Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(1,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, 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("950.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.56155 | −0.901563 | −0.450781 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450781 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.56155 | −0.637501 | ||||||||
\(7\) | −1.56155 | −0.590211 | −0.295106 | − | 0.955465i | \(-0.595355\pi\) | ||||
−0.295106 | + | 0.955465i | \(0.595355\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(12\) | −1.56155 | −0.450781 | ||||||||
\(13\) | 6.68466 | 1.85399 | 0.926995 | − | 0.375073i | \(-0.122382\pi\) | ||||
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | −1.56155 | −0.417343 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.56155 | −1.83395 | −0.916973 | − | 0.398949i | \(-0.869375\pi\) | ||||
−0.916973 | + | 0.398949i | \(0.869375\pi\) | |||||||
\(18\) | −0.561553 | −0.132359 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.43845 | 0.532113 | ||||||||
\(22\) | 4.00000 | 0.852803 | ||||||||
\(23\) | 4.68466 | 0.976819 | 0.488409 | − | 0.872615i | \(-0.337577\pi\) | ||||
0.488409 | + | 0.872615i | \(0.337577\pi\) | |||||||
\(24\) | −1.56155 | −0.318751 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.68466 | 1.31097 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | −1.56155 | −0.295106 | ||||||||
\(29\) | 6.68466 | 1.24131 | 0.620655 | − | 0.784084i | \(-0.286867\pi\) | ||||
0.620655 | + | 0.784084i | \(0.286867\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.12311 | 0.560926 | 0.280463 | − | 0.959865i | \(-0.409512\pi\) | ||||
0.280463 | + | 0.959865i | \(0.409512\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −6.24621 | −1.08733 | ||||||||
\(34\) | −7.56155 | −1.29680 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.561553 | −0.0935921 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −10.4384 | −1.67149 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.24621 | −0.663147 | −0.331573 | − | 0.943429i | \(-0.607579\pi\) | ||||
−0.331573 | + | 0.943429i | \(0.607579\pi\) | |||||||
\(42\) | 2.43845 | 0.376261 | ||||||||
\(43\) | 11.1231 | 1.69626 | 0.848129 | − | 0.529790i | \(-0.177729\pi\) | ||||
0.848129 | + | 0.529790i | \(0.177729\pi\) | |||||||
\(44\) | 4.00000 | 0.603023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.68466 | 0.690715 | ||||||||
\(47\) | 10.2462 | 1.49456 | 0.747282 | − | 0.664507i | \(-0.231359\pi\) | ||||
0.747282 | + | 0.664507i | \(0.231359\pi\) | |||||||
\(48\) | −1.56155 | −0.225391 | ||||||||
\(49\) | −4.56155 | −0.651650 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.8078 | 1.65342 | ||||||||
\(52\) | 6.68466 | 0.926995 | ||||||||
\(53\) | 0.438447 | 0.0602254 | 0.0301127 | − | 0.999547i | \(-0.490413\pi\) | ||||
0.0301127 | + | 0.999547i | \(0.490413\pi\) | |||||||
\(54\) | 5.56155 | 0.756831 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.56155 | −0.208671 | ||||||||
\(57\) | 1.56155 | 0.206833 | ||||||||
\(58\) | 6.68466 | 0.877739 | ||||||||
\(59\) | −1.56155 | −0.203297 | −0.101648 | − | 0.994820i | \(-0.532412\pi\) | ||||
−0.101648 | + | 0.994820i | \(0.532412\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.87689 | 0.368349 | 0.184174 | − | 0.982894i | \(-0.441039\pi\) | ||||
0.184174 | + | 0.982894i | \(0.441039\pi\) | |||||||
\(62\) | 3.12311 | 0.396635 | ||||||||
\(63\) | 0.876894 | 0.110478 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.24621 | −0.768855 | ||||||||
\(67\) | −1.56155 | −0.190774 | −0.0953870 | − | 0.995440i | \(-0.530409\pi\) | ||||
−0.0953870 | + | 0.995440i | \(0.530409\pi\) | |||||||
\(68\) | −7.56155 | −0.916973 | ||||||||
\(69\) | −7.31534 | −0.880664 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.24621 | −0.741289 | −0.370644 | − | 0.928775i | \(-0.620863\pi\) | ||||
−0.370644 | + | 0.928775i | \(0.620863\pi\) | |||||||
\(72\) | −0.561553 | −0.0661796 | ||||||||
\(73\) | −10.6847 | −1.25054 | −0.625272 | − | 0.780407i | \(-0.715012\pi\) | ||||
−0.625272 | + | 0.780407i | \(0.715012\pi\) | |||||||
\(74\) | 6.00000 | 0.697486 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −6.24621 | −0.711822 | ||||||||
\(78\) | −10.4384 | −1.18192 | ||||||||
\(79\) | 3.12311 | 0.351377 | 0.175688 | − | 0.984446i | \(-0.443785\pi\) | ||||
0.175688 | + | 0.984446i | \(0.443785\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | −4.24621 | −0.468916 | ||||||||
\(83\) | −11.1231 | −1.22092 | −0.610460 | − | 0.792047i | \(-0.709015\pi\) | ||||
−0.610460 | + | 0.792047i | \(0.709015\pi\) | |||||||
\(84\) | 2.43845 | 0.266056 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.1231 | 1.19944 | ||||||||
\(87\) | −10.4384 | −1.11912 | ||||||||
\(88\) | 4.00000 | 0.426401 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.4384 | −1.09425 | ||||||||
\(92\) | 4.68466 | 0.488409 | ||||||||
\(93\) | −4.87689 | −0.505710 | ||||||||
\(94\) | 10.2462 | 1.05682 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.56155 | −0.159375 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | −4.56155 | −0.460786 | ||||||||
\(99\) | −2.24621 | −0.225753 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.36932 | 0.733274 | 0.366637 | − | 0.930364i | \(-0.380509\pi\) | ||||
0.366637 | + | 0.930364i | \(0.380509\pi\) | |||||||
\(102\) | 11.8078 | 1.16914 | ||||||||
\(103\) | 14.2462 | 1.40372 | 0.701860 | − | 0.712314i | \(-0.252353\pi\) | ||||
0.701860 | + | 0.712314i | \(0.252353\pi\) | |||||||
\(104\) | 6.68466 | 0.655485 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.438447 | 0.0425858 | ||||||||
\(107\) | 9.56155 | 0.924350 | 0.462175 | − | 0.886789i | \(-0.347069\pi\) | ||||
0.462175 | + | 0.886789i | \(0.347069\pi\) | |||||||
\(108\) | 5.56155 | 0.535161 | ||||||||
\(109\) | 3.56155 | 0.341135 | 0.170567 | − | 0.985346i | \(-0.445440\pi\) | ||||
0.170567 | + | 0.985346i | \(0.445440\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.36932 | −0.889296 | ||||||||
\(112\) | −1.56155 | −0.147553 | ||||||||
\(113\) | −17.1231 | −1.61081 | −0.805403 | − | 0.592727i | \(-0.798051\pi\) | ||||
−0.805403 | + | 0.592727i | \(0.798051\pi\) | |||||||
\(114\) | 1.56155 | 0.146253 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.68466 | 0.620655 | ||||||||
\(117\) | −3.75379 | −0.347038 | ||||||||
\(118\) | −1.56155 | −0.143753 | ||||||||
\(119\) | 11.8078 | 1.08242 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 2.87689 | 0.260462 | ||||||||
\(123\) | 6.63068 | 0.597869 | ||||||||
\(124\) | 3.12311 | 0.280463 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.876894 | 0.0781200 | ||||||||
\(127\) | −4.87689 | −0.432754 | −0.216377 | − | 0.976310i | \(-0.569424\pi\) | ||||
−0.216377 | + | 0.976310i | \(0.569424\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −17.3693 | −1.52928 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.4924 | 1.44095 | 0.720475 | − | 0.693481i | \(-0.243924\pi\) | ||||
0.720475 | + | 0.693481i | \(0.243924\pi\) | |||||||
\(132\) | −6.24621 | −0.543663 | ||||||||
\(133\) | 1.56155 | 0.135404 | ||||||||
\(134\) | −1.56155 | −0.134898 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.56155 | −0.648398 | ||||||||
\(137\) | −5.80776 | −0.496191 | −0.248095 | − | 0.968736i | \(-0.579805\pi\) | ||||
−0.248095 | + | 0.968736i | \(0.579805\pi\) | |||||||
\(138\) | −7.31534 | −0.622723 | ||||||||
\(139\) | −16.4924 | −1.39887 | −0.699435 | − | 0.714697i | \(-0.746565\pi\) | ||||
−0.699435 | + | 0.714697i | \(0.746565\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.0000 | −1.34744 | ||||||||
\(142\) | −6.24621 | −0.524170 | ||||||||
\(143\) | 26.7386 | 2.23600 | ||||||||
\(144\) | −0.561553 | −0.0467961 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.6847 | −0.884269 | ||||||||
\(147\) | 7.12311 | 0.587504 | ||||||||
\(148\) | 6.00000 | 0.493197 | ||||||||
\(149\) | −11.3693 | −0.931411 | −0.465705 | − | 0.884940i | \(-0.654199\pi\) | ||||
−0.465705 | + | 0.884940i | \(0.654199\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.12311 | −0.254155 | −0.127077 | − | 0.991893i | \(-0.540560\pi\) | ||||
−0.127077 | + | 0.991893i | \(0.540560\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 4.24621 | 0.343286 | ||||||||
\(154\) | −6.24621 | −0.503334 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −10.4384 | −0.835745 | ||||||||
\(157\) | 3.75379 | 0.299585 | 0.149792 | − | 0.988717i | \(-0.452139\pi\) | ||||
0.149792 | + | 0.988717i | \(0.452139\pi\) | |||||||
\(158\) | 3.12311 | 0.248461 | ||||||||
\(159\) | −0.684658 | −0.0542969 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.31534 | −0.576530 | ||||||||
\(162\) | −7.00000 | −0.549972 | ||||||||
\(163\) | −9.36932 | −0.733862 | −0.366931 | − | 0.930248i | \(-0.619591\pi\) | ||||
−0.366931 | + | 0.930248i | \(0.619591\pi\) | |||||||
\(164\) | −4.24621 | −0.331573 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.1231 | −0.863320 | ||||||||
\(167\) | −17.3693 | −1.34408 | −0.672039 | − | 0.740516i | \(-0.734581\pi\) | ||||
−0.672039 | + | 0.740516i | \(0.734581\pi\) | |||||||
\(168\) | 2.43845 | 0.188130 | ||||||||
\(169\) | 31.6847 | 2.43728 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.561553 | 0.0429430 | ||||||||
\(172\) | 11.1231 | 0.848129 | ||||||||
\(173\) | −3.75379 | −0.285395 | −0.142698 | − | 0.989766i | \(-0.545578\pi\) | ||||
−0.142698 | + | 0.989766i | \(0.545578\pi\) | |||||||
\(174\) | −10.4384 | −0.791337 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.00000 | 0.301511 | ||||||||
\(177\) | 2.43845 | 0.183285 | ||||||||
\(178\) | 2.00000 | 0.149906 | ||||||||
\(179\) | −5.75379 | −0.430058 | −0.215029 | − | 0.976608i | \(-0.568985\pi\) | ||||
−0.215029 | + | 0.976608i | \(0.568985\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.0000 | −1.33793 | −0.668965 | − | 0.743294i | \(-0.733262\pi\) | ||||
−0.668965 | + | 0.743294i | \(0.733262\pi\) | |||||||
\(182\) | −10.4384 | −0.773749 | ||||||||
\(183\) | −4.49242 | −0.332089 | ||||||||
\(184\) | 4.68466 | 0.345358 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.87689 | −0.357591 | ||||||||
\(187\) | −30.2462 | −2.21182 | ||||||||
\(188\) | 10.2462 | 0.747282 | ||||||||
\(189\) | −8.68466 | −0.631716 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.68466 | 0.628400 | 0.314200 | − | 0.949357i | \(-0.398264\pi\) | ||||
0.314200 | + | 0.949357i | \(0.398264\pi\) | |||||||
\(192\) | −1.56155 | −0.112695 | ||||||||
\(193\) | −18.4924 | −1.33111 | −0.665557 | − | 0.746347i | \(-0.731806\pi\) | ||||
−0.665557 | + | 0.746347i | \(0.731806\pi\) | |||||||
\(194\) | −6.00000 | −0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.56155 | −0.325825 | ||||||||
\(197\) | 3.75379 | 0.267446 | 0.133723 | − | 0.991019i | \(-0.457307\pi\) | ||||
0.133723 | + | 0.991019i | \(0.457307\pi\) | |||||||
\(198\) | −2.24621 | −0.159631 | ||||||||
\(199\) | −3.80776 | −0.269925 | −0.134963 | − | 0.990851i | \(-0.543091\pi\) | ||||
−0.134963 | + | 0.990851i | \(0.543091\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.43845 | 0.171995 | ||||||||
\(202\) | 7.36932 | 0.518503 | ||||||||
\(203\) | −10.4384 | −0.732635 | ||||||||
\(204\) | 11.8078 | 0.826709 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 14.2462 | 0.992581 | ||||||||
\(207\) | −2.63068 | −0.182845 | ||||||||
\(208\) | 6.68466 | 0.463498 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.6847 | 1.42399 | 0.711995 | − | 0.702184i | \(-0.247792\pi\) | ||||
0.711995 | + | 0.702184i | \(0.247792\pi\) | |||||||
\(212\) | 0.438447 | 0.0301127 | ||||||||
\(213\) | 9.75379 | 0.668319 | ||||||||
\(214\) | 9.56155 | 0.653614 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.56155 | 0.378416 | ||||||||
\(217\) | −4.87689 | −0.331065 | ||||||||
\(218\) | 3.56155 | 0.241219 | ||||||||
\(219\) | 16.6847 | 1.12744 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −50.5464 | −3.40012 | ||||||||
\(222\) | −9.36932 | −0.628827 | ||||||||
\(223\) | −1.36932 | −0.0916962 | −0.0458481 | − | 0.998948i | \(-0.514599\pi\) | ||||
−0.0458481 | + | 0.998948i | \(0.514599\pi\) | |||||||
\(224\) | −1.56155 | −0.104336 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −17.1231 | −1.13901 | ||||||||
\(227\) | 2.93087 | 0.194529 | 0.0972643 | − | 0.995259i | \(-0.468991\pi\) | ||||
0.0972643 | + | 0.995259i | \(0.468991\pi\) | |||||||
\(228\) | 1.56155 | 0.103416 | ||||||||
\(229\) | 18.4924 | 1.22201 | 0.611007 | − | 0.791625i | \(-0.290765\pi\) | ||||
0.611007 | + | 0.791625i | \(0.290765\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.75379 | 0.641752 | ||||||||
\(232\) | 6.68466 | 0.438869 | ||||||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | −3.75379 | −0.245393 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.56155 | −0.101648 | ||||||||
\(237\) | −4.87689 | −0.316788 | ||||||||
\(238\) | 11.8078 | 0.765384 | ||||||||
\(239\) | −5.56155 | −0.359747 | −0.179873 | − | 0.983690i | \(-0.557569\pi\) | ||||
−0.179873 | + | 0.983690i | \(0.557569\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.8769 | 0.958305 | 0.479153 | − | 0.877732i | \(-0.340944\pi\) | ||||
0.479153 | + | 0.877732i | \(0.340944\pi\) | |||||||
\(242\) | 5.00000 | 0.321412 | ||||||||
\(243\) | −5.75379 | −0.369106 | ||||||||
\(244\) | 2.87689 | 0.184174 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.63068 | 0.422757 | ||||||||
\(247\) | −6.68466 | −0.425335 | ||||||||
\(248\) | 3.12311 | 0.198317 | ||||||||
\(249\) | 17.3693 | 1.10074 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.2462 | −0.646735 | −0.323368 | − | 0.946273i | \(-0.604815\pi\) | ||||
−0.323368 | + | 0.946273i | \(0.604815\pi\) | |||||||
\(252\) | 0.876894 | 0.0552392 | ||||||||
\(253\) | 18.7386 | 1.17809 | ||||||||
\(254\) | −4.87689 | −0.306004 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.0000 | −0.873296 | −0.436648 | − | 0.899632i | \(-0.643834\pi\) | ||||
−0.436648 | + | 0.899632i | \(0.643834\pi\) | |||||||
\(258\) | −17.3693 | −1.08137 | ||||||||
\(259\) | −9.36932 | −0.582181 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.75379 | −0.232354 | ||||||||
\(262\) | 16.4924 | 1.01891 | ||||||||
\(263\) | 5.75379 | 0.354794 | 0.177397 | − | 0.984139i | \(-0.443232\pi\) | ||||
0.177397 | + | 0.984139i | \(0.443232\pi\) | |||||||
\(264\) | −6.24621 | −0.384428 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.56155 | 0.0957449 | ||||||||
\(267\) | −3.12311 | −0.191131 | ||||||||
\(268\) | −1.56155 | −0.0953870 | ||||||||
\(269\) | −26.0000 | −1.58525 | −0.792624 | − | 0.609711i | \(-0.791286\pi\) | ||||
−0.792624 | + | 0.609711i | \(0.791286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.93087 | 0.421020 | 0.210510 | − | 0.977592i | \(-0.432487\pi\) | ||||
0.210510 | + | 0.977592i | \(0.432487\pi\) | |||||||
\(272\) | −7.56155 | −0.458486 | ||||||||
\(273\) | 16.3002 | 0.986532 | ||||||||
\(274\) | −5.80776 | −0.350860 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.31534 | −0.440332 | ||||||||
\(277\) | −9.12311 | −0.548154 | −0.274077 | − | 0.961708i | \(-0.588372\pi\) | ||||
−0.274077 | + | 0.961708i | \(0.588372\pi\) | |||||||
\(278\) | −16.4924 | −0.989150 | ||||||||
\(279\) | −1.75379 | −0.104997 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000 | 0.119310 | 0.0596550 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596550 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(282\) | −16.0000 | −0.952786 | ||||||||
\(283\) | 12.8769 | 0.765452 | 0.382726 | − | 0.923862i | \(-0.374985\pi\) | ||||
0.382726 | + | 0.923862i | \(0.374985\pi\) | |||||||
\(284\) | −6.24621 | −0.370644 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 26.7386 | 1.58109 | ||||||||
\(287\) | 6.63068 | 0.391397 | ||||||||
\(288\) | −0.561553 | −0.0330898 | ||||||||
\(289\) | 40.1771 | 2.36336 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.36932 | 0.549239 | ||||||||
\(292\) | −10.6847 | −0.625272 | ||||||||
\(293\) | −23.1771 | −1.35402 | −0.677010 | − | 0.735974i | \(-0.736725\pi\) | ||||
−0.677010 | + | 0.735974i | \(0.736725\pi\) | |||||||
\(294\) | 7.12311 | 0.415428 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.00000 | 0.348743 | ||||||||
\(297\) | 22.2462 | 1.29086 | ||||||||
\(298\) | −11.3693 | −0.658607 | ||||||||
\(299\) | 31.3153 | 1.81101 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.3693 | −1.00115 | ||||||||
\(302\) | −3.12311 | −0.179715 | ||||||||
\(303\) | −11.5076 | −0.661093 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.24621 | 0.242740 | ||||||||
\(307\) | 0.492423 | 0.0281040 | 0.0140520 | − | 0.999901i | \(-0.495527\pi\) | ||||
0.0140520 | + | 0.999901i | \(0.495527\pi\) | |||||||
\(308\) | −6.24621 | −0.355911 | ||||||||
\(309\) | −22.2462 | −1.26554 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.68466 | 0.492462 | 0.246231 | − | 0.969211i | \(-0.420808\pi\) | ||||
0.246231 | + | 0.969211i | \(0.420808\pi\) | |||||||
\(312\) | −10.4384 | −0.590961 | ||||||||
\(313\) | 32.0540 | 1.81180 | 0.905899 | − | 0.423494i | \(-0.139197\pi\) | ||||
0.905899 | + | 0.423494i | \(0.139197\pi\) | |||||||
\(314\) | 3.75379 | 0.211839 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.12311 | 0.175688 | ||||||||
\(317\) | 24.0540 | 1.35101 | 0.675503 | − | 0.737357i | \(-0.263927\pi\) | ||||
0.675503 | + | 0.737357i | \(0.263927\pi\) | |||||||
\(318\) | −0.684658 | −0.0383937 | ||||||||
\(319\) | 26.7386 | 1.49708 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.9309 | −0.833360 | ||||||||
\(322\) | −7.31534 | −0.407668 | ||||||||
\(323\) | 7.56155 | 0.420736 | ||||||||
\(324\) | −7.00000 | −0.388889 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.36932 | −0.518918 | ||||||||
\(327\) | −5.56155 | −0.307555 | ||||||||
\(328\) | −4.24621 | −0.234458 | ||||||||
\(329\) | −16.0000 | −0.882109 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.56155 | 0.0858307 | 0.0429154 | − | 0.999079i | \(-0.486335\pi\) | ||||
0.0429154 | + | 0.999079i | \(0.486335\pi\) | |||||||
\(332\) | −11.1231 | −0.610460 | ||||||||
\(333\) | −3.36932 | −0.184637 | ||||||||
\(334\) | −17.3693 | −0.950407 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.43845 | 0.133028 | ||||||||
\(337\) | 26.0000 | 1.41631 | 0.708155 | − | 0.706057i | \(-0.249528\pi\) | ||||
0.708155 | + | 0.706057i | \(0.249528\pi\) | |||||||
\(338\) | 31.6847 | 1.72342 | ||||||||
\(339\) | 26.7386 | 1.45224 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.4924 | 0.676503 | ||||||||
\(342\) | 0.561553 | 0.0303653 | ||||||||
\(343\) | 18.0540 | 0.974823 | ||||||||
\(344\) | 11.1231 | 0.599718 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.75379 | −0.201805 | ||||||||
\(347\) | 33.3693 | 1.79136 | 0.895679 | − | 0.444700i | \(-0.146690\pi\) | ||||
0.895679 | + | 0.444700i | \(0.146690\pi\) | |||||||
\(348\) | −10.4384 | −0.559560 | ||||||||
\(349\) | 20.2462 | 1.08375 | 0.541877 | − | 0.840458i | \(-0.317714\pi\) | ||||
0.541877 | + | 0.840458i | \(0.317714\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 37.1771 | 1.98437 | ||||||||
\(352\) | 4.00000 | 0.213201 | ||||||||
\(353\) | −24.9309 | −1.32694 | −0.663468 | − | 0.748205i | \(-0.730916\pi\) | ||||
−0.663468 | + | 0.748205i | \(0.730916\pi\) | |||||||
\(354\) | 2.43845 | 0.129602 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.00000 | 0.106000 | ||||||||
\(357\) | −18.4384 | −0.975866 | ||||||||
\(358\) | −5.75379 | −0.304097 | ||||||||
\(359\) | 5.56155 | 0.293528 | 0.146764 | − | 0.989172i | \(-0.453114\pi\) | ||||
0.146764 | + | 0.989172i | \(0.453114\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −18.0000 | −0.946059 | ||||||||
\(363\) | −7.80776 | −0.409801 | ||||||||
\(364\) | −10.4384 | −0.547123 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.49242 | −0.234823 | ||||||||
\(367\) | 10.2462 | 0.534848 | 0.267424 | − | 0.963579i | \(-0.413828\pi\) | ||||
0.267424 | + | 0.963579i | \(0.413828\pi\) | |||||||
\(368\) | 4.68466 | 0.244205 | ||||||||
\(369\) | 2.38447 | 0.124131 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.684658 | −0.0355457 | ||||||||
\(372\) | −4.87689 | −0.252855 | ||||||||
\(373\) | 27.5616 | 1.42708 | 0.713542 | − | 0.700613i | \(-0.247090\pi\) | ||||
0.713542 | + | 0.700613i | \(0.247090\pi\) | |||||||
\(374\) | −30.2462 | −1.56399 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.2462 | 0.528408 | ||||||||
\(377\) | 44.6847 | 2.30138 | ||||||||
\(378\) | −8.68466 | −0.446691 | ||||||||
\(379\) | 6.43845 | 0.330721 | 0.165360 | − | 0.986233i | \(-0.447121\pi\) | ||||
0.165360 | + | 0.986233i | \(0.447121\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.61553 | 0.390155 | ||||||||
\(382\) | 8.68466 | 0.444346 | ||||||||
\(383\) | −30.2462 | −1.54551 | −0.772755 | − | 0.634705i | \(-0.781122\pi\) | ||||
−0.772755 | + | 0.634705i | \(0.781122\pi\) | |||||||
\(384\) | −1.56155 | −0.0796877 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.4924 | −0.941240 | ||||||||
\(387\) | −6.24621 | −0.317513 | ||||||||
\(388\) | −6.00000 | −0.304604 | ||||||||
\(389\) | 1.12311 | 0.0569437 | 0.0284719 | − | 0.999595i | \(-0.490936\pi\) | ||||
0.0284719 | + | 0.999595i | \(0.490936\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.4233 | −1.79143 | ||||||||
\(392\) | −4.56155 | −0.230393 | ||||||||
\(393\) | −25.7538 | −1.29911 | ||||||||
\(394\) | 3.75379 | 0.189113 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.24621 | −0.112876 | ||||||||
\(397\) | −1.12311 | −0.0563671 | −0.0281835 | − | 0.999603i | \(-0.508972\pi\) | ||||
−0.0281835 | + | 0.999603i | \(0.508972\pi\) | |||||||
\(398\) | −3.80776 | −0.190866 | ||||||||
\(399\) | −2.43845 | −0.122075 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.2462 | −1.01105 | −0.505524 | − | 0.862813i | \(-0.668701\pi\) | ||||
−0.505524 | + | 0.862813i | \(0.668701\pi\) | |||||||
\(402\) | 2.43845 | 0.121619 | ||||||||
\(403\) | 20.8769 | 1.03995 | ||||||||
\(404\) | 7.36932 | 0.366637 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.4384 | −0.518051 | ||||||||
\(407\) | 24.0000 | 1.18964 | ||||||||
\(408\) | 11.8078 | 0.584571 | ||||||||
\(409\) | −24.7386 | −1.22325 | −0.611623 | − | 0.791149i | \(-0.709483\pi\) | ||||
−0.611623 | + | 0.791149i | \(0.709483\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.06913 | 0.447347 | ||||||||
\(412\) | 14.2462 | 0.701860 | ||||||||
\(413\) | 2.43845 | 0.119988 | ||||||||
\(414\) | −2.63068 | −0.129291 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.68466 | 0.327742 | ||||||||
\(417\) | 25.7538 | 1.26117 | ||||||||
\(418\) | −4.00000 | −0.195646 | ||||||||
\(419\) | −33.8617 | −1.65425 | −0.827127 | − | 0.562015i | \(-0.810026\pi\) | ||||
−0.827127 | + | 0.562015i | \(0.810026\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.93087 | 0.240316 | 0.120158 | − | 0.992755i | \(-0.461660\pi\) | ||||
0.120158 | + | 0.992755i | \(0.461660\pi\) | |||||||
\(422\) | 20.6847 | 1.00691 | ||||||||
\(423\) | −5.75379 | −0.279759 | ||||||||
\(424\) | 0.438447 | 0.0212929 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 9.75379 | 0.472573 | ||||||||
\(427\) | −4.49242 | −0.217404 | ||||||||
\(428\) | 9.56155 | 0.462175 | ||||||||
\(429\) | −41.7538 | −2.01589 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.0000 | −0.770693 | −0.385346 | − | 0.922772i | \(-0.625918\pi\) | ||||
−0.385346 | + | 0.922772i | \(0.625918\pi\) | |||||||
\(432\) | 5.56155 | 0.267580 | ||||||||
\(433\) | −39.3693 | −1.89197 | −0.945984 | − | 0.324212i | \(-0.894901\pi\) | ||||
−0.945984 | + | 0.324212i | \(0.894901\pi\) | |||||||
\(434\) | −4.87689 | −0.234098 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.56155 | 0.170567 | ||||||||
\(437\) | −4.68466 | −0.224098 | ||||||||
\(438\) | 16.6847 | 0.797224 | ||||||||
\(439\) | −4.87689 | −0.232761 | −0.116381 | − | 0.993205i | \(-0.537129\pi\) | ||||
−0.116381 | + | 0.993205i | \(0.537129\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.56155 | 0.121979 | ||||||||
\(442\) | −50.5464 | −2.40425 | ||||||||
\(443\) | 14.2462 | 0.676858 | 0.338429 | − | 0.940992i | \(-0.390105\pi\) | ||||
0.338429 | + | 0.940992i | \(0.390105\pi\) | |||||||
\(444\) | −9.36932 | −0.444648 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.36932 | −0.0648390 | ||||||||
\(447\) | 17.7538 | 0.839725 | ||||||||
\(448\) | −1.56155 | −0.0737764 | ||||||||
\(449\) | 20.7386 | 0.978717 | 0.489358 | − | 0.872083i | \(-0.337231\pi\) | ||||
0.489358 | + | 0.872083i | \(0.337231\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.9848 | −0.799785 | ||||||||
\(452\) | −17.1231 | −0.805403 | ||||||||
\(453\) | 4.87689 | 0.229136 | ||||||||
\(454\) | 2.93087 | 0.137553 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.56155 | 0.0731264 | ||||||||
\(457\) | −18.6847 | −0.874031 | −0.437016 | − | 0.899454i | \(-0.643965\pi\) | ||||
−0.437016 | + | 0.899454i | \(0.643965\pi\) | |||||||
\(458\) | 18.4924 | 0.864094 | ||||||||
\(459\) | −42.0540 | −1.96291 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.2462 | 0.942960 | 0.471480 | − | 0.881877i | \(-0.343720\pi\) | ||||
0.471480 | + | 0.881877i | \(0.343720\pi\) | |||||||
\(462\) | 9.75379 | 0.453787 | ||||||||
\(463\) | 13.7538 | 0.639193 | 0.319596 | − | 0.947554i | \(-0.396453\pi\) | ||||
0.319596 | + | 0.947554i | \(0.396453\pi\) | |||||||
\(464\) | 6.68466 | 0.310327 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.0000 | −0.463241 | ||||||||
\(467\) | −1.75379 | −0.0811557 | −0.0405778 | − | 0.999176i | \(-0.512920\pi\) | ||||
−0.0405778 | + | 0.999176i | \(0.512920\pi\) | |||||||
\(468\) | −3.75379 | −0.173519 | ||||||||
\(469\) | 2.43845 | 0.112597 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.86174 | −0.270095 | ||||||||
\(472\) | −1.56155 | −0.0718763 | ||||||||
\(473\) | 44.4924 | 2.04576 | ||||||||
\(474\) | −4.87689 | −0.224003 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.8078 | 0.541208 | ||||||||
\(477\) | −0.246211 | −0.0112732 | ||||||||
\(478\) | −5.56155 | −0.254380 | ||||||||
\(479\) | 32.0000 | 1.46212 | 0.731059 | − | 0.682315i | \(-0.239027\pi\) | ||||
0.731059 | + | 0.682315i | \(0.239027\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 40.1080 | 1.82877 | ||||||||
\(482\) | 14.8769 | 0.677624 | ||||||||
\(483\) | 11.4233 | 0.519778 | ||||||||
\(484\) | 5.00000 | 0.227273 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −5.75379 | −0.260997 | ||||||||
\(487\) | −23.6155 | −1.07012 | −0.535061 | − | 0.844814i | \(-0.679711\pi\) | ||||
−0.535061 | + | 0.844814i | \(0.679711\pi\) | |||||||
\(488\) | 2.87689 | 0.130231 | ||||||||
\(489\) | 14.6307 | 0.661622 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.12311 | 0.321461 | 0.160731 | − | 0.986998i | \(-0.448615\pi\) | ||||
0.160731 | + | 0.986998i | \(0.448615\pi\) | |||||||
\(492\) | 6.63068 | 0.298934 | ||||||||
\(493\) | −50.5464 | −2.27650 | ||||||||
\(494\) | −6.68466 | −0.300757 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.12311 | 0.140232 | ||||||||
\(497\) | 9.75379 | 0.437517 | ||||||||
\(498\) | 17.3693 | 0.778338 | ||||||||
\(499\) | −32.1080 | −1.43735 | −0.718675 | − | 0.695347i | \(-0.755251\pi\) | ||||
−0.718675 | + | 0.695347i | \(0.755251\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27.1231 | 1.21177 | ||||||||
\(502\) | −10.2462 | −0.457311 | ||||||||
\(503\) | −30.0540 | −1.34004 | −0.670020 | − | 0.742343i | \(-0.733715\pi\) | ||||
−0.670020 | + | 0.742343i | \(0.733715\pi\) | |||||||
\(504\) | 0.876894 | 0.0390600 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 18.7386 | 0.833034 | ||||||||
\(507\) | −49.4773 | −2.19736 | ||||||||
\(508\) | −4.87689 | −0.216377 | ||||||||
\(509\) | −30.4924 | −1.35155 | −0.675776 | − | 0.737107i | \(-0.736192\pi\) | ||||
−0.675776 | + | 0.737107i | \(0.736192\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.6847 | 0.738086 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.56155 | −0.245549 | ||||||||
\(514\) | −14.0000 | −0.617514 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −17.3693 | −0.764642 | ||||||||
\(517\) | 40.9848 | 1.80251 | ||||||||
\(518\) | −9.36932 | −0.411664 | ||||||||
\(519\) | 5.86174 | 0.257302 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.12311 | 0.224447 | 0.112224 | − | 0.993683i | \(-0.464203\pi\) | ||||
0.112224 | + | 0.993683i | \(0.464203\pi\) | |||||||
\(522\) | −3.75379 | −0.164299 | ||||||||
\(523\) | 19.3153 | 0.844601 | 0.422300 | − | 0.906456i | \(-0.361223\pi\) | ||||
0.422300 | + | 0.906456i | \(0.361223\pi\) | |||||||
\(524\) | 16.4924 | 0.720475 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.75379 | 0.250877 | ||||||||
\(527\) | −23.6155 | −1.02871 | ||||||||
\(528\) | −6.24621 | −0.271831 | ||||||||
\(529\) | −1.05398 | −0.0458250 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.876894 | 0.0380540 | ||||||||
\(532\) | 1.56155 | 0.0677019 | ||||||||
\(533\) | −28.3845 | −1.22947 | ||||||||
\(534\) | −3.12311 | −0.135150 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.56155 | −0.0674488 | ||||||||
\(537\) | 8.98485 | 0.387725 | ||||||||
\(538\) | −26.0000 | −1.12094 | ||||||||
\(539\) | −18.2462 | −0.785920 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.6155 | −1.78919 | −0.894596 | − | 0.446877i | \(-0.852536\pi\) | ||||
−0.894596 | + | 0.446877i | \(0.852536\pi\) | |||||||
\(542\) | 6.93087 | 0.297706 | ||||||||
\(543\) | 28.1080 | 1.20623 | ||||||||
\(544\) | −7.56155 | −0.324199 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 16.3002 | 0.697584 | ||||||||
\(547\) | 16.4924 | 0.705165 | 0.352583 | − | 0.935781i | \(-0.385304\pi\) | ||||
0.352583 | + | 0.935781i | \(0.385304\pi\) | |||||||
\(548\) | −5.80776 | −0.248095 | ||||||||
\(549\) | −1.61553 | −0.0689491 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.68466 | −0.284776 | ||||||||
\(552\) | −7.31534 | −0.311362 | ||||||||
\(553\) | −4.87689 | −0.207387 | ||||||||
\(554\) | −9.12311 | −0.387604 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.4924 | −0.699435 | ||||||||
\(557\) | 1.61553 | 0.0684521 | 0.0342261 | − | 0.999414i | \(-0.489103\pi\) | ||||
0.0342261 | + | 0.999414i | \(0.489103\pi\) | |||||||
\(558\) | −1.75379 | −0.0742438 | ||||||||
\(559\) | 74.3542 | 3.14485 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 47.2311 | 1.99410 | ||||||||
\(562\) | 2.00000 | 0.0843649 | ||||||||
\(563\) | −24.4924 | −1.03223 | −0.516116 | − | 0.856519i | \(-0.672623\pi\) | ||||
−0.516116 | + | 0.856519i | \(0.672623\pi\) | |||||||
\(564\) | −16.0000 | −0.673722 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 12.8769 | 0.541256 | ||||||||
\(567\) | 10.9309 | 0.459053 | ||||||||
\(568\) | −6.24621 | −0.262085 | ||||||||
\(569\) | 5.12311 | 0.214772 | 0.107386 | − | 0.994217i | \(-0.465752\pi\) | ||||
0.107386 | + | 0.994217i | \(0.465752\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.6155 | −0.820884 | −0.410442 | − | 0.911887i | \(-0.634626\pi\) | ||||
−0.410442 | + | 0.911887i | \(0.634626\pi\) | |||||||
\(572\) | 26.7386 | 1.11800 | ||||||||
\(573\) | −13.5616 | −0.566542 | ||||||||
\(574\) | 6.63068 | 0.276759 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.561553 | −0.0233980 | ||||||||
\(577\) | 22.6847 | 0.944375 | 0.472187 | − | 0.881498i | \(-0.343465\pi\) | ||||
0.472187 | + | 0.881498i | \(0.343465\pi\) | |||||||
\(578\) | 40.1771 | 1.67115 | ||||||||
\(579\) | 28.8769 | 1.20008 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.3693 | 0.720601 | ||||||||
\(582\) | 9.36932 | 0.388371 | ||||||||
\(583\) | 1.75379 | 0.0726345 | ||||||||
\(584\) | −10.6847 | −0.442134 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.1771 | −0.957436 | ||||||||
\(587\) | −17.3693 | −0.716908 | −0.358454 | − | 0.933547i | \(-0.616696\pi\) | ||||
−0.358454 | + | 0.933547i | \(0.616696\pi\) | |||||||
\(588\) | 7.12311 | 0.293752 | ||||||||
\(589\) | −3.12311 | −0.128685 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.86174 | −0.241120 | ||||||||
\(592\) | 6.00000 | 0.246598 | ||||||||
\(593\) | −24.2462 | −0.995673 | −0.497836 | − | 0.867271i | \(-0.665872\pi\) | ||||
−0.497836 | + | 0.867271i | \(0.665872\pi\) | |||||||
\(594\) | 22.2462 | 0.912773 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.3693 | −0.465705 | ||||||||
\(597\) | 5.94602 | 0.243355 | ||||||||
\(598\) | 31.3153 | 1.28058 | ||||||||
\(599\) | 45.8617 | 1.87386 | 0.936930 | − | 0.349517i | \(-0.113654\pi\) | ||||
0.936930 | + | 0.349517i | \(0.113654\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.0000 | 0.734235 | 0.367118 | − | 0.930175i | \(-0.380345\pi\) | ||||
0.367118 | + | 0.930175i | \(0.380345\pi\) | |||||||
\(602\) | −17.3693 | −0.707921 | ||||||||
\(603\) | 0.876894 | 0.0357099 | ||||||||
\(604\) | −3.12311 | −0.127077 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.5076 | −0.467463 | ||||||||
\(607\) | 12.8769 | 0.522657 | 0.261329 | − | 0.965250i | \(-0.415839\pi\) | ||||
0.261329 | + | 0.965250i | \(0.415839\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 16.3002 | 0.660517 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 68.4924 | 2.77091 | ||||||||
\(612\) | 4.24621 | 0.171643 | ||||||||
\(613\) | 19.3693 | 0.782319 | 0.391160 | − | 0.920323i | \(-0.372074\pi\) | ||||
0.391160 | + | 0.920323i | \(0.372074\pi\) | |||||||
\(614\) | 0.492423 | 0.0198726 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.24621 | −0.251667 | ||||||||
\(617\) | 4.24621 | 0.170946 | 0.0854730 | − | 0.996340i | \(-0.472760\pi\) | ||||
0.0854730 | + | 0.996340i | \(0.472760\pi\) | |||||||
\(618\) | −22.2462 | −0.894874 | ||||||||
\(619\) | −36.0000 | −1.44696 | −0.723481 | − | 0.690344i | \(-0.757459\pi\) | ||||
−0.723481 | + | 0.690344i | \(0.757459\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.0540 | 1.04551 | ||||||||
\(622\) | 8.68466 | 0.348223 | ||||||||
\(623\) | −3.12311 | −0.125125 | ||||||||
\(624\) | −10.4384 | −0.417872 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 32.0540 | 1.28113 | ||||||||
\(627\) | 6.24621 | 0.249450 | ||||||||
\(628\) | 3.75379 | 0.149792 | ||||||||
\(629\) | −45.3693 | −1.80899 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.4924 | 0.497315 | 0.248658 | − | 0.968591i | \(-0.420011\pi\) | ||||
0.248658 | + | 0.968591i | \(0.420011\pi\) | |||||||
\(632\) | 3.12311 | 0.124230 | ||||||||
\(633\) | −32.3002 | −1.28382 | ||||||||
\(634\) | 24.0540 | 0.955305 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.684658 | −0.0271485 | ||||||||
\(637\) | −30.4924 | −1.20815 | ||||||||
\(638\) | 26.7386 | 1.05859 | ||||||||
\(639\) | 3.50758 | 0.138758 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.8617 | −1.41645 | −0.708227 | − | 0.705985i | \(-0.750505\pi\) | ||||
−0.708227 | + | 0.705985i | \(0.750505\pi\) | |||||||
\(642\) | −14.9309 | −0.589274 | ||||||||
\(643\) | −7.61553 | −0.300327 | −0.150164 | − | 0.988661i | \(-0.547980\pi\) | ||||
−0.150164 | + | 0.988661i | \(0.547980\pi\) | |||||||
\(644\) | −7.31534 | −0.288265 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.56155 | 0.297505 | ||||||||
\(647\) | −9.56155 | −0.375903 | −0.187952 | − | 0.982178i | \(-0.560185\pi\) | ||||
−0.187952 | + | 0.982178i | \(0.560185\pi\) | |||||||
\(648\) | −7.00000 | −0.274986 | ||||||||
\(649\) | −6.24621 | −0.245185 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.61553 | 0.298476 | ||||||||
\(652\) | −9.36932 | −0.366931 | ||||||||
\(653\) | −1.12311 | −0.0439505 | −0.0219753 | − | 0.999759i | \(-0.506996\pi\) | ||||
−0.0219753 | + | 0.999759i | \(0.506996\pi\) | |||||||
\(654\) | −5.56155 | −0.217474 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.24621 | −0.165787 | ||||||||
\(657\) | 6.00000 | 0.234082 | ||||||||
\(658\) | −16.0000 | −0.623745 | ||||||||
\(659\) | −42.9309 | −1.67235 | −0.836175 | − | 0.548463i | \(-0.815213\pi\) | ||||
−0.836175 | + | 0.548463i | \(0.815213\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.80776 | 0.381478 | 0.190739 | − | 0.981641i | \(-0.438912\pi\) | ||||
0.190739 | + | 0.981641i | \(0.438912\pi\) | |||||||
\(662\) | 1.56155 | 0.0606915 | ||||||||
\(663\) | 78.9309 | 3.06542 | ||||||||
\(664\) | −11.1231 | −0.431660 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.36932 | −0.130558 | ||||||||
\(667\) | 31.3153 | 1.21253 | ||||||||
\(668\) | −17.3693 | −0.672039 | ||||||||
\(669\) | 2.13826 | 0.0826699 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.5076 | 0.444245 | ||||||||
\(672\) | 2.43845 | 0.0940651 | ||||||||
\(673\) | 3.36932 | 0.129878 | 0.0649388 | − | 0.997889i | \(-0.479315\pi\) | ||||
0.0649388 | + | 0.997889i | \(0.479315\pi\) | |||||||
\(674\) | 26.0000 | 1.00148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 31.6847 | 1.21864 | ||||||||
\(677\) | −36.4384 | −1.40044 | −0.700222 | − | 0.713926i | \(-0.746915\pi\) | ||||
−0.700222 | + | 0.713926i | \(0.746915\pi\) | |||||||
\(678\) | 26.7386 | 1.02689 | ||||||||
\(679\) | 9.36932 | 0.359561 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.57671 | −0.175380 | ||||||||
\(682\) | 12.4924 | 0.478360 | ||||||||
\(683\) | −4.00000 | −0.153056 | −0.0765279 | − | 0.997067i | \(-0.524383\pi\) | ||||
−0.0765279 | + | 0.997067i | \(0.524383\pi\) | |||||||
\(684\) | 0.561553 | 0.0214715 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.0540 | 0.689304 | ||||||||
\(687\) | −28.8769 | −1.10172 | ||||||||
\(688\) | 11.1231 | 0.424064 | ||||||||
\(689\) | 2.93087 | 0.111657 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.87689 | −0.337693 | −0.168846 | − | 0.985642i | \(-0.554004\pi\) | ||||
−0.168846 | + | 0.985642i | \(0.554004\pi\) | |||||||
\(692\) | −3.75379 | −0.142698 | ||||||||
\(693\) | 3.50758 | 0.133242 | ||||||||
\(694\) | 33.3693 | 1.26668 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10.4384 | −0.395668 | ||||||||
\(697\) | 32.1080 | 1.21618 | ||||||||
\(698\) | 20.2462 | 0.766330 | ||||||||
\(699\) | 15.6155 | 0.590634 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.1231 | −1.09996 | −0.549982 | − | 0.835176i | \(-0.685366\pi\) | ||||
−0.549982 | + | 0.835176i | \(0.685366\pi\) | |||||||
\(702\) | 37.1771 | 1.40316 | ||||||||
\(703\) | −6.00000 | −0.226294 | ||||||||
\(704\) | 4.00000 | 0.150756 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.9309 | −0.938286 | ||||||||
\(707\) | −11.5076 | −0.432787 | ||||||||
\(708\) | 2.43845 | 0.0916425 | ||||||||
\(709\) | 38.0000 | 1.42712 | 0.713560 | − | 0.700594i | \(-0.247082\pi\) | ||||
0.713560 | + | 0.700594i | \(0.247082\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.75379 | −0.0657722 | ||||||||
\(712\) | 2.00000 | 0.0749532 | ||||||||
\(713\) | 14.6307 | 0.547923 | ||||||||
\(714\) | −18.4384 | −0.690042 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.75379 | −0.215029 | ||||||||
\(717\) | 8.68466 | 0.324335 | ||||||||
\(718\) | 5.56155 | 0.207555 | ||||||||
\(719\) | −29.5616 | −1.10246 | −0.551230 | − | 0.834353i | \(-0.685841\pi\) | ||||
−0.551230 | + | 0.834353i | \(0.685841\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.2462 | −0.828492 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −23.2311 | −0.863972 | ||||||||
\(724\) | −18.0000 | −0.668965 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.80776 | −0.289773 | ||||||||
\(727\) | 36.6847 | 1.36056 | 0.680279 | − | 0.732953i | \(-0.261858\pi\) | ||||
0.680279 | + | 0.732953i | \(0.261858\pi\) | |||||||
\(728\) | −10.4384 | −0.386875 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −84.1080 | −3.11084 | ||||||||
\(732\) | −4.49242 | −0.166045 | ||||||||
\(733\) | 45.1231 | 1.66666 | 0.833330 | − | 0.552776i | \(-0.186431\pi\) | ||||
0.833330 | + | 0.552776i | \(0.186431\pi\) | |||||||
\(734\) | 10.2462 | 0.378195 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.68466 | 0.172679 | ||||||||
\(737\) | −6.24621 | −0.230082 | ||||||||
\(738\) | 2.38447 | 0.0877736 | ||||||||
\(739\) | 16.8769 | 0.620827 | 0.310413 | − | 0.950602i | \(-0.399533\pi\) | ||||
0.310413 | + | 0.950602i | \(0.399533\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.4384 | 0.383466 | ||||||||
\(742\) | −0.684658 | −0.0251346 | ||||||||
\(743\) | −27.1231 | −0.995050 | −0.497525 | − | 0.867450i | \(-0.665758\pi\) | ||||
−0.497525 | + | 0.867450i | \(0.665758\pi\) | |||||||
\(744\) | −4.87689 | −0.178796 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 27.5616 | 1.00910 | ||||||||
\(747\) | 6.24621 | 0.228537 | ||||||||
\(748\) | −30.2462 | −1.10591 | ||||||||
\(749\) | −14.9309 | −0.545562 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.1231 | −1.57358 | −0.786792 | − | 0.617218i | \(-0.788260\pi\) | ||||
−0.786792 | + | 0.617218i | \(0.788260\pi\) | |||||||
\(752\) | 10.2462 | 0.373641 | ||||||||
\(753\) | 16.0000 | 0.583072 | ||||||||
\(754\) | 44.6847 | 1.62732 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.68466 | −0.315858 | ||||||||
\(757\) | −9.50758 | −0.345559 | −0.172779 | − | 0.984961i | \(-0.555275\pi\) | ||||
−0.172779 | + | 0.984961i | \(0.555275\pi\) | |||||||
\(758\) | 6.43845 | 0.233855 | ||||||||
\(759\) | −29.2614 | −1.06212 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.5464 | −1.03481 | −0.517403 | − | 0.855742i | \(-0.673101\pi\) | ||||
−0.517403 | + | 0.855742i | \(0.673101\pi\) | |||||||
\(762\) | 7.61553 | 0.275881 | ||||||||
\(763\) | −5.56155 | −0.201342 | ||||||||
\(764\) | 8.68466 | 0.314200 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.2462 | −1.09284 | ||||||||
\(767\) | −10.4384 | −0.376910 | ||||||||
\(768\) | −1.56155 | −0.0563477 | ||||||||
\(769\) | 31.5616 | 1.13814 | 0.569069 | − | 0.822290i | \(-0.307304\pi\) | ||||
0.569069 | + | 0.822290i | \(0.307304\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.8617 | 0.787331 | ||||||||
\(772\) | −18.4924 | −0.665557 | ||||||||
\(773\) | 9.80776 | 0.352761 | 0.176380 | − | 0.984322i | \(-0.443561\pi\) | ||||
0.176380 | + | 0.984322i | \(0.443561\pi\) | |||||||
\(774\) | −6.24621 | −0.224515 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | 14.6307 | 0.524873 | ||||||||
\(778\) | 1.12311 | 0.0402653 | ||||||||
\(779\) | 4.24621 | 0.152136 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.9848 | −0.894028 | ||||||||
\(782\) | −35.4233 | −1.26673 | ||||||||
\(783\) | 37.1771 | 1.32860 | ||||||||
\(784\) | −4.56155 | −0.162913 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −25.7538 | −0.918607 | ||||||||
\(787\) | −31.8078 | −1.13382 | −0.566912 | − | 0.823778i | \(-0.691862\pi\) | ||||
−0.566912 | + | 0.823778i | \(0.691862\pi\) | |||||||
\(788\) | 3.75379 | 0.133723 | ||||||||
\(789\) | −8.98485 | −0.319869 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.7386 | 0.950716 | ||||||||
\(792\) | −2.24621 | −0.0798156 | ||||||||
\(793\) | 19.2311 | 0.682915 | ||||||||
\(794\) | −1.12311 | −0.0398575 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.80776 | −0.134963 | ||||||||
\(797\) | −42.3002 | −1.49835 | −0.749175 | − | 0.662372i | \(-0.769550\pi\) | ||||
−0.749175 | + | 0.662372i | \(0.769550\pi\) | |||||||
\(798\) | −2.43845 | −0.0863201 | ||||||||
\(799\) | −77.4773 | −2.74095 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.12311 | −0.0396830 | ||||||||
\(802\) | −20.2462 | −0.714919 | ||||||||
\(803\) | −42.7386 | −1.50821 | ||||||||
\(804\) | 2.43845 | 0.0859974 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.8769 | 0.735357 | ||||||||
\(807\) | 40.6004 | 1.42920 | ||||||||
\(808\) | 7.36932 | 0.259252 | ||||||||
\(809\) | −8.43845 | −0.296680 | −0.148340 | − | 0.988936i | \(-0.547393\pi\) | ||||
−0.148340 | + | 0.988936i | \(0.547393\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.192236 | −0.00675032 | −0.00337516 | − | 0.999994i | \(-0.501074\pi\) | ||||
−0.00337516 | + | 0.999994i | \(0.501074\pi\) | |||||||
\(812\) | −10.4384 | −0.366318 | ||||||||
\(813\) | −10.8229 | −0.379576 | ||||||||
\(814\) | 24.0000 | 0.841200 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 11.8078 | 0.413354 | ||||||||
\(817\) | −11.1231 | −0.389148 | ||||||||
\(818\) | −24.7386 | −0.864966 | ||||||||
\(819\) | 5.86174 | 0.204826 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.36932 | 0.257191 | 0.128595 | − | 0.991697i | \(-0.458953\pi\) | ||||
0.128595 | + | 0.991697i | \(0.458953\pi\) | |||||||
\(822\) | 9.06913 | 0.316322 | ||||||||
\(823\) | 33.5616 | 1.16988 | 0.584941 | − | 0.811076i | \(-0.301118\pi\) | ||||
0.584941 | + | 0.811076i | \(0.301118\pi\) | |||||||
\(824\) | 14.2462 | 0.496290 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.43845 | 0.0848444 | ||||||||
\(827\) | 6.43845 | 0.223887 | 0.111943 | − | 0.993715i | \(-0.464292\pi\) | ||||
0.111943 | + | 0.993715i | \(0.464292\pi\) | |||||||
\(828\) | −2.63068 | −0.0914226 | ||||||||
\(829\) | 16.0540 | 0.557578 | 0.278789 | − | 0.960352i | \(-0.410067\pi\) | ||||
0.278789 | + | 0.960352i | \(0.410067\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.2462 | 0.494196 | ||||||||
\(832\) | 6.68466 | 0.231749 | ||||||||
\(833\) | 34.4924 | 1.19509 | ||||||||
\(834\) | 25.7538 | 0.891781 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.00000 | −0.138343 | ||||||||
\(837\) | 17.3693 | 0.600371 | ||||||||
\(838\) | −33.8617 | −1.16973 | ||||||||
\(839\) | −12.4924 | −0.431286 | −0.215643 | − | 0.976472i | \(-0.569185\pi\) | ||||
−0.215643 | + | 0.976472i | \(0.569185\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6847 | 0.540850 | ||||||||
\(842\) | 4.93087 | 0.169929 | ||||||||
\(843\) | −3.12311 | −0.107565 | ||||||||
\(844\) | 20.6847 | 0.711995 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.75379 | −0.197819 | ||||||||
\(847\) | −7.80776 | −0.268278 | ||||||||
\(848\) | 0.438447 | 0.0150563 | ||||||||
\(849\) | −20.1080 | −0.690103 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.1080 | 0.963528 | ||||||||
\(852\) | 9.75379 | 0.334159 | ||||||||
\(853\) | −24.7386 | −0.847035 | −0.423517 | − | 0.905888i | \(-0.639205\pi\) | ||||
−0.423517 | + | 0.905888i | \(0.639205\pi\) | |||||||
\(854\) | −4.49242 | −0.153728 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.56155 | 0.326807 | ||||||||
\(857\) | −39.3693 | −1.34483 | −0.672415 | − | 0.740174i | \(-0.734743\pi\) | ||||
−0.672415 | + | 0.740174i | \(0.734743\pi\) | |||||||
\(858\) | −41.7538 | −1.42545 | ||||||||
\(859\) | 12.9848 | 0.443037 | 0.221519 | − | 0.975156i | \(-0.428899\pi\) | ||||
0.221519 | + | 0.975156i | \(0.428899\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.3542 | −0.352869 | ||||||||
\(862\) | −16.0000 | −0.544962 | ||||||||
\(863\) | 14.2462 | 0.484947 | 0.242473 | − | 0.970158i | \(-0.422041\pi\) | ||||
0.242473 | + | 0.970158i | \(0.422041\pi\) | |||||||
\(864\) | 5.56155 | 0.189208 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −39.3693 | −1.33782 | ||||||||
\(867\) | −62.7386 | −2.13072 | ||||||||
\(868\) | −4.87689 | −0.165533 | ||||||||
\(869\) | 12.4924 | 0.423776 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.4384 | −0.353693 | ||||||||
\(872\) | 3.56155 | 0.120609 | ||||||||
\(873\) | 3.36932 | 0.114034 | ||||||||
\(874\) | −4.68466 | −0.158461 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16.6847 | 0.563722 | ||||||||
\(877\) | −24.9309 | −0.841856 | −0.420928 | − | 0.907094i | \(-0.638295\pi\) | ||||
−0.420928 | + | 0.907094i | \(0.638295\pi\) | |||||||
\(878\) | −4.87689 | −0.164587 | ||||||||
\(879\) | 36.1922 | 1.22073 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.9848 | −0.774379 | −0.387190 | − | 0.922000i | \(-0.626554\pi\) | ||||
−0.387190 | + | 0.922000i | \(0.626554\pi\) | |||||||
\(882\) | 2.56155 | 0.0862520 | ||||||||
\(883\) | 47.6155 | 1.60239 | 0.801195 | − | 0.598403i | \(-0.204198\pi\) | ||||
0.801195 | + | 0.598403i | \(0.204198\pi\) | |||||||
\(884\) | −50.5464 | −1.70006 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.2462 | 0.478611 | ||||||||
\(887\) | 4.49242 | 0.150841 | 0.0754204 | − | 0.997152i | \(-0.475970\pi\) | ||||
0.0754204 | + | 0.997152i | \(0.475970\pi\) | |||||||
\(888\) | −9.36932 | −0.314414 | ||||||||
\(889\) | 7.61553 | 0.255417 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.0000 | −0.938035 | ||||||||
\(892\) | −1.36932 | −0.0458481 | ||||||||
\(893\) | −10.2462 | −0.342876 | ||||||||
\(894\) | 17.7538 | 0.593776 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.56155 | −0.0521678 | ||||||||
\(897\) | −48.9006 | −1.63274 | ||||||||
\(898\) | 20.7386 | 0.692057 | ||||||||
\(899\) | 20.8769 | 0.696283 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.31534 | −0.110450 | ||||||||
\(902\) | −16.9848 | −0.565533 | ||||||||
\(903\) | 27.1231 | 0.902600 | ||||||||
\(904\) | −17.1231 | −0.569506 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.87689 | 0.162024 | ||||||||
\(907\) | −25.1771 | −0.835991 | −0.417996 | − | 0.908449i | \(-0.637267\pi\) | ||||
−0.417996 | + | 0.908449i | \(0.637267\pi\) | |||||||
\(908\) | 2.93087 | 0.0972643 | ||||||||
\(909\) | −4.13826 | −0.137257 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.4924 | −0.943996 | −0.471998 | − | 0.881600i | \(-0.656467\pi\) | ||||
−0.471998 | + | 0.881600i | \(0.656467\pi\) | |||||||
\(912\) | 1.56155 | 0.0517082 | ||||||||
\(913\) | −44.4924 | −1.47248 | ||||||||
\(914\) | −18.6847 | −0.618034 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.4924 | 0.611007 | ||||||||
\(917\) | −25.7538 | −0.850465 | ||||||||
\(918\) | −42.0540 | −1.38799 | ||||||||
\(919\) | −30.9309 | −1.02032 | −0.510158 | − | 0.860081i | \(-0.670413\pi\) | ||||
−0.510158 | + | 0.860081i | \(0.670413\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.768944 | −0.0253376 | ||||||||
\(922\) | 20.2462 | 0.666773 | ||||||||
\(923\) | −41.7538 | −1.37434 | ||||||||
\(924\) | 9.75379 | 0.320876 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 13.7538 | 0.451978 | ||||||||
\(927\) | −8.00000 | −0.262754 | ||||||||
\(928\) | 6.68466 | 0.219435 | ||||||||
\(929\) | 34.3002 | 1.12535 | 0.562676 | − | 0.826677i | \(-0.309772\pi\) | ||||
0.562676 | + | 0.826677i | \(0.309772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.56155 | 0.149499 | ||||||||
\(932\) | −10.0000 | −0.327561 | ||||||||
\(933\) | −13.5616 | −0.443985 | ||||||||
\(934\) | −1.75379 | −0.0573857 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.75379 | −0.122696 | ||||||||
\(937\) | −36.4384 | −1.19039 | −0.595196 | − | 0.803580i | \(-0.702926\pi\) | ||||
−0.595196 | + | 0.803580i | \(0.702926\pi\) | |||||||
\(938\) | 2.43845 | 0.0796181 | ||||||||
\(939\) | −50.0540 | −1.63345 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.1922 | 1.11464 | 0.557318 | − | 0.830299i | \(-0.311831\pi\) | ||||
0.557318 | + | 0.830299i | \(0.311831\pi\) | |||||||
\(942\) | −5.86174 | −0.190986 | ||||||||
\(943\) | −19.8920 | −0.647774 | ||||||||
\(944\) | −1.56155 | −0.0508242 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 44.4924 | 1.44657 | ||||||||
\(947\) | 17.7538 | 0.576921 | 0.288460 | − | 0.957492i | \(-0.406857\pi\) | ||||
0.288460 | + | 0.957492i | \(0.406857\pi\) | |||||||
\(948\) | −4.87689 | −0.158394 | ||||||||
\(949\) | −71.4233 | −2.31850 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −37.5616 | −1.21802 | ||||||||
\(952\) | 11.8078 | 0.382692 | ||||||||
\(953\) | 30.1080 | 0.975292 | 0.487646 | − | 0.873041i | \(-0.337856\pi\) | ||||
0.487646 | + | 0.873041i | \(0.337856\pi\) | |||||||
\(954\) | −0.246211 | −0.00797138 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.56155 | −0.179873 | ||||||||
\(957\) | −41.7538 | −1.34971 | ||||||||
\(958\) | 32.0000 | 1.03387 | ||||||||
\(959\) | 9.06913 | 0.292857 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.2462 | −0.685362 | ||||||||
\(962\) | 40.1080 | 1.29313 | ||||||||
\(963\) | −5.36932 | −0.173024 | ||||||||
\(964\) | 14.8769 | 0.479153 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 11.4233 | 0.367538 | ||||||||
\(967\) | 48.4924 | 1.55941 | 0.779706 | − | 0.626146i | \(-0.215369\pi\) | ||||
0.779706 | + | 0.626146i | \(0.215369\pi\) | |||||||
\(968\) | 5.00000 | 0.160706 | ||||||||
\(969\) | −11.8078 | −0.379320 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.5076 | −0.754394 | −0.377197 | − | 0.926133i | \(-0.623112\pi\) | ||||
−0.377197 | + | 0.926133i | \(0.623112\pi\) | |||||||
\(972\) | −5.75379 | −0.184553 | ||||||||
\(973\) | 25.7538 | 0.825629 | ||||||||
\(974\) | −23.6155 | −0.756690 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.87689 | 0.0920871 | ||||||||
\(977\) | 20.7386 | 0.663488 | 0.331744 | − | 0.943370i | \(-0.392363\pi\) | ||||
0.331744 | + | 0.943370i | \(0.392363\pi\) | |||||||
\(978\) | 14.6307 | 0.467838 | ||||||||
\(979\) | 8.00000 | 0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | 7.12311 | 0.227307 | ||||||||
\(983\) | −27.1231 | −0.865093 | −0.432546 | − | 0.901612i | \(-0.642385\pi\) | ||||
−0.432546 | + | 0.901612i | \(0.642385\pi\) | |||||||
\(984\) | 6.63068 | 0.211378 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −50.5464 | −1.60973 | ||||||||
\(987\) | 24.9848 | 0.795276 | ||||||||
\(988\) | −6.68466 | −0.212667 | ||||||||
\(989\) | 52.1080 | 1.65694 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.1231 | 0.353337 | 0.176669 | − | 0.984270i | \(-0.443468\pi\) | ||||
0.176669 | + | 0.984270i | \(0.443468\pi\) | |||||||
\(992\) | 3.12311 | 0.0991587 | ||||||||
\(993\) | −2.43845 | −0.0773818 | ||||||||
\(994\) | 9.75379 | 0.309371 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 17.3693 | 0.550368 | ||||||||
\(997\) | −32.7386 | −1.03684 | −0.518421 | − | 0.855125i | \(-0.673480\pi\) | ||||
−0.518421 | + | 0.855125i | \(0.673480\pi\) | |||||||
\(998\) | −32.1080 | −1.01636 | ||||||||
\(999\) | 33.3693 | 1.05576 |
(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 | 950.2.a.h.1.1 | 2 | ||
3.2 | odd | 2 | 8550.2.a.br.1.1 | 2 | |||
4.3 | odd | 2 | 7600.2.a.y.1.2 | 2 | |||
5.2 | odd | 4 | 950.2.b.f.799.4 | 4 | |||
5.3 | odd | 4 | 950.2.b.f.799.1 | 4 | |||
5.4 | even | 2 | 190.2.a.d.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 1710.2.a.w.1.2 | 2 | |||
20.19 | odd | 2 | 1520.2.a.n.1.1 | 2 | |||
35.34 | odd | 2 | 9310.2.a.bc.1.1 | 2 | |||
40.19 | odd | 2 | 6080.2.a.bb.1.2 | 2 | |||
40.29 | even | 2 | 6080.2.a.bh.1.1 | 2 | |||
95.94 | odd | 2 | 3610.2.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.a.d.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
950.2.a.h.1.1 | 2 | 1.1 | even | 1 | trivial | ||
950.2.b.f.799.1 | 4 | 5.3 | odd | 4 | |||
950.2.b.f.799.4 | 4 | 5.2 | odd | 4 | |||
1520.2.a.n.1.1 | 2 | 20.19 | odd | 2 | |||
1710.2.a.w.1.2 | 2 | 15.14 | odd | 2 | |||
3610.2.a.t.1.1 | 2 | 95.94 | odd | 2 | |||
6080.2.a.bb.1.2 | 2 | 40.19 | odd | 2 | |||
6080.2.a.bh.1.1 | 2 | 40.29 | even | 2 | |||
7600.2.a.y.1.2 | 2 | 4.3 | odd | 2 | |||
8550.2.a.br.1.1 | 2 | 3.2 | odd | 2 | |||
9310.2.a.bc.1.1 | 2 | 35.34 | odd | 2 |