Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6044,2,Mod(1,6044)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6044, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6044.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6044 = 2^{2} \cdot 1511 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6044.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: | \(48.2615829817\) |
Analytic rank: | \(0\) |
Dimension: | \(63\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6044.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.50519 | −1.44637 | −0.723186 | − | 0.690653i | \(-0.757323\pi\) | ||||
−0.723186 | + | 0.690653i | \(0.757323\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.30564 | −0.583898 | −0.291949 | − | 0.956434i | \(-0.594304\pi\) | ||||
−0.291949 | + | 0.956434i | \(0.594304\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.79113 | 1.43291 | 0.716456 | − | 0.697633i | \(-0.245763\pi\) | ||||
0.716456 | + | 0.697633i | \(0.245763\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.27598 | 1.09199 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.363607 | −0.109632 | −0.0548158 | − | 0.998496i | \(-0.517457\pi\) | ||||
−0.0548158 | + | 0.998496i | \(0.517457\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.90367 | 0.527983 | 0.263992 | − | 0.964525i | \(-0.414961\pi\) | ||||
0.263992 | + | 0.964525i | \(0.414961\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.27087 | 0.844534 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.86448 | 0.937275 | 0.468637 | − | 0.883391i | \(-0.344745\pi\) | ||||
0.468637 | + | 0.883391i | \(0.344745\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.31712 | 1.67866 | 0.839331 | − | 0.543620i | \(-0.182947\pi\) | ||||
0.839331 | + | 0.543620i | \(0.182947\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.49750 | −2.07252 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.47630 | −0.516344 | −0.258172 | − | 0.966099i | \(-0.583120\pi\) | ||||
−0.258172 | + | 0.966099i | \(0.583120\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.29532 | −0.659063 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.691391 | −0.133058 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.83219 | 0.897315 | 0.448658 | − | 0.893704i | \(-0.351902\pi\) | ||||
0.448658 | + | 0.893704i | \(0.351902\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.05699 | 1.62668 | 0.813342 | − | 0.581786i | \(-0.197646\pi\) | ||||
0.813342 | + | 0.581786i | \(0.197646\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.910906 | 0.158568 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.94983 | −0.836674 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.6804 | 1.75585 | 0.877923 | − | 0.478801i | \(-0.158929\pi\) | ||||
0.877923 | + | 0.478801i | \(0.158929\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.76906 | −0.763661 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.69290 | 0.732908 | 0.366454 | − | 0.930436i | \(-0.380572\pi\) | ||||
0.366454 | + | 0.930436i | \(0.380572\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.101108 | 0.0154189 | 0.00770945 | − | 0.999970i | \(-0.497546\pi\) | ||||
0.00770945 | + | 0.999970i | \(0.497546\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.27724 | −0.637613 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.9937 | −1.89532 | −0.947662 | − | 0.319276i | \(-0.896560\pi\) | ||||
−0.947662 | + | 0.319276i | \(0.896560\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.37264 | 1.05323 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.68127 | −1.35565 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.44907 | −0.885847 | −0.442924 | − | 0.896559i | \(-0.646059\pi\) | ||||
−0.442924 | + | 0.896559i | \(0.646059\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.474738 | 0.0640137 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.3308 | −2.42797 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.2369 | 1.33273 | 0.666365 | − | 0.745626i | \(-0.267849\pi\) | ||||
0.666365 | + | 0.745626i | \(0.267849\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.80135 | 0.486713 | 0.243356 | − | 0.969937i | \(-0.421752\pi\) | ||||
0.243356 | + | 0.969937i | \(0.421752\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.4197 | 1.56473 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.48550 | −0.308288 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.43573 | −0.664081 | −0.332040 | − | 0.943265i | \(-0.607737\pi\) | ||||
−0.332040 | + | 0.943265i | \(0.607737\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.20361 | 0.746826 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.86368 | −0.695890 | −0.347945 | − | 0.937515i | \(-0.613120\pi\) | ||||
−0.347945 | + | 0.937515i | \(0.613120\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.4405 | 1.57309 | 0.786543 | − | 0.617535i | \(-0.211869\pi\) | ||||
0.786543 | + | 0.617535i | \(0.211869\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.25540 | 0.953251 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.37848 | −0.157092 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.85479 | 0.546207 | 0.273103 | − | 0.961985i | \(-0.411950\pi\) | ||||
0.273103 | + | 0.961985i | \(0.411950\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.09588 | −0.899543 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.14749 | −0.565010 | −0.282505 | − | 0.959266i | \(-0.591165\pi\) | ||||
−0.282505 | + | 0.959266i | \(0.591165\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.04560 | −0.547273 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.1056 | −1.29785 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.25481 | −0.451009 | −0.225505 | − | 0.974242i | \(-0.572403\pi\) | ||||
−0.225505 | + | 0.974242i | \(0.572403\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.21706 | 0.756553 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −22.6895 | −2.35279 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.55349 | −0.980167 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.3728 | −1.66240 | −0.831202 | − | 0.555971i | \(-0.812347\pi\) | ||||
−0.831202 | + | 0.555971i | \(0.812347\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.19117 | −0.119717 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.9032 | −1.08491 | −0.542457 | − | 0.840084i | \(-0.682506\pi\) | ||||
−0.542457 | + | 0.840084i | \(0.682506\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.12837 | 0.899445 | 0.449722 | − | 0.893168i | \(-0.351523\pi\) | ||||
0.449722 | + | 0.893168i | \(0.351523\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.4003 | 1.21014 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.86200 | 0.856722 | 0.428361 | − | 0.903608i | \(-0.359091\pi\) | ||||
0.428361 | + | 0.903608i | \(0.359091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.0160 | 1.62984 | 0.814919 | − | 0.579575i | \(-0.196782\pi\) | ||||
0.814919 | + | 0.579575i | \(0.196782\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26.7564 | −2.53961 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.85554 | 0.738987 | 0.369493 | − | 0.929233i | \(-0.379531\pi\) | ||||
0.369493 | + | 0.929233i | \(0.379531\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.23314 | 0.301492 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.23639 | 0.576555 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.6507 | 1.34303 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8678 | −0.987981 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.7566 | −1.06006 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.8307 | 0.968723 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.0754 | −0.982783 | −0.491392 | − | 0.870939i | \(-0.663512\pi\) | ||||
−0.491392 | + | 0.870939i | \(0.663512\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.253296 | −0.0223015 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.53234 | 0.133881 | 0.0669407 | − | 0.997757i | \(-0.478676\pi\) | ||||
0.0669407 | + | 0.997757i | \(0.478676\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 27.7401 | 2.40537 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.902704 | 0.0776924 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −22.7154 | −1.94071 | −0.970353 | − | 0.241693i | \(-0.922297\pi\) | ||||
−0.970353 | + | 0.241693i | \(0.922297\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.29404 | −0.364215 | −0.182108 | − | 0.983279i | \(-0.558292\pi\) | ||||
−0.182108 | + | 0.983279i | \(0.558292\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 32.5517 | 2.74134 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.692188 | −0.0578837 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.30908 | −0.523940 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −18.4699 | −1.52337 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.3655 | −1.25879 | −0.629395 | − | 0.777085i | \(-0.716697\pi\) | ||||
−0.629395 | + | 0.777085i | \(0.716697\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.62007 | 0.131840 | 0.0659198 | − | 0.997825i | \(-0.479002\pi\) | ||||
0.0659198 | + | 0.997825i | \(0.479002\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.6600 | 1.02350 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.8251 | −0.949817 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.22084 | −0.496477 | −0.248238 | − | 0.968699i | \(-0.579852\pi\) | ||||
−0.248238 | + | 0.968699i | \(0.579852\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.1561 | 1.28127 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.38797 | −0.739875 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.606523 | 0.0475066 | 0.0237533 | − | 0.999718i | \(-0.492438\pi\) | ||||
0.0237533 | + | 0.999718i | \(0.492438\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.18931 | −0.0925877 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.57408 | 0.586100 | 0.293050 | − | 0.956097i | \(-0.405330\pi\) | ||||
0.293050 | + | 0.956097i | \(0.405330\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.37604 | −0.721234 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 23.9708 | 1.83309 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.51583 | −0.495390 | −0.247695 | − | 0.968838i | \(-0.579673\pi\) | ||||
−0.247695 | + | 0.968838i | \(0.579673\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.4930 | −0.944379 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −25.6454 | −1.92762 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.1836 | 1.20962 | 0.604811 | − | 0.796369i | \(-0.293249\pi\) | ||||
0.604811 | + | 0.796369i | \(0.293249\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.78504 | −0.578657 | −0.289329 | − | 0.957230i | \(-0.593432\pi\) | ||||
−0.289329 | + | 0.957230i | \(0.593432\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.52310 | −0.703968 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.9447 | −1.02523 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.40515 | −0.102755 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.62115 | −0.190661 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.48036 | −0.613618 | −0.306809 | − | 0.951771i | \(-0.599261\pi\) | ||||
−0.306809 | + | 0.951771i | \(0.599261\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.5606 | −1.04809 | −0.524047 | − | 0.851689i | \(-0.675578\pi\) | ||||
−0.524047 | + | 0.851689i | \(0.675578\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.22665 | 0.445900 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.8459 | 1.34272 | 0.671359 | − | 0.741132i | \(-0.265711\pi\) | ||||
0.671359 | + | 0.741132i | \(0.265711\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.6566 | −1.81874 | −0.909372 | − | 0.415983i | \(-0.863438\pi\) | ||||
−0.909372 | + | 0.415983i | \(0.863438\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.6176 | 0.960508 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.3194 | 1.28577 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.12722 | −0.427944 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.11232 | −0.563845 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.66056 | −0.184035 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.97393 | 0.411262 | 0.205631 | − | 0.978630i | \(-0.434075\pi\) | ||||
0.205631 | + | 0.978630i | \(0.434075\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.6896 | 1.00652 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.132011 | −0.00900306 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 34.3362 | 2.33089 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −33.6709 | −2.27527 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.35670 | 0.494865 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.52259 | 0.570715 | 0.285357 | − | 0.958421i | \(-0.407888\pi\) | ||||
0.285357 | + | 0.958421i | \(0.407888\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.7954 | −0.719694 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 29.0376 | 1.92729 | 0.963645 | − | 0.267185i | \(-0.0860934\pi\) | ||||
0.963645 | + | 0.267185i | \(0.0860934\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.8023 | 0.713833 | 0.356917 | − | 0.934136i | \(-0.383828\pi\) | ||||
0.356917 | + | 0.934136i | \(0.383828\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.45336 | 0.227214 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.81216 | 0.249743 | 0.124872 | − | 0.992173i | \(-0.460148\pi\) | ||||
0.124872 | + | 0.992173i | \(0.460148\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.9650 | 1.10668 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.1622 | −0.790018 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.6567 | 0.818692 | 0.409346 | − | 0.912379i | \(-0.365757\pi\) | ||||
0.409346 | + | 0.912379i | \(0.365757\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.1475 | 1.74873 | 0.874363 | − | 0.485272i | \(-0.161279\pi\) | ||||
0.874363 | + | 0.485272i | \(0.161279\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3559 | 1.43413 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.62598 | −0.614981 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.9294 | 0.886306 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.8954 | 0.817215 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.89105 | −0.245601 | −0.122801 | − | 0.992431i | \(-0.539188\pi\) | ||||
−0.122801 | + | 0.992431i | \(0.539188\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.900400 | 0.0566077 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.6402 | 0.791560 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.448767 | 0.0279933 | 0.0139967 | − | 0.999902i | \(-0.495545\pi\) | ||||
0.0139967 | + | 0.999902i | \(0.495545\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 40.4907 | 2.51597 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.8302 | 0.979863 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.4410 | 1.01379 | 0.506897 | − | 0.862007i | \(-0.330792\pi\) | ||||
0.506897 | + | 0.862007i | \(0.330792\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.42013 | 0.517244 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.6591 | 0.652328 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.5178 | −1.31196 | −0.655982 | − | 0.754777i | \(-0.727745\pi\) | ||||
−0.655982 | + | 0.754777i | \(0.727745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.9037 | 1.14832 | 0.574158 | − | 0.818744i | \(-0.305329\pi\) | ||||
0.574158 | + | 0.818744i | \(0.305329\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.0801 | −1.09426 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.19820 | 0.0722542 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.37343 | −0.322858 | −0.161429 | − | 0.986884i | \(-0.551610\pi\) | ||||
−0.161429 | + | 0.986884i | \(0.551610\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 29.6706 | 1.77633 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.77169 | −0.463620 | −0.231810 | − | 0.972761i | \(-0.574465\pi\) | ||||
−0.231810 | + | 0.972761i | \(0.574465\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.2276 | 1.14296 | 0.571480 | − | 0.820616i | \(-0.306370\pi\) | ||||
0.571480 | + | 0.820616i | \(0.306370\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 23.9333 | 1.41769 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.7914 | 1.05019 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.06578 | −0.121516 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 41.0169 | 2.40446 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.5778 | −0.910062 | −0.455031 | − | 0.890476i | \(-0.650372\pi\) | ||||
−0.455031 | + | 0.890476i | \(0.650372\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.3656 | −0.778178 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.251395 | 0.0145874 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.71406 | −0.272621 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.383315 | 0.0220939 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 27.3147 | 1.56919 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.96317 | −0.284191 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.6888 | −0.952482 | −0.476241 | − | 0.879315i | \(-0.658001\pi\) | ||||
−0.476241 | + | 0.879315i | \(0.658001\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.8683 | −1.30093 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.3280 | 1.37952 | 0.689758 | − | 0.724040i | \(-0.257717\pi\) | ||||
0.689758 | + | 0.724040i | \(0.257717\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.65759 | −0.376309 | −0.188154 | − | 0.982139i | \(-0.560251\pi\) | ||||
−0.188154 | + | 0.982139i | \(0.560251\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −16.2156 | −0.913643 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.4545 | 1.03651 | 0.518255 | − | 0.855226i | \(-0.326582\pi\) | ||||
0.518255 | + | 0.855226i | \(0.326582\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.75702 | −0.0983742 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −22.2010 | −1.23914 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.2769 | 1.57337 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.27320 | −0.347974 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −42.6283 | −2.35735 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −49.2607 | −2.71583 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.5497 | −0.909654 | −0.454827 | − | 0.890580i | \(-0.650299\pi\) | ||||
−0.454827 | + | 0.890580i | \(0.650299\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 34.9888 | 1.91737 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.09709 | 0.387755 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.61696 | −0.251502 | −0.125751 | − | 0.992062i | \(-0.540134\pi\) | ||||
−0.125751 | + | 0.992062i | \(0.540134\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.6796 | −1.06885 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.29319 | −0.178336 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.41272 | 0.0762796 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.09964 | −0.436070 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.2410 | 1.03291 | 0.516456 | − | 0.856313i | \(-0.327251\pi\) | ||||
0.516456 | + | 0.856313i | \(0.327251\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.98694 | 0.266945 | 0.133472 | − | 0.991053i | \(-0.457387\pi\) | ||||
0.133472 | + | 0.991053i | \(0.457387\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.31618 | −0.0702526 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −33.8970 | −1.80416 | −0.902079 | − | 0.431572i | \(-0.857959\pi\) | ||||
−0.902079 | + | 0.431572i | \(0.857959\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.65582 | 0.406329 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −36.7029 | −1.94252 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.74759 | 0.461680 | 0.230840 | − | 0.972992i | \(-0.425853\pi\) | ||||
0.230840 | + | 0.972992i | \(0.425853\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 34.5403 | 1.81791 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 27.2259 | 1.42899 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.5483 | −0.918522 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.9781 | 1.51265 | 0.756323 | − | 0.654198i | \(-0.226994\pi\) | ||||
0.756323 | + | 0.654198i | \(0.226994\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.3739 | 0.800332 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.4492 | −1.26934 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.7879 | −0.921022 | −0.460511 | − | 0.887654i | \(-0.652334\pi\) | ||||
−0.460511 | + | 0.887654i | \(0.652334\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −27.1329 | −1.40114 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.19890 | 0.473767 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.2765 | 1.81203 | 0.906017 | − | 0.423241i | \(-0.139108\pi\) | ||||
0.906017 | + | 0.423241i | \(0.139108\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.7460 | 1.42147 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34.4048 | 1.75800 | 0.879001 | − | 0.476820i | \(-0.158211\pi\) | ||||
0.879001 | + | 0.476820i | \(0.158211\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.79979 | 0.0917259 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.331230 | 0.0168374 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.2221 | 1.22811 | 0.614055 | − | 0.789263i | \(-0.289537\pi\) | ||||
0.614055 | + | 0.789263i | \(0.289537\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.56962 | −0.483956 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.83881 | −0.193642 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.33858 | −0.318929 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.96929 | 0.199213 | 0.0996065 | − | 0.995027i | \(-0.468242\pi\) | ||||
0.0996065 | + | 0.995027i | \(0.468242\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −69.4943 | −3.47907 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.40991 | −0.0704074 | −0.0352037 | − | 0.999380i | \(-0.511208\pi\) | ||||
−0.0352037 | + | 0.999380i | \(0.511208\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.2415 | 0.858862 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.5703 | 0.525241 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.88347 | −0.192496 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.25583 | −0.111544 | −0.0557718 | − | 0.998444i | \(-0.517762\pi\) | ||||
−0.0557718 | + | 0.998444i | \(0.517762\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 56.9064 | 2.80698 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 38.8093 | 1.90968 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.72074 | 0.329908 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.7574 | 0.526791 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.6015 | −1.78810 | −0.894051 | − | 0.447965i | \(-0.852149\pi\) | ||||
−0.894051 | + | 0.447965i | \(0.852149\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0546 | −0.490030 | −0.245015 | − | 0.969519i | \(-0.578793\pi\) | ||||
−0.245015 | + | 0.969519i | \(0.578793\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −42.5671 | −2.06968 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.7347 | −0.617723 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.4114 | 0.697416 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.73406 | 0.0837214 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.6140 | 0.992940 | 0.496470 | − | 0.868054i | \(-0.334629\pi\) | ||||
0.496470 | + | 0.868054i | \(0.334629\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.7836 | 1.57548 | 0.787740 | − | 0.616008i | \(-0.211251\pi\) | ||||
0.787740 | + | 0.616008i | \(0.211251\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.8054 | 0.757813 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.1194 | −0.866768 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.18644 | −0.199808 | −0.0999038 | − | 0.994997i | \(-0.531854\pi\) | ||||
−0.0999038 | + | 0.994997i | \(0.531854\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 24.1526 | 1.15013 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.2069 | 0.484945 | 0.242473 | − | 0.970158i | \(-0.422042\pi\) | ||||
0.242473 | + | 0.970158i | \(0.422042\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.55523 | 0.263343 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 38.4935 | 1.82068 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.1229 | 1.32720 | 0.663601 | − | 0.748087i | \(-0.269027\pi\) | ||||
0.663601 | + | 0.748087i | \(0.269027\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.70637 | −0.0803500 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.05859 | −0.190689 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.42284 | −0.441750 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.6481 | 1.01265 | 0.506327 | − | 0.862342i | \(-0.331003\pi\) | ||||
0.506327 | + | 0.862342i | \(0.331003\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.67187 | −0.124712 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.6030 | 1.00615 | 0.503077 | − | 0.864242i | \(-0.332201\pi\) | ||||
0.503077 | + | 0.864242i | \(0.332201\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −42.3106 | −1.96634 | −0.983169 | − | 0.182698i | \(-0.941517\pi\) | ||||
−0.983169 | + | 0.182698i | \(0.941517\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 29.6242 | 1.37379 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.9213 | −0.551652 | −0.275826 | − | 0.961208i | \(-0.588951\pi\) | ||||
−0.275826 | + | 0.961208i | \(0.588951\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.6076 | −0.951568 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.5844 | 0.718091 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.0367638 | −0.00169040 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.1122 | −1.10635 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.1270 | −0.967340 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.33770 | −0.426650 | −0.213325 | − | 0.976981i | \(-0.568429\pi\) | ||||
−0.213325 | + | 0.976981i | \(0.568429\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.3320 | 0.927058 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 23.5187 | 1.07014 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.3769 | 0.970674 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.8697 | −0.583183 | −0.291592 | − | 0.956543i | \(-0.594185\pi\) | ||||
−0.291592 | + | 0.956543i | \(0.594185\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.51946 | −0.0687122 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.45494 | 0.291307 | 0.145654 | − | 0.989336i | \(-0.453471\pi\) | ||||
0.145654 | + | 0.989336i | \(0.453471\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.6739 | 0.841031 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.55523 | 0.0699026 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.2299 | −0.997149 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.62074 | −0.341151 | −0.170576 | − | 0.985345i | \(-0.554563\pi\) | ||||
−0.170576 | + | 0.985345i | \(0.554563\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.9745 | −0.847719 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.7140 | −1.01277 | −0.506383 | − | 0.862309i | \(-0.669018\pi\) | ||||
−0.506383 | + | 0.862309i | \(0.669018\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.2357 | 0.633478 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.4888 | 1.04317 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.4508 | 1.08376 | 0.541882 | − | 0.840454i | \(-0.317712\pi\) | ||||
0.541882 | + | 0.840454i | \(0.317712\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 50.9545 | 2.25409 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.05899 | −0.223360 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.9183 | −0.525184 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.72460 | 0.207788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.3234 | 0.716518 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.2450 | −1.06219 | −0.531097 | − | 0.847311i | \(-0.678220\pi\) | ||||
−0.531097 | + | 0.847311i | \(0.678220\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.4662 | −0.588835 | −0.294417 | − | 0.955677i | \(-0.595126\pi\) | ||||
−0.294417 | + | 0.955677i | \(0.595126\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 31.2973 | 1.36592 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.0006 | 1.52465 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8679 | −0.733389 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 33.5359 | 1.45533 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.93375 | 0.386963 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.5705 | −0.500238 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −40.5431 | −1.74956 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.68074 | −0.115468 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.7293 | −0.805236 | −0.402618 | − | 0.915368i | \(-0.631900\pi\) | ||||
−0.402618 | + | 0.915368i | \(0.631900\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.5030 | 0.836954 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −22.2167 | −0.951658 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.6607 | 1.73853 | 0.869264 | − | 0.494349i | \(-0.164593\pi\) | ||||
0.869264 | + | 0.494349i | \(0.164593\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.4532 | 0.531488 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.3577 | 1.50629 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.4051 | 0.782665 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 34.9341 | 1.48287 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.6967 | −1.17355 | −0.586774 | − | 0.809751i | \(-0.699602\pi\) | ||||
−0.586774 | + | 0.809751i | \(0.699602\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.192477 | 0.00814092 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.52018 | 0.148622 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.33718 | 0.224935 | 0.112468 | − | 0.993655i | \(-0.464125\pi\) | ||||
0.112468 | + | 0.993655i | \(0.464125\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.2565 | −0.431493 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −30.6925 | −1.28896 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.1561 | −1.18036 | −0.590182 | − | 0.807270i | \(-0.700944\pi\) | ||||
−0.590182 | + | 0.807270i | \(0.700944\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.0326 | 1.42422 | 0.712111 | − | 0.702067i | \(-0.247739\pi\) | ||||
0.712111 | + | 0.702067i | \(0.247739\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.2449 | 0.887520 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.16019 | 0.340304 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −42.7261 | −1.77871 | −0.889356 | − | 0.457216i | \(-0.848847\pi\) | ||||
−0.889356 | + | 0.457216i | \(0.848847\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 36.4771 | 1.51593 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.5148 | −0.809609 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.34493 | 0.0971169 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.14246 | −0.336649 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.8421 | −1.06662 | −0.533308 | − | 0.845921i | \(-0.679051\pi\) | ||||
−0.533308 | + | 0.845921i | \(0.679051\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 66.2711 | 2.73065 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −47.2127 | −1.94207 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.7519 | 0.934307 | 0.467154 | − | 0.884176i | \(-0.345280\pi\) | ||||
0.467154 | + | 0.884176i | \(0.345280\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.1285 | −0.784193 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 64.2746 | 2.63058 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.33632 | −0.340613 | −0.170306 | − | 0.985391i | \(-0.554476\pi\) | ||||
−0.170306 | + | 0.985391i | \(0.554476\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.43201 | −0.221576 | −0.110788 | − | 0.993844i | \(-0.535337\pi\) | ||||
−0.110788 | + | 0.993844i | \(0.535337\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.8074 | −0.725172 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.1894 | 0.576880 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.4685 | 0.749614 | 0.374807 | − | 0.927103i | \(-0.377709\pi\) | ||||
0.374807 | + | 0.927103i | \(0.377709\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −45.8937 | −1.85971 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.7357 | −1.00070 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.5726 | 0.992480 | 0.496240 | − | 0.868185i | \(-0.334714\pi\) | ||||
0.496240 | + | 0.868185i | \(0.334714\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.3499 | 0.618966 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.6795 | −0.429941 | −0.214971 | − | 0.976621i | \(-0.568966\pi\) | ||||
−0.214971 | + | 0.976621i | \(0.568966\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.35056 | 0.134670 | 0.0673352 | − | 0.997730i | \(-0.478550\pi\) | ||||
0.0673352 | + | 0.997730i | \(0.478550\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.71209 | 0.0687039 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.1305 | −0.646256 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.33570 | 0.0934279 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.66521 | 0.266183 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 41.2742 | 1.64571 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.54404 | 0.0614672 | 0.0307336 | − | 0.999528i | \(-0.490216\pi\) | ||||
0.0307336 | + | 0.999528i | \(0.490216\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.9658 | −0.594839 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.4604 | 0.573845 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.0351 | 0.556090 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.2093 | −0.759908 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.5504 | −0.851191 | −0.425595 | − | 0.904914i | \(-0.639935\pi\) | ||||
−0.425595 | + | 0.904914i | \(0.639935\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.7833 | 0.661868 | 0.330934 | − | 0.943654i | \(-0.392636\pi\) | ||||
0.330934 | + | 0.943654i | \(0.392636\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.330712 | 0.0130218 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.0708 | 0.592492 | 0.296246 | − | 0.955112i | \(-0.404265\pi\) | ||||
0.296246 | + | 0.955112i | \(0.404265\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.72221 | −0.146109 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −86.0187 | −3.37134 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.3740 | −0.640762 | −0.320381 | − | 0.947289i | \(-0.603811\pi\) | ||||
−0.320381 | + | 0.947289i | \(0.603811\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.00068 | −0.0781730 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 44.0307 | 1.71780 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.7976 | 0.654342 | 0.327171 | − | 0.944965i | \(-0.393905\pi\) | ||||
0.327171 | + | 0.944965i | \(0.393905\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.3544 | 1.37513 | 0.687563 | − | 0.726125i | \(-0.258681\pi\) | ||||
0.687563 | + | 0.726125i | \(0.258681\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.4299 | −0.715760 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −36.2185 | −1.40449 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.9660 | −0.463323 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.3507 | −0.825466 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.38220 | −0.0533591 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.7227 | 1.41556 | 0.707778 | − | 0.706435i | \(-0.249698\pi\) | ||||
0.707778 | + | 0.706435i | \(0.249698\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.27835 | 0.0876938 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.7767 | −0.875379 | −0.437690 | − | 0.899126i | \(-0.644203\pi\) | ||||
−0.437690 | + | 0.899126i | \(0.644203\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −62.0713 | −2.38208 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −72.7446 | −2.78758 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.63670 | −0.100890 | −0.0504452 | − | 0.998727i | \(-0.516064\pi\) | ||||
−0.0504452 | + | 0.998727i | \(0.516064\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.6580 | 1.13317 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.0617 | −1.03247 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.2769 | −0.467713 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.6817 | −0.520475 | −0.260237 | − | 0.965545i | \(-0.583801\pi\) | ||||
−0.260237 | + | 0.965545i | \(0.583801\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.51588 | −0.171544 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.60644 | 0.212665 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.1356 | 0.686936 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.55020 | −0.361222 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.1017 | 1.36354 | 0.681771 | − | 0.731566i | \(-0.261210\pi\) | ||||
0.681771 | + | 0.731566i | \(0.261210\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 78.1498 | 2.94747 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −42.5006 | −1.60066 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −41.3356 | −1.55458 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.14146 | −0.117980 | −0.0589900 | − | 0.998259i | \(-0.518788\pi\) | ||||
−0.0589900 | + | 0.998259i | \(0.518788\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.9042 | 0.596455 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.4278 | −0.839929 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.903746 | 0.0337982 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −31.7074 | −1.18413 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.1814 | −1.08828 | −0.544142 | − | 0.838993i | \(-0.683145\pi\) | ||||
−0.544142 | + | 0.838993i | \(0.683145\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.6068 | 1.28882 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −68.0098 | −2.52931 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.9236 | −0.591387 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −50.6424 | −1.87822 | −0.939112 | − | 0.343611i | \(-0.888350\pi\) | ||||
−0.939112 | + | 0.343611i | \(0.888350\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −31.7182 | −1.17475 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.390732 | 0.0144517 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.6083 | −0.798120 | −0.399060 | − | 0.916925i | \(-0.630664\pi\) | ||||
−0.399060 | + | 0.916925i | \(0.630664\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 24.1149 | 0.889492 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.97647 | 0.0728043 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.85134 | −0.325602 | −0.162801 | − | 0.986659i | \(-0.552053\pi\) | ||||
−0.162801 | + | 0.986659i | \(0.552053\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −34.8958 | −1.28193 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.9068 | −0.950428 | −0.475214 | − | 0.879870i | \(-0.657629\pi\) | ||||
−0.475214 | + | 0.879870i | \(0.657629\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.0617 | 0.735005 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.8631 | −0.616988 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.5970 | 1.22761 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.8156 | −0.978516 | −0.489258 | − | 0.872139i | \(-0.662732\pi\) | ||||
−0.489258 | + | 0.872139i | \(0.662732\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.74783 | 0.355231 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.11522 | −0.0769809 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −53.5837 | −1.94753 | −0.973767 | − | 0.227548i | \(-0.926929\pi\) | ||||
−0.973767 | + | 0.227548i | \(0.926929\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.25568 | −0.0818758 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.7648 | 1.22397 | 0.611987 | − | 0.790868i | \(-0.290370\pi\) | ||||
0.611987 | + | 0.790868i | \(0.290370\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 64.5098 | 2.33541 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.5293 | −0.597619 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.4877 | 0.703659 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.26570 | −0.117764 | −0.0588820 | − | 0.998265i | \(-0.518754\pi\) | ||||
−0.0588820 | + | 0.998265i | \(0.518754\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.12425 | −0.0404888 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.6645 | 1.35470 | 0.677349 | − | 0.735662i | \(-0.263129\pi\) | ||||
0.677349 | + | 0.735662i | \(0.263129\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.8457 | −1.07209 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −101.437 | −3.63903 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.3385 | 1.23031 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.13207 | 0.0762916 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.34093 | −0.119395 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.12214 | 0.289892 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.2241 | −0.364449 | −0.182225 | − | 0.983257i | \(-0.558330\pi\) | ||||
−0.182225 | + | 0.983257i | \(0.558330\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −41.1878 | −1.46632 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.7813 | 1.05890 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.23652 | 0.256976 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −21.0940 | −0.748128 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −54.5643 | −1.93277 | −0.966384 | − | 0.257103i | \(-0.917232\pi\) | ||||
−0.966384 | + | 0.257103i | \(0.917232\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −50.2139 | −1.77644 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.9387 | −0.492500 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.88705 | −0.172460 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.2573 | 0.432012 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 53.9062 | 1.89759 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.9092 | 1.61408 | 0.807041 | − | 0.590495i | \(-0.201068\pi\) | ||||
0.807041 | + | 0.590495i | \(0.201068\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.4696 | 0.648555 | 0.324278 | − | 0.945962i | \(-0.394879\pi\) | ||||
0.324278 | + | 0.945962i | \(0.394879\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −47.3573 | −1.66089 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.791898 | −0.0277390 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.739823 | 0.0258831 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 23.6430 | 0.826152 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.7998 | −1.77293 | −0.886463 | − | 0.462799i | \(-0.846845\pi\) | ||||
−0.886463 | + | 0.462799i | \(0.846845\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 55.2692 | 1.92656 | 0.963282 | − | 0.268491i | \(-0.0865248\pi\) | ||||
0.963282 | + | 0.268491i | \(0.0865248\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.00172 | −0.104507 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.6534 | 0.544322 | 0.272161 | − | 0.962252i | \(-0.412262\pi\) | ||||
0.272161 | + | 0.962252i | \(0.412262\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.8686 | −0.620601 | −0.310301 | − | 0.950638i | \(-0.600430\pi\) | ||||
−0.310301 | + | 0.950638i | \(0.600430\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.4615 | 0.466973 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.4914 | 0.987169 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.88898 | −0.342222 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.26192 | −0.216444 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.71012 | 0.128088 | 0.0640438 | − | 0.997947i | \(-0.479600\pi\) | ||||
0.0640438 | + | 0.997947i | \(0.479600\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.64995 | −0.194826 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.4696 | 0.670568 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.2417 | 0.421127 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −41.2012 | −1.41569 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −48.1687 | −1.65315 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.4479 | −0.906621 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.4140 | −0.562004 | −0.281002 | − | 0.959707i | \(-0.590667\pi\) | ||||
−0.281002 | + | 0.959707i | \(0.590667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −31.2971 | −1.07034 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38.0827 | −1.30088 | −0.650440 | − | 0.759557i | \(-0.725416\pi\) | ||||
−0.650440 | + | 0.759557i | \(0.725416\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.2033 | −1.09876 | −0.549382 | − | 0.835571i | \(-0.685137\pi\) | ||||
−0.549382 | + | 0.835571i | \(0.685137\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −44.5708 | −1.51897 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44.9612 | −1.53050 | −0.765248 | − | 0.643736i | \(-0.777384\pi\) | ||||
−0.765248 | + | 0.643736i | \(0.777384\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.50730 | 0.289257 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.17517 | 0.175758 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.76524 | −0.0598816 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.3479 | −0.350624 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −53.6369 | −1.81534 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 41.0604 | 1.38809 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.2458 | −1.52784 | −0.763922 | − | 0.645309i | \(-0.776729\pi\) | ||||
−0.763922 | + | 0.645309i | \(0.776729\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 39.0253 | 1.31629 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.2104 | −1.82640 | −0.913198 | − | 0.407516i | \(-0.866395\pi\) | ||||
−0.913198 | + | 0.407516i | \(0.866395\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 57.9733 | 1.95096 | 0.975478 | − | 0.220098i | \(-0.0706377\pi\) | ||||
0.975478 | + | 0.220098i | \(0.0706377\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 33.4835 | 1.12554 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.65363 | −0.223407 | −0.111704 | − | 0.993742i | \(-0.535631\pi\) | ||||
−0.111704 | + | 0.993742i | \(0.535631\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −41.9883 | −1.40824 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.94372 | 0.0986184 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −95.0764 | −3.18161 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.1299 | −0.706296 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.8096 | 0.394312 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 43.7651 | 1.45965 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.9223 | −0.830282 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.960278 | −0.0319560 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.1644 | 0.337877 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.1099 | −0.468511 | −0.234256 | − | 0.972175i | \(-0.575265\pi\) | ||||
−0.234256 | + | 0.972175i | \(0.575265\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −35.7188 | −1.18472 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.9469 | 0.462080 | 0.231040 | − | 0.972944i | \(-0.425787\pi\) | ||||
0.231040 | + | 0.972944i | \(0.425787\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.87166 | 0.0619430 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.4337 | 0.411045 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.80930 | 0.191840 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.6817 | 0.418330 | 0.209165 | − | 0.977880i | \(-0.432925\pi\) | ||||
0.209165 | + | 0.977880i | \(0.432925\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 41.8087 | 1.37764 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.1625 | −0.367419 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.1953 | −1.15721 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 29.9044 | 0.982188 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.03009 | −0.0337962 | −0.0168981 | − | 0.999857i | \(-0.505379\pi\) | ||||
−0.0168981 | + | 0.999857i | \(0.505379\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 53.9465 | 1.76802 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −60.9464 | −1.99529 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.83462 | 0.0599984 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.3278 | −1.64414 | −0.822068 | − | 0.569389i | \(-0.807180\pi\) | ||||
−0.822068 | + | 0.569389i | \(0.807180\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.6785 | 0.544283 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.9666 | 1.07468 | 0.537341 | − | 0.843365i | \(-0.319429\pi\) | ||||
0.537341 | + | 0.843365i | \(0.319429\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.6210 | −0.378433 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.42227 | 0.111326 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.32202 | 0.172942 | 0.0864711 | − | 0.996254i | \(-0.472441\pi\) | ||||
0.0864711 | + | 0.996254i | \(0.472441\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.5862 | 0.830564 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −46.2322 | −1.49918 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.9298 | 1.19627 | 0.598136 | − | 0.801395i | \(-0.295908\pi\) | ||||
0.598136 | + | 0.801395i | \(0.295908\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.0723 | 0.358290 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.40167 | 0.142286 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −86.1168 | −2.78086 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51.0291 | 1.64610 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 29.0318 | 0.935535 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.0108 | 0.611980 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.7250 | −0.859419 | −0.429709 | − | 0.902967i | \(-0.641384\pi\) | ||||
−0.429709 | + | 0.902967i | \(0.641384\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −70.8390 | −2.27568 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.3008 | 1.03658 | 0.518291 | − | 0.855204i | \(-0.326568\pi\) | ||||
0.518291 | + | 0.855204i | \(0.326568\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.2792 | −0.521888 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.7156 | 0.503301 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.3219 | −0.522185 | −0.261092 | − | 0.965314i | \(-0.584083\pi\) | ||||
−0.261092 | + | 0.965314i | \(0.584083\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.54708 | 0.0494449 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 55.7441 | 1.77977 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.6565 | −0.882106 | −0.441053 | − | 0.897481i | \(-0.645395\pi\) | ||||
−0.441053 | + | 0.897481i | \(0.645395\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.6059 | −0.784010 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 123.407 | 3.92810 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.250375 | −0.00796146 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.56742 | −0.0815568 | −0.0407784 | − | 0.999168i | \(-0.512984\pi\) | ||||
−0.0407784 | + | 0.999168i | \(0.512984\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 41.4602 | 1.31570 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.4981 | 1.06196 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.8210 | 1.51451 | 0.757253 | − | 0.653122i | \(-0.226541\pi\) | ||||
0.757253 | + | 0.653122i | \(0.226541\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.38433 | −0.233630 |
(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 | 6044.2.a.b.1.9 | ✓ | 63 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6044.2.a.b.1.9 | ✓ | 63 | 1.1 | even | 1 | trivial |