Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(193,252)]
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, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.l (of order \(3\), 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: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 205.6 | ||
Root | \(1.64515 - 0.541745i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.205 |
Dual form | 252.2.l.b.193.6 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 1.64515 | − | 0.541745i | 0.949827 | − | 0.312777i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.763837 | −0.341598 | −0.170799 | − | 0.985306i | \(-0.554635\pi\) | ||||
−0.170799 | + | 0.985306i | \(0.554635\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.05641 | − | 2.42569i | −0.399286 | − | 0.916826i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.41302 | − | 1.78250i | 0.804341 | − | 0.594167i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.03389 | 1.81929 | 0.909644 | − | 0.415389i | \(-0.136355\pi\) | ||||
0.909644 | + | 0.415389i | \(0.136355\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.26032 | − | 2.18294i | −0.349551 | − | 0.605440i | 0.636619 | − | 0.771179i | \(-0.280332\pi\) |
−0.986170 | + | 0.165739i | \(0.946999\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.25662 | + | 0.413805i | −0.324459 | + | 0.106844i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.94444 | + | 3.36787i | 0.471596 | + | 0.816828i | 0.999472 | − | 0.0324932i | \(-0.0103447\pi\) |
−0.527876 | + | 0.849322i | \(0.677011\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.13503 | + | 3.69798i | −0.489809 | + | 0.848375i | −0.999931 | − | 0.0117275i | \(-0.996267\pi\) |
0.510122 | + | 0.860102i | \(0.329600\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.05206 | − | 3.41832i | −0.666015 | − | 0.745939i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.46425 | −0.305317 | −0.152658 | − | 0.988279i | \(-0.548783\pi\) | ||||
−0.152658 | + | 0.988279i | \(0.548783\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.41655 | −0.883311 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.00412 | − | 4.23972i | 0.578143 | − | 0.815935i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00732 | + | 5.20884i | −0.558446 | + | 0.967257i | 0.439180 | + | 0.898399i | \(0.355269\pi\) |
−0.997626 | + | 0.0688580i | \(0.978064\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.28482 | + | 5.68948i | −0.589972 | + | 1.02186i | 0.404264 | + | 0.914642i | \(0.367528\pi\) |
−0.994235 | + | 0.107219i | \(0.965806\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.92665 | − | 3.26883i | 1.72801 | − | 0.569031i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.806926 | + | 1.85283i | 0.136395 | + | 0.313186i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.82492 | − | 8.35700i | 0.793211 | − | 1.37388i | −0.130758 | − | 0.991414i | \(-0.541741\pi\) |
0.923969 | − | 0.382468i | \(-0.124926\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.25602 | − | 2.90849i | −0.521380 | − | 0.465731i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.24844 | − | 3.89442i | −0.351148 | − | 0.608206i | 0.635303 | − | 0.772263i | \(-0.280875\pi\) |
−0.986451 | + | 0.164057i | \(0.947542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.13503 | + | 3.69798i | −0.325589 | + | 0.563937i | −0.981631 | − | 0.190787i | \(-0.938896\pi\) |
0.656042 | + | 0.754724i | \(0.272229\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.84316 | + | 1.36154i | −0.274762 | + | 0.202966i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.38924 | + | 5.87034i | 0.494372 | + | 0.856277i | 0.999979 | − | 0.00648676i | \(-0.00206481\pi\) |
−0.505607 | + | 0.862764i | \(0.668731\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.76799 | + | 5.12507i | −0.681141 | + | 0.732152i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.02342 | + | 4.48725i | 0.703419 | + | 0.628341i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.265581 | − | 0.460000i | −0.0364804 | − | 0.0631859i | 0.847209 | − | 0.531260i | \(-0.178281\pi\) |
−0.883689 | + | 0.468074i | \(0.844948\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.60891 | −0.621465 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.50908 | + | 7.24036i | −0.199882 | + | 0.959010i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.59926 | + | 9.69821i | −0.728962 | + | 1.26260i | 0.228360 | + | 0.973577i | \(0.426664\pi\) |
−0.957322 | + | 0.289023i | \(0.906670\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.19144 | − | 7.25979i | −0.536659 | − | 0.929521i | −0.999081 | − | 0.0428608i | \(-0.986353\pi\) |
0.462422 | − | 0.886660i | \(-0.346981\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.87295 | − | 3.97020i | −0.865911 | − | 0.500199i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.962681 | + | 1.66741i | 0.119406 | + | 0.206817i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.961979 | − | 1.66620i | 0.117524 | − | 0.203558i | −0.801262 | − | 0.598314i | \(-0.795838\pi\) |
0.918786 | + | 0.394756i | \(0.129171\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.40890 | + | 0.793249i | −0.289998 | + | 0.0954960i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.90353 | 1.17533 | 0.587666 | − | 0.809103i | \(-0.300047\pi\) | ||||
0.587666 | + | 0.809103i | \(0.300047\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.13099 | − | 3.69098i | −0.249413 | − | 0.431997i | 0.713950 | − | 0.700197i | \(-0.246904\pi\) |
−0.963363 | + | 0.268200i | \(0.913571\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.26588 | + | 2.39265i | −0.838992 | + | 0.276279i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.37428 | − | 14.6364i | −0.726416 | − | 1.66797i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.70372 | + | 6.41503i | 0.416701 | + | 0.721748i | 0.995605 | − | 0.0936479i | \(-0.0298528\pi\) |
−0.578904 | + | 0.815396i | \(0.696519\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.64537 | − | 8.60244i | 0.293930 | − | 0.955827i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.05178 | + | 13.9461i | −0.883798 | + | 1.53078i | −0.0367125 | + | 0.999326i | \(0.511689\pi\) |
−0.847085 | + | 0.531457i | \(0.821645\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.48523 | − | 2.57250i | −0.161096 | − | 0.279027i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.12563 | + | 10.1985i | −0.227891 | + | 1.09340i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.76310 | − | 3.05377i | 0.186888 | − | 0.323699i | −0.757323 | − | 0.653040i | \(-0.773493\pi\) |
0.944211 | + | 0.329341i | \(0.106827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.96373 | + | 5.36325i | −0.415512 | + | 0.562221i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.32177 | + | 11.1396i | −0.240757 | + | 1.15512i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.63081 | − | 2.82465i | 0.167318 | − | 0.289803i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.33513 | − | 4.04456i | 0.237096 | − | 0.410662i | −0.722784 | − | 0.691074i | \(-0.757138\pi\) |
0.959880 | + | 0.280412i | \(0.0904710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.5599 | − | 10.7554i | 1.46333 | − | 1.08096i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.71965 | −0.469623 | −0.234811 | − | 0.972041i | \(-0.575447\pi\) | ||||
−0.234811 | + | 0.972041i | \(0.575447\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.16531 | 0.311888 | 0.155944 | − | 0.987766i | \(-0.450158\pi\) | ||||
0.155944 | + | 0.987766i | \(0.450158\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.33128 | + | 2.61104i | 0.227509 | + | 0.254811i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.65537 | − | 13.2595i | 0.740073 | − | 1.28184i | −0.212389 | − | 0.977185i | \(-0.568124\pi\) |
0.952462 | − | 0.304659i | \(-0.0985424\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.65371 | + | 13.2566i | 0.733092 | + | 1.26975i | 0.955555 | + | 0.294812i | \(0.0952569\pi\) |
−0.222463 | + | 0.974941i | \(0.571410\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.41034 | − | 16.3624i | 0.323695 | − | 1.55305i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.56114 | − | 2.70397i | −0.146860 | − | 0.254368i | 0.783206 | − | 0.621763i | \(-0.213583\pi\) |
−0.930065 | + | 0.367395i | \(0.880250\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.11845 | 0.104296 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.93229 | − | 3.02097i | −0.640891 | − | 0.279289i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.11529 | − | 8.27448i | 0.560588 | − | 0.758520i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.4079 | 2.30981 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.80881 | − | 5.18881i | −0.523762 | − | 0.467859i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.19271 | 0.643335 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.27814 | 0.113416 | 0.0567082 | − | 0.998391i | \(-0.481940\pi\) | ||||
0.0567082 | + | 0.998391i | \(0.481940\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.50908 | + | 7.24036i | −0.132867 | + | 0.637479i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.77465 | 0.679274 | 0.339637 | − | 0.940557i | \(-0.389696\pi\) | ||||
0.339637 | + | 0.940557i | \(0.389696\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.2256 | + | 1.27234i | 0.973386 | + | 0.110326i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.29466 | + | 3.23846i | −0.197493 | + | 0.278722i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.82307 | 0.241191 | 0.120596 | − | 0.992702i | \(-0.461520\pi\) | ||||
0.120596 | + | 0.992702i | \(0.461520\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.2206 | − | 19.4346i | −0.951718 | − | 1.64842i | −0.741705 | − | 0.670726i | \(-0.765983\pi\) |
−0.210013 | − | 0.977699i | \(-0.567351\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.75603 | + | 7.82147i | 0.737391 | + | 0.658687i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.60466 | − | 13.1717i | −0.635933 | − | 1.10147i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.29710 | − | 3.97870i | 0.190764 | − | 0.330413i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.06757 | + | 11.0145i | −0.417966 | + | 0.908463i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.1703 | −1.65241 | −0.826206 | − | 0.563369i | \(-0.809505\pi\) | ||||
−0.826206 | + | 0.563369i | \(0.809505\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.29450 | 0.674997 | 0.337498 | − | 0.941326i | \(-0.390419\pi\) | ||||
0.337498 | + | 0.941326i | \(0.390419\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.6952 | + | 4.66078i | 0.864657 | + | 0.376802i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.50907 | − | 4.34583i | 0.201533 | − | 0.349066i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.33332 | − | 5.77348i | 0.266028 | − | 0.460774i | −0.701804 | − | 0.712370i | \(-0.747622\pi\) |
0.967832 | + | 0.251596i | \(0.0809553\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.686123 | − | 0.612891i | −0.0544131 | − | 0.0486054i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.54685 | + | 3.55182i | 0.121909 | + | 0.279922i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.69751 | − | 6.40428i | 0.289611 | − | 0.501622i | −0.684106 | − | 0.729383i | \(-0.739807\pi\) |
0.973717 | + | 0.227761i | \(0.0731406\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.58234 | + | 2.49685i | −0.590284 | + | 0.194380i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.475526 | − | 0.823635i | −0.0367973 | − | 0.0637348i | 0.847040 | − | 0.531529i | \(-0.178382\pi\) |
−0.883838 | + | 0.467794i | \(0.845049\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.32317 | − | 5.75590i | 0.255629 | − | 0.442762i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.43978 | + | 12.7290i | 0.110103 | + | 0.973411i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.33554 | − | 4.04527i | −0.177568 | − | 0.307557i | 0.763479 | − | 0.645833i | \(-0.223490\pi\) |
−0.941047 | + | 0.338276i | \(0.890156\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.66570 | + | 10.7132i | 0.352694 | + | 0.809843i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.95766 | + | 18.9884i | −0.297476 | + | 1.42725i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.49486 | − | 12.9815i | −0.560192 | − | 0.970281i | −0.997479 | − | 0.0709591i | \(-0.977394\pi\) |
0.437287 | − | 0.899322i | \(-0.355939\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.6525 | −1.01478 | −0.507391 | − | 0.861716i | \(-0.669390\pi\) | ||||
−0.507391 | + | 0.861716i | \(0.669390\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.8285 | − | 9.67273i | −0.800466 | − | 0.715029i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.68545 | + | 6.38338i | −0.270959 | + | 0.469316i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.7325 | + | 20.3214i | 0.857969 | + | 1.48605i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.4579 | − | 2.80818i | −0.978916 | − | 0.204265i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.14528 | − | 10.6439i | −0.444657 | − | 0.770168i | 0.553372 | − | 0.832934i | \(-0.313341\pi\) |
−0.998028 | + | 0.0627667i | \(0.980008\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.58578 | + | 6.21075i | −0.258110 | + | 0.447060i | −0.965736 | − | 0.259528i | \(-0.916433\pi\) |
0.707626 | + | 0.706588i | \(0.249766\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.48707 | + | 2.22161i | 0.178102 | + | 0.159093i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.0286 | −0.928247 | −0.464124 | − | 0.885770i | \(-0.653631\pi\) | ||||
−0.464124 | + | 0.885770i | \(0.653631\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.48087 | − | 4.29699i | −0.175864 | − | 0.304606i | 0.764596 | − | 0.644510i | \(-0.222939\pi\) |
−0.940460 | + | 0.339904i | \(0.889605\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.679944 | − | 3.26229i | 0.0479595 | − | 0.230104i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.8120 | + | 1.79217i | 1.10979 | + | 0.125786i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.71744 | + | 2.97470i | 0.119951 | + | 0.207762i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.53326 | + | 2.61002i | −0.245579 | + | 0.181409i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.8825 | + | 22.3132i | −0.891104 | + | 1.54344i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.07384 | + | 3.59199i | 0.142769 | + | 0.247283i | 0.928538 | − | 0.371237i | \(-0.121066\pi\) |
−0.785769 | + | 0.618519i | \(0.787733\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.2928 | − | 5.36519i | 1.11636 | − | 0.367617i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.63081 | − | 2.82465i | 0.111221 | − | 0.192640i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.2711 | + | 1.95754i | 1.17244 | + | 0.132887i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.50536 | − | 4.91776i | −0.372018 | − | 0.332311i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.90125 | − | 8.48921i | 0.329694 | − | 0.571046i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.63830 | + | 8.03378i | −0.310604 | + | 0.537982i | −0.978493 | − | 0.206279i | \(-0.933865\pi\) |
0.667889 | + | 0.744261i | \(0.267198\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.6573 | + | 7.87252i | −0.710483 | + | 0.524834i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.3602 | −1.41773 | −0.708863 | − | 0.705346i | \(-0.750792\pi\) | ||||
−0.708863 | + | 0.705346i | \(0.750792\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.0071 | −1.32210 | −0.661052 | − | 0.750340i | \(-0.729890\pi\) | ||||
−0.661052 | + | 0.750340i | \(0.729890\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.4158 | − | 20.6258i | −1.21167 | − | 1.35708i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.63657 | − | 13.2269i | 0.500288 | − | 0.866525i | −0.499712 | − | 0.866192i | \(-0.666561\pi\) |
1.00000 | 0.000332882i | \(-0.000105960\pi\) | ||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.58883 | − | 4.48398i | −0.168876 | − | 0.292503i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.56848 | + | 8.54721i | 0.621540 | + | 0.555201i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.03828 | + | 15.6548i | 0.584638 | + | 1.01262i | 0.994920 | + | 0.100664i | \(0.0320967\pi\) |
−0.410283 | + | 0.911958i | \(0.634570\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.31045 | 0.277660 | 0.138830 | − | 0.990316i | \(-0.455666\pi\) | ||||
0.138830 | + | 0.990316i | \(0.455666\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.308301 | − | 15.5854i | −0.0197775 | − | 0.999804i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.64196 | − | 3.91471i | 0.232677 | − | 0.250102i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.7633 | 0.684853 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.69114 | + | 27.3054i | −0.360662 | + | 1.73041i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.3348 | 1.03104 | 0.515521 | − | 0.856877i | \(-0.327599\pi\) | ||||
0.515521 | + | 0.856877i | \(0.327599\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.83512 | −0.555459 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.83707 | − | 3.42753i | −0.240287 | − | 0.214640i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.29540 | 0.0808046 | 0.0404023 | − | 0.999183i | \(-0.487136\pi\) | ||||
0.0404023 | + | 0.999183i | \(0.487136\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.3686 | − | 2.87534i | −1.57633 | − | 0.178665i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.02802 | + | 17.9296i | 0.125531 | + | 1.10982i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.2728 | 1.74337 | 0.871687 | − | 0.490062i | \(-0.163026\pi\) | ||||
0.871687 | + | 0.490062i | \(0.163026\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.202861 | + | 0.351365i | 0.0124616 | + | 0.0215842i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.24619 | − | 5.97906i | 0.0762655 | − | 0.365912i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.10969 | + | 12.3143i | 0.433485 | + | 0.750818i | 0.997171 | − | 0.0751711i | \(-0.0239503\pi\) |
−0.563685 | + | 0.825990i | \(0.690617\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.18914 | + | 12.4520i | −0.436709 | + | 0.756403i | −0.997433 | − | 0.0716001i | \(-0.977189\pi\) |
0.560724 | + | 0.828003i | \(0.310523\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.61542 | + | 10.9707i | −0.218815 | + | 0.663975i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −26.6490 | −1.60700 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.4361 | −0.927468 | −0.463734 | − | 0.885974i | \(-0.653491\pi\) | ||||
−0.463734 | + | 0.885974i | \(0.653491\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.21515 | + | 19.5841i | 0.132618 | + | 1.17247i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.39609 | + | 16.2745i | −0.560524 | + | 0.970856i | 0.436927 | + | 0.899497i | \(0.356067\pi\) |
−0.997451 | + | 0.0713587i | \(0.977266\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.2864 | − | 28.2089i | 0.968128 | − | 1.67685i | 0.267163 | − | 0.963651i | \(-0.413914\pi\) |
0.700965 | − | 0.713196i | \(-0.252753\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.15269 | − | 5.53046i | 0.0682793 | − | 0.327596i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.07139 | + | 9.56815i | −0.417411 | + | 0.564790i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.938304 | − | 1.62519i | 0.0551944 | − | 0.0955994i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.65051 | − | 7.91894i | 0.0967545 | − | 0.464216i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.69821 | − | 2.94138i | −0.0992103 | − | 0.171837i | 0.812148 | − | 0.583452i | \(-0.198298\pi\) |
−0.911358 | + | 0.411615i | \(0.864965\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.27692 | − | 7.40785i | 0.249012 | − | 0.431302i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.1265 | − | 25.5820i | 1.05181 | − | 1.48442i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.84543 | + | 3.19637i | 0.106724 | + | 0.184851i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.2256 | + | 1.27234i | 0.647035 | + | 0.0733364i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.76452 | + | 2.55685i | −0.446060 | + | 0.146887i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.20158 | + | 5.54529i | 0.183322 | + | 0.317523i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.69564 | 0.210921 | 0.105461 | − | 0.994423i | \(-0.466368\pi\) | ||||
0.105461 | + | 0.994423i | \(0.466368\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.20741 | − | 1.71479i | 0.296239 | − | 0.0975512i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.58119 | − | 14.8631i | 0.486594 | − | 0.842806i | −0.513287 | − | 0.858217i | \(-0.671572\pi\) |
0.999881 | + | 0.0154108i | \(0.00490561\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.64824 | − | 4.58688i | −0.149687 | − | 0.259266i | 0.781425 | − | 0.624000i | \(-0.214493\pi\) |
−0.931112 | + | 0.364734i | \(0.881160\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.24981 | + | 3.03259i | 0.295793 | + | 0.170867i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.0890 | − | 24.4028i | −0.791315 | − | 1.37060i | −0.925153 | − | 0.379594i | \(-0.876064\pi\) |
0.133838 | − | 0.991003i | \(-0.457270\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.1459 | + | 31.4296i | −1.01597 | + | 1.75972i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.41096 | − | 25.9611i | 0.302010 | − | 1.44901i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.6057 | −0.923968 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.56628 | + | 9.64109i | 0.308762 | + | 0.534791i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.7732 | + | 17.6627i | 1.09346 | + | 0.976751i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.6592 | − | 14.4228i | 0.587662 | − | 0.795153i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.5860 | − | 25.2637i | −0.801720 | − | 1.38862i | −0.918483 | − | 0.395461i | \(-0.870585\pi\) |
0.116762 | − | 0.993160i | \(-0.462748\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.25373 | − | 28.7661i | −0.178303 | − | 1.57637i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.734794 | + | 1.27270i | −0.0401461 | + | 0.0695351i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.447174 | − | 0.774528i | −0.0243591 | − | 0.0421912i | 0.853589 | − | 0.520947i | \(-0.174421\pi\) |
−0.877948 | + | 0.478756i | \(0.841088\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.03317 | − | 3.60270i | −0.219052 | − | 0.195672i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.8203 | + | 34.3297i | −1.07333 | + | 1.85906i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.4688 | + | 6.15150i | 0.943227 | + | 0.332150i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.84001 | − | 0.605913i | 0.0990627 | − | 0.0326212i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.98982 | + | 17.3029i | −0.536282 | + | 0.928867i | 0.462818 | + | 0.886453i | \(0.346838\pi\) |
−0.999100 | + | 0.0424143i | \(0.986495\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.58530 | − | 4.47788i | 0.138388 | − | 0.239695i | −0.788499 | − | 0.615037i | \(-0.789141\pi\) |
0.926887 | + | 0.375341i | \(0.122475\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.0412 | − | 1.21440i | −0.696090 | − | 0.0648201i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.1222 | 1.76292 | 0.881459 | − | 0.472261i | \(-0.156562\pi\) | ||||
0.881459 | + | 0.472261i | \(0.156562\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.56468 | −0.401491 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.57790 | − | 16.9257i | 0.295214 | − | 0.895801i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.2965 | + | 29.9584i | −0.912874 | + | 1.58114i | −0.102889 | + | 0.994693i | \(0.532809\pi\) |
−0.809985 | + | 0.586451i | \(0.800525\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.383301 | + | 0.663897i | 0.0201737 | + | 0.0349420i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 41.7997 | − | 13.7646i | 2.19392 | − | 0.722454i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.62773 | + | 2.81931i | 0.0851992 | + | 0.147569i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.29611 | −0.172055 | −0.0860277 | − | 0.996293i | \(-0.527417\pi\) | ||||
−0.0860277 | + | 0.996293i | \(0.527417\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.3674 | − | 5.38947i | −0.643819 | − | 0.280565i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.835256 | + | 1.13017i | −0.0433644 | + | 0.0586754i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.6754 | −1.22587 | −0.612933 | − | 0.790135i | \(-0.710010\pi\) | ||||
−0.612933 | + | 0.790135i | \(0.710010\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.8331 | − | 3.89661i | 0.611057 | − | 0.201220i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.1608 | 0.780821 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.4415 | −1.30684 | −0.653421 | − | 0.756995i | \(-0.726667\pi\) | ||||
−0.653421 | + | 0.756995i | \(0.726667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.10273 | − | 0.692425i | 0.107726 | − | 0.0354740i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.7278 | 1.21244 | 0.606218 | − | 0.795299i | \(-0.292686\pi\) | ||||
0.606218 | + | 0.795299i | \(0.292686\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.86891 | + | 11.1798i | 0.248142 | + | 0.569776i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.43978 | + | 12.7290i | 0.0731880 | + | 0.647052i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.5275 | 0.990082 | 0.495041 | − | 0.868870i | \(-0.335153\pi\) | ||||
0.495041 | + | 0.868870i | \(0.335153\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.84714 | − | 4.93139i | −0.143986 | − | 0.249391i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.7905 | − | 4.21188i | 0.645193 | − | 0.212461i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.82904 | − | 4.90004i | −0.142344 | − | 0.246548i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.4468 | − | 25.0226i | 0.725064 | − | 1.25585i | −0.233884 | − | 0.972265i | \(-0.575144\pi\) |
0.958948 | − | 0.283583i | \(-0.0915231\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.1571 | − | 3.98825i | 0.959056 | − | 0.199662i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.50584 | 0.274949 | 0.137474 | − | 0.990505i | \(-0.456102\pi\) | ||||
0.137474 | + | 0.990505i | \(0.456102\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.5598 | 0.824900 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.02063 | + | 6.57086i | −0.100406 | + | 0.326509i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.1130 | − | 50.4253i | 1.44308 | − | 2.49949i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.511954 | − | 0.886731i | 0.0253145 | − | 0.0438460i | −0.853091 | − | 0.521763i | \(-0.825275\pi\) |
0.878405 | + | 0.477917i | \(0.158608\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.64437 | − | 1.52938i | 0.229090 | − | 0.0754390i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.4400 | + | 3.33680i | 1.44865 | + | 0.164193i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.15025 | − | 10.6525i | 0.301904 | − | 0.522912i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −28.9882 | − | 25.8942i | −1.41956 | − | 1.26804i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.9398 | + | 29.3405i | 0.827562 | + | 1.43338i | 0.899946 | + | 0.436002i | \(0.143606\pi\) |
−0.0723837 | + | 0.997377i | \(0.523061\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.563823 | − | 0.976570i | 0.0274790 | − | 0.0475951i | −0.851959 | − | 0.523609i | \(-0.824585\pi\) |
0.879438 | + | 0.476014i | \(0.157919\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.6422 | + | 8.12394i | 0.906416 | + | 0.395000i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.58772 | − | 14.8744i | −0.416566 | − | 0.721513i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.1821 | + | 17.8365i | −0.637929 | + | 0.863168i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19.6465 | − | 17.5495i | −0.948540 | − | 0.847299i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.44172 | − | 2.49713i | −0.0694450 | − | 0.120282i | 0.829212 | − | 0.558934i | \(-0.188790\pi\) |
−0.898657 | + | 0.438652i | \(0.855456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.3808 | −0.691097 | −0.345548 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345548 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.62363 | − | 7.79000i | 0.0778473 | − | 0.373502i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.12621 | − | 5.41476i | 0.149547 | − | 0.259023i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.4958 | − | 18.1792i | −0.500936 | − | 0.867646i | −0.999999 | − | 0.00108089i | \(-0.999656\pi\) |
0.499064 | − | 0.866565i | \(-0.333677\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.36983 | + | 20.8659i | −0.112849 | + | 0.993612i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.0293 | + | 17.3713i | 0.476507 | + | 0.825335i | 0.999638 | − | 0.0269179i | \(-0.00856926\pi\) |
−0.523130 | + | 0.852253i | \(0.675236\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.34672 | + | 2.33258i | −0.0638405 | + | 0.110575i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −33.1830 | + | 10.9271i | −1.56950 | + | 0.516836i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.4192 | −0.538903 | −0.269452 | − | 0.963014i | \(-0.586842\pi\) | ||||
−0.269452 | + | 0.963014i | \(0.586842\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.5669 | − | 23.4985i | −0.638839 | − | 1.10650i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.6457 | − | 4.49350i | 0.641130 | − | 0.211123i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.02765 | − | 4.09664i | 0.141938 | − | 0.192054i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.10294 | + | 15.7667i | 0.425817 | + | 0.737537i | 0.996496 | − | 0.0836359i | \(-0.0266533\pi\) |
−0.570679 | + | 0.821173i | \(0.693320\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.1202 | + | 1.87359i | 0.939129 | + | 0.0874519i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.6430 | + | 32.2906i | −0.868289 | + | 1.50392i | −0.00454533 | + | 0.999990i | \(0.501447\pi\) |
−0.863744 | + | 0.503931i | \(0.831887\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.530345 | − | 0.918584i | −0.0246472 | − | 0.0426902i | 0.853439 | − | 0.521193i | \(-0.174513\pi\) |
−0.878086 | + | 0.478503i | \(0.841180\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.77345 | − | 8.50882i | 0.0822420 | − | 0.394587i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.0374 | + | 24.3134i | −0.649571 | + | 1.12509i | 0.333654 | + | 0.942696i | \(0.391718\pi\) |
−0.983225 | + | 0.182395i | \(0.941615\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.05793 | − | 0.573277i | −0.233553 | − | 0.0264715i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.35605 | − | 11.3040i | 0.108561 | − | 0.520863i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.8825 | + | 22.3132i | −0.592340 | + | 1.02596i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.42947 | − | 16.3323i | 0.432654 | − | 0.749378i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.46080 | − | 0.636592i | −0.0668856 | − | 0.0291476i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.23410 | 0.330535 | 0.165267 | − | 0.986249i | \(-0.447151\pi\) | ||||
0.165267 | + | 0.986249i | \(0.447151\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.3238 | −1.10907 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.46897 | + | 5.00527i | 0.203345 | + | 0.227748i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.78365 | + | 3.08938i | −0.0809916 | + | 0.140282i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.9145 | + | 29.2968i | 0.766470 | + | 1.32756i | 0.939466 | + | 0.342642i | \(0.111322\pi\) |
−0.172996 | + | 0.984922i | \(0.555345\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.61347 | − | 12.5391i | 0.118185 | − | 0.567038i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.300406 | − | 0.520319i | −0.0135572 | − | 0.0234817i | 0.859167 | − | 0.511695i | \(-0.170982\pi\) |
−0.872724 | + | 0.488213i | \(0.837649\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.3902 | −1.05344 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.1214 | + | 8.21539i | −0.499870 | + | 0.369254i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.4622 | − | 24.0229i | −0.469294 | − | 1.07758i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.64134 | 0.252541 | 0.126271 | − | 0.991996i | \(-0.459699\pi\) | ||||
0.126271 | + | 0.991996i | \(0.459699\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.22851 | − | 1.09739i | −0.0548858 | − | 0.0490276i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.0034 | −1.38237 | −0.691186 | − | 0.722677i | \(-0.742911\pi\) | ||||
−0.691186 | + | 0.722677i | \(0.742911\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.60504 | 0.160422 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.34888 | − | 11.2696i | 0.104317 | − | 0.500501i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.6959 | 1.53787 | 0.768935 | − | 0.639327i | \(-0.220787\pi\) | ||||
0.768935 | + | 0.639327i | \(0.220787\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.70199 | + | 9.06833i | −0.296479 | + | 0.401159i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.26453 | + | 20.1611i | 0.409039 | + | 0.890135i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.41778 | −0.106540 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.4503 | + | 35.4210i | 0.899405 | + | 1.55781i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.03382 | − | 5.38981i | −0.264855 | − | 0.236586i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.5083 | − | 21.6650i | −0.547998 | − | 0.949161i | −0.998412 | − | 0.0563408i | \(-0.982057\pi\) |
0.450413 | − | 0.892820i | \(-0.351277\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.59320 | + | 2.75950i | −0.0696656 | + | 0.120664i | −0.898754 | − | 0.438453i | \(-0.855527\pi\) |
0.829088 | + | 0.559117i | \(0.188860\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.4796 | + | 15.0972i | 0.588298 | + | 0.658896i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.5486 | −1.11291 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.8560 | −0.906782 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.77592 | + | 33.3827i | 0.163861 | + | 1.44869i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.66753 | + | 9.81645i | −0.245488 | + | 0.425198i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.84745 | + | 10.1281i | −0.252808 | + | 0.437875i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.3628 | − | 17.2961i | −0.835567 | − | 0.746384i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −28.7695 | + | 30.9241i | −1.23919 | + | 1.33200i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.80693 | + | 11.7900i | −0.292653 | + | 0.506890i | −0.974436 | − | 0.224664i | \(-0.927871\pi\) |
0.681783 | + | 0.731554i | \(0.261205\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.4604 | + | 7.39617i | −0.963867 | + | 0.317400i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.84618 | − | 10.1259i | −0.250423 | − | 0.433745i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.91254 | + | 10.2408i | −0.252802 | + | 0.437866i | −0.964296 | − | 0.264826i | \(-0.914685\pi\) |
0.711494 | + | 0.702692i | \(0.248019\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.0546 | − | 10.0468i | −0.983948 | − | 0.428787i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.8414 | − | 22.2420i | −0.547064 | − | 0.947543i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.6483 | − | 15.7610i | 0.495334 | − | 0.670226i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.60494 | + | 12.4982i | −0.110574 | + | 0.530518i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.32911 | − | 16.1585i | −0.395287 | − | 0.684657i | 0.597851 | − | 0.801607i | \(-0.296021\pi\) |
−0.993138 | + | 0.116950i | \(0.962688\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.7633 | 0.455239 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.3108 | + | 27.0756i | 1.27972 | + | 1.14313i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.3196 | + | 19.6060i | −0.477062 | + | 0.826296i | −0.999654 | − | 0.0262866i | \(-0.991632\pi\) |
0.522592 | + | 0.852583i | \(0.324965\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.19246 | + | 2.06539i | 0.0501670 | + | 0.0868917i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.6615 | + | 2.67086i | −0.993690 | + | 0.112165i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.45277 | − | 9.44447i | −0.228592 | − | 0.395933i | 0.728799 | − | 0.684728i | \(-0.240079\pi\) |
−0.957391 | + | 0.288795i | \(0.906745\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.8055 | − | 23.9119i | 0.577743 | − | 1.00068i | −0.417994 | − | 0.908450i | \(-0.637267\pi\) |
0.995738 | − | 0.0922313i | \(-0.0293999\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.8762 | − | 14.1817i | −0.663237 | − | 0.592448i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.46693 | 0.269690 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.2592 | − | 17.7695i | −0.427096 | − | 0.739753i | 0.569517 | − | 0.821979i | \(-0.307130\pi\) |
−0.996614 | + | 0.0822267i | \(0.973797\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.53449 | + | 12.1602i | −0.105330 | + | 0.505360i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 42.3350 | + | 4.79834i | 1.75635 | + | 0.199069i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.60249 | − | 2.77559i | −0.0663683 | − | 0.114953i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.29514 | + | 2.30753i | 0.218927 | + | 0.0954044i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.59632 | − | 13.1572i | 0.313534 | − | 0.543056i | −0.665591 | − | 0.746317i | \(-0.731820\pi\) |
0.979125 | + | 0.203260i | \(0.0651538\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.0264 | − | 24.2944i | −0.577947 | − | 1.00103i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.4339 | + | 7.05817i | −0.881674 | + | 0.290334i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.39373 | − | 5.87812i | 0.139364 | − | 0.241385i | −0.787892 | − | 0.615813i | \(-0.788828\pi\) |
0.927256 | + | 0.374428i | \(0.122161\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.67108 | + | 6.32035i | −0.191496 | + | 0.259109i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.40927 | − | 5.72519i | −0.262314 | − | 0.234316i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.32519 | + | 10.9555i | −0.258440 | + | 0.447632i | −0.965824 | − | 0.259198i | \(-0.916542\pi\) |
0.707384 | + | 0.706829i | \(0.249875\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.3699 | + | 19.6932i | −0.463787 | + | 0.803303i | −0.999146 | − | 0.0413219i | \(-0.986843\pi\) |
0.535359 | + | 0.844625i | \(0.320176\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.648720 | − | 5.73530i | −0.0264179 | − | 0.233559i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.4075 | −0.789026 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.9226 | 1.70159 | 0.850794 | − | 0.525500i | \(-0.176122\pi\) | ||||
0.850794 | + | 0.525500i | \(0.176122\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 26.9840 | − | 5.61770i | 1.09345 | − | 0.227641i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.54308 | − | 14.7971i | 0.345616 | − | 0.598625i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.7038 | − | 23.7356i | −0.553490 | − | 0.958673i | −0.998019 | − | 0.0629086i | \(-0.979962\pi\) |
0.444529 | − | 0.895764i | \(-0.353371\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.43698 | + | 3.96340i | 0.178916 | + | 0.159820i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.75420 | + | 9.96656i | 0.231655 | + | 0.401239i | 0.958295 | − | 0.285780i | \(-0.0922526\pi\) |
−0.726640 | + | 0.687018i | \(0.758919\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.7559 | 1.51754 | 0.758770 | − | 0.651359i | \(-0.225801\pi\) | ||||
0.758770 | + | 0.651359i | \(0.225801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.39878 | + | 6.20801i | −0.176517 | + | 0.249119i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.27007 | − | 1.05069i | −0.371398 | − | 0.0420951i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.5887 | 0.663549 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.10561 | + | 43.6876i | −0.363643 | + | 1.74471i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 37.5270 | 1.49630 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.4466 | 1.80920 | 0.904600 | − | 0.426262i | \(-0.140170\pi\) | ||||
0.904600 | + | 0.426262i | \(0.140170\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.35771 | + | 4.78587i | 0.212950 | + | 0.190221i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.976288 | −0.0387428 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.1969 | + | 3.94901i | 0.681367 | + | 0.156466i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.8975 | − | 17.6531i | 0.945369 | − | 0.698344i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.299606 | −0.0118337 | −0.00591687 | − | 0.999982i | \(-0.501883\pi\) | ||||
−0.00591687 | + | 0.999982i | \(0.501883\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.61580 | − | 6.26275i | −0.142593 | − | 0.246979i | 0.785879 | − | 0.618380i | \(-0.212211\pi\) |
−0.928472 | + | 0.371401i | \(0.878877\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.15269 | − | 5.53046i | 0.0453870 | − | 0.217761i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.78298 | − | 8.28437i | −0.188039 | − | 0.325692i | 0.756558 | − | 0.653927i | \(-0.226880\pi\) |
−0.944596 | + | 0.328235i | \(0.893546\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.7854 | + | 58.5180i | −1.32619 | + | 2.29703i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.4740 | − | 6.13607i | 1.15518 | − | 0.240492i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.0070 | 1.52646 | 0.763232 | − | 0.646125i | \(-0.223612\pi\) | ||||
0.763232 | + | 0.646125i | \(0.223612\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.93856 | −0.232039 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.7213 | − | 5.10794i | −0.457292 | − | 0.199280i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.251281 | + | 0.435231i | −0.00978851 | + | 0.0169542i | −0.870878 | − | 0.491499i | \(-0.836449\pi\) |
0.861090 | + | 0.508453i | \(0.169782\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.09910 | − | 1.90370i | 0.0427501 | − | 0.0740453i | −0.843859 | − | 0.536566i | \(-0.819721\pi\) |
0.886609 | + | 0.462520i | \(0.153055\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.46429 | − | 16.6212i | 0.134542 | − | 0.645515i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.57455 | − | 0.971859i | −0.332507 | − | 0.0376871i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.40347 | − | 7.62703i | 0.170503 | − | 0.295320i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.27844 | + | 15.7295i | −0.126752 | + | 0.608139i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.2907 | − | 43.8048i | −0.976337 | − | 1.69107i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.50630 | − | 13.0013i | 0.289346 | − | 0.501163i | −0.684307 | − | 0.729194i | \(-0.739895\pi\) |
0.973654 | + | 0.228031i | \(0.0732287\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −13.2679 | + | 18.7250i | −0.510680 | + | 0.720724i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.8304 | − | 25.6869i | −0.569977 | − | 0.987229i | −0.996568 | − | 0.0827841i | \(-0.973619\pi\) |
0.426591 | − | 0.904445i | \(-0.359715\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.2777 | − | 1.39158i | −0.471175 | − | 0.0534041i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −35.1407 | + | 11.5718i | −1.34659 | + | 0.443432i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.7295 | − | 22.0482i | −0.487083 | − | 0.843652i | 0.512807 | − | 0.858504i | \(-0.328606\pi\) |
−0.999890 | + | 0.0148520i | \(0.995272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.15636 | −0.0823904 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −32.9146 | + | 10.8387i | −1.25577 | + | 0.413524i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.669436 | + | 1.15950i | −0.0255035 | + | 0.0441733i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.95499 | + | 10.3143i | 0.226538 | + | 0.392376i | 0.956780 | − | 0.290813i | \(-0.0939258\pi\) |
−0.730241 | + | 0.683189i | \(0.760592\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −41.4707 | − | 23.9558i | −1.57534 | − | 0.910005i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.57070 | + | 14.8449i | 0.325105 | + | 0.563099i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.74393 | − | 15.1449i | 0.331200 | − | 0.573655i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.39766 | − | 25.8973i | 0.204158 | − | 0.979527i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.84543 | −0.145240 | −0.0726199 | − | 0.997360i | \(-0.523136\pi\) | ||||
−0.0726199 | + | 0.997360i | \(0.523136\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.6027 | + | 35.6849i | 0.777044 | + | 1.34588i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.68818 | − | 5.97433i | −0.251891 | − | 0.225006i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.98589 | + | 11.4484i | 0.187514 | + | 0.430562i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.3533 | + | 23.1286i | 0.501494 | + | 0.868614i | 0.999999 | + | 0.00172652i | \(0.000549569\pi\) |
−0.498504 | + | 0.866887i | \(0.666117\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.3720 | + | 8.87774i | 0.764009 | + | 0.332941i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.80979 | − | 8.33081i | 0.180128 | − | 0.311991i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.80872 | + | 10.0610i | 0.217234 | + | 0.376260i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.3502 | + | 20.8580i | 0.872029 | + | 0.778955i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.3611 | − | 23.1420i | 0.498284 | − | 0.863052i | −0.501715 | − | 0.865033i | \(-0.667297\pi\) |
0.999998 | + | 0.00198088i | \(0.000630534\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.34388 | − | 7.67808i | −0.124532 | − | 0.285947i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.09133 | − | 2.33516i | 0.263729 | − | 0.0868457i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.2820 | − | 23.0051i | 0.493281 | − | 0.854388i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.13012 | + | 1.95743i | −0.0419139 | + | 0.0725970i | −0.886221 | − | 0.463262i | \(-0.846679\pi\) |
0.844307 | + | 0.535859i | \(0.180012\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.95052 | − | 25.4733i | −0.331501 | − | 0.943455i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.6057 | −0.614186 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.7404 | 1.35704 | 0.678519 | − | 0.734583i | \(-0.262622\pi\) | ||||
0.678519 | + | 0.734583i | \(0.262622\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.87079 | − | 8.41330i | 0.142776 | − | 0.310329i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.80448 | − | 10.0536i | 0.213811 | − | 0.370331i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.0909 | − | 29.6022i | −0.628697 | − | 1.08894i | −0.987813 | − | 0.155643i | \(-0.950255\pi\) |
0.359116 | − | 0.933293i | \(-0.383078\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.7072 | − | 5.83097i | 0.650491 | − | 0.214206i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.56487 | − | 7.90658i | −0.167469 | − | 0.290064i | 0.770061 | − | 0.637971i | \(-0.220226\pi\) |
−0.937529 | + | 0.347907i | \(0.886893\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.4068 | 0.564461 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.42980 | + | 48.0046i | 0.198666 | + | 1.75640i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −40.2507 | − | 4.56211i | −1.47073 | − | 0.166696i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.1295 | −1.39137 | −0.695683 | − | 0.718349i | \(-0.744898\pi\) | ||||
−0.695683 | + | 0.718349i | \(0.744898\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.8731 | − | 8.84928i | 0.979311 | − | 0.322486i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.33564 | −0.230578 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.6952 | 0.679488 | 0.339744 | − | 0.940518i | \(-0.389660\pi\) | ||||
0.339744 | + | 0.940518i | \(0.389660\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14.5351 | + | 4.78638i | −0.527590 | + | 0.173735i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.1572 | −0.585697 | −0.292849 | − | 0.956159i | \(-0.594603\pi\) | ||||
−0.292849 | + | 0.956159i | \(0.594603\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.0710 | − | 32.5700i | 0.871429 | − | 1.17911i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.16940 | − | 3.56008i | −0.295365 | − | 0.128715i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.2275 | 1.01924 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.9628 | − | 29.3804i | −0.611694 | − | 1.05949i | −0.990955 | − | 0.134195i | \(-0.957155\pi\) |
0.379261 | − | 0.925290i | \(-0.376178\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.13112 | − | 0.701774i | 0.0767503 | − | 0.0252738i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.8452 | + | 34.3728i | 0.713781 | + | 1.23630i | 0.963428 | + | 0.267968i | \(0.0863522\pi\) |
−0.249647 | + | 0.968337i | \(0.580315\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.5076 | − | 25.1279i | 0.521128 | − | 0.902621i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −43.2928 | + | 9.01297i | −1.55312 | + | 0.323339i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.2020 | 0.687982 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 59.7568 | 2.13827 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.0497 | + | 28.3982i | 0.466357 | + | 1.01487i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.54611 | + | 4.41000i | −0.0908746 | + | 0.157400i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.158840 | − | 0.275119i | 0.00566204 | − | 0.00980695i | −0.863180 | − | 0.504895i | \(-0.831531\pi\) |
0.868843 | + | 0.495089i | \(0.164864\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 46.5129 | − | 15.3166i | 1.65590 | − | 0.545287i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.90980 | + | 6.64335i | −0.174573 | + | 0.236211i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.5651 | + | 18.2994i | −0.375179 | + | 0.649829i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.524086 | + | 0.468148i | 0.0185874 | + | 0.0166035i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.0702 | − | 36.4946i | −0.746344 | − | 1.29271i | −0.949564 | − | 0.313572i | \(-0.898474\pi\) |
0.203221 | − | 0.979133i | \(-0.434859\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.1804 | + | 22.8290i | −0.466288 | + | 0.807634i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.18896 | − | 10.5115i | −0.0420099 | − | 0.371407i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.8582 | − | 22.2710i | −0.453755 | − | 0.785926i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.18154 | − | 2.71301i | −0.0416438 | − | 0.0956210i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.3677 | + | 16.4073i | 0.646574 | + | 0.577563i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.40052 | − | 11.0860i | −0.225030 | − | 0.389764i | 0.731298 | − | 0.682058i | \(-0.238915\pi\) |
−0.956329 | + | 0.292294i | \(0.905581\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.1410 | 0.953051 | 0.476526 | − | 0.879161i | \(-0.341896\pi\) | ||||
0.476526 | + | 0.879161i | \(0.341896\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.08141 | + | 24.3800i | −0.178213 | + | 0.855044i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.82429 | + | 4.89182i | −0.0989307 | + | 0.171353i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.11670 | − | 15.7906i | −0.318953 | − | 0.552443i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.00458903 | + | 20.0070i | −0.000160354 | + | 0.699101i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.95924 | + | 10.3217i | 0.207979 | + | 0.360230i | 0.951078 | − | 0.308952i | \(-0.0999781\pi\) |
−0.743099 | + | 0.669182i | \(0.766645\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.26505 | − | 16.0475i | 0.322959 | − | 0.559382i | −0.658138 | − | 0.752897i | \(-0.728656\pi\) |
0.981097 | + | 0.193515i | \(0.0619890\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −43.8416 | + | 14.4370i | −1.52637 | + | 0.502631i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.64616 | 0.335430 | 0.167715 | − | 0.985836i | \(-0.446361\pi\) | ||||
0.167715 | + | 0.985836i | \(0.446361\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.2155 | + | 17.6938i | 0.354800 | + | 0.614531i | 0.987084 | − | 0.160206i | \(-0.0512158\pi\) |
−0.632284 | + | 0.774737i | \(0.717882\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.3947 | + | 8.36246i | −0.880934 | + | 0.290090i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.5316 | − | 6.09258i | −0.919266 | − | 0.211095i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.363224 | + | 0.629122i | 0.0125699 | + | 0.0217717i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.2538 | + | 31.0186i | 0.492684 | + | 1.07216i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.18866 | + | 12.4511i | −0.248180 | + | 0.429861i | −0.963021 | − | 0.269427i | \(-0.913166\pi\) |
0.714841 | + | 0.699287i | \(0.246499\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.58799 | − | 6.21459i | −0.123724 | − | 0.214296i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.64133 | + | 31.8643i | −0.228739 | + | 1.09746i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.53836 | + | 4.39657i | −0.0873222 | + | 0.151247i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.8412 | − | 61.6318i | −0.922274 | − | 2.11769i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.5115 | − | 55.2310i | 0.395075 | − | 1.89552i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.06487 | + | 12.2367i | −0.242181 | + | 0.419469i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.05636 | + | 3.56173i | −0.0704085 | + | 0.121951i | −0.899080 | − | 0.437784i | \(-0.855764\pi\) |
0.828672 | + | 0.559735i | \(0.189097\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.09975 | − | 9.72288i | −0.0376108 | − | 0.332516i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 51.1084 | 1.74583 | 0.872915 | − | 0.487873i | \(-0.162227\pi\) | ||||
0.872915 | + | 0.487873i | \(0.162227\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.3165 | 0.522592 | 0.261296 | − | 0.965259i | \(-0.415850\pi\) | ||||
0.261296 | + | 0.965259i | \(0.415850\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.44998 | + | 19.5719i | −0.219815 | + | 0.667009i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.4865 | − | 21.6272i | 0.425045 | − | 0.736199i | −0.571380 | − | 0.820686i | \(-0.693592\pi\) |
0.996425 | + | 0.0844866i | \(0.0269250\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.78397 | + | 3.08993i | 0.0606568 | + | 0.105061i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.663210 | − | 3.18200i | 0.0225238 | − | 0.108066i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.3479 | + | 38.7076i | 0.758099 | + | 1.31307i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.84962 | −0.164323 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.57471 | − | 13.9220i | −0.0532960 | − | 0.471188i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.59846 | − | 17.4473i | −0.256875 | − | 0.589827i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.3918 | 1.22886 | 0.614432 | − | 0.788970i | \(-0.289385\pi\) | ||||
0.614432 | + | 0.788970i | \(0.289385\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.38728 | − | 3.91901i | −0.147979 | − | 0.132185i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 56.1807 | 1.89277 | 0.946387 | − | 0.323035i | \(-0.104703\pi\) | ||||
0.946387 | + | 0.323035i | \(0.104703\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.7585 | −0.765884 | −0.382942 | − | 0.923772i | \(-0.625089\pi\) | ||||
−0.382942 | + | 0.923772i | \(0.625089\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.02301 | − | 14.5040i | 0.101617 | − | 0.487547i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.0314 | −0.336820 | −0.168410 | − | 0.985717i | \(-0.553863\pi\) | ||||
−0.168410 | + | 0.985717i | \(0.553863\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.35024 | − | 3.10037i | −0.0452856 | − | 0.103983i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.9619 | − | 51.9062i | 0.534744 | − | 1.73892i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.9445 | −0.968592 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.72485 | + | 9.91573i | 0.191361 | + | 0.331446i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.76762 | + | 4.25875i | 0.159186 | + | 0.142196i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.7571 | − | 34.2202i | −0.658935 | − | 1.14131i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.03281 | − | 1.78888i | 0.0344080 | − | 0.0595964i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.1571 | − | 3.98825i | 0.637509 | − | 0.132721i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.4283 | 0.346647 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.5712 | −0.683054 | −0.341527 | − | 0.939872i | \(-0.610944\pi\) | ||||
−0.341527 | + | 0.939872i | \(0.610944\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.3886 | + | 8.41278i | −0.377737 | + | 0.279034i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.19047 | + | 2.06196i | −0.0394421 | + | 0.0683157i | −0.885073 | − | 0.465453i | \(-0.845891\pi\) |
0.845630 | + | 0.533769i | \(0.179225\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48.5836 | + | 84.1493i | −1.60788 | + | 2.78493i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.27120 | + | 7.38839i | 0.273437 | + | 0.244253i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.21323 | − | 18.8589i | −0.271225 | − | 0.622777i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.8130 | + | 20.4608i | −0.389676 | + | 0.674939i | −0.992406 | − | 0.123007i | \(-0.960746\pi\) |
0.602730 | + | 0.797945i | \(0.294080\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.07988 | − | 2.00210i | 0.200339 | − | 0.0659713i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.4816 | − | 21.6188i | −0.410838 | − | 0.711593i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.3095 | + | 36.9091i | −0.700652 | + | 1.21356i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.63798 | − | 5.64218i | 0.250864 | − | 0.185313i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.6884 | + | 51.4219i | 0.974046 | + | 1.68710i | 0.683047 | + | 0.730374i | \(0.260654\pi\) |
0.290999 | + | 0.956723i | \(0.406012\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.77259 | − | 28.5741i | −0.287510 | − | 0.936478i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.06534 | − | 29.1007i | 0.198570 | − | 0.952715i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.96175 | − | 15.5222i | −0.293081 | − | 0.507630i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.1455 | 0.527451 | 0.263725 | − | 0.964598i | \(-0.415049\pi\) | ||||
0.263725 | + | 0.964598i | \(0.415049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.84166 | − | 6.11143i | −0.223269 | − | 0.199439i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.88063 | + | 17.1137i | −0.322099 | + | 0.557892i | −0.980921 | − | 0.194407i | \(-0.937722\pi\) |
0.658822 | + | 0.752299i | \(0.271055\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.29228 | + | 5.70239i | 0.107211 | + | 0.185695i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.2796 | + | 2.14499i | 0.334396 | + | 0.0697766i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.4618 | + | 42.3691i | 0.794902 | + | 1.37681i | 0.922902 | + | 0.385036i | \(0.125811\pi\) |
−0.128000 | + | 0.991774i | \(0.540856\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.37147 | + | 9.30366i | −0.174365 | + | 0.302010i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −36.3985 | − | 32.5136i | −1.18030 | − | 1.05433i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.6464 | −1.57581 | −0.787905 | − | 0.615797i | \(-0.788834\pi\) | ||||
−0.787905 | + | 0.615797i | \(0.788834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.69399 | + | 8.13022i | 0.151894 | + | 0.263088i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.8258 | + | 61.5368i | −0.414600 | + | 1.98920i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.98232 | − | 6.84790i | −0.0963043 | − | 0.221130i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.08013 | − | 10.5311i | −0.196133 | − | 0.339713i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.16248 | − | 45.6412i | −0.166358 | − | 1.47077i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.73895 | − | 4.74400i | 0.0881699 | − | 0.152715i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.1435 | + | 38.3537i | 0.712087 | + | 1.23337i | 0.964072 | + | 0.265639i | \(0.0855831\pi\) |
−0.251986 | + | 0.967731i | \(0.581084\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −27.3189 | + | 8.99608i | −0.877610 | + | 0.288996i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.6355 | + | 32.2776i | −0.598040 | + | 1.03584i | 0.395070 | + | 0.918651i | \(0.370720\pi\) |
−0.993110 | + | 0.117185i | \(0.962613\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.2889 | + | 47.7487i | −1.13131 | + | 1.53075i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.3804 | + | 12.8455i | 0.460541 | + | 0.411386i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.9312 | + | 53.5744i | −0.989577 | + | 1.71400i | −0.370078 | + | 0.929001i | \(0.620669\pi\) |
−0.619499 | + | 0.784997i | \(0.712664\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.6383 | − | 18.4261i | 0.340003 | − | 0.588902i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42.0985 | + | 18.3458i | 1.34410 | + | 0.585735i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.9765 | −0.350096 | −0.175048 | − | 0.984560i | \(-0.556008\pi\) | ||||
−0.175048 | + | 0.984560i | \(0.556008\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.95170 | 0.317088 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.72252 | − | 29.5022i | 0.309471 | − | 0.939064i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.12621 | − | 5.41476i | 0.0994077 | − | 0.172179i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.43169 | − | 9.40796i | −0.172543 | − | 0.298854i | 0.766765 | − | 0.641928i | \(-0.221865\pi\) |
−0.939308 | + | 0.343074i | \(0.888532\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −37.6827 | − | 33.6607i | −1.19582 | − | 1.06819i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.89498 | + | 3.28220i | 0.0600749 | + | 0.104053i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.9291 | −1.29624 | −0.648119 | − | 0.761539i | \(-0.724444\pi\) | ||||
−0.648119 | + | 0.761539i | \(0.724444\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.9367 | − | 45.5617i | −0.662409 | − | 1.44151i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))