Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3675,2,Mod(1,3675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3675.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3675.a (trivial) |
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: | yes |
Analytic conductor: | \(29.3450227428\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 11 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 735) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.14896\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3675.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32813 | −0.939130 | −0.469565 | − | 0.882898i | \(-0.655589\pi\) | ||||
−0.469565 | + | 0.882898i | \(0.655589\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.236068 | −0.118034 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.32813 | 0.542207 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.96979 | 1.04998 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.47214 | 1.34840 | 0.674200 | − | 0.738549i | \(-0.264489\pi\) | ||||
0.674200 | + | 0.738549i | \(0.264489\pi\) | |||||||
\(12\) | 0.236068 | 0.0681470 | ||||||||
\(13\) | −0.763932 | −0.211877 | −0.105938 | − | 0.994373i | \(-0.533785\pi\) | ||||
−0.105938 | + | 0.994373i | \(0.533785\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.47214 | −0.868034 | ||||||||
\(17\) | −5.23607 | −1.26993 | −0.634967 | − | 0.772540i | \(-0.718986\pi\) | ||||
−0.634967 | + | 0.772540i | \(0.718986\pi\) | |||||||
\(18\) | −1.32813 | −0.313043 | ||||||||
\(19\) | −1.64166 | −0.376623 | −0.188311 | − | 0.982109i | \(-0.560301\pi\) | ||||
−0.188311 | + | 0.982109i | \(0.560301\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.93958 | −1.26632 | ||||||||
\(23\) | 4.29792 | 0.896179 | 0.448089 | − | 0.893989i | \(-0.352105\pi\) | ||||
0.448089 | + | 0.893989i | \(0.352105\pi\) | |||||||
\(24\) | −2.96979 | −0.606206 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.01460 | 0.198980 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.95418 | −1.24901 | −0.624504 | − | 0.781021i | \(-0.714699\pi\) | ||||
−0.624504 | + | 0.781021i | \(0.714699\pi\) | |||||||
\(32\) | −1.32813 | −0.234783 | ||||||||
\(33\) | −4.47214 | −0.778499 | ||||||||
\(34\) | 6.95418 | 1.19263 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.236068 | −0.0393447 | ||||||||
\(37\) | −8.59584 | −1.41315 | −0.706574 | − | 0.707639i | \(-0.749760\pi\) | ||||
−0.706574 | + | 0.707639i | \(0.749760\pi\) | |||||||
\(38\) | 2.18034 | 0.353698 | ||||||||
\(39\) | 0.763932 | 0.122327 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.61045 | 1.50090 | 0.750450 | − | 0.660927i | \(-0.229837\pi\) | ||||
0.750450 | + | 0.660927i | \(0.229837\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.31252 | 0.810152 | 0.405076 | − | 0.914283i | \(-0.367245\pi\) | ||||
0.405076 | + | 0.914283i | \(0.367245\pi\) | |||||||
\(44\) | −1.05573 | −0.159157 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.70820 | −0.841629 | ||||||||
\(47\) | −12.9443 | −1.88812 | −0.944058 | − | 0.329779i | \(-0.893026\pi\) | ||||
−0.944058 | + | 0.329779i | \(0.893026\pi\) | |||||||
\(48\) | 3.47214 | 0.501160 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.23607 | 0.733196 | ||||||||
\(52\) | 0.180340 | 0.0250086 | ||||||||
\(53\) | −6.95418 | −0.955231 | −0.477615 | − | 0.878569i | \(-0.658499\pi\) | ||||
−0.477615 | + | 0.878569i | \(0.658499\pi\) | |||||||
\(54\) | 1.32813 | 0.180736 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.64166 | 0.217443 | ||||||||
\(58\) | −2.65626 | −0.348784 | ||||||||
\(59\) | −5.31252 | −0.691632 | −0.345816 | − | 0.938302i | \(-0.612398\pi\) | ||||
−0.345816 | + | 0.938302i | \(0.612398\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.9084 | 1.78078 | 0.890392 | − | 0.455194i | \(-0.150430\pi\) | ||||
0.890392 | + | 0.455194i | \(0.150430\pi\) | |||||||
\(62\) | 9.23607 | 1.17298 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.70820 | 1.08853 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.93958 | 0.731112 | ||||||||
\(67\) | 8.59584 | 1.05015 | 0.525075 | − | 0.851056i | \(-0.324037\pi\) | ||||
0.525075 | + | 0.851056i | \(0.324037\pi\) | |||||||
\(68\) | 1.23607 | 0.149895 | ||||||||
\(69\) | −4.29792 | −0.517409 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.47214 | −1.00546 | −0.502729 | − | 0.864444i | \(-0.667671\pi\) | ||||
−0.502729 | + | 0.864444i | \(0.667671\pi\) | |||||||
\(72\) | 2.96979 | 0.349993 | ||||||||
\(73\) | −7.23607 | −0.846918 | −0.423459 | − | 0.905915i | \(-0.639184\pi\) | ||||
−0.423459 | + | 0.905915i | \(0.639184\pi\) | |||||||
\(74\) | 11.4164 | 1.32713 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.387543 | 0.0444543 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.01460 | −0.114881 | ||||||||
\(79\) | −4.94427 | −0.556274 | −0.278137 | − | 0.960541i | \(-0.589717\pi\) | ||||
−0.278137 | + | 0.960541i | \(0.589717\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −12.7639 | −1.40954 | ||||||||
\(83\) | 2.47214 | 0.271352 | 0.135676 | − | 0.990753i | \(-0.456679\pi\) | ||||
0.135676 | + | 0.990753i | \(0.456679\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.05573 | −0.760839 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 13.2813 | 1.41579 | ||||||||
\(89\) | 12.8938 | 1.36674 | 0.683368 | − | 0.730074i | \(-0.260514\pi\) | ||||
0.683368 | + | 0.730074i | \(0.260514\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.01460 | −0.105780 | ||||||||
\(93\) | 6.95418 | 0.721115 | ||||||||
\(94\) | 17.1917 | 1.77319 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.32813 | 0.135552 | ||||||||
\(97\) | 12.1803 | 1.23673 | 0.618363 | − | 0.785893i | \(-0.287796\pi\) | ||||
0.618363 | + | 0.785893i | \(0.287796\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.47214 | 0.449467 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.01460 | −0.100957 | −0.0504783 | − | 0.998725i | \(-0.516075\pi\) | ||||
−0.0504783 | + | 0.998725i | \(0.516075\pi\) | |||||||
\(102\) | −6.95418 | −0.688567 | ||||||||
\(103\) | −10.4721 | −1.03185 | −0.515925 | − | 0.856634i | \(-0.672552\pi\) | ||||
−0.515925 | + | 0.856634i | \(0.672552\pi\) | |||||||
\(104\) | −2.26872 | −0.222466 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.23607 | 0.897086 | ||||||||
\(107\) | 9.61045 | 0.929077 | 0.464538 | − | 0.885553i | \(-0.346220\pi\) | ||||
0.464538 | + | 0.885553i | \(0.346220\pi\) | |||||||
\(108\) | 0.236068 | 0.0227157 | ||||||||
\(109\) | 3.52786 | 0.337908 | 0.168954 | − | 0.985624i | \(-0.445961\pi\) | ||||
0.168954 | + | 0.985624i | \(0.445961\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.59584 | 0.815881 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.5500 | −1.46282 | −0.731412 | − | 0.681936i | \(-0.761138\pi\) | ||||
−0.731412 | + | 0.681936i | \(0.761138\pi\) | |||||||
\(114\) | −2.18034 | −0.204208 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.472136 | −0.0438367 | ||||||||
\(117\) | −0.763932 | −0.0706255 | ||||||||
\(118\) | 7.05573 | 0.649532 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | −18.4721 | −1.67239 | ||||||||
\(123\) | −9.61045 | −0.866545 | ||||||||
\(124\) | 1.64166 | 0.147425 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.9084 | 1.23417 | 0.617084 | − | 0.786897i | \(-0.288314\pi\) | ||||
0.617084 | + | 0.786897i | \(0.288314\pi\) | |||||||
\(128\) | −8.90937 | −0.787485 | ||||||||
\(129\) | −5.31252 | −0.467742 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.31252 | 0.464157 | 0.232079 | − | 0.972697i | \(-0.425447\pi\) | ||||
0.232079 | + | 0.972697i | \(0.425447\pi\) | |||||||
\(132\) | 1.05573 | 0.0918893 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.4164 | −0.986227 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.5500 | −1.33340 | ||||||||
\(137\) | −1.64166 | −0.140256 | −0.0701282 | − | 0.997538i | \(-0.522341\pi\) | ||||
−0.0701282 | + | 0.997538i | \(0.522341\pi\) | |||||||
\(138\) | 5.70820 | 0.485915 | ||||||||
\(139\) | 10.2375 | 0.868334 | 0.434167 | − | 0.900832i | \(-0.357043\pi\) | ||||
0.434167 | + | 0.900832i | \(0.357043\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.9443 | 1.09010 | ||||||||
\(142\) | 11.2521 | 0.944256 | ||||||||
\(143\) | −3.41641 | −0.285694 | ||||||||
\(144\) | −3.47214 | −0.289345 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.61045 | 0.795366 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.02920 | 0.166800 | ||||||||
\(149\) | −1.05573 | −0.0864886 | −0.0432443 | − | 0.999065i | \(-0.513769\pi\) | ||||
−0.0432443 | + | 0.999065i | \(0.513769\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.94427 | 0.727875 | 0.363937 | − | 0.931423i | \(-0.381432\pi\) | ||||
0.363937 | + | 0.931423i | \(0.381432\pi\) | |||||||
\(152\) | −4.87539 | −0.395446 | ||||||||
\(153\) | −5.23607 | −0.423311 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.180340 | −0.0144387 | ||||||||
\(157\) | −22.6525 | −1.80786 | −0.903932 | − | 0.427676i | \(-0.859332\pi\) | ||||
−0.903932 | + | 0.427676i | \(0.859332\pi\) | |||||||
\(158\) | 6.56664 | 0.522414 | ||||||||
\(159\) | 6.95418 | 0.551503 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.32813 | −0.104348 | ||||||||
\(163\) | −13.9084 | −1.08939 | −0.544694 | − | 0.838635i | \(-0.683354\pi\) | ||||
−0.544694 | + | 0.838635i | \(0.683354\pi\) | |||||||
\(164\) | −2.26872 | −0.177157 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.28332 | −0.254835 | ||||||||
\(167\) | −11.4164 | −0.883428 | −0.441714 | − | 0.897156i | \(-0.645629\pi\) | ||||
−0.441714 | + | 0.897156i | \(0.645629\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4164 | −0.955108 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.64166 | −0.125541 | ||||||||
\(172\) | −1.25412 | −0.0956255 | ||||||||
\(173\) | −14.7639 | −1.12248 | −0.561240 | − | 0.827653i | \(-0.689676\pi\) | ||||
−0.561240 | + | 0.827653i | \(0.689676\pi\) | |||||||
\(174\) | 2.65626 | 0.201371 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −15.5279 | −1.17046 | ||||||||
\(177\) | 5.31252 | 0.399314 | ||||||||
\(178\) | −17.1246 | −1.28354 | ||||||||
\(179\) | −16.4721 | −1.23119 | −0.615593 | − | 0.788065i | \(-0.711083\pi\) | ||||
−0.615593 | + | 0.788065i | \(0.711083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.31252 | −0.394877 | −0.197438 | − | 0.980315i | \(-0.563262\pi\) | ||||
−0.197438 | + | 0.980315i | \(0.563262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.9084 | −1.02814 | ||||||||
\(184\) | 12.7639 | 0.940970 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.23607 | −0.677221 | ||||||||
\(187\) | −23.4164 | −1.71238 | ||||||||
\(188\) | 3.05573 | 0.222862 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.4721 | −0.902452 | −0.451226 | − | 0.892410i | \(-0.649013\pi\) | ||||
−0.451226 | + | 0.892410i | \(0.649013\pi\) | |||||||
\(192\) | −8.70820 | −0.628460 | ||||||||
\(193\) | 19.2209 | 1.38355 | 0.691775 | − | 0.722113i | \(-0.256829\pi\) | ||||
0.691775 | + | 0.722113i | \(0.256829\pi\) | |||||||
\(194\) | −16.1771 | −1.16145 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.95418 | 0.495465 | 0.247733 | − | 0.968828i | \(-0.420315\pi\) | ||||
0.247733 | + | 0.968828i | \(0.420315\pi\) | |||||||
\(198\) | −5.93958 | −0.422108 | ||||||||
\(199\) | −12.2667 | −0.869564 | −0.434782 | − | 0.900536i | \(-0.643175\pi\) | ||||
−0.434782 | + | 0.900536i | \(0.643175\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.59584 | −0.606304 | ||||||||
\(202\) | 1.34752 | 0.0948115 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.23607 | −0.0865421 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.9084 | 0.969042 | ||||||||
\(207\) | 4.29792 | 0.298726 | ||||||||
\(208\) | 2.65248 | 0.183916 | ||||||||
\(209\) | −7.34173 | −0.507838 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.94427 | 0.340378 | 0.170189 | − | 0.985411i | \(-0.445562\pi\) | ||||
0.170189 | + | 0.985411i | \(0.445562\pi\) | |||||||
\(212\) | 1.64166 | 0.112750 | ||||||||
\(213\) | 8.47214 | 0.580501 | ||||||||
\(214\) | −12.7639 | −0.872524 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.96979 | −0.202069 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.68547 | −0.317340 | ||||||||
\(219\) | 7.23607 | 0.488968 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | −11.4164 | −0.766219 | ||||||||
\(223\) | −17.8885 | −1.19791 | −0.598953 | − | 0.800784i | \(-0.704416\pi\) | ||||
−0.598953 | + | 0.800784i | \(0.704416\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.6525 | 1.37378 | ||||||||
\(227\) | 10.4721 | 0.695060 | 0.347530 | − | 0.937669i | \(-0.387020\pi\) | ||||
0.347530 | + | 0.937669i | \(0.387020\pi\) | |||||||
\(228\) | −0.387543 | −0.0256657 | ||||||||
\(229\) | −11.8792 | −0.784997 | −0.392499 | − | 0.919753i | \(-0.628389\pi\) | ||||
−0.392499 | + | 0.919753i | \(0.628389\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.93958 | 0.389953 | ||||||||
\(233\) | 12.2667 | 0.803619 | 0.401809 | − | 0.915723i | \(-0.368381\pi\) | ||||
0.401809 | + | 0.915723i | \(0.368381\pi\) | |||||||
\(234\) | 1.01460 | 0.0663266 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.25412 | 0.0816361 | ||||||||
\(237\) | 4.94427 | 0.321165 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.4721 | −1.06549 | −0.532747 | − | 0.846275i | \(-0.678840\pi\) | ||||
−0.532747 | + | 0.846275i | \(0.678840\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.59584 | 0.553707 | 0.276854 | − | 0.960912i | \(-0.410708\pi\) | ||||
0.276854 | + | 0.960912i | \(0.410708\pi\) | |||||||
\(242\) | −11.9532 | −0.768379 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.28332 | −0.210193 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.7639 | 0.813799 | ||||||||
\(247\) | 1.25412 | 0.0797975 | ||||||||
\(248\) | −20.6525 | −1.31143 | ||||||||
\(249\) | −2.47214 | −0.156665 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.5042 | −1.42045 | −0.710227 | − | 0.703973i | \(-0.751408\pi\) | ||||
−0.710227 | + | 0.703973i | \(0.751408\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.2209 | 1.20841 | ||||||||
\(254\) | −18.4721 | −1.15904 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.58359 | −0.348975 | ||||||||
\(257\) | −8.29180 | −0.517228 | −0.258614 | − | 0.965981i | \(-0.583266\pi\) | ||||
−0.258614 | + | 0.965981i | \(0.583266\pi\) | |||||||
\(258\) | 7.05573 | 0.439270 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | −7.05573 | −0.435904 | ||||||||
\(263\) | −21.4896 | −1.32511 | −0.662553 | − | 0.749015i | \(-0.730527\pi\) | ||||
−0.662553 | + | 0.749015i | \(0.730527\pi\) | |||||||
\(264\) | −13.2813 | −0.817408 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.8938 | −0.789086 | ||||||||
\(268\) | −2.02920 | −0.123953 | ||||||||
\(269\) | −9.61045 | −0.585959 | −0.292980 | − | 0.956119i | \(-0.594647\pi\) | ||||
−0.292980 | + | 0.956119i | \(0.594647\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.67086 | −0.222989 | −0.111495 | − | 0.993765i | \(-0.535564\pi\) | ||||
−0.111495 | + | 0.993765i | \(0.535564\pi\) | |||||||
\(272\) | 18.1803 | 1.10235 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.18034 | 0.131719 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.01460 | 0.0610719 | ||||||||
\(277\) | −5.31252 | −0.319199 | −0.159599 | − | 0.987182i | \(-0.551020\pi\) | ||||
−0.159599 | + | 0.987182i | \(0.551020\pi\) | |||||||
\(278\) | −13.5967 | −0.815479 | ||||||||
\(279\) | −6.95418 | −0.416336 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.0000 | −1.31241 | −0.656205 | − | 0.754583i | \(-0.727839\pi\) | ||||
−0.656205 | + | 0.754583i | \(0.727839\pi\) | |||||||
\(282\) | −17.1917 | −1.02375 | ||||||||
\(283\) | 32.3607 | 1.92364 | 0.961821 | − | 0.273678i | \(-0.0882403\pi\) | ||||
0.961821 | + | 0.273678i | \(0.0882403\pi\) | |||||||
\(284\) | 2.00000 | 0.118678 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.53744 | 0.268304 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.32813 | −0.0782609 | ||||||||
\(289\) | 10.4164 | 0.612730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.1803 | −0.714024 | ||||||||
\(292\) | 1.70820 | 0.0999651 | ||||||||
\(293\) | 2.18034 | 0.127377 | 0.0636884 | − | 0.997970i | \(-0.479714\pi\) | ||||
0.0636884 | + | 0.997970i | \(0.479714\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −25.5279 | −1.48378 | ||||||||
\(297\) | −4.47214 | −0.259500 | ||||||||
\(298\) | 1.40215 | 0.0812241 | ||||||||
\(299\) | −3.28332 | −0.189879 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −11.8792 | −0.683569 | ||||||||
\(303\) | 1.01460 | 0.0582874 | ||||||||
\(304\) | 5.70007 | 0.326921 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.95418 | 0.397544 | ||||||||
\(307\) | 6.47214 | 0.369384 | 0.184692 | − | 0.982796i | \(-0.440871\pi\) | ||||
0.184692 | + | 0.982796i | \(0.440871\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.4721 | 0.595739 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.9084 | −0.788671 | −0.394336 | − | 0.918966i | \(-0.629025\pi\) | ||||
−0.394336 | + | 0.918966i | \(0.629025\pi\) | |||||||
\(312\) | 2.26872 | 0.128441 | ||||||||
\(313\) | 6.65248 | 0.376020 | 0.188010 | − | 0.982167i | \(-0.439796\pi\) | ||||
0.188010 | + | 0.982167i | \(0.439796\pi\) | |||||||
\(314\) | 30.0855 | 1.69782 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.16718 | 0.0656592 | ||||||||
\(317\) | −24.1459 | −1.35617 | −0.678084 | − | 0.734985i | \(-0.737189\pi\) | ||||
−0.678084 | + | 0.734985i | \(0.737189\pi\) | |||||||
\(318\) | −9.23607 | −0.517933 | ||||||||
\(319\) | 8.94427 | 0.500783 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.61045 | −0.536403 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.59584 | 0.478286 | ||||||||
\(324\) | −0.236068 | −0.0131149 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 18.4721 | 1.02308 | ||||||||
\(327\) | −3.52786 | −0.195091 | ||||||||
\(328\) | 28.5410 | 1.57591 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | −0.583592 | −0.0320288 | ||||||||
\(333\) | −8.59584 | −0.471049 | ||||||||
\(334\) | 15.1625 | 0.829654 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.9084 | 0.757637 | 0.378819 | − | 0.925471i | \(-0.376330\pi\) | ||||
0.378819 | + | 0.925471i | \(0.376330\pi\) | |||||||
\(338\) | 16.4906 | 0.896971 | ||||||||
\(339\) | 15.5500 | 0.844562 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31.1001 | −1.68416 | ||||||||
\(342\) | 2.18034 | 0.117899 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 15.7771 | 0.850644 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.6084 | 1.05416 | ||||||||
\(347\) | 16.1771 | 0.868432 | 0.434216 | − | 0.900809i | \(-0.357026\pi\) | ||||
0.434216 | + | 0.900809i | \(0.357026\pi\) | |||||||
\(348\) | 0.472136 | 0.0253091 | ||||||||
\(349\) | −31.1001 | −1.66475 | −0.832374 | − | 0.554214i | \(-0.813019\pi\) | ||||
−0.832374 | + | 0.554214i | \(0.813019\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.763932 | 0.0407757 | ||||||||
\(352\) | −5.93958 | −0.316581 | ||||||||
\(353\) | −1.23607 | −0.0657893 | −0.0328946 | − | 0.999459i | \(-0.510473\pi\) | ||||
−0.0328946 | + | 0.999459i | \(0.510473\pi\) | |||||||
\(354\) | −7.05573 | −0.375008 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.04381 | −0.161321 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 21.8772 | 1.15624 | ||||||||
\(359\) | 11.5279 | 0.608417 | 0.304209 | − | 0.952605i | \(-0.401608\pi\) | ||||
0.304209 | + | 0.952605i | \(0.401608\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.3050 | −0.858155 | ||||||||
\(362\) | 7.05573 | 0.370841 | ||||||||
\(363\) | −9.00000 | −0.472377 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 18.4721 | 0.965554 | ||||||||
\(367\) | 16.0000 | 0.835193 | 0.417597 | − | 0.908633i | \(-0.362873\pi\) | ||||
0.417597 | + | 0.908633i | \(0.362873\pi\) | |||||||
\(368\) | −14.9230 | −0.777914 | ||||||||
\(369\) | 9.61045 | 0.500300 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.64166 | −0.0851161 | ||||||||
\(373\) | 6.56664 | 0.340008 | 0.170004 | − | 0.985443i | \(-0.445622\pi\) | ||||
0.170004 | + | 0.985443i | \(0.445622\pi\) | |||||||
\(374\) | 31.1001 | 1.60815 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −38.4418 | −1.98248 | ||||||||
\(377\) | −1.52786 | −0.0786890 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.9443 | 1.07583 | 0.537917 | − | 0.842997i | \(-0.319211\pi\) | ||||
0.537917 | + | 0.842997i | \(0.319211\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.9084 | −0.712547 | ||||||||
\(382\) | 16.5646 | 0.847520 | ||||||||
\(383\) | −1.52786 | −0.0780702 | −0.0390351 | − | 0.999238i | \(-0.512428\pi\) | ||||
−0.0390351 | + | 0.999238i | \(0.512428\pi\) | |||||||
\(384\) | 8.90937 | 0.454655 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.5279 | −1.29933 | ||||||||
\(387\) | 5.31252 | 0.270051 | ||||||||
\(388\) | −2.87539 | −0.145976 | ||||||||
\(389\) | 23.8885 | 1.21120 | 0.605599 | − | 0.795770i | \(-0.292934\pi\) | ||||
0.605599 | + | 0.795770i | \(0.292934\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.5042 | −1.13809 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.31252 | −0.267981 | ||||||||
\(394\) | −9.23607 | −0.465306 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.05573 | −0.0530523 | ||||||||
\(397\) | 4.76393 | 0.239095 | 0.119547 | − | 0.992828i | \(-0.461856\pi\) | ||||
0.119547 | + | 0.992828i | \(0.461856\pi\) | |||||||
\(398\) | 16.2918 | 0.816634 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.8328 | −0.840591 | −0.420295 | − | 0.907387i | \(-0.638074\pi\) | ||||
−0.420295 | + | 0.907387i | \(0.638074\pi\) | |||||||
\(402\) | 11.4164 | 0.569399 | ||||||||
\(403\) | 5.31252 | 0.264636 | ||||||||
\(404\) | 0.239515 | 0.0119163 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −38.4418 | −1.90549 | ||||||||
\(408\) | 15.5500 | 0.769841 | ||||||||
\(409\) | −29.8459 | −1.47579 | −0.737893 | − | 0.674917i | \(-0.764179\pi\) | ||||
−0.737893 | + | 0.674917i | \(0.764179\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.64166 | 0.0809771 | ||||||||
\(412\) | 2.47214 | 0.121793 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.70820 | −0.280543 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.01460 | 0.0497449 | ||||||||
\(417\) | −10.2375 | −0.501333 | ||||||||
\(418\) | 9.75078 | 0.476926 | ||||||||
\(419\) | −36.4126 | −1.77887 | −0.889436 | − | 0.457061i | \(-0.848902\pi\) | ||||
−0.889436 | + | 0.457061i | \(0.848902\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.52786 | 0.366886 | 0.183443 | − | 0.983030i | \(-0.441276\pi\) | ||||
0.183443 | + | 0.983030i | \(0.441276\pi\) | |||||||
\(422\) | −6.56664 | −0.319659 | ||||||||
\(423\) | −12.9443 | −0.629372 | ||||||||
\(424\) | −20.6525 | −1.00297 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −11.2521 | −0.545166 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.26872 | −0.109663 | ||||||||
\(429\) | 3.41641 | 0.164946 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.47214 | 0.215415 | 0.107708 | − | 0.994183i | \(-0.465649\pi\) | ||||
0.107708 | + | 0.994183i | \(0.465649\pi\) | |||||||
\(432\) | 3.47214 | 0.167053 | ||||||||
\(433\) | −22.2918 | −1.07128 | −0.535638 | − | 0.844448i | \(-0.679929\pi\) | ||||
−0.535638 | + | 0.844448i | \(0.679929\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.832816 | −0.0398846 | ||||||||
\(437\) | −7.05573 | −0.337521 | ||||||||
\(438\) | −9.61045 | −0.459205 | ||||||||
\(439\) | 4.92498 | 0.235057 | 0.117528 | − | 0.993070i | \(-0.462503\pi\) | ||||
0.117528 | + | 0.993070i | \(0.462503\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.31252 | −0.252691 | ||||||||
\(443\) | −24.7729 | −1.17700 | −0.588499 | − | 0.808498i | \(-0.700281\pi\) | ||||
−0.588499 | + | 0.808498i | \(0.700281\pi\) | |||||||
\(444\) | −2.02920 | −0.0963017 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 23.7583 | 1.12499 | ||||||||
\(447\) | 1.05573 | 0.0499342 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.9443 | −1.64912 | −0.824561 | − | 0.565773i | \(-0.808578\pi\) | ||||
−0.824561 | + | 0.565773i | \(0.808578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.9792 | 2.02381 | ||||||||
\(452\) | 3.67086 | 0.172663 | ||||||||
\(453\) | −8.94427 | −0.420239 | ||||||||
\(454\) | −13.9084 | −0.652752 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.87539 | 0.228311 | ||||||||
\(457\) | −24.5334 | −1.14762 | −0.573812 | − | 0.818987i | \(-0.694536\pi\) | ||||
−0.573812 | + | 0.818987i | \(0.694536\pi\) | |||||||
\(458\) | 15.7771 | 0.737215 | ||||||||
\(459\) | 5.23607 | 0.244399 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.5480 | −1.18989 | −0.594945 | − | 0.803766i | \(-0.702826\pi\) | ||||
−0.594945 | + | 0.803766i | \(0.702826\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.4750 | 0.951554 | 0.475777 | − | 0.879566i | \(-0.342167\pi\) | ||||
0.475777 | + | 0.879566i | \(0.342167\pi\) | |||||||
\(464\) | −6.94427 | −0.322380 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.2918 | −0.754703 | ||||||||
\(467\) | 0.583592 | 0.0270054 | 0.0135027 | − | 0.999909i | \(-0.495702\pi\) | ||||
0.0135027 | + | 0.999909i | \(0.495702\pi\) | |||||||
\(468\) | 0.180340 | 0.00833621 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.6525 | 1.04377 | ||||||||
\(472\) | −15.7771 | −0.726199 | ||||||||
\(473\) | 23.7583 | 1.09241 | ||||||||
\(474\) | −6.56664 | −0.301616 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.95418 | −0.318410 | ||||||||
\(478\) | 21.8772 | 1.00064 | ||||||||
\(479\) | 20.4750 | 0.935527 | 0.467764 | − | 0.883854i | \(-0.345060\pi\) | ||||
0.467764 | + | 0.883854i | \(0.345060\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.56664 | 0.299413 | ||||||||
\(482\) | −11.4164 | −0.520003 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.12461 | −0.0965733 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.32813 | 0.0602452 | ||||||||
\(487\) | −5.31252 | −0.240733 | −0.120367 | − | 0.992729i | \(-0.538407\pi\) | ||||
−0.120367 | + | 0.992729i | \(0.538407\pi\) | |||||||
\(488\) | 41.3050 | 1.86979 | ||||||||
\(489\) | 13.9084 | 0.628958 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.3607 | −1.18964 | −0.594820 | − | 0.803859i | \(-0.702777\pi\) | ||||
−0.594820 | + | 0.803859i | \(0.702777\pi\) | |||||||
\(492\) | 2.26872 | 0.102282 | ||||||||
\(493\) | −10.4721 | −0.471641 | ||||||||
\(494\) | −1.66563 | −0.0749403 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.1459 | 1.08418 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.28332 | 0.147129 | ||||||||
\(499\) | 8.00000 | 0.358129 | 0.179065 | − | 0.983837i | \(-0.442693\pi\) | ||||
0.179065 | + | 0.983837i | \(0.442693\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.4164 | 0.510047 | ||||||||
\(502\) | 29.8885 | 1.33399 | ||||||||
\(503\) | −38.4721 | −1.71539 | −0.857694 | − | 0.514161i | \(-0.828103\pi\) | ||||
−0.857694 | + | 0.514161i | \(0.828103\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −25.5279 | −1.13485 | ||||||||
\(507\) | 12.4164 | 0.551432 | ||||||||
\(508\) | −3.28332 | −0.145674 | ||||||||
\(509\) | −1.01460 | −0.0449714 | −0.0224857 | − | 0.999747i | \(-0.507158\pi\) | ||||
−0.0224857 | + | 0.999747i | \(0.507158\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 25.2345 | 1.11522 | ||||||||
\(513\) | 1.64166 | 0.0724811 | ||||||||
\(514\) | 11.0126 | 0.485745 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.25412 | 0.0552094 | ||||||||
\(517\) | −57.8885 | −2.54594 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.7639 | 0.648065 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.04381 | 0.133352 | 0.0666758 | − | 0.997775i | \(-0.478761\pi\) | ||||
0.0666758 | + | 0.997775i | \(0.478761\pi\) | |||||||
\(522\) | −2.65626 | −0.116261 | ||||||||
\(523\) | −32.9443 | −1.44055 | −0.720276 | − | 0.693687i | \(-0.755985\pi\) | ||||
−0.720276 | + | 0.693687i | \(0.755985\pi\) | |||||||
\(524\) | −1.25412 | −0.0547863 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.5410 | 1.24445 | ||||||||
\(527\) | 36.4126 | 1.58616 | ||||||||
\(528\) | 15.5279 | 0.675764 | ||||||||
\(529\) | −4.52786 | −0.196864 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.31252 | −0.230544 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.34173 | −0.318006 | ||||||||
\(534\) | 17.1246 | 0.741054 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 25.5279 | 1.10264 | ||||||||
\(537\) | 16.4721 | 0.710825 | ||||||||
\(538\) | 12.7639 | 0.550292 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.5279 | −0.667595 | −0.333798 | − | 0.942645i | \(-0.608330\pi\) | ||||
−0.333798 | + | 0.942645i | \(0.608330\pi\) | |||||||
\(542\) | 4.87539 | 0.209416 | ||||||||
\(543\) | 5.31252 | 0.227982 | ||||||||
\(544\) | 6.95418 | 0.298158 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.1625 | −0.648301 | −0.324151 | − | 0.946006i | \(-0.605078\pi\) | ||||
−0.324151 | + | 0.946006i | \(0.605078\pi\) | |||||||
\(548\) | 0.387543 | 0.0165550 | ||||||||
\(549\) | 13.9084 | 0.593595 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.28332 | −0.139874 | ||||||||
\(552\) | −12.7639 | −0.543269 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.05573 | 0.299769 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.41675 | −0.102493 | ||||||||
\(557\) | −13.5208 | −0.572896 | −0.286448 | − | 0.958096i | \(-0.592475\pi\) | ||||
−0.286448 | + | 0.958096i | \(0.592475\pi\) | |||||||
\(558\) | 9.23607 | 0.390994 | ||||||||
\(559\) | −4.05841 | −0.171652 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.4164 | 0.988642 | ||||||||
\(562\) | 29.2189 | 1.23252 | ||||||||
\(563\) | 21.8885 | 0.922492 | 0.461246 | − | 0.887272i | \(-0.347403\pi\) | ||||
0.461246 | + | 0.887272i | \(0.347403\pi\) | |||||||
\(564\) | −3.05573 | −0.128669 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −42.9792 | −1.80655 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −25.1605 | −1.05571 | ||||||||
\(569\) | −16.8328 | −0.705668 | −0.352834 | − | 0.935686i | \(-0.614782\pi\) | ||||
−0.352834 | + | 0.935686i | \(0.614782\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.8328 | 0.453339 | 0.226670 | − | 0.973972i | \(-0.427216\pi\) | ||||
0.226670 | + | 0.973972i | \(0.427216\pi\) | |||||||
\(572\) | 0.806504 | 0.0337216 | ||||||||
\(573\) | 12.4721 | 0.521031 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.70820 | 0.362842 | ||||||||
\(577\) | 14.6525 | 0.609991 | 0.304995 | − | 0.952354i | \(-0.401345\pi\) | ||||
0.304995 | + | 0.952354i | \(0.401345\pi\) | |||||||
\(578\) | −13.8344 | −0.575433 | ||||||||
\(579\) | −19.2209 | −0.798793 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 16.1771 | 0.670562 | ||||||||
\(583\) | −31.1001 | −1.28803 | ||||||||
\(584\) | −21.4896 | −0.889246 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.89578 | −0.119623 | ||||||||
\(587\) | 8.94427 | 0.369170 | 0.184585 | − | 0.982817i | \(-0.440906\pi\) | ||||
0.184585 | + | 0.982817i | \(0.440906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.4164 | 0.470405 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.95418 | −0.286057 | ||||||||
\(592\) | 29.8459 | 1.22666 | ||||||||
\(593\) | 4.29180 | 0.176243 | 0.0881215 | − | 0.996110i | \(-0.471914\pi\) | ||||
0.0881215 | + | 0.996110i | \(0.471914\pi\) | |||||||
\(594\) | 5.93958 | 0.243704 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.249224 | 0.0102086 | ||||||||
\(597\) | 12.2667 | 0.502043 | ||||||||
\(598\) | 4.36068 | 0.178321 | ||||||||
\(599\) | −17.4164 | −0.711615 | −0.355808 | − | 0.934559i | \(-0.615794\pi\) | ||||
−0.355808 | + | 0.934559i | \(0.615794\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.1917 | 0.701264 | 0.350632 | − | 0.936513i | \(-0.385967\pi\) | ||||
0.350632 | + | 0.936513i | \(0.385967\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.59584 | 0.350050 | ||||||||
\(604\) | −2.11146 | −0.0859139 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.34752 | −0.0547394 | ||||||||
\(607\) | 14.8328 | 0.602045 | 0.301023 | − | 0.953617i | \(-0.402672\pi\) | ||||
0.301023 | + | 0.953617i | \(0.402672\pi\) | |||||||
\(608\) | 2.18034 | 0.0884245 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.88854 | 0.400048 | ||||||||
\(612\) | 1.23607 | 0.0499651 | ||||||||
\(613\) | 23.7583 | 0.959590 | 0.479795 | − | 0.877381i | \(-0.340711\pi\) | ||||
0.479795 | + | 0.877381i | \(0.340711\pi\) | |||||||
\(614\) | −8.59584 | −0.346900 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.8333 | 0.758202 | 0.379101 | − | 0.925355i | \(-0.376233\pi\) | ||||
0.379101 | + | 0.925355i | \(0.376233\pi\) | |||||||
\(618\) | −13.9084 | −0.559477 | ||||||||
\(619\) | −41.3376 | −1.66150 | −0.830748 | − | 0.556648i | \(-0.812087\pi\) | ||||
−0.830748 | + | 0.556648i | \(0.812087\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.29792 | −0.172470 | ||||||||
\(622\) | 18.4721 | 0.740665 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.65248 | −0.106184 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.83536 | −0.353132 | ||||||||
\(627\) | 7.34173 | 0.293200 | ||||||||
\(628\) | 5.34752 | 0.213389 | ||||||||
\(629\) | 45.0084 | 1.79460 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.9443 | 1.78920 | 0.894602 | − | 0.446865i | \(-0.147459\pi\) | ||||
0.894602 | + | 0.446865i | \(0.147459\pi\) | |||||||
\(632\) | −14.6835 | −0.584076 | ||||||||
\(633\) | −4.94427 | −0.196517 | ||||||||
\(634\) | 32.0689 | 1.27362 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.64166 | −0.0650961 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.8792 | −0.470301 | ||||||||
\(639\) | −8.47214 | −0.335153 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0000 | 0.710957 | 0.355479 | − | 0.934684i | \(-0.384318\pi\) | ||||
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(642\) | 12.7639 | 0.503752 | ||||||||
\(643\) | 16.3607 | 0.645202 | 0.322601 | − | 0.946535i | \(-0.395443\pi\) | ||||
0.322601 | + | 0.946535i | \(0.395443\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.4164 | −0.449173 | ||||||||
\(647\) | 20.5836 | 0.809225 | 0.404612 | − | 0.914488i | \(-0.367406\pi\) | ||||
0.404612 | + | 0.914488i | \(0.367406\pi\) | |||||||
\(648\) | 2.96979 | 0.116664 | ||||||||
\(649\) | −23.7583 | −0.932596 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.28332 | 0.128585 | ||||||||
\(653\) | 30.7125 | 1.20187 | 0.600937 | − | 0.799297i | \(-0.294794\pi\) | ||||
0.600937 | + | 0.799297i | \(0.294794\pi\) | |||||||
\(654\) | 4.68547 | 0.183216 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −33.3688 | −1.30283 | ||||||||
\(657\) | −7.23607 | −0.282306 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.472136 | 0.0183918 | 0.00919590 | − | 0.999958i | \(-0.497073\pi\) | ||||
0.00919590 | + | 0.999958i | \(0.497073\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.9084 | −0.540973 | −0.270486 | − | 0.962724i | \(-0.587185\pi\) | ||||
−0.270486 | + | 0.962724i | \(0.587185\pi\) | |||||||
\(662\) | −10.6250 | −0.412954 | ||||||||
\(663\) | −4.00000 | −0.155347 | ||||||||
\(664\) | 7.34173 | 0.284914 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.4164 | 0.442377 | ||||||||
\(667\) | 8.59584 | 0.332832 | ||||||||
\(668\) | 2.69505 | 0.104275 | ||||||||
\(669\) | 17.8885 | 0.691611 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 62.2001 | 2.40121 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.9792 | −1.65673 | −0.828364 | − | 0.560191i | \(-0.810728\pi\) | ||||
−0.828364 | + | 0.560191i | \(0.810728\pi\) | |||||||
\(674\) | −18.4721 | −0.711520 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.93112 | 0.112735 | ||||||||
\(677\) | 17.5967 | 0.676298 | 0.338149 | − | 0.941093i | \(-0.390199\pi\) | ||||
0.338149 | + | 0.941093i | \(0.390199\pi\) | |||||||
\(678\) | −20.6525 | −0.793154 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.4721 | −0.401293 | ||||||||
\(682\) | 41.3050 | 1.58165 | ||||||||
\(683\) | 20.2355 | 0.774290 | 0.387145 | − | 0.922019i | \(-0.373461\pi\) | ||||
0.387145 | + | 0.922019i | \(0.373461\pi\) | |||||||
\(684\) | 0.387543 | 0.0148181 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.8792 | 0.453218 | ||||||||
\(688\) | −18.4458 | −0.703240 | ||||||||
\(689\) | 5.31252 | 0.202391 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.387543 | 0.0147428 | 0.00737142 | − | 0.999973i | \(-0.497654\pi\) | ||||
0.00737142 | + | 0.999973i | \(0.497654\pi\) | |||||||
\(692\) | 3.48529 | 0.132491 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.4853 | −0.815571 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.93958 | −0.225139 | ||||||||
\(697\) | −50.3210 | −1.90604 | ||||||||
\(698\) | 41.3050 | 1.56342 | ||||||||
\(699\) | −12.2667 | −0.463970 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.8328 | −1.69331 | −0.846656 | − | 0.532141i | \(-0.821388\pi\) | ||||
−0.846656 | + | 0.532141i | \(0.821388\pi\) | |||||||
\(702\) | −1.01460 | −0.0382937 | ||||||||
\(703\) | 14.1115 | 0.532224 | ||||||||
\(704\) | 38.9443 | 1.46777 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.64166 | 0.0617847 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.25412 | −0.0471326 | ||||||||
\(709\) | −34.0000 | −1.27690 | −0.638448 | − | 0.769665i | \(-0.720423\pi\) | ||||
−0.638448 | + | 0.769665i | \(0.720423\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.94427 | −0.185425 | ||||||||
\(712\) | 38.2918 | 1.43505 | ||||||||
\(713\) | −29.8885 | −1.11933 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.88854 | 0.145322 | ||||||||
\(717\) | 16.4721 | 0.615163 | ||||||||
\(718\) | −15.3105 | −0.571383 | ||||||||
\(719\) | 24.5334 | 0.914942 | 0.457471 | − | 0.889225i | \(-0.348755\pi\) | ||||
0.457471 | + | 0.889225i | \(0.348755\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 21.6551 | 0.805920 | ||||||||
\(723\) | −8.59584 | −0.319683 | ||||||||
\(724\) | 1.25412 | 0.0466089 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 11.9532 | 0.443624 | ||||||||
\(727\) | 10.4721 | 0.388390 | 0.194195 | − | 0.980963i | \(-0.437791\pi\) | ||||
0.194195 | + | 0.980963i | \(0.437791\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.8167 | −1.02884 | ||||||||
\(732\) | 3.28332 | 0.121355 | ||||||||
\(733\) | −11.8197 | −0.436569 | −0.218285 | − | 0.975885i | \(-0.570046\pi\) | ||||
−0.218285 | + | 0.975885i | \(0.570046\pi\) | |||||||
\(734\) | −21.2501 | −0.784355 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.70820 | −0.210407 | ||||||||
\(737\) | 38.4418 | 1.41602 | ||||||||
\(738\) | −12.7639 | −0.469847 | ||||||||
\(739\) | 7.05573 | 0.259549 | 0.129775 | − | 0.991544i | \(-0.458575\pi\) | ||||
0.129775 | + | 0.991544i | \(0.458575\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.25412 | −0.0460711 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.29792 | 0.157675 | 0.0788377 | − | 0.996887i | \(-0.474879\pi\) | ||||
0.0788377 | + | 0.996887i | \(0.474879\pi\) | |||||||
\(744\) | 20.6525 | 0.757157 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.72136 | −0.319312 | ||||||||
\(747\) | 2.47214 | 0.0904507 | ||||||||
\(748\) | 5.52786 | 0.202119 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.8328 | 1.56299 | 0.781496 | − | 0.623910i | \(-0.214457\pi\) | ||||
0.781496 | + | 0.623910i | \(0.214457\pi\) | |||||||
\(752\) | 44.9443 | 1.63895 | ||||||||
\(753\) | 22.5042 | 0.820099 | ||||||||
\(754\) | 2.02920 | 0.0738992 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.4750 | −0.744177 | −0.372088 | − | 0.928197i | \(-0.621358\pi\) | ||||
−0.372088 | + | 0.928197i | \(0.621358\pi\) | |||||||
\(758\) | −27.8167 | −1.01035 | ||||||||
\(759\) | −19.2209 | −0.697674 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.1147 | 1.16416 | 0.582078 | − | 0.813133i | \(-0.302240\pi\) | ||||
0.582078 | + | 0.813133i | \(0.302240\pi\) | |||||||
\(762\) | 18.4721 | 0.669175 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.94427 | 0.106520 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.02920 | 0.0733181 | ||||||||
\(767\) | 4.05841 | 0.146541 | ||||||||
\(768\) | 5.58359 | 0.201481 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.29180 | 0.298622 | ||||||||
\(772\) | −4.53744 | −0.163306 | ||||||||
\(773\) | 16.6525 | 0.598948 | 0.299474 | − | 0.954104i | \(-0.403189\pi\) | ||||
0.299474 | + | 0.954104i | \(0.403189\pi\) | |||||||
\(774\) | −7.05573 | −0.253613 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 36.1731 | 1.29854 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.7271 | −1.13747 | ||||||||
\(779\) | −15.7771 | −0.565273 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.8885 | −1.35576 | ||||||||
\(782\) | 29.8885 | 1.06881 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7.05573 | 0.251669 | ||||||||
\(787\) | 23.0557 | 0.821848 | 0.410924 | − | 0.911670i | \(-0.365206\pi\) | ||||
0.410924 | + | 0.911670i | \(0.365206\pi\) | |||||||
\(788\) | −1.64166 | −0.0584817 | ||||||||
\(789\) | 21.4896 | 0.765050 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 13.2813 | 0.471931 | ||||||||
\(793\) | −10.6250 | −0.377307 | ||||||||
\(794\) | −6.32713 | −0.224541 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.89578 | 0.102638 | ||||||||
\(797\) | −22.7639 | −0.806340 | −0.403170 | − | 0.915125i | \(-0.632092\pi\) | ||||
−0.403170 | + | 0.915125i | \(0.632092\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 67.7771 | 2.39778 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.8938 | 0.455579 | ||||||||
\(802\) | 22.3562 | 0.789424 | ||||||||
\(803\) | −32.3607 | −1.14198 | ||||||||
\(804\) | 2.02920 | 0.0715645 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.05573 | −0.248527 | ||||||||
\(807\) | 9.61045 | 0.338304 | ||||||||
\(808\) | −3.01316 | −0.106002 | ||||||||
\(809\) | −13.0557 | −0.459015 | −0.229507 | − | 0.973307i | \(-0.573712\pi\) | ||||
−0.229507 | + | 0.973307i | \(0.573712\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.5208 | −0.474780 | −0.237390 | − | 0.971414i | \(-0.576292\pi\) | ||||
−0.237390 | + | 0.971414i | \(0.576292\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.67086 | 0.128743 | ||||||||
\(814\) | 51.0557 | 1.78950 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −18.1803 | −0.636439 | ||||||||
\(817\) | −8.72136 | −0.305122 | ||||||||
\(818\) | 39.6393 | 1.38596 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.8885 | −0.973317 | −0.486658 | − | 0.873592i | \(-0.661784\pi\) | ||||
−0.486658 | + | 0.873592i | \(0.661784\pi\) | |||||||
\(822\) | −2.18034 | −0.0760481 | ||||||||
\(823\) | −41.7251 | −1.45445 | −0.727223 | − | 0.686401i | \(-0.759189\pi\) | ||||
−0.727223 | + | 0.686401i | \(0.759189\pi\) | |||||||
\(824\) | −31.1001 | −1.08342 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.8605 | 1.07313 | 0.536563 | − | 0.843860i | \(-0.319722\pi\) | ||||
0.536563 | + | 0.843860i | \(0.319722\pi\) | |||||||
\(828\) | −1.01460 | −0.0352599 | ||||||||
\(829\) | 33.1293 | 1.15063 | 0.575313 | − | 0.817933i | \(-0.304880\pi\) | ||||
0.575313 | + | 0.817933i | \(0.304880\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.31252 | 0.184289 | ||||||||
\(832\) | −6.65248 | −0.230633 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 13.5967 | 0.470817 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.73315 | 0.0599421 | ||||||||
\(837\) | 6.95418 | 0.240372 | ||||||||
\(838\) | 48.3607 | 1.67059 | ||||||||
\(839\) | 4.05841 | 0.140112 | 0.0700559 | − | 0.997543i | \(-0.477682\pi\) | ||||
0.0700559 | + | 0.997543i | \(0.477682\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | −9.99799 | −0.344553 | ||||||||
\(843\) | 22.0000 | 0.757720 | ||||||||
\(844\) | −1.16718 | −0.0401761 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17.1917 | 0.591062 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 24.1459 | 0.829173 | ||||||||
\(849\) | −32.3607 | −1.11062 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.9443 | −1.26643 | ||||||||
\(852\) | −2.00000 | −0.0685189 | ||||||||
\(853\) | −45.1246 | −1.54504 | −0.772519 | − | 0.634992i | \(-0.781003\pi\) | ||||
−0.772519 | + | 0.634992i | \(0.781003\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 28.5410 | 0.975512 | ||||||||
\(857\) | −4.87539 | −0.166540 | −0.0832700 | − | 0.996527i | \(-0.526536\pi\) | ||||
−0.0832700 | + | 0.996527i | \(0.526536\pi\) | |||||||
\(858\) | −4.53744 | −0.154906 | ||||||||
\(859\) | 29.4584 | 1.00511 | 0.502554 | − | 0.864546i | \(-0.332394\pi\) | ||||
0.502554 | + | 0.864546i | \(0.332394\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.93958 | −0.202303 | ||||||||
\(863\) | −23.5188 | −0.800590 | −0.400295 | − | 0.916386i | \(-0.631092\pi\) | ||||
−0.400295 | + | 0.916386i | \(0.631092\pi\) | |||||||
\(864\) | 1.32813 | 0.0451839 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 29.6064 | 1.00607 | ||||||||
\(867\) | −10.4164 | −0.353760 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.1115 | −0.750080 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.56664 | −0.222502 | ||||||||
\(872\) | 10.4770 | 0.354797 | ||||||||
\(873\) | 12.1803 | 0.412242 | ||||||||
\(874\) | 9.37093 | 0.316976 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.70820 | −0.0577149 | ||||||||
\(877\) | −55.6335 | −1.87861 | −0.939304 | − | 0.343085i | \(-0.888528\pi\) | ||||
−0.939304 | + | 0.343085i | \(0.888528\pi\) | |||||||
\(878\) | −6.54102 | −0.220749 | ||||||||
\(879\) | −2.18034 | −0.0735410 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.4604 | −0.655638 | −0.327819 | − | 0.944741i | \(-0.606314\pi\) | ||||
−0.327819 | + | 0.944741i | \(0.606314\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(884\) | −0.944272 | −0.0317593 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32.9017 | 1.10535 | ||||||||
\(887\) | 35.7771 | 1.20128 | 0.600639 | − | 0.799521i | \(-0.294913\pi\) | ||||
0.600639 | + | 0.799521i | \(0.294913\pi\) | |||||||
\(888\) | 25.5279 | 0.856659 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.47214 | 0.149822 | ||||||||
\(892\) | 4.22291 | 0.141394 | ||||||||
\(893\) | 21.2501 | 0.711107 | ||||||||
\(894\) | −1.40215 | −0.0468948 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.28332 | 0.109627 | ||||||||
\(898\) | 46.4106 | 1.54874 | ||||||||
\(899\) | −13.9084 | −0.463870 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.4126 | 1.21308 | ||||||||
\(902\) | −57.0820 | −1.90062 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −46.1803 | −1.53594 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11.8792 | 0.394659 | ||||||||
\(907\) | −21.2501 | −0.705598 | −0.352799 | − | 0.935699i | \(-0.614770\pi\) | ||||
−0.352799 | + | 0.935699i | \(0.614770\pi\) | |||||||
\(908\) | −2.47214 | −0.0820407 | ||||||||
\(909\) | −1.01460 | −0.0336522 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.41641 | −0.0469277 | −0.0234638 | − | 0.999725i | \(-0.507469\pi\) | ||||
−0.0234638 | + | 0.999725i | \(0.507469\pi\) | |||||||
\(912\) | −5.70007 | −0.188748 | ||||||||
\(913\) | 11.0557 | 0.365891 | ||||||||
\(914\) | 32.5836 | 1.07777 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.80429 | 0.0926564 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.95418 | −0.229522 | ||||||||
\(919\) | 4.00000 | 0.131948 | 0.0659739 | − | 0.997821i | \(-0.478985\pi\) | ||||
0.0659739 | + | 0.997821i | \(0.478985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.47214 | −0.213264 | ||||||||
\(922\) | 33.9311 | 1.11746 | ||||||||
\(923\) | 6.47214 | 0.213033 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −27.1935 | −0.893634 | ||||||||
\(927\) | −10.4721 | −0.343950 | ||||||||
\(928\) | −2.65626 | −0.0871961 | ||||||||
\(929\) | 4.29792 | 0.141010 | 0.0705051 | − | 0.997511i | \(-0.477539\pi\) | ||||
0.0705051 | + | 0.997511i | \(0.477539\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.89578 | −0.0948543 | ||||||||
\(933\) | 13.9084 | 0.455340 | ||||||||
\(934\) | −0.775087 | −0.0253616 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.26872 | −0.0741554 | ||||||||
\(937\) | −40.5410 | −1.32442 | −0.662209 | − | 0.749319i | \(-0.730381\pi\) | ||||
−0.662209 | + | 0.749319i | \(0.730381\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.65248 | −0.217095 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.8646 | 0.354175 | 0.177087 | − | 0.984195i | \(-0.443332\pi\) | ||||
0.177087 | + | 0.984195i | \(0.443332\pi\) | |||||||
\(942\) | −30.0855 | −0.980237 | ||||||||
\(943\) | 41.3050 | 1.34507 | ||||||||
\(944\) | 18.4458 | 0.600360 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31.5542 | −1.02591 | ||||||||
\(947\) | −37.4272 | −1.21622 | −0.608110 | − | 0.793853i | \(-0.708072\pi\) | ||||
−0.608110 | + | 0.793853i | \(0.708072\pi\) | |||||||
\(948\) | −1.16718 | −0.0379084 | ||||||||
\(949\) | 5.52786 | 0.179442 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.1459 | 0.782984 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.5168 | 1.08572 | 0.542858 | − | 0.839825i | \(-0.317342\pi\) | ||||
0.542858 | + | 0.839825i | \(0.317342\pi\) | |||||||
\(954\) | 9.23607 | 0.299029 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.88854 | 0.125764 | ||||||||
\(957\) | −8.94427 | −0.289127 | ||||||||
\(958\) | −27.1935 | −0.878582 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.3607 | 0.560022 | ||||||||
\(962\) | −8.72136 | −0.281188 | ||||||||
\(963\) | 9.61045 | 0.309692 | ||||||||
\(964\) | −2.02920 | −0.0653562 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.02920 | −0.0652548 | −0.0326274 | − | 0.999468i | \(-0.510387\pi\) | ||||
−0.0326274 | + | 0.999468i | \(0.510387\pi\) | |||||||
\(968\) | 26.7281 | 0.859074 | ||||||||
\(969\) | −8.59584 | −0.276138 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.53744 | 0.145613 | 0.0728066 | − | 0.997346i | \(-0.476804\pi\) | ||||
0.0728066 | + | 0.997346i | \(0.476804\pi\) | |||||||
\(972\) | 0.236068 | 0.00757188 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 7.05573 | 0.226080 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −48.2917 | −1.54578 | ||||||||
\(977\) | −4.92498 | −0.157564 | −0.0787820 | − | 0.996892i | \(-0.525103\pi\) | ||||
−0.0787820 | + | 0.996892i | \(0.525103\pi\) | |||||||
\(978\) | −18.4721 | −0.590674 | ||||||||
\(979\) | 57.6627 | 1.84291 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.52786 | 0.112636 | ||||||||
\(982\) | 35.0104 | 1.11723 | ||||||||
\(983\) | −14.8328 | −0.473093 | −0.236547 | − | 0.971620i | \(-0.576016\pi\) | ||||
−0.236547 | + | 0.971620i | \(0.576016\pi\) | |||||||
\(984\) | −28.5410 | −0.909854 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 13.9084 | 0.442933 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.296057 | −0.00941882 | ||||||||
\(989\) | 22.8328 | 0.726041 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.0000 | 1.14358 | 0.571789 | − | 0.820401i | \(-0.306250\pi\) | ||||
0.571789 | + | 0.820401i | \(0.306250\pi\) | |||||||
\(992\) | 9.23607 | 0.293245 | ||||||||
\(993\) | −8.00000 | −0.253872 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.583592 | 0.0184918 | ||||||||
\(997\) | −14.2918 | −0.452626 | −0.226313 | − | 0.974055i | \(-0.572667\pi\) | ||||
−0.226313 | + | 0.974055i | \(0.572667\pi\) | |||||||
\(998\) | −10.6250 | −0.336330 | ||||||||
\(999\) | 8.59584 | 0.271960 |
(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 | 3675.2.a.bt.1.2 | 4 | ||
5.2 | odd | 4 | 735.2.d.c.589.4 | yes | 8 | ||
5.3 | odd | 4 | 735.2.d.c.589.5 | yes | 8 | ||
5.4 | even | 2 | 3675.2.a.bv.1.3 | 4 | |||
7.6 | odd | 2 | 3675.2.a.bv.1.2 | 4 | |||
15.2 | even | 4 | 2205.2.d.m.1324.6 | 8 | |||
15.8 | even | 4 | 2205.2.d.m.1324.4 | 8 | |||
35.2 | odd | 12 | 735.2.q.h.214.3 | 16 | |||
35.3 | even | 12 | 735.2.q.h.79.4 | 16 | |||
35.12 | even | 12 | 735.2.q.h.214.4 | 16 | |||
35.13 | even | 4 | 735.2.d.c.589.6 | yes | 8 | ||
35.17 | even | 12 | 735.2.q.h.79.5 | 16 | |||
35.18 | odd | 12 | 735.2.q.h.79.3 | 16 | |||
35.23 | odd | 12 | 735.2.q.h.214.6 | 16 | |||
35.27 | even | 4 | 735.2.d.c.589.3 | ✓ | 8 | ||
35.32 | odd | 12 | 735.2.q.h.79.6 | 16 | |||
35.33 | even | 12 | 735.2.q.h.214.5 | 16 | |||
35.34 | odd | 2 | inner | 3675.2.a.bt.1.3 | 4 | ||
105.62 | odd | 4 | 2205.2.d.m.1324.5 | 8 | |||
105.83 | odd | 4 | 2205.2.d.m.1324.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
735.2.d.c.589.3 | ✓ | 8 | 35.27 | even | 4 | ||
735.2.d.c.589.4 | yes | 8 | 5.2 | odd | 4 | ||
735.2.d.c.589.5 | yes | 8 | 5.3 | odd | 4 | ||
735.2.d.c.589.6 | yes | 8 | 35.13 | even | 4 | ||
735.2.q.h.79.3 | 16 | 35.18 | odd | 12 | |||
735.2.q.h.79.4 | 16 | 35.3 | even | 12 | |||
735.2.q.h.79.5 | 16 | 35.17 | even | 12 | |||
735.2.q.h.79.6 | 16 | 35.32 | odd | 12 | |||
735.2.q.h.214.3 | 16 | 35.2 | odd | 12 | |||
735.2.q.h.214.4 | 16 | 35.12 | even | 12 | |||
735.2.q.h.214.5 | 16 | 35.33 | even | 12 | |||
735.2.q.h.214.6 | 16 | 35.23 | odd | 12 | |||
2205.2.d.m.1324.3 | 8 | 105.83 | odd | 4 | |||
2205.2.d.m.1324.4 | 8 | 15.8 | even | 4 | |||
2205.2.d.m.1324.5 | 8 | 105.62 | odd | 4 | |||
2205.2.d.m.1324.6 | 8 | 15.2 | even | 4 | |||
3675.2.a.bt.1.2 | 4 | 1.1 | even | 1 | trivial | ||
3675.2.a.bt.1.3 | 4 | 35.34 | odd | 2 | inner | ||
3675.2.a.bv.1.2 | 4 | 7.6 | odd | 2 | |||
3675.2.a.bv.1.3 | 4 | 5.4 | even | 2 |