Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,2,Mod(1549,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.1549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.d (of order \(2\), degree \(1\), 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: | \(14.3730723638\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.214798336.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 600) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1549.3 | ||
Root | \(1.23291 + 0.692769i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.1549 |
Dual form | 1800.2.d.t.1549.4 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.192769 | − | 1.40101i | −0.136308 | − | 0.990667i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.92568 | + | 0.540143i | −0.962840 | + | 0.270072i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.0802864i | − | 0.0303454i | −0.999885 | − | 0.0151727i | \(-0.995170\pi\) | ||
0.999885 | − | 0.0151727i | \(-0.00482980\pi\) | |||||||
\(8\) | 1.12796 | + | 2.59378i | 0.398794 | + | 0.917041i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.41649i | 0.728599i | 0.931282 | + | 0.364300i | \(0.118692\pi\) | ||||
−0.931282 | + | 0.364300i | \(0.881308\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.26785 | −1.46104 | −0.730520 | − | 0.682892i | \(-0.760722\pi\) | ||||
−0.730520 | + | 0.682892i | \(0.760722\pi\) | |||||||
\(14\) | −0.112482 | + | 0.0154767i | −0.0300622 | + | 0.00413632i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.41649 | − | 2.08029i | 0.854123 | − | 0.520072i | ||||
\(17\) | − | 0.255918i | − | 0.0620692i | −0.999518 | − | 0.0310346i | \(-0.990120\pi\) | ||
0.999518 | − | 0.0310346i | \(-0.00988021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.95864i | − | 1.59642i | −0.602378 | − | 0.798211i | \(-0.705780\pi\) | ||
0.602378 | − | 0.798211i | \(-0.294220\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.38554 | − | 0.465824i | 0.721799 | − | 0.0993139i | ||||
\(23\) | 1.64542i | 0.343093i | 0.985176 | + | 0.171546i | \(0.0548764\pi\) | ||||
−0.985176 | + | 0.171546i | \(0.945124\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.01548 | + | 7.38033i | 0.199151 | + | 1.44740i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.0433661 | + | 0.154606i | 0.00819543 | + | 0.0292178i | ||||
\(29\) | 4.51516i | 0.838444i | 0.907884 | + | 0.419222i | \(0.137697\pi\) | ||||
−0.907884 | + | 0.419222i | \(0.862303\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.29484 | 1.48980 | 0.744899 | − | 0.667177i | \(-0.232498\pi\) | ||||
0.744899 | + | 0.667177i | \(0.232498\pi\) | |||||||
\(32\) | −3.57310 | − | 4.38554i | −0.631641 | − | 0.775261i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.358545 | + | 0.0493330i | −0.0614899 | + | 0.00846053i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.67241 | 0.439341 | 0.219671 | − | 0.975574i | \(-0.429502\pi\) | ||||
0.219671 | + | 0.975574i | \(0.429502\pi\) | |||||||
\(38\) | −9.74915 | + | 1.34141i | −1.58152 | + | 0.217605i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.11921 | 1.26801 | 0.634004 | − | 0.773330i | \(-0.281410\pi\) | ||||
0.634004 | + | 0.773330i | \(0.281410\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.08890 | 0.623551 | 0.311776 | − | 0.950156i | \(-0.399076\pi\) | ||||
0.311776 | + | 0.950156i | \(0.399076\pi\) | |||||||
\(44\) | −1.30525 | − | 4.65339i | −0.196774 | − | 0.701525i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.30525 | − | 0.317185i | 0.339891 | − | 0.0467663i | ||||
\(47\) | 5.70272i | 0.831827i | 0.909404 | + | 0.415914i | \(0.136538\pi\) | ||||
−0.909404 | + | 0.415914i | \(0.863462\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99355 | 0.999079 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.1442 | − | 2.84539i | 1.40675 | − | 0.394585i | ||||
\(53\) | 11.5627 | 1.58826 | 0.794129 | − | 0.607749i | \(-0.207927\pi\) | ||||
0.794129 | + | 0.607749i | \(0.207927\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.208245 | − | 0.0905597i | 0.0278280 | − | 0.0121016i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.32580 | − | 0.870381i | 0.830618 | − | 0.114287i | ||||
\(59\) | 12.6963i | 1.65291i | 0.563000 | + | 0.826457i | \(0.309647\pi\) | ||||
−0.563000 | + | 0.826457i | \(0.690353\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.9403i | 1.52879i | 0.644746 | + | 0.764397i | \(0.276963\pi\) | ||||
−0.644746 | + | 0.764397i | \(0.723037\pi\) | |||||||
\(62\) | −1.59899 | − | 11.6212i | −0.203071 | − | 1.47589i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.45542 | + | 5.85136i | −0.681927 | + | 0.731420i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.27979 | −0.889367 | −0.444684 | − | 0.895688i | \(-0.646684\pi\) | ||||
−0.444684 | + | 0.895688i | \(0.646684\pi\) | |||||||
\(68\) | 0.138232 | + | 0.492816i | 0.0167631 | + | 0.0597628i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3481 | 1.34678 | 0.673388 | − | 0.739289i | \(-0.264838\pi\) | ||||
0.673388 | + | 0.739289i | \(0.264838\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.0779i | − | 1.41361i | −0.707411 | − | 0.706803i | \(-0.750137\pi\) | ||
0.707411 | − | 0.706803i | \(-0.249863\pi\) | |||||||
\(74\) | −0.515157 | − | 3.74408i | −0.0598857 | − | 0.435241i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.75866 | + | 13.4001i | 0.431148 | + | 1.53710i | ||||
\(77\) | 0.194011 | 0.0221096 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.50539 | −0.619405 | −0.309702 | − | 0.950834i | \(-0.600229\pi\) | ||||
−0.309702 | + | 0.950834i | \(0.600229\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.56513 | − | 11.3751i | −0.172840 | − | 1.25617i | ||||
\(83\) | −9.20811 | −1.01072 | −0.505361 | − | 0.862908i | \(-0.668641\pi\) | ||||
−0.505361 | + | 0.862908i | \(0.668641\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.788212 | − | 5.72861i | −0.0849950 | − | 0.617731i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.26785 | + | 2.72570i | −0.668155 | + | 0.290561i | ||||
\(89\) | 11.9173 | 1.26323 | 0.631615 | − | 0.775283i | \(-0.282393\pi\) | ||||
0.631615 | + | 0.775283i | \(0.282393\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.422937i | 0.0443358i | ||||||||
\(92\) | −0.888760 | − | 3.16855i | −0.0926597 | − | 0.330344i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.98959 | − | 1.09931i | 0.824064 | − | 0.113385i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.50539i | − | 0.863592i | −0.901971 | − | 0.431796i | \(-0.857880\pi\) | ||
0.901971 | − | 0.431796i | \(-0.142120\pi\) | |||||||
\(98\) | −1.34814 | − | 9.79807i | −0.136183 | − | 0.989754i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 7.56270i | − | 0.752516i | −0.926515 | − | 0.376258i | \(-0.877211\pi\) | ||
0.926515 | − | 0.376258i | \(-0.122789\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.78544i | − | 0.175925i | −0.996124 | − | 0.0879624i | \(-0.971964\pi\) | ||
0.996124 | − | 0.0879624i | \(-0.0280355\pi\) | |||||||
\(104\) | −5.94192 | − | 13.6637i | −0.582653 | − | 1.33983i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.22893 | − | 16.1995i | −0.216492 | − | 1.57343i | ||||
\(107\) | 10.4705 | 1.01222 | 0.506110 | − | 0.862469i | \(-0.331083\pi\) | ||||
0.506110 | + | 0.862469i | \(0.331083\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.64298i | 0.348934i | 0.984663 | + | 0.174467i | \(0.0558203\pi\) | ||||
−0.984663 | + | 0.174467i | \(0.944180\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.167019 | − | 0.274298i | −0.0157818 | − | 0.0259187i | ||||
\(113\) | − | 8.83298i | − | 0.830937i | −0.909608 | − | 0.415468i | \(-0.863618\pi\) | ||
0.909608 | − | 0.415468i | \(-0.136382\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.43883 | − | 8.69475i | −0.226440 | − | 0.807287i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.7877 | − | 2.44744i | 1.63749 | − | 0.225305i | ||||
\(119\) | −0.0205467 | −0.00188351 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.16057 | 0.469143 | ||||||||
\(122\) | 16.7285 | − | 2.30171i | 1.51452 | − | 0.208387i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.9732 | + | 4.48040i | −1.43444 | + | 0.402352i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.69628i | 0.771670i | 0.922568 | + | 0.385835i | \(0.126087\pi\) | ||||
−0.922568 | + | 0.385835i | \(0.873913\pi\) | |||||||
\(128\) | 9.24947 | + | 6.51516i | 0.817546 | + | 0.575864i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7916i | 0.942868i | 0.881901 | + | 0.471434i | \(0.156264\pi\) | ||||
−0.881901 | + | 0.471434i | \(0.843736\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.558684 | −0.0484440 | ||||||||
\(134\) | 1.40331 | + | 10.1991i | 0.121228 | + | 0.881066i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.663796 | − | 0.288665i | 0.0569200 | − | 0.0247528i | ||||
\(137\) | 11.5421i | 0.986112i | 0.869997 | + | 0.493056i | \(0.164120\pi\) | ||||
−0.869997 | + | 0.493056i | \(0.835880\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.214558i | − | 0.0181986i | −0.999959 | − | 0.00909928i | \(-0.997104\pi\) | ||
0.999959 | − | 0.00909928i | \(-0.00289643\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.18757 | − | 15.8989i | −0.183576 | − | 1.33421i | ||||
\(143\) | − | 12.7297i | − | 1.06451i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −16.9212 | + | 2.32823i | −1.40041 | + | 0.192686i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.14621 | + | 1.44348i | −0.423015 | + | 0.118654i | ||||
\(149\) | − | 23.0475i | − | 1.88813i | −0.329762 | − | 0.944064i | \(-0.606969\pi\) | ||
0.329762 | − | 0.944064i | \(-0.393031\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.48573 | 0.771938 | 0.385969 | − | 0.922512i | \(-0.373867\pi\) | ||||
0.385969 | + | 0.922512i | \(0.373867\pi\) | |||||||
\(152\) | 18.0492 | − | 7.84906i | 1.46398 | − | 0.636643i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0373993 | − | 0.271812i | −0.00301372 | − | 0.0219033i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.34413 | −0.506316 | −0.253158 | − | 0.967425i | \(-0.581469\pi\) | ||||
−0.253158 | + | 0.967425i | \(0.581469\pi\) | |||||||
\(158\) | 1.06127 | + | 7.71313i | 0.0844298 | + | 0.613624i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.132104 | 0.0104113 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.4100 | 0.972030 | 0.486015 | − | 0.873951i | \(-0.338450\pi\) | ||||
0.486015 | + | 0.873951i | \(0.338450\pi\) | |||||||
\(164\) | −15.6350 | + | 4.38554i | −1.22089 | + | 0.342453i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.77504 | + | 12.9007i | 0.137769 | + | 1.00129i | ||||
\(167\) | 23.2654i | 1.80033i | 0.435547 | + | 0.900166i | \(0.356555\pi\) | ||||
−0.435547 | + | 0.900166i | \(0.643445\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.7503 | 1.13464 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.87391 | + | 2.20859i | −0.600380 | + | 0.168403i | ||||
\(173\) | 8.63897 | 0.656809 | 0.328404 | − | 0.944537i | \(-0.393489\pi\) | ||||
0.328404 | + | 0.944537i | \(0.393489\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.02699 | + | 8.25592i | 0.378924 | + | 0.622313i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.29728 | − | 16.6963i | −0.172188 | − | 1.25144i | ||||
\(179\) | − | 9.40544i | − | 0.702996i | −0.936189 | − | 0.351498i | \(-0.885672\pi\) | ||
0.936189 | − | 0.351498i | \(-0.114328\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.43487i | − | 0.478300i | −0.970983 | − | 0.239150i | \(-0.923131\pi\) | ||
0.970983 | − | 0.239150i | \(-0.0768688\pi\) | |||||||
\(182\) | 0.592540 | − | 0.0815289i | 0.0439220 | − | 0.00604333i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.26785 | + | 1.85596i | −0.314630 | + | 0.136823i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.618423 | 0.0452236 | ||||||||
\(188\) | −3.08029 | − | 10.9816i | −0.224653 | − | 0.800917i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.56270 | 0.402503 | 0.201251 | − | 0.979540i | \(-0.435499\pi\) | ||||
0.201251 | + | 0.979540i | \(0.435499\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 18.4227i | − | 1.32609i | −0.748578 | − | 0.663046i | \(-0.769263\pi\) | ||
0.748578 | − | 0.663046i | \(-0.230737\pi\) | |||||||
\(194\) | −11.9162 | + | 1.63957i | −0.855531 | + | 0.117714i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.4674 | + | 3.77752i | −0.961954 | + | 0.269823i | ||||
\(197\) | −18.0239 | −1.28415 | −0.642074 | − | 0.766643i | \(-0.721926\pi\) | ||||
−0.642074 | + | 0.766643i | \(0.721926\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.1214 | −1.42637 | −0.713183 | − | 0.700977i | \(-0.752747\pi\) | ||||
−0.713183 | + | 0.700977i | \(0.752747\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.5954 | + | 1.45785i | −0.745493 | + | 0.102574i | ||||
\(203\) | 0.362505 | 0.0254429 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.50143 | + | 0.344177i | −0.174283 | + | 0.0239800i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −17.9976 | + | 10.9586i | −1.24791 | + | 0.759845i | ||||
\(209\) | 16.8155 | 1.16315 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.25592i | − | 0.224147i | −0.993700 | − | 0.112073i | \(-0.964251\pi\) | ||
0.993700 | − | 0.112073i | \(-0.0357492\pi\) | |||||||
\(212\) | −22.2661 | + | 6.24551i | −1.52924 | + | 0.428943i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.01838 | − | 14.6693i | −0.137974 | − | 1.00277i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.665963i | − | 0.0452085i | ||||||
\(218\) | 5.10387 | − | 0.702253i | 0.345678 | − | 0.0475626i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.34814i | 0.0906856i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.9911i | 1.80746i | 0.428104 | + | 0.903730i | \(0.359182\pi\) | ||||
−0.428104 | + | 0.903730i | \(0.640818\pi\) | |||||||
\(224\) | −0.352099 | + | 0.286871i | −0.0235256 | + | 0.0191674i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.3751 | + | 1.70272i | −0.823181 | + | 0.113263i | ||||
\(227\) | −19.8219 | −1.31563 | −0.657814 | − | 0.753180i | \(-0.728519\pi\) | ||||
−0.657814 | + | 0.753180i | \(0.728519\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.6797i | 1.43264i | 0.697773 | + | 0.716319i | \(0.254174\pi\) | ||||
−0.697773 | + | 0.716319i | \(0.745826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.7113 | + | 5.09291i | −0.768887 | + | 0.334366i | ||||
\(233\) | − | 17.2733i | − | 1.13161i | −0.824538 | − | 0.565807i | \(-0.808565\pi\) | ||
0.824538 | − | 0.565807i | \(-0.191435\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.85781 | − | 24.4490i | −0.446405 | − | 1.59149i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.00396076 | + | 0.0287862i | 0.000256738 | + | 0.00186594i | ||||
\(239\) | −16.3718 | −1.05900 | −0.529502 | − | 0.848309i | \(-0.677621\pi\) | ||||
−0.529502 | + | 0.848309i | \(0.677621\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.82654 | −0.439736 | −0.219868 | − | 0.975530i | \(-0.570563\pi\) | ||||
−0.219868 | + | 0.975530i | \(0.570563\pi\) | |||||||
\(242\) | −0.994797 | − | 7.23003i | −0.0639480 | − | 0.464764i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.44945 | − | 22.9931i | −0.412884 | − | 1.47198i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36.6571i | 2.33243i | ||||||||
\(248\) | 9.35624 | + | 21.5150i | 0.594122 | + | 1.36621i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.96969i | − | 0.187445i | −0.995598 | − | 0.0937225i | \(-0.970123\pi\) | ||
0.995598 | − | 0.0937225i | \(-0.0298766\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.97613 | −0.249977 | ||||||||
\(254\) | 12.1836 | − | 1.67637i | 0.764467 | − | 0.105185i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.34482 | − | 14.2146i | 0.459051 | − | 0.888410i | ||||
\(257\) | 5.03031i | 0.313782i | 0.987616 | + | 0.156891i | \(0.0501472\pi\) | ||||
−0.987616 | + | 0.156891i | \(0.949853\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 0.214558i | − | 0.0133320i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.1192 | − | 2.08029i | 0.934068 | − | 0.128521i | ||||
\(263\) | 2.70585i | 0.166850i | 0.996514 | + | 0.0834248i | \(0.0265859\pi\) | ||||
−0.996514 | + | 0.0834248i | \(0.973414\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.107697 | + | 0.782724i | 0.00660331 | + | 0.0479919i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.0185 | − | 3.93213i | 0.856319 | − | 0.240193i | ||||
\(269\) | 22.3718i | 1.36403i | 0.731337 | + | 0.682017i | \(0.238897\pi\) | ||||
−0.731337 | + | 0.682017i | \(0.761103\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.869741 | −0.0528330 | −0.0264165 | − | 0.999651i | \(-0.508410\pi\) | ||||
−0.0264165 | + | 0.999651i | \(0.508410\pi\) | |||||||
\(272\) | −0.532383 | − | 0.874341i | −0.0322804 | − | 0.0530147i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.1707 | − | 2.22496i | 0.976908 | − | 0.134415i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.6733 | 1.72281 | 0.861406 | − | 0.507918i | \(-0.169585\pi\) | ||||
0.861406 | + | 0.507918i | \(0.169585\pi\) | |||||||
\(278\) | −0.300599 | + | 0.0413600i | −0.0180287 | + | 0.00248061i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.1429 | −0.903349 | −0.451674 | − | 0.892183i | \(-0.649173\pi\) | ||||
−0.451674 | + | 0.892183i | \(0.649173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.23225 | 0.370469 | 0.185234 | − | 0.982694i | \(-0.440696\pi\) | ||||
0.185234 | + | 0.982694i | \(0.440696\pi\) | |||||||
\(284\) | −21.8529 | + | 6.12962i | −1.29673 | + | 0.363726i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17.8345 | + | 2.45389i | −1.05458 | + | 0.145102i | ||||
\(287\) | − | 0.651862i | − | 0.0384782i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9345 | 0.996147 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.52377 | + | 23.2581i | 0.381775 | + | 1.36108i | ||||
\(293\) | −21.5054 | −1.25636 | −0.628179 | − | 0.778069i | \(-0.716200\pi\) | ||||
−0.628179 | + | 0.778069i | \(0.716200\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.01437 | + | 6.93165i | 0.175207 | + | 0.402894i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −32.2899 | + | 4.44284i | −1.87051 | + | 0.257367i | ||||
\(299\) | − | 8.66781i | − | 0.501272i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 0.328283i | − | 0.0189219i | ||||||
\(302\) | −1.82855 | − | 13.2896i | −0.105221 | − | 0.764733i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14.4760 | − | 23.7741i | −0.830253 | − | 1.36354i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.57706 | 0.204154 | 0.102077 | − | 0.994777i | \(-0.467451\pi\) | ||||
0.102077 | + | 0.994777i | \(0.467451\pi\) | |||||||
\(308\) | −0.373604 | + | 0.104794i | −0.0212880 | + | 0.00597118i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.49461 | 0.141456 | 0.0707282 | − | 0.997496i | \(-0.477468\pi\) | ||||
0.0707282 | + | 0.997496i | \(0.477468\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.57246i | 0.541068i | 0.962710 | + | 0.270534i | \(0.0872002\pi\) | ||||
−0.962710 | + | 0.270534i | \(0.912800\pi\) | |||||||
\(314\) | 1.22295 | + | 8.88821i | 0.0690150 | + | 0.501591i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.6016 | − | 2.97370i | 0.596388 | − | 0.167284i | ||||
\(317\) | 3.16702 | 0.177877 | 0.0889387 | − | 0.996037i | \(-0.471652\pi\) | ||||
0.0889387 | + | 0.996037i | \(0.471652\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.9108 | −0.610889 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.0254656 | − | 0.185080i | −0.00141914 | − | 0.0103141i | ||||
\(323\) | −1.78084 | −0.0990887 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.39227 | − | 17.3866i | −0.132495 | − | 0.962957i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.15814 | + | 21.0595i | 0.505674 | + | 1.16281i | ||||
\(329\) | 0.457851 | 0.0252421 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 16.5118i | − | 0.907573i | −0.891111 | − | 0.453786i | \(-0.850073\pi\) | ||
0.891111 | − | 0.453786i | \(-0.149927\pi\) | |||||||
\(332\) | 17.7319 | − | 4.97370i | 0.973163 | − | 0.272967i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 32.5952 | − | 4.48484i | 1.78353 | − | 0.245400i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.8330i | 0.644584i | 0.946640 | + | 0.322292i | \(0.104453\pi\) | ||||
−0.946640 | + | 0.322292i | \(0.895547\pi\) | |||||||
\(338\) | −2.84339 | − | 20.6653i | −0.154660 | − | 1.12405i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.0444i | 1.08547i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.12349i | − | 0.0606628i | ||||||
\(344\) | 4.61211 | + | 10.6057i | 0.248668 | + | 0.571822i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.66532 | − | 12.1033i | −0.0895283 | − | 0.650678i | ||||
\(347\) | −23.9713 | −1.28684 | −0.643422 | − | 0.765511i | \(-0.722486\pi\) | ||||
−0.643422 | + | 0.765511i | \(0.722486\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8.91570i | − | 0.477247i | −0.971112 | − | 0.238623i | \(-0.923304\pi\) | ||
0.971112 | − | 0.238623i | \(-0.0766961\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.5976 | − | 8.63437i | 0.564855 | − | 0.460213i | ||||
\(353\) | 7.35606i | 0.391524i | 0.980651 | + | 0.195762i | \(0.0627179\pi\) | ||||
−0.980651 | + | 0.195762i | \(0.937282\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −22.9489 | + | 6.43704i | −1.21629 | + | 0.341162i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.1772 | + | 1.81307i | −0.696434 | + | 0.0958240i | ||||
\(359\) | 25.2114 | 1.33061 | 0.665304 | − | 0.746572i | \(-0.268302\pi\) | ||||
0.665304 | + | 0.746572i | \(0.268302\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −29.4227 | −1.54856 | ||||||||
\(362\) | −9.01534 | + | 1.24044i | −0.473836 | + | 0.0651961i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.228446 | − | 0.814441i | −0.0119738 | − | 0.0426883i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 5.86573i | − | 0.306189i | −0.988212 | − | 0.153094i | \(-0.951076\pi\) | ||
0.988212 | − | 0.153094i | \(-0.0489238\pi\) | |||||||
\(368\) | 3.42294 | + | 5.62155i | 0.178433 | + | 0.293043i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 0.928327i | − | 0.0481963i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.5063 | 1.42422 | 0.712111 | − | 0.702067i | \(-0.247739\pi\) | ||||
0.712111 | + | 0.702067i | \(0.247739\pi\) | |||||||
\(374\) | −0.119213 | − | 0.866420i | −0.00616434 | − | 0.0448015i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.7916 | + | 6.43244i | −0.762820 | + | 0.331728i | ||||
\(377\) | − | 23.7852i | − | 1.22500i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.7549i | 0.603807i | 0.953339 | + | 0.301903i | \(0.0976220\pi\) | ||||
−0.953339 | + | 0.301903i | \(0.902378\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.07231 | − | 7.79341i | −0.0548643 | − | 0.398746i | ||||
\(383\) | 34.3335i | 1.75436i | 0.480162 | + | 0.877180i | \(0.340578\pi\) | ||||
−0.480162 | + | 0.877180i | \(0.659422\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.8104 | + | 3.55131i | −1.31372 | + | 0.180757i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.59413 | + | 16.3787i | 0.233232 | + | 0.831501i | ||||
\(389\) | − | 2.89515i | − | 0.146790i | −0.997303 | − | 0.0733951i | \(-0.976617\pi\) | ||
0.997303 | − | 0.0733951i | \(-0.0233834\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.421092 | 0.0212955 | ||||||||
\(392\) | 7.88844 | + | 18.1398i | 0.398427 | + | 0.916196i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.47444 | + | 25.2517i | 0.175040 | + | 1.27216i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.9099 | −1.14982 | −0.574909 | − | 0.818218i | \(-0.694962\pi\) | ||||
−0.574909 | + | 0.818218i | \(0.694962\pi\) | |||||||
\(398\) | 3.87877 | + | 28.1903i | 0.194425 | + | 1.41305i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.4337 | 0.620910 | 0.310455 | − | 0.950588i | \(-0.399519\pi\) | ||||
0.310455 | + | 0.950588i | \(0.399519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −43.6960 | −2.17665 | ||||||||
\(404\) | 4.08494 | + | 14.5633i | 0.203233 | + | 0.724553i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0698797 | − | 0.507875i | −0.00346807 | − | 0.0252054i | ||||
\(407\) | 6.45785i | 0.320104i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.0886 | 1.58668 | 0.793340 | − | 0.608778i | \(-0.208340\pi\) | ||||
0.793340 | + | 0.608778i | \(0.208340\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.964394 | + | 3.43819i | 0.0475123 | + | 0.169388i | ||||
\(413\) | 1.01934 | 0.0501583 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 18.8226 | + | 23.1024i | 0.922853 | + | 1.13269i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.24150 | − | 23.5587i | −0.158547 | − | 1.15230i | ||||
\(419\) | − | 16.1364i | − | 0.788317i | −0.919043 | − | 0.394158i | \(-0.871036\pi\) | ||
0.919043 | − | 0.394158i | \(-0.128964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 28.7675i | − | 1.40204i | −0.713141 | − | 0.701021i | \(-0.752728\pi\) | ||
0.713141 | − | 0.701021i | \(-0.247272\pi\) | |||||||
\(422\) | −4.56159 | + | 0.627639i | −0.222055 | + | 0.0305530i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.0422 | + | 29.9911i | 0.633388 | + | 1.45650i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.958640 | 0.0463918 | ||||||||
\(428\) | −20.1628 | + | 5.65556i | −0.974605 | + | 0.273372i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.7297 | −1.19119 | −0.595594 | − | 0.803285i | \(-0.703083\pi\) | ||||
−0.595594 | + | 0.803285i | \(0.703083\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.48816i | − | 0.215687i | −0.994168 | − | 0.107844i | \(-0.965605\pi\) | ||
0.994168 | − | 0.107844i | \(-0.0343946\pi\) | |||||||
\(434\) | −0.933023 | + | 0.128377i | −0.0447865 | + | 0.00616228i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.96773 | − | 7.01522i | −0.0942373 | − | 0.335968i | ||||
\(437\) | 11.4499 | 0.547721 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.96081 | −0.284494 | −0.142247 | − | 0.989831i | \(-0.545433\pi\) | ||||
−0.142247 | + | 0.989831i | \(0.545433\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.88876 | − | 0.259879i | 0.0898392 | − | 0.0123612i | ||||
\(443\) | 14.2924 | 0.679053 | 0.339526 | − | 0.940597i | \(-0.389733\pi\) | ||||
0.339526 | + | 0.940597i | \(0.389733\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 37.8149 | − | 5.20304i | 1.79059 | − | 0.246371i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.469784 | + | 0.437996i | 0.0221952 | + | 0.0206933i | ||||
\(449\) | 24.5529 | 1.15872 | 0.579362 | − | 0.815070i | \(-0.303302\pi\) | ||||
0.579362 | + | 0.815070i | \(0.303302\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.6200i | 0.923870i | ||||||||
\(452\) | 4.77107 | + | 17.0095i | 0.224412 | + | 0.800060i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.82105 | + | 27.7708i | 0.179331 | + | 1.30335i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 28.9108i | − | 1.35239i | −0.736722 | − | 0.676196i | \(-0.763627\pi\) | ||
0.736722 | − | 0.676196i | \(-0.236373\pi\) | |||||||
\(458\) | 30.3736 | − | 4.17917i | 1.41927 | − | 0.195280i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4.35458i | − | 0.202813i | −0.994845 | − | 0.101407i | \(-0.967666\pi\) | ||
0.994845 | − | 0.101407i | \(-0.0323343\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.1303i | 0.517267i | 0.965976 | + | 0.258634i | \(0.0832722\pi\) | ||||
−0.965976 | + | 0.258634i | \(0.916728\pi\) | |||||||
\(464\) | 9.39282 | + | 15.4260i | 0.436051 | + | 0.716134i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.2002 | + | 3.32976i | −1.12105 | + | 0.154248i | ||||
\(467\) | 19.1257 | 0.885030 | 0.442515 | − | 0.896761i | \(-0.354086\pi\) | ||||
0.442515 | + | 0.896761i | \(0.354086\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.584467i | 0.0269882i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −32.9314 | + | 14.3209i | −1.51579 | + | 0.659172i | ||||
\(473\) | 9.88079i | 0.454319i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.0395664 | − | 0.0110982i | 0.00181352 | − | 0.000508684i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.15597 | + | 22.9371i | 0.144351 | + | 1.04912i | ||||
\(479\) | −25.6358 | −1.17133 | −0.585666 | − | 0.810553i | \(-0.699167\pi\) | ||||
−0.585666 | + | 0.810553i | \(0.699167\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.0779 | −0.641895 | ||||||||
\(482\) | 1.31594 | + | 9.56407i | 0.0599395 | + | 0.435632i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.93761 | + | 2.78745i | −0.451710 | + | 0.126702i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.8434i | 0.581992i | 0.956724 | + | 0.290996i | \(0.0939866\pi\) | ||||
−0.956724 | + | 0.290996i | \(0.906013\pi\) | |||||||
\(488\) | −30.9704 | + | 13.4681i | −1.40197 | + | 0.609673i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 16.9887i | − | 0.766689i | −0.923605 | − | 0.383344i | \(-0.874772\pi\) | ||
0.923605 | − | 0.383344i | \(-0.125228\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.15551 | 0.0520415 | ||||||||
\(494\) | 51.3571 | − | 7.06634i | 2.31066 | − | 0.317930i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 28.3393 | − | 17.2557i | 1.27247 | − | 0.774802i | ||||
\(497\) | − | 0.911101i | − | 0.0408684i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0521i | 0.629060i | 0.949248 | + | 0.314530i | \(0.101847\pi\) | ||||
−0.949248 | + | 0.314530i | \(0.898153\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.16057 | + | 0.572463i | −0.185695 | + | 0.0255503i | ||||
\(503\) | 9.53258i | 0.425037i | 0.977157 | + | 0.212518i | \(0.0681665\pi\) | ||||
−0.977157 | + | 0.212518i | \(0.931833\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.766474 | + | 5.57062i | 0.0340739 | + | 0.247644i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.69723 | − | 16.7462i | −0.208406 | − | 0.742995i | ||||
\(509\) | 30.3450i | 1.34502i | 0.740088 | + | 0.672510i | \(0.234784\pi\) | ||||
−0.740088 | + | 0.672510i | \(0.765216\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.969687 | −0.0428964 | ||||||||
\(512\) | −21.3306 | − | 7.55007i | −0.942690 | − | 0.333669i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.04754 | − | 0.969687i | 0.310854 | − | 0.0427710i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.7806 | −0.606069 | ||||||||
\(518\) | −0.300599 | + | 0.0413600i | −0.0132075 | + | 0.00181726i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.4245 | −0.631949 | −0.315975 | − | 0.948768i | \(-0.602331\pi\) | ||||
−0.315975 | + | 0.948768i | \(0.602331\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.2207 | −1.23401 | −0.617003 | − | 0.786961i | \(-0.711654\pi\) | ||||
−0.617003 | + | 0.786961i | \(0.711654\pi\) | |||||||
\(524\) | −5.82902 | − | 20.7812i | −0.254642 | − | 0.907832i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.79093 | − | 0.521603i | 0.165292 | − | 0.0227430i | ||||
\(527\) | − | 2.12280i | − | 0.0924706i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.2926 | 0.882287 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.07585 | − | 0.301769i | 0.0466439 | − | 0.0130834i | ||||
\(533\) | −42.7708 | −1.85261 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.21130 | − | 18.8822i | −0.354674 | − | 0.815586i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 31.3432 | − | 4.31258i | 1.35130 | − | 0.185929i | ||||
\(539\) | 16.8999i | 0.727928i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 13.4695i | − | 0.579100i | −0.957163 | − | 0.289550i | \(-0.906494\pi\) | ||
0.957163 | − | 0.289550i | \(-0.0935056\pi\) | |||||||
\(542\) | 0.167659 | + | 1.21852i | 0.00720156 | + | 0.0523399i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.12234 | + | 0.914421i | −0.0481198 | + | 0.0392055i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.42773 | 0.189316 | 0.0946581 | − | 0.995510i | \(-0.469824\pi\) | ||||
0.0946581 | + | 0.995510i | \(0.469824\pi\) | |||||||
\(548\) | −6.23441 | − | 22.2265i | −0.266321 | − | 0.949469i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.4193 | 1.33851 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.442008i | 0.0187961i | ||||||||
\(554\) | −5.52731 | − | 40.1717i | −0.234833 | − | 1.70673i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.115892 | + | 0.413170i | 0.00491492 | + | 0.0175223i | ||||
\(557\) | 40.2017 | 1.70340 | 0.851700 | − | 0.524030i | \(-0.175572\pi\) | ||||
0.851700 | + | 0.524030i | \(0.175572\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.5397 | −0.911033 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.91907 | + | 21.2154i | 0.123134 | + | 0.894917i | ||||
\(563\) | 13.1128 | 0.552637 | 0.276319 | − | 0.961066i | \(-0.410885\pi\) | ||||
0.276319 | + | 0.961066i | \(0.410885\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.20138 | − | 8.73146i | −0.0504978 | − | 0.367011i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.8002 | + | 29.4346i | 0.537086 | + | 1.23505i | ||||
\(569\) | −11.0257 | −0.462222 | −0.231111 | − | 0.972927i | \(-0.574236\pi\) | ||||
−0.231111 | + | 0.972927i | \(0.574236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.6960i | 1.91232i | 0.292847 | + | 0.956159i | \(0.405397\pi\) | ||||
−0.292847 | + | 0.956159i | \(0.594603\pi\) | |||||||
\(572\) | 6.87587 | + | 24.5134i | 0.287495 | + | 1.02496i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.913268 | + | 0.125659i | −0.0381191 | + | 0.00524489i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 17.2685i | − | 0.718899i | −0.933165 | − | 0.359449i | \(-0.882965\pi\) | ||
0.933165 | − | 0.359449i | \(-0.117035\pi\) | |||||||
\(578\) | −3.26444 | − | 23.7255i | −0.135783 | − | 0.986850i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.739286i | 0.0306707i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.9411i | 1.15720i | ||||||||
\(584\) | 31.3273 | − | 13.6233i | 1.29633 | − | 0.563737i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.14557 | + | 30.1294i | 0.171252 | + | 1.24463i | ||||
\(587\) | 34.7155 | 1.43286 | 0.716432 | − | 0.697657i | \(-0.245774\pi\) | ||||
0.716432 | + | 0.697657i | \(0.245774\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 57.7208i | − | 2.37835i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.13026 | − | 5.55938i | 0.375251 | − | 0.228489i | ||||
\(593\) | − | 9.34022i | − | 0.383557i | −0.981438 | − | 0.191778i | \(-0.938575\pi\) | ||
0.981438 | − | 0.191778i | \(-0.0614255\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.4490 | + | 44.3822i | 0.509930 | + | 1.81797i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.1437 | + | 1.67088i | −0.496594 | + | 0.0683274i | ||||
\(599\) | −13.9110 | −0.568389 | −0.284195 | − | 0.958767i | \(-0.591726\pi\) | ||||
−0.284195 | + | 0.958767i | \(0.591726\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.7330 | 0.478600 | 0.239300 | − | 0.970946i | \(-0.423082\pi\) | ||||
0.239300 | + | 0.970946i | \(0.423082\pi\) | |||||||
\(602\) | −0.459929 | + | 0.0632826i | −0.0187453 | + | 0.00257921i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −18.2665 | + | 5.12365i | −0.743253 | + | 0.208478i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 10.8158i | − | 0.438998i | −0.975613 | − | 0.219499i | \(-0.929558\pi\) | ||
0.975613 | − | 0.219499i | \(-0.0704423\pi\) | |||||||
\(608\) | −30.5174 | + | 24.8639i | −1.23764 | + | 1.00837i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 30.0411i | − | 1.21533i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.9632 | 0.725528 | 0.362764 | − | 0.931881i | \(-0.381833\pi\) | ||||
0.362764 | + | 0.931881i | \(0.381833\pi\) | |||||||
\(614\) | −0.689546 | − | 5.01152i | −0.0278278 | − | 0.202248i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.218837 | + | 0.503223i | 0.00881718 | + | 0.0202754i | ||||
\(617\) | − | 12.3576i | − | 0.497500i | −0.968568 | − | 0.248750i | \(-0.919980\pi\) | ||
0.968568 | − | 0.248750i | \(-0.0800197\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 4.99540i | − | 0.200782i | −0.994948 | − | 0.100391i | \(-0.967991\pi\) | ||
0.994948 | − | 0.100391i | \(-0.0320094\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.480883 | − | 3.49498i | −0.0192816 | − | 0.140136i | ||||
\(623\) | − | 0.956795i | − | 0.0383332i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.4112 | − | 1.84527i | 0.536018 | − | 0.0737519i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.2168 | − | 3.42674i | 0.487502 | − | 0.136742i | ||||
\(629\) | − | 0.683917i | − | 0.0272696i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.9674 | −0.715273 | −0.357636 | − | 0.933861i | \(-0.616417\pi\) | ||||
−0.357636 | + | 0.933861i | \(0.616417\pi\) | |||||||
\(632\) | −6.20985 | − | 14.2798i | −0.247015 | − | 0.568019i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.610502 | − | 4.43704i | −0.0242461 | − | 0.176217i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −36.8410 | −1.45969 | ||||||||
\(638\) | 2.10327 | + | 15.2862i | 0.0832691 | + | 0.605188i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.3638 | −1.08081 | −0.540403 | − | 0.841406i | \(-0.681728\pi\) | ||||
−0.540403 | + | 0.841406i | \(0.681728\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.27518 | −0.0897245 | −0.0448623 | − | 0.998993i | \(-0.514285\pi\) | ||||
−0.0448623 | + | 0.998993i | \(0.514285\pi\) | |||||||
\(644\) | −0.254391 | + | 0.0713553i | −0.0100244 | + | 0.00281179i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.343290 | + | 2.49498i | 0.0135066 | + | 0.0981638i | ||||
\(647\) | − | 12.4769i | − | 0.490516i | −0.969458 | − | 0.245258i | \(-0.921127\pi\) | ||
0.969458 | − | 0.245258i | \(-0.0788726\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.6804 | −1.20431 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.8978 | + | 6.70320i | −0.935909 | + | 0.262518i | ||||
\(653\) | 29.3055 | 1.14681 | 0.573406 | − | 0.819271i | \(-0.305622\pi\) | ||||
0.573406 | + | 0.819271i | \(0.305622\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 27.7392 | − | 16.8903i | 1.08303 | − | 0.659455i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.0882593 | − | 0.641455i | −0.00344070 | − | 0.0250065i | ||||
\(659\) | 18.6009i | 0.724589i | 0.932064 | + | 0.362295i | \(0.118007\pi\) | ||||
−0.932064 | + | 0.362295i | \(0.881993\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.1318i | 0.627456i | 0.949513 | + | 0.313728i | \(0.101578\pi\) | ||||
−0.949513 | + | 0.313728i | \(0.898422\pi\) | |||||||
\(662\) | −23.1333 | + | 3.18296i | −0.899102 | + | 0.123709i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.3864 | − | 23.8838i | −0.403069 | − | 0.926873i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.42931 | −0.287664 | ||||||||
\(668\) | −12.5667 | − | 44.8018i | −0.486219 | − | 1.73343i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.8535 | −1.11388 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.1385i | 1.31594i | 0.753043 | + | 0.657971i | \(0.228585\pi\) | ||||
−0.753043 | + | 0.657971i | \(0.771415\pi\) | |||||||
\(674\) | 16.5782 | − | 2.28103i | 0.638567 | − | 0.0878619i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.4043 | + | 7.96725i | −1.09247 | + | 0.306433i | ||||
\(677\) | −12.1940 | −0.468654 | −0.234327 | − | 0.972158i | \(-0.575289\pi\) | ||||
−0.234327 | + | 0.972158i | \(0.575289\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.682867 | −0.0262060 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 28.0825 | − | 3.86393i | 1.07533 | − | 0.147958i | ||||
\(683\) | 21.8567 | 0.836322 | 0.418161 | − | 0.908373i | \(-0.362675\pi\) | ||||
0.418161 | + | 0.908373i | \(0.362675\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.57403 | + | 0.216574i | −0.0600966 | + | 0.00826883i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13.9697 | − | 8.50608i | 0.532589 | − | 0.324291i | ||||
\(689\) | −60.9106 | −2.32051 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.17780i | 0.235015i | 0.993072 | + | 0.117507i | \(0.0374903\pi\) | ||||
−0.993072 | + | 0.117507i | \(0.962510\pi\) | |||||||
\(692\) | −16.6359 | + | 4.66628i | −0.632402 | + | 0.177385i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.62091 | + | 33.5841i | 0.175407 | + | 1.27483i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.07785i | − | 0.0787043i | ||||||
\(698\) | −12.4910 | + | 1.71867i | −0.472792 | + | 0.0650525i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 33.9746i | − | 1.28320i | −0.767038 | − | 0.641601i | \(-0.778270\pi\) | ||
0.767038 | − | 0.641601i | \(-0.221730\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 18.5963i | − | 0.701374i | ||||||
\(704\) | −14.1398 | − | 13.1830i | −0.532912 | − | 0.496852i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.3059 | − | 1.41802i | 0.387869 | − | 0.0533678i | ||||
\(707\) | −0.607181 | −0.0228354 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.3441i | 0.839151i | 0.907720 | + | 0.419576i | \(0.137821\pi\) | ||||
−0.907720 | + | 0.419576i | \(0.862179\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.4422 | + | 30.9108i | 0.503768 | + | 1.15843i | ||||
\(713\) | 13.6485i | 0.511139i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.08029 | + | 18.1119i | 0.189859 | + | 0.676873i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.85997 | − | 35.3216i | −0.181373 | − | 1.31819i | ||||
\(719\) | −17.8427 | −0.665422 | −0.332711 | − | 0.943029i | \(-0.607963\pi\) | ||||
−0.332711 | + | 0.943029i | \(0.607963\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.143347 | −0.00533851 | ||||||||
\(722\) | 5.67177 | + | 41.2216i | 0.211081 | + | 1.53411i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.47575 | + | 12.3915i | 0.129175 | + | 0.460527i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 23.9148i | − | 0.886953i | −0.896286 | − | 0.443476i | \(-0.853745\pi\) | ||
0.896286 | − | 0.443476i | \(-0.146255\pi\) | |||||||
\(728\) | −1.09701 | + | 0.477055i | −0.0406577 | + | 0.0176808i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.04642i | − | 0.0387034i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.6789 | −0.579112 | −0.289556 | − | 0.957161i | \(-0.593508\pi\) | ||||
−0.289556 | + | 0.957161i | \(0.593508\pi\) | |||||||
\(734\) | −8.21797 | + | 1.13073i | −0.303331 | + | 0.0417360i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.21603 | − | 5.87924i | 0.265987 | − | 0.216712i | ||||
\(737\) | − | 17.5915i | − | 0.647992i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 22.3083i | − | 0.820622i | −0.911946 | − | 0.410311i | \(-0.865420\pi\) | ||
0.911946 | − | 0.410311i | \(-0.134580\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.30060 | + | 0.178952i | −0.0477465 | + | 0.00656955i | ||||
\(743\) | 9.78057i | 0.358814i | 0.983775 | + | 0.179407i | \(0.0574180\pi\) | ||||
−0.983775 | + | 0.179407i | \(0.942582\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.30235 | − | 38.5367i | −0.194133 | − | 1.41093i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.19089 | + | 0.334037i | −0.0435431 | + | 0.0122136i | ||||
\(749\) | − | 0.840636i | − | 0.0307162i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.05399 | −0.293894 | −0.146947 | − | 0.989144i | \(-0.546945\pi\) | ||||
−0.146947 | + | 0.989144i | \(0.546945\pi\) | |||||||
\(752\) | 11.8633 | + | 19.4833i | 0.432610 | + | 0.710483i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −33.3234 | + | 4.58504i | −1.21357 | + | 0.166977i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.4889 | 1.03545 | 0.517723 | − | 0.855549i | \(-0.326780\pi\) | ||||
0.517723 | + | 0.855549i | \(0.326780\pi\) | |||||||
\(758\) | 16.4687 | − | 2.26597i | 0.598171 | − | 0.0823037i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.5005 | 0.779393 | 0.389697 | − | 0.920943i | \(-0.372580\pi\) | ||||
0.389697 | + | 0.920943i | \(0.372580\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.292482 | 0.0105886 | ||||||||
\(764\) | −10.7120 | + | 3.00465i | −0.387546 | + | 0.108705i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 48.1017 | − | 6.61842i | 1.73799 | − | 0.239133i | ||||
\(767\) | − | 66.8821i | − | 2.41497i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.5596 | −0.849580 | −0.424790 | − | 0.905292i | \(-0.639652\pi\) | ||||
−0.424790 | + | 0.905292i | \(0.639652\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.95088 | + | 35.4762i | 0.358140 | + | 1.27682i | ||||
\(773\) | −31.1655 | −1.12094 | −0.560472 | − | 0.828173i | \(-0.689380\pi\) | ||||
−0.560472 | + | 0.828173i | \(0.689380\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 22.0611 | − | 9.59373i | 0.791949 | − | 0.344395i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.05615 | + | 0.558095i | −0.145420 | + | 0.0200087i | ||||
\(779\) | − | 56.4987i | − | 2.02428i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.4227i | 0.981260i | ||||||||
\(782\) | −0.0811733 | − | 0.589955i | −0.00290275 | − | 0.0210968i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 23.8934 | − | 14.5486i | 0.853336 | − | 0.519593i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.07812 | −0.181015 | −0.0905077 | − | 0.995896i | \(-0.528849\pi\) | ||||
−0.0905077 | + | 0.995896i | \(0.528849\pi\) | |||||||
\(788\) | 34.7082 | − | 9.73547i | 1.23643 | − | 0.346812i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.709168 | −0.0252151 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 62.8995i | − | 2.23363i | ||||||
\(794\) | 4.41632 | + | 32.0972i | 0.156729 | + | 1.13909i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 38.7473 | − | 10.8684i | 1.37336 | − | 0.385221i | ||||
\(797\) | 1.43418 | 0.0508012 | 0.0254006 | − | 0.999677i | \(-0.491914\pi\) | ||||
0.0254006 | + | 0.999677i | \(0.491914\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.45943 | 0.0516309 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.39683 | − | 17.4198i | −0.0846350 | − | 0.615115i | ||||
\(803\) | 29.1860 | 1.02995 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.42322 | + | 61.2187i | 0.296695 | + | 2.15634i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 19.6160 | − | 8.53041i | 0.690088 | − | 0.300099i | ||||
\(809\) | 23.7153 | 0.833787 | 0.416894 | − | 0.908955i | \(-0.363119\pi\) | ||||
0.416894 | + | 0.908955i | \(0.363119\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 47.8394i | − | 1.67987i | −0.542689 | − | 0.839933i | \(-0.682594\pi\) | ||
0.542689 | − | 0.839933i | \(-0.317406\pi\) | |||||||
\(812\) | −0.698070 | + | 0.195805i | −0.0244974 | + | 0.00687140i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.04754 | − | 1.24487i | 0.317116 | − | 0.0436327i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 28.4532i | − | 0.995451i | ||||||
\(818\) | −6.18568 | − | 44.9566i | −0.216277 | − | 1.57187i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 51.9216i | 1.81208i | 0.423195 | + | 0.906038i | \(0.360908\pi\) | ||||
−0.423195 | + | 0.906038i | \(0.639092\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 27.8542i | − | 0.970937i | −0.874254 | − | 0.485469i | \(-0.838649\pi\) | ||
0.874254 | − | 0.485469i | \(-0.161351\pi\) | |||||||
\(824\) | 4.63105 | − | 2.01391i | 0.161330 | − | 0.0701577i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.196496 | − | 1.42811i | −0.00683698 | − | 0.0496902i | ||||
\(827\) | −43.9365 | −1.52782 | −0.763912 | − | 0.645321i | \(-0.776724\pi\) | ||||
−0.763912 | + | 0.645321i | \(0.776724\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 41.6898i | − | 1.44795i | −0.689827 | − | 0.723974i | \(-0.742314\pi\) | ||
0.689827 | − | 0.723974i | \(-0.257686\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 28.7383 | − | 30.8241i | 0.996322 | − | 1.06863i | ||||
\(833\) | − | 1.78978i | − | 0.0620121i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −32.3813 | + | 9.08277i | −1.11993 | + | 0.314134i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22.6074 | + | 3.11060i | −0.780959 | + | 0.107454i | ||||
\(839\) | −25.4733 | −0.879437 | −0.439719 | − | 0.898136i | \(-0.644922\pi\) | ||||
−0.439719 | + | 0.898136i | \(0.644922\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.61336 | 0.297012 | ||||||||
\(842\) | −40.3037 | + | 5.54547i | −1.38896 | + | 0.191110i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.75866 | + | 6.26986i | 0.0605356 | + | 0.215817i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 0.414324i | − | 0.0142363i | ||||||
\(848\) | 39.5038 | − | 24.0537i | 1.35657 | − | 0.826008i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.39722i | 0.150735i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.5366 | −0.429245 | −0.214622 | − | 0.976697i | \(-0.568852\pi\) | ||||
−0.214622 | + | 0.976697i | \(0.568852\pi\) | |||||||
\(854\) | −0.184796 | − | 1.34307i | −0.00632358 | − | 0.0459588i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.8103 | + | 27.1581i | 0.403667 | + | 0.928246i | ||||
\(857\) | − | 2.61409i | − | 0.0892956i | −0.999003 | − | 0.0446478i | \(-0.985783\pi\) | ||
0.999003 | − | 0.0446478i | \(-0.0142166\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 31.8438i | − | 1.08650i | −0.839573 | − | 0.543248i | \(-0.817195\pi\) | ||
0.839573 | − | 0.543248i | \(-0.182805\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.76711 | + | 34.6467i | 0.162369 | + | 1.18007i | ||||
\(863\) | − | 22.3335i | − | 0.760241i | −0.924937 | − | 0.380121i | \(-0.875882\pi\) | ||
0.924937 | − | 0.380121i | \(-0.124118\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.28798 | + | 0.865177i | −0.213674 | + | 0.0293999i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.359715 | + | 1.28243i | 0.0122095 | + | 0.0435286i | ||||
\(869\) | − | 13.3037i | − | 0.451298i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.3488 | 1.29940 | ||||||||
\(872\) | −9.44910 | + | 4.10913i | −0.319987 | + | 0.139153i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.20717 | − | 16.0414i | −0.0746588 | − | 0.542609i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.4408 | 1.26429 | 0.632143 | − | 0.774852i | \(-0.282176\pi\) | ||||
0.632143 | + | 0.774852i | \(0.282176\pi\) | |||||||
\(878\) | 1.14906 | + | 8.35117i | 0.0387788 | + | 0.281838i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −53.1952 | −1.79219 | −0.896096 | − | 0.443860i | \(-0.853609\pi\) | ||||
−0.896096 | + | 0.443860i | \(0.853609\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.0907 | 1.21455 | 0.607274 | − | 0.794493i | \(-0.292263\pi\) | ||||
0.607274 | + | 0.794493i | \(0.292263\pi\) | |||||||
\(884\) | −0.728188 | − | 2.59608i | −0.0244916 | − | 0.0873157i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.75513 | − | 20.0239i | −0.0925604 | − | 0.672715i | ||||
\(887\) | 43.3018i | 1.45393i | 0.686673 | + | 0.726966i | \(0.259070\pi\) | ||||
−0.686673 | + | 0.726966i | \(0.740930\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.698192 | 0.0234166 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.5791 | − | 51.9763i | −0.488143 | − | 1.74029i | ||||
\(893\) | 39.6832 | 1.32795 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.523078 | − | 0.742606i | 0.0174748 | − | 0.0248087i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.73304 | − | 34.3990i | −0.157943 | − | 1.14791i | ||||
\(899\) | 37.4525i | 1.24911i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.95910i | − | 0.0985820i | ||||||
\(902\) | 27.4879 | − | 3.78212i | 0.915247 | − | 0.125931i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22.9108 | − | 9.96324i | 0.762003 | − | 0.331372i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.75026 | 0.290548 | 0.145274 | − | 0.989391i | \(-0.453594\pi\) | ||||
0.145274 | + | 0.989391i | \(0.453594\pi\) | |||||||
\(908\) | 38.1707 | − | 10.7067i | 1.26674 | − | 0.355314i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.7438 | 0.455353 | 0.227676 | − | 0.973737i | \(-0.426887\pi\) | ||||
0.227676 | + | 0.973737i | \(0.426887\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 22.2513i | − | 0.736411i | ||||||
\(914\) | −40.5045 | + | 5.57310i | −1.33977 | + | 0.184342i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.7102 | − | 41.7483i | −0.386915 | − | 1.37940i | ||||
\(917\) | 0.866420 | 0.0286117 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.989347 | 0.0326355 | 0.0163178 | − | 0.999867i | \(-0.494806\pi\) | ||||
0.0163178 | + | 0.999867i | \(0.494806\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.10083 | + | 0.839427i | −0.200920 | + | 0.0276451i | ||||
\(923\) | −59.7803 | −1.96769 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.5936 | − | 2.14557i | 0.512439 | − | 0.0705076i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 19.8014 | − | 16.1331i | 0.650012 | − | 0.529596i | ||||
\(929\) | −8.49434 | −0.278690 | −0.139345 | − | 0.990244i | \(-0.544500\pi\) | ||||
−0.139345 | + | 0.990244i | \(0.544500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 48.6656i | − | 1.59495i | ||||||
\(932\) | 9.33008 | + | 33.2629i | 0.305617 | + | 1.08956i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.68683 | − | 26.7953i | −0.120637 | − | 0.876770i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.6912i | 0.610615i | 0.952254 | + | 0.305308i | \(0.0987593\pi\) | ||||
−0.952254 | + | 0.305308i | \(0.901241\pi\) | |||||||
\(938\) | 0.818847 | − | 0.112667i | 0.0267363 | − | 0.00367871i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.03170i | 0.0988305i | 0.998778 | + | 0.0494152i | \(0.0157358\pi\) | ||||
−0.998778 | + | 0.0494152i | \(0.984264\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.3595i | 0.435045i | ||||||||
\(944\) | 26.4119 | + | 43.3767i | 0.859634 | + | 1.41179i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.8431 | − | 1.90471i | 0.450079 | − | 0.0619273i | ||||
\(947\) | 16.8327 | 0.546990 | 0.273495 | − | 0.961873i | \(-0.411820\pi\) | ||||
0.273495 | + | 0.961873i | \(0.411820\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 63.6243i | 2.06533i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.0231759 | − | 0.0532937i | −0.000751134 | − | 0.00172726i | ||||
\(953\) | 1.73948i | 0.0563473i | 0.999603 | + | 0.0281737i | \(0.00896914\pi\) | ||||
−0.999603 | + | 0.0281737i | \(0.991031\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 31.5269 | − | 8.84312i | 1.01965 | − | 0.286007i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.94179 | + | 35.9162i | 0.159662 | + | 1.16040i | ||||
\(959\) | 0.926677 | 0.0299240 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.8044 | 1.21950 | ||||||||
\(962\) | 2.71377 | + | 19.7233i | 0.0874954 | + | 0.635904i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.1457 | − | 3.68731i | 0.423395 | − | 0.118760i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17.3399i | − | 0.557615i | −0.960347 | − | 0.278808i | \(-0.910061\pi\) | ||
0.960347 | − | 0.278808i | \(-0.0899392\pi\) | |||||||
\(968\) | 5.82091 | + | 13.3854i | 0.187091 | + | 0.430223i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.4054i | 1.45713i | 0.684977 | + | 0.728565i | \(0.259812\pi\) | ||||
−0.684977 | + | 0.728565i | \(0.740188\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.0172261 | −0.000552243 | ||||||||
\(974\) | 17.9938 | − | 2.47581i | 0.576560 | − | 0.0793302i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.8392 | + | 40.7938i | 0.795082 | + | 1.30578i | ||||
\(977\) | − | 43.4336i | − | 1.38957i | −0.719220 | − | 0.694783i | \(-0.755501\pi\) | ||
0.719220 | − | 0.694783i | \(-0.244499\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.7980i | 0.920388i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −23.8014 | + | 3.27489i | −0.759533 | + | 0.104506i | ||||
\(983\) | − | 47.4465i | − | 1.51331i | −0.653815 | − | 0.756655i | \(-0.726832\pi\) | ||
0.653815 | − | 0.756655i | \(-0.273168\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.222746 | − | 1.61889i | −0.00709368 | − | 0.0515558i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −19.8001 | − | 70.5898i | −0.629924 | − | 2.24576i | ||||
\(989\) | 6.72794i | 0.213936i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.8434 | −0.916242 | −0.458121 | − | 0.888890i | \(-0.651477\pi\) | ||||
−0.458121 | + | 0.888890i | \(0.651477\pi\) | |||||||
\(992\) | −29.6383 | − | 36.3773i | −0.941018 | − | 1.15498i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.27646 | + | 0.175632i | −0.0404870 | + | 0.00557070i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.1449 | 1.04971 | 0.524855 | − | 0.851192i | \(-0.324119\pi\) | ||||
0.524855 | + | 0.851192i | \(0.324119\pi\) | |||||||
\(998\) | 19.6872 | − | 2.70881i | 0.623189 | − | 0.0857460i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))