Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.46840000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 11x^{4} + 8x^{3} + 31x^{2} - 15x - 9 \) |
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 | 1.4 | ||
Root | \(-0.364088\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.364088 | 0.257449 | 0.128724 | − | 0.991680i | \(-0.458912\pi\) | ||||
0.128724 | + | 0.991680i | \(0.458912\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.86744 | −0.933720 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.364088 | 0.148638 | ||||||||
\(7\) | −2.24941 | −0.850196 | −0.425098 | − | 0.905147i | \(-0.639760\pi\) | ||||
−0.425098 | + | 0.905147i | \(0.639760\pi\) | |||||||
\(8\) | −1.40809 | −0.497834 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.63962 | 1.39890 | 0.699448 | − | 0.714683i | \(-0.253429\pi\) | ||||
0.699448 | + | 0.714683i | \(0.253429\pi\) | |||||||
\(12\) | −1.86744 | −0.539084 | ||||||||
\(13\) | −3.75730 | −1.04209 | −0.521044 | − | 0.853530i | \(-0.674457\pi\) | ||||
−0.521044 | + | 0.853530i | \(0.674457\pi\) | |||||||
\(14\) | −0.818981 | −0.218882 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.22221 | 0.805553 | ||||||||
\(17\) | 5.36779 | 1.30188 | 0.650940 | − | 0.759129i | \(-0.274375\pi\) | ||||
0.650940 | + | 0.759129i | \(0.274375\pi\) | |||||||
\(18\) | 0.364088 | 0.0858163 | ||||||||
\(19\) | −5.66369 | −1.29934 | −0.649669 | − | 0.760217i | \(-0.725093\pi\) | ||||
−0.649669 | + | 0.760217i | \(0.725093\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.24941 | −0.490861 | ||||||||
\(22\) | 1.68923 | 0.360144 | ||||||||
\(23\) | −1.32214 | −0.275685 | −0.137842 | − | 0.990454i | \(-0.544017\pi\) | ||||
−0.137842 | + | 0.990454i | \(0.544017\pi\) | |||||||
\(24\) | −1.40809 | −0.287425 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.36799 | −0.268284 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.20063 | 0.793845 | ||||||||
\(29\) | 8.86744 | 1.64664 | 0.823321 | − | 0.567576i | \(-0.192119\pi\) | ||||
0.823321 | + | 0.567576i | \(0.192119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.21200 | 0.217681 | 0.108841 | − | 0.994059i | \(-0.465286\pi\) | ||||
0.108841 | + | 0.994059i | \(0.465286\pi\) | |||||||
\(32\) | 3.98934 | 0.705223 | ||||||||
\(33\) | 4.63962 | 0.807653 | ||||||||
\(34\) | 1.95435 | 0.335168 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.86744 | −0.311240 | ||||||||
\(37\) | 2.15975 | 0.355061 | 0.177531 | − | 0.984115i | \(-0.443189\pi\) | ||||
0.177531 | + | 0.984115i | \(0.443189\pi\) | |||||||
\(38\) | −2.06208 | −0.334513 | ||||||||
\(39\) | −3.75730 | −0.601649 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.49965 | 0.546553 | 0.273277 | − | 0.961935i | \(-0.411893\pi\) | ||||
0.273277 | + | 0.961935i | \(0.411893\pi\) | |||||||
\(42\) | −0.818981 | −0.126372 | ||||||||
\(43\) | −1.16800 | −0.178118 | −0.0890589 | − | 0.996026i | \(-0.528386\pi\) | ||||
−0.0890589 | + | 0.996026i | \(0.528386\pi\) | |||||||
\(44\) | −8.66420 | −1.30618 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.481374 | −0.0709748 | ||||||||
\(47\) | 2.36614 | 0.345137 | 0.172568 | − | 0.984998i | \(-0.444793\pi\) | ||||
0.172568 | + | 0.984998i | \(0.444793\pi\) | |||||||
\(48\) | 3.22221 | 0.465086 | ||||||||
\(49\) | −1.94017 | −0.277167 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.36779 | 0.751641 | ||||||||
\(52\) | 7.01653 | 0.973018 | ||||||||
\(53\) | 14.1656 | 1.94580 | 0.972901 | − | 0.231223i | \(-0.0742728\pi\) | ||||
0.972901 | + | 0.231223i | \(0.0742728\pi\) | |||||||
\(54\) | 0.364088 | 0.0495461 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.16736 | 0.423256 | ||||||||
\(57\) | −5.66369 | −0.750174 | ||||||||
\(58\) | 3.22853 | 0.423926 | ||||||||
\(59\) | 0.367089 | 0.0477909 | 0.0238955 | − | 0.999714i | \(-0.492393\pi\) | ||||
0.0238955 | + | 0.999714i | \(0.492393\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.29590 | 0.678070 | 0.339035 | − | 0.940774i | \(-0.389899\pi\) | ||||
0.339035 | + | 0.940774i | \(0.389899\pi\) | |||||||
\(62\) | 0.441273 | 0.0560417 | ||||||||
\(63\) | −2.24941 | −0.283399 | ||||||||
\(64\) | −4.99195 | −0.623994 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.68923 | 0.207930 | ||||||||
\(67\) | −8.06723 | −0.985570 | −0.492785 | − | 0.870151i | \(-0.664021\pi\) | ||||
−0.492785 | + | 0.870151i | \(0.664021\pi\) | |||||||
\(68\) | −10.0240 | −1.21559 | ||||||||
\(69\) | −1.32214 | −0.159167 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4185 | 1.35513 | 0.677563 | − | 0.735465i | \(-0.263036\pi\) | ||||
0.677563 | + | 0.735465i | \(0.263036\pi\) | |||||||
\(72\) | −1.40809 | −0.165945 | ||||||||
\(73\) | 13.7580 | 1.61025 | 0.805126 | − | 0.593104i | \(-0.202098\pi\) | ||||
0.805126 | + | 0.593104i | \(0.202098\pi\) | |||||||
\(74\) | 0.786340 | 0.0914101 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.5766 | 1.21322 | ||||||||
\(77\) | −10.4364 | −1.18934 | ||||||||
\(78\) | −1.36799 | −0.154894 | ||||||||
\(79\) | 11.6247 | 1.30789 | 0.653943 | − | 0.756544i | \(-0.273114\pi\) | ||||
0.653943 | + | 0.756544i | \(0.273114\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.27418 | 0.140710 | ||||||||
\(83\) | −11.1027 | −1.21868 | −0.609338 | − | 0.792910i | \(-0.708565\pi\) | ||||
−0.609338 | + | 0.792910i | \(0.708565\pi\) | |||||||
\(84\) | 4.20063 | 0.458326 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.425253 | −0.0458562 | ||||||||
\(87\) | 8.86744 | 0.950689 | ||||||||
\(88\) | −6.53299 | −0.696419 | ||||||||
\(89\) | 16.6526 | 1.76518 | 0.882588 | − | 0.470148i | \(-0.155799\pi\) | ||||
0.882588 | + | 0.470148i | \(0.155799\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.45169 | 0.885978 | ||||||||
\(92\) | 2.46901 | 0.257412 | ||||||||
\(93\) | 1.21200 | 0.125678 | ||||||||
\(94\) | 0.861482 | 0.0888551 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.98934 | 0.407161 | ||||||||
\(97\) | −14.4790 | −1.47012 | −0.735061 | − | 0.678001i | \(-0.762847\pi\) | ||||
−0.735061 | + | 0.678001i | \(0.762847\pi\) | |||||||
\(98\) | −0.706393 | −0.0713565 | ||||||||
\(99\) | 4.63962 | 0.466299 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.16089 | 0.215017 | 0.107508 | − | 0.994204i | \(-0.465713\pi\) | ||||
0.107508 | + | 0.994204i | \(0.465713\pi\) | |||||||
\(102\) | 1.95435 | 0.193509 | ||||||||
\(103\) | 7.13512 | 0.703044 | 0.351522 | − | 0.936180i | \(-0.385664\pi\) | ||||
0.351522 | + | 0.936180i | \(0.385664\pi\) | |||||||
\(104\) | 5.29061 | 0.518787 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.15754 | 0.500944 | ||||||||
\(107\) | 14.3985 | 1.39196 | 0.695979 | − | 0.718062i | \(-0.254971\pi\) | ||||
0.695979 | + | 0.718062i | \(0.254971\pi\) | |||||||
\(108\) | −1.86744 | −0.179695 | ||||||||
\(109\) | 16.4693 | 1.57748 | 0.788738 | − | 0.614730i | \(-0.210735\pi\) | ||||
0.788738 | + | 0.614730i | \(0.210735\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.15975 | 0.204995 | ||||||||
\(112\) | −7.24806 | −0.684878 | ||||||||
\(113\) | −16.2639 | −1.52998 | −0.764990 | − | 0.644042i | \(-0.777256\pi\) | ||||
−0.764990 | + | 0.644042i | \(0.777256\pi\) | |||||||
\(114\) | −2.06208 | −0.193131 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −16.5594 | −1.53750 | ||||||||
\(117\) | −3.75730 | −0.347362 | ||||||||
\(118\) | 0.133653 | 0.0123037 | ||||||||
\(119\) | −12.0743 | −1.10685 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5260 | 0.956912 | ||||||||
\(122\) | 1.92817 | 0.174568 | ||||||||
\(123\) | 3.49965 | 0.315553 | ||||||||
\(124\) | −2.26333 | −0.203253 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.818981 | −0.0729606 | ||||||||
\(127\) | −5.14048 | −0.456144 | −0.228072 | − | 0.973644i | \(-0.573242\pi\) | ||||
−0.228072 | + | 0.973644i | \(0.573242\pi\) | |||||||
\(128\) | −9.79620 | −0.865870 | ||||||||
\(129\) | −1.16800 | −0.102836 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.52438 | 0.570038 | 0.285019 | − | 0.958522i | \(-0.408000\pi\) | ||||
0.285019 | + | 0.958522i | \(0.408000\pi\) | |||||||
\(132\) | −8.66420 | −0.754122 | ||||||||
\(133\) | 12.7399 | 1.10469 | ||||||||
\(134\) | −2.93718 | −0.253734 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.55832 | −0.648121 | ||||||||
\(137\) | −13.5071 | −1.15399 | −0.576993 | − | 0.816749i | \(-0.695774\pi\) | ||||
−0.576993 | + | 0.816749i | \(0.695774\pi\) | |||||||
\(138\) | −0.481374 | −0.0409773 | ||||||||
\(139\) | −21.1376 | −1.79287 | −0.896435 | − | 0.443176i | \(-0.853852\pi\) | ||||
−0.896435 | + | 0.443176i | \(0.853852\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.36614 | 0.199265 | ||||||||
\(142\) | 4.15733 | 0.348876 | ||||||||
\(143\) | −17.4324 | −1.45777 | ||||||||
\(144\) | 3.22221 | 0.268518 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.00912 | 0.414558 | ||||||||
\(147\) | −1.94017 | −0.160023 | ||||||||
\(148\) | −4.03321 | −0.331528 | ||||||||
\(149\) | −3.22853 | −0.264491 | −0.132246 | − | 0.991217i | \(-0.542219\pi\) | ||||
−0.132246 | + | 0.991217i | \(0.542219\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.9240 | −1.29588 | −0.647939 | − | 0.761692i | \(-0.724369\pi\) | ||||
−0.647939 | + | 0.761692i | \(0.724369\pi\) | |||||||
\(152\) | 7.97497 | 0.646855 | ||||||||
\(153\) | 5.36779 | 0.433960 | ||||||||
\(154\) | −3.79976 | −0.306193 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.01653 | 0.561772 | ||||||||
\(157\) | −3.21251 | −0.256387 | −0.128193 | − | 0.991749i | \(-0.540918\pi\) | ||||
−0.128193 | + | 0.991749i | \(0.540918\pi\) | |||||||
\(158\) | 4.23243 | 0.336714 | ||||||||
\(159\) | 14.1656 | 1.12341 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.97403 | 0.234386 | ||||||||
\(162\) | 0.364088 | 0.0286054 | ||||||||
\(163\) | 13.7482 | 1.07685 | 0.538423 | − | 0.842675i | \(-0.319020\pi\) | ||||
0.538423 | + | 0.842675i | \(0.319020\pi\) | |||||||
\(164\) | −6.53538 | −0.510328 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.04235 | −0.313747 | ||||||||
\(167\) | −0.787486 | −0.0609375 | −0.0304688 | − | 0.999536i | \(-0.509700\pi\) | ||||
−0.0304688 | + | 0.999536i | \(0.509700\pi\) | |||||||
\(168\) | 3.16736 | 0.244367 | ||||||||
\(169\) | 1.11729 | 0.0859456 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.66369 | −0.433113 | ||||||||
\(172\) | 2.18116 | 0.166312 | ||||||||
\(173\) | −2.58986 | −0.196904 | −0.0984518 | − | 0.995142i | \(-0.531389\pi\) | ||||
−0.0984518 | + | 0.995142i | \(0.531389\pi\) | |||||||
\(174\) | 3.22853 | 0.244754 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.9498 | 1.12689 | ||||||||
\(177\) | 0.367089 | 0.0275921 | ||||||||
\(178\) | 6.06302 | 0.454443 | ||||||||
\(179\) | 15.0630 | 1.12586 | 0.562930 | − | 0.826505i | \(-0.309674\pi\) | ||||
0.562930 | + | 0.826505i | \(0.309674\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.5492 | −0.932771 | −0.466386 | − | 0.884582i | \(-0.654444\pi\) | ||||
−0.466386 | + | 0.884582i | \(0.654444\pi\) | |||||||
\(182\) | 3.07716 | 0.228094 | ||||||||
\(183\) | 5.29590 | 0.391484 | ||||||||
\(184\) | 1.86169 | 0.137245 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.441273 | 0.0323557 | ||||||||
\(187\) | 24.9045 | 1.82120 | ||||||||
\(188\) | −4.41862 | −0.322261 | ||||||||
\(189\) | −2.24941 | −0.163620 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.0684 | 1.16267 | 0.581334 | − | 0.813665i | \(-0.302531\pi\) | ||||
0.581334 | + | 0.813665i | \(0.302531\pi\) | |||||||
\(192\) | −4.99195 | −0.360263 | ||||||||
\(193\) | −8.48878 | −0.611036 | −0.305518 | − | 0.952186i | \(-0.598830\pi\) | ||||
−0.305518 | + | 0.952186i | \(0.598830\pi\) | |||||||
\(194\) | −5.27164 | −0.378481 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.62316 | 0.258797 | ||||||||
\(197\) | 4.68061 | 0.333479 | 0.166740 | − | 0.986001i | \(-0.446676\pi\) | ||||
0.166740 | + | 0.986001i | \(0.446676\pi\) | |||||||
\(198\) | 1.68923 | 0.120048 | ||||||||
\(199\) | 1.45880 | 0.103411 | 0.0517057 | − | 0.998662i | \(-0.483534\pi\) | ||||
0.0517057 | + | 0.998662i | \(0.483534\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.06723 | −0.569019 | ||||||||
\(202\) | 0.786753 | 0.0553558 | ||||||||
\(203\) | −19.9465 | −1.39997 | ||||||||
\(204\) | −10.0240 | −0.701822 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.59781 | 0.180998 | ||||||||
\(207\) | −1.32214 | −0.0918950 | ||||||||
\(208\) | −12.1068 | −0.839457 | ||||||||
\(209\) | −26.2773 | −1.81764 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.8107 | 0.881926 | 0.440963 | − | 0.897525i | \(-0.354637\pi\) | ||||
0.440963 | + | 0.897525i | \(0.354637\pi\) | |||||||
\(212\) | −26.4535 | −1.81683 | ||||||||
\(213\) | 11.4185 | 0.782382 | ||||||||
\(214\) | 5.24233 | 0.358358 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.40809 | −0.0958082 | ||||||||
\(217\) | −2.72627 | −0.185071 | ||||||||
\(218\) | 5.99628 | 0.406119 | ||||||||
\(219\) | 13.7580 | 0.929680 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.1684 | −1.35667 | ||||||||
\(222\) | 0.786340 | 0.0527757 | ||||||||
\(223\) | 0.223725 | 0.0149817 | 0.00749086 | − | 0.999972i | \(-0.497616\pi\) | ||||
0.00749086 | + | 0.999972i | \(0.497616\pi\) | |||||||
\(224\) | −8.97365 | −0.599577 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.92149 | −0.393892 | ||||||||
\(227\) | −28.2672 | −1.87616 | −0.938081 | − | 0.346416i | \(-0.887398\pi\) | ||||
−0.938081 | + | 0.346416i | \(0.887398\pi\) | |||||||
\(228\) | 10.5766 | 0.700452 | ||||||||
\(229\) | −16.6618 | −1.10104 | −0.550521 | − | 0.834821i | \(-0.685571\pi\) | ||||
−0.550521 | + | 0.834821i | \(0.685571\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.4364 | −0.686663 | ||||||||
\(232\) | −12.4861 | −0.819755 | ||||||||
\(233\) | −19.9807 | −1.30898 | −0.654491 | − | 0.756070i | \(-0.727117\pi\) | ||||
−0.654491 | + | 0.756070i | \(0.727117\pi\) | |||||||
\(234\) | −1.36799 | −0.0894281 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.685517 | −0.0446233 | ||||||||
\(237\) | 11.6247 | 0.755108 | ||||||||
\(238\) | −4.39612 | −0.284958 | ||||||||
\(239\) | 18.6586 | 1.20692 | 0.603462 | − | 0.797392i | \(-0.293788\pi\) | ||||
0.603462 | + | 0.797392i | \(0.293788\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.10919 | 0.457943 | 0.228972 | − | 0.973433i | \(-0.426464\pi\) | ||||
0.228972 | + | 0.973433i | \(0.426464\pi\) | |||||||
\(242\) | 3.83240 | 0.246356 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −9.88977 | −0.633128 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.27418 | 0.0812387 | ||||||||
\(247\) | 21.2802 | 1.35402 | ||||||||
\(248\) | −1.70660 | −0.108369 | ||||||||
\(249\) | −11.1027 | −0.703603 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.5636 | −0.666767 | −0.333384 | − | 0.942791i | \(-0.608190\pi\) | ||||
−0.333384 | + | 0.942791i | \(0.608190\pi\) | |||||||
\(252\) | 4.20063 | 0.264615 | ||||||||
\(253\) | −6.13421 | −0.385655 | ||||||||
\(254\) | −1.87159 | −0.117434 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.41723 | 0.401077 | ||||||||
\(257\) | 2.94764 | 0.183869 | 0.0919344 | − | 0.995765i | \(-0.470695\pi\) | ||||
0.0919344 | + | 0.995765i | \(0.470695\pi\) | |||||||
\(258\) | −0.425253 | −0.0264751 | ||||||||
\(259\) | −4.85816 | −0.301872 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.86744 | 0.548881 | ||||||||
\(262\) | 2.37545 | 0.146756 | ||||||||
\(263\) | 0.220418 | 0.0135916 | 0.00679578 | − | 0.999977i | \(-0.497837\pi\) | ||||
0.00679578 | + | 0.999977i | \(0.497837\pi\) | |||||||
\(264\) | −6.53299 | −0.402077 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.63845 | 0.284402 | ||||||||
\(267\) | 16.6526 | 1.01912 | ||||||||
\(268\) | 15.0651 | 0.920246 | ||||||||
\(269\) | 10.4148 | 0.634999 | 0.317499 | − | 0.948258i | \(-0.397157\pi\) | ||||
0.317499 | + | 0.948258i | \(0.397157\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.4416 | −1.42397 | −0.711987 | − | 0.702193i | \(-0.752205\pi\) | ||||
−0.711987 | + | 0.702193i | \(0.752205\pi\) | |||||||
\(272\) | 17.2962 | 1.04873 | ||||||||
\(273\) | 8.45169 | 0.511520 | ||||||||
\(274\) | −4.91775 | −0.297092 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.46901 | 0.148617 | ||||||||
\(277\) | 18.4064 | 1.10593 | 0.552966 | − | 0.833204i | \(-0.313496\pi\) | ||||
0.552966 | + | 0.833204i | \(0.313496\pi\) | |||||||
\(278\) | −7.69595 | −0.461572 | ||||||||
\(279\) | 1.21200 | 0.0725603 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.120288 | 0.00717577 | 0.00358789 | − | 0.999994i | \(-0.498858\pi\) | ||||
0.00358789 | + | 0.999994i | \(0.498858\pi\) | |||||||
\(282\) | 0.861482 | 0.0513005 | ||||||||
\(283\) | −0.0913058 | −0.00542756 | −0.00271378 | − | 0.999996i | \(-0.500864\pi\) | ||||
−0.00271378 | + | 0.999996i | \(0.500864\pi\) | |||||||
\(284\) | −21.3234 | −1.26531 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.34693 | −0.375302 | ||||||||
\(287\) | −7.87213 | −0.464677 | ||||||||
\(288\) | 3.98934 | 0.235074 | ||||||||
\(289\) | 11.8132 | 0.694893 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.4790 | −0.848776 | ||||||||
\(292\) | −25.6922 | −1.50352 | ||||||||
\(293\) | 19.6709 | 1.14919 | 0.574593 | − | 0.818439i | \(-0.305160\pi\) | ||||
0.574593 | + | 0.818439i | \(0.305160\pi\) | |||||||
\(294\) | −0.706393 | −0.0411977 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.04112 | −0.176762 | ||||||||
\(297\) | 4.63962 | 0.269218 | ||||||||
\(298\) | −1.17547 | −0.0680930 | ||||||||
\(299\) | 4.96767 | 0.287288 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.62730 | 0.151435 | ||||||||
\(302\) | −5.79774 | −0.333623 | ||||||||
\(303\) | 2.16089 | 0.124140 | ||||||||
\(304\) | −18.2496 | −1.04669 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.95435 | 0.111723 | ||||||||
\(307\) | −9.01250 | −0.514371 | −0.257185 | − | 0.966362i | \(-0.582795\pi\) | ||||
−0.257185 | + | 0.966362i | \(0.582795\pi\) | |||||||
\(308\) | 19.4893 | 1.11051 | ||||||||
\(309\) | 7.13512 | 0.405903 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.0844 | −1.30899 | −0.654497 | − | 0.756065i | \(-0.727119\pi\) | ||||
−0.654497 | + | 0.756065i | \(0.727119\pi\) | |||||||
\(312\) | 5.29061 | 0.299522 | ||||||||
\(313\) | 6.87528 | 0.388614 | 0.194307 | − | 0.980941i | \(-0.437754\pi\) | ||||
0.194307 | + | 0.980941i | \(0.437754\pi\) | |||||||
\(314\) | −1.16964 | −0.0660064 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −21.7085 | −1.22120 | ||||||||
\(317\) | 12.9741 | 0.728696 | 0.364348 | − | 0.931263i | \(-0.381292\pi\) | ||||
0.364348 | + | 0.931263i | \(0.381292\pi\) | |||||||
\(318\) | 5.15754 | 0.289220 | ||||||||
\(319\) | 41.1415 | 2.30348 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.3985 | 0.803647 | ||||||||
\(322\) | 1.08281 | 0.0603424 | ||||||||
\(323\) | −30.4015 | −1.69158 | ||||||||
\(324\) | −1.86744 | −0.103747 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.00557 | 0.277233 | ||||||||
\(327\) | 16.4693 | 0.910756 | ||||||||
\(328\) | −4.92781 | −0.272093 | ||||||||
\(329\) | −5.32241 | −0.293434 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.77297 | −0.317311 | −0.158656 | − | 0.987334i | \(-0.550716\pi\) | ||||
−0.158656 | + | 0.987334i | \(0.550716\pi\) | |||||||
\(332\) | 20.7336 | 1.13790 | ||||||||
\(333\) | 2.15975 | 0.118354 | ||||||||
\(334\) | −0.286714 | −0.0156883 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.24806 | −0.395414 | ||||||||
\(337\) | 13.1047 | 0.713860 | 0.356930 | − | 0.934131i | \(-0.383823\pi\) | ||||
0.356930 | + | 0.934131i | \(0.383823\pi\) | |||||||
\(338\) | 0.406792 | 0.0221266 | ||||||||
\(339\) | −16.2639 | −0.883335 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.62320 | 0.304513 | ||||||||
\(342\) | −2.06208 | −0.111504 | ||||||||
\(343\) | 20.1101 | 1.08584 | ||||||||
\(344\) | 1.64464 | 0.0886731 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.942937 | −0.0506926 | ||||||||
\(347\) | −30.8690 | −1.65713 | −0.828567 | − | 0.559890i | \(-0.810843\pi\) | ||||
−0.828567 | + | 0.559890i | \(0.810843\pi\) | |||||||
\(348\) | −16.5594 | −0.887678 | ||||||||
\(349\) | 28.0753 | 1.50284 | 0.751419 | − | 0.659825i | \(-0.229370\pi\) | ||||
0.751419 | + | 0.659825i | \(0.229370\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.75730 | −0.200550 | ||||||||
\(352\) | 18.5090 | 0.986534 | ||||||||
\(353\) | −13.5595 | −0.721697 | −0.360849 | − | 0.932624i | \(-0.617513\pi\) | ||||
−0.360849 | + | 0.932624i | \(0.617513\pi\) | |||||||
\(354\) | 0.133653 | 0.00710356 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −31.0978 | −1.64818 | ||||||||
\(357\) | −12.0743 | −0.639042 | ||||||||
\(358\) | 5.48425 | 0.289851 | ||||||||
\(359\) | −1.81642 | −0.0958672 | −0.0479336 | − | 0.998851i | \(-0.515264\pi\) | ||||
−0.0479336 | + | 0.998851i | \(0.515264\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0773 | 0.688282 | ||||||||
\(362\) | −4.56899 | −0.240141 | ||||||||
\(363\) | 10.5260 | 0.552473 | ||||||||
\(364\) | −15.7830 | −0.827255 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.92817 | 0.100787 | ||||||||
\(367\) | 31.2892 | 1.63328 | 0.816640 | − | 0.577147i | \(-0.195834\pi\) | ||||
0.816640 | + | 0.577147i | \(0.195834\pi\) | |||||||
\(368\) | −4.26021 | −0.222079 | ||||||||
\(369\) | 3.49965 | 0.182184 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.8643 | −1.65431 | ||||||||
\(372\) | −2.26333 | −0.117348 | ||||||||
\(373\) | −24.2034 | −1.25321 | −0.626603 | − | 0.779338i | \(-0.715555\pi\) | ||||
−0.626603 | + | 0.779338i | \(0.715555\pi\) | |||||||
\(374\) | 9.06742 | 0.468865 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.33173 | −0.171821 | ||||||||
\(377\) | −33.3176 | −1.71594 | ||||||||
\(378\) | −0.818981 | −0.0421239 | ||||||||
\(379\) | 0.676661 | 0.0347577 | 0.0173789 | − | 0.999849i | \(-0.494468\pi\) | ||||
0.0173789 | + | 0.999849i | \(0.494468\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.14048 | −0.263355 | ||||||||
\(382\) | 5.85030 | 0.299327 | ||||||||
\(383\) | 8.32588 | 0.425433 | 0.212716 | − | 0.977114i | \(-0.431769\pi\) | ||||
0.212716 | + | 0.977114i | \(0.431769\pi\) | |||||||
\(384\) | −9.79620 | −0.499910 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.09066 | −0.157311 | ||||||||
\(387\) | −1.16800 | −0.0593726 | ||||||||
\(388\) | 27.0387 | 1.37268 | ||||||||
\(389\) | 34.8213 | 1.76551 | 0.882754 | − | 0.469835i | \(-0.155687\pi\) | ||||
0.882754 | + | 0.469835i | \(0.155687\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.09696 | −0.358909 | ||||||||
\(392\) | 2.73193 | 0.137983 | ||||||||
\(393\) | 6.52438 | 0.329111 | ||||||||
\(394\) | 1.70415 | 0.0858539 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.66420 | −0.435393 | ||||||||
\(397\) | −24.3197 | −1.22057 | −0.610286 | − | 0.792182i | \(-0.708945\pi\) | ||||
−0.610286 | + | 0.792182i | \(0.708945\pi\) | |||||||
\(398\) | 0.531130 | 0.0266232 | ||||||||
\(399\) | 12.7399 | 0.637794 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.0996 | −1.05367 | −0.526833 | − | 0.849969i | \(-0.676621\pi\) | ||||
−0.526833 | + | 0.849969i | \(0.676621\pi\) | |||||||
\(402\) | −2.93718 | −0.146493 | ||||||||
\(403\) | −4.55383 | −0.226843 | ||||||||
\(404\) | −4.03533 | −0.200765 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.26227 | −0.360420 | ||||||||
\(407\) | 10.0204 | 0.496694 | ||||||||
\(408\) | −7.55832 | −0.374193 | ||||||||
\(409\) | 1.03583 | 0.0512184 | 0.0256092 | − | 0.999672i | \(-0.491847\pi\) | ||||
0.0256092 | + | 0.999672i | \(0.491847\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.5071 | −0.666254 | ||||||||
\(412\) | −13.3244 | −0.656447 | ||||||||
\(413\) | −0.825732 | −0.0406316 | ||||||||
\(414\) | −0.481374 | −0.0236583 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −14.9892 | −0.734904 | ||||||||
\(417\) | −21.1376 | −1.03511 | ||||||||
\(418\) | −9.56725 | −0.467950 | ||||||||
\(419\) | 2.57098 | 0.125601 | 0.0628004 | − | 0.998026i | \(-0.479997\pi\) | ||||
0.0628004 | + | 0.998026i | \(0.479997\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.4929 | 0.950025 | 0.475012 | − | 0.879979i | \(-0.342444\pi\) | ||||
0.475012 | + | 0.879979i | \(0.342444\pi\) | |||||||
\(422\) | 4.66423 | 0.227051 | ||||||||
\(423\) | 2.36614 | 0.115046 | ||||||||
\(424\) | −19.9465 | −0.968686 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.15733 | 0.201424 | ||||||||
\(427\) | −11.9126 | −0.576492 | ||||||||
\(428\) | −26.8884 | −1.29970 | ||||||||
\(429\) | −17.4324 | −0.841645 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.8376 | −0.522026 | −0.261013 | − | 0.965335i | \(-0.584057\pi\) | ||||
−0.261013 | + | 0.965335i | \(0.584057\pi\) | |||||||
\(432\) | 3.22221 | 0.155029 | ||||||||
\(433\) | −29.8688 | −1.43540 | −0.717701 | − | 0.696351i | \(-0.754806\pi\) | ||||
−0.717701 | + | 0.696351i | \(0.754806\pi\) | |||||||
\(434\) | −0.992603 | −0.0476464 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −30.7555 | −1.47292 | ||||||||
\(437\) | 7.48818 | 0.358208 | ||||||||
\(438\) | 5.00912 | 0.239345 | ||||||||
\(439\) | 13.0354 | 0.622148 | 0.311074 | − | 0.950386i | \(-0.399311\pi\) | ||||
0.311074 | + | 0.950386i | \(0.399311\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.94017 | −0.0923892 | ||||||||
\(442\) | −7.34307 | −0.349274 | ||||||||
\(443\) | −18.1333 | −0.861539 | −0.430770 | − | 0.902462i | \(-0.641758\pi\) | ||||
−0.430770 | + | 0.902462i | \(0.641758\pi\) | |||||||
\(444\) | −4.03321 | −0.191408 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.0814555 | 0.00385703 | ||||||||
\(447\) | −3.22853 | −0.152704 | ||||||||
\(448\) | 11.2289 | 0.530517 | ||||||||
\(449\) | 13.7087 | 0.646954 | 0.323477 | − | 0.946236i | \(-0.395148\pi\) | ||||
0.323477 | + | 0.946236i | \(0.395148\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.2370 | 0.764572 | ||||||||
\(452\) | 30.3719 | 1.42857 | ||||||||
\(453\) | −15.9240 | −0.748176 | ||||||||
\(454\) | −10.2918 | −0.483016 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.97497 | 0.373462 | ||||||||
\(457\) | 17.8434 | 0.834680 | 0.417340 | − | 0.908750i | \(-0.362962\pi\) | ||||
0.417340 | + | 0.908750i | \(0.362962\pi\) | |||||||
\(458\) | −6.06635 | −0.283462 | ||||||||
\(459\) | 5.36779 | 0.250547 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.25912 | 0.0586430 | 0.0293215 | − | 0.999570i | \(-0.490665\pi\) | ||||
0.0293215 | + | 0.999570i | \(0.490665\pi\) | |||||||
\(462\) | −3.79976 | −0.176781 | ||||||||
\(463\) | 22.6971 | 1.05482 | 0.527412 | − | 0.849610i | \(-0.323162\pi\) | ||||
0.527412 | + | 0.849610i | \(0.323162\pi\) | |||||||
\(464\) | 28.5728 | 1.32646 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.27474 | −0.336996 | ||||||||
\(467\) | −10.1460 | −0.469501 | −0.234751 | − | 0.972056i | \(-0.575427\pi\) | ||||
−0.234751 | + | 0.972056i | \(0.575427\pi\) | |||||||
\(468\) | 7.01653 | 0.324339 | ||||||||
\(469\) | 18.1465 | 0.837927 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.21251 | −0.148025 | ||||||||
\(472\) | −0.516894 | −0.0237920 | ||||||||
\(473\) | −5.41906 | −0.249168 | ||||||||
\(474\) | 4.23243 | 0.194402 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 22.5481 | 1.03349 | ||||||||
\(477\) | 14.1656 | 0.648600 | ||||||||
\(478\) | 6.79337 | 0.310721 | ||||||||
\(479\) | −8.86088 | −0.404864 | −0.202432 | − | 0.979296i | \(-0.564884\pi\) | ||||
−0.202432 | + | 0.979296i | \(0.564884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.11484 | −0.370005 | ||||||||
\(482\) | 2.58837 | 0.117897 | ||||||||
\(483\) | 2.97403 | 0.135323 | ||||||||
\(484\) | −19.6567 | −0.893488 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.364088 | 0.0165154 | ||||||||
\(487\) | −8.37280 | −0.379408 | −0.189704 | − | 0.981841i | \(-0.560753\pi\) | ||||
−0.189704 | + | 0.981841i | \(0.560753\pi\) | |||||||
\(488\) | −7.45709 | −0.337566 | ||||||||
\(489\) | 13.7482 | 0.621717 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.44669 | 0.155547 | 0.0777734 | − | 0.996971i | \(-0.475219\pi\) | ||||
0.0777734 | + | 0.996971i | \(0.475219\pi\) | |||||||
\(492\) | −6.53538 | −0.294638 | ||||||||
\(493\) | 47.5986 | 2.14373 | ||||||||
\(494\) | 7.74785 | 0.348592 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.90531 | 0.175354 | ||||||||
\(497\) | −25.6848 | −1.15212 | ||||||||
\(498\) | −4.04235 | −0.181142 | ||||||||
\(499\) | −0.476153 | −0.0213155 | −0.0106578 | − | 0.999943i | \(-0.503393\pi\) | ||||
−0.0106578 | + | 0.999943i | \(0.503393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.787486 | −0.0351823 | ||||||||
\(502\) | −3.84607 | −0.171658 | ||||||||
\(503\) | −9.90779 | −0.441766 | −0.220883 | − | 0.975300i | \(-0.570894\pi\) | ||||
−0.220883 | + | 0.975300i | \(0.570894\pi\) | |||||||
\(504\) | 3.16736 | 0.141085 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.23339 | −0.0992864 | ||||||||
\(507\) | 1.11729 | 0.0496207 | ||||||||
\(508\) | 9.59955 | 0.425911 | ||||||||
\(509\) | −11.8211 | −0.523963 | −0.261981 | − | 0.965073i | \(-0.584376\pi\) | ||||
−0.261981 | + | 0.965073i | \(0.584376\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.9473 | −1.36903 | ||||||||
\(512\) | 21.9288 | 0.969126 | ||||||||
\(513\) | −5.66369 | −0.250058 | ||||||||
\(514\) | 1.07320 | 0.0473368 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.18116 | 0.0960204 | ||||||||
\(517\) | 10.9780 | 0.482811 | ||||||||
\(518\) | −1.76880 | −0.0777165 | ||||||||
\(519\) | −2.58986 | −0.113682 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.0561 | 1.09773 | 0.548863 | − | 0.835912i | \(-0.315061\pi\) | ||||
0.548863 | + | 0.835912i | \(0.315061\pi\) | |||||||
\(522\) | 3.22853 | 0.141309 | ||||||||
\(523\) | 19.5306 | 0.854012 | 0.427006 | − | 0.904249i | \(-0.359568\pi\) | ||||
0.427006 | + | 0.904249i | \(0.359568\pi\) | |||||||
\(524\) | −12.1839 | −0.532256 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.0802515 | 0.00349913 | ||||||||
\(527\) | 6.50574 | 0.283395 | ||||||||
\(528\) | 14.9498 | 0.650608 | ||||||||
\(529\) | −21.2520 | −0.923998 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.367089 | 0.0159303 | ||||||||
\(532\) | −23.7911 | −1.03147 | ||||||||
\(533\) | −13.1492 | −0.569556 | ||||||||
\(534\) | 6.06302 | 0.262373 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.3594 | 0.490650 | ||||||||
\(537\) | 15.0630 | 0.650015 | ||||||||
\(538\) | 3.79188 | 0.163480 | ||||||||
\(539\) | −9.00165 | −0.387729 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.96076 | −0.385253 | −0.192627 | − | 0.981272i | \(-0.561701\pi\) | ||||
−0.192627 | + | 0.981272i | \(0.561701\pi\) | |||||||
\(542\) | −8.53479 | −0.366601 | ||||||||
\(543\) | −12.5492 | −0.538536 | ||||||||
\(544\) | 21.4140 | 0.918116 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.07716 | 0.131690 | ||||||||
\(547\) | 6.82992 | 0.292026 | 0.146013 | − | 0.989283i | \(-0.453356\pi\) | ||||
0.146013 | + | 0.989283i | \(0.453356\pi\) | |||||||
\(548\) | 25.2236 | 1.07750 | ||||||||
\(549\) | 5.29590 | 0.226023 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −50.2224 | −2.13955 | ||||||||
\(552\) | 1.86169 | 0.0792386 | ||||||||
\(553\) | −26.1488 | −1.11196 | ||||||||
\(554\) | 6.70153 | 0.284721 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 39.4732 | 1.67404 | ||||||||
\(557\) | −5.53535 | −0.234540 | −0.117270 | − | 0.993100i | \(-0.537414\pi\) | ||||
−0.117270 | + | 0.993100i | \(0.537414\pi\) | |||||||
\(558\) | 0.441273 | 0.0186806 | ||||||||
\(559\) | 4.38851 | 0.185614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.9045 | 1.05147 | ||||||||
\(562\) | 0.0437954 | 0.00184740 | ||||||||
\(563\) | 39.1974 | 1.65198 | 0.825988 | − | 0.563688i | \(-0.190618\pi\) | ||||
0.825988 | + | 0.563688i | \(0.190618\pi\) | |||||||
\(564\) | −4.41862 | −0.186058 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.0332433 | −0.00139732 | ||||||||
\(567\) | −2.24941 | −0.0944662 | ||||||||
\(568\) | −16.0782 | −0.674628 | ||||||||
\(569\) | 19.8092 | 0.830444 | 0.415222 | − | 0.909720i | \(-0.363704\pi\) | ||||
0.415222 | + | 0.909720i | \(0.363704\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.9768 | −0.961548 | −0.480774 | − | 0.876845i | \(-0.659644\pi\) | ||||
−0.480774 | + | 0.876845i | \(0.659644\pi\) | |||||||
\(572\) | 32.5540 | 1.36115 | ||||||||
\(573\) | 16.0684 | 0.671266 | ||||||||
\(574\) | −2.86615 | −0.119631 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.99195 | −0.207998 | ||||||||
\(577\) | −12.1833 | −0.507198 | −0.253599 | − | 0.967309i | \(-0.581614\pi\) | ||||
−0.253599 | + | 0.967309i | \(0.581614\pi\) | |||||||
\(578\) | 4.30103 | 0.178899 | ||||||||
\(579\) | −8.48878 | −0.352782 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.9744 | 1.03611 | ||||||||
\(582\) | −5.27164 | −0.218516 | ||||||||
\(583\) | 65.7232 | 2.72198 | ||||||||
\(584\) | −19.3725 | −0.801639 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.16194 | 0.295857 | ||||||||
\(587\) | −12.0991 | −0.499384 | −0.249692 | − | 0.968325i | \(-0.580329\pi\) | ||||
−0.249692 | + | 0.968325i | \(0.580329\pi\) | |||||||
\(588\) | 3.62316 | 0.149416 | ||||||||
\(589\) | −6.86437 | −0.282841 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.68061 | 0.192534 | ||||||||
\(592\) | 6.95918 | 0.286021 | ||||||||
\(593\) | 26.8465 | 1.10245 | 0.551227 | − | 0.834355i | \(-0.314160\pi\) | ||||
0.551227 | + | 0.834355i | \(0.314160\pi\) | |||||||
\(594\) | 1.68923 | 0.0693098 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.02908 | 0.246961 | ||||||||
\(597\) | 1.45880 | 0.0597046 | ||||||||
\(598\) | 1.80867 | 0.0739619 | ||||||||
\(599\) | 5.16011 | 0.210836 | 0.105418 | − | 0.994428i | \(-0.466382\pi\) | ||||
0.105418 | + | 0.994428i | \(0.466382\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.5481 | −0.838173 | −0.419086 | − | 0.907946i | \(-0.637650\pi\) | ||||
−0.419086 | + | 0.907946i | \(0.637650\pi\) | |||||||
\(602\) | 0.956567 | 0.0389868 | ||||||||
\(603\) | −8.06723 | −0.328523 | ||||||||
\(604\) | 29.7372 | 1.20999 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.786753 | 0.0319597 | ||||||||
\(607\) | −7.83380 | −0.317964 | −0.158982 | − | 0.987281i | \(-0.550821\pi\) | ||||
−0.158982 | + | 0.987281i | \(0.550821\pi\) | |||||||
\(608\) | −22.5944 | −0.916324 | ||||||||
\(609\) | −19.9465 | −0.808272 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.89029 | −0.359663 | ||||||||
\(612\) | −10.0240 | −0.405197 | ||||||||
\(613\) | −21.4304 | −0.865564 | −0.432782 | − | 0.901499i | \(-0.642468\pi\) | ||||
−0.432782 | + | 0.901499i | \(0.642468\pi\) | |||||||
\(614\) | −3.28134 | −0.132424 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.6953 | 0.592092 | ||||||||
\(617\) | 7.08270 | 0.285139 | 0.142569 | − | 0.989785i | \(-0.454464\pi\) | ||||
0.142569 | + | 0.989785i | \(0.454464\pi\) | |||||||
\(618\) | 2.59781 | 0.104499 | ||||||||
\(619\) | −38.5317 | −1.54872 | −0.774360 | − | 0.632745i | \(-0.781928\pi\) | ||||
−0.774360 | + | 0.632745i | \(0.781928\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.32214 | −0.0530556 | ||||||||
\(622\) | −8.40473 | −0.336999 | ||||||||
\(623\) | −37.4585 | −1.50074 | ||||||||
\(624\) | −12.1068 | −0.484660 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.50321 | 0.100048 | ||||||||
\(627\) | −26.2773 | −1.04942 | ||||||||
\(628\) | 5.99918 | 0.239393 | ||||||||
\(629\) | 11.5931 | 0.462247 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.1731 | −1.40022 | −0.700110 | − | 0.714035i | \(-0.746866\pi\) | ||||
−0.700110 | + | 0.714035i | \(0.746866\pi\) | |||||||
\(632\) | −16.3687 | −0.651110 | ||||||||
\(633\) | 12.8107 | 0.509180 | ||||||||
\(634\) | 4.72370 | 0.187602 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −26.4535 | −1.04895 | ||||||||
\(637\) | 7.28981 | 0.288833 | ||||||||
\(638\) | 14.9791 | 0.593029 | ||||||||
\(639\) | 11.4185 | 0.451709 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.9089 | −0.509872 | −0.254936 | − | 0.966958i | \(-0.582054\pi\) | ||||
−0.254936 | + | 0.966958i | \(0.582054\pi\) | |||||||
\(642\) | 5.24233 | 0.206898 | ||||||||
\(643\) | −42.0703 | −1.65909 | −0.829546 | − | 0.558438i | \(-0.811401\pi\) | ||||
−0.829546 | + | 0.558438i | \(0.811401\pi\) | |||||||
\(644\) | −5.55381 | −0.218851 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.0688 | −0.435497 | ||||||||
\(647\) | −2.45766 | −0.0966207 | −0.0483103 | − | 0.998832i | \(-0.515384\pi\) | ||||
−0.0483103 | + | 0.998832i | \(0.515384\pi\) | |||||||
\(648\) | −1.40809 | −0.0553149 | ||||||||
\(649\) | 1.70315 | 0.0668546 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.72627 | −0.106851 | ||||||||
\(652\) | −25.6740 | −1.00547 | ||||||||
\(653\) | 42.7727 | 1.67382 | 0.836912 | − | 0.547337i | \(-0.184359\pi\) | ||||
0.836912 | + | 0.547337i | \(0.184359\pi\) | |||||||
\(654\) | 5.99628 | 0.234473 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.2766 | 0.440278 | ||||||||
\(657\) | 13.7580 | 0.536751 | ||||||||
\(658\) | −1.93782 | −0.0755442 | ||||||||
\(659\) | 3.41659 | 0.133092 | 0.0665458 | − | 0.997783i | \(-0.478802\pi\) | ||||
0.0665458 | + | 0.997783i | \(0.478802\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.6380 | 1.65843 | 0.829213 | − | 0.558933i | \(-0.188789\pi\) | ||||
0.829213 | + | 0.558933i | \(0.188789\pi\) | |||||||
\(662\) | −2.10187 | −0.0816914 | ||||||||
\(663\) | −20.1684 | −0.783276 | ||||||||
\(664\) | 15.6335 | 0.606699 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.786340 | 0.0304700 | ||||||||
\(667\) | −11.7240 | −0.453954 | ||||||||
\(668\) | 1.47058 | 0.0568986 | ||||||||
\(669\) | 0.223725 | 0.00864970 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.5709 | 0.948550 | ||||||||
\(672\) | −8.97365 | −0.346166 | ||||||||
\(673\) | 7.02233 | 0.270691 | 0.135345 | − | 0.990798i | \(-0.456786\pi\) | ||||
0.135345 | + | 0.990798i | \(0.456786\pi\) | |||||||
\(674\) | 4.77127 | 0.183782 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.08648 | −0.0802491 | ||||||||
\(677\) | −4.96936 | −0.190988 | −0.0954941 | − | 0.995430i | \(-0.530443\pi\) | ||||
−0.0954941 | + | 0.995430i | \(0.530443\pi\) | |||||||
\(678\) | −5.92149 | −0.227414 | ||||||||
\(679\) | 32.5692 | 1.24989 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.2672 | −1.08320 | ||||||||
\(682\) | 2.04734 | 0.0783966 | ||||||||
\(683\) | 2.27348 | 0.0869922 | 0.0434961 | − | 0.999054i | \(-0.486150\pi\) | ||||
0.0434961 | + | 0.999054i | \(0.486150\pi\) | |||||||
\(684\) | 10.5766 | 0.404406 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.32183 | 0.279549 | ||||||||
\(687\) | −16.6618 | −0.635687 | ||||||||
\(688\) | −3.76353 | −0.143483 | ||||||||
\(689\) | −53.2246 | −2.02769 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.7141 | −0.635836 | −0.317918 | − | 0.948118i | \(-0.602984\pi\) | ||||
−0.317918 | + | 0.948118i | \(0.602984\pi\) | |||||||
\(692\) | 4.83641 | 0.183853 | ||||||||
\(693\) | −10.4364 | −0.396445 | ||||||||
\(694\) | −11.2390 | −0.426627 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.4861 | −0.473286 | ||||||||
\(697\) | 18.7854 | 0.711547 | ||||||||
\(698\) | 10.2219 | 0.386904 | ||||||||
\(699\) | −19.9807 | −0.755741 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.4650 | 0.395256 | 0.197628 | − | 0.980277i | \(-0.436676\pi\) | ||||
0.197628 | + | 0.980277i | \(0.436676\pi\) | |||||||
\(702\) | −1.36799 | −0.0516313 | ||||||||
\(703\) | −12.2322 | −0.461345 | ||||||||
\(704\) | −23.1607 | −0.872904 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.93683 | −0.185800 | ||||||||
\(707\) | −4.86072 | −0.182806 | ||||||||
\(708\) | −0.685517 | −0.0257633 | ||||||||
\(709\) | 10.4906 | 0.393984 | 0.196992 | − | 0.980405i | \(-0.436883\pi\) | ||||
0.196992 | + | 0.980405i | \(0.436883\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.6247 | 0.435962 | ||||||||
\(712\) | −23.4484 | −0.878765 | ||||||||
\(713\) | −1.60243 | −0.0600114 | ||||||||
\(714\) | −4.39612 | −0.164521 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −28.1292 | −1.05124 | ||||||||
\(717\) | 18.6586 | 0.696818 | ||||||||
\(718\) | −0.661338 | −0.0246809 | ||||||||
\(719\) | −51.8986 | −1.93549 | −0.967746 | − | 0.251929i | \(-0.918935\pi\) | ||||
−0.967746 | + | 0.251929i | \(0.918935\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0498 | −0.597725 | ||||||||
\(722\) | 4.76130 | 0.177197 | ||||||||
\(723\) | 7.10919 | 0.264394 | ||||||||
\(724\) | 23.4348 | 0.870947 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.83240 | 0.142234 | ||||||||
\(727\) | 36.1382 | 1.34029 | 0.670145 | − | 0.742230i | \(-0.266232\pi\) | ||||
0.670145 | + | 0.742230i | \(0.266232\pi\) | |||||||
\(728\) | −11.9007 | −0.441070 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.26956 | −0.231888 | ||||||||
\(732\) | −9.88977 | −0.365536 | ||||||||
\(733\) | −49.1978 | −1.81716 | −0.908581 | − | 0.417709i | \(-0.862833\pi\) | ||||
−0.908581 | + | 0.417709i | \(0.862833\pi\) | |||||||
\(734\) | 11.3920 | 0.420486 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.27446 | −0.194419 | ||||||||
\(737\) | −37.4289 | −1.37871 | ||||||||
\(738\) | 1.27418 | 0.0469032 | ||||||||
\(739\) | −0.931024 | −0.0342483 | −0.0171241 | − | 0.999853i | \(-0.505451\pi\) | ||||
−0.0171241 | + | 0.999853i | \(0.505451\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.2802 | 0.781746 | ||||||||
\(742\) | −11.6014 | −0.425901 | ||||||||
\(743\) | −7.46765 | −0.273962 | −0.136981 | − | 0.990574i | \(-0.543740\pi\) | ||||
−0.136981 | + | 0.990574i | \(0.543740\pi\) | |||||||
\(744\) | −1.70660 | −0.0625669 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.81218 | −0.322637 | ||||||||
\(747\) | −11.1027 | −0.406225 | ||||||||
\(748\) | −46.5076 | −1.70049 | ||||||||
\(749\) | −32.3881 | −1.18344 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.8157 | −0.431160 | −0.215580 | − | 0.976486i | \(-0.569164\pi\) | ||||
−0.215580 | + | 0.976486i | \(0.569164\pi\) | |||||||
\(752\) | 7.62420 | 0.278026 | ||||||||
\(753\) | −10.5636 | −0.384958 | ||||||||
\(754\) | −12.1305 | −0.441768 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.20063 | 0.152775 | ||||||||
\(757\) | −36.5733 | −1.32928 | −0.664640 | − | 0.747163i | \(-0.731415\pi\) | ||||
−0.664640 | + | 0.747163i | \(0.731415\pi\) | |||||||
\(758\) | 0.246364 | 0.00894834 | ||||||||
\(759\) | −6.13421 | −0.222658 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.9848 | 0.470700 | 0.235350 | − | 0.971911i | \(-0.424376\pi\) | ||||
0.235350 | + | 0.971911i | \(0.424376\pi\) | |||||||
\(762\) | −1.87159 | −0.0678005 | ||||||||
\(763\) | −37.0462 | −1.34116 | ||||||||
\(764\) | −30.0067 | −1.08561 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.03135 | 0.109527 | ||||||||
\(767\) | −1.37926 | −0.0498023 | ||||||||
\(768\) | 6.41723 | 0.231562 | ||||||||
\(769\) | 0.337323 | 0.0121642 | 0.00608208 | − | 0.999982i | \(-0.498064\pi\) | ||||
0.00608208 | + | 0.999982i | \(0.498064\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.94764 | 0.106157 | ||||||||
\(772\) | 15.8523 | 0.570536 | ||||||||
\(773\) | 32.7655 | 1.17849 | 0.589246 | − | 0.807953i | \(-0.299425\pi\) | ||||
0.589246 | + | 0.807953i | \(0.299425\pi\) | |||||||
\(774\) | −0.425253 | −0.0152854 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 20.3877 | 0.731877 | ||||||||
\(777\) | −4.85816 | −0.174286 | ||||||||
\(778\) | 12.6780 | 0.454528 | ||||||||
\(779\) | −19.8209 | −0.710158 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.9774 | 1.89568 | ||||||||
\(782\) | −2.58392 | −0.0924007 | ||||||||
\(783\) | 8.86744 | 0.316896 | ||||||||
\(784\) | −6.25165 | −0.223273 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.37545 | 0.0847294 | ||||||||
\(787\) | 24.6230 | 0.877715 | 0.438857 | − | 0.898557i | \(-0.355383\pi\) | ||||
0.438857 | + | 0.898557i | \(0.355383\pi\) | |||||||
\(788\) | −8.74075 | −0.311376 | ||||||||
\(789\) | 0.220418 | 0.00784709 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.5842 | 1.30078 | ||||||||
\(792\) | −6.53299 | −0.232140 | ||||||||
\(793\) | −19.8983 | −0.706608 | ||||||||
\(794\) | −8.85451 | −0.314235 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.72422 | −0.0965573 | ||||||||
\(797\) | 28.1988 | 0.998852 | 0.499426 | − | 0.866357i | \(-0.333544\pi\) | ||||
0.499426 | + | 0.866357i | \(0.333544\pi\) | |||||||
\(798\) | 4.63845 | 0.164199 | ||||||||
\(799\) | 12.7009 | 0.449327 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.6526 | 0.588392 | ||||||||
\(802\) | −7.68212 | −0.271265 | ||||||||
\(803\) | 63.8318 | 2.25258 | ||||||||
\(804\) | 15.0651 | 0.531304 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.65799 | −0.0584004 | ||||||||
\(807\) | 10.4148 | 0.366617 | ||||||||
\(808\) | −3.04272 | −0.107043 | ||||||||
\(809\) | 46.0975 | 1.62070 | 0.810352 | − | 0.585944i | \(-0.199276\pi\) | ||||
0.810352 | + | 0.585944i | \(0.199276\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.6551 | 0.690183 | 0.345092 | − | 0.938569i | \(-0.387848\pi\) | ||||
0.345092 | + | 0.938569i | \(0.387848\pi\) | |||||||
\(812\) | 37.2488 | 1.30718 | ||||||||
\(813\) | −23.4416 | −0.822132 | ||||||||
\(814\) | 3.64831 | 0.127873 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 17.2962 | 0.605487 | ||||||||
\(817\) | 6.61517 | 0.231435 | ||||||||
\(818\) | 0.377132 | 0.0131861 | ||||||||
\(819\) | 8.45169 | 0.295326 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.8469 | 1.00676 | 0.503382 | − | 0.864064i | \(-0.332089\pi\) | ||||
0.503382 | + | 0.864064i | \(0.332089\pi\) | |||||||
\(822\) | −4.91775 | −0.171526 | ||||||||
\(823\) | 4.32008 | 0.150589 | 0.0752943 | − | 0.997161i | \(-0.476010\pi\) | ||||
0.0752943 | + | 0.997161i | \(0.476010\pi\) | |||||||
\(824\) | −10.0469 | −0.349999 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.300639 | −0.0104606 | ||||||||
\(827\) | 54.9133 | 1.90952 | 0.954762 | − | 0.297371i | \(-0.0961098\pi\) | ||||
0.954762 | + | 0.297371i | \(0.0961098\pi\) | |||||||
\(828\) | 2.46901 | 0.0858042 | ||||||||
\(829\) | −15.8046 | −0.548916 | −0.274458 | − | 0.961599i | \(-0.588498\pi\) | ||||
−0.274458 | + | 0.961599i | \(0.588498\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.4064 | 0.638510 | ||||||||
\(832\) | 18.7563 | 0.650256 | ||||||||
\(833\) | −10.4144 | −0.360839 | ||||||||
\(834\) | −7.69595 | −0.266489 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 49.0713 | 1.69717 | ||||||||
\(837\) | 1.21200 | 0.0418927 | ||||||||
\(838\) | 0.936064 | 0.0323358 | ||||||||
\(839\) | −20.7086 | −0.714939 | −0.357469 | − | 0.933925i | \(-0.616360\pi\) | ||||
−0.357469 | + | 0.933925i | \(0.616360\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49.6315 | 1.71143 | ||||||||
\(842\) | 7.09712 | 0.244583 | ||||||||
\(843\) | 0.120288 | 0.00414294 | ||||||||
\(844\) | −23.9233 | −0.823472 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.861482 | 0.0296184 | ||||||||
\(847\) | −23.6773 | −0.813562 | ||||||||
\(848\) | 45.6447 | 1.56745 | ||||||||
\(849\) | −0.0913058 | −0.00313361 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.85549 | −0.0978850 | ||||||||
\(852\) | −21.3234 | −0.730526 | ||||||||
\(853\) | −8.27523 | −0.283338 | −0.141669 | − | 0.989914i | \(-0.545247\pi\) | ||||
−0.141669 | + | 0.989914i | \(0.545247\pi\) | |||||||
\(854\) | −4.33724 | −0.148417 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.2744 | −0.692964 | ||||||||
\(857\) | 6.29920 | 0.215177 | 0.107588 | − | 0.994196i | \(-0.465687\pi\) | ||||
0.107588 | + | 0.994196i | \(0.465687\pi\) | |||||||
\(858\) | −6.34693 | −0.216681 | ||||||||
\(859\) | 26.4130 | 0.901200 | 0.450600 | − | 0.892726i | \(-0.351210\pi\) | ||||
0.450600 | + | 0.892726i | \(0.351210\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.87213 | −0.268282 | ||||||||
\(862\) | −3.94582 | −0.134395 | ||||||||
\(863\) | −34.5355 | −1.17560 | −0.587802 | − | 0.809005i | \(-0.700007\pi\) | ||||
−0.587802 | + | 0.809005i | \(0.700007\pi\) | |||||||
\(864\) | 3.98934 | 0.135720 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −10.8749 | −0.369543 | ||||||||
\(867\) | 11.8132 | 0.401197 | ||||||||
\(868\) | 5.09115 | 0.172805 | ||||||||
\(869\) | 53.9343 | 1.82960 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.3110 | 1.02705 | ||||||||
\(872\) | −23.1903 | −0.785321 | ||||||||
\(873\) | −14.4790 | −0.490041 | ||||||||
\(874\) | 2.72635 | 0.0922203 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −25.6922 | −0.868060 | ||||||||
\(877\) | −44.1083 | −1.48943 | −0.744716 | − | 0.667382i | \(-0.767415\pi\) | ||||
−0.744716 | + | 0.667382i | \(0.767415\pi\) | |||||||
\(878\) | 4.74605 | 0.160171 | ||||||||
\(879\) | 19.6709 | 0.663483 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.5724 | 1.16477 | 0.582386 | − | 0.812912i | \(-0.302119\pi\) | ||||
0.582386 | + | 0.812912i | \(0.302119\pi\) | |||||||
\(882\) | −0.706393 | −0.0237855 | ||||||||
\(883\) | −3.56120 | −0.119844 | −0.0599220 | − | 0.998203i | \(-0.519085\pi\) | ||||
−0.0599220 | + | 0.998203i | \(0.519085\pi\) | |||||||
\(884\) | 37.6633 | 1.26675 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.60212 | −0.221802 | ||||||||
\(887\) | 53.6149 | 1.80021 | 0.900106 | − | 0.435671i | \(-0.143489\pi\) | ||||
0.900106 | + | 0.435671i | \(0.143489\pi\) | |||||||
\(888\) | −3.04112 | −0.102053 | ||||||||
\(889\) | 11.5630 | 0.387812 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.63962 | 0.155433 | ||||||||
\(892\) | −0.417793 | −0.0139887 | ||||||||
\(893\) | −13.4011 | −0.448450 | ||||||||
\(894\) | −1.17547 | −0.0393135 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 22.0356 | 0.736159 | ||||||||
\(897\) | 4.96767 | 0.165866 | ||||||||
\(898\) | 4.99117 | 0.166558 | ||||||||
\(899\) | 10.7473 | 0.358443 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 76.0382 | 2.53320 | ||||||||
\(902\) | 5.91170 | 0.196838 | ||||||||
\(903\) | 2.62730 | 0.0874310 | ||||||||
\(904\) | 22.9010 | 0.761677 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.79774 | −0.192617 | ||||||||
\(907\) | 41.7962 | 1.38782 | 0.693909 | − | 0.720062i | \(-0.255887\pi\) | ||||
0.693909 | + | 0.720062i | \(0.255887\pi\) | |||||||
\(908\) | 52.7874 | 1.75181 | ||||||||
\(909\) | 2.16089 | 0.0716722 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.8484 | −1.51903 | −0.759513 | − | 0.650492i | \(-0.774563\pi\) | ||||
−0.759513 | + | 0.650492i | \(0.774563\pi\) | |||||||
\(912\) | −18.2496 | −0.604305 | ||||||||
\(913\) | −51.5121 | −1.70480 | ||||||||
\(914\) | 6.49657 | 0.214887 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 31.1149 | 1.02806 | ||||||||
\(917\) | −14.6760 | −0.484644 | ||||||||
\(918\) | 1.95435 | 0.0645031 | ||||||||
\(919\) | −28.3017 | −0.933588 | −0.466794 | − | 0.884366i | \(-0.654591\pi\) | ||||
−0.466794 | + | 0.884366i | \(0.654591\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.01250 | −0.296972 | ||||||||
\(922\) | 0.458429 | 0.0150976 | ||||||||
\(923\) | −42.9027 | −1.41216 | ||||||||
\(924\) | 19.4893 | 0.641151 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 8.26374 | 0.271563 | ||||||||
\(927\) | 7.13512 | 0.234348 | ||||||||
\(928\) | 35.3753 | 1.16125 | ||||||||
\(929\) | 14.0835 | 0.462064 | 0.231032 | − | 0.972946i | \(-0.425790\pi\) | ||||
0.231032 | + | 0.972946i | \(0.425790\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.9885 | 0.360134 | ||||||||
\(932\) | 37.3128 | 1.22222 | ||||||||
\(933\) | −23.0844 | −0.755748 | ||||||||
\(934\) | −3.69404 | −0.120873 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.29061 | 0.172929 | ||||||||
\(937\) | −17.7320 | −0.579280 | −0.289640 | − | 0.957136i | \(-0.593536\pi\) | ||||
−0.289640 | + | 0.957136i | \(0.593536\pi\) | |||||||
\(938\) | 6.60691 | 0.215723 | ||||||||
\(939\) | 6.87528 | 0.224366 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.8982 | −0.453068 | −0.226534 | − | 0.974003i | \(-0.572739\pi\) | ||||
−0.226534 | + | 0.974003i | \(0.572739\pi\) | |||||||
\(942\) | −1.16964 | −0.0381088 | ||||||||
\(943\) | −4.62702 | −0.150676 | ||||||||
\(944\) | 1.18284 | 0.0384981 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.97301 | −0.0641482 | ||||||||
\(947\) | 28.7291 | 0.933571 | 0.466786 | − | 0.884371i | \(-0.345412\pi\) | ||||
0.466786 | + | 0.884371i | \(0.345412\pi\) | |||||||
\(948\) | −21.7085 | −0.705059 | ||||||||
\(949\) | −51.6929 | −1.67802 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.9741 | 0.420713 | ||||||||
\(952\) | 17.0017 | 0.551029 | ||||||||
\(953\) | 40.5303 | 1.31291 | 0.656453 | − | 0.754367i | \(-0.272056\pi\) | ||||
0.656453 | + | 0.754367i | \(0.272056\pi\) | |||||||
\(954\) | 5.15754 | 0.166981 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −34.8438 | −1.12693 | ||||||||
\(957\) | 41.1415 | 1.32992 | ||||||||
\(958\) | −3.22614 | −0.104232 | ||||||||
\(959\) | 30.3829 | 0.981114 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5311 | −0.952615 | ||||||||
\(962\) | −2.95451 | −0.0952573 | ||||||||
\(963\) | 14.3985 | 0.463986 | ||||||||
\(964\) | −13.2760 | −0.427591 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.08281 | 0.0348387 | ||||||||
\(967\) | 21.1771 | 0.681010 | 0.340505 | − | 0.940243i | \(-0.389402\pi\) | ||||
0.340505 | + | 0.940243i | \(0.389402\pi\) | |||||||
\(968\) | −14.8216 | −0.476383 | ||||||||
\(969\) | −30.4015 | −0.976636 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.7880 | −1.34104 | −0.670520 | − | 0.741891i | \(-0.733929\pi\) | ||||
−0.670520 | + | 0.741891i | \(0.733929\pi\) | |||||||
\(972\) | −1.86744 | −0.0598982 | ||||||||
\(973\) | 47.5471 | 1.52429 | ||||||||
\(974\) | −3.04843 | −0.0976781 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17.0645 | 0.546221 | ||||||||
\(977\) | 20.1059 | 0.643245 | 0.321623 | − | 0.946868i | \(-0.395772\pi\) | ||||
0.321623 | + | 0.946868i | \(0.395772\pi\) | |||||||
\(978\) | 5.00557 | 0.160060 | ||||||||
\(979\) | 77.2618 | 2.46930 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.4693 | 0.525825 | ||||||||
\(982\) | 1.25490 | 0.0400454 | ||||||||
\(983\) | −1.74028 | −0.0555063 | −0.0277531 | − | 0.999615i | \(-0.508835\pi\) | ||||
−0.0277531 | + | 0.999615i | \(0.508835\pi\) | |||||||
\(984\) | −4.92781 | −0.157093 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 17.3301 | 0.551901 | ||||||||
\(987\) | −5.32241 | −0.169414 | ||||||||
\(988\) | −39.7394 | −1.26428 | ||||||||
\(989\) | 1.54425 | 0.0491044 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.8725 | −0.440676 | −0.220338 | − | 0.975424i | \(-0.570716\pi\) | ||||
−0.220338 | + | 0.975424i | \(0.570716\pi\) | |||||||
\(992\) | 4.83507 | 0.153514 | ||||||||
\(993\) | −5.77297 | −0.183200 | ||||||||
\(994\) | −9.35153 | −0.296613 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 20.7336 | 0.656968 | ||||||||
\(997\) | 23.7256 | 0.751399 | 0.375699 | − | 0.926742i | \(-0.377403\pi\) | ||||
0.375699 | + | 0.926742i | \(0.377403\pi\) | |||||||
\(998\) | −0.173362 | −0.00548766 | ||||||||
\(999\) | 2.15975 | 0.0683316 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1875.2.a.i.1.4 | ✓ | 6 | |
3.2 | odd | 2 | 5625.2.a.r.1.3 | 6 | |||
5.2 | odd | 4 | 1875.2.b.e.1249.7 | 12 | |||
5.3 | odd | 4 | 1875.2.b.e.1249.6 | 12 | |||
5.4 | even | 2 | 1875.2.a.l.1.3 | yes | 6 | ||
15.14 | odd | 2 | 5625.2.a.o.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.i.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1875.2.a.l.1.3 | yes | 6 | 5.4 | even | 2 | ||
1875.2.b.e.1249.6 | 12 | 5.3 | odd | 4 | |||
1875.2.b.e.1249.7 | 12 | 5.2 | odd | 4 | |||
5625.2.a.o.1.4 | 6 | 15.14 | odd | 2 | |||
5625.2.a.r.1.3 | 6 | 3.2 | odd | 2 |