Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, 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("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.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: | \(32.1477718538\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7537.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.15976\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.66454 | −0.744407 | −0.372204 | − | 0.928151i | \(-0.621398\pi\) | ||||
−0.372204 | + | 0.928151i | \(0.621398\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.43525 | −0.920440 | −0.460220 | − | 0.887805i | \(-0.652229\pi\) | ||||
−0.460220 | + | 0.887805i | \(0.652229\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.66454 | 0.526375 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 6.41931 | 1.78040 | 0.890198 | − | 0.455573i | \(-0.150566\pi\) | ||||
0.890198 | + | 0.455573i | \(0.150566\pi\) | |||||||
\(14\) | 2.43525 | 0.650849 | ||||||||
\(15\) | −1.66454 | −0.429784 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.265921 | −0.0644952 | −0.0322476 | − | 0.999480i | \(-0.510267\pi\) | ||||
−0.0322476 | + | 0.999480i | \(0.510267\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −4.82430 | −1.10677 | −0.553385 | − | 0.832925i | \(-0.686664\pi\) | ||||
−0.553385 | + | 0.832925i | \(0.686664\pi\) | |||||||
\(20\) | −1.66454 | −0.372204 | ||||||||
\(21\) | −2.43525 | −0.531416 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 5.37530 | 1.12083 | 0.560414 | − | 0.828213i | \(-0.310642\pi\) | ||||
0.560414 | + | 0.828213i | \(0.310642\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.22929 | −0.445858 | ||||||||
\(26\) | −6.41931 | −1.25893 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.43525 | −0.460220 | ||||||||
\(29\) | 2.75477 | 0.511547 | 0.255774 | − | 0.966737i | \(-0.417670\pi\) | ||||
0.255774 | + | 0.966737i | \(0.417670\pi\) | |||||||
\(30\) | 1.66454 | 0.303903 | ||||||||
\(31\) | −4.15018 | −0.745394 | −0.372697 | − | 0.927953i | \(-0.621567\pi\) | ||||
−0.372697 | + | 0.927953i | \(0.621567\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0.265921 | 0.0456050 | ||||||||
\(35\) | 4.05359 | 0.685182 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.27330 | −1.03132 | −0.515662 | − | 0.856792i | \(-0.672454\pi\) | ||||
−0.515662 | + | 0.856792i | \(0.672454\pi\) | |||||||
\(38\) | 4.82430 | 0.782605 | ||||||||
\(39\) | 6.41931 | 1.02791 | ||||||||
\(40\) | 1.66454 | 0.263188 | ||||||||
\(41\) | 7.91452 | 1.23604 | 0.618020 | − | 0.786162i | \(-0.287935\pi\) | ||||
0.618020 | + | 0.786162i | \(0.287935\pi\) | |||||||
\(42\) | 2.43525 | 0.375768 | ||||||||
\(43\) | −10.7086 | −1.63304 | −0.816520 | − | 0.577317i | \(-0.804100\pi\) | ||||
−0.816520 | + | 0.577317i | \(0.804100\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −1.66454 | −0.248136 | ||||||||
\(46\) | −5.37530 | −0.792545 | ||||||||
\(47\) | 0.474524 | 0.0692164 | 0.0346082 | − | 0.999401i | \(-0.488982\pi\) | ||||
0.0346082 | + | 0.999401i | \(0.488982\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −1.06953 | −0.152791 | ||||||||
\(50\) | 2.22929 | 0.315269 | ||||||||
\(51\) | −0.265921 | −0.0372363 | ||||||||
\(52\) | 6.41931 | 0.890198 | ||||||||
\(53\) | −10.2691 | −1.41057 | −0.705287 | − | 0.708922i | \(-0.749182\pi\) | ||||
−0.705287 | + | 0.708922i | \(0.749182\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 1.66454 | 0.224447 | ||||||||
\(56\) | 2.43525 | 0.325425 | ||||||||
\(57\) | −4.82430 | −0.638994 | ||||||||
\(58\) | −2.75477 | −0.361719 | ||||||||
\(59\) | 10.8275 | 1.40962 | 0.704811 | − | 0.709395i | \(-0.251032\pi\) | ||||
0.704811 | + | 0.709395i | \(0.251032\pi\) | |||||||
\(60\) | −1.66454 | −0.214892 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 4.15018 | 0.527073 | ||||||||
\(63\) | −2.43525 | −0.306813 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −10.6852 | −1.32534 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 1.15976 | 0.141687 | 0.0708434 | − | 0.997487i | \(-0.477431\pi\) | ||||
0.0708434 | + | 0.997487i | \(0.477431\pi\) | |||||||
\(68\) | −0.265921 | −0.0322476 | ||||||||
\(69\) | 5.37530 | 0.647110 | ||||||||
\(70\) | −4.05359 | −0.484497 | ||||||||
\(71\) | 6.34978 | 0.753580 | 0.376790 | − | 0.926299i | \(-0.377028\pi\) | ||||
0.376790 | + | 0.926299i | \(0.377028\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 14.8153 | 1.73400 | 0.867000 | − | 0.498309i | \(-0.166045\pi\) | ||||
0.867000 | + | 0.498309i | \(0.166045\pi\) | |||||||
\(74\) | 6.27330 | 0.729257 | ||||||||
\(75\) | −2.22929 | −0.257416 | ||||||||
\(76\) | −4.82430 | −0.553385 | ||||||||
\(77\) | 2.43525 | 0.277523 | ||||||||
\(78\) | −6.41931 | −0.726844 | ||||||||
\(79\) | −13.9607 | −1.57070 | −0.785352 | − | 0.619049i | \(-0.787518\pi\) | ||||
−0.785352 | + | 0.619049i | \(0.787518\pi\) | |||||||
\(80\) | −1.66454 | −0.186102 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.91452 | −0.874013 | ||||||||
\(83\) | 7.07428 | 0.776503 | 0.388251 | − | 0.921553i | \(-0.373079\pi\) | ||||
0.388251 | + | 0.921553i | \(0.373079\pi\) | |||||||
\(84\) | −2.43525 | −0.265708 | ||||||||
\(85\) | 0.442637 | 0.0480107 | ||||||||
\(86\) | 10.7086 | 1.15473 | ||||||||
\(87\) | 2.75477 | 0.295342 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 4.10397 | 0.435020 | 0.217510 | − | 0.976058i | \(-0.430207\pi\) | ||||
0.217510 | + | 0.976058i | \(0.430207\pi\) | |||||||
\(90\) | 1.66454 | 0.175458 | ||||||||
\(91\) | −15.6327 | −1.63875 | ||||||||
\(92\) | 5.37530 | 0.560414 | ||||||||
\(93\) | −4.15018 | −0.430353 | ||||||||
\(94\) | −0.474524 | −0.0489434 | ||||||||
\(95\) | 8.03027 | 0.823888 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 4.25736 | 0.432269 | 0.216135 | − | 0.976364i | \(-0.430655\pi\) | ||||
0.216135 | + | 0.976364i | \(0.430655\pi\) | |||||||
\(98\) | 1.06953 | 0.108039 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −2.22929 | −0.222929 | ||||||||
\(101\) | −0.316298 | −0.0314729 | −0.0157364 | − | 0.999876i | \(-0.505009\pi\) | ||||
−0.0157364 | + | 0.999876i | \(0.505009\pi\) | |||||||
\(102\) | 0.265921 | 0.0263301 | ||||||||
\(103\) | 1.55297 | 0.153019 | 0.0765094 | − | 0.997069i | \(-0.475622\pi\) | ||||
0.0765094 | + | 0.997069i | \(0.475622\pi\) | |||||||
\(104\) | −6.41931 | −0.629465 | ||||||||
\(105\) | 4.05359 | 0.395590 | ||||||||
\(106\) | 10.2691 | 0.997426 | ||||||||
\(107\) | −18.5998 | −1.79811 | −0.899053 | − | 0.437840i | \(-0.855744\pi\) | ||||
−0.899053 | + | 0.437840i | \(0.855744\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −5.78029 | −0.553651 | −0.276826 | − | 0.960920i | \(-0.589282\pi\) | ||||
−0.276826 | + | 0.960920i | \(0.589282\pi\) | |||||||
\(110\) | −1.66454 | −0.158708 | ||||||||
\(111\) | −6.27330 | −0.595436 | ||||||||
\(112\) | −2.43525 | −0.230110 | ||||||||
\(113\) | 2.38905 | 0.224743 | 0.112371 | − | 0.993666i | \(-0.464155\pi\) | ||||
0.112371 | + | 0.993666i | \(0.464155\pi\) | |||||||
\(114\) | 4.82430 | 0.451837 | ||||||||
\(115\) | −8.94743 | −0.834352 | ||||||||
\(116\) | 2.75477 | 0.255774 | ||||||||
\(117\) | 6.41931 | 0.593466 | ||||||||
\(118\) | −10.8275 | −0.996753 | ||||||||
\(119\) | 0.647584 | 0.0593640 | ||||||||
\(120\) | 1.66454 | 0.151951 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | 7.91452 | 0.713628 | ||||||||
\(124\) | −4.15018 | −0.372697 | ||||||||
\(125\) | 12.0335 | 1.07631 | ||||||||
\(126\) | 2.43525 | 0.216950 | ||||||||
\(127\) | −15.7341 | −1.39617 | −0.698087 | − | 0.716013i | \(-0.745965\pi\) | ||||
−0.698087 | + | 0.716013i | \(0.745965\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −10.7086 | −0.942836 | ||||||||
\(130\) | 10.6852 | 0.937157 | ||||||||
\(131\) | −4.72771 | −0.413062 | −0.206531 | − | 0.978440i | \(-0.566217\pi\) | ||||
−0.206531 | + | 0.978440i | \(0.566217\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 11.7484 | 1.01872 | ||||||||
\(134\) | −1.15976 | −0.100188 | ||||||||
\(135\) | −1.66454 | −0.143261 | ||||||||
\(136\) | 0.265921 | 0.0228025 | ||||||||
\(137\) | −14.3137 | −1.22290 | −0.611452 | − | 0.791282i | \(-0.709414\pi\) | ||||
−0.611452 | + | 0.791282i | \(0.709414\pi\) | |||||||
\(138\) | −5.37530 | −0.457576 | ||||||||
\(139\) | −18.7388 | −1.58941 | −0.794703 | − | 0.606998i | \(-0.792373\pi\) | ||||
−0.794703 | + | 0.606998i | \(0.792373\pi\) | |||||||
\(140\) | 4.05359 | 0.342591 | ||||||||
\(141\) | 0.474524 | 0.0399621 | ||||||||
\(142\) | −6.34978 | −0.532861 | ||||||||
\(143\) | −6.41931 | −0.536810 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −4.58543 | −0.380799 | ||||||||
\(146\) | −14.8153 | −1.22612 | ||||||||
\(147\) | −1.06953 | −0.0882137 | ||||||||
\(148\) | −6.27330 | −0.515662 | ||||||||
\(149\) | −9.36352 | −0.767090 | −0.383545 | − | 0.923522i | \(-0.625297\pi\) | ||||
−0.383545 | + | 0.923522i | \(0.625297\pi\) | |||||||
\(150\) | 2.22929 | 0.182021 | ||||||||
\(151\) | −22.6721 | −1.84503 | −0.922513 | − | 0.385966i | \(-0.873868\pi\) | ||||
−0.922513 | + | 0.385966i | \(0.873868\pi\) | |||||||
\(152\) | 4.82430 | 0.391302 | ||||||||
\(153\) | −0.265921 | −0.0214984 | ||||||||
\(154\) | −2.43525 | −0.196238 | ||||||||
\(155\) | 6.90816 | 0.554877 | ||||||||
\(156\) | 6.41931 | 0.513956 | ||||||||
\(157\) | 8.87468 | 0.708276 | 0.354138 | − | 0.935193i | \(-0.384774\pi\) | ||||
0.354138 | + | 0.935193i | \(0.384774\pi\) | |||||||
\(158\) | 13.9607 | 1.11066 | ||||||||
\(159\) | −10.2691 | −0.814395 | ||||||||
\(160\) | 1.66454 | 0.131594 | ||||||||
\(161\) | −13.0902 | −1.03165 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −0.454411 | −0.0355922 | −0.0177961 | − | 0.999842i | \(-0.505665\pi\) | ||||
−0.0177961 | + | 0.999842i | \(0.505665\pi\) | |||||||
\(164\) | 7.91452 | 0.618020 | ||||||||
\(165\) | 1.66454 | 0.129585 | ||||||||
\(166\) | −7.07428 | −0.549070 | ||||||||
\(167\) | −17.4592 | −1.35103 | −0.675515 | − | 0.737346i | \(-0.736079\pi\) | ||||
−0.675515 | + | 0.737346i | \(0.736079\pi\) | |||||||
\(168\) | 2.43525 | 0.187884 | ||||||||
\(169\) | 28.2076 | 2.16981 | ||||||||
\(170\) | −0.442637 | −0.0339487 | ||||||||
\(171\) | −4.82430 | −0.368923 | ||||||||
\(172\) | −10.7086 | −0.816520 | ||||||||
\(173\) | −17.7516 | −1.34963 | −0.674815 | − | 0.737987i | \(-0.735777\pi\) | ||||
−0.674815 | + | 0.737987i | \(0.735777\pi\) | |||||||
\(174\) | −2.75477 | −0.208838 | ||||||||
\(175\) | 5.42889 | 0.410385 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 10.8275 | 0.813846 | ||||||||
\(178\) | −4.10397 | −0.307605 | ||||||||
\(179\) | −24.8418 | −1.85677 | −0.928383 | − | 0.371625i | \(-0.878801\pi\) | ||||
−0.928383 | + | 0.371625i | \(0.878801\pi\) | |||||||
\(180\) | −1.66454 | −0.124068 | ||||||||
\(181\) | −25.7352 | −1.91288 | −0.956442 | − | 0.291922i | \(-0.905705\pi\) | ||||
−0.956442 | + | 0.291922i | \(0.905705\pi\) | |||||||
\(182\) | 15.6327 | 1.15877 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | −5.37530 | −0.396272 | ||||||||
\(185\) | 10.4422 | 0.767725 | ||||||||
\(186\) | 4.15018 | 0.304306 | ||||||||
\(187\) | 0.265921 | 0.0194460 | ||||||||
\(188\) | 0.474524 | 0.0346082 | ||||||||
\(189\) | −2.43525 | −0.177139 | ||||||||
\(190\) | −8.03027 | −0.582577 | ||||||||
\(191\) | −22.6603 | −1.63964 | −0.819820 | − | 0.572621i | \(-0.805927\pi\) | ||||
−0.819820 | + | 0.572621i | \(0.805927\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −19.8646 | −1.42988 | −0.714942 | − | 0.699184i | \(-0.753547\pi\) | ||||
−0.714942 | + | 0.699184i | \(0.753547\pi\) | |||||||
\(194\) | −4.25736 | −0.305661 | ||||||||
\(195\) | −10.6852 | −0.765185 | ||||||||
\(196\) | −1.06953 | −0.0763953 | ||||||||
\(197\) | −4.40776 | −0.314040 | −0.157020 | − | 0.987595i | \(-0.550189\pi\) | ||||
−0.157020 | + | 0.987595i | \(0.550189\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 9.74936 | 0.691114 | 0.345557 | − | 0.938398i | \(-0.387690\pi\) | ||||
0.345557 | + | 0.938398i | \(0.387690\pi\) | |||||||
\(200\) | 2.22929 | 0.157635 | ||||||||
\(201\) | 1.15976 | 0.0818029 | ||||||||
\(202\) | 0.316298 | 0.0222547 | ||||||||
\(203\) | −6.70856 | −0.470848 | ||||||||
\(204\) | −0.265921 | −0.0186182 | ||||||||
\(205\) | −13.1741 | −0.920117 | ||||||||
\(206\) | −1.55297 | −0.108201 | ||||||||
\(207\) | 5.37530 | 0.373609 | ||||||||
\(208\) | 6.41931 | 0.445099 | ||||||||
\(209\) | 4.82430 | 0.333704 | ||||||||
\(210\) | −4.05359 | −0.279724 | ||||||||
\(211\) | 22.5478 | 1.55225 | 0.776126 | − | 0.630578i | \(-0.217182\pi\) | ||||
0.776126 | + | 0.630578i | \(0.217182\pi\) | |||||||
\(212\) | −10.2691 | −0.705287 | ||||||||
\(213\) | 6.34978 | 0.435080 | ||||||||
\(214\) | 18.5998 | 1.27145 | ||||||||
\(215\) | 17.8249 | 1.21565 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 10.1067 | 0.686090 | ||||||||
\(218\) | 5.78029 | 0.391491 | ||||||||
\(219\) | 14.8153 | 1.00112 | ||||||||
\(220\) | 1.66454 | 0.112224 | ||||||||
\(221\) | −1.70703 | −0.114827 | ||||||||
\(222\) | 6.27330 | 0.421037 | ||||||||
\(223\) | 22.9878 | 1.53938 | 0.769690 | − | 0.638418i | \(-0.220411\pi\) | ||||
0.769690 | + | 0.638418i | \(0.220411\pi\) | |||||||
\(224\) | 2.43525 | 0.162712 | ||||||||
\(225\) | −2.22929 | −0.148619 | ||||||||
\(226\) | −2.38905 | −0.158917 | ||||||||
\(227\) | −13.5329 | −0.898207 | −0.449104 | − | 0.893480i | \(-0.648257\pi\) | ||||
−0.449104 | + | 0.893480i | \(0.648257\pi\) | |||||||
\(228\) | −4.82430 | −0.319497 | ||||||||
\(229\) | −4.39321 | −0.290312 | −0.145156 | − | 0.989409i | \(-0.546368\pi\) | ||||
−0.145156 | + | 0.989409i | \(0.546368\pi\) | |||||||
\(230\) | 8.94743 | 0.589976 | ||||||||
\(231\) | 2.43525 | 0.160228 | ||||||||
\(232\) | −2.75477 | −0.180859 | ||||||||
\(233\) | −10.2601 | −0.672163 | −0.336082 | − | 0.941833i | \(-0.609102\pi\) | ||||
−0.336082 | + | 0.941833i | \(0.609102\pi\) | |||||||
\(234\) | −6.41931 | −0.419643 | ||||||||
\(235\) | −0.789866 | −0.0515252 | ||||||||
\(236\) | 10.8275 | 0.704811 | ||||||||
\(237\) | −13.9607 | −0.906847 | ||||||||
\(238\) | −0.647584 | −0.0419767 | ||||||||
\(239\) | 20.2952 | 1.31279 | 0.656395 | − | 0.754418i | \(-0.272081\pi\) | ||||
0.656395 | + | 0.754418i | \(0.272081\pi\) | |||||||
\(240\) | −1.66454 | −0.107446 | ||||||||
\(241\) | −4.10674 | −0.264538 | −0.132269 | − | 0.991214i | \(-0.542226\pi\) | ||||
−0.132269 | + | 0.991214i | \(0.542226\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | 1.78029 | 0.113738 | ||||||||
\(246\) | −7.91452 | −0.504611 | ||||||||
\(247\) | −30.9687 | −1.97049 | ||||||||
\(248\) | 4.15018 | 0.263537 | ||||||||
\(249\) | 7.07428 | 0.448314 | ||||||||
\(250\) | −12.0335 | −0.761064 | ||||||||
\(251\) | −0.778315 | −0.0491268 | −0.0245634 | − | 0.999698i | \(-0.507820\pi\) | ||||
−0.0245634 | + | 0.999698i | \(0.507820\pi\) | |||||||
\(252\) | −2.43525 | −0.153407 | ||||||||
\(253\) | −5.37530 | −0.337942 | ||||||||
\(254\) | 15.7341 | 0.987244 | ||||||||
\(255\) | 0.442637 | 0.0277190 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.1418 | 1.00690 | 0.503450 | − | 0.864024i | \(-0.332064\pi\) | ||||
0.503450 | + | 0.864024i | \(0.332064\pi\) | |||||||
\(258\) | 10.7086 | 0.666686 | ||||||||
\(259\) | 15.2771 | 0.949272 | ||||||||
\(260\) | −10.6852 | −0.662670 | ||||||||
\(261\) | 2.75477 | 0.170516 | ||||||||
\(262\) | 4.72771 | 0.292079 | ||||||||
\(263\) | −6.31095 | −0.389150 | −0.194575 | − | 0.980888i | \(-0.562333\pi\) | ||||
−0.194575 | + | 0.980888i | \(0.562333\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | 17.0934 | 1.05004 | ||||||||
\(266\) | −11.7484 | −0.720341 | ||||||||
\(267\) | 4.10397 | 0.251159 | ||||||||
\(268\) | 1.15976 | 0.0708434 | ||||||||
\(269\) | 22.7531 | 1.38728 | 0.693642 | − | 0.720320i | \(-0.256005\pi\) | ||||
0.693642 | + | 0.720320i | \(0.256005\pi\) | |||||||
\(270\) | 1.66454 | 0.101301 | ||||||||
\(271\) | −7.33699 | −0.445690 | −0.222845 | − | 0.974854i | \(-0.571534\pi\) | ||||
−0.222845 | + | 0.974854i | \(0.571534\pi\) | |||||||
\(272\) | −0.265921 | −0.0161238 | ||||||||
\(273\) | −15.6327 | −0.946131 | ||||||||
\(274\) | 14.3137 | 0.864723 | ||||||||
\(275\) | 2.22929 | 0.134431 | ||||||||
\(276\) | 5.37530 | 0.323555 | ||||||||
\(277\) | −8.14645 | −0.489473 | −0.244736 | − | 0.969590i | \(-0.578701\pi\) | ||||
−0.244736 | + | 0.969590i | \(0.578701\pi\) | |||||||
\(278\) | 18.7388 | 1.12388 | ||||||||
\(279\) | −4.15018 | −0.248465 | ||||||||
\(280\) | −4.05359 | −0.242248 | ||||||||
\(281\) | −15.4404 | −0.921099 | −0.460550 | − | 0.887634i | \(-0.652348\pi\) | ||||
−0.460550 | + | 0.887634i | \(0.652348\pi\) | |||||||
\(282\) | −0.474524 | −0.0282575 | ||||||||
\(283\) | 5.37947 | 0.319776 | 0.159888 | − | 0.987135i | \(-0.448887\pi\) | ||||
0.159888 | + | 0.987135i | \(0.448887\pi\) | |||||||
\(284\) | 6.34978 | 0.376790 | ||||||||
\(285\) | 8.03027 | 0.475672 | ||||||||
\(286\) | 6.41931 | 0.379582 | ||||||||
\(287\) | −19.2739 | −1.13770 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.9293 | −0.995840 | ||||||||
\(290\) | 4.58543 | 0.269266 | ||||||||
\(291\) | 4.25736 | 0.249571 | ||||||||
\(292\) | 14.8153 | 0.867000 | ||||||||
\(293\) | 25.2818 | 1.47698 | 0.738488 | − | 0.674266i | \(-0.235540\pi\) | ||||
0.738488 | + | 0.674266i | \(0.235540\pi\) | |||||||
\(294\) | 1.06953 | 0.0623765 | ||||||||
\(295\) | −18.0229 | −1.04933 | ||||||||
\(296\) | 6.27330 | 0.364628 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 9.36352 | 0.542414 | ||||||||
\(299\) | 34.5057 | 1.99552 | ||||||||
\(300\) | −2.22929 | −0.128708 | ||||||||
\(301\) | 26.0781 | 1.50311 | ||||||||
\(302\) | 22.6721 | 1.30463 | ||||||||
\(303\) | −0.316298 | −0.0181709 | ||||||||
\(304\) | −4.82430 | −0.276693 | ||||||||
\(305\) | −1.66454 | −0.0953116 | ||||||||
\(306\) | 0.265921 | 0.0152017 | ||||||||
\(307\) | −19.0780 | −1.08884 | −0.544420 | − | 0.838813i | \(-0.683250\pi\) | ||||
−0.544420 | + | 0.838813i | \(0.683250\pi\) | |||||||
\(308\) | 2.43525 | 0.138762 | ||||||||
\(309\) | 1.55297 | 0.0883454 | ||||||||
\(310\) | −6.90816 | −0.392357 | ||||||||
\(311\) | 32.0099 | 1.81512 | 0.907558 | − | 0.419926i | \(-0.137944\pi\) | ||||
0.907558 | + | 0.419926i | \(0.137944\pi\) | |||||||
\(312\) | −6.41931 | −0.363422 | ||||||||
\(313\) | −23.9824 | −1.35557 | −0.677784 | − | 0.735261i | \(-0.737059\pi\) | ||||
−0.677784 | + | 0.735261i | \(0.737059\pi\) | |||||||
\(314\) | −8.87468 | −0.500827 | ||||||||
\(315\) | 4.05359 | 0.228394 | ||||||||
\(316\) | −13.9607 | −0.785352 | ||||||||
\(317\) | 3.15237 | 0.177055 | 0.0885275 | − | 0.996074i | \(-0.471784\pi\) | ||||
0.0885275 | + | 0.996074i | \(0.471784\pi\) | |||||||
\(318\) | 10.2691 | 0.575864 | ||||||||
\(319\) | −2.75477 | −0.154237 | ||||||||
\(320\) | −1.66454 | −0.0930509 | ||||||||
\(321\) | −18.5998 | −1.03814 | ||||||||
\(322\) | 13.0902 | 0.729490 | ||||||||
\(323\) | 1.28288 | 0.0713814 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −14.3105 | −0.793804 | ||||||||
\(326\) | 0.454411 | 0.0251675 | ||||||||
\(327\) | −5.78029 | −0.319651 | ||||||||
\(328\) | −7.91452 | −0.437006 | ||||||||
\(329\) | −1.15559 | −0.0637096 | ||||||||
\(330\) | −1.66454 | −0.0916302 | ||||||||
\(331\) | −35.5079 | −1.95169 | −0.975846 | − | 0.218461i | \(-0.929896\pi\) | ||||
−0.975846 | + | 0.218461i | \(0.929896\pi\) | |||||||
\(332\) | 7.07428 | 0.388251 | ||||||||
\(333\) | −6.27330 | −0.343775 | ||||||||
\(334\) | 17.4592 | 0.955322 | ||||||||
\(335\) | −1.93047 | −0.105473 | ||||||||
\(336\) | −2.43525 | −0.132854 | ||||||||
\(337\) | −10.3992 | −0.566480 | −0.283240 | − | 0.959049i | \(-0.591409\pi\) | ||||
−0.283240 | + | 0.959049i | \(0.591409\pi\) | |||||||
\(338\) | −28.2076 | −1.53429 | ||||||||
\(339\) | 2.38905 | 0.129755 | ||||||||
\(340\) | 0.442637 | 0.0240054 | ||||||||
\(341\) | 4.15018 | 0.224745 | ||||||||
\(342\) | 4.82430 | 0.260868 | ||||||||
\(343\) | 19.6514 | 1.06107 | ||||||||
\(344\) | 10.7086 | 0.577367 | ||||||||
\(345\) | −8.94743 | −0.481713 | ||||||||
\(346\) | 17.7516 | 0.954333 | ||||||||
\(347\) | −19.5319 | −1.04853 | −0.524264 | − | 0.851556i | \(-0.675659\pi\) | ||||
−0.524264 | + | 0.851556i | \(0.675659\pi\) | |||||||
\(348\) | 2.75477 | 0.147671 | ||||||||
\(349\) | −9.23667 | −0.494428 | −0.247214 | − | 0.968961i | \(-0.579515\pi\) | ||||
−0.247214 | + | 0.968961i | \(0.579515\pi\) | |||||||
\(350\) | −5.42889 | −0.290186 | ||||||||
\(351\) | 6.41931 | 0.342637 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −8.02126 | −0.426929 | −0.213464 | − | 0.976951i | \(-0.568475\pi\) | ||||
−0.213464 | + | 0.976951i | \(0.568475\pi\) | |||||||
\(354\) | −10.8275 | −0.575476 | ||||||||
\(355\) | −10.5695 | −0.560970 | ||||||||
\(356\) | 4.10397 | 0.217510 | ||||||||
\(357\) | 0.647584 | 0.0342738 | ||||||||
\(358\) | 24.8418 | 1.31293 | ||||||||
\(359\) | 32.7129 | 1.72652 | 0.863261 | − | 0.504758i | \(-0.168418\pi\) | ||||
0.863261 | + | 0.504758i | \(0.168418\pi\) | |||||||
\(360\) | 1.66454 | 0.0877292 | ||||||||
\(361\) | 4.27388 | 0.224941 | ||||||||
\(362\) | 25.7352 | 1.35261 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −15.6327 | −0.819374 | ||||||||
\(365\) | −24.6607 | −1.29080 | ||||||||
\(366\) | −1.00000 | −0.0522708 | ||||||||
\(367\) | 11.7532 | 0.613514 | 0.306757 | − | 0.951788i | \(-0.400756\pi\) | ||||
0.306757 | + | 0.951788i | \(0.400756\pi\) | |||||||
\(368\) | 5.37530 | 0.280207 | ||||||||
\(369\) | 7.91452 | 0.412014 | ||||||||
\(370\) | −10.4422 | −0.542864 | ||||||||
\(371\) | 25.0080 | 1.29835 | ||||||||
\(372\) | −4.15018 | −0.215177 | ||||||||
\(373\) | 21.7119 | 1.12420 | 0.562100 | − | 0.827069i | \(-0.309994\pi\) | ||||
0.562100 | + | 0.827069i | \(0.309994\pi\) | |||||||
\(374\) | −0.265921 | −0.0137504 | ||||||||
\(375\) | 12.0335 | 0.621406 | ||||||||
\(376\) | −0.474524 | −0.0244717 | ||||||||
\(377\) | 17.6837 | 0.910757 | ||||||||
\(378\) | 2.43525 | 0.125256 | ||||||||
\(379\) | −28.2596 | −1.45160 | −0.725799 | − | 0.687906i | \(-0.758530\pi\) | ||||
−0.725799 | + | 0.687906i | \(0.758530\pi\) | |||||||
\(380\) | 8.03027 | 0.411944 | ||||||||
\(381\) | −15.7341 | −0.806081 | ||||||||
\(382\) | 22.6603 | 1.15940 | ||||||||
\(383\) | −30.0875 | −1.53740 | −0.768700 | − | 0.639609i | \(-0.779096\pi\) | ||||
−0.768700 | + | 0.639609i | \(0.779096\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −4.05359 | −0.206590 | ||||||||
\(386\) | 19.8646 | 1.01108 | ||||||||
\(387\) | −10.7086 | −0.544347 | ||||||||
\(388\) | 4.25736 | 0.216135 | ||||||||
\(389\) | 3.01375 | 0.152803 | 0.0764015 | − | 0.997077i | \(-0.475657\pi\) | ||||
0.0764015 | + | 0.997077i | \(0.475657\pi\) | |||||||
\(390\) | 10.6852 | 0.541068 | ||||||||
\(391\) | −1.42940 | −0.0722880 | ||||||||
\(392\) | 1.06953 | 0.0540196 | ||||||||
\(393\) | −4.72771 | −0.238482 | ||||||||
\(394\) | 4.40776 | 0.222060 | ||||||||
\(395\) | 23.2383 | 1.16924 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 31.0546 | 1.55859 | 0.779293 | − | 0.626660i | \(-0.215578\pi\) | ||||
0.779293 | + | 0.626660i | \(0.215578\pi\) | |||||||
\(398\) | −9.74936 | −0.488691 | ||||||||
\(399\) | 11.7484 | 0.588156 | ||||||||
\(400\) | −2.22929 | −0.111465 | ||||||||
\(401\) | 17.0466 | 0.851265 | 0.425632 | − | 0.904896i | \(-0.360052\pi\) | ||||
0.425632 | + | 0.904896i | \(0.360052\pi\) | |||||||
\(402\) | −1.15976 | −0.0578434 | ||||||||
\(403\) | −26.6413 | −1.32710 | ||||||||
\(404\) | −0.316298 | −0.0157364 | ||||||||
\(405\) | −1.66454 | −0.0827119 | ||||||||
\(406\) | 6.70856 | 0.332940 | ||||||||
\(407\) | 6.27330 | 0.310956 | ||||||||
\(408\) | 0.265921 | 0.0131650 | ||||||||
\(409\) | −2.40082 | −0.118713 | −0.0593565 | − | 0.998237i | \(-0.518905\pi\) | ||||
−0.0593565 | + | 0.998237i | \(0.518905\pi\) | |||||||
\(410\) | 13.1741 | 0.650621 | ||||||||
\(411\) | −14.3137 | −0.706044 | ||||||||
\(412\) | 1.55297 | 0.0765094 | ||||||||
\(413\) | −26.3678 | −1.29747 | ||||||||
\(414\) | −5.37530 | −0.264182 | ||||||||
\(415\) | −11.7755 | −0.578034 | ||||||||
\(416\) | −6.41931 | −0.314733 | ||||||||
\(417\) | −18.7388 | −0.917644 | ||||||||
\(418\) | −4.82430 | −0.235964 | ||||||||
\(419\) | 10.8918 | 0.532098 | 0.266049 | − | 0.963960i | \(-0.414282\pi\) | ||||
0.266049 | + | 0.963960i | \(0.414282\pi\) | |||||||
\(420\) | 4.05359 | 0.197795 | ||||||||
\(421\) | 39.8498 | 1.94216 | 0.971080 | − | 0.238754i | \(-0.0767391\pi\) | ||||
0.971080 | + | 0.238754i | \(0.0767391\pi\) | |||||||
\(422\) | −22.5478 | −1.09761 | ||||||||
\(423\) | 0.474524 | 0.0230721 | ||||||||
\(424\) | 10.2691 | 0.498713 | ||||||||
\(425\) | 0.592814 | 0.0287557 | ||||||||
\(426\) | −6.34978 | −0.307648 | ||||||||
\(427\) | −2.43525 | −0.117850 | ||||||||
\(428\) | −18.5998 | −0.899053 | ||||||||
\(429\) | −6.41931 | −0.309927 | ||||||||
\(430\) | −17.8249 | −0.859592 | ||||||||
\(431\) | −24.3923 | −1.17493 | −0.587467 | − | 0.809248i | \(-0.699875\pi\) | ||||
−0.587467 | + | 0.809248i | \(0.699875\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −17.4973 | −0.840867 | −0.420434 | − | 0.907323i | \(-0.638122\pi\) | ||||
−0.420434 | + | 0.907323i | \(0.638122\pi\) | |||||||
\(434\) | −10.1067 | −0.485139 | ||||||||
\(435\) | −4.58543 | −0.219855 | ||||||||
\(436\) | −5.78029 | −0.276826 | ||||||||
\(437\) | −25.9321 | −1.24050 | ||||||||
\(438\) | −14.8153 | −0.707902 | ||||||||
\(439\) | 21.4162 | 1.02214 | 0.511069 | − | 0.859540i | \(-0.329250\pi\) | ||||
0.511069 | + | 0.859540i | \(0.329250\pi\) | |||||||
\(440\) | −1.66454 | −0.0793541 | ||||||||
\(441\) | −1.06953 | −0.0509302 | ||||||||
\(442\) | 1.70703 | 0.0811950 | ||||||||
\(443\) | −5.25612 | −0.249726 | −0.124863 | − | 0.992174i | \(-0.539849\pi\) | ||||
−0.124863 | + | 0.992174i | \(0.539849\pi\) | |||||||
\(444\) | −6.27330 | −0.297718 | ||||||||
\(445\) | −6.83124 | −0.323832 | ||||||||
\(446\) | −22.9878 | −1.08851 | ||||||||
\(447\) | −9.36352 | −0.442879 | ||||||||
\(448\) | −2.43525 | −0.115055 | ||||||||
\(449\) | 5.87430 | 0.277225 | 0.138613 | − | 0.990347i | \(-0.455736\pi\) | ||||
0.138613 | + | 0.990347i | \(0.455736\pi\) | |||||||
\(450\) | 2.22929 | 0.105090 | ||||||||
\(451\) | −7.91452 | −0.372680 | ||||||||
\(452\) | 2.38905 | 0.112371 | ||||||||
\(453\) | −22.6721 | −1.06523 | ||||||||
\(454\) | 13.5329 | 0.635129 | ||||||||
\(455\) | 26.0213 | 1.21990 | ||||||||
\(456\) | 4.82430 | 0.225919 | ||||||||
\(457\) | 13.4282 | 0.628146 | 0.314073 | − | 0.949399i | \(-0.398306\pi\) | ||||
0.314073 | + | 0.949399i | \(0.398306\pi\) | |||||||
\(458\) | 4.39321 | 0.205281 | ||||||||
\(459\) | −0.265921 | −0.0124121 | ||||||||
\(460\) | −8.94743 | −0.417176 | ||||||||
\(461\) | −38.8023 | −1.80721 | −0.903603 | − | 0.428372i | \(-0.859087\pi\) | ||||
−0.903603 | + | 0.428372i | \(0.859087\pi\) | |||||||
\(462\) | −2.43525 | −0.113298 | ||||||||
\(463\) | −15.2240 | −0.707520 | −0.353760 | − | 0.935336i | \(-0.615097\pi\) | ||||
−0.353760 | + | 0.935336i | \(0.615097\pi\) | |||||||
\(464\) | 2.75477 | 0.127887 | ||||||||
\(465\) | 6.90816 | 0.320358 | ||||||||
\(466\) | 10.2601 | 0.475291 | ||||||||
\(467\) | 36.6004 | 1.69366 | 0.846832 | − | 0.531860i | \(-0.178507\pi\) | ||||
0.846832 | + | 0.531860i | \(0.178507\pi\) | |||||||
\(468\) | 6.41931 | 0.296733 | ||||||||
\(469\) | −2.82430 | −0.130414 | ||||||||
\(470\) | 0.789866 | 0.0364338 | ||||||||
\(471\) | 8.87468 | 0.408924 | ||||||||
\(472\) | −10.8275 | −0.498377 | ||||||||
\(473\) | 10.7086 | 0.492380 | ||||||||
\(474\) | 13.9607 | 0.641238 | ||||||||
\(475\) | 10.7548 | 0.493463 | ||||||||
\(476\) | 0.647584 | 0.0296820 | ||||||||
\(477\) | −10.2691 | −0.470191 | ||||||||
\(478\) | −20.2952 | −0.928282 | ||||||||
\(479\) | 15.5333 | 0.709735 | 0.354867 | − | 0.934917i | \(-0.384526\pi\) | ||||
0.354867 | + | 0.934917i | \(0.384526\pi\) | |||||||
\(480\) | 1.66454 | 0.0759757 | ||||||||
\(481\) | −40.2703 | −1.83617 | ||||||||
\(482\) | 4.10674 | 0.187057 | ||||||||
\(483\) | −13.0902 | −0.595626 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −7.08657 | −0.321784 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 2.55632 | 0.115838 | 0.0579189 | − | 0.998321i | \(-0.481554\pi\) | ||||
0.0579189 | + | 0.998321i | \(0.481554\pi\) | |||||||
\(488\) | −1.00000 | −0.0452679 | ||||||||
\(489\) | −0.454411 | −0.0205492 | ||||||||
\(490\) | −1.78029 | −0.0804252 | ||||||||
\(491\) | −18.8074 | −0.848766 | −0.424383 | − | 0.905483i | \(-0.639509\pi\) | ||||
−0.424383 | + | 0.905483i | \(0.639509\pi\) | |||||||
\(492\) | 7.91452 | 0.356814 | ||||||||
\(493\) | −0.732549 | −0.0329924 | ||||||||
\(494\) | 30.9687 | 1.39335 | ||||||||
\(495\) | 1.66454 | 0.0748157 | ||||||||
\(496\) | −4.15018 | −0.186348 | ||||||||
\(497\) | −15.4633 | −0.693625 | ||||||||
\(498\) | −7.07428 | −0.317006 | ||||||||
\(499\) | 26.3269 | 1.17855 | 0.589277 | − | 0.807931i | \(-0.299413\pi\) | ||||
0.589277 | + | 0.807931i | \(0.299413\pi\) | |||||||
\(500\) | 12.0335 | 0.538154 | ||||||||
\(501\) | −17.4592 | −0.780018 | ||||||||
\(502\) | 0.778315 | 0.0347379 | ||||||||
\(503\) | −23.5590 | −1.05044 | −0.525221 | − | 0.850966i | \(-0.676017\pi\) | ||||
−0.525221 | + | 0.850966i | \(0.676017\pi\) | |||||||
\(504\) | 2.43525 | 0.108475 | ||||||||
\(505\) | 0.526493 | 0.0234286 | ||||||||
\(506\) | 5.37530 | 0.238961 | ||||||||
\(507\) | 28.2076 | 1.25274 | ||||||||
\(508\) | −15.7341 | −0.698087 | ||||||||
\(509\) | −30.1737 | −1.33743 | −0.668713 | − | 0.743521i | \(-0.733154\pi\) | ||||
−0.668713 | + | 0.743521i | \(0.733154\pi\) | |||||||
\(510\) | −0.442637 | −0.0196003 | ||||||||
\(511\) | −36.0790 | −1.59604 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.82430 | −0.212998 | ||||||||
\(514\) | −16.1418 | −0.711986 | ||||||||
\(515\) | −2.58499 | −0.113908 | ||||||||
\(516\) | −10.7086 | −0.471418 | ||||||||
\(517\) | −0.474524 | −0.0208695 | ||||||||
\(518\) | −15.2771 | −0.671237 | ||||||||
\(519\) | −17.7516 | −0.779209 | ||||||||
\(520\) | 10.6852 | 0.468578 | ||||||||
\(521\) | −12.9022 | −0.565254 | −0.282627 | − | 0.959230i | \(-0.591206\pi\) | ||||
−0.282627 | + | 0.959230i | \(0.591206\pi\) | |||||||
\(522\) | −2.75477 | −0.120573 | ||||||||
\(523\) | −31.8933 | −1.39460 | −0.697298 | − | 0.716781i | \(-0.745615\pi\) | ||||
−0.697298 | + | 0.716781i | \(0.745615\pi\) | |||||||
\(524\) | −4.72771 | −0.206531 | ||||||||
\(525\) | 5.42889 | 0.236936 | ||||||||
\(526\) | 6.31095 | 0.275170 | ||||||||
\(527\) | 1.10362 | 0.0480743 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 5.89384 | 0.256254 | ||||||||
\(530\) | −17.0934 | −0.742491 | ||||||||
\(531\) | 10.8275 | 0.469874 | ||||||||
\(532\) | 11.7484 | 0.509358 | ||||||||
\(533\) | 50.8058 | 2.20064 | ||||||||
\(534\) | −4.10397 | −0.177596 | ||||||||
\(535\) | 30.9601 | 1.33852 | ||||||||
\(536\) | −1.15976 | −0.0500938 | ||||||||
\(537\) | −24.8418 | −1.07200 | ||||||||
\(538\) | −22.7531 | −0.980958 | ||||||||
\(539\) | 1.06953 | 0.0460681 | ||||||||
\(540\) | −1.66454 | −0.0716306 | ||||||||
\(541\) | −7.86994 | −0.338355 | −0.169177 | − | 0.985586i | \(-0.554111\pi\) | ||||
−0.169177 | + | 0.985586i | \(0.554111\pi\) | |||||||
\(542\) | 7.33699 | 0.315151 | ||||||||
\(543\) | −25.7352 | −1.10440 | ||||||||
\(544\) | 0.265921 | 0.0114013 | ||||||||
\(545\) | 9.62155 | 0.412142 | ||||||||
\(546\) | 15.6327 | 0.669016 | ||||||||
\(547\) | 13.7814 | 0.589252 | 0.294626 | − | 0.955613i | \(-0.404805\pi\) | ||||
0.294626 | + | 0.955613i | \(0.404805\pi\) | |||||||
\(548\) | −14.3137 | −0.611452 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | −2.22929 | −0.0950573 | ||||||||
\(551\) | −13.2898 | −0.566165 | ||||||||
\(552\) | −5.37530 | −0.228788 | ||||||||
\(553\) | 33.9979 | 1.44574 | ||||||||
\(554\) | 8.14645 | 0.346110 | ||||||||
\(555\) | 10.4422 | 0.443246 | ||||||||
\(556\) | −18.7388 | −0.794703 | ||||||||
\(557\) | 29.1736 | 1.23613 | 0.618063 | − | 0.786128i | \(-0.287918\pi\) | ||||
0.618063 | + | 0.786128i | \(0.287918\pi\) | |||||||
\(558\) | 4.15018 | 0.175691 | ||||||||
\(559\) | −68.7416 | −2.90746 | ||||||||
\(560\) | 4.05359 | 0.171295 | ||||||||
\(561\) | 0.265921 | 0.0112272 | ||||||||
\(562\) | 15.4404 | 0.651316 | ||||||||
\(563\) | 28.9527 | 1.22021 | 0.610106 | − | 0.792320i | \(-0.291127\pi\) | ||||
0.610106 | + | 0.792320i | \(0.291127\pi\) | |||||||
\(564\) | 0.474524 | 0.0199811 | ||||||||
\(565\) | −3.97667 | −0.167300 | ||||||||
\(566\) | −5.37947 | −0.226116 | ||||||||
\(567\) | −2.43525 | −0.102271 | ||||||||
\(568\) | −6.34978 | −0.266431 | ||||||||
\(569\) | 31.3358 | 1.31367 | 0.656833 | − | 0.754036i | \(-0.271896\pi\) | ||||
0.656833 | + | 0.754036i | \(0.271896\pi\) | |||||||
\(570\) | −8.03027 | −0.336351 | ||||||||
\(571\) | −12.3865 | −0.518359 | −0.259179 | − | 0.965829i | \(-0.583452\pi\) | ||||
−0.259179 | + | 0.965829i | \(0.583452\pi\) | |||||||
\(572\) | −6.41931 | −0.268405 | ||||||||
\(573\) | −22.6603 | −0.946647 | ||||||||
\(574\) | 19.2739 | 0.804476 | ||||||||
\(575\) | −11.9831 | −0.499730 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −34.5015 | −1.43632 | −0.718159 | − | 0.695879i | \(-0.755015\pi\) | ||||
−0.718159 | + | 0.695879i | \(0.755015\pi\) | |||||||
\(578\) | 16.9293 | 0.704165 | ||||||||
\(579\) | −19.8646 | −0.825544 | ||||||||
\(580\) | −4.58543 | −0.190400 | ||||||||
\(581\) | −17.2277 | −0.714724 | ||||||||
\(582\) | −4.25736 | −0.176473 | ||||||||
\(583\) | 10.2691 | 0.425304 | ||||||||
\(584\) | −14.8153 | −0.613061 | ||||||||
\(585\) | −10.6852 | −0.441780 | ||||||||
\(586\) | −25.2818 | −1.04438 | ||||||||
\(587\) | 8.09913 | 0.334287 | 0.167144 | − | 0.985933i | \(-0.446546\pi\) | ||||
0.167144 | + | 0.985933i | \(0.446546\pi\) | |||||||
\(588\) | −1.06953 | −0.0441069 | ||||||||
\(589\) | 20.0217 | 0.824980 | ||||||||
\(590\) | 18.0229 | 0.741990 | ||||||||
\(591\) | −4.40776 | −0.181311 | ||||||||
\(592\) | −6.27330 | −0.257831 | ||||||||
\(593\) | 43.5483 | 1.78832 | 0.894158 | − | 0.447752i | \(-0.147775\pi\) | ||||
0.894158 | + | 0.447752i | \(0.147775\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | −1.07793 | −0.0441910 | ||||||||
\(596\) | −9.36352 | −0.383545 | ||||||||
\(597\) | 9.74936 | 0.399015 | ||||||||
\(598\) | −34.5057 | −1.41104 | ||||||||
\(599\) | −9.14433 | −0.373627 | −0.186814 | − | 0.982395i | \(-0.559816\pi\) | ||||
−0.186814 | + | 0.982395i | \(0.559816\pi\) | |||||||
\(600\) | 2.22929 | 0.0910104 | ||||||||
\(601\) | −0.590710 | −0.0240956 | −0.0120478 | − | 0.999927i | \(-0.503835\pi\) | ||||
−0.0120478 | + | 0.999927i | \(0.503835\pi\) | |||||||
\(602\) | −26.0781 | −1.06286 | ||||||||
\(603\) | 1.15976 | 0.0472289 | ||||||||
\(604\) | −22.6721 | −0.922513 | ||||||||
\(605\) | −1.66454 | −0.0676734 | ||||||||
\(606\) | 0.316298 | 0.0128487 | ||||||||
\(607\) | −7.74423 | −0.314329 | −0.157164 | − | 0.987572i | \(-0.550235\pi\) | ||||
−0.157164 | + | 0.987572i | \(0.550235\pi\) | |||||||
\(608\) | 4.82430 | 0.195651 | ||||||||
\(609\) | −6.70856 | −0.271844 | ||||||||
\(610\) | 1.66454 | 0.0673955 | ||||||||
\(611\) | 3.04612 | 0.123233 | ||||||||
\(612\) | −0.265921 | −0.0107492 | ||||||||
\(613\) | 42.0390 | 1.69794 | 0.848970 | − | 0.528441i | \(-0.177223\pi\) | ||||
0.848970 | + | 0.528441i | \(0.177223\pi\) | |||||||
\(614\) | 19.0780 | 0.769926 | ||||||||
\(615\) | −13.1741 | −0.531230 | ||||||||
\(616\) | −2.43525 | −0.0981192 | ||||||||
\(617\) | 13.2644 | 0.534004 | 0.267002 | − | 0.963696i | \(-0.413967\pi\) | ||||
0.267002 | + | 0.963696i | \(0.413967\pi\) | |||||||
\(618\) | −1.55297 | −0.0624696 | ||||||||
\(619\) | 7.29399 | 0.293170 | 0.146585 | − | 0.989198i | \(-0.453172\pi\) | ||||
0.146585 | + | 0.989198i | \(0.453172\pi\) | |||||||
\(620\) | 6.90816 | 0.277438 | ||||||||
\(621\) | 5.37530 | 0.215703 | ||||||||
\(622\) | −32.0099 | −1.28348 | ||||||||
\(623\) | −9.99421 | −0.400410 | ||||||||
\(624\) | 6.41931 | 0.256978 | ||||||||
\(625\) | −8.88381 | −0.355353 | ||||||||
\(626\) | 23.9824 | 0.958531 | ||||||||
\(627\) | 4.82430 | 0.192664 | ||||||||
\(628\) | 8.87468 | 0.354138 | ||||||||
\(629\) | 1.66820 | 0.0665155 | ||||||||
\(630\) | −4.05359 | −0.161499 | ||||||||
\(631\) | 27.8402 | 1.10830 | 0.554149 | − | 0.832417i | \(-0.313044\pi\) | ||||
0.554149 | + | 0.832417i | \(0.313044\pi\) | |||||||
\(632\) | 13.9607 | 0.555328 | ||||||||
\(633\) | 22.5478 | 0.896193 | ||||||||
\(634\) | −3.15237 | −0.125197 | ||||||||
\(635\) | 26.1901 | 1.03932 | ||||||||
\(636\) | −10.2691 | −0.407198 | ||||||||
\(637\) | −6.86567 | −0.272028 | ||||||||
\(638\) | 2.75477 | 0.109062 | ||||||||
\(639\) | 6.34978 | 0.251193 | ||||||||
\(640\) | 1.66454 | 0.0657969 | ||||||||
\(641\) | −24.8992 | −0.983457 | −0.491729 | − | 0.870748i | \(-0.663635\pi\) | ||||
−0.491729 | + | 0.870748i | \(0.663635\pi\) | |||||||
\(642\) | 18.5998 | 0.734074 | ||||||||
\(643\) | 14.6561 | 0.577981 | 0.288990 | − | 0.957332i | \(-0.406680\pi\) | ||||
0.288990 | + | 0.957332i | \(0.406680\pi\) | |||||||
\(644\) | −13.0902 | −0.515827 | ||||||||
\(645\) | 17.8249 | 0.701854 | ||||||||
\(646\) | −1.28288 | −0.0504743 | ||||||||
\(647\) | 39.5453 | 1.55468 | 0.777342 | − | 0.629078i | \(-0.216567\pi\) | ||||
0.777342 | + | 0.629078i | \(0.216567\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −10.8275 | −0.425017 | ||||||||
\(650\) | 14.3105 | 0.561304 | ||||||||
\(651\) | 10.1067 | 0.396114 | ||||||||
\(652\) | −0.454411 | −0.0177961 | ||||||||
\(653\) | 16.2690 | 0.636654 | 0.318327 | − | 0.947981i | \(-0.396879\pi\) | ||||
0.318327 | + | 0.947981i | \(0.396879\pi\) | |||||||
\(654\) | 5.78029 | 0.226027 | ||||||||
\(655\) | 7.86949 | 0.307487 | ||||||||
\(656\) | 7.91452 | 0.309010 | ||||||||
\(657\) | 14.8153 | 0.578000 | ||||||||
\(658\) | 1.15559 | 0.0450495 | ||||||||
\(659\) | 34.8015 | 1.35567 | 0.677836 | − | 0.735213i | \(-0.262918\pi\) | ||||
0.677836 | + | 0.735213i | \(0.262918\pi\) | |||||||
\(660\) | 1.66454 | 0.0647923 | ||||||||
\(661\) | −7.62155 | −0.296444 | −0.148222 | − | 0.988954i | \(-0.547355\pi\) | ||||
−0.148222 | + | 0.988954i | \(0.547355\pi\) | |||||||
\(662\) | 35.5079 | 1.38005 | ||||||||
\(663\) | −1.70703 | −0.0662954 | ||||||||
\(664\) | −7.07428 | −0.274535 | ||||||||
\(665\) | −19.5557 | −0.758339 | ||||||||
\(666\) | 6.27330 | 0.243086 | ||||||||
\(667\) | 14.8077 | 0.573356 | ||||||||
\(668\) | −17.4592 | −0.675515 | ||||||||
\(669\) | 22.9878 | 0.888761 | ||||||||
\(670\) | 1.93047 | 0.0745804 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 2.43525 | 0.0939420 | ||||||||
\(673\) | 35.6135 | 1.37280 | 0.686400 | − | 0.727224i | \(-0.259190\pi\) | ||||
0.686400 | + | 0.727224i | \(0.259190\pi\) | |||||||
\(674\) | 10.3992 | 0.400562 | ||||||||
\(675\) | −2.22929 | −0.0858054 | ||||||||
\(676\) | 28.2076 | 1.08491 | ||||||||
\(677\) | −43.2410 | −1.66189 | −0.830944 | − | 0.556356i | \(-0.812199\pi\) | ||||
−0.830944 | + | 0.556356i | \(0.812199\pi\) | |||||||
\(678\) | −2.38905 | −0.0917508 | ||||||||
\(679\) | −10.3678 | −0.397878 | ||||||||
\(680\) | −0.442637 | −0.0169743 | ||||||||
\(681\) | −13.5329 | −0.518580 | ||||||||
\(682\) | −4.15018 | −0.158919 | ||||||||
\(683\) | −21.4393 | −0.820353 | −0.410177 | − | 0.912006i | \(-0.634533\pi\) | ||||
−0.410177 | + | 0.912006i | \(0.634533\pi\) | |||||||
\(684\) | −4.82430 | −0.184462 | ||||||||
\(685\) | 23.8258 | 0.910338 | ||||||||
\(686\) | −19.6514 | −0.750293 | ||||||||
\(687\) | −4.39321 | −0.167612 | ||||||||
\(688\) | −10.7086 | −0.408260 | ||||||||
\(689\) | −65.9208 | −2.51138 | ||||||||
\(690\) | 8.94743 | 0.340623 | ||||||||
\(691\) | 37.9995 | 1.44557 | 0.722785 | − | 0.691073i | \(-0.242862\pi\) | ||||
0.722785 | + | 0.691073i | \(0.242862\pi\) | |||||||
\(692\) | −17.7516 | −0.674815 | ||||||||
\(693\) | 2.43525 | 0.0925077 | ||||||||
\(694\) | 19.5319 | 0.741421 | ||||||||
\(695\) | 31.1916 | 1.18317 | ||||||||
\(696\) | −2.75477 | −0.104419 | ||||||||
\(697\) | −2.10463 | −0.0797187 | ||||||||
\(698\) | 9.23667 | 0.349613 | ||||||||
\(699\) | −10.2601 | −0.388074 | ||||||||
\(700\) | 5.42889 | 0.205193 | ||||||||
\(701\) | −10.7427 | −0.405746 | −0.202873 | − | 0.979205i | \(-0.565028\pi\) | ||||
−0.202873 | + | 0.979205i | \(0.565028\pi\) | |||||||
\(702\) | −6.41931 | −0.242281 | ||||||||
\(703\) | 30.2643 | 1.14144 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −0.789866 | −0.0297481 | ||||||||
\(706\) | 8.02126 | 0.301884 | ||||||||
\(707\) | 0.770267 | 0.0289689 | ||||||||
\(708\) | 10.8275 | 0.406923 | ||||||||
\(709\) | 26.5299 | 0.996352 | 0.498176 | − | 0.867076i | \(-0.334003\pi\) | ||||
0.498176 | + | 0.867076i | \(0.334003\pi\) | |||||||
\(710\) | 10.5695 | 0.396666 | ||||||||
\(711\) | −13.9607 | −0.523568 | ||||||||
\(712\) | −4.10397 | −0.153803 | ||||||||
\(713\) | −22.3084 | −0.835458 | ||||||||
\(714\) | −0.647584 | −0.0242352 | ||||||||
\(715\) | 10.6852 | 0.399605 | ||||||||
\(716\) | −24.8418 | −0.928383 | ||||||||
\(717\) | 20.2952 | 0.757939 | ||||||||
\(718\) | −32.7129 | −1.22084 | ||||||||
\(719\) | −1.14521 | −0.0427092 | −0.0213546 | − | 0.999772i | \(-0.506798\pi\) | ||||
−0.0213546 | + | 0.999772i | \(0.506798\pi\) | |||||||
\(720\) | −1.66454 | −0.0620339 | ||||||||
\(721\) | −3.78188 | −0.140845 | ||||||||
\(722\) | −4.27388 | −0.159057 | ||||||||
\(723\) | −4.10674 | −0.152731 | ||||||||
\(724\) | −25.7352 | −0.956442 | ||||||||
\(725\) | −6.14117 | −0.228077 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | 26.7828 | 0.993318 | 0.496659 | − | 0.867946i | \(-0.334560\pi\) | ||||
0.496659 | + | 0.867946i | \(0.334560\pi\) | |||||||
\(728\) | 15.6327 | 0.579385 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 24.6607 | 0.912734 | ||||||||
\(731\) | 2.84763 | 0.105323 | ||||||||
\(732\) | 1.00000 | 0.0369611 | ||||||||
\(733\) | −5.28082 | −0.195051 | −0.0975257 | − | 0.995233i | \(-0.531093\pi\) | ||||
−0.0975257 | + | 0.995233i | \(0.531093\pi\) | |||||||
\(734\) | −11.7532 | −0.433820 | ||||||||
\(735\) | 1.78029 | 0.0656669 | ||||||||
\(736\) | −5.37530 | −0.198136 | ||||||||
\(737\) | −1.15976 | −0.0427202 | ||||||||
\(738\) | −7.91452 | −0.291338 | ||||||||
\(739\) | 9.85355 | 0.362469 | 0.181234 | − | 0.983440i | \(-0.441991\pi\) | ||||
0.181234 | + | 0.983440i | \(0.441991\pi\) | |||||||
\(740\) | 10.4422 | 0.383863 | ||||||||
\(741\) | −30.9687 | −1.13766 | ||||||||
\(742\) | −25.0080 | −0.918071 | ||||||||
\(743\) | 11.5351 | 0.423182 | 0.211591 | − | 0.977358i | \(-0.432135\pi\) | ||||
0.211591 | + | 0.977358i | \(0.432135\pi\) | |||||||
\(744\) | 4.15018 | 0.152153 | ||||||||
\(745\) | 15.5860 | 0.571027 | ||||||||
\(746\) | −21.7119 | −0.794929 | ||||||||
\(747\) | 7.07428 | 0.258834 | ||||||||
\(748\) | 0.265921 | 0.00972302 | ||||||||
\(749\) | 45.2951 | 1.65505 | ||||||||
\(750\) | −12.0335 | −0.439401 | ||||||||
\(751\) | −3.37895 | −0.123300 | −0.0616499 | − | 0.998098i | \(-0.519636\pi\) | ||||
−0.0616499 | + | 0.998098i | \(0.519636\pi\) | |||||||
\(752\) | 0.474524 | 0.0173041 | ||||||||
\(753\) | −0.778315 | −0.0283634 | ||||||||
\(754\) | −17.6837 | −0.644002 | ||||||||
\(755\) | 37.7387 | 1.37345 | ||||||||
\(756\) | −2.43525 | −0.0885694 | ||||||||
\(757\) | −10.5487 | −0.383401 | −0.191700 | − | 0.981454i | \(-0.561400\pi\) | ||||
−0.191700 | + | 0.981454i | \(0.561400\pi\) | |||||||
\(758\) | 28.2596 | 1.02644 | ||||||||
\(759\) | −5.37530 | −0.195111 | ||||||||
\(760\) | −8.03027 | −0.291288 | ||||||||
\(761\) | −26.6125 | −0.964702 | −0.482351 | − | 0.875978i | \(-0.660217\pi\) | ||||
−0.482351 | + | 0.875978i | \(0.660217\pi\) | |||||||
\(762\) | 15.7341 | 0.569986 | ||||||||
\(763\) | 14.0765 | 0.509603 | ||||||||
\(764\) | −22.6603 | −0.819820 | ||||||||
\(765\) | 0.442637 | 0.0160036 | ||||||||
\(766\) | 30.0875 | 1.08711 | ||||||||
\(767\) | 69.5052 | 2.50969 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −46.8000 | −1.68765 | −0.843825 | − | 0.536618i | \(-0.819702\pi\) | ||||
−0.843825 | + | 0.536618i | \(0.819702\pi\) | |||||||
\(770\) | 4.05359 | 0.146081 | ||||||||
\(771\) | 16.1418 | 0.581334 | ||||||||
\(772\) | −19.8646 | −0.714942 | ||||||||
\(773\) | 34.6050 | 1.24466 | 0.622328 | − | 0.782756i | \(-0.286187\pi\) | ||||
0.622328 | + | 0.782756i | \(0.286187\pi\) | |||||||
\(774\) | 10.7086 | 0.384911 | ||||||||
\(775\) | 9.25195 | 0.332340 | ||||||||
\(776\) | −4.25736 | −0.152830 | ||||||||
\(777\) | 15.2771 | 0.548063 | ||||||||
\(778\) | −3.01375 | −0.108048 | ||||||||
\(779\) | −38.1820 | −1.36801 | ||||||||
\(780\) | −10.6852 | −0.382593 | ||||||||
\(781\) | −6.34978 | −0.227213 | ||||||||
\(782\) | 1.42940 | 0.0511153 | ||||||||
\(783\) | 2.75477 | 0.0984473 | ||||||||
\(784\) | −1.06953 | −0.0381977 | ||||||||
\(785\) | −14.7723 | −0.527246 | ||||||||
\(786\) | 4.72771 | 0.168632 | ||||||||
\(787\) | −46.4840 | −1.65698 | −0.828488 | − | 0.560007i | \(-0.810799\pi\) | ||||
−0.828488 | + | 0.560007i | \(0.810799\pi\) | |||||||
\(788\) | −4.40776 | −0.157020 | ||||||||
\(789\) | −6.31095 | −0.224676 | ||||||||
\(790\) | −23.2383 | −0.826780 | ||||||||
\(791\) | −5.81794 | −0.206862 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 6.41931 | 0.227956 | ||||||||
\(794\) | −31.0546 | −1.10209 | ||||||||
\(795\) | 17.0934 | 0.606242 | ||||||||
\(796\) | 9.74936 | 0.345557 | ||||||||
\(797\) | 10.7058 | 0.379218 | 0.189609 | − | 0.981860i | \(-0.439278\pi\) | ||||
0.189609 | + | 0.981860i | \(0.439278\pi\) | |||||||
\(798\) | −11.7484 | −0.415889 | ||||||||
\(799\) | −0.126186 | −0.00446413 | ||||||||
\(800\) | 2.22929 | 0.0788173 | ||||||||
\(801\) | 4.10397 | 0.145007 | ||||||||
\(802\) | −17.0466 | −0.601935 | ||||||||
\(803\) | −14.8153 | −0.522820 | ||||||||
\(804\) | 1.15976 | 0.0409014 | ||||||||
\(805\) | 21.7893 | 0.767971 | ||||||||
\(806\) | 26.6413 | 0.938399 | ||||||||
\(807\) | 22.7531 | 0.800949 | ||||||||
\(808\) | 0.316298 | 0.0111273 | ||||||||
\(809\) | −6.21321 | −0.218445 | −0.109223 | − | 0.994017i | \(-0.534836\pi\) | ||||
−0.109223 | + | 0.994017i | \(0.534836\pi\) | |||||||
\(810\) | 1.66454 | 0.0584861 | ||||||||
\(811\) | −6.31006 | −0.221576 | −0.110788 | − | 0.993844i | \(-0.535338\pi\) | ||||
−0.110788 | + | 0.993844i | \(0.535338\pi\) | |||||||
\(812\) | −6.70856 | −0.235424 | ||||||||
\(813\) | −7.33699 | −0.257319 | ||||||||
\(814\) | −6.27330 | −0.219879 | ||||||||
\(815\) | 0.756388 | 0.0264951 | ||||||||
\(816\) | −0.265921 | −0.00930908 | ||||||||
\(817\) | 51.6613 | 1.80740 | ||||||||
\(818\) | 2.40082 | 0.0839427 | ||||||||
\(819\) | −15.6327 | −0.546249 | ||||||||
\(820\) | −13.1741 | −0.460059 | ||||||||
\(821\) | 18.9399 | 0.661007 | 0.330503 | − | 0.943805i | \(-0.392781\pi\) | ||||
0.330503 | + | 0.943805i | \(0.392781\pi\) | |||||||
\(822\) | 14.3137 | 0.499248 | ||||||||
\(823\) | −35.7429 | −1.24592 | −0.622960 | − | 0.782254i | \(-0.714070\pi\) | ||||
−0.622960 | + | 0.782254i | \(0.714070\pi\) | |||||||
\(824\) | −1.55297 | −0.0541003 | ||||||||
\(825\) | 2.22929 | 0.0776139 | ||||||||
\(826\) | 26.3678 | 0.917452 | ||||||||
\(827\) | −31.1136 | −1.08193 | −0.540963 | − | 0.841047i | \(-0.681940\pi\) | ||||
−0.540963 | + | 0.841047i | \(0.681940\pi\) | |||||||
\(828\) | 5.37530 | 0.186805 | ||||||||
\(829\) | 0.559046 | 0.0194165 | 0.00970824 | − | 0.999953i | \(-0.496910\pi\) | ||||
0.00970824 | + | 0.999953i | \(0.496910\pi\) | |||||||
\(830\) | 11.7755 | 0.408732 | ||||||||
\(831\) | −8.14645 | −0.282597 | ||||||||
\(832\) | 6.41931 | 0.222550 | ||||||||
\(833\) | 0.284411 | 0.00985427 | ||||||||
\(834\) | 18.7388 | 0.648872 | ||||||||
\(835\) | 29.0615 | 1.00572 | ||||||||
\(836\) | 4.82430 | 0.166852 | ||||||||
\(837\) | −4.15018 | −0.143451 | ||||||||
\(838\) | −10.8918 | −0.376250 | ||||||||
\(839\) | −19.8577 | −0.685563 | −0.342782 | − | 0.939415i | \(-0.611369\pi\) | ||||
−0.342782 | + | 0.939415i | \(0.611369\pi\) | |||||||
\(840\) | −4.05359 | −0.139862 | ||||||||
\(841\) | −21.4113 | −0.738319 | ||||||||
\(842\) | −39.8498 | −1.37331 | ||||||||
\(843\) | −15.4404 | −0.531797 | ||||||||
\(844\) | 22.5478 | 0.776126 | ||||||||
\(845\) | −46.9527 | −1.61522 | ||||||||
\(846\) | −0.474524 | −0.0163145 | ||||||||
\(847\) | −2.43525 | −0.0836763 | ||||||||
\(848\) | −10.2691 | −0.352644 | ||||||||
\(849\) | 5.37947 | 0.184623 | ||||||||
\(850\) | −0.592814 | −0.0203334 | ||||||||
\(851\) | −33.7209 | −1.15594 | ||||||||
\(852\) | 6.34978 | 0.217540 | ||||||||
\(853\) | 29.8486 | 1.02200 | 0.510999 | − | 0.859581i | \(-0.329276\pi\) | ||||
0.510999 | + | 0.859581i | \(0.329276\pi\) | |||||||
\(854\) | 2.43525 | 0.0833327 | ||||||||
\(855\) | 8.03027 | 0.274629 | ||||||||
\(856\) | 18.5998 | 0.635726 | ||||||||
\(857\) | −28.8335 | −0.984934 | −0.492467 | − | 0.870331i | \(-0.663905\pi\) | ||||
−0.492467 | + | 0.870331i | \(0.663905\pi\) | |||||||
\(858\) | 6.41931 | 0.219152 | ||||||||
\(859\) | 2.04481 | 0.0697680 | 0.0348840 | − | 0.999391i | \(-0.488894\pi\) | ||||
0.0348840 | + | 0.999391i | \(0.488894\pi\) | |||||||
\(860\) | 17.8249 | 0.607823 | ||||||||
\(861\) | −19.2739 | −0.656852 | ||||||||
\(862\) | 24.3923 | 0.830804 | ||||||||
\(863\) | 32.2334 | 1.09724 | 0.548618 | − | 0.836073i | \(-0.315154\pi\) | ||||
0.548618 | + | 0.836073i | \(0.315154\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 29.5484 | 1.00467 | ||||||||
\(866\) | 17.4973 | 0.594583 | ||||||||
\(867\) | −16.9293 | −0.574949 | ||||||||
\(868\) | 10.1067 | 0.343045 | ||||||||
\(869\) | 13.9607 | 0.473585 | ||||||||
\(870\) | 4.58543 | 0.155461 | ||||||||
\(871\) | 7.44483 | 0.252259 | ||||||||
\(872\) | 5.78029 | 0.195745 | ||||||||
\(873\) | 4.25736 | 0.144090 | ||||||||
\(874\) | 25.9321 | 0.877165 | ||||||||
\(875\) | −29.3046 | −0.990676 | ||||||||
\(876\) | 14.8153 | 0.500562 | ||||||||
\(877\) | −25.8087 | −0.871498 | −0.435749 | − | 0.900068i | \(-0.643516\pi\) | ||||
−0.435749 | + | 0.900068i | \(0.643516\pi\) | |||||||
\(878\) | −21.4162 | −0.722760 | ||||||||
\(879\) | 25.2818 | 0.852733 | ||||||||
\(880\) | 1.66454 | 0.0561118 | ||||||||
\(881\) | 39.7123 | 1.33794 | 0.668971 | − | 0.743288i | \(-0.266735\pi\) | ||||
0.668971 | + | 0.743288i | \(0.266735\pi\) | |||||||
\(882\) | 1.06953 | 0.0360131 | ||||||||
\(883\) | −33.9378 | −1.14210 | −0.571049 | − | 0.820916i | \(-0.693463\pi\) | ||||
−0.571049 | + | 0.820916i | \(0.693463\pi\) | |||||||
\(884\) | −1.70703 | −0.0574135 | ||||||||
\(885\) | −18.0229 | −0.605833 | ||||||||
\(886\) | 5.25612 | 0.176583 | ||||||||
\(887\) | −4.86619 | −0.163391 | −0.0816953 | − | 0.996657i | \(-0.526033\pi\) | ||||
−0.0816953 | + | 0.996657i | \(0.526033\pi\) | |||||||
\(888\) | 6.27330 | 0.210518 | ||||||||
\(889\) | 38.3165 | 1.28509 | ||||||||
\(890\) | 6.83124 | 0.228984 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 22.9878 | 0.769690 | ||||||||
\(893\) | −2.28925 | −0.0766067 | ||||||||
\(894\) | 9.36352 | 0.313163 | ||||||||
\(895\) | 41.3504 | 1.38219 | ||||||||
\(896\) | 2.43525 | 0.0813562 | ||||||||
\(897\) | 34.5057 | 1.15211 | ||||||||
\(898\) | −5.87430 | −0.196028 | ||||||||
\(899\) | −11.4328 | −0.381304 | ||||||||
\(900\) | −2.22929 | −0.0743097 | ||||||||
\(901\) | 2.73077 | 0.0909753 | ||||||||
\(902\) | 7.91452 | 0.263525 | ||||||||
\(903\) | 26.0781 | 0.867824 | ||||||||
\(904\) | −2.38905 | −0.0794585 | ||||||||
\(905\) | 42.8374 | 1.42396 | ||||||||
\(906\) | 22.6721 | 0.753229 | ||||||||
\(907\) | 9.01696 | 0.299403 | 0.149702 | − | 0.988731i | \(-0.452169\pi\) | ||||
0.149702 | + | 0.988731i | \(0.452169\pi\) | |||||||
\(908\) | −13.5329 | −0.449104 | ||||||||
\(909\) | −0.316298 | −0.0104910 | ||||||||
\(910\) | −26.0213 | −0.862596 | ||||||||
\(911\) | 0.412595 | 0.0136699 | 0.00683494 | − | 0.999977i | \(-0.497824\pi\) | ||||
0.00683494 | + | 0.999977i | \(0.497824\pi\) | |||||||
\(912\) | −4.82430 | −0.159749 | ||||||||
\(913\) | −7.07428 | −0.234124 | ||||||||
\(914\) | −13.4282 | −0.444166 | ||||||||
\(915\) | −1.66454 | −0.0550282 | ||||||||
\(916\) | −4.39321 | −0.145156 | ||||||||
\(917\) | 11.5132 | 0.380199 | ||||||||
\(918\) | 0.265921 | 0.00877669 | ||||||||
\(919\) | −37.1635 | −1.22591 | −0.612955 | − | 0.790118i | \(-0.710019\pi\) | ||||
−0.612955 | + | 0.790118i | \(0.710019\pi\) | |||||||
\(920\) | 8.94743 | 0.294988 | ||||||||
\(921\) | −19.0780 | −0.628642 | ||||||||
\(922\) | 38.8023 | 1.27789 | ||||||||
\(923\) | 40.7612 | 1.34167 | ||||||||
\(924\) | 2.43525 | 0.0801140 | ||||||||
\(925\) | 13.9850 | 0.459824 | ||||||||
\(926\) | 15.2240 | 0.500292 | ||||||||
\(927\) | 1.55297 | 0.0510063 | ||||||||
\(928\) | −2.75477 | −0.0904296 | ||||||||
\(929\) | −39.4005 | −1.29269 | −0.646344 | − | 0.763046i | \(-0.723703\pi\) | ||||
−0.646344 | + | 0.763046i | \(0.723703\pi\) | |||||||
\(930\) | −6.90816 | −0.226527 | ||||||||
\(931\) | 5.15976 | 0.169104 | ||||||||
\(932\) | −10.2601 | −0.336082 | ||||||||
\(933\) | 32.0099 | 1.04796 | ||||||||
\(934\) | −36.6004 | −1.19760 | ||||||||
\(935\) | −0.442637 | −0.0144758 | ||||||||
\(936\) | −6.41931 | −0.209822 | ||||||||
\(937\) | −32.6053 | −1.06517 | −0.532584 | − | 0.846377i | \(-0.678779\pi\) | ||||
−0.532584 | + | 0.846377i | \(0.678779\pi\) | |||||||
\(938\) | 2.82430 | 0.0922167 | ||||||||
\(939\) | −23.9824 | −0.782637 | ||||||||
\(940\) | −0.789866 | −0.0257626 | ||||||||
\(941\) | −45.5906 | −1.48621 | −0.743106 | − | 0.669174i | \(-0.766648\pi\) | ||||
−0.743106 | + | 0.669174i | \(0.766648\pi\) | |||||||
\(942\) | −8.87468 | −0.289153 | ||||||||
\(943\) | 42.5429 | 1.38539 | ||||||||
\(944\) | 10.8275 | 0.352406 | ||||||||
\(945\) | 4.05359 | 0.131863 | ||||||||
\(946\) | −10.7086 | −0.348165 | ||||||||
\(947\) | 32.2802 | 1.04897 | 0.524483 | − | 0.851421i | \(-0.324258\pi\) | ||||
0.524483 | + | 0.851421i | \(0.324258\pi\) | |||||||
\(948\) | −13.9607 | −0.453423 | ||||||||
\(949\) | 95.1040 | 3.08721 | ||||||||
\(950\) | −10.7548 | −0.348931 | ||||||||
\(951\) | 3.15237 | 0.102223 | ||||||||
\(952\) | −0.647584 | −0.0209883 | ||||||||
\(953\) | 33.3741 | 1.08109 | 0.540547 | − | 0.841314i | \(-0.318217\pi\) | ||||
0.540547 | + | 0.841314i | \(0.318217\pi\) | |||||||
\(954\) | 10.2691 | 0.332475 | ||||||||
\(955\) | 37.7191 | 1.22056 | ||||||||
\(956\) | 20.2952 | 0.656395 | ||||||||
\(957\) | −2.75477 | −0.0890489 | ||||||||
\(958\) | −15.5333 | −0.501858 | ||||||||
\(959\) | 34.8576 | 1.12561 | ||||||||
\(960\) | −1.66454 | −0.0537230 | ||||||||
\(961\) | −13.7760 | −0.444388 | ||||||||
\(962\) | 40.2703 | 1.29837 | ||||||||
\(963\) | −18.5998 | −0.599369 | ||||||||
\(964\) | −4.10674 | −0.132269 | ||||||||
\(965\) | 33.0655 | 1.06442 | ||||||||
\(966\) | 13.0902 | 0.421171 | ||||||||
\(967\) | −28.1252 | −0.904446 | −0.452223 | − | 0.891905i | \(-0.649369\pi\) | ||||
−0.452223 | + | 0.891905i | \(0.649369\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 1.28288 | 0.0412121 | ||||||||
\(970\) | 7.08657 | 0.227536 | ||||||||
\(971\) | −37.7925 | −1.21282 | −0.606409 | − | 0.795153i | \(-0.707391\pi\) | ||||
−0.606409 | + | 0.795153i | \(0.707391\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 45.6338 | 1.46295 | ||||||||
\(974\) | −2.55632 | −0.0819096 | ||||||||
\(975\) | −14.3105 | −0.458303 | ||||||||
\(976\) | 1.00000 | 0.0320092 | ||||||||
\(977\) | −41.0126 | −1.31211 | −0.656055 | − | 0.754713i | \(-0.727776\pi\) | ||||
−0.656055 | + | 0.754713i | \(0.727776\pi\) | |||||||
\(978\) | 0.454411 | 0.0145305 | ||||||||
\(979\) | −4.10397 | −0.131163 | ||||||||
\(980\) | 1.78029 | 0.0568692 | ||||||||
\(981\) | −5.78029 | −0.184550 | ||||||||
\(982\) | 18.8074 | 0.600168 | ||||||||
\(983\) | 13.3748 | 0.426589 | 0.213295 | − | 0.976988i | \(-0.431581\pi\) | ||||
0.213295 | + | 0.976988i | \(0.431581\pi\) | |||||||
\(984\) | −7.91452 | −0.252306 | ||||||||
\(985\) | 7.33691 | 0.233774 | ||||||||
\(986\) | 0.732549 | 0.0233291 | ||||||||
\(987\) | −1.15559 | −0.0367827 | ||||||||
\(988\) | −30.9687 | −0.985245 | ||||||||
\(989\) | −57.5617 | −1.83036 | ||||||||
\(990\) | −1.66454 | −0.0529027 | ||||||||
\(991\) | 29.8651 | 0.948695 | 0.474348 | − | 0.880338i | \(-0.342684\pi\) | ||||
0.474348 | + | 0.880338i | \(0.342684\pi\) | |||||||
\(992\) | 4.15018 | 0.131768 | ||||||||
\(993\) | −35.5079 | −1.12681 | ||||||||
\(994\) | 15.4633 | 0.490467 | ||||||||
\(995\) | −16.2282 | −0.514470 | ||||||||
\(996\) | 7.07428 | 0.224157 | ||||||||
\(997\) | −21.2637 | −0.673428 | −0.336714 | − | 0.941607i | \(-0.609316\pi\) | ||||
−0.336714 | + | 0.941607i | \(0.609316\pi\) | |||||||
\(998\) | −26.3269 | −0.833363 | ||||||||
\(999\) | −6.27330 | −0.198479 |
(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 | 4026.2.a.r.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.r.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial |