Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3750,2,Mod(1,3750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3750, 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("3750.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3750 = 2 \cdot 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3750.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: | \(29.9439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.71684000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 18x^{6} + 10x^{5} + 101x^{4} + 40x^{3} - 132x^{2} - 96x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | no (minimal twist has level 150) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.37243\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3750.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.329315 | 0.124469 | 0.0622347 | − | 0.998062i | \(-0.480177\pi\) | ||||
0.0622347 | + | 0.998062i | \(0.480177\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.03339 | −1.51762 | −0.758812 | − | 0.651309i | \(-0.774220\pi\) | ||||
−0.758812 | + | 0.651309i | \(0.774220\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0.482152 | 0.133725 | 0.0668625 | − | 0.997762i | \(-0.478701\pi\) | ||||
0.0668625 | + | 0.997762i | \(0.478701\pi\) | |||||||
\(14\) | −0.329315 | −0.0880131 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.78610 | −1.64587 | −0.822935 | − | 0.568135i | \(-0.807665\pi\) | ||||
−0.822935 | + | 0.568135i | \(0.807665\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.44012 | 1.24805 | 0.624025 | − | 0.781404i | \(-0.285496\pi\) | ||||
0.624025 | + | 0.781404i | \(0.285496\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.329315 | −0.0718624 | ||||||||
\(22\) | 5.03339 | 1.07312 | ||||||||
\(23\) | −6.50055 | −1.35546 | −0.677729 | − | 0.735312i | \(-0.737036\pi\) | ||||
−0.677729 | + | 0.735312i | \(0.737036\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.482152 | −0.0945578 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.329315 | 0.0622347 | ||||||||
\(29\) | −6.02216 | −1.11829 | −0.559144 | − | 0.829071i | \(-0.688870\pi\) | ||||
−0.559144 | + | 0.829071i | \(0.688870\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.31869 | 0.236844 | 0.118422 | − | 0.992963i | \(-0.462216\pi\) | ||||
0.118422 | + | 0.992963i | \(0.462216\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.03339 | 0.876201 | ||||||||
\(34\) | 6.78610 | 1.16381 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.780139 | −0.128254 | −0.0641270 | − | 0.997942i | \(-0.520426\pi\) | ||||
−0.0641270 | + | 0.997942i | \(0.520426\pi\) | |||||||
\(38\) | −5.44012 | −0.882504 | ||||||||
\(39\) | −0.482152 | −0.0772061 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.5205 | 1.95538 | 0.977689 | − | 0.210059i | \(-0.0673657\pi\) | ||||
0.977689 | + | 0.210059i | \(0.0673657\pi\) | |||||||
\(42\) | 0.329315 | 0.0508144 | ||||||||
\(43\) | 2.47582 | 0.377559 | 0.188779 | − | 0.982020i | \(-0.439547\pi\) | ||||
0.188779 | + | 0.982020i | \(0.439547\pi\) | |||||||
\(44\) | −5.03339 | −0.758812 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.50055 | 0.958454 | ||||||||
\(47\) | 4.38040 | 0.638946 | 0.319473 | − | 0.947595i | \(-0.396494\pi\) | ||||
0.319473 | + | 0.947595i | \(0.396494\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.89155 | −0.984507 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.78610 | 0.950244 | ||||||||
\(52\) | 0.482152 | 0.0668625 | ||||||||
\(53\) | 1.68591 | 0.231578 | 0.115789 | − | 0.993274i | \(-0.463060\pi\) | ||||
0.115789 | + | 0.993274i | \(0.463060\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.329315 | −0.0440066 | ||||||||
\(57\) | −5.44012 | −0.720562 | ||||||||
\(58\) | 6.02216 | 0.790749 | ||||||||
\(59\) | 1.01583 | 0.132250 | 0.0661250 | − | 0.997811i | \(-0.478936\pi\) | ||||
0.0661250 | + | 0.997811i | \(0.478936\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.18808 | 0.536229 | 0.268114 | − | 0.963387i | \(-0.413599\pi\) | ||||
0.268114 | + | 0.963387i | \(0.413599\pi\) | |||||||
\(62\) | −1.31869 | −0.167474 | ||||||||
\(63\) | 0.329315 | 0.0414898 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.03339 | −0.619568 | ||||||||
\(67\) | −3.14433 | −0.384141 | −0.192070 | − | 0.981381i | \(-0.561520\pi\) | ||||
−0.192070 | + | 0.981381i | \(0.561520\pi\) | |||||||
\(68\) | −6.78610 | −0.822935 | ||||||||
\(69\) | 6.50055 | 0.782574 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.71189 | 0.677876 | 0.338938 | − | 0.940809i | \(-0.389932\pi\) | ||||
0.338938 | + | 0.940809i | \(0.389932\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −2.94269 | −0.344415 | −0.172208 | − | 0.985061i | \(-0.555090\pi\) | ||||
−0.172208 | + | 0.985061i | \(0.555090\pi\) | |||||||
\(74\) | 0.780139 | 0.0906893 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.44012 | 0.624025 | ||||||||
\(77\) | −1.65757 | −0.188898 | ||||||||
\(78\) | 0.482152 | 0.0545930 | ||||||||
\(79\) | 8.48510 | 0.954648 | 0.477324 | − | 0.878727i | \(-0.341607\pi\) | ||||
0.477324 | + | 0.878727i | \(0.341607\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −12.5205 | −1.38266 | ||||||||
\(83\) | −17.1955 | −1.88745 | −0.943725 | − | 0.330730i | \(-0.892705\pi\) | ||||
−0.943725 | + | 0.330730i | \(0.892705\pi\) | |||||||
\(84\) | −0.329315 | −0.0359312 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.47582 | −0.266974 | ||||||||
\(87\) | 6.02216 | 0.645644 | ||||||||
\(88\) | 5.03339 | 0.536561 | ||||||||
\(89\) | 3.45233 | 0.365946 | 0.182973 | − | 0.983118i | \(-0.441428\pi\) | ||||
0.182973 | + | 0.983118i | \(0.441428\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.158780 | 0.0166447 | ||||||||
\(92\) | −6.50055 | −0.677729 | ||||||||
\(93\) | −1.31869 | −0.136742 | ||||||||
\(94\) | −4.38040 | −0.451803 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 9.51004 | 0.965598 | 0.482799 | − | 0.875731i | \(-0.339620\pi\) | ||||
0.482799 | + | 0.875731i | \(0.339620\pi\) | |||||||
\(98\) | 6.89155 | 0.696152 | ||||||||
\(99\) | −5.03339 | −0.505875 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.2435 | 1.91480 | 0.957400 | − | 0.288765i | \(-0.0932447\pi\) | ||||
0.957400 | + | 0.288765i | \(0.0932447\pi\) | |||||||
\(102\) | −6.78610 | −0.671924 | ||||||||
\(103\) | −5.10689 | −0.503196 | −0.251598 | − | 0.967832i | \(-0.580956\pi\) | ||||
−0.251598 | + | 0.967832i | \(0.580956\pi\) | |||||||
\(104\) | −0.482152 | −0.0472789 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.68591 | −0.163750 | ||||||||
\(107\) | 15.3340 | 1.48239 | 0.741194 | − | 0.671290i | \(-0.234260\pi\) | ||||
0.741194 | + | 0.671290i | \(0.234260\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −9.76027 | −0.934865 | −0.467432 | − | 0.884029i | \(-0.654821\pi\) | ||||
−0.467432 | + | 0.884029i | \(0.654821\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.780139 | 0.0740475 | ||||||||
\(112\) | 0.329315 | 0.0311173 | ||||||||
\(113\) | −1.51566 | −0.142581 | −0.0712905 | − | 0.997456i | \(-0.522712\pi\) | ||||
−0.0712905 | + | 0.997456i | \(0.522712\pi\) | |||||||
\(114\) | 5.44012 | 0.509514 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.02216 | −0.559144 | ||||||||
\(117\) | 0.482152 | 0.0445750 | ||||||||
\(118\) | −1.01583 | −0.0935149 | ||||||||
\(119\) | −2.23476 | −0.204860 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.3350 | 1.30319 | ||||||||
\(122\) | −4.18808 | −0.379171 | ||||||||
\(123\) | −12.5205 | −1.12894 | ||||||||
\(124\) | 1.31869 | 0.118422 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.329315 | −0.0293377 | ||||||||
\(127\) | −12.6056 | −1.11856 | −0.559282 | − | 0.828977i | \(-0.688923\pi\) | ||||
−0.559282 | + | 0.828977i | \(0.688923\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.47582 | −0.217984 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.0559 | 1.22807 | 0.614036 | − | 0.789278i | \(-0.289545\pi\) | ||||
0.614036 | + | 0.789278i | \(0.289545\pi\) | |||||||
\(132\) | 5.03339 | 0.438101 | ||||||||
\(133\) | 1.79151 | 0.155344 | ||||||||
\(134\) | 3.14433 | 0.271629 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.78610 | 0.581903 | ||||||||
\(137\) | 6.68863 | 0.571448 | 0.285724 | − | 0.958312i | \(-0.407766\pi\) | ||||
0.285724 | + | 0.958312i | \(0.407766\pi\) | |||||||
\(138\) | −6.50055 | −0.553364 | ||||||||
\(139\) | −3.07799 | −0.261072 | −0.130536 | − | 0.991444i | \(-0.541670\pi\) | ||||
−0.130536 | + | 0.991444i | \(0.541670\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.38040 | −0.368896 | ||||||||
\(142\) | −5.71189 | −0.479331 | ||||||||
\(143\) | −2.42686 | −0.202944 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.94269 | 0.243538 | ||||||||
\(147\) | 6.89155 | 0.568406 | ||||||||
\(148\) | −0.780139 | −0.0641270 | ||||||||
\(149\) | 5.06465 | 0.414912 | 0.207456 | − | 0.978244i | \(-0.433482\pi\) | ||||
0.207456 | + | 0.978244i | \(0.433482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.9581 | −1.38003 | −0.690015 | − | 0.723795i | \(-0.742396\pi\) | ||||
−0.690015 | + | 0.723795i | \(0.742396\pi\) | |||||||
\(152\) | −5.44012 | −0.441252 | ||||||||
\(153\) | −6.78610 | −0.548623 | ||||||||
\(154\) | 1.65757 | 0.133571 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.482152 | −0.0386031 | ||||||||
\(157\) | 22.8284 | 1.82190 | 0.910952 | − | 0.412513i | \(-0.135349\pi\) | ||||
0.910952 | + | 0.412513i | \(0.135349\pi\) | |||||||
\(158\) | −8.48510 | −0.675038 | ||||||||
\(159\) | −1.68591 | −0.133701 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.14073 | −0.168713 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −7.95823 | −0.623337 | −0.311668 | − | 0.950191i | \(-0.600888\pi\) | ||||
−0.311668 | + | 0.950191i | \(0.600888\pi\) | |||||||
\(164\) | 12.5205 | 0.977689 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.1955 | 1.33463 | ||||||||
\(167\) | −13.9503 | −1.07951 | −0.539754 | − | 0.841823i | \(-0.681483\pi\) | ||||
−0.539754 | + | 0.841823i | \(0.681483\pi\) | |||||||
\(168\) | 0.329315 | 0.0254072 | ||||||||
\(169\) | −12.7675 | −0.982118 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.44012 | 0.416017 | ||||||||
\(172\) | 2.47582 | 0.188779 | ||||||||
\(173\) | 19.5009 | 1.48262 | 0.741312 | − | 0.671161i | \(-0.234204\pi\) | ||||
0.741312 | + | 0.671161i | \(0.234204\pi\) | |||||||
\(174\) | −6.02216 | −0.456539 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.03339 | −0.379406 | ||||||||
\(177\) | −1.01583 | −0.0763546 | ||||||||
\(178\) | −3.45233 | −0.258763 | ||||||||
\(179\) | −18.9911 | −1.41946 | −0.709731 | − | 0.704473i | \(-0.751183\pi\) | ||||
−0.709731 | + | 0.704473i | \(0.751183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.9484 | −1.40842 | −0.704211 | − | 0.709991i | \(-0.748699\pi\) | ||||
−0.704211 | + | 0.709991i | \(0.748699\pi\) | |||||||
\(182\) | −0.158780 | −0.0117695 | ||||||||
\(183\) | −4.18808 | −0.309592 | ||||||||
\(184\) | 6.50055 | 0.479227 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.31869 | 0.0966913 | ||||||||
\(187\) | 34.1571 | 2.49781 | ||||||||
\(188\) | 4.38040 | 0.319473 | ||||||||
\(189\) | −0.329315 | −0.0239541 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0933 | −0.875040 | −0.437520 | − | 0.899209i | \(-0.644143\pi\) | ||||
−0.437520 | + | 0.899209i | \(0.644143\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 11.0357 | 0.794368 | 0.397184 | − | 0.917739i | \(-0.369987\pi\) | ||||
0.397184 | + | 0.917739i | \(0.369987\pi\) | |||||||
\(194\) | −9.51004 | −0.682781 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.89155 | −0.492254 | ||||||||
\(197\) | 20.6212 | 1.46920 | 0.734599 | − | 0.678502i | \(-0.237370\pi\) | ||||
0.734599 | + | 0.678502i | \(0.237370\pi\) | |||||||
\(198\) | 5.03339 | 0.357708 | ||||||||
\(199\) | 18.5313 | 1.31365 | 0.656826 | − | 0.754042i | \(-0.271899\pi\) | ||||
0.656826 | + | 0.754042i | \(0.271899\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.14433 | 0.221784 | ||||||||
\(202\) | −19.2435 | −1.35397 | ||||||||
\(203\) | −1.98319 | −0.139193 | ||||||||
\(204\) | 6.78610 | 0.475122 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.10689 | 0.355814 | ||||||||
\(207\) | −6.50055 | −0.451819 | ||||||||
\(208\) | 0.482152 | 0.0334312 | ||||||||
\(209\) | −27.3823 | −1.89407 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.7638 | 1.08523 | 0.542613 | − | 0.839983i | \(-0.317435\pi\) | ||||
0.542613 | + | 0.839983i | \(0.317435\pi\) | |||||||
\(212\) | 1.68591 | 0.115789 | ||||||||
\(213\) | −5.71189 | −0.391372 | ||||||||
\(214\) | −15.3340 | −1.04821 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0.434265 | 0.0294799 | ||||||||
\(218\) | 9.76027 | 0.661049 | ||||||||
\(219\) | 2.94269 | 0.198848 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.27193 | −0.220094 | ||||||||
\(222\) | −0.780139 | −0.0523595 | ||||||||
\(223\) | 22.1782 | 1.48516 | 0.742582 | − | 0.669755i | \(-0.233601\pi\) | ||||
0.742582 | + | 0.669755i | \(0.233601\pi\) | |||||||
\(224\) | −0.329315 | −0.0220033 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.51566 | 0.100820 | ||||||||
\(227\) | −11.0969 | −0.736528 | −0.368264 | − | 0.929721i | \(-0.620048\pi\) | ||||
−0.368264 | + | 0.929721i | \(0.620048\pi\) | |||||||
\(228\) | −5.44012 | −0.360281 | ||||||||
\(229\) | 1.79879 | 0.118867 | 0.0594337 | − | 0.998232i | \(-0.481071\pi\) | ||||
0.0594337 | + | 0.998232i | \(0.481071\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.65757 | 0.109060 | ||||||||
\(232\) | 6.02216 | 0.395374 | ||||||||
\(233\) | −3.70579 | −0.242774 | −0.121387 | − | 0.992605i | \(-0.538734\pi\) | ||||
−0.121387 | + | 0.992605i | \(0.538734\pi\) | |||||||
\(234\) | −0.482152 | −0.0315193 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.01583 | 0.0661250 | ||||||||
\(237\) | −8.48510 | −0.551167 | ||||||||
\(238\) | 2.23476 | 0.144858 | ||||||||
\(239\) | −16.8733 | −1.09145 | −0.545723 | − | 0.837966i | \(-0.683745\pi\) | ||||
−0.545723 | + | 0.837966i | \(0.683745\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.6256 | 1.32861 | 0.664306 | − | 0.747461i | \(-0.268727\pi\) | ||||
0.664306 | + | 0.747461i | \(0.268727\pi\) | |||||||
\(242\) | −14.3350 | −0.921491 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.18808 | 0.268114 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.5205 | 0.798279 | ||||||||
\(247\) | 2.62297 | 0.166895 | ||||||||
\(248\) | −1.31869 | −0.0837371 | ||||||||
\(249\) | 17.1955 | 1.08972 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.69615 | 0.548896 | 0.274448 | − | 0.961602i | \(-0.411505\pi\) | ||||
0.274448 | + | 0.961602i | \(0.411505\pi\) | |||||||
\(252\) | 0.329315 | 0.0207449 | ||||||||
\(253\) | 32.7198 | 2.05708 | ||||||||
\(254\) | 12.6056 | 0.790945 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.10714 | −0.443331 | −0.221666 | − | 0.975123i | \(-0.571149\pi\) | ||||
−0.221666 | + | 0.975123i | \(0.571149\pi\) | |||||||
\(258\) | 2.47582 | 0.154138 | ||||||||
\(259\) | −0.256911 | −0.0159637 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.02216 | −0.372763 | ||||||||
\(262\) | −14.0559 | −0.868378 | ||||||||
\(263\) | 15.8609 | 0.978028 | 0.489014 | − | 0.872276i | \(-0.337357\pi\) | ||||
0.489014 | + | 0.872276i | \(0.337357\pi\) | |||||||
\(264\) | −5.03339 | −0.309784 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.79151 | −0.109845 | ||||||||
\(267\) | −3.45233 | −0.211279 | ||||||||
\(268\) | −3.14433 | −0.192070 | ||||||||
\(269\) | 4.51935 | 0.275550 | 0.137775 | − | 0.990464i | \(-0.456005\pi\) | ||||
0.137775 | + | 0.990464i | \(0.456005\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.1314 | 0.676186 | 0.338093 | − | 0.941113i | \(-0.390218\pi\) | ||||
0.338093 | + | 0.941113i | \(0.390218\pi\) | |||||||
\(272\) | −6.78610 | −0.411468 | ||||||||
\(273\) | −0.158780 | −0.00960980 | ||||||||
\(274\) | −6.68863 | −0.404075 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.50055 | 0.391287 | ||||||||
\(277\) | 22.8338 | 1.37195 | 0.685975 | − | 0.727625i | \(-0.259376\pi\) | ||||
0.685975 | + | 0.727625i | \(0.259376\pi\) | |||||||
\(278\) | 3.07799 | 0.184605 | ||||||||
\(279\) | 1.31869 | 0.0789481 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.7548 | 1.71537 | 0.857683 | − | 0.514179i | \(-0.171903\pi\) | ||||
0.857683 | + | 0.514179i | \(0.171903\pi\) | |||||||
\(282\) | 4.38040 | 0.260849 | ||||||||
\(283\) | 19.3471 | 1.15007 | 0.575034 | − | 0.818130i | \(-0.304989\pi\) | ||||
0.575034 | + | 0.818130i | \(0.304989\pi\) | |||||||
\(284\) | 5.71189 | 0.338938 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.42686 | 0.143503 | ||||||||
\(287\) | 4.12320 | 0.243385 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 29.0511 | 1.70889 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.51004 | −0.557488 | ||||||||
\(292\) | −2.94269 | −0.172208 | ||||||||
\(293\) | −15.0301 | −0.878069 | −0.439035 | − | 0.898470i | \(-0.644679\pi\) | ||||
−0.439035 | + | 0.898470i | \(0.644679\pi\) | |||||||
\(294\) | −6.89155 | −0.401923 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.780139 | 0.0453446 | ||||||||
\(297\) | 5.03339 | 0.292067 | ||||||||
\(298\) | −5.06465 | −0.293387 | ||||||||
\(299\) | −3.13425 | −0.181259 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.815324 | 0.0469945 | ||||||||
\(302\) | 16.9581 | 0.975829 | ||||||||
\(303\) | −19.2435 | −1.10551 | ||||||||
\(304\) | 5.44012 | 0.312012 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.78610 | 0.387935 | ||||||||
\(307\) | −19.7061 | −1.12468 | −0.562342 | − | 0.826905i | \(-0.690100\pi\) | ||||
−0.562342 | + | 0.826905i | \(0.690100\pi\) | |||||||
\(308\) | −1.65757 | −0.0944489 | ||||||||
\(309\) | 5.10689 | 0.290521 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.2393 | 1.60130 | 0.800651 | − | 0.599130i | \(-0.204487\pi\) | ||||
0.800651 | + | 0.599130i | \(0.204487\pi\) | |||||||
\(312\) | 0.482152 | 0.0272965 | ||||||||
\(313\) | 11.2478 | 0.635764 | 0.317882 | − | 0.948130i | \(-0.397028\pi\) | ||||
0.317882 | + | 0.948130i | \(0.397028\pi\) | |||||||
\(314\) | −22.8284 | −1.28828 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.48510 | 0.477324 | ||||||||
\(317\) | 23.2917 | 1.30819 | 0.654095 | − | 0.756412i | \(-0.273050\pi\) | ||||
0.654095 | + | 0.756412i | \(0.273050\pi\) | |||||||
\(318\) | 1.68591 | 0.0945412 | ||||||||
\(319\) | 30.3119 | 1.69714 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.3340 | −0.855858 | ||||||||
\(322\) | 2.14073 | 0.119298 | ||||||||
\(323\) | −36.9172 | −2.05413 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.95823 | 0.440766 | ||||||||
\(327\) | 9.76027 | 0.539744 | ||||||||
\(328\) | −12.5205 | −0.691330 | ||||||||
\(329\) | 1.44253 | 0.0795292 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.129334 | 0.00710883 | 0.00355441 | − | 0.999994i | \(-0.498869\pi\) | ||||
0.00355441 | + | 0.999994i | \(0.498869\pi\) | |||||||
\(332\) | −17.1955 | −0.943725 | ||||||||
\(333\) | −0.780139 | −0.0427513 | ||||||||
\(334\) | 13.9503 | 0.763327 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.329315 | −0.0179656 | ||||||||
\(337\) | −0.538069 | −0.0293105 | −0.0146552 | − | 0.999893i | \(-0.504665\pi\) | ||||
−0.0146552 | + | 0.999893i | \(0.504665\pi\) | |||||||
\(338\) | 12.7675 | 0.694462 | ||||||||
\(339\) | 1.51566 | 0.0823192 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.63750 | −0.359441 | ||||||||
\(342\) | −5.44012 | −0.294168 | ||||||||
\(343\) | −4.57470 | −0.247010 | ||||||||
\(344\) | −2.47582 | −0.133487 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.5009 | −1.04837 | ||||||||
\(347\) | 22.7156 | 1.21944 | 0.609719 | − | 0.792618i | \(-0.291282\pi\) | ||||
0.609719 | + | 0.792618i | \(0.291282\pi\) | |||||||
\(348\) | 6.02216 | 0.322822 | ||||||||
\(349\) | 6.84350 | 0.366324 | 0.183162 | − | 0.983083i | \(-0.441367\pi\) | ||||
0.183162 | + | 0.983083i | \(0.441367\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.482152 | −0.0257354 | ||||||||
\(352\) | 5.03339 | 0.268281 | ||||||||
\(353\) | 16.7789 | 0.893049 | 0.446524 | − | 0.894771i | \(-0.352662\pi\) | ||||
0.446524 | + | 0.894771i | \(0.352662\pi\) | |||||||
\(354\) | 1.01583 | 0.0539909 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.45233 | 0.182973 | ||||||||
\(357\) | 2.23476 | 0.118276 | ||||||||
\(358\) | 18.9911 | 1.00371 | ||||||||
\(359\) | −7.46364 | −0.393916 | −0.196958 | − | 0.980412i | \(-0.563106\pi\) | ||||
−0.196958 | + | 0.980412i | \(0.563106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.5949 | 0.557628 | ||||||||
\(362\) | 18.9484 | 0.995905 | ||||||||
\(363\) | −14.3350 | −0.752395 | ||||||||
\(364\) | 0.158780 | 0.00832233 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.18808 | 0.218914 | ||||||||
\(367\) | −6.15474 | −0.321275 | −0.160637 | − | 0.987013i | \(-0.551355\pi\) | ||||
−0.160637 | + | 0.987013i | \(0.551355\pi\) | |||||||
\(368\) | −6.50055 | −0.338865 | ||||||||
\(369\) | 12.5205 | 0.651792 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.555196 | 0.0288243 | ||||||||
\(372\) | −1.31869 | −0.0683711 | ||||||||
\(373\) | 9.16928 | 0.474767 | 0.237384 | − | 0.971416i | \(-0.423710\pi\) | ||||
0.237384 | + | 0.971416i | \(0.423710\pi\) | |||||||
\(374\) | −34.1571 | −1.76622 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.38040 | −0.225902 | ||||||||
\(377\) | −2.90360 | −0.149543 | ||||||||
\(378\) | 0.329315 | 0.0169381 | ||||||||
\(379\) | −34.6321 | −1.77893 | −0.889465 | − | 0.457004i | \(-0.848923\pi\) | ||||
−0.889465 | + | 0.457004i | \(0.848923\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.6056 | 0.645804 | ||||||||
\(382\) | 12.0933 | 0.618746 | ||||||||
\(383\) | 9.52044 | 0.486472 | 0.243236 | − | 0.969967i | \(-0.421791\pi\) | ||||
0.243236 | + | 0.969967i | \(0.421791\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.0357 | −0.561703 | ||||||||
\(387\) | 2.47582 | 0.125853 | ||||||||
\(388\) | 9.51004 | 0.482799 | ||||||||
\(389\) | −17.4454 | −0.884515 | −0.442258 | − | 0.896888i | \(-0.645822\pi\) | ||||
−0.442258 | + | 0.896888i | \(0.645822\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44.1134 | 2.23091 | ||||||||
\(392\) | 6.89155 | 0.348076 | ||||||||
\(393\) | −14.0559 | −0.709028 | ||||||||
\(394\) | −20.6212 | −1.03888 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.03339 | −0.252937 | ||||||||
\(397\) | 13.5551 | 0.680313 | 0.340157 | − | 0.940369i | \(-0.389520\pi\) | ||||
0.340157 | + | 0.940369i | \(0.389520\pi\) | |||||||
\(398\) | −18.5313 | −0.928892 | ||||||||
\(399\) | −1.79151 | −0.0896879 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.1105 | 0.704642 | 0.352321 | − | 0.935879i | \(-0.385392\pi\) | ||||
0.352321 | + | 0.935879i | \(0.385392\pi\) | |||||||
\(402\) | −3.14433 | −0.156825 | ||||||||
\(403\) | 0.635811 | 0.0316720 | ||||||||
\(404\) | 19.2435 | 0.957400 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.98319 | 0.0984240 | ||||||||
\(407\) | 3.92674 | 0.194641 | ||||||||
\(408\) | −6.78610 | −0.335962 | ||||||||
\(409\) | −16.5637 | −0.819024 | −0.409512 | − | 0.912305i | \(-0.634301\pi\) | ||||
−0.409512 | + | 0.912305i | \(0.634301\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.68863 | −0.329926 | ||||||||
\(412\) | −5.10689 | −0.251598 | ||||||||
\(413\) | 0.334529 | 0.0164611 | ||||||||
\(414\) | 6.50055 | 0.319485 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.482152 | −0.0236395 | ||||||||
\(417\) | 3.07799 | 0.150730 | ||||||||
\(418\) | 27.3823 | 1.33931 | ||||||||
\(419\) | 16.9705 | 0.829062 | 0.414531 | − | 0.910035i | \(-0.363946\pi\) | ||||
0.414531 | + | 0.910035i | \(0.363946\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.06240 | −0.344200 | −0.172100 | − | 0.985079i | \(-0.555055\pi\) | ||||
−0.172100 | + | 0.985079i | \(0.555055\pi\) | |||||||
\(422\) | −15.7638 | −0.767371 | ||||||||
\(423\) | 4.38040 | 0.212982 | ||||||||
\(424\) | −1.68591 | −0.0818751 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.71189 | 0.276742 | ||||||||
\(427\) | 1.37920 | 0.0667440 | ||||||||
\(428\) | 15.3340 | 0.741194 | ||||||||
\(429\) | 2.42686 | 0.117170 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.8582 | −0.860199 | −0.430099 | − | 0.902782i | \(-0.641521\pi\) | ||||
−0.430099 | + | 0.902782i | \(0.641521\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 24.1797 | 1.16200 | 0.581000 | − | 0.813903i | \(-0.302661\pi\) | ||||
0.581000 | + | 0.813903i | \(0.302661\pi\) | |||||||
\(434\) | −0.434265 | −0.0208454 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.76027 | −0.467432 | ||||||||
\(437\) | −35.3638 | −1.69168 | ||||||||
\(438\) | −2.94269 | −0.140607 | ||||||||
\(439\) | −18.9103 | −0.902537 | −0.451269 | − | 0.892388i | \(-0.649028\pi\) | ||||
−0.451269 | + | 0.892388i | \(0.649028\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.89155 | −0.328169 | ||||||||
\(442\) | 3.27193 | 0.155630 | ||||||||
\(443\) | −4.05769 | −0.192787 | −0.0963933 | − | 0.995343i | \(-0.530731\pi\) | ||||
−0.0963933 | + | 0.995343i | \(0.530731\pi\) | |||||||
\(444\) | 0.780139 | 0.0370237 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −22.1782 | −1.05017 | ||||||||
\(447\) | −5.06465 | −0.239550 | ||||||||
\(448\) | 0.329315 | 0.0155587 | ||||||||
\(449\) | −6.26150 | −0.295498 | −0.147749 | − | 0.989025i | \(-0.547203\pi\) | ||||
−0.147749 | + | 0.989025i | \(0.547203\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −63.0207 | −2.96753 | ||||||||
\(452\) | −1.51566 | −0.0712905 | ||||||||
\(453\) | 16.9581 | 0.796761 | ||||||||
\(454\) | 11.0969 | 0.520804 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.44012 | 0.254757 | ||||||||
\(457\) | −1.94229 | −0.0908564 | −0.0454282 | − | 0.998968i | \(-0.514465\pi\) | ||||
−0.0454282 | + | 0.998968i | \(0.514465\pi\) | |||||||
\(458\) | −1.79879 | −0.0840520 | ||||||||
\(459\) | 6.78610 | 0.316748 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.12391 | 0.145495 | 0.0727475 | − | 0.997350i | \(-0.476823\pi\) | ||||
0.0727475 | + | 0.997350i | \(0.476823\pi\) | |||||||
\(462\) | −1.65757 | −0.0771172 | ||||||||
\(463\) | 8.26641 | 0.384173 | 0.192086 | − | 0.981378i | \(-0.438475\pi\) | ||||
0.192086 | + | 0.981378i | \(0.438475\pi\) | |||||||
\(464\) | −6.02216 | −0.279572 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.70579 | 0.171667 | ||||||||
\(467\) | 30.6192 | 1.41689 | 0.708445 | − | 0.705766i | \(-0.249397\pi\) | ||||
0.708445 | + | 0.705766i | \(0.249397\pi\) | |||||||
\(468\) | 0.482152 | 0.0222875 | ||||||||
\(469\) | −1.03547 | −0.0478137 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.8284 | −1.05188 | ||||||||
\(472\) | −1.01583 | −0.0467575 | ||||||||
\(473\) | −12.4618 | −0.572993 | ||||||||
\(474\) | 8.48510 | 0.389734 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.23476 | −0.102430 | ||||||||
\(477\) | 1.68591 | 0.0771925 | ||||||||
\(478\) | 16.8733 | 0.771769 | ||||||||
\(479\) | −1.17289 | −0.0535907 | −0.0267953 | − | 0.999641i | \(-0.508530\pi\) | ||||
−0.0267953 | + | 0.999641i | \(0.508530\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.376146 | −0.0171508 | ||||||||
\(482\) | −20.6256 | −0.939471 | ||||||||
\(483\) | 2.14073 | 0.0974065 | ||||||||
\(484\) | 14.3350 | 0.651593 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −11.7556 | −0.532695 | −0.266348 | − | 0.963877i | \(-0.585817\pi\) | ||||
−0.266348 | + | 0.963877i | \(0.585817\pi\) | |||||||
\(488\) | −4.18808 | −0.189585 | ||||||||
\(489\) | 7.95823 | 0.359884 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.13052 | 0.186408 | 0.0932038 | − | 0.995647i | \(-0.470289\pi\) | ||||
0.0932038 | + | 0.995647i | \(0.470289\pi\) | |||||||
\(492\) | −12.5205 | −0.564469 | ||||||||
\(493\) | 40.8670 | 1.84056 | ||||||||
\(494\) | −2.62297 | −0.118013 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.31869 | 0.0592111 | ||||||||
\(497\) | 1.88101 | 0.0843748 | ||||||||
\(498\) | −17.1955 | −0.770549 | ||||||||
\(499\) | 9.59154 | 0.429376 | 0.214688 | − | 0.976683i | \(-0.431127\pi\) | ||||
0.214688 | + | 0.976683i | \(0.431127\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.9503 | 0.623254 | ||||||||
\(502\) | −8.69615 | −0.388128 | ||||||||
\(503\) | −16.9453 | −0.755555 | −0.377777 | − | 0.925896i | \(-0.623312\pi\) | ||||
−0.377777 | + | 0.925896i | \(0.623312\pi\) | |||||||
\(504\) | −0.329315 | −0.0146689 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −32.7198 | −1.45457 | ||||||||
\(507\) | 12.7675 | 0.567026 | ||||||||
\(508\) | −12.6056 | −0.559282 | ||||||||
\(509\) | 34.3000 | 1.52032 | 0.760161 | − | 0.649735i | \(-0.225120\pi\) | ||||
0.760161 | + | 0.649735i | \(0.225120\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.969070 | −0.0428691 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.44012 | −0.240187 | ||||||||
\(514\) | 7.10714 | 0.313483 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.47582 | −0.108992 | ||||||||
\(517\) | −22.0482 | −0.969681 | ||||||||
\(518\) | 0.256911 | 0.0112880 | ||||||||
\(519\) | −19.5009 | −0.855993 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.2832 | 0.932436 | 0.466218 | − | 0.884670i | \(-0.345616\pi\) | ||||
0.466218 | + | 0.884670i | \(0.345616\pi\) | |||||||
\(522\) | 6.02216 | 0.263583 | ||||||||
\(523\) | 41.3492 | 1.80807 | 0.904037 | − | 0.427454i | \(-0.140589\pi\) | ||||
0.904037 | + | 0.427454i | \(0.140589\pi\) | |||||||
\(524\) | 14.0559 | 0.614036 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.8609 | −0.691570 | ||||||||
\(527\) | −8.94878 | −0.389815 | ||||||||
\(528\) | 5.03339 | 0.219050 | ||||||||
\(529\) | 19.2571 | 0.837267 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.01583 | 0.0440833 | ||||||||
\(532\) | 1.79151 | 0.0776720 | ||||||||
\(533\) | 6.03680 | 0.261483 | ||||||||
\(534\) | 3.45233 | 0.149397 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.14433 | 0.135814 | ||||||||
\(537\) | 18.9911 | 0.819526 | ||||||||
\(538\) | −4.51935 | −0.194843 | ||||||||
\(539\) | 34.6879 | 1.49411 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.8217 | −1.54010 | −0.770048 | − | 0.637987i | \(-0.779768\pi\) | ||||
−0.770048 | + | 0.637987i | \(0.779768\pi\) | |||||||
\(542\) | −11.1314 | −0.478136 | ||||||||
\(543\) | 18.9484 | 0.813153 | ||||||||
\(544\) | 6.78610 | 0.290951 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.158780 | 0.00679515 | ||||||||
\(547\) | −8.36253 | −0.357556 | −0.178778 | − | 0.983889i | \(-0.557214\pi\) | ||||
−0.178778 | + | 0.983889i | \(0.557214\pi\) | |||||||
\(548\) | 6.68863 | 0.285724 | ||||||||
\(549\) | 4.18808 | 0.178743 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.7613 | −1.39568 | ||||||||
\(552\) | −6.50055 | −0.276682 | ||||||||
\(553\) | 2.79427 | 0.118824 | ||||||||
\(554\) | −22.8338 | −0.970115 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.07799 | −0.130536 | ||||||||
\(557\) | 28.1467 | 1.19262 | 0.596308 | − | 0.802756i | \(-0.296634\pi\) | ||||
0.596308 | + | 0.802756i | \(0.296634\pi\) | |||||||
\(558\) | −1.31869 | −0.0558247 | ||||||||
\(559\) | 1.19372 | 0.0504890 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −34.1571 | −1.44211 | ||||||||
\(562\) | −28.7548 | −1.21295 | ||||||||
\(563\) | 3.45072 | 0.145431 | 0.0727153 | − | 0.997353i | \(-0.476834\pi\) | ||||
0.0727153 | + | 0.997353i | \(0.476834\pi\) | |||||||
\(564\) | −4.38040 | −0.184448 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −19.3471 | −0.813220 | ||||||||
\(567\) | 0.329315 | 0.0138299 | ||||||||
\(568\) | −5.71189 | −0.239665 | ||||||||
\(569\) | 17.4040 | 0.729614 | 0.364807 | − | 0.931083i | \(-0.381135\pi\) | ||||
0.364807 | + | 0.931083i | \(0.381135\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.2213 | −1.55766 | −0.778831 | − | 0.627234i | \(-0.784187\pi\) | ||||
−0.778831 | + | 0.627234i | \(0.784187\pi\) | |||||||
\(572\) | −2.42686 | −0.101472 | ||||||||
\(573\) | 12.0933 | 0.505204 | ||||||||
\(574\) | −4.12320 | −0.172099 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 20.1041 | 0.836943 | 0.418472 | − | 0.908230i | \(-0.362566\pi\) | ||||
0.418472 | + | 0.908230i | \(0.362566\pi\) | |||||||
\(578\) | −29.0511 | −1.20837 | ||||||||
\(579\) | −11.0357 | −0.458629 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.66273 | −0.234930 | ||||||||
\(582\) | 9.51004 | 0.394204 | ||||||||
\(583\) | −8.48585 | −0.351448 | ||||||||
\(584\) | 2.94269 | 0.121769 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.0301 | 0.620889 | ||||||||
\(587\) | 6.11838 | 0.252533 | 0.126266 | − | 0.991996i | \(-0.459701\pi\) | ||||
0.126266 | + | 0.991996i | \(0.459701\pi\) | |||||||
\(588\) | 6.89155 | 0.284203 | ||||||||
\(589\) | 7.17385 | 0.295593 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.6212 | −0.848242 | ||||||||
\(592\) | −0.780139 | −0.0320635 | ||||||||
\(593\) | −24.9458 | −1.02440 | −0.512201 | − | 0.858866i | \(-0.671170\pi\) | ||||
−0.512201 | + | 0.858866i | \(0.671170\pi\) | |||||||
\(594\) | −5.03339 | −0.206523 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.06465 | 0.207456 | ||||||||
\(597\) | −18.5313 | −0.758437 | ||||||||
\(598\) | 3.13425 | 0.128169 | ||||||||
\(599\) | −0.941228 | −0.0384575 | −0.0192288 | − | 0.999815i | \(-0.506121\pi\) | ||||
−0.0192288 | + | 0.999815i | \(0.506121\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.2333 | 0.417426 | 0.208713 | − | 0.977977i | \(-0.433073\pi\) | ||||
0.208713 | + | 0.977977i | \(0.433073\pi\) | |||||||
\(602\) | −0.815324 | −0.0332301 | ||||||||
\(603\) | −3.14433 | −0.128047 | ||||||||
\(604\) | −16.9581 | −0.690015 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 19.2435 | 0.781714 | ||||||||
\(607\) | −6.80623 | −0.276256 | −0.138128 | − | 0.990414i | \(-0.544109\pi\) | ||||
−0.138128 | + | 0.990414i | \(0.544109\pi\) | |||||||
\(608\) | −5.44012 | −0.220626 | ||||||||
\(609\) | 1.98319 | 0.0803629 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.11202 | 0.0854431 | ||||||||
\(612\) | −6.78610 | −0.274312 | ||||||||
\(613\) | 1.13944 | 0.0460215 | 0.0230107 | − | 0.999735i | \(-0.492675\pi\) | ||||
0.0230107 | + | 0.999735i | \(0.492675\pi\) | |||||||
\(614\) | 19.7061 | 0.795272 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.65757 | 0.0667854 | ||||||||
\(617\) | 14.3577 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(618\) | −5.10689 | −0.205429 | ||||||||
\(619\) | 0.476518 | 0.0191529 | 0.00957644 | − | 0.999954i | \(-0.496952\pi\) | ||||
0.00957644 | + | 0.999954i | \(0.496952\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.50055 | 0.260858 | ||||||||
\(622\) | −28.2393 | −1.13229 | ||||||||
\(623\) | 1.13690 | 0.0455491 | ||||||||
\(624\) | −0.482152 | −0.0193015 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.2478 | −0.449553 | ||||||||
\(627\) | 27.3823 | 1.09354 | ||||||||
\(628\) | 22.8284 | 0.910952 | ||||||||
\(629\) | 5.29410 | 0.211089 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.0525 | −0.678850 | −0.339425 | − | 0.940633i | \(-0.610232\pi\) | ||||
−0.339425 | + | 0.940633i | \(0.610232\pi\) | |||||||
\(632\) | −8.48510 | −0.337519 | ||||||||
\(633\) | −15.7638 | −0.626556 | ||||||||
\(634\) | −23.2917 | −0.925030 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.68591 | −0.0668507 | ||||||||
\(637\) | −3.32278 | −0.131653 | ||||||||
\(638\) | −30.3119 | −1.20006 | ||||||||
\(639\) | 5.71189 | 0.225959 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.7254 | −1.29258 | −0.646288 | − | 0.763094i | \(-0.723680\pi\) | ||||
−0.646288 | + | 0.763094i | \(0.723680\pi\) | |||||||
\(642\) | 15.3340 | 0.605183 | ||||||||
\(643\) | 12.5844 | 0.496281 | 0.248141 | − | 0.968724i | \(-0.420180\pi\) | ||||
0.248141 | + | 0.968724i | \(0.420180\pi\) | |||||||
\(644\) | −2.14073 | −0.0843565 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 36.9172 | 1.45249 | ||||||||
\(647\) | −25.6397 | −1.00800 | −0.504000 | − | 0.863703i | \(-0.668139\pi\) | ||||
−0.504000 | + | 0.863703i | \(0.668139\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −5.11308 | −0.200706 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.434265 | −0.0170202 | ||||||||
\(652\) | −7.95823 | −0.311668 | ||||||||
\(653\) | −30.0568 | −1.17621 | −0.588107 | − | 0.808783i | \(-0.700127\pi\) | ||||
−0.588107 | + | 0.808783i | \(0.700127\pi\) | |||||||
\(654\) | −9.76027 | −0.381657 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 12.5205 | 0.488844 | ||||||||
\(657\) | −2.94269 | −0.114805 | ||||||||
\(658\) | −1.44253 | −0.0562357 | ||||||||
\(659\) | −8.04829 | −0.313517 | −0.156759 | − | 0.987637i | \(-0.550104\pi\) | ||||
−0.156759 | + | 0.987637i | \(0.550104\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.728568 | −0.0283380 | −0.0141690 | − | 0.999900i | \(-0.504510\pi\) | ||||
−0.0141690 | + | 0.999900i | \(0.504510\pi\) | |||||||
\(662\) | −0.129334 | −0.00502670 | ||||||||
\(663\) | 3.27193 | 0.127071 | ||||||||
\(664\) | 17.1955 | 0.667315 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.780139 | 0.0302298 | ||||||||
\(667\) | 39.1474 | 1.51579 | ||||||||
\(668\) | −13.9503 | −0.539754 | ||||||||
\(669\) | −22.1782 | −0.857460 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.0803 | −0.813794 | ||||||||
\(672\) | 0.329315 | 0.0127036 | ||||||||
\(673\) | −7.40821 | −0.285566 | −0.142783 | − | 0.989754i | \(-0.545605\pi\) | ||||
−0.142783 | + | 0.989754i | \(0.545605\pi\) | |||||||
\(674\) | 0.538069 | 0.0207256 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.7675 | −0.491059 | ||||||||
\(677\) | −9.79504 | −0.376454 | −0.188227 | − | 0.982126i | \(-0.560274\pi\) | ||||
−0.188227 | + | 0.982126i | \(0.560274\pi\) | |||||||
\(678\) | −1.51566 | −0.0582084 | ||||||||
\(679\) | 3.13180 | 0.120187 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.0969 | 0.425235 | ||||||||
\(682\) | 6.63750 | 0.254163 | ||||||||
\(683\) | −33.5847 | −1.28508 | −0.642542 | − | 0.766250i | \(-0.722120\pi\) | ||||
−0.642542 | + | 0.766250i | \(0.722120\pi\) | |||||||
\(684\) | 5.44012 | 0.208008 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.57470 | 0.174663 | ||||||||
\(687\) | −1.79879 | −0.0686281 | ||||||||
\(688\) | 2.47582 | 0.0943897 | ||||||||
\(689\) | 0.812865 | 0.0309677 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.1110 | 0.993309 | 0.496655 | − | 0.867948i | \(-0.334562\pi\) | ||||
0.496655 | + | 0.867948i | \(0.334562\pi\) | |||||||
\(692\) | 19.5009 | 0.741312 | ||||||||
\(693\) | −1.65757 | −0.0629659 | ||||||||
\(694\) | −22.7156 | −0.862273 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.02216 | −0.228270 | ||||||||
\(697\) | −84.9655 | −3.21830 | ||||||||
\(698\) | −6.84350 | −0.259030 | ||||||||
\(699\) | 3.70579 | 0.140166 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.8212 | 1.57956 | 0.789782 | − | 0.613388i | \(-0.210194\pi\) | ||||
0.789782 | + | 0.613388i | \(0.210194\pi\) | |||||||
\(702\) | 0.482152 | 0.0181977 | ||||||||
\(703\) | −4.24405 | −0.160067 | ||||||||
\(704\) | −5.03339 | −0.189703 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.7789 | −0.631481 | ||||||||
\(707\) | 6.33717 | 0.238334 | ||||||||
\(708\) | −1.01583 | −0.0381773 | ||||||||
\(709\) | −8.86903 | −0.333083 | −0.166542 | − | 0.986034i | \(-0.553260\pi\) | ||||
−0.166542 | + | 0.986034i | \(0.553260\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.48510 | 0.318216 | ||||||||
\(712\) | −3.45233 | −0.129382 | ||||||||
\(713\) | −8.57223 | −0.321033 | ||||||||
\(714\) | −2.23476 | −0.0836339 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.9911 | −0.709731 | ||||||||
\(717\) | 16.8733 | 0.630146 | ||||||||
\(718\) | 7.46364 | 0.278541 | ||||||||
\(719\) | −2.65509 | −0.0990182 | −0.0495091 | − | 0.998774i | \(-0.515766\pi\) | ||||
−0.0495091 | + | 0.998774i | \(0.515766\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.68177 | −0.0626325 | ||||||||
\(722\) | −10.5949 | −0.394303 | ||||||||
\(723\) | −20.6256 | −0.767075 | ||||||||
\(724\) | −18.9484 | −0.704211 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 14.3350 | 0.532023 | ||||||||
\(727\) | 7.03681 | 0.260981 | 0.130490 | − | 0.991450i | \(-0.458345\pi\) | ||||
0.130490 | + | 0.991450i | \(0.458345\pi\) | |||||||
\(728\) | −0.158780 | −0.00588477 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.8011 | −0.621413 | ||||||||
\(732\) | −4.18808 | −0.154796 | ||||||||
\(733\) | −20.2601 | −0.748324 | −0.374162 | − | 0.927363i | \(-0.622070\pi\) | ||||
−0.374162 | + | 0.927363i | \(0.622070\pi\) | |||||||
\(734\) | 6.15474 | 0.227176 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.50055 | 0.239613 | ||||||||
\(737\) | 15.8266 | 0.582982 | ||||||||
\(738\) | −12.5205 | −0.460887 | ||||||||
\(739\) | 17.1512 | 0.630919 | 0.315459 | − | 0.948939i | \(-0.397841\pi\) | ||||
0.315459 | + | 0.948939i | \(0.397841\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.62297 | −0.0963571 | ||||||||
\(742\) | −0.555196 | −0.0203819 | ||||||||
\(743\) | 9.94252 | 0.364756 | 0.182378 | − | 0.983229i | \(-0.441621\pi\) | ||||
0.182378 | + | 0.983229i | \(0.441621\pi\) | |||||||
\(744\) | 1.31869 | 0.0483456 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.16928 | −0.335711 | ||||||||
\(747\) | −17.1955 | −0.629150 | ||||||||
\(748\) | 34.1571 | 1.24891 | ||||||||
\(749\) | 5.04970 | 0.184512 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.6941 | −0.645667 | −0.322833 | − | 0.946456i | \(-0.604635\pi\) | ||||
−0.322833 | + | 0.946456i | \(0.604635\pi\) | |||||||
\(752\) | 4.38040 | 0.159737 | ||||||||
\(753\) | −8.69615 | −0.316905 | ||||||||
\(754\) | 2.90360 | 0.105743 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.329315 | −0.0119771 | ||||||||
\(757\) | −37.1272 | −1.34941 | −0.674706 | − | 0.738087i | \(-0.735729\pi\) | ||||
−0.674706 | + | 0.738087i | \(0.735729\pi\) | |||||||
\(758\) | 34.6321 | 1.25789 | ||||||||
\(759\) | −32.7198 | −1.18765 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −49.5640 | −1.79669 | −0.898346 | − | 0.439289i | \(-0.855230\pi\) | ||||
−0.898346 | + | 0.439289i | \(0.855230\pi\) | |||||||
\(762\) | −12.6056 | −0.456652 | ||||||||
\(763\) | −3.21420 | −0.116362 | ||||||||
\(764\) | −12.0933 | −0.437520 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.52044 | −0.343987 | ||||||||
\(767\) | 0.489786 | 0.0176851 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 34.3645 | 1.23922 | 0.619608 | − | 0.784911i | \(-0.287291\pi\) | ||||
0.619608 | + | 0.784911i | \(0.287291\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.10714 | 0.255957 | ||||||||
\(772\) | 11.0357 | 0.397184 | ||||||||
\(773\) | 22.9926 | 0.826985 | 0.413493 | − | 0.910507i | \(-0.364309\pi\) | ||||
0.413493 | + | 0.910507i | \(0.364309\pi\) | |||||||
\(774\) | −2.47582 | −0.0889915 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9.51004 | −0.341390 | ||||||||
\(777\) | 0.256911 | 0.00921664 | ||||||||
\(778\) | 17.4454 | 0.625447 | ||||||||
\(779\) | 68.1132 | 2.44041 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.7502 | −1.02876 | ||||||||
\(782\) | −44.1134 | −1.57749 | ||||||||
\(783\) | 6.02216 | 0.215215 | ||||||||
\(784\) | −6.89155 | −0.246127 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 14.0559 | 0.501358 | ||||||||
\(787\) | 8.41183 | 0.299849 | 0.149925 | − | 0.988697i | \(-0.452097\pi\) | ||||
0.149925 | + | 0.988697i | \(0.452097\pi\) | |||||||
\(788\) | 20.6212 | 0.734599 | ||||||||
\(789\) | −15.8609 | −0.564665 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.499128 | −0.0177470 | ||||||||
\(792\) | 5.03339 | 0.178854 | ||||||||
\(793\) | 2.01929 | 0.0717072 | ||||||||
\(794\) | −13.5551 | −0.481054 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.5313 | 0.656826 | ||||||||
\(797\) | −38.2745 | −1.35575 | −0.677875 | − | 0.735177i | \(-0.737099\pi\) | ||||
−0.677875 | + | 0.735177i | \(0.737099\pi\) | |||||||
\(798\) | 1.79151 | 0.0634189 | ||||||||
\(799\) | −29.7258 | −1.05162 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.45233 | 0.121982 | ||||||||
\(802\) | −14.1105 | −0.498257 | ||||||||
\(803\) | 14.8117 | 0.522693 | ||||||||
\(804\) | 3.14433 | 0.110892 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.635811 | −0.0223955 | ||||||||
\(807\) | −4.51935 | −0.159089 | ||||||||
\(808\) | −19.2435 | −0.676984 | ||||||||
\(809\) | −30.8014 | −1.08292 | −0.541461 | − | 0.840726i | \(-0.682128\pi\) | ||||
−0.541461 | + | 0.840726i | \(0.682128\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.787233 | −0.0276435 | −0.0138217 | − | 0.999904i | \(-0.504400\pi\) | ||||
−0.0138217 | + | 0.999904i | \(0.504400\pi\) | |||||||
\(812\) | −1.98319 | −0.0695963 | ||||||||
\(813\) | −11.1314 | −0.390396 | ||||||||
\(814\) | −3.92674 | −0.137632 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.78610 | 0.237561 | ||||||||
\(817\) | 13.4688 | 0.471212 | ||||||||
\(818\) | 16.5637 | 0.579138 | ||||||||
\(819\) | 0.158780 | 0.00554822 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.4710 | 0.609743 | 0.304872 | − | 0.952393i | \(-0.401386\pi\) | ||||
0.304872 | + | 0.952393i | \(0.401386\pi\) | |||||||
\(822\) | 6.68863 | 0.233293 | ||||||||
\(823\) | −37.4268 | −1.30462 | −0.652309 | − | 0.757953i | \(-0.726199\pi\) | ||||
−0.652309 | + | 0.757953i | \(0.726199\pi\) | |||||||
\(824\) | 5.10689 | 0.177907 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.334529 | −0.0116397 | ||||||||
\(827\) | 11.7918 | 0.410041 | 0.205020 | − | 0.978758i | \(-0.434274\pi\) | ||||
0.205020 | + | 0.978758i | \(0.434274\pi\) | |||||||
\(828\) | −6.50055 | −0.225910 | ||||||||
\(829\) | −35.0287 | −1.21660 | −0.608298 | − | 0.793708i | \(-0.708148\pi\) | ||||
−0.608298 | + | 0.793708i | \(0.708148\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.8338 | −0.792096 | ||||||||
\(832\) | 0.482152 | 0.0167156 | ||||||||
\(833\) | 46.7667 | 1.62037 | ||||||||
\(834\) | −3.07799 | −0.106582 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −27.3823 | −0.947036 | ||||||||
\(837\) | −1.31869 | −0.0455807 | ||||||||
\(838\) | −16.9705 | −0.586235 | ||||||||
\(839\) | 0.498658 | 0.0172156 | 0.00860779 | − | 0.999963i | \(-0.497260\pi\) | ||||
0.00860779 | + | 0.999963i | \(0.497260\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.26647 | 0.250568 | ||||||||
\(842\) | 7.06240 | 0.243386 | ||||||||
\(843\) | −28.7548 | −0.990367 | ||||||||
\(844\) | 15.7638 | 0.542613 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.38040 | −0.150601 | ||||||||
\(847\) | 4.72074 | 0.162207 | ||||||||
\(848\) | 1.68591 | 0.0578944 | ||||||||
\(849\) | −19.3471 | −0.663992 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.07133 | 0.173843 | ||||||||
\(852\) | −5.71189 | −0.195686 | ||||||||
\(853\) | −21.3584 | −0.731298 | −0.365649 | − | 0.930753i | \(-0.619153\pi\) | ||||
−0.365649 | + | 0.930753i | \(0.619153\pi\) | |||||||
\(854\) | −1.37920 | −0.0471952 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.3340 | −0.524104 | ||||||||
\(857\) | 33.4831 | 1.14376 | 0.571880 | − | 0.820337i | \(-0.306214\pi\) | ||||
0.571880 | + | 0.820337i | \(0.306214\pi\) | |||||||
\(858\) | −2.42686 | −0.0828517 | ||||||||
\(859\) | 45.4873 | 1.55201 | 0.776003 | − | 0.630729i | \(-0.217244\pi\) | ||||
0.776003 | + | 0.630729i | \(0.217244\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.12320 | −0.140518 | ||||||||
\(862\) | 17.8582 | 0.608252 | ||||||||
\(863\) | −14.4689 | −0.492529 | −0.246264 | − | 0.969203i | \(-0.579203\pi\) | ||||
−0.246264 | + | 0.969203i | \(0.579203\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −24.1797 | −0.821659 | ||||||||
\(867\) | −29.0511 | −0.986627 | ||||||||
\(868\) | 0.434265 | 0.0147399 | ||||||||
\(869\) | −42.7088 | −1.44880 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.51604 | −0.0513692 | ||||||||
\(872\) | 9.76027 | 0.330525 | ||||||||
\(873\) | 9.51004 | 0.321866 | ||||||||
\(874\) | 35.3638 | 1.19620 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.94269 | 0.0994241 | ||||||||
\(877\) | 45.1991 | 1.52626 | 0.763132 | − | 0.646243i | \(-0.223661\pi\) | ||||
0.763132 | + | 0.646243i | \(0.223661\pi\) | |||||||
\(878\) | 18.9103 | 0.638190 | ||||||||
\(879\) | 15.0301 | 0.506954 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.9752 | 0.470836 | 0.235418 | − | 0.971894i | \(-0.424354\pi\) | ||||
0.235418 | + | 0.971894i | \(0.424354\pi\) | |||||||
\(882\) | 6.89155 | 0.232051 | ||||||||
\(883\) | 11.7349 | 0.394911 | 0.197455 | − | 0.980312i | \(-0.436732\pi\) | ||||
0.197455 | + | 0.980312i | \(0.436732\pi\) | |||||||
\(884\) | −3.27193 | −0.110047 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.05769 | 0.136321 | ||||||||
\(887\) | −19.7512 | −0.663180 | −0.331590 | − | 0.943424i | \(-0.607585\pi\) | ||||
−0.331590 | + | 0.943424i | \(0.607585\pi\) | |||||||
\(888\) | −0.780139 | −0.0261797 | ||||||||
\(889\) | −4.15121 | −0.139227 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.03339 | −0.168625 | ||||||||
\(892\) | 22.1782 | 0.742582 | ||||||||
\(893\) | 23.8299 | 0.797437 | ||||||||
\(894\) | 5.06465 | 0.169387 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.329315 | −0.0110016 | ||||||||
\(897\) | 3.13425 | 0.104650 | ||||||||
\(898\) | 6.26150 | 0.208949 | ||||||||
\(899\) | −7.94139 | −0.264860 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.4408 | −0.381147 | ||||||||
\(902\) | 63.0207 | 2.09836 | ||||||||
\(903\) | −0.815324 | −0.0271323 | ||||||||
\(904\) | 1.51566 | 0.0504100 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −16.9581 | −0.563395 | ||||||||
\(907\) | 21.0111 | 0.697661 | 0.348831 | − | 0.937186i | \(-0.386579\pi\) | ||||
0.348831 | + | 0.937186i | \(0.386579\pi\) | |||||||
\(908\) | −11.0969 | −0.368264 | ||||||||
\(909\) | 19.2435 | 0.638267 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.8288 | 0.822614 | 0.411307 | − | 0.911497i | \(-0.365072\pi\) | ||||
0.411307 | + | 0.911497i | \(0.365072\pi\) | |||||||
\(912\) | −5.44012 | −0.180140 | ||||||||
\(913\) | 86.5517 | 2.86444 | ||||||||
\(914\) | 1.94229 | 0.0642452 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.79879 | 0.0594337 | ||||||||
\(917\) | 4.62883 | 0.152857 | ||||||||
\(918\) | −6.78610 | −0.223975 | ||||||||
\(919\) | −36.0292 | −1.18849 | −0.594247 | − | 0.804283i | \(-0.702550\pi\) | ||||
−0.594247 | + | 0.804283i | \(0.702550\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.7061 | 0.649337 | ||||||||
\(922\) | −3.12391 | −0.102881 | ||||||||
\(923\) | 2.75400 | 0.0906490 | ||||||||
\(924\) | 1.65757 | 0.0545301 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.26641 | −0.271651 | ||||||||
\(927\) | −5.10689 | −0.167732 | ||||||||
\(928\) | 6.02216 | 0.197687 | ||||||||
\(929\) | −56.9634 | −1.86891 | −0.934454 | − | 0.356084i | \(-0.884112\pi\) | ||||
−0.934454 | + | 0.356084i | \(0.884112\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37.4909 | −1.22871 | ||||||||
\(932\) | −3.70579 | −0.121387 | ||||||||
\(933\) | −28.2393 | −0.924513 | ||||||||
\(934\) | −30.6192 | −1.00189 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.482152 | −0.0157596 | ||||||||
\(937\) | −41.7570 | −1.36414 | −0.682071 | − | 0.731286i | \(-0.738920\pi\) | ||||
−0.682071 | + | 0.731286i | \(0.738920\pi\) | |||||||
\(938\) | 1.03547 | 0.0338094 | ||||||||
\(939\) | −11.2478 | −0.367059 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.8232 | −0.744014 | −0.372007 | − | 0.928230i | \(-0.621330\pi\) | ||||
−0.372007 | + | 0.928230i | \(0.621330\pi\) | |||||||
\(942\) | 22.8284 | 0.743789 | ||||||||
\(943\) | −81.3903 | −2.65043 | ||||||||
\(944\) | 1.01583 | 0.0330625 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.4618 | 0.405167 | ||||||||
\(947\) | 8.46744 | 0.275155 | 0.137577 | − | 0.990491i | \(-0.456068\pi\) | ||||
0.137577 | + | 0.990491i | \(0.456068\pi\) | |||||||
\(948\) | −8.48510 | −0.275583 | ||||||||
\(949\) | −1.41882 | −0.0460569 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.2917 | −0.755284 | ||||||||
\(952\) | 2.23476 | 0.0724291 | ||||||||
\(953\) | −24.8878 | −0.806195 | −0.403097 | − | 0.915157i | \(-0.632066\pi\) | ||||
−0.403097 | + | 0.915157i | \(0.632066\pi\) | |||||||
\(954\) | −1.68591 | −0.0545834 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −16.8733 | −0.545723 | ||||||||
\(957\) | −30.3119 | −0.979845 | ||||||||
\(958\) | 1.17289 | 0.0378943 | ||||||||
\(959\) | 2.20267 | 0.0711278 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.2610 | −0.943905 | ||||||||
\(962\) | 0.376146 | 0.0121274 | ||||||||
\(963\) | 15.3340 | 0.494130 | ||||||||
\(964\) | 20.6256 | 0.664306 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.14073 | −0.0688768 | ||||||||
\(967\) | 22.1247 | 0.711483 | 0.355742 | − | 0.934584i | \(-0.384228\pi\) | ||||
0.355742 | + | 0.934584i | \(0.384228\pi\) | |||||||
\(968\) | −14.3350 | −0.460746 | ||||||||
\(969\) | 36.9172 | 1.18595 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.0050 | −0.545716 | −0.272858 | − | 0.962054i | \(-0.587969\pi\) | ||||
−0.272858 | + | 0.962054i | \(0.587969\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −1.01363 | −0.0324954 | ||||||||
\(974\) | 11.7556 | 0.376672 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.18808 | 0.134057 | ||||||||
\(977\) | −41.3030 | −1.32140 | −0.660701 | − | 0.750650i | \(-0.729741\pi\) | ||||
−0.660701 | + | 0.750650i | \(0.729741\pi\) | |||||||
\(978\) | −7.95823 | −0.254476 | ||||||||
\(979\) | −17.3769 | −0.555369 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.76027 | −0.311622 | ||||||||
\(982\) | −4.13052 | −0.131810 | ||||||||
\(983\) | −61.9160 | −1.97481 | −0.987407 | − | 0.158199i | \(-0.949431\pi\) | ||||
−0.987407 | + | 0.158199i | \(0.949431\pi\) | |||||||
\(984\) | 12.5205 | 0.399140 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −40.8670 | −1.30147 | ||||||||
\(987\) | −1.44253 | −0.0459162 | ||||||||
\(988\) | 2.62297 | 0.0834477 | ||||||||
\(989\) | −16.0942 | −0.511765 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.93098 | 0.156638 | 0.0783188 | − | 0.996928i | \(-0.475045\pi\) | ||||
0.0783188 | + | 0.996928i | \(0.475045\pi\) | |||||||
\(992\) | −1.31869 | −0.0418686 | ||||||||
\(993\) | −0.129334 | −0.00410428 | ||||||||
\(994\) | −1.88101 | −0.0596620 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 17.1955 | 0.544860 | ||||||||
\(997\) | 49.5596 | 1.56957 | 0.784784 | − | 0.619769i | \(-0.212774\pi\) | ||||
0.784784 | + | 0.619769i | \(0.212774\pi\) | |||||||
\(998\) | −9.59154 | −0.303615 | ||||||||
\(999\) | 0.780139 | 0.0246825 |
(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 | 3750.2.a.u.1.5 | 8 | ||
5.2 | odd | 4 | 3750.2.c.k.1249.5 | 16 | |||
5.3 | odd | 4 | 3750.2.c.k.1249.12 | 16 | |||
5.4 | even | 2 | 3750.2.a.v.1.4 | 8 | |||
25.2 | odd | 20 | 750.2.h.d.649.2 | 16 | |||
25.9 | even | 10 | 750.2.g.f.151.2 | 16 | |||
25.11 | even | 5 | 750.2.g.g.601.3 | 16 | |||
25.12 | odd | 20 | 150.2.h.b.19.4 | ✓ | 16 | ||
25.13 | odd | 20 | 750.2.h.d.349.1 | 16 | |||
25.14 | even | 10 | 750.2.g.f.601.2 | 16 | |||
25.16 | even | 5 | 750.2.g.g.151.3 | 16 | |||
25.23 | odd | 20 | 150.2.h.b.79.4 | yes | 16 | ||
75.23 | even | 20 | 450.2.l.c.379.1 | 16 | |||
75.62 | even | 20 | 450.2.l.c.19.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.h.b.19.4 | ✓ | 16 | 25.12 | odd | 20 | ||
150.2.h.b.79.4 | yes | 16 | 25.23 | odd | 20 | ||
450.2.l.c.19.1 | 16 | 75.62 | even | 20 | |||
450.2.l.c.379.1 | 16 | 75.23 | even | 20 | |||
750.2.g.f.151.2 | 16 | 25.9 | even | 10 | |||
750.2.g.f.601.2 | 16 | 25.14 | even | 10 | |||
750.2.g.g.151.3 | 16 | 25.16 | even | 5 | |||
750.2.g.g.601.3 | 16 | 25.11 | even | 5 | |||
750.2.h.d.349.1 | 16 | 25.13 | odd | 20 | |||
750.2.h.d.649.2 | 16 | 25.2 | odd | 20 | |||
3750.2.a.u.1.5 | 8 | 1.1 | even | 1 | trivial | ||
3750.2.a.v.1.4 | 8 | 5.4 | even | 2 | |||
3750.2.c.k.1249.5 | 16 | 5.2 | odd | 4 | |||
3750.2.c.k.1249.12 | 16 | 5.3 | odd | 4 |