Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, 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("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.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: | \(48.1977026600\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.244833 | −0.109493 | −0.0547463 | − | 0.998500i | \(-0.517435\pi\) | ||||
−0.0547463 | + | 0.998500i | \(0.517435\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.69533 | 1.01874 | 0.509369 | − | 0.860548i | \(-0.329879\pi\) | ||||
0.509369 | + | 0.860548i | \(0.329879\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.17525 | 1.25888 | 0.629442 | − | 0.777047i | \(-0.283283\pi\) | ||||
0.629442 | + | 0.777047i | \(0.283283\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.50565 | −1.24964 | −0.624822 | − | 0.780768i | \(-0.714828\pi\) | ||||
−0.624822 | + | 0.780768i | \(0.714828\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.244833 | 0.0632156 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.19780 | 0.290509 | 0.145255 | − | 0.989394i | \(-0.453600\pi\) | ||||
0.145255 | + | 0.989394i | \(0.453600\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.55525 | 0.586214 | 0.293107 | − | 0.956080i | \(-0.405311\pi\) | ||||
0.293107 | + | 0.956080i | \(0.405311\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.69533 | −0.588168 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.82577 | 1.00624 | 0.503122 | − | 0.864216i | \(-0.332185\pi\) | ||||
0.503122 | + | 0.864216i | \(0.332185\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.94006 | −0.988011 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.33354 | −0.433328 | −0.216664 | − | 0.976246i | \(-0.569518\pi\) | ||||
−0.216664 | + | 0.976246i | \(0.569518\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.83643 | 1.58707 | 0.793535 | − | 0.608525i | \(-0.208238\pi\) | ||||
0.793535 | + | 0.608525i | \(0.208238\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.17525 | −0.726817 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.659904 | −0.111544 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.02074 | 0.989803 | 0.494902 | − | 0.868949i | \(-0.335204\pi\) | ||||
0.494902 | + | 0.868949i | \(0.335204\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.50565 | 0.721482 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.45996 | −1.47740 | −0.738699 | − | 0.674036i | \(-0.764559\pi\) | ||||
−0.738699 | + | 0.674036i | \(0.764559\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.71148 | 1.17599 | 0.587995 | − | 0.808864i | \(-0.299917\pi\) | ||||
0.587995 | + | 0.808864i | \(0.299917\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.244833 | −0.0364975 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.80134 | 0.408618 | 0.204309 | − | 0.978906i | \(-0.434505\pi\) | ||||
0.204309 | + | 0.978906i | \(0.434505\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.264777 | 0.0378253 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.19780 | −0.167725 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.72490 | 0.511655 | 0.255827 | − | 0.966722i | \(-0.417652\pi\) | ||||
0.255827 | + | 0.966722i | \(0.417652\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.02224 | −0.137839 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.55525 | −0.338451 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.71732 | 0.874520 | 0.437260 | − | 0.899335i | \(-0.355949\pi\) | ||||
0.437260 | + | 0.899335i | \(0.355949\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.0509 | −1.28689 | −0.643443 | − | 0.765494i | \(-0.722495\pi\) | ||||
−0.643443 | + | 0.765494i | \(0.722495\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.69533 | 0.339579 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.10313 | 0.136827 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.48628 | −0.670256 | −0.335128 | − | 0.942173i | \(-0.608780\pi\) | ||||
−0.335128 | + | 0.942173i | \(0.608780\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.82577 | −0.580955 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.35862 | 0.279916 | 0.139958 | − | 0.990157i | \(-0.455303\pi\) | ||||
0.139958 | + | 0.990157i | \(0.455303\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.1415 | 1.18697 | 0.593485 | − | 0.804845i | \(-0.297752\pi\) | ||||
0.593485 | + | 0.804845i | \(0.297752\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.94006 | 0.570429 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.2536 | 1.28247 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.84247 | 0.207294 | 0.103647 | − | 0.994614i | \(-0.466949\pi\) | ||||
0.103647 | + | 0.994614i | \(0.466949\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.03637 | −0.662578 | −0.331289 | − | 0.943529i | \(-0.607483\pi\) | ||||
−0.331289 | + | 0.943529i | \(0.607483\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.293261 | −0.0318086 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.33354 | 0.250182 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.866842 | −0.0918851 | −0.0459425 | − | 0.998944i | \(-0.514629\pi\) | ||||
−0.0459425 | + | 0.998944i | \(0.514629\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.1442 | −1.27306 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.83643 | −0.916295 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.625608 | −0.0641861 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.72995 | 0.784858 | 0.392429 | − | 0.919782i | \(-0.371635\pi\) | ||||
0.392429 | + | 0.919782i | \(0.371635\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.17525 | 0.419628 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.545900 | −0.0543191 | −0.0271595 | − | 0.999631i | \(-0.508646\pi\) | ||||
−0.0271595 | + | 0.999631i | \(0.508646\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.90518 | −0.384789 | −0.192394 | − | 0.981318i | \(-0.561625\pi\) | ||||
−0.192394 | + | 0.981318i | \(0.561625\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.659904 | 0.0644001 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.18330 | 0.887783 | 0.443891 | − | 0.896081i | \(-0.353598\pi\) | ||||
0.443891 | + | 0.896081i | \(0.353598\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.00728 | −0.862741 | −0.431371 | − | 0.902175i | \(-0.641970\pi\) | ||||
−0.431371 | + | 0.902175i | \(0.641970\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.02074 | −0.571463 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.71190 | 0.443258 | 0.221629 | − | 0.975131i | \(-0.428863\pi\) | ||||
0.221629 | + | 0.975131i | \(0.428863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.18151 | −0.110176 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.50565 | −0.416548 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.22846 | 0.295952 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.43268 | 0.584790 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.45996 | 0.852976 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.43365 | 0.217673 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.6498 | −1.03375 | −0.516877 | − | 0.856060i | \(-0.672906\pi\) | ||||
−0.516877 | + | 0.856060i | \(0.672906\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.71148 | −0.678958 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.83085 | −0.159962 | −0.0799809 | − | 0.996796i | \(-0.525486\pi\) | ||||
−0.0799809 | + | 0.996796i | \(0.525486\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.88722 | 0.597198 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.244833 | 0.0210719 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.4853 | 1.15213 | 0.576065 | − | 0.817404i | \(-0.304587\pi\) | ||||
0.576065 | + | 0.817404i | \(0.304587\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.1740 | 0.947769 | 0.473885 | − | 0.880587i | \(-0.342851\pi\) | ||||
0.473885 | + | 0.880587i | \(0.342851\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.80134 | −0.235916 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.8122 | −1.57316 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.571328 | 0.0474462 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.264777 | −0.0218385 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −23.8442 | −1.95339 | −0.976696 | − | 0.214629i | \(-0.931146\pi\) | ||||
−0.976696 | + | 0.214629i | \(0.931146\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.56968 | −0.616011 | −0.308006 | − | 0.951385i | \(-0.599662\pi\) | ||||
−0.308006 | + | 0.951385i | \(0.599662\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.19780 | 0.0968363 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.16345 | −0.173772 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.6508 | 1.72792 | 0.863960 | − | 0.503561i | \(-0.167977\pi\) | ||||
0.863960 | + | 0.503561i | \(0.167977\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.72490 | −0.295404 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.0070 | 1.02510 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0454 | −1.25677 | −0.628386 | − | 0.777902i | \(-0.716284\pi\) | ||||
−0.628386 | + | 0.777902i | \(0.716284\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.02224 | 0.0795811 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.20314 | 0.712160 | 0.356080 | − | 0.934455i | \(-0.384113\pi\) | ||||
0.356080 | + | 0.934455i | \(0.384113\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.30091 | 0.561608 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.55525 | 0.195405 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.14157 | −0.695021 | −0.347510 | − | 0.937676i | \(-0.612973\pi\) | ||||
−0.347510 | + | 0.937676i | \(0.612973\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.3151 | −1.00652 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.71732 | −0.504904 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.68254 | −0.424733 | −0.212366 | − | 0.977190i | \(-0.568117\pi\) | ||||
−0.212366 | + | 0.977190i | \(0.568117\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.5449 | 1.67575 | 0.837874 | − | 0.545864i | \(-0.183798\pi\) | ||||
0.837874 | + | 0.545864i | \(0.183798\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.0509 | 0.742984 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.47407 | −0.108376 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.00111 | 0.365717 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.69533 | −0.196056 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.8900 | −1.00504 | −0.502521 | − | 0.864565i | \(-0.667594\pi\) | ||||
−0.502521 | + | 0.864565i | \(0.667594\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8571 | −0.853491 | −0.426745 | − | 0.904372i | \(-0.640340\pi\) | ||||
−0.426745 | + | 0.904372i | \(0.640340\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.10313 | −0.0789969 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.71344 | −0.549560 | −0.274780 | − | 0.961507i | \(-0.588605\pi\) | ||||
−0.274780 | + | 0.961507i | \(0.588605\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.8647 | 0.841068 | 0.420534 | − | 0.907277i | \(-0.361843\pi\) | ||||
0.420534 | + | 0.907277i | \(0.361843\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.48628 | 0.386972 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.28965 | −0.441447 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.31611 | 0.161764 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.82577 | 0.335415 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.6688 | 0.737975 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.8342 | 0.883545 | 0.441773 | − | 0.897127i | \(-0.354350\pi\) | ||||
0.441773 | + | 0.897127i | \(0.354350\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.35862 | −0.161610 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.88803 | −0.128762 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.8171 | 1.61681 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.1415 | −0.685298 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.39687 | −0.363033 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.5846 | 1.37844 | 0.689222 | − | 0.724550i | \(-0.257953\pi\) | ||||
0.689222 | + | 0.724550i | \(0.257953\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.94006 | −0.329337 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.9870 | −1.72482 | −0.862410 | − | 0.506211i | \(-0.831046\pi\) | ||||
−0.862410 | + | 0.506211i | \(0.831046\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.2462 | 1.07358 | 0.536791 | − | 0.843715i | \(-0.319636\pi\) | ||||
0.536791 | + | 0.843715i | \(0.319636\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.2536 | −0.740436 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.61228 | 0.564209 | 0.282104 | − | 0.959384i | \(-0.408968\pi\) | ||||
0.282104 | + | 0.959384i | \(0.408968\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.685861 | −0.0447406 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.84247 | −0.119681 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.0577 | 1.75022 | 0.875110 | − | 0.483924i | \(-0.160789\pi\) | ||||
0.875110 | + | 0.483924i | \(0.160789\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.99854 | 0.321985 | 0.160992 | − | 0.986956i | \(-0.448531\pi\) | ||||
0.160992 | + | 0.986956i | \(0.448531\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.0648262 | −0.00414160 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.5131 | −0.732558 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.03637 | 0.382539 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.14507 | 0.514113 | 0.257056 | − | 0.966396i | \(-0.417247\pi\) | ||||
0.257056 | + | 0.966396i | \(0.417247\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.1488 | 1.26674 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.293261 | 0.0183647 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.67847 | 0.541348 | 0.270674 | − | 0.962671i | \(-0.412753\pi\) | ||||
0.270674 | + | 0.962671i | \(0.412753\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.2278 | 1.00835 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.33354 | −0.144443 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.7470 | −0.971003 | −0.485501 | − | 0.874236i | \(-0.661363\pi\) | ||||
−0.485501 | + | 0.874236i | \(0.661363\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.911979 | −0.0560224 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.866842 | 0.0530499 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.5710 | 0.827440 | 0.413720 | − | 0.910404i | \(-0.364229\pi\) | ||||
0.413720 | + | 0.910404i | \(0.364229\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.8147 | 1.56813 | 0.784064 | − | 0.620679i | \(-0.213143\pi\) | ||||
0.784064 | + | 0.620679i | \(0.213143\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.1442 | 0.735000 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.6260 | −1.24379 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.9744 | −0.959809 | −0.479905 | − | 0.877321i | \(-0.659329\pi\) | ||||
−0.479905 | + | 0.877321i | \(0.659329\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.83643 | 0.529023 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.06969 | −0.183122 | −0.0915611 | − | 0.995799i | \(-0.529186\pi\) | ||||
−0.0915611 | + | 0.995799i | \(0.529186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.9714 | 1.90050 | 0.950250 | − | 0.311487i | \(-0.100827\pi\) | ||||
0.950250 | + | 0.311487i | \(0.100827\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.625608 | 0.0370578 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.4977 | −1.50508 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5653 | −0.915605 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.72995 | −0.453138 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.2704 | −1.12579 | −0.562893 | − | 0.826530i | \(-0.690312\pi\) | ||||
−0.562893 | + | 0.826530i | \(0.690312\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.64462 | −0.0957535 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.17525 | −0.242272 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.7433 | −1.25745 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.7850 | 1.19803 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.545900 | 0.0313611 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.46079 | 0.140905 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.36581 | 0.363316 | 0.181658 | − | 0.983362i | \(-0.441854\pi\) | ||||
0.181658 | + | 0.983362i | \(0.441854\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.90518 | 0.222158 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.4669 | 1.67092 | 0.835458 | − | 0.549554i | \(-0.185202\pi\) | ||||
0.835458 | + | 0.549554i | \(0.185202\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.9018 | 1.29448 | 0.647242 | − | 0.762285i | \(-0.275922\pi\) | ||||
0.647242 | + | 0.762285i | \(0.275922\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.659904 | −0.0371814 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.7613 | −1.67156 | −0.835780 | − | 0.549065i | \(-0.814984\pi\) | ||||
−0.835780 | + | 0.549065i | \(0.814984\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.74311 | −0.545510 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.18330 | −0.512562 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.06067 | 0.170300 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.2582 | 1.23466 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.00728 | 0.498104 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.55053 | 0.416274 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.56891 | −0.361060 | −0.180530 | − | 0.983569i | \(-0.557781\pi\) | ||||
−0.180530 | + | 0.983569i | \(0.557781\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.02074 | 0.329934 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.34322 | 0.0733881 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.65801 | 0.417159 | 0.208579 | − | 0.978005i | \(-0.433116\pi\) | ||||
0.208579 | + | 0.978005i | \(0.433116\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.71190 | −0.255915 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36.8943 | 1.99794 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.1536 | −0.980203 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.18151 | 0.0636103 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.1422 | −0.705512 | −0.352756 | − | 0.935715i | \(-0.614755\pi\) | ||||
−0.352756 | + | 0.935715i | \(0.614755\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.85668 | 0.313501 | 0.156750 | − | 0.987638i | \(-0.449898\pi\) | ||||
0.156750 | + | 0.987638i | \(0.449898\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.50565 | 0.240494 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.81238 | −0.522260 | −0.261130 | − | 0.965304i | \(-0.584095\pi\) | ||||
−0.261130 | + | 0.965304i | \(0.584095\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.577467 | −0.0306488 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.22846 | −0.170868 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.9807 | 1.26565 | 0.632825 | − | 0.774295i | \(-0.281895\pi\) | ||||
0.632825 | + | 0.774295i | \(0.281895\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.4707 | −0.656354 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.43268 | −0.337628 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.48297 | −0.129964 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.4318 | 1.43193 | 0.715963 | − | 0.698138i | \(-0.245988\pi\) | ||||
0.715963 | + | 0.698138i | \(0.245988\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.45996 | −0.492466 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.0398 | 0.521242 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.9189 | 0.876028 | 0.438014 | − | 0.898968i | \(-0.355682\pi\) | ||||
0.438014 | + | 0.898968i | \(0.355682\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.43365 | −0.125673 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.5141 | 0.541505 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.6865 | 1.88446 | 0.942229 | − | 0.334968i | \(-0.108726\pi\) | ||||
0.942229 | + | 0.334968i | \(0.108726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.6498 | 0.596838 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.57033 | −0.0802403 | −0.0401201 | − | 0.999195i | \(-0.512774\pi\) | ||||
−0.0401201 | + | 0.999195i | \(0.512774\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.75526 | −0.140421 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.71148 | 0.391997 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.54858 | 0.484132 | 0.242066 | − | 0.970260i | \(-0.422175\pi\) | ||||
0.242066 | + | 0.970260i | \(0.422175\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.78031 | 0.292323 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.83085 | 0.0923540 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.451096 | −0.0226971 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.85597 | 0.293903 | 0.146951 | − | 0.989144i | \(-0.453054\pi\) | ||||
0.146951 | + | 0.989144i | \(0.453054\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.88722 | −0.344792 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.88455 | 0.393735 | 0.196868 | − | 0.980430i | \(-0.436923\pi\) | ||||
0.196868 | + | 0.980430i | \(0.436923\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −39.8139 | −1.98327 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.244833 | −0.0121658 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.1381 | 1.24605 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.8972 | 1.52777 | 0.763884 | − | 0.645353i | \(-0.223290\pi\) | ||||
0.763884 | + | 0.645353i | \(0.223290\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.4853 | −0.665183 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.1054 | 0.890906 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.47790 | 0.0725474 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.1740 | −0.547195 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.8669 | 1.70336 | 0.851679 | − | 0.524063i | \(-0.175585\pi\) | ||||
0.851679 | + | 0.524063i | \(0.175585\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.2800 | 1.18334 | 0.591668 | − | 0.806182i | \(-0.298470\pi\) | ||||
0.591668 | + | 0.806182i | \(0.298470\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.80134 | 0.136206 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.91720 | −0.287026 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.0905 | −1.31100 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.8122 | 0.908262 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.0586 | −1.49604 | −0.748020 | − | 0.663676i | \(-0.768995\pi\) | ||||
−0.748020 | + | 0.663676i | \(0.768995\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.40142 | 0.115405 | 0.0577025 | − | 0.998334i | \(-0.481623\pi\) | ||||
0.0577025 | + | 0.998334i | \(0.481623\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.571328 | −0.0273931 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.3310 | 0.589874 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.0664 | 0.719081 | 0.359540 | − | 0.933129i | \(-0.382933\pi\) | ||||
0.359540 | + | 0.933129i | \(0.382933\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.264777 | 0.0126084 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.31651 | −0.157572 | −0.0787861 | − | 0.996892i | \(-0.525104\pi\) | ||||
−0.0787861 | + | 0.996892i | \(0.525104\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.212231 | 0.0100607 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 23.8442 | 1.12779 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.9427 | 0.988347 | 0.494174 | − | 0.869363i | \(-0.335471\pi\) | ||||
0.494174 | + | 0.869363i | \(0.335471\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −39.4977 | −1.85987 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.56968 | 0.355654 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.97330 | 0.139390 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.5175 | 0.491988 | 0.245994 | − | 0.969271i | \(-0.420886\pi\) | ||||
0.245994 | + | 0.969271i | \(0.420886\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.19780 | −0.0559085 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.6364 | −0.821408 | −0.410704 | − | 0.911769i | \(-0.634717\pi\) | ||||
−0.410704 | + | 0.911769i | \(0.634717\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.71983 | 0.172875 | 0.0864375 | − | 0.996257i | \(-0.472452\pi\) | ||||
0.0864375 | + | 0.996257i | \(0.472452\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.16345 | 0.100328 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.4817 | −1.36425 | −0.682125 | − | 0.731236i | \(-0.738944\pi\) | ||||
−0.682125 | + | 0.731236i | \(0.738944\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.7873 | −0.682815 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.6508 | −0.997615 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.1974 | 1.48044 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.6231 | −0.579186 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.72490 | 0.170552 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.4820 | 1.62122 | 0.810608 | − | 0.585590i | \(-0.199137\pi\) | ||||
0.810608 | + | 0.585590i | \(0.199137\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.1274 | −1.23690 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.0070 | −0.591840 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.89255 | −0.0859361 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.19988 | 0.0996862 | 0.0498431 | − | 0.998757i | \(-0.484128\pi\) | ||||
0.0498431 | + | 0.998757i | \(0.484128\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.0454 | 0.725598 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.81164 | 0.126888 | 0.0634438 | − | 0.997985i | \(-0.479792\pi\) | ||||
0.0634438 | + | 0.997985i | \(0.479792\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.79511 | −0.125886 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.02224 | −0.0459462 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.35724 | 0.285161 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.4483 | 1.13922 | 0.569612 | − | 0.821914i | \(-0.307094\pi\) | ||||
0.569612 | + | 0.821914i | \(0.307094\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.20314 | −0.411166 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.133654 | 0.00594754 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.30091 | −0.324245 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.89029 | 0.172434 | 0.0862170 | − | 0.996276i | \(-0.472522\pi\) | ||||
0.0862170 | + | 0.996276i | \(0.472522\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.3346 | 1.20921 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.55525 | −0.112817 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.956116 | 0.0421315 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.6963 | 0.514402 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.14157 | 0.401270 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.72429 | −0.119353 | −0.0596767 | − | 0.998218i | \(-0.519007\pi\) | ||||
−0.0596767 | + | 0.998218i | \(0.519007\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.6255 | −1.20798 | −0.603990 | − | 0.796992i | \(-0.706423\pi\) | ||||
−0.603990 | + | 0.796992i | \(0.706423\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.3151 | 0.581117 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.5843 | 0.461058 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.288101 | 0.0125261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.71732 | 0.291507 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.6233 | 1.84622 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.24837 | −0.0972057 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.68254 | 0.245220 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.10551 | 0.0476177 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.0276 | −0.904048 | −0.452024 | − | 0.892006i | \(-0.649298\pi\) | ||||
−0.452024 | + | 0.892006i | \(0.649298\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.5449 | −0.967493 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.20528 | 0.0944638 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.1019 | −0.688470 | −0.344235 | − | 0.938884i | \(-0.611862\pi\) | ||||
−0.344235 | + | 0.938884i | \(0.611862\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.0509 | −0.428962 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.96277 | −0.254023 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.96605 | 0.211178 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.47407 | 0.0625710 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.8272 | 1.05196 | 0.525981 | − | 0.850496i | \(-0.323698\pi\) | ||||
0.525981 | + | 0.850496i | \(0.323698\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −34.7453 | −1.46957 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.00111 | −0.211147 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.5378 | −0.781276 | −0.390638 | − | 0.920544i | \(-0.627746\pi\) | ||||
−0.390638 | + | 0.920544i | \(0.627746\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.15363 | −0.0485335 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.69533 | 0.113193 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.86399 | 0.0781424 | 0.0390712 | − | 0.999236i | \(-0.487560\pi\) | ||||
0.0390712 | + | 0.999236i | \(0.487560\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.01062 | 0.167839 | 0.0839197 | − | 0.996473i | \(-0.473256\pi\) | ||||
0.0839197 | + | 0.996473i | \(0.473256\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.8900 | 0.580262 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.8396 | −0.994180 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.58184 | 0.0658527 | 0.0329264 | − | 0.999458i | \(-0.489517\pi\) | ||||
0.0329264 | + | 0.999458i | \(0.489517\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.8571 | 0.492763 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.2700 | −0.674993 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.5524 | 0.644114 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.10313 | 0.0456089 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.5921 | −1.22140 | −0.610698 | − | 0.791863i | \(-0.709111\pi\) | ||||
−0.610698 | + | 0.791863i | \(0.709111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.5793 | 0.930362 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.71344 | 0.317289 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.9349 | −1.06502 | −0.532510 | − | 0.846424i | \(-0.678751\pi\) | ||||
−0.532510 | + | 0.846424i | \(0.678751\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.790433 | −0.0324046 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.8647 | −0.485591 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.9091 | 1.46721 | 0.733604 | − | 0.679578i | \(-0.237837\pi\) | ||||
0.733604 | + | 0.679578i | \(0.237837\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.35909 | 0.381765 | 0.190883 | − | 0.981613i | \(-0.438865\pi\) | ||||
0.190883 | + | 0.981613i | \(0.438865\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.48628 | −0.223419 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.57493 | −0.0640301 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.5857 | 0.997902 | 0.498951 | − | 0.866630i | \(-0.333719\pi\) | ||||
0.498951 | + | 0.866630i | \(0.333719\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.28965 | 0.254870 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.6219 | −0.510626 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.5654 | −1.07297 | −0.536483 | − | 0.843911i | \(-0.680248\pi\) | ||||
−0.536483 | + | 0.843911i | \(0.680248\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.31611 | −0.0933945 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.2929 | −1.09877 | −0.549385 | − | 0.835570i | \(-0.685138\pi\) | ||||
−0.549385 | + | 0.835570i | \(0.685138\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.6654 | 0.710032 | 0.355016 | − | 0.934860i | \(-0.384475\pi\) | ||||
0.355016 | + | 0.934860i | \(0.384475\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.82577 | −0.193652 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.33642 | −0.0936067 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.1044 | 0.964178 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.6688 | −0.426070 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.21164 | 0.287547 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.3134 | 1.72428 | 0.862139 | − | 0.506672i | \(-0.169124\pi\) | ||||
0.862139 | + | 0.506672i | \(0.169124\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.8342 | −0.510115 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.85226 | 0.113188 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.19300 | −0.0472682 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.35862 | 0.0933054 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.0104 | 0.434884 | 0.217442 | − | 0.976073i | \(-0.430229\pi\) | ||||
0.217442 | + | 0.976073i | \(0.430229\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.4543 | 0.885513 | 0.442756 | − | 0.896642i | \(-0.354001\pi\) | ||||
0.442756 | + | 0.896642i | \(0.354001\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.88803 | 0.0743409 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.60853 | −0.181180 | −0.0905900 | − | 0.995888i | \(-0.528875\pi\) | ||||
−0.0905900 | + | 0.995888i | \(0.528875\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.0465 | 1.10092 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.8171 | −0.933464 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.19941 | 0.242602 | 0.121301 | − | 0.992616i | \(-0.461293\pi\) | ||||
0.121301 | + | 0.992616i | \(0.461293\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.448251 | 0.0175146 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.1415 | 0.395657 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.6675 | −1.77895 | −0.889477 | − | 0.456980i | \(-0.848931\pi\) | ||||
−0.889477 | + | 0.456980i | \(0.848931\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.1949 | −1.56340 | −0.781701 | − | 0.623654i | \(-0.785648\pi\) | ||||
−0.781701 | + | 0.623654i | \(0.785648\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.39687 | 0.209597 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.68622 | −0.0653887 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.2611 | −0.436033 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.5846 | −0.795845 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.9650 | −1.62004 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.7682 | −0.530727 | −0.265363 | − | 0.964148i | \(-0.585492\pi\) | ||||
−0.265363 | + | 0.964148i | \(0.585492\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.94006 | 0.190143 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −48.3502 | −1.85825 | −0.929124 | − | 0.369768i | \(-0.879437\pi\) | ||||
−0.929124 | + | 0.369768i | \(0.879437\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.8347 | 0.799564 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.9870 | 0.995825 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.3798 | −1.50683 | −0.753414 | − | 0.657547i | \(-0.771594\pi\) | ||||
−0.753414 | + | 0.657547i | \(0.771594\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.30166 | −0.126150 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.2462 | −0.619833 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.7831 | −0.639386 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.0610 | −1.48595 | −0.742975 | − | 0.669319i | \(-0.766586\pi\) | ||||
−0.742975 | + | 0.669319i | \(0.766586\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.2536 | 0.427491 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.73577 | −0.103774 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.3311 | −0.429197 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.61228 | −0.325746 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −47.4853 | −1.79349 | −0.896747 | − | 0.442543i | \(-0.854076\pi\) | ||||
−0.896747 | + | 0.442543i | \(0.854076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.3845 | 0.580236 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.685861 | 0.0258310 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.47138 | −0.0553369 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.0321 | 0.414319 | 0.207160 | − | 0.978307i | \(-0.433578\pi\) | ||||
0.207160 | + | 0.978307i | \(0.433578\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.84247 | 0.0690979 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 42.6426 | 1.59698 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.60585 | 0.172249 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.0577 | −1.01049 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.9644 | 0.595371 | 0.297686 | − | 0.954664i | \(-0.403785\pi\) | ||||
0.297686 | + | 0.954664i | \(0.403785\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.5257 | −0.391998 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.99854 | −0.185898 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.5278 | 0.428133 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.5597 | −1.65263 | −0.826315 | − | 0.563209i | \(-0.809567\pi\) | ||||
−0.826315 | + | 0.563209i | \(0.809567\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.23681 | 0.341636 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.4408 | −1.67839 | −0.839196 | − | 0.543828i | \(-0.816974\pi\) | ||||
−0.839196 | + | 0.543828i | \(0.816974\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.0648262 | 0.00239115 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.9066 | −0.843775 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.70406 | 0.283398 | 0.141699 | − | 0.989910i | \(-0.454743\pi\) | ||||
0.141699 | + | 0.989910i | \(0.454743\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.5131 | 0.422943 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.0135 | −0.404047 | −0.202024 | − | 0.979381i | \(-0.564752\pi\) | ||||
−0.202024 | + | 0.979381i | \(0.564752\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.83784 | 0.213882 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.03637 | −0.220859 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.7520 | 0.904417 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.3053 | −0.813933 | −0.406967 | − | 0.913443i | \(-0.633413\pi\) | ||||
−0.406967 | + | 0.913443i | \(0.633413\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.14507 | −0.296823 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.85331 | 0.0674487 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.29421 | 0.228767 | 0.114383 | − | 0.993437i | \(-0.463511\pi\) | ||||
0.114383 | + | 0.993437i | \(0.463511\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20.1488 | −0.731355 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.7260 | 0.533817 | 0.266909 | − | 0.963722i | \(-0.413998\pi\) | ||||
0.266909 | + | 0.963722i | \(0.413998\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.2776 | −0.878906 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.293261 | −0.0106029 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −30.2659 | −1.09284 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.6883 | 1.14271 | 0.571354 | − | 0.820704i | \(-0.306418\pi\) | ||||
0.571354 | + | 0.820704i | \(0.306418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.67847 | −0.312547 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.7530 | 1.21401 | 0.607005 | − | 0.794698i | \(-0.292371\pi\) | ||||
0.607005 | + | 0.794698i | \(0.292371\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −43.6525 | −1.56804 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.2278 | −0.582171 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.1725 | −0.866071 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.84781 | 0.352382 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.33354 | 0.0833940 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.30082 | −0.189194 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.27299 | 0.330546 | 0.165273 | − | 0.986248i | \(-0.447149\pi\) | ||||
0.165273 | + | 0.986248i | \(0.447149\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.7470 | 0.560609 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.7001 | 0.451564 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45.2859 | 1.60815 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.911979 | 0.0323446 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.7808 | 1.47995 | 0.739976 | − | 0.672633i | \(-0.234837\pi\) | ||||
0.739976 | + | 0.672633i | \(0.234837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.35545 | 0.118707 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.866842 | −0.0306284 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 42.3432 | 1.49426 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.18455 | −0.112241 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.5710 | −0.477723 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.07013 | 0.178256 | 0.0891282 | − | 0.996020i | \(-0.471592\pi\) | ||||
0.0891282 | + | 0.996020i | \(0.471592\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.4918 | −0.649334 | −0.324667 | − | 0.945828i | \(-0.605252\pi\) | ||||
−0.324667 | + | 0.945828i | \(0.605252\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.8147 | −0.905360 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.92844 | 0.137607 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.7047 | 0.689382 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.1442 | −0.424353 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.55963 | 0.298733 | 0.149367 | − | 0.988782i | \(-0.452277\pi\) | ||||
0.149367 | + | 0.988782i | \(0.452277\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.229162 | 0.00798809 | 0.00399405 | − | 0.999992i | \(-0.498729\pi\) | ||||
0.00399405 | + | 0.999992i | \(0.498729\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20.6260 | 0.718104 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.2949 | −0.357987 | −0.178994 | − | 0.983850i | \(-0.557284\pi\) | ||||
−0.178994 | + | 0.983850i | \(0.557284\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.42281 | 0.153611 | 0.0768053 | − | 0.997046i | \(-0.475528\pi\) | ||||
0.0768053 | + | 0.997046i | \(0.475528\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.9744 | 0.554146 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.317150 | 0.0109886 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.25323 | −0.0779763 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.83643 | −0.305432 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.2460 | −1.04421 | −0.522103 | − | 0.852882i | \(-0.674852\pi\) | ||||
−0.522103 | + | 0.852882i | \(0.674852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.5546 | −0.812227 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.06969 | 0.105726 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.78750 | −0.0614920 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.3382 | 0.595747 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.9714 | −1.09725 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.0547 | 0.995983 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.7512 | 0.813227 | 0.406613 | − | 0.913600i | \(-0.366710\pi\) | ||||
0.406613 | + | 0.913600i | \(0.366710\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.625608 | −0.0213954 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.2245 | −0.895813 | −0.447906 | − | 0.894080i | \(-0.647830\pi\) | ||||
−0.447906 | + | 0.894080i | \(0.647830\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.5067 | 1.21147 | 0.605736 | − | 0.795665i | \(-0.292879\pi\) | ||||
0.605736 | + | 0.795665i | \(0.292879\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.4977 | 0.868958 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.2621 | −0.825891 | −0.412945 | − | 0.910756i | \(-0.635500\pi\) | ||||
−0.412945 | + | 0.910756i | \(0.635500\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.23816 | 0.0760996 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.5653 | 0.528625 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.69275 | 0.260959 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.7193 | 0.837581 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.72995 | 0.261619 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.55949 | 0.221751 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.06096 | −0.305967 | −0.152983 | − | 0.988229i | \(-0.548888\pi\) | ||||
−0.152983 | + | 0.988229i | \(0.548888\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.2704 | 0.649973 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.6812 | −1.53904 | −0.769519 | − | 0.638624i | \(-0.779504\pi\) | ||||
−0.769519 | + | 0.638624i | \(0.779504\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.1800 | −1.38582 | −0.692909 | − | 0.721025i | \(-0.743671\pi\) | ||||
−0.692909 | + | 0.721025i | \(0.743671\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.64462 | 0.0552833 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.3278 | 0.716119 | 0.358059 | − | 0.933699i | \(-0.383438\pi\) | ||||
0.358059 | + | 0.933699i | \(0.383438\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.4000 | −1.05312 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.17525 | 0.139876 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.15812 | 0.239537 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.39127 | 0.0465051 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21.7433 | 0.725987 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.6202 | −0.687721 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.46169 | 0.148640 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.7850 | −0.691680 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.51973 | −0.183482 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.9012 | 1.75656 | 0.878278 | − | 0.478151i | \(-0.158693\pi\) | ||||
0.878278 | + | 0.478151i | \(0.158693\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.545900 | −0.0181064 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.5751 | −0.549159 | −0.274579 | − | 0.961564i | \(-0.588539\pi\) | ||||
−0.274579 | + | 0.961564i | \(0.588539\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.2033 | −0.834109 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.46079 | −0.0813513 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.93473 | −0.162959 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.8122 | −1.14835 | −0.574174 | − | 0.818733i | \(-0.694677\pi\) | ||||
−0.574174 | + | 0.818733i | \(0.694677\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.36581 | −0.209761 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.6271 | −0.349796 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.7428 | −0.977937 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.90518 | −0.128263 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.6853 | 1.66293 | 0.831466 | − | 0.555576i | \(-0.187502\pi\) | ||||
0.831466 | + | 0.555576i | \(0.187502\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.676571 | 0.0221737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −29.4669 | −0.964704 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.22444 | −0.0400433 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.2435 | 0.367310 | 0.183655 | − | 0.982991i | \(-0.441207\pi\) | ||||
0.183655 | + | 0.982991i | \(0.441207\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.9018 | −0.747371 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.98689 | −0.195167 | −0.0975836 | − | 0.995227i | \(-0.531111\pi\) | ||||
−0.0975836 | + | 0.995227i | \(0.531111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −45.6516 | −1.48662 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.659904 | 0.0214667 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.43436 | 0.176593 | 0.0882965 | − | 0.996094i | \(-0.471858\pi\) | ||||
0.0882965 | + | 0.996094i | \(0.471858\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.6940 | −1.48329 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.7613 | 0.965075 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.33785 | −0.205303 | −0.102652 | − | 0.994717i | \(-0.532733\pi\) | ||||
−0.102652 | + | 0.994717i | \(0.532733\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.40072 | 0.110045 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.74311 | 0.314950 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36.3474 | 1.17372 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 47.0825 | 1.51879 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.18330 | 0.295928 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.90300 | 0.0934509 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8182 | 0.412206 | 0.206103 | − | 0.978530i | \(-0.433922\pi\) | ||||
0.206103 | + | 0.978530i | \(0.433922\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.06067 | −0.0983230 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.2204 | −1.41910 | −0.709549 | − | 0.704656i | \(-0.751101\pi\) | ||||
−0.709549 | + | 0.704656i | \(0.751101\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.1177 | 0.965528 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22.2582 | −0.712832 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.9512 | −0.382354 | −0.191177 | − | 0.981556i | \(-0.561230\pi\) | ||||
−0.191177 | + | 0.981556i | \(0.561230\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.61928 | −0.115673 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.00728 | −0.287580 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.5494 | −0.495950 | −0.247975 | − | 0.968766i | \(-0.579765\pi\) | ||||
−0.247975 | + | 0.968766i | \(0.579765\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.88850 | 0.0601728 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.55053 | −0.240336 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.2139 | 1.18333 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.6255 | 0.464594 | 0.232297 | − | 0.972645i | \(-0.425376\pi\) | ||||
0.232297 | + | 0.972645i | \(0.425376\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.56891 | 0.208458 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.90488 | −0.0920908 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.0004 | −0.633420 | −0.316710 | − | 0.948522i | \(-0.602578\pi\) | ||||
−0.316710 | + | 0.948522i | \(0.602578\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.02074 | −0.190488 |
(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 | 6036.2.a.i.1.12 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.i.1.12 | ✓ | 26 | 1.1 | even | 1 | trivial |