Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(1469,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.1469");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.d (of order \(2\), degree \(1\), 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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1469.1 | ||
Root | \(1.68614 + 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.1469 |
Dual form | 1470.2.d.a.1469.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.68614 | − | 0.396143i | −0.973494 | − | 0.228714i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.18614 | − | 0.469882i | 0.977672 | − | 0.210138i | ||||
\(6\) | 1.68614 | + | 0.396143i | 0.688364 | + | 0.161725i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.68614 | + | 1.33591i | 0.895380 | + | 0.445302i | ||||
\(10\) | −2.18614 | + | 0.469882i | −0.691318 | + | 0.148590i | ||||
\(11\) | − | 0.939764i | − | 0.283349i | −0.989913 | − | 0.141675i | \(-0.954751\pi\) | ||
0.989913 | − | 0.141675i | \(-0.0452487\pi\) | |||||||
\(12\) | −1.68614 | − | 0.396143i | −0.486747 | − | 0.114357i | ||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.87228 | − | 0.0737384i | −0.999819 | − | 0.0190392i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.63325i | 1.60880i | 0.594089 | + | 0.804400i | \(0.297513\pi\) | ||||
−0.594089 | + | 0.804400i | \(0.702487\pi\) | |||||||
\(18\) | −2.68614 | − | 1.33591i | −0.633129 | − | 0.314876i | ||||
\(19\) | 3.46410i | 0.794719i | 0.917663 | + | 0.397360i | \(0.130073\pi\) | ||||
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 2.18614 | − | 0.469882i | 0.488836 | − | 0.105069i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.939764i | 0.200358i | ||||||||
\(23\) | 1.37228 | 0.286140 | 0.143070 | − | 0.989713i | \(-0.454303\pi\) | ||||
0.143070 | + | 0.989713i | \(0.454303\pi\) | |||||||
\(24\) | 1.68614 | + | 0.396143i | 0.344182 | + | 0.0808625i | ||||
\(25\) | 4.55842 | − | 2.05446i | 0.911684 | − | 0.410891i | ||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | −4.00000 | − | 3.31662i | −0.769800 | − | 0.638285i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.31662i | − | 0.615882i | −0.951405 | − | 0.307941i | \(-0.900360\pi\) | ||
0.951405 | − | 0.307941i | \(-0.0996399\pi\) | |||||||
\(30\) | 3.87228 | + | 0.0737384i | 0.706979 | + | 0.0134627i | ||||
\(31\) | 7.57301i | 1.36015i | 0.733141 | + | 0.680077i | \(0.238054\pi\) | ||||
−0.733141 | + | 0.680077i | \(0.761946\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.372281 | + | 1.58457i | −0.0648059 | + | 0.275839i | ||||
\(34\) | − | 6.63325i | − | 1.13759i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.68614 | + | 1.33591i | 0.447690 | + | 0.222651i | ||||
\(37\) | 8.21782i | 1.35100i | 0.737359 | + | 0.675501i | \(0.236073\pi\) | ||||
−0.737359 | + | 0.675501i | \(0.763927\pi\) | |||||||
\(38\) | − | 3.46410i | − | 0.561951i | ||||||
\(39\) | −3.37228 | − | 0.792287i | −0.539997 | − | 0.126867i | ||||
\(40\) | −2.18614 | + | 0.469882i | −0.345659 | + | 0.0742949i | ||||
\(41\) | −7.37228 | −1.15136 | −0.575678 | − | 0.817676i | \(-0.695262\pi\) | ||||
−0.575678 | + | 0.817676i | \(0.695262\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.08724i | − | 0.165803i | −0.996558 | − | 0.0829013i | \(-0.973581\pi\) | ||
0.996558 | − | 0.0829013i | \(-0.0264186\pi\) | |||||||
\(44\) | − | 0.939764i | − | 0.141675i | ||||||
\(45\) | 6.50000 | + | 1.65831i | 0.968963 | + | 0.247207i | ||||
\(46\) | −1.37228 | −0.202332 | ||||||||
\(47\) | − | 8.51278i | − | 1.24172i | −0.783923 | − | 0.620858i | \(-0.786784\pi\) | ||
0.783923 | − | 0.620858i | \(-0.213216\pi\) | |||||||
\(48\) | −1.68614 | − | 0.396143i | −0.243373 | − | 0.0571784i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.55842 | + | 2.05446i | −0.644658 | + | 0.290544i | ||||
\(51\) | 2.62772 | − | 11.1846i | 0.367954 | − | 1.56616i | ||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 4.37228 | 0.600579 | 0.300290 | − | 0.953848i | \(-0.402917\pi\) | ||||
0.300290 | + | 0.953848i | \(0.402917\pi\) | |||||||
\(54\) | 4.00000 | + | 3.31662i | 0.544331 | + | 0.451335i | ||||
\(55\) | −0.441578 | − | 2.05446i | −0.0595424 | − | 0.277023i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.37228 | − | 5.84096i | 0.181763 | − | 0.773654i | ||||
\(58\) | 3.31662i | 0.435494i | ||||||||
\(59\) | −13.1168 | −1.70767 | −0.853834 | − | 0.520546i | \(-0.825729\pi\) | ||||
−0.853834 | + | 0.520546i | \(0.825729\pi\) | |||||||
\(60\) | −3.87228 | − | 0.0737384i | −0.499909 | − | 0.00951959i | ||||
\(61\) | 12.7692i | 1.63492i | 0.575982 | + | 0.817462i | \(0.304620\pi\) | ||||
−0.575982 | + | 0.817462i | \(0.695380\pi\) | |||||||
\(62\) | − | 7.57301i | − | 0.961774i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.37228 | − | 0.939764i | 0.542315 | − | 0.116563i | ||||
\(66\) | 0.372281 | − | 1.58457i | 0.0458247 | − | 0.195048i | ||||
\(67\) | 2.37686i | 0.290380i | 0.989404 | + | 0.145190i | \(0.0463793\pi\) | ||||
−0.989404 | + | 0.145190i | \(0.953621\pi\) | |||||||
\(68\) | 6.63325i | 0.804400i | ||||||||
\(69\) | −2.31386 | − | 0.543620i | −0.278556 | − | 0.0654442i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.51278i | − | 1.01028i | −0.863037 | − | 0.505140i | \(-0.831441\pi\) | ||
0.863037 | − | 0.505140i | \(-0.168559\pi\) | |||||||
\(72\) | −2.68614 | − | 1.33591i | −0.316565 | − | 0.157438i | ||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | − | 8.21782i | − | 0.955303i | ||||||
\(75\) | −8.50000 | + | 1.65831i | −0.981495 | + | 0.191485i | ||||
\(76\) | 3.46410i | 0.397360i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.37228 | + | 0.792287i | 0.381836 | + | 0.0897088i | ||||
\(79\) | 9.11684 | 1.02573 | 0.512863 | − | 0.858471i | \(-0.328585\pi\) | ||||
0.512863 | + | 0.858471i | \(0.328585\pi\) | |||||||
\(80\) | 2.18614 | − | 0.469882i | 0.244418 | − | 0.0525344i | ||||
\(81\) | 5.43070 | + | 7.17687i | 0.603411 | + | 0.797430i | ||||
\(82\) | 7.37228 | 0.814132 | ||||||||
\(83\) | 11.8294i | 1.29845i | 0.760598 | + | 0.649223i | \(0.224906\pi\) | ||||
−0.760598 | + | 0.649223i | \(0.775094\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.11684 | + | 14.5012i | 0.338069 | + | 1.57288i | ||||
\(86\) | 1.08724i | 0.117240i | ||||||||
\(87\) | −1.31386 | + | 5.59230i | −0.140861 | + | 0.599557i | ||||
\(88\) | 0.939764i | 0.100179i | ||||||||
\(89\) | −1.37228 | −0.145462 | −0.0727308 | − | 0.997352i | \(-0.523171\pi\) | ||||
−0.0727308 | + | 0.997352i | \(0.523171\pi\) | |||||||
\(90\) | −6.50000 | − | 1.65831i | −0.685160 | − | 0.174801i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.37228 | 0.143070 | ||||||||
\(93\) | 3.00000 | − | 12.7692i | 0.311086 | − | 1.32410i | ||||
\(94\) | 8.51278i | 0.878026i | ||||||||
\(95\) | 1.62772 | + | 7.57301i | 0.167000 | + | 0.776975i | ||||
\(96\) | 1.68614 | + | 0.396143i | 0.172091 | + | 0.0404312i | ||||
\(97\) | 15.1168 | 1.53488 | 0.767441 | − | 0.641119i | \(-0.221530\pi\) | ||||
0.767441 | + | 0.641119i | \(0.221530\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.25544 | − | 2.52434i | 0.126176 | − | 0.253705i | ||||
\(100\) | 4.55842 | − | 2.05446i | 0.455842 | − | 0.205446i | ||||
\(101\) | 10.6277 | 1.05750 | 0.528749 | − | 0.848778i | \(-0.322661\pi\) | ||||
0.528749 | + | 0.848778i | \(0.322661\pi\) | |||||||
\(102\) | −2.62772 | + | 11.1846i | −0.260183 | + | 1.10744i | ||||
\(103\) | −2.11684 | −0.208579 | −0.104289 | − | 0.994547i | \(-0.533257\pi\) | ||||
−0.104289 | + | 0.994547i | \(0.533257\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.37228 | −0.424674 | ||||||||
\(107\) | −6.25544 | −0.604736 | −0.302368 | − | 0.953191i | \(-0.597777\pi\) | ||||
−0.302368 | + | 0.953191i | \(0.597777\pi\) | |||||||
\(108\) | −4.00000 | − | 3.31662i | −0.384900 | − | 0.319142i | ||||
\(109\) | −8.11684 | −0.777453 | −0.388726 | − | 0.921353i | \(-0.627085\pi\) | ||||
−0.388726 | + | 0.921353i | \(0.627085\pi\) | |||||||
\(110\) | 0.441578 | + | 2.05446i | 0.0421028 | + | 0.195885i | ||||
\(111\) | 3.25544 | − | 13.8564i | 0.308992 | − | 1.31519i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.7446 | 1.38705 | 0.693526 | − | 0.720432i | \(-0.256056\pi\) | ||||
0.693526 | + | 0.720432i | \(0.256056\pi\) | |||||||
\(114\) | −1.37228 | + | 5.84096i | −0.128526 | + | 0.547056i | ||||
\(115\) | 3.00000 | − | 0.644810i | 0.279751 | − | 0.0601289i | ||||
\(116\) | − | 3.31662i | − | 0.307941i | ||||||
\(117\) | 5.37228 | + | 2.67181i | 0.496668 | + | 0.247009i | ||||
\(118\) | 13.1168 | 1.20750 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.87228 | + | 0.0737384i | 0.353489 | + | 0.00673137i | ||||
\(121\) | 10.1168 | 0.919713 | ||||||||
\(122\) | − | 12.7692i | − | 1.15607i | ||||||
\(123\) | 12.4307 | + | 2.92048i | 1.12084 | + | 0.263331i | ||||
\(124\) | 7.57301i | 0.680077i | ||||||||
\(125\) | 9.00000 | − | 6.63325i | 0.804984 | − | 0.593296i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.57301i | 0.671996i | 0.941863 | + | 0.335998i | \(0.109074\pi\) | ||||
−0.941863 | + | 0.335998i | \(0.890926\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.430703 | + | 1.83324i | −0.0379213 | + | 0.161408i | ||||
\(130\) | −4.37228 | + | 0.939764i | −0.383474 | + | 0.0824227i | ||||
\(131\) | 10.3723 | 0.906230 | 0.453115 | − | 0.891452i | \(-0.350313\pi\) | ||||
0.453115 | + | 0.891452i | \(0.350313\pi\) | |||||||
\(132\) | −0.372281 | + | 1.58457i | −0.0324029 | + | 0.137919i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 2.37686i | − | 0.205330i | ||||||
\(135\) | −10.3030 | − | 5.37108i | −0.886740 | − | 0.462269i | ||||
\(136\) | − | 6.63325i | − | 0.568796i | ||||||
\(137\) | 8.74456 | 0.747098 | 0.373549 | − | 0.927610i | \(-0.378141\pi\) | ||||
0.373549 | + | 0.927610i | \(0.378141\pi\) | |||||||
\(138\) | 2.31386 | + | 0.543620i | 0.196969 | + | 0.0462760i | ||||
\(139\) | 8.21782i | 0.697027i | 0.937304 | + | 0.348513i | \(0.113313\pi\) | ||||
−0.937304 | + | 0.348513i | \(0.886687\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.37228 | + | 14.3537i | −0.283997 | + | 1.20880i | ||||
\(142\) | 8.51278i | 0.714376i | ||||||||
\(143\) | − | 1.87953i | − | 0.157174i | ||||||
\(144\) | 2.68614 | + | 1.33591i | 0.223845 | + | 0.111326i | ||||
\(145\) | −1.55842 | − | 7.25061i | −0.129420 | − | 0.602130i | ||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.21782i | 0.675501i | ||||||||
\(149\) | 9.01011i | 0.738137i | 0.929402 | + | 0.369069i | \(0.120323\pi\) | ||||
−0.929402 | + | 0.369069i | \(0.879677\pi\) | |||||||
\(150\) | 8.50000 | − | 1.65831i | 0.694022 | − | 0.135401i | ||||
\(151\) | 9.11684 | 0.741918 | 0.370959 | − | 0.928649i | \(-0.379029\pi\) | ||||
0.370959 | + | 0.928649i | \(0.379029\pi\) | |||||||
\(152\) | − | 3.46410i | − | 0.280976i | ||||||
\(153\) | −8.86141 | + | 17.8178i | −0.716402 | + | 1.44049i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.55842 | + | 16.5557i | 0.285819 | + | 1.32978i | ||||
\(156\) | −3.37228 | − | 0.792287i | −0.269999 | − | 0.0634337i | ||||
\(157\) | 8.00000 | 0.638470 | 0.319235 | − | 0.947676i | \(-0.396574\pi\) | ||||
0.319235 | + | 0.947676i | \(0.396574\pi\) | |||||||
\(158\) | −9.11684 | −0.725297 | ||||||||
\(159\) | −7.37228 | − | 1.73205i | −0.584660 | − | 0.137361i | ||||
\(160\) | −2.18614 | + | 0.469882i | −0.172830 | + | 0.0371474i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.43070 | − | 7.17687i | −0.426676 | − | 0.563868i | ||||
\(163\) | 3.46410i | 0.271329i | 0.990755 | + | 0.135665i | \(0.0433170\pi\) | ||||
−0.990755 | + | 0.135665i | \(0.956683\pi\) | |||||||
\(164\) | −7.37228 | −0.575678 | ||||||||
\(165\) | −0.0692967 | + | 3.63903i | −0.00539474 | + | 0.283298i | ||||
\(166\) | − | 11.8294i | − | 0.918140i | ||||||
\(167\) | 14.6487i | 1.13355i | 0.823873 | + | 0.566775i | \(0.191809\pi\) | ||||
−0.823873 | + | 0.566775i | \(0.808191\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −3.11684 | − | 14.5012i | −0.239051 | − | 1.11219i | ||||
\(171\) | −4.62772 | + | 9.30506i | −0.353890 | + | 0.711576i | ||||
\(172\) | − | 1.08724i | − | 0.0829013i | ||||||
\(173\) | 17.0256i | 1.29443i | 0.762308 | + | 0.647214i | \(0.224066\pi\) | ||||
−0.762308 | + | 0.647214i | \(0.775934\pi\) | |||||||
\(174\) | 1.31386 | − | 5.59230i | 0.0996034 | − | 0.423951i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.939764i | − | 0.0708374i | ||||||
\(177\) | 22.1168 | + | 5.19615i | 1.66240 | + | 0.390567i | ||||
\(178\) | 1.37228 | 0.102857 | ||||||||
\(179\) | − | 23.6588i | − | 1.76834i | −0.467163 | − | 0.884171i | \(-0.654724\pi\) | ||
0.467163 | − | 0.884171i | \(-0.345276\pi\) | |||||||
\(180\) | 6.50000 | + | 1.65831i | 0.484481 | + | 0.123603i | ||||
\(181\) | 8.01544i | 0.595783i | 0.954600 | + | 0.297892i | \(0.0962834\pi\) | ||||
−0.954600 | + | 0.297892i | \(0.903717\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.05842 | − | 21.5306i | 0.373929 | − | 1.59159i | ||||
\(184\) | −1.37228 | −0.101166 | ||||||||
\(185\) | 3.86141 | + | 17.9653i | 0.283896 | + | 1.32084i | ||||
\(186\) | −3.00000 | + | 12.7692i | −0.219971 | + | 0.936281i | ||||
\(187\) | 6.23369 | 0.455852 | ||||||||
\(188\) | − | 8.51278i | − | 0.620858i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.62772 | − | 7.57301i | −0.118087 | − | 0.549404i | ||||
\(191\) | 17.0256i | 1.23193i | 0.787775 | + | 0.615963i | \(0.211233\pi\) | ||||
−0.787775 | + | 0.615963i | \(0.788767\pi\) | |||||||
\(192\) | −1.68614 | − | 0.396143i | −0.121687 | − | 0.0285892i | ||||
\(193\) | − | 17.9653i | − | 1.29317i | −0.762841 | − | 0.646586i | \(-0.776196\pi\) | ||
0.762841 | − | 0.646586i | \(-0.223804\pi\) | |||||||
\(194\) | −15.1168 | −1.08533 | ||||||||
\(195\) | −7.74456 | − | 0.147477i | −0.554600 | − | 0.0105610i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.2337 | −1.01411 | −0.507054 | − | 0.861914i | \(-0.669266\pi\) | ||||
−0.507054 | + | 0.861914i | \(0.669266\pi\) | |||||||
\(198\) | −1.25544 | + | 2.52434i | −0.0892200 | + | 0.179397i | ||||
\(199\) | 1.28962i | 0.0914188i | 0.998955 | + | 0.0457094i | \(0.0145548\pi\) | ||||
−0.998955 | + | 0.0457094i | \(0.985445\pi\) | |||||||
\(200\) | −4.55842 | + | 2.05446i | −0.322329 | + | 0.145272i | ||||
\(201\) | 0.941578 | − | 4.00772i | 0.0664138 | − | 0.282683i | ||||
\(202\) | −10.6277 | −0.747764 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.62772 | − | 11.1846i | 0.183977 | − | 0.783078i | ||||
\(205\) | −16.1168 | + | 3.46410i | −1.12565 | + | 0.241943i | ||||
\(206\) | 2.11684 | 0.147488 | ||||||||
\(207\) | 3.68614 | + | 1.83324i | 0.256204 | + | 0.127419i | ||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | 3.25544 | 0.225183 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.2337 | 1.11757 | 0.558787 | − | 0.829311i | \(-0.311267\pi\) | ||||
0.558787 | + | 0.829311i | \(0.311267\pi\) | |||||||
\(212\) | 4.37228 | 0.300290 | ||||||||
\(213\) | −3.37228 | + | 14.3537i | −0.231065 | + | 0.983502i | ||||
\(214\) | 6.25544 | 0.427613 | ||||||||
\(215\) | −0.510875 | − | 2.37686i | −0.0348414 | − | 0.162101i | ||||
\(216\) | 4.00000 | + | 3.31662i | 0.272166 | + | 0.225668i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.11684 | 0.549742 | ||||||||
\(219\) | −3.37228 | − | 0.792287i | −0.227878 | − | 0.0535378i | ||||
\(220\) | −0.441578 | − | 2.05446i | −0.0297712 | − | 0.138511i | ||||
\(221\) | 13.2665i | 0.892401i | ||||||||
\(222\) | −3.25544 | + | 13.8564i | −0.218491 | + | 0.929981i | ||||
\(223\) | 0.883156 | 0.0591405 | 0.0295703 | − | 0.999563i | \(-0.490586\pi\) | ||||
0.0295703 | + | 0.999563i | \(0.490586\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.9891 | + | 0.571072i | 0.999275 | + | 0.0380715i | ||||
\(226\) | −14.7446 | −0.980794 | ||||||||
\(227\) | − | 20.8395i | − | 1.38317i | −0.722297 | − | 0.691584i | \(-0.756913\pi\) | ||
0.722297 | − | 0.691584i | \(-0.243087\pi\) | |||||||
\(228\) | 1.37228 | − | 5.84096i | 0.0908816 | − | 0.386827i | ||||
\(229\) | − | 13.8564i | − | 0.915657i | −0.889041 | − | 0.457829i | \(-0.848627\pi\) | ||
0.889041 | − | 0.457829i | \(-0.151373\pi\) | |||||||
\(230\) | −3.00000 | + | 0.644810i | −0.197814 | + | 0.0425175i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.31662i | 0.217747i | ||||||||
\(233\) | 0.510875 | 0.0334685 | 0.0167343 | − | 0.999860i | \(-0.494673\pi\) | ||||
0.0167343 | + | 0.999860i | \(0.494673\pi\) | |||||||
\(234\) | −5.37228 | − | 2.67181i | −0.351197 | − | 0.174662i | ||||
\(235\) | −4.00000 | − | 18.6101i | −0.260931 | − | 1.21399i | ||||
\(236\) | −13.1168 | −0.853834 | ||||||||
\(237\) | −15.3723 | − | 3.61158i | −0.998537 | − | 0.234597i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 23.6588i | − | 1.53036i | −0.643816 | − | 0.765180i | \(-0.722650\pi\) | ||
0.643816 | − | 0.765180i | \(-0.277350\pi\) | |||||||
\(240\) | −3.87228 | − | 0.0737384i | −0.249955 | − | 0.00475979i | ||||
\(241\) | − | 19.2549i | − | 1.24032i | −0.784475 | − | 0.620160i | \(-0.787068\pi\) | ||
0.784475 | − | 0.620160i | \(-0.212932\pi\) | |||||||
\(242\) | −10.1168 | −0.650335 | ||||||||
\(243\) | −6.31386 | − | 14.2525i | −0.405034 | − | 0.914302i | ||||
\(244\) | 12.7692i | 0.817462i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −12.4307 | − | 2.92048i | −0.792553 | − | 0.186203i | ||||
\(247\) | 6.92820i | 0.440831i | ||||||||
\(248\) | − | 7.57301i | − | 0.480887i | ||||||
\(249\) | 4.68614 | − | 19.9460i | 0.296972 | − | 1.26403i | ||||
\(250\) | −9.00000 | + | 6.63325i | −0.569210 | + | 0.419524i | ||||
\(251\) | 1.11684 | 0.0704946 | 0.0352473 | − | 0.999379i | \(-0.488778\pi\) | ||||
0.0352473 | + | 0.999379i | \(0.488778\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.28962i | − | 0.0810777i | ||||||
\(254\) | − | 7.57301i | − | 0.475173i | ||||||
\(255\) | 0.489125 | − | 25.6858i | 0.0306302 | − | 1.60851i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.87953i | 0.117242i | 0.998280 | + | 0.0586209i | \(0.0186703\pi\) | ||||
−0.998280 | + | 0.0586209i | \(0.981330\pi\) | |||||||
\(258\) | 0.430703 | − | 1.83324i | 0.0268144 | − | 0.114133i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.37228 | − | 0.939764i | 0.271157 | − | 0.0582817i | ||||
\(261\) | 4.43070 | − | 8.90892i | 0.274254 | − | 0.551448i | ||||
\(262\) | −10.3723 | −0.640802 | ||||||||
\(263\) | −7.37228 | −0.454594 | −0.227297 | − | 0.973825i | \(-0.572989\pi\) | ||||
−0.227297 | + | 0.973825i | \(0.572989\pi\) | |||||||
\(264\) | 0.372281 | − | 1.58457i | 0.0229123 | − | 0.0975238i | ||||
\(265\) | 9.55842 | − | 2.05446i | 0.587169 | − | 0.126204i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.31386 | + | 0.543620i | 0.141606 | + | 0.0332690i | ||||
\(268\) | 2.37686i | 0.145190i | ||||||||
\(269\) | −25.9783 | −1.58392 | −0.791961 | − | 0.610572i | \(-0.790940\pi\) | ||||
−0.791961 | + | 0.610572i | \(0.790940\pi\) | |||||||
\(270\) | 10.3030 | + | 5.37108i | 0.627020 | + | 0.326874i | ||||
\(271\) | − | 8.86263i | − | 0.538367i | −0.963089 | − | 0.269183i | \(-0.913246\pi\) | ||
0.963089 | − | 0.269183i | \(-0.0867538\pi\) | |||||||
\(272\) | 6.63325i | 0.402200i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.74456 | −0.528278 | ||||||||
\(275\) | −1.93070 | − | 4.28384i | −0.116426 | − | 0.258325i | ||||
\(276\) | −2.31386 | − | 0.543620i | −0.139278 | − | 0.0327221i | ||||
\(277\) | 9.10268i | 0.546927i | 0.961882 | + | 0.273464i | \(0.0881693\pi\) | ||||
−0.961882 | + | 0.273464i | \(0.911831\pi\) | |||||||
\(278\) | − | 8.21782i | − | 0.492872i | ||||||
\(279\) | −10.1168 | + | 20.3422i | −0.605680 | + | 1.21785i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.3870i | 0.679290i | 0.940554 | + | 0.339645i | \(0.110307\pi\) | ||||
−0.940554 | + | 0.339645i | \(0.889693\pi\) | |||||||
\(282\) | 3.37228 | − | 14.3537i | 0.200816 | − | 0.854753i | ||||
\(283\) | −16.0000 | −0.951101 | −0.475551 | − | 0.879688i | \(-0.657751\pi\) | ||||
−0.475551 | + | 0.879688i | \(0.657751\pi\) | |||||||
\(284\) | − | 8.51278i | − | 0.505140i | ||||||
\(285\) | 0.255437 | − | 13.4140i | 0.0151308 | − | 0.794575i | ||||
\(286\) | 1.87953i | 0.111139i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.68614 | − | 1.33591i | −0.158282 | − | 0.0787191i | ||||
\(289\) | −27.0000 | −1.58824 | ||||||||
\(290\) | 1.55842 | + | 7.25061i | 0.0915137 | + | 0.425770i | ||||
\(291\) | −25.4891 | − | 5.98844i | −1.49420 | − | 0.351049i | ||||
\(292\) | 2.00000 | 0.117041 | ||||||||
\(293\) | − | 21.7244i | − | 1.26915i | −0.772861 | − | 0.634576i | \(-0.781175\pi\) | ||
0.772861 | − | 0.634576i | \(-0.218825\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.6753 | + | 6.16337i | −1.66954 | + | 0.358845i | ||||
\(296\) | − | 8.21782i | − | 0.477651i | ||||||
\(297\) | −3.11684 | + | 3.75906i | −0.180858 | + | 0.218123i | ||||
\(298\) | − | 9.01011i | − | 0.521942i | ||||||
\(299\) | 2.74456 | 0.158722 | ||||||||
\(300\) | −8.50000 | + | 1.65831i | −0.490748 | + | 0.0957427i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.11684 | −0.524615 | ||||||||
\(303\) | −17.9198 | − | 4.21010i | −1.02947 | − | 0.241864i | ||||
\(304\) | 3.46410i | 0.198680i | ||||||||
\(305\) | 6.00000 | + | 27.9152i | 0.343559 | + | 1.59842i | ||||
\(306\) | 8.86141 | − | 17.8178i | 0.506573 | − | 1.01858i | ||||
\(307\) | 24.1168 | 1.37642 | 0.688210 | − | 0.725511i | \(-0.258397\pi\) | ||||
0.688210 | + | 0.725511i | \(0.258397\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.56930 | + | 0.838574i | 0.203050 | + | 0.0477048i | ||||
\(310\) | −3.55842 | − | 16.5557i | −0.202105 | − | 0.940299i | ||||
\(311\) | 20.2337 | 1.14735 | 0.573674 | − | 0.819084i | \(-0.305518\pi\) | ||||
0.573674 | + | 0.819084i | \(0.305518\pi\) | |||||||
\(312\) | 3.37228 | + | 0.792287i | 0.190918 | + | 0.0448544i | ||||
\(313\) | 3.11684 | 0.176174 | 0.0880872 | − | 0.996113i | \(-0.471925\pi\) | ||||
0.0880872 | + | 0.996113i | \(0.471925\pi\) | |||||||
\(314\) | −8.00000 | −0.451466 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.11684 | 0.512863 | ||||||||
\(317\) | 1.11684 | 0.0627282 | 0.0313641 | − | 0.999508i | \(-0.490015\pi\) | ||||
0.0313641 | + | 0.999508i | \(0.490015\pi\) | |||||||
\(318\) | 7.37228 | + | 1.73205i | 0.413417 | + | 0.0971286i | ||||
\(319\) | −3.11684 | −0.174510 | ||||||||
\(320\) | 2.18614 | − | 0.469882i | 0.122209 | − | 0.0262672i | ||||
\(321\) | 10.5475 | + | 2.47805i | 0.588707 | + | 0.138311i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.9783 | −1.27854 | ||||||||
\(324\) | 5.43070 | + | 7.17687i | 0.301706 | + | 0.398715i | ||||
\(325\) | 9.11684 | − | 4.10891i | 0.505712 | − | 0.227921i | ||||
\(326\) | − | 3.46410i | − | 0.191859i | ||||||
\(327\) | 13.6861 | + | 3.21543i | 0.756845 | + | 0.177814i | ||||
\(328\) | 7.37228 | 0.407066 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.0692967 | − | 3.63903i | 0.00381466 | − | 0.200322i | ||||
\(331\) | −24.2337 | −1.33200 | −0.666002 | − | 0.745950i | \(-0.731996\pi\) | ||||
−0.666002 | + | 0.745950i | \(0.731996\pi\) | |||||||
\(332\) | 11.8294i | 0.649223i | ||||||||
\(333\) | −10.9783 | + | 22.0742i | −0.601604 | + | 1.20966i | ||||
\(334\) | − | 14.6487i | − | 0.801541i | ||||||
\(335\) | 1.11684 | + | 5.19615i | 0.0610197 | + | 0.283896i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.644810i | 0.0351250i | 0.999846 | + | 0.0175625i | \(0.00559061\pi\) | ||||
−0.999846 | + | 0.0175625i | \(0.994409\pi\) | |||||||
\(338\) | 9.00000 | 0.489535 | ||||||||
\(339\) | −24.8614 | − | 5.84096i | −1.35029 | − | 0.317238i | ||||
\(340\) | 3.11684 | + | 14.5012i | 0.169035 | + | 0.786439i | ||||
\(341\) | 7.11684 | 0.385399 | ||||||||
\(342\) | 4.62772 | − | 9.30506i | 0.250238 | − | 0.503160i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.08724i | 0.0586201i | ||||||||
\(345\) | −5.31386 | − | 0.101190i | −0.286089 | − | 0.00544788i | ||||
\(346\) | − | 17.0256i | − | 0.915299i | ||||||
\(347\) | −1.88316 | −0.101093 | −0.0505466 | − | 0.998722i | \(-0.516096\pi\) | ||||
−0.0505466 | + | 0.998722i | \(0.516096\pi\) | |||||||
\(348\) | −1.31386 | + | 5.59230i | −0.0704303 | + | 0.299779i | ||||
\(349\) | − | 25.7407i | − | 1.37787i | −0.724824 | − | 0.688934i | \(-0.758079\pi\) | ||
0.724824 | − | 0.688934i | \(-0.241921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.00000 | − | 6.63325i | −0.427008 | − | 0.354057i | ||||
\(352\) | 0.939764i | 0.0500896i | ||||||||
\(353\) | 12.2718i | 0.653164i | 0.945169 | + | 0.326582i | \(0.105897\pi\) | ||||
−0.945169 | + | 0.326582i | \(0.894103\pi\) | |||||||
\(354\) | −22.1168 | − | 5.19615i | −1.17550 | − | 0.276172i | ||||
\(355\) | −4.00000 | − | 18.6101i | −0.212298 | − | 0.987723i | ||||
\(356\) | −1.37228 | −0.0727308 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23.6588i | 1.25041i | ||||||||
\(359\) | 27.4179i | 1.44706i | 0.690293 | + | 0.723530i | \(0.257481\pi\) | ||||
−0.690293 | + | 0.723530i | \(0.742519\pi\) | |||||||
\(360\) | −6.50000 | − | 1.65831i | −0.342580 | − | 0.0874007i | ||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | − | 8.01544i | − | 0.421282i | ||||||
\(363\) | −17.0584 | − | 4.00772i | −0.895335 | − | 0.210351i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.37228 | − | 0.939764i | 0.228856 | − | 0.0491895i | ||||
\(366\) | −5.05842 | + | 21.5306i | −0.264408 | + | 1.12542i | ||||
\(367\) | 13.2337 | 0.690793 | 0.345396 | − | 0.938457i | \(-0.387744\pi\) | ||||
0.345396 | + | 0.938457i | \(0.387744\pi\) | |||||||
\(368\) | 1.37228 | 0.0715351 | ||||||||
\(369\) | −19.8030 | − | 9.84868i | −1.03090 | − | 0.512702i | ||||
\(370\) | −3.86141 | − | 17.9653i | −0.200745 | − | 0.933972i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.00000 | − | 12.7692i | 0.155543 | − | 0.662050i | ||||
\(373\) | − | 23.3639i | − | 1.20973i | −0.796326 | − | 0.604867i | \(-0.793226\pi\) | ||
0.796326 | − | 0.604867i | \(-0.206774\pi\) | |||||||
\(374\) | −6.23369 | −0.322336 | ||||||||
\(375\) | −17.8030 | + | 7.61930i | −0.919342 | + | 0.393459i | ||||
\(376\) | 8.51278i | 0.439013i | ||||||||
\(377\) | − | 6.63325i | − | 0.341630i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.2337 | −0.628402 | −0.314201 | − | 0.949356i | \(-0.601737\pi\) | ||||
−0.314201 | + | 0.949356i | \(0.601737\pi\) | |||||||
\(380\) | 1.62772 | + | 7.57301i | 0.0835002 | + | 0.388487i | ||||
\(381\) | 3.00000 | − | 12.7692i | 0.153695 | − | 0.654184i | ||||
\(382\) | − | 17.0256i | − | 0.871103i | ||||||
\(383\) | − | 15.6434i | − | 0.799338i | −0.916659 | − | 0.399669i | \(-0.869125\pi\) | ||
0.916659 | − | 0.399669i | \(-0.130875\pi\) | |||||||
\(384\) | 1.68614 | + | 0.396143i | 0.0860455 | + | 0.0202156i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.9653i | 0.914411i | ||||||||
\(387\) | 1.45245 | − | 2.92048i | 0.0738323 | − | 0.148456i | ||||
\(388\) | 15.1168 | 0.767441 | ||||||||
\(389\) | 7.51811i | 0.381183i | 0.981669 | + | 0.190592i | \(0.0610406\pi\) | ||||
−0.981669 | + | 0.190592i | \(0.938959\pi\) | |||||||
\(390\) | 7.74456 | + | 0.147477i | 0.392161 | + | 0.00746778i | ||||
\(391\) | 9.10268i | 0.460343i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.4891 | − | 4.10891i | −0.882210 | − | 0.207267i | ||||
\(394\) | 14.2337 | 0.717083 | ||||||||
\(395\) | 19.9307 | − | 4.28384i | 1.00282 | − | 0.215543i | ||||
\(396\) | 1.25544 | − | 2.52434i | 0.0630881 | − | 0.126853i | ||||
\(397\) | 8.00000 | 0.401508 | 0.200754 | − | 0.979642i | \(-0.435661\pi\) | ||||
0.200754 | + | 0.979642i | \(0.435661\pi\) | |||||||
\(398\) | − | 1.28962i | − | 0.0646428i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.55842 | − | 2.05446i | 0.227921 | − | 0.102723i | ||||
\(401\) | − | 16.5282i | − | 0.825380i | −0.910872 | − | 0.412690i | \(-0.864589\pi\) | ||
0.910872 | − | 0.412690i | \(-0.135411\pi\) | |||||||
\(402\) | −0.941578 | + | 4.00772i | −0.0469616 | + | 0.199887i | ||||
\(403\) | 15.1460i | 0.754477i | ||||||||
\(404\) | 10.6277 | 0.528749 | ||||||||
\(405\) | 15.2446 | + | 13.1379i | 0.757508 | + | 0.652825i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.72281 | 0.382806 | ||||||||
\(408\) | −2.62772 | + | 11.1846i | −0.130091 | + | 0.553720i | ||||
\(409\) | 4.31129i | 0.213180i | 0.994303 | + | 0.106590i | \(0.0339932\pi\) | ||||
−0.994303 | + | 0.106590i | \(0.966007\pi\) | |||||||
\(410\) | 16.1168 | − | 3.46410i | 0.795954 | − | 0.171080i | ||||
\(411\) | −14.7446 | − | 3.46410i | −0.727296 | − | 0.170872i | ||||
\(412\) | −2.11684 | −0.104289 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.68614 | − | 1.83324i | −0.181164 | − | 0.0900989i | ||||
\(415\) | 5.55842 | + | 25.8607i | 0.272852 | + | 1.26945i | ||||
\(416\) | −2.00000 | −0.0980581 | ||||||||
\(417\) | 3.25544 | − | 13.8564i | 0.159419 | − | 0.678551i | ||||
\(418\) | −3.25544 | −0.159229 | ||||||||
\(419\) | 6.51087 | 0.318077 | 0.159039 | − | 0.987272i | \(-0.449161\pi\) | ||||
0.159039 | + | 0.987272i | \(0.449161\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.11684 | −0.103169 | −0.0515843 | − | 0.998669i | \(-0.516427\pi\) | ||||
−0.0515843 | + | 0.998669i | \(0.516427\pi\) | |||||||
\(422\) | −16.2337 | −0.790244 | ||||||||
\(423\) | 11.3723 | − | 22.8665i | 0.552939 | − | 1.11181i | ||||
\(424\) | −4.37228 | −0.212337 | ||||||||
\(425\) | 13.6277 | + | 30.2372i | 0.661041 | + | 1.46672i | ||||
\(426\) | 3.37228 | − | 14.3537i | 0.163388 | − | 0.695441i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.25544 | −0.302368 | ||||||||
\(429\) | −0.744563 | + | 3.16915i | −0.0359478 | + | 0.153008i | ||||
\(430\) | 0.510875 | + | 2.37686i | 0.0246366 | + | 0.114622i | ||||
\(431\) | 17.0256i | 0.820092i | 0.912065 | + | 0.410046i | \(0.134487\pi\) | ||||
−0.912065 | + | 0.410046i | \(0.865513\pi\) | |||||||
\(432\) | −4.00000 | − | 3.31662i | −0.192450 | − | 0.159571i | ||||
\(433\) | −34.0000 | −1.63394 | −0.816968 | − | 0.576683i | \(-0.804347\pi\) | ||||
−0.816968 | + | 0.576683i | \(0.804347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.244563 | + | 12.8429i | −0.0117259 | + | 0.615770i | ||||
\(436\) | −8.11684 | −0.388726 | ||||||||
\(437\) | 4.75372i | 0.227401i | ||||||||
\(438\) | 3.37228 | + | 0.792287i | 0.161134 | + | 0.0378569i | ||||
\(439\) | 2.81929i | 0.134557i | 0.997734 | + | 0.0672787i | \(0.0214317\pi\) | ||||
−0.997734 | + | 0.0672787i | \(0.978568\pi\) | |||||||
\(440\) | 0.441578 | + | 2.05446i | 0.0210514 | + | 0.0979423i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 13.2665i | − | 0.631023i | ||||||
\(443\) | −9.00000 | −0.427603 | −0.213801 | − | 0.976877i | \(-0.568585\pi\) | ||||
−0.213801 | + | 0.976877i | \(0.568585\pi\) | |||||||
\(444\) | 3.25544 | − | 13.8564i | 0.154496 | − | 0.657596i | ||||
\(445\) | −3.00000 | + | 0.644810i | −0.142214 | + | 0.0305669i | ||||
\(446\) | −0.883156 | −0.0418187 | ||||||||
\(447\) | 3.56930 | − | 15.1923i | 0.168822 | − | 0.718572i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 20.3971i | − | 0.962598i | −0.876557 | − | 0.481299i | \(-0.840165\pi\) | ||
0.876557 | − | 0.481299i | \(-0.159835\pi\) | |||||||
\(450\) | −14.9891 | − | 0.571072i | −0.706594 | − | 0.0269206i | ||||
\(451\) | 6.92820i | 0.326236i | ||||||||
\(452\) | 14.7446 | 0.693526 | ||||||||
\(453\) | −15.3723 | − | 3.61158i | −0.722253 | − | 0.169687i | ||||
\(454\) | 20.8395i | 0.978047i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.37228 | + | 5.84096i | −0.0642630 | + | 0.273528i | ||||
\(457\) | − | 2.81929i | − | 0.131881i | −0.997824 | − | 0.0659404i | \(-0.978995\pi\) | ||
0.997824 | − | 0.0659404i | \(-0.0210047\pi\) | |||||||
\(458\) | 13.8564i | 0.647467i | ||||||||
\(459\) | 22.0000 | − | 26.5330i | 1.02687 | − | 1.23845i | ||||
\(460\) | 3.00000 | − | 0.644810i | 0.139876 | − | 0.0300644i | ||||
\(461\) | 23.4891 | 1.09400 | 0.546999 | − | 0.837133i | \(-0.315770\pi\) | ||||
0.546999 | + | 0.837133i | \(0.315770\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.72582i | 0.312576i | 0.987712 | + | 0.156288i | \(0.0499527\pi\) | ||||
−0.987712 | + | 0.156288i | \(0.950047\pi\) | |||||||
\(464\) | − | 3.31662i | − | 0.153970i | ||||||
\(465\) | 0.558422 | − | 29.3248i | 0.0258962 | − | 1.35991i | ||||
\(466\) | −0.510875 | −0.0236658 | ||||||||
\(467\) | − | 36.4280i | − | 1.68569i | −0.538160 | − | 0.842843i | \(-0.680880\pi\) | ||
0.538160 | − | 0.842843i | \(-0.319120\pi\) | |||||||
\(468\) | 5.37228 | + | 2.67181i | 0.248334 | + | 0.123505i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.00000 | + | 18.6101i | 0.184506 | + | 0.858421i | ||||
\(471\) | −13.4891 | − | 3.16915i | −0.621546 | − | 0.146027i | ||||
\(472\) | 13.1168 | 0.603752 | ||||||||
\(473\) | −1.02175 | −0.0469801 | ||||||||
\(474\) | 15.3723 | + | 3.61158i | 0.706072 | + | 0.165885i | ||||
\(475\) | 7.11684 | + | 15.7908i | 0.326543 | + | 0.724533i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.7446 | + | 5.84096i | 0.537747 | + | 0.267439i | ||||
\(478\) | 23.6588i | 1.08213i | ||||||||
\(479\) | 2.74456 | 0.125402 | 0.0627011 | − | 0.998032i | \(-0.480029\pi\) | ||||
0.0627011 | + | 0.998032i | \(0.480029\pi\) | |||||||
\(480\) | 3.87228 | + | 0.0737384i | 0.176745 | + | 0.00336568i | ||||
\(481\) | 16.4356i | 0.749401i | ||||||||
\(482\) | 19.2549i | 0.877038i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.1168 | 0.459857 | ||||||||
\(485\) | 33.0475 | − | 7.10313i | 1.50061 | − | 0.322537i | ||||
\(486\) | 6.31386 | + | 14.2525i | 0.286402 | + | 0.646509i | ||||
\(487\) | 14.5012i | 0.657113i | 0.944484 | + | 0.328556i | \(0.106562\pi\) | ||||
−0.944484 | + | 0.328556i | \(0.893438\pi\) | |||||||
\(488\) | − | 12.7692i | − | 0.578033i | ||||||
\(489\) | 1.37228 | − | 5.84096i | 0.0620567 | − | 0.264137i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.2372i | 1.36458i | 0.731080 | + | 0.682292i | \(0.239017\pi\) | ||||
−0.731080 | + | 0.682292i | \(0.760983\pi\) | |||||||
\(492\) | 12.4307 | + | 2.92048i | 0.560419 | + | 0.131665i | ||||
\(493\) | 22.0000 | 0.990830 | ||||||||
\(494\) | − | 6.92820i | − | 0.311715i | ||||||
\(495\) | 1.55842 | − | 6.10846i | 0.0700459 | − | 0.274555i | ||||
\(496\) | 7.57301i | 0.340038i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.68614 | + | 19.9460i | −0.209991 | + | 0.893803i | ||||
\(499\) | −6.23369 | −0.279058 | −0.139529 | − | 0.990218i | \(-0.544559\pi\) | ||||
−0.139529 | + | 0.990218i | \(0.544559\pi\) | |||||||
\(500\) | 9.00000 | − | 6.63325i | 0.402492 | − | 0.296648i | ||||
\(501\) | 5.80298 | − | 24.6998i | 0.259258 | − | 1.10350i | ||||
\(502\) | −1.11684 | −0.0498472 | ||||||||
\(503\) | − | 6.13592i | − | 0.273587i | −0.990600 | − | 0.136793i | \(-0.956320\pi\) | ||
0.990600 | − | 0.136793i | \(-0.0436797\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.2337 | − | 4.99377i | 1.03389 | − | 0.222220i | ||||
\(506\) | 1.28962i | 0.0573306i | ||||||||
\(507\) | 15.1753 | + | 3.56529i | 0.673957 | + | 0.158340i | ||||
\(508\) | 7.57301i | 0.335998i | ||||||||
\(509\) | −11.7446 | −0.520569 | −0.260284 | − | 0.965532i | \(-0.583816\pi\) | ||||
−0.260284 | + | 0.965532i | \(0.583816\pi\) | |||||||
\(510\) | −0.489125 | + | 25.6858i | −0.0216588 | + | 1.13739i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 11.4891 | − | 13.8564i | 0.507257 | − | 0.611775i | ||||
\(514\) | − | 1.87953i | − | 0.0829024i | ||||||
\(515\) | −4.62772 | + | 0.994667i | −0.203922 | + | 0.0438303i | ||||
\(516\) | −0.430703 | + | 1.83324i | −0.0189607 | + | 0.0807039i | ||||
\(517\) | −8.00000 | −0.351840 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.74456 | − | 28.7075i | 0.296053 | − | 1.26012i | ||||
\(520\) | −4.37228 | + | 0.939764i | −0.191737 | + | 0.0412114i | ||||
\(521\) | −14.7446 | −0.645971 | −0.322986 | − | 0.946404i | \(-0.604687\pi\) | ||||
−0.322986 | + | 0.946404i | \(0.604687\pi\) | |||||||
\(522\) | −4.43070 | + | 8.90892i | −0.193927 | + | 0.389933i | ||||
\(523\) | 10.2337 | 0.447488 | 0.223744 | − | 0.974648i | \(-0.428172\pi\) | ||||
0.223744 | + | 0.974648i | \(0.428172\pi\) | |||||||
\(524\) | 10.3723 | 0.453115 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.37228 | 0.321447 | ||||||||
\(527\) | −50.2337 | −2.18821 | ||||||||
\(528\) | −0.372281 | + | 1.58457i | −0.0162015 | + | 0.0689597i | ||||
\(529\) | −21.1168 | −0.918124 | ||||||||
\(530\) | −9.55842 | + | 2.05446i | −0.415191 | + | 0.0892399i | ||||
\(531\) | −35.2337 | − | 17.5229i | −1.52901 | − | 0.760429i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.7446 | −0.638658 | ||||||||
\(534\) | −2.31386 | − | 0.543620i | −0.100130 | − | 0.0235248i | ||||
\(535\) | −13.6753 | + | 2.93932i | −0.591233 | + | 0.127078i | ||||
\(536\) | − | 2.37686i | − | 0.102665i | ||||||
\(537\) | −9.37228 | + | 39.8921i | −0.404444 | + | 1.72147i | ||||
\(538\) | 25.9783 | 1.12000 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −10.3030 | − | 5.37108i | −0.443370 | − | 0.231135i | ||||
\(541\) | 38.3505 | 1.64882 | 0.824409 | − | 0.565994i | \(-0.191508\pi\) | ||||
0.824409 | + | 0.565994i | \(0.191508\pi\) | |||||||
\(542\) | 8.86263i | 0.380683i | ||||||||
\(543\) | 3.17527 | − | 13.5152i | 0.136264 | − | 0.579991i | ||||
\(544\) | − | 6.63325i | − | 0.284398i | ||||||
\(545\) | −17.7446 | + | 3.81396i | −0.760094 | + | 0.163372i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.30506i | 0.397856i | 0.980014 | + | 0.198928i | \(0.0637460\pi\) | ||||
−0.980014 | + | 0.198928i | \(0.936254\pi\) | |||||||
\(548\) | 8.74456 | 0.373549 | ||||||||
\(549\) | −17.0584 | + | 34.2998i | −0.728036 | + | 1.46388i | ||||
\(550\) | 1.93070 | + | 4.28384i | 0.0823255 | + | 0.182664i | ||||
\(551\) | 11.4891 | 0.489453 | ||||||||
\(552\) | 2.31386 | + | 0.543620i | 0.0984844 | + | 0.0231380i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 9.10268i | − | 0.386736i | ||||||
\(555\) | 0.605969 | − | 31.8217i | 0.0257220 | − | 1.35076i | ||||
\(556\) | 8.21782i | 0.348513i | ||||||||
\(557\) | −27.8614 | −1.18053 | −0.590263 | − | 0.807211i | \(-0.700976\pi\) | ||||
−0.590263 | + | 0.807211i | \(0.700976\pi\) | |||||||
\(558\) | 10.1168 | − | 20.3422i | 0.428280 | − | 0.861153i | ||||
\(559\) | − | 2.17448i | − | 0.0919708i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.5109 | − | 2.46943i | −0.443769 | − | 0.104260i | ||||
\(562\) | − | 11.3870i | − | 0.480330i | ||||||
\(563\) | 1.43710i | 0.0605664i | 0.999541 | + | 0.0302832i | \(0.00964092\pi\) | ||||
−0.999541 | + | 0.0302832i | \(0.990359\pi\) | |||||||
\(564\) | −3.37228 | + | 14.3537i | −0.141999 | + | 0.604401i | ||||
\(565\) | 32.2337 | − | 6.92820i | 1.35608 | − | 0.291472i | ||||
\(566\) | 16.0000 | 0.672530 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.51278i | 0.357188i | ||||||||
\(569\) | 11.3870i | 0.477367i | 0.971097 | + | 0.238683i | \(0.0767158\pi\) | ||||
−0.971097 | + | 0.238683i | \(0.923284\pi\) | |||||||
\(570\) | −0.255437 | + | 13.4140i | −0.0106991 | + | 0.561850i | ||||
\(571\) | −0.233688 | −0.00977954 | −0.00488977 | − | 0.999988i | \(-0.501556\pi\) | ||||
−0.00488977 | + | 0.999988i | \(0.501556\pi\) | |||||||
\(572\) | − | 1.87953i | − | 0.0785870i | ||||||
\(573\) | 6.74456 | − | 28.7075i | 0.281758 | − | 1.19927i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.25544 | − | 2.81929i | 0.260870 | − | 0.117573i | ||||
\(576\) | 2.68614 | + | 1.33591i | 0.111923 | + | 0.0556628i | ||||
\(577\) | −35.1168 | −1.46193 | −0.730967 | − | 0.682413i | \(-0.760931\pi\) | ||||
−0.730967 | + | 0.682413i | \(0.760931\pi\) | |||||||
\(578\) | 27.0000 | 1.12305 | ||||||||
\(579\) | −7.11684 | + | 30.2921i | −0.295766 | + | 1.25889i | ||||
\(580\) | −1.55842 | − | 7.25061i | −0.0647100 | − | 0.301065i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 25.4891 | + | 5.98844i | 1.05656 | + | 0.248229i | ||||
\(583\) | − | 4.10891i | − | 0.170174i | ||||||
\(584\) | −2.00000 | −0.0827606 | ||||||||
\(585\) | 13.0000 | + | 3.31662i | 0.537484 | + | 0.137126i | ||||
\(586\) | 21.7244i | 0.897426i | ||||||||
\(587\) | − | 0.0549029i | − | 0.00226608i | −0.999999 | − | 0.00113304i | \(-0.999639\pi\) | ||
0.999999 | − | 0.00113304i | \(-0.000360659\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.2337 | −1.08094 | ||||||||
\(590\) | 28.6753 | − | 6.16337i | 1.18054 | − | 0.253742i | ||||
\(591\) | 24.0000 | + | 5.63858i | 0.987228 | + | 0.231940i | ||||
\(592\) | 8.21782i | 0.337750i | ||||||||
\(593\) | 27.4179i | 1.12592i | 0.826485 | + | 0.562958i | \(0.190337\pi\) | ||||
−0.826485 | + | 0.562958i | \(0.809663\pi\) | |||||||
\(594\) | 3.11684 | − | 3.75906i | 0.127886 | − | 0.154236i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.01011i | 0.369069i | ||||||||
\(597\) | 0.510875 | − | 2.17448i | 0.0209087 | − | 0.0889956i | ||||
\(598\) | −2.74456 | −0.112234 | ||||||||
\(599\) | 1.87953i | 0.0767954i | 0.999263 | + | 0.0383977i | \(0.0122254\pi\) | ||||
−0.999263 | + | 0.0383977i | \(0.987775\pi\) | |||||||
\(600\) | 8.50000 | − | 1.65831i | 0.347011 | − | 0.0677003i | ||||
\(601\) | 19.2549i | 0.785425i | 0.919661 | + | 0.392713i | \(0.128463\pi\) | ||||
−0.919661 | + | 0.392713i | \(0.871537\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.17527 | + | 6.38458i | −0.129307 | + | 0.260000i | ||||
\(604\) | 9.11684 | 0.370959 | ||||||||
\(605\) | 22.1168 | − | 4.75372i | 0.899178 | − | 0.193266i | ||||
\(606\) | 17.9198 | + | 4.21010i | 0.727943 | + | 0.171024i | ||||
\(607\) | −41.4674 | −1.68311 | −0.841554 | − | 0.540172i | \(-0.818359\pi\) | ||||
−0.841554 | + | 0.540172i | \(0.818359\pi\) | |||||||
\(608\) | − | 3.46410i | − | 0.140488i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.00000 | − | 27.9152i | −0.242933 | − | 1.13025i | ||||
\(611\) | − | 17.0256i | − | 0.688780i | ||||||
\(612\) | −8.86141 | + | 17.8178i | −0.358201 | + | 0.720244i | ||||
\(613\) | 26.8280i | 1.08357i | 0.840517 | + | 0.541785i | \(0.182251\pi\) | ||||
−0.840517 | + | 0.541785i | \(0.817749\pi\) | |||||||
\(614\) | −24.1168 | −0.973277 | ||||||||
\(615\) | 28.5475 | + | 0.543620i | 1.15115 | + | 0.0219209i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.9783 | 1.89127 | 0.945637 | − | 0.325225i | \(-0.105440\pi\) | ||||
0.945637 | + | 0.325225i | \(0.105440\pi\) | |||||||
\(618\) | −3.56930 | − | 0.838574i | −0.143578 | − | 0.0337324i | ||||
\(619\) | − | 16.4356i | − | 0.660604i | −0.943875 | − | 0.330302i | \(-0.892849\pi\) | ||
0.943875 | − | 0.330302i | \(-0.107151\pi\) | |||||||
\(620\) | 3.55842 | + | 16.5557i | 0.142910 | + | 0.664892i | ||||
\(621\) | −5.48913 | − | 4.55134i | −0.220271 | − | 0.182639i | ||||
\(622\) | −20.2337 | −0.811297 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.37228 | − | 0.792287i | −0.134999 | − | 0.0317169i | ||||
\(625\) | 16.5584 | − | 18.7302i | 0.662337 | − | 0.749206i | ||||
\(626\) | −3.11684 | −0.124574 | ||||||||
\(627\) | −5.48913 | − | 1.28962i | −0.219215 | − | 0.0515025i | ||||
\(628\) | 8.00000 | 0.319235 | ||||||||
\(629\) | −54.5109 | −2.17349 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.8832 | 0.512870 | 0.256435 | − | 0.966561i | \(-0.417452\pi\) | ||||
0.256435 | + | 0.966561i | \(0.417452\pi\) | |||||||
\(632\) | −9.11684 | −0.362649 | ||||||||
\(633\) | −27.3723 | − | 6.43087i | −1.08795 | − | 0.255604i | ||||
\(634\) | −1.11684 | −0.0443555 | ||||||||
\(635\) | 3.55842 | + | 16.5557i | 0.141212 | + | 0.656992i | ||||
\(636\) | −7.37228 | − | 1.73205i | −0.292330 | − | 0.0686803i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.11684 | 0.123397 | ||||||||
\(639\) | 11.3723 | − | 22.8665i | 0.449880 | − | 0.904585i | ||||
\(640\) | −2.18614 | + | 0.469882i | −0.0864148 | + | 0.0185737i | ||||
\(641\) | 9.01011i | 0.355878i | 0.984042 | + | 0.177939i | \(0.0569430\pi\) | ||||
−0.984042 | + | 0.177939i | \(0.943057\pi\) | |||||||
\(642\) | −10.5475 | − | 2.47805i | −0.416278 | − | 0.0978009i | ||||
\(643\) | −18.2337 | −0.719066 | −0.359533 | − | 0.933132i | \(-0.617064\pi\) | ||||
−0.359533 | + | 0.933132i | \(0.617064\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.0801714 | + | 4.21010i | −0.00315675 | + | 0.165773i | ||||
\(646\) | 22.9783 | 0.904067 | ||||||||
\(647\) | − | 42.0666i | − | 1.65381i | −0.562344 | − | 0.826903i | \(-0.690100\pi\) | ||
0.562344 | − | 0.826903i | \(-0.309900\pi\) | |||||||
\(648\) | −5.43070 | − | 7.17687i | −0.213338 | − | 0.281934i | ||||
\(649\) | 12.3267i | 0.483867i | ||||||||
\(650\) | −9.11684 | + | 4.10891i | −0.357592 | + | 0.161165i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.46410i | 0.135665i | ||||||||
\(653\) | 16.3723 | 0.640697 | 0.320348 | − | 0.947300i | \(-0.396200\pi\) | ||||
0.320348 | + | 0.947300i | \(0.396200\pi\) | |||||||
\(654\) | −13.6861 | − | 3.21543i | −0.535170 | − | 0.125733i | ||||
\(655\) | 22.6753 | − | 4.87375i | 0.885996 | − | 0.190433i | ||||
\(656\) | −7.37228 | −0.287839 | ||||||||
\(657\) | 5.37228 | + | 2.67181i | 0.209593 | + | 0.104237i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.1407i | 0.628752i | 0.949299 | + | 0.314376i | \(0.101795\pi\) | ||||
−0.949299 | + | 0.314376i | \(0.898205\pi\) | |||||||
\(660\) | −0.0692967 | + | 3.63903i | −0.00269737 | + | 0.141649i | ||||
\(661\) | 12.7692i | 0.496663i | 0.968675 | + | 0.248331i | \(0.0798822\pi\) | ||||
−0.968675 | + | 0.248331i | \(0.920118\pi\) | |||||||
\(662\) | 24.2337 | 0.941869 | ||||||||
\(663\) | 5.25544 | − | 22.3692i | 0.204104 | − | 0.868747i | ||||
\(664\) | − | 11.8294i | − | 0.459070i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.9783 | − | 22.0742i | 0.425399 | − | 0.855359i | ||||
\(667\) | − | 4.55134i | − | 0.176229i | ||||||
\(668\) | 14.6487i | 0.566775i | ||||||||
\(669\) | −1.48913 | − | 0.349857i | −0.0575729 | − | 0.0135262i | ||||
\(670\) | −1.11684 | − | 5.19615i | −0.0431474 | − | 0.200745i | ||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 46.9678i | − | 1.81047i | −0.424907 | − | 0.905237i | \(-0.639693\pi\) | ||
0.424907 | − | 0.905237i | \(-0.360307\pi\) | |||||||
\(674\) | − | 0.644810i | − | 0.0248372i | ||||||
\(675\) | −25.0475 | − | 6.90075i | −0.964081 | − | 0.265610i | ||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | − | 1.82462i | − | 0.0701260i | −0.999385 | − | 0.0350630i | \(-0.988837\pi\) | ||
0.999385 | − | 0.0350630i | \(-0.0111632\pi\) | |||||||
\(678\) | 24.8614 | + | 5.84096i | 0.954797 | + | 0.224321i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.11684 | − | 14.5012i | −0.119526 | − | 0.556096i | ||||
\(681\) | −8.25544 | + | 35.1383i | −0.316349 | + | 1.34650i | ||||
\(682\) | −7.11684 | −0.272518 | ||||||||
\(683\) | −31.9783 | −1.22361 | −0.611807 | − | 0.791007i | \(-0.709557\pi\) | ||||
−0.611807 | + | 0.791007i | \(0.709557\pi\) | |||||||
\(684\) | −4.62772 | + | 9.30506i | −0.176945 | + | 0.355788i | ||||
\(685\) | 19.1168 | − | 4.10891i | 0.730417 | − | 0.156993i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.48913 | + | 23.3639i | −0.209423 | + | 0.891386i | ||||
\(688\) | − | 1.08724i | − | 0.0414507i | ||||||
\(689\) | 8.74456 | 0.333141 | ||||||||
\(690\) | 5.31386 | + | 0.101190i | 0.202295 | + | 0.00385223i | ||||
\(691\) | − | 9.50744i | − | 0.361680i | −0.983513 | − | 0.180840i | \(-0.942118\pi\) | ||
0.983513 | − | 0.180840i | \(-0.0578817\pi\) | |||||||
\(692\) | 17.0256i | 0.647214i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.88316 | 0.0714836 | ||||||||
\(695\) | 3.86141 | + | 17.9653i | 0.146472 | + | 0.681463i | ||||
\(696\) | 1.31386 | − | 5.59230i | 0.0498017 | − | 0.211975i | ||||
\(697\) | − | 48.9022i | − | 1.85230i | ||||||
\(698\) | 25.7407i | 0.974300i | ||||||||
\(699\) | −0.861407 | − | 0.202380i | −0.0325814 | − | 0.00765470i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 39.2473i | − | 1.48235i | −0.671313 | − | 0.741174i | \(-0.734269\pi\) | ||
0.671313 | − | 0.741174i | \(-0.265731\pi\) | |||||||
\(702\) | 8.00000 | + | 6.63325i | 0.301941 | + | 0.250356i | ||||
\(703\) | −28.4674 | −1.07367 | ||||||||
\(704\) | − | 0.939764i | − | 0.0354187i | ||||||
\(705\) | −0.627719 | + | 32.9639i | −0.0236413 | + | 1.24149i | ||||
\(706\) | − | 12.2718i | − | 0.461857i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 22.1168 | + | 5.19615i | 0.831202 | + | 0.195283i | ||||
\(709\) | 12.1168 | 0.455058 | 0.227529 | − | 0.973771i | \(-0.426935\pi\) | ||||
0.227529 | + | 0.973771i | \(0.426935\pi\) | |||||||
\(710\) | 4.00000 | + | 18.6101i | 0.150117 | + | 0.698426i | ||||
\(711\) | 24.4891 | + | 12.1793i | 0.918414 | + | 0.456758i | ||||
\(712\) | 1.37228 | 0.0514284 | ||||||||
\(713\) | 10.3923i | 0.389195i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.883156 | − | 4.10891i | −0.0330282 | − | 0.153665i | ||||
\(716\) | − | 23.6588i | − | 0.884171i | ||||||
\(717\) | −9.37228 | + | 39.8921i | −0.350014 | + | 1.48980i | ||||
\(718\) | − | 27.4179i | − | 1.02323i | ||||||
\(719\) | 44.7446 | 1.66869 | 0.834345 | − | 0.551242i | \(-0.185846\pi\) | ||||
0.834345 | + | 0.551242i | \(0.185846\pi\) | |||||||
\(720\) | 6.50000 | + | 1.65831i | 0.242241 | + | 0.0618017i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.00000 | −0.260513 | ||||||||
\(723\) | −7.62772 | + | 32.4665i | −0.283678 | + | 1.20744i | ||||
\(724\) | 8.01544i | 0.297892i | ||||||||
\(725\) | −6.81386 | − | 15.1186i | −0.253060 | − | 0.561490i | ||||
\(726\) | 17.0584 | + | 4.00772i | 0.633097 | + | 0.148741i | ||||
\(727\) | −19.0000 | −0.704671 | −0.352335 | − | 0.935874i | \(-0.614612\pi\) | ||||
−0.352335 | + | 0.935874i | \(0.614612\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.00000 | + | 26.5330i | 0.185185 | + | 0.982704i | ||||
\(730\) | −4.37228 | + | 0.939764i | −0.161825 | + | 0.0347822i | ||||
\(731\) | 7.21194 | 0.266743 | ||||||||
\(732\) | 5.05842 | − | 21.5306i | 0.186965 | − | 0.795794i | ||||
\(733\) | −32.4674 | −1.19921 | −0.599605 | − | 0.800296i | \(-0.704676\pi\) | ||||
−0.599605 | + | 0.800296i | \(0.704676\pi\) | |||||||
\(734\) | −13.2337 | −0.488464 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.37228 | −0.0505830 | ||||||||
\(737\) | 2.23369 | 0.0822790 | ||||||||
\(738\) | 19.8030 | + | 9.84868i | 0.728958 | + | 0.362535i | ||||
\(739\) | −1.76631 | −0.0649748 | −0.0324874 | − | 0.999472i | \(-0.510343\pi\) | ||||
−0.0324874 | + | 0.999472i | \(0.510343\pi\) | |||||||
\(740\) | 3.86141 | + | 17.9653i | 0.141948 | + | 0.660418i | ||||
\(741\) | 2.74456 | − | 11.6819i | 0.100824 | − | 0.429146i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.6060 | −0.792646 | −0.396323 | − | 0.918111i | \(-0.629714\pi\) | ||||
−0.396323 | + | 0.918111i | \(0.629714\pi\) | |||||||
\(744\) | −3.00000 | + | 12.7692i | −0.109985 | + | 0.468140i | ||||
\(745\) | 4.23369 | + | 19.6974i | 0.155110 | + | 0.721656i | ||||
\(746\) | 23.3639i | 0.855411i | ||||||||
\(747\) | −15.8030 | + | 31.7754i | −0.578201 | + | 1.16260i | ||||
\(748\) | 6.23369 | 0.227926 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 17.8030 | − | 7.61930i | 0.650073 | − | 0.278218i | ||||
\(751\) | 24.8832 | 0.907999 | 0.454000 | − | 0.891002i | \(-0.349997\pi\) | ||||
0.454000 | + | 0.891002i | \(0.349997\pi\) | |||||||
\(752\) | − | 8.51278i | − | 0.310429i | ||||||
\(753\) | −1.88316 | − | 0.442430i | −0.0686260 | − | 0.0161231i | ||||
\(754\) | 6.63325i | 0.241569i | ||||||||
\(755\) | 19.9307 | − | 4.28384i | 0.725353 | − | 0.155905i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 25.5383i | − | 0.928206i | −0.885781 | − | 0.464103i | \(-0.846377\pi\) | ||
0.885781 | − | 0.464103i | \(-0.153623\pi\) | |||||||
\(758\) | 12.2337 | 0.444348 | ||||||||
\(759\) | −0.510875 | + | 2.17448i | −0.0185436 | + | 0.0789287i | ||||
\(760\) | −1.62772 | − | 7.57301i | −0.0590436 | − | 0.274702i | ||||
\(761\) | 7.02175 | 0.254538 | 0.127269 | − | 0.991868i | \(-0.459379\pi\) | ||||
0.127269 | + | 0.991868i | \(0.459379\pi\) | |||||||
\(762\) | −3.00000 | + | 12.7692i | −0.108679 | + | 0.462578i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17.0256i | 0.615963i | ||||||||
\(765\) | −11.0000 | + | 43.1161i | −0.397706 | + | 1.55887i | ||||
\(766\) | 15.6434i | 0.565218i | ||||||||
\(767\) | −26.2337 | −0.947244 | ||||||||
\(768\) | −1.68614 | − | 0.396143i | −0.0608434 | − | 0.0142946i | ||||
\(769\) | − | 30.5321i | − | 1.10102i | −0.834830 | − | 0.550508i | \(-0.814434\pi\) | ||
0.834830 | − | 0.550508i | \(-0.185566\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.744563 | − | 3.16915i | 0.0268148 | − | 0.114134i | ||||
\(772\) | − | 17.9653i | − | 0.646586i | ||||||
\(773\) | − | 8.51278i | − | 0.306183i | −0.988212 | − | 0.153092i | \(-0.951077\pi\) | ||
0.988212 | − | 0.153092i | \(-0.0489230\pi\) | |||||||
\(774\) | −1.45245 | + | 2.92048i | −0.0522073 | + | 0.104975i | ||||
\(775\) | 15.5584 | + | 34.5210i | 0.558875 | + | 1.24003i | ||||
\(776\) | −15.1168 | −0.542663 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 7.51811i | − | 0.269537i | ||||||
\(779\) | − | 25.5383i | − | 0.915006i | ||||||
\(780\) | −7.74456 | − | 0.147477i | −0.277300 | − | 0.00528052i | ||||
\(781\) | −8.00000 | −0.286263 | ||||||||
\(782\) | − | 9.10268i | − | 0.325511i | ||||||
\(783\) | −11.0000 | + | 13.2665i | −0.393108 | + | 0.474106i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.4891 | − | 3.75906i | 0.624214 | − | 0.134166i | ||||
\(786\) | 17.4891 | + | 4.10891i | 0.623816 | + | 0.146560i | ||||
\(787\) | 9.88316 | 0.352296 | 0.176148 | − | 0.984364i | \(-0.443636\pi\) | ||||
0.176148 | + | 0.984364i | \(0.443636\pi\) | |||||||
\(788\) | −14.2337 | −0.507054 | ||||||||
\(789\) | 12.4307 | + | 2.92048i | 0.442545 | + | 0.103972i | ||||
\(790\) | −19.9307 | + | 4.28384i | −0.709103 | + | 0.152412i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.25544 | + | 2.52434i | −0.0446100 | + | 0.0896984i | ||||
\(793\) | 25.5383i | 0.906893i | ||||||||
\(794\) | −8.00000 | −0.283909 | ||||||||
\(795\) | −16.9307 | − | 0.322405i | −0.600470 | − | 0.0114345i | ||||
\(796\) | 1.28962i | 0.0457094i | ||||||||
\(797\) | − | 0.939764i | − | 0.0332881i | −0.999861 | − | 0.0166441i | \(-0.994702\pi\) | ||
0.999861 | − | 0.0166441i | \(-0.00529822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 56.4674 | 1.99767 | ||||||||
\(800\) | −4.55842 | + | 2.05446i | −0.161165 | + | 0.0726360i | ||||
\(801\) | −3.68614 | − | 1.83324i | −0.130243 | − | 0.0647744i | ||||
\(802\) | 16.5282i | 0.583632i | ||||||||
\(803\) | − | 1.87953i | − | 0.0663271i | ||||||
\(804\) | 0.941578 | − | 4.00772i | 0.0332069 | − | 0.141341i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 15.1460i | − | 0.533496i | ||||||
\(807\) | 43.8030 | + | 10.2911i | 1.54194 | + | 0.362264i | ||||
\(808\) | −10.6277 | −0.373882 | ||||||||
\(809\) | − | 42.0666i | − | 1.47898i | −0.673167 | − | 0.739491i | \(-0.735066\pi\) | ||
0.673167 | − | 0.739491i | \(-0.264934\pi\) | |||||||
\(810\) | −15.2446 | − | 13.1379i | −0.535639 | − | 0.461617i | ||||
\(811\) | − | 10.3923i | − | 0.364923i | −0.983213 | − | 0.182462i | \(-0.941593\pi\) | ||
0.983213 | − | 0.182462i | \(-0.0584065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.51087 | + | 14.9436i | −0.123132 | + | 0.524097i | ||||
\(814\) | −7.72281 | −0.270684 | ||||||||
\(815\) | 1.62772 | + | 7.57301i | 0.0570165 | + | 0.265271i | ||||
\(816\) | 2.62772 | − | 11.1846i | 0.0919886 | − | 0.391539i | ||||
\(817\) | 3.76631 | 0.131767 | ||||||||
\(818\) | − | 4.31129i | − | 0.150741i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16.1168 | + | 3.46410i | −0.562825 | + | 0.120972i | ||||
\(821\) | 4.69882i | 0.163990i | 0.996633 | + | 0.0819950i | \(0.0261291\pi\) | ||||
−0.996633 | + | 0.0819950i | \(0.973871\pi\) | |||||||
\(822\) | 14.7446 | + | 3.46410i | 0.514276 | + | 0.120824i | ||||
\(823\) | 13.6540i | 0.475949i | 0.971271 | + | 0.237975i | \(0.0764835\pi\) | ||||
−0.971271 | + | 0.237975i | \(0.923516\pi\) | |||||||
\(824\) | 2.11684 | 0.0737438 | ||||||||
\(825\) | 1.55842 | + | 7.98799i | 0.0542573 | + | 0.278106i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.0000 | −1.14752 | −0.573761 | − | 0.819023i | \(-0.694516\pi\) | ||||
−0.573761 | + | 0.819023i | \(0.694516\pi\) | |||||||
\(828\) | 3.68614 | + | 1.83324i | 0.128102 | + | 0.0637095i | ||||
\(829\) | 1.28962i | 0.0447904i | 0.999749 | + | 0.0223952i | \(0.00712920\pi\) | ||||
−0.999749 | + | 0.0223952i | \(0.992871\pi\) | |||||||
\(830\) | −5.55842 | − | 25.8607i | −0.192936 | − | 0.897639i | ||||
\(831\) | 3.60597 | − | 15.3484i | 0.125090 | − | 0.532430i | ||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.25544 | + | 13.8564i | −0.112727 | + | 0.479808i | ||||
\(835\) | 6.88316 | + | 32.0241i | 0.238201 | + | 1.10824i | ||||
\(836\) | 3.25544 | 0.112592 | ||||||||
\(837\) | 25.1168 | − | 30.2921i | 0.868165 | − | 1.04705i | ||||
\(838\) | −6.51087 | −0.224914 | ||||||||
\(839\) | 55.7228 | 1.92377 | 0.961883 | − | 0.273463i | \(-0.0881690\pi\) | ||||
0.961883 | + | 0.273463i | \(0.0881690\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.0000 | 0.620690 | ||||||||
\(842\) | 2.11684 | 0.0729513 | ||||||||
\(843\) | 4.51087 | − | 19.2000i | 0.155363 | − | 0.661284i | ||||
\(844\) | 16.2337 | 0.558787 | ||||||||
\(845\) | −19.6753 | + | 4.22894i | −0.676850 | + | 0.145480i | ||||
\(846\) | −11.3723 | + | 22.8665i | −0.390987 | + | 0.786167i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.37228 | 0.150145 | ||||||||
\(849\) | 26.9783 | + | 6.33830i | 0.925891 | + | 0.217530i | ||||
\(850\) | −13.6277 | − | 30.2372i | −0.467427 | − | 1.03713i | ||||
\(851\) | 11.2772i | 0.386576i | ||||||||
\(852\) | −3.37228 | + | 14.3537i | −0.115532 | + | 0.491751i | ||||
\(853\) | −38.4674 | −1.31710 | −0.658549 | − | 0.752538i | \(-0.728829\pi\) | ||||
−0.658549 | + | 0.752538i | \(0.728829\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.74456 | + | 22.5167i | −0.196460 | + | 0.770054i | ||||
\(856\) | 6.25544 | 0.213806 | ||||||||
\(857\) | − | 24.5437i | − | 0.838396i | −0.907895 | − | 0.419198i | \(-0.862311\pi\) | ||
0.907895 | − | 0.419198i | \(-0.137689\pi\) | |||||||
\(858\) | 0.744563 | − | 3.16915i | 0.0254189 | − | 0.108193i | ||||
\(859\) | 46.7277i | 1.59433i | 0.603762 | + | 0.797164i | \(0.293668\pi\) | ||||
−0.603762 | + | 0.797164i | \(0.706332\pi\) | |||||||
\(860\) | −0.510875 | − | 2.37686i | −0.0174207 | − | 0.0810503i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 17.0256i | − | 0.579893i | ||||||
\(863\) | −13.3723 | −0.455198 | −0.227599 | − | 0.973755i | \(-0.573087\pi\) | ||||
−0.227599 | + | 0.973755i | \(0.573087\pi\) | |||||||
\(864\) | 4.00000 | + | 3.31662i | 0.136083 | + | 0.112834i | ||||
\(865\) | 8.00000 | + | 37.2203i | 0.272008 | + | 1.26553i | ||||
\(866\) | 34.0000 | 1.15537 | ||||||||
\(867\) | 45.5258 | + | 10.6959i | 1.54614 | + | 0.363251i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 8.56768i | − | 0.290639i | ||||||
\(870\) | 0.244563 | − | 12.8429i | 0.00829145 | − | 0.435415i | ||||
\(871\) | 4.75372i | 0.161074i | ||||||||
\(872\) | 8.11684 | 0.274871 | ||||||||
\(873\) | 40.6060 | + | 20.1947i | 1.37430 | + | 0.683487i | ||||
\(874\) | − | 4.75372i | − | 0.160797i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.37228 | − | 0.792287i | −0.113939 | − | 0.0267689i | ||||
\(877\) | − | 28.1176i | − | 0.949463i | −0.880131 | − | 0.474731i | \(-0.842545\pi\) | ||
0.880131 | − | 0.474731i | \(-0.157455\pi\) | |||||||
\(878\) | − | 2.81929i | − | 0.0951465i | ||||||
\(879\) | −8.60597 | + | 36.6303i | −0.290272 | + | 1.23551i | ||||
\(880\) | −0.441578 | − | 2.05446i | −0.0148856 | − | 0.0692557i | ||||
\(881\) | −0.350532 | −0.0118097 | −0.00590486 | − | 0.999983i | \(-0.501880\pi\) | ||||
−0.00590486 | + | 0.999983i | \(0.501880\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 44.5532i | − | 1.49934i | −0.661815 | − | 0.749668i | \(-0.730213\pi\) | ||
0.661815 | − | 0.749668i | \(-0.269787\pi\) | |||||||
\(884\) | 13.2665i | 0.446201i | ||||||||
\(885\) | 50.7921 | + | 0.967215i | 1.70736 | + | 0.0325126i | ||||
\(886\) | 9.00000 | 0.302361 | ||||||||
\(887\) | 8.12525i | 0.272819i | 0.990653 | + | 0.136410i | \(0.0435563\pi\) | ||||
−0.990653 | + | 0.136410i | \(0.956444\pi\) | |||||||
\(888\) | −3.25544 | + | 13.8564i | −0.109245 | + | 0.464991i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.00000 | − | 0.644810i | 0.100560 | − | 0.0216141i | ||||
\(891\) | 6.74456 | − | 5.10358i | 0.225951 | − | 0.170976i | ||||
\(892\) | 0.883156 | 0.0295703 | ||||||||
\(893\) | 29.4891 | 0.986816 | ||||||||
\(894\) | −3.56930 | + | 15.1923i | −0.119375 | + | 0.508107i | ||||
\(895\) | −11.1168 | − | 51.7215i | −0.371595 | − | 1.72886i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.62772 | − | 1.08724i | −0.154515 | − | 0.0363019i | ||||
\(898\) | 20.3971i | 0.680659i | ||||||||
\(899\) | 25.1168 | 0.837694 | ||||||||
\(900\) | 14.9891 | + | 0.571072i | 0.499638 | + | 0.0190357i | ||||
\(901\) | 29.0024i | 0.966211i | ||||||||
\(902\) | − | 6.92820i | − | 0.230684i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.7446 | −0.490397 | ||||||||
\(905\) | 3.76631 | + | 17.5229i | 0.125196 | + | 0.582480i | ||||
\(906\) | 15.3723 | + | 3.61158i | 0.510710 | + | 0.119987i | ||||
\(907\) | 4.95610i | 0.164565i | 0.996609 | + | 0.0822823i | \(0.0262209\pi\) | ||||
−0.996609 | + | 0.0822823i | \(0.973779\pi\) | |||||||
\(908\) | − | 20.8395i | − | 0.691584i | ||||||
\(909\) | 28.5475 | + | 14.1976i | 0.946862 | + | 0.470906i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.8102i | 1.25271i | 0.779539 | + | 0.626353i | \(0.215453\pi\) | ||||
−0.779539 | + | 0.626353i | \(0.784547\pi\) | |||||||
\(912\) | 1.37228 | − | 5.84096i | 0.0454408 | − | 0.193414i | ||||
\(913\) | 11.1168 | 0.367914 | ||||||||
\(914\) | 2.81929i | 0.0932539i | ||||||||
\(915\) | 0.941578 | − | 49.4458i | 0.0311276 | − | 1.63463i | ||||
\(916\) | − | 13.8564i | − | 0.457829i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −22.0000 | + | 26.5330i | −0.726108 | + | 0.875719i | ||||
\(919\) | 16.2337 | 0.535500 | 0.267750 | − | 0.963488i | \(-0.413720\pi\) | ||||
0.267750 | + | 0.963488i | \(0.413720\pi\) | |||||||
\(920\) | −3.00000 | + | 0.644810i | −0.0989071 | + | 0.0212588i | ||||
\(921\) | −40.6644 | − | 9.55373i | −1.33994 | − | 0.314806i | ||||
\(922\) | −23.4891 | −0.773573 | ||||||||
\(923\) | − | 17.0256i | − | 0.560403i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.8832 | + | 37.4603i | 0.555115 | + | 1.23169i | ||||
\(926\) | − | 6.72582i | − | 0.221024i | ||||||
\(927\) | −5.68614 | − | 2.82791i | −0.186757 | − | 0.0928807i | ||||
\(928\) | 3.31662i | 0.108874i | ||||||||
\(929\) | −34.1168 | −1.11934 | −0.559669 | − | 0.828716i | \(-0.689072\pi\) | ||||
−0.559669 | + | 0.828716i | \(0.689072\pi\) | |||||||
\(930\) | −0.558422 | + | 29.3248i | −0.0183114 | + | 0.961599i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.510875 | 0.0167343 | ||||||||
\(933\) | −34.1168 | − | 8.01544i | −1.11694 | − | 0.262414i | ||||
\(934\) | 36.4280i | 1.19196i | ||||||||
\(935\) | 13.6277 | − | 2.92910i | 0.445674 | − | 0.0957917i | ||||
\(936\) | −5.37228 | − | 2.67181i | −0.175599 | − | 0.0873310i | ||||
\(937\) | −1.35053 | −0.0441200 | −0.0220600 | − | 0.999757i | \(-0.507022\pi\) | ||||
−0.0220600 | + | 0.999757i | \(0.507022\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.25544 | − | 1.23472i | −0.171505 | − | 0.0402935i | ||||
\(940\) | −4.00000 | − | 18.6101i | −0.130466 | − | 0.606995i | ||||
\(941\) | −27.3505 | −0.891602 | −0.445801 | − | 0.895132i | \(-0.647081\pi\) | ||||
−0.445801 | + | 0.895132i | \(0.647081\pi\) | |||||||
\(942\) | 13.4891 | + | 3.16915i | 0.439499 | + | 0.103256i | ||||
\(943\) | −10.1168 | −0.329450 | ||||||||
\(944\) | −13.1168 | −0.426917 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.02175 | 0.0332199 | ||||||||
\(947\) | −25.8832 | −0.841090 | −0.420545 | − | 0.907272i | \(-0.638161\pi\) | ||||
−0.420545 | + | 0.907272i | \(0.638161\pi\) | |||||||
\(948\) | −15.3723 | − | 3.61158i | −0.499268 | − | 0.117299i | ||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | −7.11684 | − | 15.7908i | −0.230901 | − | 0.512322i | ||||
\(951\) | −1.88316 | − | 0.442430i | −0.0610655 | − | 0.0143468i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.0000 | 1.55487 | 0.777436 | − | 0.628962i | \(-0.216520\pi\) | ||||
0.777436 | + | 0.628962i | \(0.216520\pi\) | |||||||
\(954\) | −11.7446 | − | 5.84096i | −0.380244 | − | 0.189108i | ||||
\(955\) | 8.00000 | + | 37.2203i | 0.258874 | + | 1.20442i | ||||
\(956\) | − | 23.6588i | − | 0.765180i | ||||||
\(957\) | 5.25544 | + | 1.23472i | 0.169884 | + | 0.0399127i | ||||
\(958\) | −2.74456 | −0.0886728 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.87228 | − | 0.0737384i | −0.124977 | − | 0.00237990i | ||||
\(961\) | −26.3505 | −0.850017 | ||||||||
\(962\) | − | 16.4356i | − | 0.529907i | ||||||
\(963\) | −16.8030 | − | 8.35668i | −0.541469 | − | 0.269290i | ||||
\(964\) | − | 19.2549i | − | 0.620160i | ||||||
\(965\) | −8.44158 | − | 39.2747i | −0.271744 | − | 1.26430i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.6751i | 0.889973i | 0.895537 | + | 0.444986i | \(0.146791\pi\) | ||||
−0.895537 | + | 0.444986i | \(0.853209\pi\) | |||||||
\(968\) | −10.1168 | −0.325168 | ||||||||
\(969\) | 38.7446 | + | 9.10268i | 1.24465 | + | 0.292420i | ||||
\(970\) | −33.0475 | + | 7.10313i | −1.06109 | + | 0.228068i | ||||
\(971\) | −34.3723 | −1.10306 | −0.551530 | − | 0.834155i | \(-0.685956\pi\) | ||||
−0.551530 | + | 0.834155i | \(0.685956\pi\) | |||||||
\(972\) | −6.31386 | − | 14.2525i | −0.202517 | − | 0.457151i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 14.5012i | − | 0.464649i | ||||||
\(975\) | −17.0000 | + | 3.31662i | −0.544436 | + | 0.106217i | ||||
\(976\) | 12.7692i | 0.408731i | ||||||||
\(977\) | −28.4674 | −0.910752 | −0.455376 | − | 0.890299i | \(-0.650495\pi\) | ||||
−0.455376 | + | 0.890299i | \(0.650495\pi\) | |||||||
\(978\) | −1.37228 | + | 5.84096i | −0.0438807 | + | 0.186773i | ||||
\(979\) | 1.28962i | 0.0412164i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.8030 | − | 10.8434i | −0.696116 | − | 0.346202i | ||||
\(982\) | − | 30.2372i | − | 0.964906i | ||||||
\(983\) | 25.0410i | 0.798684i | 0.916802 | + | 0.399342i | \(0.130761\pi\) | ||||
−0.916802 | + | 0.399342i | \(0.869239\pi\) | |||||||
\(984\) | −12.4307 | − | 2.92048i | −0.396276 | − | 0.0931015i | ||||
\(985\) | −31.1168 | + | 6.68815i | −0.991465 | + | 0.213102i | ||||
\(986\) | −22.0000 | −0.700623 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.92820i | 0.220416i | ||||||||
\(989\) | − | 1.49200i | − | 0.0474428i | ||||||
\(990\) | −1.55842 | + | 6.10846i | −0.0495299 | + | 0.194140i | ||||
\(991\) | 23.3505 | 0.741754 | 0.370877 | − | 0.928682i | \(-0.379057\pi\) | ||||
0.370877 | + | 0.928682i | \(0.379057\pi\) | |||||||
\(992\) | − | 7.57301i | − | 0.240443i | ||||||
\(993\) | 40.8614 | + | 9.60002i | 1.29670 | + | 0.304647i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.605969 | + | 2.81929i | 0.0192105 | + | 0.0893775i | ||||
\(996\) | 4.68614 | − | 19.9460i | 0.148486 | − | 0.632014i | ||||
\(997\) | −38.4674 | −1.21827 | −0.609137 | − | 0.793065i | \(-0.708484\pi\) | ||||
−0.609137 | + | 0.793065i | \(0.708484\pi\) | |||||||
\(998\) | 6.23369 | 0.197324 | ||||||||
\(999\) | 27.2554 | − | 32.8713i | 0.862324 | − | 1.04000i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1470.2.d.a.1469.1 | 4 | ||
3.2 | odd | 2 | 1470.2.d.c.1469.2 | 4 | |||
5.4 | even | 2 | 1470.2.d.d.1469.4 | 4 | |||
7.4 | even | 3 | 210.2.t.d.89.2 | yes | 4 | ||
7.5 | odd | 6 | 210.2.t.c.59.1 | yes | 4 | ||
7.6 | odd | 2 | 1470.2.d.b.1469.4 | 4 | |||
15.14 | odd | 2 | 1470.2.d.b.1469.3 | 4 | |||
21.5 | even | 6 | 210.2.t.a.59.2 | ✓ | 4 | ||
21.11 | odd | 6 | 210.2.t.b.89.2 | yes | 4 | ||
21.20 | even | 2 | 1470.2.d.d.1469.3 | 4 | |||
35.4 | even | 6 | 210.2.t.a.89.1 | yes | 4 | ||
35.12 | even | 12 | 1050.2.s.d.101.2 | 8 | |||
35.18 | odd | 12 | 1050.2.s.e.551.1 | 8 | |||
35.19 | odd | 6 | 210.2.t.b.59.2 | yes | 4 | ||
35.32 | odd | 12 | 1050.2.s.e.551.4 | 8 | |||
35.33 | even | 12 | 1050.2.s.d.101.3 | 8 | |||
35.34 | odd | 2 | 1470.2.d.c.1469.1 | 4 | |||
105.32 | even | 12 | 1050.2.s.d.551.2 | 8 | |||
105.47 | odd | 12 | 1050.2.s.e.101.4 | 8 | |||
105.53 | even | 12 | 1050.2.s.d.551.3 | 8 | |||
105.68 | odd | 12 | 1050.2.s.e.101.1 | 8 | |||
105.74 | odd | 6 | 210.2.t.c.89.1 | yes | 4 | ||
105.89 | even | 6 | 210.2.t.d.59.1 | yes | 4 | ||
105.104 | even | 2 | inner | 1470.2.d.a.1469.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.t.a.59.2 | ✓ | 4 | 21.5 | even | 6 | ||
210.2.t.a.89.1 | yes | 4 | 35.4 | even | 6 | ||
210.2.t.b.59.2 | yes | 4 | 35.19 | odd | 6 | ||
210.2.t.b.89.2 | yes | 4 | 21.11 | odd | 6 | ||
210.2.t.c.59.1 | yes | 4 | 7.5 | odd | 6 | ||
210.2.t.c.89.1 | yes | 4 | 105.74 | odd | 6 | ||
210.2.t.d.59.1 | yes | 4 | 105.89 | even | 6 | ||
210.2.t.d.89.2 | yes | 4 | 7.4 | even | 3 | ||
1050.2.s.d.101.2 | 8 | 35.12 | even | 12 | |||
1050.2.s.d.101.3 | 8 | 35.33 | even | 12 | |||
1050.2.s.d.551.2 | 8 | 105.32 | even | 12 | |||
1050.2.s.d.551.3 | 8 | 105.53 | even | 12 | |||
1050.2.s.e.101.1 | 8 | 105.68 | odd | 12 | |||
1050.2.s.e.101.4 | 8 | 105.47 | odd | 12 | |||
1050.2.s.e.551.1 | 8 | 35.18 | odd | 12 | |||
1050.2.s.e.551.4 | 8 | 35.32 | odd | 12 | |||
1470.2.d.a.1469.1 | 4 | 1.1 | even | 1 | trivial | ||
1470.2.d.a.1469.2 | 4 | 105.104 | even | 2 | inner | ||
1470.2.d.b.1469.3 | 4 | 15.14 | odd | 2 | |||
1470.2.d.b.1469.4 | 4 | 7.6 | odd | 2 | |||
1470.2.d.c.1469.1 | 4 | 35.34 | odd | 2 | |||
1470.2.d.c.1469.2 | 4 | 3.2 | odd | 2 | |||
1470.2.d.d.1469.3 | 4 | 21.20 | even | 2 | |||
1470.2.d.d.1469.4 | 4 | 5.4 | even | 2 |