Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, 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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 5 x^{14} - 16 x^{13} + 123 x^{12} - 76 x^{11} - 630 x^{10} + 937 x^{9} + 1083 x^{8} - 2602 x^{7} - 249 x^{6} + 2736 x^{5} - 801 x^{4} - 900 x^{3} + 429 x^{2} - 36 x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(1.82373\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.66529 | 1.53880 | 0.769402 | − | 0.638764i | \(-0.220554\pi\) | ||||
0.769402 | + | 0.638764i | \(0.220554\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.22875 | 0.549515 | 0.274757 | − | 0.961514i | \(-0.411402\pi\) | ||||
0.274757 | + | 0.961514i | \(0.411402\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.12758 | −1.18211 | −0.591056 | − | 0.806630i | \(-0.701289\pi\) | ||||
−0.591056 | + | 0.806630i | \(0.701289\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.10376 | 1.36792 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.80947 | −0.545577 | −0.272788 | − | 0.962074i | \(-0.587946\pi\) | ||||
−0.272788 | + | 0.962074i | \(0.587946\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.05098 | −1.12354 | −0.561770 | − | 0.827293i | \(-0.689880\pi\) | ||||
−0.561770 | + | 0.827293i | \(0.689880\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.27498 | 0.845596 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.41700 | −1.24275 | −0.621373 | − | 0.783515i | \(-0.713425\pi\) | ||||
−0.621373 | + | 0.783515i | \(0.713425\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.33589 | −1.81904 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.32843 | −1.94511 | −0.972556 | − | 0.232670i | \(-0.925254\pi\) | ||||
−0.972556 | + | 0.232670i | \(0.925254\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.49017 | −0.698034 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.94184 | 0.566158 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.0200 | 1.86067 | 0.930336 | − | 0.366709i | \(-0.119516\pi\) | ||||
0.930336 | + | 0.366709i | \(0.119516\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.429720 | 0.0771800 | 0.0385900 | − | 0.999255i | \(-0.487713\pi\) | ||||
0.0385900 | + | 0.999255i | \(0.487713\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.82277 | −0.839536 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.84302 | −0.649588 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.26089 | 0.700486 | 0.350243 | − | 0.936659i | \(-0.386099\pi\) | ||||
0.350243 | + | 0.936659i | \(0.386099\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.7970 | −1.72891 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0793498 | 0.0123923 | 0.00619617 | − | 0.999981i | \(-0.498028\pi\) | ||||
0.00619617 | + | 0.999981i | \(0.498028\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.41857 | −1.43632 | −0.718160 | − | 0.695878i | \(-0.755015\pi\) | ||||
−0.718160 | + | 0.695878i | \(0.755015\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.04251 | 0.751693 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.21591 | −0.323224 | −0.161612 | − | 0.986854i | \(-0.551669\pi\) | ||||
−0.161612 | + | 0.986854i | \(0.551669\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.78173 | 0.397390 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.66529 | 0.373215 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.34332 | −1.14604 | −0.573022 | − | 0.819540i | \(-0.694229\pi\) | ||||
−0.573022 | + | 0.819540i | \(0.694229\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.22339 | −0.299802 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.4379 | −1.91234 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.967357 | 0.123857 | 0.0619287 | − | 0.998081i | \(-0.480275\pi\) | ||||
0.0619287 | + | 0.998081i | \(0.480275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.8348 | −1.61704 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.97766 | −0.617402 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.09029 | −0.988386 | −0.494193 | − | 0.869352i | \(-0.664536\pi\) | ||||
−0.494193 | + | 0.869352i | \(0.664536\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −24.8629 | −2.99315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0748 | 1.19565 | 0.597827 | − | 0.801625i | \(-0.296031\pi\) | ||||
0.597827 | + | 0.801625i | \(0.296031\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.10494 | 0.363406 | 0.181703 | − | 0.983353i | \(-0.441839\pi\) | ||||
0.181703 | + | 0.983353i | \(0.441839\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.30230 | −1.07414 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.65926 | 0.644933 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.46026 | 0.951854 | 0.475927 | − | 0.879485i | \(-0.342113\pi\) | ||||
0.475927 | + | 0.879485i | \(0.342113\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.47043 | −0.496714 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.3705 | −1.35784 | −0.678921 | − | 0.734211i | \(-0.737552\pi\) | ||||
−0.678921 | + | 0.734211i | \(0.737552\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.22875 | 0.133277 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 26.7062 | 2.86321 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.7521 | 1.35171 | 0.675857 | − | 0.737032i | \(-0.263774\pi\) | ||||
0.675857 | + | 0.737032i | \(0.263774\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.6698 | 1.32815 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.14533 | 0.118765 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.65615 | −0.682907 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.26348 | −0.534425 | −0.267213 | − | 0.963638i | \(-0.586103\pi\) | ||||
−0.267213 | + | 0.963638i | \(0.586103\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.42565 | −0.746306 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.4756 | 1.14187 | 0.570935 | − | 0.820996i | \(-0.306581\pi\) | ||||
0.570935 | + | 0.820996i | \(0.306581\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.3684 | −1.61283 | −0.806416 | − | 0.591349i | \(-0.798596\pi\) | ||||
−0.806416 | + | 0.591349i | \(0.798596\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.2427 | −0.999590 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.0759 | 1.84414 | 0.922069 | − | 0.387025i | \(-0.126497\pi\) | ||||
0.922069 | + | 0.387025i | \(0.126497\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.5619 | 1.29899 | 0.649495 | − | 0.760365i | \(-0.274980\pi\) | ||||
0.649495 | + | 0.760365i | \(0.274980\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.3565 | 1.07791 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.6150 | 0.998580 | 0.499290 | − | 0.866435i | \(-0.333594\pi\) | ||||
0.499290 | + | 0.866435i | \(0.333594\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.4623 | −1.06887 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.6243 | −1.53691 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.12758 | −0.286704 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.72581 | −0.702346 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.211490 | 0.0190694 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.4323 | −0.933095 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0668 | −0.893287 | −0.446644 | − | 0.894712i | \(-0.647381\pi\) | ||||
−0.446644 | + | 0.894712i | \(0.647381\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −25.1032 | −2.21022 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.26722 | −0.285458 | −0.142729 | − | 0.989762i | \(-0.545588\pi\) | ||||
−0.142729 | + | 0.989762i | \(0.545588\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.9421 | 1.46906 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.61480 | 0.311112 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.87323 | −0.843527 | −0.421764 | − | 0.906706i | \(-0.638589\pi\) | ||||
−0.421764 | + | 0.906706i | \(0.638589\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.63396 | −0.562685 | −0.281343 | − | 0.959607i | \(-0.590780\pi\) | ||||
−0.281343 | + | 0.959607i | \(0.590780\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.90605 | −0.497379 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.33015 | 0.612978 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.3121 | 1.02247 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.41411 | 0.611506 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.51433 | 0.451751 | 0.225876 | − | 0.974156i | \(-0.427476\pi\) | ||||
0.225876 | + | 0.974156i | \(0.427476\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.9784 | −1.05617 | −0.528083 | − | 0.849193i | \(-0.677089\pi\) | ||||
−0.528083 | + | 0.849193i | \(0.677089\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.10376 | 0.331769 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.528019 | 0.0424115 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.9176 | −1.82902 | −0.914511 | − | 0.404562i | \(-0.867424\pi\) | ||||
−0.914511 | + | 0.404562i | \(0.867424\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −22.2374 | −1.76354 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 29.1754 | 2.29934 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.8633 | −1.63414 | −0.817069 | − | 0.576540i | \(-0.804402\pi\) | ||||
−0.817069 | + | 0.576540i | \(0.804402\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.92599 | −0.461337 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.0402 | 1.55076 | 0.775379 | − | 0.631496i | \(-0.217559\pi\) | ||||
0.775379 | + | 0.631496i | \(0.217559\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.41046 | 0.262343 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −22.2301 | −1.69998 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.65014 | −0.277515 | −0.138757 | − | 0.990326i | \(-0.544311\pi\) | ||||
−0.138757 | + | 0.990326i | \(0.544311\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.9158 | 0.825154 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.66529 | −0.200335 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.2813 | 1.29167 | 0.645833 | − | 0.763478i | \(-0.276510\pi\) | ||||
0.645833 | + | 0.763478i | \(0.276510\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.4288 | 0.998156 | 0.499078 | − | 0.866557i | \(-0.333672\pi\) | ||||
0.499078 | + | 0.866557i | \(0.333672\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.57828 | 0.190592 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.23558 | 0.384927 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.80947 | −0.132322 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.20084 | −0.669262 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.80814 | 0.275547 | 0.137774 | − | 0.990464i | \(-0.456005\pi\) | ||||
0.137774 | + | 0.990464i | \(0.456005\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.5574 | −0.903898 | −0.451949 | − | 0.892044i | \(-0.649271\pi\) | ||||
−0.451949 | + | 0.892044i | \(0.649271\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.2669 | −0.950061 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.95161 | 0.709023 | 0.354512 | − | 0.935052i | \(-0.384647\pi\) | ||||
0.354512 | + | 0.935052i | \(0.384647\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.4079 | 1.51757 | 0.758783 | − | 0.651343i | \(-0.225794\pi\) | ||||
0.758783 | + | 0.651343i | \(0.225794\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.5630 | −1.52093 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −31.3384 | −2.19952 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0975012 | 0.00680978 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −38.2816 | −2.66076 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.80192 | 0.678013 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.1461 | 0.836169 | 0.418084 | − | 0.908408i | \(-0.362702\pi\) | ||||
0.418084 | + | 0.908408i | \(0.362702\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 26.8521 | 1.83988 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.5731 | −0.789279 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.34398 | −0.0912354 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.27556 | 0.559211 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.05098 | −0.272499 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.89663 | 0.327903 | 0.163951 | − | 0.986468i | \(-0.447576\pi\) | ||||
0.163951 | + | 0.986468i | \(0.447576\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.3228 | −0.954854 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.2524 | −0.680472 | −0.340236 | − | 0.940340i | \(-0.610507\pi\) | ||||
−0.340236 | + | 0.940340i | \(0.610507\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.8844 | 1.11575 | 0.557876 | − | 0.829924i | \(-0.311616\pi\) | ||||
0.557876 | + | 0.829924i | \(0.311616\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.0836 | 0.992426 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.2195 | −1.19360 | −0.596799 | − | 0.802391i | \(-0.703561\pi\) | ||||
−0.596799 | + | 0.802391i | \(0.703561\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.72281 | −0.177616 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 22.5490 | 1.46472 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.6352 | −1.59352 | −0.796758 | − | 0.604298i | \(-0.793454\pi\) | ||||
−0.796758 | + | 0.604298i | \(0.793454\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.95060 | 0.576559 | 0.288279 | − | 0.957546i | \(-0.406917\pi\) | ||||
0.288279 | + | 0.957546i | \(0.406917\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −20.7405 | −1.33050 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.41806 | 0.218372 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.9442 | 1.39627 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −32.9710 | −2.08945 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.74174 | 0.362416 | 0.181208 | − | 0.983445i | \(-0.441999\pi\) | ||||
0.181208 | + | 0.983445i | \(0.441999\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.8795 | 1.06121 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.27498 | 0.205087 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.7469 | −0.732749 | −0.366375 | − | 0.930467i | \(-0.619401\pi\) | ||||
−0.366375 | + | 0.930467i | \(0.619401\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.3262 | −0.828053 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 41.1198 | 2.54525 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.1564 | 1.55121 | 0.775604 | − | 0.631219i | \(-0.217445\pi\) | ||||
0.775604 | + | 0.631219i | \(0.217445\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.2519 | −0.629768 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 33.9879 | 2.08003 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.3493 | −0.691981 | −0.345990 | − | 0.938238i | \(-0.612457\pi\) | ||||
−0.345990 | + | 0.938238i | \(0.612457\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.8351 | −1.26565 | −0.632823 | − | 0.774297i | \(-0.718104\pi\) | ||||
−0.632823 | + | 0.774297i | \(0.718104\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 33.7686 | 2.04377 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.31536 | 0.380831 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.7728 | 0.947694 | 0.473847 | − | 0.880607i | \(-0.342865\pi\) | ||||
0.473847 | + | 0.880607i | \(0.342865\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.76347 | 0.105576 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.989841 | 0.0590490 | 0.0295245 | − | 0.999564i | \(-0.490601\pi\) | ||||
0.0295245 | + | 0.999564i | \(0.490601\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.0067 | 1.12983 | 0.564916 | − | 0.825148i | \(-0.308908\pi\) | ||||
0.564916 | + | 0.825148i | \(0.308908\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.7406 | −1.05086 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.248172 | −0.0146492 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.0287 | −0.822376 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.5161 | 1.43224 | 0.716122 | − | 0.697975i | \(-0.245915\pi\) | ||||
0.716122 | + | 0.697975i | \(0.245915\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.22875 | −0.0715407 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.32319 | −0.308883 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 37.7893 | 2.18541 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 29.4573 | 1.69789 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 30.5859 | 1.75711 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.18864 | 0.0680614 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.5879 | −0.832577 | −0.416289 | − | 0.909232i | \(-0.636669\pi\) | ||||
−0.416289 | + | 0.909232i | \(0.636669\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −43.6266 | −2.48183 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0198 | 1.13522 | 0.567609 | − | 0.823298i | \(-0.307869\pi\) | ||||
0.567609 | + | 0.823298i | \(0.307869\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.42363 | 0.136992 | 0.0684959 | − | 0.997651i | \(-0.478180\pi\) | ||||
0.0684959 | + | 0.997651i | \(0.478180\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −15.7708 | −0.888585 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.2630 | −0.576427 | −0.288214 | − | 0.957566i | \(-0.593061\pi\) | ||||
−0.288214 | + | 0.957566i | \(0.593061\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.1310 | −1.01514 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 50.8428 | 2.83777 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.41700 | −0.301410 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.1386 | 0.784269 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 36.1463 | 1.99889 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.93043 | 0.382087 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.32736 | 0.237853 | 0.118927 | − | 0.992903i | \(-0.462055\pi\) | ||||
0.118927 | + | 0.992903i | \(0.462055\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.4857 | 0.958209 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.94096 | −0.543133 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −36.5048 | −1.98854 | −0.994270 | − | 0.106895i | \(-0.965909\pi\) | ||||
−0.994270 | + | 0.106895i | \(0.965909\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 28.2922 | 1.53662 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.777567 | −0.0421076 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.1930 | 0.712353 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −30.5504 | −1.64478 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.63200 | −0.302342 | −0.151171 | − | 0.988508i | \(-0.548304\pi\) | ||||
−0.151171 | + | 0.988508i | \(0.548304\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.6802 | −1.85639 | −0.928194 | − | 0.372096i | \(-0.878639\pi\) | ||||
−0.928194 | + | 0.372096i | \(0.878639\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.9174 | −0.636101 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.970983 | −0.0516802 | −0.0258401 | − | 0.999666i | \(-0.508226\pi\) | ||||
−0.0258401 | + | 0.999666i | \(0.508226\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.3794 | 0.657029 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.33589 | −0.441182 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.6141 | 1.08797 | 0.543985 | − | 0.839095i | \(-0.316915\pi\) | ||||
0.543985 | + | 0.839095i | \(0.316915\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.3439 | 0.544416 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.5915 | −1.08077 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.81520 | 0.199697 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.85365 | −0.305558 | −0.152779 | − | 0.988260i | \(-0.548822\pi\) | ||||
−0.152779 | + | 0.988260i | \(0.548822\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.325632 | 0.0169517 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.0944 | 1.35475 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.59866 | −0.186331 | −0.0931657 | − | 0.995651i | \(-0.529699\pi\) | ||||
−0.0931657 | + | 0.995651i | \(0.529699\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −27.8051 | −1.43585 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40.5909 | −2.09054 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.9701 | 0.768960 | 0.384480 | − | 0.923133i | \(-0.374381\pi\) | ||||
0.384480 | + | 0.923133i | \(0.374381\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.8310 | −1.37459 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.43186 | −0.124262 | −0.0621311 | − | 0.998068i | \(-0.519790\pi\) | ||||
−0.0621311 | + | 0.998068i | \(0.519790\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.95383 | 0.354400 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −38.6516 | −1.96477 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.1743 | −1.37779 | −0.688895 | − | 0.724861i | \(-0.741904\pi\) | ||||
−0.688895 | + | 0.724861i | \(0.741904\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.32843 | −0.471759 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.70807 | −0.439264 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.3956 | 0.523058 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.95557 | −0.399279 | −0.199639 | − | 0.979869i | \(-0.563977\pi\) | ||||
−0.199639 | + | 0.979869i | \(0.563977\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 45.1555 | 2.26060 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.2089 | −1.40868 | −0.704342 | − | 0.709861i | \(-0.748758\pi\) | ||||
−0.704342 | + | 0.709861i | \(0.748758\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.74079 | −0.0867148 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.49305 | −0.272952 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.70996 | −0.382169 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.84972 | −0.289250 | −0.144625 | − | 0.989487i | \(-0.546198\pi\) | ||||
−0.144625 | + | 0.989487i | \(0.546198\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −26.3150 | −1.29802 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.12758 | 0.153898 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.2003 | −0.746154 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.6814 | −0.865863 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.6156 | −1.39797 | −0.698983 | − | 0.715139i | \(-0.746364\pi\) | ||||
−0.698983 | + | 0.715139i | \(0.746364\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.28918 | −0.452727 | −0.226363 | − | 0.974043i | \(-0.572684\pi\) | ||||
−0.226363 | + | 0.974043i | \(0.572684\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.09358 | −0.442145 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.49017 | −0.169298 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.02548 | −0.146413 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 19.5370 | 0.943253 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.70573 | −0.130330 | −0.0651651 | − | 0.997874i | \(-0.520757\pi\) | ||||
−0.0651651 | + | 0.997874i | \(0.520757\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.0687 | 1.15667 | 0.578335 | − | 0.815800i | \(-0.303703\pi\) | ||||
0.578335 | + | 0.815800i | \(0.303703\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 32.8154 | 1.57338 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 50.5321 | 2.41728 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.3843 | 1.64107 | 0.820536 | − | 0.571594i | \(-0.193675\pi\) | ||||
0.820536 | + | 0.571594i | \(0.193675\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.4156 | 0.543598 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.7999 | 1.17828 | 0.589140 | − | 0.808031i | \(-0.299467\pi\) | ||||
0.589140 | + | 0.808031i | \(0.299467\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.6691 | 0.742787 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.6973 | 0.695157 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.6807 | −1.40072 | −0.700359 | − | 0.713791i | \(-0.746977\pi\) | ||||
−0.700359 | + | 0.713791i | \(0.746977\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.143581 | −0.00676098 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −34.5912 | −1.62523 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.5680 | 0.729839 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0512 | 1.03151 | 0.515757 | − | 0.856735i | \(-0.327511\pi\) | ||||
0.515757 | + | 0.856735i | \(0.327511\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.94184 | 0.137313 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.3620 | −1.60040 | −0.800199 | − | 0.599735i | \(-0.795273\pi\) | ||||
−0.800199 | + | 0.599735i | \(0.795273\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.5944 | 1.09653 | 0.548263 | − | 0.836306i | \(-0.315289\pi\) | ||||
0.548263 | + | 0.836306i | \(0.315289\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.40732 | 0.0652631 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.4674 | −1.22476 | −0.612382 | − | 0.790562i | \(-0.709789\pi\) | ||||
−0.612382 | + | 0.790562i | \(0.709789\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.3030 | 1.16838 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −61.0819 | −2.81451 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.0427 | 0.783622 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.9062 | 0.867478 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −34.2390 | −1.56770 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.29484 | 0.104854 | 0.0524269 | − | 0.998625i | \(-0.483304\pi\) | ||||
0.0524269 | + | 0.998625i | \(0.483304\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.2608 | −0.787024 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 77.7608 | 3.53824 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.46751 | −0.293675 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.4074 | −0.607546 | −0.303773 | − | 0.952744i | \(-0.598246\pi\) | ||||
−0.303773 | + | 0.952744i | \(0.598246\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −55.6066 | −2.51462 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.1949 | 1.31755 | 0.658774 | − | 0.752341i | \(-0.271075\pi\) | ||||
0.658774 | + | 0.752341i | \(0.271075\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0200 | 0.451279 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.12428 | −0.410106 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −31.5096 | −1.41340 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −43.3041 | −1.93856 | −0.969278 | − | 0.245966i | \(-0.920895\pi\) | ||||
−0.969278 | + | 0.245966i | \(0.920895\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 53.4129 | 2.38631 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.2316 | −1.12502 | −0.562510 | − | 0.826790i | \(-0.690164\pi\) | ||||
−0.562510 | + | 0.826790i | \(0.690164\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.1007 | 0.627474 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.08987 | 0.403695 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.0390 | 1.37578 | 0.687890 | − | 0.725815i | \(-0.258537\pi\) | ||||
0.687890 | + | 0.725815i | \(0.258537\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.71094 | −0.429586 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.9360 | −0.703590 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.1128 | −0.886275 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.00963 | 0.176344 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.72867 | −0.427041 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.4542 | 0.896115 | 0.448057 | − | 0.894005i | \(-0.352116\pi\) | ||||
0.448057 | + | 0.894005i | \(0.352116\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.6091 | −0.507629 | −0.253815 | − | 0.967253i | \(-0.581685\pi\) | ||||
−0.253815 | + | 0.967253i | \(0.581685\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 29.0937 | 1.26975 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.429720 | 0.0187189 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 64.0196 | 2.78346 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.10376 | −0.178088 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.321445 | −0.0139233 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.4396 | 1.01338 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 46.0597 | 1.98762 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.03346 | −0.216807 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.7202 | −1.06280 | −0.531402 | − | 0.847120i | \(-0.678334\pi\) | ||||
−0.531402 | + | 0.847120i | \(0.678334\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 35.7917 | 1.53597 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.6642 | 0.713815 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.4519 | 0.617918 | 0.308959 | − | 0.951075i | \(-0.400019\pi\) | ||||
0.308959 | + | 0.951075i | \(0.400019\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.96980 | 0.169427 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −54.2785 | −2.31234 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.4601 | −1.12520 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.9543 | 0.592328 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 42.1816 | 1.78729 | 0.893645 | − | 0.448774i | \(-0.148139\pi\) | ||||
0.893645 | + | 0.448774i | \(0.148139\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.1545 | 1.61376 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.82277 | −0.203617 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.10583 | −0.0466054 | −0.0233027 | − | 0.999728i | \(-0.507418\pi\) | ||||
−0.0233027 | + | 0.999728i | \(0.507418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.0433 | 0.548734 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.9816 | 0.587172 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.6702 | 0.656929 | 0.328464 | − | 0.944516i | \(-0.393469\pi\) | ||||
0.328464 | + | 0.944516i | \(0.393469\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.31950 | −0.390009 | −0.195005 | − | 0.980802i | \(-0.562472\pi\) | ||||
−0.195005 | + | 0.980802i | \(0.562472\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.1498 | 0.424013 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.5578 | 1.35775 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.7254 | −1.11259 | −0.556297 | − | 0.830984i | \(-0.687778\pi\) | ||||
−0.556297 | + | 0.830984i | \(0.687778\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −33.4690 | −1.39092 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.6898 | 1.60512 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.0970 | 0.625255 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −20.4271 | −0.844557 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.9112 | −0.491627 | −0.245813 | − | 0.969317i | \(-0.579055\pi\) | ||||
−0.245813 | + | 0.969317i | \(0.579055\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.32779 | −0.0959151 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.5239 | 1.09105 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.2850 | −1.36685 | −0.683426 | − | 0.730020i | \(-0.739511\pi\) | ||||
−0.683426 | + | 0.730020i | \(0.739511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.84302 | −0.157548 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 57.0582 | 2.33524 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.2912 | 1.27852 | 0.639262 | − | 0.768989i | \(-0.279240\pi\) | ||||
0.639262 | + | 0.768989i | \(0.279240\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.4347 | −1.36383 | −0.681915 | − | 0.731432i | \(-0.738852\pi\) | ||||
−0.681915 | + | 0.731432i | \(0.738852\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33.2006 | −1.35203 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.49310 | −0.385950 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −39.4291 | −1.60038 | −0.800189 | − | 0.599748i | \(-0.795267\pi\) | ||||
−0.800189 | + | 0.599748i | \(0.795267\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −83.5258 | −3.38464 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.97662 | 0.363155 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.4169 | −1.18814 | −0.594068 | − | 0.804415i | \(-0.702479\pi\) | ||||
−0.594068 | + | 0.804415i | \(0.702479\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.259869 | 0.0104789 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.4580 | −1.42748 | −0.713742 | − | 0.700409i | \(-0.753001\pi\) | ||||
−0.713742 | + | 0.700409i | \(0.753001\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.46718 | 0.380518 | 0.190259 | − | 0.981734i | \(-0.439067\pi\) | ||||
0.190259 | + | 0.981734i | \(0.439067\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.4428 | −1.10124 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −39.8830 | −1.59788 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.63211 | 0.185284 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 26.1249 | 1.04333 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.26089 | 0.169893 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.2080 | −0.764660 | −0.382330 | − | 0.924026i | \(-0.624878\pi\) | ||||
−0.382330 | + | 0.924026i | \(0.624878\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.3727 | 1.28670 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.3696 | −0.490875 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.2687 | −0.446484 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 41.3444 | 1.63556 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.5997 | −0.537155 | −0.268577 | − | 0.963258i | \(-0.586553\pi\) | ||||
−0.268577 | + | 0.963258i | \(0.586553\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.19490 | 0.0471225 | 0.0235612 | − | 0.999722i | \(-0.492500\pi\) | ||||
0.0235612 | + | 0.999722i | \(0.492500\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −30.8456 | −1.21455 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.5758 | −1.67383 | −0.836914 | − | 0.547334i | \(-0.815643\pi\) | ||||
−0.836914 | + | 0.547334i | \(0.815643\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.80947 | 0.0710280 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.58210 | −0.140393 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.772012 | −0.0302112 | −0.0151056 | − | 0.999886i | \(-0.504808\pi\) | ||||
−0.0151056 | + | 0.999886i | \(0.504808\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.01460 | −0.156863 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.7419 | 0.497110 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.8835 | −0.891416 | −0.445708 | − | 0.895178i | \(-0.647048\pi\) | ||||
−0.445708 | + | 0.895178i | \(0.647048\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.0916 | −1.20932 | −0.604662 | − | 0.796482i | \(-0.706692\pi\) | ||||
−0.604662 | + | 0.796482i | \(0.706692\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.7970 | −0.419322 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.8176 | 0.807273 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −93.4710 | −3.61921 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.0509 | 0.504578 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.75041 | −0.0675737 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.2250 | 1.35782 | 0.678912 | − | 0.734219i | \(-0.262452\pi\) | ||||
0.678912 | + | 0.734219i | \(0.262452\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.2675 | −0.395197 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.7097 | 0.411607 | 0.205804 | − | 0.978593i | \(-0.434019\pi\) | ||||
0.205804 | + | 0.978593i | \(0.434019\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.4619 | 0.631751 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27.3255 | −1.04711 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.79463 | −0.374781 | −0.187391 | − | 0.982285i | \(-0.560003\pi\) | ||||
−0.187391 | + | 0.982285i | \(0.560003\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.1318 | −0.463531 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 45.0018 | 1.71692 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 33.7987 | 1.28763 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.38249 | 0.242801 | 0.121401 | − | 0.992604i | \(-0.461261\pi\) | ||||
0.121401 | + | 0.992604i | \(0.461261\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.2243 | 0.882217 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.15149 | −0.309204 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.0793498 | 0.00300559 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −48.5602 | −1.83671 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.9980 | −0.604235 | −0.302117 | − | 0.953271i | \(-0.597693\pi\) | ||||
−0.302117 | + | 0.953271i | \(0.597693\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.0812 | −0.870525 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.25707 | −0.273317 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −35.8909 | −1.34982 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.1141 | 0.379843 | 0.189922 | − | 0.981799i | \(-0.439177\pi\) | ||||
0.189922 | + | 0.981799i | \(0.439177\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 34.7189 | 1.30206 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.00861 | −0.150124 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.00693 | 0.336840 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −65.6598 | −2.45211 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.6802 | −0.845829 | −0.422915 | − | 0.906170i | \(-0.638993\pi\) | ||||
−0.422915 | + | 0.906170i | \(0.638993\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 51.1936 | 1.90655 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.8559 | 0.887211 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −34.9715 | −1.29881 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.9601 | 0.591929 | 0.295964 | − | 0.955199i | \(-0.404359\pi\) | ||||
0.295964 | + | 0.955199i | \(0.404359\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.8681 | −1.55067 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.41857 | −0.348359 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.2409 | 0.969229 | 0.484615 | − | 0.874728i | \(-0.338960\pi\) | ||||
0.484615 | + | 0.874728i | \(0.338960\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.11011 | 0.336031 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.6392 | 0.539240 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.5569 | 1.01370 | 0.506848 | − | 0.862036i | \(-0.330811\pi\) | ||||
0.506848 | + | 0.862036i | \(0.330811\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 58.4876 | 2.14859 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.2489 | 0.706174 | 0.353087 | − | 0.935591i | \(-0.385132\pi\) | ||||
0.353087 | + | 0.935591i | \(0.385132\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.77574 | 0.248244 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −50.7657 | −1.85742 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −59.6614 | −2.17998 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.78247 | 0.101534 | 0.0507668 | − | 0.998711i | \(-0.483833\pi\) | ||||
0.0507668 | + | 0.998711i | \(0.483833\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.3034 | 0.557687 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.9472 | −0.580379 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.55489 | −0.165550 | −0.0827751 | − | 0.996568i | \(-0.526378\pi\) | ||||
−0.0827751 | + | 0.996568i | \(0.526378\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 44.9888 | 1.63299 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.0049 | 1.74017 | 0.870087 | − | 0.492898i | \(-0.164062\pi\) | ||||
0.870087 | + | 0.492898i | \(0.164062\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42.4158 | −1.53555 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.04251 | 0.182312 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.05098 | 0.146273 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.6711 | 1.50270 | 0.751350 | − | 0.659904i | \(-0.229403\pi\) | ||||
0.751350 | + | 0.659904i | \(0.229403\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.3088 | −1.12756 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.4436 | −0.627403 | −0.313701 | − | 0.949522i | \(-0.601569\pi\) | ||||
−0.313701 | + | 0.949522i | \(0.601569\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.49979 | −0.0538742 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −35.5183 | −1.27421 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.429838 | −0.0154005 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.2300 | −0.652321 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 29.4773 | 1.05343 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28.1600 | −1.00507 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.0109 | −0.784604 | −0.392302 | − | 0.919837i | \(-0.628321\pi\) | ||||
−0.392302 | + | 0.919837i | \(0.628321\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 67.0490 | 2.38701 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.1994 | −1.18043 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.91875 | −0.139159 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27.3242 | −0.969090 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.6652 | −1.08622 | −0.543108 | − | 0.839663i | \(-0.682753\pi\) | ||||
−0.543108 | + | 0.839663i | \(0.682753\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.21591 | −0.0783933 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 52.3314 | 1.84904 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.61831 | −0.198266 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35.8493 | 1.26352 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.2492 | −1.06482 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.4843 | 0.966298 | 0.483149 | − | 0.875538i | \(-0.339493\pi\) | ||||
0.483149 | + | 0.875538i | \(0.339493\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.53676 | −0.264651 | −0.132326 | − | 0.991206i | \(-0.542244\pi\) | ||||
−0.132326 | + | 0.991206i | \(0.542244\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −55.5317 | −1.94758 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.6358 | −0.897983 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51.0204 | 1.78498 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 51.9937 | 1.81681 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.99702 | 0.0696964 | 0.0348482 | − | 0.999393i | \(-0.488905\pi\) | ||||
0.0348482 | + | 0.999393i | \(0.488905\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.2296 | −0.391439 | −0.195720 | − | 0.980660i | \(-0.562704\pi\) | ||||
−0.195720 | + | 0.980660i | \(0.562704\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16.8323 | 0.586024 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.09139 | −0.316139 | −0.158069 | − | 0.987428i | \(-0.550527\pi\) | ||||
−0.158069 | + | 0.987428i | \(0.550527\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −54.6984 | −1.89975 | −0.949877 | − | 0.312622i | \(-0.898793\pi\) | ||||
−0.949877 | + | 0.312622i | \(0.898793\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.0390 | 1.45832 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.78173 | 0.0963812 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.6245 | 0.852164 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.26417 | 0.0436960 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.6343 | 1.33380 | 0.666902 | − | 0.745145i | \(-0.267620\pi\) | ||||
0.666902 | + | 0.745145i | \(0.267620\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 71.4008 | 2.46210 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.63821 | 0.0908649 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.19062 | 0.144162 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.1630 | 0.830252 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 50.6584 | 1.73859 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −39.7474 | −1.36252 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.7301 | −0.470111 | −0.235055 | − | 0.971982i | \(-0.575527\pi\) | ||||
−0.235055 | + | 0.971982i | \(0.575527\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −27.3153 | −0.934162 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.5782 | 1.04453 | 0.522266 | − | 0.852783i | \(-0.325087\pi\) | ||||
0.522266 | + | 0.852783i | \(0.325087\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.2853 | −0.794485 | −0.397243 | − | 0.917714i | \(-0.630033\pi\) | ||||
−0.397243 | + | 0.917714i | \(0.630033\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.661451 | −0.0225422 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.15746 | −0.0394005 | −0.0197002 | − | 0.999806i | \(-0.506271\pi\) | ||||
−0.0197002 | + | 0.999806i | \(0.506271\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.48511 | −0.152498 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.66529 | 0.0905179 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.3086 | −0.519309 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.7736 | 1.11049 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.6001 | −0.731051 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 32.6279 | 1.10302 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.85805 | −0.197812 | −0.0989061 | − | 0.995097i | \(-0.531534\pi\) | ||||
−0.0989061 | + | 0.995097i | \(0.531534\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 65.3424 | 2.20395 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.15450 | −0.308423 | −0.154212 | − | 0.988038i | \(-0.549284\pi\) | ||||
−0.154212 | + | 0.988038i | \(0.549284\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.4140 | 1.76387 | 0.881935 | − | 0.471371i | \(-0.156241\pi\) | ||||
0.881935 | + | 0.471371i | \(0.156241\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.27498 | −0.110087 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.3427 | −0.347275 | −0.173637 | − | 0.984810i | \(-0.555552\pi\) | ||||
−0.173637 | + | 0.984810i | \(0.555552\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.4848 | 1.05597 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.08912 | 0.270996 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.0036 | 0.401685 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.2345 | 0.709790 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 100.719 | 3.36292 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.30580 | 0.143607 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.34332 | −0.277956 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 78.5122 | 2.61272 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.5007 | 0.548502 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.54200 | 0.250428 | 0.125214 | − | 0.992130i | \(-0.460038\pi\) | ||||
0.125214 | + | 0.992130i | \(0.460038\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 47.0933 | 1.56199 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.5967 | 0.417349 | 0.208674 | − | 0.977985i | \(-0.433085\pi\) | ||||
0.208674 | + | 0.977985i | \(0.433085\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.3841 | 0.740807 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.16807 | 0.104733 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.2185 | 0.337443 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.1436 | 0.994347 | 0.497174 | − | 0.867651i | \(-0.334371\pi\) | ||||
0.497174 | + | 0.867651i | \(0.334371\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −38.8811 | −1.28117 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −40.8127 | −1.34337 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.8712 | −0.488962 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −67.1722 | −2.20622 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.2975 | 0.698750 | 0.349375 | − | 0.936983i | \(-0.386394\pi\) | ||||
0.349375 | + | 0.936983i | \(0.386394\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.0686 | −0.493855 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 53.3585 | 1.74688 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.22339 | −0.0727128 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.5345 | 0.964851 | 0.482426 | − | 0.875937i | \(-0.339756\pi\) | ||||
0.482426 | + | 0.875937i | \(0.339756\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.45968 | 0.210804 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.7209 | 0.773281 | 0.386640 | − | 0.922231i | \(-0.373635\pi\) | ||||
0.386640 | + | 0.922231i | \(0.373635\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.740208 | −0.0241045 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.3055 | −0.367770 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.01806 | −0.228056 | −0.114028 | − | 0.993478i | \(-0.536375\pi\) | ||||
−0.114028 | + | 0.993478i | \(0.536375\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.5781 | −0.408301 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.3538 | −0.887009 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.5749 | 1.15238 | 0.576192 | − | 0.817314i | \(-0.304538\pi\) | ||||
0.576192 | + | 0.817314i | \(0.304538\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.67926 | 0.151417 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −48.3242 | −1.56210 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30.8793 | 0.997144 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8153 | −0.994043 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 78.2830 | 2.52263 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.4299 | −0.496705 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.5148 | −0.852658 | −0.426329 | − | 0.904568i | \(-0.640193\pi\) | ||||
−0.426329 | + | 0.904568i | \(0.640193\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.4379 | −0.463811 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.7636 | −1.30816 | −0.654082 | − | 0.756423i | \(-0.726945\pi\) | ||||
−0.654082 | + | 0.756423i | \(0.726945\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.7482 | 0.665157 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 37.6835 | 1.20684 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.3207 | −1.48193 | −0.740966 | − | 0.671543i | \(-0.765632\pi\) | ||||
−0.740966 | + | 0.671543i | \(0.765632\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.0745 | −0.737464 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 55.6547 | 1.77692 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.0236923 | −0.000755668 0 | −0.000377834 | − | 1.00000i | \(-0.500120\pi\) | ||||
−0.000377834 | 1.00000i | \(0.500120\pi\) | ||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.2281 | 0.389619 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.4716 | 0.587958 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 87.8605 | 2.79380 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.8366 | 0.820726 | 0.410363 | − | 0.911922i | \(-0.365402\pi\) | ||||
0.410363 | + | 0.911922i | \(0.365402\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.5337 | 0.366010 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.3050 | 0.833925 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.76142 | −0.119125 | −0.0595627 | − | 0.998225i | \(-0.518971\pi\) | ||||
−0.0595627 | + | 0.998225i | \(0.518971\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.5349 | 0.396585 |
(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 | 4012.2.a.h.1.15 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.h.1.15 | ✓ | 15 | 1.1 | even | 1 | trivial |