Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, 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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.5822000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 8x^{4} + 5x^{3} + 14x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.47848\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.860448 | −0.608429 | −0.304214 | − | 0.952604i | \(-0.598394\pi\) | ||||
−0.304214 | + | 0.952604i | \(0.598394\pi\) | |||||||
\(3\) | 0.867394 | 0.500790 | 0.250395 | − | 0.968144i | \(-0.419440\pi\) | ||||
0.250395 | + | 0.968144i | \(0.419440\pi\) | |||||||
\(4\) | −1.25963 | −0.629814 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.746348 | −0.304695 | ||||||||
\(7\) | −0.263921 | −0.0997528 | −0.0498764 | − | 0.998755i | \(-0.515883\pi\) | ||||
−0.0498764 | + | 0.998755i | \(0.515883\pi\) | |||||||
\(8\) | 2.80474 | 0.991626 | ||||||||
\(9\) | −2.24763 | −0.749209 | ||||||||
\(10\) | 0.860448 | 0.272098 | ||||||||
\(11\) | −5.32135 | −1.60445 | −0.802223 | − | 0.597024i | \(-0.796350\pi\) | ||||
−0.802223 | + | 0.597024i | \(0.796350\pi\) | |||||||
\(12\) | −1.09259 | −0.315405 | ||||||||
\(13\) | 1.19606 | 0.331726 | 0.165863 | − | 0.986149i | \(-0.446959\pi\) | ||||
0.165863 | + | 0.986149i | \(0.446959\pi\) | |||||||
\(14\) | 0.227090 | 0.0606925 | ||||||||
\(15\) | −0.867394 | −0.223960 | ||||||||
\(16\) | 0.105921 | 0.0264803 | ||||||||
\(17\) | 4.46010 | 1.08173 | 0.540867 | − | 0.841108i | \(-0.318096\pi\) | ||||
0.540867 | + | 0.841108i | \(0.318096\pi\) | |||||||
\(18\) | 1.93397 | 0.455841 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.25963 | 0.281662 | ||||||||
\(21\) | −0.228924 | −0.0499552 | ||||||||
\(22\) | 4.57874 | 0.976191 | ||||||||
\(23\) | −0.920897 | −0.192020 | −0.0960101 | − | 0.995380i | \(-0.530608\pi\) | ||||
−0.0960101 | + | 0.995380i | \(0.530608\pi\) | |||||||
\(24\) | 2.43282 | 0.496596 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.02914 | −0.201832 | ||||||||
\(27\) | −4.55176 | −0.875987 | ||||||||
\(28\) | 0.332443 | 0.0628257 | ||||||||
\(29\) | −9.87581 | −1.83389 | −0.916946 | − | 0.399012i | \(-0.869353\pi\) | ||||
−0.916946 | + | 0.399012i | \(0.869353\pi\) | |||||||
\(30\) | 0.746348 | 0.136264 | ||||||||
\(31\) | −0.0400121 | −0.00718639 | −0.00359319 | − | 0.999994i | \(-0.501144\pi\) | ||||
−0.00359319 | + | 0.999994i | \(0.501144\pi\) | |||||||
\(32\) | −5.70062 | −1.00774 | ||||||||
\(33\) | −4.61570 | −0.803491 | ||||||||
\(34\) | −3.83769 | −0.658158 | ||||||||
\(35\) | 0.263921 | 0.0446108 | ||||||||
\(36\) | 2.83118 | 0.471863 | ||||||||
\(37\) | 7.76091 | 1.27589 | 0.637943 | − | 0.770084i | \(-0.279786\pi\) | ||||
0.637943 | + | 0.770084i | \(0.279786\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.03745 | 0.166125 | ||||||||
\(40\) | −2.80474 | −0.443469 | ||||||||
\(41\) | 6.27419 | 0.979864 | 0.489932 | − | 0.871761i | \(-0.337022\pi\) | ||||
0.489932 | + | 0.871761i | \(0.337022\pi\) | |||||||
\(42\) | 0.196977 | 0.0303942 | ||||||||
\(43\) | 10.0853 | 1.53799 | 0.768995 | − | 0.639254i | \(-0.220757\pi\) | ||||
0.768995 | + | 0.639254i | \(0.220757\pi\) | |||||||
\(44\) | 6.70292 | 1.01050 | ||||||||
\(45\) | 2.24763 | 0.335057 | ||||||||
\(46\) | 0.792384 | 0.116831 | ||||||||
\(47\) | 8.44271 | 1.23150 | 0.615748 | − | 0.787943i | \(-0.288854\pi\) | ||||
0.615748 | + | 0.787943i | \(0.288854\pi\) | |||||||
\(48\) | 0.0918755 | 0.0132611 | ||||||||
\(49\) | −6.93035 | −0.990049 | ||||||||
\(50\) | −0.860448 | −0.121686 | ||||||||
\(51\) | 3.86866 | 0.541721 | ||||||||
\(52\) | −1.50659 | −0.208926 | ||||||||
\(53\) | 4.20047 | 0.576979 | 0.288490 | − | 0.957483i | \(-0.406847\pi\) | ||||
0.288490 | + | 0.957483i | \(0.406847\pi\) | |||||||
\(54\) | 3.91655 | 0.532976 | ||||||||
\(55\) | 5.32135 | 0.717530 | ||||||||
\(56\) | −0.740231 | −0.0989175 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.49762 | 1.11579 | ||||||||
\(59\) | −8.10775 | −1.05554 | −0.527770 | − | 0.849387i | \(-0.676972\pi\) | ||||
−0.527770 | + | 0.849387i | \(0.676972\pi\) | |||||||
\(60\) | 1.09259 | 0.141053 | ||||||||
\(61\) | 0.218505 | 0.0279768 | 0.0139884 | − | 0.999902i | \(-0.495547\pi\) | ||||
0.0139884 | + | 0.999902i | \(0.495547\pi\) | |||||||
\(62\) | 0.0344283 | 0.00437240 | ||||||||
\(63\) | 0.593196 | 0.0747357 | ||||||||
\(64\) | 4.69325 | 0.586656 | ||||||||
\(65\) | −1.19606 | −0.148352 | ||||||||
\(66\) | 3.97157 | 0.488867 | ||||||||
\(67\) | 3.76600 | 0.460090 | 0.230045 | − | 0.973180i | \(-0.426113\pi\) | ||||
0.230045 | + | 0.973180i | \(0.426113\pi\) | |||||||
\(68\) | −5.61807 | −0.681291 | ||||||||
\(69\) | −0.798780 | −0.0961618 | ||||||||
\(70\) | −0.227090 | −0.0271425 | ||||||||
\(71\) | 10.1077 | 1.19956 | 0.599780 | − | 0.800165i | \(-0.295255\pi\) | ||||
0.599780 | + | 0.800165i | \(0.295255\pi\) | |||||||
\(72\) | −6.30402 | −0.742936 | ||||||||
\(73\) | 9.91093 | 1.15999 | 0.579993 | − | 0.814621i | \(-0.303055\pi\) | ||||
0.579993 | + | 0.814621i | \(0.303055\pi\) | |||||||
\(74\) | −6.67786 | −0.776286 | ||||||||
\(75\) | 0.867394 | 0.100158 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.40442 | 0.160048 | ||||||||
\(78\) | −0.892673 | −0.101075 | ||||||||
\(79\) | 0.00558375 | 0.000628221 0 | 0.000314111 | − | 1.00000i | \(-0.499900\pi\) | ||||
0.000314111 | 1.00000i | \(0.499900\pi\) | ||||||||
\(80\) | −0.105921 | −0.0118424 | ||||||||
\(81\) | 2.79472 | 0.310524 | ||||||||
\(82\) | −5.39862 | −0.596177 | ||||||||
\(83\) | 8.82190 | 0.968329 | 0.484165 | − | 0.874977i | \(-0.339124\pi\) | ||||
0.484165 | + | 0.874977i | \(0.339124\pi\) | |||||||
\(84\) | 0.288359 | 0.0314625 | ||||||||
\(85\) | −4.46010 | −0.483766 | ||||||||
\(86\) | −8.67786 | −0.935758 | ||||||||
\(87\) | −8.56621 | −0.918395 | ||||||||
\(88\) | −14.9250 | −1.59101 | ||||||||
\(89\) | −0.431648 | −0.0457546 | −0.0228773 | − | 0.999738i | \(-0.507283\pi\) | ||||
−0.0228773 | + | 0.999738i | \(0.507283\pi\) | |||||||
\(90\) | −1.93397 | −0.203858 | ||||||||
\(91\) | −0.315664 | −0.0330906 | ||||||||
\(92\) | 1.15999 | 0.120937 | ||||||||
\(93\) | −0.0347063 | −0.00359887 | ||||||||
\(94\) | −7.26452 | −0.749278 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.94469 | −0.504665 | ||||||||
\(97\) | −17.3729 | −1.76395 | −0.881973 | − | 0.471299i | \(-0.843785\pi\) | ||||
−0.881973 | + | 0.471299i | \(0.843785\pi\) | |||||||
\(98\) | 5.96320 | 0.602375 | ||||||||
\(99\) | 11.9604 | 1.20207 | ||||||||
\(100\) | −1.25963 | −0.125963 | ||||||||
\(101\) | −8.95142 | −0.890699 | −0.445350 | − | 0.895357i | \(-0.646921\pi\) | ||||
−0.445350 | + | 0.895357i | \(0.646921\pi\) | |||||||
\(102\) | −3.32879 | −0.329599 | ||||||||
\(103\) | 5.66535 | 0.558224 | 0.279112 | − | 0.960259i | \(-0.409960\pi\) | ||||
0.279112 | + | 0.960259i | \(0.409960\pi\) | |||||||
\(104\) | 3.35463 | 0.328948 | ||||||||
\(105\) | 0.228924 | 0.0223406 | ||||||||
\(106\) | −3.61429 | −0.351051 | ||||||||
\(107\) | 8.52693 | 0.824329 | 0.412165 | − | 0.911109i | \(-0.364773\pi\) | ||||
0.412165 | + | 0.911109i | \(0.364773\pi\) | |||||||
\(108\) | 5.73353 | 0.551709 | ||||||||
\(109\) | 7.01751 | 0.672156 | 0.336078 | − | 0.941834i | \(-0.390899\pi\) | ||||
0.336078 | + | 0.941834i | \(0.390899\pi\) | |||||||
\(110\) | −4.57874 | −0.436566 | ||||||||
\(111\) | 6.73176 | 0.638951 | ||||||||
\(112\) | −0.0279549 | −0.00264149 | ||||||||
\(113\) | 8.74027 | 0.822215 | 0.411108 | − | 0.911587i | \(-0.365142\pi\) | ||||
0.411108 | + | 0.911587i | \(0.365142\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.920897 | 0.0858741 | ||||||||
\(116\) | 12.4398 | 1.15501 | ||||||||
\(117\) | −2.68829 | −0.248532 | ||||||||
\(118\) | 6.97630 | 0.642221 | ||||||||
\(119\) | −1.17711 | −0.107906 | ||||||||
\(120\) | −2.43282 | −0.222085 | ||||||||
\(121\) | 17.3167 | 1.57425 | ||||||||
\(122\) | −0.188013 | −0.0170219 | ||||||||
\(123\) | 5.44219 | 0.490706 | ||||||||
\(124\) | 0.0504004 | 0.00452609 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.510415 | −0.0454714 | ||||||||
\(127\) | 6.80930 | 0.604228 | 0.302114 | − | 0.953272i | \(-0.402308\pi\) | ||||
0.302114 | + | 0.953272i | \(0.402308\pi\) | |||||||
\(128\) | 7.36295 | 0.650799 | ||||||||
\(129\) | 8.74791 | 0.770210 | ||||||||
\(130\) | 1.02914 | 0.0902619 | ||||||||
\(131\) | 11.4004 | 0.996055 | 0.498028 | − | 0.867161i | \(-0.334058\pi\) | ||||
0.498028 | + | 0.867161i | \(0.334058\pi\) | |||||||
\(132\) | 5.81407 | 0.506050 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.24045 | −0.279932 | ||||||||
\(135\) | 4.55176 | 0.391753 | ||||||||
\(136\) | 12.5094 | 1.07267 | ||||||||
\(137\) | −17.1356 | −1.46400 | −0.731998 | − | 0.681307i | \(-0.761412\pi\) | ||||
−0.731998 | + | 0.681307i | \(0.761412\pi\) | |||||||
\(138\) | 0.687309 | 0.0585076 | ||||||||
\(139\) | 13.4272 | 1.13888 | 0.569439 | − | 0.822034i | \(-0.307160\pi\) | ||||
0.569439 | + | 0.822034i | \(0.307160\pi\) | |||||||
\(140\) | −0.332443 | −0.0280965 | ||||||||
\(141\) | 7.32316 | 0.616721 | ||||||||
\(142\) | −8.69713 | −0.729847 | ||||||||
\(143\) | −6.36463 | −0.532237 | ||||||||
\(144\) | −0.238072 | −0.0198393 | ||||||||
\(145\) | 9.87581 | 0.820141 | ||||||||
\(146\) | −8.52784 | −0.705769 | ||||||||
\(147\) | −6.01134 | −0.495807 | ||||||||
\(148\) | −9.77586 | −0.803571 | ||||||||
\(149\) | 19.3771 | 1.58743 | 0.793716 | − | 0.608289i | \(-0.208144\pi\) | ||||
0.793716 | + | 0.608289i | \(0.208144\pi\) | |||||||
\(150\) | −0.746348 | −0.0609390 | ||||||||
\(151\) | −15.2903 | −1.24431 | −0.622153 | − | 0.782896i | \(-0.713742\pi\) | ||||
−0.622153 | + | 0.782896i | \(0.713742\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.0246 | −0.810445 | ||||||||
\(154\) | −1.20843 | −0.0973778 | ||||||||
\(155\) | 0.0400121 | 0.00321385 | ||||||||
\(156\) | −1.30680 | −0.104628 | ||||||||
\(157\) | 16.7845 | 1.33955 | 0.669773 | − | 0.742566i | \(-0.266392\pi\) | ||||
0.669773 | + | 0.742566i | \(0.266392\pi\) | |||||||
\(158\) | −0.00480453 | −0.000382228 0 | ||||||||
\(159\) | 3.64346 | 0.288945 | ||||||||
\(160\) | 5.70062 | 0.450674 | ||||||||
\(161\) | 0.243044 | 0.0191546 | ||||||||
\(162\) | −2.40471 | −0.188932 | ||||||||
\(163\) | 20.1558 | 1.57872 | 0.789361 | − | 0.613929i | \(-0.210412\pi\) | ||||
0.789361 | + | 0.613929i | \(0.210412\pi\) | |||||||
\(164\) | −7.90315 | −0.617132 | ||||||||
\(165\) | 4.61570 | 0.359332 | ||||||||
\(166\) | −7.59079 | −0.589159 | ||||||||
\(167\) | −23.6089 | −1.82691 | −0.913454 | − | 0.406942i | \(-0.866595\pi\) | ||||
−0.913454 | + | 0.406942i | \(0.866595\pi\) | |||||||
\(168\) | −0.642071 | −0.0495369 | ||||||||
\(169\) | −11.5695 | −0.889958 | ||||||||
\(170\) | 3.83769 | 0.294337 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.7037 | −0.968648 | ||||||||
\(173\) | 7.10025 | 0.539822 | 0.269911 | − | 0.962885i | \(-0.413006\pi\) | ||||
0.269911 | + | 0.962885i | \(0.413006\pi\) | |||||||
\(174\) | 7.37079 | 0.558778 | ||||||||
\(175\) | −0.263921 | −0.0199506 | ||||||||
\(176\) | −0.563644 | −0.0424863 | ||||||||
\(177\) | −7.03262 | −0.528604 | ||||||||
\(178\) | 0.371411 | 0.0278384 | ||||||||
\(179\) | −3.65176 | −0.272946 | −0.136473 | − | 0.990644i | \(-0.543577\pi\) | ||||
−0.136473 | + | 0.990644i | \(0.543577\pi\) | |||||||
\(180\) | −2.83118 | −0.211023 | ||||||||
\(181\) | 8.74210 | 0.649796 | 0.324898 | − | 0.945749i | \(-0.394670\pi\) | ||||
0.324898 | + | 0.945749i | \(0.394670\pi\) | |||||||
\(182\) | 0.271613 | 0.0201333 | ||||||||
\(183\) | 0.189530 | 0.0140105 | ||||||||
\(184\) | −2.58288 | −0.190412 | ||||||||
\(185\) | −7.76091 | −0.570593 | ||||||||
\(186\) | 0.0298629 | 0.00218966 | ||||||||
\(187\) | −23.7337 | −1.73558 | ||||||||
\(188\) | −10.6347 | −0.775614 | ||||||||
\(189\) | 1.20131 | 0.0873821 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.41340 | 0.246985 | 0.123492 | − | 0.992346i | \(-0.460591\pi\) | ||||
0.123492 | + | 0.992346i | \(0.460591\pi\) | |||||||
\(192\) | 4.07090 | 0.293792 | ||||||||
\(193\) | −13.7389 | −0.988946 | −0.494473 | − | 0.869193i | \(-0.664639\pi\) | ||||
−0.494473 | + | 0.869193i | \(0.664639\pi\) | |||||||
\(194\) | 14.9485 | 1.07324 | ||||||||
\(195\) | −1.03745 | −0.0742934 | ||||||||
\(196\) | 8.72966 | 0.623547 | ||||||||
\(197\) | −12.4598 | −0.887722 | −0.443861 | − | 0.896096i | \(-0.646392\pi\) | ||||
−0.443861 | + | 0.896096i | \(0.646392\pi\) | |||||||
\(198\) | −10.2913 | −0.731372 | ||||||||
\(199\) | 27.1939 | 1.92772 | 0.963861 | − | 0.266407i | \(-0.0858364\pi\) | ||||
0.963861 | + | 0.266407i | \(0.0858364\pi\) | |||||||
\(200\) | 2.80474 | 0.198325 | ||||||||
\(201\) | 3.26660 | 0.230409 | ||||||||
\(202\) | 7.70223 | 0.541927 | ||||||||
\(203\) | 2.60643 | 0.182936 | ||||||||
\(204\) | −4.87308 | −0.341184 | ||||||||
\(205\) | −6.27419 | −0.438208 | ||||||||
\(206\) | −4.87474 | −0.339640 | ||||||||
\(207\) | 2.06983 | 0.143863 | ||||||||
\(208\) | 0.126688 | 0.00878422 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.196977 | −0.0135927 | ||||||||
\(211\) | −15.6319 | −1.07614 | −0.538071 | − | 0.842899i | \(-0.680847\pi\) | ||||
−0.538071 | + | 0.842899i | \(0.680847\pi\) | |||||||
\(212\) | −5.29103 | −0.363390 | ||||||||
\(213\) | 8.76733 | 0.600728 | ||||||||
\(214\) | −7.33698 | −0.501546 | ||||||||
\(215\) | −10.0853 | −0.687810 | ||||||||
\(216\) | −12.7665 | −0.868651 | ||||||||
\(217\) | 0.0105600 | 0.000716862 0 | ||||||||
\(218\) | −6.03821 | −0.408959 | ||||||||
\(219\) | 8.59668 | 0.580910 | ||||||||
\(220\) | −6.70292 | −0.451911 | ||||||||
\(221\) | 5.33453 | 0.358839 | ||||||||
\(222\) | −5.79234 | −0.388756 | ||||||||
\(223\) | 19.1486 | 1.28229 | 0.641143 | − | 0.767421i | \(-0.278460\pi\) | ||||
0.641143 | + | 0.767421i | \(0.278460\pi\) | |||||||
\(224\) | 1.50451 | 0.100525 | ||||||||
\(225\) | −2.24763 | −0.149842 | ||||||||
\(226\) | −7.52055 | −0.500259 | ||||||||
\(227\) | 27.9989 | 1.85835 | 0.929175 | − | 0.369641i | \(-0.120519\pi\) | ||||
0.929175 | + | 0.369641i | \(0.120519\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.43209 | 0.491126 | 0.245563 | − | 0.969381i | \(-0.421027\pi\) | ||||
0.245563 | + | 0.969381i | \(0.421027\pi\) | |||||||
\(230\) | −0.792384 | −0.0522483 | ||||||||
\(231\) | 1.21818 | 0.0801505 | ||||||||
\(232\) | −27.6991 | −1.81853 | ||||||||
\(233\) | −14.2940 | −0.936431 | −0.468215 | − | 0.883614i | \(-0.655103\pi\) | ||||
−0.468215 | + | 0.883614i | \(0.655103\pi\) | |||||||
\(234\) | 2.31313 | 0.151214 | ||||||||
\(235\) | −8.44271 | −0.550742 | ||||||||
\(236\) | 10.2128 | 0.664794 | ||||||||
\(237\) | 0.00484331 | 0.000314607 0 | ||||||||
\(238\) | 1.01285 | 0.0656531 | ||||||||
\(239\) | 1.04233 | 0.0674225 | 0.0337113 | − | 0.999432i | \(-0.489267\pi\) | ||||
0.0337113 | + | 0.999432i | \(0.489267\pi\) | |||||||
\(240\) | −0.0918755 | −0.00593054 | ||||||||
\(241\) | 18.2225 | 1.17381 | 0.586907 | − | 0.809655i | \(-0.300346\pi\) | ||||
0.586907 | + | 0.809655i | \(0.300346\pi\) | |||||||
\(242\) | −14.9001 | −0.957818 | ||||||||
\(243\) | 16.0794 | 1.03149 | ||||||||
\(244\) | −0.275236 | −0.0176202 | ||||||||
\(245\) | 6.93035 | 0.442764 | ||||||||
\(246\) | −4.68273 | −0.298560 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.112224 | −0.00712621 | ||||||||
\(249\) | 7.65206 | 0.484930 | ||||||||
\(250\) | 0.860448 | 0.0544195 | ||||||||
\(251\) | 2.92399 | 0.184561 | 0.0922804 | − | 0.995733i | \(-0.470584\pi\) | ||||
0.0922804 | + | 0.995733i | \(0.470584\pi\) | |||||||
\(252\) | −0.747207 | −0.0470696 | ||||||||
\(253\) | 4.90041 | 0.308086 | ||||||||
\(254\) | −5.85905 | −0.367630 | ||||||||
\(255\) | −3.86866 | −0.242265 | ||||||||
\(256\) | −15.7219 | −0.982621 | ||||||||
\(257\) | 13.8615 | 0.864659 | 0.432330 | − | 0.901716i | \(-0.357692\pi\) | ||||
0.432330 | + | 0.901716i | \(0.357692\pi\) | |||||||
\(258\) | −7.52712 | −0.468618 | ||||||||
\(259\) | −2.04827 | −0.127273 | ||||||||
\(260\) | 1.50659 | 0.0934345 | ||||||||
\(261\) | 22.1971 | 1.37397 | ||||||||
\(262\) | −9.80944 | −0.606029 | ||||||||
\(263\) | −12.4674 | −0.768776 | −0.384388 | − | 0.923172i | \(-0.625587\pi\) | ||||
−0.384388 | + | 0.923172i | \(0.625587\pi\) | |||||||
\(264\) | −12.9459 | −0.796762 | ||||||||
\(265\) | −4.20047 | −0.258033 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.374409 | −0.0229134 | ||||||||
\(268\) | −4.74376 | −0.289771 | ||||||||
\(269\) | −27.2482 | −1.66135 | −0.830676 | − | 0.556755i | \(-0.812046\pi\) | ||||
−0.830676 | + | 0.556755i | \(0.812046\pi\) | |||||||
\(270\) | −3.91655 | −0.238354 | ||||||||
\(271\) | −25.6315 | −1.55700 | −0.778501 | − | 0.627644i | \(-0.784020\pi\) | ||||
−0.778501 | + | 0.627644i | \(0.784020\pi\) | |||||||
\(272\) | 0.472420 | 0.0286446 | ||||||||
\(273\) | −0.273805 | −0.0165715 | ||||||||
\(274\) | 14.7443 | 0.890737 | ||||||||
\(275\) | −5.32135 | −0.320889 | ||||||||
\(276\) | 1.00617 | 0.0605641 | ||||||||
\(277\) | 21.1317 | 1.26968 | 0.634841 | − | 0.772643i | \(-0.281066\pi\) | ||||
0.634841 | + | 0.772643i | \(0.281066\pi\) | |||||||
\(278\) | −11.5534 | −0.692926 | ||||||||
\(279\) | 0.0899323 | 0.00538411 | ||||||||
\(280\) | 0.740231 | 0.0442372 | ||||||||
\(281\) | −1.59925 | −0.0954033 | −0.0477017 | − | 0.998862i | \(-0.515190\pi\) | ||||
−0.0477017 | + | 0.998862i | \(0.515190\pi\) | |||||||
\(282\) | −6.30120 | −0.375231 | ||||||||
\(283\) | 2.19141 | 0.130266 | 0.0651328 | − | 0.997877i | \(-0.479253\pi\) | ||||
0.0651328 | + | 0.997877i | \(0.479253\pi\) | |||||||
\(284\) | −12.7319 | −0.755500 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.47643 | 0.323828 | ||||||||
\(287\) | −1.65589 | −0.0977442 | ||||||||
\(288\) | 12.8129 | 0.755006 | ||||||||
\(289\) | 2.89249 | 0.170147 | ||||||||
\(290\) | −8.49762 | −0.498998 | ||||||||
\(291\) | −15.0691 | −0.883367 | ||||||||
\(292\) | −12.4841 | −0.730576 | ||||||||
\(293\) | −14.0044 | −0.818145 | −0.409073 | − | 0.912502i | \(-0.634148\pi\) | ||||
−0.409073 | + | 0.912502i | \(0.634148\pi\) | |||||||
\(294\) | 5.17245 | 0.301663 | ||||||||
\(295\) | 8.10775 | 0.472052 | ||||||||
\(296\) | 21.7673 | 1.26520 | ||||||||
\(297\) | 24.2215 | 1.40547 | ||||||||
\(298\) | −16.6730 | −0.965839 | ||||||||
\(299\) | −1.10144 | −0.0636982 | ||||||||
\(300\) | −1.09259 | −0.0630809 | ||||||||
\(301\) | −2.66172 | −0.153419 | ||||||||
\(302\) | 13.1565 | 0.757072 | ||||||||
\(303\) | −7.76440 | −0.446053 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.218505 | −0.0125116 | ||||||||
\(306\) | 8.62569 | 0.493098 | ||||||||
\(307\) | 4.81646 | 0.274890 | 0.137445 | − | 0.990509i | \(-0.456111\pi\) | ||||
0.137445 | + | 0.990509i | \(0.456111\pi\) | |||||||
\(308\) | −1.76904 | −0.100801 | ||||||||
\(309\) | 4.91409 | 0.279553 | ||||||||
\(310\) | −0.0344283 | −0.00195540 | ||||||||
\(311\) | 19.4101 | 1.10064 | 0.550322 | − | 0.834952i | \(-0.314505\pi\) | ||||
0.550322 | + | 0.834952i | \(0.314505\pi\) | |||||||
\(312\) | 2.90978 | 0.164734 | ||||||||
\(313\) | −5.71724 | −0.323157 | −0.161579 | − | 0.986860i | \(-0.551659\pi\) | ||||
−0.161579 | + | 0.986860i | \(0.551659\pi\) | |||||||
\(314\) | −14.4422 | −0.815018 | ||||||||
\(315\) | −0.593196 | −0.0334228 | ||||||||
\(316\) | −0.00703346 | −0.000395663 0 | ||||||||
\(317\) | −14.8729 | −0.835348 | −0.417674 | − | 0.908597i | \(-0.637155\pi\) | ||||
−0.417674 | + | 0.908597i | \(0.637155\pi\) | |||||||
\(318\) | −3.13501 | −0.175803 | ||||||||
\(319\) | 52.5526 | 2.94238 | ||||||||
\(320\) | −4.69325 | −0.262361 | ||||||||
\(321\) | 7.39621 | 0.412816 | ||||||||
\(322\) | −0.209127 | −0.0116542 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −3.52030 | −0.195572 | ||||||||
\(325\) | 1.19606 | 0.0663452 | ||||||||
\(326\) | −17.3430 | −0.960540 | ||||||||
\(327\) | 6.08695 | 0.336609 | ||||||||
\(328\) | 17.5975 | 0.971659 | ||||||||
\(329\) | −2.22821 | −0.122845 | ||||||||
\(330\) | −3.97157 | −0.218628 | ||||||||
\(331\) | 0.0342375 | 0.00188187 | 0.000940933 | − | 1.00000i | \(-0.499700\pi\) | ||||
0.000940933 | 1.00000i | \(0.499700\pi\) | ||||||||
\(332\) | −11.1123 | −0.609868 | ||||||||
\(333\) | −17.4436 | −0.955905 | ||||||||
\(334\) | 20.3142 | 1.11154 | ||||||||
\(335\) | −3.76600 | −0.205759 | ||||||||
\(336\) | −0.0242479 | −0.00132283 | ||||||||
\(337\) | −23.8249 | −1.29782 | −0.648911 | − | 0.760864i | \(-0.724775\pi\) | ||||
−0.648911 | + | 0.760864i | \(0.724775\pi\) | |||||||
\(338\) | 9.95491 | 0.541476 | ||||||||
\(339\) | 7.58125 | 0.411757 | ||||||||
\(340\) | 5.61807 | 0.304683 | ||||||||
\(341\) | 0.212918 | 0.0115302 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.67651 | 0.198513 | ||||||||
\(344\) | 28.2866 | 1.52511 | ||||||||
\(345\) | 0.798780 | 0.0430049 | ||||||||
\(346\) | −6.10940 | −0.328443 | ||||||||
\(347\) | −32.4568 | −1.74237 | −0.871186 | − | 0.490952i | \(-0.836649\pi\) | ||||
−0.871186 | + | 0.490952i | \(0.836649\pi\) | |||||||
\(348\) | 10.7902 | 0.578418 | ||||||||
\(349\) | 2.59566 | 0.138943 | 0.0694713 | − | 0.997584i | \(-0.477869\pi\) | ||||
0.0694713 | + | 0.997584i | \(0.477869\pi\) | |||||||
\(350\) | 0.227090 | 0.0121385 | ||||||||
\(351\) | −5.44416 | −0.290588 | ||||||||
\(352\) | 30.3350 | 1.61686 | ||||||||
\(353\) | 2.39072 | 0.127245 | 0.0636226 | − | 0.997974i | \(-0.479735\pi\) | ||||
0.0636226 | + | 0.997974i | \(0.479735\pi\) | |||||||
\(354\) | 6.05120 | 0.321618 | ||||||||
\(355\) | −10.1077 | −0.536459 | ||||||||
\(356\) | 0.543716 | 0.0288169 | ||||||||
\(357\) | −1.02102 | −0.0540382 | ||||||||
\(358\) | 3.14215 | 0.166068 | ||||||||
\(359\) | −15.6300 | −0.824918 | −0.412459 | − | 0.910976i | \(-0.635330\pi\) | ||||
−0.412459 | + | 0.910976i | \(0.635330\pi\) | |||||||
\(360\) | 6.30402 | 0.332251 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −7.52213 | −0.395354 | ||||||||
\(363\) | 15.0204 | 0.788368 | ||||||||
\(364\) | 0.397620 | 0.0208409 | ||||||||
\(365\) | −9.91093 | −0.518762 | ||||||||
\(366\) | −0.163081 | −0.00852438 | ||||||||
\(367\) | −6.19364 | −0.323305 | −0.161653 | − | 0.986848i | \(-0.551682\pi\) | ||||
−0.161653 | + | 0.986848i | \(0.551682\pi\) | |||||||
\(368\) | −0.0975426 | −0.00508476 | ||||||||
\(369\) | −14.1020 | −0.734123 | ||||||||
\(370\) | 6.67786 | 0.347165 | ||||||||
\(371\) | −1.10859 | −0.0575553 | ||||||||
\(372\) | 0.0437170 | 0.00226662 | ||||||||
\(373\) | 26.9063 | 1.39316 | 0.696578 | − | 0.717481i | \(-0.254705\pi\) | ||||
0.696578 | + | 0.717481i | \(0.254705\pi\) | |||||||
\(374\) | 20.4217 | 1.05598 | ||||||||
\(375\) | −0.867394 | −0.0447920 | ||||||||
\(376\) | 23.6796 | 1.22118 | ||||||||
\(377\) | −11.8120 | −0.608350 | ||||||||
\(378\) | −1.03366 | −0.0531658 | ||||||||
\(379\) | −27.0655 | −1.39026 | −0.695129 | − | 0.718885i | \(-0.744653\pi\) | ||||
−0.695129 | + | 0.718885i | \(0.744653\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.90634 | 0.302591 | ||||||||
\(382\) | −2.93705 | −0.150273 | ||||||||
\(383\) | −30.5061 | −1.55879 | −0.779394 | − | 0.626533i | \(-0.784473\pi\) | ||||
−0.779394 | + | 0.626533i | \(0.784473\pi\) | |||||||
\(384\) | 6.38658 | 0.325914 | ||||||||
\(385\) | −1.40442 | −0.0715756 | ||||||||
\(386\) | 11.8216 | 0.601704 | ||||||||
\(387\) | −22.6680 | −1.15228 | ||||||||
\(388\) | 21.8834 | 1.11096 | ||||||||
\(389\) | −13.3023 | −0.674453 | −0.337226 | − | 0.941424i | \(-0.609489\pi\) | ||||
−0.337226 | + | 0.941424i | \(0.609489\pi\) | |||||||
\(390\) | 0.892673 | 0.0452023 | ||||||||
\(391\) | −4.10729 | −0.207715 | ||||||||
\(392\) | −19.4378 | −0.981759 | ||||||||
\(393\) | 9.88862 | 0.498815 | ||||||||
\(394\) | 10.7210 | 0.540116 | ||||||||
\(395\) | −0.00558375 | −0.000280949 0 | ||||||||
\(396\) | −15.0657 | −0.757078 | ||||||||
\(397\) | 23.0108 | 1.15488 | 0.577440 | − | 0.816433i | \(-0.304052\pi\) | ||||
0.577440 | + | 0.816433i | \(0.304052\pi\) | |||||||
\(398\) | −23.3989 | −1.17288 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.105921 | 0.00529606 | ||||||||
\(401\) | 35.9215 | 1.79383 | 0.896917 | − | 0.442199i | \(-0.145802\pi\) | ||||
0.896917 | + | 0.442199i | \(0.145802\pi\) | |||||||
\(402\) | −2.81074 | −0.140187 | ||||||||
\(403\) | −0.0478567 | −0.00238391 | ||||||||
\(404\) | 11.2755 | 0.560975 | ||||||||
\(405\) | −2.79472 | −0.138871 | ||||||||
\(406\) | −2.24270 | −0.111303 | ||||||||
\(407\) | −41.2985 | −2.04709 | ||||||||
\(408\) | 10.8506 | 0.537185 | ||||||||
\(409\) | −32.3379 | −1.59900 | −0.799502 | − | 0.600663i | \(-0.794903\pi\) | ||||
−0.799502 | + | 0.600663i | \(0.794903\pi\) | |||||||
\(410\) | 5.39862 | 0.266619 | ||||||||
\(411\) | −14.8633 | −0.733154 | ||||||||
\(412\) | −7.13624 | −0.351577 | ||||||||
\(413\) | 2.13981 | 0.105293 | ||||||||
\(414\) | −1.78098 | −0.0875306 | ||||||||
\(415\) | −8.82190 | −0.433050 | ||||||||
\(416\) | −6.81826 | −0.334293 | ||||||||
\(417\) | 11.6466 | 0.570339 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.6510 | 0.618041 | 0.309021 | − | 0.951055i | \(-0.399999\pi\) | ||||
0.309021 | + | 0.951055i | \(0.399999\pi\) | |||||||
\(420\) | −0.288359 | −0.0140705 | ||||||||
\(421\) | −14.6787 | −0.715396 | −0.357698 | − | 0.933837i | \(-0.616438\pi\) | ||||
−0.357698 | + | 0.933837i | \(0.616438\pi\) | |||||||
\(422\) | 13.4504 | 0.654756 | ||||||||
\(423\) | −18.9761 | −0.922649 | ||||||||
\(424\) | 11.7812 | 0.572148 | ||||||||
\(425\) | 4.46010 | 0.216347 | ||||||||
\(426\) | −7.54384 | −0.365500 | ||||||||
\(427\) | −0.0576682 | −0.00279076 | ||||||||
\(428\) | −10.7408 | −0.519174 | ||||||||
\(429\) | −5.52064 | −0.266539 | ||||||||
\(430\) | 8.67786 | 0.418484 | ||||||||
\(431\) | −12.9971 | −0.626049 | −0.313025 | − | 0.949745i | \(-0.601342\pi\) | ||||
−0.313025 | + | 0.949745i | \(0.601342\pi\) | |||||||
\(432\) | −0.482128 | −0.0231964 | ||||||||
\(433\) | 25.3993 | 1.22061 | 0.610305 | − | 0.792166i | \(-0.291047\pi\) | ||||
0.610305 | + | 0.792166i | \(0.291047\pi\) | |||||||
\(434\) | −0.00908637 | −0.000436160 0 | ||||||||
\(435\) | 8.56621 | 0.410719 | ||||||||
\(436\) | −8.83946 | −0.423333 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −7.39700 | −0.353442 | ||||||||
\(439\) | −18.6099 | −0.888203 | −0.444101 | − | 0.895977i | \(-0.646477\pi\) | ||||
−0.444101 | + | 0.895977i | \(0.646477\pi\) | |||||||
\(440\) | 14.9250 | 0.711522 | ||||||||
\(441\) | 15.5768 | 0.741754 | ||||||||
\(442\) | −4.59009 | −0.218328 | ||||||||
\(443\) | −10.3665 | −0.492527 | −0.246263 | − | 0.969203i | \(-0.579203\pi\) | ||||
−0.246263 | + | 0.969203i | \(0.579203\pi\) | |||||||
\(444\) | −8.47952 | −0.402420 | ||||||||
\(445\) | 0.431648 | 0.0204621 | ||||||||
\(446\) | −16.4764 | −0.780180 | ||||||||
\(447\) | 16.8075 | 0.794970 | ||||||||
\(448\) | −1.23865 | −0.0585206 | ||||||||
\(449\) | −12.9229 | −0.609869 | −0.304934 | − | 0.952373i | \(-0.598635\pi\) | ||||
−0.304934 | + | 0.952373i | \(0.598635\pi\) | |||||||
\(450\) | 1.93397 | 0.0911681 | ||||||||
\(451\) | −33.3871 | −1.57214 | ||||||||
\(452\) | −11.0095 | −0.517843 | ||||||||
\(453\) | −13.2627 | −0.623136 | ||||||||
\(454\) | −24.0916 | −1.13067 | ||||||||
\(455\) | 0.315664 | 0.0147986 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.6446 | 1.01249 | 0.506246 | − | 0.862389i | \(-0.331033\pi\) | ||||
0.506246 | + | 0.862389i | \(0.331033\pi\) | |||||||
\(458\) | −6.39493 | −0.298815 | ||||||||
\(459\) | −20.3013 | −0.947584 | ||||||||
\(460\) | −1.15999 | −0.0540847 | ||||||||
\(461\) | 25.6902 | 1.19651 | 0.598255 | − | 0.801306i | \(-0.295861\pi\) | ||||
0.598255 | + | 0.801306i | \(0.295861\pi\) | |||||||
\(462\) | −1.04818 | −0.0487659 | ||||||||
\(463\) | −5.30550 | −0.246567 | −0.123284 | − | 0.992371i | \(-0.539343\pi\) | ||||
−0.123284 | + | 0.992371i | \(0.539343\pi\) | |||||||
\(464\) | −1.04606 | −0.0485620 | ||||||||
\(465\) | 0.0347063 | 0.00160946 | ||||||||
\(466\) | 12.2992 | 0.569751 | ||||||||
\(467\) | 0.970711 | 0.0449191 | 0.0224596 | − | 0.999748i | \(-0.492850\pi\) | ||||
0.0224596 | + | 0.999748i | \(0.492850\pi\) | |||||||
\(468\) | 3.38625 | 0.156529 | ||||||||
\(469\) | −0.993927 | −0.0458953 | ||||||||
\(470\) | 7.26452 | 0.335087 | ||||||||
\(471\) | 14.5587 | 0.670831 | ||||||||
\(472\) | −22.7402 | −1.04670 | ||||||||
\(473\) | −53.6673 | −2.46762 | ||||||||
\(474\) | −0.00416742 | −0.000191416 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.48273 | 0.0679607 | ||||||||
\(477\) | −9.44110 | −0.432278 | ||||||||
\(478\) | −0.896868 | −0.0410218 | ||||||||
\(479\) | 0.227190 | 0.0103806 | 0.00519030 | − | 0.999987i | \(-0.498348\pi\) | ||||
0.00519030 | + | 0.999987i | \(0.498348\pi\) | |||||||
\(480\) | 4.94469 | 0.225693 | ||||||||
\(481\) | 9.28248 | 0.423245 | ||||||||
\(482\) | −15.6795 | −0.714182 | ||||||||
\(483\) | 0.210815 | 0.00959241 | ||||||||
\(484\) | −21.8126 | −0.991484 | ||||||||
\(485\) | 17.3729 | 0.788861 | ||||||||
\(486\) | −13.8355 | −0.627591 | ||||||||
\(487\) | −16.5677 | −0.750753 | −0.375376 | − | 0.926872i | \(-0.622487\pi\) | ||||
−0.375376 | + | 0.926872i | \(0.622487\pi\) | |||||||
\(488\) | 0.612851 | 0.0277425 | ||||||||
\(489\) | 17.4830 | 0.790608 | ||||||||
\(490\) | −5.96320 | −0.269390 | ||||||||
\(491\) | 22.0413 | 0.994709 | 0.497354 | − | 0.867547i | \(-0.334305\pi\) | ||||
0.497354 | + | 0.867547i | \(0.334305\pi\) | |||||||
\(492\) | −6.85514 | −0.309054 | ||||||||
\(493\) | −44.0471 | −1.98378 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.9604 | −0.537580 | ||||||||
\(496\) | −0.00423813 | −0.000190298 0 | ||||||||
\(497\) | −2.66763 | −0.119659 | ||||||||
\(498\) | −6.58420 | −0.295045 | ||||||||
\(499\) | 25.3168 | 1.13334 | 0.566669 | − | 0.823946i | \(-0.308232\pi\) | ||||
0.566669 | + | 0.823946i | \(0.308232\pi\) | |||||||
\(500\) | 1.25963 | 0.0563323 | ||||||||
\(501\) | −20.4782 | −0.914897 | ||||||||
\(502\) | −2.51595 | −0.112292 | ||||||||
\(503\) | 17.2941 | 0.771104 | 0.385552 | − | 0.922686i | \(-0.374011\pi\) | ||||
0.385552 | + | 0.922686i | \(0.374011\pi\) | |||||||
\(504\) | 1.66376 | 0.0741099 | ||||||||
\(505\) | 8.95142 | 0.398333 | ||||||||
\(506\) | −4.21655 | −0.187449 | ||||||||
\(507\) | −10.0353 | −0.445682 | ||||||||
\(508\) | −8.57719 | −0.380551 | ||||||||
\(509\) | 11.2867 | 0.500272 | 0.250136 | − | 0.968211i | \(-0.419525\pi\) | ||||
0.250136 | + | 0.968211i | \(0.419525\pi\) | |||||||
\(510\) | 3.32879 | 0.147401 | ||||||||
\(511\) | −2.61570 | −0.115712 | ||||||||
\(512\) | −1.19798 | −0.0529438 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.9271 | −0.526084 | ||||||||
\(515\) | −5.66535 | −0.249645 | ||||||||
\(516\) | −11.0191 | −0.485090 | ||||||||
\(517\) | −44.9266 | −1.97587 | ||||||||
\(518\) | 1.76243 | 0.0774367 | ||||||||
\(519\) | 6.15872 | 0.270338 | ||||||||
\(520\) | −3.35463 | −0.147110 | ||||||||
\(521\) | −19.6658 | −0.861573 | −0.430787 | − | 0.902454i | \(-0.641764\pi\) | ||||
−0.430787 | + | 0.902454i | \(0.641764\pi\) | |||||||
\(522\) | −19.0995 | −0.835962 | ||||||||
\(523\) | 35.4632 | 1.55070 | 0.775349 | − | 0.631534i | \(-0.217574\pi\) | ||||
0.775349 | + | 0.631534i | \(0.217574\pi\) | |||||||
\(524\) | −14.3602 | −0.627330 | ||||||||
\(525\) | −0.228924 | −0.00999104 | ||||||||
\(526\) | 10.7276 | 0.467745 | ||||||||
\(527\) | −0.178458 | −0.00777375 | ||||||||
\(528\) | −0.488901 | −0.0212767 | ||||||||
\(529\) | −22.1519 | −0.963128 | ||||||||
\(530\) | 3.61429 | 0.156995 | ||||||||
\(531\) | 18.2232 | 0.790820 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.50428 | 0.325047 | ||||||||
\(534\) | 0.322159 | 0.0139412 | ||||||||
\(535\) | −8.52693 | −0.368651 | ||||||||
\(536\) | 10.5627 | 0.456237 | ||||||||
\(537\) | −3.16752 | −0.136688 | ||||||||
\(538\) | 23.4457 | 1.01082 | ||||||||
\(539\) | 36.8788 | 1.58848 | ||||||||
\(540\) | −5.73353 | −0.246732 | ||||||||
\(541\) | 7.58701 | 0.326191 | 0.163095 | − | 0.986610i | \(-0.447852\pi\) | ||||
0.163095 | + | 0.986610i | \(0.447852\pi\) | |||||||
\(542\) | 22.0546 | 0.947325 | ||||||||
\(543\) | 7.58285 | 0.325411 | ||||||||
\(544\) | −25.4254 | −1.09010 | ||||||||
\(545\) | −7.01751 | −0.300597 | ||||||||
\(546\) | 0.235595 | 0.0100826 | ||||||||
\(547\) | −16.6909 | −0.713650 | −0.356825 | − | 0.934171i | \(-0.616141\pi\) | ||||
−0.356825 | + | 0.934171i | \(0.616141\pi\) | |||||||
\(548\) | 21.5845 | 0.922045 | ||||||||
\(549\) | −0.491119 | −0.0209604 | ||||||||
\(550\) | 4.57874 | 0.195238 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −2.24037 | −0.0953566 | ||||||||
\(553\) | −0.00147367 | −6.26668e−5 0 | ||||||||
\(554\) | −18.1828 | −0.772511 | ||||||||
\(555\) | −6.73176 | −0.285747 | ||||||||
\(556\) | −16.9133 | −0.717282 | ||||||||
\(557\) | −18.6607 | −0.790680 | −0.395340 | − | 0.918535i | \(-0.629373\pi\) | ||||
−0.395340 | + | 0.918535i | \(0.629373\pi\) | |||||||
\(558\) | −0.0773821 | −0.00327585 | ||||||||
\(559\) | 12.0626 | 0.510192 | ||||||||
\(560\) | 0.0279549 | 0.00118131 | ||||||||
\(561\) | −20.5865 | −0.869163 | ||||||||
\(562\) | 1.37607 | 0.0580462 | ||||||||
\(563\) | −6.21513 | −0.261936 | −0.130968 | − | 0.991387i | \(-0.541809\pi\) | ||||
−0.130968 | + | 0.991387i | \(0.541809\pi\) | |||||||
\(564\) | −9.22446 | −0.388420 | ||||||||
\(565\) | −8.74027 | −0.367706 | ||||||||
\(566\) | −1.88559 | −0.0792573 | ||||||||
\(567\) | −0.737584 | −0.0309756 | ||||||||
\(568\) | 28.3494 | 1.18951 | ||||||||
\(569\) | −16.6738 | −0.699003 | −0.349501 | − | 0.936936i | \(-0.613649\pi\) | ||||
−0.349501 | + | 0.936936i | \(0.613649\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.4171 | −0.603337 | −0.301669 | − | 0.953413i | \(-0.597544\pi\) | ||||
−0.301669 | + | 0.953413i | \(0.597544\pi\) | |||||||
\(572\) | 8.01707 | 0.335210 | ||||||||
\(573\) | 2.96076 | 0.123688 | ||||||||
\(574\) | 1.42481 | 0.0594704 | ||||||||
\(575\) | −0.920897 | −0.0384041 | ||||||||
\(576\) | −10.5487 | −0.439528 | ||||||||
\(577\) | 22.2199 | 0.925028 | 0.462514 | − | 0.886612i | \(-0.346947\pi\) | ||||
0.462514 | + | 0.886612i | \(0.346947\pi\) | |||||||
\(578\) | −2.48884 | −0.103522 | ||||||||
\(579\) | −11.9170 | −0.495255 | ||||||||
\(580\) | −12.4398 | −0.516537 | ||||||||
\(581\) | −2.32829 | −0.0965936 | ||||||||
\(582\) | 12.9662 | 0.537466 | ||||||||
\(583\) | −22.3522 | −0.925732 | ||||||||
\(584\) | 27.7976 | 1.15027 | ||||||||
\(585\) | 2.68829 | 0.111147 | ||||||||
\(586\) | 12.0501 | 0.497783 | ||||||||
\(587\) | 41.5186 | 1.71366 | 0.856828 | − | 0.515602i | \(-0.172432\pi\) | ||||
0.856828 | + | 0.515602i | \(0.172432\pi\) | |||||||
\(588\) | 7.57205 | 0.312266 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −6.97630 | −0.287210 | ||||||||
\(591\) | −10.8075 | −0.444562 | ||||||||
\(592\) | 0.822045 | 0.0337859 | ||||||||
\(593\) | −8.48062 | −0.348257 | −0.174129 | − | 0.984723i | \(-0.555711\pi\) | ||||
−0.174129 | + | 0.984723i | \(0.555711\pi\) | |||||||
\(594\) | −20.8413 | −0.855131 | ||||||||
\(595\) | 1.17711 | 0.0482570 | ||||||||
\(596\) | −24.4079 | −0.999787 | ||||||||
\(597\) | 23.5878 | 0.965384 | ||||||||
\(598\) | 0.947736 | 0.0387558 | ||||||||
\(599\) | −15.1403 | −0.618614 | −0.309307 | − | 0.950962i | \(-0.600097\pi\) | ||||
−0.309307 | + | 0.950962i | \(0.600097\pi\) | |||||||
\(600\) | 2.43282 | 0.0993193 | ||||||||
\(601\) | 24.4130 | 0.995826 | 0.497913 | − | 0.867227i | \(-0.334100\pi\) | ||||
0.497913 | + | 0.867227i | \(0.334100\pi\) | |||||||
\(602\) | 2.29027 | 0.0933445 | ||||||||
\(603\) | −8.46457 | −0.344704 | ||||||||
\(604\) | 19.2601 | 0.783682 | ||||||||
\(605\) | −17.3167 | −0.704025 | ||||||||
\(606\) | 6.68087 | 0.271392 | ||||||||
\(607\) | 22.1867 | 0.900532 | 0.450266 | − | 0.892894i | \(-0.351329\pi\) | ||||
0.450266 | + | 0.892894i | \(0.351329\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.26080 | 0.0916124 | ||||||||
\(610\) | 0.188013 | 0.00761241 | ||||||||
\(611\) | 10.0980 | 0.408520 | ||||||||
\(612\) | 12.6273 | 0.510430 | ||||||||
\(613\) | 11.2934 | 0.456135 | 0.228068 | − | 0.973645i | \(-0.426759\pi\) | ||||
0.228068 | + | 0.973645i | \(0.426759\pi\) | |||||||
\(614\) | −4.14432 | −0.167251 | ||||||||
\(615\) | −5.44219 | −0.219450 | ||||||||
\(616\) | 3.93902 | 0.158708 | ||||||||
\(617\) | −8.72864 | −0.351402 | −0.175701 | − | 0.984444i | \(-0.556219\pi\) | ||||
−0.175701 | + | 0.984444i | \(0.556219\pi\) | |||||||
\(618\) | −4.22832 | −0.170088 | ||||||||
\(619\) | 46.3421 | 1.86265 | 0.931323 | − | 0.364194i | \(-0.118655\pi\) | ||||
0.931323 | + | 0.364194i | \(0.118655\pi\) | |||||||
\(620\) | −0.0504004 | −0.00202413 | ||||||||
\(621\) | 4.19170 | 0.168207 | ||||||||
\(622\) | −16.7014 | −0.669664 | ||||||||
\(623\) | 0.113921 | 0.00456415 | ||||||||
\(624\) | 0.109888 | 0.00439905 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 4.91939 | 0.196618 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.1422 | −0.843665 | ||||||||
\(629\) | 34.6144 | 1.38017 | ||||||||
\(630\) | 0.510415 | 0.0203354 | ||||||||
\(631\) | 14.1200 | 0.562108 | 0.281054 | − | 0.959692i | \(-0.409316\pi\) | ||||
0.281054 | + | 0.959692i | \(0.409316\pi\) | |||||||
\(632\) | 0.0156610 | 0.000622961 0 | ||||||||
\(633\) | −13.5590 | −0.538922 | ||||||||
\(634\) | 12.7974 | 0.508250 | ||||||||
\(635\) | −6.80930 | −0.270219 | ||||||||
\(636\) | −4.58941 | −0.181982 | ||||||||
\(637\) | −8.28908 | −0.328425 | ||||||||
\(638\) | −45.2188 | −1.79023 | ||||||||
\(639\) | −22.7183 | −0.898721 | ||||||||
\(640\) | −7.36295 | −0.291046 | ||||||||
\(641\) | −14.0331 | −0.554273 | −0.277136 | − | 0.960831i | \(-0.589385\pi\) | ||||
−0.277136 | + | 0.960831i | \(0.589385\pi\) | |||||||
\(642\) | −6.36405 | −0.251169 | ||||||||
\(643\) | 20.4083 | 0.804823 | 0.402411 | − | 0.915459i | \(-0.368172\pi\) | ||||
0.402411 | + | 0.915459i | \(0.368172\pi\) | |||||||
\(644\) | −0.306145 | −0.0120638 | ||||||||
\(645\) | −8.74791 | −0.344449 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.5688 | −0.572757 | −0.286379 | − | 0.958117i | \(-0.592452\pi\) | ||||
−0.286379 | + | 0.958117i | \(0.592452\pi\) | |||||||
\(648\) | 7.83846 | 0.307924 | ||||||||
\(649\) | 43.1442 | 1.69356 | ||||||||
\(650\) | −1.02914 | −0.0403664 | ||||||||
\(651\) | 0.00915971 | 0.000358997 0 | ||||||||
\(652\) | −25.3888 | −0.994302 | ||||||||
\(653\) | −26.9592 | −1.05500 | −0.527498 | − | 0.849556i | \(-0.676870\pi\) | ||||
−0.527498 | + | 0.849556i | \(0.676870\pi\) | |||||||
\(654\) | −5.23751 | −0.204803 | ||||||||
\(655\) | −11.4004 | −0.445450 | ||||||||
\(656\) | 0.664570 | 0.0259471 | ||||||||
\(657\) | −22.2761 | −0.869073 | ||||||||
\(658\) | 1.91726 | 0.0747426 | ||||||||
\(659\) | −14.3259 | −0.558059 | −0.279029 | − | 0.960283i | \(-0.590013\pi\) | ||||
−0.279029 | + | 0.960283i | \(0.590013\pi\) | |||||||
\(660\) | −5.81407 | −0.226312 | ||||||||
\(661\) | −45.9785 | −1.78836 | −0.894179 | − | 0.447710i | \(-0.852240\pi\) | ||||
−0.894179 | + | 0.447710i | \(0.852240\pi\) | |||||||
\(662\) | −0.0294596 | −0.00114498 | ||||||||
\(663\) | 4.62714 | 0.179703 | ||||||||
\(664\) | 24.7432 | 0.960221 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.0093 | 0.581600 | ||||||||
\(667\) | 9.09460 | 0.352144 | ||||||||
\(668\) | 29.7384 | 1.15061 | ||||||||
\(669\) | 16.6094 | 0.642156 | ||||||||
\(670\) | 3.24045 | 0.125189 | ||||||||
\(671\) | −1.16274 | −0.0448872 | ||||||||
\(672\) | 1.30501 | 0.0503417 | ||||||||
\(673\) | 3.81843 | 0.147190 | 0.0735948 | − | 0.997288i | \(-0.476553\pi\) | ||||
0.0735948 | + | 0.997288i | \(0.476553\pi\) | |||||||
\(674\) | 20.5001 | 0.789633 | ||||||||
\(675\) | −4.55176 | −0.175197 | ||||||||
\(676\) | 14.5732 | 0.560508 | ||||||||
\(677\) | 48.8890 | 1.87896 | 0.939479 | − | 0.342607i | \(-0.111310\pi\) | ||||
0.939479 | + | 0.342607i | \(0.111310\pi\) | |||||||
\(678\) | −6.52328 | −0.250525 | ||||||||
\(679\) | 4.58506 | 0.175959 | ||||||||
\(680\) | −12.5094 | −0.479715 | ||||||||
\(681\) | 24.2860 | 0.930643 | ||||||||
\(682\) | −0.183205 | −0.00701529 | ||||||||
\(683\) | −15.9118 | −0.608849 | −0.304425 | − | 0.952536i | \(-0.598464\pi\) | ||||
−0.304425 | + | 0.952536i | \(0.598464\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.1356 | 0.654719 | ||||||||
\(686\) | −3.16345 | −0.120781 | ||||||||
\(687\) | 6.44655 | 0.245951 | ||||||||
\(688\) | 1.06825 | 0.0407265 | ||||||||
\(689\) | 5.02400 | 0.191399 | ||||||||
\(690\) | −0.687309 | −0.0261654 | ||||||||
\(691\) | 36.6387 | 1.39380 | 0.696902 | − | 0.717167i | \(-0.254561\pi\) | ||||
0.696902 | + | 0.717167i | \(0.254561\pi\) | |||||||
\(692\) | −8.94368 | −0.339988 | ||||||||
\(693\) | −3.15660 | −0.119909 | ||||||||
\(694\) | 27.9274 | 1.06011 | ||||||||
\(695\) | −13.4272 | −0.509322 | ||||||||
\(696\) | −24.0260 | −0.910704 | ||||||||
\(697\) | 27.9835 | 1.05995 | ||||||||
\(698\) | −2.23343 | −0.0845367 | ||||||||
\(699\) | −12.3985 | −0.468955 | ||||||||
\(700\) | 0.332443 | 0.0125651 | ||||||||
\(701\) | −17.6715 | −0.667442 | −0.333721 | − | 0.942672i | \(-0.608304\pi\) | ||||
−0.333721 | + | 0.942672i | \(0.608304\pi\) | |||||||
\(702\) | 4.68442 | 0.176802 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −24.9744 | −0.941258 | ||||||||
\(705\) | −7.32316 | −0.275806 | ||||||||
\(706\) | −2.05709 | −0.0774196 | ||||||||
\(707\) | 2.36247 | 0.0888497 | ||||||||
\(708\) | 8.85848 | 0.332922 | ||||||||
\(709\) | 15.3223 | 0.575442 | 0.287721 | − | 0.957714i | \(-0.407102\pi\) | ||||
0.287721 | + | 0.957714i | \(0.407102\pi\) | |||||||
\(710\) | 8.69713 | 0.326397 | ||||||||
\(711\) | −0.0125502 | −0.000470669 0 | ||||||||
\(712\) | −1.21066 | −0.0453714 | ||||||||
\(713\) | 0.0368470 | 0.00137993 | ||||||||
\(714\) | 0.878537 | 0.0328784 | ||||||||
\(715\) | 6.36463 | 0.238024 | ||||||||
\(716\) | 4.59986 | 0.171905 | ||||||||
\(717\) | 0.904108 | 0.0337645 | ||||||||
\(718\) | 13.4488 | 0.501904 | ||||||||
\(719\) | 1.62082 | 0.0604462 | 0.0302231 | − | 0.999543i | \(-0.490378\pi\) | ||||
0.0302231 | + | 0.999543i | \(0.490378\pi\) | |||||||
\(720\) | 0.238072 | 0.00887241 | ||||||||
\(721\) | −1.49521 | −0.0556844 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.8061 | 0.587834 | ||||||||
\(724\) | −11.0118 | −0.409250 | ||||||||
\(725\) | −9.87581 | −0.366778 | ||||||||
\(726\) | −12.9243 | −0.479666 | ||||||||
\(727\) | 11.1635 | 0.414031 | 0.207016 | − | 0.978338i | \(-0.433625\pi\) | ||||
0.207016 | + | 0.978338i | \(0.433625\pi\) | |||||||
\(728\) | −0.885357 | −0.0328135 | ||||||||
\(729\) | 5.56303 | 0.206038 | ||||||||
\(730\) | 8.52784 | 0.315630 | ||||||||
\(731\) | 44.9813 | 1.66370 | ||||||||
\(732\) | −0.238738 | −0.00882400 | ||||||||
\(733\) | 12.1110 | 0.447331 | 0.223666 | − | 0.974666i | \(-0.428198\pi\) | ||||
0.223666 | + | 0.974666i | \(0.428198\pi\) | |||||||
\(734\) | 5.32931 | 0.196708 | ||||||||
\(735\) | 6.01134 | 0.221732 | ||||||||
\(736\) | 5.24969 | 0.193506 | ||||||||
\(737\) | −20.0402 | −0.738190 | ||||||||
\(738\) | 12.1341 | 0.446662 | ||||||||
\(739\) | 40.0688 | 1.47395 | 0.736977 | − | 0.675918i | \(-0.236253\pi\) | ||||
0.736977 | + | 0.675918i | \(0.236253\pi\) | |||||||
\(740\) | 9.77586 | 0.359368 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.953887 | 0.0350183 | ||||||||
\(743\) | −23.3715 | −0.857416 | −0.428708 | − | 0.903443i | \(-0.641031\pi\) | ||||
−0.428708 | + | 0.903443i | \(0.641031\pi\) | |||||||
\(744\) | −0.0973421 | −0.00356873 | ||||||||
\(745\) | −19.3771 | −0.709921 | ||||||||
\(746\) | −23.1515 | −0.847636 | ||||||||
\(747\) | −19.8283 | −0.725481 | ||||||||
\(748\) | 29.8957 | 1.09309 | ||||||||
\(749\) | −2.25044 | −0.0822292 | ||||||||
\(750\) | 0.746348 | 0.0272528 | ||||||||
\(751\) | 16.6615 | 0.607986 | 0.303993 | − | 0.952674i | \(-0.401680\pi\) | ||||
0.303993 | + | 0.952674i | \(0.401680\pi\) | |||||||
\(752\) | 0.894263 | 0.0326104 | ||||||||
\(753\) | 2.53625 | 0.0924262 | ||||||||
\(754\) | 10.1636 | 0.370138 | ||||||||
\(755\) | 15.2903 | 0.556470 | ||||||||
\(756\) | −1.51320 | −0.0550345 | ||||||||
\(757\) | 23.5257 | 0.855057 | 0.427528 | − | 0.904002i | \(-0.359384\pi\) | ||||
0.427528 | + | 0.904002i | \(0.359384\pi\) | |||||||
\(758\) | 23.2884 | 0.845874 | ||||||||
\(759\) | 4.25059 | 0.154287 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.20495 | −0.297429 | −0.148715 | − | 0.988880i | \(-0.547514\pi\) | ||||
−0.148715 | + | 0.988880i | \(0.547514\pi\) | |||||||
\(762\) | −5.08210 | −0.184105 | ||||||||
\(763\) | −1.85207 | −0.0670494 | ||||||||
\(764\) | −4.29961 | −0.155555 | ||||||||
\(765\) | 10.0246 | 0.362442 | ||||||||
\(766\) | 26.2489 | 0.948412 | ||||||||
\(767\) | −9.69733 | −0.350150 | ||||||||
\(768\) | −13.6371 | −0.492087 | ||||||||
\(769\) | 18.8871 | 0.681087 | 0.340544 | − | 0.940229i | \(-0.389389\pi\) | ||||
0.340544 | + | 0.940229i | \(0.389389\pi\) | |||||||
\(770\) | 1.20843 | 0.0435487 | ||||||||
\(771\) | 12.0234 | 0.433013 | ||||||||
\(772\) | 17.3059 | 0.622853 | ||||||||
\(773\) | 42.4983 | 1.52856 | 0.764279 | − | 0.644886i | \(-0.223095\pi\) | ||||
0.764279 | + | 0.644886i | \(0.223095\pi\) | |||||||
\(774\) | 19.5046 | 0.701079 | ||||||||
\(775\) | −0.0400121 | −0.00143728 | ||||||||
\(776\) | −48.7264 | −1.74918 | ||||||||
\(777\) | −1.77665 | −0.0637371 | ||||||||
\(778\) | 11.4459 | 0.410356 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 1.30680 | 0.0467911 | ||||||||
\(781\) | −53.7864 | −1.92463 | ||||||||
\(782\) | 3.53411 | 0.126380 | ||||||||
\(783\) | 44.9523 | 1.60646 | ||||||||
\(784\) | −0.734071 | −0.0262168 | ||||||||
\(785\) | −16.7845 | −0.599063 | ||||||||
\(786\) | −8.50864 | −0.303493 | ||||||||
\(787\) | 44.4450 | 1.58429 | 0.792146 | − | 0.610331i | \(-0.208964\pi\) | ||||
0.792146 | + | 0.610331i | \(0.208964\pi\) | |||||||
\(788\) | 15.6947 | 0.559100 | ||||||||
\(789\) | −10.8142 | −0.384995 | ||||||||
\(790\) | 0.00480453 | 0.000170938 0 | ||||||||
\(791\) | −2.30674 | −0.0820183 | ||||||||
\(792\) | 33.5459 | 1.19200 | ||||||||
\(793\) | 0.261345 | 0.00928062 | ||||||||
\(794\) | −19.7996 | −0.702662 | ||||||||
\(795\) | −3.64346 | −0.129220 | ||||||||
\(796\) | −34.2542 | −1.21411 | ||||||||
\(797\) | −0.711060 | −0.0251870 | −0.0125935 | − | 0.999921i | \(-0.504009\pi\) | ||||
−0.0125935 | + | 0.999921i | \(0.504009\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.6554 | 1.33215 | ||||||||
\(800\) | −5.70062 | −0.201547 | ||||||||
\(801\) | 0.970184 | 0.0342798 | ||||||||
\(802\) | −30.9086 | −1.09142 | ||||||||
\(803\) | −52.7395 | −1.86114 | ||||||||
\(804\) | −4.11471 | −0.145115 | ||||||||
\(805\) | −0.243044 | −0.00856618 | ||||||||
\(806\) | 0.0411782 | 0.00145044 | ||||||||
\(807\) | −23.6349 | −0.831989 | ||||||||
\(808\) | −25.1064 | −0.883241 | ||||||||
\(809\) | −37.2669 | −1.31023 | −0.655117 | − | 0.755528i | \(-0.727381\pi\) | ||||
−0.655117 | + | 0.755528i | \(0.727381\pi\) | |||||||
\(810\) | 2.40471 | 0.0844928 | ||||||||
\(811\) | −26.0182 | −0.913622 | −0.456811 | − | 0.889564i | \(-0.651008\pi\) | ||||
−0.456811 | + | 0.889564i | \(0.651008\pi\) | |||||||
\(812\) | −3.28314 | −0.115216 | ||||||||
\(813\) | −22.2326 | −0.779731 | ||||||||
\(814\) | 35.5352 | 1.24551 | ||||||||
\(815\) | −20.1558 | −0.706026 | ||||||||
\(816\) | 0.409774 | 0.0143450 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 27.8251 | 0.972881 | ||||||||
\(819\) | 0.709496 | 0.0247918 | ||||||||
\(820\) | 7.90315 | 0.275990 | ||||||||
\(821\) | 1.15939 | 0.0404631 | 0.0202316 | − | 0.999795i | \(-0.493560\pi\) | ||||
0.0202316 | + | 0.999795i | \(0.493560\pi\) | |||||||
\(822\) | 12.7891 | 0.446072 | ||||||||
\(823\) | 15.4136 | 0.537284 | 0.268642 | − | 0.963240i | \(-0.413425\pi\) | ||||
0.268642 | + | 0.963240i | \(0.413425\pi\) | |||||||
\(824\) | 15.8899 | 0.553549 | ||||||||
\(825\) | −4.61570 | −0.160698 | ||||||||
\(826\) | −1.84119 | −0.0640633 | ||||||||
\(827\) | −37.9042 | −1.31806 | −0.659029 | − | 0.752118i | \(-0.729032\pi\) | ||||
−0.659029 | + | 0.752118i | \(0.729032\pi\) | |||||||
\(828\) | −2.60722 | −0.0906072 | ||||||||
\(829\) | −12.1577 | −0.422254 | −0.211127 | − | 0.977459i | \(-0.567713\pi\) | ||||
−0.211127 | + | 0.977459i | \(0.567713\pi\) | |||||||
\(830\) | 7.59079 | 0.263480 | ||||||||
\(831\) | 18.3295 | 0.635844 | ||||||||
\(832\) | 5.61339 | 0.194609 | ||||||||
\(833\) | −30.9100 | −1.07097 | ||||||||
\(834\) | −10.0213 | −0.347011 | ||||||||
\(835\) | 23.6089 | 0.817018 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.182125 | 0.00629518 | ||||||||
\(838\) | −10.8855 | −0.376034 | ||||||||
\(839\) | 47.7649 | 1.64903 | 0.824513 | − | 0.565843i | \(-0.191449\pi\) | ||||
0.824513 | + | 0.565843i | \(0.191449\pi\) | |||||||
\(840\) | 0.642071 | 0.0221536 | ||||||||
\(841\) | 68.5316 | 2.36316 | ||||||||
\(842\) | 12.6303 | 0.435267 | ||||||||
\(843\) | −1.38718 | −0.0477770 | ||||||||
\(844\) | 19.6904 | 0.677770 | ||||||||
\(845\) | 11.5695 | 0.398001 | ||||||||
\(846\) | 16.3279 | 0.561366 | ||||||||
\(847\) | −4.57025 | −0.157036 | ||||||||
\(848\) | 0.444919 | 0.0152786 | ||||||||
\(849\) | 1.90081 | 0.0652357 | ||||||||
\(850\) | −3.83769 | −0.131632 | ||||||||
\(851\) | −7.14700 | −0.244996 | ||||||||
\(852\) | −11.0436 | −0.378347 | ||||||||
\(853\) | −27.5081 | −0.941859 | −0.470930 | − | 0.882171i | \(-0.656081\pi\) | ||||
−0.470930 | + | 0.882171i | \(0.656081\pi\) | |||||||
\(854\) | 0.0496205 | 0.00169798 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23.9158 | 0.817427 | ||||||||
\(857\) | −7.97761 | −0.272510 | −0.136255 | − | 0.990674i | \(-0.543507\pi\) | ||||
−0.136255 | + | 0.990674i | \(0.543507\pi\) | |||||||
\(858\) | 4.75022 | 0.162170 | ||||||||
\(859\) | 2.43789 | 0.0831798 | 0.0415899 | − | 0.999135i | \(-0.486758\pi\) | ||||
0.0415899 | + | 0.999135i | \(0.486758\pi\) | |||||||
\(860\) | 12.7037 | 0.433193 | ||||||||
\(861\) | −1.43631 | −0.0489493 | ||||||||
\(862\) | 11.1833 | 0.380906 | ||||||||
\(863\) | 19.8250 | 0.674852 | 0.337426 | − | 0.941352i | \(-0.390444\pi\) | ||||
0.337426 | + | 0.941352i | \(0.390444\pi\) | |||||||
\(864\) | 25.9479 | 0.882765 | ||||||||
\(865\) | −7.10025 | −0.241416 | ||||||||
\(866\) | −21.8547 | −0.742655 | ||||||||
\(867\) | 2.50893 | 0.0852077 | ||||||||
\(868\) | −0.0133017 | −0.000451490 0 | ||||||||
\(869\) | −0.0297131 | −0.00100795 | ||||||||
\(870\) | −7.37079 | −0.249893 | ||||||||
\(871\) | 4.50435 | 0.152624 | ||||||||
\(872\) | 19.6823 | 0.666527 | ||||||||
\(873\) | 39.0477 | 1.32157 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.263921 | 0.00892216 | ||||||||
\(876\) | −10.8286 | −0.365865 | ||||||||
\(877\) | 8.63651 | 0.291634 | 0.145817 | − | 0.989312i | \(-0.453419\pi\) | ||||
0.145817 | + | 0.989312i | \(0.453419\pi\) | |||||||
\(878\) | 16.0129 | 0.540408 | ||||||||
\(879\) | −12.1473 | −0.409719 | ||||||||
\(880\) | 0.563644 | 0.0190004 | ||||||||
\(881\) | −6.78634 | −0.228638 | −0.114319 | − | 0.993444i | \(-0.536469\pi\) | ||||
−0.114319 | + | 0.993444i | \(0.536469\pi\) | |||||||
\(882\) | −13.4031 | −0.451305 | ||||||||
\(883\) | 22.2213 | 0.747807 | 0.373904 | − | 0.927468i | \(-0.378019\pi\) | ||||
0.373904 | + | 0.927468i | \(0.378019\pi\) | |||||||
\(884\) | −6.71952 | −0.226002 | ||||||||
\(885\) | 7.03262 | 0.236399 | ||||||||
\(886\) | 8.91983 | 0.299668 | ||||||||
\(887\) | −3.22267 | −0.108207 | −0.0541033 | − | 0.998535i | \(-0.517230\pi\) | ||||
−0.0541033 | + | 0.998535i | \(0.517230\pi\) | |||||||
\(888\) | 18.8809 | 0.633600 | ||||||||
\(889\) | −1.79712 | −0.0602734 | ||||||||
\(890\) | −0.371411 | −0.0124497 | ||||||||
\(891\) | −14.8716 | −0.498219 | ||||||||
\(892\) | −24.1202 | −0.807602 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −14.4620 | −0.483683 | ||||||||
\(895\) | 3.65176 | 0.122065 | ||||||||
\(896\) | −1.94324 | −0.0649190 | ||||||||
\(897\) | −0.955386 | −0.0318994 | ||||||||
\(898\) | 11.1195 | 0.371062 | ||||||||
\(899\) | 0.395152 | 0.0131791 | ||||||||
\(900\) | 2.83118 | 0.0943725 | ||||||||
\(901\) | 18.7345 | 0.624137 | ||||||||
\(902\) | 28.7279 | 0.956535 | ||||||||
\(903\) | −2.30876 | −0.0768306 | ||||||||
\(904\) | 24.5142 | 0.815330 | ||||||||
\(905\) | −8.74210 | −0.290597 | ||||||||
\(906\) | 11.4119 | 0.379134 | ||||||||
\(907\) | 0.911956 | 0.0302810 | 0.0151405 | − | 0.999885i | \(-0.495180\pi\) | ||||
0.0151405 | + | 0.999885i | \(0.495180\pi\) | |||||||
\(908\) | −35.2682 | −1.17042 | ||||||||
\(909\) | 20.1195 | 0.667320 | ||||||||
\(910\) | −0.271613 | −0.00900388 | ||||||||
\(911\) | 51.6358 | 1.71077 | 0.855385 | − | 0.517992i | \(-0.173320\pi\) | ||||
0.855385 | + | 0.517992i | \(0.173320\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −46.9444 | −1.55363 | ||||||||
\(914\) | −18.6241 | −0.616029 | ||||||||
\(915\) | −0.189530 | −0.00626568 | ||||||||
\(916\) | −9.36167 | −0.309318 | ||||||||
\(917\) | −3.00880 | −0.0993593 | ||||||||
\(918\) | 17.4682 | 0.576537 | ||||||||
\(919\) | −16.5629 | −0.546361 | −0.273180 | − | 0.961963i | \(-0.588076\pi\) | ||||
−0.273180 | + | 0.961963i | \(0.588076\pi\) | |||||||
\(920\) | 2.58288 | 0.0851550 | ||||||||
\(921\) | 4.17777 | 0.137662 | ||||||||
\(922\) | −22.1051 | −0.727991 | ||||||||
\(923\) | 12.0893 | 0.397925 | ||||||||
\(924\) | −1.53446 | −0.0504799 | ||||||||
\(925\) | 7.76091 | 0.255177 | ||||||||
\(926\) | 4.56511 | 0.150019 | ||||||||
\(927\) | −12.7336 | −0.418227 | ||||||||
\(928\) | 56.2983 | 1.84808 | ||||||||
\(929\) | −25.5753 | −0.839098 | −0.419549 | − | 0.907733i | \(-0.637812\pi\) | ||||
−0.419549 | + | 0.907733i | \(0.637812\pi\) | |||||||
\(930\) | −0.0298629 | −0.000979244 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 18.0051 | 0.589777 | ||||||||
\(933\) | 16.8362 | 0.551192 | ||||||||
\(934\) | −0.835247 | −0.0273301 | ||||||||
\(935\) | 23.7337 | 0.776176 | ||||||||
\(936\) | −7.53996 | −0.246451 | ||||||||
\(937\) | −1.00369 | −0.0327890 | −0.0163945 | − | 0.999866i | \(-0.505219\pi\) | ||||
−0.0163945 | + | 0.999866i | \(0.505219\pi\) | |||||||
\(938\) | 0.855223 | 0.0279240 | ||||||||
\(939\) | −4.95910 | −0.161834 | ||||||||
\(940\) | 10.6347 | 0.346865 | ||||||||
\(941\) | −55.6685 | −1.81474 | −0.907371 | − | 0.420331i | \(-0.861914\pi\) | ||||
−0.907371 | + | 0.420331i | \(0.861914\pi\) | |||||||
\(942\) | −12.5270 | −0.408153 | ||||||||
\(943\) | −5.77788 | −0.188154 | ||||||||
\(944\) | −0.858784 | −0.0279510 | ||||||||
\(945\) | −1.20131 | −0.0390785 | ||||||||
\(946\) | 46.1779 | 1.50137 | ||||||||
\(947\) | 28.8174 | 0.936438 | 0.468219 | − | 0.883612i | \(-0.344896\pi\) | ||||
0.468219 | + | 0.883612i | \(0.344896\pi\) | |||||||
\(948\) | −0.00610078 | −0.000198144 0 | ||||||||
\(949\) | 11.8540 | 0.384798 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.9007 | −0.418334 | ||||||||
\(952\) | −3.30150 | −0.107002 | ||||||||
\(953\) | −8.08279 | −0.261827 | −0.130914 | − | 0.991394i | \(-0.541791\pi\) | ||||
−0.130914 | + | 0.991394i | \(0.541791\pi\) | |||||||
\(954\) | 8.12358 | 0.263011 | ||||||||
\(955\) | −3.41340 | −0.110455 | ||||||||
\(956\) | −1.31294 | −0.0424637 | ||||||||
\(957\) | 45.5838 | 1.47351 | ||||||||
\(958\) | −0.195486 | −0.00631585 | ||||||||
\(959\) | 4.52245 | 0.146038 | ||||||||
\(960\) | −4.07090 | −0.131388 | ||||||||
\(961\) | −30.9984 | −0.999948 | ||||||||
\(962\) | −7.98710 | −0.257514 | ||||||||
\(963\) | −19.1654 | −0.617595 | ||||||||
\(964\) | −22.9536 | −0.739285 | ||||||||
\(965\) | 13.7389 | 0.442270 | ||||||||
\(966\) | −0.181395 | −0.00583630 | ||||||||
\(967\) | 9.84792 | 0.316688 | 0.158344 | − | 0.987384i | \(-0.449385\pi\) | ||||
0.158344 | + | 0.987384i | \(0.449385\pi\) | |||||||
\(968\) | 48.5690 | 1.56107 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.9485 | −0.479966 | ||||||||
\(971\) | −1.84777 | −0.0592979 | −0.0296489 | − | 0.999560i | \(-0.509439\pi\) | ||||
−0.0296489 | + | 0.999560i | \(0.509439\pi\) | |||||||
\(972\) | −20.2541 | −0.649650 | ||||||||
\(973\) | −3.54371 | −0.113606 | ||||||||
\(974\) | 14.2556 | 0.456780 | ||||||||
\(975\) | 1.03745 | 0.0332250 | ||||||||
\(976\) | 0.0231444 | 0.000740833 0 | ||||||||
\(977\) | 26.4611 | 0.846567 | 0.423283 | − | 0.905997i | \(-0.360877\pi\) | ||||
0.423283 | + | 0.905997i | \(0.360877\pi\) | |||||||
\(978\) | −15.0432 | −0.481029 | ||||||||
\(979\) | 2.29695 | 0.0734108 | ||||||||
\(980\) | −8.72966 | −0.278859 | ||||||||
\(981\) | −15.7728 | −0.503586 | ||||||||
\(982\) | −18.9654 | −0.605210 | ||||||||
\(983\) | 35.5543 | 1.13401 | 0.567003 | − | 0.823716i | \(-0.308103\pi\) | ||||
0.567003 | + | 0.823716i | \(0.308103\pi\) | |||||||
\(984\) | 15.2639 | 0.486597 | ||||||||
\(985\) | 12.4598 | 0.397001 | ||||||||
\(986\) | 37.9002 | 1.20699 | ||||||||
\(987\) | −1.93274 | −0.0615197 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.28750 | −0.295325 | ||||||||
\(990\) | 10.2913 | 0.327079 | ||||||||
\(991\) | 39.1942 | 1.24504 | 0.622522 | − | 0.782603i | \(-0.286108\pi\) | ||||
0.622522 | + | 0.782603i | \(0.286108\pi\) | |||||||
\(992\) | 0.228094 | 0.00724199 | ||||||||
\(993\) | 0.0296974 | 0.000942420 0 | ||||||||
\(994\) | 2.29536 | 0.0728043 | ||||||||
\(995\) | −27.1939 | −0.862103 | ||||||||
\(996\) | −9.63875 | −0.305416 | ||||||||
\(997\) | −3.55869 | −0.112705 | −0.0563524 | − | 0.998411i | \(-0.517947\pi\) | ||||
−0.0563524 | + | 0.998411i | \(0.517947\pi\) | |||||||
\(998\) | −21.7838 | −0.689555 | ||||||||
\(999\) | −35.3258 | −1.11766 |
(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 | 1805.2.a.r.1.2 | yes | 6 | |
5.4 | even | 2 | 9025.2.a.bq.1.5 | 6 | |||
19.18 | odd | 2 | 1805.2.a.q.1.5 | ✓ | 6 | ||
95.94 | odd | 2 | 9025.2.a.ca.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.a.q.1.5 | ✓ | 6 | 19.18 | odd | 2 | ||
1805.2.a.r.1.2 | yes | 6 | 1.1 | even | 1 | trivial | |
9025.2.a.bq.1.5 | 6 | 5.4 | even | 2 | |||
9025.2.a.ca.1.2 | 6 | 95.94 | odd | 2 |