Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, 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("1875.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(14.9719503790\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.5444000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 2x^{6} + 20x^{5} - 4x^{4} - 30x^{3} + 7x^{2} + 12x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.08982\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0898194 | 0.0635119 | 0.0317560 | − | 0.999496i | \(-0.489890\pi\) | ||||
0.0317560 | + | 0.999496i | \(0.489890\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.99193 | −0.995966 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0898194 | 0.0366686 | ||||||||
\(7\) | −4.36070 | −1.64819 | −0.824095 | − | 0.566451i | \(-0.808316\pi\) | ||||
−0.824095 | + | 0.566451i | \(0.808316\pi\) | |||||||
\(8\) | −0.358553 | −0.126768 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.39094 | 1.32392 | 0.661959 | − | 0.749540i | \(-0.269725\pi\) | ||||
0.661959 | + | 0.749540i | \(0.269725\pi\) | |||||||
\(12\) | −1.99193 | −0.575021 | ||||||||
\(13\) | 1.98166 | 0.549612 | 0.274806 | − | 0.961500i | \(-0.411386\pi\) | ||||
0.274806 | + | 0.961500i | \(0.411386\pi\) | |||||||
\(14\) | −0.391676 | −0.104680 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.95166 | 0.987915 | ||||||||
\(17\) | −0.997022 | −0.241813 | −0.120907 | − | 0.992664i | \(-0.538580\pi\) | ||||
−0.120907 | + | 0.992664i | \(0.538580\pi\) | |||||||
\(18\) | 0.0898194 | 0.0211706 | ||||||||
\(19\) | 1.35096 | 0.309931 | 0.154965 | − | 0.987920i | \(-0.450473\pi\) | ||||
0.154965 | + | 0.987920i | \(0.450473\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.36070 | −0.951583 | ||||||||
\(22\) | 0.394392 | 0.0840846 | ||||||||
\(23\) | −2.35651 | −0.491366 | −0.245683 | − | 0.969350i | \(-0.579012\pi\) | ||||
−0.245683 | + | 0.969350i | \(0.579012\pi\) | |||||||
\(24\) | −0.358553 | −0.0731893 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.177991 | 0.0349069 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 8.68622 | 1.64154 | ||||||||
\(29\) | −7.97856 | −1.48158 | −0.740790 | − | 0.671736i | \(-0.765549\pi\) | ||||
−0.740790 | + | 0.671736i | \(0.765549\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.67761 | −0.660519 | −0.330259 | − | 0.943890i | \(-0.607136\pi\) | ||||
−0.330259 | + | 0.943890i | \(0.607136\pi\) | |||||||
\(32\) | 1.07204 | 0.189512 | ||||||||
\(33\) | 4.39094 | 0.764365 | ||||||||
\(34\) | −0.0895519 | −0.0153580 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.99193 | −0.331989 | ||||||||
\(37\) | 1.43706 | 0.236251 | 0.118125 | − | 0.992999i | \(-0.462312\pi\) | ||||
0.118125 | + | 0.992999i | \(0.462312\pi\) | |||||||
\(38\) | 0.121342 | 0.0196843 | ||||||||
\(39\) | 1.98166 | 0.317319 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.98248 | −0.934306 | −0.467153 | − | 0.884177i | \(-0.654720\pi\) | ||||
−0.467153 | + | 0.884177i | \(0.654720\pi\) | |||||||
\(42\) | −0.391676 | −0.0604369 | ||||||||
\(43\) | −2.68554 | −0.409541 | −0.204770 | − | 0.978810i | \(-0.565645\pi\) | ||||
−0.204770 | + | 0.978810i | \(0.565645\pi\) | |||||||
\(44\) | −8.74646 | −1.31858 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.211660 | −0.0312076 | ||||||||
\(47\) | −10.9393 | −1.59566 | −0.797829 | − | 0.602883i | \(-0.794018\pi\) | ||||
−0.797829 | + | 0.602883i | \(0.794018\pi\) | |||||||
\(48\) | 3.95166 | 0.570373 | ||||||||
\(49\) | 12.0157 | 1.71653 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.997022 | −0.139611 | ||||||||
\(52\) | −3.94732 | −0.547395 | ||||||||
\(53\) | −11.0510 | −1.51798 | −0.758989 | − | 0.651104i | \(-0.774306\pi\) | ||||
−0.758989 | + | 0.651104i | \(0.774306\pi\) | |||||||
\(54\) | 0.0898194 | 0.0122229 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.56354 | 0.208937 | ||||||||
\(57\) | 1.35096 | 0.178938 | ||||||||
\(58\) | −0.716629 | −0.0940980 | ||||||||
\(59\) | 6.68895 | 0.870827 | 0.435414 | − | 0.900231i | \(-0.356602\pi\) | ||||
0.435414 | + | 0.900231i | \(0.356602\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.45570 | −1.21068 | −0.605339 | − | 0.795967i | \(-0.706963\pi\) | ||||
−0.605339 | + | 0.795967i | \(0.706963\pi\) | |||||||
\(62\) | −0.330321 | −0.0419508 | ||||||||
\(63\) | −4.36070 | −0.549397 | ||||||||
\(64\) | −7.80703 | −0.975879 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.394392 | 0.0485463 | ||||||||
\(67\) | −12.9219 | −1.57866 | −0.789328 | − | 0.613972i | \(-0.789571\pi\) | ||||
−0.789328 | + | 0.613972i | \(0.789571\pi\) | |||||||
\(68\) | 1.98600 | 0.240838 | ||||||||
\(69\) | −2.35651 | −0.283690 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.32257 | 0.869029 | 0.434515 | − | 0.900665i | \(-0.356920\pi\) | ||||
0.434515 | + | 0.900665i | \(0.356920\pi\) | |||||||
\(72\) | −0.358553 | −0.0422559 | ||||||||
\(73\) | 0.424804 | 0.0497195 | 0.0248598 | − | 0.999691i | \(-0.492086\pi\) | ||||
0.0248598 | + | 0.999691i | \(0.492086\pi\) | |||||||
\(74\) | 0.129076 | 0.0150047 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.69101 | −0.308680 | ||||||||
\(77\) | −19.1476 | −2.18207 | ||||||||
\(78\) | 0.177991 | 0.0201535 | ||||||||
\(79\) | −6.35531 | −0.715028 | −0.357514 | − | 0.933908i | \(-0.616376\pi\) | ||||
−0.357514 | + | 0.933908i | \(0.616376\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.537343 | −0.0593396 | ||||||||
\(83\) | −0.737011 | −0.0808975 | −0.0404487 | − | 0.999182i | \(-0.512879\pi\) | ||||
−0.0404487 | + | 0.999182i | \(0.512879\pi\) | |||||||
\(84\) | 8.68622 | 0.947745 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.241213 | −0.0260107 | ||||||||
\(87\) | −7.97856 | −0.855391 | ||||||||
\(88\) | −1.57439 | −0.167830 | ||||||||
\(89\) | −9.78736 | −1.03746 | −0.518729 | − | 0.854939i | \(-0.673595\pi\) | ||||
−0.518729 | + | 0.854939i | \(0.673595\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.64141 | −0.905866 | ||||||||
\(92\) | 4.69401 | 0.489384 | ||||||||
\(93\) | −3.67761 | −0.381351 | ||||||||
\(94\) | −0.982560 | −0.101343 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.07204 | 0.109415 | ||||||||
\(97\) | −0.0337081 | −0.00342254 | −0.00171127 | − | 0.999999i | \(-0.500545\pi\) | ||||
−0.00171127 | + | 0.999999i | \(0.500545\pi\) | |||||||
\(98\) | 1.07925 | 0.109020 | ||||||||
\(99\) | 4.39094 | 0.441306 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.19390 | 0.317805 | 0.158902 | − | 0.987294i | \(-0.449204\pi\) | ||||
0.158902 | + | 0.987294i | \(0.449204\pi\) | |||||||
\(102\) | −0.0895519 | −0.00886696 | ||||||||
\(103\) | −8.55342 | −0.842794 | −0.421397 | − | 0.906876i | \(-0.638460\pi\) | ||||
−0.421397 | + | 0.906876i | \(0.638460\pi\) | |||||||
\(104\) | −0.710529 | −0.0696731 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.992598 | −0.0964097 | ||||||||
\(107\) | −2.22136 | −0.214747 | −0.107373 | − | 0.994219i | \(-0.534244\pi\) | ||||
−0.107373 | + | 0.994219i | \(0.534244\pi\) | |||||||
\(108\) | −1.99193 | −0.191674 | ||||||||
\(109\) | 11.0023 | 1.05383 | 0.526916 | − | 0.849917i | \(-0.323348\pi\) | ||||
0.526916 | + | 0.849917i | \(0.323348\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.43706 | 0.136399 | ||||||||
\(112\) | −17.2320 | −1.62827 | ||||||||
\(113\) | −1.71021 | −0.160883 | −0.0804415 | − | 0.996759i | \(-0.525633\pi\) | ||||
−0.0804415 | + | 0.996759i | \(0.525633\pi\) | |||||||
\(114\) | 0.121342 | 0.0113647 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 15.8927 | 1.47560 | ||||||||
\(117\) | 1.98166 | 0.183204 | ||||||||
\(118\) | 0.600798 | 0.0553079 | ||||||||
\(119\) | 4.34771 | 0.398554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.28037 | 0.752761 | ||||||||
\(122\) | −0.849306 | −0.0768925 | ||||||||
\(123\) | −5.98248 | −0.539422 | ||||||||
\(124\) | 7.32556 | 0.657855 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.391676 | −0.0348933 | ||||||||
\(127\) | 12.5570 | 1.11425 | 0.557125 | − | 0.830429i | \(-0.311905\pi\) | ||||
0.557125 | + | 0.830429i | \(0.311905\pi\) | |||||||
\(128\) | −2.84531 | −0.251492 | ||||||||
\(129\) | −2.68554 | −0.236448 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.4718 | 1.43915 | 0.719574 | − | 0.694416i | \(-0.244337\pi\) | ||||
0.719574 | + | 0.694416i | \(0.244337\pi\) | |||||||
\(132\) | −8.74646 | −0.761282 | ||||||||
\(133\) | −5.89112 | −0.510825 | ||||||||
\(134\) | −1.16063 | −0.100263 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.357485 | 0.0306541 | ||||||||
\(137\) | 9.66732 | 0.825935 | 0.412967 | − | 0.910746i | \(-0.364492\pi\) | ||||
0.412967 | + | 0.910746i | \(0.364492\pi\) | |||||||
\(138\) | −0.211660 | −0.0180177 | ||||||||
\(139\) | 13.5327 | 1.14783 | 0.573913 | − | 0.818916i | \(-0.305425\pi\) | ||||
0.573913 | + | 0.818916i | \(0.305425\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.9393 | −0.921254 | ||||||||
\(142\) | 0.657709 | 0.0551937 | ||||||||
\(143\) | 8.70133 | 0.727642 | ||||||||
\(144\) | 3.95166 | 0.329305 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.0381557 | 0.00315778 | ||||||||
\(147\) | 12.0157 | 0.991040 | ||||||||
\(148\) | −2.86252 | −0.235298 | ||||||||
\(149\) | 13.6843 | 1.12106 | 0.560529 | − | 0.828134i | \(-0.310598\pi\) | ||||
0.560529 | + | 0.828134i | \(0.310598\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.3204 | −0.921237 | −0.460619 | − | 0.887598i | \(-0.652372\pi\) | ||||
−0.460619 | + | 0.887598i | \(0.652372\pi\) | |||||||
\(152\) | −0.484389 | −0.0392892 | ||||||||
\(153\) | −0.997022 | −0.0806044 | ||||||||
\(154\) | −1.71983 | −0.138587 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.94732 | −0.316039 | ||||||||
\(157\) | −8.56070 | −0.683219 | −0.341609 | − | 0.939842i | \(-0.610972\pi\) | ||||
−0.341609 | + | 0.939842i | \(0.610972\pi\) | |||||||
\(158\) | −0.570830 | −0.0454128 | ||||||||
\(159\) | −11.0510 | −0.876405 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.2760 | 0.809865 | ||||||||
\(162\) | 0.0898194 | 0.00705688 | ||||||||
\(163\) | −4.58509 | −0.359132 | −0.179566 | − | 0.983746i | \(-0.557469\pi\) | ||||
−0.179566 | + | 0.983746i | \(0.557469\pi\) | |||||||
\(164\) | 11.9167 | 0.930537 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.0661979 | −0.00513795 | ||||||||
\(167\) | −7.21792 | −0.558540 | −0.279270 | − | 0.960213i | \(-0.590092\pi\) | ||||
−0.279270 | + | 0.960213i | \(0.590092\pi\) | |||||||
\(168\) | 1.56354 | 0.120630 | ||||||||
\(169\) | −9.07304 | −0.697926 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.35096 | 0.103310 | ||||||||
\(172\) | 5.34941 | 0.407889 | ||||||||
\(173\) | 4.65009 | 0.353540 | 0.176770 | − | 0.984252i | \(-0.443435\pi\) | ||||
0.176770 | + | 0.984252i | \(0.443435\pi\) | |||||||
\(174\) | −0.716629 | −0.0543275 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 17.3515 | 1.30792 | ||||||||
\(177\) | 6.68895 | 0.502772 | ||||||||
\(178\) | −0.879095 | −0.0658909 | ||||||||
\(179\) | −7.20338 | −0.538406 | −0.269203 | − | 0.963083i | \(-0.586760\pi\) | ||||
−0.269203 | + | 0.963083i | \(0.586760\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.80424 | −0.282767 | −0.141383 | − | 0.989955i | \(-0.545155\pi\) | ||||
−0.141383 | + | 0.989955i | \(0.545155\pi\) | |||||||
\(182\) | −0.776167 | −0.0575333 | ||||||||
\(183\) | −9.45570 | −0.698986 | ||||||||
\(184\) | 0.844934 | 0.0622893 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.330321 | −0.0242203 | ||||||||
\(187\) | −4.37786 | −0.320141 | ||||||||
\(188\) | 21.7903 | 1.58922 | ||||||||
\(189\) | −4.36070 | −0.317194 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.5541 | 1.55960 | 0.779801 | − | 0.626027i | \(-0.215320\pi\) | ||||
0.779801 | + | 0.626027i | \(0.215320\pi\) | |||||||
\(192\) | −7.80703 | −0.563424 | ||||||||
\(193\) | −3.15029 | −0.226763 | −0.113381 | − | 0.993552i | \(-0.536168\pi\) | ||||
−0.113381 | + | 0.993552i | \(0.536168\pi\) | |||||||
\(194\) | −0.00302764 | −0.000217372 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −23.9345 | −1.70961 | ||||||||
\(197\) | −26.0837 | −1.85839 | −0.929195 | − | 0.369590i | \(-0.879498\pi\) | ||||
−0.929195 | + | 0.369590i | \(0.879498\pi\) | |||||||
\(198\) | 0.394392 | 0.0280282 | ||||||||
\(199\) | −24.2662 | −1.72018 | −0.860092 | − | 0.510139i | \(-0.829594\pi\) | ||||
−0.860092 | + | 0.510139i | \(0.829594\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.9219 | −0.911437 | ||||||||
\(202\) | 0.286874 | 0.0201844 | ||||||||
\(203\) | 34.7921 | 2.44193 | ||||||||
\(204\) | 1.98600 | 0.139048 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.768264 | −0.0535275 | ||||||||
\(207\) | −2.35651 | −0.163789 | ||||||||
\(208\) | 7.83083 | 0.542970 | ||||||||
\(209\) | 5.93197 | 0.410323 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.3783 | 1.12753 | 0.563765 | − | 0.825935i | \(-0.309352\pi\) | ||||
0.563765 | + | 0.825935i | \(0.309352\pi\) | |||||||
\(212\) | 22.0129 | 1.51185 | ||||||||
\(213\) | 7.32257 | 0.501734 | ||||||||
\(214\) | −0.199521 | −0.0136390 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.358553 | −0.0243964 | ||||||||
\(217\) | 16.0370 | 1.08866 | ||||||||
\(218\) | 0.988224 | 0.0669310 | ||||||||
\(219\) | 0.424804 | 0.0287056 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.97575 | −0.132904 | ||||||||
\(222\) | 0.129076 | 0.00866299 | ||||||||
\(223\) | 5.68295 | 0.380558 | 0.190279 | − | 0.981730i | \(-0.439061\pi\) | ||||
0.190279 | + | 0.981730i | \(0.439061\pi\) | |||||||
\(224\) | −4.67486 | −0.312352 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.153610 | −0.0102180 | ||||||||
\(227\) | −3.64374 | −0.241844 | −0.120922 | − | 0.992662i | \(-0.538585\pi\) | ||||
−0.120922 | + | 0.992662i | \(0.538585\pi\) | |||||||
\(228\) | −2.69101 | −0.178217 | ||||||||
\(229\) | 1.66125 | 0.109779 | 0.0548893 | − | 0.998492i | \(-0.482519\pi\) | ||||
0.0548893 | + | 0.998492i | \(0.482519\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.1476 | −1.25982 | ||||||||
\(232\) | 2.86074 | 0.187817 | ||||||||
\(233\) | −7.85899 | −0.514860 | −0.257430 | − | 0.966297i | \(-0.582876\pi\) | ||||
−0.257430 | + | 0.966297i | \(0.582876\pi\) | |||||||
\(234\) | 0.177991 | 0.0116356 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.3239 | −0.867314 | ||||||||
\(237\) | −6.35531 | −0.412821 | ||||||||
\(238\) | 0.390509 | 0.0253130 | ||||||||
\(239\) | −0.567301 | −0.0366956 | −0.0183478 | − | 0.999832i | \(-0.505841\pi\) | ||||
−0.0183478 | + | 0.999832i | \(0.505841\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.0081 | −1.22442 | −0.612211 | − | 0.790695i | \(-0.709720\pi\) | ||||
−0.612211 | + | 0.790695i | \(0.709720\pi\) | |||||||
\(242\) | 0.743738 | 0.0478093 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 18.8351 | 1.20580 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.537343 | −0.0342597 | ||||||||
\(247\) | 2.67713 | 0.170342 | ||||||||
\(248\) | 1.31862 | 0.0837324 | ||||||||
\(249\) | −0.737011 | −0.0467062 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.02533 | 0.190957 | 0.0954787 | − | 0.995431i | \(-0.469562\pi\) | ||||
0.0954787 | + | 0.995431i | \(0.469562\pi\) | |||||||
\(252\) | 8.68622 | 0.547181 | ||||||||
\(253\) | −10.3473 | −0.650529 | ||||||||
\(254\) | 1.12786 | 0.0707681 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.3585 | 0.959906 | ||||||||
\(257\) | 19.8613 | 1.23891 | 0.619456 | − | 0.785032i | \(-0.287353\pi\) | ||||
0.619456 | + | 0.785032i | \(0.287353\pi\) | |||||||
\(258\) | −0.241213 | −0.0150173 | ||||||||
\(259\) | −6.26658 | −0.389386 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.97856 | −0.493860 | ||||||||
\(262\) | 1.47949 | 0.0914030 | ||||||||
\(263\) | −22.8299 | −1.40775 | −0.703876 | − | 0.710323i | \(-0.748549\pi\) | ||||
−0.703876 | + | 0.710323i | \(0.748549\pi\) | |||||||
\(264\) | −1.57439 | −0.0968968 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.529137 | −0.0324435 | ||||||||
\(267\) | −9.78736 | −0.598977 | ||||||||
\(268\) | 25.7395 | 1.57229 | ||||||||
\(269\) | 14.8324 | 0.904347 | 0.452174 | − | 0.891930i | \(-0.350649\pi\) | ||||
0.452174 | + | 0.891930i | \(0.350649\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.43720 | −0.391032 | −0.195516 | − | 0.980701i | \(-0.562638\pi\) | ||||
−0.195516 | + | 0.980701i | \(0.562638\pi\) | |||||||
\(272\) | −3.93989 | −0.238891 | ||||||||
\(273\) | −8.64141 | −0.523002 | ||||||||
\(274\) | 0.868313 | 0.0524567 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.69401 | 0.282546 | ||||||||
\(277\) | −6.70976 | −0.403150 | −0.201575 | − | 0.979473i | \(-0.564606\pi\) | ||||
−0.201575 | + | 0.979473i | \(0.564606\pi\) | |||||||
\(278\) | 1.21550 | 0.0729006 | ||||||||
\(279\) | −3.67761 | −0.220173 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.4867 | −1.22214 | −0.611068 | − | 0.791578i | \(-0.709260\pi\) | ||||
−0.611068 | + | 0.791578i | \(0.709260\pi\) | |||||||
\(282\) | −0.982560 | −0.0585106 | ||||||||
\(283\) | 11.4177 | 0.678715 | 0.339357 | − | 0.940658i | \(-0.389790\pi\) | ||||
0.339357 | + | 0.940658i | \(0.389790\pi\) | |||||||
\(284\) | −14.5861 | −0.865524 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.781549 | 0.0462140 | ||||||||
\(287\) | 26.0878 | 1.53991 | ||||||||
\(288\) | 1.07204 | 0.0631707 | ||||||||
\(289\) | −16.0059 | −0.941526 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.0337081 | −0.00197600 | ||||||||
\(292\) | −0.846181 | −0.0495190 | ||||||||
\(293\) | −28.5505 | −1.66794 | −0.833968 | − | 0.551812i | \(-0.813937\pi\) | ||||
−0.833968 | + | 0.551812i | \(0.813937\pi\) | |||||||
\(294\) | 1.07925 | 0.0629429 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.515261 | −0.0299489 | ||||||||
\(297\) | 4.39094 | 0.254788 | ||||||||
\(298\) | 1.22911 | 0.0712006 | ||||||||
\(299\) | −4.66979 | −0.270061 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.7108 | 0.675001 | ||||||||
\(302\) | −1.01679 | −0.0585095 | ||||||||
\(303\) | 3.19390 | 0.183485 | ||||||||
\(304\) | 5.33852 | 0.306185 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.0895519 | −0.00511934 | ||||||||
\(307\) | 20.5417 | 1.17238 | 0.586188 | − | 0.810175i | \(-0.300628\pi\) | ||||
0.586188 | + | 0.810175i | \(0.300628\pi\) | |||||||
\(308\) | 38.1407 | 2.17327 | ||||||||
\(309\) | −8.55342 | −0.486587 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.5496 | 0.995146 | 0.497573 | − | 0.867422i | \(-0.334225\pi\) | ||||
0.497573 | + | 0.867422i | \(0.334225\pi\) | |||||||
\(312\) | −0.710529 | −0.0402258 | ||||||||
\(313\) | 2.98564 | 0.168758 | 0.0843790 | − | 0.996434i | \(-0.473109\pi\) | ||||
0.0843790 | + | 0.996434i | \(0.473109\pi\) | |||||||
\(314\) | −0.768918 | −0.0433925 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.6593 | 0.712143 | ||||||||
\(317\) | 16.1708 | 0.908244 | 0.454122 | − | 0.890940i | \(-0.349953\pi\) | ||||
0.454122 | + | 0.890940i | \(0.349953\pi\) | |||||||
\(318\) | −0.992598 | −0.0556621 | ||||||||
\(319\) | −35.0334 | −1.96149 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.22136 | −0.123984 | ||||||||
\(322\) | 0.922988 | 0.0514361 | ||||||||
\(323\) | −1.34693 | −0.0749453 | ||||||||
\(324\) | −1.99193 | −0.110663 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.411830 | −0.0228092 | ||||||||
\(327\) | 11.0023 | 0.608431 | ||||||||
\(328\) | 2.14504 | 0.118440 | ||||||||
\(329\) | 47.7030 | 2.62995 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0705 | −0.718418 | −0.359209 | − | 0.933257i | \(-0.616953\pi\) | ||||
−0.359209 | + | 0.933257i | \(0.616953\pi\) | |||||||
\(332\) | 1.46808 | 0.0805711 | ||||||||
\(333\) | 1.43706 | 0.0787502 | ||||||||
\(334\) | −0.648310 | −0.0354739 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −17.2320 | −0.940083 | ||||||||
\(337\) | −26.8049 | −1.46015 | −0.730077 | − | 0.683365i | \(-0.760516\pi\) | ||||
−0.730077 | + | 0.683365i | \(0.760516\pi\) | |||||||
\(338\) | −0.814935 | −0.0443266 | ||||||||
\(339\) | −1.71021 | −0.0928858 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.1482 | −0.874473 | ||||||||
\(342\) | 0.121342 | 0.00656143 | ||||||||
\(343\) | −21.8721 | −1.18098 | ||||||||
\(344\) | 0.962908 | 0.0519165 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.417669 | 0.0224540 | ||||||||
\(347\) | 25.4859 | 1.36815 | 0.684077 | − | 0.729410i | \(-0.260205\pi\) | ||||
0.684077 | + | 0.729410i | \(0.260205\pi\) | |||||||
\(348\) | 15.8927 | 0.851941 | ||||||||
\(349\) | −28.0435 | −1.50113 | −0.750566 | − | 0.660795i | \(-0.770219\pi\) | ||||
−0.750566 | + | 0.660795i | \(0.770219\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.98166 | 0.105773 | ||||||||
\(352\) | 4.70727 | 0.250899 | ||||||||
\(353\) | −14.6667 | −0.780630 | −0.390315 | − | 0.920681i | \(-0.627634\pi\) | ||||
−0.390315 | + | 0.920681i | \(0.627634\pi\) | |||||||
\(354\) | 0.600798 | 0.0319320 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 19.4958 | 1.03327 | ||||||||
\(357\) | 4.34771 | 0.230105 | ||||||||
\(358\) | −0.647004 | −0.0341952 | ||||||||
\(359\) | −14.6205 | −0.771642 | −0.385821 | − | 0.922574i | \(-0.626082\pi\) | ||||
−0.385821 | + | 0.922574i | \(0.626082\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1749 | −0.903943 | ||||||||
\(362\) | −0.341694 | −0.0179591 | ||||||||
\(363\) | 8.28037 | 0.434607 | ||||||||
\(364\) | 17.2131 | 0.902212 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.849306 | −0.0443939 | ||||||||
\(367\) | 17.6940 | 0.923617 | 0.461808 | − | 0.886980i | \(-0.347201\pi\) | ||||
0.461808 | + | 0.886980i | \(0.347201\pi\) | |||||||
\(368\) | −9.31212 | −0.485428 | ||||||||
\(369\) | −5.98248 | −0.311435 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 48.1903 | 2.50192 | ||||||||
\(372\) | 7.32556 | 0.379813 | ||||||||
\(373\) | −12.2293 | −0.633210 | −0.316605 | − | 0.948557i | \(-0.602543\pi\) | ||||
−0.316605 | + | 0.948557i | \(0.602543\pi\) | |||||||
\(374\) | −0.393217 | −0.0203328 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.92231 | 0.202278 | ||||||||
\(377\) | −15.8107 | −0.814295 | ||||||||
\(378\) | −0.391676 | −0.0201456 | ||||||||
\(379\) | 28.0951 | 1.44315 | 0.721574 | − | 0.692338i | \(-0.243419\pi\) | ||||
0.721574 | + | 0.692338i | \(0.243419\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.5570 | 0.643312 | ||||||||
\(382\) | 1.93598 | 0.0990533 | ||||||||
\(383\) | −34.4334 | −1.75947 | −0.879733 | − | 0.475468i | \(-0.842279\pi\) | ||||
−0.879733 | + | 0.475468i | \(0.842279\pi\) | |||||||
\(384\) | −2.84531 | −0.145199 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.282957 | −0.0144021 | ||||||||
\(387\) | −2.68554 | −0.136514 | ||||||||
\(388\) | 0.0671442 | 0.00340873 | ||||||||
\(389\) | 13.5225 | 0.685619 | 0.342809 | − | 0.939405i | \(-0.388622\pi\) | ||||
0.342809 | + | 0.939405i | \(0.388622\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.34949 | 0.118819 | ||||||||
\(392\) | −4.30827 | −0.217601 | ||||||||
\(393\) | 16.4718 | 0.830892 | ||||||||
\(394\) | −2.34283 | −0.118030 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.74646 | −0.439526 | ||||||||
\(397\) | 35.9744 | 1.80550 | 0.902751 | − | 0.430164i | \(-0.141544\pi\) | ||||
0.902751 | + | 0.430164i | \(0.141544\pi\) | |||||||
\(398\) | −2.17958 | −0.109252 | ||||||||
\(399\) | −5.89112 | −0.294925 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.35977 | 0.217717 | 0.108858 | − | 0.994057i | \(-0.465281\pi\) | ||||
0.108858 | + | 0.994057i | \(0.465281\pi\) | |||||||
\(402\) | −1.16063 | −0.0578871 | ||||||||
\(403\) | −7.28776 | −0.363029 | ||||||||
\(404\) | −6.36203 | −0.316523 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.12501 | 0.155092 | ||||||||
\(407\) | 6.31003 | 0.312777 | ||||||||
\(408\) | 0.357485 | 0.0176982 | ||||||||
\(409\) | −18.1138 | −0.895668 | −0.447834 | − | 0.894117i | \(-0.647804\pi\) | ||||
−0.447834 | + | 0.894117i | \(0.647804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.66732 | 0.476854 | ||||||||
\(412\) | 17.0378 | 0.839394 | ||||||||
\(413\) | −29.1685 | −1.43529 | ||||||||
\(414\) | −0.211660 | −0.0104025 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.12442 | 0.104158 | ||||||||
\(417\) | 13.5327 | 0.662698 | ||||||||
\(418\) | 0.532806 | 0.0260604 | ||||||||
\(419\) | 0.527867 | 0.0257880 | 0.0128940 | − | 0.999917i | \(-0.495896\pi\) | ||||
0.0128940 | + | 0.999917i | \(0.495896\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.6586 | 0.909365 | 0.454682 | − | 0.890654i | \(-0.349753\pi\) | ||||
0.454682 | + | 0.890654i | \(0.349753\pi\) | |||||||
\(422\) | 1.47109 | 0.0716117 | ||||||||
\(423\) | −10.9393 | −0.531886 | ||||||||
\(424\) | 3.96239 | 0.192430 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.657709 | 0.0318661 | ||||||||
\(427\) | 41.2335 | 1.99543 | ||||||||
\(428\) | 4.42480 | 0.213881 | ||||||||
\(429\) | 8.70133 | 0.420104 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.9913 | 1.01112 | 0.505559 | − | 0.862792i | \(-0.331286\pi\) | ||||
0.505559 | + | 0.862792i | \(0.331286\pi\) | |||||||
\(432\) | 3.95166 | 0.190124 | ||||||||
\(433\) | 13.6639 | 0.656647 | 0.328324 | − | 0.944565i | \(-0.393516\pi\) | ||||
0.328324 | + | 0.944565i | \(0.393516\pi\) | |||||||
\(434\) | 1.44043 | 0.0691430 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −21.9159 | −1.04958 | ||||||||
\(437\) | −3.18354 | −0.152289 | ||||||||
\(438\) | 0.0381557 | 0.00182315 | ||||||||
\(439\) | −4.33339 | −0.206821 | −0.103411 | − | 0.994639i | \(-0.532976\pi\) | ||||
−0.103411 | + | 0.994639i | \(0.532976\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.0157 | 0.572177 | ||||||||
\(442\) | −0.177461 | −0.00844096 | ||||||||
\(443\) | 1.60742 | 0.0763707 | 0.0381854 | − | 0.999271i | \(-0.487842\pi\) | ||||
0.0381854 | + | 0.999271i | \(0.487842\pi\) | |||||||
\(444\) | −2.86252 | −0.135849 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.510439 | 0.0241700 | ||||||||
\(447\) | 13.6843 | 0.647244 | ||||||||
\(448\) | 34.0441 | 1.60843 | ||||||||
\(449\) | −13.8291 | −0.652634 | −0.326317 | − | 0.945260i | \(-0.605808\pi\) | ||||
−0.326317 | + | 0.945260i | \(0.605808\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.2687 | −1.23694 | ||||||||
\(452\) | 3.40662 | 0.160234 | ||||||||
\(453\) | −11.3204 | −0.531876 | ||||||||
\(454\) | −0.327279 | −0.0153600 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.484389 | −0.0226836 | ||||||||
\(457\) | −20.1345 | −0.941850 | −0.470925 | − | 0.882173i | \(-0.656080\pi\) | ||||
−0.470925 | + | 0.882173i | \(0.656080\pi\) | |||||||
\(458\) | 0.149213 | 0.00697225 | ||||||||
\(459\) | −0.997022 | −0.0465370 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.5264 | 1.46833 | 0.734166 | − | 0.678970i | \(-0.237573\pi\) | ||||
0.734166 | + | 0.678970i | \(0.237573\pi\) | |||||||
\(462\) | −1.71983 | −0.0800135 | ||||||||
\(463\) | 0.0451697 | 0.00209921 | 0.00104961 | − | 0.999999i | \(-0.499666\pi\) | ||||
0.00104961 | + | 0.999999i | \(0.499666\pi\) | |||||||
\(464\) | −31.5285 | −1.46368 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.705890 | −0.0326997 | ||||||||
\(467\) | 32.8349 | 1.51942 | 0.759708 | − | 0.650265i | \(-0.225342\pi\) | ||||
0.759708 | + | 0.650265i | \(0.225342\pi\) | |||||||
\(468\) | −3.94732 | −0.182465 | ||||||||
\(469\) | 56.3484 | 2.60193 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.56070 | −0.394456 | ||||||||
\(472\) | −2.39834 | −0.110393 | ||||||||
\(473\) | −11.7920 | −0.542198 | ||||||||
\(474\) | −0.570830 | −0.0262191 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.66035 | −0.396947 | ||||||||
\(477\) | −11.0510 | −0.505992 | ||||||||
\(478\) | −0.0509546 | −0.00233061 | ||||||||
\(479\) | 7.48576 | 0.342033 | 0.171017 | − | 0.985268i | \(-0.445295\pi\) | ||||
0.171017 | + | 0.985268i | \(0.445295\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.84775 | 0.129846 | ||||||||
\(482\) | −1.70730 | −0.0777654 | ||||||||
\(483\) | 10.2760 | 0.467576 | ||||||||
\(484\) | −16.4939 | −0.749724 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.0898194 | 0.00407429 | ||||||||
\(487\) | 25.4295 | 1.15232 | 0.576160 | − | 0.817337i | \(-0.304551\pi\) | ||||
0.576160 | + | 0.817337i | \(0.304551\pi\) | |||||||
\(488\) | 3.39037 | 0.153475 | ||||||||
\(489\) | −4.58509 | −0.207345 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.0668 | −0.499438 | −0.249719 | − | 0.968318i | \(-0.580338\pi\) | ||||
−0.249719 | + | 0.968318i | \(0.580338\pi\) | |||||||
\(492\) | 11.9167 | 0.537246 | ||||||||
\(493\) | 7.95479 | 0.358266 | ||||||||
\(494\) | 0.240458 | 0.0108187 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.5327 | −0.652537 | ||||||||
\(497\) | −31.9315 | −1.43233 | ||||||||
\(498\) | −0.0661979 | −0.00296640 | ||||||||
\(499\) | 4.68157 | 0.209576 | 0.104788 | − | 0.994495i | \(-0.466584\pi\) | ||||
0.104788 | + | 0.994495i | \(0.466584\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.21792 | −0.322473 | ||||||||
\(502\) | 0.271734 | 0.0121281 | ||||||||
\(503\) | −10.8285 | −0.482818 | −0.241409 | − | 0.970423i | \(-0.577609\pi\) | ||||
−0.241409 | + | 0.970423i | \(0.577609\pi\) | |||||||
\(504\) | 1.56354 | 0.0696458 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.929388 | −0.0413163 | ||||||||
\(507\) | −9.07304 | −0.402948 | ||||||||
\(508\) | −25.0126 | −1.10975 | ||||||||
\(509\) | 11.5007 | 0.509757 | 0.254879 | − | 0.966973i | \(-0.417964\pi\) | ||||
0.254879 | + | 0.966973i | \(0.417964\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.85244 | −0.0819473 | ||||||||
\(512\) | 7.07011 | 0.312457 | ||||||||
\(513\) | 1.35096 | 0.0596462 | ||||||||
\(514\) | 1.78393 | 0.0786856 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.34941 | 0.235495 | ||||||||
\(517\) | −48.0338 | −2.11252 | ||||||||
\(518\) | −0.562860 | −0.0247307 | ||||||||
\(519\) | 4.65009 | 0.204116 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.797807 | 0.0349525 | 0.0174763 | − | 0.999847i | \(-0.494437\pi\) | ||||
0.0174763 | + | 0.999847i | \(0.494437\pi\) | |||||||
\(522\) | −0.716629 | −0.0313660 | ||||||||
\(523\) | −40.1429 | −1.75533 | −0.877663 | − | 0.479279i | \(-0.840898\pi\) | ||||
−0.877663 | + | 0.479279i | \(0.840898\pi\) | |||||||
\(524\) | −32.8107 | −1.43334 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.05057 | −0.0894090 | ||||||||
\(527\) | 3.66666 | 0.159722 | ||||||||
\(528\) | 17.3515 | 0.755127 | ||||||||
\(529\) | −17.4469 | −0.758559 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.68895 | 0.290276 | ||||||||
\(532\) | 11.7347 | 0.508764 | ||||||||
\(533\) | −11.8552 | −0.513506 | ||||||||
\(534\) | −0.879095 | −0.0380422 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.63317 | 0.200123 | ||||||||
\(537\) | −7.20338 | −0.310849 | ||||||||
\(538\) | 1.33224 | 0.0574369 | ||||||||
\(539\) | 52.7603 | 2.27255 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.41016 | 0.0606277 | 0.0303138 | − | 0.999540i | \(-0.490349\pi\) | ||||
0.0303138 | + | 0.999540i | \(0.490349\pi\) | |||||||
\(542\) | −0.578185 | −0.0248352 | ||||||||
\(543\) | −3.80424 | −0.163255 | ||||||||
\(544\) | −1.06885 | −0.0458265 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.776167 | −0.0332169 | ||||||||
\(547\) | −15.4621 | −0.661110 | −0.330555 | − | 0.943787i | \(-0.607236\pi\) | ||||
−0.330555 | + | 0.943787i | \(0.607236\pi\) | |||||||
\(548\) | −19.2566 | −0.822603 | ||||||||
\(549\) | −9.45570 | −0.403560 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.7787 | −0.459187 | ||||||||
\(552\) | 0.844934 | 0.0359628 | ||||||||
\(553\) | 27.7136 | 1.17850 | ||||||||
\(554\) | −0.602667 | −0.0256049 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −26.9562 | −1.14320 | ||||||||
\(557\) | 18.0445 | 0.764568 | 0.382284 | − | 0.924045i | \(-0.375138\pi\) | ||||
0.382284 | + | 0.924045i | \(0.375138\pi\) | |||||||
\(558\) | −0.330321 | −0.0139836 | ||||||||
\(559\) | −5.32181 | −0.225089 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.37786 | −0.184834 | ||||||||
\(562\) | −1.84011 | −0.0776202 | ||||||||
\(563\) | 28.5327 | 1.20251 | 0.601254 | − | 0.799058i | \(-0.294668\pi\) | ||||
0.601254 | + | 0.799058i | \(0.294668\pi\) | |||||||
\(564\) | 21.7903 | 0.917538 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.02554 | 0.0431065 | ||||||||
\(567\) | −4.36070 | −0.183132 | ||||||||
\(568\) | −2.62553 | −0.110165 | ||||||||
\(569\) | 16.4072 | 0.687826 | 0.343913 | − | 0.939001i | \(-0.388247\pi\) | ||||
0.343913 | + | 0.939001i | \(0.388247\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.34705 | −0.349313 | −0.174657 | − | 0.984629i | \(-0.555882\pi\) | ||||
−0.174657 | + | 0.984629i | \(0.555882\pi\) | |||||||
\(572\) | −17.3325 | −0.724707 | ||||||||
\(573\) | 21.5541 | 0.900437 | ||||||||
\(574\) | 2.34319 | 0.0978029 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.80703 | −0.325293 | ||||||||
\(577\) | −8.43531 | −0.351167 | −0.175583 | − | 0.984465i | \(-0.556181\pi\) | ||||
−0.175583 | + | 0.984465i | \(0.556181\pi\) | |||||||
\(578\) | −1.43765 | −0.0597982 | ||||||||
\(579\) | −3.15029 | −0.130921 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.21389 | 0.133334 | ||||||||
\(582\) | −0.00302764 | −0.000125500 0 | ||||||||
\(583\) | −48.5245 | −2.00968 | ||||||||
\(584\) | −0.152315 | −0.00630283 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.56439 | −0.105934 | ||||||||
\(587\) | 24.2852 | 1.00236 | 0.501179 | − | 0.865344i | \(-0.332900\pi\) | ||||
0.501179 | + | 0.865344i | \(0.332900\pi\) | |||||||
\(588\) | −23.9345 | −0.987042 | ||||||||
\(589\) | −4.96829 | −0.204715 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.0837 | −1.07294 | ||||||||
\(592\) | 5.67876 | 0.233396 | ||||||||
\(593\) | 28.4653 | 1.16893 | 0.584466 | − | 0.811418i | \(-0.301304\pi\) | ||||
0.584466 | + | 0.811418i | \(0.301304\pi\) | |||||||
\(594\) | 0.394392 | 0.0161821 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −27.2581 | −1.11654 | ||||||||
\(597\) | −24.2662 | −0.993149 | ||||||||
\(598\) | −0.419438 | −0.0171521 | ||||||||
\(599\) | 16.0387 | 0.655323 | 0.327662 | − | 0.944795i | \(-0.393739\pi\) | ||||
0.327662 | + | 0.944795i | \(0.393739\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.09005 | −0.330000 | −0.165000 | − | 0.986294i | \(-0.552762\pi\) | ||||
−0.165000 | + | 0.986294i | \(0.552762\pi\) | |||||||
\(602\) | 1.05186 | 0.0428706 | ||||||||
\(603\) | −12.9219 | −0.526219 | ||||||||
\(604\) | 22.5494 | 0.917521 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.286874 | 0.0116535 | ||||||||
\(607\) | 0.434608 | 0.0176402 | 0.00882010 | − | 0.999961i | \(-0.497192\pi\) | ||||
0.00882010 | + | 0.999961i | \(0.497192\pi\) | |||||||
\(608\) | 1.44828 | 0.0587356 | ||||||||
\(609\) | 34.7921 | 1.40985 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.6779 | −0.876994 | ||||||||
\(612\) | 1.98600 | 0.0802793 | ||||||||
\(613\) | 39.3962 | 1.59120 | 0.795599 | − | 0.605824i | \(-0.207156\pi\) | ||||
0.795599 | + | 0.605824i | \(0.207156\pi\) | |||||||
\(614\) | 1.84504 | 0.0744599 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.86543 | 0.276616 | ||||||||
\(617\) | −15.4146 | −0.620568 | −0.310284 | − | 0.950644i | \(-0.600424\pi\) | ||||
−0.310284 | + | 0.950644i | \(0.600424\pi\) | |||||||
\(618\) | −0.768264 | −0.0309041 | ||||||||
\(619\) | −10.6718 | −0.428935 | −0.214468 | − | 0.976731i | \(-0.568802\pi\) | ||||
−0.214468 | + | 0.976731i | \(0.568802\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.35651 | −0.0945635 | ||||||||
\(622\) | 1.57629 | 0.0632036 | ||||||||
\(623\) | 42.6797 | 1.70993 | ||||||||
\(624\) | 7.83083 | 0.313484 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.268168 | 0.0107182 | ||||||||
\(627\) | 5.93197 | 0.236900 | ||||||||
\(628\) | 17.0523 | 0.680463 | ||||||||
\(629\) | −1.43278 | −0.0571285 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.4347 | −0.733874 | −0.366937 | − | 0.930246i | \(-0.619594\pi\) | ||||
−0.366937 | + | 0.930246i | \(0.619594\pi\) | |||||||
\(632\) | 2.27871 | 0.0906424 | ||||||||
\(633\) | 16.3783 | 0.650980 | ||||||||
\(634\) | 1.45245 | 0.0576843 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 22.0129 | 0.872869 | ||||||||
\(637\) | 23.8110 | 0.943427 | ||||||||
\(638\) | −3.14668 | −0.124578 | ||||||||
\(639\) | 7.32257 | 0.289676 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.4281 | 0.490882 | 0.245441 | − | 0.969412i | \(-0.421067\pi\) | ||||
0.245441 | + | 0.969412i | \(0.421067\pi\) | |||||||
\(642\) | −0.199521 | −0.00787447 | ||||||||
\(643\) | 1.84657 | 0.0728218 | 0.0364109 | − | 0.999337i | \(-0.488407\pi\) | ||||
0.0364109 | + | 0.999337i | \(0.488407\pi\) | |||||||
\(644\) | −20.4692 | −0.806598 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.120981 | −0.00475992 | ||||||||
\(647\) | 38.9760 | 1.53230 | 0.766152 | − | 0.642660i | \(-0.222169\pi\) | ||||
0.766152 | + | 0.642660i | \(0.222169\pi\) | |||||||
\(648\) | −0.358553 | −0.0140853 | ||||||||
\(649\) | 29.3708 | 1.15290 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.0370 | 0.628539 | ||||||||
\(652\) | 9.13319 | 0.357683 | ||||||||
\(653\) | −28.3389 | −1.10899 | −0.554493 | − | 0.832189i | \(-0.687088\pi\) | ||||
−0.554493 | + | 0.832189i | \(0.687088\pi\) | |||||||
\(654\) | 0.988224 | 0.0386426 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −23.6407 | −0.923015 | ||||||||
\(657\) | 0.424804 | 0.0165732 | ||||||||
\(658\) | 4.28465 | 0.167033 | ||||||||
\(659\) | −22.3561 | −0.870868 | −0.435434 | − | 0.900221i | \(-0.643405\pi\) | ||||
−0.435434 | + | 0.900221i | \(0.643405\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.2143 | 1.13631 | 0.568153 | − | 0.822923i | \(-0.307658\pi\) | ||||
0.568153 | + | 0.822923i | \(0.307658\pi\) | |||||||
\(662\) | −1.17398 | −0.0456281 | ||||||||
\(663\) | −1.97575 | −0.0767319 | ||||||||
\(664\) | 0.264258 | 0.0102552 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.129076 | 0.00500158 | ||||||||
\(667\) | 18.8015 | 0.727998 | ||||||||
\(668\) | 14.3776 | 0.556287 | ||||||||
\(669\) | 5.68295 | 0.219715 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.5194 | −1.60284 | ||||||||
\(672\) | −4.67486 | −0.180336 | ||||||||
\(673\) | −3.21546 | −0.123947 | −0.0619735 | − | 0.998078i | \(-0.519739\pi\) | ||||
−0.0619735 | + | 0.998078i | \(0.519739\pi\) | |||||||
\(674\) | −2.40760 | −0.0927372 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.0729 | 0.695111 | ||||||||
\(677\) | 47.2470 | 1.81585 | 0.907925 | − | 0.419133i | \(-0.137666\pi\) | ||||
0.907925 | + | 0.419133i | \(0.137666\pi\) | |||||||
\(678\) | −0.153610 | −0.00589936 | ||||||||
\(679\) | 0.146991 | 0.00564099 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.64374 | −0.139629 | ||||||||
\(682\) | −1.45042 | −0.0555395 | ||||||||
\(683\) | 37.2527 | 1.42543 | 0.712717 | − | 0.701452i | \(-0.247464\pi\) | ||||
0.712717 | + | 0.701452i | \(0.247464\pi\) | |||||||
\(684\) | −2.69101 | −0.102893 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.96454 | −0.0750064 | ||||||||
\(687\) | 1.66125 | 0.0633807 | ||||||||
\(688\) | −10.6123 | −0.404591 | ||||||||
\(689\) | −21.8994 | −0.834299 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.9827 | −0.417803 | −0.208901 | − | 0.977937i | \(-0.566989\pi\) | ||||
−0.208901 | + | 0.977937i | \(0.566989\pi\) | |||||||
\(692\) | −9.26267 | −0.352114 | ||||||||
\(693\) | −19.1476 | −0.727357 | ||||||||
\(694\) | 2.28913 | 0.0868941 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.86074 | 0.108436 | ||||||||
\(697\) | 5.96466 | 0.225928 | ||||||||
\(698\) | −2.51885 | −0.0953399 | ||||||||
\(699\) | −7.85899 | −0.297254 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.4086 | 0.846361 | 0.423180 | − | 0.906046i | \(-0.360914\pi\) | ||||
0.423180 | + | 0.906046i | \(0.360914\pi\) | |||||||
\(702\) | 0.177991 | 0.00671784 | ||||||||
\(703\) | 1.94140 | 0.0732213 | ||||||||
\(704\) | −34.2802 | −1.29198 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.31736 | −0.0495793 | ||||||||
\(707\) | −13.9276 | −0.523803 | ||||||||
\(708\) | −13.3239 | −0.500744 | ||||||||
\(709\) | −14.6297 | −0.549431 | −0.274716 | − | 0.961526i | \(-0.588584\pi\) | ||||
−0.274716 | + | 0.961526i | \(0.588584\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.35531 | −0.238343 | ||||||||
\(712\) | 3.50929 | 0.131516 | ||||||||
\(713\) | 8.66633 | 0.324557 | ||||||||
\(714\) | 0.390509 | 0.0146144 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.3486 | 0.536234 | ||||||||
\(717\) | −0.567301 | −0.0211862 | ||||||||
\(718\) | −1.31321 | −0.0490085 | ||||||||
\(719\) | −28.4977 | −1.06278 | −0.531392 | − | 0.847126i | \(-0.678331\pi\) | ||||
−0.531392 | + | 0.847126i | \(0.678331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.2989 | 1.38908 | ||||||||
\(722\) | −1.54264 | −0.0574112 | ||||||||
\(723\) | −19.0081 | −0.706920 | ||||||||
\(724\) | 7.57778 | 0.281626 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.743738 | 0.0276027 | ||||||||
\(727\) | −44.0064 | −1.63211 | −0.816054 | − | 0.577976i | \(-0.803843\pi\) | ||||
−0.816054 | + | 0.577976i | \(0.803843\pi\) | |||||||
\(728\) | 3.09840 | 0.114835 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.67754 | 0.0990324 | ||||||||
\(732\) | 18.8351 | 0.696166 | ||||||||
\(733\) | 27.3227 | 1.00919 | 0.504593 | − | 0.863357i | \(-0.331643\pi\) | ||||
0.504593 | + | 0.863357i | \(0.331643\pi\) | |||||||
\(734\) | 1.58926 | 0.0586607 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.52628 | −0.0931198 | ||||||||
\(737\) | −56.7391 | −2.09001 | ||||||||
\(738\) | −0.537343 | −0.0197799 | ||||||||
\(739\) | 16.4678 | 0.605776 | 0.302888 | − | 0.953026i | \(-0.402049\pi\) | ||||
0.302888 | + | 0.953026i | \(0.402049\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.67713 | 0.0983468 | ||||||||
\(742\) | 4.32843 | 0.158901 | ||||||||
\(743\) | 35.6012 | 1.30608 | 0.653041 | − | 0.757322i | \(-0.273493\pi\) | ||||
0.653041 | + | 0.757322i | \(0.273493\pi\) | |||||||
\(744\) | 1.31862 | 0.0483430 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.09843 | −0.0402164 | ||||||||
\(747\) | −0.737011 | −0.0269658 | ||||||||
\(748\) | 8.72041 | 0.318850 | ||||||||
\(749\) | 9.68668 | 0.353944 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.0748 | 1.68129 | 0.840647 | − | 0.541583i | \(-0.182175\pi\) | ||||
0.840647 | + | 0.541583i | \(0.182175\pi\) | |||||||
\(752\) | −43.2283 | −1.57638 | ||||||||
\(753\) | 3.02533 | 0.110249 | ||||||||
\(754\) | −1.42011 | −0.0517174 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.68622 | 0.315915 | ||||||||
\(757\) | −36.6482 | −1.33200 | −0.666000 | − | 0.745951i | \(-0.731995\pi\) | ||||
−0.666000 | + | 0.745951i | \(0.731995\pi\) | |||||||
\(758\) | 2.52348 | 0.0916571 | ||||||||
\(759\) | −10.3473 | −0.375583 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.2078 | −0.986282 | −0.493141 | − | 0.869949i | \(-0.664151\pi\) | ||||
−0.493141 | + | 0.869949i | \(0.664151\pi\) | |||||||
\(762\) | 1.12786 | 0.0408580 | ||||||||
\(763\) | −47.9779 | −1.73692 | ||||||||
\(764\) | −42.9344 | −1.55331 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.09279 | −0.111747 | ||||||||
\(767\) | 13.2552 | 0.478617 | ||||||||
\(768\) | 15.3585 | 0.554202 | ||||||||
\(769\) | 26.5327 | 0.956794 | 0.478397 | − | 0.878144i | \(-0.341218\pi\) | ||||
0.478397 | + | 0.878144i | \(0.341218\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.8613 | 0.715286 | ||||||||
\(772\) | 6.27516 | 0.225848 | ||||||||
\(773\) | 28.7677 | 1.03470 | 0.517351 | − | 0.855773i | \(-0.326918\pi\) | ||||
0.517351 | + | 0.855773i | \(0.326918\pi\) | |||||||
\(774\) | −0.241213 | −0.00867024 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.0120861 | 0.000433867 0 | ||||||||
\(777\) | −6.26658 | −0.224812 | ||||||||
\(778\) | 1.21458 | 0.0435450 | ||||||||
\(779\) | −8.08206 | −0.289570 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.1530 | 1.15052 | ||||||||
\(782\) | 0.211030 | 0.00754641 | ||||||||
\(783\) | −7.97856 | −0.285130 | ||||||||
\(784\) | 47.4820 | 1.69579 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.47949 | 0.0527716 | ||||||||
\(787\) | −24.8663 | −0.886387 | −0.443193 | − | 0.896426i | \(-0.646155\pi\) | ||||
−0.443193 | + | 0.896426i | \(0.646155\pi\) | |||||||
\(788\) | 51.9571 | 1.85089 | ||||||||
\(789\) | −22.8299 | −0.812766 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.45771 | 0.265166 | ||||||||
\(792\) | −1.57439 | −0.0559434 | ||||||||
\(793\) | −18.7379 | −0.665404 | ||||||||
\(794\) | 3.23120 | 0.114671 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 48.3366 | 1.71325 | ||||||||
\(797\) | 31.4206 | 1.11298 | 0.556488 | − | 0.830856i | \(-0.312149\pi\) | ||||
0.556488 | + | 0.830856i | \(0.312149\pi\) | |||||||
\(798\) | −0.529137 | −0.0187312 | ||||||||
\(799\) | 10.9067 | 0.385851 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.78736 | −0.345819 | ||||||||
\(802\) | 0.391592 | 0.0138276 | ||||||||
\(803\) | 1.86529 | 0.0658246 | ||||||||
\(804\) | 25.7395 | 0.907761 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.654583 | −0.0230567 | ||||||||
\(807\) | 14.8324 | 0.522125 | ||||||||
\(808\) | −1.14518 | −0.0402874 | ||||||||
\(809\) | 50.5027 | 1.77558 | 0.887790 | − | 0.460249i | \(-0.152240\pi\) | ||||
0.887790 | + | 0.460249i | \(0.152240\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.1612 | 0.883528 | 0.441764 | − | 0.897131i | \(-0.354353\pi\) | ||||
0.441764 | + | 0.897131i | \(0.354353\pi\) | |||||||
\(812\) | −69.3035 | −2.43208 | ||||||||
\(813\) | −6.43720 | −0.225762 | ||||||||
\(814\) | 0.566763 | 0.0198650 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.93989 | −0.137924 | ||||||||
\(817\) | −3.62804 | −0.126929 | ||||||||
\(818\) | −1.62697 | −0.0568856 | ||||||||
\(819\) | −8.64141 | −0.301955 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.6307 | −0.720017 | −0.360009 | − | 0.932949i | \(-0.617226\pi\) | ||||
−0.360009 | + | 0.932949i | \(0.617226\pi\) | |||||||
\(822\) | 0.868313 | 0.0302859 | ||||||||
\(823\) | 35.8618 | 1.25006 | 0.625032 | − | 0.780599i | \(-0.285086\pi\) | ||||
0.625032 | + | 0.780599i | \(0.285086\pi\) | |||||||
\(824\) | 3.06686 | 0.106839 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.61990 | −0.0911580 | ||||||||
\(827\) | −4.73642 | −0.164701 | −0.0823507 | − | 0.996603i | \(-0.526243\pi\) | ||||
−0.0823507 | + | 0.996603i | \(0.526243\pi\) | |||||||
\(828\) | 4.69401 | 0.163128 | ||||||||
\(829\) | −28.4768 | −0.989039 | −0.494520 | − | 0.869166i | \(-0.664656\pi\) | ||||
−0.494520 | + | 0.869166i | \(0.664656\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.70976 | −0.232759 | ||||||||
\(832\) | −15.4708 | −0.536355 | ||||||||
\(833\) | −11.9799 | −0.415080 | ||||||||
\(834\) | 1.21550 | 0.0420892 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −11.8161 | −0.408668 | ||||||||
\(837\) | −3.67761 | −0.127117 | ||||||||
\(838\) | 0.0474127 | 0.00163784 | ||||||||
\(839\) | −0.765715 | −0.0264354 | −0.0132177 | − | 0.999913i | \(-0.504207\pi\) | ||||
−0.0132177 | + | 0.999913i | \(0.504207\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.6574 | 1.19508 | ||||||||
\(842\) | 1.67591 | 0.0577555 | ||||||||
\(843\) | −20.4867 | −0.705600 | ||||||||
\(844\) | −32.6245 | −1.12298 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.982560 | −0.0337811 | ||||||||
\(847\) | −36.1082 | −1.24069 | ||||||||
\(848\) | −43.6700 | −1.49963 | ||||||||
\(849\) | 11.4177 | 0.391856 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.38644 | −0.116086 | ||||||||
\(852\) | −14.5861 | −0.499710 | ||||||||
\(853\) | −34.7289 | −1.18910 | −0.594548 | − | 0.804060i | \(-0.702669\pi\) | ||||
−0.594548 | + | 0.804060i | \(0.702669\pi\) | |||||||
\(854\) | 3.70357 | 0.126734 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.796475 | 0.0272230 | ||||||||
\(857\) | −54.2561 | −1.85335 | −0.926676 | − | 0.375860i | \(-0.877347\pi\) | ||||
−0.926676 | + | 0.375860i | \(0.877347\pi\) | |||||||
\(858\) | 0.781549 | 0.0266816 | ||||||||
\(859\) | 15.9095 | 0.542824 | 0.271412 | − | 0.962463i | \(-0.412509\pi\) | ||||
0.271412 | + | 0.962463i | \(0.412509\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.0878 | 0.889070 | ||||||||
\(862\) | 1.88543 | 0.0642180 | ||||||||
\(863\) | −22.4714 | −0.764935 | −0.382467 | − | 0.923969i | \(-0.624926\pi\) | ||||
−0.382467 | + | 0.923969i | \(0.624926\pi\) | |||||||
\(864\) | 1.07204 | 0.0364716 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.22729 | 0.0417049 | ||||||||
\(867\) | −16.0059 | −0.543590 | ||||||||
\(868\) | −31.9446 | −1.08427 | ||||||||
\(869\) | −27.9058 | −0.946639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.6067 | −0.867649 | ||||||||
\(872\) | −3.94492 | −0.133592 | ||||||||
\(873\) | −0.0337081 | −0.00114085 | ||||||||
\(874\) | −0.285944 | −0.00967219 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.846181 | −0.0285898 | ||||||||
\(877\) | −27.0756 | −0.914278 | −0.457139 | − | 0.889395i | \(-0.651126\pi\) | ||||
−0.457139 | + | 0.889395i | \(0.651126\pi\) | |||||||
\(878\) | −0.389222 | −0.0131356 | ||||||||
\(879\) | −28.5505 | −0.962984 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.81317 | −0.263232 | −0.131616 | − | 0.991301i | \(-0.542017\pi\) | ||||
−0.131616 | + | 0.991301i | \(0.542017\pi\) | |||||||
\(882\) | 1.07925 | 0.0363401 | ||||||||
\(883\) | 58.3010 | 1.96199 | 0.980993 | − | 0.194042i | \(-0.0621598\pi\) | ||||
0.980993 | + | 0.194042i | \(0.0621598\pi\) | |||||||
\(884\) | 3.93557 | 0.132367 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.144377 | 0.00485045 | ||||||||
\(887\) | 8.64610 | 0.290307 | 0.145154 | − | 0.989409i | \(-0.453632\pi\) | ||||
0.145154 | + | 0.989409i | \(0.453632\pi\) | |||||||
\(888\) | −0.515261 | −0.0172910 | ||||||||
\(889\) | −54.7571 | −1.83650 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.39094 | 0.147102 | ||||||||
\(892\) | −11.3200 | −0.379023 | ||||||||
\(893\) | −14.7785 | −0.494543 | ||||||||
\(894\) | 1.22911 | 0.0411077 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 12.4075 | 0.414507 | ||||||||
\(897\) | −4.66979 | −0.155920 | ||||||||
\(898\) | −1.24212 | −0.0414500 | ||||||||
\(899\) | 29.3420 | 0.978612 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.0181 | 0.367067 | ||||||||
\(902\) | −2.35944 | −0.0785608 | ||||||||
\(903\) | 11.7108 | 0.389712 | ||||||||
\(904\) | 0.613201 | 0.0203948 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.01679 | −0.0337805 | ||||||||
\(907\) | 40.4367 | 1.34268 | 0.671339 | − | 0.741151i | \(-0.265720\pi\) | ||||
0.671339 | + | 0.741151i | \(0.265720\pi\) | |||||||
\(908\) | 7.25809 | 0.240868 | ||||||||
\(909\) | 3.19390 | 0.105935 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.5643 | −1.67527 | −0.837635 | − | 0.546230i | \(-0.816063\pi\) | ||||
−0.837635 | + | 0.546230i | \(0.816063\pi\) | |||||||
\(912\) | 5.33852 | 0.176776 | ||||||||
\(913\) | −3.23617 | −0.107102 | ||||||||
\(914\) | −1.80847 | −0.0598187 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.30910 | −0.109336 | ||||||||
\(917\) | −71.8286 | −2.37199 | ||||||||
\(918\) | −0.0895519 | −0.00295565 | ||||||||
\(919\) | −43.3566 | −1.43020 | −0.715101 | − | 0.699021i | \(-0.753619\pi\) | ||||
−0.715101 | + | 0.699021i | \(0.753619\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.5417 | 0.676871 | ||||||||
\(922\) | 2.83169 | 0.0932566 | ||||||||
\(923\) | 14.5108 | 0.477629 | ||||||||
\(924\) | 38.1407 | 1.25474 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.00405712 | 0.000133325 0 | ||||||||
\(927\) | −8.55342 | −0.280931 | ||||||||
\(928\) | −8.55335 | −0.280777 | ||||||||
\(929\) | −34.1746 | −1.12123 | −0.560617 | − | 0.828075i | \(-0.689436\pi\) | ||||
−0.560617 | + | 0.828075i | \(0.689436\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.2327 | 0.532006 | ||||||||
\(932\) | 15.6546 | 0.512783 | ||||||||
\(933\) | 17.5496 | 0.574548 | ||||||||
\(934\) | 2.94921 | 0.0965010 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.710529 | −0.0232244 | ||||||||
\(937\) | −27.8996 | −0.911441 | −0.455720 | − | 0.890123i | \(-0.650618\pi\) | ||||
−0.455720 | + | 0.890123i | \(0.650618\pi\) | |||||||
\(938\) | 5.06118 | 0.165253 | ||||||||
\(939\) | 2.98564 | 0.0974325 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −54.3261 | −1.77098 | −0.885490 | − | 0.464659i | \(-0.846177\pi\) | ||||
−0.885490 | + | 0.464659i | \(0.846177\pi\) | |||||||
\(942\) | −0.768918 | −0.0250527 | ||||||||
\(943\) | 14.0978 | 0.459086 | ||||||||
\(944\) | 26.4325 | 0.860303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.05915 | −0.0344361 | ||||||||
\(947\) | −4.23171 | −0.137512 | −0.0687561 | − | 0.997633i | \(-0.521903\pi\) | ||||
−0.0687561 | + | 0.997633i | \(0.521903\pi\) | |||||||
\(948\) | 12.6593 | 0.411156 | ||||||||
\(949\) | 0.841815 | 0.0273265 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.1708 | 0.524375 | ||||||||
\(952\) | −1.55889 | −0.0505238 | ||||||||
\(953\) | 47.9307 | 1.55263 | 0.776314 | − | 0.630346i | \(-0.217087\pi\) | ||||
0.776314 | + | 0.630346i | \(0.217087\pi\) | |||||||
\(954\) | −0.992598 | −0.0321366 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.13002 | 0.0365476 | ||||||||
\(957\) | −35.0334 | −1.13247 | ||||||||
\(958\) | 0.672367 | 0.0217232 | ||||||||
\(959\) | −42.1563 | −1.36130 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.4752 | −0.563715 | ||||||||
\(962\) | 0.255783 | 0.00824679 | ||||||||
\(963\) | −2.22136 | −0.0715823 | ||||||||
\(964\) | 37.8629 | 1.21948 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.922988 | 0.0296966 | ||||||||
\(967\) | 20.8827 | 0.671544 | 0.335772 | − | 0.941943i | \(-0.391003\pi\) | ||||
0.335772 | + | 0.941943i | \(0.391003\pi\) | |||||||
\(968\) | −2.96895 | −0.0954257 | ||||||||
\(969\) | −1.34693 | −0.0432697 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.0740 | 0.515838 | 0.257919 | − | 0.966167i | \(-0.416963\pi\) | ||||
0.257919 | + | 0.966167i | \(0.416963\pi\) | |||||||
\(972\) | −1.99193 | −0.0638913 | ||||||||
\(973\) | −59.0119 | −1.89184 | ||||||||
\(974\) | 2.28406 | 0.0731860 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37.3657 | −1.19605 | ||||||||
\(977\) | 35.5665 | 1.13787 | 0.568937 | − | 0.822381i | \(-0.307355\pi\) | ||||
0.568937 | + | 0.822381i | \(0.307355\pi\) | |||||||
\(978\) | −0.411830 | −0.0131689 | ||||||||
\(979\) | −42.9757 | −1.37351 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.0023 | 0.351278 | ||||||||
\(982\) | −0.994014 | −0.0317202 | ||||||||
\(983\) | −18.4711 | −0.589138 | −0.294569 | − | 0.955630i | \(-0.595176\pi\) | ||||
−0.294569 | + | 0.955630i | \(0.595176\pi\) | |||||||
\(984\) | 2.14504 | 0.0683812 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.714495 | 0.0227542 | ||||||||
\(987\) | 47.7030 | 1.51840 | ||||||||
\(988\) | −5.33266 | −0.169655 | ||||||||
\(989\) | 6.32849 | 0.201234 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.5907 | −1.32117 | −0.660586 | − | 0.750750i | \(-0.729692\pi\) | ||||
−0.660586 | + | 0.750750i | \(0.729692\pi\) | |||||||
\(992\) | −3.94256 | −0.125176 | ||||||||
\(993\) | −13.0705 | −0.414779 | ||||||||
\(994\) | −2.86807 | −0.0909698 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.46808 | 0.0465178 | ||||||||
\(997\) | −31.8374 | −1.00830 | −0.504151 | − | 0.863616i | \(-0.668194\pi\) | ||||
−0.504151 | + | 0.863616i | \(0.668194\pi\) | |||||||
\(998\) | 0.420496 | 0.0133106 | ||||||||
\(999\) | 1.43706 | 0.0454665 |
(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 | 1875.2.a.m.1.5 | 8 | ||
3.2 | odd | 2 | 5625.2.a.bd.1.4 | 8 | |||
5.2 | odd | 4 | 1875.2.b.h.1249.9 | 16 | |||
5.3 | odd | 4 | 1875.2.b.h.1249.8 | 16 | |||
5.4 | even | 2 | 1875.2.a.p.1.4 | 8 | |||
15.14 | odd | 2 | 5625.2.a.t.1.5 | 8 | |||
25.3 | odd | 20 | 375.2.i.c.49.2 | 16 | |||
25.4 | even | 10 | 375.2.g.d.76.3 | 16 | |||
25.6 | even | 5 | 375.2.g.e.301.2 | 16 | |||
25.8 | odd | 20 | 75.2.i.a.64.3 | yes | 16 | ||
25.17 | odd | 20 | 375.2.i.c.199.2 | 16 | |||
25.19 | even | 10 | 375.2.g.d.301.3 | 16 | |||
25.21 | even | 5 | 375.2.g.e.76.2 | 16 | |||
25.22 | odd | 20 | 75.2.i.a.34.3 | ✓ | 16 | ||
75.8 | even | 20 | 225.2.m.b.64.2 | 16 | |||
75.47 | even | 20 | 225.2.m.b.109.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.34.3 | ✓ | 16 | 25.22 | odd | 20 | ||
75.2.i.a.64.3 | yes | 16 | 25.8 | odd | 20 | ||
225.2.m.b.64.2 | 16 | 75.8 | even | 20 | |||
225.2.m.b.109.2 | 16 | 75.47 | even | 20 | |||
375.2.g.d.76.3 | 16 | 25.4 | even | 10 | |||
375.2.g.d.301.3 | 16 | 25.19 | even | 10 | |||
375.2.g.e.76.2 | 16 | 25.21 | even | 5 | |||
375.2.g.e.301.2 | 16 | 25.6 | even | 5 | |||
375.2.i.c.49.2 | 16 | 25.3 | odd | 20 | |||
375.2.i.c.199.2 | 16 | 25.17 | odd | 20 | |||
1875.2.a.m.1.5 | 8 | 1.1 | even | 1 | trivial | ||
1875.2.a.p.1.4 | 8 | 5.4 | even | 2 | |||
1875.2.b.h.1249.8 | 16 | 5.3 | odd | 4 | |||
1875.2.b.h.1249.9 | 16 | 5.2 | odd | 4 | |||
5625.2.a.t.1.5 | 8 | 15.14 | odd | 2 | |||
5625.2.a.bd.1.4 | 8 | 3.2 | odd | 2 |