Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} - 36 x^{14} + 196 x^{13} + 498 x^{12} - 3101 x^{11} - 3150 x^{10} + 25368 x^{9} + 6763 x^{8} - 113788 x^{7} + 19731 x^{6} + 270913 x^{5} - 122680 x^{4} + \cdots - 66432 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(3.75055\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.75055 | 1.67730 | 0.838649 | − | 0.544672i | \(-0.183346\pi\) | ||||
0.838649 | + | 0.544672i | \(0.183346\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.75149 | −1.03996 | −0.519982 | − | 0.854177i | \(-0.674061\pi\) | ||||
−0.519982 | + | 0.854177i | \(0.674061\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.75055 | 1.18603 | ||||||||
\(11\) | 1.40678 | 0.424159 | 0.212080 | − | 0.977252i | \(-0.431976\pi\) | ||||
0.212080 | + | 0.977252i | \(0.431976\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −2.75149 | −0.735366 | ||||||||
\(15\) | 3.75055 | 0.968389 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.85100 | 1.17654 | 0.588270 | − | 0.808664i | \(-0.299809\pi\) | ||||
0.588270 | + | 0.808664i | \(0.299809\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −4.50999 | −1.03466 | −0.517331 | − | 0.855785i | \(-0.673074\pi\) | ||||
−0.517331 | + | 0.855785i | \(0.673074\pi\) | |||||||
\(20\) | 3.75055 | 0.838649 | ||||||||
\(21\) | −2.75149 | −0.600424 | ||||||||
\(22\) | 1.40678 | 0.299926 | ||||||||
\(23\) | −4.42327 | −0.922315 | −0.461157 | − | 0.887318i | \(-0.652566\pi\) | ||||
−0.461157 | + | 0.887318i | \(0.652566\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 9.06665 | 1.81333 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.75149 | −0.519982 | ||||||||
\(29\) | 6.19385 | 1.15017 | 0.575085 | − | 0.818094i | \(-0.304969\pi\) | ||||
0.575085 | + | 0.818094i | \(0.304969\pi\) | |||||||
\(30\) | 3.75055 | 0.684754 | ||||||||
\(31\) | −8.77193 | −1.57549 | −0.787743 | − | 0.616005i | \(-0.788750\pi\) | ||||
−0.787743 | + | 0.616005i | \(0.788750\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.40678 | 0.244889 | ||||||||
\(34\) | 4.85100 | 0.831940 | ||||||||
\(35\) | −10.3196 | −1.74433 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.12167 | 0.677599 | 0.338800 | − | 0.940859i | \(-0.389979\pi\) | ||||
0.338800 | + | 0.940859i | \(0.389979\pi\) | |||||||
\(38\) | −4.50999 | −0.731617 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 3.75055 | 0.593015 | ||||||||
\(41\) | −1.99643 | −0.311790 | −0.155895 | − | 0.987774i | \(-0.549826\pi\) | ||||
−0.155895 | + | 0.987774i | \(0.549826\pi\) | |||||||
\(42\) | −2.75149 | −0.424564 | ||||||||
\(43\) | 11.5347 | 1.75903 | 0.879515 | − | 0.475871i | \(-0.157867\pi\) | ||||
0.879515 | + | 0.475871i | \(0.157867\pi\) | |||||||
\(44\) | 1.40678 | 0.212080 | ||||||||
\(45\) | 3.75055 | 0.559099 | ||||||||
\(46\) | −4.42327 | −0.652175 | ||||||||
\(47\) | 11.3867 | 1.66092 | 0.830462 | − | 0.557076i | \(-0.188077\pi\) | ||||
0.830462 | + | 0.557076i | \(0.188077\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0.570676 | 0.0815252 | ||||||||
\(50\) | 9.06665 | 1.28222 | ||||||||
\(51\) | 4.85100 | 0.679276 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 6.40341 | 0.879576 | 0.439788 | − | 0.898102i | \(-0.355054\pi\) | ||||
0.439788 | + | 0.898102i | \(0.355054\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 5.27619 | 0.711442 | ||||||||
\(56\) | −2.75149 | −0.367683 | ||||||||
\(57\) | −4.50999 | −0.597363 | ||||||||
\(58\) | 6.19385 | 0.813293 | ||||||||
\(59\) | −9.19555 | −1.19716 | −0.598579 | − | 0.801064i | \(-0.704268\pi\) | ||||
−0.598579 | + | 0.801064i | \(0.704268\pi\) | |||||||
\(60\) | 3.75055 | 0.484194 | ||||||||
\(61\) | 14.5433 | 1.86208 | 0.931040 | − | 0.364918i | \(-0.118903\pi\) | ||||
0.931040 | + | 0.364918i | \(0.118903\pi\) | |||||||
\(62\) | −8.77193 | −1.11404 | ||||||||
\(63\) | −2.75149 | −0.346655 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.75055 | −0.465199 | ||||||||
\(66\) | 1.40678 | 0.173162 | ||||||||
\(67\) | 6.93725 | 0.847520 | 0.423760 | − | 0.905775i | \(-0.360710\pi\) | ||||
0.423760 | + | 0.905775i | \(0.360710\pi\) | |||||||
\(68\) | 4.85100 | 0.588270 | ||||||||
\(69\) | −4.42327 | −0.532499 | ||||||||
\(70\) | −10.3196 | −1.23343 | ||||||||
\(71\) | 14.4592 | 1.71599 | 0.857996 | − | 0.513656i | \(-0.171709\pi\) | ||||
0.857996 | + | 0.513656i | \(0.171709\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −5.76412 | −0.674639 | −0.337319 | − | 0.941390i | \(-0.609520\pi\) | ||||
−0.337319 | + | 0.941390i | \(0.609520\pi\) | |||||||
\(74\) | 4.12167 | 0.479135 | ||||||||
\(75\) | 9.06665 | 1.04693 | ||||||||
\(76\) | −4.50999 | −0.517331 | ||||||||
\(77\) | −3.87073 | −0.441111 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −3.87580 | −0.436061 | −0.218031 | − | 0.975942i | \(-0.569963\pi\) | ||||
−0.218031 | + | 0.975942i | \(0.569963\pi\) | |||||||
\(80\) | 3.75055 | 0.419325 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.99643 | −0.220469 | ||||||||
\(83\) | 10.5152 | 1.15420 | 0.577098 | − | 0.816675i | \(-0.304185\pi\) | ||||
0.577098 | + | 0.816675i | \(0.304185\pi\) | |||||||
\(84\) | −2.75149 | −0.300212 | ||||||||
\(85\) | 18.1939 | 1.97341 | ||||||||
\(86\) | 11.5347 | 1.24382 | ||||||||
\(87\) | 6.19385 | 0.664051 | ||||||||
\(88\) | 1.40678 | 0.149963 | ||||||||
\(89\) | 7.07682 | 0.750142 | 0.375071 | − | 0.926996i | \(-0.377618\pi\) | ||||
0.375071 | + | 0.926996i | \(0.377618\pi\) | |||||||
\(90\) | 3.75055 | 0.395343 | ||||||||
\(91\) | 2.75149 | 0.288434 | ||||||||
\(92\) | −4.42327 | −0.461157 | ||||||||
\(93\) | −8.77193 | −0.909607 | ||||||||
\(94\) | 11.3867 | 1.17445 | ||||||||
\(95\) | −16.9150 | −1.73544 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 17.8888 | 1.81633 | 0.908164 | − | 0.418614i | \(-0.137484\pi\) | ||||
0.908164 | + | 0.418614i | \(0.137484\pi\) | |||||||
\(98\) | 0.570676 | 0.0576470 | ||||||||
\(99\) | 1.40678 | 0.141386 | ||||||||
\(100\) | 9.06665 | 0.906665 | ||||||||
\(101\) | −7.86666 | −0.782762 | −0.391381 | − | 0.920229i | \(-0.628003\pi\) | ||||
−0.391381 | + | 0.920229i | \(0.628003\pi\) | |||||||
\(102\) | 4.85100 | 0.480321 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −10.3196 | −1.00709 | ||||||||
\(106\) | 6.40341 | 0.621954 | ||||||||
\(107\) | −11.1912 | −1.08189 | −0.540946 | − | 0.841058i | \(-0.681933\pi\) | ||||
−0.540946 | + | 0.841058i | \(0.681933\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −9.76772 | −0.935578 | −0.467789 | − | 0.883840i | \(-0.654949\pi\) | ||||
−0.467789 | + | 0.883840i | \(0.654949\pi\) | |||||||
\(110\) | 5.27619 | 0.503065 | ||||||||
\(111\) | 4.12167 | 0.391212 | ||||||||
\(112\) | −2.75149 | −0.259991 | ||||||||
\(113\) | −11.9388 | −1.12311 | −0.561555 | − | 0.827440i | \(-0.689797\pi\) | ||||
−0.561555 | + | 0.827440i | \(0.689797\pi\) | |||||||
\(114\) | −4.50999 | −0.422399 | ||||||||
\(115\) | −16.5897 | −1.54700 | ||||||||
\(116\) | 6.19385 | 0.575085 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −9.19555 | −0.846519 | ||||||||
\(119\) | −13.3475 | −1.22356 | ||||||||
\(120\) | 3.75055 | 0.342377 | ||||||||
\(121\) | −9.02098 | −0.820089 | ||||||||
\(122\) | 14.5433 | 1.31669 | ||||||||
\(123\) | −1.99643 | −0.180012 | ||||||||
\(124\) | −8.77193 | −0.787743 | ||||||||
\(125\) | 15.2522 | 1.36420 | ||||||||
\(126\) | −2.75149 | −0.245122 | ||||||||
\(127\) | 13.6249 | 1.20901 | 0.604506 | − | 0.796600i | \(-0.293370\pi\) | ||||
0.604506 | + | 0.796600i | \(0.293370\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 11.5347 | 1.01558 | ||||||||
\(130\) | −3.75055 | −0.328945 | ||||||||
\(131\) | −2.27585 | −0.198842 | −0.0994209 | − | 0.995045i | \(-0.531699\pi\) | ||||
−0.0994209 | + | 0.995045i | \(0.531699\pi\) | |||||||
\(132\) | 1.40678 | 0.122444 | ||||||||
\(133\) | 12.4092 | 1.07601 | ||||||||
\(134\) | 6.93725 | 0.599287 | ||||||||
\(135\) | 3.75055 | 0.322796 | ||||||||
\(136\) | 4.85100 | 0.415970 | ||||||||
\(137\) | −11.7402 | −1.00303 | −0.501516 | − | 0.865149i | \(-0.667224\pi\) | ||||
−0.501516 | + | 0.865149i | \(0.667224\pi\) | |||||||
\(138\) | −4.42327 | −0.376533 | ||||||||
\(139\) | 1.88819 | 0.160154 | 0.0800770 | − | 0.996789i | \(-0.474483\pi\) | ||||
0.0800770 | + | 0.996789i | \(0.474483\pi\) | |||||||
\(140\) | −10.3196 | −0.872165 | ||||||||
\(141\) | 11.3867 | 0.958934 | ||||||||
\(142\) | 14.4592 | 1.21339 | ||||||||
\(143\) | −1.40678 | −0.117641 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 23.2304 | 1.92918 | ||||||||
\(146\) | −5.76412 | −0.477042 | ||||||||
\(147\) | 0.570676 | 0.0470686 | ||||||||
\(148\) | 4.12167 | 0.338800 | ||||||||
\(149\) | 20.1646 | 1.65195 | 0.825973 | − | 0.563710i | \(-0.190627\pi\) | ||||
0.825973 | + | 0.563710i | \(0.190627\pi\) | |||||||
\(150\) | 9.06665 | 0.740289 | ||||||||
\(151\) | −4.02291 | −0.327380 | −0.163690 | − | 0.986512i | \(-0.552340\pi\) | ||||
−0.163690 | + | 0.986512i | \(0.552340\pi\) | |||||||
\(152\) | −4.50999 | −0.365808 | ||||||||
\(153\) | 4.85100 | 0.392180 | ||||||||
\(154\) | −3.87073 | −0.311912 | ||||||||
\(155\) | −32.8996 | −2.64256 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −12.3376 | −0.984645 | −0.492322 | − | 0.870413i | \(-0.663852\pi\) | ||||
−0.492322 | + | 0.870413i | \(0.663852\pi\) | |||||||
\(158\) | −3.87580 | −0.308342 | ||||||||
\(159\) | 6.40341 | 0.507823 | ||||||||
\(160\) | 3.75055 | 0.296507 | ||||||||
\(161\) | 12.1706 | 0.959174 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 6.87000 | 0.538100 | 0.269050 | − | 0.963126i | \(-0.413290\pi\) | ||||
0.269050 | + | 0.963126i | \(0.413290\pi\) | |||||||
\(164\) | −1.99643 | −0.155895 | ||||||||
\(165\) | 5.27619 | 0.410751 | ||||||||
\(166\) | 10.5152 | 0.816139 | ||||||||
\(167\) | −22.2739 | −1.72361 | −0.861803 | − | 0.507243i | \(-0.830665\pi\) | ||||
−0.861803 | + | 0.507243i | \(0.830665\pi\) | |||||||
\(168\) | −2.75149 | −0.212282 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 18.1939 | 1.39541 | ||||||||
\(171\) | −4.50999 | −0.344887 | ||||||||
\(172\) | 11.5347 | 0.879515 | ||||||||
\(173\) | 4.21358 | 0.320353 | 0.160176 | − | 0.987088i | \(-0.448794\pi\) | ||||
0.160176 | + | 0.987088i | \(0.448794\pi\) | |||||||
\(174\) | 6.19385 | 0.469555 | ||||||||
\(175\) | −24.9468 | −1.88580 | ||||||||
\(176\) | 1.40678 | 0.106040 | ||||||||
\(177\) | −9.19555 | −0.691180 | ||||||||
\(178\) | 7.07682 | 0.530430 | ||||||||
\(179\) | −25.2297 | −1.88576 | −0.942878 | − | 0.333139i | \(-0.891892\pi\) | ||||
−0.942878 | + | 0.333139i | \(0.891892\pi\) | |||||||
\(180\) | 3.75055 | 0.279550 | ||||||||
\(181\) | −1.22302 | −0.0909060 | −0.0454530 | − | 0.998966i | \(-0.514473\pi\) | ||||
−0.0454530 | + | 0.998966i | \(0.514473\pi\) | |||||||
\(182\) | 2.75149 | 0.203954 | ||||||||
\(183\) | 14.5433 | 1.07507 | ||||||||
\(184\) | −4.42327 | −0.326087 | ||||||||
\(185\) | 15.4586 | 1.13654 | ||||||||
\(186\) | −8.77193 | −0.643189 | ||||||||
\(187\) | 6.82428 | 0.499041 | ||||||||
\(188\) | 11.3867 | 0.830462 | ||||||||
\(189\) | −2.75149 | −0.200141 | ||||||||
\(190\) | −16.9150 | −1.22714 | ||||||||
\(191\) | −16.9267 | −1.22477 | −0.612385 | − | 0.790560i | \(-0.709790\pi\) | ||||
−0.612385 | + | 0.790560i | \(0.709790\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 22.1717 | 1.59595 | 0.797977 | − | 0.602688i | \(-0.205904\pi\) | ||||
0.797977 | + | 0.602688i | \(0.205904\pi\) | |||||||
\(194\) | 17.8888 | 1.28434 | ||||||||
\(195\) | −3.75055 | −0.268583 | ||||||||
\(196\) | 0.570676 | 0.0407626 | ||||||||
\(197\) | −4.41932 | −0.314864 | −0.157432 | − | 0.987530i | \(-0.550321\pi\) | ||||
−0.157432 | + | 0.987530i | \(0.550321\pi\) | |||||||
\(198\) | 1.40678 | 0.0999753 | ||||||||
\(199\) | −15.6553 | −1.10977 | −0.554887 | − | 0.831926i | \(-0.687238\pi\) | ||||
−0.554887 | + | 0.831926i | \(0.687238\pi\) | |||||||
\(200\) | 9.06665 | 0.641109 | ||||||||
\(201\) | 6.93725 | 0.489316 | ||||||||
\(202\) | −7.86666 | −0.553496 | ||||||||
\(203\) | −17.0423 | −1.19614 | ||||||||
\(204\) | 4.85100 | 0.339638 | ||||||||
\(205\) | −7.48771 | −0.522965 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −4.42327 | −0.307438 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −6.34455 | −0.438862 | ||||||||
\(210\) | −10.3196 | −0.712120 | ||||||||
\(211\) | −11.3565 | −0.781814 | −0.390907 | − | 0.920430i | \(-0.627839\pi\) | ||||
−0.390907 | + | 0.920430i | \(0.627839\pi\) | |||||||
\(212\) | 6.40341 | 0.439788 | ||||||||
\(213\) | 14.4592 | 0.990729 | ||||||||
\(214\) | −11.1912 | −0.765012 | ||||||||
\(215\) | 43.2616 | 2.95042 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 24.1358 | 1.63845 | ||||||||
\(218\) | −9.76772 | −0.661553 | ||||||||
\(219\) | −5.76412 | −0.389503 | ||||||||
\(220\) | 5.27619 | 0.355721 | ||||||||
\(221\) | −4.85100 | −0.326314 | ||||||||
\(222\) | 4.12167 | 0.276629 | ||||||||
\(223\) | −18.6322 | −1.24770 | −0.623852 | − | 0.781543i | \(-0.714433\pi\) | ||||
−0.623852 | + | 0.781543i | \(0.714433\pi\) | |||||||
\(224\) | −2.75149 | −0.183841 | ||||||||
\(225\) | 9.06665 | 0.604443 | ||||||||
\(226\) | −11.9388 | −0.794158 | ||||||||
\(227\) | −16.1448 | −1.07157 | −0.535785 | − | 0.844355i | \(-0.679984\pi\) | ||||
−0.535785 | + | 0.844355i | \(0.679984\pi\) | |||||||
\(228\) | −4.50999 | −0.298681 | ||||||||
\(229\) | 13.4124 | 0.886318 | 0.443159 | − | 0.896443i | \(-0.353858\pi\) | ||||
0.443159 | + | 0.896443i | \(0.353858\pi\) | |||||||
\(230\) | −16.5897 | −1.09389 | ||||||||
\(231\) | −3.87073 | −0.254675 | ||||||||
\(232\) | 6.19385 | 0.406646 | ||||||||
\(233\) | 6.75929 | 0.442816 | 0.221408 | − | 0.975181i | \(-0.428935\pi\) | ||||
0.221408 | + | 0.975181i | \(0.428935\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 42.7065 | 2.78586 | ||||||||
\(236\) | −9.19555 | −0.598579 | ||||||||
\(237\) | −3.87580 | −0.251760 | ||||||||
\(238\) | −13.3475 | −0.865187 | ||||||||
\(239\) | 12.9876 | 0.840099 | 0.420049 | − | 0.907501i | \(-0.362013\pi\) | ||||
0.420049 | + | 0.907501i | \(0.362013\pi\) | |||||||
\(240\) | 3.75055 | 0.242097 | ||||||||
\(241\) | −3.25984 | −0.209985 | −0.104992 | − | 0.994473i | \(-0.533482\pi\) | ||||
−0.104992 | + | 0.994473i | \(0.533482\pi\) | |||||||
\(242\) | −9.02098 | −0.579890 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 14.5433 | 0.931040 | ||||||||
\(245\) | 2.14035 | 0.136742 | ||||||||
\(246\) | −1.99643 | −0.127288 | ||||||||
\(247\) | 4.50999 | 0.286964 | ||||||||
\(248\) | −8.77193 | −0.557018 | ||||||||
\(249\) | 10.5152 | 0.666375 | ||||||||
\(250\) | 15.2522 | 0.964633 | ||||||||
\(251\) | −12.0501 | −0.760597 | −0.380299 | − | 0.924864i | \(-0.624179\pi\) | ||||
−0.380299 | + | 0.924864i | \(0.624179\pi\) | |||||||
\(252\) | −2.75149 | −0.173327 | ||||||||
\(253\) | −6.22255 | −0.391209 | ||||||||
\(254\) | 13.6249 | 0.854901 | ||||||||
\(255\) | 18.1939 | 1.13935 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.5708 | −0.846525 | −0.423263 | − | 0.906007i | \(-0.639115\pi\) | ||||
−0.423263 | + | 0.906007i | \(0.639115\pi\) | |||||||
\(258\) | 11.5347 | 0.718121 | ||||||||
\(259\) | −11.3407 | −0.704679 | ||||||||
\(260\) | −3.75055 | −0.232599 | ||||||||
\(261\) | 6.19385 | 0.383390 | ||||||||
\(262\) | −2.27585 | −0.140602 | ||||||||
\(263\) | 13.2870 | 0.819310 | 0.409655 | − | 0.912241i | \(-0.365649\pi\) | ||||
0.409655 | + | 0.912241i | \(0.365649\pi\) | |||||||
\(264\) | 1.40678 | 0.0865812 | ||||||||
\(265\) | 24.0163 | 1.47531 | ||||||||
\(266\) | 12.4092 | 0.760855 | ||||||||
\(267\) | 7.07682 | 0.433094 | ||||||||
\(268\) | 6.93725 | 0.423760 | ||||||||
\(269\) | −22.3684 | −1.36383 | −0.681913 | − | 0.731434i | \(-0.738852\pi\) | ||||
−0.681913 | + | 0.731434i | \(0.738852\pi\) | |||||||
\(270\) | 3.75055 | 0.228251 | ||||||||
\(271\) | 27.7261 | 1.68424 | 0.842121 | − | 0.539288i | \(-0.181307\pi\) | ||||
0.842121 | + | 0.539288i | \(0.181307\pi\) | |||||||
\(272\) | 4.85100 | 0.294135 | ||||||||
\(273\) | 2.75149 | 0.166528 | ||||||||
\(274\) | −11.7402 | −0.709250 | ||||||||
\(275\) | 12.7548 | 0.769141 | ||||||||
\(276\) | −4.42327 | −0.266249 | ||||||||
\(277\) | 19.8500 | 1.19267 | 0.596335 | − | 0.802735i | \(-0.296623\pi\) | ||||
0.596335 | + | 0.802735i | \(0.296623\pi\) | |||||||
\(278\) | 1.88819 | 0.113246 | ||||||||
\(279\) | −8.77193 | −0.525162 | ||||||||
\(280\) | −10.3196 | −0.616714 | ||||||||
\(281\) | 7.52692 | 0.449018 | 0.224509 | − | 0.974472i | \(-0.427922\pi\) | ||||
0.224509 | + | 0.974472i | \(0.427922\pi\) | |||||||
\(282\) | 11.3867 | 0.678069 | ||||||||
\(283\) | −23.8501 | −1.41774 | −0.708871 | − | 0.705338i | \(-0.750795\pi\) | ||||
−0.708871 | + | 0.705338i | \(0.750795\pi\) | |||||||
\(284\) | 14.4592 | 0.857996 | ||||||||
\(285\) | −16.9150 | −1.00196 | ||||||||
\(286\) | −1.40678 | −0.0831845 | ||||||||
\(287\) | 5.49315 | 0.324250 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 6.53220 | 0.384247 | ||||||||
\(290\) | 23.2304 | 1.36413 | ||||||||
\(291\) | 17.8888 | 1.04866 | ||||||||
\(292\) | −5.76412 | −0.337319 | ||||||||
\(293\) | −2.38503 | −0.139335 | −0.0696676 | − | 0.997570i | \(-0.522194\pi\) | ||||
−0.0696676 | + | 0.997570i | \(0.522194\pi\) | |||||||
\(294\) | 0.570676 | 0.0332825 | ||||||||
\(295\) | −34.4884 | −2.00799 | ||||||||
\(296\) | 4.12167 | 0.239567 | ||||||||
\(297\) | 1.40678 | 0.0816295 | ||||||||
\(298\) | 20.1646 | 1.16810 | ||||||||
\(299\) | 4.42327 | 0.255804 | ||||||||
\(300\) | 9.06665 | 0.523463 | ||||||||
\(301\) | −31.7377 | −1.82933 | ||||||||
\(302\) | −4.02291 | −0.231493 | ||||||||
\(303\) | −7.86666 | −0.451928 | ||||||||
\(304\) | −4.50999 | −0.258666 | ||||||||
\(305\) | 54.5454 | 3.12326 | ||||||||
\(306\) | 4.85100 | 0.277313 | ||||||||
\(307\) | −12.7915 | −0.730050 | −0.365025 | − | 0.930998i | \(-0.618940\pi\) | ||||
−0.365025 | + | 0.930998i | \(0.618940\pi\) | |||||||
\(308\) | −3.87073 | −0.220555 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −32.8996 | −1.86857 | ||||||||
\(311\) | −10.9137 | −0.618857 | −0.309428 | − | 0.950923i | \(-0.600138\pi\) | ||||
−0.309428 | + | 0.950923i | \(0.600138\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −5.14958 | −0.291072 | −0.145536 | − | 0.989353i | \(-0.546491\pi\) | ||||
−0.145536 | + | 0.989353i | \(0.546491\pi\) | |||||||
\(314\) | −12.3376 | −0.696249 | ||||||||
\(315\) | −10.3196 | −0.581443 | ||||||||
\(316\) | −3.87580 | −0.218031 | ||||||||
\(317\) | 34.4704 | 1.93605 | 0.968025 | − | 0.250855i | \(-0.0807118\pi\) | ||||
0.968025 | + | 0.250855i | \(0.0807118\pi\) | |||||||
\(318\) | 6.40341 | 0.359085 | ||||||||
\(319\) | 8.71337 | 0.487855 | ||||||||
\(320\) | 3.75055 | 0.209662 | ||||||||
\(321\) | −11.1912 | −0.624630 | ||||||||
\(322\) | 12.1706 | 0.678239 | ||||||||
\(323\) | −21.8780 | −1.21732 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −9.06665 | −0.502927 | ||||||||
\(326\) | 6.87000 | 0.380494 | ||||||||
\(327\) | −9.76772 | −0.540156 | ||||||||
\(328\) | −1.99643 | −0.110234 | ||||||||
\(329\) | −31.3304 | −1.72730 | ||||||||
\(330\) | 5.27619 | 0.290445 | ||||||||
\(331\) | 14.9647 | 0.822537 | 0.411268 | − | 0.911514i | \(-0.365086\pi\) | ||||
0.411268 | + | 0.911514i | \(0.365086\pi\) | |||||||
\(332\) | 10.5152 | 0.577098 | ||||||||
\(333\) | 4.12167 | 0.225866 | ||||||||
\(334\) | −22.2739 | −1.21877 | ||||||||
\(335\) | 26.0185 | 1.42154 | ||||||||
\(336\) | −2.75149 | −0.150106 | ||||||||
\(337\) | −25.1159 | −1.36815 | −0.684074 | − | 0.729413i | \(-0.739793\pi\) | ||||
−0.684074 | + | 0.729413i | \(0.739793\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −11.9388 | −0.648427 | ||||||||
\(340\) | 18.1939 | 0.986705 | ||||||||
\(341\) | −12.3402 | −0.668257 | ||||||||
\(342\) | −4.50999 | −0.243872 | ||||||||
\(343\) | 17.6902 | 0.955181 | ||||||||
\(344\) | 11.5347 | 0.621911 | ||||||||
\(345\) | −16.5897 | −0.893159 | ||||||||
\(346\) | 4.21358 | 0.226524 | ||||||||
\(347\) | −17.6919 | −0.949751 | −0.474875 | − | 0.880053i | \(-0.657507\pi\) | ||||
−0.474875 | + | 0.880053i | \(0.657507\pi\) | |||||||
\(348\) | 6.19385 | 0.332025 | ||||||||
\(349\) | −30.3608 | −1.62518 | −0.812589 | − | 0.582837i | \(-0.801943\pi\) | ||||
−0.812589 | + | 0.582837i | \(0.801943\pi\) | |||||||
\(350\) | −24.9468 | −1.33346 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 1.40678 | 0.0749815 | ||||||||
\(353\) | −28.0436 | −1.49261 | −0.746306 | − | 0.665603i | \(-0.768174\pi\) | ||||
−0.746306 | + | 0.665603i | \(0.768174\pi\) | |||||||
\(354\) | −9.19555 | −0.488738 | ||||||||
\(355\) | 54.2300 | 2.87823 | ||||||||
\(356\) | 7.07682 | 0.375071 | ||||||||
\(357\) | −13.3475 | −0.706422 | ||||||||
\(358\) | −25.2297 | −1.33343 | ||||||||
\(359\) | −15.6900 | −0.828084 | −0.414042 | − | 0.910258i | \(-0.635883\pi\) | ||||
−0.414042 | + | 0.910258i | \(0.635883\pi\) | |||||||
\(360\) | 3.75055 | 0.197672 | ||||||||
\(361\) | 1.34000 | 0.0705263 | ||||||||
\(362\) | −1.22302 | −0.0642803 | ||||||||
\(363\) | −9.02098 | −0.473478 | ||||||||
\(364\) | 2.75149 | 0.144217 | ||||||||
\(365\) | −21.6186 | −1.13157 | ||||||||
\(366\) | 14.5433 | 0.760191 | ||||||||
\(367\) | −33.6308 | −1.75552 | −0.877758 | − | 0.479105i | \(-0.840961\pi\) | ||||
−0.877758 | + | 0.479105i | \(0.840961\pi\) | |||||||
\(368\) | −4.42327 | −0.230579 | ||||||||
\(369\) | −1.99643 | −0.103930 | ||||||||
\(370\) | 15.4586 | 0.803652 | ||||||||
\(371\) | −17.6189 | −0.914727 | ||||||||
\(372\) | −8.77193 | −0.454803 | ||||||||
\(373\) | −17.0354 | −0.882059 | −0.441030 | − | 0.897493i | \(-0.645387\pi\) | ||||
−0.441030 | + | 0.897493i | \(0.645387\pi\) | |||||||
\(374\) | 6.82428 | 0.352875 | ||||||||
\(375\) | 15.2522 | 0.787619 | ||||||||
\(376\) | 11.3867 | 0.587225 | ||||||||
\(377\) | −6.19385 | −0.319000 | ||||||||
\(378\) | −2.75149 | −0.141521 | ||||||||
\(379\) | 24.5883 | 1.26301 | 0.631507 | − | 0.775370i | \(-0.282437\pi\) | ||||
0.631507 | + | 0.775370i | \(0.282437\pi\) | |||||||
\(380\) | −16.9150 | −0.867719 | ||||||||
\(381\) | 13.6249 | 0.698024 | ||||||||
\(382\) | −16.9267 | −0.866043 | ||||||||
\(383\) | −7.75115 | −0.396065 | −0.198033 | − | 0.980195i | \(-0.563455\pi\) | ||||
−0.198033 | + | 0.980195i | \(0.563455\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −14.5174 | −0.739874 | ||||||||
\(386\) | 22.1717 | 1.12851 | ||||||||
\(387\) | 11.5347 | 0.586343 | ||||||||
\(388\) | 17.8888 | 0.908164 | ||||||||
\(389\) | −31.5554 | −1.59992 | −0.799961 | − | 0.600052i | \(-0.795147\pi\) | ||||
−0.799961 | + | 0.600052i | \(0.795147\pi\) | |||||||
\(390\) | −3.75055 | −0.189917 | ||||||||
\(391\) | −21.4573 | −1.08514 | ||||||||
\(392\) | 0.570676 | 0.0288235 | ||||||||
\(393\) | −2.27585 | −0.114801 | ||||||||
\(394\) | −4.41932 | −0.222642 | ||||||||
\(395\) | −14.5364 | −0.731405 | ||||||||
\(396\) | 1.40678 | 0.0706932 | ||||||||
\(397\) | 18.1186 | 0.909346 | 0.454673 | − | 0.890658i | \(-0.349756\pi\) | ||||
0.454673 | + | 0.890658i | \(0.349756\pi\) | |||||||
\(398\) | −15.6553 | −0.784728 | ||||||||
\(399\) | 12.4092 | 0.621236 | ||||||||
\(400\) | 9.06665 | 0.453332 | ||||||||
\(401\) | −13.1398 | −0.656172 | −0.328086 | − | 0.944648i | \(-0.606404\pi\) | ||||
−0.328086 | + | 0.944648i | \(0.606404\pi\) | |||||||
\(402\) | 6.93725 | 0.345999 | ||||||||
\(403\) | 8.77193 | 0.436961 | ||||||||
\(404\) | −7.86666 | −0.391381 | ||||||||
\(405\) | 3.75055 | 0.186366 | ||||||||
\(406\) | −17.0423 | −0.845795 | ||||||||
\(407\) | 5.79828 | 0.287410 | ||||||||
\(408\) | 4.85100 | 0.240160 | ||||||||
\(409\) | −2.70569 | −0.133788 | −0.0668939 | − | 0.997760i | \(-0.521309\pi\) | ||||
−0.0668939 | + | 0.997760i | \(0.521309\pi\) | |||||||
\(410\) | −7.48771 | −0.369792 | ||||||||
\(411\) | −11.7402 | −0.579100 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | 25.3014 | 1.24500 | ||||||||
\(414\) | −4.42327 | −0.217392 | ||||||||
\(415\) | 39.4379 | 1.93593 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 1.88819 | 0.0924650 | ||||||||
\(418\) | −6.34455 | −0.310322 | ||||||||
\(419\) | 20.1362 | 0.983718 | 0.491859 | − | 0.870675i | \(-0.336318\pi\) | ||||
0.491859 | + | 0.870675i | \(0.336318\pi\) | |||||||
\(420\) | −10.3196 | −0.503545 | ||||||||
\(421\) | 8.01317 | 0.390538 | 0.195269 | − | 0.980750i | \(-0.437442\pi\) | ||||
0.195269 | + | 0.980750i | \(0.437442\pi\) | |||||||
\(422\) | −11.3565 | −0.552826 | ||||||||
\(423\) | 11.3867 | 0.553641 | ||||||||
\(424\) | 6.40341 | 0.310977 | ||||||||
\(425\) | 43.9823 | 2.13346 | ||||||||
\(426\) | 14.4592 | 0.700551 | ||||||||
\(427\) | −40.0157 | −1.93650 | ||||||||
\(428\) | −11.1912 | −0.540946 | ||||||||
\(429\) | −1.40678 | −0.0679199 | ||||||||
\(430\) | 43.2616 | 2.08626 | ||||||||
\(431\) | 26.7201 | 1.28706 | 0.643530 | − | 0.765421i | \(-0.277469\pi\) | ||||
0.643530 | + | 0.765421i | \(0.277469\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 24.8075 | 1.19217 | 0.596087 | − | 0.802920i | \(-0.296721\pi\) | ||||
0.596087 | + | 0.802920i | \(0.296721\pi\) | |||||||
\(434\) | 24.1358 | 1.15856 | ||||||||
\(435\) | 23.2304 | 1.11381 | ||||||||
\(436\) | −9.76772 | −0.467789 | ||||||||
\(437\) | 19.9489 | 0.954284 | ||||||||
\(438\) | −5.76412 | −0.275420 | ||||||||
\(439\) | −25.4088 | −1.21270 | −0.606348 | − | 0.795199i | \(-0.707366\pi\) | ||||
−0.606348 | + | 0.795199i | \(0.707366\pi\) | |||||||
\(440\) | 5.27619 | 0.251533 | ||||||||
\(441\) | 0.570676 | 0.0271751 | ||||||||
\(442\) | −4.85100 | −0.230739 | ||||||||
\(443\) | 30.5178 | 1.44995 | 0.724973 | − | 0.688778i | \(-0.241852\pi\) | ||||
0.724973 | + | 0.688778i | \(0.241852\pi\) | |||||||
\(444\) | 4.12167 | 0.195606 | ||||||||
\(445\) | 26.5420 | 1.25821 | ||||||||
\(446\) | −18.6322 | −0.882260 | ||||||||
\(447\) | 20.1646 | 0.953751 | ||||||||
\(448\) | −2.75149 | −0.129996 | ||||||||
\(449\) | −7.30121 | −0.344565 | −0.172283 | − | 0.985048i | \(-0.555114\pi\) | ||||
−0.172283 | + | 0.985048i | \(0.555114\pi\) | |||||||
\(450\) | 9.06665 | 0.427406 | ||||||||
\(451\) | −2.80853 | −0.132249 | ||||||||
\(452\) | −11.9388 | −0.561555 | ||||||||
\(453\) | −4.02291 | −0.189013 | ||||||||
\(454\) | −16.1448 | −0.757714 | ||||||||
\(455\) | 10.3196 | 0.483790 | ||||||||
\(456\) | −4.50999 | −0.211200 | ||||||||
\(457\) | −2.46773 | −0.115435 | −0.0577177 | − | 0.998333i | \(-0.518382\pi\) | ||||
−0.0577177 | + | 0.998333i | \(0.518382\pi\) | |||||||
\(458\) | 13.4124 | 0.626721 | ||||||||
\(459\) | 4.85100 | 0.226425 | ||||||||
\(460\) | −16.5897 | −0.773498 | ||||||||
\(461\) | −20.1050 | −0.936384 | −0.468192 | − | 0.883627i | \(-0.655095\pi\) | ||||
−0.468192 | + | 0.883627i | \(0.655095\pi\) | |||||||
\(462\) | −3.87073 | −0.180083 | ||||||||
\(463\) | −4.99320 | −0.232054 | −0.116027 | − | 0.993246i | \(-0.537016\pi\) | ||||
−0.116027 | + | 0.993246i | \(0.537016\pi\) | |||||||
\(464\) | 6.19385 | 0.287542 | ||||||||
\(465\) | −32.8996 | −1.52568 | ||||||||
\(466\) | 6.75929 | 0.313118 | ||||||||
\(467\) | 12.2694 | 0.567760 | 0.283880 | − | 0.958860i | \(-0.408378\pi\) | ||||
0.283880 | + | 0.958860i | \(0.408378\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −19.0877 | −0.881390 | ||||||||
\(470\) | 42.7065 | 1.96990 | ||||||||
\(471\) | −12.3376 | −0.568485 | ||||||||
\(472\) | −9.19555 | −0.423259 | ||||||||
\(473\) | 16.2268 | 0.746109 | ||||||||
\(474\) | −3.87580 | −0.178021 | ||||||||
\(475\) | −40.8905 | −1.87618 | ||||||||
\(476\) | −13.3475 | −0.611780 | ||||||||
\(477\) | 6.40341 | 0.293192 | ||||||||
\(478\) | 12.9876 | 0.594039 | ||||||||
\(479\) | −26.9745 | −1.23250 | −0.616248 | − | 0.787552i | \(-0.711348\pi\) | ||||
−0.616248 | + | 0.787552i | \(0.711348\pi\) | |||||||
\(480\) | 3.75055 | 0.171189 | ||||||||
\(481\) | −4.12167 | −0.187932 | ||||||||
\(482\) | −3.25984 | −0.148482 | ||||||||
\(483\) | 12.1706 | 0.553779 | ||||||||
\(484\) | −9.02098 | −0.410044 | ||||||||
\(485\) | 67.0927 | 3.04652 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −13.0202 | −0.590002 | −0.295001 | − | 0.955497i | \(-0.595320\pi\) | ||||
−0.295001 | + | 0.955497i | \(0.595320\pi\) | |||||||
\(488\) | 14.5433 | 0.658344 | ||||||||
\(489\) | 6.87000 | 0.310672 | ||||||||
\(490\) | 2.14035 | 0.0966913 | ||||||||
\(491\) | 9.57244 | 0.431998 | 0.215999 | − | 0.976394i | \(-0.430699\pi\) | ||||
0.215999 | + | 0.976394i | \(0.430699\pi\) | |||||||
\(492\) | −1.99643 | −0.0900060 | ||||||||
\(493\) | 30.0464 | 1.35322 | ||||||||
\(494\) | 4.50999 | 0.202914 | ||||||||
\(495\) | 5.27619 | 0.237147 | ||||||||
\(496\) | −8.77193 | −0.393871 | ||||||||
\(497\) | −39.7843 | −1.78457 | ||||||||
\(498\) | 10.5152 | 0.471198 | ||||||||
\(499\) | 39.4882 | 1.76773 | 0.883866 | − | 0.467740i | \(-0.154931\pi\) | ||||
0.883866 | + | 0.467740i | \(0.154931\pi\) | |||||||
\(500\) | 15.2522 | 0.682098 | ||||||||
\(501\) | −22.2739 | −0.995125 | ||||||||
\(502\) | −12.0501 | −0.537824 | ||||||||
\(503\) | −6.33659 | −0.282534 | −0.141267 | − | 0.989972i | \(-0.545118\pi\) | ||||
−0.141267 | + | 0.989972i | \(0.545118\pi\) | |||||||
\(504\) | −2.75149 | −0.122561 | ||||||||
\(505\) | −29.5043 | −1.31293 | ||||||||
\(506\) | −6.22255 | −0.276626 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 13.6249 | 0.604506 | ||||||||
\(509\) | −23.6417 | −1.04790 | −0.523950 | − | 0.851749i | \(-0.675542\pi\) | ||||
−0.523950 | + | 0.851749i | \(0.675542\pi\) | |||||||
\(510\) | 18.1939 | 0.805641 | ||||||||
\(511\) | 15.8599 | 0.701600 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.50999 | −0.199121 | ||||||||
\(514\) | −13.5708 | −0.598584 | ||||||||
\(515\) | 3.75055 | 0.165269 | ||||||||
\(516\) | 11.5347 | 0.507788 | ||||||||
\(517\) | 16.0186 | 0.704496 | ||||||||
\(518\) | −11.3407 | −0.498283 | ||||||||
\(519\) | 4.21358 | 0.184956 | ||||||||
\(520\) | −3.75055 | −0.164473 | ||||||||
\(521\) | −27.3043 | −1.19622 | −0.598111 | − | 0.801413i | \(-0.704082\pi\) | ||||
−0.598111 | + | 0.801413i | \(0.704082\pi\) | |||||||
\(522\) | 6.19385 | 0.271098 | ||||||||
\(523\) | 17.4180 | 0.761634 | 0.380817 | − | 0.924650i | \(-0.375643\pi\) | ||||
0.380817 | + | 0.924650i | \(0.375643\pi\) | |||||||
\(524\) | −2.27585 | −0.0994209 | ||||||||
\(525\) | −24.9468 | −1.08877 | ||||||||
\(526\) | 13.2870 | 0.579339 | ||||||||
\(527\) | −42.5526 | −1.85362 | ||||||||
\(528\) | 1.40678 | 0.0612221 | ||||||||
\(529\) | −3.43472 | −0.149336 | ||||||||
\(530\) | 24.0163 | 1.04320 | ||||||||
\(531\) | −9.19555 | −0.399053 | ||||||||
\(532\) | 12.4092 | 0.538006 | ||||||||
\(533\) | 1.99643 | 0.0864749 | ||||||||
\(534\) | 7.07682 | 0.306244 | ||||||||
\(535\) | −41.9731 | −1.81465 | ||||||||
\(536\) | 6.93725 | 0.299644 | ||||||||
\(537\) | −25.2297 | −1.08874 | ||||||||
\(538\) | −22.3684 | −0.964370 | ||||||||
\(539\) | 0.802815 | 0.0345797 | ||||||||
\(540\) | 3.75055 | 0.161398 | ||||||||
\(541\) | −10.6788 | −0.459119 | −0.229560 | − | 0.973295i | \(-0.573729\pi\) | ||||
−0.229560 | + | 0.973295i | \(0.573729\pi\) | |||||||
\(542\) | 27.7261 | 1.19094 | ||||||||
\(543\) | −1.22302 | −0.0524846 | ||||||||
\(544\) | 4.85100 | 0.207985 | ||||||||
\(545\) | −36.6343 | −1.56924 | ||||||||
\(546\) | 2.75149 | 0.117753 | ||||||||
\(547\) | −2.35594 | −0.100733 | −0.0503665 | − | 0.998731i | \(-0.516039\pi\) | ||||
−0.0503665 | + | 0.998731i | \(0.516039\pi\) | |||||||
\(548\) | −11.7402 | −0.501516 | ||||||||
\(549\) | 14.5433 | 0.620693 | ||||||||
\(550\) | 12.7548 | 0.543865 | ||||||||
\(551\) | −27.9342 | −1.19004 | ||||||||
\(552\) | −4.42327 | −0.188267 | ||||||||
\(553\) | 10.6642 | 0.453488 | ||||||||
\(554\) | 19.8500 | 0.843345 | ||||||||
\(555\) | 15.4586 | 0.656179 | ||||||||
\(556\) | 1.88819 | 0.0800770 | ||||||||
\(557\) | −15.2342 | −0.645492 | −0.322746 | − | 0.946486i | \(-0.604606\pi\) | ||||
−0.322746 | + | 0.946486i | \(0.604606\pi\) | |||||||
\(558\) | −8.77193 | −0.371345 | ||||||||
\(559\) | −11.5347 | −0.487867 | ||||||||
\(560\) | −10.3196 | −0.436083 | ||||||||
\(561\) | 6.82428 | 0.288121 | ||||||||
\(562\) | 7.52692 | 0.317504 | ||||||||
\(563\) | 28.8572 | 1.21619 | 0.608093 | − | 0.793866i | \(-0.291935\pi\) | ||||
0.608093 | + | 0.793866i | \(0.291935\pi\) | |||||||
\(564\) | 11.3867 | 0.479467 | ||||||||
\(565\) | −44.7772 | −1.88379 | ||||||||
\(566\) | −23.8501 | −1.00249 | ||||||||
\(567\) | −2.75149 | −0.115552 | ||||||||
\(568\) | 14.4592 | 0.606695 | ||||||||
\(569\) | 26.4704 | 1.10970 | 0.554849 | − | 0.831951i | \(-0.312776\pi\) | ||||
0.554849 | + | 0.831951i | \(0.312776\pi\) | |||||||
\(570\) | −16.9150 | −0.708489 | ||||||||
\(571\) | −13.0509 | −0.546163 | −0.273082 | − | 0.961991i | \(-0.588043\pi\) | ||||
−0.273082 | + | 0.961991i | \(0.588043\pi\) | |||||||
\(572\) | −1.40678 | −0.0588203 | ||||||||
\(573\) | −16.9267 | −0.707122 | ||||||||
\(574\) | 5.49315 | 0.229279 | ||||||||
\(575\) | −40.1042 | −1.67246 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 31.9196 | 1.32883 | 0.664415 | − | 0.747364i | \(-0.268681\pi\) | ||||
0.664415 | + | 0.747364i | \(0.268681\pi\) | |||||||
\(578\) | 6.53220 | 0.271704 | ||||||||
\(579\) | 22.1717 | 0.921424 | ||||||||
\(580\) | 23.2304 | 0.964589 | ||||||||
\(581\) | −28.9325 | −1.20032 | ||||||||
\(582\) | 17.8888 | 0.741513 | ||||||||
\(583\) | 9.00817 | 0.373080 | ||||||||
\(584\) | −5.76412 | −0.238521 | ||||||||
\(585\) | −3.75055 | −0.155066 | ||||||||
\(586\) | −2.38503 | −0.0985248 | ||||||||
\(587\) | −0.597564 | −0.0246641 | −0.0123321 | − | 0.999924i | \(-0.503926\pi\) | ||||
−0.0123321 | + | 0.999924i | \(0.503926\pi\) | |||||||
\(588\) | 0.570676 | 0.0235343 | ||||||||
\(589\) | 39.5613 | 1.63010 | ||||||||
\(590\) | −34.4884 | −1.41986 | ||||||||
\(591\) | −4.41932 | −0.181787 | ||||||||
\(592\) | 4.12167 | 0.169400 | ||||||||
\(593\) | 12.0593 | 0.495217 | 0.247608 | − | 0.968860i | \(-0.420355\pi\) | ||||
0.247608 | + | 0.968860i | \(0.420355\pi\) | |||||||
\(594\) | 1.40678 | 0.0577208 | ||||||||
\(595\) | −50.0604 | −2.05227 | ||||||||
\(596\) | 20.1646 | 0.825973 | ||||||||
\(597\) | −15.6553 | −0.640728 | ||||||||
\(598\) | 4.42327 | 0.180881 | ||||||||
\(599\) | −17.3205 | −0.707695 | −0.353847 | − | 0.935303i | \(-0.615127\pi\) | ||||
−0.353847 | + | 0.935303i | \(0.615127\pi\) | |||||||
\(600\) | 9.06665 | 0.370144 | ||||||||
\(601\) | −2.24987 | −0.0917740 | −0.0458870 | − | 0.998947i | \(-0.514611\pi\) | ||||
−0.0458870 | + | 0.998947i | \(0.514611\pi\) | |||||||
\(602\) | −31.7377 | −1.29353 | ||||||||
\(603\) | 6.93725 | 0.282507 | ||||||||
\(604\) | −4.02291 | −0.163690 | ||||||||
\(605\) | −33.8337 | −1.37553 | ||||||||
\(606\) | −7.86666 | −0.319561 | ||||||||
\(607\) | −15.6789 | −0.636386 | −0.318193 | − | 0.948026i | \(-0.603076\pi\) | ||||
−0.318193 | + | 0.948026i | \(0.603076\pi\) | |||||||
\(608\) | −4.50999 | −0.182904 | ||||||||
\(609\) | −17.0423 | −0.690589 | ||||||||
\(610\) | 54.5454 | 2.20848 | ||||||||
\(611\) | −11.3867 | −0.460657 | ||||||||
\(612\) | 4.85100 | 0.196090 | ||||||||
\(613\) | −2.57938 | −0.104180 | −0.0520900 | − | 0.998642i | \(-0.516588\pi\) | ||||
−0.0520900 | + | 0.998642i | \(0.516588\pi\) | |||||||
\(614\) | −12.7915 | −0.516223 | ||||||||
\(615\) | −7.48771 | −0.301934 | ||||||||
\(616\) | −3.87073 | −0.155956 | ||||||||
\(617\) | 45.9164 | 1.84853 | 0.924263 | − | 0.381756i | \(-0.124681\pi\) | ||||
0.924263 | + | 0.381756i | \(0.124681\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | 22.6301 | 0.909579 | 0.454790 | − | 0.890599i | \(-0.349714\pi\) | ||||
0.454790 | + | 0.890599i | \(0.349714\pi\) | |||||||
\(620\) | −32.8996 | −1.32128 | ||||||||
\(621\) | −4.42327 | −0.177500 | ||||||||
\(622\) | −10.9137 | −0.437598 | ||||||||
\(623\) | −19.4718 | −0.780120 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 11.8709 | 0.474835 | ||||||||
\(626\) | −5.14958 | −0.205819 | ||||||||
\(627\) | −6.34455 | −0.253377 | ||||||||
\(628\) | −12.3376 | −0.492322 | ||||||||
\(629\) | 19.9942 | 0.797223 | ||||||||
\(630\) | −10.3196 | −0.411143 | ||||||||
\(631\) | 37.5836 | 1.49618 | 0.748089 | − | 0.663598i | \(-0.230972\pi\) | ||||
0.748089 | + | 0.663598i | \(0.230972\pi\) | |||||||
\(632\) | −3.87580 | −0.154171 | ||||||||
\(633\) | −11.3565 | −0.451380 | ||||||||
\(634\) | 34.4704 | 1.36899 | ||||||||
\(635\) | 51.1008 | 2.02787 | ||||||||
\(636\) | 6.40341 | 0.253912 | ||||||||
\(637\) | −0.570676 | −0.0226110 | ||||||||
\(638\) | 8.71337 | 0.344966 | ||||||||
\(639\) | 14.4592 | 0.571998 | ||||||||
\(640\) | 3.75055 | 0.148254 | ||||||||
\(641\) | 18.8532 | 0.744658 | 0.372329 | − | 0.928101i | \(-0.378559\pi\) | ||||
0.372329 | + | 0.928101i | \(0.378559\pi\) | |||||||
\(642\) | −11.1912 | −0.441680 | ||||||||
\(643\) | −17.7100 | −0.698413 | −0.349207 | − | 0.937046i | \(-0.613549\pi\) | ||||
−0.349207 | + | 0.937046i | \(0.613549\pi\) | |||||||
\(644\) | 12.1706 | 0.479587 | ||||||||
\(645\) | 43.2616 | 1.70342 | ||||||||
\(646\) | −21.8780 | −0.860777 | ||||||||
\(647\) | −5.52460 | −0.217194 | −0.108597 | − | 0.994086i | \(-0.534636\pi\) | ||||
−0.108597 | + | 0.994086i | \(0.534636\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −12.9361 | −0.507786 | ||||||||
\(650\) | −9.06665 | −0.355623 | ||||||||
\(651\) | 24.1358 | 0.945958 | ||||||||
\(652\) | 6.87000 | 0.269050 | ||||||||
\(653\) | −37.9594 | −1.48546 | −0.742732 | − | 0.669589i | \(-0.766470\pi\) | ||||
−0.742732 | + | 0.669589i | \(0.766470\pi\) | |||||||
\(654\) | −9.76772 | −0.381948 | ||||||||
\(655\) | −8.53569 | −0.333517 | ||||||||
\(656\) | −1.99643 | −0.0779474 | ||||||||
\(657\) | −5.76412 | −0.224880 | ||||||||
\(658\) | −31.3304 | −1.22139 | ||||||||
\(659\) | −12.5990 | −0.490788 | −0.245394 | − | 0.969423i | \(-0.578917\pi\) | ||||
−0.245394 | + | 0.969423i | \(0.578917\pi\) | |||||||
\(660\) | 5.27619 | 0.205376 | ||||||||
\(661\) | −27.3101 | −1.06224 | −0.531120 | − | 0.847297i | \(-0.678228\pi\) | ||||
−0.531120 | + | 0.847297i | \(0.678228\pi\) | |||||||
\(662\) | 14.9647 | 0.581621 | ||||||||
\(663\) | −4.85100 | −0.188397 | ||||||||
\(664\) | 10.5152 | 0.408070 | ||||||||
\(665\) | 46.5413 | 1.80479 | ||||||||
\(666\) | 4.12167 | 0.159712 | ||||||||
\(667\) | −27.3971 | −1.06082 | ||||||||
\(668\) | −22.2739 | −0.861803 | ||||||||
\(669\) | −18.6322 | −0.720362 | ||||||||
\(670\) | 26.0185 | 1.00518 | ||||||||
\(671\) | 20.4592 | 0.789819 | ||||||||
\(672\) | −2.75149 | −0.106141 | ||||||||
\(673\) | 10.1922 | 0.392880 | 0.196440 | − | 0.980516i | \(-0.437062\pi\) | ||||
0.196440 | + | 0.980516i | \(0.437062\pi\) | |||||||
\(674\) | −25.1159 | −0.967427 | ||||||||
\(675\) | 9.06665 | 0.348975 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 31.7391 | 1.21983 | 0.609917 | − | 0.792466i | \(-0.291203\pi\) | ||||
0.609917 | + | 0.792466i | \(0.291203\pi\) | |||||||
\(678\) | −11.9388 | −0.458507 | ||||||||
\(679\) | −49.2207 | −1.88892 | ||||||||
\(680\) | 18.1939 | 0.697705 | ||||||||
\(681\) | −16.1448 | −0.618671 | ||||||||
\(682\) | −12.3402 | −0.472529 | ||||||||
\(683\) | 9.40345 | 0.359813 | 0.179906 | − | 0.983684i | \(-0.442421\pi\) | ||||
0.179906 | + | 0.983684i | \(0.442421\pi\) | |||||||
\(684\) | −4.50999 | −0.172444 | ||||||||
\(685\) | −44.0322 | −1.68238 | ||||||||
\(686\) | 17.6902 | 0.675415 | ||||||||
\(687\) | 13.4124 | 0.511716 | ||||||||
\(688\) | 11.5347 | 0.439758 | ||||||||
\(689\) | −6.40341 | −0.243950 | ||||||||
\(690\) | −16.5897 | −0.631559 | ||||||||
\(691\) | −29.7503 | −1.13175 | −0.565877 | − | 0.824490i | \(-0.691462\pi\) | ||||
−0.565877 | + | 0.824490i | \(0.691462\pi\) | |||||||
\(692\) | 4.21358 | 0.160176 | ||||||||
\(693\) | −3.87073 | −0.147037 | ||||||||
\(694\) | −17.6919 | −0.671575 | ||||||||
\(695\) | 7.08175 | 0.268626 | ||||||||
\(696\) | 6.19385 | 0.234777 | ||||||||
\(697\) | −9.68468 | −0.366833 | ||||||||
\(698\) | −30.3608 | −1.14917 | ||||||||
\(699\) | 6.75929 | 0.255660 | ||||||||
\(700\) | −24.9468 | −0.942899 | ||||||||
\(701\) | −27.3803 | −1.03414 | −0.517070 | − | 0.855943i | \(-0.672977\pi\) | ||||
−0.517070 | + | 0.855943i | \(0.672977\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −18.5887 | −0.701086 | ||||||||
\(704\) | 1.40678 | 0.0530199 | ||||||||
\(705\) | 42.7065 | 1.60842 | ||||||||
\(706\) | −28.0436 | −1.05544 | ||||||||
\(707\) | 21.6450 | 0.814044 | ||||||||
\(708\) | −9.19555 | −0.345590 | ||||||||
\(709\) | 16.0203 | 0.601655 | 0.300827 | − | 0.953679i | \(-0.402737\pi\) | ||||
0.300827 | + | 0.953679i | \(0.402737\pi\) | |||||||
\(710\) | 54.2300 | 2.03522 | ||||||||
\(711\) | −3.87580 | −0.145354 | ||||||||
\(712\) | 7.07682 | 0.265215 | ||||||||
\(713\) | 38.8006 | 1.45309 | ||||||||
\(714\) | −13.3475 | −0.499516 | ||||||||
\(715\) | −5.27619 | −0.197319 | ||||||||
\(716\) | −25.2297 | −0.942878 | ||||||||
\(717\) | 12.9876 | 0.485031 | ||||||||
\(718\) | −15.6900 | −0.585544 | ||||||||
\(719\) | −21.7279 | −0.810314 | −0.405157 | − | 0.914247i | \(-0.632783\pi\) | ||||
−0.405157 | + | 0.914247i | \(0.632783\pi\) | |||||||
\(720\) | 3.75055 | 0.139775 | ||||||||
\(721\) | −2.75149 | −0.102471 | ||||||||
\(722\) | 1.34000 | 0.0498696 | ||||||||
\(723\) | −3.25984 | −0.121235 | ||||||||
\(724\) | −1.22302 | −0.0454530 | ||||||||
\(725\) | 56.1575 | 2.08564 | ||||||||
\(726\) | −9.02098 | −0.334800 | ||||||||
\(727\) | −15.2089 | −0.564068 | −0.282034 | − | 0.959404i | \(-0.591009\pi\) | ||||
−0.282034 | + | 0.959404i | \(0.591009\pi\) | |||||||
\(728\) | 2.75149 | 0.101977 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −21.6186 | −0.800141 | ||||||||
\(731\) | 55.9550 | 2.06957 | ||||||||
\(732\) | 14.5433 | 0.537536 | ||||||||
\(733\) | −12.2944 | −0.454104 | −0.227052 | − | 0.973883i | \(-0.572909\pi\) | ||||
−0.227052 | + | 0.973883i | \(0.572909\pi\) | |||||||
\(734\) | −33.6308 | −1.24134 | ||||||||
\(735\) | 2.14035 | 0.0789481 | ||||||||
\(736\) | −4.42327 | −0.163044 | ||||||||
\(737\) | 9.75917 | 0.359484 | ||||||||
\(738\) | −1.99643 | −0.0734896 | ||||||||
\(739\) | −41.3497 | −1.52107 | −0.760537 | − | 0.649294i | \(-0.775064\pi\) | ||||
−0.760537 | + | 0.649294i | \(0.775064\pi\) | |||||||
\(740\) | 15.4586 | 0.568268 | ||||||||
\(741\) | 4.50999 | 0.165679 | ||||||||
\(742\) | −17.6189 | −0.646810 | ||||||||
\(743\) | −26.0556 | −0.955888 | −0.477944 | − | 0.878390i | \(-0.658618\pi\) | ||||
−0.477944 | + | 0.878390i | \(0.658618\pi\) | |||||||
\(744\) | −8.77193 | −0.321595 | ||||||||
\(745\) | 75.6283 | 2.77080 | ||||||||
\(746\) | −17.0354 | −0.623710 | ||||||||
\(747\) | 10.5152 | 0.384732 | ||||||||
\(748\) | 6.82428 | 0.249520 | ||||||||
\(749\) | 30.7923 | 1.12513 | ||||||||
\(750\) | 15.2522 | 0.556931 | ||||||||
\(751\) | 32.2491 | 1.17679 | 0.588394 | − | 0.808575i | \(-0.299761\pi\) | ||||
0.588394 | + | 0.808575i | \(0.299761\pi\) | |||||||
\(752\) | 11.3867 | 0.415231 | ||||||||
\(753\) | −12.0501 | −0.439131 | ||||||||
\(754\) | −6.19385 | −0.225567 | ||||||||
\(755\) | −15.0882 | −0.549114 | ||||||||
\(756\) | −2.75149 | −0.100071 | ||||||||
\(757\) | −42.6448 | −1.54995 | −0.774977 | − | 0.631990i | \(-0.782238\pi\) | ||||
−0.774977 | + | 0.631990i | \(0.782238\pi\) | |||||||
\(758\) | 24.5883 | 0.893086 | ||||||||
\(759\) | −6.22255 | −0.225864 | ||||||||
\(760\) | −16.9150 | −0.613570 | ||||||||
\(761\) | −33.4844 | −1.21381 | −0.606904 | − | 0.794775i | \(-0.707589\pi\) | ||||
−0.606904 | + | 0.794775i | \(0.707589\pi\) | |||||||
\(762\) | 13.6249 | 0.493577 | ||||||||
\(763\) | 26.8757 | 0.972967 | ||||||||
\(764\) | −16.9267 | −0.612385 | ||||||||
\(765\) | 18.1939 | 0.657803 | ||||||||
\(766\) | −7.75115 | −0.280060 | ||||||||
\(767\) | 9.19555 | 0.332032 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −4.78372 | −0.172505 | −0.0862527 | − | 0.996273i | \(-0.527489\pi\) | ||||
−0.0862527 | + | 0.996273i | \(0.527489\pi\) | |||||||
\(770\) | −14.5174 | −0.523170 | ||||||||
\(771\) | −13.5708 | −0.488741 | ||||||||
\(772\) | 22.1717 | 0.797977 | ||||||||
\(773\) | −9.82103 | −0.353238 | −0.176619 | − | 0.984279i | \(-0.556516\pi\) | ||||
−0.176619 | + | 0.984279i | \(0.556516\pi\) | |||||||
\(774\) | 11.5347 | 0.414607 | ||||||||
\(775\) | −79.5320 | −2.85687 | ||||||||
\(776\) | 17.8888 | 0.642169 | ||||||||
\(777\) | −11.3407 | −0.406846 | ||||||||
\(778\) | −31.5554 | −1.13132 | ||||||||
\(779\) | 9.00387 | 0.322597 | ||||||||
\(780\) | −3.75055 | −0.134291 | ||||||||
\(781\) | 20.3409 | 0.727855 | ||||||||
\(782\) | −21.4573 | −0.767310 | ||||||||
\(783\) | 6.19385 | 0.221350 | ||||||||
\(784\) | 0.570676 | 0.0203813 | ||||||||
\(785\) | −46.2727 | −1.65154 | ||||||||
\(786\) | −2.27585 | −0.0811769 | ||||||||
\(787\) | 26.0077 | 0.927073 | 0.463536 | − | 0.886078i | \(-0.346580\pi\) | ||||
0.463536 | + | 0.886078i | \(0.346580\pi\) | |||||||
\(788\) | −4.41932 | −0.157432 | ||||||||
\(789\) | 13.2870 | 0.473029 | ||||||||
\(790\) | −14.5364 | −0.517181 | ||||||||
\(791\) | 32.8495 | 1.16799 | ||||||||
\(792\) | 1.40678 | 0.0499877 | ||||||||
\(793\) | −14.5433 | −0.516448 | ||||||||
\(794\) | 18.1186 | 0.643005 | ||||||||
\(795\) | 24.0163 | 0.851771 | ||||||||
\(796\) | −15.6553 | −0.554887 | ||||||||
\(797\) | −1.21383 | −0.0429961 | −0.0214980 | − | 0.999769i | \(-0.506844\pi\) | ||||
−0.0214980 | + | 0.999769i | \(0.506844\pi\) | |||||||
\(798\) | 12.4092 | 0.439280 | ||||||||
\(799\) | 55.2370 | 1.95414 | ||||||||
\(800\) | 9.06665 | 0.320554 | ||||||||
\(801\) | 7.07682 | 0.250047 | ||||||||
\(802\) | −13.1398 | −0.463984 | ||||||||
\(803\) | −8.10883 | −0.286154 | ||||||||
\(804\) | 6.93725 | 0.244658 | ||||||||
\(805\) | 45.6463 | 1.60882 | ||||||||
\(806\) | 8.77193 | 0.308978 | ||||||||
\(807\) | −22.3684 | −0.787405 | ||||||||
\(808\) | −7.86666 | −0.276748 | ||||||||
\(809\) | −36.6451 | −1.28837 | −0.644186 | − | 0.764869i | \(-0.722804\pi\) | ||||
−0.644186 | + | 0.764869i | \(0.722804\pi\) | |||||||
\(810\) | 3.75055 | 0.131781 | ||||||||
\(811\) | 39.2571 | 1.37850 | 0.689252 | − | 0.724522i | \(-0.257939\pi\) | ||||
0.689252 | + | 0.724522i | \(0.257939\pi\) | |||||||
\(812\) | −17.0423 | −0.598068 | ||||||||
\(813\) | 27.7261 | 0.972398 | ||||||||
\(814\) | 5.79828 | 0.203230 | ||||||||
\(815\) | 25.7663 | 0.902554 | ||||||||
\(816\) | 4.85100 | 0.169819 | ||||||||
\(817\) | −52.0215 | −1.82000 | ||||||||
\(818\) | −2.70569 | −0.0946023 | ||||||||
\(819\) | 2.75149 | 0.0961447 | ||||||||
\(820\) | −7.48771 | −0.261482 | ||||||||
\(821\) | −13.8433 | −0.483136 | −0.241568 | − | 0.970384i | \(-0.577662\pi\) | ||||
−0.241568 | + | 0.970384i | \(0.577662\pi\) | |||||||
\(822\) | −11.7402 | −0.409486 | ||||||||
\(823\) | 14.6944 | 0.512215 | 0.256107 | − | 0.966648i | \(-0.417560\pi\) | ||||
0.256107 | + | 0.966648i | \(0.417560\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | 12.7548 | 0.444064 | ||||||||
\(826\) | 25.3014 | 0.880349 | ||||||||
\(827\) | 22.2035 | 0.772092 | 0.386046 | − | 0.922480i | \(-0.373841\pi\) | ||||
0.386046 | + | 0.922480i | \(0.373841\pi\) | |||||||
\(828\) | −4.42327 | −0.153719 | ||||||||
\(829\) | 36.1214 | 1.25455 | 0.627273 | − | 0.778799i | \(-0.284171\pi\) | ||||
0.627273 | + | 0.778799i | \(0.284171\pi\) | |||||||
\(830\) | 39.4379 | 1.36891 | ||||||||
\(831\) | 19.8500 | 0.688589 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 2.76835 | 0.0959177 | ||||||||
\(834\) | 1.88819 | 0.0653826 | ||||||||
\(835\) | −83.5395 | −2.89100 | ||||||||
\(836\) | −6.34455 | −0.219431 | ||||||||
\(837\) | −8.77193 | −0.303202 | ||||||||
\(838\) | 20.1362 | 0.695594 | ||||||||
\(839\) | 49.0119 | 1.69208 | 0.846040 | − | 0.533120i | \(-0.178981\pi\) | ||||
0.846040 | + | 0.533120i | \(0.178981\pi\) | |||||||
\(840\) | −10.3196 | −0.356060 | ||||||||
\(841\) | 9.36381 | 0.322890 | ||||||||
\(842\) | 8.01317 | 0.276152 | ||||||||
\(843\) | 7.52692 | 0.259241 | ||||||||
\(844\) | −11.3565 | −0.390907 | ||||||||
\(845\) | 3.75055 | 0.129023 | ||||||||
\(846\) | 11.3867 | 0.391483 | ||||||||
\(847\) | 24.8211 | 0.852863 | ||||||||
\(848\) | 6.40341 | 0.219894 | ||||||||
\(849\) | −23.8501 | −0.818534 | ||||||||
\(850\) | 43.9823 | 1.50858 | ||||||||
\(851\) | −18.2313 | −0.624960 | ||||||||
\(852\) | 14.4592 | 0.495364 | ||||||||
\(853\) | −17.5841 | −0.602068 | −0.301034 | − | 0.953613i | \(-0.597332\pi\) | ||||
−0.301034 | + | 0.953613i | \(0.597332\pi\) | |||||||
\(854\) | −40.0157 | −1.36931 | ||||||||
\(855\) | −16.9150 | −0.578479 | ||||||||
\(856\) | −11.1912 | −0.382506 | ||||||||
\(857\) | 49.6481 | 1.69595 | 0.847973 | − | 0.530040i | \(-0.177823\pi\) | ||||
0.847973 | + | 0.530040i | \(0.177823\pi\) | |||||||
\(858\) | −1.40678 | −0.0480266 | ||||||||
\(859\) | −32.3009 | −1.10209 | −0.551046 | − | 0.834475i | \(-0.685771\pi\) | ||||
−0.551046 | + | 0.834475i | \(0.685771\pi\) | |||||||
\(860\) | 43.2616 | 1.47521 | ||||||||
\(861\) | 5.49315 | 0.187206 | ||||||||
\(862\) | 26.7201 | 0.910089 | ||||||||
\(863\) | 36.0519 | 1.22722 | 0.613610 | − | 0.789609i | \(-0.289717\pi\) | ||||
0.613610 | + | 0.789609i | \(0.289717\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 15.8033 | 0.537327 | ||||||||
\(866\) | 24.8075 | 0.842994 | ||||||||
\(867\) | 6.53220 | 0.221845 | ||||||||
\(868\) | 24.1358 | 0.819224 | ||||||||
\(869\) | −5.45239 | −0.184960 | ||||||||
\(870\) | 23.2304 | 0.787583 | ||||||||
\(871\) | −6.93725 | −0.235060 | ||||||||
\(872\) | −9.76772 | −0.330777 | ||||||||
\(873\) | 17.8888 | 0.605443 | ||||||||
\(874\) | 19.9489 | 0.674781 | ||||||||
\(875\) | −41.9662 | −1.41872 | ||||||||
\(876\) | −5.76412 | −0.194751 | ||||||||
\(877\) | −7.30397 | −0.246638 | −0.123319 | − | 0.992367i | \(-0.539354\pi\) | ||||
−0.123319 | + | 0.992367i | \(0.539354\pi\) | |||||||
\(878\) | −25.4088 | −0.857506 | ||||||||
\(879\) | −2.38503 | −0.0804452 | ||||||||
\(880\) | 5.27619 | 0.177860 | ||||||||
\(881\) | 31.8389 | 1.07268 | 0.536340 | − | 0.844002i | \(-0.319806\pi\) | ||||
0.536340 | + | 0.844002i | \(0.319806\pi\) | |||||||
\(882\) | 0.570676 | 0.0192157 | ||||||||
\(883\) | 38.2054 | 1.28571 | 0.642857 | − | 0.765986i | \(-0.277749\pi\) | ||||
0.642857 | + | 0.765986i | \(0.277749\pi\) | |||||||
\(884\) | −4.85100 | −0.163157 | ||||||||
\(885\) | −34.4884 | −1.15931 | ||||||||
\(886\) | 30.5178 | 1.02527 | ||||||||
\(887\) | 16.8560 | 0.565969 | 0.282985 | − | 0.959124i | \(-0.408675\pi\) | ||||
0.282985 | + | 0.959124i | \(0.408675\pi\) | |||||||
\(888\) | 4.12167 | 0.138314 | ||||||||
\(889\) | −37.4887 | −1.25733 | ||||||||
\(890\) | 26.5420 | 0.889690 | ||||||||
\(891\) | 1.40678 | 0.0471288 | ||||||||
\(892\) | −18.6322 | −0.623852 | ||||||||
\(893\) | −51.3540 | −1.71849 | ||||||||
\(894\) | 20.1646 | 0.674404 | ||||||||
\(895\) | −94.6253 | −3.16297 | ||||||||
\(896\) | −2.75149 | −0.0919207 | ||||||||
\(897\) | 4.42327 | 0.147689 | ||||||||
\(898\) | −7.30121 | −0.243645 | ||||||||
\(899\) | −54.3320 | −1.81208 | ||||||||
\(900\) | 9.06665 | 0.302222 | ||||||||
\(901\) | 31.0629 | 1.03486 | ||||||||
\(902\) | −2.80853 | −0.0935139 | ||||||||
\(903\) | −31.7377 | −1.05616 | ||||||||
\(904\) | −11.9388 | −0.397079 | ||||||||
\(905\) | −4.58698 | −0.152477 | ||||||||
\(906\) | −4.02291 | −0.133652 | ||||||||
\(907\) | −27.5492 | −0.914756 | −0.457378 | − | 0.889272i | \(-0.651211\pi\) | ||||
−0.457378 | + | 0.889272i | \(0.651211\pi\) | |||||||
\(908\) | −16.1448 | −0.535785 | ||||||||
\(909\) | −7.86666 | −0.260921 | ||||||||
\(910\) | 10.3196 | 0.342091 | ||||||||
\(911\) | −23.2797 | −0.771291 | −0.385646 | − | 0.922647i | \(-0.626021\pi\) | ||||
−0.385646 | + | 0.922647i | \(0.626021\pi\) | |||||||
\(912\) | −4.50999 | −0.149341 | ||||||||
\(913\) | 14.7926 | 0.489563 | ||||||||
\(914\) | −2.46773 | −0.0816252 | ||||||||
\(915\) | 54.5454 | 1.80322 | ||||||||
\(916\) | 13.4124 | 0.443159 | ||||||||
\(917\) | 6.26197 | 0.206788 | ||||||||
\(918\) | 4.85100 | 0.160107 | ||||||||
\(919\) | 41.8555 | 1.38068 | 0.690342 | − | 0.723483i | \(-0.257460\pi\) | ||||
0.690342 | + | 0.723483i | \(0.257460\pi\) | |||||||
\(920\) | −16.5897 | −0.546946 | ||||||||
\(921\) | −12.7915 | −0.421495 | ||||||||
\(922\) | −20.1050 | −0.662124 | ||||||||
\(923\) | −14.4592 | −0.475931 | ||||||||
\(924\) | −3.87073 | −0.127338 | ||||||||
\(925\) | 37.3698 | 1.22871 | ||||||||
\(926\) | −4.99320 | −0.164087 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 6.19385 | 0.203323 | ||||||||
\(929\) | 3.17728 | 0.104243 | 0.0521216 | − | 0.998641i | \(-0.483402\pi\) | ||||
0.0521216 | + | 0.998641i | \(0.483402\pi\) | |||||||
\(930\) | −32.8996 | −1.07882 | ||||||||
\(931\) | −2.57374 | −0.0843511 | ||||||||
\(932\) | 6.75929 | 0.221408 | ||||||||
\(933\) | −10.9137 | −0.357297 | ||||||||
\(934\) | 12.2694 | 0.401467 | ||||||||
\(935\) | 25.5948 | 0.837040 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 14.2743 | 0.466322 | 0.233161 | − | 0.972438i | \(-0.425093\pi\) | ||||
0.233161 | + | 0.972438i | \(0.425093\pi\) | |||||||
\(938\) | −19.0877 | −0.623237 | ||||||||
\(939\) | −5.14958 | −0.168050 | ||||||||
\(940\) | 42.7065 | 1.39293 | ||||||||
\(941\) | 17.1305 | 0.558439 | 0.279220 | − | 0.960227i | \(-0.409924\pi\) | ||||
0.279220 | + | 0.960227i | \(0.409924\pi\) | |||||||
\(942\) | −12.3376 | −0.401980 | ||||||||
\(943\) | 8.83074 | 0.287568 | ||||||||
\(944\) | −9.19555 | −0.299290 | ||||||||
\(945\) | −10.3196 | −0.335696 | ||||||||
\(946\) | 16.2268 | 0.527579 | ||||||||
\(947\) | 3.68806 | 0.119846 | 0.0599229 | − | 0.998203i | \(-0.480915\pi\) | ||||
0.0599229 | + | 0.998203i | \(0.480915\pi\) | |||||||
\(948\) | −3.87580 | −0.125880 | ||||||||
\(949\) | 5.76412 | 0.187111 | ||||||||
\(950\) | −40.8905 | −1.32666 | ||||||||
\(951\) | 34.4704 | 1.11778 | ||||||||
\(952\) | −13.3475 | −0.432594 | ||||||||
\(953\) | −26.0185 | −0.842820 | −0.421410 | − | 0.906870i | \(-0.638465\pi\) | ||||
−0.421410 | + | 0.906870i | \(0.638465\pi\) | |||||||
\(954\) | 6.40341 | 0.207318 | ||||||||
\(955\) | −63.4844 | −2.05431 | ||||||||
\(956\) | 12.9876 | 0.420049 | ||||||||
\(957\) | 8.71337 | 0.281663 | ||||||||
\(958\) | −26.9745 | −0.871506 | ||||||||
\(959\) | 32.3029 | 1.04312 | ||||||||
\(960\) | 3.75055 | 0.121049 | ||||||||
\(961\) | 45.9468 | 1.48215 | ||||||||
\(962\) | −4.12167 | −0.132888 | ||||||||
\(963\) | −11.1912 | −0.360630 | ||||||||
\(964\) | −3.25984 | −0.104992 | ||||||||
\(965\) | 83.1561 | 2.67689 | ||||||||
\(966\) | 12.1706 | 0.391581 | ||||||||
\(967\) | 9.62259 | 0.309442 | 0.154721 | − | 0.987958i | \(-0.450552\pi\) | ||||
0.154721 | + | 0.987958i | \(0.450552\pi\) | |||||||
\(968\) | −9.02098 | −0.289945 | ||||||||
\(969\) | −21.8780 | −0.702821 | ||||||||
\(970\) | 67.0927 | 2.15422 | ||||||||
\(971\) | 41.4954 | 1.33165 | 0.665825 | − | 0.746108i | \(-0.268080\pi\) | ||||
0.665825 | + | 0.746108i | \(0.268080\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −5.19532 | −0.166554 | ||||||||
\(974\) | −13.0202 | −0.417194 | ||||||||
\(975\) | −9.06665 | −0.290365 | ||||||||
\(976\) | 14.5433 | 0.465520 | ||||||||
\(977\) | 61.1349 | 1.95588 | 0.977939 | − | 0.208893i | \(-0.0669859\pi\) | ||||
0.977939 | + | 0.208893i | \(0.0669859\pi\) | |||||||
\(978\) | 6.87000 | 0.219678 | ||||||||
\(979\) | 9.95552 | 0.318180 | ||||||||
\(980\) | 2.14035 | 0.0683711 | ||||||||
\(981\) | −9.76772 | −0.311859 | ||||||||
\(982\) | 9.57244 | 0.305469 | ||||||||
\(983\) | −51.6042 | −1.64592 | −0.822960 | − | 0.568100i | \(-0.807679\pi\) | ||||
−0.822960 | + | 0.568100i | \(0.807679\pi\) | |||||||
\(984\) | −1.99643 | −0.0636438 | ||||||||
\(985\) | −16.5749 | −0.528120 | ||||||||
\(986\) | 30.0464 | 0.956872 | ||||||||
\(987\) | −31.3304 | −0.997257 | ||||||||
\(988\) | 4.50999 | 0.143482 | ||||||||
\(989\) | −51.0212 | −1.62238 | ||||||||
\(990\) | 5.27619 | 0.167688 | ||||||||
\(991\) | 36.0436 | 1.14496 | 0.572482 | − | 0.819918i | \(-0.305981\pi\) | ||||
0.572482 | + | 0.819918i | \(0.305981\pi\) | |||||||
\(992\) | −8.77193 | −0.278509 | ||||||||
\(993\) | 14.9647 | 0.474892 | ||||||||
\(994\) | −39.7843 | −1.26188 | ||||||||
\(995\) | −58.7160 | −1.86142 | ||||||||
\(996\) | 10.5152 | 0.333188 | ||||||||
\(997\) | −53.4859 | −1.69391 | −0.846957 | − | 0.531661i | \(-0.821568\pi\) | ||||
−0.846957 | + | 0.531661i | \(0.821568\pi\) | |||||||
\(998\) | 39.4882 | 1.24998 | ||||||||
\(999\) | 4.12167 | 0.130404 |
(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 | 8034.2.a.bd.1.15 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bd.1.15 | ✓ | 16 | 1.1 | even | 1 | trivial |