Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,2,Mod(541,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.541");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.9357651274\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1081.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1081 |
Dual form | 1620.2.i.m.541.2 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.36603 | + | 2.36603i | 0.516309 | + | 0.894274i | 0.999821 | + | 0.0189356i | \(0.00602775\pi\) |
−0.483512 | + | 0.875338i | \(0.660639\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.866025 | + | 1.50000i | 0.261116 | + | 0.452267i | 0.966539 | − | 0.256520i | \(-0.0825760\pi\) |
−0.705422 | + | 0.708787i | \(0.749243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.73205 | + | 4.73205i | −0.757735 | + | 1.31243i | 0.186269 | + | 0.982499i | \(0.440360\pi\) |
−0.944003 | + | 0.329936i | \(0.892973\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.73205 | 1.14769 | 0.573845 | − | 0.818964i | \(-0.305451\pi\) | ||||
0.573845 | + | 0.818964i | \(0.305451\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.46410 | −1.02414 | −0.512068 | − | 0.858945i | \(-0.671120\pi\) | ||||
−0.512068 | + | 0.858945i | \(0.671120\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.73205 | − | 3.00000i | 0.361158 | − | 0.625543i | −0.626994 | − | 0.779024i | \(-0.715715\pi\) |
0.988152 | + | 0.153481i | \(0.0490483\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.86603 | − | 6.69615i | −0.717903 | − | 1.24344i | −0.961829 | − | 0.273651i | \(-0.911769\pi\) |
0.243926 | − | 0.969794i | \(-0.421564\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.96410 | + | 5.13397i | −0.532368 | + | 0.922089i | 0.466917 | + | 0.884301i | \(0.345365\pi\) |
−0.999286 | + | 0.0377881i | \(0.987969\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.73205 | −0.461801 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.19615 | −1.01864 | −0.509321 | − | 0.860577i | \(-0.670103\pi\) | ||||
−0.509321 | + | 0.860577i | \(0.670103\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.59808 | + | 9.69615i | −0.874273 | + | 1.51428i | −0.0167371 | + | 0.999860i | \(0.505328\pi\) |
−0.857536 | + | 0.514425i | \(0.828006\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.63397 | − | 2.83013i | −0.249179 | − | 0.431590i | 0.714119 | − | 0.700024i | \(-0.246827\pi\) |
−0.963298 | + | 0.268434i | \(0.913494\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.633975 | − | 1.09808i | −0.0924747 | − | 0.160171i | 0.816077 | − | 0.577943i | \(-0.196144\pi\) |
−0.908552 | + | 0.417772i | \(0.862811\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.232051 | + | 0.401924i | −0.0331501 | + | 0.0574177i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.26795 | 0.998330 | 0.499165 | − | 0.866507i | \(-0.333640\pi\) | ||||
0.499165 | + | 0.866507i | \(0.333640\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.73205 | −0.233550 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.86603 | + | 6.69615i | −0.503314 | + | 0.871765i | 0.496679 | + | 0.867934i | \(0.334553\pi\) |
−0.999993 | + | 0.00383049i | \(0.998781\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | + | 3.46410i | 0.256074 | + | 0.443533i | 0.965187 | − | 0.261562i | \(-0.0842377\pi\) |
−0.709113 | + | 0.705095i | \(0.750904\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.73205 | − | 4.73205i | −0.338869 | − | 0.586939i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.19615 | + | 5.53590i | −0.390472 | + | 0.676318i | −0.992512 | − | 0.122149i | \(-0.961022\pi\) |
0.602040 | + | 0.798466i | \(0.294355\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1962 | 1.32874 | 0.664369 | − | 0.747404i | \(-0.268700\pi\) | ||||
0.664369 | + | 0.747404i | \(0.268700\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.196152 | −0.0229579 | −0.0114790 | − | 0.999934i | \(-0.503654\pi\) | ||||
−0.0114790 | + | 0.999934i | \(0.503654\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.36603 | + | 4.09808i | −0.269634 | + | 0.467019i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.19615 | + | 12.4641i | 0.809630 | + | 1.40232i | 0.913120 | + | 0.407690i | \(0.133666\pi\) |
−0.103490 | + | 0.994631i | \(0.533001\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.56218 | − | 13.0981i | −0.830057 | − | 1.43770i | −0.897992 | − | 0.440011i | \(-0.854975\pi\) |
0.0679356 | − | 0.997690i | \(-0.478359\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.36603 | + | 4.09808i | −0.256631 | + | 0.444499i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.19615 | −0.550791 | −0.275396 | − | 0.961331i | \(-0.588809\pi\) | ||||
−0.275396 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.9282 | −1.56490 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.23205 | − | 3.86603i | 0.229004 | − | 0.396646i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.366025 | − | 0.633975i | −0.0371642 | − | 0.0643704i | 0.846845 | − | 0.531840i | \(-0.178499\pi\) |
−0.884009 | + | 0.467469i | \(0.845166\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.06218 | + | 5.30385i | 0.304698 | + | 0.527753i | 0.977194 | − | 0.212348i | \(-0.0681111\pi\) |
−0.672496 | + | 0.740101i | \(0.734778\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.19615 | + | 15.9282i | −0.906124 | + | 1.56945i | −0.0867223 | + | 0.996233i | \(0.527639\pi\) |
−0.819402 | + | 0.573220i | \(0.805694\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.46410 | −0.334887 | −0.167444 | − | 0.985882i | \(-0.553551\pi\) | ||||
−0.167444 | + | 0.985882i | \(0.553551\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.92820 | −0.759384 | −0.379692 | − | 0.925113i | \(-0.623970\pi\) | ||||
−0.379692 | + | 0.925113i | \(0.623970\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.169873 | + | 0.294229i | −0.0159803 | + | 0.0276787i | −0.873905 | − | 0.486097i | \(-0.838420\pi\) |
0.857925 | + | 0.513776i | \(0.171754\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.73205 | + | 3.00000i | 0.161515 | + | 0.279751i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.46410 | + | 11.1962i | 0.592563 | + | 1.02635i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.00000 | − | 6.92820i | 0.363636 | − | 0.629837i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.19615 | 0.372348 | 0.186174 | − | 0.982517i | \(-0.440391\pi\) | ||||
0.186174 | + | 0.982517i | \(0.440391\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.13397 | − | 8.89230i | 0.448557 | − | 0.776924i | −0.549735 | − | 0.835339i | \(-0.685271\pi\) |
0.998292 | + | 0.0584149i | \(0.0186046\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.09808 | − | 10.5622i | −0.528770 | − | 0.915857i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.19615 | + | 3.80385i | 0.187630 | + | 0.324985i | 0.944460 | − | 0.328628i | \(-0.106586\pi\) |
−0.756830 | + | 0.653612i | \(0.773253\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.69615 | + | 13.3301i | −0.652779 | + | 1.13065i | 0.329666 | + | 0.944097i | \(0.393064\pi\) |
−0.982446 | + | 0.186549i | \(0.940270\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.46410 | −0.791428 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.73205 | 0.642112 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.69615 | + | 15.0622i | 0.707683 | + | 1.22574i | 0.965715 | + | 0.259606i | \(0.0835928\pi\) |
−0.258032 | + | 0.966136i | \(0.583074\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.96410 | − | 5.13397i | −0.238082 | − | 0.412371i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.63397 | + | 2.83013i | −0.130405 | + | 0.225869i | −0.923833 | − | 0.382796i | \(-0.874961\pi\) |
0.793428 | + | 0.608665i | \(0.208295\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.46410 | 0.745876 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.7321 | 1.46721 | 0.733604 | − | 0.679577i | \(-0.237837\pi\) | ||||
0.733604 | + | 0.679577i | \(0.237837\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.5622 | + | 18.2942i | −0.817326 | + | 1.41565i | 0.0903199 | + | 0.995913i | \(0.471211\pi\) |
−0.907646 | + | 0.419737i | \(0.862122\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.42820 | − | 14.5981i | −0.648323 | − | 1.12293i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.1244 | − | 21.0000i | −0.921798 | − | 1.59660i | −0.796632 | − | 0.604465i | \(-0.793387\pi\) |
−0.125166 | − | 0.992136i | \(-0.539946\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.36603 | − | 2.36603i | 0.103262 | − | 0.178855i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1244 | 0.906217 | 0.453108 | − | 0.891455i | \(-0.350315\pi\) | ||||
0.453108 | + | 0.891455i | \(0.350315\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.4641 | −1.22377 | −0.611884 | − | 0.790948i | \(-0.709588\pi\) | ||||
−0.611884 | + | 0.790948i | \(0.709588\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.09808 | − | 5.36603i | 0.227775 | − | 0.394518i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.09808 | + | 7.09808i | 0.299681 | + | 0.519063i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.52628 | + | 16.5000i | 0.689297 | + | 1.19390i | 0.972065 | + | 0.234710i | \(0.0754140\pi\) |
−0.282768 | + | 0.959188i | \(0.591253\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.29423 | − | 9.16987i | 0.381087 | − | 0.660062i | −0.610131 | − | 0.792301i | \(-0.708883\pi\) |
0.991218 | + | 0.132239i | \(0.0422165\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.8564 | 0.987228 | 0.493614 | − | 0.869681i | \(-0.335676\pi\) | ||||
0.493614 | + | 0.869681i | \(0.335676\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.8564 | 1.12403 | 0.562015 | − | 0.827127i | \(-0.310026\pi\) | ||||
0.562015 | + | 0.827127i | \(0.310026\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.5622 | − | 18.2942i | 0.741320 | − | 1.28400i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.59808 | − | 9.69615i | −0.390987 | − | 0.677209i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.86603 | − | 6.69615i | −0.267419 | − | 0.463183i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.96410 | − | 17.2583i | 0.685957 | − | 1.18811i | −0.287178 | − | 0.957877i | \(-0.592717\pi\) |
0.973135 | − | 0.230235i | \(-0.0739496\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.26795 | 0.222872 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.1962 | −1.09947 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.9282 | + | 22.3923i | −0.869645 | + | 1.50627i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.92820 | + | 5.07180i | 0.196087 | + | 0.339633i | 0.947256 | − | 0.320477i | \(-0.103843\pi\) |
−0.751169 | + | 0.660110i | \(0.770510\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.0981 | + | 22.6865i | 0.869350 | + | 1.50576i | 0.862662 | + | 0.505780i | \(0.168795\pi\) |
0.00668763 | + | 0.999978i | \(0.497871\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.92820 | − | 15.4641i | 0.589992 | − | 1.02190i | −0.404240 | − | 0.914653i | \(-0.632464\pi\) |
0.994233 | − | 0.107244i | \(-0.0342026\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.5885 | −1.61084 | −0.805422 | − | 0.592702i | \(-0.798061\pi\) | ||||
−0.805422 | + | 0.592702i | \(0.798061\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.26795 | 0.0827119 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.26795 | − | 7.39230i | 0.276071 | − | 0.478168i | −0.694334 | − | 0.719653i | \(-0.744301\pi\) |
0.970405 | + | 0.241484i | \(0.0776343\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.16025 | − | 8.93782i | −0.332401 | − | 0.575736i | 0.650581 | − | 0.759437i | \(-0.274525\pi\) |
−0.982982 | + | 0.183701i | \(0.941192\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.232051 | − | 0.401924i | −0.0148252 | − | 0.0256780i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.1962 | − | 21.1244i | 0.776023 | − | 1.34411i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.5359 | −1.29621 | −0.648107 | − | 0.761549i | \(-0.724439\pi\) | ||||
−0.648107 | + | 0.761549i | \(0.724439\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | 0.377217 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.73205 | − | 13.3923i | 0.482312 | − | 0.835389i | −0.517482 | − | 0.855694i | \(-0.673130\pi\) |
0.999794 | + | 0.0203052i | \(0.00646380\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.46410 | − | 14.6603i | −0.525934 | − | 0.910944i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.1244 | − | 21.0000i | −0.747620 | − | 1.29492i | −0.948961 | − | 0.315394i | \(-0.897863\pi\) |
0.201341 | − | 0.979521i | \(-0.435470\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.63397 | + | 6.29423i | −0.223233 | + | 0.386651i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.2679 | 0.991874 | 0.495937 | − | 0.868358i | \(-0.334825\pi\) | ||||
0.495937 | + | 0.868358i | \(0.334825\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.7846 | 1.01959 | 0.509796 | − | 0.860295i | \(-0.329721\pi\) | ||||
0.509796 | + | 0.860295i | \(0.329721\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.866025 | − | 1.50000i | 0.0522233 | − | 0.0904534i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.56218 | − | 4.43782i | −0.153946 | − | 0.266643i | 0.778729 | − | 0.627361i | \(-0.215865\pi\) |
−0.932675 | + | 0.360718i | \(0.882532\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.6603 | + | 25.3923i | 0.874557 | + | 1.51478i | 0.857233 | + | 0.514928i | \(0.172181\pi\) |
0.0173240 | + | 0.999850i | \(0.494485\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.26795 | + | 14.3205i | −0.491479 | + | 0.851266i | −0.999952 | − | 0.00981191i | \(-0.996877\pi\) |
0.508473 | + | 0.861078i | \(0.330210\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.5885 | −1.80558 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.39230 | 0.317194 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.2942 | − | 21.2942i | 0.718237 | − | 1.24402i | −0.243461 | − | 0.969911i | \(-0.578283\pi\) |
0.961698 | − | 0.274112i | \(-0.0883837\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.86603 | − | 6.69615i | −0.225089 | − | 0.389865i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.46410 | + | 16.3923i | 0.547323 | + | 0.947991i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.46410 | − | 7.73205i | 0.257307 | − | 0.445668i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.00000 | −0.229039 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.80385 | −0.102951 | −0.0514755 | − | 0.998674i | \(-0.516392\pi\) | ||||
−0.0514755 | + | 0.998674i | \(0.516392\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.25833 | + | 14.3038i | −0.468287 | + | 0.811097i | −0.999343 | − | 0.0362398i | \(-0.988462\pi\) |
0.531056 | + | 0.847337i | \(0.321795\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.46410 | − | 12.9282i | −0.421896 | − | 0.730745i | 0.574229 | − | 0.818695i | \(-0.305302\pi\) |
−0.996125 | + | 0.0879495i | \(0.971969\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.56218 | + | 2.70577i | 0.0877406 | + | 0.151971i | 0.906556 | − | 0.422086i | \(-0.138702\pi\) |
−0.818815 | + | 0.574057i | \(0.805369\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.69615 | − | 11.5981i | 0.374913 | − | 0.649368i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.1244 | −1.17539 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.46410 | 0.303094 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.73205 | − | 3.00000i | 0.0954911 | − | 0.165395i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.6962 | + | 25.4545i | 0.807774 | + | 1.39910i | 0.914403 | + | 0.404806i | \(0.132661\pi\) |
−0.106629 | + | 0.994299i | \(0.534006\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.19615 | − | 5.53590i | −0.174624 | − | 0.302458i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1244 | − | 29.6603i | 0.932823 | − | 1.61570i | 0.154353 | − | 0.988016i | \(-0.450671\pi\) |
0.778471 | − | 0.627681i | \(-0.215996\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.2679 | −0.556041 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8564 | 0.964155 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.9019 | − | 18.8827i | 0.585246 | − | 1.01368i | −0.409599 | − | 0.912266i | \(-0.634331\pi\) |
0.994845 | − | 0.101410i | \(-0.0323354\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.5000 | + | 21.6506i | 0.669110 | + | 1.15893i | 0.978153 | + | 0.207884i | \(0.0666577\pi\) |
−0.309044 | + | 0.951048i | \(0.600009\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.4904 | − | 25.0981i | −0.771245 | − | 1.33584i | −0.936881 | − | 0.349649i | \(-0.886301\pi\) |
0.165636 | − | 0.986187i | \(-0.447032\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.59808 | + | 9.69615i | −0.297115 | + | 0.514618i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.33975 | −0.492933 | −0.246466 | − | 0.969151i | \(-0.579270\pi\) | ||||
−0.246466 | + | 0.969151i | \(0.579270\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.928203 | 0.0488528 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.0980762 | − | 0.169873i | 0.00513354 | − | 0.00889156i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.1962 | + | 22.8564i | 0.688834 | + | 1.19309i | 0.972216 | + | 0.234088i | \(0.0752102\pi\) |
−0.283382 | + | 0.959007i | \(0.591456\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.92820 | + | 17.1962i | 0.515447 | + | 0.892780i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.02628 | − | 12.1699i | 0.363807 | − | 0.630132i | −0.624777 | − | 0.780803i | \(-0.714810\pi\) |
0.988584 | + | 0.150671i | \(0.0481434\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 42.2487 | 2.17592 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.53590 | 0.232993 | 0.116497 | − | 0.993191i | \(-0.462834\pi\) | ||||
0.116497 | + | 0.993191i | \(0.462834\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.12436 | − | 15.8038i | 0.466233 | − | 0.807539i | −0.533023 | − | 0.846100i | \(-0.678944\pi\) |
0.999256 | + | 0.0385616i | \(0.0122776\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.36603 | − | 4.09808i | −0.120584 | − | 0.208857i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.7321 | + | 23.7846i | 0.696243 | + | 1.20593i | 0.969760 | + | 0.244061i | \(0.0784796\pi\) |
−0.273517 | + | 0.961867i | \(0.588187\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.19615 | − | 14.1962i | 0.414497 | − | 0.717930i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.3923 | −0.724155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.3205 | 1.87306 | 0.936531 | − | 0.350584i | \(-0.114017\pi\) | ||||
0.936531 | + | 0.350584i | \(0.114017\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.39230 | + | 12.8038i | −0.369154 | + | 0.639394i | −0.989434 | − | 0.144987i | \(-0.953686\pi\) |
0.620279 | + | 0.784381i | \(0.287019\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.1962 | − | 28.0526i | −0.806788 | − | 1.39740i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.36603 | − | 9.29423i | −0.265984 | − | 0.460698i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.92820 | − | 15.4641i | 0.441471 | − | 0.764651i | −0.556328 | − | 0.830963i | \(-0.687790\pi\) |
0.997799 | + | 0.0663124i | \(0.0211234\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.1244 | −1.03946 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.1244 | 0.742425 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.7321 | − | 18.5885i | 0.524295 | − | 0.908106i | −0.475305 | − | 0.879821i | \(-0.657662\pi\) |
0.999600 | − | 0.0282844i | \(-0.00900441\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.89230 | − | 11.9378i | −0.335910 | − | 0.581814i | 0.647749 | − | 0.761854i | \(-0.275711\pi\) |
−0.983659 | + | 0.180040i | \(0.942377\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.36603 | − | 4.09808i | −0.114769 | − | 0.198786i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.46410 | + | 9.46410i | −0.264426 | + | 0.458000i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.5885 | 1.61790 | 0.808950 | − | 0.587878i | \(-0.200037\pi\) | ||||
0.808950 | + | 0.587878i | \(0.200037\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.4641 | 0.550930 | 0.275465 | − | 0.961311i | \(-0.411168\pi\) | ||||
0.275465 | + | 0.961311i | \(0.411168\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.73205 | + | 13.3923i | −0.369874 | + | 0.640641i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.30385 | − | 5.72243i | −0.157684 | − | 0.273117i | 0.776349 | − | 0.630303i | \(-0.217069\pi\) |
−0.934033 | + | 0.357186i | \(0.883736\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.6340 | + | 32.2750i | 0.885327 | + | 1.53343i | 0.845339 | + | 0.534231i | \(0.179399\pi\) |
0.0399883 | + | 0.999200i | \(0.487268\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.59808 | − | 4.50000i | 0.123161 | − | 0.213320i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.1244 | −1.13850 | −0.569249 | − | 0.822165i | \(-0.692766\pi\) | ||||
−0.569249 | + | 0.822165i | \(0.692766\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.3923 | −0.913148 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.46410 | − | 12.9282i | 0.349922 | − | 0.606084i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0981 | − | 19.2224i | −0.519146 | − | 0.899187i | −0.999752 | − | 0.0222510i | \(-0.992917\pi\) |
0.480606 | − | 0.876936i | \(-0.340417\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.79423 | + | 8.30385i | 0.223289 | + | 0.386749i | 0.955805 | − | 0.294002i | \(-0.0949871\pi\) |
−0.732515 | + | 0.680750i | \(0.761654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.19615 | − | 2.07180i | 0.0555899 | − | 0.0962846i | −0.836891 | − | 0.547369i | \(-0.815629\pi\) |
0.892481 | + | 0.451085i | \(0.148963\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.1962 | −1.21221 | −0.606107 | − | 0.795383i | \(-0.707270\pi\) | ||||
−0.606107 | + | 0.795383i | \(0.707270\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.4641 | −0.806417 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.83013 | − | 4.90192i | 0.130129 | − | 0.225391i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.23205 | + | 3.86603i | 0.102414 | + | 0.177385i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.66987 | − | 2.89230i | −0.0762984 | − | 0.132153i | 0.825352 | − | 0.564619i | \(-0.190977\pi\) |
−0.901650 | + | 0.432466i | \(0.857644\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.9282 | − | 29.3205i | 0.771860 | − | 1.33690i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.732051 | 0.0332407 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.5359 | −1.38371 | −0.691857 | − | 0.722035i | \(-0.743207\pi\) | ||||
−0.691857 | + | 0.722035i | \(0.743207\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.13397 | + | 3.69615i | −0.0963049 | + | 0.166805i | −0.910152 | − | 0.414273i | \(-0.864036\pi\) |
0.813848 | + | 0.581078i | \(0.197369\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.2942 | − | 31.6865i | −0.823931 | − | 1.42709i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.2942 | + | 26.4904i | 0.686040 | + | 1.18826i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.6962 | + | 23.7224i | −0.613124 | + | 1.06196i | 0.377587 | + | 0.925974i | \(0.376754\pi\) |
−0.990711 | + | 0.135988i | \(0.956579\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.3205 | 1.57486 | 0.787432 | − | 0.616402i | \(-0.211410\pi\) | ||||
0.787432 | + | 0.616402i | \(0.211410\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.12436 | −0.272530 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.3923 | + | 23.1962i | −0.593603 | + | 1.02815i | 0.400139 | + | 0.916455i | \(0.368962\pi\) |
−0.993742 | + | 0.111697i | \(0.964371\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.267949 | − | 0.464102i | −0.0118534 | − | 0.0205306i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.19615 | − | 15.9282i | −0.405231 | − | 0.701880i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.09808 | − | 1.90192i | 0.0482933 | − | 0.0836465i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.3923 | 0.455295 | 0.227648 | − | 0.973744i | \(-0.426897\pi\) | ||||
0.227648 | + | 0.973744i | \(0.426897\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.60770 | 0.157753 | 0.0788767 | − | 0.996884i | \(-0.474867\pi\) | ||||
0.0788767 | + | 0.996884i | \(0.474867\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.0263 | + | 24.2942i | −0.610994 | + | 1.05827i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.50000 | + | 9.52628i | 0.239130 | + | 0.414186i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.5885 | − | 52.9808i | −1.32493 | − | 2.29485i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.73205 | − | 3.00000i | 0.0748831 | − | 0.129701i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.803848 | −0.0346242 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.46410 | 0.105940 | 0.0529700 | − | 0.998596i | \(-0.483131\pi\) | ||||
0.0529700 | + | 0.998596i | \(0.483131\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.96410 | − | 6.86603i | 0.169803 | − | 0.294108i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.39230 | − | 4.14359i | −0.102288 | − | 0.177167i | 0.810339 | − | 0.585961i | \(-0.199283\pi\) |
−0.912627 | + | 0.408794i | \(0.865950\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.2583 | + | 29.8923i | 0.735230 | + | 1.27346i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.6603 | + | 34.0526i | −0.836039 | + | 1.44806i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.39230 | 0.186108 | 0.0930540 | − | 0.995661i | \(-0.470337\pi\) | ||||
0.0930540 | + | 0.995661i | \(0.470337\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.8564 | 0.755246 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.3660 | − | 19.6865i | 0.479021 | − | 0.829688i | −0.520690 | − | 0.853746i | \(-0.674325\pi\) |
0.999711 | + | 0.0240575i | \(0.00765849\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.169873 | − | 0.294229i | −0.00714661 | − | 0.0123783i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.5263 | − | 37.2846i | −0.902429 | − | 1.56305i | −0.824332 | − | 0.566106i | \(-0.808449\pi\) |
−0.0780964 | − | 0.996946i | \(-0.524884\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.428203 | + | 0.741670i | −0.0179197 | + | 0.0310379i | −0.874846 | − | 0.484401i | \(-0.839038\pi\) |
0.856926 | + | 0.515439i | \(0.172371\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.46410 | −0.144463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.8038 | 0.491401 | 0.245700 | − | 0.969346i | \(-0.420982\pi\) | ||||
0.245700 | + | 0.969346i | \(0.420982\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.6603 | − | 35.7846i | 0.857132 | − | 1.48460i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.29423 | + | 10.9019i | 0.260680 | + | 0.451512i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.90192 | + | 3.29423i | 0.0785008 | + | 0.135967i | 0.902603 | − | 0.430473i | \(-0.141653\pi\) |
−0.824102 | + | 0.566441i | \(0.808320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.2321 | − | 22.9186i | 0.545217 | − | 0.944344i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.0718 | 0.947445 | 0.473723 | − | 0.880674i | \(-0.342910\pi\) | ||||
0.473723 | + | 0.880674i | \(0.342910\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.9282 | −0.530005 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.20577 | + | 12.4808i | −0.294420 | + | 0.509950i | −0.974850 | − | 0.222863i | \(-0.928460\pi\) |
0.680430 | + | 0.732813i | \(0.261793\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.1603 | + | 21.0622i | 0.496027 | + | 0.859144i | 0.999990 | − | 0.00458144i | \(-0.00145832\pi\) |
−0.503962 | + | 0.863726i | \(0.668125\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.00000 | + | 6.92820i | 0.162623 | + | 0.281672i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.29423 | + | 2.24167i | −0.0525311 | + | 0.0909866i | −0.891095 | − | 0.453816i | \(-0.850062\pi\) |
0.838564 | + | 0.544803i | \(0.183396\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.92820 | 0.280285 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.3923 | 0.985196 | 0.492598 | − | 0.870257i | \(-0.336047\pi\) | ||||
0.492598 | + | 0.870257i | \(0.336047\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.00000 | + | 10.3923i | −0.241551 | + | 0.418378i | −0.961156 | − | 0.276005i | \(-0.910989\pi\) |
0.719605 | + | 0.694383i | \(0.244323\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.00000 | + | 8.66025i | 0.200967 | + | 0.348085i | 0.948840 | − | 0.315757i | \(-0.102258\pi\) |
−0.747873 | + | 0.663842i | \(0.768925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.09808 | − | 12.2942i | −0.284378 | − | 0.492558i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.3205 | −1.16909 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.0717968 | −0.00285818 | −0.00142909 | − | 0.999999i | \(-0.500455\pi\) | ||||
−0.00142909 | + | 0.999999i | \(0.500455\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.09808 | + | 3.63397i | −0.0832596 | + | 0.144210i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.26795 | − | 2.19615i | −0.0502380 | − | 0.0870147i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.40192 | − | 11.0885i | −0.252861 | − | 0.437968i | 0.711451 | − | 0.702735i | \(-0.248038\pi\) |
−0.964312 | + | 0.264767i | \(0.914705\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.29423 | + | 12.6340i | −0.287656 | + | 0.498235i | −0.973250 | − | 0.229749i | \(-0.926209\pi\) |
0.685594 | + | 0.727985i | \(0.259543\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.248711 | −0.00977785 | −0.00488893 | − | 0.999988i | \(-0.501556\pi\) | ||||
−0.00488893 | + | 0.999988i | \(0.501556\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.3923 | −0.525694 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.26795 | + | 2.19615i | −0.0496187 | + | 0.0859421i | −0.889768 | − | 0.456413i | \(-0.849134\pi\) |
0.840149 | + | 0.542355i | \(0.182467\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.13397 | + | 8.89230i | 0.200601 | + | 0.347451i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.26795 | − | 2.19615i | −0.0493923 | − | 0.0855500i | 0.840272 | − | 0.542165i | \(-0.182395\pi\) |
−0.889665 | + | 0.456615i | \(0.849062\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.69615 | + | 13.3301i | −0.299346 | + | 0.518482i | −0.975986 | − | 0.217831i | \(-0.930102\pi\) |
0.676641 | + | 0.736313i | \(0.263435\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.1962 | 0.472947 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.7846 | −1.03710 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.46410 | + | 6.00000i | −0.133730 | + | 0.231627i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.1962 | + | 33.2487i | 0.739957 | + | 1.28164i | 0.952514 | + | 0.304495i | \(0.0984877\pi\) |
−0.212557 | + | 0.977149i | \(0.568179\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.3205 | + | 35.1962i | 0.780981 | + | 1.35270i | 0.931371 | + | 0.364071i | \(0.118614\pi\) |
−0.150390 | + | 0.988627i | \(0.548053\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.00000 | − | 1.73205i | 0.0383765 | − | 0.0664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.4641 | −0.821301 | −0.410651 | − | 0.911793i | \(-0.634698\pi\) | ||||
−0.410651 | + | 0.911793i | \(0.634698\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.39230 | −0.167821 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.8564 | + | 34.3923i | −0.756469 | + | 1.31024i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.00000 | + | 8.66025i | 0.190209 | + | 0.329452i | 0.945319 | − | 0.326146i | \(-0.105750\pi\) |
−0.755110 | + | 0.655598i | \(0.772417\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.69615 | − | 13.3301i | −0.291932 | − | 0.505641i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.4904 | + | 45.8827i | −1.00339 | + | 1.73793i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.8756 | 0.675154 | 0.337577 | − | 0.941298i | \(-0.390393\pi\) | ||||
0.337577 | + | 0.941298i | \(0.390393\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.6603 | 1.04323 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.36603 | + | 14.4904i | −0.314637 | + | 0.544967i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.26795 | − | 9.12436i | −0.197842 | − | 0.342672i | 0.749986 | − | 0.661453i | \(-0.230060\pi\) |
−0.947828 | + | 0.318781i | \(0.896727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.2679 | + | 17.7846i | 0.384538 | + | 0.666039i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.73205 | − | 8.19615i | 0.176969 | − | 0.306519i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.1962 | 0.641308 | 0.320654 | − | 0.947196i | \(-0.396097\pi\) | ||||
0.320654 | + | 0.947196i | \(0.396097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.2487 | −1.87136 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.86603 | + | 6.69615i | −0.143581 | + | 0.248689i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.5885 | + | 25.2679i | 0.541056 | + | 0.937136i | 0.998844 | + | 0.0480749i | \(0.0153086\pi\) |
−0.457788 | + | 0.889061i | \(0.651358\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.73205 | − | 13.3923i | −0.285980 | − | 0.495332i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.7846 | + | 37.7321i | −0.804633 | + | 1.39367i | 0.111906 | + | 0.993719i | \(0.464305\pi\) |
−0.916539 | + | 0.399946i | \(0.869029\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.0718 | −0.407835 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.1769 | −0.962933 | −0.481467 | − | 0.876464i | \(-0.659896\pi\) | ||||
−0.481467 | + | 0.876464i | \(0.659896\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.70577 | + | 4.68653i | −0.0992651 | + | 0.171932i | −0.911381 | − | 0.411564i | \(-0.864983\pi\) |
0.812116 | + | 0.583497i | \(0.198316\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.73205 | − | 8.19615i | −0.172905 | − | 0.299481i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.3923 | + | 35.3205i | −0.744126 | + | 1.28886i | 0.206476 | + | 0.978452i | \(0.433800\pi\) |
−0.950602 | + | 0.310412i | \(0.899533\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.3923 | −0.632971 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.3923 | −0.741171 | −0.370585 | − | 0.928798i | \(-0.620843\pi\) | ||||
−0.370585 | + | 0.928798i | \(0.620843\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.0622 | + | 26.0885i | −0.546004 | + | 0.945706i | 0.452539 | + | 0.891744i | \(0.350518\pi\) |
−0.998543 | + | 0.0539615i | \(0.982815\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.8301 | − | 18.7583i | −0.392077 | − | 0.679097i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.1244 | − | 36.5885i | −0.762756 | − | 1.32113i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.6244 | + | 30.5263i | −0.635551 | + | 1.10081i | 0.350848 | + | 0.936433i | \(0.385893\pi\) |
−0.986398 | + | 0.164373i | \(0.947440\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.6603 | −0.635195 | −0.317598 | − | 0.948226i | \(-0.602876\pi\) | ||||
−0.317598 | + | 0.948226i | \(0.602876\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.92820 | 0.212947 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.9904 | − | 43.2846i | 0.895373 | − | 1.55083i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.69615 | + | 16.7942i | 0.346956 | + | 0.600945i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.63397 | − | 2.83013i | −0.0583191 | − | 0.101012i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.0981 | − | 31.3468i | 0.645127 | − | 1.11739i | −0.339145 | − | 0.940734i | \(-0.610138\pi\) |
0.984272 | − | 0.176658i | \(-0.0565288\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.928203 | −0.0330031 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.8564 | −0.776144 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.6603 | − | 20.1962i | 0.413027 | − | 0.715384i | −0.582192 | − | 0.813052i | \(-0.697805\pi\) |
0.995219 | + | <