Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(173,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.173");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.bm (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.01223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 185.6 | ||
Root | \(-0.544978 + 1.64408i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.185 |
Dual form | 252.2.bm.a.173.6 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0.615921 | + | 1.61884i | 0.355602 | + | 0.934637i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.91482 | −1.75076 | −0.875381 | − | 0.483434i | \(-0.839389\pi\) | ||||
−0.875381 | + | 0.483434i | \(0.839389\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.51757 | − | 0.813537i | −0.951552 | − | 0.307488i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.24128 | + | 1.99416i | −0.747094 | + | 0.664718i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.69456i | 1.11395i | 0.830529 | + | 0.556976i | \(0.188038\pi\) | ||||
−0.830529 | + | 0.556976i | \(0.811962\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.480242 | − | 0.277268i | −0.133195 | − | 0.0769002i | 0.431922 | − | 0.901911i | \(-0.357836\pi\) |
−0.565117 | + | 0.825011i | \(0.691169\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.41122 | − | 6.33747i | −0.622575 | − | 1.63633i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.91916 | + | 5.05613i | −0.708000 | + | 1.22629i | 0.257598 | + | 0.966252i | \(0.417069\pi\) |
−0.965598 | + | 0.260040i | \(0.916264\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.62434 | − | 2.66986i | 1.06090 | − | 0.612509i | 0.135216 | − | 0.990816i | \(-0.456827\pi\) |
0.925680 | + | 0.378307i | \(0.123494\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.233638 | − | 4.57662i | −0.0509841 | − | 0.998699i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.27435i | − | 0.474236i | −0.971481 | − | 0.237118i | \(-0.923797\pi\) | ||
0.971481 | − | 0.237118i | \(-0.0762027\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.3258 | 2.06516 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.60867 | − | 2.40003i | −0.886939 | − | 0.461887i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.53638 | − | 2.04173i | 0.656690 | − | 0.379140i | −0.134325 | − | 0.990937i | \(-0.542887\pi\) |
0.791014 | + | 0.611797i | \(0.209553\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.00132 | + | 4.04222i | −1.25748 | + | 0.726004i | −0.972583 | − | 0.232556i | \(-0.925291\pi\) |
−0.284892 | + | 0.958560i | \(0.591958\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.98090 | + | 2.27556i | −1.04114 | + | 0.396124i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.85583 | + | 3.18485i | 1.66594 | + | 0.538338i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.89849 | + | 6.75239i | 0.640909 | + | 1.11009i | 0.985230 | + | 0.171235i | \(0.0547756\pi\) |
−0.344322 | + | 0.938852i | \(0.611891\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.153061 | − | 0.948209i | 0.0245093 | − | 0.151835i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.59234 | + | 6.22212i | −0.561030 | + | 0.971732i | 0.436377 | + | 0.899764i | \(0.356261\pi\) |
−0.997407 | + | 0.0719684i | \(0.977072\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.754009 | − | 1.30598i | −0.114985 | − | 0.199160i | 0.802789 | − | 0.596264i | \(-0.203349\pi\) |
−0.917774 | + | 0.397103i | \(0.870015\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.77422 | − | 7.80676i | 1.30798 | − | 1.16376i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.41416 | + | 2.44940i | −0.206277 | + | 0.357282i | −0.950539 | − | 0.310606i | \(-0.899468\pi\) |
0.744262 | + | 0.667888i | \(0.232801\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.67631 | + | 4.09627i | 0.810902 | + | 0.585182i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.98304 | − | 1.61147i | −1.39790 | − | 0.225651i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.0415658 | + | 0.0239980i | 0.00570950 | + | 0.00329638i | 0.502852 | − | 0.864373i | \(-0.332284\pi\) |
−0.497143 | + | 0.867669i | \(0.665617\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 14.4635i | − | 1.95026i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.17031 | + | 5.84164i | 0.949731 | + | 0.773744i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.45656 | − | 7.71900i | −0.580195 | − | 1.00493i | −0.995456 | − | 0.0952251i | \(-0.969643\pi\) |
0.415261 | − | 0.909703i | \(-0.363690\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.03343 | + | 3.48340i | 0.772501 | + | 0.446004i | 0.833766 | − | 0.552118i | \(-0.186180\pi\) |
−0.0612648 | + | 0.998122i | \(0.519513\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.26490 | − | 3.19706i | 0.915292 | − | 0.402791i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.88006 | + | 1.08545i | 0.233193 | + | 0.134634i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.587402 | − | 1.01741i | −0.0717626 | − | 0.124296i | 0.827911 | − | 0.560859i | \(-0.189529\pi\) |
−0.899674 | + | 0.436563i | \(0.856196\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.68181 | − | 1.40082i | 0.443238 | − | 0.168639i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.71061i | 0.796403i | 0.917298 | + | 0.398202i | \(0.130366\pi\) | ||||
−0.917298 | + | 0.398202i | \(0.869634\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.52692 | − | 2.03627i | −0.412795 | − | 0.238327i | 0.279195 | − | 0.960234i | \(-0.409932\pi\) |
−0.691990 | + | 0.721907i | \(0.743266\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.35989 | + | 16.7158i | 0.734377 | + | 1.93018i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.00566 | − | 9.30131i | 0.342527 | − | 1.05998i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.97374 | − | 3.41861i | 0.222063 | − | 0.384624i | −0.733371 | − | 0.679828i | \(-0.762054\pi\) |
0.955434 | + | 0.295204i | \(0.0953877\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.04669 | − | 8.93893i | 0.116299 | − | 0.993214i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.84674 | − | 6.66275i | −0.422235 | − | 0.731332i | 0.573923 | − | 0.818909i | \(-0.305421\pi\) |
−0.996158 | + | 0.0875774i | \(0.972087\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.4280 | − | 19.7938i | 1.23954 | − | 2.14694i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.48337 | + | 4.46729i | 0.587879 | + | 0.478944i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.71300 | + | 4.69905i | 0.287577 | + | 0.498099i | 0.973231 | − | 0.229829i | \(-0.0738168\pi\) |
−0.685654 | + | 0.727928i | \(0.740483\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.983474 | + | 1.08874i | 0.103096 | + | 0.114130i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.8560 | − | 8.84433i | −1.12571 | − | 0.917115i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.1035 | + | 10.4520i | −1.85738 | + | 1.07236i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.9874 | + | 8.07563i | −1.42021 | + | 0.819956i | −0.996316 | − | 0.0857571i | \(-0.972669\pi\) |
−0.423890 | + | 0.905714i | \(0.639336\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.36753 | − | 8.28055i | −0.740464 | − | 0.832227i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.62350 | 0.161544 | 0.0807722 | − | 0.996733i | \(-0.474261\pi\) | ||||
0.0807722 | + | 0.996733i | \(0.474261\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.395662i | 0.0389857i | 0.999810 | + | 0.0194929i | \(0.00620517\pi\) | ||||
−0.999810 | + | 0.0194929i | \(0.993795\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.914653 | + | 17.9166i | 0.0892610 | + | 1.74848i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.90777 | − | 2.83350i | 0.474452 | − | 0.273925i | −0.243650 | − | 0.969863i | \(-0.578345\pi\) |
0.718101 | + | 0.695938i | \(0.245011\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.75667 | + | 11.7029i | −0.647171 | + | 1.12093i | 0.336624 | + | 0.941639i | \(0.390715\pi\) |
−0.983795 | + | 0.179294i | \(0.942619\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.52987 | + | 10.4700i | −0.809619 | + | 0.993766i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.13651 | + | 0.656162i | 0.106913 | + | 0.0617265i | 0.552503 | − | 0.833511i | \(-0.313673\pi\) |
−0.445590 | + | 0.895237i | \(0.647006\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.90369i | 0.830273i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.62927 | − | 0.336241i | 0.150626 | − | 0.0310855i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.4625 | − | 10.3543i | 1.05077 | − | 0.949179i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.64977 | −0.240888 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.2852 | − | 1.98309i | −1.10772 | − | 0.178809i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −20.8496 | −1.86485 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.3935 | −1.54342 | −0.771710 | − | 0.635975i | \(-0.780598\pi\) | ||||
−0.771710 | + | 0.635975i | \(0.780598\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.64976 | − | 2.02500i | 0.145254 | − | 0.178291i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.9072 | 0.952968 | 0.476484 | − | 0.879183i | \(-0.341911\pi\) | ||||
0.476484 | + | 0.879183i | \(0.341911\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.8141 | + | 2.95950i | −1.19784 | + | 0.256621i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.0421 | + | 9.39570i | 1.55282 | + | 0.808653i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.80514i | − | 0.752274i | −0.926564 | − | 0.376137i | \(-0.877252\pi\) | ||
0.926564 | − | 0.376137i | \(-0.122748\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.2352 | + | 8.21869i | 1.20741 | + | 0.697100i | 0.962193 | − | 0.272367i | \(-0.0878066\pi\) |
0.245220 | + | 0.969468i | \(0.421140\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.83621 | − | 0.780664i | −0.407282 | − | 0.0657438i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.02438 | − | 1.77428i | 0.0856631 | − | 0.148373i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.8443 | + | 7.99301i | −1.14971 | + | 0.663783i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.13505 | + | 11.7120i | −0.258574 | + | 0.965991i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.5278i | 1.19016i | 0.803665 | + | 0.595082i | \(0.202880\pi\) | ||||
−0.803665 | + | 0.595082i | \(0.797120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.60613 | 0.456221 | 0.228110 | − | 0.973635i | \(-0.426745\pi\) | ||||
0.228110 | + | 0.973635i | \(0.426745\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.54005 | − | 17.1535i | −0.286196 | − | 1.38678i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.4089 | − | 15.8246i | 2.20154 | − | 1.27106i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.4411 | + | 8.91493i | −1.23233 | + | 0.711489i | −0.967516 | − | 0.252809i | \(-0.918645\pi\) |
−0.264819 | + | 0.964298i | \(0.585312\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0132477 | + | 0.0820692i | −0.00105061 | + | 0.00650851i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.85027 | + | 5.72584i | −0.145822 | + | 0.451260i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.576994 | − | 0.999383i | −0.0451937 | − | 0.0782777i | 0.842544 | − | 0.538628i | \(-0.181057\pi\) |
−0.887737 | + | 0.460350i | \(0.847724\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 23.4141 | − | 8.90840i | 1.82279 | − | 0.693518i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.95550 | − | 15.5114i | 0.692997 | − | 1.20031i | −0.277854 | − | 0.960623i | \(-0.589623\pi\) |
0.970851 | − | 0.239683i | \(-0.0770435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.34625 | − | 10.9920i | −0.488173 | − | 0.845540i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.04033 | + | 15.2056i | −0.385443 | + | 1.16280i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.74814 | − | 6.49197i | 0.284966 | − | 0.493576i | −0.687635 | − | 0.726057i | \(-0.741351\pi\) |
0.972601 | + | 0.232481i | \(0.0746843\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −25.9960 | − | 8.40044i | −1.96511 | − | 0.635014i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.75092 | − | 11.9688i | 0.732924 | − | 0.899627i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.624382 | − | 0.360487i | −0.0466685 | − | 0.0269441i | 0.476484 | − | 0.879183i | \(-0.341911\pi\) |
−0.523153 | + | 0.852239i | \(0.675244\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.07121i | 0.376940i | 0.982079 | + | 0.188470i | \(0.0603529\pi\) | ||||
−0.982079 | + | 0.188470i | \(0.939647\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.92295 | + | 11.9127i | −0.142149 | + | 0.880609i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.2619 | − | 26.4344i | −1.12208 | − | 1.94350i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.6802 | − | 10.7850i | −1.36603 | − | 0.788678i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.65013 | + | 9.79158i | 0.701944 | + | 0.712232i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.0005 | − | 6.35111i | −0.795965 | − | 0.459551i | 0.0460934 | − | 0.998937i | \(-0.485323\pi\) |
−0.842058 | + | 0.539387i | \(0.818656\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.4076 | + | 19.7586i | 0.821140 | + | 1.42226i | 0.904834 | + | 0.425765i | \(0.139995\pi\) |
−0.0836931 | + | 0.996492i | \(0.526672\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.599205 | + | 3.71207i | −0.0429100 | + | 0.265827i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.0311360i | 0.00221835i | 0.999999 | + | 0.00110918i | \(0.000353062\pi\) | ||||
−0.999999 | + | 0.00110918i | \(0.999647\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.9144 | + | 11.4976i | 1.41169 | + | 0.815042i | 0.995548 | − | 0.0942556i | \(-0.0300471\pi\) |
0.416146 | + | 0.909298i | \(0.363380\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.28523 | − | 1.57755i | 0.0906532 | − | 0.111272i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.5641 | + | 2.26322i | −0.741455 | + | 0.158847i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.0634 | − | 24.3585i | 0.982229 | − | 1.70127i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.53542 | + | 5.09747i | 0.315233 | + | 0.354299i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.86397 | + | 17.0849i | 0.682305 | + | 1.18179i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.55841 | − | 14.8236i | 0.589185 | − | 1.02050i | −0.405154 | − | 0.914248i | \(-0.632782\pi\) |
0.994339 | − | 0.106250i | \(-0.0338845\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.8634 | + | 4.13321i | −0.744348 | + | 0.283203i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.95181 | + | 5.11268i | 0.201312 | + | 0.348682i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.9148 | − | 4.48072i | 1.41979 | − | 0.304171i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.12409 | − | 6.96369i | 0.0759587 | − | 0.470563i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.80380 | − | 1.61878i | 0.188604 | − | 0.108891i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.25230 | + | 0.723016i | −0.0838602 | + | 0.0484167i | −0.541344 | − | 0.840801i | \(-0.682084\pi\) |
0.457484 | + | 0.889218i | \(0.348751\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −23.1431 | + | 20.5913i | −1.54287 | + | 1.37275i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.47193 | −0.296812 | −0.148406 | − | 0.988926i | \(-0.547414\pi\) | ||||
−0.148406 | + | 0.988926i | \(0.547414\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.58736i | − | 0.170978i | −0.996339 | − | 0.0854888i | \(-0.972755\pi\) | ||
0.996339 | − | 0.0854888i | \(-0.0272452\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.9086 | − | 0.863191i | 1.11250 | − | 0.0567938i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.0756 | + | 8.70389i | −0.987634 | + | 0.570211i | −0.904566 | − | 0.426333i | \(-0.859805\pi\) |
−0.0830679 | + | 0.996544i | \(0.526472\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.53620 | − | 9.58898i | 0.361142 | − | 0.625516i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.74985 | + | 1.08957i | 0.438450 | + | 0.0707750i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.23642 | + | 2.44590i | 0.274031 | + | 0.158212i | 0.630718 | − | 0.776012i | \(-0.282760\pi\) |
−0.356687 | + | 0.934224i | \(0.616094\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.13235i | 0.523851i | 0.965088 | + | 0.261925i | \(0.0843574\pi\) | ||||
−0.965088 | + | 0.261925i | \(0.915643\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.1154 | − | 3.81125i | 0.969651 | − | 0.244492i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −22.2218 | − | 16.0362i | −1.41970 | − | 1.02451i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.96107 | −0.188408 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.41663 | − | 10.3310i | 0.533382 | − | 0.654699i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.9341 | 1.63694 | 0.818472 | − | 0.574546i | \(-0.194821\pi\) | ||||
0.818472 | + | 0.574546i | \(0.194821\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.40274 | 0.528276 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 39.0818 | + | 6.30862i | 2.44740 | + | 0.395061i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 30.8230 | 1.92269 | 0.961344 | − | 0.275349i | \(-0.0887934\pi\) | ||||
0.961344 | + | 0.275349i | \(0.0887934\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.32141 | − | 20.1712i | −0.268519 | − | 1.25338i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.85450 | + | 11.6282i | −0.238588 | + | 0.719767i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.0855i | 1.11520i | 0.830110 | + | 0.557600i | \(0.188278\pi\) | ||||
−0.830110 | + | 0.557600i | \(0.811722\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.162723 | − | 0.0939479i | −0.00999597 | − | 0.00577117i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.93602 | + | 7.28616i | −0.363278 | + | 0.445906i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.8203 | − | 18.7413i | 0.659725 | − | 1.14268i | −0.320961 | − | 0.947092i | \(-0.604006\pi\) |
0.980687 | − | 0.195585i | \(-0.0626607\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.3453 | + | 7.12756i | −0.749923 | + | 0.432968i | −0.825666 | − | 0.564159i | \(-0.809200\pi\) |
0.0757430 | + | 0.997127i | \(0.475867\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.15674 | + | 2.26266i | −0.0700094 | + | 0.136943i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 38.1494i | 2.30049i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.80327 | 0.528937 | 0.264469 | − | 0.964394i | \(-0.414803\pi\) | ||||
0.264469 | + | 0.964394i | \(0.414803\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.63113 | − | 23.0215i | 0.456864 | − | 1.37826i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.6889 | + | 9.63537i | −0.995579 | + | 0.574798i | −0.906937 | − | 0.421266i | \(-0.861586\pi\) |
−0.0886417 | + | 0.996064i | \(0.528253\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.32822 | + | 4.80830i | −0.495061 | + | 0.285824i | −0.726672 | − | 0.686985i | \(-0.758934\pi\) |
0.231611 | + | 0.972809i | \(0.425601\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −28.0705 | − | 22.8690i | −1.66275 | − | 1.35464i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.1059 | − | 12.7421i | 0.832645 | − | 0.752144i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.54297 | − | 14.7969i | −0.502528 | − | 0.870404i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.6883 | − | 17.6694i | −1.27139 | − | 1.03580i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.22598 | + | 2.12346i | −0.0716225 | + | 0.124054i | −0.899613 | − | 0.436689i | \(-0.856151\pi\) |
0.827990 | + | 0.560743i | \(0.189484\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.4467 | + | 30.2185i | 1.01578 | + | 1.75939i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.86706 | − | 17.0270i | 0.514519 | − | 0.988007i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.630605 | + | 1.09224i | −0.0364688 | + | 0.0631658i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.835805 | + | 3.90131i | 0.0481750 | + | 0.224868i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.999949 | + | 2.62819i | 0.0574455 | + | 0.150985i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −23.6198 | − | 13.6369i | −1.35247 | − | 0.780846i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.6839i | 0.609760i | 0.952391 | + | 0.304880i | \(0.0986163\pi\) | ||||
−0.952391 | + | 0.304880i | \(0.901384\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.640513 | + | 0.243697i | −0.0364375 | + | 0.0138634i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.3833 | − | 17.9843i | −0.588780 | − | 1.01980i | −0.994393 | − | 0.105752i | \(-0.966275\pi\) |
0.405612 | − | 0.914045i | \(-0.367058\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.40449 | + | 1.96558i | 0.192433 | + | 0.111101i | 0.593121 | − | 0.805113i | \(-0.297896\pi\) |
−0.400688 | + | 0.916215i | \(0.631229\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −28.4408 | + | 12.5159i | −1.60246 | + | 0.705192i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.98369 | + | 1.14528i | 0.111415 | + | 0.0643256i | 0.554672 | − | 0.832069i | \(-0.312844\pi\) |
−0.443257 | + | 0.896395i | \(0.646177\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.54330 | + | 13.0654i | 0.422344 | + | 0.731521i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.60978 | + | 6.19967i | 0.424736 | + | 0.346032i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 31.1750i | 1.73462i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.95889 | − | 2.86302i | −0.275070 | − | 0.158812i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.1067 | − | 3.72990i | −1.27780 | − | 0.206264i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.55294 | − | 5.01607i | 0.306143 | − | 0.276545i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.46788 | + | 6.00655i | −0.190612 | + | 0.330150i | −0.945453 | − | 0.325758i | \(-0.894381\pi\) |
0.754841 | + | 0.655908i | \(0.227714\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −22.2029 | − | 7.35981i | −1.21671 | − | 0.403315i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.29957 | + | 3.98298i | 0.125639 | + | 0.217613i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.59771 | + | 16.6237i | −0.522821 | + | 0.905552i | 0.476827 | + | 0.878997i | \(0.341787\pi\) |
−0.999647 | + | 0.0265545i | \(0.991546\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.362223 | + | 2.24396i | −0.0196732 | + | 0.121875i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.9342 | − | 25.8668i | −0.808733 | − | 1.40077i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.9580 | − | 14.9305i | −0.591679 | − | 0.806174i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14.4136 | + | 5.48397i | −0.776004 | + | 0.295247i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.35287 | + | 4.24518i | −0.394723 | + | 0.227893i | −0.684204 | − | 0.729290i | \(-0.739850\pi\) |
0.289482 | + | 0.957184i | \(0.406517\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.5478 | − | 9.55386i | 0.885782 | − | 0.511407i | 0.0132216 | − | 0.999913i | \(-0.495791\pi\) |
0.872560 | + | 0.488506i | \(0.162458\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.54782 | + | 2.43043i | 0.0826167 | + | 0.129727i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.6590 | 0.726996 | 0.363498 | − | 0.931595i | \(-0.381582\pi\) | ||||
0.363498 | + | 0.931595i | \(0.381582\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 26.2708i | − | 1.39431i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 23.8220 | + | 12.1786i | 1.26079 | + | 0.644558i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.8909 | − | 8.59724i | 0.785909 | − | 0.453745i | −0.0526113 | − | 0.998615i | \(-0.516754\pi\) |
0.838520 | + | 0.544870i | \(0.183421\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.75635 | − | 8.23824i | 0.250334 | − | 0.433592i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.63205 | − | 4.28955i | −0.0856604 | − | 0.225143i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.8073 | + | 7.97162i | 0.722705 | + | 0.417254i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.8587i | 0.880018i | 0.897993 | + | 0.440009i | \(0.145025\pi\) | ||||
−0.897993 | + | 0.440009i | \(0.854975\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.35642 | − | 21.1092i | −0.226786 | − | 1.09890i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0851215 | − | 0.0942320i | −0.00441929 | − | 0.00489228i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.40858 | −0.0729333 | −0.0364667 | − | 0.999335i | \(-0.511610\pi\) | ||||
−0.0364667 | + | 0.999335i | \(0.511610\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.8417 | − | 33.7522i | −0.663144 | − | 1.74296i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.26442 | −0.116624 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.598572 | −0.0307466 | −0.0153733 | − | 0.999882i | \(-0.504894\pi\) | ||||
−0.0153733 | + | 0.999882i | \(0.504894\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.7130 | − | 28.1572i | −0.548844 | − | 1.44254i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.52077 | −0.435391 | −0.217696 | − | 0.976017i | \(-0.569854\pi\) | ||||
−0.217696 | + | 0.976017i | \(0.569854\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.7666 | + | 36.4130i | −0.599683 | + | 1.85578i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.29428 | + | 1.42346i | 0.218290 | + | 0.0723586i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 34.5976i | 1.75417i | 0.480336 | + | 0.877084i | \(0.340515\pi\) | ||||
−0.480336 | + | 0.877084i | \(0.659485\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.4994 | + | 6.63920i | 0.581551 | + | 0.335759i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.71799 | + | 17.6570i | 0.338878 | + | 0.890680i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.72683 | + | 13.3833i | −0.388779 | + | 0.673385i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.9571 | − | 16.1411i | 1.40313 | − | 0.810097i | 0.408416 | − | 0.912796i | \(-0.366081\pi\) |
0.994712 | + | 0.102699i | \(0.0327478\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.2994 | − | 20.5400i | −0.665801 | − | 1.02829i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.1028i | 0.654321i | 0.944969 | + | 0.327161i | \(0.106092\pi\) | ||||
−0.944969 | + | 0.327161i | \(0.893908\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.48310 | 0.223319 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.09760 | + | 34.9943i | −0.203611 | + | 1.73888i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.9471 | + | 14.4032i | −1.23658 | + | 0.713941i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.3493 | − | 18.6769i | 1.59957 | − | 0.923513i | 0.608002 | − | 0.793936i | \(-0.291971\pi\) |
0.991569 | − | 0.129577i | \(-0.0413620\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.2541 | − | 5.42327i | 0.703103 | − | 0.267510i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.94002 | + | 23.0587i | 0.243082 | + | 1.13464i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.0593 | + | 26.0835i | 0.739232 | + | 1.28039i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.53698 | + | 28.1066i | −0.222177 | + | 1.37638i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.1954 | + | 24.5871i | −0.693490 | + | 1.20116i | 0.277198 | + | 0.960813i | \(0.410594\pi\) |
−0.970687 | + | 0.240346i | \(0.922739\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.3359 | − | 30.0267i | −0.844901 | − | 1.46341i | −0.885707 | − | 0.464245i | \(-0.846326\pi\) |
0.0408054 | − | 0.999167i | \(-0.487008\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.71495 | − | 8.30987i | −0.0833838 | − | 0.404040i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −30.1427 | + | 52.2087i | −1.46214 | + | 2.53249i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.3557 | − | 13.6781i | −0.597934 | − | 0.661931i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.50322 | + | 0.565492i | 0.169137 | + | 0.0273022i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.1844 | − | 7.61200i | −0.635069 | − | 0.366657i | 0.147643 | − | 0.989041i | \(-0.452831\pi\) |
−0.782713 | + | 0.622383i | \(0.786165\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.97041i | − | 0.190806i | −0.995439 | − | 0.0954028i | \(-0.969586\pi\) | ||
0.995439 | − | 0.0954028i | \(-0.0304139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.4664 | − | 17.4886i | −1.02924 | − | 0.838516i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.07222 | − | 10.5174i | −0.290474 | − | 0.503115i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.21910 | + | 4.74530i | 0.392276 | + | 0.226481i | 0.683146 | − | 0.730282i | \(-0.260611\pi\) |
−0.290870 | + | 0.956763i | \(0.593945\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.8908 | + | 2.13855i | −0.994801 | + | 0.101836i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.3955 | − | 16.3942i | −1.34911 | − | 0.778910i | −0.360989 | − | 0.932570i | \(-0.617561\pi\) |
−0.988124 | + | 0.153660i | \(0.950894\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.6209 | − | 18.3960i | −0.503479 | − | 0.872052i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.5182 | + | 8.94798i | −1.11237 | + | 0.423225i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 0.658896i | − | 0.0310952i | −0.999879 | − | 0.0155476i | \(-0.995051\pi\) | ||
0.999879 | − | 0.0155476i | \(-0.00494916\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.9880 | − | 13.2721i | −1.08246 | − | 0.624960i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.45294 | + | 9.07543i | 0.162233 | + | 0.426401i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.85013 | − | 4.26220i | −0.180497 | − | 0.199815i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.94514 | + | 13.7614i | −0.371658 | + | 0.643730i | −0.989821 | − | 0.142320i | \(-0.954544\pi\) |
0.618163 | + | 0.786050i | \(0.287877\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.5883 | − | 16.2960i | 1.19436 | − | 0.760630i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.81626 | + | 17.0023i | 0.457189 | + | 0.791874i | 0.998811 | − | 0.0487477i | \(-0.0155230\pi\) |
−0.541622 | + | 0.840622i | \(0.682190\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.600159 | − | 1.03951i | 0.0278918 | − | 0.0483099i | −0.851743 | − | 0.523960i | \(-0.824454\pi\) |
0.879634 | + | 0.475651i | \(0.157787\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 42.4992 | + | 34.6240i | 1.97085 | + | 1.60565i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.2809 | − | 33.3955i | −0.892213 | − | 1.54536i | −0.837216 | − | 0.546872i | \(-0.815818\pi\) |
−0.0549972 | − | 0.998487i | \(-0.517515\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.651124 | + | 3.03927i | 0.0300661 | + | 0.140341i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.9424 | − | 19.5058i | −1.10321 | − | 0.898779i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.82503 | − | 2.78573i | 0.221855 | − | 0.128088i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 47.7501 | − | 27.5685i | 2.19093 | − | 1.26493i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.141016 | + | 0.0291023i | −0.00645670 | + | 0.00133250i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.22578 | −0.330154 | −0.165077 | − | 0.986281i | \(-0.552787\pi\) | ||||
−0.165077 | + | 0.986281i | \(0.552787\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 4.32371i | − | 0.197144i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.4088 | + | 0.531377i | −0.473619 | + | 0.0241785i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 54.7582 | − | 31.6147i | 2.48644 | − | 1.43555i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.85770 | − | 8.41378i | 0.220123 | − | 0.381265i | −0.734722 | − | 0.678368i | \(-0.762687\pi\) |
0.954845 | + | 0.297104i | \(0.0960207\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.26246 | − | 1.54960i | 0.0570903 | − | 0.0700754i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.2480 | + | 9.95814i | 0.778392 | + | 0.449405i | 0.835860 | − | 0.548943i | \(-0.184969\pi\) |
−0.0574682 | + | 0.998347i | \(0.518303\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.8405i | 1.07372i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 28.8425 | + | 32.4169i | 1.29638 | + | 1.45703i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.45933 | − | 16.8944i | 0.244885 | − | 0.757819i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.3840 | 1.53924 | 0.769619 | − | 0.638503i | \(-0.220446\pi\) | ||||
0.769619 | + | 0.638503i | \(0.220446\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 30.6263 | + | 4.94372i | 1.36828 | + | 0.220869i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.22542 | −0.0546388 | −0.0273194 | − | 0.999627i | \(-0.508697\pi\) | ||||
−0.0273194 | + | 0.999627i | \(0.508697\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.35571 | −0.282826 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.8855 | − | 17.0438i | 0.616678 | − | 0.756940i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.1016 | 0.447744 | 0.223872 | − | 0.974619i | \(-0.428130\pi\) | ||||
0.223872 | + | 0.974619i | \(0.428130\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.22268 | + | 7.99572i | 0.319513 | + | 0.353710i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.7198 | + | 1.20596i | −1.22386 | + | 0.0532442i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 1.54895i | − | 0.0682547i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.04947 | − | 5.22471i | −0.397995 | − | 0.229783i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.8180 | + | 2.06910i | 0.562649 | + | 0.0908233i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.5390 | + | 18.2541i | −0.461723 | + | 0.799728i | −0.999047 | − | 0.0436480i | \(-0.986102\pi\) |
0.537324 | + | 0.843376i | \(0.319435\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.0733 | − | 9.85727i | 0.746563 | − | 0.431028i | −0.0778877 | − | 0.996962i | \(-0.524818\pi\) |
0.824451 | + | 0.565934i | \(0.191484\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.41251 | − | 47.2573i | −0.105291 | − | 2.06248i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 47.1995i | − | 2.05604i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.8273 | 0.775101 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.3813 | + | 8.41336i | 1.10145 | + | 0.365109i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.45039 | − | 1.99208i | 0.149453 | − | 0.0862866i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.2130 | + | 11.0926i | −0.830652 | + | 0.479577i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.199000 | − | 1.23281i | 0.00858750 | − | 0.0531995i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.1339 | + | 20.9715i | −0.651864 | + | 0.903306i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.22475 | − | 7.31748i | −0.181636 | − | 0.314603i | 0.760802 | − | 0.648984i | \(-0.224806\pi\) |
−0.942438 | + | 0.334381i | \(0.891473\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.20948 | + | 3.12347i | −0.352302 | + | 0.134041i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.4511 | − | 45.8147i | 1.13304 | − | 1.96249i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.02889 | − | 6.97824i | −0.172263 | − | 0.298368i | 0.766948 | − | 0.641709i | \(-0.221774\pi\) |
−0.939211 | + | 0.343342i | \(0.888441\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20.4691 | + | 4.22431i | −0.873598 | + | 0.180289i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.9023 | − | 18.8833i | 0.464453 | − | 0.804456i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.75019 | + | 7.00089i | −0.329572 | + | 0.297708i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 33.3929 | − | 40.9881i | 1.41745 | − | 1.73985i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.2294 | + | 10.5247i | 0.772403 | + | 0.445947i | 0.833731 | − | 0.552170i | \(-0.186200\pi\) |
−0.0613279 | + | 0.998118i | \(0.519534\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.836249i | 0.0353696i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.95367 | − | 36.8829i | 0.251364 | − | 1.55720i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.6410 | + | 35.7513i | 0.869916 | + | 1.50674i | 0.862082 | + | 0.506769i | \(0.169160\pi\) |
0.00783378 | + | 0.999969i | \(0.497506\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.44922 | − | 2.56876i | −0.187180 | − | 0.108068i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.90727 | + | 21.6529i | −0.416066 | + | 0.909334i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.2691 | + | 18.0532i | 1.31087 | + | 0.756829i | 0.982240 | − | 0.187630i | \(-0.0600807\pi\) |
0.328627 | + | 0.944460i | \(0.393414\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.62111 | + | 16.6642i | 0.402631 | + | 0.697377i | 0.994043 | − | 0.108993i | \(-0.0347625\pi\) |
−0.591412 | + | 0.806370i | \(0.701429\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.50602 | − | 21.7198i | 0.146466 | − | 0.907356i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 23.4846i | − | 0.979375i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.8102 | − | 14.9015i | −1.07449 | − | 0.620359i | −0.145088 | − | 0.989419i | \(-0.546346\pi\) |
−0.929406 | + | 0.369060i | \(0.879680\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.9598 | + | 30.6369i | −1.03730 | + | 1.27323i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.26404 | + | 19.9034i | 0.176902 | + | 0.825732i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.0886621 | + | 0.153567i | −0.00367201 | + | 0.00636010i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.37831 | + | 1.31633i | −0.263711 | + | 0.0544233i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.72218 | − | 8.17905i | −0.194905 | − | 0.337586i | 0.751964 | − | 0.659204i | \(-0.229107\pi\) |
−0.946869 | + | 0.321618i | \(0.895773\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.5843 | + | 37.3852i | −0.889367 | + | 1.54043i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0504043 | + | 0.0191774i | −0.00207335 | + | 0.000788851i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.4176 | − | 21.5079i | −0.509929 | − | 0.883223i | −0.999934 | − | 0.0115033i | \(-0.996338\pi\) |
0.490005 | − | 0.871720i | \(-0.336995\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −44.8738 | + | 40.5353i | −1.83965 | + | 1.66179i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.34704 | + | 39.3198i | −0.259767 | + | 1.60925i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.3052 | + | 5.94974i | −0.421061 | + | 0.243100i | −0.695531 | − | 0.718496i | \(-0.744831\pi\) |
0.274470 | + | 0.961596i | \(0.411498\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.1276 | + | 12.7754i | −0.902604 | + | 0.521118i | −0.878044 | − | 0.478580i | \(-0.841152\pi\) |
−0.0245596 | + | 0.999698i | \(0.507818\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.34541 | + | 1.10893i | 0.136236 | + | 0.0451592i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.3734 | 0.421738 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.5794i | 0.916471i | 0.888831 | + | 0.458235i | \(0.151518\pi\) | ||||
−0.888831 | + | 0.458235i | \(0.848482\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.1705 | − | 15.7076i | −0.412128 | − | 0.636506i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.35828 | − | 0.784204i | 0.0549502 | − | 0.0317255i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.4294 | + | 19.7963i | −0.461628 | + | 0.799564i | −0.999042 | − | 0.0437549i | \(-0.986068\pi\) |
0.537414 | + | 0.843319i | \(0.319401\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 48.0944 | + | 7.76344i | 1.93935 | + | 0.313052i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.78792 | + | 1.03226i | 0.0719791 | + | 0.0415572i | 0.535558 | − | 0.844499i | \(-0.320101\pi\) |
−0.463578 | + | 0.886056i | \(0.653435\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 32.5894i | − | 1.30988i | −0.755681 | − | 0.654940i | \(-0.772694\pi\) | ||
0.755681 | − | 0.654940i | \(-0.227306\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.45852 | + | 10.4817i | −0.219043 | + | 0.420618i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.00731 | − | 14.0373i | −0.120485 | − | 0.562393i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 29.9935 | 1.19974 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21.5823 | + | 26.4911i | −0.861913 | + | 1.05795i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −45.5213 | −1.81505 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.4706 | 1.53149 | 0.765744 | − | 0.643145i | \(-0.222371\pi\) | ||||
0.765744 | + | 0.643145i | \(0.222371\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 29.2683 | + | 4.72452i | 1.16331 | + | 0.187783i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 68.0923 | 2.70216 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.59024 | − | 3.54106i | −0.0630075 | − | 0.140302i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.3820 | − | 15.0404i | −0.529384 | − | 0.594988i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 47.7636i | − | 1.88655i | −0.332014 | − | 0.943274i | \(-0.607728\pi\) | ||
0.332014 | − | 0.943274i | \(-0.392272\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.2346 | − | 16.8786i | −1.15290 | − | 0.665626i | −0.203306 | − | 0.979115i | \(-0.565169\pi\) |
−0.949592 | + | 0.313489i | \(0.898502\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.45853 | + | 7.92752i | −0.254304 | + | 0.312146i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.536008 | + | 0.928393i | −0.0210727 | + | 0.0364989i | −0.876369 | − | 0.481640i | \(-0.840041\pi\) |
0.855297 | + | 0.518138i | \(0.173375\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.5183 | − | 16.4650i | 1.11944 | − | 0.646309i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.1355 | + | 31.0980i | 0.789171 | + | 1.21882i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.3135i | 1.30366i | 0.758367 | + | 0.651828i | \(0.225998\pi\) | ||||
−0.758367 | + | 0.651828i | \(0.774002\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −42.6998 | −1.66842 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.9654 | − | 2.46937i | 0.466817 | − | 0.0963394i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.41890 | + | 4.86065i | −0.327954 | + | 0.189344i | −0.654932 | − | 0.755688i | \(-0.727303\pi\) |
0.326979 | + | 0.945032i | \(0.393969\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.7856 | + | 8.53647i | −0.575093 | + | 0.332030i | −0.759181 | − | 0.650880i | \(-0.774400\pi\) |
0.184088 | + | 0.982910i | \(0.441067\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.34746 | + | 3.54187i | 0.168841 | + | 0.137555i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 54.0799 | − | 11.5859i | 2.09713 | − | 0.449282i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.64362 | − | 8.04298i | −0.179802 | − | 0.311426i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.94176 | − | 1.58195i | −0.0750730 | − | 0.0611618i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.8696 | + | 22.2909i | −0.496827 | + | 0.860529i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.3359 | − | 31.7588i | −0.706798 | − | 1.22421i | −0.966039 | − | 0.258398i | \(-0.916805\pi\) |
0.259240 | − | 0.965813i | \(-0.416528\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −47.5883 | − | 24.7823i | −1.83167 | − | 0.953872i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.1769 | + | 34.9474i | −0.775461 | + | 1.34314i | 0.159073 | + | 0.987267i | \(0.449149\pi\) |
−0.934535 | + | 0.355872i | \(0.884184\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.7841 | − | 8.95169i | 1.60353 | − | 0.343534i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.75436 | − | 7.23933i | −0.105547 | − | 0.277412i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.23662 | − | 4.75541i | −0.315165 | − | 0.181961i | 0.334070 | − | 0.942548i | \(-0.391578\pi\) |
−0.649236 | + | 0.760587i | \(0.724911\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.4705i | 1.31705i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.18852 | − | 1.59361i | 0.159802 | − | 0.0608000i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.0133077 | − | 0.0230497i | −0.000506985 | − | 0.000878123i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.67519 | − | 3.85392i | −0.253936 | − | 0.146610i | 0.367629 | − | 0.929972i | \(-0.380170\pi\) |
−0.621565 | + | 0.783362i | \(0.713503\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.8117 | + | 26.8406i | 0.448690 | + | 1.01959i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −55.7282 | − | 32.1747i | −2.11389 | − | 1.22046i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.9732 | − | 36.3267i | −0.794418 | − | 1.37597i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.3756 | − | 19.0440i | −0.884145 | − | 0.720311i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 15.6388i | − | 0.590671i | −0.955394 | − | 0.295336i | \(-0.904569\pi\) | ||
0.955394 | − | 0.295336i | \(-0.0954314\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.0559 | + | 20.8169i | 1.35988 | + | 0.785124i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.9329 | + | 3.05616i | 0.713053 | + | 0.115102i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.08728 | − | 1.32078i | −0.153718 | − | 0.0496730i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.72025 | + | 11.6398i | −0.252384 | + | 0.437142i | −0.964182 | − | 0.265242i | \(-0.914548\pi\) |
0.711797 | + | 0.702385i | \(0.247881\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.39354 | + | 11.5980i | 0.0897649 | + | 0.434959i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.19343 | + | 15.9235i | 0.344297 | + | 0.596339i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.01027 | + | 6.94599i | −0.149976 | + | 0.259765i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.35021 | + | 8.36456i | −0.0504247 | + | 0.312380i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.0309 | − | 34.6946i | −0.747027 | − | 1.29389i | −0.949242 | − | 0.314548i | \(-0.898147\pi\) |
0.202214 | − | 0.979341i | \(-0.435186\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.321886 | − | 0.996107i | 0.0119877 | − | 0.0370970i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.1650 | + | 5.00889i | −0.489610 | + | 0.186283i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 36.5161 | − | 21.0826i | 1.35617 | − | 0.782986i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.2091 | + | 24.9468i | −1.60254 | + | 0.925225i | −0.611560 | + | 0.791198i | \(0.709458\pi\) |
−0.990978 | + | 0.134027i | \(0.957209\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.4797 | + | 22.1219i | 0.573322 | + | 0.819330i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.80428 | 0.325638 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.4480i | 0.422843i | 0.977395 | + | 0.211422i | \(0.0678093\pi\) | ||||
−0.977395 | + | 0.211422i | \(0.932191\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.2731 | − | 45.8505i | 0.452702 | − | 1.69122i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.75888 | − | 2.17019i | 0.138460 | − | 0.0799400i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.46303 | − | 7.73020i | 0.164175 | − | 0.284360i | −0.772187 | − | 0.635396i | \(-0.780837\pi\) |
0.936362 | + | 0.351036i | \(0.114170\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.82378 | − | 4.79349i | −0.0669984 | − | 0.176093i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.8621 | − | 26.4785i | −1.68252 | − | 0.971403i | −0.959979 | − | 0.280074i | \(-0.909641\pi\) |
−0.722540 | − | 0.691329i | \(-0.757026\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 56.8737i | − | 2.08369i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.9082 | + | 7.26210i | 0.801579 | + | 0.265706i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.6608 | + | 3.14088i | −0.535694 | + | 0.114765i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.4652 | −0.965729 | −0.482865 | − | 0.875695i | \(-0.660404\pi\) | ||||
−0.482865 | + | 0.875695i | \(0.660404\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.9734 | + | 41.9831i | 0.582101 | + | 1.52995i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.9470 | −0.798733 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.46749 | 0.307756 | 0.153878 | − | 0.988090i | \(-0.450824\pi\) | ||||
0.153878 | + | 0.988090i | \(0.450824\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.17542 | + | 13.6027i | 0.187856 | + | 0.493746i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −53.9937 | −1.95727 | −0.978635 | − | 0.205605i | \(-0.934084\pi\) | ||||
−0.978635 | + | 0.205605i | \(0.934084\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.5311 | − | 23.9660i | 0.960491 | − | 0.867629i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.8587 | + | 67.1528i | 0.501061 | + | 2.42791i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.94264i | 0.178469i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.1912 | − | 17.4309i | −1.08872 | − | 0.628575i | −0.155487 | − | 0.987838i | \(-0.549695\pi\) |
−0.933236 | + | 0.359263i | \(0.883028\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.9846 | + | 49.8976i | 0.683713 | + | 1.79702i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.06375 | − | 1.84246i | 0.0382603 | − | 0.0662688i | −0.846261 | − | 0.532768i | \(-0.821152\pi\) |
0.884521 | + | 0.466499i | \(0.154485\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −72.2944 | + | 41.7392i | −2.59689 | + | 1.49932i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 29.9923 | − | 19.4195i | 1.07597 | − | 0.696672i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 38.3643i | 1.37454i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.7928 | −0.887155 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.1982 | + | 0.922233i | −0.757563 | + | 0.0329579i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 60.4492 | − | 34.9004i | 2.15752 | − | 1.24565i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.5457 | − | 14.1715i | 0.874959 | − | 0.505158i | 0.00596615 | − | 0.999982i | \(-0.498101\pi\) |
0.868993 | + | 0.494824i | \(0.164768\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.2775 | + | 11.1393i | −1.04231 | + | 0.396568i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.32742 | − | 2.57652i | −0.0827535 | − | 0.0916106i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.93167 | − | 3.34575i | −0.0685956 | − | 0.118811i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.0518623 | − | 0.321286i | 0.00183937 | − | 0.0113948i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.9123 | − | 32.7570i | 0.669907 | − | 1.16031i | −0.308022 | − | 0.951379i | \(-0.599667\pi\) |
0.977930 | − | 0.208935i | \(-0.0669996\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.25634 | − | 14.3004i | −0.292088 | − | 0.505912i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.4512 | − | 5.12176i | −0.545943 | − | 0.180969i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.52311 | − | 13.0304i | 0.265485 | − | 0.459833i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.24348 | − | 22.4157i | 0.255299 | − | 0.790048i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 37.0036 | + | 5.97316i | 1.30259 | + | 0.210265i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.2475 | − | 22.6595i | −1.37987 | − | 0.796667i | −0.387724 | − | 0.921776i | \(-0.626739\pi\) |
−0.992143 | + | 0.125109i | \(0.960072\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.45145i | 0.191426i | 0.995409 | + | 0.0957132i | \(0.0305132\pi\) | ||||
−0.995409 | + | 0.0957132i | \(0.969487\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.1421 | − | 15.5950i | −0.671343 | − | 0.546942i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.25883 | + | 3.91241i | 0.0791233 | + | 0.137046i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.97359 | − | 4.02620i | −0.243975 | − | 0.140859i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.37535 | − | 0.478962i | −0.152887 | − | 0.0167363i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.7121 | − | 24.6598i | −1.49066 | − | 0.860634i | −0.490718 | − | 0.871318i | \(-0.663266\pi\) |
−0.999943 | + | 0.0106847i | \(0.996599\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.8496 | + | 20.5241i | 0.413050 | + | 0.715424i | 0.995222 | − | 0.0976419i | \(-0.0311300\pi\) |
−0.582171 | + | 0.813066i | \(0.697797\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −61.7577 | + | 23.4970i | −2.15013 | + | 0.818061i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.9706i | 0.694445i | 0.937783 | + | 0.347222i | \(0.112875\pi\) | ||||
−0.937783 | + | 0.347222i | \(0.887125\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.3741 | − | 7.72155i | −0.464503 | − | 0.268181i | 0.249433 | − | 0.968392i | \(-0.419756\pi\) |
−0.713936 | + | 0.700211i | \(0.753089\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.42212 | + | 14.2511i | 0.188091 | + | 0.494365i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −37.2814 | + | 16.7425i | −1.29172 | + | 0.580094i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.0592 | + | 60.7242i | −1.21327 | + | 2.10145i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 41.9682 | − | 1.82584i | 1.45063 | − | 0.0631101i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.53910 | + | 9.59401i | 0.191231 | + | 0.331222i | 0.945658 | − | 0.325162i | \(-0.105419\pi\) |
−0.754427 | + | 0.656383i | \(0.772085\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.16267 | + | 10.6741i | −0.212506 | + | 0.368071i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.8772 | − | 21.0821i | −0.891258 | − | 0.726106i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24.8444 | + | 43.0318i | 0.854674 | + | 1.48034i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.67098 | + | 2.15569i | 0.229218 | + | 0.0740703i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.9134 | − | 10.5205i | −0.443186 | − | 0.361063i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.3573 | − | 8.86656i | 0.526442 | − | 0.303942i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.1706 | − | 24.3472i | 1.44389 | − | 0.833633i | 0.445788 | − | 0.895139i | \(-0.352924\pi\) |
0.998107 | + | 0.0615058i | \(0.0195903\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.7320 | − | 59.5271i | 0.674819 | − | 2.03578i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.7826 | 0.573283 | 0.286641 | − | 0.958038i | \(-0.407461\pi\) | ||||
0.286641 | + | 0.958038i | \(0.407461\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.1358i | 0.857622i | 0.903394 | + | 0.428811i | \(0.141067\pi\) | ||||
−0.903394 | + | 0.428811i | \(0.858933\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.3156 | + | 14.9871i | 0.999072 | + | 0.510757i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.87377 | + | 3.39122i | −0.199945 | + | 0.115438i | −0.596630 | − | 0.802516i | \(-0.703494\pi\) |
0.396685 | + | 0.917955i | \(0.370161\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.6733 | + | 25.4149i | −0.498907 | + | 0.864133i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.6919 | − | 22.9434i | 0.634812 | − | 0.779199i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.6303 | + | 7.29209i | 0.428452 | + | 0.247367i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.651470i | 0.0220742i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.2457 | − | 45.9928i | 0.515987 | − | 1.55662i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 52.4904 | + | 16.9620i | 1.77450 | + | 0.573419i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.7259 | −1.47652 | −0.738260 | − | 0.674517i | \(-0.764352\pi\) | ||||
−0.738260 | + | 0.674517i | \(0.764352\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.19264 | − | 0.676780i | −0.141414 | − | 0.0228272i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.5307 | 0.927531 | 0.463766 | − | 0.885958i | \(-0.346498\pi\) | ||||
0.463766 | + | 0.885958i | \(0.346498\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.56040 | 0.187122 | 0.0935612 | − | 0.995614i | \(-0.470175\pi\) | ||||
0.0935612 | + | 0.995614i | \(0.470175\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −38.1731 | + | 46.8555i | −1.28318 | + | 1.57503i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.6185 | 0.826607 | 0.413303 | − | 0.910593i | \(-0.364375\pi\) | ||||
0.413303 | + | 0.910593i | \(0.364375\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43.7892 | + | 14.1502i | 1.46864 | + | 0.474583i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.0254 | + | 3.86706i | 1.10639 | + | 0.129551i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.1025i | 0.505386i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.44434 | + | 1.41124i | 0.0817054 | + | 0.0471726i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.15656 | − | 0.348114i | −0.0720056 | − | 0.0116232i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.5062 | + | 28.5896i | −0.550514 | + | 0.953518i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.242674 | + | 0.140108i | −0.00808465 | + | 0.00466767i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.80081 | + | 3.75594i | −0.193039 | + | 0.124990i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 19.8529i | − | 0.659932i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.0867 | −0.334925 | −0.167462 | − | 0.985878i | \(-0.553557\pi\) | ||||
−0.167462 | + | 0.985878i | \(0.553557\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.63872 | + | 3.23751i | −0.120689 | + | 0.107381i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.5808 | − | 13.6144i | 0.781267 | − | 0.451065i | −0.0556121 | − | 0.998452i | \(-0.517711\pi\) |
0.836879 | + | 0.547388i | \(0.184378\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.6159 | − | 14.2120i | 0.814668 | − | 0.470349i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.52801 | − | 46.6359i | 0.248868 | − | 1.54174i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −27.4597 | − | 8.87343i | −0.906799 | − | 0.293026i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.8493 | − | 34.3800i | −0.654769 | − | 1.13409i | −0.981952 | − | 0.189132i | \(-0.939433\pi\) |
0.327183 | − | 0.944961i | \(-0.393901\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.2954 | + | 6.58041i | −0.569904 | + | 0.216832i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.86064 | − | 3.22272i | 0.0612436 | − | 0.106077i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40.2552 | + | 69.7240i | 1.32358 | + | 2.29251i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.789012 | − | 0.886790i | −0.0259145 | − | 0.0291260i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.142283 | + | 0.246442i | −0.00466816 | + | 0.00808550i | −0.868350 | − | 0.495952i | \(-0.834819\pi\) |
0.863682 | + | 0.504037i | \(0.168153\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.1857 | + | 3.78758i | 1.21871 | + | 0.124133i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.7185 | − | 27.8857i | 0.743769 | − | 0.912938i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 73.1295 | + | 42.2214i | 2.39159 | + | 1.38079i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 21.7298i | − | 0.709881i | −0.934889 | − | 0.354940i | \(-0.884501\pi\) | ||
0.934889 | − | 0.354940i | \(-0.115499\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.08507 | + | 6.72197i | −0.0354098 | + | 0.219363i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.64242 | − | 9.77295i | −0.183938 | − | 0.318589i | 0.759280 | − | 0.650764i | \(-0.225551\pi\) |
−0.943218 | + | 0.332174i | \(0.892218\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.1513 | + | 8.17026i | 0.460830 | + | 0.266060i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −37.7785 | − | 38.3323i | −1.22894 | − | 1.24695i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.6701 | + | 11.3566i | 0.639194 | + | 0.369039i | 0.784304 | − | 0.620377i | \(-0.213020\pi\) |
−0.145110 | + | 0.989416i | \(0.546354\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.12918 | + | 1.95580i | 0.0366548 | + | 0.0634880i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.632234 | + | 3.91668i | −0.0205016 | + | 0.127007i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16.5638i | − | 0.536554i | −0.963342 | − | 0.268277i | \(-0.913546\pi\) | ||
0.963342 | − | 0.268277i | \(-0.0864543\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.0648 | + | 24.8635i | 1.39354 | + | 0.804563i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.5047 | + | 20.2586i | −0.533520 | + | 0.654868i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.16331 | + | 22.1675i | −0.231315 | + | 0.715827i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.1790 | − | 29.7550i | 0.554162 | − | 0.959837i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.34925 | + | 16.1375i | −0.172377 | + | 0.520024i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −44.6589 | − | 77.3515i | −1.43762 | − | 2.49003i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.38867 | − | 14.5296i | 0.269762 | − | 0.467241i | −0.699039 | − | 0.715084i | \(-0.746388\pi\) |
0.968800 | + | 0.247843i | \(0.0797218\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −50.4674 | + | 19.2014i | −1.62125 | + | 0.616837i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.6820 | + | 27.1620i | 0.503259 | + | 0.871670i | 0.999993 | + | 0.00376705i | \(0.00119909\pi\) |
−0.496734 | + | 0.867903i | \(0.665468\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.1519 | − | 32.2720i | −0.934566 | − | 1.03459i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.58048 | − | 9.79104i | 0.0506158 | − | 0.313564i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49.0953 | − | 28.3452i | 1.57070 | − | 0.906843i | 0.574614 | − | 0.818424i | \(-0.305152\pi\) |
0.996083 | − | 0.0884183i | \(-0.0281812\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.3609 | + | 10.0233i | −0.554858 | + | 0.320347i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.19378 | − | 39.7033i | −0.261607 | − | 1.26763i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.8408 | 1.27072 | 0.635362 | − | 0.772214i | \(-0.280851\pi\) | ||||
0.635362 | + | 0.772214i | \(0.280851\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 0.121892i | − | 0.00388380i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.5404 | + | 5.89981i | 0.367334 | + | 0.187793i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.97026 | + | 1.71488i | −0.0944489 | + | 0.0545301i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.2975 | − | 54.2089i | 0.994199 | − | 1.72200i | 0.403952 | − | 0.914780i | \(-0.367636\pi\) |
0.590247 | − | 0.807223i | \(-0.299030\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.8596 | − | 1.91438i | −0.376352 | − | 0.0607511i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −77.9613 | − | 45.0110i | −2.47154 | − | 1.42694i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.1041i | 1.42846i | 0.699911 | + | 0.714230i | \(0.253223\pi\) | ||||
−0.699911 | + | 0.714230i | \(0.746777\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.76092 | − | 40.4761i | −0.0557130 | − | 1.28061i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))