Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(1,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1183.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.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: | \(9.44630255912\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.1279733.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 6x^{4} + 10x^{3} + 10x^{2} - 11x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.0849355\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.10591 | −0.781998 | −0.390999 | − | 0.920391i | \(-0.627870\pi\) | ||||
−0.390999 | + | 0.920391i | \(0.627870\pi\) | |||||||
\(3\) | 1.33192 | 0.768982 | 0.384491 | − | 0.923129i | \(-0.374377\pi\) | ||||
0.384491 | + | 0.923129i | \(0.374377\pi\) | |||||||
\(4\) | −0.776957 | −0.388478 | ||||||||
\(5\) | 1.90785 | 0.853217 | 0.426608 | − | 0.904436i | \(-0.359708\pi\) | ||||
0.426608 | + | 0.904436i | \(0.359708\pi\) | |||||||
\(6\) | −1.47298 | −0.601342 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.07107 | 1.08579 | ||||||||
\(9\) | −1.22600 | −0.408667 | ||||||||
\(10\) | −2.10992 | −0.667214 | ||||||||
\(11\) | −6.49608 | −1.95864 | −0.979321 | − | 0.202312i | \(-0.935154\pi\) | ||||
−0.979321 | + | 0.202312i | \(0.935154\pi\) | |||||||
\(12\) | −1.03484 | −0.298733 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.10591 | −0.295568 | ||||||||
\(15\) | 2.54109 | 0.656108 | ||||||||
\(16\) | −1.84242 | −0.460606 | ||||||||
\(17\) | −7.14583 | −1.73312 | −0.866560 | − | 0.499073i | \(-0.833674\pi\) | ||||
−0.866560 | + | 0.499073i | \(0.833674\pi\) | |||||||
\(18\) | 1.35585 | 0.319577 | ||||||||
\(19\) | 4.93001 | 1.13102 | 0.565510 | − | 0.824741i | \(-0.308679\pi\) | ||||
0.565510 | + | 0.824741i | \(0.308679\pi\) | |||||||
\(20\) | −1.48232 | −0.331456 | ||||||||
\(21\) | 1.33192 | 0.290648 | ||||||||
\(22\) | 7.18410 | 1.53166 | ||||||||
\(23\) | −6.24377 | −1.30192 | −0.650958 | − | 0.759114i | \(-0.725633\pi\) | ||||
−0.650958 | + | 0.759114i | \(0.725633\pi\) | |||||||
\(24\) | 4.09041 | 0.834951 | ||||||||
\(25\) | −1.36011 | −0.272021 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.62868 | −1.08324 | ||||||||
\(28\) | −0.776957 | −0.146831 | ||||||||
\(29\) | −0.505701 | −0.0939063 | −0.0469531 | − | 0.998897i | \(-0.514951\pi\) | ||||
−0.0469531 | + | 0.998897i | \(0.514951\pi\) | |||||||
\(30\) | −2.81023 | −0.513075 | ||||||||
\(31\) | −5.66349 | −1.01719 | −0.508596 | − | 0.861005i | \(-0.669835\pi\) | ||||
−0.508596 | + | 0.861005i | \(0.669835\pi\) | |||||||
\(32\) | −4.10458 | −0.725595 | ||||||||
\(33\) | −8.65223 | −1.50616 | ||||||||
\(34\) | 7.90267 | 1.35530 | ||||||||
\(35\) | 1.90785 | 0.322486 | ||||||||
\(36\) | 0.952551 | 0.158758 | ||||||||
\(37\) | −0.0345893 | −0.00568644 | −0.00284322 | − | 0.999996i | \(-0.500905\pi\) | ||||
−0.00284322 | + | 0.999996i | \(0.500905\pi\) | |||||||
\(38\) | −5.45216 | −0.884456 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.85915 | 0.926412 | ||||||||
\(41\) | 2.58588 | 0.403847 | 0.201924 | − | 0.979401i | \(-0.435281\pi\) | ||||
0.201924 | + | 0.979401i | \(0.435281\pi\) | |||||||
\(42\) | −1.47298 | −0.227286 | ||||||||
\(43\) | 0.374663 | 0.0571355 | 0.0285678 | − | 0.999592i | \(-0.490905\pi\) | ||||
0.0285678 | + | 0.999592i | \(0.490905\pi\) | |||||||
\(44\) | 5.04718 | 0.760890 | ||||||||
\(45\) | −2.33903 | −0.348682 | ||||||||
\(46\) | 6.90506 | 1.01810 | ||||||||
\(47\) | 10.3893 | 1.51543 | 0.757715 | − | 0.652586i | \(-0.226316\pi\) | ||||
0.757715 | + | 0.652586i | \(0.226316\pi\) | |||||||
\(48\) | −2.45395 | −0.354198 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.50416 | 0.212720 | ||||||||
\(51\) | −9.51764 | −1.33274 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.66712 | 0.366357 | 0.183179 | − | 0.983080i | \(-0.441361\pi\) | ||||
0.183179 | + | 0.983080i | \(0.441361\pi\) | |||||||
\(54\) | 6.22482 | 0.847091 | ||||||||
\(55\) | −12.3936 | −1.67115 | ||||||||
\(56\) | 3.07107 | 0.410389 | ||||||||
\(57\) | 6.56635 | 0.869734 | ||||||||
\(58\) | 0.559261 | 0.0734346 | ||||||||
\(59\) | −1.28549 | −0.167357 | −0.0836784 | − | 0.996493i | \(-0.526667\pi\) | ||||
−0.0836784 | + | 0.996493i | \(0.526667\pi\) | |||||||
\(60\) | −1.97432 | −0.254884 | ||||||||
\(61\) | −5.66025 | −0.724720 | −0.362360 | − | 0.932038i | \(-0.618029\pi\) | ||||
−0.362360 | + | 0.932038i | \(0.618029\pi\) | |||||||
\(62\) | 6.26333 | 0.795443 | ||||||||
\(63\) | −1.22600 | −0.154462 | ||||||||
\(64\) | 8.22416 | 1.02802 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.56861 | 1.17781 | ||||||||
\(67\) | 12.8913 | 1.57492 | 0.787461 | − | 0.616365i | \(-0.211395\pi\) | ||||
0.787461 | + | 0.616365i | \(0.211395\pi\) | |||||||
\(68\) | 5.55201 | 0.673280 | ||||||||
\(69\) | −8.31617 | −1.00115 | ||||||||
\(70\) | −2.10992 | −0.252183 | ||||||||
\(71\) | −9.38877 | −1.11424 | −0.557121 | − | 0.830431i | \(-0.688094\pi\) | ||||
−0.557121 | + | 0.830431i | \(0.688094\pi\) | |||||||
\(72\) | −3.76514 | −0.443726 | ||||||||
\(73\) | −4.37566 | −0.512132 | −0.256066 | − | 0.966659i | \(-0.582426\pi\) | ||||
−0.256066 | + | 0.966659i | \(0.582426\pi\) | |||||||
\(74\) | 0.0382527 | 0.00444679 | ||||||||
\(75\) | −1.81155 | −0.209179 | ||||||||
\(76\) | −3.83040 | −0.439377 | ||||||||
\(77\) | −6.49608 | −0.740297 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.870391 | 0.0979266 | 0.0489633 | − | 0.998801i | \(-0.484408\pi\) | ||||
0.0489633 | + | 0.998801i | \(0.484408\pi\) | |||||||
\(80\) | −3.51507 | −0.392997 | ||||||||
\(81\) | −3.81891 | −0.424324 | ||||||||
\(82\) | −2.85976 | −0.315808 | ||||||||
\(83\) | −7.76117 | −0.851899 | −0.425950 | − | 0.904747i | \(-0.640060\pi\) | ||||
−0.425950 | + | 0.904747i | \(0.640060\pi\) | |||||||
\(84\) | −1.03484 | −0.112910 | ||||||||
\(85\) | −13.6332 | −1.47873 | ||||||||
\(86\) | −0.414344 | −0.0446799 | ||||||||
\(87\) | −0.673550 | −0.0722122 | ||||||||
\(88\) | −19.9499 | −2.12667 | ||||||||
\(89\) | −9.16906 | −0.971918 | −0.485959 | − | 0.873982i | \(-0.661530\pi\) | ||||
−0.485959 | + | 0.873982i | \(0.661530\pi\) | |||||||
\(90\) | 2.58676 | 0.272669 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.85114 | 0.505766 | ||||||||
\(93\) | −7.54329 | −0.782202 | ||||||||
\(94\) | −11.4896 | −1.18506 | ||||||||
\(95\) | 9.40571 | 0.965006 | ||||||||
\(96\) | −5.46696 | −0.557969 | ||||||||
\(97\) | −1.40381 | −0.142535 | −0.0712675 | − | 0.997457i | \(-0.522704\pi\) | ||||
−0.0712675 | + | 0.997457i | \(0.522704\pi\) | |||||||
\(98\) | −1.10591 | −0.111714 | ||||||||
\(99\) | 7.96421 | 0.800433 | ||||||||
\(100\) | 1.05674 | 0.105674 | ||||||||
\(101\) | 7.91948 | 0.788018 | 0.394009 | − | 0.919107i | \(-0.371088\pi\) | ||||
0.394009 | + | 0.919107i | \(0.371088\pi\) | |||||||
\(102\) | 10.5257 | 1.04220 | ||||||||
\(103\) | 5.39342 | 0.531429 | 0.265715 | − | 0.964052i | \(-0.414392\pi\) | ||||
0.265715 | + | 0.964052i | \(0.414392\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.54109 | 0.247985 | ||||||||
\(106\) | −2.94960 | −0.286491 | ||||||||
\(107\) | −1.27332 | −0.123096 | −0.0615482 | − | 0.998104i | \(-0.519604\pi\) | ||||
−0.0615482 | + | 0.998104i | \(0.519604\pi\) | |||||||
\(108\) | 4.37324 | 0.420815 | ||||||||
\(109\) | −12.6746 | −1.21401 | −0.607004 | − | 0.794699i | \(-0.707629\pi\) | ||||
−0.607004 | + | 0.794699i | \(0.707629\pi\) | |||||||
\(110\) | 13.7062 | 1.30683 | ||||||||
\(111\) | −0.0460700 | −0.00437277 | ||||||||
\(112\) | −1.84242 | −0.174093 | ||||||||
\(113\) | 0.833601 | 0.0784186 | 0.0392093 | − | 0.999231i | \(-0.487516\pi\) | ||||
0.0392093 | + | 0.999231i | \(0.487516\pi\) | |||||||
\(114\) | −7.26181 | −0.680131 | ||||||||
\(115\) | −11.9122 | −1.11082 | ||||||||
\(116\) | 0.392908 | 0.0364806 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.42164 | 0.130873 | ||||||||
\(119\) | −7.14583 | −0.655058 | ||||||||
\(120\) | 7.80389 | 0.712394 | ||||||||
\(121\) | 31.1991 | 2.83628 | ||||||||
\(122\) | 6.25974 | 0.566730 | ||||||||
\(123\) | 3.44418 | 0.310551 | ||||||||
\(124\) | 4.40029 | 0.395158 | ||||||||
\(125\) | −12.1341 | −1.08531 | ||||||||
\(126\) | 1.35585 | 0.120789 | ||||||||
\(127\) | −7.97017 | −0.707238 | −0.353619 | − | 0.935390i | \(-0.615049\pi\) | ||||
−0.353619 | + | 0.935390i | \(0.615049\pi\) | |||||||
\(128\) | −0.886036 | −0.0783152 | ||||||||
\(129\) | 0.499019 | 0.0439362 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.5538 | −1.35894 | −0.679472 | − | 0.733702i | \(-0.737791\pi\) | ||||
−0.679472 | + | 0.733702i | \(0.737791\pi\) | |||||||
\(132\) | 6.72241 | 0.585111 | ||||||||
\(133\) | 4.93001 | 0.427486 | ||||||||
\(134\) | −14.2566 | −1.23159 | ||||||||
\(135\) | −10.7387 | −0.924238 | ||||||||
\(136\) | −21.9454 | −1.88180 | ||||||||
\(137\) | 17.7435 | 1.51593 | 0.757965 | − | 0.652295i | \(-0.226194\pi\) | ||||
0.757965 | + | 0.652295i | \(0.226194\pi\) | |||||||
\(138\) | 9.19696 | 0.782897 | ||||||||
\(139\) | −17.3421 | −1.47094 | −0.735468 | − | 0.677560i | \(-0.763038\pi\) | ||||
−0.735468 | + | 0.677560i | \(0.763038\pi\) | |||||||
\(140\) | −1.48232 | −0.125279 | ||||||||
\(141\) | 13.8376 | 1.16534 | ||||||||
\(142\) | 10.3832 | 0.871335 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.25882 | 0.188235 | ||||||||
\(145\) | −0.964801 | −0.0801224 | ||||||||
\(146\) | 4.83910 | 0.400487 | ||||||||
\(147\) | 1.33192 | 0.109855 | ||||||||
\(148\) | 0.0268744 | 0.00220906 | ||||||||
\(149\) | −3.45543 | −0.283080 | −0.141540 | − | 0.989933i | \(-0.545205\pi\) | ||||
−0.141540 | + | 0.989933i | \(0.545205\pi\) | |||||||
\(150\) | 2.00341 | 0.163578 | ||||||||
\(151\) | −4.65219 | −0.378590 | −0.189295 | − | 0.981920i | \(-0.560620\pi\) | ||||
−0.189295 | + | 0.981920i | \(0.560620\pi\) | |||||||
\(152\) | 15.1404 | 1.22805 | ||||||||
\(153\) | 8.76081 | 0.708269 | ||||||||
\(154\) | 7.18410 | 0.578911 | ||||||||
\(155\) | −10.8051 | −0.867886 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.24284 | −0.178998 | −0.0894992 | − | 0.995987i | \(-0.528527\pi\) | ||||
−0.0894992 | + | 0.995987i | \(0.528527\pi\) | |||||||
\(158\) | −0.962576 | −0.0765785 | ||||||||
\(159\) | 3.55238 | 0.281722 | ||||||||
\(160\) | −7.83093 | −0.619090 | ||||||||
\(161\) | −6.24377 | −0.492078 | ||||||||
\(162\) | 4.22338 | 0.331820 | ||||||||
\(163\) | 9.85924 | 0.772235 | 0.386118 | − | 0.922450i | \(-0.373816\pi\) | ||||
0.386118 | + | 0.922450i | \(0.373816\pi\) | |||||||
\(164\) | −2.00912 | −0.156886 | ||||||||
\(165\) | −16.5072 | −1.28508 | ||||||||
\(166\) | 8.58318 | 0.666184 | ||||||||
\(167\) | 8.60457 | 0.665841 | 0.332921 | − | 0.942955i | \(-0.391966\pi\) | ||||
0.332921 | + | 0.942955i | \(0.391966\pi\) | |||||||
\(168\) | 4.09041 | 0.315582 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 15.0771 | 1.15636 | ||||||||
\(171\) | −6.04420 | −0.462211 | ||||||||
\(172\) | −0.291097 | −0.0221959 | ||||||||
\(173\) | −15.0786 | −1.14640 | −0.573202 | − | 0.819414i | \(-0.694299\pi\) | ||||
−0.573202 | + | 0.819414i | \(0.694299\pi\) | |||||||
\(174\) | 0.744888 | 0.0564698 | ||||||||
\(175\) | −1.36011 | −0.102814 | ||||||||
\(176\) | 11.9685 | 0.902162 | ||||||||
\(177\) | −1.71217 | −0.128694 | ||||||||
\(178\) | 10.1402 | 0.760039 | ||||||||
\(179\) | 2.60788 | 0.194922 | 0.0974610 | − | 0.995239i | \(-0.468928\pi\) | ||||
0.0974610 | + | 0.995239i | \(0.468928\pi\) | |||||||
\(180\) | 1.81732 | 0.135455 | ||||||||
\(181\) | −16.2821 | −1.21024 | −0.605119 | − | 0.796135i | \(-0.706874\pi\) | ||||
−0.605119 | + | 0.796135i | \(0.706874\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.53897 | −0.557297 | ||||||||
\(184\) | −19.1751 | −1.41360 | ||||||||
\(185\) | −0.0659912 | −0.00485177 | ||||||||
\(186\) | 8.34222 | 0.611681 | ||||||||
\(187\) | 46.4199 | 3.39456 | ||||||||
\(188\) | −8.07201 | −0.588712 | ||||||||
\(189\) | −5.62868 | −0.409426 | ||||||||
\(190\) | −10.4019 | −0.754633 | ||||||||
\(191\) | 12.8226 | 0.927811 | 0.463906 | − | 0.885885i | \(-0.346448\pi\) | ||||
0.463906 | + | 0.885885i | \(0.346448\pi\) | |||||||
\(192\) | 10.9539 | 0.790528 | ||||||||
\(193\) | −3.15790 | −0.227311 | −0.113655 | − | 0.993520i | \(-0.536256\pi\) | ||||
−0.113655 | + | 0.993520i | \(0.536256\pi\) | |||||||
\(194\) | 1.55249 | 0.111462 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.776957 | −0.0554969 | ||||||||
\(197\) | −13.9283 | −0.992350 | −0.496175 | − | 0.868223i | \(-0.665263\pi\) | ||||
−0.496175 | + | 0.868223i | \(0.665263\pi\) | |||||||
\(198\) | −8.80772 | −0.625938 | ||||||||
\(199\) | 22.9738 | 1.62857 | 0.814285 | − | 0.580465i | \(-0.197129\pi\) | ||||
0.814285 | + | 0.580465i | \(0.197129\pi\) | |||||||
\(200\) | −4.17698 | −0.295357 | ||||||||
\(201\) | 17.1701 | 1.21109 | ||||||||
\(202\) | −8.75825 | −0.616229 | ||||||||
\(203\) | −0.505701 | −0.0354932 | ||||||||
\(204\) | 7.39480 | 0.517740 | ||||||||
\(205\) | 4.93348 | 0.344569 | ||||||||
\(206\) | −5.96465 | −0.415577 | ||||||||
\(207\) | 7.65488 | 0.532051 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −32.0257 | −2.21526 | ||||||||
\(210\) | −2.81023 | −0.193924 | ||||||||
\(211\) | 23.8461 | 1.64164 | 0.820818 | − | 0.571190i | \(-0.193518\pi\) | ||||
0.820818 | + | 0.571190i | \(0.193518\pi\) | |||||||
\(212\) | −2.07224 | −0.142322 | ||||||||
\(213\) | −12.5050 | −0.856831 | ||||||||
\(214\) | 1.40818 | 0.0962611 | ||||||||
\(215\) | 0.714800 | 0.0487490 | ||||||||
\(216\) | −17.2861 | −1.17617 | ||||||||
\(217\) | −5.66349 | −0.384463 | ||||||||
\(218\) | 14.0170 | 0.949352 | ||||||||
\(219\) | −5.82801 | −0.393820 | ||||||||
\(220\) | 9.62926 | 0.649204 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.0509494 | 0.00341950 | ||||||||
\(223\) | 19.3348 | 1.29475 | 0.647375 | − | 0.762171i | \(-0.275867\pi\) | ||||
0.647375 | + | 0.762171i | \(0.275867\pi\) | |||||||
\(224\) | −4.10458 | −0.274249 | ||||||||
\(225\) | 1.66749 | 0.111166 | ||||||||
\(226\) | −0.921890 | −0.0613232 | ||||||||
\(227\) | 9.40454 | 0.624201 | 0.312100 | − | 0.950049i | \(-0.398967\pi\) | ||||
0.312100 | + | 0.950049i | \(0.398967\pi\) | |||||||
\(228\) | −5.10177 | −0.337873 | ||||||||
\(229\) | −7.01784 | −0.463752 | −0.231876 | − | 0.972745i | \(-0.574486\pi\) | ||||
−0.231876 | + | 0.972745i | \(0.574486\pi\) | |||||||
\(230\) | 13.1738 | 0.868657 | ||||||||
\(231\) | −8.65223 | −0.569275 | ||||||||
\(232\) | −1.55304 | −0.101962 | ||||||||
\(233\) | −1.34066 | −0.0878293 | −0.0439147 | − | 0.999035i | \(-0.513983\pi\) | ||||
−0.0439147 | + | 0.999035i | \(0.513983\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.8212 | 1.29299 | ||||||||
\(236\) | 0.998772 | 0.0650145 | ||||||||
\(237\) | 1.15929 | 0.0753038 | ||||||||
\(238\) | 7.90267 | 0.512254 | ||||||||
\(239\) | 4.15222 | 0.268585 | 0.134293 | − | 0.990942i | \(-0.457124\pi\) | ||||
0.134293 | + | 0.990942i | \(0.457124\pi\) | |||||||
\(240\) | −4.68177 | −0.302207 | ||||||||
\(241\) | 4.32286 | 0.278460 | 0.139230 | − | 0.990260i | \(-0.455537\pi\) | ||||
0.139230 | + | 0.990260i | \(0.455537\pi\) | |||||||
\(242\) | −34.5034 | −2.21797 | ||||||||
\(243\) | 11.7996 | 0.756942 | ||||||||
\(244\) | 4.39777 | 0.281538 | ||||||||
\(245\) | 1.90785 | 0.121888 | ||||||||
\(246\) | −3.80896 | −0.242850 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −17.3930 | −1.10446 | ||||||||
\(249\) | −10.3372 | −0.655095 | ||||||||
\(250\) | 13.4193 | 0.848711 | ||||||||
\(251\) | −20.2440 | −1.27779 | −0.638895 | − | 0.769294i | \(-0.720608\pi\) | ||||
−0.638895 | + | 0.769294i | \(0.720608\pi\) | |||||||
\(252\) | 0.952551 | 0.0600051 | ||||||||
\(253\) | 40.5600 | 2.54999 | ||||||||
\(254\) | 8.81431 | 0.553059 | ||||||||
\(255\) | −18.1582 | −1.13711 | ||||||||
\(256\) | −15.4684 | −0.966778 | ||||||||
\(257\) | −4.03630 | −0.251778 | −0.125889 | − | 0.992044i | \(-0.540178\pi\) | ||||
−0.125889 | + | 0.992044i | \(0.540178\pi\) | |||||||
\(258\) | −0.551871 | −0.0343580 | ||||||||
\(259\) | −0.0345893 | −0.00214927 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.619990 | 0.0383764 | ||||||||
\(262\) | 17.2012 | 1.06269 | ||||||||
\(263\) | −23.7353 | −1.46358 | −0.731792 | − | 0.681528i | \(-0.761316\pi\) | ||||
−0.731792 | + | 0.681528i | \(0.761316\pi\) | |||||||
\(264\) | −26.5716 | −1.63537 | ||||||||
\(265\) | 5.08847 | 0.312582 | ||||||||
\(266\) | −5.45216 | −0.334293 | ||||||||
\(267\) | −12.2124 | −0.747387 | ||||||||
\(268\) | −10.0160 | −0.611823 | ||||||||
\(269\) | −21.2888 | −1.29800 | −0.649000 | − | 0.760789i | \(-0.724812\pi\) | ||||
−0.649000 | + | 0.760789i | \(0.724812\pi\) | |||||||
\(270\) | 11.8760 | 0.722752 | ||||||||
\(271\) | −9.20572 | −0.559208 | −0.279604 | − | 0.960115i | \(-0.590203\pi\) | ||||
−0.279604 | + | 0.960115i | \(0.590203\pi\) | |||||||
\(272\) | 13.1657 | 0.798285 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.6228 | −1.18545 | ||||||||
\(275\) | 8.83536 | 0.532792 | ||||||||
\(276\) | 6.46131 | 0.388925 | ||||||||
\(277\) | 4.85993 | 0.292005 | 0.146002 | − | 0.989284i | \(-0.453359\pi\) | ||||
0.146002 | + | 0.989284i | \(0.453359\pi\) | |||||||
\(278\) | 19.1788 | 1.15027 | ||||||||
\(279\) | 6.94345 | 0.415694 | ||||||||
\(280\) | 5.85915 | 0.350151 | ||||||||
\(281\) | 25.1410 | 1.49979 | 0.749894 | − | 0.661558i | \(-0.230105\pi\) | ||||
0.749894 | + | 0.661558i | \(0.230105\pi\) | |||||||
\(282\) | −15.3032 | −0.911292 | ||||||||
\(283\) | 10.1245 | 0.601838 | 0.300919 | − | 0.953650i | \(-0.402707\pi\) | ||||
0.300919 | + | 0.953650i | \(0.402707\pi\) | |||||||
\(284\) | 7.29467 | 0.432859 | ||||||||
\(285\) | 12.5276 | 0.742072 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.58588 | 0.152640 | ||||||||
\(288\) | 5.03223 | 0.296527 | ||||||||
\(289\) | 34.0629 | 2.00370 | ||||||||
\(290\) | 1.06699 | 0.0626556 | ||||||||
\(291\) | −1.86975 | −0.109607 | ||||||||
\(292\) | 3.39970 | 0.198952 | ||||||||
\(293\) | 25.0544 | 1.46369 | 0.731846 | − | 0.681470i | \(-0.238659\pi\) | ||||
0.731846 | + | 0.681470i | \(0.238659\pi\) | |||||||
\(294\) | −1.47298 | −0.0859060 | ||||||||
\(295\) | −2.45253 | −0.142792 | ||||||||
\(296\) | −0.106226 | −0.00617427 | ||||||||
\(297\) | 36.5643 | 2.12168 | ||||||||
\(298\) | 3.82140 | 0.221368 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.40749 | 0.0812617 | ||||||||
\(301\) | 0.374663 | 0.0215952 | ||||||||
\(302\) | 5.14491 | 0.296057 | ||||||||
\(303\) | 10.5481 | 0.605971 | ||||||||
\(304\) | −9.08316 | −0.520955 | ||||||||
\(305\) | −10.7989 | −0.618343 | ||||||||
\(306\) | −9.68869 | −0.553866 | ||||||||
\(307\) | 31.8849 | 1.81977 | 0.909883 | − | 0.414864i | \(-0.136171\pi\) | ||||
0.909883 | + | 0.414864i | \(0.136171\pi\) | |||||||
\(308\) | 5.04718 | 0.287589 | ||||||||
\(309\) | 7.18357 | 0.408659 | ||||||||
\(310\) | 11.9495 | 0.678685 | ||||||||
\(311\) | −2.23201 | −0.126566 | −0.0632828 | − | 0.997996i | \(-0.520157\pi\) | ||||
−0.0632828 | + | 0.997996i | \(0.520157\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.1644 | −0.913668 | −0.456834 | − | 0.889552i | \(-0.651017\pi\) | ||||
−0.456834 | + | 0.889552i | \(0.651017\pi\) | |||||||
\(314\) | 2.48039 | 0.139976 | ||||||||
\(315\) | −2.33903 | −0.131789 | ||||||||
\(316\) | −0.676256 | −0.0380424 | ||||||||
\(317\) | −7.95078 | −0.446560 | −0.223280 | − | 0.974754i | \(-0.571676\pi\) | ||||
−0.223280 | + | 0.974754i | \(0.571676\pi\) | |||||||
\(318\) | −3.92862 | −0.220306 | ||||||||
\(319\) | 3.28507 | 0.183929 | ||||||||
\(320\) | 15.6905 | 0.877124 | ||||||||
\(321\) | −1.69595 | −0.0946588 | ||||||||
\(322\) | 6.90506 | 0.384804 | ||||||||
\(323\) | −35.2290 | −1.96019 | ||||||||
\(324\) | 2.96713 | 0.164841 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.9035 | −0.603887 | ||||||||
\(327\) | −16.8815 | −0.933550 | ||||||||
\(328\) | 7.94144 | 0.438492 | ||||||||
\(329\) | 10.3893 | 0.572779 | ||||||||
\(330\) | 18.2555 | 1.00493 | ||||||||
\(331\) | 14.0809 | 0.773954 | 0.386977 | − | 0.922089i | \(-0.373519\pi\) | ||||
0.386977 | + | 0.922089i | \(0.373519\pi\) | |||||||
\(332\) | 6.03010 | 0.330944 | ||||||||
\(333\) | 0.0424065 | 0.00232386 | ||||||||
\(334\) | −9.51590 | −0.520687 | ||||||||
\(335\) | 24.5947 | 1.34375 | ||||||||
\(336\) | −2.45395 | −0.133874 | ||||||||
\(337\) | 21.3763 | 1.16444 | 0.582220 | − | 0.813032i | \(-0.302184\pi\) | ||||
0.582220 | + | 0.813032i | \(0.302184\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.11029 | 0.0603024 | ||||||||
\(340\) | 10.5924 | 0.574453 | ||||||||
\(341\) | 36.7905 | 1.99232 | ||||||||
\(342\) | 6.68436 | 0.361449 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 1.15062 | 0.0620371 | ||||||||
\(345\) | −15.8660 | −0.854197 | ||||||||
\(346\) | 16.6756 | 0.896487 | ||||||||
\(347\) | 8.96438 | 0.481233 | 0.240617 | − | 0.970620i | \(-0.422650\pi\) | ||||
0.240617 | + | 0.970620i | \(0.422650\pi\) | |||||||
\(348\) | 0.523320 | 0.0280529 | ||||||||
\(349\) | 5.83019 | 0.312083 | 0.156041 | − | 0.987751i | \(-0.450127\pi\) | ||||
0.156041 | + | 0.987751i | \(0.450127\pi\) | |||||||
\(350\) | 1.50416 | 0.0804007 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 26.6637 | 1.42118 | ||||||||
\(353\) | −22.1854 | −1.18081 | −0.590406 | − | 0.807107i | \(-0.701032\pi\) | ||||
−0.590406 | + | 0.807107i | \(0.701032\pi\) | |||||||
\(354\) | 1.89351 | 0.100639 | ||||||||
\(355\) | −17.9124 | −0.950689 | ||||||||
\(356\) | 7.12396 | 0.377569 | ||||||||
\(357\) | −9.51764 | −0.503727 | ||||||||
\(358\) | −2.88409 | −0.152429 | ||||||||
\(359\) | −14.3644 | −0.758123 | −0.379062 | − | 0.925371i | \(-0.623753\pi\) | ||||
−0.379062 | + | 0.925371i | \(0.623753\pi\) | |||||||
\(360\) | −7.18333 | −0.378595 | ||||||||
\(361\) | 5.30495 | 0.279208 | ||||||||
\(362\) | 18.0066 | 0.946404 | ||||||||
\(363\) | 41.5545 | 2.18105 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.34811 | −0.436960 | ||||||||
\(366\) | 8.33744 | 0.435805 | ||||||||
\(367\) | −22.0395 | −1.15045 | −0.575226 | − | 0.817994i | \(-0.695086\pi\) | ||||
−0.575226 | + | 0.817994i | \(0.695086\pi\) | |||||||
\(368\) | 11.5037 | 0.599670 | ||||||||
\(369\) | −3.17030 | −0.165039 | ||||||||
\(370\) | 0.0729805 | 0.00379408 | ||||||||
\(371\) | 2.66712 | 0.138470 | ||||||||
\(372\) | 5.86081 | 0.303869 | ||||||||
\(373\) | 10.5232 | 0.544873 | 0.272436 | − | 0.962174i | \(-0.412171\pi\) | ||||
0.272436 | + | 0.962174i | \(0.412171\pi\) | |||||||
\(374\) | −51.3364 | −2.65454 | ||||||||
\(375\) | −16.1616 | −0.834583 | ||||||||
\(376\) | 31.9062 | 1.64544 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 6.22482 | 0.320170 | ||||||||
\(379\) | 2.24826 | 0.115485 | 0.0577427 | − | 0.998331i | \(-0.481610\pi\) | ||||
0.0577427 | + | 0.998331i | \(0.481610\pi\) | |||||||
\(380\) | −7.30783 | −0.374884 | ||||||||
\(381\) | −10.6156 | −0.543853 | ||||||||
\(382\) | −14.1807 | −0.725547 | ||||||||
\(383\) | 8.17316 | 0.417629 | 0.208815 | − | 0.977955i | \(-0.433039\pi\) | ||||
0.208815 | + | 0.977955i | \(0.433039\pi\) | |||||||
\(384\) | −1.18012 | −0.0602230 | ||||||||
\(385\) | −12.3936 | −0.631634 | ||||||||
\(386\) | 3.49237 | 0.177757 | ||||||||
\(387\) | −0.459337 | −0.0233494 | ||||||||
\(388\) | 1.09070 | 0.0553718 | ||||||||
\(389\) | −21.0561 | −1.06758 | −0.533792 | − | 0.845616i | \(-0.679234\pi\) | ||||
−0.533792 | + | 0.845616i | \(0.679234\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44.6169 | 2.25638 | ||||||||
\(392\) | 3.07107 | 0.155113 | ||||||||
\(393\) | −20.7164 | −1.04500 | ||||||||
\(394\) | 15.4035 | 0.776016 | ||||||||
\(395\) | 1.66058 | 0.0835526 | ||||||||
\(396\) | −6.18785 | −0.310951 | ||||||||
\(397\) | −28.4290 | −1.42681 | −0.713405 | − | 0.700752i | \(-0.752848\pi\) | ||||
−0.713405 | + | 0.700752i | \(0.752848\pi\) | |||||||
\(398\) | −25.4070 | −1.27354 | ||||||||
\(399\) | 6.56635 | 0.328729 | ||||||||
\(400\) | 2.50589 | 0.125295 | ||||||||
\(401\) | 26.8409 | 1.34037 | 0.670185 | − | 0.742194i | \(-0.266215\pi\) | ||||
0.670185 | + | 0.742194i | \(0.266215\pi\) | |||||||
\(402\) | −18.9886 | −0.947067 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.15310 | −0.306128 | ||||||||
\(405\) | −7.28591 | −0.362040 | ||||||||
\(406\) | 0.559261 | 0.0277557 | ||||||||
\(407\) | 0.224695 | 0.0111377 | ||||||||
\(408\) | −29.2294 | −1.44707 | ||||||||
\(409\) | 18.9796 | 0.938483 | 0.469242 | − | 0.883070i | \(-0.344527\pi\) | ||||
0.469242 | + | 0.883070i | \(0.344527\pi\) | |||||||
\(410\) | −5.45600 | −0.269453 | ||||||||
\(411\) | 23.6328 | 1.16572 | ||||||||
\(412\) | −4.19045 | −0.206449 | ||||||||
\(413\) | −1.28549 | −0.0632549 | ||||||||
\(414\) | −8.46562 | −0.416063 | ||||||||
\(415\) | −14.8072 | −0.726855 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −23.0982 | −1.13112 | ||||||||
\(418\) | 35.4176 | 1.73233 | ||||||||
\(419\) | −14.7355 | −0.719874 | −0.359937 | − | 0.932977i | \(-0.617202\pi\) | ||||
−0.359937 | + | 0.932977i | \(0.617202\pi\) | |||||||
\(420\) | −1.97432 | −0.0963370 | ||||||||
\(421\) | 1.07189 | 0.0522408 | 0.0261204 | − | 0.999659i | \(-0.491685\pi\) | ||||
0.0261204 | + | 0.999659i | \(0.491685\pi\) | |||||||
\(422\) | −26.3717 | −1.28376 | ||||||||
\(423\) | −12.7373 | −0.619307 | ||||||||
\(424\) | 8.19092 | 0.397786 | ||||||||
\(425\) | 9.71910 | 0.471445 | ||||||||
\(426\) | 13.8295 | 0.670041 | ||||||||
\(427\) | −5.66025 | −0.273919 | ||||||||
\(428\) | 0.989313 | 0.0478203 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.790507 | −0.0381216 | ||||||||
\(431\) | −28.0271 | −1.35002 | −0.675008 | − | 0.737810i | \(-0.735860\pi\) | ||||
−0.675008 | + | 0.737810i | \(0.735860\pi\) | |||||||
\(432\) | 10.3704 | 0.498947 | ||||||||
\(433\) | −17.9880 | −0.864446 | −0.432223 | − | 0.901767i | \(-0.642271\pi\) | ||||
−0.432223 | + | 0.901767i | \(0.642271\pi\) | |||||||
\(434\) | 6.26333 | 0.300649 | ||||||||
\(435\) | −1.28503 | −0.0616126 | ||||||||
\(436\) | 9.84763 | 0.471616 | ||||||||
\(437\) | −30.7818 | −1.47249 | ||||||||
\(438\) | 6.44527 | 0.307967 | ||||||||
\(439\) | 33.5023 | 1.59898 | 0.799489 | − | 0.600681i | \(-0.205104\pi\) | ||||
0.799489 | + | 0.600681i | \(0.205104\pi\) | |||||||
\(440\) | −38.0615 | −1.81451 | ||||||||
\(441\) | −1.22600 | −0.0583811 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.2578 | −1.39008 | −0.695040 | − | 0.718971i | \(-0.744613\pi\) | ||||
−0.695040 | + | 0.718971i | \(0.744613\pi\) | |||||||
\(444\) | 0.0357944 | 0.00169873 | ||||||||
\(445\) | −17.4932 | −0.829257 | ||||||||
\(446\) | −21.3826 | −1.01249 | ||||||||
\(447\) | −4.60233 | −0.217683 | ||||||||
\(448\) | 8.22416 | 0.388555 | ||||||||
\(449\) | −19.3050 | −0.911058 | −0.455529 | − | 0.890221i | \(-0.650550\pi\) | ||||
−0.455529 | + | 0.890221i | \(0.650550\pi\) | |||||||
\(450\) | −1.84410 | −0.0869318 | ||||||||
\(451\) | −16.7981 | −0.790992 | ||||||||
\(452\) | −0.647672 | −0.0304639 | ||||||||
\(453\) | −6.19632 | −0.291129 | ||||||||
\(454\) | −10.4006 | −0.488124 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 20.1657 | 0.944347 | ||||||||
\(457\) | −17.4861 | −0.817964 | −0.408982 | − | 0.912542i | \(-0.634116\pi\) | ||||
−0.408982 | + | 0.912542i | \(0.634116\pi\) | |||||||
\(458\) | 7.76112 | 0.362653 | ||||||||
\(459\) | 40.2216 | 1.87738 | ||||||||
\(460\) | 9.25525 | 0.431528 | ||||||||
\(461\) | 18.5263 | 0.862858 | 0.431429 | − | 0.902147i | \(-0.358010\pi\) | ||||
0.431429 | + | 0.902147i | \(0.358010\pi\) | |||||||
\(462\) | 9.56861 | 0.445172 | ||||||||
\(463\) | 2.68708 | 0.124879 | 0.0624395 | − | 0.998049i | \(-0.480112\pi\) | ||||
0.0624395 | + | 0.998049i | \(0.480112\pi\) | |||||||
\(464\) | 0.931715 | 0.0432538 | ||||||||
\(465\) | −14.3915 | −0.667388 | ||||||||
\(466\) | 1.48265 | 0.0686824 | ||||||||
\(467\) | −16.0186 | −0.741251 | −0.370625 | − | 0.928782i | \(-0.620857\pi\) | ||||
−0.370625 | + | 0.928782i | \(0.620857\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.8913 | 0.595264 | ||||||||
\(470\) | −21.9205 | −1.01112 | ||||||||
\(471\) | −2.98728 | −0.137646 | ||||||||
\(472\) | −3.94784 | −0.181714 | ||||||||
\(473\) | −2.43384 | −0.111908 | ||||||||
\(474\) | −1.28207 | −0.0588874 | ||||||||
\(475\) | −6.70533 | −0.307662 | ||||||||
\(476\) | 5.55201 | 0.254476 | ||||||||
\(477\) | −3.26990 | −0.149718 | ||||||||
\(478\) | −4.59200 | −0.210033 | ||||||||
\(479\) | 4.25810 | 0.194557 | 0.0972787 | − | 0.995257i | \(-0.468986\pi\) | ||||
0.0972787 | + | 0.995257i | \(0.468986\pi\) | |||||||
\(480\) | −10.4301 | −0.476068 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −4.78070 | −0.217755 | ||||||||
\(483\) | −8.31617 | −0.378399 | ||||||||
\(484\) | −24.2403 | −1.10183 | ||||||||
\(485\) | −2.67825 | −0.121613 | ||||||||
\(486\) | −13.0493 | −0.591928 | ||||||||
\(487\) | −43.0637 | −1.95140 | −0.975702 | − | 0.219103i | \(-0.929687\pi\) | ||||
−0.975702 | + | 0.219103i | \(0.929687\pi\) | |||||||
\(488\) | −17.3830 | −0.786893 | ||||||||
\(489\) | 13.1317 | 0.593835 | ||||||||
\(490\) | −2.10992 | −0.0953163 | ||||||||
\(491\) | 9.44176 | 0.426101 | 0.213050 | − | 0.977041i | \(-0.431660\pi\) | ||||
0.213050 | + | 0.977041i | \(0.431660\pi\) | |||||||
\(492\) | −2.67598 | −0.120642 | ||||||||
\(493\) | 3.61365 | 0.162751 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.1945 | 0.682943 | ||||||||
\(496\) | 10.4346 | 0.468525 | ||||||||
\(497\) | −9.38877 | −0.421144 | ||||||||
\(498\) | 11.4321 | 0.512283 | ||||||||
\(499\) | −0.400211 | −0.0179159 | −0.00895795 | − | 0.999960i | \(-0.502851\pi\) | ||||
−0.00895795 | + | 0.999960i | \(0.502851\pi\) | |||||||
\(500\) | 9.42770 | 0.421619 | ||||||||
\(501\) | 11.4606 | 0.512020 | ||||||||
\(502\) | 22.3881 | 0.999229 | ||||||||
\(503\) | 18.5562 | 0.827378 | 0.413689 | − | 0.910418i | \(-0.364240\pi\) | ||||
0.413689 | + | 0.910418i | \(0.364240\pi\) | |||||||
\(504\) | −3.76514 | −0.167713 | ||||||||
\(505\) | 15.1092 | 0.672350 | ||||||||
\(506\) | −44.8559 | −1.99409 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.19248 | 0.274747 | ||||||||
\(509\) | 39.7624 | 1.76244 | 0.881219 | − | 0.472709i | \(-0.156724\pi\) | ||||
0.881219 | + | 0.472709i | \(0.156724\pi\) | |||||||
\(510\) | 20.0814 | 0.889221 | ||||||||
\(511\) | −4.37566 | −0.193568 | ||||||||
\(512\) | 18.8788 | 0.834334 | ||||||||
\(513\) | −27.7494 | −1.22517 | ||||||||
\(514\) | 4.46380 | 0.196890 | ||||||||
\(515\) | 10.2898 | 0.453424 | ||||||||
\(516\) | −0.387716 | −0.0170683 | ||||||||
\(517\) | −67.4895 | −2.96818 | ||||||||
\(518\) | 0.0382527 | 0.00168073 | ||||||||
\(519\) | −20.0834 | −0.881564 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.7880 | 0.998359 | 0.499180 | − | 0.866499i | \(-0.333635\pi\) | ||||
0.499180 | + | 0.866499i | \(0.333635\pi\) | |||||||
\(522\) | −0.685655 | −0.0300103 | ||||||||
\(523\) | −26.9862 | −1.18003 | −0.590013 | − | 0.807394i | \(-0.700877\pi\) | ||||
−0.590013 | + | 0.807394i | \(0.700877\pi\) | |||||||
\(524\) | 12.0847 | 0.527920 | ||||||||
\(525\) | −1.81155 | −0.0790624 | ||||||||
\(526\) | 26.2492 | 1.14452 | ||||||||
\(527\) | 40.4704 | 1.76292 | ||||||||
\(528\) | 15.9411 | 0.693746 | ||||||||
\(529\) | 15.9847 | 0.694985 | ||||||||
\(530\) | −5.62740 | −0.244439 | ||||||||
\(531\) | 1.57602 | 0.0683933 | ||||||||
\(532\) | −3.83040 | −0.166069 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 13.5059 | 0.584456 | ||||||||
\(535\) | −2.42930 | −0.105028 | ||||||||
\(536\) | 39.5901 | 1.71003 | ||||||||
\(537\) | 3.47347 | 0.149891 | ||||||||
\(538\) | 23.5435 | 1.01503 | ||||||||
\(539\) | −6.49608 | −0.279806 | ||||||||
\(540\) | 8.34349 | 0.359046 | ||||||||
\(541\) | 1.35736 | 0.0583574 | 0.0291787 | − | 0.999574i | \(-0.490711\pi\) | ||||
0.0291787 | + | 0.999574i | \(0.490711\pi\) | |||||||
\(542\) | 10.1807 | 0.437299 | ||||||||
\(543\) | −21.6864 | −0.930651 | ||||||||
\(544\) | 29.3307 | 1.25754 | ||||||||
\(545\) | −24.1813 | −1.03581 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.66512 | 0.199466 | 0.0997330 | − | 0.995014i | \(-0.468201\pi\) | ||||
0.0997330 | + | 0.995014i | \(0.468201\pi\) | |||||||
\(548\) | −13.7859 | −0.588906 | ||||||||
\(549\) | 6.93948 | 0.296170 | ||||||||
\(550\) | −9.77114 | −0.416643 | ||||||||
\(551\) | −2.49311 | −0.106210 | ||||||||
\(552\) | −25.5396 | −1.08704 | ||||||||
\(553\) | 0.870391 | 0.0370128 | ||||||||
\(554\) | −5.37466 | −0.228347 | ||||||||
\(555\) | −0.0878947 | −0.00373092 | ||||||||
\(556\) | 13.4740 | 0.571427 | ||||||||
\(557\) | 9.60851 | 0.407126 | 0.203563 | − | 0.979062i | \(-0.434748\pi\) | ||||
0.203563 | + | 0.979062i | \(0.434748\pi\) | |||||||
\(558\) | −7.67885 | −0.325072 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.51507 | −0.148539 | ||||||||
\(561\) | 61.8274 | 2.61035 | ||||||||
\(562\) | −27.8038 | −1.17283 | ||||||||
\(563\) | 33.1683 | 1.39788 | 0.698938 | − | 0.715183i | \(-0.253656\pi\) | ||||
0.698938 | + | 0.715183i | \(0.253656\pi\) | |||||||
\(564\) | −10.7512 | −0.452709 | ||||||||
\(565\) | 1.59039 | 0.0669080 | ||||||||
\(566\) | −11.1968 | −0.470636 | ||||||||
\(567\) | −3.81891 | −0.160379 | ||||||||
\(568\) | −28.8336 | −1.20983 | ||||||||
\(569\) | −44.4353 | −1.86282 | −0.931411 | − | 0.363968i | \(-0.881422\pi\) | ||||
−0.931411 | + | 0.363968i | \(0.881422\pi\) | |||||||
\(570\) | −13.8544 | −0.580299 | ||||||||
\(571\) | −15.0146 | −0.628341 | −0.314170 | − | 0.949367i | \(-0.601726\pi\) | ||||
−0.314170 | + | 0.949367i | \(0.601726\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.0786 | 0.713470 | ||||||||
\(574\) | −2.85976 | −0.119364 | ||||||||
\(575\) | 8.49219 | 0.354149 | ||||||||
\(576\) | −10.0828 | −0.420118 | ||||||||
\(577\) | −11.7372 | −0.488625 | −0.244312 | − | 0.969697i | \(-0.578562\pi\) | ||||
−0.244312 | + | 0.969697i | \(0.578562\pi\) | |||||||
\(578\) | −37.6707 | −1.56689 | ||||||||
\(579\) | −4.20606 | −0.174798 | ||||||||
\(580\) | 0.749609 | 0.0311258 | ||||||||
\(581\) | −7.76117 | −0.321988 | ||||||||
\(582\) | 2.06778 | 0.0857123 | ||||||||
\(583\) | −17.3258 | −0.717563 | ||||||||
\(584\) | −13.4380 | −0.556067 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.7079 | −1.14460 | ||||||||
\(587\) | −1.87115 | −0.0772306 | −0.0386153 | − | 0.999254i | \(-0.512295\pi\) | ||||
−0.0386153 | + | 0.999254i | \(0.512295\pi\) | |||||||
\(588\) | −1.03484 | −0.0426761 | ||||||||
\(589\) | −27.9210 | −1.15047 | ||||||||
\(590\) | 2.71228 | 0.111663 | ||||||||
\(591\) | −18.5513 | −0.763099 | ||||||||
\(592\) | 0.0637281 | 0.00261921 | ||||||||
\(593\) | −5.06081 | −0.207823 | −0.103911 | − | 0.994587i | \(-0.533136\pi\) | ||||
−0.103911 | + | 0.994587i | \(0.533136\pi\) | |||||||
\(594\) | −40.4370 | −1.65915 | ||||||||
\(595\) | −13.6332 | −0.558906 | ||||||||
\(596\) | 2.68472 | 0.109970 | ||||||||
\(597\) | 30.5992 | 1.25234 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.98581 | 0.162856 | 0.0814280 | − | 0.996679i | \(-0.474052\pi\) | ||||
0.0814280 | + | 0.996679i | \(0.474052\pi\) | |||||||
\(600\) | −5.56339 | −0.227124 | ||||||||
\(601\) | −12.2004 | −0.497666 | −0.248833 | − | 0.968546i | \(-0.580047\pi\) | ||||
−0.248833 | + | 0.968546i | \(0.580047\pi\) | |||||||
\(602\) | −0.414344 | −0.0168874 | ||||||||
\(603\) | −15.8048 | −0.643619 | ||||||||
\(604\) | 3.61455 | 0.147074 | ||||||||
\(605\) | 59.5232 | 2.41996 | ||||||||
\(606\) | −11.6653 | −0.473868 | ||||||||
\(607\) | 11.0021 | 0.446560 | 0.223280 | − | 0.974754i | \(-0.428324\pi\) | ||||
0.223280 | + | 0.974754i | \(0.428324\pi\) | |||||||
\(608\) | −20.2356 | −0.820663 | ||||||||
\(609\) | −0.673550 | −0.0272936 | ||||||||
\(610\) | 11.9426 | 0.483544 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −6.80677 | −0.275147 | ||||||||
\(613\) | −23.9685 | −0.968080 | −0.484040 | − | 0.875046i | \(-0.660831\pi\) | ||||
−0.484040 | + | 0.875046i | \(0.660831\pi\) | |||||||
\(614\) | −35.2619 | −1.42305 | ||||||||
\(615\) | 6.57098 | 0.264967 | ||||||||
\(616\) | −19.9499 | −0.803806 | ||||||||
\(617\) | −7.63127 | −0.307223 | −0.153612 | − | 0.988131i | \(-0.549090\pi\) | ||||
−0.153612 | + | 0.988131i | \(0.549090\pi\) | |||||||
\(618\) | −7.94441 | −0.319571 | ||||||||
\(619\) | 12.1904 | 0.489972 | 0.244986 | − | 0.969527i | \(-0.421217\pi\) | ||||
0.244986 | + | 0.969527i | \(0.421217\pi\) | |||||||
\(620\) | 8.39509 | 0.337155 | ||||||||
\(621\) | 35.1442 | 1.41029 | ||||||||
\(622\) | 2.46841 | 0.0989740 | ||||||||
\(623\) | −9.16906 | −0.367351 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.3496 | −0.653983 | ||||||||
\(626\) | 17.8764 | 0.714487 | ||||||||
\(627\) | −42.6555 | −1.70350 | ||||||||
\(628\) | 1.74259 | 0.0695370 | ||||||||
\(629\) | 0.247169 | 0.00985529 | ||||||||
\(630\) | 2.58676 | 0.103059 | ||||||||
\(631\) | 12.1308 | 0.482921 | 0.241461 | − | 0.970411i | \(-0.422374\pi\) | ||||
0.241461 | + | 0.970411i | \(0.422374\pi\) | |||||||
\(632\) | 2.67303 | 0.106328 | ||||||||
\(633\) | 31.7610 | 1.26239 | ||||||||
\(634\) | 8.79287 | 0.349209 | ||||||||
\(635\) | −15.2059 | −0.603427 | ||||||||
\(636\) | −2.76005 | −0.109443 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.63300 | −0.143832 | ||||||||
\(639\) | 11.5106 | 0.455354 | ||||||||
\(640\) | −1.69042 | −0.0668199 | ||||||||
\(641\) | −49.5578 | −1.95742 | −0.978708 | − | 0.205259i | \(-0.934196\pi\) | ||||
−0.978708 | + | 0.205259i | \(0.934196\pi\) | |||||||
\(642\) | 1.87557 | 0.0740230 | ||||||||
\(643\) | 27.1873 | 1.07216 | 0.536080 | − | 0.844167i | \(-0.319904\pi\) | ||||
0.536080 | + | 0.844167i | \(0.319904\pi\) | |||||||
\(644\) | 4.85114 | 0.191162 | ||||||||
\(645\) | 0.952053 | 0.0374871 | ||||||||
\(646\) | 38.9602 | 1.53287 | ||||||||
\(647\) | −23.1148 | −0.908738 | −0.454369 | − | 0.890814i | \(-0.650135\pi\) | ||||
−0.454369 | + | 0.890814i | \(0.650135\pi\) | |||||||
\(648\) | −11.7282 | −0.460725 | ||||||||
\(649\) | 8.35066 | 0.327792 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.54329 | −0.295645 | ||||||||
\(652\) | −7.66021 | −0.299997 | ||||||||
\(653\) | −35.9335 | −1.40619 | −0.703093 | − | 0.711098i | \(-0.748198\pi\) | ||||
−0.703093 | + | 0.711098i | \(0.748198\pi\) | |||||||
\(654\) | 18.6695 | 0.730034 | ||||||||
\(655\) | −29.6744 | −1.15947 | ||||||||
\(656\) | −4.76429 | −0.186014 | ||||||||
\(657\) | 5.36457 | 0.209292 | ||||||||
\(658\) | −11.4896 | −0.447912 | ||||||||
\(659\) | 0.915223 | 0.0356520 | 0.0178260 | − | 0.999841i | \(-0.494326\pi\) | ||||
0.0178260 | + | 0.999841i | \(0.494326\pi\) | |||||||
\(660\) | 12.8254 | 0.499226 | ||||||||
\(661\) | −44.7114 | −1.73907 | −0.869536 | − | 0.493869i | \(-0.835582\pi\) | ||||
−0.869536 | + | 0.493869i | \(0.835582\pi\) | |||||||
\(662\) | −15.5722 | −0.605231 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −23.8351 | −0.924982 | ||||||||
\(665\) | 9.40571 | 0.364738 | ||||||||
\(666\) | −0.0468979 | −0.00181726 | ||||||||
\(667\) | 3.15748 | 0.122258 | ||||||||
\(668\) | −6.68538 | −0.258665 | ||||||||
\(669\) | 25.7522 | 0.995639 | ||||||||
\(670\) | −27.1995 | −1.05081 | ||||||||
\(671\) | 36.7694 | 1.41947 | ||||||||
\(672\) | −5.46696 | −0.210892 | ||||||||
\(673\) | −34.0405 | −1.31216 | −0.656082 | − | 0.754690i | \(-0.727787\pi\) | ||||
−0.656082 | + | 0.754690i | \(0.727787\pi\) | |||||||
\(674\) | −23.6403 | −0.910590 | ||||||||
\(675\) | 7.65560 | 0.294664 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.9457 | 1.41994 | 0.709969 | − | 0.704233i | \(-0.248709\pi\) | ||||
0.709969 | + | 0.704233i | \(0.248709\pi\) | |||||||
\(678\) | −1.22788 | −0.0471564 | ||||||||
\(679\) | −1.40381 | −0.0538732 | ||||||||
\(680\) | −41.8685 | −1.60558 | ||||||||
\(681\) | 12.5260 | 0.479999 | ||||||||
\(682\) | −40.6871 | −1.55799 | ||||||||
\(683\) | −22.6057 | −0.864982 | −0.432491 | − | 0.901638i | \(-0.642365\pi\) | ||||
−0.432491 | + | 0.901638i | \(0.642365\pi\) | |||||||
\(684\) | 4.69608 | 0.179559 | ||||||||
\(685\) | 33.8519 | 1.29342 | ||||||||
\(686\) | −1.10591 | −0.0422239 | ||||||||
\(687\) | −9.34716 | −0.356617 | ||||||||
\(688\) | −0.690287 | −0.0263170 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 17.5464 | 0.667981 | ||||||||
\(691\) | 5.83440 | 0.221951 | 0.110976 | − | 0.993823i | \(-0.464602\pi\) | ||||
0.110976 | + | 0.993823i | \(0.464602\pi\) | |||||||
\(692\) | 11.7154 | 0.445354 | ||||||||
\(693\) | 7.96421 | 0.302535 | ||||||||
\(694\) | −9.91382 | −0.376324 | ||||||||
\(695\) | −33.0861 | −1.25503 | ||||||||
\(696\) | −2.06852 | −0.0784071 | ||||||||
\(697\) | −18.4783 | −0.699915 | ||||||||
\(698\) | −6.44768 | −0.244048 | ||||||||
\(699\) | −1.78564 | −0.0675391 | ||||||||
\(700\) | 1.05674 | 0.0399412 | ||||||||
\(701\) | −17.5715 | −0.663667 | −0.331834 | − | 0.943338i | \(-0.607667\pi\) | ||||
−0.331834 | + | 0.943338i | \(0.607667\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.170525 | −0.00643149 | ||||||||
\(704\) | −53.4248 | −2.01352 | ||||||||
\(705\) | 26.4001 | 0.994285 | ||||||||
\(706\) | 24.5352 | 0.923393 | ||||||||
\(707\) | 7.91948 | 0.297843 | ||||||||
\(708\) | 1.33028 | 0.0499950 | ||||||||
\(709\) | −41.7153 | −1.56665 | −0.783325 | − | 0.621612i | \(-0.786478\pi\) | ||||
−0.783325 | + | 0.621612i | \(0.786478\pi\) | |||||||
\(710\) | 19.8095 | 0.743438 | ||||||||
\(711\) | −1.06710 | −0.0400194 | ||||||||
\(712\) | −28.1588 | −1.05530 | ||||||||
\(713\) | 35.3615 | 1.32430 | ||||||||
\(714\) | 10.5257 | 0.393914 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.02621 | −0.0757230 | ||||||||
\(717\) | 5.53041 | 0.206537 | ||||||||
\(718\) | 15.8858 | 0.592851 | ||||||||
\(719\) | −36.1319 | −1.34749 | −0.673746 | − | 0.738963i | \(-0.735316\pi\) | ||||
−0.673746 | + | 0.738963i | \(0.735316\pi\) | |||||||
\(720\) | 4.30948 | 0.160605 | ||||||||
\(721\) | 5.39342 | 0.200861 | ||||||||
\(722\) | −5.86681 | −0.218340 | ||||||||
\(723\) | 5.75768 | 0.214130 | ||||||||
\(724\) | 12.6505 | 0.470151 | ||||||||
\(725\) | 0.687807 | 0.0255445 | ||||||||
\(726\) | −45.9557 | −1.70557 | ||||||||
\(727\) | 23.7414 | 0.880520 | 0.440260 | − | 0.897870i | \(-0.354886\pi\) | ||||
0.440260 | + | 0.897870i | \(0.354886\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.1727 | 1.00640 | ||||||||
\(730\) | 9.23228 | 0.341702 | ||||||||
\(731\) | −2.67728 | −0.0990227 | ||||||||
\(732\) | 5.85745 | 0.216498 | ||||||||
\(733\) | −18.1355 | −0.669849 | −0.334925 | − | 0.942245i | \(-0.608711\pi\) | ||||
−0.334925 | + | 0.942245i | \(0.608711\pi\) | |||||||
\(734\) | 24.3738 | 0.899652 | ||||||||
\(735\) | 2.54109 | 0.0937297 | ||||||||
\(736\) | 25.6281 | 0.944663 | ||||||||
\(737\) | −83.7429 | −3.08471 | ||||||||
\(738\) | 3.50607 | 0.129060 | ||||||||
\(739\) | 33.8316 | 1.24451 | 0.622257 | − | 0.782813i | \(-0.286216\pi\) | ||||
0.622257 | + | 0.782813i | \(0.286216\pi\) | |||||||
\(740\) | 0.0512723 | 0.00188481 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.94960 | −0.108283 | ||||||||
\(743\) | 16.6098 | 0.609353 | 0.304677 | − | 0.952456i | \(-0.401452\pi\) | ||||
0.304677 | + | 0.952456i | \(0.401452\pi\) | |||||||
\(744\) | −23.1660 | −0.849306 | ||||||||
\(745\) | −6.59244 | −0.241528 | ||||||||
\(746\) | −11.6378 | −0.426090 | ||||||||
\(747\) | 9.51521 | 0.348143 | ||||||||
\(748\) | −36.0663 | −1.31871 | ||||||||
\(749\) | −1.27332 | −0.0465260 | ||||||||
\(750\) | 17.8734 | 0.652643 | ||||||||
\(751\) | 41.9317 | 1.53011 | 0.765054 | − | 0.643966i | \(-0.222712\pi\) | ||||
0.765054 | + | 0.643966i | \(0.222712\pi\) | |||||||
\(752\) | −19.1414 | −0.698016 | ||||||||
\(753\) | −26.9633 | −0.982596 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.87568 | −0.323019 | ||||||||
\(756\) | 4.37324 | 0.159053 | ||||||||
\(757\) | 46.3278 | 1.68381 | 0.841907 | − | 0.539623i | \(-0.181433\pi\) | ||||
0.841907 | + | 0.539623i | \(0.181433\pi\) | |||||||
\(758\) | −2.48638 | −0.0903094 | ||||||||
\(759\) | 54.0225 | 1.96089 | ||||||||
\(760\) | 28.8856 | 1.04779 | ||||||||
\(761\) | 29.5269 | 1.07035 | 0.535174 | − | 0.844742i | \(-0.320246\pi\) | ||||
0.535174 | + | 0.844742i | \(0.320246\pi\) | |||||||
\(762\) | 11.7399 | 0.425292 | ||||||||
\(763\) | −12.6746 | −0.458852 | ||||||||
\(764\) | −9.96261 | −0.360435 | ||||||||
\(765\) | 16.7143 | 0.604307 | ||||||||
\(766\) | −9.03880 | −0.326585 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −20.6027 | −0.743434 | ||||||||
\(769\) | −39.4542 | −1.42275 | −0.711377 | − | 0.702811i | \(-0.751928\pi\) | ||||
−0.711377 | + | 0.702811i | \(0.751928\pi\) | |||||||
\(770\) | 13.7062 | 0.493937 | ||||||||
\(771\) | −5.37601 | −0.193612 | ||||||||
\(772\) | 2.45356 | 0.0883054 | ||||||||
\(773\) | −3.97395 | −0.142933 | −0.0714666 | − | 0.997443i | \(-0.522768\pi\) | ||||
−0.0714666 | + | 0.997443i | \(0.522768\pi\) | |||||||
\(774\) | 0.507987 | 0.0182592 | ||||||||
\(775\) | 7.70295 | 0.276698 | ||||||||
\(776\) | −4.31119 | −0.154763 | ||||||||
\(777\) | −0.0460700 | −0.00165275 | ||||||||
\(778\) | 23.2862 | 0.834849 | ||||||||
\(779\) | 12.7484 | 0.456760 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 60.9902 | 2.18240 | ||||||||
\(782\) | −49.3424 | −1.76448 | ||||||||
\(783\) | 2.84643 | 0.101723 | ||||||||
\(784\) | −1.84242 | −0.0658009 | ||||||||
\(785\) | −4.27901 | −0.152724 | ||||||||
\(786\) | 22.9105 | 0.817190 | ||||||||
\(787\) | 0.698671 | 0.0249049 | 0.0124525 | − | 0.999922i | \(-0.496036\pi\) | ||||
0.0124525 | + | 0.999922i | \(0.496036\pi\) | |||||||
\(788\) | 10.8217 | 0.385507 | ||||||||
\(789\) | −31.6134 | −1.12547 | ||||||||
\(790\) | −1.83645 | −0.0653380 | ||||||||
\(791\) | 0.833601 | 0.0296394 | ||||||||
\(792\) | 24.4587 | 0.869101 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 31.4400 | 1.11576 | ||||||||
\(795\) | 6.77741 | 0.240370 | ||||||||
\(796\) | −17.8497 | −0.632664 | ||||||||
\(797\) | −6.12095 | −0.216815 | −0.108408 | − | 0.994107i | \(-0.534575\pi\) | ||||
−0.108408 | + | 0.994107i | \(0.534575\pi\) | |||||||
\(798\) | −7.26181 | −0.257065 | ||||||||
\(799\) | −74.2400 | −2.62642 | ||||||||
\(800\) | 5.58267 | 0.197377 | ||||||||
\(801\) | 11.2413 | 0.397191 | ||||||||
\(802\) | −29.6837 | −1.04817 | ||||||||
\(803\) | 28.4246 | 1.00308 | ||||||||
\(804\) | −13.3404 | −0.470481 | ||||||||
\(805\) | −11.9122 | −0.419849 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.3548 | −0.998137 | ||||||||
\(808\) | 24.3213 | 0.855620 | ||||||||
\(809\) | −21.8694 | −0.768886 | −0.384443 | − | 0.923149i | \(-0.625606\pi\) | ||||
−0.384443 | + | 0.923149i | \(0.625606\pi\) | |||||||
\(810\) | 8.05758 | 0.283115 | ||||||||
\(811\) | −4.38772 | −0.154074 | −0.0770368 | − | 0.997028i | \(-0.524546\pi\) | ||||
−0.0770368 | + | 0.997028i | \(0.524546\pi\) | |||||||
\(812\) | 0.392908 | 0.0137884 | ||||||||
\(813\) | −12.2612 | −0.430020 | ||||||||
\(814\) | −0.248493 | −0.00870967 | ||||||||
\(815\) | 18.8100 | 0.658884 | ||||||||
\(816\) | 17.5355 | 0.613867 | ||||||||
\(817\) | 1.84709 | 0.0646215 | ||||||||
\(818\) | −20.9898 | −0.733892 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.83310 | −0.133858 | ||||||||
\(821\) | 31.5599 | 1.10145 | 0.550724 | − | 0.834687i | \(-0.314352\pi\) | ||||
0.550724 | + | 0.834687i | \(0.314352\pi\) | |||||||
\(822\) | −26.1359 | −0.911593 | ||||||||
\(823\) | −13.6727 | −0.476600 | −0.238300 | − | 0.971192i | \(-0.576590\pi\) | ||||
−0.238300 | + | 0.971192i | \(0.576590\pi\) | |||||||
\(824\) | 16.5636 | 0.577020 | ||||||||
\(825\) | 11.7680 | 0.409707 | ||||||||
\(826\) | 1.42164 | 0.0494653 | ||||||||
\(827\) | −13.5727 | −0.471970 | −0.235985 | − | 0.971757i | \(-0.575832\pi\) | ||||
−0.235985 | + | 0.971757i | \(0.575832\pi\) | |||||||
\(828\) | −5.94751 | −0.206690 | ||||||||
\(829\) | 51.0839 | 1.77422 | 0.887109 | − | 0.461560i | \(-0.152710\pi\) | ||||
0.887109 | + | 0.461560i | \(0.152710\pi\) | |||||||
\(830\) | 16.3754 | 0.568399 | ||||||||
\(831\) | 6.47301 | 0.224546 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.14583 | −0.247588 | ||||||||
\(834\) | 25.5446 | 0.884536 | ||||||||
\(835\) | 16.4162 | 0.568107 | ||||||||
\(836\) | 24.8826 | 0.860583 | ||||||||
\(837\) | 31.8780 | 1.10186 | ||||||||
\(838\) | 16.2961 | 0.562940 | ||||||||
\(839\) | −7.39574 | −0.255329 | −0.127665 | − | 0.991817i | \(-0.540748\pi\) | ||||
−0.127665 | + | 0.991817i | \(0.540748\pi\) | |||||||
\(840\) | 7.80389 | 0.269260 | ||||||||
\(841\) | −28.7443 | −0.991182 | ||||||||
\(842\) | −1.18542 | −0.0408522 | ||||||||
\(843\) | 33.4857 | 1.15331 | ||||||||
\(844\) | −18.5274 | −0.637740 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 14.0863 | 0.484297 | ||||||||
\(847\) | 31.1991 | 1.07201 | ||||||||
\(848\) | −4.91397 | −0.168746 | ||||||||
\(849\) | 13.4849 | 0.462802 | ||||||||
\(850\) | −10.7485 | −0.368670 | ||||||||
\(851\) | 0.215968 | 0.00740327 | ||||||||
\(852\) | 9.71588 | 0.332860 | ||||||||
\(853\) | −12.0552 | −0.412762 | −0.206381 | − | 0.978472i | \(-0.566169\pi\) | ||||
−0.206381 | + | 0.978472i | \(0.566169\pi\) | |||||||
\(854\) | 6.25974 | 0.214204 | ||||||||
\(855\) | −11.5314 | −0.394366 | ||||||||
\(856\) | −3.91045 | −0.133656 | ||||||||
\(857\) | 46.7924 | 1.59840 | 0.799199 | − | 0.601066i | \(-0.205257\pi\) | ||||
0.799199 | + | 0.601066i | \(0.205257\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.5870 | −1.48717 | −0.743585 | − | 0.668641i | \(-0.766876\pi\) | ||||
−0.743585 | + | 0.668641i | \(0.766876\pi\) | |||||||
\(860\) | −0.555369 | −0.0189379 | ||||||||
\(861\) | 3.44418 | 0.117377 | ||||||||
\(862\) | 30.9955 | 1.05571 | ||||||||
\(863\) | −0.0785410 | −0.00267357 | −0.00133678 | − | 0.999999i | \(-0.500426\pi\) | ||||
−0.00133678 | + | 0.999999i | \(0.500426\pi\) | |||||||
\(864\) | 23.1034 | 0.785993 | ||||||||
\(865\) | −28.7677 | −0.978132 | ||||||||
\(866\) | 19.8931 | 0.675995 | ||||||||
\(867\) | 45.3690 | 1.54081 | ||||||||
\(868\) | 4.40029 | 0.149356 | ||||||||
\(869\) | −5.65413 | −0.191803 | ||||||||
\(870\) | 1.42114 | 0.0481810 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −38.9247 | −1.31816 | ||||||||
\(873\) | 1.72107 | 0.0582494 | ||||||||
\(874\) | 34.0420 | 1.15149 | ||||||||
\(875\) | −12.1341 | −0.410209 | ||||||||
\(876\) | 4.52811 | 0.152991 | ||||||||
\(877\) | −32.1903 | −1.08699 | −0.543495 | − | 0.839413i | \(-0.682899\pi\) | ||||
−0.543495 | + | 0.839413i | \(0.682899\pi\) | |||||||
\(878\) | −37.0506 | −1.25040 | ||||||||
\(879\) | 33.3703 | 1.12555 | ||||||||
\(880\) | 22.8342 | 0.769740 | ||||||||
\(881\) | −10.4114 | −0.350770 | −0.175385 | − | 0.984500i | \(-0.556117\pi\) | ||||
−0.175385 | + | 0.984500i | \(0.556117\pi\) | |||||||
\(882\) | 1.35585 | 0.0456539 | ||||||||
\(883\) | 21.5238 | 0.724334 | 0.362167 | − | 0.932113i | \(-0.382037\pi\) | ||||
0.362167 | + | 0.932113i | \(0.382037\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.26656 | −0.109804 | ||||||||
\(886\) | 32.3566 | 1.08704 | ||||||||
\(887\) | 45.5964 | 1.53098 | 0.765489 | − | 0.643449i | \(-0.222497\pi\) | ||||
0.765489 | + | 0.643449i | \(0.222497\pi\) | |||||||
\(888\) | −0.141484 | −0.00474790 | ||||||||
\(889\) | −7.97017 | −0.267311 | ||||||||
\(890\) | 19.3459 | 0.648478 | ||||||||
\(891\) | 24.8080 | 0.831098 | ||||||||
\(892\) | −15.0223 | −0.502983 | ||||||||
\(893\) | 51.2191 | 1.71398 | ||||||||
\(894\) | 5.08978 | 0.170228 | ||||||||
\(895\) | 4.97544 | 0.166311 | ||||||||
\(896\) | −0.886036 | −0.0296004 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.3496 | 0.712446 | ||||||||
\(899\) | 2.86403 | 0.0955208 | ||||||||
\(900\) | −1.29557 | −0.0431857 | ||||||||
\(901\) | −19.0588 | −0.634941 | ||||||||
\(902\) | 18.5772 | 0.618555 | ||||||||
\(903\) | 0.499019 | 0.0166063 | ||||||||
\(904\) | 2.56005 | 0.0851460 | ||||||||
\(905\) | −31.0638 | −1.03260 | ||||||||
\(906\) | 6.85259 | 0.227662 | ||||||||
\(907\) | 19.0080 | 0.631150 | 0.315575 | − | 0.948901i | \(-0.397803\pi\) | ||||
0.315575 | + | 0.948901i | \(0.397803\pi\) | |||||||
\(908\) | −7.30692 | −0.242489 | ||||||||
\(909\) | −9.70930 | −0.322037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.6010 | −1.11325 | −0.556626 | − | 0.830763i | \(-0.687904\pi\) | ||||
−0.556626 | + | 0.830763i | \(0.687904\pi\) | |||||||
\(912\) | −12.0980 | −0.400605 | ||||||||
\(913\) | 50.4172 | 1.66857 | ||||||||
\(914\) | 19.3381 | 0.639647 | ||||||||
\(915\) | −14.3832 | −0.475495 | ||||||||
\(916\) | 5.45256 | 0.180158 | ||||||||
\(917\) | −15.5538 | −0.513632 | ||||||||
\(918\) | −44.4816 | −1.46811 | ||||||||
\(919\) | 19.9752 | 0.658921 | 0.329461 | − | 0.944169i | \(-0.393133\pi\) | ||||
0.329461 | + | 0.944169i | \(0.393133\pi\) | |||||||
\(920\) | −36.5832 | −1.20611 | ||||||||
\(921\) | 42.4680 | 1.39937 | ||||||||
\(922\) | −20.4885 | −0.674754 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 6.72241 | 0.221151 | ||||||||
\(925\) | 0.0470451 | 0.00154683 | ||||||||
\(926\) | −2.97167 | −0.0976552 | ||||||||
\(927\) | −6.61234 | −0.217178 | ||||||||
\(928\) | 2.07569 | 0.0681379 | ||||||||
\(929\) | 1.73612 | 0.0569602 | 0.0284801 | − | 0.999594i | \(-0.490933\pi\) | ||||
0.0284801 | + | 0.999594i | \(0.490933\pi\) | |||||||
\(930\) | 15.9157 | 0.521897 | ||||||||
\(931\) | 4.93001 | 0.161574 | ||||||||
\(932\) | 1.04163 | 0.0341198 | ||||||||
\(933\) | −2.97284 | −0.0973265 | ||||||||
\(934\) | 17.7151 | 0.579657 | ||||||||
\(935\) | 88.5623 | 2.89630 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.46161 | 0.145754 | 0.0728772 | − | 0.997341i | \(-0.476782\pi\) | ||||
0.0728772 | + | 0.997341i | \(0.476782\pi\) | |||||||
\(938\) | −14.2566 | −0.465496 | ||||||||
\(939\) | −21.5296 | −0.702593 | ||||||||
\(940\) | −15.4002 | −0.502299 | ||||||||
\(941\) | 5.31110 | 0.173137 | 0.0865685 | − | 0.996246i | \(-0.472410\pi\) | ||||
0.0865685 | + | 0.996246i | \(0.472410\pi\) | |||||||
\(942\) | 3.30367 | 0.107639 | ||||||||
\(943\) | −16.1457 | −0.525775 | ||||||||
\(944\) | 2.36842 | 0.0770856 | ||||||||
\(945\) | −10.7387 | −0.349329 | ||||||||
\(946\) | 2.69161 | 0.0875119 | ||||||||
\(947\) | −15.0901 | −0.490364 | −0.245182 | − | 0.969477i | \(-0.578848\pi\) | ||||
−0.245182 | + | 0.969477i | \(0.578848\pi\) | |||||||
\(948\) | −0.900716 | −0.0292539 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.41551 | 0.240591 | ||||||||
\(951\) | −10.5898 | −0.343397 | ||||||||
\(952\) | −21.9454 | −0.711254 | ||||||||
\(953\) | −38.5139 | −1.24759 | −0.623794 | − | 0.781589i | \(-0.714409\pi\) | ||||
−0.623794 | + | 0.781589i | \(0.714409\pi\) | |||||||
\(954\) | 3.61622 | 0.117079 | ||||||||
\(955\) | 24.4636 | 0.791624 | ||||||||
\(956\) | −3.22610 | −0.104339 | ||||||||
\(957\) | 4.37544 | 0.141438 | ||||||||
\(958\) | −4.70909 | −0.152144 | ||||||||
\(959\) | 17.7435 | 0.572968 | ||||||||
\(960\) | 20.8984 | 0.674492 | ||||||||
\(961\) | 1.07512 | 0.0346813 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.56109 | 0.0503055 | ||||||||
\(964\) | −3.35868 | −0.108176 | ||||||||
\(965\) | −6.02481 | −0.193945 | ||||||||
\(966\) | 9.19696 | 0.295907 | ||||||||
\(967\) | 46.8859 | 1.50775 | 0.753874 | − | 0.657019i | \(-0.228183\pi\) | ||||
0.753874 | + | 0.657019i | \(0.228183\pi\) | |||||||
\(968\) | 95.8146 | 3.07960 | ||||||||
\(969\) | −46.9220 | −1.50735 | ||||||||
\(970\) | 2.96191 | 0.0951014 | ||||||||
\(971\) | 2.39329 | 0.0768045 | 0.0384022 | − | 0.999262i | \(-0.487773\pi\) | ||||
0.0384022 | + | 0.999262i | \(0.487773\pi\) | |||||||
\(972\) | −9.16775 | −0.294056 | ||||||||
\(973\) | −17.3421 | −0.555961 | ||||||||
\(974\) | 47.6247 | 1.52599 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.4286 | 0.333811 | ||||||||
\(977\) | 33.4315 | 1.06957 | 0.534784 | − | 0.844988i | \(-0.320393\pi\) | ||||
0.534784 | + | 0.844988i | \(0.320393\pi\) | |||||||
\(978\) | −14.5225 | −0.464378 | ||||||||
\(979\) | 59.5629 | 1.90364 | ||||||||
\(980\) | −1.48232 | −0.0473509 | ||||||||
\(981\) | 15.5391 | 0.496125 | ||||||||
\(982\) | −10.4418 | −0.333210 | ||||||||
\(983\) | −48.2644 | −1.53940 | −0.769698 | − | 0.638408i | \(-0.779593\pi\) | ||||
−0.769698 | + | 0.638408i | \(0.779593\pi\) | |||||||
\(984\) | 10.5773 | 0.337193 | ||||||||
\(985\) | −26.5731 | −0.846689 | ||||||||
\(986\) | −3.99639 | −0.127271 | ||||||||
\(987\) | 13.8376 | 0.440456 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.33931 | −0.0743856 | ||||||||
\(990\) | −16.8038 | −0.534060 | ||||||||
\(991\) | 57.0084 | 1.81093 | 0.905466 | − | 0.424418i | \(-0.139521\pi\) | ||||
0.905466 | + | 0.424418i | \(0.139521\pi\) | |||||||
\(992\) | 23.2463 | 0.738070 | ||||||||
\(993\) | 18.7545 | 0.595157 | ||||||||
\(994\) | 10.3832 | 0.329334 | ||||||||
\(995\) | 43.8306 | 1.38952 | ||||||||
\(996\) | 8.03158 | 0.254490 | ||||||||
\(997\) | −42.4795 | −1.34534 | −0.672670 | − | 0.739943i | \(-0.734853\pi\) | ||||
−0.672670 | + | 0.739943i | \(0.734853\pi\) | |||||||
\(998\) | 0.442598 | 0.0140102 | ||||||||
\(999\) | 0.194692 | 0.00615978 |
(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 | 1183.2.a.n.1.3 | ✓ | 6 | |
7.6 | odd | 2 | 8281.2.a.cb.1.3 | 6 | |||
13.5 | odd | 4 | 1183.2.c.h.337.8 | 12 | |||
13.8 | odd | 4 | 1183.2.c.h.337.5 | 12 | |||
13.12 | even | 2 | 1183.2.a.o.1.4 | yes | 6 | ||
91.90 | odd | 2 | 8281.2.a.cg.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.a.n.1.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1183.2.a.o.1.4 | yes | 6 | 13.12 | even | 2 | ||
1183.2.c.h.337.5 | 12 | 13.8 | odd | 4 | |||
1183.2.c.h.337.8 | 12 | 13.5 | odd | 4 | |||
8281.2.a.cb.1.3 | 6 | 7.6 | odd | 2 | |||
8281.2.a.cg.1.4 | 6 | 91.90 | odd | 2 |