Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(1,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, 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("4014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.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: | \(32.0519513713\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.356173.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 7x^{3} + 9x^{2} + 14x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1338) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.253142\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4014.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.686428 | −0.306980 | −0.153490 | − | 0.988150i | \(-0.549051\pi\) | ||||
−0.153490 | + | 0.988150i | \(0.549051\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.87549 | 1.08683 | 0.543416 | − | 0.839463i | \(-0.317130\pi\) | ||||
0.543416 | + | 0.839463i | \(0.317130\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.686428 | −0.217068 | ||||||||
\(11\) | −5.51891 | −1.66402 | −0.832008 | − | 0.554764i | \(-0.812808\pi\) | ||||
−0.832008 | + | 0.554764i | \(0.812808\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.329853 | 0.0914848 | 0.0457424 | − | 0.998953i | \(-0.485435\pi\) | ||||
0.0457424 | + | 0.998953i | \(0.485435\pi\) | |||||||
\(14\) | 2.87549 | 0.768507 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.44220 | −1.07739 | −0.538696 | − | 0.842500i | \(-0.681083\pi\) | ||||
−0.538696 | + | 0.842500i | \(0.681083\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.53786 | −0.352810 | −0.176405 | − | 0.984318i | \(-0.556447\pi\) | ||||
−0.176405 | + | 0.984318i | \(0.556447\pi\) | |||||||
\(20\) | −0.686428 | −0.153490 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.51891 | −1.17664 | ||||||||
\(23\) | 3.17011 | 0.661014 | 0.330507 | − | 0.943804i | \(-0.392780\pi\) | ||||
0.330507 | + | 0.943804i | \(0.392780\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.52882 | −0.905763 | ||||||||
\(26\) | 0.329853 | 0.0646895 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.87549 | 0.543416 | ||||||||
\(29\) | −7.03297 | −1.30599 | −0.652995 | − | 0.757362i | \(-0.726488\pi\) | ||||
−0.652995 | + | 0.757362i | \(0.726488\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.43855 | −1.33600 | −0.668002 | − | 0.744160i | \(-0.732850\pi\) | ||||
−0.668002 | + | 0.744160i | \(0.732850\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.44220 | −0.761832 | ||||||||
\(35\) | −1.97382 | −0.333636 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.58613 | −1.24715 | −0.623576 | − | 0.781762i | \(-0.714321\pi\) | ||||
−0.623576 | + | 0.781762i | \(0.714321\pi\) | |||||||
\(38\) | −1.53786 | −0.249474 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.686428 | −0.108534 | ||||||||
\(41\) | 2.51679 | 0.393056 | 0.196528 | − | 0.980498i | \(-0.437033\pi\) | ||||
0.196528 | + | 0.980498i | \(0.437033\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.97369 | 1.06348 | 0.531739 | − | 0.846908i | \(-0.321539\pi\) | ||||
0.531739 | + | 0.846908i | \(0.321539\pi\) | |||||||
\(44\) | −5.51891 | −0.832008 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.17011 | 0.467408 | ||||||||
\(47\) | −6.00990 | −0.876634 | −0.438317 | − | 0.898820i | \(-0.644425\pi\) | ||||
−0.438317 | + | 0.898820i | \(0.644425\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.26844 | 0.181206 | ||||||||
\(50\) | −4.52882 | −0.640471 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.329853 | 0.0457424 | ||||||||
\(53\) | 0.840259 | 0.115419 | 0.0577093 | − | 0.998333i | \(-0.481620\pi\) | ||||
0.0577093 | + | 0.998333i | \(0.481620\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.78834 | 0.510819 | ||||||||
\(56\) | 2.87549 | 0.384253 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.03297 | −0.923475 | ||||||||
\(59\) | 3.14631 | 0.409614 | 0.204807 | − | 0.978802i | \(-0.434343\pi\) | ||||
0.204807 | + | 0.978802i | \(0.434343\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.68741 | −0.344088 | −0.172044 | − | 0.985089i | \(-0.555037\pi\) | ||||
−0.172044 | + | 0.985089i | \(0.555037\pi\) | |||||||
\(62\) | −7.43855 | −0.944697 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.226420 | −0.0280840 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.9815 | −1.70811 | −0.854057 | − | 0.520179i | \(-0.825865\pi\) | ||||
−0.854057 | + | 0.520179i | \(0.825865\pi\) | |||||||
\(68\) | −4.44220 | −0.538696 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.97382 | −0.235916 | ||||||||
\(71\) | 6.67275 | 0.791909 | 0.395955 | − | 0.918270i | \(-0.370414\pi\) | ||||
0.395955 | + | 0.918270i | \(0.370414\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.9575 | 1.39952 | 0.699758 | − | 0.714380i | \(-0.253291\pi\) | ||||
0.699758 | + | 0.714380i | \(0.253291\pi\) | |||||||
\(74\) | −7.58613 | −0.881870 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.53786 | −0.176405 | ||||||||
\(77\) | −15.8696 | −1.80851 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.1543 | 1.36747 | 0.683733 | − | 0.729732i | \(-0.260355\pi\) | ||||
0.683733 | + | 0.729732i | \(0.260355\pi\) | |||||||
\(80\) | −0.686428 | −0.0767450 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.51679 | 0.277932 | ||||||||
\(83\) | 5.22743 | 0.573785 | 0.286892 | − | 0.957963i | \(-0.407378\pi\) | ||||
0.286892 | + | 0.957963i | \(0.407378\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.04925 | 0.330738 | ||||||||
\(86\) | 6.97369 | 0.751992 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.51891 | −0.588318 | ||||||||
\(89\) | −8.29874 | −0.879665 | −0.439833 | − | 0.898080i | \(-0.644962\pi\) | ||||
−0.439833 | + | 0.898080i | \(0.644962\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.948489 | 0.0994286 | ||||||||
\(92\) | 3.17011 | 0.330507 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.00990 | −0.619874 | ||||||||
\(95\) | 1.05563 | 0.108306 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.45112 | 0.451943 | 0.225971 | − | 0.974134i | \(-0.427444\pi\) | ||||
0.225971 | + | 0.974134i | \(0.427444\pi\) | |||||||
\(98\) | 1.26844 | 0.128132 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.52882 | −0.452882 | ||||||||
\(101\) | 3.23632 | 0.322026 | 0.161013 | − | 0.986952i | \(-0.448524\pi\) | ||||
0.161013 | + | 0.986952i | \(0.448524\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.7274 | −1.25407 | −0.627034 | − | 0.778992i | \(-0.715731\pi\) | ||||
−0.627034 | + | 0.778992i | \(0.715731\pi\) | |||||||
\(104\) | 0.329853 | 0.0323447 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.840259 | 0.0816132 | ||||||||
\(107\) | −4.52529 | −0.437477 | −0.218738 | − | 0.975784i | \(-0.570194\pi\) | ||||
−0.218738 | + | 0.975784i | \(0.570194\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.5371 | −1.00927 | −0.504637 | − | 0.863332i | \(-0.668374\pi\) | ||||
−0.504637 | + | 0.863332i | \(0.668374\pi\) | |||||||
\(110\) | 3.78834 | 0.361204 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.87549 | 0.271708 | ||||||||
\(113\) | −2.93690 | −0.276281 | −0.138140 | − | 0.990413i | \(-0.544112\pi\) | ||||
−0.138140 | + | 0.990413i | \(0.544112\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.17605 | −0.202918 | ||||||||
\(116\) | −7.03297 | −0.652995 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.14631 | 0.289641 | ||||||||
\(119\) | −12.7735 | −1.17095 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.4584 | 1.76895 | ||||||||
\(122\) | −2.68741 | −0.243307 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.43855 | −0.668002 | ||||||||
\(125\) | 6.54085 | 0.585031 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.04306 | 0.358764 | 0.179382 | − | 0.983780i | \(-0.442590\pi\) | ||||
0.179382 | + | 0.983780i | \(0.442590\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.226420 | −0.0198584 | ||||||||
\(131\) | −6.64749 | −0.580794 | −0.290397 | − | 0.956906i | \(-0.593787\pi\) | ||||
−0.290397 | + | 0.956906i | \(0.593787\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.42211 | −0.383446 | ||||||||
\(134\) | −13.9815 | −1.20782 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.44220 | −0.380916 | ||||||||
\(137\) | −10.9737 | −0.937545 | −0.468773 | − | 0.883319i | \(-0.655304\pi\) | ||||
−0.468773 | + | 0.883319i | \(0.655304\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.2142 | −1.29045 | −0.645225 | − | 0.763992i | \(-0.723237\pi\) | ||||
−0.645225 | + | 0.763992i | \(0.723237\pi\) | |||||||
\(140\) | −1.97382 | −0.166818 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.67275 | 0.559964 | ||||||||
\(143\) | −1.82043 | −0.152232 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.82763 | 0.400913 | ||||||||
\(146\) | 11.9575 | 0.989607 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.58613 | −0.623576 | ||||||||
\(149\) | −2.90167 | −0.237714 | −0.118857 | − | 0.992911i | \(-0.537923\pi\) | ||||
−0.118857 | + | 0.992911i | \(0.537923\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.66399 | 0.216792 | 0.108396 | − | 0.994108i | \(-0.465429\pi\) | ||||
0.108396 | + | 0.994108i | \(0.465429\pi\) | |||||||
\(152\) | −1.53786 | −0.124737 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −15.8696 | −1.27881 | ||||||||
\(155\) | 5.10603 | 0.410126 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.2048 | 1.21347 | 0.606736 | − | 0.794903i | \(-0.292478\pi\) | ||||
0.606736 | + | 0.794903i | \(0.292478\pi\) | |||||||
\(158\) | 12.1543 | 0.966944 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.686428 | −0.0542669 | ||||||||
\(161\) | 9.11562 | 0.718412 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.4990 | 0.978996 | 0.489498 | − | 0.872004i | \(-0.337180\pi\) | ||||
0.489498 | + | 0.872004i | \(0.337180\pi\) | |||||||
\(164\) | 2.51679 | 0.196528 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.22743 | 0.405727 | ||||||||
\(167\) | −6.88133 | −0.532493 | −0.266247 | − | 0.963905i | \(-0.585784\pi\) | ||||
−0.266247 | + | 0.963905i | \(0.585784\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8912 | −0.991631 | ||||||||
\(170\) | 3.04925 | 0.233867 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.97369 | 0.531739 | ||||||||
\(173\) | 3.65630 | 0.277984 | 0.138992 | − | 0.990294i | \(-0.455614\pi\) | ||||
0.138992 | + | 0.990294i | \(0.455614\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.0226 | −0.984413 | ||||||||
\(176\) | −5.51891 | −0.416004 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.29874 | −0.622017 | ||||||||
\(179\) | −11.6410 | −0.870090 | −0.435045 | − | 0.900409i | \(-0.643267\pi\) | ||||
−0.435045 | + | 0.900409i | \(0.643267\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.8301 | −1.02798 | −0.513990 | − | 0.857796i | \(-0.671833\pi\) | ||||
−0.513990 | + | 0.857796i | \(0.671833\pi\) | |||||||
\(182\) | 0.948489 | 0.0703067 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.17011 | 0.233704 | ||||||||
\(185\) | 5.20733 | 0.382851 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.5161 | 1.79280 | ||||||||
\(188\) | −6.00990 | −0.438317 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.05563 | 0.0765836 | ||||||||
\(191\) | 15.4332 | 1.11671 | 0.558354 | − | 0.829603i | \(-0.311433\pi\) | ||||
0.558354 | + | 0.829603i | \(0.311433\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.86292 | −0.134096 | −0.0670479 | − | 0.997750i | \(-0.521358\pi\) | ||||
−0.0670479 | + | 0.997750i | \(0.521358\pi\) | |||||||
\(194\) | 4.45112 | 0.319572 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.26844 | 0.0906028 | ||||||||
\(197\) | 18.0327 | 1.28477 | 0.642387 | − | 0.766381i | \(-0.277944\pi\) | ||||
0.642387 | + | 0.766381i | \(0.277944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0118 | 1.70215 | 0.851077 | − | 0.525042i | \(-0.175950\pi\) | ||||
0.851077 | + | 0.525042i | \(0.175950\pi\) | |||||||
\(200\) | −4.52882 | −0.320236 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.23632 | 0.227707 | ||||||||
\(203\) | −20.2232 | −1.41939 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.72759 | −0.120660 | ||||||||
\(206\) | −12.7274 | −0.886760 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.329853 | 0.0228712 | ||||||||
\(209\) | 8.48734 | 0.587081 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.05163 | 0.416611 | 0.208306 | − | 0.978064i | \(-0.433205\pi\) | ||||
0.208306 | + | 0.978064i | \(0.433205\pi\) | |||||||
\(212\) | 0.840259 | 0.0577093 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.52529 | −0.309343 | ||||||||
\(215\) | −4.78694 | −0.326466 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.3895 | −1.45201 | ||||||||
\(218\) | −10.5371 | −0.713664 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.78834 | 0.255410 | ||||||||
\(221\) | −1.46527 | −0.0985650 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | ||||||||
\(224\) | 2.87549 | 0.192127 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.93690 | −0.195360 | ||||||||
\(227\) | −24.3730 | −1.61769 | −0.808846 | − | 0.588021i | \(-0.799907\pi\) | ||||
−0.808846 | + | 0.588021i | \(0.799907\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.57496 | 0.500567 | 0.250284 | − | 0.968173i | \(-0.419476\pi\) | ||||
0.250284 | + | 0.968173i | \(0.419476\pi\) | |||||||
\(230\) | −2.17605 | −0.143485 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.03297 | −0.461737 | ||||||||
\(233\) | −1.91430 | −0.125410 | −0.0627050 | − | 0.998032i | \(-0.519973\pi\) | ||||
−0.0627050 | + | 0.998032i | \(0.519973\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.12537 | 0.269109 | ||||||||
\(236\) | 3.14631 | 0.204807 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.7735 | −0.827984 | ||||||||
\(239\) | 18.8018 | 1.21619 | 0.608094 | − | 0.793865i | \(-0.291934\pi\) | ||||
0.608094 | + | 0.793865i | \(0.291934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.7202 | −0.819378 | −0.409689 | − | 0.912225i | \(-0.634363\pi\) | ||||
−0.409689 | + | 0.912225i | \(0.634363\pi\) | |||||||
\(242\) | 19.4584 | 1.25083 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.68741 | −0.172044 | ||||||||
\(245\) | −0.870693 | −0.0556265 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.507269 | −0.0322767 | ||||||||
\(248\) | −7.43855 | −0.472349 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.54085 | 0.413680 | ||||||||
\(251\) | −8.40005 | −0.530206 | −0.265103 | − | 0.964220i | \(-0.585406\pi\) | ||||
−0.265103 | + | 0.964220i | \(0.585406\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.4956 | −1.09994 | ||||||||
\(254\) | 4.04306 | 0.253684 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.1611 | 1.44475 | 0.722375 | − | 0.691502i | \(-0.243051\pi\) | ||||
0.722375 | + | 0.691502i | \(0.243051\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.8138 | −1.35545 | ||||||||
\(260\) | −0.226420 | −0.0140420 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.64749 | −0.410683 | ||||||||
\(263\) | −6.61626 | −0.407976 | −0.203988 | − | 0.978973i | \(-0.565390\pi\) | ||||
−0.203988 | + | 0.978973i | \(0.565390\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.576778 | −0.0354312 | ||||||||
\(266\) | −4.42211 | −0.271137 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.9815 | −0.854057 | ||||||||
\(269\) | 4.44005 | 0.270715 | 0.135357 | − | 0.990797i | \(-0.456782\pi\) | ||||
0.135357 | + | 0.990797i | \(0.456782\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.05643 | −0.367902 | −0.183951 | − | 0.982935i | \(-0.558889\pi\) | ||||
−0.183951 | + | 0.982935i | \(0.558889\pi\) | |||||||
\(272\) | −4.44220 | −0.269348 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.9737 | −0.662945 | ||||||||
\(275\) | 24.9942 | 1.50720 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.7454 | −1.54689 | −0.773446 | − | 0.633862i | \(-0.781469\pi\) | ||||
−0.773446 | + | 0.633862i | \(0.781469\pi\) | |||||||
\(278\) | −15.2142 | −0.912487 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.97382 | −0.117958 | ||||||||
\(281\) | 14.7983 | 0.882790 | 0.441395 | − | 0.897313i | \(-0.354484\pi\) | ||||
0.441395 | + | 0.897313i | \(0.354484\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.17776 | −0.248342 | −0.124171 | − | 0.992261i | \(-0.539627\pi\) | ||||
−0.124171 | + | 0.992261i | \(0.539627\pi\) | |||||||
\(284\) | 6.67275 | 0.395955 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.82043 | −0.107644 | ||||||||
\(287\) | 7.23699 | 0.427186 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.73318 | 0.160775 | ||||||||
\(290\) | 4.82763 | 0.283488 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.9575 | 0.699758 | ||||||||
\(293\) | 12.6202 | 0.737281 | 0.368641 | − | 0.929572i | \(-0.379823\pi\) | ||||
0.368641 | + | 0.929572i | \(0.379823\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.15971 | −0.125743 | ||||||||
\(296\) | −7.58613 | −0.440935 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.90167 | −0.168089 | ||||||||
\(299\) | 1.04567 | 0.0604727 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0528 | 1.15582 | ||||||||
\(302\) | 2.66399 | 0.153295 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.53786 | −0.0882025 | ||||||||
\(305\) | 1.84472 | 0.105628 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.7514 | −1.86922 | −0.934612 | − | 0.355669i | \(-0.884253\pi\) | ||||
−0.934612 | + | 0.355669i | \(0.884253\pi\) | |||||||
\(308\) | −15.8696 | −0.904253 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.10603 | 0.290003 | ||||||||
\(311\) | 5.09711 | 0.289031 | 0.144515 | − | 0.989503i | \(-0.453838\pi\) | ||||
0.144515 | + | 0.989503i | \(0.453838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.70513 | 0.209426 | 0.104713 | − | 0.994502i | \(-0.466608\pi\) | ||||
0.104713 | + | 0.994502i | \(0.466608\pi\) | |||||||
\(314\) | 15.2048 | 0.858055 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.1543 | 0.683733 | ||||||||
\(317\) | −11.1944 | −0.628743 | −0.314371 | − | 0.949300i | \(-0.601794\pi\) | ||||
−0.314371 | + | 0.949300i | \(0.601794\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 38.8144 | 2.17319 | ||||||||
\(320\) | −0.686428 | −0.0383725 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.11562 | 0.507994 | ||||||||
\(323\) | 6.83150 | 0.380115 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.49384 | −0.0828635 | ||||||||
\(326\) | 12.4990 | 0.692255 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.51679 | 0.138966 | ||||||||
\(329\) | −17.2814 | −0.952755 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.7807 | −1.69186 | −0.845930 | − | 0.533293i | \(-0.820954\pi\) | ||||
−0.845930 | + | 0.533293i | \(0.820954\pi\) | |||||||
\(332\) | 5.22743 | 0.286892 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.88133 | −0.376530 | ||||||||
\(335\) | 9.59731 | 0.524357 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.0781 | −1.52951 | −0.764755 | − | 0.644322i | \(-0.777140\pi\) | ||||
−0.764755 | + | 0.644322i | \(0.777140\pi\) | |||||||
\(338\) | −12.8912 | −0.701189 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.04925 | 0.165369 | ||||||||
\(341\) | 41.0527 | 2.22313 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.4810 | −0.889893 | ||||||||
\(344\) | 6.97369 | 0.375996 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.65630 | 0.196564 | ||||||||
\(347\) | −4.81474 | −0.258469 | −0.129234 | − | 0.991614i | \(-0.541252\pi\) | ||||
−0.129234 | + | 0.991614i | \(0.541252\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.7579 | 1.11114 | 0.555571 | − | 0.831469i | \(-0.312500\pi\) | ||||
0.555571 | + | 0.831469i | \(0.312500\pi\) | |||||||
\(350\) | −13.0226 | −0.696085 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.51891 | −0.294159 | ||||||||
\(353\) | 3.21876 | 0.171317 | 0.0856587 | − | 0.996325i | \(-0.472701\pi\) | ||||
0.0856587 | + | 0.996325i | \(0.472701\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.58036 | −0.243100 | ||||||||
\(356\) | −8.29874 | −0.439833 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.6410 | −0.615246 | ||||||||
\(359\) | −25.5107 | −1.34641 | −0.673203 | − | 0.739458i | \(-0.735082\pi\) | ||||
−0.673203 | + | 0.739458i | \(0.735082\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.6350 | −0.875525 | ||||||||
\(362\) | −13.8301 | −0.726892 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.948489 | 0.0497143 | ||||||||
\(365\) | −8.20794 | −0.429623 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.4579 | −1.27669 | −0.638346 | − | 0.769750i | \(-0.720381\pi\) | ||||
−0.638346 | + | 0.769750i | \(0.720381\pi\) | |||||||
\(368\) | 3.17011 | 0.165254 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.20733 | 0.270716 | ||||||||
\(371\) | 2.41616 | 0.125441 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.79830 | −0.507337 | −0.253668 | − | 0.967291i | \(-0.581637\pi\) | ||||
−0.253668 | + | 0.967291i | \(0.581637\pi\) | |||||||
\(374\) | 24.5161 | 1.26770 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00990 | −0.309937 | ||||||||
\(377\) | −2.31985 | −0.119478 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.3632 | 1.20009 | 0.600043 | − | 0.799968i | \(-0.295150\pi\) | ||||
0.600043 | + | 0.799968i | \(0.295150\pi\) | |||||||
\(380\) | 1.05563 | 0.0541528 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.4332 | 0.789632 | ||||||||
\(383\) | −26.1424 | −1.33582 | −0.667908 | − | 0.744244i | \(-0.732810\pi\) | ||||
−0.667908 | + | 0.744244i | \(0.732810\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.8933 | 0.555175 | ||||||||
\(386\) | −1.86292 | −0.0948201 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.45112 | 0.225971 | ||||||||
\(389\) | −3.73549 | −0.189397 | −0.0946985 | − | 0.995506i | \(-0.530189\pi\) | ||||
−0.0946985 | + | 0.995506i | \(0.530189\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.0823 | −0.712172 | ||||||||
\(392\) | 1.26844 | 0.0640659 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.0327 | 0.908472 | ||||||||
\(395\) | −8.34305 | −0.419785 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.6199 | 0.884316 | 0.442158 | − | 0.896937i | \(-0.354213\pi\) | ||||
0.442158 | + | 0.896937i | \(0.354213\pi\) | |||||||
\(398\) | 24.0118 | 1.20360 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.52882 | −0.226441 | ||||||||
\(401\) | 22.5232 | 1.12475 | 0.562376 | − | 0.826881i | \(-0.309887\pi\) | ||||
0.562376 | + | 0.826881i | \(0.309887\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.45363 | −0.122224 | ||||||||
\(404\) | 3.23632 | 0.161013 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.2232 | −1.00366 | ||||||||
\(407\) | 41.8672 | 2.07528 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.4542 | −0.615821 | −0.307910 | − | 0.951415i | \(-0.599630\pi\) | ||||
−0.307910 | + | 0.951415i | \(0.599630\pi\) | |||||||
\(410\) | −1.72759 | −0.0853197 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.7274 | −0.627034 | ||||||||
\(413\) | 9.04717 | 0.445182 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.58825 | −0.176140 | ||||||||
\(416\) | 0.329853 | 0.0161724 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.48734 | 0.415129 | ||||||||
\(419\) | 30.5170 | 1.49086 | 0.745428 | − | 0.666586i | \(-0.232245\pi\) | ||||
0.745428 | + | 0.666586i | \(0.232245\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.17369 | 0.252150 | 0.126075 | − | 0.992021i | \(-0.459762\pi\) | ||||
0.126075 | + | 0.992021i | \(0.459762\pi\) | |||||||
\(422\) | 6.05163 | 0.294589 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.840259 | 0.0408066 | ||||||||
\(425\) | 20.1179 | 0.975863 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.72762 | −0.373966 | ||||||||
\(428\) | −4.52529 | −0.218738 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.78694 | −0.230847 | ||||||||
\(431\) | 11.8685 | 0.571686 | 0.285843 | − | 0.958277i | \(-0.407726\pi\) | ||||
0.285843 | + | 0.958277i | \(0.407726\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.77072 | 0.133152 | 0.0665762 | − | 0.997781i | \(-0.478792\pi\) | ||||
0.0665762 | + | 0.997781i | \(0.478792\pi\) | |||||||
\(434\) | −21.3895 | −1.02673 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.5371 | −0.504637 | ||||||||
\(437\) | −4.87520 | −0.233212 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.5404 | −0.646248 | −0.323124 | − | 0.946357i | \(-0.604733\pi\) | ||||
−0.323124 | + | 0.946357i | \(0.604733\pi\) | |||||||
\(440\) | 3.78834 | 0.180602 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.46527 | −0.0696960 | ||||||||
\(443\) | −38.7298 | −1.84011 | −0.920054 | − | 0.391791i | \(-0.871856\pi\) | ||||
−0.920054 | + | 0.391791i | \(0.871856\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.69649 | 0.270040 | ||||||||
\(446\) | −1.00000 | −0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.87549 | 0.135854 | ||||||||
\(449\) | 35.2746 | 1.66471 | 0.832356 | − | 0.554241i | \(-0.186992\pi\) | ||||
0.832356 | + | 0.554241i | \(0.186992\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.8899 | −0.654051 | ||||||||
\(452\) | −2.93690 | −0.138140 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −24.3730 | −1.14388 | ||||||||
\(455\) | −0.651069 | −0.0305226 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.7179 | −0.735251 | −0.367626 | − | 0.929974i | \(-0.619829\pi\) | ||||
−0.367626 | + | 0.929974i | \(0.619829\pi\) | |||||||
\(458\) | 7.57496 | 0.353955 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.17605 | −0.101459 | ||||||||
\(461\) | 15.4964 | 0.721739 | 0.360869 | − | 0.932616i | \(-0.382480\pi\) | ||||
0.360869 | + | 0.932616i | \(0.382480\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.0979 | 1.58466 | 0.792331 | − | 0.610091i | \(-0.208867\pi\) | ||||
0.792331 | + | 0.610091i | \(0.208867\pi\) | |||||||
\(464\) | −7.03297 | −0.326498 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.91430 | −0.0886783 | ||||||||
\(467\) | −5.76270 | −0.266666 | −0.133333 | − | 0.991071i | \(-0.542568\pi\) | ||||
−0.133333 | + | 0.991071i | \(0.542568\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.2037 | −1.85644 | ||||||||
\(470\) | 4.12537 | 0.190289 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.14631 | 0.144821 | ||||||||
\(473\) | −38.4872 | −1.76964 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.96470 | 0.319562 | ||||||||
\(476\) | −12.7735 | −0.585473 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.8018 | 0.859975 | ||||||||
\(479\) | 0.892156 | 0.0407637 | 0.0203818 | − | 0.999792i | \(-0.493512\pi\) | ||||
0.0203818 | + | 0.999792i | \(0.493512\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.50231 | −0.114095 | ||||||||
\(482\) | −12.7202 | −0.579387 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.4584 | 0.884473 | ||||||||
\(485\) | −3.05538 | −0.138737 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.83587 | 0.219134 | 0.109567 | − | 0.993979i | \(-0.465054\pi\) | ||||
0.109567 | + | 0.993979i | \(0.465054\pi\) | |||||||
\(488\) | −2.68741 | −0.121653 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.870693 | −0.0393339 | ||||||||
\(491\) | 14.5280 | 0.655640 | 0.327820 | − | 0.944740i | \(-0.393686\pi\) | ||||
0.327820 | + | 0.944740i | \(0.393686\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.2419 | 1.40706 | ||||||||
\(494\) | −0.507269 | −0.0228231 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.43855 | −0.334001 | ||||||||
\(497\) | 19.1874 | 0.860673 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 42.7043 | 1.91171 | 0.955854 | − | 0.293842i | \(-0.0949339\pi\) | ||||
0.955854 | + | 0.293842i | \(0.0949339\pi\) | |||||||
\(500\) | 6.54085 | 0.292516 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.40005 | −0.374912 | ||||||||
\(503\) | 28.7298 | 1.28100 | 0.640499 | − | 0.767959i | \(-0.278727\pi\) | ||||
0.640499 | + | 0.767959i | \(0.278727\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.22150 | −0.0988556 | ||||||||
\(506\) | −17.4956 | −0.777773 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.04306 | 0.179382 | ||||||||
\(509\) | 31.9400 | 1.41572 | 0.707858 | − | 0.706355i | \(-0.249662\pi\) | ||||
0.707858 | + | 0.706355i | \(0.249662\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.3836 | 1.52104 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 23.1611 | 1.02159 | ||||||||
\(515\) | 8.73644 | 0.384974 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.1681 | 1.45873 | ||||||||
\(518\) | −21.8138 | −0.958445 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.226420 | −0.00992919 | ||||||||
\(521\) | −34.5500 | −1.51366 | −0.756832 | − | 0.653609i | \(-0.773254\pi\) | ||||
−0.756832 | + | 0.653609i | \(0.773254\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.3878 | 0.891498 | 0.445749 | − | 0.895158i | \(-0.352937\pi\) | ||||
0.445749 | + | 0.895158i | \(0.352937\pi\) | |||||||
\(524\) | −6.64749 | −0.290397 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.61626 | −0.288483 | ||||||||
\(527\) | 33.0436 | 1.43940 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.9504 | −0.563060 | ||||||||
\(530\) | −0.576778 | −0.0250536 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.42211 | −0.191723 | ||||||||
\(533\) | 0.830169 | 0.0359586 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.10629 | 0.134297 | ||||||||
\(536\) | −13.9815 | −0.603910 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.44005 | 0.191424 | ||||||||
\(539\) | −7.00041 | −0.301529 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.5035 | −1.13948 | −0.569738 | − | 0.821827i | \(-0.692955\pi\) | ||||
−0.569738 | + | 0.821827i | \(0.692955\pi\) | |||||||
\(542\) | −6.05643 | −0.260146 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.44220 | −0.190458 | ||||||||
\(545\) | 7.23298 | 0.309827 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.362415 | −0.0154958 | −0.00774788 | − | 0.999970i | \(-0.502466\pi\) | ||||
−0.00774788 | + | 0.999970i | \(0.502466\pi\) | |||||||
\(548\) | −10.9737 | −0.468773 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 24.9942 | 1.06575 | ||||||||
\(551\) | 10.8158 | 0.460766 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 34.9496 | 1.48621 | ||||||||
\(554\) | −25.7454 | −1.09382 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.2142 | −0.645225 | ||||||||
\(557\) | 17.2544 | 0.731092 | 0.365546 | − | 0.930793i | \(-0.380882\pi\) | ||||
0.365546 | + | 0.930793i | \(0.380882\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.30029 | 0.0972920 | ||||||||
\(560\) | −1.97382 | −0.0834090 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.7983 | 0.624227 | ||||||||
\(563\) | −38.1428 | −1.60753 | −0.803764 | − | 0.594948i | \(-0.797173\pi\) | ||||
−0.803764 | + | 0.594948i | \(0.797173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.01597 | 0.0848126 | ||||||||
\(566\) | −4.17776 | −0.175604 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.67275 | 0.279982 | ||||||||
\(569\) | 9.79988 | 0.410832 | 0.205416 | − | 0.978675i | \(-0.434145\pi\) | ||||
0.205416 | + | 0.978675i | \(0.434145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.2196 | 1.18095 | 0.590476 | − | 0.807055i | \(-0.298940\pi\) | ||||
0.590476 | + | 0.807055i | \(0.298940\pi\) | |||||||
\(572\) | −1.82043 | −0.0761160 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.23699 | 0.302066 | ||||||||
\(575\) | −14.3569 | −0.598722 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.2068 | 1.17427 | 0.587133 | − | 0.809491i | \(-0.300257\pi\) | ||||
0.587133 | + | 0.809491i | \(0.300257\pi\) | |||||||
\(578\) | 2.73318 | 0.113685 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.82763 | 0.200456 | ||||||||
\(581\) | 15.0314 | 0.623608 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.63732 | −0.192058 | ||||||||
\(584\) | 11.9575 | 0.494803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.6202 | 0.521337 | ||||||||
\(587\) | 12.2413 | 0.505251 | 0.252626 | − | 0.967564i | \(-0.418706\pi\) | ||||
0.252626 | + | 0.967564i | \(0.418706\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.4395 | 0.471355 | ||||||||
\(590\) | −2.15971 | −0.0889140 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.58613 | −0.311788 | ||||||||
\(593\) | −28.6547 | −1.17671 | −0.588353 | − | 0.808604i | \(-0.700223\pi\) | ||||
−0.588353 | + | 0.808604i | \(0.700223\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.76810 | 0.359457 | ||||||||
\(596\) | −2.90167 | −0.118857 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.04567 | 0.0427607 | ||||||||
\(599\) | 6.02231 | 0.246065 | 0.123032 | − | 0.992403i | \(-0.460738\pi\) | ||||
0.123032 | + | 0.992403i | \(0.460738\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.1083 | 1.35052 | 0.675258 | − | 0.737582i | \(-0.264032\pi\) | ||||
0.675258 | + | 0.737582i | \(0.264032\pi\) | |||||||
\(602\) | 20.0528 | 0.817290 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.66399 | 0.108396 | ||||||||
\(605\) | −13.3568 | −0.543031 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.7642 | 1.45163 | 0.725813 | − | 0.687892i | \(-0.241464\pi\) | ||||
0.725813 | + | 0.687892i | \(0.241464\pi\) | |||||||
\(608\) | −1.53786 | −0.0623686 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.84472 | 0.0746903 | ||||||||
\(611\) | −1.98238 | −0.0801987 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.7521 | −0.959339 | −0.479669 | − | 0.877449i | \(-0.659243\pi\) | ||||
−0.479669 | + | 0.877449i | \(0.659243\pi\) | |||||||
\(614\) | −32.7514 | −1.32174 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.8696 | −0.639404 | ||||||||
\(617\) | 37.5379 | 1.51122 | 0.755609 | − | 0.655023i | \(-0.227341\pi\) | ||||
0.755609 | + | 0.655023i | \(0.227341\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.6282 | 1.87415 | 0.937073 | − | 0.349132i | \(-0.113524\pi\) | ||||
0.937073 | + | 0.349132i | \(0.113524\pi\) | |||||||
\(620\) | 5.10603 | 0.205063 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.09711 | 0.204376 | ||||||||
\(623\) | −23.8630 | −0.956049 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.1543 | 0.726170 | ||||||||
\(626\) | 3.70513 | 0.148087 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.2048 | 0.606736 | ||||||||
\(629\) | 33.6991 | 1.34367 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.3815 | 1.12985 | 0.564926 | − | 0.825142i | \(-0.308905\pi\) | ||||
0.564926 | + | 0.825142i | \(0.308905\pi\) | |||||||
\(632\) | 12.1543 | 0.483472 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.1944 | −0.444588 | ||||||||
\(635\) | −2.77527 | −0.110133 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.418399 | 0.0165776 | ||||||||
\(638\) | 38.8144 | 1.53668 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.686428 | −0.0271335 | ||||||||
\(641\) | −11.2437 | −0.444098 | −0.222049 | − | 0.975036i | \(-0.571274\pi\) | ||||
−0.222049 | + | 0.975036i | \(0.571274\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.473139 | −0.0186588 | −0.00932940 | − | 0.999956i | \(-0.502970\pi\) | ||||
−0.00932940 | + | 0.999956i | \(0.502970\pi\) | |||||||
\(644\) | 9.11562 | 0.359206 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.83150 | 0.268782 | ||||||||
\(647\) | 44.1533 | 1.73585 | 0.867923 | − | 0.496699i | \(-0.165455\pi\) | ||||
0.867923 | + | 0.496699i | \(0.165455\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.3642 | −0.681604 | ||||||||
\(650\) | −1.49384 | −0.0585934 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.4990 | 0.489498 | ||||||||
\(653\) | −17.7560 | −0.694847 | −0.347423 | − | 0.937708i | \(-0.612943\pi\) | ||||
−0.347423 | + | 0.937708i | \(0.612943\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.56302 | 0.178292 | ||||||||
\(656\) | 2.51679 | 0.0982640 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −17.2814 | −0.673700 | ||||||||
\(659\) | −28.1314 | −1.09584 | −0.547921 | − | 0.836530i | \(-0.684581\pi\) | ||||
−0.547921 | + | 0.836530i | \(0.684581\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.7180 | 0.533567 | 0.266784 | − | 0.963756i | \(-0.414039\pi\) | ||||
0.266784 | + | 0.963756i | \(0.414039\pi\) | |||||||
\(662\) | −30.7807 | −1.19633 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.22743 | 0.202864 | ||||||||
\(665\) | 3.03546 | 0.117710 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.2953 | −0.863278 | ||||||||
\(668\) | −6.88133 | −0.266247 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.59731 | 0.370776 | ||||||||
\(671\) | 14.8316 | 0.572567 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.1670 | 0.469002 | 0.234501 | − | 0.972116i | \(-0.424654\pi\) | ||||
0.234501 | + | 0.972116i | \(0.424654\pi\) | |||||||
\(674\) | −28.0781 | −1.08153 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.8912 | −0.495815 | ||||||||
\(677\) | −42.3323 | −1.62696 | −0.813481 | − | 0.581592i | \(-0.802430\pi\) | ||||
−0.813481 | + | 0.581592i | \(0.802430\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.7992 | 0.491186 | ||||||||
\(680\) | 3.04925 | 0.116934 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 41.0527 | 1.57199 | ||||||||
\(683\) | −32.6141 | −1.24794 | −0.623972 | − | 0.781446i | \(-0.714482\pi\) | ||||
−0.623972 | + | 0.781446i | \(0.714482\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.53265 | 0.287808 | ||||||||
\(686\) | −16.4810 | −0.629249 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.97369 | 0.265869 | ||||||||
\(689\) | 0.277162 | 0.0105590 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.87327 | 0.261472 | 0.130736 | − | 0.991417i | \(-0.458266\pi\) | ||||
0.130736 | + | 0.991417i | \(0.458266\pi\) | |||||||
\(692\) | 3.65630 | 0.138992 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.81474 | −0.182765 | ||||||||
\(695\) | 10.4434 | 0.396143 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.1801 | −0.423475 | ||||||||
\(698\) | 20.7579 | 0.785697 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.0226 | −0.492207 | ||||||||
\(701\) | 30.3022 | 1.14450 | 0.572249 | − | 0.820080i | \(-0.306071\pi\) | ||||
0.572249 | + | 0.820080i | \(0.306071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.6664 | 0.440008 | ||||||||
\(704\) | −5.51891 | −0.208002 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.21876 | 0.121140 | ||||||||
\(707\) | 9.30601 | 0.349989 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.6605 | −1.71482 | −0.857408 | − | 0.514638i | \(-0.827926\pi\) | ||||
−0.857408 | + | 0.514638i | \(0.827926\pi\) | |||||||
\(710\) | −4.58036 | −0.171898 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.29874 | −0.311009 | ||||||||
\(713\) | −23.5810 | −0.883117 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.24959 | 0.0467322 | ||||||||
\(716\) | −11.6410 | −0.435045 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −25.5107 | −0.952053 | ||||||||
\(719\) | 4.43820 | 0.165517 | 0.0827584 | − | 0.996570i | \(-0.473627\pi\) | ||||
0.0827584 | + | 0.996570i | \(0.473627\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.5975 | −1.36296 | ||||||||
\(722\) | −16.6350 | −0.619090 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.8301 | −0.513990 | ||||||||
\(725\) | 31.8510 | 1.18292 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.18844 | 0.118253 | 0.0591263 | − | 0.998251i | \(-0.481169\pi\) | ||||
0.0591263 | + | 0.998251i | \(0.481169\pi\) | |||||||
\(728\) | 0.948489 | 0.0351533 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.20794 | −0.303790 | ||||||||
\(731\) | −30.9785 | −1.14578 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.01336 | 0.259045 | 0.129522 | − | 0.991577i | \(-0.458656\pi\) | ||||
0.129522 | + | 0.991577i | \(0.458656\pi\) | |||||||
\(734\) | −24.4579 | −0.902758 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.17011 | 0.116852 | ||||||||
\(737\) | 77.1628 | 2.84233 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.9587 | −0.918122 | −0.459061 | − | 0.888405i | \(-0.651814\pi\) | ||||
−0.459061 | + | 0.888405i | \(0.651814\pi\) | |||||||
\(740\) | 5.20733 | 0.191425 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.41616 | 0.0886999 | ||||||||
\(743\) | −28.8093 | −1.05691 | −0.528456 | − | 0.848961i | \(-0.677229\pi\) | ||||
−0.528456 | + | 0.848961i | \(0.677229\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.99179 | 0.0729735 | ||||||||
\(746\) | −9.79830 | −0.358741 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 24.5161 | 0.896399 | ||||||||
\(749\) | −13.0124 | −0.475464 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −51.0813 | −1.86398 | −0.931992 | − | 0.362479i | \(-0.881931\pi\) | ||||
−0.931992 | + | 0.362479i | \(0.881931\pi\) | |||||||
\(752\) | −6.00990 | −0.219159 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.31985 | −0.0844838 | ||||||||
\(755\) | −1.82864 | −0.0665509 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.0243 | 0.546068 | 0.273034 | − | 0.962004i | \(-0.411973\pi\) | ||||
0.273034 | + | 0.962004i | \(0.411973\pi\) | |||||||
\(758\) | 23.3632 | 0.848588 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.05563 | 0.0382918 | ||||||||
\(761\) | −6.31216 | −0.228816 | −0.114408 | − | 0.993434i | \(-0.536497\pi\) | ||||
−0.114408 | + | 0.993434i | \(0.536497\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.2994 | −1.09691 | ||||||||
\(764\) | 15.4332 | 0.558354 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.1424 | −0.944564 | ||||||||
\(767\) | 1.03782 | 0.0374735 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.2449 | 0.874293 | 0.437147 | − | 0.899390i | \(-0.355989\pi\) | ||||
0.437147 | + | 0.899390i | \(0.355989\pi\) | |||||||
\(770\) | 10.8933 | 0.392568 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.86292 | −0.0670479 | ||||||||
\(773\) | −14.1903 | −0.510390 | −0.255195 | − | 0.966890i | \(-0.582140\pi\) | ||||
−0.255195 | + | 0.966890i | \(0.582140\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33.6878 | 1.21010 | ||||||||
\(776\) | 4.45112 | 0.159786 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.73549 | −0.133924 | ||||||||
\(779\) | −3.87047 | −0.138674 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.8263 | −1.31775 | ||||||||
\(782\) | −14.0823 | −0.503582 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.26844 | 0.0453014 | ||||||||
\(785\) | −10.4370 | −0.372512 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.2608 | −0.615280 | −0.307640 | − | 0.951503i | \(-0.599539\pi\) | ||||
−0.307640 | + | 0.951503i | \(0.599539\pi\) | |||||||
\(788\) | 18.0327 | 0.642387 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.34305 | −0.296833 | ||||||||
\(791\) | −8.44503 | −0.300271 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.886451 | −0.0314788 | ||||||||
\(794\) | 17.6199 | 0.625306 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.0118 | 0.851077 | ||||||||
\(797\) | 13.2887 | 0.470710 | 0.235355 | − | 0.971909i | \(-0.424375\pi\) | ||||
0.235355 | + | 0.971909i | \(0.424375\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.6972 | 0.944479 | ||||||||
\(800\) | −4.52882 | −0.160118 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.5232 | 0.795320 | ||||||||
\(803\) | −65.9922 | −2.32882 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.25722 | −0.220538 | ||||||||
\(806\) | −2.45363 | −0.0864254 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.23632 | 0.113853 | ||||||||
\(809\) | 9.08056 | 0.319255 | 0.159628 | − | 0.987177i | \(-0.448971\pi\) | ||||
0.159628 | + | 0.987177i | \(0.448971\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.9105 | −1.75260 | −0.876298 | − | 0.481770i | \(-0.839994\pi\) | ||||
−0.876298 | + | 0.481770i | \(0.839994\pi\) | |||||||
\(812\) | −20.2232 | −0.709697 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 41.8672 | 1.46745 | ||||||||
\(815\) | −8.57965 | −0.300532 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.7246 | −0.375206 | ||||||||
\(818\) | −12.4542 | −0.435451 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.72759 | −0.0603301 | ||||||||
\(821\) | −9.08016 | −0.316900 | −0.158450 | − | 0.987367i | \(-0.550650\pi\) | ||||
−0.158450 | + | 0.987367i | \(0.550650\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.7767 | 0.689371 | 0.344686 | − | 0.938718i | \(-0.387986\pi\) | ||||
0.344686 | + | 0.938718i | \(0.387986\pi\) | |||||||
\(824\) | −12.7274 | −0.443380 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.04717 | 0.314791 | ||||||||
\(827\) | −37.8945 | −1.31772 | −0.658860 | − | 0.752266i | \(-0.728961\pi\) | ||||
−0.658860 | + | 0.752266i | \(0.728961\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.13822 | −0.213189 | −0.106595 | − | 0.994303i | \(-0.533995\pi\) | ||||
−0.106595 | + | 0.994303i | \(0.533995\pi\) | |||||||
\(830\) | −3.58825 | −0.124550 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.329853 | 0.0114356 | ||||||||
\(833\) | −5.63467 | −0.195230 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.72354 | 0.163465 | ||||||||
\(836\) | 8.48734 | 0.293541 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 30.5170 | 1.05419 | ||||||||
\(839\) | −37.2877 | −1.28731 | −0.643657 | − | 0.765314i | \(-0.722584\pi\) | ||||
−0.643657 | + | 0.765314i | \(0.722584\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.4627 | 0.705610 | ||||||||
\(842\) | 5.17369 | 0.178297 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.05163 | 0.208306 | ||||||||
\(845\) | 8.84888 | 0.304411 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 55.9525 | 1.92255 | ||||||||
\(848\) | 0.840259 | 0.0288546 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 20.1179 | 0.690039 | ||||||||
\(851\) | −24.0489 | −0.824385 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.19329 | −0.177815 | −0.0889075 | − | 0.996040i | \(-0.528338\pi\) | ||||
−0.0889075 | + | 0.996040i | \(0.528338\pi\) | |||||||
\(854\) | −7.72762 | −0.264434 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.52529 | −0.154671 | ||||||||
\(857\) | −33.5933 | −1.14753 | −0.573763 | − | 0.819022i | \(-0.694517\pi\) | ||||
−0.573763 | + | 0.819022i | \(0.694517\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.4008 | 0.354872 | 0.177436 | − | 0.984132i | \(-0.443220\pi\) | ||||
0.177436 | + | 0.984132i | \(0.443220\pi\) | |||||||
\(860\) | −4.78694 | −0.163233 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.8685 | 0.404243 | ||||||||
\(863\) | 37.4393 | 1.27445 | 0.637224 | − | 0.770679i | \(-0.280083\pi\) | ||||
0.637224 | + | 0.770679i | \(0.280083\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.50979 | −0.0853354 | ||||||||
\(866\) | 2.77072 | 0.0941530 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −21.3895 | −0.726006 | ||||||||
\(869\) | −67.0785 | −2.27548 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.61185 | −0.156266 | ||||||||
\(872\) | −10.5371 | −0.356832 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.87520 | −0.164906 | ||||||||
\(875\) | 18.8081 | 0.635831 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.1976 | 1.66129 | 0.830643 | − | 0.556805i | \(-0.187973\pi\) | ||||
0.830643 | + | 0.556805i | \(0.187973\pi\) | |||||||
\(878\) | −13.5404 | −0.456966 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.78834 | 0.127705 | ||||||||
\(881\) | 42.7892 | 1.44161 | 0.720803 | − | 0.693140i | \(-0.243773\pi\) | ||||
0.720803 | + | 0.693140i | \(0.243773\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.3874 | −0.416870 | −0.208435 | − | 0.978036i | \(-0.566837\pi\) | ||||
−0.208435 | + | 0.978036i | \(0.566837\pi\) | |||||||
\(884\) | −1.46527 | −0.0492825 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −38.7298 | −1.30115 | ||||||||
\(887\) | 1.39064 | 0.0466930 | 0.0233465 | − | 0.999727i | \(-0.492568\pi\) | ||||
0.0233465 | + | 0.999727i | \(0.492568\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.6258 | 0.389916 | ||||||||
\(890\) | 5.69649 | 0.190947 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | 9.24241 | 0.309285 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.99071 | 0.267100 | ||||||||
\(896\) | 2.87549 | 0.0960634 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 35.2746 | 1.17713 | ||||||||
\(899\) | 52.3151 | 1.74481 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.73260 | −0.124351 | ||||||||
\(902\) | −13.8899 | −0.462484 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.93690 | −0.0976799 | ||||||||
\(905\) | 9.49335 | 0.315570 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.8327 | −0.558921 | −0.279460 | − | 0.960157i | \(-0.590156\pi\) | ||||
−0.279460 | + | 0.960157i | \(0.590156\pi\) | |||||||
\(908\) | −24.3730 | −0.808846 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.651069 | −0.0215827 | ||||||||
\(911\) | −25.6813 | −0.850860 | −0.425430 | − | 0.904991i | \(-0.639877\pi\) | ||||
−0.425430 | + | 0.904991i | \(0.639877\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.8497 | −0.954787 | ||||||||
\(914\) | −15.7179 | −0.519901 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.57496 | 0.250284 | ||||||||
\(917\) | −19.1148 | −0.631226 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.0182 | −1.12216 | −0.561079 | − | 0.827762i | \(-0.689614\pi\) | ||||
−0.561079 | + | 0.827762i | \(0.689614\pi\) | |||||||
\(920\) | −2.17605 | −0.0717424 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.4964 | 0.510346 | ||||||||
\(923\) | 2.20103 | 0.0724476 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.3562 | 1.12963 | ||||||||
\(926\) | 34.0979 | 1.12053 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.03297 | −0.230869 | ||||||||
\(929\) | 16.0961 | 0.528096 | 0.264048 | − | 0.964510i | \(-0.414942\pi\) | ||||
0.264048 | + | 0.964510i | \(0.414942\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.95069 | −0.0639312 | ||||||||
\(932\) | −1.91430 | −0.0627050 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.76270 | −0.188561 | ||||||||
\(935\) | −16.8286 | −0.550353 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.1780 | −0.365169 | −0.182584 | − | 0.983190i | \(-0.558446\pi\) | ||||
−0.182584 | + | 0.983190i | \(0.558446\pi\) | |||||||
\(938\) | −40.2037 | −1.31270 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.12537 | 0.134555 | ||||||||
\(941\) | 55.8606 | 1.82101 | 0.910503 | − | 0.413504i | \(-0.135695\pi\) | ||||
0.910503 | + | 0.413504i | \(0.135695\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.97849 | 0.259815 | ||||||||
\(944\) | 3.14631 | 0.102404 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.4872 | −1.25133 | ||||||||
\(947\) | −33.1983 | −1.07880 | −0.539400 | − | 0.842050i | \(-0.681349\pi\) | ||||
−0.539400 | + | 0.842050i | \(0.681349\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.94421 | 0.128034 | ||||||||
\(950\) | 6.96470 | 0.225965 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.7735 | −0.413992 | ||||||||
\(953\) | 52.1647 | 1.68978 | 0.844891 | − | 0.534939i | \(-0.179665\pi\) | ||||
0.844891 | + | 0.534939i | \(0.179665\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.5938 | −0.342807 | ||||||||
\(956\) | 18.8018 | 0.608094 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.892156 | 0.0288243 | ||||||||
\(959\) | −31.5547 | −1.01896 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.3321 | 0.784905 | ||||||||
\(962\) | −2.50231 | −0.0806777 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.7202 | −0.409689 | ||||||||
\(965\) | 1.27876 | 0.0411648 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.32108 | −0.203272 | −0.101636 | − | 0.994822i | \(-0.532408\pi\) | ||||
−0.101636 | + | 0.994822i | \(0.532408\pi\) | |||||||
\(968\) | 19.4584 | 0.625417 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.05538 | −0.0981022 | ||||||||
\(971\) | −24.4643 | −0.785098 | −0.392549 | − | 0.919731i | \(-0.628407\pi\) | ||||
−0.392549 | + | 0.919731i | \(0.628407\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −43.7482 | −1.40250 | ||||||||
\(974\) | 4.83587 | 0.154951 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.68741 | −0.0860220 | ||||||||
\(977\) | 23.1983 | 0.742181 | 0.371090 | − | 0.928597i | \(-0.378984\pi\) | ||||
0.371090 | + | 0.928597i | \(0.378984\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.8001 | 1.46378 | ||||||||
\(980\) | −0.870693 | −0.0278133 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14.5280 | 0.463608 | ||||||||
\(983\) | 44.9757 | 1.43450 | 0.717252 | − | 0.696814i | \(-0.245400\pi\) | ||||
0.717252 | + | 0.696814i | \(0.245400\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.3781 | −0.394400 | ||||||||
\(986\) | 31.2419 | 0.994945 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.507269 | −0.0161384 | ||||||||
\(989\) | 22.1074 | 0.702974 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.4523 | −1.72973 | −0.864867 | − | 0.502001i | \(-0.832597\pi\) | ||||
−0.864867 | + | 0.502001i | \(0.832597\pi\) | |||||||
\(992\) | −7.43855 | −0.236174 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 19.1874 | 0.608588 | ||||||||
\(995\) | −16.4824 | −0.522527 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.4748 | 0.648444 | 0.324222 | − | 0.945981i | \(-0.394898\pi\) | ||||
0.324222 | + | 0.945981i | \(0.394898\pi\) | |||||||
\(998\) | 42.7043 | 1.35178 | ||||||||
\(999\) | 0 | 0 |
(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 | 4014.2.a.r.1.4 | 5 | ||
3.2 | odd | 2 | 1338.2.a.h.1.2 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1338.2.a.h.1.2 | ✓ | 5 | 3.2 | odd | 2 | ||
4014.2.a.r.1.4 | 5 | 1.1 | even | 1 | trivial |