Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [456,2,Mod(11,456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(456, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("456.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 456 = 2^{3} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 456.u (of order \(6\), degree \(2\), 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: | \(3.64117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.4857532416.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + x^{6} - 14x^{5} + 96x^{4} - 82x^{3} - 17x^{2} + 86x + 31 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(2.39325 - 1.62089i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 456.11 |
Dual form | 456.2.u.c.83.1 |
$q$-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 \(\left(\mathbb{Z}/456\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(343\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 1.22474i | −0.500000 | + | 0.866025i | ||||
\(3\) | −1.18614 | − | 1.26217i | −0.684819 | − | 0.728714i | ||||
\(4\) | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0.707107 | − | 1.22474i | 0.316228 | − | 0.547723i | −0.663470 | − | 0.748203i | \(-0.730917\pi\) |
0.979698 | + | 0.200480i | \(0.0642503\pi\) | |||||||
\(6\) | 2.38456 | − | 0.560232i | 0.973494 | − | 0.228714i | ||||
\(7\) | − | 4.69042i | − | 1.77281i | −0.462910 | − | 0.886405i | \(-0.653195\pi\) | ||
0.462910 | − | 0.886405i | \(-0.346805\pi\) | |||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | −0.186141 | + | 2.99422i | −0.0620469 | + | 0.998073i | ||||
\(10\) | 1.00000 | + | 1.73205i | 0.316228 | + | 0.547723i | ||||
\(11\) | 3.31662i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | −1.00000 | + | 3.31662i | −0.288675 | + | 0.957427i | ||||
\(13\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(14\) | 5.74456 | + | 3.31662i | 1.53530 | + | 0.886405i | ||||
\(15\) | −2.38456 | + | 0.560232i | −0.615692 | + | 0.144651i | ||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | −5.74456 | − | 3.31662i | −1.39326 | − | 0.804400i | −0.399586 | − | 0.916696i | \(-0.630846\pi\) |
−0.993675 | + | 0.112296i | \(0.964180\pi\) | |||||||
\(18\) | −3.53553 | − | 2.34521i | −0.833333 | − | 0.552771i | ||||
\(19\) | −3.50000 | − | 2.59808i | −0.802955 | − | 0.596040i | ||||
\(20\) | −2.82843 | −0.632456 | ||||||||
\(21\) | −5.92010 | + | 5.56349i | −1.29187 | + | 1.21405i | ||||
\(22\) | −4.06202 | − | 2.34521i | −0.866025 | − | 0.500000i | ||||
\(23\) | −2.12132 | − | 3.67423i | −0.442326 | − | 0.766131i | 0.555536 | − | 0.831493i | \(-0.312513\pi\) |
−0.997862 | + | 0.0653618i | \(0.979180\pi\) | |||||||
\(24\) | −3.35491 | − | 3.56995i | −0.684819 | − | 0.728714i | ||||
\(25\) | 1.50000 | + | 2.59808i | 0.300000 | + | 0.519615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | − | 3.31662i | 0.769800 | − | 0.638285i | ||||
\(28\) | −8.12404 | + | 4.69042i | −1.53530 | + | 0.886405i | ||||
\(29\) | 3.53553 | + | 6.12372i | 0.656532 | + | 1.13715i | 0.981507 | + | 0.191425i | \(0.0613107\pi\) |
−0.324975 | + | 0.945723i | \(0.605356\pi\) | |||||||
\(30\) | 1.00000 | − | 3.31662i | 0.182574 | − | 0.605530i | ||||
\(31\) | − | 4.69042i | − | 0.842424i | −0.906962 | − | 0.421212i | \(-0.861605\pi\) | ||
0.906962 | − | 0.421212i | \(-0.138395\pi\) | |||||||
\(32\) | −2.82843 | − | 4.89898i | −0.500000 | − | 0.866025i | ||||
\(33\) | 4.18614 | − | 3.93398i | 0.728714 | − | 0.684819i | ||||
\(34\) | 8.12404 | − | 4.69042i | 1.39326 | − | 0.804400i | ||||
\(35\) | −5.74456 | − | 3.31662i | −0.971008 | − | 0.560612i | ||||
\(36\) | 5.37228 | − | 2.67181i | 0.895380 | − | 0.445302i | ||||
\(37\) | 4.69042i | 0.771100i | 0.922687 | + | 0.385550i | \(0.125988\pi\) | ||||
−0.922687 | + | 0.385550i | \(0.874012\pi\) | |||||||
\(38\) | 5.65685 | − | 2.44949i | 0.917663 | − | 0.397360i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.00000 | − | 3.46410i | 0.316228 | − | 0.547723i | ||||
\(41\) | −2.87228 | − | 1.65831i | −0.448575 | − | 0.258985i | 0.258653 | − | 0.965970i | \(-0.416721\pi\) |
−0.707228 | + | 0.706985i | \(0.750055\pi\) | |||||||
\(42\) | −2.62772 | − | 11.1846i | −0.405466 | − | 1.72582i | ||||
\(43\) | −3.00000 | + | 5.19615i | −0.457496 | + | 0.792406i | −0.998828 | − | 0.0484030i | \(-0.984587\pi\) |
0.541332 | + | 0.840809i | \(0.317920\pi\) | |||||||
\(44\) | 5.74456 | − | 3.31662i | 0.866025 | − | 0.500000i | ||||
\(45\) | 3.53553 | + | 2.34521i | 0.527046 | + | 0.349603i | ||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | −3.53553 | − | 6.12372i | −0.515711 | − | 0.893237i | −0.999834 | − | 0.0182371i | \(-0.994195\pi\) |
0.484123 | − | 0.875000i | \(-0.339139\pi\) | |||||||
\(48\) | 6.74456 | − | 1.58457i | 0.973494 | − | 0.228714i | ||||
\(49\) | −15.0000 | −2.14286 | ||||||||
\(50\) | −4.24264 | −0.600000 | ||||||||
\(51\) | 2.62772 | + | 11.1846i | 0.367954 | + | 1.56616i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.65685 | − | 9.79796i | −0.777029 | − | 1.34585i | −0.933647 | − | 0.358194i | \(-0.883393\pi\) |
0.156618 | − | 0.987659i | \(-0.449941\pi\) | |||||||
\(54\) | 1.23359 | + | 7.24419i | 0.167871 | + | 0.985809i | ||||
\(55\) | 4.06202 | + | 2.34521i | 0.547723 | + | 0.316228i | ||||
\(56\) | − | 13.2665i | − | 1.77281i | ||||||
\(57\) | 0.872281 | + | 7.49927i | 0.115536 | + | 0.993303i | ||||
\(58\) | −10.0000 | −1.31306 | ||||||||
\(59\) | 2.87228 | + | 1.65831i | 0.373939 | + | 0.215894i | 0.675178 | − | 0.737655i | \(-0.264067\pi\) |
−0.301239 | + | 0.953549i | \(0.597400\pi\) | |||||||
\(60\) | 3.35491 | + | 3.56995i | 0.433117 | + | 0.460879i | ||||
\(61\) | −4.06202 | + | 2.34521i | −0.520088 | + | 0.300273i | −0.736971 | − | 0.675925i | \(-0.763744\pi\) |
0.216883 | + | 0.976198i | \(0.430411\pi\) | |||||||
\(62\) | 5.74456 | + | 3.31662i | 0.729560 | + | 0.421212i | ||||
\(63\) | 14.0441 | + | 0.873077i | 1.76939 | + | 0.109997i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.85808 | + | 7.90870i | 0.228714 | + | 0.973494i | ||||
\(67\) | −2.50000 | − | 4.33013i | −0.305424 | − | 0.529009i | 0.671932 | − | 0.740613i | \(-0.265465\pi\) |
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | 13.2665i | 1.60880i | ||||||||
\(69\) | −2.12132 | + | 7.03562i | −0.255377 | + | 0.846990i | ||||
\(70\) | 8.12404 | − | 4.69042i | 0.971008 | − | 0.560612i | ||||
\(71\) | 2.82843 | − | 4.89898i | 0.335673 | − | 0.581402i | −0.647941 | − | 0.761690i | \(-0.724370\pi\) |
0.983614 | + | 0.180288i | \(0.0577031\pi\) | |||||||
\(72\) | −0.526485 | + | 8.46893i | −0.0620469 | + | 0.998073i | ||||
\(73\) | −0.500000 | + | 0.866025i | −0.0585206 | + | 0.101361i | −0.893801 | − | 0.448463i | \(-0.851972\pi\) |
0.835281 | + | 0.549823i | \(0.185305\pi\) | |||||||
\(74\) | −5.74456 | − | 3.31662i | −0.667792 | − | 0.385550i | ||||
\(75\) | 1.50000 | − | 4.97494i | 0.173205 | − | 0.574456i | ||||
\(76\) | −1.00000 | + | 8.66025i | −0.114708 | + | 0.993399i | ||||
\(77\) | 15.5563 | 1.77281 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(80\) | 2.82843 | + | 4.89898i | 0.316228 | + | 0.547723i | ||||
\(81\) | −8.93070 | − | 1.11469i | −0.992300 | − | 0.123855i | ||||
\(82\) | 4.06202 | − | 2.34521i | 0.448575 | − | 0.258985i | ||||
\(83\) | 3.31662i | 0.364047i | 0.983294 | + | 0.182023i | \(0.0582647\pi\) | ||||
−0.983294 | + | 0.182023i | \(0.941735\pi\) | |||||||
\(84\) | 15.5563 | + | 4.69042i | 1.69734 | + | 0.511766i | ||||
\(85\) | −8.12404 | + | 4.69042i | −0.881176 | + | 0.508747i | ||||
\(86\) | −4.24264 | − | 7.34847i | −0.457496 | − | 0.792406i | ||||
\(87\) | 3.53553 | − | 11.7260i | 0.379049 | − | 1.25716i | ||||
\(88\) | 9.38083i | 1.00000i | ||||||||
\(89\) | 5.74456 | − | 3.31662i | 0.608922 | − | 0.351562i | −0.163621 | − | 0.986523i | \(-0.552317\pi\) |
0.772544 | + | 0.634962i | \(0.218984\pi\) | |||||||
\(90\) | −5.37228 | + | 2.67181i | −0.566288 | + | 0.281634i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.24264 | + | 7.34847i | −0.442326 | + | 0.766131i | ||||
\(93\) | −5.92010 | + | 5.56349i | −0.613885 | + | 0.576907i | ||||
\(94\) | 10.0000 | 1.03142 | ||||||||
\(95\) | −5.65685 | + | 2.44949i | −0.580381 | + | 0.251312i | ||||
\(96\) | −2.82843 | + | 9.38083i | −0.288675 | + | 0.957427i | ||||
\(97\) | 7.50000 | − | 12.9904i | 0.761510 | − | 1.31897i | −0.180563 | − | 0.983563i | \(-0.557792\pi\) |
0.942072 | − | 0.335410i | \(-0.108875\pi\) | |||||||
\(98\) | 10.6066 | − | 18.3712i | 1.07143 | − | 1.85577i | ||||
\(99\) | −9.93070 | − | 0.617359i | −0.998073 | − | 0.0620469i | ||||
\(100\) | 3.00000 | − | 5.19615i | 0.300000 | − | 0.519615i | ||||
\(101\) | −3.53553 | − | 6.12372i | −0.351799 | − | 0.609333i | 0.634766 | − | 0.772704i | \(-0.281097\pi\) |
−0.986565 | + | 0.163371i | \(0.947763\pi\) | |||||||
\(102\) | −15.5563 | − | 4.69042i | −1.54031 | − | 0.464420i | ||||
\(103\) | 9.38083i | 0.924321i | 0.886796 | + | 0.462160i | \(0.152926\pi\) | ||||
−0.886796 | + | 0.462160i | \(0.847074\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.62772 | + | 11.1846i | 0.256439 | + | 1.09150i | ||||
\(106\) | 16.0000 | 1.55406 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | −9.74456 | − | 3.61158i | −0.937671 | − | 0.347524i | ||||
\(109\) | 8.12404 | + | 4.69042i | 0.778142 | + | 0.449260i | 0.835771 | − | 0.549078i | \(-0.185021\pi\) |
−0.0576296 | + | 0.998338i | \(0.518354\pi\) | |||||||
\(110\) | −5.74456 | + | 3.31662i | −0.547723 | + | 0.316228i | ||||
\(111\) | 5.92010 | − | 5.56349i | 0.561911 | − | 0.528063i | ||||
\(112\) | 16.2481 | + | 9.38083i | 1.53530 | + | 0.886405i | ||||
\(113\) | 16.5831i | 1.56001i | 0.625774 | + | 0.780005i | \(0.284783\pi\) | ||||
−0.625774 | + | 0.780005i | \(0.715217\pi\) | |||||||
\(114\) | −9.80149 | − | 4.23447i | −0.917994 | − | 0.396594i | ||||
\(115\) | −6.00000 | −0.559503 | ||||||||
\(116\) | 7.07107 | − | 12.2474i | 0.656532 | − | 1.13715i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.06202 | + | 2.34521i | −0.373939 | + | 0.215894i | ||||
\(119\) | −15.5563 | + | 26.9444i | −1.42605 | + | 2.46999i | ||||
\(120\) | −6.74456 | + | 1.58457i | −0.615692 | + | 0.144651i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 6.63325i | − | 0.600546i | ||||||
\(123\) | 1.31386 | + | 5.59230i | 0.118467 | + | 0.504240i | ||||
\(124\) | −8.12404 | + | 4.69042i | −0.729560 | + | 0.421212i | ||||
\(125\) | 11.3137 | 1.01193 | ||||||||
\(126\) | −11.0000 | + | 16.5831i | −0.979958 | + | 1.47734i | ||||
\(127\) | 16.2481 | − | 9.38083i | 1.44178 | − | 0.832414i | 0.443815 | − | 0.896119i | \(-0.353625\pi\) |
0.997969 | + | 0.0637043i | \(0.0202915\pi\) | |||||||
\(128\) | −5.65685 | + | 9.79796i | −0.500000 | + | 0.866025i | ||||
\(129\) | 10.1168 | − | 2.37686i | 0.890738 | − | 0.209271i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.87228 | − | 1.65831i | −0.250952 | − | 0.144887i | 0.369248 | − | 0.929331i | \(-0.379615\pi\) |
−0.620200 | + | 0.784444i | \(0.712949\pi\) | |||||||
\(132\) | −11.0000 | − | 3.31662i | −0.957427 | − | 0.288675i | ||||
\(133\) | −12.1861 | + | 16.4165i | −1.05667 | + | 1.42349i | ||||
\(134\) | 7.07107 | 0.610847 | ||||||||
\(135\) | −1.23359 | − | 7.24419i | −0.106171 | − | 0.623480i | ||||
\(136\) | −16.2481 | − | 9.38083i | −1.39326 | − | 0.804400i | ||||
\(137\) | 14.3614 | − | 8.29156i | 1.22698 | − | 0.708396i | 0.260581 | − | 0.965452i | \(-0.416086\pi\) |
0.966397 | + | 0.257056i | \(0.0827525\pi\) | |||||||
\(138\) | −7.11684 | − | 7.57301i | −0.605826 | − | 0.644658i | ||||
\(139\) | −7.50000 | − | 12.9904i | −0.636142 | − | 1.10183i | −0.986272 | − | 0.165129i | \(-0.947196\pi\) |
0.350130 | − | 0.936701i | \(-0.386137\pi\) | |||||||
\(140\) | 13.2665i | 1.12122i | ||||||||
\(141\) | −3.53553 | + | 11.7260i | −0.297746 | + | 0.987511i | ||||
\(142\) | 4.00000 | + | 6.92820i | 0.335673 | + | 0.581402i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −10.0000 | − | 6.63325i | −0.833333 | − | 0.552771i | ||||
\(145\) | 10.0000 | 0.830455 | ||||||||
\(146\) | −0.707107 | − | 1.22474i | −0.0585206 | − | 0.101361i | ||||
\(147\) | 17.7921 | + | 18.9325i | 1.46747 | + | 1.56153i | ||||
\(148\) | 8.12404 | − | 4.69042i | 0.667792 | − | 0.385550i | ||||
\(149\) | 3.53553 | − | 6.12372i | 0.289642 | − | 0.501675i | −0.684082 | − | 0.729405i | \(-0.739797\pi\) |
0.973724 | + | 0.227730i | \(0.0731303\pi\) | |||||||
\(150\) | 5.03237 | + | 5.35493i | 0.410891 | + | 0.437228i | ||||
\(151\) | − | 4.69042i | − | 0.381701i | −0.981619 | − | 0.190850i | \(-0.938875\pi\) | ||
0.981619 | − | 0.190850i | \(-0.0611245\pi\) | |||||||
\(152\) | −9.89949 | − | 7.34847i | −0.802955 | − | 0.596040i | ||||
\(153\) | 11.0000 | − | 16.5831i | 0.889297 | − | 1.34067i | ||||
\(154\) | −11.0000 | + | 19.0526i | −0.886405 | + | 1.53530i | ||||
\(155\) | −5.74456 | − | 3.31662i | −0.461414 | − | 0.266398i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.2481 | − | 9.38083i | −1.29674 | − | 0.748672i | −0.316898 | − | 0.948459i | \(-0.602641\pi\) |
−0.979839 | + | 0.199788i | \(0.935975\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.65685 | + | 18.7617i | −0.448618 | + | 1.48790i | ||||
\(160\) | −8.00000 | −0.632456 | ||||||||
\(161\) | −17.2337 | + | 9.94987i | −1.35820 | + | 0.784160i | ||||
\(162\) | 7.68017 | − | 10.1496i | 0.603411 | − | 0.797430i | ||||
\(163\) | 15.0000 | 1.17489 | 0.587445 | − | 0.809264i | \(-0.300134\pi\) | ||||
0.587445 | + | 0.809264i | \(0.300134\pi\) | |||||||
\(164\) | 6.63325i | 0.517970i | ||||||||
\(165\) | −1.85808 | − | 7.90870i | −0.144651 | − | 0.615692i | ||||
\(166\) | −4.06202 | − | 2.34521i | −0.315274 | − | 0.182023i | ||||
\(167\) | −4.24264 | − | 7.34847i | −0.328305 | − | 0.568642i | 0.653870 | − | 0.756607i | \(-0.273144\pi\) |
−0.982176 | + | 0.187965i | \(0.939811\pi\) | |||||||
\(168\) | −16.7446 | + | 15.7359i | −1.29187 | + | 1.21405i | ||||
\(169\) | −6.50000 | + | 11.2583i | −0.500000 | + | 0.866025i | ||||
\(170\) | − | 13.2665i | − | 1.01749i | ||||||
\(171\) | 8.43070 | − | 9.99616i | 0.644712 | − | 0.764426i | ||||
\(172\) | 12.0000 | 0.914991 | ||||||||
\(173\) | 1.41421 | − | 2.44949i | 0.107521 | − | 0.186231i | −0.807245 | − | 0.590217i | \(-0.799042\pi\) |
0.914765 | + | 0.403986i | \(0.132375\pi\) | |||||||
\(174\) | 11.8614 | + | 12.6217i | 0.899211 | + | 0.956848i | ||||
\(175\) | 12.1861 | − | 7.03562i | 0.921179 | − | 0.531843i | ||||
\(176\) | −11.4891 | − | 6.63325i | −0.866025 | − | 0.500000i | ||||
\(177\) | −1.31386 | − | 5.59230i | −0.0987557 | − | 0.420343i | ||||
\(178\) | 9.38083i | 0.703123i | ||||||||
\(179\) | − | 9.94987i | − | 0.743689i | −0.928295 | − | 0.371844i | \(-0.878726\pi\) | ||
0.928295 | − | 0.371844i | \(-0.121274\pi\) | |||||||
\(180\) | 0.526485 | − | 8.46893i | 0.0392419 | − | 0.631237i | ||||
\(181\) | 20.3101 | − | 11.7260i | 1.50964 | − | 0.871590i | 0.509701 | − | 0.860352i | \(-0.329756\pi\) |
0.999937 | − | 0.0112379i | \(-0.00357720\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.77817 | + | 2.34521i | 0.574979 | + | 0.173363i | ||||
\(184\) | −6.00000 | − | 10.3923i | −0.442326 | − | 0.766131i | ||||
\(185\) | 5.74456 | + | 3.31662i | 0.422349 | + | 0.243843i | ||||
\(186\) | −2.62772 | − | 11.1846i | −0.192674 | − | 0.820094i | ||||
\(187\) | 11.0000 | − | 19.0526i | 0.804400 | − | 1.39326i | ||||
\(188\) | −7.07107 | + | 12.2474i | −0.515711 | + | 0.893237i | ||||
\(189\) | −15.5563 | − | 18.7617i | −1.13156 | − | 1.36471i | ||||
\(190\) | 1.00000 | − | 8.66025i | 0.0725476 | − | 0.628281i | ||||
\(191\) | 5.65685 | 0.409316 | 0.204658 | − | 0.978834i | \(-0.434392\pi\) | ||||
0.204658 | + | 0.978834i | \(0.434392\pi\) | |||||||
\(192\) | −9.48913 | − | 10.0974i | −0.684819 | − | 0.728714i | ||||
\(193\) | 10.0000 | − | 17.3205i | 0.719816 | − | 1.24676i | −0.241257 | − | 0.970461i | \(-0.577560\pi\) |
0.961073 | − | 0.276296i | \(-0.0891071\pi\) | |||||||
\(194\) | 10.6066 | + | 18.3712i | 0.761510 | + | 1.31897i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.0000 | + | 25.9808i | 1.07143 | + | 1.85577i | ||||
\(197\) | 12.7279 | 0.906827 | 0.453413 | − | 0.891300i | \(-0.350206\pi\) | ||||
0.453413 | + | 0.891300i | \(0.350206\pi\) | |||||||
\(198\) | 7.77817 | − | 11.7260i | 0.552771 | − | 0.833333i | ||||
\(199\) | −8.12404 | + | 4.69042i | −0.575898 | + | 0.332495i | −0.759501 | − | 0.650506i | \(-0.774557\pi\) |
0.183604 | + | 0.983000i | \(0.441224\pi\) | |||||||
\(200\) | 4.24264 | + | 7.34847i | 0.300000 | + | 0.519615i | ||||
\(201\) | −2.50000 | + | 8.29156i | −0.176336 | + | 0.584842i | ||||
\(202\) | 10.0000 | 0.703598 | ||||||||
\(203\) | 28.7228 | − | 16.5831i | 2.01595 | − | 1.16391i | ||||
\(204\) | 16.7446 | − | 15.7359i | 1.17235 | − | 1.10174i | ||||
\(205\) | −4.06202 | + | 2.34521i | −0.283704 | + | 0.163796i | ||||
\(206\) | −11.4891 | − | 6.63325i | −0.800485 | − | 0.462160i | ||||
\(207\) | 11.3963 | − | 5.66777i | 0.792100 | − | 0.393938i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.61684 | − | 11.6082i | 0.596040 | − | 0.802955i | ||||
\(210\) | −15.5563 | − | 4.69042i | −1.07349 | − | 0.323669i | ||||
\(211\) | −8.00000 | + | 13.8564i | −0.550743 | + | 0.953914i | 0.447478 | + | 0.894295i | \(0.352322\pi\) |
−0.998221 | + | 0.0596196i | \(0.981011\pi\) | |||||||
\(212\) | −11.3137 | + | 19.5959i | −0.777029 | + | 1.34585i | ||||
\(213\) | −9.53825 | + | 2.24093i | −0.653550 | + | 0.153546i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.24264 | + | 7.34847i | 0.289346 | + | 0.501161i | ||||
\(216\) | 11.3137 | − | 9.38083i | 0.769800 | − | 0.638285i | ||||
\(217\) | −22.0000 | −1.49346 | ||||||||
\(218\) | −11.4891 | + | 6.63325i | −0.778142 | + | 0.449260i | ||||
\(219\) | 1.68614 | − | 0.396143i | 0.113939 | − | 0.0267689i | ||||
\(220\) | − | 9.38083i | − | 0.632456i | ||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.62772 | + | 11.1846i | 0.176361 | + | 0.750661i | ||||
\(223\) | −12.1861 | − | 7.03562i | −0.816039 | − | 0.471140i | 0.0330098 | − | 0.999455i | \(-0.489491\pi\) |
−0.849049 | + | 0.528315i | \(0.822824\pi\) | |||||||
\(224\) | −22.9783 | + | 13.2665i | −1.53530 | + | 0.886405i | ||||
\(225\) | −8.05842 | + | 4.00772i | −0.537228 | + | 0.267181i | ||||
\(226\) | −20.3101 | − | 11.7260i | −1.35101 | − | 0.780005i | ||||
\(227\) | 16.5831i | 1.10066i | 0.834947 | + | 0.550330i | \(0.185498\pi\) | ||||
−0.834947 | + | 0.550330i | \(0.814502\pi\) | |||||||
\(228\) | 12.1168 | − | 9.01011i | 0.802458 | − | 0.596709i | ||||
\(229\) | − | 9.38083i | − | 0.619903i | −0.950752 | − | 0.309951i | \(-0.899687\pi\) | ||
0.950752 | − | 0.309951i | \(-0.100313\pi\) | |||||||
\(230\) | 4.24264 | − | 7.34847i | 0.279751 | − | 0.484544i | ||||
\(231\) | −18.4520 | − | 19.6347i | −1.21405 | − | 1.29187i | ||||
\(232\) | 10.0000 | + | 17.3205i | 0.656532 | + | 1.13715i | ||||
\(233\) | 14.3614 | + | 8.29156i | 0.940847 | + | 0.543198i | 0.890226 | − | 0.455520i | \(-0.150547\pi\) |
0.0506213 | + | 0.998718i | \(0.483880\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.0000 | −0.652328 | ||||||||
\(236\) | − | 6.63325i | − | 0.431788i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −22.0000 | − | 38.1051i | −1.42605 | − | 2.46999i | ||||
\(239\) | −14.1421 | −0.914779 | −0.457389 | − | 0.889267i | \(-0.651215\pi\) | ||||
−0.457389 | + | 0.889267i | \(0.651215\pi\) | |||||||
\(240\) | 2.82843 | − | 9.38083i | 0.182574 | − | 0.605530i | ||||
\(241\) | −12.5000 | − | 21.6506i | −0.805196 | − | 1.39464i | −0.916159 | − | 0.400815i | \(-0.868727\pi\) |
0.110963 | − | 0.993825i | \(-0.464606\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.18614 | + | 12.5942i | 0.589291 | + | 0.807921i | ||||
\(244\) | 8.12404 | + | 4.69042i | 0.520088 | + | 0.300273i | ||||
\(245\) | −10.6066 | + | 18.3712i | −0.677631 | + | 1.17369i | ||||
\(246\) | −7.77817 | − | 2.34521i | −0.495918 | − | 0.149525i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 13.2665i | − | 0.842424i | ||||||
\(249\) | 4.18614 | − | 3.93398i | 0.265286 | − | 0.249306i | ||||
\(250\) | −8.00000 | + | 13.8564i | −0.505964 | + | 0.876356i | ||||
\(251\) | 14.3614 | − | 8.29156i | 0.906484 | − | 0.523359i | 0.0271858 | − | 0.999630i | \(-0.491345\pi\) |
0.879298 | + | 0.476272i | \(0.158012\pi\) | |||||||
\(252\) | −12.5319 | − | 25.1982i | −0.789437 | − | 1.58734i | ||||
\(253\) | 12.1861 | − | 7.03562i | 0.766131 | − | 0.442326i | ||||
\(254\) | 26.5330i | 1.66483i | ||||||||
\(255\) | 15.5563 | + | 4.69042i | 0.974176 | + | 0.293725i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 8.61684 | − | 4.97494i | 0.537504 | − | 0.310328i | −0.206563 | − | 0.978433i | \(-0.566228\pi\) |
0.744067 | + | 0.668105i | \(0.232894\pi\) | |||||||
\(258\) | −4.24264 | + | 14.0712i | −0.264135 | + | 0.876038i | ||||
\(259\) | 22.0000 | 1.36701 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.9939 | + | 9.44629i | −1.17569 | + | 0.584711i | ||||
\(262\) | 4.06202 | − | 2.34521i | 0.250952 | − | 0.144887i | ||||
\(263\) | −2.12132 | + | 3.67423i | −0.130806 | + | 0.226563i | −0.923988 | − | 0.382422i | \(-0.875090\pi\) |
0.793181 | + | 0.608985i | \(0.208423\pi\) | |||||||
\(264\) | 11.8402 | − | 11.1270i | 0.728714 | − | 0.684819i | ||||
\(265\) | −16.0000 | −0.982872 | ||||||||
\(266\) | −11.4891 | − | 26.5330i | −0.704443 | − | 1.62684i | ||||
\(267\) | −11.0000 | − | 3.31662i | −0.673189 | − | 0.202974i | ||||
\(268\) | −5.00000 | + | 8.66025i | −0.305424 | + | 0.529009i | ||||
\(269\) | −5.65685 | + | 9.79796i | −0.344904 | + | 0.597392i | −0.985336 | − | 0.170623i | \(-0.945422\pi\) |
0.640432 | + | 0.768015i | \(0.278755\pi\) | |||||||
\(270\) | 9.74456 | + | 3.61158i | 0.593035 | + | 0.219794i | ||||
\(271\) | −20.3101 | − | 11.7260i | −1.23375 | − | 0.712306i | −0.265941 | − | 0.963989i | \(-0.585683\pi\) |
−0.967810 | + | 0.251683i | \(0.919016\pi\) | |||||||
\(272\) | 22.9783 | − | 13.2665i | 1.39326 | − | 0.804400i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 23.4521i | 1.41679i | ||||||||
\(275\) | −8.61684 | + | 4.97494i | −0.519615 | + | 0.300000i | ||||
\(276\) | 14.3074 | − | 3.36139i | 0.861203 | − | 0.202332i | ||||
\(277\) | − | 23.4521i | − | 1.40910i | −0.709655 | − | 0.704549i | \(-0.751149\pi\) | ||
0.709655 | − | 0.704549i | \(-0.248851\pi\) | |||||||
\(278\) | 21.2132 | 1.27228 | ||||||||
\(279\) | 14.0441 | + | 0.873077i | 0.840800 | + | 0.0522698i | ||||
\(280\) | −16.2481 | − | 9.38083i | −0.971008 | − | 0.560612i | ||||
\(281\) | 2.87228 | − | 1.65831i | 0.171346 | − | 0.0989266i | −0.411874 | − | 0.911241i | \(-0.635126\pi\) |
0.583220 | + | 0.812314i | \(0.301792\pi\) | |||||||
\(282\) | −11.8614 | − | 12.6217i | −0.706336 | − | 0.751611i | ||||
\(283\) | −12.5000 | + | 21.6506i | −0.743048 | + | 1.28700i | 0.208053 | + | 0.978117i | \(0.433287\pi\) |
−0.951101 | + | 0.308879i | \(0.900046\pi\) | |||||||
\(284\) | −11.3137 | −0.671345 | ||||||||
\(285\) | 9.80149 | + | 4.23447i | 0.580590 | + | 0.250828i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.77817 | + | 13.4722i | −0.459131 | + | 0.795238i | ||||
\(288\) | 15.1951 | − | 7.55703i | 0.895380 | − | 0.445302i | ||||
\(289\) | 13.5000 | + | 23.3827i | 0.794118 | + | 1.37545i | ||||
\(290\) | −7.07107 | + | 12.2474i | −0.415227 | + | 0.719195i | ||||
\(291\) | −25.2921 | + | 5.94215i | −1.48265 | + | 0.348335i | ||||
\(292\) | 2.00000 | 0.117041 | ||||||||
\(293\) | 9.89949 | 0.578335 | 0.289167 | − | 0.957279i | \(-0.406622\pi\) | ||||
0.289167 | + | 0.957279i | \(0.406622\pi\) | |||||||
\(294\) | −35.7684 | + | 8.40347i | −2.08606 | + | 0.490100i | ||||
\(295\) | 4.06202 | − | 2.34521i | 0.236500 | − | 0.136543i | ||||
\(296\) | 13.2665i | 0.771100i | ||||||||
\(297\) | 11.0000 | + | 13.2665i | 0.638285 | + | 0.769800i | ||||
\(298\) | 5.00000 | + | 8.66025i | 0.289642 | + | 0.501675i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −10.1168 | + | 2.37686i | −0.584096 | + | 0.137228i | ||||
\(301\) | 24.3721 | + | 14.0712i | 1.40479 | + | 0.811053i | ||||
\(302\) | 5.74456 | + | 3.31662i | 0.330562 | + | 0.190850i | ||||
\(303\) | −3.53553 | + | 11.7260i | −0.203111 | + | 0.673643i | ||||
\(304\) | 16.0000 | − | 6.92820i | 0.917663 | − | 0.397360i | ||||
\(305\) | 6.63325i | 0.379819i | ||||||||
\(306\) | 12.5319 | + | 25.1982i | 0.716402 | + | 1.44049i | ||||
\(307\) | −2.50000 | + | 4.33013i | −0.142683 | + | 0.247133i | −0.928506 | − | 0.371318i | \(-0.878906\pi\) |
0.785823 | + | 0.618451i | \(0.212239\pi\) | |||||||
\(308\) | −15.5563 | − | 26.9444i | −0.886405 | − | 1.53530i | ||||
\(309\) | 11.8402 | − | 11.1270i | 0.673565 | − | 0.632992i | ||||
\(310\) | 8.12404 | − | 4.69042i | 0.461414 | − | 0.266398i | ||||
\(311\) | −7.07107 | −0.400963 | −0.200482 | − | 0.979697i | \(-0.564251\pi\) | ||||
−0.200482 | + | 0.979697i | \(0.564251\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.50000 | − | 9.52628i | −0.310878 | − | 0.538457i | 0.667674 | − | 0.744453i | \(-0.267290\pi\) |
−0.978553 | + | 0.205996i | \(0.933957\pi\) | |||||||
\(314\) | 22.9783 | − | 13.2665i | 1.29674 | − | 0.748672i | ||||
\(315\) | 11.0000 | − | 16.5831i | 0.619780 | − | 0.934353i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.89949 | − | 17.1464i | −0.556011 | − | 0.963039i | −0.997824 | − | 0.0659322i | \(-0.978998\pi\) |
0.441813 | − | 0.897107i | \(-0.354335\pi\) | |||||||
\(318\) | −18.9783 | − | 20.1947i | −1.06425 | − | 1.13246i | ||||
\(319\) | −20.3101 | + | 11.7260i | −1.13715 | + | 0.656532i | ||||
\(320\) | 5.65685 | − | 9.79796i | 0.316228 | − | 0.547723i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 28.1425i | − | 1.56832i | ||||||
\(323\) | 11.4891 | + | 26.5330i | 0.639272 | + | 1.47634i | ||||
\(324\) | 7.00000 | + | 16.5831i | 0.388889 | + | 0.921285i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.6066 | + | 18.3712i | −0.587445 | + | 1.01749i | ||||
\(327\) | −3.71616 | − | 15.8174i | −0.205504 | − | 0.874704i | ||||
\(328\) | −8.12404 | − | 4.69042i | −0.448575 | − | 0.258985i | ||||
\(329\) | −28.7228 | + | 16.5831i | −1.58354 | + | 0.914257i | ||||
\(330\) | 11.0000 | + | 3.31662i | 0.605530 | + | 0.182574i | ||||
\(331\) | −11.0000 | −0.604615 | −0.302307 | − | 0.953211i | \(-0.597757\pi\) | ||||
−0.302307 | + | 0.953211i | \(0.597757\pi\) | |||||||
\(332\) | 5.74456 | − | 3.31662i | 0.315274 | − | 0.182023i | ||||
\(333\) | −14.0441 | − | 0.873077i | −0.769614 | − | 0.0478443i | ||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | −7.07107 | −0.386334 | ||||||||
\(336\) | −7.43231 | − | 31.6348i | −0.405466 | − | 1.72582i | ||||
\(337\) | −2.50000 | + | 4.33013i | −0.136184 | + | 0.235877i | −0.926049 | − | 0.377403i | \(-0.876817\pi\) |
0.789865 | + | 0.613280i | \(0.210150\pi\) | |||||||
\(338\) | −9.19239 | − | 15.9217i | −0.500000 | − | 0.866025i | ||||
\(339\) | 20.9307 | − | 19.6699i | 1.13680 | − | 1.06832i | ||||
\(340\) | 16.2481 | + | 9.38083i | 0.881176 | + | 0.508747i | ||||
\(341\) | 15.5563 | 0.842424 | ||||||||
\(342\) | 6.28134 | + | 17.3938i | 0.339656 | + | 0.940550i | ||||
\(343\) | 37.5233i | 2.02607i | ||||||||
\(344\) | −8.48528 | + | 14.6969i | −0.457496 | + | 0.792406i | ||||
\(345\) | 7.11684 | + | 7.57301i | 0.383158 | + | 0.407717i | ||||
\(346\) | 2.00000 | + | 3.46410i | 0.107521 | + | 0.186231i | ||||
\(347\) | −14.3614 | − | 8.29156i | −0.770961 | − | 0.445114i | 0.0622565 | − | 0.998060i | \(-0.480170\pi\) |
−0.833217 | + | 0.552946i | \(0.813504\pi\) | |||||||
\(348\) | −23.8456 | + | 5.60232i | −1.27826 | + | 0.300316i | ||||
\(349\) | 9.38083i | 0.502144i | 0.967968 | + | 0.251072i | \(0.0807832\pi\) | ||||
−0.967968 | + | 0.251072i | \(0.919217\pi\) | |||||||
\(350\) | 19.8997i | 1.06369i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.2481 | − | 9.38083i | 0.866025 | − | 0.500000i | ||||
\(353\) | − | 16.5831i | − | 0.882631i | −0.897352 | − | 0.441315i | \(-0.854512\pi\) | ||
0.897352 | − | 0.441315i | \(-0.145488\pi\) | |||||||
\(354\) | 7.77817 | + | 2.34521i | 0.413405 | + | 0.124646i | ||||
\(355\) | −4.00000 | − | 6.92820i | −0.212298 | − | 0.367711i | ||||
\(356\) | −11.4891 | − | 6.63325i | −0.608922 | − | 0.351562i | ||||
\(357\) | 52.4604 | − | 12.3251i | 2.77650 | − | 0.652313i | ||||
\(358\) | 12.1861 | + | 7.03562i | 0.644053 | + | 0.371844i | ||||
\(359\) | 12.0208 | − | 20.8207i | 0.634434 | − | 1.09887i | −0.352200 | − | 0.935925i | \(-0.614566\pi\) |
0.986635 | − | 0.162948i | \(-0.0521003\pi\) | |||||||
\(360\) | 10.0000 | + | 6.63325i | 0.527046 | + | 0.349603i | ||||
\(361\) | 5.50000 | + | 18.1865i | 0.289474 | + | 0.957186i | ||||
\(362\) | 33.1662i | 1.74318i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.707107 | + | 1.22474i | 0.0370117 | + | 0.0641061i | ||||
\(366\) | −8.37228 | + | 7.86797i | −0.437626 | + | 0.411265i | ||||
\(367\) | −20.3101 | + | 11.7260i | −1.06018 | + | 0.612094i | −0.925482 | − | 0.378793i | \(-0.876339\pi\) |
−0.134697 | + | 0.990887i | \(0.543006\pi\) | |||||||
\(368\) | 16.9706 | 0.884652 | ||||||||
\(369\) | 5.50000 | − | 8.29156i | 0.286319 | − | 0.431641i | ||||
\(370\) | −8.12404 | + | 4.69042i | −0.422349 | + | 0.243843i | ||||
\(371\) | −45.9565 | + | 26.5330i | −2.38594 | + | 1.37752i | ||||
\(372\) | 15.5563 | + | 4.69042i | 0.806559 | + | 0.243187i | ||||
\(373\) | − | 9.38083i | − | 0.485721i | −0.970061 | − | 0.242861i | \(-0.921914\pi\) | ||
0.970061 | − | 0.242861i | \(-0.0780857\pi\) | |||||||
\(374\) | 15.5563 | + | 26.9444i | 0.804400 | + | 1.39326i | ||||
\(375\) | −13.4196 | − | 14.2798i | −0.692988 | − | 0.737406i | ||||
\(376\) | −10.0000 | − | 17.3205i | −0.515711 | − | 0.893237i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 33.9783 | − | 5.78606i | 1.74765 | − | 0.297603i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 9.89949 | + | 7.34847i | 0.507833 | + | 0.376969i | ||||
\(381\) | −31.1127 | − | 9.38083i | −1.59395 | − | 0.480595i | ||||
\(382\) | −4.00000 | + | 6.92820i | −0.204658 | + | 0.354478i | ||||
\(383\) | 3.53553 | − | 6.12372i | 0.180657 | − | 0.312908i | −0.761447 | − | 0.648227i | \(-0.775511\pi\) |
0.942105 | + | 0.335319i | \(0.108844\pi\) | |||||||
\(384\) | 19.0765 | − | 4.48185i | 0.973494 | − | 0.228714i | ||||
\(385\) | 11.0000 | − | 19.0526i | 0.560612 | − | 0.971008i | ||||
\(386\) | 14.1421 | + | 24.4949i | 0.719816 | + | 1.24676i | ||||
\(387\) | −15.0000 | − | 9.94987i | −0.762493 | − | 0.505781i | ||||
\(388\) | −30.0000 | −1.52302 | ||||||||
\(389\) | 1.41421 | + | 2.44949i | 0.0717035 | + | 0.124194i | 0.899648 | − | 0.436616i | \(-0.143823\pi\) |
−0.827945 | + | 0.560810i | \(0.810490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.1425i | 1.42323i | ||||||||
\(392\) | −42.4264 | −2.14286 | ||||||||
\(393\) | 1.31386 | + | 5.59230i | 0.0662754 | + | 0.282094i | ||||
\(394\) | −9.00000 | + | 15.5885i | −0.453413 | + | 0.785335i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.86141 | + | 17.8178i | 0.445302 | + | 0.895380i | ||||
\(397\) | −4.06202 | − | 2.34521i | −0.203867 | − | 0.117703i | 0.394591 | − | 0.918857i | \(-0.370886\pi\) |
−0.598458 | + | 0.801154i | \(0.704220\pi\) | |||||||
\(398\) | − | 13.2665i | − | 0.664990i | ||||||
\(399\) | 35.1747 | − | 4.09136i | 1.76094 | − | 0.204824i | ||||
\(400\) | −12.0000 | −0.600000 | ||||||||
\(401\) | −14.3614 | − | 8.29156i | −0.717174 | − | 0.414061i | 0.0965374 | − | 0.995329i | \(-0.469223\pi\) |
−0.813712 | + | 0.581269i | \(0.802557\pi\) | |||||||
\(402\) | −8.38728 | − | 8.92488i | −0.418320 | − | 0.445133i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −7.07107 | + | 12.2474i | −0.351799 | + | 0.609333i | ||||
\(405\) | −7.68017 | + | 10.1496i | −0.381631 | + | 0.504339i | ||||
\(406\) | 46.9042i | 2.32781i | ||||||||
\(407\) | −15.5563 | −0.771100 | ||||||||
\(408\) | 7.43231 | + | 31.6348i | 0.367954 | + | 1.56616i | ||||
\(409\) | 13.5000 | + | 23.3827i | 0.667532 | + | 1.15620i | 0.978592 | + | 0.205809i | \(0.0659826\pi\) |
−0.311060 | + | 0.950390i | \(0.600684\pi\) | |||||||
\(410\) | − | 6.63325i | − | 0.327593i | ||||||
\(411\) | −27.5000 | − | 8.29156i | −1.35647 | − | 0.408993i | ||||
\(412\) | 16.2481 | − | 9.38083i | 0.800485 | − | 0.462160i | ||||
\(413\) | 7.77817 | − | 13.4722i | 0.382739 | − | 0.662923i | ||||
\(414\) | −1.11684 | + | 17.9653i | −0.0548899 | + | 0.882947i | ||||
\(415\) | 4.06202 | + | 2.34521i | 0.199397 | + | 0.115122i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.50000 | + | 24.8747i | −0.367277 | + | 1.21812i | ||||
\(418\) | 8.12404 | + | 18.7617i | 0.397360 | + | 0.917663i | ||||
\(419\) | − | 26.5330i | − | 1.29622i | −0.761546 | − | 0.648111i | \(-0.775559\pi\) | ||
0.761546 | − | 0.648111i | \(-0.224441\pi\) | |||||||
\(420\) | 16.7446 | − | 15.7359i | 0.817051 | − | 0.767835i | ||||
\(421\) | 20.3101 | + | 11.7260i | 0.989854 | + | 0.571492i | 0.905231 | − | 0.424921i | \(-0.139698\pi\) |
0.0846230 | + | 0.996413i | \(0.473031\pi\) | |||||||
\(422\) | −11.3137 | − | 19.5959i | −0.550743 | − | 0.953914i | ||||
\(423\) | 18.9939 | − | 9.44629i | 0.923514 | − | 0.459294i | ||||
\(424\) | −16.0000 | − | 27.7128i | −0.777029 | − | 1.34585i | ||||
\(425\) | − | 19.8997i | − | 0.965280i | ||||||
\(426\) | 4.00000 | − | 13.2665i | 0.193801 | − | 0.642764i | ||||
\(427\) | 11.0000 | + | 19.0526i | 0.532327 | + | 0.922018i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.0000 | −0.578691 | ||||||||
\(431\) | 7.07107 | + | 12.2474i | 0.340601 | + | 0.589939i | 0.984545 | − | 0.175134i | \(-0.0560360\pi\) |
−0.643943 | + | 0.765073i | \(0.722703\pi\) | |||||||
\(432\) | 3.48913 | + | 20.4897i | 0.167871 | + | 0.985809i | ||||
\(433\) | 10.0000 | + | 17.3205i | 0.480569 | + | 0.832370i | 0.999751 | − | 0.0222931i | \(-0.00709671\pi\) |
−0.519182 | + | 0.854664i | \(0.673763\pi\) | |||||||
\(434\) | 15.5563 | − | 26.9444i | 0.746729 | − | 1.29337i | ||||
\(435\) | −11.8614 | − | 12.6217i | −0.568711 | − | 0.605164i | ||||
\(436\) | − | 18.7617i | − | 0.898521i | ||||||
\(437\) | −2.12132 | + | 18.3712i | −0.101477 | + | 0.878812i | ||||
\(438\) | −0.707107 | + | 2.34521i | −0.0337869 | + | 0.112058i | ||||
\(439\) | 20.3101 | + | 11.7260i | 0.969348 | + | 0.559653i | 0.899037 | − | 0.437872i | \(-0.144268\pi\) |
0.0703106 | + | 0.997525i | \(0.477601\pi\) | |||||||
\(440\) | 11.4891 | + | 6.63325i | 0.547723 | + | 0.316228i | ||||
\(441\) | 2.79211 | − | 44.9133i | 0.132958 | − | 2.13873i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.87228 | − | 1.65831i | 0.136466 | − | 0.0787888i | −0.430213 | − | 0.902728i | \(-0.641561\pi\) |
0.566679 | + | 0.823939i | \(0.308228\pi\) | |||||||
\(444\) | −15.5563 | − | 4.69042i | −0.738272 | − | 0.222597i | ||||
\(445\) | − | 9.38083i | − | 0.444694i | ||||||
\(446\) | 17.2337 | − | 9.94987i | 0.816039 | − | 0.471140i | ||||
\(447\) | −11.9228 | + | 2.80116i | −0.563930 | + | 0.132490i | ||||
\(448\) | − | 37.5233i | − | 1.77281i | ||||||
\(449\) | − | 9.94987i | − | 0.469564i | −0.972048 | − | 0.234782i | \(-0.924562\pi\) | ||
0.972048 | − | 0.234782i | \(-0.0754376\pi\) | |||||||
\(450\) | 0.789728 | − | 12.7034i | 0.0372281 | − | 0.598844i | ||||
\(451\) | 5.50000 | − | 9.52628i | 0.258985 | − | 0.448575i | ||||
\(452\) | 28.7228 | − | 16.5831i | 1.35101 | − | 0.780005i | ||||
\(453\) | −5.92010 | + | 5.56349i | −0.278150 | + | 0.261396i | ||||
\(454\) | −20.3101 | − | 11.7260i | −0.953200 | − | 0.550330i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.46718 | + | 21.2112i | 0.115536 | + | 0.993303i | ||||
\(457\) | 25.0000 | 1.16945 | 0.584725 | − | 0.811231i | \(-0.301202\pi\) | ||||
0.584725 | + | 0.811231i | \(0.301202\pi\) | |||||||
\(458\) | 11.4891 | + | 6.63325i | 0.536852 | + | 0.309951i | ||||
\(459\) | −33.9783 | + | 5.78606i | −1.58597 | + | 0.270070i | ||||
\(460\) | 6.00000 | + | 10.3923i | 0.279751 | + | 0.484544i | ||||
\(461\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(462\) | 37.0951 | − | 8.71516i | 1.72582 | − | 0.405466i | ||||
\(463\) | − | 9.38083i | − | 0.435964i | −0.975953 | − | 0.217982i | \(-0.930053\pi\) | ||
0.975953 | − | 0.217982i | \(-0.0699474\pi\) | |||||||
\(464\) | −28.2843 | −1.31306 | ||||||||
\(465\) | 2.62772 | + | 11.1846i | 0.121858 | + | 0.518673i | ||||
\(466\) | −20.3101 | + | 11.7260i | −0.940847 | + | 0.543198i | ||||
\(467\) | 16.5831i | 0.767375i | 0.923463 | + | 0.383688i | \(0.125346\pi\) | ||||
−0.923463 | + | 0.383688i | \(0.874654\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.3101 | + | 11.7260i | −0.937833 | + | 0.541458i | ||||
\(470\) | 7.07107 | − | 12.2474i | 0.326164 | − | 0.564933i | ||||
\(471\) | 7.43231 | + | 31.6348i | 0.342463 | + | 1.45765i | ||||
\(472\) | 8.12404 | + | 4.69042i | 0.373939 | + | 0.215894i | ||||
\(473\) | −17.2337 | − | 9.94987i | −0.792406 | − | 0.457496i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.50000 | − | 12.9904i | 0.0688247 | − | 0.596040i | ||||
\(476\) | 62.2254 | 2.85210 | ||||||||
\(477\) | 30.3902 | − | 15.1141i | 1.39147 | − | 0.692026i | ||||
\(478\) | 10.0000 | − | 17.3205i | 0.457389 | − | 0.792222i | ||||
\(479\) | 19.7990 | + | 34.2929i | 0.904639 | + | 1.56688i | 0.821401 | + | 0.570351i | \(0.193193\pi\) |
0.0832378 | + | 0.996530i | \(0.473474\pi\) | |||||||
\(480\) | 9.48913 | + | 10.0974i | 0.433117 | + | 0.460879i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 35.3553 | 1.61039 | ||||||||
\(483\) | 33.0000 | + | 9.94987i | 1.50155 | + | 0.452735i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.6066 | − | 18.3712i | −0.481621 | − | 0.834192i | ||||
\(486\) | −21.9203 | + | 2.34521i | −0.994325 | + | 0.106381i | ||||
\(487\) | − | 4.69042i | − | 0.212543i | −0.994337 | − | 0.106272i | \(-0.966109\pi\) | ||
0.994337 | − | 0.106272i | \(-0.0338913\pi\) | |||||||
\(488\) | −11.4891 | + | 6.63325i | −0.520088 | + | 0.300273i | ||||
\(489\) | −17.7921 | − | 18.9325i | −0.804587 | − | 0.856159i | ||||
\(490\) | −15.0000 | − | 25.9808i | −0.677631 | − | 1.17369i | ||||
\(491\) | 11.4891 | + | 6.63325i | 0.518497 | + | 0.299354i | 0.736319 | − | 0.676634i | \(-0.236562\pi\) |
−0.217823 | + | 0.975988i | \(0.569895\pi\) | |||||||
\(492\) | 8.37228 | − | 7.86797i | 0.377452 | − | 0.354715i | ||||
\(493\) | − | 46.9042i | − | 2.11246i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.77817 | + | 11.7260i | −0.349603 | + | 0.527046i | ||||
\(496\) | 16.2481 | + | 9.38083i | 0.729560 | + | 0.421212i | ||||
\(497\) | −22.9783 | − | 13.2665i | −1.03072 | − | 0.595084i | ||||
\(498\) | 1.85808 | + | 7.90870i | 0.0832625 | + | 0.354397i | ||||
\(499\) | 6.50000 | − | 11.2583i | 0.290980 | − | 0.503992i | −0.683062 | − | 0.730361i | \(-0.739352\pi\) |
0.974042 | + | 0.226369i | \(0.0726854\pi\) | |||||||
\(500\) | −11.3137 | − | 19.5959i | −0.505964 | − | 0.876356i | ||||
\(501\) | −4.24264 | + | 14.0712i | −0.189547 | + | 0.628657i | ||||
\(502\) | 23.4521i | 1.04672i | ||||||||
\(503\) | 16.2635 | + | 28.1691i | 0.725152 | + | 1.25600i | 0.958912 | + | 0.283705i | \(0.0915637\pi\) |
−0.233760 | + | 0.972294i | \(0.575103\pi\) | |||||||
\(504\) | 39.7228 | + | 2.46943i | 1.76939 | + | 0.109997i | ||||
\(505\) | −10.0000 | −0.444994 | ||||||||
\(506\) | 19.8997i | 0.884652i | ||||||||
\(507\) | 21.9198 | − | 5.14987i | 0.973494 | − | 0.228714i | ||||
\(508\) | −32.4962 | − | 18.7617i | −1.44178 | − | 0.832414i | ||||
\(509\) | 8.48528 | + | 14.6969i | 0.376103 | + | 0.651430i | 0.990492 | − | 0.137574i | \(-0.0439304\pi\) |
−0.614388 | + | 0.789004i | \(0.710597\pi\) | |||||||
\(510\) | −16.7446 | + | 15.7359i | −0.741462 | + | 0.696799i | ||||
\(511\) | 4.06202 | + | 2.34521i | 0.179693 | + | 0.103746i | ||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | −22.6168 | + | 1.21588i | −0.998558 | + | 0.0536825i | ||||
\(514\) | 14.0712i | 0.620656i | ||||||||
\(515\) | 11.4891 | + | 6.63325i | 0.506271 | + | 0.292296i | ||||
\(516\) | −14.2337 | − | 15.1460i | −0.626603 | − | 0.666767i | ||||
\(517\) | 20.3101 | − | 11.7260i | 0.893237 | − | 0.515711i | ||||
\(518\) | −15.5563 | + | 26.9444i | −0.683507 | + | 1.18387i | ||||
\(519\) | −4.76913 | + | 1.12046i | −0.209341 | + | 0.0491829i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.5831i | 0.726520i | 0.931688 | + | 0.363260i | \(0.118336\pi\) | ||||
−0.931688 | + | 0.363260i | \(0.881664\pi\) | |||||||
\(522\) | 1.86141 | − | 29.9422i | 0.0814716 | − | 1.31053i | ||||
\(523\) | 5.00000 | + | 8.66025i | 0.218635 | + | 0.378686i | 0.954391 | − | 0.298560i | \(-0.0965063\pi\) |
−0.735756 | + | 0.677247i | \(0.763173\pi\) | |||||||
\(524\) | 6.63325i | 0.289775i | ||||||||
\(525\) | −23.3345 | − | 7.03562i | −1.01840 | − | 0.307060i | ||||
\(526\) | −3.00000 | − | 5.19615i | −0.130806 | − | 0.226563i | ||||
\(527\) | −15.5563 | + | 26.9444i | −0.677645 | + | 1.17372i | ||||
\(528\) | 5.25544 | + | 22.3692i | 0.228714 | + | 0.973494i | ||||
\(529\) | 2.50000 | − | 4.33013i | 0.108696 | − | 0.188266i | ||||
\(530\) | 11.3137 | − | 19.5959i | 0.491436 | − | 0.851192i | ||||
\(531\) | −5.50000 | + | 8.29156i | −0.238680 | + | 0.359823i | ||||
\(532\) | 40.6202 | + | 4.69042i | 1.76111 | + | 0.203355i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 11.8402 | − | 11.1270i | 0.512375 | − | 0.481512i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.07107 | − | 12.2474i | −0.305424 | − | 0.529009i | ||||
\(537\) | −12.5584 | + | 11.8020i | −0.541936 | + | 0.509292i | ||||
\(538\) | −8.00000 | − | 13.8564i | −0.344904 | − | 0.597392i | ||||
\(539\) | − | 49.7494i | − | 2.14286i | ||||||
\(540\) | −11.3137 | + | 9.38083i | −0.486864 | + | 0.403687i | ||||
\(541\) | −16.2481 | + | 9.38083i | −0.698559 | + | 0.403313i | −0.806811 | − | 0.590810i | \(-0.798808\pi\) |
0.108251 | + | 0.994124i | \(0.465475\pi\) | |||||||
\(542\) | 28.7228 | − | 16.5831i | 1.23375 | − | 0.712306i | ||||
\(543\) | −38.8909 | − | 11.7260i | −1.66897 | − | 0.503213i | ||||
\(544\) | 37.5233i | 1.60880i | ||||||||
\(545\) | 11.4891 | − | 6.63325i | 0.492140 | − | 0.284137i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.00000 | + | 8.66025i | 0.213785 | + | 0.370286i | 0.952896 | − | 0.303298i | \(-0.0980876\pi\) |
−0.739111 | + | 0.673583i | \(0.764754\pi\) | |||||||
\(548\) | −28.7228 | − | 16.5831i | −1.22698 | − | 0.708396i | ||||
\(549\) | −6.26596 | − | 12.5991i | −0.267425 | − | 0.537717i | ||||
\(550\) | − | 14.0712i | − | 0.600000i | ||||||
\(551\) | 3.53553 | − | 30.6186i | 0.150619 | − | 1.30440i | ||||
\(552\) | −6.00000 | + | 19.8997i | −0.255377 | + | 0.846990i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 28.7228 | + | 16.5831i | 1.22032 | + | 0.704549i | ||||
\(555\) | −2.62772 | − | 11.1846i | −0.111540 | − | 0.474759i | ||||
\(556\) | −15.0000 | + | 25.9808i | −0.636142 | + | 1.10183i | ||||
\(557\) | −18.3848 | − | 31.8434i | −0.778988 | − | 1.34925i | −0.932526 | − | 0.361104i | \(-0.882400\pi\) |
0.153538 | − | 0.988143i | \(-0.450933\pi\) | |||||||
\(558\) | −11.0000 | + | 16.5831i | −0.465667 | + | 0.702020i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 22.9783 | − | 13.2665i | 0.971008 | − | 0.560612i | ||||
\(561\) | −37.0951 | + | 8.71516i | −1.56616 | + | 0.367954i | ||||
\(562\) | 4.69042i | 0.197853i | ||||||||
\(563\) | 16.5831i | 0.698895i | 0.936956 | + | 0.349448i | \(0.113631\pi\) | ||||
−0.936956 | + | 0.349448i | \(0.886369\pi\) | |||||||
\(564\) | 23.8456 | − | 5.60232i | 1.00408 | − | 0.235900i | ||||
\(565\) | 20.3101 | + | 11.7260i | 0.854452 | + | 0.493318i | ||||
\(566\) | −17.6777 | − | 30.6186i | −0.743048 | − | 1.28700i | ||||
\(567\) | −5.22837 | + | 41.8887i | −0.219571 | + | 1.75916i | ||||
\(568\) | 8.00000 | − | 13.8564i | 0.335673 | − | 0.581402i | ||||
\(569\) | 6.63325i | 0.278080i | 0.990287 | + | 0.139040i | \(0.0444017\pi\) | ||||
−0.990287 | + | 0.139040i | \(0.955598\pi\) | |||||||
\(570\) | −12.1168 | + | 9.01011i | −0.507519 | + | 0.377392i | ||||
\(571\) | 25.0000 | 1.04622 | 0.523109 | − | 0.852266i | \(-0.324772\pi\) | ||||
0.523109 | + | 0.852266i | \(0.324772\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.70982 | − | 7.13991i | −0.280307 | − | 0.298274i | ||||
\(574\) | −11.0000 | − | 19.0526i | −0.459131 | − | 0.795238i | ||||
\(575\) | 6.36396 | − | 11.0227i | 0.265396 | − | 0.459679i | ||||
\(576\) | −1.48913 | + | 23.9538i | −0.0620469 | + | 0.998073i | ||||
\(577\) | −15.0000 | −0.624458 | −0.312229 | − | 0.950007i | \(-0.601076\pi\) | ||||
−0.312229 | + | 0.950007i | \(0.601076\pi\) | |||||||
\(578\) | −38.1838 | −1.58824 | ||||||||
\(579\) | −33.7228 | + | 7.92287i | −1.40147 | + | 0.329263i | ||||
\(580\) | −10.0000 | − | 17.3205i | −0.415227 | − | 0.719195i | ||||
\(581\) | 15.5563 | 0.645386 | ||||||||
\(582\) | 10.6066 | − | 35.1781i | 0.439658 | − | 1.45818i | ||||
\(583\) | 32.4962 | − | 18.7617i | 1.34585 | − | 0.777029i | ||||
\(584\) | −1.41421 | + | 2.44949i | −0.0585206 | + | 0.101361i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.00000 | + | 12.1244i | −0.289167 | + | 0.500853i | ||||
\(587\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(588\) | 15.0000 | − | 49.7494i | 0.618590 | − | 2.05163i | ||||
\(589\) | −12.1861 | + | 16.4165i | −0.502118 | + | 0.676428i | ||||
\(590\) | 6.63325i | 0.273087i | ||||||||
\(591\) | −15.0971 | − | 16.0648i | −0.621012 | − | 0.660817i | ||||
\(592\) | −16.2481 | − | 9.38083i | −0.667792 | − | 0.385550i | ||||
\(593\) | −14.3614 | + | 8.29156i | −0.589752 | + | 0.340494i | −0.765000 | − | 0.644031i | \(-0.777261\pi\) |
0.175247 | + | 0.984524i | \(0.443928\pi\) | |||||||
\(594\) | −24.0263 | + | 4.09136i | −0.985809 | + | 0.167871i | ||||
\(595\) | 22.0000 | + | 38.1051i | 0.901912 | + | 1.56216i | ||||
\(596\) | −14.1421 | −0.579284 | ||||||||
\(597\) | 15.5563 | + | 4.69042i | 0.636679 | + | 0.191966i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.12132 | − | 3.67423i | −0.0866748 | − | 0.150125i | 0.819429 | − | 0.573181i | \(-0.194291\pi\) |
−0.906104 | + | 0.423056i | \(0.860957\pi\) | |||||||
\(600\) | 4.24264 | − | 14.0712i | 0.173205 | − | 0.574456i | ||||
\(601\) | 1.00000 | 0.0407909 | 0.0203954 | − | 0.999792i | \(-0.493507\pi\) | ||||
0.0203954 | + | 0.999792i | \(0.493507\pi\) | |||||||
\(602\) | −34.4674 | + | 19.8997i | −1.40479 | + | 0.811053i | ||||
\(603\) | 13.4307 | − | 6.67954i | 0.546941 | − | 0.272012i | ||||
\(604\) | −8.12404 | + | 4.69042i | −0.330562 | + | 0.190850i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.8614 | − | 12.6217i | −0.481837 | − | 0.512721i | ||||
\(607\) | − | 4.69042i | − | 0.190378i | −0.995459 | − | 0.0951891i | \(-0.969654\pi\) | ||
0.995459 | − | 0.0951891i | \(-0.0303456\pi\) | |||||||
\(608\) | −2.82843 | + | 24.4949i | −0.114708 | + | 0.993399i | ||||
\(609\) | −55.0000 | − | 16.5831i | −2.22871 | − | 0.671982i | ||||
\(610\) | −8.12404 | − | 4.69042i | −0.328933 | − | 0.189909i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −39.7228 | − | 2.46943i | −1.60570 | − | 0.0998210i | ||||
\(613\) | −32.4962 | − | 18.7617i | −1.31251 | − | 0.757776i | −0.329997 | − | 0.943982i | \(-0.607048\pi\) |
−0.982511 | + | 0.186206i | \(0.940381\pi\) | |||||||
\(614\) | −3.53553 | − | 6.12372i | −0.142683 | − | 0.247133i | ||||
\(615\) | 7.77817 | + | 2.34521i | 0.313646 | + | 0.0945679i | ||||
\(616\) | 44.0000 | 1.77281 | ||||||||
\(617\) | −8.61684 | + | 4.97494i | −0.346901 | + | 0.200283i | −0.663320 | − | 0.748336i | \(-0.730853\pi\) |
0.316418 | + | 0.948620i | \(0.397520\pi\) | |||||||
\(618\) | 5.25544 | + | 22.3692i | 0.211405 | + | 0.899821i | ||||
\(619\) | −38.0000 | −1.52735 | −0.763674 | − | 0.645601i | \(-0.776607\pi\) | ||||
−0.763674 | + | 0.645601i | \(0.776607\pi\) | |||||||
\(620\) | 13.2665i | 0.532795i | ||||||||
\(621\) | −20.6713 | − | 7.66131i | −0.829512 | − | 0.307438i | ||||
\(622\) | 5.00000 | − | 8.66025i | 0.200482 | − | 0.347245i | ||||
\(623\) | −15.5563 | − | 26.9444i | −0.623252 | − | 1.07950i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.500000 | − | 0.866025i | 0.0200000 | − | 0.0346410i | ||||
\(626\) | 15.5563 | 0.621757 | ||||||||
\(627\) | −24.8723 | + | 2.89303i | −0.993303 | + | 0.115536i | ||||
\(628\) | 37.5233i | 1.49734i | ||||||||
\(629\) | 15.5563 | − | 26.9444i | 0.620272 | − | 1.07434i | ||||
\(630\) | 12.5319 | + | 25.1982i | 0.499284 | + | 1.00392i | ||||
\(631\) | −4.06202 | + | 2.34521i | −0.161706 | + | 0.0933613i | −0.578669 | − | 0.815562i | \(-0.696428\pi\) |
0.416963 | + | 0.908923i | \(0.363094\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.9783 | − | 6.33830i | 1.07229 | − | 0.251925i | ||||
\(634\) | 28.0000 | 1.11202 | ||||||||
\(635\) | − | 26.5330i | − | 1.05293i | ||||||
\(636\) | 38.1530 | − | 8.96370i | 1.51287 | − | 0.355434i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 33.1662i | − | 1.31306i | ||||||
\(639\) | 14.1421 | + | 9.38083i | 0.559454 | + | 0.371100i | ||||
\(640\) | 8.00000 | + | 13.8564i | 0.316228 | + | 0.547723i | ||||
\(641\) | 43.0842 | + | 24.8747i | 1.70172 | + | 0.982491i | 0.944017 | + | 0.329896i | \(0.107014\pi\) |
0.757707 | + | 0.652595i | \(0.226320\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5000 | + | 25.1147i | −0.571824 | + | 0.990429i | 0.424555 | + | 0.905402i | \(0.360431\pi\) |
−0.996379 | + | 0.0850262i | \(0.972903\pi\) | |||||||
\(644\) | 34.4674 | + | 19.8997i | 1.35820 | + | 0.784160i | ||||
\(645\) | 4.24264 | − | 14.0712i | 0.167054 | − | 0.554055i | ||||
\(646\) | −40.6202 | − | 4.69042i | −1.59818 | − | 0.184542i | ||||
\(647\) | −8.48528 | −0.333591 | −0.166795 | − | 0.985992i | \(-0.553342\pi\) | ||||
−0.166795 | + | 0.985992i | \(0.553342\pi\) | |||||||
\(648\) | −25.2598 | − | 3.15283i | −0.992300 | − | 0.123855i | ||||
\(649\) | −5.50000 | + | 9.52628i | −0.215894 | + | 0.373939i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.0951 | + | 27.7677i | 1.02275 | + | 1.08830i | ||||
\(652\) | −15.0000 | − | 25.9808i | −0.587445 | − | 1.01749i | ||||
\(653\) | −2.82843 | −0.110685 | −0.0553425 | − | 0.998467i | \(-0.517625\pi\) | ||||
−0.0553425 | + | 0.998467i | \(0.517625\pi\) | |||||||
\(654\) | 22.0000 | + | 6.63325i | 0.860268 | + | 0.259381i | ||||
\(655\) | −4.06202 | + | 2.34521i | −0.158716 | + | 0.0916349i | ||||
\(656\) | 11.4891 | − | 6.63325i | 0.448575 | − | 0.258985i | ||||
\(657\) | −2.50000 | − | 1.65831i | −0.0975343 | − | 0.0646969i | ||||
\(658\) | − | 46.9042i | − | 1.82851i | ||||||
\(659\) | −22.9783 | + | 13.2665i | −0.895106 | + | 0.516789i | −0.875609 | − | 0.483020i | \(-0.839540\pi\) |
−0.0194965 | + | 0.999810i | \(0.506206\pi\) | |||||||
\(660\) | −11.8402 | + | 11.1270i | −0.460879 | + | 0.433117i | ||||
\(661\) | 36.5582 | − | 21.1069i | 1.42195 | − | 0.820962i | 0.425483 | − | 0.904967i | \(-0.360104\pi\) |
0.996465 | + | 0.0840044i | \(0.0267710\pi\) | |||||||
\(662\) | 7.77817 | − | 13.4722i | 0.302307 | − | 0.523612i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.38083i | 0.364047i | ||||||||
\(665\) | 11.4891 | + | 26.5330i | 0.445529 | + | 1.02891i | ||||
\(666\) | 11.0000 | − | 16.5831i | 0.426241 | − | 0.642583i | ||||
\(667\) | 15.0000 | − | 25.9808i | 0.580802 | − | 1.00598i | ||||
\(668\) | −8.48528 | + | 14.6969i | −0.328305 | + | 0.568642i | ||||
\(669\) | 5.57423 | + | 23.7261i | 0.215512 | + | 0.917304i | ||||
\(670\) | 5.00000 | − | 8.66025i | 0.193167 | − | 0.334575i | ||||
\(671\) | −7.77817 | − | 13.4722i | −0.300273 | − | 0.520088i | ||||
\(672\) | 44.0000 | + | 13.2665i | 1.69734 | + | 0.511766i | ||||
\(673\) | 20.0000 | 0.770943 | 0.385472 | − | 0.922720i | \(-0.374039\pi\) | ||||
0.385472 | + | 0.922720i | \(0.374039\pi\) | |||||||
\(674\) | −3.53553 | − | 6.12372i | −0.136184 | − | 0.235877i | ||||
\(675\) | 14.6168 | + | 5.41737i | 0.562603 | + | 0.208515i | ||||
\(676\) | 26.0000 | 1.00000 | ||||||||
\(677\) | −19.7990 | −0.760937 | −0.380468 | − | 0.924794i | \(-0.624237\pi\) | ||||
−0.380468 | + | 0.924794i | \(0.624237\pi\) | |||||||
\(678\) | 9.29039 | + | 39.5435i | 0.356795 | + | 1.51866i | ||||
\(679\) | −60.9303 | − | 35.1781i | −2.33829 | − | 1.35001i | ||||
\(680\) | −22.9783 | + | 13.2665i | −0.881176 | + | 0.508747i | ||||
\(681\) | 20.9307 | − | 19.6699i | 0.802066 | − | 0.753753i | ||||
\(682\) | −11.0000 | + | 19.0526i | −0.421212 | + | 0.729560i | ||||
\(683\) | 13.2665i | 0.507628i | 0.967253 | + | 0.253814i | \(0.0816852\pi\) | ||||
−0.967253 | + | 0.253814i | \(0.918315\pi\) | |||||||
\(684\) | −25.7446 | − | 4.60625i | −0.984368 | − | 0.176124i | ||||
\(685\) | − | 23.4521i | − | 0.896058i | ||||||
\(686\) | −45.9565 | − | 26.5330i | −1.75463 | − | 1.01303i | ||||
\(687\) | −11.8402 | + | 11.1270i | −0.451732 | + | 0.424521i | ||||
\(688\) | −12.0000 | − | 20.7846i | −0.457496 | − | 0.792406i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −14.3074 | + | 3.36139i | −0.544673 | + | 0.127966i | ||||
\(691\) | 14.0000 | 0.532585 | 0.266293 | − | 0.963892i | \(-0.414201\pi\) | ||||
0.266293 | + | 0.963892i | \(0.414201\pi\) | |||||||
\(692\) | −5.65685 | −0.215041 | ||||||||
\(693\) | −2.89567 | + | 46.5791i | −0.109997 | + | 1.76939i | ||||
\(694\) | 20.3101 | − | 11.7260i | 0.770961 | − | 0.445114i | ||||
\(695\) | −21.2132 | −0.804663 | ||||||||
\(696\) | 10.0000 | − | 33.1662i | 0.379049 | − | 1.25716i | ||||
\(697\) | 11.0000 | + | 19.0526i | 0.416655 | + | 0.721667i | ||||
\(698\) | −11.4891 | − | 6.63325i | −0.434870 | − | 0.251072i | ||||
\(699\) | −6.56930 | − | 27.9615i | −0.248474 | − | 1.05760i | ||||
\(700\) | −24.3721 | − | 14.0712i | −0.921179 | − | 0.531843i | ||||
\(701\) | 0.707107 | − | 1.22474i | 0.0267071 | − | 0.0462580i | −0.852363 | − | 0.522951i | \(-0.824831\pi\) |
0.879070 | + | 0.476693i | \(0.158165\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.1861 | − | 16.4165i | 0.459606 | − | 0.619158i | ||||
\(704\) | 26.5330i | 1.00000i | ||||||||
\(705\) | 11.8614 | + | 12.6217i | 0.446726 | + | 0.475360i | ||||
\(706\) | 20.3101 | + | 11.7260i | 0.764381 | + | 0.441315i | ||||
\(707\) | −28.7228 | + | 16.5831i | −1.08023 | + | 0.623673i | ||||
\(708\) | −8.37228 | + | 7.86797i | −0.314650 | + | 0.295696i | ||||
\(709\) | −28.4341 | + | 16.4165i | −1.06787 | + | 0.616533i | −0.927598 | − | 0.373581i | \(-0.878130\pi\) |
−0.140269 | + | 0.990113i | \(0.544797\pi\) | |||||||
\(710\) | 11.3137 | 0.424596 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.2481 | − | 9.38083i | 0.608922 | − | 0.351562i | ||||
\(713\) | −17.2337 | + | 9.94987i | −0.645407 | + | 0.372626i | ||||
\(714\) | −22.0000 | + | 72.9657i | −0.823329 | + | 2.73067i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.2337 | + | 9.94987i | −0.644053 | + | 0.371844i | ||||
\(717\) | 16.7746 | + | 17.8498i | 0.626458 | + | 0.666612i | ||||
\(718\) | 17.0000 | + | 29.4449i | 0.634434 | + | 1.09887i | ||||
\(719\) | 19.7990 | − | 34.2929i | 0.738378 | − | 1.27891i | −0.214848 | − | 0.976648i | \(-0.568926\pi\) |
0.953225 | − | 0.302260i | \(-0.0977411\pi\) | |||||||
\(720\) | −15.1951 | + | 7.55703i | −0.566288 | + | 0.281634i | ||||
\(721\) | 44.0000 | 1.63865 | ||||||||
\(722\) | −26.1630 | − | 6.12372i | −0.973684 | − | 0.227901i | ||||
\(723\) | −12.5000 | + | 41.4578i | −0.464880 | + | 1.54183i | ||||
\(724\) | −40.6202 | − | 23.4521i | −1.50964 | − | 0.871590i | ||||
\(725\) | −10.6066 | + | 18.3712i | −0.393919 | + | 0.682288i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.00000 | − | 26.5330i | 0.185185 | − | 0.982704i | ||||
\(730\) | −2.00000 | −0.0740233 | ||||||||
\(731\) | 34.4674 | − | 19.8997i | 1.27482 | − | 0.736019i | ||||
\(732\) | −3.71616 | − | 15.8174i | −0.137353 | − | 0.584628i | ||||
\(733\) | 32.8329i | 1.21271i | 0.795194 | + | 0.606356i | \(0.207369\pi\) | ||||
−0.795194 | + | 0.606356i | \(0.792631\pi\) | |||||||
\(734\) | − | 33.1662i | − | 1.22419i | ||||||
\(735\) | 35.7684 | − | 8.40347i | 1.31934 | − | 0.309967i | ||||
\(736\) | −12.0000 | + | 20.7846i | −0.442326 | + | 0.766131i | ||||
\(737\) | 14.3614 | − | 8.29156i | 0.529009 | − | 0.305424i | ||||
\(738\) | 6.26596 | + | 12.5991i | 0.230653 | + | 0.463780i | ||||
\(739\) | 3.50000 | − | 6.06218i | 0.128750 | − | 0.223001i | −0.794443 | − | 0.607339i | \(-0.792237\pi\) |
0.923192 | + | 0.384338i | \(0.125570\pi\) | |||||||
\(740\) | − | 13.2665i | − | 0.487686i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 75.0467i | − | 2.75505i | ||||||
\(743\) | −12.0208 | + | 20.8207i | −0.441001 | + | 0.763836i | −0.997764 | − | 0.0668353i | \(-0.978710\pi\) |
0.556763 | + | 0.830671i | \(0.312043\pi\) | |||||||
\(744\) | −16.7446 | + | 15.7359i | −0.613885 | + | 0.576907i | ||||
\(745\) | −5.00000 | − | 8.66025i | −0.183186 | − | 0.317287i | ||||
\(746\) | 11.4891 | + | 6.63325i | 0.420647 | + | 0.242861i | ||||
\(747\) | −9.93070 | − | 0.617359i | −0.363345 | − | 0.0225880i | ||||
\(748\) | −44.0000 | −1.60880 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 26.9783 | − | 6.33830i | 0.985106 | − | 0.231442i | ||||
\(751\) | 24.3721 | − | 14.0712i | 0.889351 | − | 0.513467i | 0.0156209 | − | 0.999878i | \(-0.495028\pi\) |
0.873730 | + | 0.486411i | \(0.161694\pi\) | |||||||
\(752\) | 28.2843 | 1.03142 | ||||||||
\(753\) | −27.5000 | − | 8.29156i | −1.00216 | − | 0.302161i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.74456 | − | 3.31662i | −0.209066 | − | 0.120704i | ||||
\(756\) | −16.9398 | + | 45.7061i | −0.616095 | + | 1.66231i | ||||
\(757\) | −16.2481 | − | 9.38083i | −0.590546 | − | 0.340952i | 0.174767 | − | 0.984610i | \(-0.444083\pi\) |
−0.765314 | + | 0.643658i | \(0.777416\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −23.3345 | − | 7.03562i | −0.846990 | − | 0.255377i | ||||
\(760\) | −16.0000 | + | 6.92820i | −0.580381 | + | 0.251312i | ||||
\(761\) | 3.31662i | 0.120228i | 0.998192 | + | 0.0601138i | \(0.0191464\pi\) | ||||
−0.998192 | + | 0.0601138i | \(0.980854\pi\) | |||||||
\(762\) | 33.4891 | − | 31.4719i | 1.21318 | − | 1.14011i | ||||
\(763\) | 22.0000 | − | 38.1051i | 0.796453 | − | 1.37950i | ||||
\(764\) | −5.65685 | − | 9.79796i | −0.204658 | − | 0.354478i | ||||
\(765\) | −12.5319 | − | 25.1982i | −0.453093 | − | 0.911044i | ||||
\(766\) | 5.00000 | + | 8.66025i | 0.180657 | + | 0.312908i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −8.00000 | + | 26.5330i | −0.288675 | + | 0.957427i | ||||
\(769\) | 12.0000 | + | 20.7846i | 0.432731 | + | 0.749512i | 0.997107 | − | 0.0760054i | \(-0.0242166\pi\) |
−0.564376 | + | 0.825518i | \(0.690883\pi\) | |||||||
\(770\) | 15.5563 | + | 26.9444i | 0.560612 | + | 0.971008i | ||||
\(771\) | −16.5000 | − | 4.97494i | −0.594233 | − | 0.179168i | ||||
\(772\) | −40.0000 | −1.43963 | ||||||||
\(773\) | 12.0208 | + | 20.8207i | 0.432359 | + | 0.748867i | 0.997076 | − | 0.0764173i | \(-0.0243481\pi\) |
−0.564717 | + | 0.825284i | \(0.691015\pi\) | |||||||
\(774\) | 22.7927 | − | 11.3355i | 0.819265 | − | 0.407448i | ||||
\(775\) | 12.1861 | − | 7.03562i | 0.437736 | − | 0.252727i | ||||
\(776\) | 21.2132 | − | 36.7423i | 0.761510 | − | 1.31897i | ||||
\(777\) | −26.0951 | − | 27.7677i | −0.936156 | − | 0.996161i | ||||
\(778\) | −4.00000 | −0.143407 | ||||||||
\(779\) | 5.74456 | + | 13.2665i | 0.205820 | + | 0.475322i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.2481 | + | 9.38083i | 0.581402 | + | 0.335673i | ||||
\(782\) | −34.4674 | − | 19.8997i | −1.23255 | − | 0.711614i | ||||
\(783\) | 34.4522 | + | 12.7689i | 1.23122 | + | 0.456322i | ||||
\(784\) | 30.0000 | − | 51.9615i | 1.07143 | − | 1.85577i | ||||
\(785\) | −22.9783 | + | 13.2665i | −0.820129 | + | 0.473502i | ||||
\(786\) | −7.77817 | − | 2.34521i | −0.277438 | − | 0.0836508i | ||||
\(787\) | −35.0000 | −1.24762 | −0.623808 | − | 0.781578i | \(-0.714415\pi\) | ||||
−0.623808 | + | 0.781578i | \(0.714415\pi\) | |||||||
\(788\) | −12.7279 | − | 22.0454i | −0.453413 | − | 0.785335i | ||||
\(789\) | 7.15369 | − | 1.68069i | 0.254678 | − | 0.0598343i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 77.7817 | 2.76560 | ||||||||
\(792\) | −28.0883 | − | 1.74615i | −0.998073 | − | 0.0620469i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 5.74456 | − | 3.31662i | 0.203867 | − | 0.117703i | ||||
\(795\) | 18.9783 | + | 20.1947i | 0.673089 | + | 0.716232i | ||||
\(796\) | 16.2481 | + | 9.38083i | 0.575898 | + | 0.332495i | ||||
\(797\) | −26.8701 | −0.951786 | −0.475893 | − | 0.879503i | \(-0.657875\pi\) | ||||
−0.475893 | + | 0.879503i | \(0.657875\pi\) | |||||||
\(798\) | −19.8614 | + | 45.9731i | −0.703086 | + | 1.62743i | ||||
\(799\) | 46.9042i | 1.65935i | ||||||||
\(800\) | 8.48528 | − | 14.6969i | 0.300000 | − | 0.519615i | ||||
\(801\) | 8.86141 | + | 17.8178i | 0.313102 | + | 0.629562i | ||||
\(802\) | 20.3101 | − | 11.7260i | 0.717174 | − | 0.414061i | ||||
\(803\) | −2.87228 | − | 1.65831i | −0.101361 | − | 0.0585206i | ||||
\(804\) | 16.8614 | − | 3.96143i | 0.594656 | − | 0.139709i | ||||
\(805\) | 28.1425i | 0.991893i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.0765 | − | 4.48185i | 0.671525 | − | 0.157769i | ||||
\(808\) | −10.0000 | − | 17.3205i | −0.351799 | − | 0.609333i | ||||
\(809\) | − | 49.7494i | − | 1.74909i | −0.484940 | − | 0.874547i | \(-0.661159\pi\) | ||
0.484940 | − | 0.874547i | \(-0.338841\pi\) | |||||||
\(810\) | −7.00000 | − | 16.5831i | −0.245955 | − | 0.582672i | ||||
\(811\) | −7.00000 | − | 12.1244i | −0.245803 | − | 0.425744i | 0.716554 | − | 0.697532i | \(-0.245718\pi\) |
−0.962357 | + | 0.271788i | \(0.912385\pi\) | |||||||
\(812\) | −57.4456 | − | 33.1662i | −2.01595 | − | 1.16391i | ||||
\(813\) | 9.29039 | + | 39.5435i | 0.325828 | + | 1.38685i | ||||
\(814\) | 11.0000 | − | 19.0526i | 0.385550 | − | 0.667792i | ||||
\(815\) | 10.6066 | − | 18.3712i | 0.371533 | − | 0.643514i | ||||
\(816\) | −44.0000 | − | 13.2665i | −1.54031 | − | 0.464420i | ||||
\(817\) | 24.0000 | − | 10.3923i | 0.839654 | − | 0.363581i | ||||
\(818\) | −38.1838 | −1.33506 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.12404 | + | 4.69042i | 0.283704 | + | 0.163796i | ||||
\(821\) | −28.2843 | − | 48.9898i | −0.987128 | − | 1.70976i | −0.632070 | − | 0.774911i | \(-0.717794\pi\) |
−0.355058 | − | 0.934844i | \(-0.615539\pi\) | |||||||
\(822\) | 29.6005 | − | 27.8175i | 1.03244 | − | 0.970245i | ||||
\(823\) | 8.12404 | − | 4.69042i | 0.283186 | − | 0.163498i | −0.351679 | − | 0.936121i | \(-0.614389\pi\) |
0.634865 | + | 0.772623i | \(0.281056\pi\) | |||||||
\(824\) | 26.5330i | 0.924321i | ||||||||
\(825\) | 16.5000 | + | 4.97494i | 0.574456 | + | 0.173205i | ||||
\(826\) | 11.0000 | + | 19.0526i | 0.382739 | + | 0.662923i | ||||
\(827\) | −14.3614 | + | 8.29156i | −0.499395 | + | 0.288326i | −0.728464 | − | 0.685084i | \(-0.759765\pi\) |
0.229069 | + | 0.973410i | \(0.426432\pi\) | |||||||
\(828\) | −21.2132 | − | 14.0712i | −0.737210 | − | 0.489010i | ||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | −5.74456 | + | 3.31662i | −0.199397 | + | 0.115122i | ||||
\(831\) | −29.6005 | + | 27.8175i | −1.02683 | + | 0.964977i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 86.1684 | + | 49.7494i | 2.98556 | + | 1.72371i | ||||
\(834\) | −25.1618 | − | 26.7746i | −0.871283 | − | 0.927130i | ||||
\(835\) | −12.0000 | −0.415277 | ||||||||
\(836\) | −28.7228 | − | 3.31662i | −0.993399 | − | 0.114708i | ||||
\(837\) | −15.5563 | − | 18.7617i | −0.537706 | − | 0.648498i | ||||
\(838\) | 32.4962 | + | 18.7617i | 1.12256 | + | 0.648111i | ||||
\(839\) | −4.94975 | + | 8.57321i | −0.170884 | + | 0.295980i | −0.938729 | − | 0.344655i | \(-0.887996\pi\) |
0.767845 | + | 0.640636i | \(0.221329\pi\) | |||||||
\(840\) | 7.43231 | + | 31.6348i | 0.256439 | + | 1.09150i | ||||
\(841\) | −10.5000 | + | 18.1865i | −0.362069 | + | 0.627122i | ||||
\(842\) | −28.7228 | + | 16.5831i | −0.989854 | + | 0.571492i | ||||
\(843\) | −5.50000 | − | 1.65831i | −0.189430 | − | 0.0571153i | ||||
\(844\) | 32.0000 | 1.10149 | ||||||||
\(845\) | 9.19239 | + | 15.9217i | 0.316228 | + | 0.547723i | ||||
\(846\) | −1.86141 | + | 29.9422i | −0.0639965 | + | 1.02943i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 45.2548 | 1.55406 | ||||||||
\(849\) | 42.1535 | − | 9.90359i | 1.44670 | − | 0.339890i | ||||
\(850\) | 24.3721 | + | 14.0712i | 0.835957 | + | 0.482640i | ||||
\(851\) | 17.2337 | − | 9.94987i | 0.590763 | − | 0.341077i | ||||
\(852\) | 13.4196 | + | 14.2798i | 0.459750 | + | 0.489218i | ||||
\(853\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(854\) | −31.1127 | −1.06465 | ||||||||
\(855\) | −6.28134 | − | 17.3938i | −0.214817 | − | 0.594856i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.0842 | + | 24.8747i | 1.47173 | + | 0.849703i | 0.999495 | − | 0.0317703i | \(-0.0101145\pi\) |
0.472234 | + | 0.881473i | \(0.343448\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.5000 | + | 28.5788i | 0.562973 | + | 0.975097i | 0.997235 | + | 0.0743110i | \(0.0236757\pi\) |
−0.434262 | + | 0.900786i | \(0.642991\pi\) | |||||||
\(860\) | 8.48528 | − | 14.6969i | 0.289346 | − | 0.501161i | ||||
\(861\) | 26.2302 | − | 6.16255i | 0.893923 | − | 0.210019i | ||||
\(862\) | −20.0000 | −0.681203 | ||||||||
\(863\) | −4.24264 | −0.144421 | −0.0722106 | − | 0.997389i | \(-0.523005\pi\) | ||||
−0.0722106 | + | 0.997389i | \(0.523005\pi\) | |||||||
\(864\) | −27.5618 | − | 10.2151i | −0.937671 | − | 0.347524i | ||||
\(865\) | −2.00000 | − | 3.46410i | −0.0680020 | − | 0.117783i | ||||
\(866\) | −28.2843 | −0.961139 | ||||||||
\(867\) | 13.5000 | − | 44.7744i | 0.458484 | − | 1.52062i | ||||
\(868\) | 22.0000 | + | 38.1051i | 0.746729 | + | 1.29337i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 23.8456 | − | 5.60232i | 0.808443 | − | 0.189936i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 22.9783 | + | 13.2665i | 0.778142 | + | 0.449260i | ||||
\(873\) | 37.5000 | + | 24.8747i | 1.26918 | + | 0.841881i | ||||
\(874\) | −21.0000 | − | 15.5885i | −0.710336 | − | 0.527287i | ||||
\(875\) | − | 53.0660i | − | 1.79396i | ||||||
\(876\) | −2.37228 | − | 2.52434i | −0.0801520 | − | 0.0852895i | ||||
\(877\) | −4.06202 | − | 2.34521i | −0.137165 | − | 0.0791920i | 0.429847 | − | 0.902902i | \(-0.358567\pi\) |
−0.567012 | + | 0.823710i | \(0.691901\pi\) | |||||||
\(878\) | −28.7228 | + | 16.5831i | −0.969348 | + | 0.559653i | ||||
\(879\) | −11.7422 | − | 12.4948i | −0.396054 | − | 0.421440i | ||||
\(880\) | −16.2481 | + | 9.38083i | −0.547723 | + | 0.316228i | ||||
\(881\) | − | 29.8496i | − | 1.00566i | −0.864386 | − | 0.502830i | \(-0.832292\pi\) | ||
0.864386 | − | 0.502830i | \(-0.167708\pi\) | |||||||
\(882\) | 53.0330 | + | 35.1781i | 1.78571 | + | 1.18451i | ||||
\(883\) | −12.5000 | − | 21.6506i | −0.420658 | − | 0.728602i | 0.575346 | − | 0.817910i | \(-0.304868\pi\) |
−0.996004 | + | 0.0893086i | \(0.971534\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.77817 | − | 2.34521i | −0.261460 | − | 0.0788333i | ||||
\(886\) | 4.69042i | 0.157578i | ||||||||
\(887\) | −21.2132 | − | 36.7423i | −0.712270 | − | 1.23369i | −0.964003 | − | 0.265891i | \(-0.914334\pi\) |
0.251734 | − | 0.967797i | \(-0.418999\pi\) | |||||||
\(888\) | 16.7446 | − | 15.7359i | 0.561911 | − | 0.528063i | ||||
\(889\) | −44.0000 | − | 76.2102i | −1.47571 | − | 2.55601i | ||||
\(890\) | 11.4891 | + | 6.63325i | 0.385116 | + | 0.222347i | ||||
\(891\) | 3.69702 | − | 29.6198i | 0.123855 | − | 0.992300i | ||||
\(892\) | 28.1425i | 0.942280i | ||||||||
\(893\) | −3.53553 | + | 30.6186i | −0.118312 | + | 1.02461i | ||||
\(894\) | 5.00000 | − | 16.5831i | 0.167225 | − | 0.554623i | ||||
\(895\) | −12.1861 | − | 7.03562i | −0.407335 | − | 0.235175i | ||||
\(896\) | 45.9565 | + | 26.5330i | 1.53530 | + | 0.886405i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.1861 | + | 7.03562i | 0.406654 | + | 0.234782i | ||||
\(899\) | 28.7228 | − | 16.5831i | 0.957959 | − | 0.553078i | ||||
\(900\) | 15.0000 | + | 9.94987i | 0.500000 | + | 0.331662i | ||||
\(901\) | 75.0467i | 2.50017i | ||||||||
\(902\) | 7.77817 | + | 13.4722i | 0.258985 | + | 0.448575i | ||||
\(903\) | −11.1485 | − | 47.4522i | −0.370998 | − | 1.57911i | ||||
\(904\) | 46.9042i | 1.56001i | ||||||||
\(905\) | − | 33.1662i | − | 1.10248i | ||||||
\(906\) | −2.62772 | − | 11.1846i | −0.0873001 | − | 0.371583i | ||||
\(907\) | 1.50000 | − | 2.59808i | 0.0498067 | − | 0.0862677i | −0.840047 | − | 0.542513i | \(-0.817473\pi\) |
0.889854 | + | 0.456246i | \(0.150806\pi\) | |||||||
\(908\) | 28.7228 | − | 16.5831i | 0.953200 | − | 0.550330i | ||||
\(909\) | 18.9939 | − | 9.44629i | 0.629987 | − | 0.313314i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.3553 | 1.17137 | 0.585687 | − | 0.810537i | \(-0.300825\pi\) | ||||
0.585687 | + | 0.810537i | \(0.300825\pi\) | |||||||
\(912\) | −27.7228 | − | 11.9769i | −0.917994 | − | 0.396594i | ||||
\(913\) | −11.0000 | −0.364047 | ||||||||
\(914\) | −17.6777 | + | 30.6186i | −0.584725 | + | 1.01277i | ||||
\(915\) | 8.37228 | − | 7.86797i | 0.276779 | − | 0.260107i | ||||
\(916\) | −16.2481 | + | 9.38083i | −0.536852 | + | 0.309951i | ||||
\(917\) | −7.77817 | + | 13.4722i | −0.256858 | + | 0.444891i | ||||
\(918\) | 16.9398 | − | 45.7061i | 0.559097 | − | 1.50852i | ||||
\(919\) | − | 56.2850i | − | 1.85667i | −0.371744 | − | 0.928335i | \(-0.621240\pi\) | ||
0.371744 | − | 0.928335i | \(-0.378760\pi\) | |||||||
\(920\) | −16.9706 | −0.559503 | ||||||||
\(921\) | 8.43070 | − | 1.98072i | 0.277801 | − | 0.0652669i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −15.5563 | + | 51.5946i | −0.511766 | + | 1.69734i | ||||
\(925\) | −12.1861 | + | 7.03562i | −0.400675 | + | 0.231330i | ||||
\(926\) | 11.4891 | + | 6.63325i | 0.377556 | + | 0.217982i | ||||
\(927\) | −28.0883 | − | 1.74615i | −0.922540 | − | 0.0573512i | ||||
\(928\) | 20.0000 | − | 34.6410i | 0.656532 | − | 1.13715i | ||||
\(929\) | −8.61684 | − | 4.97494i | −0.282709 | − | 0.163222i | 0.351940 | − | 0.936023i | \(-0.385522\pi\) |
−0.634649 | + | 0.772800i | \(0.718855\pi\) | |||||||
\(930\) | −15.5563 | − | 4.69042i | −0.510113 | − | 0.153805i | ||||
\(931\) | 52.5000 | + | 38.9711i | 1.72062 | + | 1.27723i | ||||
\(932\) | − | 33.1662i | − | 1.08640i | ||||||
\(933\) | 8.38728 | + | 8.92488i | 0.274587 | + | 0.292188i | ||||
\(934\) | −20.3101 | − | 11.7260i | −0.664567 | − | 0.383688i | ||||
\(935\) | −15.5563 | − | 26.9444i | −0.508747 | − | 0.881176i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.50000 | − | 6.06218i | −0.114340 | − | 0.198043i | 0.803176 | − | 0.595742i | \(-0.203142\pi\) |
−0.917516 | + | 0.397699i | \(0.869809\pi\) | |||||||
\(938\) | − | 33.1662i | − | 1.08292i | ||||||
\(939\) | −5.50000 | + | 18.2414i | −0.179486 | + | 0.595287i | ||||
\(940\) | 10.0000 | + | 17.3205i | 0.326164 | + | 0.564933i | ||||
\(941\) | 21.2132 | + | 36.7423i | 0.691531 | + | 1.19777i | 0.971336 | + | 0.237710i | \(0.0763966\pi\) |
−0.279806 | + | 0.960057i | \(0.590270\pi\) | |||||||
\(942\) | −44.0000 | − | 13.2665i | −1.43360 | − | 0.432246i | ||||
\(943\) | 14.0712i | 0.458223i | ||||||||
\(944\) | −11.4891 | + | 6.63325i | −0.373939 | + | 0.215894i | ||||
\(945\) | −33.9783 | + | 5.78606i | −1.10531 | + | 0.188221i | ||||
\(946\) | 24.3721 | − | 14.0712i | 0.792406 | − | 0.457496i | ||||
\(947\) | 34.4674 | + | 19.8997i | 1.12004 | + | 0.646655i | 0.941411 | − | 0.337262i | \(-0.109501\pi\) |
0.178628 | + | 0.983917i | \(0.442834\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 14.8492 | + | 11.0227i | 0.481773 | + | 0.357624i | ||||
\(951\) | −9.89949 | + | 32.8329i | −0.321013 | + | 1.06468i | ||||
\(952\) | −44.0000 | + | 76.2102i | −1.42605 | + | 2.46999i | ||||
\(953\) | −14.3614 | − | 8.29156i | −0.465212 | − | 0.268590i | 0.249021 | − | 0.968498i | \(-0.419891\pi\) |
−0.714233 | + | 0.699908i | \(0.753224\pi\) | |||||||
\(954\) | −2.97825 | + | 47.9075i | −0.0964244 | + | 1.55106i | ||||
\(955\) | 4.00000 | − | 6.92820i | 0.129437 | − | 0.224191i | ||||
\(956\) | 14.1421 | + | 24.4949i | 0.457389 | + | 0.792222i | ||||
\(957\) | 38.8909 | + | 11.7260i | 1.25716 | + | 0.379049i | ||||
\(958\) | −56.0000 | −1.80928 | ||||||||
\(959\) | −38.8909 | − | 67.3610i | −1.25585 | − | 2.17520i | ||||
\(960\) | −19.0765 | + | 4.48185i | −0.615692 | + | 0.144651i | ||||
\(961\) | 9.00000 | 0.290323 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −25.0000 | + | 43.3013i | −0.805196 | + | 1.39464i | ||||
\(965\) | −14.1421 | − | 24.4949i | −0.455251 | − | 0.788519i | ||||
\(966\) | −35.5206 | + | 33.3810i | −1.14286 | + | 1.07401i | ||||
\(967\) | 40.6202 | + | 23.4521i | 1.30626 | + | 0.754168i | 0.981469 | − | 0.191619i | \(-0.0613737\pi\) |
0.324788 | + | 0.945787i | \(0.394707\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.8614 | − | 45.9731i | 0.638040 | − | 1.47687i | ||||
\(970\) | 30.0000 | 0.963242 | ||||||||
\(971\) | 14.3614 | + | 8.29156i | 0.460879 | + | 0.266089i | 0.712414 | − | 0.701759i | \(-0.247602\pi\) |
−0.251535 | + | 0.967848i | \(0.580935\pi\) | |||||||
\(972\) | 12.6277 | − | 28.5051i | 0.405034 | − | 0.914302i | ||||
\(973\) | −60.9303 | + | 35.1781i | −1.95334 | + | 1.12776i | ||||
\(974\) | 5.74456 | + | 3.31662i | 0.184068 | + | 0.106272i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 18.7617i | − | 0.600546i | ||||||
\(977\) | − | 16.5831i | − | 0.530541i | −0.964174 | − | 0.265271i | \(-0.914539\pi\) | ||
0.964174 | − | 0.265271i | \(-0.0854613\pi\) | |||||||
\(978\) | 35.7684 | − | 8.40347i | 1.14375 | − | 0.268713i | ||||
\(979\) | 11.0000 | + | 19.0526i | 0.351562 | + | 0.608922i | ||||
\(980\) | 42.4264 | 1.35526 | ||||||||
\(981\) | −15.5563 | + | 23.4521i | −0.496676 | + | 0.748767i | ||||
\(982\) | −16.2481 | + | 9.38083i | −0.518497 | + | 0.299354i | ||||
\(983\) | 29.6985 | − | 51.4393i | 0.947235 | − | 1.64066i | 0.196020 | − | 0.980600i | \(-0.437198\pi\) |
0.751214 | − | 0.660059i | \(-0.229469\pi\) | |||||||
\(984\) | 3.71616 | + | 15.8174i | 0.118467 | + | 0.504240i | ||||
\(985\) | 9.00000 | − | 15.5885i | 0.286764 | − | 0.496690i | ||||
\(986\) | 57.4456 | + | 33.1662i | 1.82944 | + | 1.05623i | ||||
\(987\) | 55.0000 | + | 16.5831i | 1.75067 | + | 0.527847i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.4558 | 0.809449 | ||||||||
\(990\) | −8.86141 | − | 17.8178i | −0.281634 | − | 0.566288i | ||||
\(991\) | −40.6202 | − | 23.4521i | −1.29034 | − | 0.744980i | −0.311628 | − | 0.950204i | \(-0.600874\pi\) |
−0.978715 | + | 0.205224i | \(0.934208\pi\) | |||||||
\(992\) | −22.9783 | + | 13.2665i | −0.729560 | + | 0.421212i | ||||
\(993\) | 13.0475 | + | 13.8839i | 0.414051 | + | 0.440591i | ||||
\(994\) | 32.4962 | − | 18.7617i | 1.03072 | − | 0.595084i | ||||
\(995\) | 13.2665i | 0.420576i | ||||||||
\(996\) | −11.0000 | − | 3.31662i | −0.348548 | − | 0.105091i | ||||
\(997\) | −4.06202 | + | 2.34521i | −0.128645 | + | 0.0742735i | −0.562942 | − | 0.826497i | \(-0.690330\pi\) |
0.434296 | + | 0.900770i | \(0.356997\pi\) | |||||||
\(998\) | 9.19239 | + | 15.9217i | 0.290980 | + | 0.503992i | ||||
\(999\) | 15.5563 | + | 18.7617i | 0.492181 | + | 0.593593i |
(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 | 456.2.u.c.11.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 456.2.u.c.11.4 | yes | 8 | |
8.3 | odd | 2 | inner | 456.2.u.c.11.3 | yes | 8 | |
19.7 | even | 3 | inner | 456.2.u.c.83.2 | yes | 8 | |
24.11 | even | 2 | inner | 456.2.u.c.11.2 | yes | 8 | |
57.26 | odd | 6 | inner | 456.2.u.c.83.3 | yes | 8 | |
152.83 | odd | 6 | inner | 456.2.u.c.83.4 | yes | 8 | |
456.83 | even | 6 | inner | 456.2.u.c.83.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.u.c.11.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
456.2.u.c.11.2 | yes | 8 | 24.11 | even | 2 | inner | |
456.2.u.c.11.3 | yes | 8 | 8.3 | odd | 2 | inner | |
456.2.u.c.11.4 | yes | 8 | 3.2 | odd | 2 | inner | |
456.2.u.c.83.1 | yes | 8 | 456.83 | even | 6 | inner | |
456.2.u.c.83.2 | yes | 8 | 19.7 | even | 3 | inner | |
456.2.u.c.83.3 | yes | 8 | 57.26 | odd | 6 | inner | |
456.2.u.c.83.4 | yes | 8 | 152.83 | odd | 6 | inner |