Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.34292\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.14637 | 0.661854 | 0.330927 | − | 0.943656i | \(-0.392639\pi\) | ||||
0.330927 | + | 0.943656i | \(0.392639\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.14637 | 0.468002 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.68585 | −0.561949 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.14637 | 0.330927 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.14637 | 0.295990 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.68585 | −0.651413 | −0.325707 | − | 0.945471i | \(-0.605602\pi\) | ||||
−0.325707 | + | 0.945471i | \(0.605602\pi\) | |||||||
\(18\) | −1.68585 | −0.397358 | ||||||||
\(19\) | 5.53948 | 1.27084 | 0.635422 | − | 0.772165i | \(-0.280826\pi\) | ||||
0.635422 | + | 0.772165i | \(0.280826\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.14637 | 0.250157 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.83221 | −0.382043 | −0.191021 | − | 0.981586i | \(-0.561180\pi\) | ||||
−0.191021 | + | 0.981586i | \(0.561180\pi\) | |||||||
\(24\) | 1.14637 | 0.234001 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.37169 | −1.03378 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 3.83221 | 0.711624 | 0.355812 | − | 0.934558i | \(-0.384204\pi\) | ||||
0.355812 | + | 0.934558i | \(0.384204\pi\) | |||||||
\(30\) | 1.14637 | 0.209297 | ||||||||
\(31\) | 9.66442 | 1.73578 | 0.867891 | − | 0.496755i | \(-0.165475\pi\) | ||||
0.867891 | + | 0.496755i | \(0.165475\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.68585 | −0.460619 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −1.68585 | −0.280974 | ||||||||
\(37\) | −1.83221 | −0.301214 | −0.150607 | − | 0.988594i | \(-0.548123\pi\) | ||||
−0.150607 | + | 0.988594i | \(0.548123\pi\) | |||||||
\(38\) | 5.53948 | 0.898622 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −1.43910 | −0.224749 | −0.112375 | − | 0.993666i | \(-0.535846\pi\) | ||||
−0.112375 | + | 0.993666i | \(0.535846\pi\) | |||||||
\(42\) | 1.14637 | 0.176888 | ||||||||
\(43\) | 4.97858 | 0.759226 | 0.379613 | − | 0.925145i | \(-0.376057\pi\) | ||||
0.379613 | + | 0.925145i | \(0.376057\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.68585 | −0.251311 | ||||||||
\(46\) | −1.83221 | −0.270145 | ||||||||
\(47\) | −0.393115 | −0.0573417 | −0.0286709 | − | 0.999589i | \(-0.509127\pi\) | ||||
−0.0286709 | + | 0.999589i | \(0.509127\pi\) | |||||||
\(48\) | 1.14637 | 0.165464 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −3.07896 | −0.431141 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.4966 | 1.85391 | 0.926953 | − | 0.375178i | \(-0.122418\pi\) | ||||
0.926953 | + | 0.375178i | \(0.122418\pi\) | |||||||
\(54\) | −5.37169 | −0.730995 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 6.35027 | 0.841114 | ||||||||
\(58\) | 3.83221 | 0.503194 | ||||||||
\(59\) | 0.685846 | 0.0892896 | 0.0446448 | − | 0.999003i | \(-0.485784\pi\) | ||||
0.0446448 | + | 0.999003i | \(0.485784\pi\) | |||||||
\(60\) | 1.14637 | 0.147995 | ||||||||
\(61\) | 2.39312 | 0.306407 | 0.153204 | − | 0.988195i | \(-0.451041\pi\) | ||||
0.153204 | + | 0.988195i | \(0.451041\pi\) | |||||||
\(62\) | 9.66442 | 1.22738 | ||||||||
\(63\) | −1.68585 | −0.212397 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.37169 | 0.411918 | 0.205959 | − | 0.978561i | \(-0.433969\pi\) | ||||
0.205959 | + | 0.978561i | \(0.433969\pi\) | |||||||
\(68\) | −2.68585 | −0.325707 | ||||||||
\(69\) | −2.10038 | −0.252857 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | −0.585462 | −0.0694816 | −0.0347408 | − | 0.999396i | \(-0.511061\pi\) | ||||
−0.0347408 | + | 0.999396i | \(0.511061\pi\) | |||||||
\(72\) | −1.68585 | −0.198679 | ||||||||
\(73\) | −8.97858 | −1.05086 | −0.525431 | − | 0.850836i | \(-0.676096\pi\) | ||||
−0.525431 | + | 0.850836i | \(0.676096\pi\) | |||||||
\(74\) | −1.83221 | −0.212990 | ||||||||
\(75\) | 1.14637 | 0.132371 | ||||||||
\(76\) | 5.53948 | 0.635422 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.2039 | −1.48556 | −0.742778 | − | 0.669538i | \(-0.766492\pi\) | ||||
−0.742778 | + | 0.669538i | \(0.766492\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −1.10038 | −0.122265 | ||||||||
\(82\) | −1.43910 | −0.158922 | ||||||||
\(83\) | 9.37169 | 1.02868 | 0.514338 | − | 0.857587i | \(-0.328038\pi\) | ||||
0.514338 | + | 0.857587i | \(0.328038\pi\) | |||||||
\(84\) | 1.14637 | 0.125079 | ||||||||
\(85\) | −2.68585 | −0.291321 | ||||||||
\(86\) | 4.97858 | 0.536854 | ||||||||
\(87\) | 4.39312 | 0.470991 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.58546 | 0.698058 | 0.349029 | − | 0.937112i | \(-0.386512\pi\) | ||||
0.349029 | + | 0.937112i | \(0.386512\pi\) | |||||||
\(90\) | −1.68585 | −0.177704 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.83221 | −0.191021 | ||||||||
\(93\) | 11.0790 | 1.14883 | ||||||||
\(94\) | −0.393115 | −0.0405467 | ||||||||
\(95\) | 5.53948 | 0.568339 | ||||||||
\(96\) | 1.14637 | 0.117000 | ||||||||
\(97\) | 10.1678 | 1.03238 | 0.516191 | − | 0.856473i | \(-0.327349\pi\) | ||||
0.516191 | + | 0.856473i | \(0.327349\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −1.02142 | −0.101635 | −0.0508177 | − | 0.998708i | \(-0.516183\pi\) | ||||
−0.0508177 | + | 0.998708i | \(0.516183\pi\) | |||||||
\(102\) | −3.07896 | −0.304863 | ||||||||
\(103\) | 2.68585 | 0.264644 | 0.132322 | − | 0.991207i | \(-0.457757\pi\) | ||||
0.132322 | + | 0.991207i | \(0.457757\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.14637 | 0.111874 | ||||||||
\(106\) | 13.4966 | 1.31091 | ||||||||
\(107\) | 0.393115 | 0.0380039 | 0.0190019 | − | 0.999819i | \(-0.493951\pi\) | ||||
0.0190019 | + | 0.999819i | \(0.493951\pi\) | |||||||
\(108\) | −5.37169 | −0.516891 | ||||||||
\(109\) | 4.41767 | 0.423136 | 0.211568 | − | 0.977363i | \(-0.432143\pi\) | ||||
0.211568 | + | 0.977363i | \(0.432143\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.10038 | −0.199360 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 11.3717 | 1.06976 | 0.534879 | − | 0.844928i | \(-0.320357\pi\) | ||||
0.534879 | + | 0.844928i | \(0.320357\pi\) | |||||||
\(114\) | 6.35027 | 0.594757 | ||||||||
\(115\) | −1.83221 | −0.170855 | ||||||||
\(116\) | 3.83221 | 0.355812 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.685846 | 0.0631373 | ||||||||
\(119\) | −2.68585 | −0.246211 | ||||||||
\(120\) | 1.14637 | 0.104648 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 2.39312 | 0.216662 | ||||||||
\(123\) | −1.64973 | −0.148751 | ||||||||
\(124\) | 9.66442 | 0.867891 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.68585 | −0.150187 | ||||||||
\(127\) | 16.4507 | 1.45976 | 0.729880 | − | 0.683576i | \(-0.239576\pi\) | ||||
0.729880 | + | 0.683576i | \(0.239576\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.70727 | 0.502497 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.20390 | −0.454667 | −0.227334 | − | 0.973817i | \(-0.573001\pi\) | ||||
−0.227334 | + | 0.973817i | \(0.573001\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.53948 | 0.480334 | ||||||||
\(134\) | 3.37169 | 0.291270 | ||||||||
\(135\) | −5.37169 | −0.462322 | ||||||||
\(136\) | −2.68585 | −0.230309 | ||||||||
\(137\) | 1.41454 | 0.120852 | 0.0604261 | − | 0.998173i | \(-0.480754\pi\) | ||||
0.0604261 | + | 0.998173i | \(0.480754\pi\) | |||||||
\(138\) | −2.10038 | −0.178797 | ||||||||
\(139\) | −13.2039 | −1.11994 | −0.559970 | − | 0.828513i | \(-0.689187\pi\) | ||||
−0.559970 | + | 0.828513i | \(0.689187\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | −0.450654 | −0.0379519 | ||||||||
\(142\) | −0.585462 | −0.0491309 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.68585 | −0.140487 | ||||||||
\(145\) | 3.83221 | 0.318248 | ||||||||
\(146\) | −8.97858 | −0.743072 | ||||||||
\(147\) | 1.14637 | 0.0945506 | ||||||||
\(148\) | −1.83221 | −0.150607 | ||||||||
\(149\) | −0.417674 | −0.0342172 | −0.0171086 | − | 0.999854i | \(-0.505446\pi\) | ||||
−0.0171086 | + | 0.999854i | \(0.505446\pi\) | |||||||
\(150\) | 1.14637 | 0.0936004 | ||||||||
\(151\) | −6.91117 | −0.562423 | −0.281212 | − | 0.959646i | \(-0.590736\pi\) | ||||
−0.281212 | + | 0.959646i | \(0.590736\pi\) | |||||||
\(152\) | 5.53948 | 0.449311 | ||||||||
\(153\) | 4.52792 | 0.366061 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.66442 | 0.776265 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.2499 | 1.13726 | 0.568632 | − | 0.822592i | \(-0.307473\pi\) | ||||
0.568632 | + | 0.822592i | \(0.307473\pi\) | |||||||
\(158\) | −13.2039 | −1.05045 | ||||||||
\(159\) | 15.4721 | 1.22702 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −1.83221 | −0.144399 | ||||||||
\(162\) | −1.10038 | −0.0864543 | ||||||||
\(163\) | 0.628308 | 0.0492129 | 0.0246064 | − | 0.999697i | \(-0.492167\pi\) | ||||
0.0246064 | + | 0.999697i | \(0.492167\pi\) | |||||||
\(164\) | −1.43910 | −0.112375 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.37169 | 0.727384 | ||||||||
\(167\) | −18.5426 | −1.43487 | −0.717435 | − | 0.696625i | \(-0.754684\pi\) | ||||
−0.717435 | + | 0.696625i | \(0.754684\pi\) | |||||||
\(168\) | 1.14637 | 0.0884440 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | −2.68585 | −0.205995 | ||||||||
\(171\) | −9.33871 | −0.714149 | ||||||||
\(172\) | 4.97858 | 0.379613 | ||||||||
\(173\) | 10.3503 | 0.786916 | 0.393458 | − | 0.919343i | \(-0.371279\pi\) | ||||
0.393458 | + | 0.919343i | \(0.371279\pi\) | |||||||
\(174\) | 4.39312 | 0.333041 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.786230 | 0.0590967 | ||||||||
\(178\) | 6.58546 | 0.493601 | ||||||||
\(179\) | 12.6430 | 0.944982 | 0.472491 | − | 0.881335i | \(-0.343355\pi\) | ||||
0.472491 | + | 0.881335i | \(0.343355\pi\) | |||||||
\(180\) | −1.68585 | −0.125656 | ||||||||
\(181\) | −2.58546 | −0.192176 | −0.0960879 | − | 0.995373i | \(-0.530633\pi\) | ||||
−0.0960879 | + | 0.995373i | \(0.530633\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.74338 | 0.202797 | ||||||||
\(184\) | −1.83221 | −0.135072 | ||||||||
\(185\) | −1.83221 | −0.134707 | ||||||||
\(186\) | 11.0790 | 0.812349 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.393115 | −0.0286709 | ||||||||
\(189\) | −5.37169 | −0.390733 | ||||||||
\(190\) | 5.53948 | 0.401876 | ||||||||
\(191\) | 2.87819 | 0.208259 | 0.104129 | − | 0.994564i | \(-0.466794\pi\) | ||||
0.104129 | + | 0.994564i | \(0.466794\pi\) | |||||||
\(192\) | 1.14637 | 0.0827318 | ||||||||
\(193\) | −11.1793 | −0.804707 | −0.402353 | − | 0.915484i | \(-0.631808\pi\) | ||||
−0.402353 | + | 0.915484i | \(0.631808\pi\) | |||||||
\(194\) | 10.1678 | 0.730005 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 15.6216 | 1.11299 | 0.556496 | − | 0.830851i | \(-0.312146\pi\) | ||||
0.556496 | + | 0.830851i | \(0.312146\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.7220 | −1.53983 | −0.769915 | − | 0.638147i | \(-0.779701\pi\) | ||||
−0.769915 | + | 0.638147i | \(0.779701\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 3.86519 | 0.272630 | ||||||||
\(202\) | −1.02142 | −0.0718671 | ||||||||
\(203\) | 3.83221 | 0.268969 | ||||||||
\(204\) | −3.07896 | −0.215570 | ||||||||
\(205\) | −1.43910 | −0.100511 | ||||||||
\(206\) | 2.68585 | 0.187132 | ||||||||
\(207\) | 3.08883 | 0.214688 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.14637 | 0.0791067 | ||||||||
\(211\) | −18.5426 | −1.27653 | −0.638263 | − | 0.769818i | \(-0.720347\pi\) | ||||
−0.638263 | + | 0.769818i | \(0.720347\pi\) | |||||||
\(212\) | 13.4966 | 0.926953 | ||||||||
\(213\) | −0.671153 | −0.0459867 | ||||||||
\(214\) | 0.393115 | 0.0268728 | ||||||||
\(215\) | 4.97858 | 0.339536 | ||||||||
\(216\) | −5.37169 | −0.365497 | ||||||||
\(217\) | 9.66442 | 0.656064 | ||||||||
\(218\) | 4.41767 | 0.299203 | ||||||||
\(219\) | −10.2927 | −0.695518 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.10038 | −0.140969 | ||||||||
\(223\) | 1.31415 | 0.0880022 | 0.0440011 | − | 0.999031i | \(-0.485989\pi\) | ||||
0.0440011 | + | 0.999031i | \(0.485989\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −1.68585 | −0.112390 | ||||||||
\(226\) | 11.3717 | 0.756434 | ||||||||
\(227\) | −6.87819 | −0.456522 | −0.228261 | − | 0.973600i | \(-0.573304\pi\) | ||||
−0.228261 | + | 0.973600i | \(0.573304\pi\) | |||||||
\(228\) | 6.35027 | 0.420557 | ||||||||
\(229\) | 14.0575 | 0.928948 | 0.464474 | − | 0.885587i | \(-0.346243\pi\) | ||||
0.464474 | + | 0.885587i | \(0.346243\pi\) | |||||||
\(230\) | −1.83221 | −0.120812 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.83221 | 0.251597 | ||||||||
\(233\) | −4.04285 | −0.264856 | −0.132428 | − | 0.991193i | \(-0.542277\pi\) | ||||
−0.132428 | + | 0.991193i | \(0.542277\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.393115 | −0.0256440 | ||||||||
\(236\) | 0.685846 | 0.0446448 | ||||||||
\(237\) | −15.1365 | −0.983221 | ||||||||
\(238\) | −2.68585 | −0.174098 | ||||||||
\(239\) | 24.4177 | 1.57945 | 0.789724 | − | 0.613462i | \(-0.210224\pi\) | ||||
0.789724 | + | 0.613462i | \(0.210224\pi\) | |||||||
\(240\) | 1.14637 | 0.0739976 | ||||||||
\(241\) | −3.73183 | −0.240388 | −0.120194 | − | 0.992750i | \(-0.538352\pi\) | ||||
−0.120194 | + | 0.992750i | \(0.538352\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8536 | 0.952861 | ||||||||
\(244\) | 2.39312 | 0.153204 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −1.64973 | −0.105183 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9.66442 | 0.613691 | ||||||||
\(249\) | 10.7434 | 0.680834 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 23.5640 | 1.48735 | 0.743674 | − | 0.668542i | \(-0.233081\pi\) | ||||
0.743674 | + | 0.668542i | \(0.233081\pi\) | |||||||
\(252\) | −1.68585 | −0.106198 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 16.4507 | 1.03221 | ||||||||
\(255\) | −3.07896 | −0.192812 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.0821 | −0.878417 | −0.439209 | − | 0.898385i | \(-0.644741\pi\) | ||||
−0.439209 | + | 0.898385i | \(0.644741\pi\) | |||||||
\(258\) | 5.70727 | 0.355319 | ||||||||
\(259\) | −1.83221 | −0.113848 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.46052 | −0.399896 | ||||||||
\(262\) | −5.20390 | −0.321498 | ||||||||
\(263\) | 15.6644 | 0.965910 | 0.482955 | − | 0.875645i | \(-0.339564\pi\) | ||||
0.482955 | + | 0.875645i | \(0.339564\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.4966 | 0.829092 | ||||||||
\(266\) | 5.53948 | 0.339647 | ||||||||
\(267\) | 7.54935 | 0.462012 | ||||||||
\(268\) | 3.37169 | 0.205959 | ||||||||
\(269\) | 22.0575 | 1.34487 | 0.672436 | − | 0.740155i | \(-0.265248\pi\) | ||||
0.672436 | + | 0.740155i | \(0.265248\pi\) | |||||||
\(270\) | −5.37169 | −0.326911 | ||||||||
\(271\) | −13.0361 | −0.791888 | −0.395944 | − | 0.918275i | \(-0.629583\pi\) | ||||
−0.395944 | + | 0.918275i | \(0.629583\pi\) | |||||||
\(272\) | −2.68585 | −0.162853 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.41454 | 0.0854554 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.10038 | −0.126428 | ||||||||
\(277\) | −18.2499 | −1.09653 | −0.548265 | − | 0.836305i | \(-0.684711\pi\) | ||||
−0.548265 | + | 0.836305i | \(0.684711\pi\) | |||||||
\(278\) | −13.2039 | −0.791918 | ||||||||
\(279\) | −16.2927 | −0.975420 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −18.4078 | −1.09812 | −0.549059 | − | 0.835784i | \(-0.685014\pi\) | ||||
−0.549059 | + | 0.835784i | \(0.685014\pi\) | |||||||
\(282\) | −0.450654 | −0.0268360 | ||||||||
\(283\) | −9.62158 | −0.571943 | −0.285972 | − | 0.958238i | \(-0.592316\pi\) | ||||
−0.285972 | + | 0.958238i | \(0.592316\pi\) | |||||||
\(284\) | −0.585462 | −0.0347408 | ||||||||
\(285\) | 6.35027 | 0.376157 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.43910 | −0.0849472 | ||||||||
\(288\) | −1.68585 | −0.0993394 | ||||||||
\(289\) | −9.78623 | −0.575661 | ||||||||
\(290\) | 3.83221 | 0.225035 | ||||||||
\(291\) | 11.6560 | 0.683287 | ||||||||
\(292\) | −8.97858 | −0.525431 | ||||||||
\(293\) | −31.9143 | −1.86445 | −0.932227 | − | 0.361874i | \(-0.882137\pi\) | ||||
−0.932227 | + | 0.361874i | \(0.882137\pi\) | |||||||
\(294\) | 1.14637 | 0.0668574 | ||||||||
\(295\) | 0.685846 | 0.0399315 | ||||||||
\(296\) | −1.83221 | −0.106495 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.417674 | −0.0241952 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.14637 | 0.0661854 | ||||||||
\(301\) | 4.97858 | 0.286960 | ||||||||
\(302\) | −6.91117 | −0.397693 | ||||||||
\(303\) | −1.17092 | −0.0672678 | ||||||||
\(304\) | 5.53948 | 0.317711 | ||||||||
\(305\) | 2.39312 | 0.137029 | ||||||||
\(306\) | 4.52792 | 0.258844 | ||||||||
\(307\) | −9.03612 | −0.515718 | −0.257859 | − | 0.966183i | \(-0.583017\pi\) | ||||
−0.257859 | + | 0.966183i | \(0.583017\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.07896 | 0.175156 | ||||||||
\(310\) | 9.66442 | 0.548902 | ||||||||
\(311\) | −13.6644 | −0.774838 | −0.387419 | − | 0.921904i | \(-0.626633\pi\) | ||||
−0.387419 | + | 0.921904i | \(0.626633\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.71040 | −0.266248 | −0.133124 | − | 0.991099i | \(-0.542501\pi\) | ||||
−0.133124 | + | 0.991099i | \(0.542501\pi\) | |||||||
\(314\) | 14.2499 | 0.804168 | ||||||||
\(315\) | −1.68585 | −0.0949867 | ||||||||
\(316\) | −13.2039 | −0.742778 | ||||||||
\(317\) | 20.9112 | 1.17449 | 0.587244 | − | 0.809410i | \(-0.300213\pi\) | ||||
0.587244 | + | 0.809410i | \(0.300213\pi\) | |||||||
\(318\) | 15.4721 | 0.867631 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0.450654 | 0.0251530 | ||||||||
\(322\) | −1.83221 | −0.102105 | ||||||||
\(323\) | −14.8782 | −0.827845 | ||||||||
\(324\) | −1.10038 | −0.0611325 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.628308 | 0.0347987 | ||||||||
\(327\) | 5.06427 | 0.280055 | ||||||||
\(328\) | −1.43910 | −0.0794608 | ||||||||
\(329\) | −0.393115 | −0.0216731 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.4721 | −0.850422 | −0.425211 | − | 0.905094i | \(-0.639800\pi\) | ||||
−0.425211 | + | 0.905094i | \(0.639800\pi\) | |||||||
\(332\) | 9.37169 | 0.514338 | ||||||||
\(333\) | 3.08883 | 0.169267 | ||||||||
\(334\) | −18.5426 | −1.01461 | ||||||||
\(335\) | 3.37169 | 0.184215 | ||||||||
\(336\) | 1.14637 | 0.0625394 | ||||||||
\(337\) | −35.9572 | −1.95871 | −0.979356 | − | 0.202145i | \(-0.935209\pi\) | ||||
−0.979356 | + | 0.202145i | \(0.935209\pi\) | |||||||
\(338\) | −13.0000 | −0.707107 | ||||||||
\(339\) | 13.0361 | 0.708025 | ||||||||
\(340\) | −2.68585 | −0.145660 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −9.33871 | −0.504980 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.97858 | 0.268427 | ||||||||
\(345\) | −2.10038 | −0.113081 | ||||||||
\(346\) | 10.3503 | 0.556434 | ||||||||
\(347\) | −2.23519 | −0.119991 | −0.0599957 | − | 0.998199i | \(-0.519109\pi\) | ||||
−0.0599957 | + | 0.998199i | \(0.519109\pi\) | |||||||
\(348\) | 4.39312 | 0.235496 | ||||||||
\(349\) | 12.0147 | 0.643132 | 0.321566 | − | 0.946887i | \(-0.395791\pi\) | ||||
0.321566 | + | 0.946887i | \(0.395791\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.2039 | 1.66082 | 0.830408 | − | 0.557156i | \(-0.188107\pi\) | ||||
0.830408 | + | 0.557156i | \(0.188107\pi\) | |||||||
\(354\) | 0.786230 | 0.0417877 | ||||||||
\(355\) | −0.585462 | −0.0310731 | ||||||||
\(356\) | 6.58546 | 0.349029 | ||||||||
\(357\) | −3.07896 | −0.162956 | ||||||||
\(358\) | 12.6430 | 0.668203 | ||||||||
\(359\) | 20.8683 | 1.10139 | 0.550694 | − | 0.834707i | \(-0.314363\pi\) | ||||
0.550694 | + | 0.834707i | \(0.314363\pi\) | |||||||
\(360\) | −1.68585 | −0.0888519 | ||||||||
\(361\) | 11.6858 | 0.615045 | ||||||||
\(362\) | −2.58546 | −0.135889 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.97858 | −0.469960 | ||||||||
\(366\) | 2.74338 | 0.143399 | ||||||||
\(367\) | −33.2285 | −1.73451 | −0.867256 | − | 0.497863i | \(-0.834118\pi\) | ||||
−0.867256 | + | 0.497863i | \(0.834118\pi\) | |||||||
\(368\) | −1.83221 | −0.0955106 | ||||||||
\(369\) | 2.42610 | 0.126297 | ||||||||
\(370\) | −1.83221 | −0.0952521 | ||||||||
\(371\) | 13.4966 | 0.700710 | ||||||||
\(372\) | 11.0790 | 0.574417 | ||||||||
\(373\) | −9.66442 | −0.500405 | −0.250202 | − | 0.968194i | \(-0.580497\pi\) | ||||
−0.250202 | + | 0.968194i | \(0.580497\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.14637 | 0.0591981 | ||||||||
\(376\) | −0.393115 | −0.0202734 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −5.37169 | −0.276290 | ||||||||
\(379\) | −3.21377 | −0.165080 | −0.0825401 | − | 0.996588i | \(-0.526303\pi\) | ||||
−0.0825401 | + | 0.996588i | \(0.526303\pi\) | |||||||
\(380\) | 5.53948 | 0.284169 | ||||||||
\(381\) | 18.8585 | 0.966148 | ||||||||
\(382\) | 2.87819 | 0.147261 | ||||||||
\(383\) | −24.6430 | −1.25920 | −0.629599 | − | 0.776920i | \(-0.716781\pi\) | ||||
−0.629599 | + | 0.776920i | \(0.716781\pi\) | |||||||
\(384\) | 1.14637 | 0.0585002 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.1793 | −0.569014 | ||||||||
\(387\) | −8.39312 | −0.426646 | ||||||||
\(388\) | 10.1678 | 0.516191 | ||||||||
\(389\) | −6.92104 | −0.350911 | −0.175455 | − | 0.984487i | \(-0.556140\pi\) | ||||
−0.175455 | + | 0.984487i | \(0.556140\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.92104 | 0.248868 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −5.96558 | −0.300923 | ||||||||
\(394\) | 15.6216 | 0.787004 | ||||||||
\(395\) | −13.2039 | −0.664361 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.92104 | 0.347357 | 0.173678 | − | 0.984802i | \(-0.444435\pi\) | ||||
0.173678 | + | 0.984802i | \(0.444435\pi\) | |||||||
\(398\) | −21.7220 | −1.08882 | ||||||||
\(399\) | 6.35027 | 0.317911 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 18.6430 | 0.930987 | 0.465494 | − | 0.885051i | \(-0.345877\pi\) | ||||
0.465494 | + | 0.885051i | \(0.345877\pi\) | |||||||
\(402\) | 3.86519 | 0.192778 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.02142 | −0.0508177 | ||||||||
\(405\) | −1.10038 | −0.0546785 | ||||||||
\(406\) | 3.83221 | 0.190189 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −3.07896 | −0.152431 | ||||||||
\(409\) | 33.6890 | 1.66581 | 0.832906 | − | 0.553414i | \(-0.186675\pi\) | ||||
0.832906 | + | 0.553414i | \(0.186675\pi\) | |||||||
\(410\) | −1.43910 | −0.0710719 | ||||||||
\(411\) | 1.62158 | 0.0799865 | ||||||||
\(412\) | 2.68585 | 0.132322 | ||||||||
\(413\) | 0.685846 | 0.0337483 | ||||||||
\(414\) | 3.08883 | 0.151808 | ||||||||
\(415\) | 9.37169 | 0.460038 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.1365 | −0.741238 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.0214 | 1.02696 | 0.513482 | − | 0.858100i | \(-0.328355\pi\) | ||||
0.513482 | + | 0.858100i | \(0.328355\pi\) | |||||||
\(420\) | 1.14637 | 0.0559369 | ||||||||
\(421\) | −10.8353 | −0.528083 | −0.264041 | − | 0.964511i | \(-0.585056\pi\) | ||||
−0.264041 | + | 0.964511i | \(0.585056\pi\) | |||||||
\(422\) | −18.5426 | −0.902640 | ||||||||
\(423\) | 0.662732 | 0.0322231 | ||||||||
\(424\) | 13.4966 | 0.655455 | ||||||||
\(425\) | −2.68585 | −0.130283 | ||||||||
\(426\) | −0.671153 | −0.0325175 | ||||||||
\(427\) | 2.39312 | 0.115811 | ||||||||
\(428\) | 0.393115 | 0.0190019 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.97858 | 0.240088 | ||||||||
\(431\) | −32.6676 | −1.57354 | −0.786770 | − | 0.617246i | \(-0.788248\pi\) | ||||
−0.786770 | + | 0.617246i | \(0.788248\pi\) | |||||||
\(432\) | −5.37169 | −0.258446 | ||||||||
\(433\) | −16.3748 | −0.786924 | −0.393462 | − | 0.919341i | \(-0.628723\pi\) | ||||
−0.393462 | + | 0.919341i | \(0.628723\pi\) | |||||||
\(434\) | 9.66442 | 0.463907 | ||||||||
\(435\) | 4.39312 | 0.210634 | ||||||||
\(436\) | 4.41767 | 0.211568 | ||||||||
\(437\) | −10.1495 | −0.485516 | ||||||||
\(438\) | −10.2927 | −0.491806 | ||||||||
\(439\) | 0.450654 | 0.0215085 | 0.0107543 | − | 0.999942i | \(-0.496577\pi\) | ||||
0.0107543 | + | 0.999942i | \(0.496577\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.68585 | −0.0802784 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.7862 | 0.512469 | 0.256235 | − | 0.966615i | \(-0.417518\pi\) | ||||
0.256235 | + | 0.966615i | \(0.417518\pi\) | |||||||
\(444\) | −2.10038 | −0.0996798 | ||||||||
\(445\) | 6.58546 | 0.312181 | ||||||||
\(446\) | 1.31415 | 0.0622270 | ||||||||
\(447\) | −0.478807 | −0.0226468 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −19.8139 | −0.935077 | −0.467538 | − | 0.883973i | \(-0.654859\pi\) | ||||
−0.467538 | + | 0.883973i | \(0.654859\pi\) | |||||||
\(450\) | −1.68585 | −0.0794716 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 11.3717 | 0.534879 | ||||||||
\(453\) | −7.92273 | −0.372242 | ||||||||
\(454\) | −6.87819 | −0.322810 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.35027 | 0.297379 | ||||||||
\(457\) | 23.9572 | 1.12067 | 0.560334 | − | 0.828267i | \(-0.310673\pi\) | ||||
0.560334 | + | 0.828267i | \(0.310673\pi\) | |||||||
\(458\) | 14.0575 | 0.656866 | ||||||||
\(459\) | 14.4275 | 0.673420 | ||||||||
\(460\) | −1.83221 | −0.0854273 | ||||||||
\(461\) | 26.6430 | 1.24089 | 0.620444 | − | 0.784251i | \(-0.286952\pi\) | ||||
0.620444 | + | 0.784251i | \(0.286952\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.75325 | 0.127954 | 0.0639772 | − | 0.997951i | \(-0.479622\pi\) | ||||
0.0639772 | + | 0.997951i | \(0.479622\pi\) | |||||||
\(464\) | 3.83221 | 0.177906 | ||||||||
\(465\) | 11.0790 | 0.513775 | ||||||||
\(466\) | −4.04285 | −0.187281 | ||||||||
\(467\) | −20.1396 | −0.931951 | −0.465976 | − | 0.884798i | \(-0.654297\pi\) | ||||
−0.465976 | + | 0.884798i | \(0.654297\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.37169 | 0.155690 | ||||||||
\(470\) | −0.393115 | −0.0181331 | ||||||||
\(471\) | 16.3356 | 0.752704 | ||||||||
\(472\) | 0.685846 | 0.0315686 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −15.1365 | −0.695242 | ||||||||
\(475\) | 5.53948 | 0.254169 | ||||||||
\(476\) | −2.68585 | −0.123106 | ||||||||
\(477\) | −22.7533 | −1.04180 | ||||||||
\(478\) | 24.4177 | 1.11684 | ||||||||
\(479\) | −4.58546 | −0.209515 | −0.104758 | − | 0.994498i | \(-0.533407\pi\) | ||||
−0.104758 | + | 0.994498i | \(0.533407\pi\) | |||||||
\(480\) | 1.14637 | 0.0523242 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −3.73183 | −0.169980 | ||||||||
\(483\) | −2.10038 | −0.0955708 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.1678 | 0.461695 | ||||||||
\(486\) | 14.8536 | 0.673775 | ||||||||
\(487\) | 33.1611 | 1.50267 | 0.751335 | − | 0.659920i | \(-0.229410\pi\) | ||||
0.751335 | + | 0.659920i | \(0.229410\pi\) | |||||||
\(488\) | 2.39312 | 0.108331 | ||||||||
\(489\) | 0.720270 | 0.0325717 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 23.9143 | 1.07924 | 0.539619 | − | 0.841909i | \(-0.318568\pi\) | ||||
0.539619 | + | 0.841909i | \(0.318568\pi\) | |||||||
\(492\) | −1.64973 | −0.0743756 | ||||||||
\(493\) | −10.2927 | −0.463561 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.66442 | 0.433945 | ||||||||
\(497\) | −0.585462 | −0.0262616 | ||||||||
\(498\) | 10.7434 | 0.481423 | ||||||||
\(499\) | −39.3864 | −1.76318 | −0.881588 | − | 0.472019i | \(-0.843525\pi\) | ||||
−0.881588 | + | 0.472019i | \(0.843525\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −21.2566 | −0.949676 | ||||||||
\(502\) | 23.5640 | 1.05171 | ||||||||
\(503\) | −23.5296 | −1.04913 | −0.524567 | − | 0.851369i | \(-0.675773\pi\) | ||||
−0.524567 | + | 0.851369i | \(0.675773\pi\) | |||||||
\(504\) | −1.68585 | −0.0750936 | ||||||||
\(505\) | −1.02142 | −0.0454527 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.9028 | −0.661854 | ||||||||
\(508\) | 16.4507 | 0.729880 | ||||||||
\(509\) | −20.5426 | −0.910535 | −0.455268 | − | 0.890355i | \(-0.650456\pi\) | ||||
−0.455268 | + | 0.890355i | \(0.650456\pi\) | |||||||
\(510\) | −3.07896 | −0.136339 | ||||||||
\(511\) | −8.97858 | −0.397189 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −29.7564 | −1.31378 | ||||||||
\(514\) | −14.0821 | −0.621135 | ||||||||
\(515\) | 2.68585 | 0.118353 | ||||||||
\(516\) | 5.70727 | 0.251249 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.83221 | −0.0805028 | ||||||||
\(519\) | 11.8652 | 0.520824 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.53635 | −0.286362 | −0.143181 | − | 0.989696i | \(-0.545733\pi\) | ||||
−0.143181 | + | 0.989696i | \(0.545733\pi\) | |||||||
\(522\) | −6.46052 | −0.282769 | ||||||||
\(523\) | −37.7367 | −1.65011 | −0.825054 | − | 0.565053i | \(-0.808856\pi\) | ||||
−0.825054 | + | 0.565053i | \(0.808856\pi\) | |||||||
\(524\) | −5.20390 | −0.227334 | ||||||||
\(525\) | 1.14637 | 0.0500315 | ||||||||
\(526\) | 15.6644 | 0.683001 | ||||||||
\(527\) | −25.9572 | −1.13071 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.6430 | −0.854043 | ||||||||
\(530\) | 13.4966 | 0.586256 | ||||||||
\(531\) | −1.15623 | −0.0501762 | ||||||||
\(532\) | 5.53948 | 0.240167 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 7.54935 | 0.326692 | ||||||||
\(535\) | 0.393115 | 0.0169959 | ||||||||
\(536\) | 3.37169 | 0.145635 | ||||||||
\(537\) | 14.4935 | 0.625441 | ||||||||
\(538\) | 22.0575 | 0.950968 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.37169 | −0.231161 | ||||||||
\(541\) | −2.99686 | −0.128845 | −0.0644226 | − | 0.997923i | \(-0.520521\pi\) | ||||
−0.0644226 | + | 0.997923i | \(0.520521\pi\) | |||||||
\(542\) | −13.0361 | −0.559949 | ||||||||
\(543\) | −2.96388 | −0.127192 | ||||||||
\(544\) | −2.68585 | −0.115155 | ||||||||
\(545\) | 4.41767 | 0.189232 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.0856914 | 0.00366390 | 0.00183195 | − | 0.999998i | \(-0.499417\pi\) | ||||
0.00183195 | + | 0.999998i | \(0.499417\pi\) | |||||||
\(548\) | 1.41454 | 0.0604261 | ||||||||
\(549\) | −4.03442 | −0.172185 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.2285 | 0.904363 | ||||||||
\(552\) | −2.10038 | −0.0893983 | ||||||||
\(553\) | −13.2039 | −0.561487 | ||||||||
\(554\) | −18.2499 | −0.775363 | ||||||||
\(555\) | −2.10038 | −0.0891563 | ||||||||
\(556\) | −13.2039 | −0.559970 | ||||||||
\(557\) | −27.2860 | −1.15614 | −0.578072 | − | 0.815985i | \(-0.696195\pi\) | ||||
−0.578072 | + | 0.815985i | \(0.696195\pi\) | |||||||
\(558\) | −16.2927 | −0.689726 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.4078 | −0.776487 | ||||||||
\(563\) | 29.0852 | 1.22580 | 0.612898 | − | 0.790162i | \(-0.290004\pi\) | ||||
0.612898 | + | 0.790162i | \(0.290004\pi\) | |||||||
\(564\) | −0.450654 | −0.0189759 | ||||||||
\(565\) | 11.3717 | 0.478411 | ||||||||
\(566\) | −9.62158 | −0.404425 | ||||||||
\(567\) | −1.10038 | −0.0462118 | ||||||||
\(568\) | −0.585462 | −0.0245654 | ||||||||
\(569\) | −23.9143 | −1.00254 | −0.501270 | − | 0.865291i | \(-0.667134\pi\) | ||||
−0.501270 | + | 0.865291i | \(0.667134\pi\) | |||||||
\(570\) | 6.35027 | 0.265984 | ||||||||
\(571\) | −15.2797 | −0.639437 | −0.319718 | − | 0.947513i | \(-0.603588\pi\) | ||||
−0.319718 | + | 0.947513i | \(0.603588\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.29946 | 0.137837 | ||||||||
\(574\) | −1.43910 | −0.0600667 | ||||||||
\(575\) | −1.83221 | −0.0764085 | ||||||||
\(576\) | −1.68585 | −0.0702436 | ||||||||
\(577\) | −9.58233 | −0.398917 | −0.199459 | − | 0.979906i | \(-0.563918\pi\) | ||||
−0.199459 | + | 0.979906i | \(0.563918\pi\) | |||||||
\(578\) | −9.78623 | −0.407054 | ||||||||
\(579\) | −12.8156 | −0.532599 | ||||||||
\(580\) | 3.83221 | 0.159124 | ||||||||
\(581\) | 9.37169 | 0.388803 | ||||||||
\(582\) | 11.6560 | 0.483157 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −8.97858 | −0.371536 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −31.9143 | −1.31837 | ||||||||
\(587\) | 0.176210 | 0.00727296 | 0.00363648 | − | 0.999993i | \(-0.498842\pi\) | ||||
0.00363648 | + | 0.999993i | \(0.498842\pi\) | |||||||
\(588\) | 1.14637 | 0.0472753 | ||||||||
\(589\) | 53.5359 | 2.20591 | ||||||||
\(590\) | 0.685846 | 0.0282358 | ||||||||
\(591\) | 17.9080 | 0.736638 | ||||||||
\(592\) | −1.83221 | −0.0753034 | ||||||||
\(593\) | 0.863500 | 0.0354597 | 0.0177299 | − | 0.999843i | \(-0.494356\pi\) | ||||
0.0177299 | + | 0.999843i | \(0.494356\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.68585 | −0.110109 | ||||||||
\(596\) | −0.417674 | −0.0171086 | ||||||||
\(597\) | −24.9013 | −1.01914 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.4145 | 0.956692 | 0.478346 | − | 0.878171i | \(-0.341236\pi\) | ||||
0.478346 | + | 0.878171i | \(0.341236\pi\) | |||||||
\(600\) | 1.14637 | 0.0468002 | ||||||||
\(601\) | −13.1892 | −0.537999 | −0.269000 | − | 0.963140i | \(-0.586693\pi\) | ||||
−0.269000 | + | 0.963140i | \(0.586693\pi\) | |||||||
\(602\) | 4.97858 | 0.202912 | ||||||||
\(603\) | −5.68415 | −0.231477 | ||||||||
\(604\) | −6.91117 | −0.281212 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.17092 | −0.0475655 | ||||||||
\(607\) | 11.8077 | 0.479258 | 0.239629 | − | 0.970865i | \(-0.422974\pi\) | ||||
0.239629 | + | 0.970865i | \(0.422974\pi\) | |||||||
\(608\) | 5.53948 | 0.224656 | ||||||||
\(609\) | 4.39312 | 0.178018 | ||||||||
\(610\) | 2.39312 | 0.0968944 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.52792 | 0.183030 | ||||||||
\(613\) | 39.4868 | 1.59486 | 0.797428 | − | 0.603414i | \(-0.206193\pi\) | ||||
0.797428 | + | 0.603414i | \(0.206193\pi\) | |||||||
\(614\) | −9.03612 | −0.364668 | ||||||||
\(615\) | −1.64973 | −0.0665236 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.3650 | −1.54452 | −0.772258 | − | 0.635310i | \(-0.780873\pi\) | ||||
−0.772258 | + | 0.635310i | \(0.780873\pi\) | |||||||
\(618\) | 3.07896 | 0.123854 | ||||||||
\(619\) | −5.52119 | −0.221915 | −0.110958 | − | 0.993825i | \(-0.535392\pi\) | ||||
−0.110958 | + | 0.993825i | \(0.535392\pi\) | |||||||
\(620\) | 9.66442 | 0.388133 | ||||||||
\(621\) | 9.84208 | 0.394949 | ||||||||
\(622\) | −13.6644 | −0.547893 | ||||||||
\(623\) | 6.58546 | 0.263841 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −4.71040 | −0.188266 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.2499 | 0.568632 | ||||||||
\(629\) | 4.92104 | 0.196215 | ||||||||
\(630\) | −1.68585 | −0.0671657 | ||||||||
\(631\) | −46.2730 | −1.84210 | −0.921050 | − | 0.389445i | \(-0.872667\pi\) | ||||
−0.921050 | + | 0.389445i | \(0.872667\pi\) | |||||||
\(632\) | −13.2039 | −0.525223 | ||||||||
\(633\) | −21.2566 | −0.844875 | ||||||||
\(634\) | 20.9112 | 0.830489 | ||||||||
\(635\) | 16.4507 | 0.652824 | ||||||||
\(636\) | 15.4721 | 0.613508 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.986999 | 0.0390451 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −39.0852 | −1.54377 | −0.771887 | − | 0.635760i | \(-0.780687\pi\) | ||||
−0.771887 | + | 0.635760i | \(0.780687\pi\) | |||||||
\(642\) | 0.450654 | 0.0177859 | ||||||||
\(643\) | 40.3404 | 1.59087 | 0.795435 | − | 0.606039i | \(-0.207242\pi\) | ||||
0.795435 | + | 0.606039i | \(0.207242\pi\) | |||||||
\(644\) | −1.83221 | −0.0721993 | ||||||||
\(645\) | 5.70727 | 0.224723 | ||||||||
\(646\) | −14.8782 | −0.585375 | ||||||||
\(647\) | −6.48508 | −0.254955 | −0.127477 | − | 0.991841i | \(-0.540688\pi\) | ||||
−0.127477 | + | 0.991841i | \(0.540688\pi\) | |||||||
\(648\) | −1.10038 | −0.0432272 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.0790 | 0.434219 | ||||||||
\(652\) | 0.628308 | 0.0246064 | ||||||||
\(653\) | 18.7533 | 0.733871 | 0.366936 | − | 0.930246i | \(-0.380407\pi\) | ||||
0.366936 | + | 0.930246i | \(0.380407\pi\) | |||||||
\(654\) | 5.06427 | 0.198029 | ||||||||
\(655\) | −5.20390 | −0.203333 | ||||||||
\(656\) | −1.43910 | −0.0561873 | ||||||||
\(657\) | 15.1365 | 0.590531 | ||||||||
\(658\) | −0.393115 | −0.0153252 | ||||||||
\(659\) | −6.37842 | −0.248468 | −0.124234 | − | 0.992253i | \(-0.539647\pi\) | ||||
−0.124234 | + | 0.992253i | \(0.539647\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.6148 | 1.19078 | 0.595390 | − | 0.803437i | \(-0.296998\pi\) | ||||
0.595390 | + | 0.803437i | \(0.296998\pi\) | |||||||
\(662\) | −15.4721 | −0.601339 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.37169 | 0.363692 | ||||||||
\(665\) | 5.53948 | 0.214812 | ||||||||
\(666\) | 3.08883 | 0.119690 | ||||||||
\(667\) | −7.02142 | −0.271871 | ||||||||
\(668\) | −18.5426 | −0.717435 | ||||||||
\(669\) | 1.50650 | 0.0582447 | ||||||||
\(670\) | 3.37169 | 0.130260 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.14637 | 0.0442220 | ||||||||
\(673\) | −5.91431 | −0.227980 | −0.113990 | − | 0.993482i | \(-0.536363\pi\) | ||||
−0.113990 | + | 0.993482i | \(0.536363\pi\) | |||||||
\(674\) | −35.9572 | −1.38502 | ||||||||
\(675\) | −5.37169 | −0.206757 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | −29.9656 | −1.15167 | −0.575835 | − | 0.817566i | \(-0.695323\pi\) | ||||
−0.575835 | + | 0.817566i | \(0.695323\pi\) | |||||||
\(678\) | 13.0361 | 0.500649 | ||||||||
\(679\) | 10.1678 | 0.390204 | ||||||||
\(680\) | −2.68585 | −0.102997 | ||||||||
\(681\) | −7.88492 | −0.302151 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.0790 | 1.26573 | 0.632866 | − | 0.774262i | \(-0.281879\pi\) | ||||
0.632866 | + | 0.774262i | \(0.281879\pi\) | |||||||
\(684\) | −9.33871 | −0.357075 | ||||||||
\(685\) | 1.41454 | 0.0540467 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 16.1151 | 0.614829 | ||||||||
\(688\) | 4.97858 | 0.189806 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2.10038 | −0.0799603 | ||||||||
\(691\) | 35.9656 | 1.36819 | 0.684097 | − | 0.729391i | \(-0.260196\pi\) | ||||
0.684097 | + | 0.729391i | \(0.260196\pi\) | |||||||
\(692\) | 10.3503 | 0.393458 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.23519 | −0.0848467 | ||||||||
\(695\) | −13.2039 | −0.500853 | ||||||||
\(696\) | 4.39312 | 0.166521 | ||||||||
\(697\) | 3.86519 | 0.146405 | ||||||||
\(698\) | 12.0147 | 0.454763 | ||||||||
\(699\) | −4.63458 | −0.175296 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −4.95402 | −0.187111 | −0.0935554 | − | 0.995614i | \(-0.529823\pi\) | ||||
−0.0935554 | + | 0.995614i | \(0.529823\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.1495 | −0.382796 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.450654 | −0.0169726 | ||||||||
\(706\) | 31.2039 | 1.17437 | ||||||||
\(707\) | −1.02142 | −0.0384146 | ||||||||
\(708\) | 0.786230 | 0.0295483 | ||||||||
\(709\) | −23.5725 | −0.885282 | −0.442641 | − | 0.896699i | \(-0.645958\pi\) | ||||
−0.442641 | + | 0.896699i | \(0.645958\pi\) | |||||||
\(710\) | −0.585462 | −0.0219720 | ||||||||
\(711\) | 22.2598 | 0.834806 | ||||||||
\(712\) | 6.58546 | 0.246801 | ||||||||
\(713\) | −17.7073 | −0.663142 | ||||||||
\(714\) | −3.07896 | −0.115227 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.6430 | 0.472491 | ||||||||
\(717\) | 27.9916 | 1.04536 | ||||||||
\(718\) | 20.8683 | 0.778799 | ||||||||
\(719\) | 43.2944 | 1.61461 | 0.807305 | − | 0.590135i | \(-0.200925\pi\) | ||||
0.807305 | + | 0.590135i | \(0.200925\pi\) | |||||||
\(720\) | −1.68585 | −0.0628278 | ||||||||
\(721\) | 2.68585 | 0.100026 | ||||||||
\(722\) | 11.6858 | 0.434902 | ||||||||
\(723\) | −4.27804 | −0.159102 | ||||||||
\(724\) | −2.58546 | −0.0960879 | ||||||||
\(725\) | 3.83221 | 0.142325 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.8370 | 1.47747 | 0.738737 | − | 0.673994i | \(-0.235423\pi\) | ||||
0.738737 | + | 0.673994i | \(0.235423\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.3288 | 0.752920 | ||||||||
\(730\) | −8.97858 | −0.332312 | ||||||||
\(731\) | −13.3717 | −0.494570 | ||||||||
\(732\) | 2.74338 | 0.101398 | ||||||||
\(733\) | 13.6791 | 0.505250 | 0.252625 | − | 0.967564i | \(-0.418706\pi\) | ||||
0.252625 | + | 0.967564i | \(0.418706\pi\) | |||||||
\(734\) | −33.2285 | −1.22648 | ||||||||
\(735\) | 1.14637 | 0.0422843 | ||||||||
\(736\) | −1.83221 | −0.0675362 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 2.42610 | 0.0893058 | ||||||||
\(739\) | 1.25662 | 0.0462253 | 0.0231127 | − | 0.999733i | \(-0.492642\pi\) | ||||
0.0231127 | + | 0.999733i | \(0.492642\pi\) | |||||||
\(740\) | −1.83221 | −0.0673534 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.4966 | 0.495477 | ||||||||
\(743\) | −1.90804 | −0.0699991 | −0.0349996 | − | 0.999387i | \(-0.511143\pi\) | ||||
−0.0349996 | + | 0.999387i | \(0.511143\pi\) | |||||||
\(744\) | 11.0790 | 0.406174 | ||||||||
\(745\) | −0.417674 | −0.0153024 | ||||||||
\(746\) | −9.66442 | −0.353840 | ||||||||
\(747\) | −15.7992 | −0.578064 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.393115 | 0.0143641 | ||||||||
\(750\) | 1.14637 | 0.0418593 | ||||||||
\(751\) | −41.0852 | −1.49922 | −0.749611 | − | 0.661879i | \(-0.769759\pi\) | ||||
−0.749611 | + | 0.661879i | \(0.769759\pi\) | |||||||
\(752\) | −0.393115 | −0.0143354 | ||||||||
\(753\) | 27.0130 | 0.984408 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.91117 | −0.251523 | ||||||||
\(756\) | −5.37169 | −0.195367 | ||||||||
\(757\) | 4.07583 | 0.148138 | 0.0740692 | − | 0.997253i | \(-0.476401\pi\) | ||||
0.0740692 | + | 0.997253i | \(0.476401\pi\) | |||||||
\(758\) | −3.21377 | −0.116729 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.53948 | 0.200938 | ||||||||
\(761\) | 5.10352 | 0.185002 | 0.0925012 | − | 0.995713i | \(-0.470514\pi\) | ||||
0.0925012 | + | 0.995713i | \(0.470514\pi\) | |||||||
\(762\) | 18.8585 | 0.683170 | ||||||||
\(763\) | 4.41767 | 0.159931 | ||||||||
\(764\) | 2.87819 | 0.104129 | ||||||||
\(765\) | 4.52792 | 0.163707 | ||||||||
\(766\) | −24.6430 | −0.890388 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.14637 | 0.0413659 | ||||||||
\(769\) | −21.8406 | −0.787593 | −0.393797 | − | 0.919198i | \(-0.628839\pi\) | ||||
−0.393797 | + | 0.919198i | \(0.628839\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.1432 | −0.581384 | ||||||||
\(772\) | −11.1793 | −0.402353 | ||||||||
\(773\) | 34.0294 | 1.22395 | 0.611976 | − | 0.790876i | \(-0.290375\pi\) | ||||
0.611976 | + | 0.790876i | \(0.290375\pi\) | |||||||
\(774\) | −8.39312 | −0.301684 | ||||||||
\(775\) | 9.66442 | 0.347156 | ||||||||
\(776\) | 10.1678 | 0.365002 | ||||||||
\(777\) | −2.10038 | −0.0753509 | ||||||||
\(778\) | −6.92104 | −0.248131 | ||||||||
\(779\) | −7.97185 | −0.285621 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 4.92104 | 0.175976 | ||||||||
\(783\) | −20.5855 | −0.735664 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 14.2499 | 0.508600 | ||||||||
\(786\) | −5.96558 | −0.212785 | ||||||||
\(787\) | −16.4998 | −0.588153 | −0.294077 | − | 0.955782i | \(-0.595012\pi\) | ||||
−0.294077 | + | 0.955782i | \(0.595012\pi\) | |||||||
\(788\) | 15.6216 | 0.556496 | ||||||||
\(789\) | 17.9572 | 0.639292 | ||||||||
\(790\) | −13.2039 | −0.469774 | ||||||||
\(791\) | 11.3717 | 0.404331 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 6.92104 | 0.245618 | ||||||||
\(795\) | 15.4721 | 0.548738 | ||||||||
\(796\) | −21.7220 | −0.769915 | ||||||||
\(797\) | 32.3221 | 1.14491 | 0.572454 | − | 0.819937i | \(-0.305991\pi\) | ||||
0.572454 | + | 0.819937i | \(0.305991\pi\) | |||||||
\(798\) | 6.35027 | 0.224797 | ||||||||
\(799\) | 1.05585 | 0.0373532 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −11.1021 | −0.392273 | ||||||||
\(802\) | 18.6430 | 0.658307 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 3.86519 | 0.136315 | ||||||||
\(805\) | −1.83221 | −0.0645770 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.2860 | 0.890109 | ||||||||
\(808\) | −1.02142 | −0.0359335 | ||||||||
\(809\) | −24.6514 | −0.866698 | −0.433349 | − | 0.901226i | \(-0.642668\pi\) | ||||
−0.433349 | + | 0.901226i | \(0.642668\pi\) | |||||||
\(810\) | −1.10038 | −0.0386636 | ||||||||
\(811\) | −6.66129 | −0.233909 | −0.116955 | − | 0.993137i | \(-0.537313\pi\) | ||||
−0.116955 | + | 0.993137i | \(0.537313\pi\) | |||||||
\(812\) | 3.83221 | 0.134484 | ||||||||
\(813\) | −14.9442 | −0.524114 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.628308 | 0.0220087 | ||||||||
\(816\) | −3.07896 | −0.107785 | ||||||||
\(817\) | 27.5787 | 0.964858 | ||||||||
\(818\) | 33.6890 | 1.17791 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.43910 | −0.0502554 | ||||||||
\(821\) | −42.2400 | −1.47419 | −0.737093 | − | 0.675791i | \(-0.763802\pi\) | ||||
−0.737093 | + | 0.675791i | \(0.763802\pi\) | |||||||
\(822\) | 1.62158 | 0.0565590 | ||||||||
\(823\) | −26.2829 | −0.916163 | −0.458082 | − | 0.888910i | \(-0.651463\pi\) | ||||
−0.458082 | + | 0.888910i | \(0.651463\pi\) | |||||||
\(824\) | 2.68585 | 0.0935659 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.685846 | 0.0238636 | ||||||||
\(827\) | 0.986999 | 0.0343213 | 0.0171607 | − | 0.999853i | \(-0.494537\pi\) | ||||
0.0171607 | + | 0.999853i | \(0.494537\pi\) | |||||||
\(828\) | 3.08883 | 0.107344 | ||||||||
\(829\) | −1.07054 | −0.0371814 | −0.0185907 | − | 0.999827i | \(-0.505918\pi\) | ||||
−0.0185907 | + | 0.999827i | \(0.505918\pi\) | |||||||
\(830\) | 9.37169 | 0.325296 | ||||||||
\(831\) | −20.9210 | −0.725743 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.68585 | −0.0930591 | ||||||||
\(834\) | −15.1365 | −0.524134 | ||||||||
\(835\) | −18.5426 | −0.641694 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −51.9143 | −1.79442 | ||||||||
\(838\) | 21.0214 | 0.726173 | ||||||||
\(839\) | −30.4507 | −1.05127 | −0.525637 | − | 0.850709i | \(-0.676173\pi\) | ||||
−0.525637 | + | 0.850709i | \(0.676173\pi\) | |||||||
\(840\) | 1.14637 | 0.0395534 | ||||||||
\(841\) | −14.3142 | −0.493592 | ||||||||
\(842\) | −10.8353 | −0.373411 | ||||||||
\(843\) | −21.1021 | −0.726794 | ||||||||
\(844\) | −18.5426 | −0.638263 | ||||||||
\(845\) | −13.0000 | −0.447214 | ||||||||
\(846\) | 0.662732 | 0.0227852 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 13.4966 | 0.463476 | ||||||||
\(849\) | −11.0298 | −0.378543 | ||||||||
\(850\) | −2.68585 | −0.0921238 | ||||||||
\(851\) | 3.35700 | 0.115076 | ||||||||
\(852\) | −0.671153 | −0.0229933 | ||||||||
\(853\) | −6.43596 | −0.220363 | −0.110182 | − | 0.993911i | \(-0.535143\pi\) | ||||
−0.110182 | + | 0.993911i | \(0.535143\pi\) | |||||||
\(854\) | 2.39312 | 0.0818907 | ||||||||
\(855\) | −9.33871 | −0.319377 | ||||||||
\(856\) | 0.393115 | 0.0134364 | ||||||||
\(857\) | 1.26504 | 0.0432128 | 0.0216064 | − | 0.999767i | \(-0.493122\pi\) | ||||
0.0216064 | + | 0.999767i | \(0.493122\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.13650 | 0.0387769 | 0.0193884 | − | 0.999812i | \(-0.493828\pi\) | ||||
0.0193884 | + | 0.999812i | \(0.493828\pi\) | |||||||
\(860\) | 4.97858 | 0.169768 | ||||||||
\(861\) | −1.64973 | −0.0562227 | ||||||||
\(862\) | −32.6676 | −1.11266 | ||||||||
\(863\) | 44.7764 | 1.52421 | 0.762103 | − | 0.647456i | \(-0.224167\pi\) | ||||
0.762103 | + | 0.647456i | \(0.224167\pi\) | |||||||
\(864\) | −5.37169 | −0.182749 | ||||||||
\(865\) | 10.3503 | 0.351920 | ||||||||
\(866\) | −16.3748 | −0.556439 | ||||||||
\(867\) | −11.2186 | −0.381004 | ||||||||
\(868\) | 9.66442 | 0.328032 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 4.39312 | 0.148941 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 4.41767 | 0.149601 | ||||||||
\(873\) | −17.1413 | −0.580146 | ||||||||
\(874\) | −10.1495 | −0.343312 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −10.2927 | −0.347759 | ||||||||
\(877\) | −53.6644 | −1.81212 | −0.906059 | − | 0.423151i | \(-0.860924\pi\) | ||||
−0.906059 | + | 0.423151i | \(0.860924\pi\) | |||||||
\(878\) | 0.450654 | 0.0152088 | ||||||||
\(879\) | −36.5855 | −1.23400 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.42754 | 0.149168 | 0.0745838 | − | 0.997215i | \(-0.476237\pi\) | ||||
0.0745838 | + | 0.997215i | \(0.476237\pi\) | |||||||
\(882\) | −1.68585 | −0.0567654 | ||||||||
\(883\) | 31.7073 | 1.06703 | 0.533517 | − | 0.845789i | \(-0.320870\pi\) | ||||
0.533517 | + | 0.845789i | \(0.320870\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.786230 | 0.0264288 | ||||||||
\(886\) | 10.7862 | 0.362370 | ||||||||
\(887\) | 45.9865 | 1.54408 | 0.772038 | − | 0.635576i | \(-0.219237\pi\) | ||||
0.772038 | + | 0.635576i | \(0.219237\pi\) | |||||||
\(888\) | −2.10038 | −0.0704843 | ||||||||
\(889\) | 16.4507 | 0.551737 | ||||||||
\(890\) | 6.58546 | 0.220745 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.31415 | 0.0440011 | ||||||||
\(893\) | −2.17765 | −0.0728724 | ||||||||
\(894\) | −0.478807 | −0.0160137 | ||||||||
\(895\) | 12.6430 | 0.422609 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.8139 | −0.661199 | ||||||||
\(899\) | 37.0361 | 1.23522 | ||||||||
\(900\) | −1.68585 | −0.0561949 | ||||||||
\(901\) | −36.2499 | −1.20766 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.70727 | 0.189926 | ||||||||
\(904\) | 11.3717 | 0.378217 | ||||||||
\(905\) | −2.58546 | −0.0859437 | ||||||||
\(906\) | −7.92273 | −0.263215 | ||||||||
\(907\) | −11.5065 | −0.382067 | −0.191034 | − | 0.981584i | \(-0.561184\pi\) | ||||
−0.191034 | + | 0.981584i | \(0.561184\pi\) | |||||||
\(908\) | −6.87819 | −0.228261 | ||||||||
\(909\) | 1.72196 | 0.0571139 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.8353 | 0.557780 | 0.278890 | − | 0.960323i | \(-0.410034\pi\) | ||||
0.278890 | + | 0.960323i | \(0.410034\pi\) | |||||||
\(912\) | 6.35027 | 0.210278 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 23.9572 | 0.792432 | ||||||||
\(915\) | 2.74338 | 0.0906935 | ||||||||
\(916\) | 14.0575 | 0.464474 | ||||||||
\(917\) | −5.20390 | −0.171848 | ||||||||
\(918\) | 14.4275 | 0.476180 | ||||||||
\(919\) | 48.6184 | 1.60377 | 0.801887 | − | 0.597475i | \(-0.203829\pi\) | ||||
0.801887 | + | 0.597475i | \(0.203829\pi\) | |||||||
\(920\) | −1.83221 | −0.0604062 | ||||||||
\(921\) | −10.3587 | −0.341330 | ||||||||
\(922\) | 26.6430 | 0.877440 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.83221 | −0.0602427 | ||||||||
\(926\) | 2.75325 | 0.0904774 | ||||||||
\(927\) | −4.52792 | −0.148717 | ||||||||
\(928\) | 3.83221 | 0.125799 | ||||||||
\(929\) | −5.57873 | −0.183032 | −0.0915161 | − | 0.995804i | \(-0.529171\pi\) | ||||
−0.0915161 | + | 0.995804i | \(0.529171\pi\) | |||||||
\(930\) | 11.0790 | 0.363293 | ||||||||
\(931\) | 5.53948 | 0.181549 | ||||||||
\(932\) | −4.04285 | −0.132428 | ||||||||
\(933\) | −15.6644 | −0.512830 | ||||||||
\(934\) | −20.1396 | −0.658989 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.6430 | 0.674377 | 0.337189 | − | 0.941437i | \(-0.390524\pi\) | ||||
0.337189 | + | 0.941437i | \(0.390524\pi\) | |||||||
\(938\) | 3.37169 | 0.110090 | ||||||||
\(939\) | −5.39985 | −0.176217 | ||||||||
\(940\) | −0.393115 | −0.0128220 | ||||||||
\(941\) | −45.0214 | −1.46766 | −0.733828 | − | 0.679335i | \(-0.762268\pi\) | ||||
−0.733828 | + | 0.679335i | \(0.762268\pi\) | |||||||
\(942\) | 16.3356 | 0.532242 | ||||||||
\(943\) | 2.63673 | 0.0858637 | ||||||||
\(944\) | 0.685846 | 0.0223224 | ||||||||
\(945\) | −5.37169 | −0.174741 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.45065 | −0.209618 | −0.104809 | − | 0.994492i | \(-0.533423\pi\) | ||||
−0.104809 | + | 0.994492i | \(0.533423\pi\) | |||||||
\(948\) | −15.1365 | −0.491611 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 5.53948 | 0.179724 | ||||||||
\(951\) | 23.9718 | 0.777340 | ||||||||
\(952\) | −2.68585 | −0.0870488 | ||||||||
\(953\) | −28.5510 | −0.924859 | −0.462429 | − | 0.886656i | \(-0.653022\pi\) | ||||
−0.462429 | + | 0.886656i | \(0.653022\pi\) | |||||||
\(954\) | −22.7533 | −0.736664 | ||||||||
\(955\) | 2.87819 | 0.0931361 | ||||||||
\(956\) | 24.4177 | 0.789724 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.58546 | −0.148150 | ||||||||
\(959\) | 1.41454 | 0.0456778 | ||||||||
\(960\) | 1.14637 | 0.0369988 | ||||||||
\(961\) | 62.4011 | 2.01294 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.662732 | −0.0213562 | ||||||||
\(964\) | −3.73183 | −0.120194 | ||||||||
\(965\) | −11.1793 | −0.359876 | ||||||||
\(966\) | −2.10038 | −0.0675788 | ||||||||
\(967\) | −1.90804 | −0.0613583 | −0.0306792 | − | 0.999529i | \(-0.509767\pi\) | ||||
−0.0306792 | + | 0.999529i | \(0.509767\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.0558 | −0.547913 | ||||||||
\(970\) | 10.1678 | 0.326468 | ||||||||
\(971\) | −31.8996 | −1.02371 | −0.511854 | − | 0.859073i | \(-0.671041\pi\) | ||||
−0.511854 | + | 0.859073i | \(0.671041\pi\) | |||||||
\(972\) | 14.8536 | 0.476431 | ||||||||
\(973\) | −13.2039 | −0.423298 | ||||||||
\(974\) | 33.1611 | 1.06255 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.39312 | 0.0766018 | ||||||||
\(977\) | 28.5426 | 0.913159 | 0.456580 | − | 0.889683i | \(-0.349074\pi\) | ||||
0.456580 | + | 0.889683i | \(0.349074\pi\) | |||||||
\(978\) | 0.720270 | 0.0230317 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −7.44752 | −0.237781 | ||||||||
\(982\) | 23.9143 | 0.763136 | ||||||||
\(983\) | −36.0869 | −1.15099 | −0.575497 | − | 0.817804i | \(-0.695191\pi\) | ||||
−0.575497 | + | 0.817804i | \(0.695191\pi\) | |||||||
\(984\) | −1.64973 | −0.0525915 | ||||||||
\(985\) | 15.6216 | 0.497745 | ||||||||
\(986\) | −10.2927 | −0.327787 | ||||||||
\(987\) | −0.450654 | −0.0143445 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.12181 | −0.290057 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.2369 | −1.81819 | −0.909095 | − | 0.416589i | \(-0.863225\pi\) | ||||
−0.909095 | + | 0.416589i | \(0.863225\pi\) | |||||||
\(992\) | 9.66442 | 0.306846 | ||||||||
\(993\) | −17.7367 | −0.562856 | ||||||||
\(994\) | −0.585462 | −0.0185697 | ||||||||
\(995\) | −21.7220 | −0.688632 | ||||||||
\(996\) | 10.7434 | 0.340417 | ||||||||
\(997\) | −34.0638 | −1.07881 | −0.539406 | − | 0.842046i | \(-0.681351\pi\) | ||||
−0.539406 | + | 0.842046i | \(0.681351\pi\) | |||||||
\(998\) | −39.3864 | −1.24675 | ||||||||
\(999\) | 9.84208 | 0.311390 |
(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 | 8470.2.a.cn.1.2 | yes | 3 | |
11.10 | odd | 2 | 8470.2.a.ch.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.ch.1.2 | ✓ | 3 | 11.10 | odd | 2 | ||
8470.2.a.cn.1.2 | yes | 3 | 1.1 | even | 1 | trivial |