Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, 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("5070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.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: | \(40.4841538248\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.24698\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.04892 | 1.15238 | 0.576191 | − | 0.817315i | \(-0.304538\pi\) | ||||
0.576191 | + | 0.817315i | \(0.304538\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −6.24698 | −1.88354 | −0.941768 | − | 0.336264i | \(-0.890836\pi\) | ||||
−0.941768 | + | 0.336264i | \(0.890836\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.04892 | 0.814857 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.69202 | 0.652911 | 0.326456 | − | 0.945213i | \(-0.394146\pi\) | ||||
0.326456 | + | 0.945213i | \(0.394146\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −5.82908 | −1.33728 | −0.668642 | − | 0.743585i | \(-0.733124\pi\) | ||||
−0.668642 | + | 0.743585i | \(0.733124\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −3.04892 | −0.665328 | ||||||||
\(22\) | −6.24698 | −1.33186 | ||||||||
\(23\) | −5.62565 | −1.17303 | −0.586514 | − | 0.809939i | \(-0.699500\pi\) | ||||
−0.586514 | + | 0.809939i | \(0.699500\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.04892 | 0.576191 | ||||||||
\(29\) | −5.14675 | −0.955728 | −0.477864 | − | 0.878434i | \(-0.658589\pi\) | ||||
−0.477864 | + | 0.878434i | \(0.658589\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −3.53319 | −0.634579 | −0.317290 | − | 0.948329i | \(-0.602773\pi\) | ||||
−0.317290 | + | 0.948329i | \(0.602773\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.24698 | 1.08746 | ||||||||
\(34\) | 2.69202 | 0.461678 | ||||||||
\(35\) | 3.04892 | 0.515361 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.65279 | −0.764914 | −0.382457 | − | 0.923973i | \(-0.624922\pi\) | ||||
−0.382457 | + | 0.923973i | \(0.624922\pi\) | |||||||
\(38\) | −5.82908 | −0.945602 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −3.77479 | −0.589523 | −0.294762 | − | 0.955571i | \(-0.595240\pi\) | ||||
−0.294762 | + | 0.955571i | \(0.595240\pi\) | |||||||
\(42\) | −3.04892 | −0.470458 | ||||||||
\(43\) | 2.85086 | 0.434751 | 0.217376 | − | 0.976088i | \(-0.430250\pi\) | ||||
0.217376 | + | 0.976088i | \(0.430250\pi\) | |||||||
\(44\) | −6.24698 | −0.941768 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −5.62565 | −0.829456 | ||||||||
\(47\) | −3.61596 | −0.527442 | −0.263721 | − | 0.964599i | \(-0.584950\pi\) | ||||
−0.263721 | + | 0.964599i | \(0.584950\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 2.29590 | 0.327985 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −2.69202 | −0.376958 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.664874 | 0.0913275 | 0.0456638 | − | 0.998957i | \(-0.485460\pi\) | ||||
0.0456638 | + | 0.998957i | \(0.485460\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −6.24698 | −0.842343 | ||||||||
\(56\) | 3.04892 | 0.407429 | ||||||||
\(57\) | 5.82908 | 0.772081 | ||||||||
\(58\) | −5.14675 | −0.675802 | ||||||||
\(59\) | −12.9487 | −1.68578 | −0.842888 | − | 0.538089i | \(-0.819146\pi\) | ||||
−0.842888 | + | 0.538089i | \(0.819146\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −7.91723 | −1.01370 | −0.506849 | − | 0.862035i | \(-0.669190\pi\) | ||||
−0.506849 | + | 0.862035i | \(0.669190\pi\) | |||||||
\(62\) | −3.53319 | −0.448715 | ||||||||
\(63\) | 3.04892 | 0.384127 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.24698 | 0.768950 | ||||||||
\(67\) | −0.198062 | −0.0241972 | −0.0120986 | − | 0.999927i | \(-0.503851\pi\) | ||||
−0.0120986 | + | 0.999927i | \(0.503851\pi\) | |||||||
\(68\) | 2.69202 | 0.326456 | ||||||||
\(69\) | 5.62565 | 0.677248 | ||||||||
\(70\) | 3.04892 | 0.364415 | ||||||||
\(71\) | −0.374354 | −0.0444277 | −0.0222138 | − | 0.999753i | \(-0.507071\pi\) | ||||
−0.0222138 | + | 0.999753i | \(0.507071\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 14.6136 | 1.71039 | 0.855194 | − | 0.518308i | \(-0.173438\pi\) | ||||
0.855194 | + | 0.518308i | \(0.173438\pi\) | |||||||
\(74\) | −4.65279 | −0.540876 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −5.82908 | −0.668642 | ||||||||
\(77\) | −19.0465 | −2.17055 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.2567 | −1.26647 | −0.633237 | − | 0.773958i | \(-0.718274\pi\) | ||||
−0.633237 | + | 0.773958i | \(0.718274\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.77479 | −0.416856 | ||||||||
\(83\) | 6.83877 | 0.750653 | 0.375326 | − | 0.926893i | \(-0.377531\pi\) | ||||
0.375326 | + | 0.926893i | \(0.377531\pi\) | |||||||
\(84\) | −3.04892 | −0.332664 | ||||||||
\(85\) | 2.69202 | 0.291991 | ||||||||
\(86\) | 2.85086 | 0.307416 | ||||||||
\(87\) | 5.14675 | 0.551790 | ||||||||
\(88\) | −6.24698 | −0.665930 | ||||||||
\(89\) | 9.50365 | 1.00738 | 0.503692 | − | 0.863883i | \(-0.331975\pi\) | ||||
0.503692 | + | 0.863883i | \(0.331975\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.62565 | −0.586514 | ||||||||
\(93\) | 3.53319 | 0.366375 | ||||||||
\(94\) | −3.61596 | −0.372957 | ||||||||
\(95\) | −5.82908 | −0.598051 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −0.335126 | −0.0340268 | −0.0170134 | − | 0.999855i | \(-0.505416\pi\) | ||||
−0.0170134 | + | 0.999855i | \(0.505416\pi\) | |||||||
\(98\) | 2.29590 | 0.231921 | ||||||||
\(99\) | −6.24698 | −0.627845 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 0.274127 | 0.0272766 | 0.0136383 | − | 0.999907i | \(-0.495659\pi\) | ||||
0.0136383 | + | 0.999907i | \(0.495659\pi\) | |||||||
\(102\) | −2.69202 | −0.266550 | ||||||||
\(103\) | −9.00000 | −0.886796 | −0.443398 | − | 0.896325i | \(-0.646227\pi\) | ||||
−0.443398 | + | 0.896325i | \(0.646227\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.04892 | −0.297544 | ||||||||
\(106\) | 0.664874 | 0.0645783 | ||||||||
\(107\) | −10.8509 | −1.04899 | −0.524496 | − | 0.851413i | \(-0.675746\pi\) | ||||
−0.524496 | + | 0.851413i | \(0.675746\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −1.02177 | −0.0978678 | −0.0489339 | − | 0.998802i | \(-0.515582\pi\) | ||||
−0.0489339 | + | 0.998802i | \(0.515582\pi\) | |||||||
\(110\) | −6.24698 | −0.595626 | ||||||||
\(111\) | 4.65279 | 0.441624 | ||||||||
\(112\) | 3.04892 | 0.288096 | ||||||||
\(113\) | 19.6383 | 1.84742 | 0.923709 | − | 0.383095i | \(-0.125142\pi\) | ||||
0.923709 | + | 0.383095i | \(0.125142\pi\) | |||||||
\(114\) | 5.82908 | 0.545944 | ||||||||
\(115\) | −5.62565 | −0.524594 | ||||||||
\(116\) | −5.14675 | −0.477864 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.9487 | −1.19202 | ||||||||
\(119\) | 8.20775 | 0.752403 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 28.0248 | 2.54770 | ||||||||
\(122\) | −7.91723 | −0.716792 | ||||||||
\(123\) | 3.77479 | 0.340361 | ||||||||
\(124\) | −3.53319 | −0.317290 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 3.04892 | 0.271619 | ||||||||
\(127\) | 18.5187 | 1.64327 | 0.821635 | − | 0.570014i | \(-0.193062\pi\) | ||||
0.821635 | + | 0.570014i | \(0.193062\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.85086 | −0.251004 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.2349 | −1.06897 | −0.534484 | − | 0.845179i | \(-0.679494\pi\) | ||||
−0.534484 | + | 0.845179i | \(0.679494\pi\) | |||||||
\(132\) | 6.24698 | 0.543730 | ||||||||
\(133\) | −17.7724 | −1.54106 | ||||||||
\(134\) | −0.198062 | −0.0171100 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 2.69202 | 0.230839 | ||||||||
\(137\) | −19.3002 | −1.64893 | −0.824464 | − | 0.565914i | \(-0.808523\pi\) | ||||
−0.824464 | + | 0.565914i | \(0.808523\pi\) | |||||||
\(138\) | 5.62565 | 0.478887 | ||||||||
\(139\) | 19.5133 | 1.65510 | 0.827550 | − | 0.561392i | \(-0.189734\pi\) | ||||
0.827550 | + | 0.561392i | \(0.189734\pi\) | |||||||
\(140\) | 3.04892 | 0.257681 | ||||||||
\(141\) | 3.61596 | 0.304519 | ||||||||
\(142\) | −0.374354 | −0.0314151 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −5.14675 | −0.427414 | ||||||||
\(146\) | 14.6136 | 1.20943 | ||||||||
\(147\) | −2.29590 | −0.189362 | ||||||||
\(148\) | −4.65279 | −0.382457 | ||||||||
\(149\) | −18.0248 | −1.47665 | −0.738323 | − | 0.674448i | \(-0.764382\pi\) | ||||
−0.738323 | + | 0.674448i | \(0.764382\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 5.30127 | 0.431412 | 0.215706 | − | 0.976458i | \(-0.430795\pi\) | ||||
0.215706 | + | 0.976458i | \(0.430795\pi\) | |||||||
\(152\) | −5.82908 | −0.472801 | ||||||||
\(153\) | 2.69202 | 0.217637 | ||||||||
\(154\) | −19.0465 | −1.53481 | ||||||||
\(155\) | −3.53319 | −0.283792 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.41789 | 0.592012 | 0.296006 | − | 0.955186i | \(-0.404345\pi\) | ||||
0.296006 | + | 0.955186i | \(0.404345\pi\) | |||||||
\(158\) | −11.2567 | −0.895532 | ||||||||
\(159\) | −0.664874 | −0.0527280 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −17.1521 | −1.35178 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 24.0151 | 1.88101 | 0.940503 | − | 0.339787i | \(-0.110355\pi\) | ||||
0.940503 | + | 0.339787i | \(0.110355\pi\) | |||||||
\(164\) | −3.77479 | −0.294762 | ||||||||
\(165\) | 6.24698 | 0.486327 | ||||||||
\(166\) | 6.83877 | 0.530792 | ||||||||
\(167\) | 11.9922 | 0.927987 | 0.463993 | − | 0.885839i | \(-0.346416\pi\) | ||||
0.463993 | + | 0.885839i | \(0.346416\pi\) | |||||||
\(168\) | −3.04892 | −0.235229 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.69202 | 0.206469 | ||||||||
\(171\) | −5.82908 | −0.445761 | ||||||||
\(172\) | 2.85086 | 0.217376 | ||||||||
\(173\) | 19.8823 | 1.51162 | 0.755812 | − | 0.654788i | \(-0.227242\pi\) | ||||
0.755812 | + | 0.654788i | \(0.227242\pi\) | |||||||
\(174\) | 5.14675 | 0.390174 | ||||||||
\(175\) | 3.04892 | 0.230476 | ||||||||
\(176\) | −6.24698 | −0.470884 | ||||||||
\(177\) | 12.9487 | 0.973283 | ||||||||
\(178\) | 9.50365 | 0.712329 | ||||||||
\(179\) | 16.7453 | 1.25160 | 0.625799 | − | 0.779984i | \(-0.284773\pi\) | ||||
0.625799 | + | 0.779984i | \(0.284773\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −3.93900 | −0.292784 | −0.146392 | − | 0.989227i | \(-0.546766\pi\) | ||||
−0.146392 | + | 0.989227i | \(0.546766\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.91723 | 0.585259 | ||||||||
\(184\) | −5.62565 | −0.414728 | ||||||||
\(185\) | −4.65279 | −0.342080 | ||||||||
\(186\) | 3.53319 | 0.259066 | ||||||||
\(187\) | −16.8170 | −1.22978 | ||||||||
\(188\) | −3.61596 | −0.263721 | ||||||||
\(189\) | −3.04892 | −0.221776 | ||||||||
\(190\) | −5.82908 | −0.422886 | ||||||||
\(191\) | −27.1540 | −1.96480 | −0.982399 | − | 0.186795i | \(-0.940190\pi\) | ||||
−0.982399 | + | 0.186795i | \(0.940190\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 15.3937 | 1.10807 | 0.554033 | − | 0.832495i | \(-0.313088\pi\) | ||||
0.554033 | + | 0.832495i | \(0.313088\pi\) | |||||||
\(194\) | −0.335126 | −0.0240606 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.29590 | 0.163993 | ||||||||
\(197\) | −23.5036 | −1.67457 | −0.837283 | − | 0.546770i | \(-0.815857\pi\) | ||||
−0.837283 | + | 0.546770i | \(0.815857\pi\) | |||||||
\(198\) | −6.24698 | −0.443954 | ||||||||
\(199\) | −20.8442 | −1.47760 | −0.738801 | − | 0.673923i | \(-0.764608\pi\) | ||||
−0.738801 | + | 0.673923i | \(0.764608\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0.198062 | 0.0139702 | ||||||||
\(202\) | 0.274127 | 0.0192875 | ||||||||
\(203\) | −15.6920 | −1.10136 | ||||||||
\(204\) | −2.69202 | −0.188479 | ||||||||
\(205\) | −3.77479 | −0.263643 | ||||||||
\(206\) | −9.00000 | −0.627060 | ||||||||
\(207\) | −5.62565 | −0.391009 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 36.4142 | 2.51882 | ||||||||
\(210\) | −3.04892 | −0.210395 | ||||||||
\(211\) | −19.0073 | −1.30852 | −0.654258 | − | 0.756271i | \(-0.727019\pi\) | ||||
−0.654258 | + | 0.756271i | \(0.727019\pi\) | |||||||
\(212\) | 0.664874 | 0.0456638 | ||||||||
\(213\) | 0.374354 | 0.0256503 | ||||||||
\(214\) | −10.8509 | −0.741749 | ||||||||
\(215\) | 2.85086 | 0.194427 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −10.7724 | −0.731278 | ||||||||
\(218\) | −1.02177 | −0.0692030 | ||||||||
\(219\) | −14.6136 | −0.987493 | ||||||||
\(220\) | −6.24698 | −0.421171 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.65279 | 0.312275 | ||||||||
\(223\) | −20.9433 | −1.40247 | −0.701234 | − | 0.712931i | \(-0.747367\pi\) | ||||
−0.701234 | + | 0.712931i | \(0.747367\pi\) | |||||||
\(224\) | 3.04892 | 0.203714 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 19.6383 | 1.30632 | ||||||||
\(227\) | −19.0978 | −1.26757 | −0.633784 | − | 0.773510i | \(-0.718499\pi\) | ||||
−0.633784 | + | 0.773510i | \(0.718499\pi\) | |||||||
\(228\) | 5.82908 | 0.386041 | ||||||||
\(229\) | −9.33513 | −0.616882 | −0.308441 | − | 0.951243i | \(-0.599807\pi\) | ||||
−0.308441 | + | 0.951243i | \(0.599807\pi\) | |||||||
\(230\) | −5.62565 | −0.370944 | ||||||||
\(231\) | 19.0465 | 1.25317 | ||||||||
\(232\) | −5.14675 | −0.337901 | ||||||||
\(233\) | −14.3599 | −0.940747 | −0.470374 | − | 0.882467i | \(-0.655881\pi\) | ||||
−0.470374 | + | 0.882467i | \(0.655881\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.61596 | −0.235879 | ||||||||
\(236\) | −12.9487 | −0.842888 | ||||||||
\(237\) | 11.2567 | 0.731199 | ||||||||
\(238\) | 8.20775 | 0.532029 | ||||||||
\(239\) | −27.7482 | −1.79488 | −0.897442 | − | 0.441132i | \(-0.854577\pi\) | ||||
−0.897442 | + | 0.441132i | \(0.854577\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 14.5579 | 0.937759 | 0.468880 | − | 0.883262i | \(-0.344658\pi\) | ||||
0.468880 | + | 0.883262i | \(0.344658\pi\) | |||||||
\(242\) | 28.0248 | 1.80150 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −7.91723 | −0.506849 | ||||||||
\(245\) | 2.29590 | 0.146679 | ||||||||
\(246\) | 3.77479 | 0.240672 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.53319 | −0.224358 | ||||||||
\(249\) | −6.83877 | −0.433390 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 27.8756 | 1.75949 | 0.879746 | − | 0.475443i | \(-0.157712\pi\) | ||||
0.879746 | + | 0.475443i | \(0.157712\pi\) | |||||||
\(252\) | 3.04892 | 0.192064 | ||||||||
\(253\) | 35.1433 | 2.20944 | ||||||||
\(254\) | 18.5187 | 1.16197 | ||||||||
\(255\) | −2.69202 | −0.168581 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.64848 | −0.352343 | −0.176171 | − | 0.984360i | \(-0.556371\pi\) | ||||
−0.176171 | + | 0.984360i | \(0.556371\pi\) | |||||||
\(258\) | −2.85086 | −0.177486 | ||||||||
\(259\) | −14.1860 | −0.881474 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.14675 | −0.318576 | ||||||||
\(262\) | −12.2349 | −0.755875 | ||||||||
\(263\) | 6.06100 | 0.373737 | 0.186869 | − | 0.982385i | \(-0.440166\pi\) | ||||
0.186869 | + | 0.982385i | \(0.440166\pi\) | |||||||
\(264\) | 6.24698 | 0.384475 | ||||||||
\(265\) | 0.664874 | 0.0408429 | ||||||||
\(266\) | −17.7724 | −1.08970 | ||||||||
\(267\) | −9.50365 | −0.581614 | ||||||||
\(268\) | −0.198062 | −0.0120986 | ||||||||
\(269\) | 8.19136 | 0.499436 | 0.249718 | − | 0.968319i | \(-0.419662\pi\) | ||||
0.249718 | + | 0.968319i | \(0.419662\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 12.8006 | 0.777582 | 0.388791 | − | 0.921326i | \(-0.372893\pi\) | ||||
0.388791 | + | 0.921326i | \(0.372893\pi\) | |||||||
\(272\) | 2.69202 | 0.163228 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.3002 | −1.16597 | ||||||||
\(275\) | −6.24698 | −0.376707 | ||||||||
\(276\) | 5.62565 | 0.338624 | ||||||||
\(277\) | −7.88338 | −0.473666 | −0.236833 | − | 0.971550i | \(-0.576109\pi\) | ||||
−0.236833 | + | 0.971550i | \(0.576109\pi\) | |||||||
\(278\) | 19.5133 | 1.17033 | ||||||||
\(279\) | −3.53319 | −0.211526 | ||||||||
\(280\) | 3.04892 | 0.182208 | ||||||||
\(281\) | 7.16182 | 0.427238 | 0.213619 | − | 0.976917i | \(-0.431475\pi\) | ||||
0.213619 | + | 0.976917i | \(0.431475\pi\) | |||||||
\(282\) | 3.61596 | 0.215327 | ||||||||
\(283\) | 11.7342 | 0.697528 | 0.348764 | − | 0.937211i | \(-0.386602\pi\) | ||||
0.348764 | + | 0.937211i | \(0.386602\pi\) | |||||||
\(284\) | −0.374354 | −0.0222138 | ||||||||
\(285\) | 5.82908 | 0.345285 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.5090 | −0.679356 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −9.75302 | −0.573707 | ||||||||
\(290\) | −5.14675 | −0.302228 | ||||||||
\(291\) | 0.335126 | 0.0196454 | ||||||||
\(292\) | 14.6136 | 0.855194 | ||||||||
\(293\) | −26.4456 | −1.54497 | −0.772485 | − | 0.635033i | \(-0.780987\pi\) | ||||
−0.772485 | + | 0.635033i | \(0.780987\pi\) | |||||||
\(294\) | −2.29590 | −0.133899 | ||||||||
\(295\) | −12.9487 | −0.753902 | ||||||||
\(296\) | −4.65279 | −0.270438 | ||||||||
\(297\) | 6.24698 | 0.362487 | ||||||||
\(298\) | −18.0248 | −1.04415 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 8.69202 | 0.501000 | ||||||||
\(302\) | 5.30127 | 0.305054 | ||||||||
\(303\) | −0.274127 | −0.0157482 | ||||||||
\(304\) | −5.82908 | −0.334321 | ||||||||
\(305\) | −7.91723 | −0.453339 | ||||||||
\(306\) | 2.69202 | 0.153893 | ||||||||
\(307\) | −10.8562 | −0.619598 | −0.309799 | − | 0.950802i | \(-0.600262\pi\) | ||||
−0.309799 | + | 0.950802i | \(0.600262\pi\) | |||||||
\(308\) | −19.0465 | −1.08528 | ||||||||
\(309\) | 9.00000 | 0.511992 | ||||||||
\(310\) | −3.53319 | −0.200672 | ||||||||
\(311\) | 11.5453 | 0.654672 | 0.327336 | − | 0.944908i | \(-0.393849\pi\) | ||||
0.327336 | + | 0.944908i | \(0.393849\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.4862 | 1.04490 | 0.522451 | − | 0.852670i | \(-0.325018\pi\) | ||||
0.522451 | + | 0.852670i | \(0.325018\pi\) | |||||||
\(314\) | 7.41789 | 0.418616 | ||||||||
\(315\) | 3.04892 | 0.171787 | ||||||||
\(316\) | −11.2567 | −0.633237 | ||||||||
\(317\) | −3.05131 | −0.171379 | −0.0856893 | − | 0.996322i | \(-0.527309\pi\) | ||||
−0.0856893 | + | 0.996322i | \(0.527309\pi\) | |||||||
\(318\) | −0.664874 | −0.0372843 | ||||||||
\(319\) | 32.1517 | 1.80015 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 10.8509 | 0.605636 | ||||||||
\(322\) | −17.1521 | −0.955851 | ||||||||
\(323\) | −15.6920 | −0.873127 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.0151 | 1.33007 | ||||||||
\(327\) | 1.02177 | 0.0565040 | ||||||||
\(328\) | −3.77479 | −0.208428 | ||||||||
\(329\) | −11.0248 | −0.607814 | ||||||||
\(330\) | 6.24698 | 0.343885 | ||||||||
\(331\) | −12.1575 | −0.668237 | −0.334118 | − | 0.942531i | \(-0.608439\pi\) | ||||
−0.334118 | + | 0.942531i | \(0.608439\pi\) | |||||||
\(332\) | 6.83877 | 0.375326 | ||||||||
\(333\) | −4.65279 | −0.254971 | ||||||||
\(334\) | 11.9922 | 0.656186 | ||||||||
\(335\) | −0.198062 | −0.0108213 | ||||||||
\(336\) | −3.04892 | −0.166332 | ||||||||
\(337\) | 6.48188 | 0.353090 | 0.176545 | − | 0.984293i | \(-0.443508\pi\) | ||||
0.176545 | + | 0.984293i | \(0.443508\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.6383 | −1.06661 | ||||||||
\(340\) | 2.69202 | 0.145995 | ||||||||
\(341\) | 22.0718 | 1.19525 | ||||||||
\(342\) | −5.82908 | −0.315201 | ||||||||
\(343\) | −14.3424 | −0.774418 | ||||||||
\(344\) | 2.85086 | 0.153708 | ||||||||
\(345\) | 5.62565 | 0.302875 | ||||||||
\(346\) | 19.8823 | 1.06888 | ||||||||
\(347\) | 19.1933 | 1.03035 | 0.515175 | − | 0.857085i | \(-0.327727\pi\) | ||||
0.515175 | + | 0.857085i | \(0.327727\pi\) | |||||||
\(348\) | 5.14675 | 0.275895 | ||||||||
\(349\) | −11.5767 | −0.619688 | −0.309844 | − | 0.950787i | \(-0.600277\pi\) | ||||
−0.309844 | + | 0.950787i | \(0.600277\pi\) | |||||||
\(350\) | 3.04892 | 0.162971 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.24698 | −0.332965 | ||||||||
\(353\) | −21.6963 | −1.15478 | −0.577390 | − | 0.816469i | \(-0.695929\pi\) | ||||
−0.577390 | + | 0.816469i | \(0.695929\pi\) | |||||||
\(354\) | 12.9487 | 0.688215 | ||||||||
\(355\) | −0.374354 | −0.0198687 | ||||||||
\(356\) | 9.50365 | 0.503692 | ||||||||
\(357\) | −8.20775 | −0.434400 | ||||||||
\(358\) | 16.7453 | 0.885014 | ||||||||
\(359\) | 13.0476 | 0.688625 | 0.344313 | − | 0.938855i | \(-0.388112\pi\) | ||||
0.344313 | + | 0.938855i | \(0.388112\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 14.9782 | 0.788328 | ||||||||
\(362\) | −3.93900 | −0.207029 | ||||||||
\(363\) | −28.0248 | −1.47092 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.6136 | 0.764909 | ||||||||
\(366\) | 7.91723 | 0.413840 | ||||||||
\(367\) | 1.76377 | 0.0920683 | 0.0460341 | − | 0.998940i | \(-0.485342\pi\) | ||||
0.0460341 | + | 0.998940i | \(0.485342\pi\) | |||||||
\(368\) | −5.62565 | −0.293257 | ||||||||
\(369\) | −3.77479 | −0.196508 | ||||||||
\(370\) | −4.65279 | −0.241887 | ||||||||
\(371\) | 2.02715 | 0.105244 | ||||||||
\(372\) | 3.53319 | 0.183187 | ||||||||
\(373\) | 15.5013 | 0.802625 | 0.401312 | − | 0.915941i | \(-0.368554\pi\) | ||||
0.401312 | + | 0.915941i | \(0.368554\pi\) | |||||||
\(374\) | −16.8170 | −0.869587 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −3.61596 | −0.186479 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −3.04892 | −0.156819 | ||||||||
\(379\) | 8.62863 | 0.443223 | 0.221611 | − | 0.975135i | \(-0.428868\pi\) | ||||
0.221611 | + | 0.975135i | \(0.428868\pi\) | |||||||
\(380\) | −5.82908 | −0.299026 | ||||||||
\(381\) | −18.5187 | −0.948742 | ||||||||
\(382\) | −27.1540 | −1.38932 | ||||||||
\(383\) | 31.1008 | 1.58918 | 0.794589 | − | 0.607148i | \(-0.207686\pi\) | ||||
0.794589 | + | 0.607148i | \(0.207686\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −19.0465 | −0.970701 | ||||||||
\(386\) | 15.3937 | 0.783520 | ||||||||
\(387\) | 2.85086 | 0.144917 | ||||||||
\(388\) | −0.335126 | −0.0170134 | ||||||||
\(389\) | 7.07069 | 0.358498 | 0.179249 | − | 0.983804i | \(-0.442633\pi\) | ||||
0.179249 | + | 0.983804i | \(0.442633\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.1444 | −0.765883 | ||||||||
\(392\) | 2.29590 | 0.115960 | ||||||||
\(393\) | 12.2349 | 0.617169 | ||||||||
\(394\) | −23.5036 | −1.18410 | ||||||||
\(395\) | −11.2567 | −0.566384 | ||||||||
\(396\) | −6.24698 | −0.313923 | ||||||||
\(397\) | −28.5948 | −1.43513 | −0.717565 | − | 0.696491i | \(-0.754744\pi\) | ||||
−0.717565 | + | 0.696491i | \(0.754744\pi\) | |||||||
\(398\) | −20.8442 | −1.04482 | ||||||||
\(399\) | 17.7724 | 0.889733 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −11.8267 | −0.590597 | −0.295298 | − | 0.955405i | \(-0.595419\pi\) | ||||
−0.295298 | + | 0.955405i | \(0.595419\pi\) | |||||||
\(402\) | 0.198062 | 0.00987845 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.274127 | 0.0136383 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −15.6920 | −0.778782 | ||||||||
\(407\) | 29.0659 | 1.44074 | ||||||||
\(408\) | −2.69202 | −0.133275 | ||||||||
\(409\) | −9.00000 | −0.445021 | −0.222511 | − | 0.974930i | \(-0.571425\pi\) | ||||
−0.222511 | + | 0.974930i | \(0.571425\pi\) | |||||||
\(410\) | −3.77479 | −0.186424 | ||||||||
\(411\) | 19.3002 | 0.952009 | ||||||||
\(412\) | −9.00000 | −0.443398 | ||||||||
\(413\) | −39.4795 | −1.94266 | ||||||||
\(414\) | −5.62565 | −0.276485 | ||||||||
\(415\) | 6.83877 | 0.335702 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.5133 | −0.955572 | ||||||||
\(418\) | 36.4142 | 1.78108 | ||||||||
\(419\) | 19.7735 | 0.965997 | 0.482998 | − | 0.875621i | \(-0.339548\pi\) | ||||
0.482998 | + | 0.875621i | \(0.339548\pi\) | |||||||
\(420\) | −3.04892 | −0.148772 | ||||||||
\(421\) | −21.0127 | −1.02409 | −0.512047 | − | 0.858957i | \(-0.671113\pi\) | ||||
−0.512047 | + | 0.858957i | \(0.671113\pi\) | |||||||
\(422\) | −19.0073 | −0.925261 | ||||||||
\(423\) | −3.61596 | −0.175814 | ||||||||
\(424\) | 0.664874 | 0.0322892 | ||||||||
\(425\) | 2.69202 | 0.130582 | ||||||||
\(426\) | 0.374354 | 0.0181375 | ||||||||
\(427\) | −24.1390 | −1.16817 | ||||||||
\(428\) | −10.8509 | −0.524496 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.85086 | 0.137480 | ||||||||
\(431\) | −26.5633 | −1.27951 | −0.639755 | − | 0.768579i | \(-0.720964\pi\) | ||||
−0.639755 | + | 0.768579i | \(0.720964\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −14.7047 | −0.706662 | −0.353331 | − | 0.935498i | \(-0.614951\pi\) | ||||
−0.353331 | + | 0.935498i | \(0.614951\pi\) | |||||||
\(434\) | −10.7724 | −0.517092 | ||||||||
\(435\) | 5.14675 | 0.246768 | ||||||||
\(436\) | −1.02177 | −0.0489339 | ||||||||
\(437\) | 32.7924 | 1.56867 | ||||||||
\(438\) | −14.6136 | −0.698263 | ||||||||
\(439\) | −28.2640 | −1.34897 | −0.674483 | − | 0.738291i | \(-0.735633\pi\) | ||||
−0.674483 | + | 0.738291i | \(0.735633\pi\) | |||||||
\(440\) | −6.24698 | −0.297813 | ||||||||
\(441\) | 2.29590 | 0.109328 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.5109 | 0.974504 | 0.487252 | − | 0.873261i | \(-0.337999\pi\) | ||||
0.487252 | + | 0.873261i | \(0.337999\pi\) | |||||||
\(444\) | 4.65279 | 0.220812 | ||||||||
\(445\) | 9.50365 | 0.450516 | ||||||||
\(446\) | −20.9433 | −0.991695 | ||||||||
\(447\) | 18.0248 | 0.852542 | ||||||||
\(448\) | 3.04892 | 0.144048 | ||||||||
\(449\) | −3.19806 | −0.150926 | −0.0754629 | − | 0.997149i | \(-0.524043\pi\) | ||||
−0.0754629 | + | 0.997149i | \(0.524043\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 23.5810 | 1.11039 | ||||||||
\(452\) | 19.6383 | 0.923709 | ||||||||
\(453\) | −5.30127 | −0.249076 | ||||||||
\(454\) | −19.0978 | −0.896306 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.82908 | 0.272972 | ||||||||
\(457\) | 8.65710 | 0.404962 | 0.202481 | − | 0.979286i | \(-0.435100\pi\) | ||||
0.202481 | + | 0.979286i | \(0.435100\pi\) | |||||||
\(458\) | −9.33513 | −0.436202 | ||||||||
\(459\) | −2.69202 | −0.125653 | ||||||||
\(460\) | −5.62565 | −0.262297 | ||||||||
\(461\) | −11.1239 | −0.518092 | −0.259046 | − | 0.965865i | \(-0.583408\pi\) | ||||
−0.259046 | + | 0.965865i | \(0.583408\pi\) | |||||||
\(462\) | 19.0465 | 0.886125 | ||||||||
\(463\) | −33.0659 | −1.53670 | −0.768351 | − | 0.640028i | \(-0.778923\pi\) | ||||
−0.768351 | + | 0.640028i | \(0.778923\pi\) | |||||||
\(464\) | −5.14675 | −0.238932 | ||||||||
\(465\) | 3.53319 | 0.163848 | ||||||||
\(466\) | −14.3599 | −0.665209 | ||||||||
\(467\) | 15.3937 | 0.712337 | 0.356168 | − | 0.934422i | \(-0.384083\pi\) | ||||
0.356168 | + | 0.934422i | \(0.384083\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.603875 | −0.0278844 | ||||||||
\(470\) | −3.61596 | −0.166792 | ||||||||
\(471\) | −7.41789 | −0.341799 | ||||||||
\(472\) | −12.9487 | −0.596012 | ||||||||
\(473\) | −17.8092 | −0.818869 | ||||||||
\(474\) | 11.2567 | 0.517036 | ||||||||
\(475\) | −5.82908 | −0.267457 | ||||||||
\(476\) | 8.20775 | 0.376202 | ||||||||
\(477\) | 0.664874 | 0.0304425 | ||||||||
\(478\) | −27.7482 | −1.26917 | ||||||||
\(479\) | 42.2137 | 1.92879 | 0.964397 | − | 0.264459i | \(-0.0851933\pi\) | ||||
0.964397 | + | 0.264459i | \(0.0851933\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 14.5579 | 0.663096 | ||||||||
\(483\) | 17.1521 | 0.780449 | ||||||||
\(484\) | 28.0248 | 1.27385 | ||||||||
\(485\) | −0.335126 | −0.0152173 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 14.9903 | 0.679276 | 0.339638 | − | 0.940556i | \(-0.389695\pi\) | ||||
0.339638 | + | 0.940556i | \(0.389695\pi\) | |||||||
\(488\) | −7.91723 | −0.358396 | ||||||||
\(489\) | −24.0151 | −1.08600 | ||||||||
\(490\) | 2.29590 | 0.103718 | ||||||||
\(491\) | −21.3706 | −0.964443 | −0.482222 | − | 0.876049i | \(-0.660170\pi\) | ||||
−0.482222 | + | 0.876049i | \(0.660170\pi\) | |||||||
\(492\) | 3.77479 | 0.170181 | ||||||||
\(493\) | −13.8552 | −0.624005 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.24698 | −0.280781 | ||||||||
\(496\) | −3.53319 | −0.158645 | ||||||||
\(497\) | −1.14138 | −0.0511977 | ||||||||
\(498\) | −6.83877 | −0.306453 | ||||||||
\(499\) | −26.6160 | −1.19149 | −0.595747 | − | 0.803172i | \(-0.703144\pi\) | ||||
−0.595747 | + | 0.803172i | \(0.703144\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −11.9922 | −0.535773 | ||||||||
\(502\) | 27.8756 | 1.24415 | ||||||||
\(503\) | −25.2218 | −1.12458 | −0.562291 | − | 0.826939i | \(-0.690080\pi\) | ||||
−0.562291 | + | 0.826939i | \(0.690080\pi\) | |||||||
\(504\) | 3.04892 | 0.135810 | ||||||||
\(505\) | 0.274127 | 0.0121985 | ||||||||
\(506\) | 35.1433 | 1.56231 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.5187 | 0.821635 | ||||||||
\(509\) | −17.3797 | −0.770343 | −0.385172 | − | 0.922845i | \(-0.625858\pi\) | ||||
−0.385172 | + | 0.922845i | \(0.625858\pi\) | |||||||
\(510\) | −2.69202 | −0.119205 | ||||||||
\(511\) | 44.5555 | 1.97102 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.82908 | 0.257360 | ||||||||
\(514\) | −5.64848 | −0.249144 | ||||||||
\(515\) | −9.00000 | −0.396587 | ||||||||
\(516\) | −2.85086 | −0.125502 | ||||||||
\(517\) | 22.5888 | 0.993455 | ||||||||
\(518\) | −14.1860 | −0.623296 | ||||||||
\(519\) | −19.8823 | −0.872737 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.27114 | 0.362365 | 0.181183 | − | 0.983449i | \(-0.442007\pi\) | ||||
0.181183 | + | 0.983449i | \(0.442007\pi\) | |||||||
\(522\) | −5.14675 | −0.225267 | ||||||||
\(523\) | −40.9154 | −1.78911 | −0.894553 | − | 0.446961i | \(-0.852506\pi\) | ||||
−0.894553 | + | 0.446961i | \(0.852506\pi\) | |||||||
\(524\) | −12.2349 | −0.534484 | ||||||||
\(525\) | −3.04892 | −0.133066 | ||||||||
\(526\) | 6.06100 | 0.264272 | ||||||||
\(527\) | −9.51142 | −0.414324 | ||||||||
\(528\) | 6.24698 | 0.271865 | ||||||||
\(529\) | 8.64789 | 0.375995 | ||||||||
\(530\) | 0.664874 | 0.0288803 | ||||||||
\(531\) | −12.9487 | −0.561925 | ||||||||
\(532\) | −17.7724 | −0.770531 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −9.50365 | −0.411263 | ||||||||
\(535\) | −10.8509 | −0.469123 | ||||||||
\(536\) | −0.198062 | −0.00855499 | ||||||||
\(537\) | −16.7453 | −0.722611 | ||||||||
\(538\) | 8.19136 | 0.353154 | ||||||||
\(539\) | −14.3424 | −0.617772 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 27.2252 | 1.17050 | 0.585252 | − | 0.810852i | \(-0.300996\pi\) | ||||
0.585252 | + | 0.810852i | \(0.300996\pi\) | |||||||
\(542\) | 12.8006 | 0.549833 | ||||||||
\(543\) | 3.93900 | 0.169039 | ||||||||
\(544\) | 2.69202 | 0.115419 | ||||||||
\(545\) | −1.02177 | −0.0437678 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.7023 | −1.39825 | −0.699125 | − | 0.715000i | \(-0.746427\pi\) | ||||
−0.699125 | + | 0.715000i | \(0.746427\pi\) | |||||||
\(548\) | −19.3002 | −0.824464 | ||||||||
\(549\) | −7.91723 | −0.337899 | ||||||||
\(550\) | −6.24698 | −0.266372 | ||||||||
\(551\) | 30.0009 | 1.27808 | ||||||||
\(552\) | 5.62565 | 0.239443 | ||||||||
\(553\) | −34.3207 | −1.45946 | ||||||||
\(554\) | −7.88338 | −0.334933 | ||||||||
\(555\) | 4.65279 | 0.197500 | ||||||||
\(556\) | 19.5133 | 0.827550 | ||||||||
\(557\) | 0.225209 | 0.00954243 | 0.00477121 | − | 0.999989i | \(-0.498481\pi\) | ||||
0.00477121 | + | 0.999989i | \(0.498481\pi\) | |||||||
\(558\) | −3.53319 | −0.149572 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.04892 | 0.128840 | ||||||||
\(561\) | 16.8170 | 0.710014 | ||||||||
\(562\) | 7.16182 | 0.302103 | ||||||||
\(563\) | −9.55735 | −0.402794 | −0.201397 | − | 0.979510i | \(-0.564548\pi\) | ||||
−0.201397 | + | 0.979510i | \(0.564548\pi\) | |||||||
\(564\) | 3.61596 | 0.152259 | ||||||||
\(565\) | 19.6383 | 0.826190 | ||||||||
\(566\) | 11.7342 | 0.493227 | ||||||||
\(567\) | 3.04892 | 0.128042 | ||||||||
\(568\) | −0.374354 | −0.0157076 | ||||||||
\(569\) | 34.8455 | 1.46080 | 0.730399 | − | 0.683020i | \(-0.239334\pi\) | ||||
0.730399 | + | 0.683020i | \(0.239334\pi\) | |||||||
\(570\) | 5.82908 | 0.244153 | ||||||||
\(571\) | 36.5472 | 1.52945 | 0.764726 | − | 0.644355i | \(-0.222874\pi\) | ||||
0.764726 | + | 0.644355i | \(0.222874\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.1540 | 1.13438 | ||||||||
\(574\) | −11.5090 | −0.480377 | ||||||||
\(575\) | −5.62565 | −0.234606 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 18.3284 | 0.763022 | 0.381511 | − | 0.924364i | \(-0.375404\pi\) | ||||
0.381511 | + | 0.924364i | \(0.375404\pi\) | |||||||
\(578\) | −9.75302 | −0.405672 | ||||||||
\(579\) | −15.3937 | −0.639742 | ||||||||
\(580\) | −5.14675 | −0.213707 | ||||||||
\(581\) | 20.8509 | 0.865039 | ||||||||
\(582\) | 0.335126 | 0.0138914 | ||||||||
\(583\) | −4.15346 | −0.172019 | ||||||||
\(584\) | 14.6136 | 0.604714 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.4456 | −1.09246 | ||||||||
\(587\) | −17.3937 | −0.717916 | −0.358958 | − | 0.933354i | \(-0.616868\pi\) | ||||
−0.358958 | + | 0.933354i | \(0.616868\pi\) | |||||||
\(588\) | −2.29590 | −0.0946812 | ||||||||
\(589\) | 20.5953 | 0.848613 | ||||||||
\(590\) | −12.9487 | −0.533089 | ||||||||
\(591\) | 23.5036 | 0.966811 | ||||||||
\(592\) | −4.65279 | −0.191229 | ||||||||
\(593\) | −19.5362 | −0.802254 | −0.401127 | − | 0.916022i | \(-0.631381\pi\) | ||||
−0.401127 | + | 0.916022i | \(0.631381\pi\) | |||||||
\(594\) | 6.24698 | 0.256317 | ||||||||
\(595\) | 8.20775 | 0.336485 | ||||||||
\(596\) | −18.0248 | −0.738323 | ||||||||
\(597\) | 20.8442 | 0.853094 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.6364 | −0.598027 | −0.299014 | − | 0.954249i | \(-0.596658\pi\) | ||||
−0.299014 | + | 0.954249i | \(0.596658\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | 33.3980 | 1.36233 | 0.681167 | − | 0.732128i | \(-0.261473\pi\) | ||||
0.681167 | + | 0.732128i | \(0.261473\pi\) | |||||||
\(602\) | 8.69202 | 0.354260 | ||||||||
\(603\) | −0.198062 | −0.00806572 | ||||||||
\(604\) | 5.30127 | 0.215706 | ||||||||
\(605\) | 28.0248 | 1.13937 | ||||||||
\(606\) | −0.274127 | −0.0111356 | ||||||||
\(607\) | 29.9694 | 1.21642 | 0.608210 | − | 0.793776i | \(-0.291888\pi\) | ||||
0.608210 | + | 0.793776i | \(0.291888\pi\) | |||||||
\(608\) | −5.82908 | −0.236401 | ||||||||
\(609\) | 15.6920 | 0.635873 | ||||||||
\(610\) | −7.91723 | −0.320559 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.69202 | 0.108819 | ||||||||
\(613\) | 1.58748 | 0.0641178 | 0.0320589 | − | 0.999486i | \(-0.489794\pi\) | ||||
0.0320589 | + | 0.999486i | \(0.489794\pi\) | |||||||
\(614\) | −10.8562 | −0.438122 | ||||||||
\(615\) | 3.77479 | 0.152214 | ||||||||
\(616\) | −19.0465 | −0.767406 | ||||||||
\(617\) | −12.9511 | −0.521391 | −0.260695 | − | 0.965421i | \(-0.583952\pi\) | ||||
−0.260695 | + | 0.965421i | \(0.583952\pi\) | |||||||
\(618\) | 9.00000 | 0.362033 | ||||||||
\(619\) | 23.9554 | 0.962849 | 0.481424 | − | 0.876488i | \(-0.340120\pi\) | ||||
0.481424 | + | 0.876488i | \(0.340120\pi\) | |||||||
\(620\) | −3.53319 | −0.141896 | ||||||||
\(621\) | 5.62565 | 0.225749 | ||||||||
\(622\) | 11.5453 | 0.462923 | ||||||||
\(623\) | 28.9758 | 1.16089 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 18.4862 | 0.738857 | ||||||||
\(627\) | −36.4142 | −1.45424 | ||||||||
\(628\) | 7.41789 | 0.296006 | ||||||||
\(629\) | −12.5254 | −0.499421 | ||||||||
\(630\) | 3.04892 | 0.121472 | ||||||||
\(631\) | 35.4601 | 1.41164 | 0.705822 | − | 0.708389i | \(-0.250578\pi\) | ||||
0.705822 | + | 0.708389i | \(0.250578\pi\) | |||||||
\(632\) | −11.2567 | −0.447766 | ||||||||
\(633\) | 19.0073 | 0.755472 | ||||||||
\(634\) | −3.05131 | −0.121183 | ||||||||
\(635\) | 18.5187 | 0.734893 | ||||||||
\(636\) | −0.664874 | −0.0263640 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 32.1517 | 1.27290 | ||||||||
\(639\) | −0.374354 | −0.0148092 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 16.8358 | 0.664974 | 0.332487 | − | 0.943108i | \(-0.392112\pi\) | ||||
0.332487 | + | 0.943108i | \(0.392112\pi\) | |||||||
\(642\) | 10.8509 | 0.428249 | ||||||||
\(643\) | 18.4838 | 0.728930 | 0.364465 | − | 0.931217i | \(-0.381252\pi\) | ||||
0.364465 | + | 0.931217i | \(0.381252\pi\) | |||||||
\(644\) | −17.1521 | −0.675889 | ||||||||
\(645\) | −2.85086 | −0.112252 | ||||||||
\(646\) | −15.6920 | −0.617394 | ||||||||
\(647\) | −1.20237 | −0.0472702 | −0.0236351 | − | 0.999721i | \(-0.507524\pi\) | ||||
−0.0236351 | + | 0.999721i | \(0.507524\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 80.8902 | 3.17522 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.7724 | 0.422204 | ||||||||
\(652\) | 24.0151 | 0.940503 | ||||||||
\(653\) | −36.9530 | −1.44608 | −0.723041 | − | 0.690805i | \(-0.757256\pi\) | ||||
−0.723041 | + | 0.690805i | \(0.757256\pi\) | |||||||
\(654\) | 1.02177 | 0.0399544 | ||||||||
\(655\) | −12.2349 | −0.478057 | ||||||||
\(656\) | −3.77479 | −0.147381 | ||||||||
\(657\) | 14.6136 | 0.570129 | ||||||||
\(658\) | −11.0248 | −0.429790 | ||||||||
\(659\) | −26.4494 | −1.03032 | −0.515160 | − | 0.857094i | \(-0.672268\pi\) | ||||
−0.515160 | + | 0.857094i | \(0.672268\pi\) | |||||||
\(660\) | 6.24698 | 0.243163 | ||||||||
\(661\) | −2.21073 | −0.0859876 | −0.0429938 | − | 0.999075i | \(-0.513690\pi\) | ||||
−0.0429938 | + | 0.999075i | \(0.513690\pi\) | |||||||
\(662\) | −12.1575 | −0.472515 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.83877 | 0.265396 | ||||||||
\(665\) | −17.7724 | −0.689184 | ||||||||
\(666\) | −4.65279 | −0.180292 | ||||||||
\(667\) | 28.9538 | 1.12110 | ||||||||
\(668\) | 11.9922 | 0.463993 | ||||||||
\(669\) | 20.9433 | 0.809715 | ||||||||
\(670\) | −0.198062 | −0.00765181 | ||||||||
\(671\) | 49.4588 | 1.90934 | ||||||||
\(672\) | −3.04892 | −0.117615 | ||||||||
\(673\) | 16.5555 | 0.638170 | 0.319085 | − | 0.947726i | \(-0.396625\pi\) | ||||
0.319085 | + | 0.947726i | \(0.396625\pi\) | |||||||
\(674\) | 6.48188 | 0.249673 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.53617 | −0.328072 | −0.164036 | − | 0.986454i | \(-0.552451\pi\) | ||||
−0.164036 | + | 0.986454i | \(0.552451\pi\) | |||||||
\(678\) | −19.6383 | −0.754205 | ||||||||
\(679\) | −1.02177 | −0.0392119 | ||||||||
\(680\) | 2.69202 | 0.103234 | ||||||||
\(681\) | 19.0978 | 0.731831 | ||||||||
\(682\) | 22.0718 | 0.845171 | ||||||||
\(683\) | 0.204767 | 0.00783519 | 0.00391760 | − | 0.999992i | \(-0.498753\pi\) | ||||
0.00391760 | + | 0.999992i | \(0.498753\pi\) | |||||||
\(684\) | −5.82908 | −0.222881 | ||||||||
\(685\) | −19.3002 | −0.737423 | ||||||||
\(686\) | −14.3424 | −0.547596 | ||||||||
\(687\) | 9.33513 | 0.356157 | ||||||||
\(688\) | 2.85086 | 0.108688 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 5.62565 | 0.214165 | ||||||||
\(691\) | 33.5187 | 1.27511 | 0.637556 | − | 0.770404i | \(-0.279945\pi\) | ||||
0.637556 | + | 0.770404i | \(0.279945\pi\) | |||||||
\(692\) | 19.8823 | 0.755812 | ||||||||
\(693\) | −19.0465 | −0.723518 | ||||||||
\(694\) | 19.1933 | 0.728567 | ||||||||
\(695\) | 19.5133 | 0.740183 | ||||||||
\(696\) | 5.14675 | 0.195087 | ||||||||
\(697\) | −10.1618 | −0.384906 | ||||||||
\(698\) | −11.5767 | −0.438186 | ||||||||
\(699\) | 14.3599 | 0.543141 | ||||||||
\(700\) | 3.04892 | 0.115238 | ||||||||
\(701\) | 19.0271 | 0.718645 | 0.359323 | − | 0.933213i | \(-0.383008\pi\) | ||||
0.359323 | + | 0.933213i | \(0.383008\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.1215 | 1.02291 | ||||||||
\(704\) | −6.24698 | −0.235442 | ||||||||
\(705\) | 3.61596 | 0.136185 | ||||||||
\(706\) | −21.6963 | −0.816552 | ||||||||
\(707\) | 0.835790 | 0.0314331 | ||||||||
\(708\) | 12.9487 | 0.486642 | ||||||||
\(709\) | 42.5760 | 1.59897 | 0.799487 | − | 0.600683i | \(-0.205105\pi\) | ||||
0.799487 | + | 0.600683i | \(0.205105\pi\) | |||||||
\(710\) | −0.374354 | −0.0140493 | ||||||||
\(711\) | −11.2567 | −0.422158 | ||||||||
\(712\) | 9.50365 | 0.356164 | ||||||||
\(713\) | 19.8765 | 0.744379 | ||||||||
\(714\) | −8.20775 | −0.307167 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.7453 | 0.625799 | ||||||||
\(717\) | 27.7482 | 1.03628 | ||||||||
\(718\) | 13.0476 | 0.486932 | ||||||||
\(719\) | 7.51632 | 0.280311 | 0.140156 | − | 0.990129i | \(-0.455240\pi\) | ||||
0.140156 | + | 0.990129i | \(0.455240\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −27.4403 | −1.02193 | ||||||||
\(722\) | 14.9782 | 0.557432 | ||||||||
\(723\) | −14.5579 | −0.541416 | ||||||||
\(724\) | −3.93900 | −0.146392 | ||||||||
\(725\) | −5.14675 | −0.191146 | ||||||||
\(726\) | −28.0248 | −1.04010 | ||||||||
\(727\) | 39.6558 | 1.47075 | 0.735376 | − | 0.677660i | \(-0.237006\pi\) | ||||
0.735376 | + | 0.677660i | \(0.237006\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.6136 | 0.540872 | ||||||||
\(731\) | 7.67456 | 0.283854 | ||||||||
\(732\) | 7.91723 | 0.292629 | ||||||||
\(733\) | 24.4886 | 0.904506 | 0.452253 | − | 0.891890i | \(-0.350620\pi\) | ||||
0.452253 | + | 0.891890i | \(0.350620\pi\) | |||||||
\(734\) | 1.76377 | 0.0651021 | ||||||||
\(735\) | −2.29590 | −0.0846854 | ||||||||
\(736\) | −5.62565 | −0.207364 | ||||||||
\(737\) | 1.23729 | 0.0455762 | ||||||||
\(738\) | −3.77479 | −0.138952 | ||||||||
\(739\) | −41.9842 | −1.54441 | −0.772207 | − | 0.635371i | \(-0.780847\pi\) | ||||
−0.772207 | + | 0.635371i | \(0.780847\pi\) | |||||||
\(740\) | −4.65279 | −0.171040 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.02715 | 0.0744189 | ||||||||
\(743\) | 29.7711 | 1.09219 | 0.546097 | − | 0.837722i | \(-0.316113\pi\) | ||||
0.546097 | + | 0.837722i | \(0.316113\pi\) | |||||||
\(744\) | 3.53319 | 0.129533 | ||||||||
\(745\) | −18.0248 | −0.660376 | ||||||||
\(746\) | 15.5013 | 0.567541 | ||||||||
\(747\) | 6.83877 | 0.250218 | ||||||||
\(748\) | −16.8170 | −0.614891 | ||||||||
\(749\) | −33.0834 | −1.20884 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 35.4999 | 1.29541 | 0.647705 | − | 0.761891i | \(-0.275729\pi\) | ||||
0.647705 | + | 0.761891i | \(0.275729\pi\) | |||||||
\(752\) | −3.61596 | −0.131860 | ||||||||
\(753\) | −27.8756 | −1.01584 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.30127 | 0.192933 | ||||||||
\(756\) | −3.04892 | −0.110888 | ||||||||
\(757\) | 2.73258 | 0.0993172 | 0.0496586 | − | 0.998766i | \(-0.484187\pi\) | ||||
0.0496586 | + | 0.998766i | \(0.484187\pi\) | |||||||
\(758\) | 8.62863 | 0.313406 | ||||||||
\(759\) | −35.1433 | −1.27562 | ||||||||
\(760\) | −5.82908 | −0.211443 | ||||||||
\(761\) | −30.2349 | −1.09601 | −0.548007 | − | 0.836474i | \(-0.684613\pi\) | ||||
−0.548007 | + | 0.836474i | \(0.684613\pi\) | |||||||
\(762\) | −18.5187 | −0.670862 | ||||||||
\(763\) | −3.11529 | −0.112781 | ||||||||
\(764\) | −27.1540 | −0.982399 | ||||||||
\(765\) | 2.69202 | 0.0973302 | ||||||||
\(766\) | 31.1008 | 1.12372 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −35.3183 | −1.27361 | −0.636804 | − | 0.771025i | \(-0.719744\pi\) | ||||
−0.636804 | + | 0.771025i | \(0.719744\pi\) | |||||||
\(770\) | −19.0465 | −0.686389 | ||||||||
\(771\) | 5.64848 | 0.203425 | ||||||||
\(772\) | 15.3937 | 0.554033 | ||||||||
\(773\) | −32.0551 | −1.15294 | −0.576472 | − | 0.817117i | \(-0.695571\pi\) | ||||
−0.576472 | + | 0.817117i | \(0.695571\pi\) | |||||||
\(774\) | 2.85086 | 0.102472 | ||||||||
\(775\) | −3.53319 | −0.126916 | ||||||||
\(776\) | −0.335126 | −0.0120303 | ||||||||
\(777\) | 14.1860 | 0.508919 | ||||||||
\(778\) | 7.07069 | 0.253496 | ||||||||
\(779\) | 22.0036 | 0.788360 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.33858 | 0.0836811 | ||||||||
\(782\) | −15.1444 | −0.541561 | ||||||||
\(783\) | 5.14675 | 0.183930 | ||||||||
\(784\) | 2.29590 | 0.0819963 | ||||||||
\(785\) | 7.41789 | 0.264756 | ||||||||
\(786\) | 12.2349 | 0.436404 | ||||||||
\(787\) | −43.9235 | −1.56570 | −0.782851 | − | 0.622209i | \(-0.786235\pi\) | ||||
−0.782851 | + | 0.622209i | \(0.786235\pi\) | |||||||
\(788\) | −23.5036 | −0.837283 | ||||||||
\(789\) | −6.06100 | −0.215777 | ||||||||
\(790\) | −11.2567 | −0.400494 | ||||||||
\(791\) | 59.8756 | 2.12893 | ||||||||
\(792\) | −6.24698 | −0.221977 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −28.5948 | −1.01479 | ||||||||
\(795\) | −0.664874 | −0.0235807 | ||||||||
\(796\) | −20.8442 | −0.738801 | ||||||||
\(797\) | −26.4523 | −0.936990 | −0.468495 | − | 0.883466i | \(-0.655204\pi\) | ||||
−0.468495 | + | 0.883466i | \(0.655204\pi\) | |||||||
\(798\) | 17.7724 | 0.629136 | ||||||||
\(799\) | −9.73423 | −0.344372 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 9.50365 | 0.335795 | ||||||||
\(802\) | −11.8267 | −0.417615 | ||||||||
\(803\) | −91.2906 | −3.22158 | ||||||||
\(804\) | 0.198062 | 0.00698512 | ||||||||
\(805\) | −17.1521 | −0.604533 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.19136 | −0.288349 | ||||||||
\(808\) | 0.274127 | 0.00964374 | ||||||||
\(809\) | 41.4634 | 1.45777 | 0.728887 | − | 0.684634i | \(-0.240038\pi\) | ||||
0.728887 | + | 0.684634i | \(0.240038\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 24.9095 | 0.874689 | 0.437345 | − | 0.899294i | \(-0.355919\pi\) | ||||
0.437345 | + | 0.899294i | \(0.355919\pi\) | |||||||
\(812\) | −15.6920 | −0.550682 | ||||||||
\(813\) | −12.8006 | −0.448937 | ||||||||
\(814\) | 29.0659 | 1.01876 | ||||||||
\(815\) | 24.0151 | 0.841211 | ||||||||
\(816\) | −2.69202 | −0.0942396 | ||||||||
\(817\) | −16.6179 | −0.581386 | ||||||||
\(818\) | −9.00000 | −0.314678 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.77479 | −0.131821 | ||||||||
\(821\) | 3.11901 | 0.108854 | 0.0544272 | − | 0.998518i | \(-0.482667\pi\) | ||||
0.0544272 | + | 0.998518i | \(0.482667\pi\) | |||||||
\(822\) | 19.3002 | 0.673172 | ||||||||
\(823\) | 36.4077 | 1.26909 | 0.634547 | − | 0.772884i | \(-0.281187\pi\) | ||||
0.634547 | + | 0.772884i | \(0.281187\pi\) | |||||||
\(824\) | −9.00000 | −0.313530 | ||||||||
\(825\) | 6.24698 | 0.217492 | ||||||||
\(826\) | −39.4795 | −1.37367 | ||||||||
\(827\) | −8.04785 | −0.279851 | −0.139926 | − | 0.990162i | \(-0.544686\pi\) | ||||
−0.139926 | + | 0.990162i | \(0.544686\pi\) | |||||||
\(828\) | −5.62565 | −0.195505 | ||||||||
\(829\) | 28.7006 | 0.996815 | 0.498407 | − | 0.866943i | \(-0.333918\pi\) | ||||
0.498407 | + | 0.866943i | \(0.333918\pi\) | |||||||
\(830\) | 6.83877 | 0.237377 | ||||||||
\(831\) | 7.88338 | 0.273471 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.18060 | 0.214145 | ||||||||
\(834\) | −19.5133 | −0.675692 | ||||||||
\(835\) | 11.9922 | 0.415008 | ||||||||
\(836\) | 36.4142 | 1.25941 | ||||||||
\(837\) | 3.53319 | 0.122125 | ||||||||
\(838\) | 19.7735 | 0.683063 | ||||||||
\(839\) | −34.8491 | −1.20312 | −0.601561 | − | 0.798827i | \(-0.705455\pi\) | ||||
−0.601561 | + | 0.798827i | \(0.705455\pi\) | |||||||
\(840\) | −3.04892 | −0.105198 | ||||||||
\(841\) | −2.51094 | −0.0865843 | ||||||||
\(842\) | −21.0127 | −0.724145 | ||||||||
\(843\) | −7.16182 | −0.246666 | ||||||||
\(844\) | −19.0073 | −0.654258 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.61596 | −0.124319 | ||||||||
\(847\) | 85.4452 | 2.93593 | ||||||||
\(848\) | 0.664874 | 0.0228319 | ||||||||
\(849\) | −11.7342 | −0.402718 | ||||||||
\(850\) | 2.69202 | 0.0923356 | ||||||||
\(851\) | 26.1750 | 0.897266 | ||||||||
\(852\) | 0.374354 | 0.0128252 | ||||||||
\(853\) | 0.0779834 | 0.00267010 | 0.00133505 | − | 0.999999i | \(-0.499575\pi\) | ||||
0.00133505 | + | 0.999999i | \(0.499575\pi\) | |||||||
\(854\) | −24.1390 | −0.826019 | ||||||||
\(855\) | −5.82908 | −0.199350 | ||||||||
\(856\) | −10.8509 | −0.370875 | ||||||||
\(857\) | 18.3811 | 0.627885 | 0.313943 | − | 0.949442i | \(-0.398350\pi\) | ||||
0.313943 | + | 0.949442i | \(0.398350\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.871297 | 0.0297283 | 0.0148641 | − | 0.999890i | \(-0.495268\pi\) | ||||
0.0148641 | + | 0.999890i | \(0.495268\pi\) | |||||||
\(860\) | 2.85086 | 0.0972134 | ||||||||
\(861\) | 11.5090 | 0.392227 | ||||||||
\(862\) | −26.5633 | −0.904750 | ||||||||
\(863\) | 1.88172 | 0.0640546 | 0.0320273 | − | 0.999487i | \(-0.489804\pi\) | ||||
0.0320273 | + | 0.999487i | \(0.489804\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 19.8823 | 0.676019 | ||||||||
\(866\) | −14.7047 | −0.499686 | ||||||||
\(867\) | 9.75302 | 0.331230 | ||||||||
\(868\) | −10.7724 | −0.365639 | ||||||||
\(869\) | 70.3202 | 2.38545 | ||||||||
\(870\) | 5.14675 | 0.174491 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.02177 | −0.0346015 | ||||||||
\(873\) | −0.335126 | −0.0113423 | ||||||||
\(874\) | 32.7924 | 1.10922 | ||||||||
\(875\) | 3.04892 | 0.103072 | ||||||||
\(876\) | −14.6136 | −0.493747 | ||||||||
\(877\) | 46.6859 | 1.57647 | 0.788236 | − | 0.615374i | \(-0.210995\pi\) | ||||
0.788236 | + | 0.615374i | \(0.210995\pi\) | |||||||
\(878\) | −28.2640 | −0.953863 | ||||||||
\(879\) | 26.4456 | 0.891989 | ||||||||
\(880\) | −6.24698 | −0.210586 | ||||||||
\(881\) | 51.9821 | 1.75132 | 0.875660 | − | 0.482928i | \(-0.160427\pi\) | ||||
0.875660 | + | 0.482928i | \(0.160427\pi\) | |||||||
\(882\) | 2.29590 | 0.0773069 | ||||||||
\(883\) | 22.3889 | 0.753448 | 0.376724 | − | 0.926326i | \(-0.377051\pi\) | ||||
0.376724 | + | 0.926326i | \(0.377051\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.9487 | 0.435265 | ||||||||
\(886\) | 20.5109 | 0.689079 | ||||||||
\(887\) | −20.7332 | −0.696152 | −0.348076 | − | 0.937466i | \(-0.613165\pi\) | ||||
−0.348076 | + | 0.937466i | \(0.613165\pi\) | |||||||
\(888\) | 4.65279 | 0.156138 | ||||||||
\(889\) | 56.4620 | 1.89368 | ||||||||
\(890\) | 9.50365 | 0.318563 | ||||||||
\(891\) | −6.24698 | −0.209282 | ||||||||
\(892\) | −20.9433 | −0.701234 | ||||||||
\(893\) | 21.0777 | 0.705339 | ||||||||
\(894\) | 18.0248 | 0.602838 | ||||||||
\(895\) | 16.7453 | 0.559732 | ||||||||
\(896\) | 3.04892 | 0.101857 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.19806 | −0.106721 | ||||||||
\(899\) | 18.1844 | 0.606485 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 1.78986 | 0.0596288 | ||||||||
\(902\) | 23.5810 | 0.785163 | ||||||||
\(903\) | −8.69202 | −0.289252 | ||||||||
\(904\) | 19.6383 | 0.653161 | ||||||||
\(905\) | −3.93900 | −0.130937 | ||||||||
\(906\) | −5.30127 | −0.176123 | ||||||||
\(907\) | −9.27365 | −0.307927 | −0.153963 | − | 0.988077i | \(-0.549204\pi\) | ||||
−0.153963 | + | 0.988077i | \(0.549204\pi\) | |||||||
\(908\) | −19.0978 | −0.633784 | ||||||||
\(909\) | 0.274127 | 0.00909221 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.87071 | −0.128242 | −0.0641211 | − | 0.997942i | \(-0.520424\pi\) | ||||
−0.0641211 | + | 0.997942i | \(0.520424\pi\) | |||||||
\(912\) | 5.82908 | 0.193020 | ||||||||
\(913\) | −42.7217 | −1.41388 | ||||||||
\(914\) | 8.65710 | 0.286352 | ||||||||
\(915\) | 7.91723 | 0.261736 | ||||||||
\(916\) | −9.33513 | −0.308441 | ||||||||
\(917\) | −37.3032 | −1.23186 | ||||||||
\(918\) | −2.69202 | −0.0888499 | ||||||||
\(919\) | −33.2644 | −1.09729 | −0.548646 | − | 0.836055i | \(-0.684857\pi\) | ||||
−0.548646 | + | 0.836055i | \(0.684857\pi\) | |||||||
\(920\) | −5.62565 | −0.185472 | ||||||||
\(921\) | 10.8562 | 0.357725 | ||||||||
\(922\) | −11.1239 | −0.366347 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 19.0465 | 0.626585 | ||||||||
\(925\) | −4.65279 | −0.152983 | ||||||||
\(926\) | −33.0659 | −1.08661 | ||||||||
\(927\) | −9.00000 | −0.295599 | ||||||||
\(928\) | −5.14675 | −0.168950 | ||||||||
\(929\) | −1.92095 | −0.0630244 | −0.0315122 | − | 0.999503i | \(-0.510032\pi\) | ||||
−0.0315122 | + | 0.999503i | \(0.510032\pi\) | |||||||
\(930\) | 3.53319 | 0.115858 | ||||||||
\(931\) | −13.3830 | −0.438609 | ||||||||
\(932\) | −14.3599 | −0.470374 | ||||||||
\(933\) | −11.5453 | −0.377975 | ||||||||
\(934\) | 15.3937 | 0.503698 | ||||||||
\(935\) | −16.8170 | −0.549975 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.6886 | 0.871877 | 0.435939 | − | 0.899976i | \(-0.356416\pi\) | ||||
0.435939 | + | 0.899976i | \(0.356416\pi\) | |||||||
\(938\) | −0.603875 | −0.0197172 | ||||||||
\(939\) | −18.4862 | −0.603274 | ||||||||
\(940\) | −3.61596 | −0.117940 | ||||||||
\(941\) | 2.69309 | 0.0877921 | 0.0438961 | − | 0.999036i | \(-0.486023\pi\) | ||||
0.0438961 | + | 0.999036i | \(0.486023\pi\) | |||||||
\(942\) | −7.41789 | −0.241688 | ||||||||
\(943\) | 21.2356 | 0.691527 | ||||||||
\(944\) | −12.9487 | −0.421444 | ||||||||
\(945\) | −3.04892 | −0.0991813 | ||||||||
\(946\) | −17.8092 | −0.579028 | ||||||||
\(947\) | −23.1226 | −0.751383 | −0.375692 | − | 0.926745i | \(-0.622595\pi\) | ||||
−0.375692 | + | 0.926745i | \(0.622595\pi\) | |||||||
\(948\) | 11.2567 | 0.365600 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −5.82908 | −0.189120 | ||||||||
\(951\) | 3.05131 | 0.0989455 | ||||||||
\(952\) | 8.20775 | 0.266015 | ||||||||
\(953\) | −31.7313 | −1.02788 | −0.513938 | − | 0.857827i | \(-0.671814\pi\) | ||||
−0.513938 | + | 0.857827i | \(0.671814\pi\) | |||||||
\(954\) | 0.664874 | 0.0215261 | ||||||||
\(955\) | −27.1540 | −0.878684 | ||||||||
\(956\) | −27.7482 | −0.897442 | ||||||||
\(957\) | −32.1517 | −1.03932 | ||||||||
\(958\) | 42.2137 | 1.36386 | ||||||||
\(959\) | −58.8447 | −1.90020 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −18.5166 | −0.597309 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.8509 | −0.349664 | ||||||||
\(964\) | 14.5579 | 0.468880 | ||||||||
\(965\) | 15.3937 | 0.495542 | ||||||||
\(966\) | 17.1521 | 0.551861 | ||||||||
\(967\) | −29.7095 | −0.955392 | −0.477696 | − | 0.878525i | \(-0.658528\pi\) | ||||
−0.477696 | + | 0.878525i | \(0.658528\pi\) | |||||||
\(968\) | 28.0248 | 0.900750 | ||||||||
\(969\) | 15.6920 | 0.504100 | ||||||||
\(970\) | −0.335126 | −0.0107602 | ||||||||
\(971\) | −50.0428 | −1.60595 | −0.802975 | − | 0.596013i | \(-0.796751\pi\) | ||||
−0.802975 | + | 0.596013i | \(0.796751\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 59.4946 | 1.90731 | ||||||||
\(974\) | 14.9903 | 0.480321 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.91723 | −0.253424 | ||||||||
\(977\) | −15.4800 | −0.495248 | −0.247624 | − | 0.968856i | \(-0.579650\pi\) | ||||
−0.247624 | + | 0.968856i | \(0.579650\pi\) | |||||||
\(978\) | −24.0151 | −0.767917 | ||||||||
\(979\) | −59.3691 | −1.89744 | ||||||||
\(980\) | 2.29590 | 0.0733397 | ||||||||
\(981\) | −1.02177 | −0.0326226 | ||||||||
\(982\) | −21.3706 | −0.681964 | ||||||||
\(983\) | 24.3080 | 0.775304 | 0.387652 | − | 0.921806i | \(-0.373286\pi\) | ||||
0.387652 | + | 0.921806i | \(0.373286\pi\) | |||||||
\(984\) | 3.77479 | 0.120336 | ||||||||
\(985\) | −23.5036 | −0.748888 | ||||||||
\(986\) | −13.8552 | −0.441238 | ||||||||
\(987\) | 11.0248 | 0.350922 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.0379 | −0.509976 | ||||||||
\(990\) | −6.24698 | −0.198542 | ||||||||
\(991\) | 41.1196 | 1.30621 | 0.653104 | − | 0.757269i | \(-0.273467\pi\) | ||||
0.653104 | + | 0.757269i | \(0.273467\pi\) | |||||||
\(992\) | −3.53319 | −0.112179 | ||||||||
\(993\) | 12.1575 | 0.385807 | ||||||||
\(994\) | −1.14138 | −0.0362022 | ||||||||
\(995\) | −20.8442 | −0.660804 | ||||||||
\(996\) | −6.83877 | −0.216695 | ||||||||
\(997\) | 8.75063 | 0.277135 | 0.138568 | − | 0.990353i | \(-0.455750\pi\) | ||||
0.138568 | + | 0.990353i | \(0.455750\pi\) | |||||||
\(998\) | −26.6160 | −0.842513 | ||||||||
\(999\) | 4.65279 | 0.147208 |
(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 | 5070.2.a.bt.1.3 | yes | 3 | |
13.5 | odd | 4 | 5070.2.b.s.1351.3 | 6 | |||
13.8 | odd | 4 | 5070.2.b.s.1351.4 | 6 | |||
13.12 | even | 2 | 5070.2.a.bk.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bk.1.1 | ✓ | 3 | 13.12 | even | 2 | ||
5070.2.a.bt.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
5070.2.b.s.1351.3 | 6 | 13.5 | odd | 4 | |||
5070.2.b.s.1351.4 | 6 | 13.8 | odd | 4 |