Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(1,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.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: | \(4.99065012633\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.14884000000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 11x^{6} + 36x^{4} - 31x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.183172\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.183172 | −0.129522 | −0.0647611 | − | 0.997901i | \(-0.520629\pi\) | ||||
−0.0647611 | + | 0.997901i | \(0.520629\pi\) | |||||||
\(3\) | −1.47195 | −0.849830 | −0.424915 | − | 0.905233i | \(-0.639696\pi\) | ||||
−0.424915 | + | 0.905233i | \(0.639696\pi\) | |||||||
\(4\) | −1.96645 | −0.983224 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.269620 | 0.110072 | ||||||||
\(7\) | −3.26086 | −1.23249 | −0.616244 | − | 0.787555i | \(-0.711346\pi\) | ||||
−0.616244 | + | 0.787555i | \(0.711346\pi\) | |||||||
\(8\) | 0.726543 | 0.256872 | ||||||||
\(9\) | −0.833366 | −0.277789 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 2.89451 | 0.835573 | ||||||||
\(13\) | −0.296379 | −0.0822006 | −0.0411003 | − | 0.999155i | \(-0.513086\pi\) | ||||
−0.0411003 | + | 0.999155i | \(0.513086\pi\) | |||||||
\(14\) | 0.597298 | 0.159635 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.79981 | 0.949953 | ||||||||
\(17\) | −5.16297 | −1.25220 | −0.626102 | − | 0.779741i | \(-0.715351\pi\) | ||||
−0.626102 | + | 0.779741i | \(0.715351\pi\) | |||||||
\(18\) | 0.152649 | 0.0359798 | ||||||||
\(19\) | 1.73038 | 0.396976 | 0.198488 | − | 0.980103i | \(-0.436397\pi\) | ||||
0.198488 | + | 0.980103i | \(0.436397\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.79981 | 1.04741 | ||||||||
\(22\) | −0.366344 | −0.0781048 | ||||||||
\(23\) | 0.879192 | 0.183324 | 0.0916621 | − | 0.995790i | \(-0.470782\pi\) | ||||
0.0916621 | + | 0.995790i | \(0.470782\pi\) | |||||||
\(24\) | −1.06943 | −0.218297 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.0542883 | 0.0106468 | ||||||||
\(27\) | 5.64252 | 1.08590 | ||||||||
\(28\) | 6.41230 | 1.21181 | ||||||||
\(29\) | 5.91216 | 1.09786 | 0.548930 | − | 0.835868i | \(-0.315035\pi\) | ||||
0.548930 | + | 0.835868i | \(0.315035\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.09953 | 1.09551 | 0.547754 | − | 0.836639i | \(-0.315483\pi\) | ||||
0.547754 | + | 0.836639i | \(0.315483\pi\) | |||||||
\(32\) | −2.14910 | −0.379912 | ||||||||
\(33\) | −2.94390 | −0.512467 | ||||||||
\(34\) | 0.945712 | 0.162188 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.63877 | 0.273128 | ||||||||
\(37\) | 8.08800 | 1.32966 | 0.664830 | − | 0.746995i | \(-0.268504\pi\) | ||||
0.664830 | + | 0.746995i | \(0.268504\pi\) | |||||||
\(38\) | −0.316957 | −0.0514173 | ||||||||
\(39\) | 0.436254 | 0.0698566 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.01515 | −0.158539 | −0.0792695 | − | 0.996853i | \(-0.525259\pi\) | ||||
−0.0792695 | + | 0.996853i | \(0.525259\pi\) | |||||||
\(42\) | −0.879192 | −0.135662 | ||||||||
\(43\) | −3.24199 | −0.494399 | −0.247200 | − | 0.968965i | \(-0.579510\pi\) | ||||
−0.247200 | + | 0.968965i | \(0.579510\pi\) | |||||||
\(44\) | −3.93290 | −0.592906 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.161043 | −0.0237446 | ||||||||
\(47\) | 4.21996 | 0.615544 | 0.307772 | − | 0.951460i | \(-0.400417\pi\) | ||||
0.307772 | + | 0.951460i | \(0.400417\pi\) | |||||||
\(48\) | −5.59313 | −0.807299 | ||||||||
\(49\) | 3.63318 | 0.519026 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.59963 | 1.06416 | ||||||||
\(52\) | 0.582813 | 0.0808216 | ||||||||
\(53\) | −8.10072 | −1.11272 | −0.556360 | − | 0.830941i | \(-0.687802\pi\) | ||||
−0.556360 | + | 0.830941i | \(0.687802\pi\) | |||||||
\(54\) | −1.03355 | −0.140649 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.36915 | −0.316591 | ||||||||
\(57\) | −2.54703 | −0.337363 | ||||||||
\(58\) | −1.08294 | −0.142197 | ||||||||
\(59\) | 5.93635 | 0.772847 | 0.386424 | − | 0.922321i | \(-0.373710\pi\) | ||||
0.386424 | + | 0.922321i | \(0.373710\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.915615 | 0.117232 | 0.0586162 | − | 0.998281i | \(-0.481331\pi\) | ||||
0.0586162 | + | 0.998281i | \(0.481331\pi\) | |||||||
\(62\) | −1.11726 | −0.141893 | ||||||||
\(63\) | 2.71749 | 0.342371 | ||||||||
\(64\) | −7.20597 | −0.900746 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.539240 | 0.0663759 | ||||||||
\(67\) | 6.88806 | 0.841510 | 0.420755 | − | 0.907174i | \(-0.361765\pi\) | ||||
0.420755 | + | 0.907174i | \(0.361765\pi\) | |||||||
\(68\) | 10.1527 | 1.23120 | ||||||||
\(69\) | −1.29413 | −0.155794 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.96878 | −0.708364 | −0.354182 | − | 0.935177i | \(-0.615241\pi\) | ||||
−0.354182 | + | 0.935177i | \(0.615241\pi\) | |||||||
\(72\) | −0.605476 | −0.0713560 | ||||||||
\(73\) | 8.83341 | 1.03387 | 0.516936 | − | 0.856024i | \(-0.327072\pi\) | ||||
0.516936 | + | 0.856024i | \(0.327072\pi\) | |||||||
\(74\) | −1.48150 | −0.172220 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.40270 | −0.390317 | ||||||||
\(77\) | −6.52171 | −0.743218 | ||||||||
\(78\) | −0.0799096 | −0.00904798 | ||||||||
\(79\) | −7.76067 | −0.873144 | −0.436572 | − | 0.899669i | \(-0.643808\pi\) | ||||
−0.436572 | + | 0.899669i | \(0.643808\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.80540 | −0.645045 | ||||||||
\(82\) | 0.185946 | 0.0205343 | ||||||||
\(83\) | 14.5154 | 1.59327 | 0.796635 | − | 0.604461i | \(-0.206612\pi\) | ||||
0.796635 | + | 0.604461i | \(0.206612\pi\) | |||||||
\(84\) | −9.43858 | −1.02983 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.593842 | 0.0640357 | ||||||||
\(87\) | −8.70240 | −0.932995 | ||||||||
\(88\) | 1.45309 | 0.154899 | ||||||||
\(89\) | 7.52642 | 0.797799 | 0.398900 | − | 0.916995i | \(-0.369392\pi\) | ||||
0.398900 | + | 0.916995i | \(0.369392\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.966448 | 0.101311 | ||||||||
\(92\) | −1.72889 | −0.180249 | ||||||||
\(93\) | −8.97820 | −0.930996 | ||||||||
\(94\) | −0.772978 | −0.0797266 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.16337 | 0.322860 | ||||||||
\(97\) | −6.72649 | −0.682971 | −0.341486 | − | 0.939887i | \(-0.610930\pi\) | ||||
−0.341486 | + | 0.939887i | \(0.610930\pi\) | |||||||
\(98\) | −0.665497 | −0.0672254 | ||||||||
\(99\) | −1.66673 | −0.167513 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.1955 | −1.21350 | −0.606748 | − | 0.794894i | \(-0.707526\pi\) | ||||
−0.606748 | + | 0.794894i | \(0.707526\pi\) | |||||||
\(102\) | −1.39204 | −0.137832 | ||||||||
\(103\) | 1.38140 | 0.136114 | 0.0680569 | − | 0.997681i | \(-0.478320\pi\) | ||||
0.0680569 | + | 0.997681i | \(0.478320\pi\) | |||||||
\(104\) | −0.215332 | −0.0211150 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.48383 | 0.144122 | ||||||||
\(107\) | 15.8285 | 1.53020 | 0.765101 | − | 0.643911i | \(-0.222689\pi\) | ||||
0.765101 | + | 0.643911i | \(0.222689\pi\) | |||||||
\(108\) | −11.0957 | −1.06769 | ||||||||
\(109\) | −2.00377 | −0.191926 | −0.0959632 | − | 0.995385i | \(-0.530593\pi\) | ||||
−0.0959632 | + | 0.995385i | \(0.530593\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.9051 | −1.12998 | ||||||||
\(112\) | −12.3906 | −1.17081 | ||||||||
\(113\) | −10.4275 | −0.980935 | −0.490468 | − | 0.871459i | \(-0.663174\pi\) | ||||
−0.490468 | + | 0.871459i | \(0.663174\pi\) | |||||||
\(114\) | 0.466545 | 0.0436959 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −11.6260 | −1.07944 | ||||||||
\(117\) | 0.246992 | 0.0228344 | ||||||||
\(118\) | −1.08737 | −0.100101 | ||||||||
\(119\) | 16.8357 | 1.54333 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −0.167715 | −0.0151842 | ||||||||
\(123\) | 1.49424 | 0.134731 | ||||||||
\(124\) | −11.9944 | −1.07713 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.497767 | −0.0443446 | ||||||||
\(127\) | −5.85007 | −0.519110 | −0.259555 | − | 0.965728i | \(-0.583576\pi\) | ||||
−0.259555 | + | 0.965728i | \(0.583576\pi\) | |||||||
\(128\) | 5.61814 | 0.496578 | ||||||||
\(129\) | 4.77205 | 0.420155 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.49664 | −0.130762 | −0.0653811 | − | 0.997860i | \(-0.520826\pi\) | ||||
−0.0653811 | + | 0.997860i | \(0.520826\pi\) | |||||||
\(132\) | 5.78902 | 0.503870 | ||||||||
\(133\) | −5.64252 | −0.489268 | ||||||||
\(134\) | −1.26170 | −0.108994 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.75112 | −0.321656 | ||||||||
\(137\) | −7.84887 | −0.670574 | −0.335287 | − | 0.942116i | \(-0.608833\pi\) | ||||
−0.335287 | + | 0.942116i | \(0.608833\pi\) | |||||||
\(138\) | 0.237048 | 0.0201788 | ||||||||
\(139\) | 5.39152 | 0.457303 | 0.228651 | − | 0.973508i | \(-0.426568\pi\) | ||||
0.228651 | + | 0.973508i | \(0.426568\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.21156 | −0.523108 | ||||||||
\(142\) | 1.09331 | 0.0917488 | ||||||||
\(143\) | −0.592757 | −0.0495689 | ||||||||
\(144\) | −3.16663 | −0.263886 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.61803 | −0.133909 | ||||||||
\(147\) | −5.34786 | −0.441084 | ||||||||
\(148\) | −15.9046 | −1.30735 | ||||||||
\(149\) | 18.8229 | 1.54203 | 0.771015 | − | 0.636817i | \(-0.219749\pi\) | ||||
0.771015 | + | 0.636817i | \(0.219749\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.88797 | −0.316398 | −0.158199 | − | 0.987407i | \(-0.550569\pi\) | ||||
−0.158199 | + | 0.987407i | \(0.550569\pi\) | |||||||
\(152\) | 1.25719 | 0.101972 | ||||||||
\(153\) | 4.30264 | 0.347848 | ||||||||
\(154\) | 1.19460 | 0.0962632 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.857871 | −0.0686847 | ||||||||
\(157\) | 4.28378 | 0.341883 | 0.170941 | − | 0.985281i | \(-0.445319\pi\) | ||||
0.170941 | + | 0.985281i | \(0.445319\pi\) | |||||||
\(158\) | 1.42154 | 0.113092 | ||||||||
\(159\) | 11.9238 | 0.945623 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.86692 | −0.225945 | ||||||||
\(162\) | 1.06339 | 0.0835477 | ||||||||
\(163\) | 15.7263 | 1.23178 | 0.615890 | − | 0.787832i | \(-0.288796\pi\) | ||||
0.615890 | + | 0.787832i | \(0.288796\pi\) | |||||||
\(164\) | 1.99623 | 0.155879 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.65881 | −0.206364 | ||||||||
\(167\) | 21.0330 | 1.62758 | 0.813792 | − | 0.581156i | \(-0.197399\pi\) | ||||
0.813792 | + | 0.581156i | \(0.197399\pi\) | |||||||
\(168\) | 3.48727 | 0.269049 | ||||||||
\(169\) | −12.9122 | −0.993243 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.44204 | −0.110276 | ||||||||
\(172\) | 6.37521 | 0.486105 | ||||||||
\(173\) | 7.16663 | 0.544869 | 0.272434 | − | 0.962174i | \(-0.412171\pi\) | ||||
0.272434 | + | 0.962174i | \(0.412171\pi\) | |||||||
\(174\) | 1.59404 | 0.120844 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.59963 | 0.572843 | ||||||||
\(177\) | −8.73801 | −0.656789 | ||||||||
\(178\) | −1.37863 | −0.103333 | ||||||||
\(179\) | 8.03934 | 0.600888 | 0.300444 | − | 0.953799i | \(-0.402865\pi\) | ||||
0.300444 | + | 0.953799i | \(0.402865\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.6171 | −1.53246 | −0.766229 | − | 0.642568i | \(-0.777869\pi\) | ||||
−0.766229 | + | 0.642568i | \(0.777869\pi\) | |||||||
\(182\) | −0.177026 | −0.0131221 | ||||||||
\(183\) | −1.34774 | −0.0996277 | ||||||||
\(184\) | 0.638770 | 0.0470908 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.64456 | 0.120585 | ||||||||
\(187\) | −10.3259 | −0.755107 | ||||||||
\(188\) | −8.29833 | −0.605218 | ||||||||
\(189\) | −18.3994 | −1.33836 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.0303 | 1.30463 | 0.652313 | − | 0.757950i | \(-0.273799\pi\) | ||||
0.652313 | + | 0.757950i | \(0.273799\pi\) | |||||||
\(192\) | 10.6068 | 0.765482 | ||||||||
\(193\) | 6.78859 | 0.488653 | 0.244327 | − | 0.969693i | \(-0.421433\pi\) | ||||
0.244327 | + | 0.969693i | \(0.421433\pi\) | |||||||
\(194\) | 1.23210 | 0.0884599 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.14446 | −0.510318 | ||||||||
\(197\) | 7.99537 | 0.569647 | 0.284823 | − | 0.958580i | \(-0.408065\pi\) | ||||
0.284823 | + | 0.958580i | \(0.408065\pi\) | |||||||
\(198\) | 0.305299 | 0.0216966 | ||||||||
\(199\) | −5.20485 | −0.368962 | −0.184481 | − | 0.982836i | \(-0.559060\pi\) | ||||
−0.184481 | + | 0.982836i | \(0.559060\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.1389 | −0.715141 | ||||||||
\(202\) | 2.23387 | 0.157175 | ||||||||
\(203\) | −19.2787 | −1.35310 | ||||||||
\(204\) | −14.9443 | −1.04631 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.253035 | −0.0176298 | ||||||||
\(207\) | −0.732688 | −0.0509254 | ||||||||
\(208\) | −1.12618 | −0.0780868 | ||||||||
\(209\) | 3.46076 | 0.239386 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.6020 | 1.14293 | 0.571463 | − | 0.820628i | \(-0.306376\pi\) | ||||
0.571463 | + | 0.820628i | \(0.306376\pi\) | |||||||
\(212\) | 15.9296 | 1.09405 | ||||||||
\(213\) | 8.78574 | 0.601989 | ||||||||
\(214\) | −2.89934 | −0.198195 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.09953 | 0.278938 | ||||||||
\(217\) | −19.8897 | −1.35020 | ||||||||
\(218\) | 0.367035 | 0.0248587 | ||||||||
\(219\) | −13.0023 | −0.878616 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.53019 | 0.102932 | ||||||||
\(222\) | 2.18069 | 0.146358 | ||||||||
\(223\) | 6.62808 | 0.443849 | 0.221925 | − | 0.975064i | \(-0.428766\pi\) | ||||
0.221925 | + | 0.975064i | \(0.428766\pi\) | |||||||
\(224\) | 7.00792 | 0.468236 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.91002 | 0.127053 | ||||||||
\(227\) | 13.3919 | 0.888853 | 0.444427 | − | 0.895815i | \(-0.353407\pi\) | ||||
0.444427 | + | 0.895815i | \(0.353407\pi\) | |||||||
\(228\) | 5.00860 | 0.331703 | ||||||||
\(229\) | 10.0867 | 0.666549 | 0.333274 | − | 0.942830i | \(-0.391846\pi\) | ||||
0.333274 | + | 0.942830i | \(0.391846\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.59963 | 0.631609 | ||||||||
\(232\) | 4.29544 | 0.282009 | ||||||||
\(233\) | 22.0055 | 1.44163 | 0.720814 | − | 0.693129i | \(-0.243768\pi\) | ||||
0.720814 | + | 0.693129i | \(0.243768\pi\) | |||||||
\(234\) | −0.0452420 | −0.00295756 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.6735 | −0.759882 | ||||||||
\(237\) | 11.4233 | 0.742024 | ||||||||
\(238\) | −3.08383 | −0.199895 | ||||||||
\(239\) | 7.56029 | 0.489035 | 0.244517 | − | 0.969645i | \(-0.421371\pi\) | ||||
0.244517 | + | 0.969645i | \(0.421371\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.3945 | −1.31373 | −0.656864 | − | 0.754009i | \(-0.728117\pi\) | ||||
−0.656864 | + | 0.754009i | \(0.728117\pi\) | |||||||
\(242\) | 1.28220 | 0.0824232 | ||||||||
\(243\) | −8.38230 | −0.537725 | ||||||||
\(244\) | −1.80051 | −0.115266 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.273703 | −0.0174507 | ||||||||
\(247\) | −0.512848 | −0.0326317 | ||||||||
\(248\) | 4.43157 | 0.281405 | ||||||||
\(249\) | −21.3659 | −1.35401 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.5717 | 0.667278 | 0.333639 | − | 0.942701i | \(-0.391723\pi\) | ||||
0.333639 | + | 0.942701i | \(0.391723\pi\) | |||||||
\(252\) | −5.34379 | −0.336627 | ||||||||
\(253\) | 1.75838 | 0.110549 | ||||||||
\(254\) | 1.07157 | 0.0672362 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.3829 | 0.836428 | ||||||||
\(257\) | −20.2700 | −1.26441 | −0.632205 | − | 0.774801i | \(-0.717850\pi\) | ||||
−0.632205 | + | 0.774801i | \(0.717850\pi\) | |||||||
\(258\) | −0.874106 | −0.0544194 | ||||||||
\(259\) | −26.3738 | −1.63879 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.92699 | −0.304973 | ||||||||
\(262\) | 0.274143 | 0.0169366 | ||||||||
\(263\) | −28.0909 | −1.73216 | −0.866079 | − | 0.499906i | \(-0.833368\pi\) | ||||
−0.866079 | + | 0.499906i | \(0.833368\pi\) | |||||||
\(264\) | −2.13887 | −0.131638 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.03355 | 0.0633711 | ||||||||
\(267\) | −11.0785 | −0.677994 | ||||||||
\(268\) | −13.5450 | −0.827393 | ||||||||
\(269\) | 20.3230 | 1.23911 | 0.619557 | − | 0.784952i | \(-0.287312\pi\) | ||||
0.619557 | + | 0.784952i | \(0.287312\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.4467 | 1.91025 | 0.955125 | − | 0.296202i | \(-0.0957200\pi\) | ||||
0.955125 | + | 0.296202i | \(0.0957200\pi\) | |||||||
\(272\) | −19.6183 | −1.18954 | ||||||||
\(273\) | −1.42256 | −0.0860974 | ||||||||
\(274\) | 1.43769 | 0.0868543 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.54483 | 0.153181 | ||||||||
\(277\) | 13.9305 | 0.837001 | 0.418501 | − | 0.908217i | \(-0.362556\pi\) | ||||
0.418501 | + | 0.908217i | \(0.362556\pi\) | |||||||
\(278\) | −0.987576 | −0.0592309 | ||||||||
\(279\) | −5.08314 | −0.304320 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.8777 | 1.54373 | 0.771866 | − | 0.635785i | \(-0.219323\pi\) | ||||
0.771866 | + | 0.635785i | \(0.219323\pi\) | |||||||
\(282\) | 1.13778 | 0.0677541 | ||||||||
\(283\) | −23.7316 | −1.41070 | −0.705350 | − | 0.708859i | \(-0.749210\pi\) | ||||
−0.705350 | + | 0.708859i | \(0.749210\pi\) | |||||||
\(284\) | 11.7373 | 0.696480 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.108577 | 0.00642027 | ||||||||
\(287\) | 3.31024 | 0.195397 | ||||||||
\(288\) | 1.79099 | 0.105535 | ||||||||
\(289\) | 9.65625 | 0.568014 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.90105 | 0.580410 | ||||||||
\(292\) | −17.3704 | −1.01653 | ||||||||
\(293\) | 12.3029 | 0.718742 | 0.359371 | − | 0.933195i | \(-0.382991\pi\) | ||||
0.359371 | + | 0.933195i | \(0.382991\pi\) | |||||||
\(294\) | 0.979578 | 0.0571301 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.87628 | 0.341552 | ||||||||
\(297\) | 11.2850 | 0.654824 | ||||||||
\(298\) | −3.44783 | −0.199727 | ||||||||
\(299\) | −0.260574 | −0.0150694 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.5717 | 0.609341 | ||||||||
\(302\) | 0.712167 | 0.0409806 | ||||||||
\(303\) | 17.9511 | 1.03127 | ||||||||
\(304\) | 6.57512 | 0.377109 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.788124 | −0.0450540 | ||||||||
\(307\) | −4.28249 | −0.244415 | −0.122207 | − | 0.992505i | \(-0.538997\pi\) | ||||
−0.122207 | + | 0.992505i | \(0.538997\pi\) | |||||||
\(308\) | 12.8246 | 0.730750 | ||||||||
\(309\) | −2.03336 | −0.115674 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.6467 | 1.45429 | 0.727145 | − | 0.686484i | \(-0.240847\pi\) | ||||
0.727145 | + | 0.686484i | \(0.240847\pi\) | |||||||
\(312\) | 0.316957 | 0.0179442 | ||||||||
\(313\) | 22.3513 | 1.26337 | 0.631684 | − | 0.775226i | \(-0.282364\pi\) | ||||
0.631684 | + | 0.775226i | \(0.282364\pi\) | |||||||
\(314\) | −0.784668 | −0.0442814 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.2610 | 0.858496 | ||||||||
\(317\) | −21.9228 | −1.23131 | −0.615655 | − | 0.788016i | \(-0.711108\pi\) | ||||
−0.615655 | + | 0.788016i | \(0.711108\pi\) | |||||||
\(318\) | −2.18412 | −0.122479 | ||||||||
\(319\) | 11.8243 | 0.662035 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −23.2988 | −1.30041 | ||||||||
\(322\) | 0.525139 | 0.0292649 | ||||||||
\(323\) | −8.93390 | −0.497095 | ||||||||
\(324\) | 11.4160 | 0.634224 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.88062 | −0.159543 | ||||||||
\(327\) | 2.94945 | 0.163105 | ||||||||
\(328\) | −0.737546 | −0.0407242 | ||||||||
\(329\) | −13.7607 | −0.758650 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.96299 | −0.492651 | −0.246325 | − | 0.969187i | \(-0.579223\pi\) | ||||
−0.246325 | + | 0.969187i | \(0.579223\pi\) | |||||||
\(332\) | −28.5437 | −1.56654 | ||||||||
\(333\) | −6.74026 | −0.369364 | ||||||||
\(334\) | −3.85266 | −0.210808 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 18.2384 | 0.994986 | ||||||||
\(337\) | 29.0836 | 1.58428 | 0.792141 | − | 0.610338i | \(-0.208966\pi\) | ||||
0.792141 | + | 0.610338i | \(0.208966\pi\) | |||||||
\(338\) | 2.36515 | 0.128647 | ||||||||
\(339\) | 15.3487 | 0.833628 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.1991 | 0.660616 | ||||||||
\(342\) | 0.264141 | 0.0142831 | ||||||||
\(343\) | 10.9787 | 0.592795 | ||||||||
\(344\) | −2.35544 | −0.126997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.31273 | −0.0705726 | ||||||||
\(347\) | −14.2972 | −0.767513 | −0.383757 | − | 0.923434i | \(-0.625370\pi\) | ||||
−0.383757 | + | 0.923434i | \(0.625370\pi\) | |||||||
\(348\) | 17.1128 | 0.917343 | ||||||||
\(349\) | 5.62382 | 0.301036 | 0.150518 | − | 0.988607i | \(-0.451906\pi\) | ||||
0.150518 | + | 0.988607i | \(0.451906\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.67232 | −0.0892620 | ||||||||
\(352\) | −4.29821 | −0.229095 | ||||||||
\(353\) | −1.90997 | −0.101658 | −0.0508288 | − | 0.998707i | \(-0.516186\pi\) | ||||
−0.0508288 | + | 0.998707i | \(0.516186\pi\) | |||||||
\(354\) | 1.60056 | 0.0850688 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −14.8003 | −0.784415 | ||||||||
\(357\) | −24.7813 | −1.31156 | ||||||||
\(358\) | −1.47258 | −0.0778284 | ||||||||
\(359\) | 22.2047 | 1.17192 | 0.585958 | − | 0.810341i | \(-0.300718\pi\) | ||||
0.585958 | + | 0.810341i | \(0.300718\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.0058 | −0.842410 | ||||||||
\(362\) | 3.77648 | 0.198487 | ||||||||
\(363\) | 10.3036 | 0.540801 | ||||||||
\(364\) | −1.90047 | −0.0996117 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.246868 | 0.0129040 | ||||||||
\(367\) | 21.4450 | 1.11942 | 0.559709 | − | 0.828689i | \(-0.310913\pi\) | ||||
0.559709 | + | 0.828689i | \(0.310913\pi\) | |||||||
\(368\) | 3.34077 | 0.174149 | ||||||||
\(369\) | 0.845987 | 0.0440403 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.4153 | 1.37141 | ||||||||
\(372\) | 17.6552 | 0.915377 | ||||||||
\(373\) | −23.1399 | −1.19814 | −0.599070 | − | 0.800697i | \(-0.704463\pi\) | ||||
−0.599070 | + | 0.800697i | \(0.704463\pi\) | |||||||
\(374\) | 1.89142 | 0.0978032 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.06598 | 0.158116 | ||||||||
\(377\) | −1.75224 | −0.0902448 | ||||||||
\(378\) | 3.37026 | 0.173348 | ||||||||
\(379\) | −21.6501 | −1.11209 | −0.556047 | − | 0.831151i | \(-0.687682\pi\) | ||||
−0.556047 | + | 0.831151i | \(0.687682\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.61100 | 0.441155 | ||||||||
\(382\) | −3.30265 | −0.168978 | ||||||||
\(383\) | −5.65481 | −0.288947 | −0.144474 | − | 0.989509i | \(-0.546149\pi\) | ||||
−0.144474 | + | 0.989509i | \(0.546149\pi\) | |||||||
\(384\) | −8.26962 | −0.422007 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.24348 | −0.0632915 | ||||||||
\(387\) | 2.70176 | 0.137338 | ||||||||
\(388\) | 13.2273 | 0.671514 | ||||||||
\(389\) | −8.12605 | −0.412007 | −0.206004 | − | 0.978551i | \(-0.566046\pi\) | ||||
−0.206004 | + | 0.978551i | \(0.566046\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.53924 | −0.229559 | ||||||||
\(392\) | 2.63966 | 0.133323 | ||||||||
\(393\) | 2.20298 | 0.111126 | ||||||||
\(394\) | −1.46453 | −0.0737819 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.27754 | 0.164703 | ||||||||
\(397\) | 20.7689 | 1.04236 | 0.521180 | − | 0.853447i | \(-0.325492\pi\) | ||||
0.521180 | + | 0.853447i | \(0.325492\pi\) | |||||||
\(398\) | 0.953382 | 0.0477887 | ||||||||
\(399\) | 8.30550 | 0.415795 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.1195 | 1.50410 | 0.752049 | − | 0.659107i | \(-0.229066\pi\) | ||||
0.752049 | + | 0.659107i | \(0.229066\pi\) | |||||||
\(402\) | 1.85716 | 0.0926266 | ||||||||
\(403\) | −1.80777 | −0.0900515 | ||||||||
\(404\) | 23.9818 | 1.19314 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.53132 | 0.175256 | ||||||||
\(407\) | 16.1760 | 0.801815 | ||||||||
\(408\) | 5.52145 | 0.273353 | ||||||||
\(409\) | 11.0452 | 0.546152 | 0.273076 | − | 0.961992i | \(-0.411959\pi\) | ||||
0.273076 | + | 0.961992i | \(0.411959\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.5531 | 0.569874 | ||||||||
\(412\) | −2.71646 | −0.133830 | ||||||||
\(413\) | −19.3576 | −0.952524 | ||||||||
\(414\) | 0.134208 | 0.00659597 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.636949 | 0.0312290 | ||||||||
\(417\) | −7.93604 | −0.388630 | ||||||||
\(418\) | −0.633915 | −0.0310058 | ||||||||
\(419\) | −32.9212 | −1.60830 | −0.804152 | − | 0.594424i | \(-0.797380\pi\) | ||||
−0.804152 | + | 0.594424i | \(0.797380\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.2647 | −0.987642 | −0.493821 | − | 0.869564i | \(-0.664400\pi\) | ||||
−0.493821 | + | 0.869564i | \(0.664400\pi\) | |||||||
\(422\) | −3.04101 | −0.148034 | ||||||||
\(423\) | −3.51677 | −0.170991 | ||||||||
\(424\) | −5.88552 | −0.285826 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.60930 | −0.0779709 | ||||||||
\(427\) | −2.98569 | −0.144488 | ||||||||
\(428\) | −31.1260 | −1.50453 | ||||||||
\(429\) | 0.872509 | 0.0421251 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.15526 | 0.344657 | 0.172328 | − | 0.985040i | \(-0.444871\pi\) | ||||
0.172328 | + | 0.985040i | \(0.444871\pi\) | |||||||
\(432\) | 21.4405 | 1.03156 | ||||||||
\(433\) | 5.48264 | 0.263479 | 0.131739 | − | 0.991284i | \(-0.457944\pi\) | ||||
0.131739 | + | 0.991284i | \(0.457944\pi\) | |||||||
\(434\) | 3.64324 | 0.174881 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.94031 | 0.188707 | ||||||||
\(437\) | 1.52134 | 0.0727754 | ||||||||
\(438\) | 2.38166 | 0.113800 | ||||||||
\(439\) | −30.7561 | −1.46791 | −0.733954 | − | 0.679199i | \(-0.762327\pi\) | ||||
−0.733954 | + | 0.679199i | \(0.762327\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.02777 | −0.144179 | ||||||||
\(442\) | −0.280289 | −0.0133320 | ||||||||
\(443\) | −11.3527 | −0.539381 | −0.269691 | − | 0.962947i | \(-0.586921\pi\) | ||||
−0.269691 | + | 0.962947i | \(0.586921\pi\) | |||||||
\(444\) | 23.4108 | 1.11103 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.21408 | −0.0574883 | ||||||||
\(447\) | −27.7063 | −1.31046 | ||||||||
\(448\) | 23.4976 | 1.11016 | ||||||||
\(449\) | −15.7661 | −0.744050 | −0.372025 | − | 0.928223i | \(-0.621336\pi\) | ||||
−0.372025 | + | 0.928223i | \(0.621336\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.03029 | −0.0956027 | ||||||||
\(452\) | 20.5051 | 0.964479 | ||||||||
\(453\) | 5.72289 | 0.268885 | ||||||||
\(454\) | −2.45303 | −0.115126 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.85053 | −0.0866588 | ||||||||
\(457\) | 4.16714 | 0.194931 | 0.0974653 | − | 0.995239i | \(-0.468926\pi\) | ||||
0.0974653 | + | 0.995239i | \(0.468926\pi\) | |||||||
\(458\) | −1.84760 | −0.0863329 | ||||||||
\(459\) | −29.1322 | −1.35977 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.9714 | −1.11646 | −0.558230 | − | 0.829686i | \(-0.688519\pi\) | ||||
−0.558230 | + | 0.829686i | \(0.688519\pi\) | |||||||
\(462\) | −1.75838 | −0.0818074 | ||||||||
\(463\) | −41.3247 | −1.92052 | −0.960260 | − | 0.279107i | \(-0.909962\pi\) | ||||
−0.960260 | + | 0.279107i | \(0.909962\pi\) | |||||||
\(464\) | 22.4651 | 1.04292 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.03079 | −0.186723 | ||||||||
\(467\) | 10.3966 | 0.481097 | 0.240548 | − | 0.970637i | \(-0.422673\pi\) | ||||
0.240548 | + | 0.970637i | \(0.422673\pi\) | |||||||
\(468\) | −0.485697 | −0.0224513 | ||||||||
\(469\) | −22.4610 | −1.03715 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.30550 | −0.290542 | ||||||||
\(472\) | 4.31301 | 0.198522 | ||||||||
\(473\) | −6.48398 | −0.298134 | ||||||||
\(474\) | −2.09243 | −0.0961086 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −33.1065 | −1.51743 | ||||||||
\(477\) | 6.75086 | 0.309101 | ||||||||
\(478\) | −1.38483 | −0.0633408 | ||||||||
\(479\) | 36.0081 | 1.64525 | 0.822626 | − | 0.568582i | \(-0.192508\pi\) | ||||
0.822626 | + | 0.568582i | \(0.192508\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.39711 | −0.109299 | ||||||||
\(482\) | 3.73571 | 0.170157 | ||||||||
\(483\) | 4.21996 | 0.192015 | ||||||||
\(484\) | 13.7651 | 0.625688 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.53540 | 0.0696473 | ||||||||
\(487\) | −10.6378 | −0.482045 | −0.241023 | − | 0.970520i | \(-0.577483\pi\) | ||||
−0.241023 | + | 0.970520i | \(0.577483\pi\) | |||||||
\(488\) | 0.665233 | 0.0301137 | ||||||||
\(489\) | −23.1483 | −1.04680 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.6693 | −0.797402 | −0.398701 | − | 0.917081i | \(-0.630539\pi\) | ||||
−0.398701 | + | 0.917081i | \(0.630539\pi\) | |||||||
\(492\) | −2.93835 | −0.132471 | ||||||||
\(493\) | −30.5243 | −1.37475 | ||||||||
\(494\) | 0.0939394 | 0.00422653 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.1771 | 1.04068 | ||||||||
\(497\) | 19.4633 | 0.873049 | ||||||||
\(498\) | 3.91363 | 0.175374 | ||||||||
\(499\) | −9.41734 | −0.421578 | −0.210789 | − | 0.977532i | \(-0.567603\pi\) | ||||
−0.210789 | + | 0.977532i | \(0.567603\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.9595 | −1.38317 | ||||||||
\(502\) | −1.93643 | −0.0864273 | ||||||||
\(503\) | 18.0133 | 0.803172 | 0.401586 | − | 0.915821i | \(-0.368459\pi\) | ||||
0.401586 | + | 0.915821i | \(0.368459\pi\) | |||||||
\(504\) | 1.97437 | 0.0879454 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.322087 | −0.0143185 | ||||||||
\(507\) | 19.0060 | 0.844088 | ||||||||
\(508\) | 11.5039 | 0.510401 | ||||||||
\(509\) | −16.0485 | −0.711337 | −0.355669 | − | 0.934612i | \(-0.615747\pi\) | ||||
−0.355669 | + | 0.934612i | \(0.615747\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.8045 | −1.27423 | ||||||||
\(512\) | −13.6877 | −0.604914 | ||||||||
\(513\) | 9.76370 | 0.431078 | ||||||||
\(514\) | 3.71291 | 0.163769 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.38398 | −0.413107 | ||||||||
\(517\) | 8.43991 | 0.371187 | ||||||||
\(518\) | 4.83095 | 0.212260 | ||||||||
\(519\) | −10.5489 | −0.463046 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.20069 | −0.0964142 | −0.0482071 | − | 0.998837i | \(-0.515351\pi\) | ||||
−0.0482071 | + | 0.998837i | \(0.515351\pi\) | |||||||
\(522\) | 0.902487 | 0.0395008 | ||||||||
\(523\) | 7.43588 | 0.325148 | 0.162574 | − | 0.986696i | \(-0.448020\pi\) | ||||
0.162574 | + | 0.986696i | \(0.448020\pi\) | |||||||
\(524\) | 2.94307 | 0.128569 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.14547 | 0.224353 | ||||||||
\(527\) | −31.4917 | −1.37180 | ||||||||
\(528\) | −11.1863 | −0.486820 | ||||||||
\(529\) | −22.2270 | −0.966392 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.94715 | −0.214688 | ||||||||
\(532\) | 11.0957 | 0.481061 | ||||||||
\(533\) | 0.300867 | 0.0130320 | ||||||||
\(534\) | 2.02927 | 0.0878153 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.00447 | 0.216160 | ||||||||
\(537\) | −11.8335 | −0.510653 | ||||||||
\(538\) | −3.72260 | −0.160493 | ||||||||
\(539\) | 7.26636 | 0.312984 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.6474 | 0.887701 | 0.443850 | − | 0.896101i | \(-0.353612\pi\) | ||||
0.443850 | + | 0.896101i | \(0.353612\pi\) | |||||||
\(542\) | −5.76016 | −0.247420 | ||||||||
\(543\) | 30.3473 | 1.30233 | ||||||||
\(544\) | 11.0958 | 0.475727 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.260574 | 0.0111515 | ||||||||
\(547\) | −31.3762 | −1.34155 | −0.670774 | − | 0.741662i | \(-0.734038\pi\) | ||||
−0.670774 | + | 0.741662i | \(0.734038\pi\) | |||||||
\(548\) | 15.4344 | 0.659325 | ||||||||
\(549\) | −0.763042 | −0.0325658 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.2303 | 0.435825 | ||||||||
\(552\) | −0.940237 | −0.0400192 | ||||||||
\(553\) | 25.3064 | 1.07614 | ||||||||
\(554\) | −2.55167 | −0.108410 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.6021 | −0.449631 | ||||||||
\(557\) | 22.3515 | 0.947064 | 0.473532 | − | 0.880776i | \(-0.342979\pi\) | ||||
0.473532 | + | 0.880776i | \(0.342979\pi\) | |||||||
\(558\) | 0.931089 | 0.0394161 | ||||||||
\(559\) | 0.960857 | 0.0406399 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.1993 | 0.641713 | ||||||||
\(562\) | −4.74007 | −0.199948 | ||||||||
\(563\) | 34.3663 | 1.44837 | 0.724184 | − | 0.689607i | \(-0.242217\pi\) | ||||
0.724184 | + | 0.689607i | \(0.242217\pi\) | |||||||
\(564\) | 12.2147 | 0.514332 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.34697 | 0.182717 | ||||||||
\(567\) | 18.9306 | 0.795010 | ||||||||
\(568\) | −4.33657 | −0.181958 | ||||||||
\(569\) | 32.1662 | 1.34848 | 0.674239 | − | 0.738513i | \(-0.264472\pi\) | ||||
0.674239 | + | 0.738513i | \(0.264472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.1668 | −1.13690 | −0.568448 | − | 0.822719i | \(-0.692456\pi\) | ||||
−0.568448 | + | 0.822719i | \(0.692456\pi\) | |||||||
\(572\) | 1.16563 | 0.0487373 | ||||||||
\(573\) | −26.5397 | −1.10871 | ||||||||
\(574\) | −0.606344 | −0.0253083 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.00521 | 0.250217 | ||||||||
\(577\) | −13.8503 | −0.576596 | −0.288298 | − | 0.957541i | \(-0.593089\pi\) | ||||
−0.288298 | + | 0.957541i | \(0.593089\pi\) | |||||||
\(578\) | −1.76875 | −0.0735705 | ||||||||
\(579\) | −9.99246 | −0.415273 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −47.3325 | −1.96368 | ||||||||
\(582\) | −1.81360 | −0.0751759 | ||||||||
\(583\) | −16.2014 | −0.670995 | ||||||||
\(584\) | 6.41785 | 0.265572 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.25354 | −0.0930930 | ||||||||
\(587\) | −44.1499 | −1.82226 | −0.911131 | − | 0.412118i | \(-0.864789\pi\) | ||||
−0.911131 | + | 0.412118i | \(0.864789\pi\) | |||||||
\(588\) | 10.5163 | 0.433684 | ||||||||
\(589\) | 10.5545 | 0.434891 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.7688 | −0.484103 | ||||||||
\(592\) | 30.7329 | 1.26311 | ||||||||
\(593\) | 16.2531 | 0.667437 | 0.333718 | − | 0.942673i | \(-0.391697\pi\) | ||||
0.333718 | + | 0.942673i | \(0.391697\pi\) | |||||||
\(594\) | −2.06710 | −0.0848143 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −37.0142 | −1.51616 | ||||||||
\(597\) | 7.66127 | 0.313555 | ||||||||
\(598\) | 0.0477298 | 0.00195182 | ||||||||
\(599\) | 30.4822 | 1.24547 | 0.622734 | − | 0.782433i | \(-0.286022\pi\) | ||||
0.622734 | + | 0.782433i | \(0.286022\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.9162 | −1.17952 | −0.589758 | − | 0.807580i | \(-0.700777\pi\) | ||||
−0.589758 | + | 0.807580i | \(0.700777\pi\) | |||||||
\(602\) | −1.93643 | −0.0789232 | ||||||||
\(603\) | −5.74027 | −0.233762 | ||||||||
\(604\) | 7.64549 | 0.311090 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.28815 | −0.133572 | ||||||||
\(607\) | −8.23276 | −0.334157 | −0.167079 | − | 0.985944i | \(-0.553433\pi\) | ||||
−0.167079 | + | 0.985944i | \(0.553433\pi\) | |||||||
\(608\) | −3.71877 | −0.150816 | ||||||||
\(609\) | 28.3773 | 1.14990 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.25071 | −0.0505981 | ||||||||
\(612\) | −8.46092 | −0.342012 | ||||||||
\(613\) | −4.79811 | −0.193794 | −0.0968969 | − | 0.995294i | \(-0.530892\pi\) | ||||
−0.0968969 | + | 0.995294i | \(0.530892\pi\) | |||||||
\(614\) | 0.784432 | 0.0316571 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.73830 | −0.190912 | ||||||||
\(617\) | 2.03184 | 0.0817986 | 0.0408993 | − | 0.999163i | \(-0.486978\pi\) | ||||
0.0408993 | + | 0.999163i | \(0.486978\pi\) | |||||||
\(618\) | 0.372454 | 0.0149823 | ||||||||
\(619\) | 8.14100 | 0.327215 | 0.163607 | − | 0.986526i | \(-0.447687\pi\) | ||||
0.163607 | + | 0.986526i | \(0.447687\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.96086 | 0.199072 | ||||||||
\(622\) | −4.69776 | −0.188363 | ||||||||
\(623\) | −24.5426 | −0.983278 | ||||||||
\(624\) | 1.65769 | 0.0663605 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.09413 | −0.163634 | ||||||||
\(627\) | −5.09406 | −0.203437 | ||||||||
\(628\) | −8.42382 | −0.336147 | ||||||||
\(629\) | −41.7581 | −1.66500 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.2847 | 1.32504 | 0.662522 | − | 0.749042i | \(-0.269486\pi\) | ||||
0.662522 | + | 0.749042i | \(0.269486\pi\) | |||||||
\(632\) | −5.63846 | −0.224286 | ||||||||
\(633\) | −24.4372 | −0.971293 | ||||||||
\(634\) | 4.01565 | 0.159482 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −23.4476 | −0.929759 | ||||||||
\(637\) | −1.07680 | −0.0426642 | ||||||||
\(638\) | −2.16589 | −0.0857482 | ||||||||
\(639\) | 4.97417 | 0.196775 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.0481 | −1.58180 | −0.790902 | − | 0.611943i | \(-0.790388\pi\) | ||||
−0.790902 | + | 0.611943i | \(0.790388\pi\) | |||||||
\(642\) | 4.26769 | 0.168432 | ||||||||
\(643\) | 11.6870 | 0.460890 | 0.230445 | − | 0.973085i | \(-0.425982\pi\) | ||||
0.230445 | + | 0.973085i | \(0.425982\pi\) | |||||||
\(644\) | 5.63764 | 0.222154 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.63644 | 0.0643849 | ||||||||
\(647\) | 7.94936 | 0.312522 | 0.156261 | − | 0.987716i | \(-0.450056\pi\) | ||||
0.156261 | + | 0.987716i | \(0.450056\pi\) | |||||||
\(648\) | −4.21787 | −0.165694 | ||||||||
\(649\) | 11.8727 | 0.466044 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.2766 | 1.14744 | ||||||||
\(652\) | −30.9250 | −1.21112 | ||||||||
\(653\) | −3.33736 | −0.130601 | −0.0653005 | − | 0.997866i | \(-0.520801\pi\) | ||||
−0.0653005 | + | 0.997866i | \(0.520801\pi\) | |||||||
\(654\) | −0.540256 | −0.0211257 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.85736 | −0.150605 | ||||||||
\(657\) | −7.36146 | −0.287198 | ||||||||
\(658\) | 2.52057 | 0.0982621 | ||||||||
\(659\) | −30.0508 | −1.17061 | −0.585306 | − | 0.810812i | \(-0.699026\pi\) | ||||
−0.585306 | + | 0.810812i | \(0.699026\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.58417 | −0.256094 | −0.128047 | − | 0.991768i | \(-0.540871\pi\) | ||||
−0.128047 | + | 0.991768i | \(0.540871\pi\) | |||||||
\(662\) | 1.64177 | 0.0638092 | ||||||||
\(663\) | −2.25237 | −0.0874747 | ||||||||
\(664\) | 10.5460 | 0.409266 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.23463 | 0.0478409 | ||||||||
\(667\) | 5.19792 | 0.201264 | ||||||||
\(668\) | −41.3603 | −1.60028 | ||||||||
\(669\) | −9.75620 | −0.377196 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.83123 | 0.0706939 | ||||||||
\(672\) | −10.3153 | −0.397921 | ||||||||
\(673\) | −6.73140 | −0.259476 | −0.129738 | − | 0.991548i | \(-0.541414\pi\) | ||||
−0.129738 | + | 0.991548i | \(0.541414\pi\) | |||||||
\(674\) | −5.32730 | −0.205200 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25.3911 | 0.976580 | ||||||||
\(677\) | −13.6478 | −0.524529 | −0.262265 | − | 0.964996i | \(-0.584469\pi\) | ||||
−0.262265 | + | 0.964996i | \(0.584469\pi\) | |||||||
\(678\) | −2.81146 | −0.107973 | ||||||||
\(679\) | 21.9341 | 0.841753 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.7122 | −0.755374 | ||||||||
\(682\) | −2.23453 | −0.0855645 | ||||||||
\(683\) | −1.17220 | −0.0448529 | −0.0224265 | − | 0.999748i | \(-0.507139\pi\) | ||||
−0.0224265 | + | 0.999748i | \(0.507139\pi\) | |||||||
\(684\) | 2.83570 | 0.108426 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.01099 | −0.0767801 | ||||||||
\(687\) | −14.8471 | −0.566453 | ||||||||
\(688\) | −12.3190 | −0.469656 | ||||||||
\(689\) | 2.40088 | 0.0914663 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.2674 | 0.466673 | 0.233336 | − | 0.972396i | \(-0.425036\pi\) | ||||
0.233336 | + | 0.972396i | \(0.425036\pi\) | |||||||
\(692\) | −14.0928 | −0.535728 | ||||||||
\(693\) | 5.43497 | 0.206457 | ||||||||
\(694\) | 2.61885 | 0.0994100 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.32266 | −0.239660 | ||||||||
\(697\) | 5.24116 | 0.198523 | ||||||||
\(698\) | −1.03013 | −0.0389909 | ||||||||
\(699\) | −32.3910 | −1.22514 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.0271 | −0.756415 | −0.378207 | − | 0.925721i | \(-0.623459\pi\) | ||||
−0.378207 | + | 0.925721i | \(0.623459\pi\) | |||||||
\(702\) | 0.306323 | 0.0115614 | ||||||||
\(703\) | 13.9953 | 0.527843 | ||||||||
\(704\) | −14.4119 | −0.543171 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.349854 | 0.0131669 | ||||||||
\(707\) | 39.7677 | 1.49562 | ||||||||
\(708\) | 17.1828 | 0.645771 | ||||||||
\(709\) | −4.39510 | −0.165061 | −0.0825306 | − | 0.996589i | \(-0.526300\pi\) | ||||
−0.0825306 | + | 0.996589i | \(0.526300\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.46748 | 0.242549 | ||||||||
\(712\) | 5.46827 | 0.204932 | ||||||||
\(713\) | 5.36266 | 0.200833 | ||||||||
\(714\) | 4.53924 | 0.169877 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.8089 | −0.590808 | ||||||||
\(717\) | −11.1284 | −0.415596 | ||||||||
\(718\) | −4.06727 | −0.151789 | ||||||||
\(719\) | −10.9283 | −0.407557 | −0.203779 | − | 0.979017i | \(-0.565322\pi\) | ||||
−0.203779 | + | 0.979017i | \(0.565322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.50456 | −0.167759 | ||||||||
\(722\) | 2.93181 | 0.109111 | ||||||||
\(723\) | 30.0197 | 1.11645 | ||||||||
\(724\) | 40.5425 | 1.50675 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.88734 | −0.0700458 | ||||||||
\(727\) | 32.9032 | 1.22031 | 0.610156 | − | 0.792281i | \(-0.291107\pi\) | ||||
0.610156 | + | 0.792281i | \(0.291107\pi\) | |||||||
\(728\) | 0.702166 | 0.0260240 | ||||||||
\(729\) | 29.7545 | 1.10202 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.7383 | 0.619088 | ||||||||
\(732\) | 2.65026 | 0.0979564 | ||||||||
\(733\) | 13.7498 | 0.507859 | 0.253929 | − | 0.967223i | \(-0.418277\pi\) | ||||
0.253929 | + | 0.967223i | \(0.418277\pi\) | |||||||
\(734\) | −3.92812 | −0.144990 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.88948 | −0.0696470 | ||||||||
\(737\) | 13.7761 | 0.507450 | ||||||||
\(738\) | −0.154961 | −0.00570420 | ||||||||
\(739\) | −43.1893 | −1.58874 | −0.794372 | − | 0.607432i | \(-0.792200\pi\) | ||||
−0.794372 | + | 0.607432i | \(0.792200\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.754886 | 0.0277314 | ||||||||
\(742\) | −4.83854 | −0.177628 | ||||||||
\(743\) | 31.8479 | 1.16838 | 0.584192 | − | 0.811615i | \(-0.301411\pi\) | ||||
0.584192 | + | 0.811615i | \(0.301411\pi\) | |||||||
\(744\) | −6.52304 | −0.239146 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.23859 | 0.155186 | ||||||||
\(747\) | −12.0966 | −0.442592 | ||||||||
\(748\) | 20.3054 | 0.742440 | ||||||||
\(749\) | −51.6145 | −1.88595 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.5952 | −1.07995 | −0.539973 | − | 0.841682i | \(-0.681565\pi\) | ||||
−0.539973 | + | 0.841682i | \(0.681565\pi\) | |||||||
\(752\) | 16.0351 | 0.584738 | ||||||||
\(753\) | −15.5610 | −0.567073 | ||||||||
\(754\) | 0.320961 | 0.0116887 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 36.1815 | 1.31591 | ||||||||
\(757\) | −0.0984401 | −0.00357786 | −0.00178893 | − | 0.999998i | \(-0.500569\pi\) | ||||
−0.00178893 | + | 0.999998i | \(0.500569\pi\) | |||||||
\(758\) | 3.96570 | 0.144041 | ||||||||
\(759\) | −2.58825 | −0.0939476 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.54402 | −0.128471 | −0.0642353 | − | 0.997935i | \(-0.520461\pi\) | ||||
−0.0642353 | + | 0.997935i | \(0.520461\pi\) | |||||||
\(762\) | −1.57730 | −0.0571394 | ||||||||
\(763\) | 6.53400 | 0.236547 | ||||||||
\(764\) | −35.4556 | −1.28274 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.03580 | 0.0374251 | ||||||||
\(767\) | −1.75941 | −0.0635285 | ||||||||
\(768\) | −19.6989 | −0.710822 | ||||||||
\(769\) | 1.42759 | 0.0514802 | 0.0257401 | − | 0.999669i | \(-0.491806\pi\) | ||||
0.0257401 | + | 0.999669i | \(0.491806\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.8365 | 1.07453 | ||||||||
\(772\) | −13.3494 | −0.480456 | ||||||||
\(773\) | 33.7807 | 1.21501 | 0.607504 | − | 0.794317i | \(-0.292171\pi\) | ||||
0.607504 | + | 0.794317i | \(0.292171\pi\) | |||||||
\(774\) | −0.494888 | −0.0177884 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.88708 | −0.175436 | ||||||||
\(777\) | 38.8209 | 1.39269 | ||||||||
\(778\) | 1.48847 | 0.0533641 | ||||||||
\(779\) | −1.75659 | −0.0629363 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.9376 | −0.427159 | ||||||||
\(782\) | 0.831462 | 0.0297330 | ||||||||
\(783\) | 33.3595 | 1.19217 | ||||||||
\(784\) | 13.8054 | 0.493050 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.403525 | −0.0143932 | ||||||||
\(787\) | 2.18030 | 0.0777192 | 0.0388596 | − | 0.999245i | \(-0.487627\pi\) | ||||
0.0388596 | + | 0.999245i | \(0.487627\pi\) | |||||||
\(788\) | −15.7225 | −0.560090 | ||||||||
\(789\) | 41.3484 | 1.47204 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.0025 | 1.20899 | ||||||||
\(792\) | −1.21095 | −0.0430293 | ||||||||
\(793\) | −0.271369 | −0.00963659 | ||||||||
\(794\) | −3.80428 | −0.135009 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.2351 | 0.362772 | ||||||||
\(797\) | 23.4919 | 0.832124 | 0.416062 | − | 0.909336i | \(-0.363410\pi\) | ||||
0.416062 | + | 0.909336i | \(0.363410\pi\) | |||||||
\(798\) | −1.52134 | −0.0538547 | ||||||||
\(799\) | −21.7875 | −0.770787 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.27226 | −0.221620 | ||||||||
\(802\) | −5.51706 | −0.194814 | ||||||||
\(803\) | 17.6668 | 0.623449 | ||||||||
\(804\) | 19.9376 | 0.703143 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.331133 | 0.0116637 | ||||||||
\(807\) | −29.9144 | −1.05304 | ||||||||
\(808\) | −8.86054 | −0.311713 | ||||||||
\(809\) | −38.1509 | −1.34132 | −0.670658 | − | 0.741767i | \(-0.733988\pi\) | ||||
−0.670658 | + | 0.741767i | \(0.733988\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.9069 | 1.68224 | 0.841120 | − | 0.540849i | \(-0.181897\pi\) | ||||
0.841120 | + | 0.540849i | \(0.181897\pi\) | |||||||
\(812\) | 37.9106 | 1.33040 | ||||||||
\(813\) | −46.2879 | −1.62339 | ||||||||
\(814\) | −2.96299 | −0.103853 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 28.8772 | 1.01090 | ||||||||
\(817\) | −5.60988 | −0.196265 | ||||||||
\(818\) | −2.02318 | −0.0707388 | ||||||||
\(819\) | −0.805405 | −0.0281431 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.9808 | 0.662434 | 0.331217 | − | 0.943555i | \(-0.392541\pi\) | ||||
0.331217 | + | 0.943555i | \(0.392541\pi\) | |||||||
\(822\) | −2.11621 | −0.0738114 | ||||||||
\(823\) | −22.1681 | −0.772732 | −0.386366 | − | 0.922345i | \(-0.626270\pi\) | ||||
−0.386366 | + | 0.922345i | \(0.626270\pi\) | |||||||
\(824\) | 1.00365 | 0.0349638 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.54577 | 0.123373 | ||||||||
\(827\) | −4.72938 | −0.164457 | −0.0822283 | − | 0.996614i | \(-0.526204\pi\) | ||||
−0.0822283 | + | 0.996614i | \(0.526204\pi\) | |||||||
\(828\) | 1.44079 | 0.0500710 | ||||||||
\(829\) | 16.4400 | 0.570986 | 0.285493 | − | 0.958381i | \(-0.407843\pi\) | ||||
0.285493 | + | 0.958381i | \(0.407843\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.5050 | −0.711309 | ||||||||
\(832\) | 2.13570 | 0.0740419 | ||||||||
\(833\) | −18.7580 | −0.649926 | ||||||||
\(834\) | 1.45366 | 0.0503362 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.80540 | −0.235370 | ||||||||
\(837\) | 34.4167 | 1.18962 | ||||||||
\(838\) | 6.03024 | 0.208311 | ||||||||
\(839\) | −5.60083 | −0.193362 | −0.0966811 | − | 0.995315i | \(-0.530823\pi\) | ||||
−0.0966811 | + | 0.995315i | \(0.530823\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.95363 | 0.205298 | ||||||||
\(842\) | 3.71193 | 0.127922 | ||||||||
\(843\) | −38.0906 | −1.31191 | ||||||||
\(844\) | −32.6469 | −1.12375 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.644174 | 0.0221471 | ||||||||
\(847\) | 22.8260 | 0.784310 | ||||||||
\(848\) | −30.7812 | −1.05703 | ||||||||
\(849\) | 34.9318 | 1.19886 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.11091 | 0.243759 | ||||||||
\(852\) | −17.2767 | −0.591890 | ||||||||
\(853\) | −17.8905 | −0.612559 | −0.306279 | − | 0.951942i | \(-0.599084\pi\) | ||||
−0.306279 | + | 0.951942i | \(0.599084\pi\) | |||||||
\(854\) | 0.546895 | 0.0187144 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.5001 | 0.393065 | ||||||||
\(857\) | 3.19536 | 0.109151 | 0.0545757 | − | 0.998510i | \(-0.482619\pi\) | ||||
0.0545757 | + | 0.998510i | \(0.482619\pi\) | |||||||
\(858\) | −0.159819 | −0.00545614 | ||||||||
\(859\) | 43.4196 | 1.48146 | 0.740728 | − | 0.671805i | \(-0.234481\pi\) | ||||
0.740728 | + | 0.671805i | \(0.234481\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.87251 | −0.166055 | ||||||||
\(862\) | −1.31064 | −0.0446407 | ||||||||
\(863\) | 43.2724 | 1.47301 | 0.736504 | − | 0.676433i | \(-0.236475\pi\) | ||||
0.736504 | + | 0.676433i | \(0.236475\pi\) | |||||||
\(864\) | −12.1264 | −0.412547 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.00427 | −0.0341264 | ||||||||
\(867\) | −14.2135 | −0.482716 | ||||||||
\(868\) | 39.1120 | 1.32755 | ||||||||
\(869\) | −15.5213 | −0.526525 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.04147 | −0.0691727 | ||||||||
\(872\) | −1.45582 | −0.0493004 | ||||||||
\(873\) | 5.60562 | 0.189722 | ||||||||
\(874\) | −0.278666 | −0.00942603 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 25.5684 | 0.863876 | ||||||||
\(877\) | 34.2339 | 1.15600 | 0.577999 | − | 0.816038i | \(-0.303834\pi\) | ||||
0.577999 | + | 0.816038i | \(0.303834\pi\) | |||||||
\(878\) | 5.63366 | 0.190127 | ||||||||
\(879\) | −18.1092 | −0.610808 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.6270 | 0.930779 | 0.465389 | − | 0.885106i | \(-0.345914\pi\) | ||||
0.465389 | + | 0.885106i | \(0.345914\pi\) | |||||||
\(882\) | 0.554602 | 0.0186744 | ||||||||
\(883\) | 25.8990 | 0.871571 | 0.435786 | − | 0.900051i | \(-0.356471\pi\) | ||||
0.435786 | + | 0.900051i | \(0.356471\pi\) | |||||||
\(884\) | −3.00905 | −0.101205 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.07949 | 0.0698618 | ||||||||
\(887\) | 17.2449 | 0.579027 | 0.289514 | − | 0.957174i | \(-0.406506\pi\) | ||||
0.289514 | + | 0.957174i | \(0.406506\pi\) | |||||||
\(888\) | −8.64958 | −0.290261 | ||||||||
\(889\) | 19.0762 | 0.639796 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.6108 | −0.388977 | ||||||||
\(892\) | −13.0338 | −0.436403 | ||||||||
\(893\) | 7.30213 | 0.244356 | ||||||||
\(894\) | 5.07502 | 0.169734 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −18.3200 | −0.612027 | ||||||||
\(897\) | 0.383551 | 0.0128064 | ||||||||
\(898\) | 2.88792 | 0.0963710 | ||||||||
\(899\) | 36.0614 | 1.20271 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.8238 | 1.39335 | ||||||||
\(902\) | 0.371893 | 0.0123827 | ||||||||
\(903\) | −15.5610 | −0.517836 | ||||||||
\(904\) | −7.57601 | −0.251974 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.04827 | −0.0348266 | ||||||||
\(907\) | −57.0465 | −1.89420 | −0.947099 | − | 0.320940i | \(-0.896001\pi\) | ||||
−0.947099 | + | 0.320940i | \(0.896001\pi\) | |||||||
\(908\) | −26.3345 | −0.873942 | ||||||||
\(909\) | 10.1633 | 0.337095 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.8683 | 0.658267 | 0.329133 | − | 0.944283i | \(-0.393243\pi\) | ||||
0.329133 | + | 0.944283i | \(0.393243\pi\) | |||||||
\(912\) | −9.67824 | −0.320479 | ||||||||
\(913\) | 29.0307 | 0.960777 | ||||||||
\(914\) | −0.763304 | −0.0252478 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.8350 | −0.655367 | ||||||||
\(917\) | 4.88033 | 0.161163 | ||||||||
\(918\) | 5.33620 | 0.176121 | ||||||||
\(919\) | 27.9785 | 0.922924 | 0.461462 | − | 0.887160i | \(-0.347325\pi\) | ||||
0.461462 | + | 0.887160i | \(0.347325\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.30361 | 0.207711 | ||||||||
\(922\) | 4.39090 | 0.144606 | ||||||||
\(923\) | 1.76902 | 0.0582279 | ||||||||
\(924\) | −18.8772 | −0.621013 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.56952 | 0.248750 | ||||||||
\(927\) | −1.15122 | −0.0378109 | ||||||||
\(928\) | −12.7059 | −0.417090 | ||||||||
\(929\) | −14.1249 | −0.463424 | −0.231712 | − | 0.972784i | \(-0.574433\pi\) | ||||
−0.231712 | + | 0.972784i | \(0.574433\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.28678 | 0.206041 | ||||||||
\(932\) | −43.2727 | −1.41744 | ||||||||
\(933\) | −37.7506 | −1.23590 | ||||||||
\(934\) | −1.90437 | −0.0623127 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.179450 | 0.00586551 | ||||||||
\(937\) | 35.9546 | 1.17459 | 0.587293 | − | 0.809374i | \(-0.300194\pi\) | ||||
0.587293 | + | 0.809374i | \(0.300194\pi\) | |||||||
\(938\) | 4.11422 | 0.134334 | ||||||||
\(939\) | −32.8999 | −1.07365 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.6979 | 0.870327 | 0.435164 | − | 0.900351i | \(-0.356691\pi\) | ||||
0.435164 | + | 0.900351i | \(0.356691\pi\) | |||||||
\(942\) | 1.15499 | 0.0376317 | ||||||||
\(943\) | −0.892508 | −0.0290640 | ||||||||
\(944\) | 22.5570 | 0.734169 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.18768 | 0.0386150 | ||||||||
\(947\) | 17.3102 | 0.562506 | 0.281253 | − | 0.959634i | \(-0.409250\pi\) | ||||
0.281253 | + | 0.959634i | \(0.409250\pi\) | |||||||
\(948\) | −22.4634 | −0.729576 | ||||||||
\(949\) | −2.61803 | −0.0849850 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.2693 | 1.04640 | ||||||||
\(952\) | 12.2318 | 0.396436 | ||||||||
\(953\) | 24.2622 | 0.785931 | 0.392965 | − | 0.919553i | \(-0.371449\pi\) | ||||
0.392965 | + | 0.919553i | \(0.371449\pi\) | |||||||
\(954\) | −1.23657 | −0.0400354 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.8669 | −0.480830 | ||||||||
\(957\) | −17.4048 | −0.562617 | ||||||||
\(958\) | −6.59568 | −0.213097 | ||||||||
\(959\) | 25.5940 | 0.826475 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.20427 | 0.200138 | ||||||||
\(962\) | 0.439084 | 0.0141566 | ||||||||
\(963\) | −13.1910 | −0.425072 | ||||||||
\(964\) | 40.1048 | 1.29169 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.772978 | −0.0248702 | ||||||||
\(967\) | −31.1143 | −1.00057 | −0.500284 | − | 0.865861i | \(-0.666771\pi\) | ||||
−0.500284 | + | 0.865861i | \(0.666771\pi\) | |||||||
\(968\) | −5.08580 | −0.163464 | ||||||||
\(969\) | 13.1502 | 0.422447 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.3721 | −0.557497 | −0.278749 | − | 0.960364i | \(-0.589920\pi\) | ||||
−0.278749 | + | 0.960364i | \(0.589920\pi\) | |||||||
\(972\) | 16.4834 | 0.528704 | ||||||||
\(973\) | −17.5810 | −0.563620 | ||||||||
\(974\) | 1.94855 | 0.0624356 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.47917 | 0.111365 | ||||||||
\(977\) | −42.8929 | −1.37227 | −0.686133 | − | 0.727476i | \(-0.740693\pi\) | ||||
−0.686133 | + | 0.727476i | \(0.740693\pi\) | |||||||
\(978\) | 4.24013 | 0.135584 | ||||||||
\(979\) | 15.0528 | 0.481091 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.66987 | 0.0533149 | ||||||||
\(982\) | 3.23651 | 0.103281 | ||||||||
\(983\) | −37.4533 | −1.19457 | −0.597287 | − | 0.802028i | \(-0.703755\pi\) | ||||
−0.597287 | + | 0.802028i | \(0.703755\pi\) | |||||||
\(984\) | 1.08563 | 0.0346086 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.59120 | 0.178060 | ||||||||
\(987\) | 20.2550 | 0.644724 | ||||||||
\(988\) | 1.00849 | 0.0320843 | ||||||||
\(989\) | −2.85033 | −0.0906353 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.7624 | 0.532476 | 0.266238 | − | 0.963907i | \(-0.414219\pi\) | ||||
0.266238 | + | 0.963907i | \(0.414219\pi\) | |||||||
\(992\) | −13.1085 | −0.416196 | ||||||||
\(993\) | 13.1931 | 0.418669 | ||||||||
\(994\) | −3.56514 | −0.113079 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 42.0149 | 1.33129 | ||||||||
\(997\) | −59.8595 | −1.89577 | −0.947884 | − | 0.318615i | \(-0.896782\pi\) | ||||
−0.947884 | + | 0.318615i | \(0.896782\pi\) | |||||||
\(998\) | 1.72499 | 0.0546037 | ||||||||
\(999\) | 45.6367 | 1.44388 |
(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 | 625.2.a.f.1.4 | 8 | ||
3.2 | odd | 2 | 5625.2.a.x.1.5 | 8 | |||
4.3 | odd | 2 | 10000.2.a.bj.1.6 | 8 | |||
5.2 | odd | 4 | 625.2.b.c.624.4 | 8 | |||
5.3 | odd | 4 | 625.2.b.c.624.5 | 8 | |||
5.4 | even | 2 | inner | 625.2.a.f.1.5 | 8 | ||
15.14 | odd | 2 | 5625.2.a.x.1.4 | 8 | |||
20.19 | odd | 2 | 10000.2.a.bj.1.3 | 8 | |||
25.2 | odd | 20 | 125.2.e.b.24.1 | 8 | |||
25.3 | odd | 20 | 625.2.e.a.249.2 | 8 | |||
25.4 | even | 10 | 625.2.d.o.376.2 | 16 | |||
25.6 | even | 5 | 625.2.d.o.251.3 | 16 | |||
25.8 | odd | 20 | 625.2.e.i.374.1 | 8 | |||
25.9 | even | 10 | 125.2.d.b.26.3 | 16 | |||
25.11 | even | 5 | 125.2.d.b.101.2 | 16 | |||
25.12 | odd | 20 | 25.2.e.a.19.2 | yes | 8 | ||
25.13 | odd | 20 | 125.2.e.b.99.1 | 8 | |||
25.14 | even | 10 | 125.2.d.b.101.3 | 16 | |||
25.16 | even | 5 | 125.2.d.b.26.2 | 16 | |||
25.17 | odd | 20 | 625.2.e.a.374.2 | 8 | |||
25.19 | even | 10 | 625.2.d.o.251.2 | 16 | |||
25.21 | even | 5 | 625.2.d.o.376.3 | 16 | |||
25.22 | odd | 20 | 625.2.e.i.249.1 | 8 | |||
25.23 | odd | 20 | 25.2.e.a.4.2 | ✓ | 8 | ||
75.23 | even | 20 | 225.2.m.a.154.1 | 8 | |||
75.62 | even | 20 | 225.2.m.a.19.1 | 8 | |||
100.23 | even | 20 | 400.2.y.c.129.2 | 8 | |||
100.87 | even | 20 | 400.2.y.c.369.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.e.a.4.2 | ✓ | 8 | 25.23 | odd | 20 | ||
25.2.e.a.19.2 | yes | 8 | 25.12 | odd | 20 | ||
125.2.d.b.26.2 | 16 | 25.16 | even | 5 | |||
125.2.d.b.26.3 | 16 | 25.9 | even | 10 | |||
125.2.d.b.101.2 | 16 | 25.11 | even | 5 | |||
125.2.d.b.101.3 | 16 | 25.14 | even | 10 | |||
125.2.e.b.24.1 | 8 | 25.2 | odd | 20 | |||
125.2.e.b.99.1 | 8 | 25.13 | odd | 20 | |||
225.2.m.a.19.1 | 8 | 75.62 | even | 20 | |||
225.2.m.a.154.1 | 8 | 75.23 | even | 20 | |||
400.2.y.c.129.2 | 8 | 100.23 | even | 20 | |||
400.2.y.c.369.2 | 8 | 100.87 | even | 20 | |||
625.2.a.f.1.4 | 8 | 1.1 | even | 1 | trivial | ||
625.2.a.f.1.5 | 8 | 5.4 | even | 2 | inner | ||
625.2.b.c.624.4 | 8 | 5.2 | odd | 4 | |||
625.2.b.c.624.5 | 8 | 5.3 | odd | 4 | |||
625.2.d.o.251.2 | 16 | 25.19 | even | 10 | |||
625.2.d.o.251.3 | 16 | 25.6 | even | 5 | |||
625.2.d.o.376.2 | 16 | 25.4 | even | 10 | |||
625.2.d.o.376.3 | 16 | 25.21 | even | 5 | |||
625.2.e.a.249.2 | 8 | 25.3 | odd | 20 | |||
625.2.e.a.374.2 | 8 | 25.17 | odd | 20 | |||
625.2.e.i.249.1 | 8 | 25.22 | odd | 20 | |||
625.2.e.i.374.1 | 8 | 25.8 | odd | 20 | |||
5625.2.a.x.1.4 | 8 | 15.14 | odd | 2 | |||
5625.2.a.x.1.5 | 8 | 3.2 | odd | 2 | |||
10000.2.a.bj.1.3 | 8 | 20.19 | odd | 2 | |||
10000.2.a.bj.1.6 | 8 | 4.3 | odd | 2 |