Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2738,2,Mod(1,2738)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2738, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2738.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2738 = 2 \cdot 37^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2738.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: | \(21.8630400734\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.37902897.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 15x^{4} - x^{3} + 60x^{2} - 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.90773\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2738.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.90773 | 1.67878 | 0.839390 | − | 0.543530i | \(-0.182913\pi\) | ||||
0.839390 | + | 0.543530i | \(0.182913\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.347296 | −0.155316 | −0.0776578 | − | 0.996980i | \(-0.524744\pi\) | ||||
−0.0776578 | + | 0.996980i | \(0.524744\pi\) | |||||||
\(6\) | −2.90773 | −1.18708 | ||||||||
\(7\) | 1.00984 | 0.381685 | 0.190843 | − | 0.981621i | \(-0.438878\pi\) | ||||
0.190843 | + | 0.981621i | \(0.438878\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 5.45490 | 1.81830 | ||||||||
\(10\) | 0.347296 | 0.109825 | ||||||||
\(11\) | −5.46475 | −1.64768 | −0.823842 | − | 0.566820i | \(-0.808174\pi\) | ||||
−0.823842 | + | 0.566820i | \(0.808174\pi\) | |||||||
\(12\) | 2.90773 | 0.839390 | ||||||||
\(13\) | −6.36263 | −1.76468 | −0.882339 | − | 0.470615i | \(-0.844032\pi\) | ||||
−0.882339 | + | 0.470615i | \(0.844032\pi\) | |||||||
\(14\) | −1.00984 | −0.269892 | ||||||||
\(15\) | −1.00984 | −0.260741 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.522244 | −0.126663 | −0.0633314 | − | 0.997993i | \(-0.520173\pi\) | ||||
−0.0633314 | + | 0.997993i | \(0.520173\pi\) | |||||||
\(18\) | −5.45490 | −1.28573 | ||||||||
\(19\) | −5.00984 | −1.14934 | −0.574669 | − | 0.818386i | \(-0.694869\pi\) | ||||
−0.574669 | + | 0.818386i | \(0.694869\pi\) | |||||||
\(20\) | −0.347296 | −0.0776578 | ||||||||
\(21\) | 2.93636 | 0.640766 | ||||||||
\(22\) | 5.46475 | 1.16509 | ||||||||
\(23\) | −1.44298 | −0.300883 | −0.150441 | − | 0.988619i | \(-0.548070\pi\) | ||||
−0.150441 | + | 0.988619i | \(0.548070\pi\) | |||||||
\(24\) | −2.90773 | −0.593538 | ||||||||
\(25\) | −4.87939 | −0.975877 | ||||||||
\(26\) | 6.36263 | 1.24782 | ||||||||
\(27\) | 7.13820 | 1.37375 | ||||||||
\(28\) | 1.00984 | 0.190843 | ||||||||
\(29\) | 6.33429 | 1.17625 | 0.588124 | − | 0.808771i | \(-0.299867\pi\) | ||||
0.588124 | + | 0.808771i | \(0.299867\pi\) | |||||||
\(30\) | 1.00984 | 0.184372 | ||||||||
\(31\) | −3.30777 | −0.594092 | −0.297046 | − | 0.954863i | \(-0.596002\pi\) | ||||
−0.297046 | + | 0.954863i | \(0.596002\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −15.8900 | −2.76610 | ||||||||
\(34\) | 0.522244 | 0.0895642 | ||||||||
\(35\) | −0.350715 | −0.0592817 | ||||||||
\(36\) | 5.45490 | 0.909151 | ||||||||
\(37\) | 0 | 0 | ||||||||
\(38\) | 5.00984 | 0.812704 | ||||||||
\(39\) | −18.5008 | −2.96250 | ||||||||
\(40\) | 0.347296 | 0.0549124 | ||||||||
\(41\) | −1.10049 | −0.171868 | −0.0859338 | − | 0.996301i | \(-0.527387\pi\) | ||||
−0.0859338 | + | 0.996301i | \(0.527387\pi\) | |||||||
\(42\) | −2.93636 | −0.453090 | ||||||||
\(43\) | 6.27037 | 0.956222 | 0.478111 | − | 0.878299i | \(-0.341322\pi\) | ||||
0.478111 | + | 0.878299i | \(0.341322\pi\) | |||||||
\(44\) | −5.46475 | −0.823842 | ||||||||
\(45\) | −1.89447 | −0.282411 | ||||||||
\(46\) | 1.44298 | 0.212756 | ||||||||
\(47\) | −11.4382 | −1.66843 | −0.834216 | − | 0.551437i | \(-0.814080\pi\) | ||||
−0.834216 | + | 0.551437i | \(0.814080\pi\) | |||||||
\(48\) | 2.90773 | 0.419695 | ||||||||
\(49\) | −5.98021 | −0.854316 | ||||||||
\(50\) | 4.87939 | 0.690049 | ||||||||
\(51\) | −1.51855 | −0.212639 | ||||||||
\(52\) | −6.36263 | −0.882339 | ||||||||
\(53\) | 0.0922684 | 0.0126740 | 0.00633702 | − | 0.999980i | \(-0.497983\pi\) | ||||
0.00633702 | + | 0.999980i | \(0.497983\pi\) | |||||||
\(54\) | −7.13820 | −0.971386 | ||||||||
\(55\) | 1.89789 | 0.255911 | ||||||||
\(56\) | −1.00984 | −0.134946 | ||||||||
\(57\) | −14.5673 | −1.92948 | ||||||||
\(58\) | −6.33429 | −0.831733 | ||||||||
\(59\) | −2.99016 | −0.389285 | −0.194643 | − | 0.980874i | \(-0.562355\pi\) | ||||
−0.194643 | + | 0.980874i | \(0.562355\pi\) | |||||||
\(60\) | −1.00984 | −0.130370 | ||||||||
\(61\) | −3.81583 | −0.488567 | −0.244284 | − | 0.969704i | \(-0.578553\pi\) | ||||
−0.244284 | + | 0.969704i | \(0.578553\pi\) | |||||||
\(62\) | 3.30777 | 0.420087 | ||||||||
\(63\) | 5.50860 | 0.694019 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.20972 | 0.274082 | ||||||||
\(66\) | 15.8900 | 1.95593 | ||||||||
\(67\) | −1.16475 | −0.142297 | −0.0711485 | − | 0.997466i | \(-0.522666\pi\) | ||||
−0.0711485 | + | 0.997466i | \(0.522666\pi\) | |||||||
\(68\) | −0.522244 | −0.0633314 | ||||||||
\(69\) | −4.19581 | −0.505116 | ||||||||
\(70\) | 0.350715 | 0.0419185 | ||||||||
\(71\) | 0.312892 | 0.0371335 | 0.0185667 | − | 0.999828i | \(-0.494090\pi\) | ||||
0.0185667 | + | 0.999828i | \(0.494090\pi\) | |||||||
\(72\) | −5.45490 | −0.642867 | ||||||||
\(73\) | 13.2325 | 1.54875 | 0.774376 | − | 0.632726i | \(-0.218064\pi\) | ||||
0.774376 | + | 0.632726i | \(0.218064\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.1879 | −1.63828 | ||||||||
\(76\) | −5.00984 | −0.574669 | ||||||||
\(77\) | −5.51855 | −0.628897 | ||||||||
\(78\) | 18.5008 | 2.09481 | ||||||||
\(79\) | −9.30676 | −1.04709 | −0.523546 | − | 0.851997i | \(-0.675391\pi\) | ||||
−0.523546 | + | 0.851997i | \(0.675391\pi\) | |||||||
\(80\) | −0.347296 | −0.0388289 | ||||||||
\(81\) | 4.39126 | 0.487918 | ||||||||
\(82\) | 1.10049 | 0.121529 | ||||||||
\(83\) | 9.46475 | 1.03889 | 0.519446 | − | 0.854504i | \(-0.326139\pi\) | ||||
0.519446 | + | 0.854504i | \(0.326139\pi\) | |||||||
\(84\) | 2.93636 | 0.320383 | ||||||||
\(85\) | 0.181374 | 0.0196727 | ||||||||
\(86\) | −6.27037 | −0.676151 | ||||||||
\(87\) | 18.4184 | 1.97466 | ||||||||
\(88\) | 5.46475 | 0.582544 | ||||||||
\(89\) | 15.7678 | 1.67138 | 0.835692 | − | 0.549198i | \(-0.185067\pi\) | ||||
0.835692 | + | 0.549198i | \(0.185067\pi\) | |||||||
\(90\) | 1.89447 | 0.199694 | ||||||||
\(91\) | −6.42527 | −0.673552 | ||||||||
\(92\) | −1.44298 | −0.150441 | ||||||||
\(93\) | −9.61810 | −0.997350 | ||||||||
\(94\) | 11.4382 | 1.17976 | ||||||||
\(95\) | 1.73990 | 0.178510 | ||||||||
\(96\) | −2.90773 | −0.296769 | ||||||||
\(97\) | 0.929128 | 0.0943387 | 0.0471693 | − | 0.998887i | \(-0.484980\pi\) | ||||
0.0471693 | + | 0.998887i | \(0.484980\pi\) | |||||||
\(98\) | 5.98021 | 0.604093 | ||||||||
\(99\) | −29.8097 | −2.99598 | ||||||||
\(100\) | −4.87939 | −0.487939 | ||||||||
\(101\) | 8.56186 | 0.851937 | 0.425969 | − | 0.904738i | \(-0.359933\pi\) | ||||
0.425969 | + | 0.904738i | \(0.359933\pi\) | |||||||
\(102\) | 1.51855 | 0.150358 | ||||||||
\(103\) | −4.95913 | −0.488637 | −0.244319 | − | 0.969695i | \(-0.578564\pi\) | ||||
−0.244319 | + | 0.969695i | \(0.578564\pi\) | |||||||
\(104\) | 6.36263 | 0.623908 | ||||||||
\(105\) | −1.01979 | −0.0995209 | ||||||||
\(106\) | −0.0922684 | −0.00896189 | ||||||||
\(107\) | −3.56826 | −0.344957 | −0.172478 | − | 0.985013i | \(-0.555177\pi\) | ||||
−0.172478 | + | 0.985013i | \(0.555177\pi\) | |||||||
\(108\) | 7.13820 | 0.686874 | ||||||||
\(109\) | 0.978688 | 0.0937413 | 0.0468706 | − | 0.998901i | \(-0.485075\pi\) | ||||
0.0468706 | + | 0.998901i | \(0.485075\pi\) | |||||||
\(110\) | −1.89789 | −0.180956 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00984 | 0.0954213 | ||||||||
\(113\) | −9.23702 | −0.868946 | −0.434473 | − | 0.900685i | \(-0.643065\pi\) | ||||
−0.434473 | + | 0.900685i | \(0.643065\pi\) | |||||||
\(114\) | 14.5673 | 1.36435 | ||||||||
\(115\) | 0.501143 | 0.0467318 | ||||||||
\(116\) | 6.33429 | 0.588124 | ||||||||
\(117\) | −34.7076 | −3.20871 | ||||||||
\(118\) | 2.99016 | 0.275266 | ||||||||
\(119\) | −0.527386 | −0.0483454 | ||||||||
\(120\) | 1.00984 | 0.0921858 | ||||||||
\(121\) | 18.8635 | 1.71486 | ||||||||
\(122\) | 3.81583 | 0.345469 | ||||||||
\(123\) | −3.19993 | −0.288528 | ||||||||
\(124\) | −3.30777 | −0.297046 | ||||||||
\(125\) | 3.43107 | 0.306885 | ||||||||
\(126\) | −5.50860 | −0.490746 | ||||||||
\(127\) | 6.77151 | 0.600874 | 0.300437 | − | 0.953802i | \(-0.402867\pi\) | ||||
0.300437 | + | 0.953802i | \(0.402867\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 18.2325 | 1.60529 | ||||||||
\(130\) | −2.20972 | −0.193805 | ||||||||
\(131\) | 15.1485 | 1.32353 | 0.661764 | − | 0.749712i | \(-0.269808\pi\) | ||||
0.661764 | + | 0.749712i | \(0.269808\pi\) | |||||||
\(132\) | −15.8900 | −1.38305 | ||||||||
\(133\) | −5.05916 | −0.438685 | ||||||||
\(134\) | 1.16475 | 0.100619 | ||||||||
\(135\) | −2.47907 | −0.213364 | ||||||||
\(136\) | 0.522244 | 0.0447821 | ||||||||
\(137\) | −8.48173 | −0.724643 | −0.362321 | − | 0.932053i | \(-0.618016\pi\) | ||||
−0.362321 | + | 0.932053i | \(0.618016\pi\) | |||||||
\(138\) | 4.19581 | 0.357171 | ||||||||
\(139\) | −18.3384 | −1.55544 | −0.777720 | − | 0.628611i | \(-0.783624\pi\) | ||||
−0.777720 | + | 0.628611i | \(0.783624\pi\) | |||||||
\(140\) | −0.350715 | −0.0296409 | ||||||||
\(141\) | −33.2592 | −2.80093 | ||||||||
\(142\) | −0.312892 | −0.0262573 | ||||||||
\(143\) | 34.7702 | 2.90763 | ||||||||
\(144\) | 5.45490 | 0.454575 | ||||||||
\(145\) | −2.19988 | −0.182690 | ||||||||
\(146\) | −13.2325 | −1.09513 | ||||||||
\(147\) | −17.3889 | −1.43421 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.45291 | 0.446720 | 0.223360 | − | 0.974736i | \(-0.428297\pi\) | ||||
0.223360 | + | 0.974736i | \(0.428297\pi\) | |||||||
\(150\) | 14.1879 | 1.15844 | ||||||||
\(151\) | −15.5554 | −1.26588 | −0.632939 | − | 0.774202i | \(-0.718152\pi\) | ||||
−0.632939 | + | 0.774202i | \(0.718152\pi\) | |||||||
\(152\) | 5.00984 | 0.406352 | ||||||||
\(153\) | −2.84879 | −0.230311 | ||||||||
\(154\) | 5.51855 | 0.444697 | ||||||||
\(155\) | 1.14878 | 0.0922719 | ||||||||
\(156\) | −18.5008 | −1.48125 | ||||||||
\(157\) | −4.00822 | −0.319891 | −0.159945 | − | 0.987126i | \(-0.551132\pi\) | ||||
−0.159945 | + | 0.987126i | \(0.551132\pi\) | |||||||
\(158\) | 9.30676 | 0.740406 | ||||||||
\(159\) | 0.268292 | 0.0212769 | ||||||||
\(160\) | 0.347296 | 0.0274562 | ||||||||
\(161\) | −1.45719 | −0.114843 | ||||||||
\(162\) | −4.39126 | −0.345010 | ||||||||
\(163\) | −4.69223 | −0.367524 | −0.183762 | − | 0.982971i | \(-0.558828\pi\) | ||||
−0.183762 | + | 0.982971i | \(0.558828\pi\) | |||||||
\(164\) | −1.10049 | −0.0859338 | ||||||||
\(165\) | 5.51855 | 0.429618 | ||||||||
\(166\) | −9.46475 | −0.734607 | ||||||||
\(167\) | 0.776993 | 0.0601255 | 0.0300628 | − | 0.999548i | \(-0.490429\pi\) | ||||
0.0300628 | + | 0.999548i | \(0.490429\pi\) | |||||||
\(168\) | −2.93636 | −0.226545 | ||||||||
\(169\) | 27.4831 | 2.11409 | ||||||||
\(170\) | −0.181374 | −0.0139107 | ||||||||
\(171\) | −27.3282 | −2.08984 | ||||||||
\(172\) | 6.27037 | 0.478111 | ||||||||
\(173\) | 10.7333 | 0.816041 | 0.408021 | − | 0.912973i | \(-0.366219\pi\) | ||||
0.408021 | + | 0.912973i | \(0.366219\pi\) | |||||||
\(174\) | −18.4184 | −1.39630 | ||||||||
\(175\) | −4.92742 | −0.372478 | ||||||||
\(176\) | −5.46475 | −0.411921 | ||||||||
\(177\) | −8.69457 | −0.653524 | ||||||||
\(178\) | −15.7678 | −1.18185 | ||||||||
\(179\) | 11.8976 | 0.889267 | 0.444633 | − | 0.895713i | \(-0.353334\pi\) | ||||
0.444633 | + | 0.895713i | \(0.353334\pi\) | |||||||
\(180\) | −1.89447 | −0.141205 | ||||||||
\(181\) | 4.38667 | 0.326059 | 0.163029 | − | 0.986621i | \(-0.447873\pi\) | ||||
0.163029 | + | 0.986621i | \(0.447873\pi\) | |||||||
\(182\) | 6.42527 | 0.476273 | ||||||||
\(183\) | −11.0954 | −0.820197 | ||||||||
\(184\) | 1.44298 | 0.106378 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.61810 | 0.705233 | ||||||||
\(187\) | 2.85393 | 0.208700 | ||||||||
\(188\) | −11.4382 | −0.834216 | ||||||||
\(189\) | 7.20847 | 0.524339 | ||||||||
\(190\) | −1.73990 | −0.126226 | ||||||||
\(191\) | 10.4903 | 0.759053 | 0.379527 | − | 0.925181i | \(-0.376087\pi\) | ||||
0.379527 | + | 0.925181i | \(0.376087\pi\) | |||||||
\(192\) | 2.90773 | 0.209847 | ||||||||
\(193\) | −9.82949 | −0.707542 | −0.353771 | − | 0.935332i | \(-0.615101\pi\) | ||||
−0.353771 | + | 0.935332i | \(0.615101\pi\) | |||||||
\(194\) | −0.929128 | −0.0667075 | ||||||||
\(195\) | 6.42527 | 0.460123 | ||||||||
\(196\) | −5.98021 | −0.427158 | ||||||||
\(197\) | −12.0631 | −0.859460 | −0.429730 | − | 0.902958i | \(-0.641391\pi\) | ||||
−0.429730 | + | 0.902958i | \(0.641391\pi\) | |||||||
\(198\) | 29.8097 | 2.11848 | ||||||||
\(199\) | 9.29990 | 0.659252 | 0.329626 | − | 0.944112i | \(-0.393077\pi\) | ||||
0.329626 | + | 0.944112i | \(0.393077\pi\) | |||||||
\(200\) | 4.87939 | 0.345025 | ||||||||
\(201\) | −3.38678 | −0.238885 | ||||||||
\(202\) | −8.56186 | −0.602411 | ||||||||
\(203\) | 6.39665 | 0.448957 | ||||||||
\(204\) | −1.51855 | −0.106320 | ||||||||
\(205\) | 0.382196 | 0.0266937 | ||||||||
\(206\) | 4.95913 | 0.345519 | ||||||||
\(207\) | −7.87134 | −0.547096 | ||||||||
\(208\) | −6.36263 | −0.441169 | ||||||||
\(209\) | 27.3775 | 1.89374 | ||||||||
\(210\) | 1.01979 | 0.0703719 | ||||||||
\(211\) | −4.40004 | −0.302911 | −0.151455 | − | 0.988464i | \(-0.548396\pi\) | ||||
−0.151455 | + | 0.988464i | \(0.548396\pi\) | |||||||
\(212\) | 0.0922684 | 0.00633702 | ||||||||
\(213\) | 0.909807 | 0.0623389 | ||||||||
\(214\) | 3.56826 | 0.243921 | ||||||||
\(215\) | −2.17768 | −0.148516 | ||||||||
\(216\) | −7.13820 | −0.485693 | ||||||||
\(217\) | −3.34033 | −0.226756 | ||||||||
\(218\) | −0.978688 | −0.0662851 | ||||||||
\(219\) | 38.4767 | 2.60001 | ||||||||
\(220\) | 1.89789 | 0.127956 | ||||||||
\(221\) | 3.32285 | 0.223519 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.2311 | 0.752092 | 0.376046 | − | 0.926601i | \(-0.377283\pi\) | ||||
0.376046 | + | 0.926601i | \(0.377283\pi\) | |||||||
\(224\) | −1.00984 | −0.0674731 | ||||||||
\(225\) | −26.6166 | −1.77444 | ||||||||
\(226\) | 9.23702 | 0.614438 | ||||||||
\(227\) | 15.1539 | 1.00580 | 0.502901 | − | 0.864344i | \(-0.332266\pi\) | ||||
0.502901 | + | 0.864344i | \(0.332266\pi\) | |||||||
\(228\) | −14.5673 | −0.964742 | ||||||||
\(229\) | −15.5617 | −1.02835 | −0.514173 | − | 0.857686i | \(-0.671901\pi\) | ||||
−0.514173 | + | 0.857686i | \(0.671901\pi\) | |||||||
\(230\) | −0.501143 | −0.0330444 | ||||||||
\(231\) | −16.0465 | −1.05578 | ||||||||
\(232\) | −6.33429 | −0.415866 | ||||||||
\(233\) | 13.5871 | 0.890122 | 0.445061 | − | 0.895500i | \(-0.353182\pi\) | ||||
0.445061 | + | 0.895500i | \(0.353182\pi\) | |||||||
\(234\) | 34.7076 | 2.26890 | ||||||||
\(235\) | 3.97244 | 0.259134 | ||||||||
\(236\) | −2.99016 | −0.194643 | ||||||||
\(237\) | −27.0616 | −1.75784 | ||||||||
\(238\) | 0.527386 | 0.0341853 | ||||||||
\(239\) | 19.4945 | 1.26099 | 0.630496 | − | 0.776192i | \(-0.282852\pi\) | ||||
0.630496 | + | 0.776192i | \(0.282852\pi\) | |||||||
\(240\) | −1.00984 | −0.0651852 | ||||||||
\(241\) | −1.44363 | −0.0929924 | −0.0464962 | − | 0.998918i | \(-0.514806\pi\) | ||||
−0.0464962 | + | 0.998918i | \(0.514806\pi\) | |||||||
\(242\) | −18.8635 | −1.21259 | ||||||||
\(243\) | −8.64599 | −0.554641 | ||||||||
\(244\) | −3.81583 | −0.244284 | ||||||||
\(245\) | 2.07691 | 0.132689 | ||||||||
\(246\) | 3.19993 | 0.204020 | ||||||||
\(247\) | 31.8758 | 2.02821 | ||||||||
\(248\) | 3.30777 | 0.210043 | ||||||||
\(249\) | 27.5209 | 1.74407 | ||||||||
\(250\) | −3.43107 | −0.217000 | ||||||||
\(251\) | −10.0729 | −0.635797 | −0.317898 | − | 0.948125i | \(-0.602977\pi\) | ||||
−0.317898 | + | 0.948125i | \(0.602977\pi\) | |||||||
\(252\) | 5.50860 | 0.347009 | ||||||||
\(253\) | 7.88554 | 0.495760 | ||||||||
\(254\) | −6.77151 | −0.424882 | ||||||||
\(255\) | 0.527386 | 0.0330262 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.98500 | 0.435712 | 0.217856 | − | 0.975981i | \(-0.430094\pi\) | ||||
0.217856 | + | 0.975981i | \(0.430094\pi\) | |||||||
\(258\) | −18.2325 | −1.13511 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.20972 | 0.137041 | ||||||||
\(261\) | 34.5529 | 2.13877 | ||||||||
\(262\) | −15.1485 | −0.935875 | ||||||||
\(263\) | 2.66284 | 0.164198 | 0.0820990 | − | 0.996624i | \(-0.473838\pi\) | ||||
0.0820990 | + | 0.996624i | \(0.473838\pi\) | |||||||
\(264\) | 15.8900 | 0.977963 | ||||||||
\(265\) | −0.0320445 | −0.00196848 | ||||||||
\(266\) | 5.05916 | 0.310197 | ||||||||
\(267\) | 45.8486 | 2.80589 | ||||||||
\(268\) | −1.16475 | −0.0711485 | ||||||||
\(269\) | 2.41504 | 0.147247 | 0.0736236 | − | 0.997286i | \(-0.476544\pi\) | ||||
0.0736236 | + | 0.997286i | \(0.476544\pi\) | |||||||
\(270\) | 2.47907 | 0.150871 | ||||||||
\(271\) | −25.2506 | −1.53386 | −0.766932 | − | 0.641729i | \(-0.778218\pi\) | ||||
−0.766932 | + | 0.641729i | \(0.778218\pi\) | |||||||
\(272\) | −0.522244 | −0.0316657 | ||||||||
\(273\) | −18.6830 | −1.13074 | ||||||||
\(274\) | 8.48173 | 0.512400 | ||||||||
\(275\) | 26.6646 | 1.60794 | ||||||||
\(276\) | −4.19581 | −0.252558 | ||||||||
\(277\) | 17.7320 | 1.06541 | 0.532706 | − | 0.846301i | \(-0.321175\pi\) | ||||
0.532706 | + | 0.846301i | \(0.321175\pi\) | |||||||
\(278\) | 18.3384 | 1.09986 | ||||||||
\(279\) | −18.0435 | −1.08024 | ||||||||
\(280\) | 0.350715 | 0.0209593 | ||||||||
\(281\) | −19.7493 | −1.17815 | −0.589073 | − | 0.808080i | \(-0.700507\pi\) | ||||
−0.589073 | + | 0.808080i | \(0.700507\pi\) | |||||||
\(282\) | 33.2592 | 1.98056 | ||||||||
\(283\) | −24.3494 | −1.44742 | −0.723711 | − | 0.690103i | \(-0.757565\pi\) | ||||
−0.723711 | + | 0.690103i | \(0.757565\pi\) | |||||||
\(284\) | 0.312892 | 0.0185667 | ||||||||
\(285\) | 5.05916 | 0.299679 | ||||||||
\(286\) | −34.7702 | −2.05600 | ||||||||
\(287\) | −1.11132 | −0.0655994 | ||||||||
\(288\) | −5.45490 | −0.321433 | ||||||||
\(289\) | −16.7273 | −0.983957 | ||||||||
\(290\) | 2.19988 | 0.129181 | ||||||||
\(291\) | 2.70165 | 0.158374 | ||||||||
\(292\) | 13.2325 | 0.774376 | ||||||||
\(293\) | −23.2486 | −1.35820 | −0.679098 | − | 0.734048i | \(-0.737629\pi\) | ||||
−0.679098 | + | 0.734048i | \(0.737629\pi\) | |||||||
\(294\) | 17.3889 | 1.01414 | ||||||||
\(295\) | 1.03847 | 0.0604621 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −39.0085 | −2.26350 | ||||||||
\(298\) | −5.45291 | −0.315879 | ||||||||
\(299\) | 9.18118 | 0.530961 | ||||||||
\(300\) | −14.1879 | −0.819141 | ||||||||
\(301\) | 6.33210 | 0.364976 | ||||||||
\(302\) | 15.5554 | 0.895111 | ||||||||
\(303\) | 24.8956 | 1.43021 | ||||||||
\(304\) | −5.00984 | −0.287334 | ||||||||
\(305\) | 1.32522 | 0.0758821 | ||||||||
\(306\) | 2.84879 | 0.162855 | ||||||||
\(307\) | −10.6702 | −0.608978 | −0.304489 | − | 0.952516i | \(-0.598486\pi\) | ||||
−0.304489 | + | 0.952516i | \(0.598486\pi\) | |||||||
\(308\) | −5.51855 | −0.314448 | ||||||||
\(309\) | −14.4198 | −0.820314 | ||||||||
\(310\) | −1.14878 | −0.0652461 | ||||||||
\(311\) | −17.0201 | −0.965122 | −0.482561 | − | 0.875862i | \(-0.660293\pi\) | ||||
−0.482561 | + | 0.875862i | \(0.660293\pi\) | |||||||
\(312\) | 18.5008 | 1.04740 | ||||||||
\(313\) | −10.9104 | −0.616694 | −0.308347 | − | 0.951274i | \(-0.599776\pi\) | ||||
−0.308347 | + | 0.951274i | \(0.599776\pi\) | |||||||
\(314\) | 4.00822 | 0.226197 | ||||||||
\(315\) | −1.91312 | −0.107792 | ||||||||
\(316\) | −9.30676 | −0.523546 | ||||||||
\(317\) | −28.8403 | −1.61983 | −0.809917 | − | 0.586545i | \(-0.800488\pi\) | ||||
−0.809917 | + | 0.586545i | \(0.800488\pi\) | |||||||
\(318\) | −0.268292 | −0.0150450 | ||||||||
\(319\) | −34.6153 | −1.93808 | ||||||||
\(320\) | −0.347296 | −0.0194145 | ||||||||
\(321\) | −10.3755 | −0.579106 | ||||||||
\(322\) | 1.45719 | 0.0812060 | ||||||||
\(323\) | 2.61636 | 0.145578 | ||||||||
\(324\) | 4.39126 | 0.243959 | ||||||||
\(325\) | 31.0457 | 1.72211 | ||||||||
\(326\) | 4.69223 | 0.259879 | ||||||||
\(327\) | 2.84576 | 0.157371 | ||||||||
\(328\) | 1.10049 | 0.0607644 | ||||||||
\(329\) | −11.5508 | −0.636816 | ||||||||
\(330\) | −5.51855 | −0.303786 | ||||||||
\(331\) | −3.95955 | −0.217637 | −0.108818 | − | 0.994062i | \(-0.534707\pi\) | ||||
−0.108818 | + | 0.994062i | \(0.534707\pi\) | |||||||
\(332\) | 9.46475 | 0.519446 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.776993 | −0.0425152 | ||||||||
\(335\) | 0.404514 | 0.0221009 | ||||||||
\(336\) | 2.93636 | 0.160191 | ||||||||
\(337\) | −4.27678 | −0.232971 | −0.116485 | − | 0.993192i | \(-0.537163\pi\) | ||||
−0.116485 | + | 0.993192i | \(0.537163\pi\) | |||||||
\(338\) | −27.4831 | −1.49488 | ||||||||
\(339\) | −26.8588 | −1.45877 | ||||||||
\(340\) | 0.181374 | 0.00983636 | ||||||||
\(341\) | 18.0761 | 0.978876 | ||||||||
\(342\) | 27.3282 | 1.47774 | ||||||||
\(343\) | −13.1080 | −0.707765 | ||||||||
\(344\) | −6.27037 | −0.338076 | ||||||||
\(345\) | 1.45719 | 0.0784524 | ||||||||
\(346\) | −10.7333 | −0.577028 | ||||||||
\(347\) | 10.1280 | 0.543701 | 0.271850 | − | 0.962339i | \(-0.412364\pi\) | ||||
0.271850 | + | 0.962339i | \(0.412364\pi\) | |||||||
\(348\) | 18.4184 | 0.987330 | ||||||||
\(349\) | −7.19087 | −0.384918 | −0.192459 | − | 0.981305i | \(-0.561646\pi\) | ||||
−0.192459 | + | 0.981305i | \(0.561646\pi\) | |||||||
\(350\) | 4.92742 | 0.263382 | ||||||||
\(351\) | −45.4178 | −2.42422 | ||||||||
\(352\) | 5.46475 | 0.291272 | ||||||||
\(353\) | 34.0550 | 1.81256 | 0.906282 | − | 0.422674i | \(-0.138908\pi\) | ||||
0.906282 | + | 0.422674i | \(0.138908\pi\) | |||||||
\(354\) | 8.69457 | 0.462111 | ||||||||
\(355\) | −0.108666 | −0.00576741 | ||||||||
\(356\) | 15.7678 | 0.835692 | ||||||||
\(357\) | −1.53350 | −0.0811612 | ||||||||
\(358\) | −11.8976 | −0.628807 | ||||||||
\(359\) | 9.87953 | 0.521422 | 0.260711 | − | 0.965417i | \(-0.416043\pi\) | ||||
0.260711 | + | 0.965417i | \(0.416043\pi\) | |||||||
\(360\) | 1.89447 | 0.0998472 | ||||||||
\(361\) | 6.09854 | 0.320976 | ||||||||
\(362\) | −4.38667 | −0.230559 | ||||||||
\(363\) | 54.8499 | 2.87887 | ||||||||
\(364\) | −6.42527 | −0.336776 | ||||||||
\(365\) | −4.59561 | −0.240545 | ||||||||
\(366\) | 11.0954 | 0.579967 | ||||||||
\(367\) | −33.9039 | −1.76977 | −0.884885 | − | 0.465809i | \(-0.845763\pi\) | ||||
−0.884885 | + | 0.465809i | \(0.845763\pi\) | |||||||
\(368\) | −1.44298 | −0.0752207 | ||||||||
\(369\) | −6.00307 | −0.312507 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.0931767 | 0.00483749 | ||||||||
\(372\) | −9.61810 | −0.498675 | ||||||||
\(373\) | 31.3540 | 1.62345 | 0.811725 | − | 0.584039i | \(-0.198529\pi\) | ||||
0.811725 | + | 0.584039i | \(0.198529\pi\) | |||||||
\(374\) | −2.85393 | −0.147573 | ||||||||
\(375\) | 9.97664 | 0.515192 | ||||||||
\(376\) | 11.4382 | 0.589880 | ||||||||
\(377\) | −40.3028 | −2.07570 | ||||||||
\(378\) | −7.20847 | −0.370764 | ||||||||
\(379\) | 10.6544 | 0.547281 | 0.273641 | − | 0.961832i | \(-0.411772\pi\) | ||||
0.273641 | + | 0.961832i | \(0.411772\pi\) | |||||||
\(380\) | 1.73990 | 0.0892550 | ||||||||
\(381\) | 19.6897 | 1.00874 | ||||||||
\(382\) | −10.4903 | −0.536732 | ||||||||
\(383\) | −19.4015 | −0.991372 | −0.495686 | − | 0.868502i | \(-0.665083\pi\) | ||||
−0.495686 | + | 0.868502i | \(0.665083\pi\) | |||||||
\(384\) | −2.90773 | −0.148385 | ||||||||
\(385\) | 1.91657 | 0.0976775 | ||||||||
\(386\) | 9.82949 | 0.500308 | ||||||||
\(387\) | 34.2042 | 1.73870 | ||||||||
\(388\) | 0.929128 | 0.0471693 | ||||||||
\(389\) | −18.6990 | −0.948078 | −0.474039 | − | 0.880504i | \(-0.657204\pi\) | ||||
−0.474039 | + | 0.880504i | \(0.657204\pi\) | |||||||
\(390\) | −6.42527 | −0.325356 | ||||||||
\(391\) | 0.753590 | 0.0381107 | ||||||||
\(392\) | 5.98021 | 0.302046 | ||||||||
\(393\) | 44.0477 | 2.22191 | ||||||||
\(394\) | 12.0631 | 0.607730 | ||||||||
\(395\) | 3.23220 | 0.162630 | ||||||||
\(396\) | −29.8097 | −1.49799 | ||||||||
\(397\) | −23.8632 | −1.19766 | −0.598829 | − | 0.800877i | \(-0.704367\pi\) | ||||
−0.598829 | + | 0.800877i | \(0.704367\pi\) | |||||||
\(398\) | −9.29990 | −0.466162 | ||||||||
\(399\) | −14.7107 | −0.736456 | ||||||||
\(400\) | −4.87939 | −0.243969 | ||||||||
\(401\) | −17.8350 | −0.890638 | −0.445319 | − | 0.895372i | \(-0.646910\pi\) | ||||
−0.445319 | + | 0.895372i | \(0.646910\pi\) | |||||||
\(402\) | 3.38678 | 0.168917 | ||||||||
\(403\) | 21.0461 | 1.04838 | ||||||||
\(404\) | 8.56186 | 0.425969 | ||||||||
\(405\) | −1.52507 | −0.0757813 | ||||||||
\(406\) | −6.39665 | −0.317460 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.51855 | 0.0751792 | ||||||||
\(409\) | 9.98668 | 0.493810 | 0.246905 | − | 0.969040i | \(-0.420586\pi\) | ||||
0.246905 | + | 0.969040i | \(0.420586\pi\) | |||||||
\(410\) | −0.382196 | −0.0188753 | ||||||||
\(411\) | −24.6626 | −1.21652 | ||||||||
\(412\) | −4.95913 | −0.244319 | ||||||||
\(413\) | −3.01959 | −0.148584 | ||||||||
\(414\) | 7.87134 | 0.386855 | ||||||||
\(415\) | −3.28707 | −0.161356 | ||||||||
\(416\) | 6.36263 | 0.311954 | ||||||||
\(417\) | −53.3231 | −2.61124 | ||||||||
\(418\) | −27.3775 | −1.33908 | ||||||||
\(419\) | 36.0291 | 1.76014 | 0.880068 | − | 0.474848i | \(-0.157497\pi\) | ||||
0.880068 | + | 0.474848i | \(0.157497\pi\) | |||||||
\(420\) | −1.01979 | −0.0497605 | ||||||||
\(421\) | −22.3336 | −1.08847 | −0.544235 | − | 0.838933i | \(-0.683180\pi\) | ||||
−0.544235 | + | 0.838933i | \(0.683180\pi\) | |||||||
\(422\) | 4.40004 | 0.214190 | ||||||||
\(423\) | −62.3943 | −3.03371 | ||||||||
\(424\) | −0.0922684 | −0.00448095 | ||||||||
\(425\) | 2.54823 | 0.123607 | ||||||||
\(426\) | −0.909807 | −0.0440803 | ||||||||
\(427\) | −3.85340 | −0.186479 | ||||||||
\(428\) | −3.56826 | −0.172478 | ||||||||
\(429\) | 101.102 | 4.88127 | ||||||||
\(430\) | 2.17768 | 0.105017 | ||||||||
\(431\) | −31.2560 | −1.50555 | −0.752774 | − | 0.658279i | \(-0.771285\pi\) | ||||
−0.752774 | + | 0.658279i | \(0.771285\pi\) | |||||||
\(432\) | 7.13820 | 0.343437 | ||||||||
\(433\) | 5.42187 | 0.260558 | 0.130279 | − | 0.991477i | \(-0.458413\pi\) | ||||
0.130279 | + | 0.991477i | \(0.458413\pi\) | |||||||
\(434\) | 3.34033 | 0.160341 | ||||||||
\(435\) | −6.39665 | −0.306696 | ||||||||
\(436\) | 0.978688 | 0.0468706 | ||||||||
\(437\) | 7.22912 | 0.345816 | ||||||||
\(438\) | −38.4767 | −1.83849 | ||||||||
\(439\) | 15.4292 | 0.736397 | 0.368199 | − | 0.929747i | \(-0.379975\pi\) | ||||
0.368199 | + | 0.929747i | \(0.379975\pi\) | |||||||
\(440\) | −1.89789 | −0.0904782 | ||||||||
\(441\) | −32.6215 | −1.55340 | ||||||||
\(442\) | −3.32285 | −0.158052 | ||||||||
\(443\) | −8.45523 | −0.401720 | −0.200860 | − | 0.979620i | \(-0.564374\pi\) | ||||
−0.200860 | + | 0.979620i | \(0.564374\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.47610 | −0.259592 | ||||||||
\(446\) | −11.2311 | −0.531810 | ||||||||
\(447\) | 15.8556 | 0.749944 | ||||||||
\(448\) | 1.00984 | 0.0477107 | ||||||||
\(449\) | −36.3945 | −1.71756 | −0.858782 | − | 0.512342i | \(-0.828778\pi\) | ||||
−0.858782 | + | 0.512342i | \(0.828778\pi\) | |||||||
\(450\) | 26.6166 | 1.25472 | ||||||||
\(451\) | 6.01390 | 0.283183 | ||||||||
\(452\) | −9.23702 | −0.434473 | ||||||||
\(453\) | −45.2308 | −2.12513 | ||||||||
\(454\) | −15.1539 | −0.711209 | ||||||||
\(455\) | 2.23147 | 0.104613 | ||||||||
\(456\) | 14.5673 | 0.682176 | ||||||||
\(457\) | −13.0415 | −0.610054 | −0.305027 | − | 0.952344i | \(-0.598665\pi\) | ||||
−0.305027 | + | 0.952344i | \(0.598665\pi\) | |||||||
\(458\) | 15.5617 | 0.727151 | ||||||||
\(459\) | −3.72788 | −0.174003 | ||||||||
\(460\) | 0.501143 | 0.0233659 | ||||||||
\(461\) | −17.6483 | −0.821964 | −0.410982 | − | 0.911644i | \(-0.634814\pi\) | ||||
−0.410982 | + | 0.911644i | \(0.634814\pi\) | |||||||
\(462\) | 16.0465 | 0.746548 | ||||||||
\(463\) | −26.4940 | −1.23128 | −0.615640 | − | 0.788028i | \(-0.711102\pi\) | ||||
−0.615640 | + | 0.788028i | \(0.711102\pi\) | |||||||
\(464\) | 6.33429 | 0.294062 | ||||||||
\(465\) | 3.34033 | 0.154904 | ||||||||
\(466\) | −13.5871 | −0.629411 | ||||||||
\(467\) | 19.0975 | 0.883727 | 0.441864 | − | 0.897082i | \(-0.354317\pi\) | ||||
0.441864 | + | 0.897082i | \(0.354317\pi\) | |||||||
\(468\) | −34.7076 | −1.60436 | ||||||||
\(469\) | −1.17622 | −0.0543127 | ||||||||
\(470\) | −3.97244 | −0.183235 | ||||||||
\(471\) | −11.6548 | −0.537026 | ||||||||
\(472\) | 2.99016 | 0.137633 | ||||||||
\(473\) | −34.2660 | −1.57555 | ||||||||
\(474\) | 27.0616 | 1.24298 | ||||||||
\(475\) | 24.4450 | 1.12161 | ||||||||
\(476\) | −0.527386 | −0.0241727 | ||||||||
\(477\) | 0.503315 | 0.0230452 | ||||||||
\(478\) | −19.4945 | −0.891656 | ||||||||
\(479\) | −19.1825 | −0.876471 | −0.438236 | − | 0.898860i | \(-0.644396\pi\) | ||||
−0.438236 | + | 0.898860i | \(0.644396\pi\) | |||||||
\(480\) | 1.00984 | 0.0460929 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.44363 | 0.0657556 | ||||||||
\(483\) | −4.23712 | −0.192795 | ||||||||
\(484\) | 18.8635 | 0.857430 | ||||||||
\(485\) | −0.322683 | −0.0146523 | ||||||||
\(486\) | 8.64599 | 0.392190 | ||||||||
\(487\) | 35.7577 | 1.62034 | 0.810168 | − | 0.586197i | \(-0.199376\pi\) | ||||
0.810168 | + | 0.586197i | \(0.199376\pi\) | |||||||
\(488\) | 3.81583 | 0.172735 | ||||||||
\(489\) | −13.6438 | −0.616992 | ||||||||
\(490\) | −2.07691 | −0.0938251 | ||||||||
\(491\) | 29.7732 | 1.34364 | 0.671822 | − | 0.740713i | \(-0.265512\pi\) | ||||
0.671822 | + | 0.740713i | \(0.265512\pi\) | |||||||
\(492\) | −3.19993 | −0.144264 | ||||||||
\(493\) | −3.30805 | −0.148987 | ||||||||
\(494\) | −31.8758 | −1.43416 | ||||||||
\(495\) | 10.3528 | 0.465323 | ||||||||
\(496\) | −3.30777 | −0.148523 | ||||||||
\(497\) | 0.315973 | 0.0141733 | ||||||||
\(498\) | −27.5209 | −1.23324 | ||||||||
\(499\) | −24.8179 | −1.11100 | −0.555501 | − | 0.831516i | \(-0.687473\pi\) | ||||
−0.555501 | + | 0.831516i | \(0.687473\pi\) | |||||||
\(500\) | 3.43107 | 0.153442 | ||||||||
\(501\) | 2.25929 | 0.100938 | ||||||||
\(502\) | 10.0729 | 0.449576 | ||||||||
\(503\) | −13.6252 | −0.607518 | −0.303759 | − | 0.952749i | \(-0.598242\pi\) | ||||
−0.303759 | + | 0.952749i | \(0.598242\pi\) | |||||||
\(504\) | −5.50860 | −0.245373 | ||||||||
\(505\) | −2.97350 | −0.132319 | ||||||||
\(506\) | −7.88554 | −0.350555 | ||||||||
\(507\) | 79.9135 | 3.54909 | ||||||||
\(508\) | 6.77151 | 0.300437 | ||||||||
\(509\) | 21.1010 | 0.935285 | 0.467643 | − | 0.883918i | \(-0.345103\pi\) | ||||
0.467643 | + | 0.883918i | \(0.345103\pi\) | |||||||
\(510\) | −0.527386 | −0.0233530 | ||||||||
\(511\) | 13.3628 | 0.591136 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −35.7613 | −1.57890 | ||||||||
\(514\) | −6.98500 | −0.308095 | ||||||||
\(515\) | 1.72229 | 0.0758930 | ||||||||
\(516\) | 18.2325 | 0.802643 | ||||||||
\(517\) | 62.5069 | 2.74905 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.2097 | 1.36995 | ||||||||
\(520\) | −2.20972 | −0.0969026 | ||||||||
\(521\) | 2.94157 | 0.128872 | 0.0644362 | − | 0.997922i | \(-0.479475\pi\) | ||||
0.0644362 | + | 0.997922i | \(0.479475\pi\) | |||||||
\(522\) | −34.5529 | −1.51234 | ||||||||
\(523\) | −10.8441 | −0.474180 | −0.237090 | − | 0.971488i | \(-0.576194\pi\) | ||||
−0.237090 | + | 0.971488i | \(0.576194\pi\) | |||||||
\(524\) | 15.1485 | 0.661764 | ||||||||
\(525\) | −14.3276 | −0.625308 | ||||||||
\(526\) | −2.66284 | −0.116105 | ||||||||
\(527\) | 1.72746 | 0.0752494 | ||||||||
\(528\) | −15.8900 | −0.691524 | ||||||||
\(529\) | −20.9178 | −0.909469 | ||||||||
\(530\) | 0.0320445 | 0.00139192 | ||||||||
\(531\) | −16.3110 | −0.707837 | ||||||||
\(532\) | −5.05916 | −0.219343 | ||||||||
\(533\) | 7.00202 | 0.303291 | ||||||||
\(534\) | −45.8486 | −1.98406 | ||||||||
\(535\) | 1.23924 | 0.0535772 | ||||||||
\(536\) | 1.16475 | 0.0503096 | ||||||||
\(537\) | 34.5950 | 1.49288 | ||||||||
\(538\) | −2.41504 | −0.104120 | ||||||||
\(539\) | 32.6804 | 1.40764 | ||||||||
\(540\) | −2.47907 | −0.106682 | ||||||||
\(541\) | −8.87735 | −0.381667 | −0.190834 | − | 0.981622i | \(-0.561119\pi\) | ||||
−0.190834 | + | 0.981622i | \(0.561119\pi\) | |||||||
\(542\) | 25.2506 | 1.08461 | ||||||||
\(543\) | 12.7553 | 0.547381 | ||||||||
\(544\) | 0.522244 | 0.0223910 | ||||||||
\(545\) | −0.339895 | −0.0145595 | ||||||||
\(546\) | 18.6830 | 0.799557 | ||||||||
\(547\) | 36.5299 | 1.56190 | 0.780952 | − | 0.624591i | \(-0.214734\pi\) | ||||
0.780952 | + | 0.624591i | \(0.214734\pi\) | |||||||
\(548\) | −8.48173 | −0.362321 | ||||||||
\(549\) | −20.8150 | −0.888362 | ||||||||
\(550\) | −26.6646 | −1.13698 | ||||||||
\(551\) | −31.7338 | −1.35191 | ||||||||
\(552\) | 4.19581 | 0.178586 | ||||||||
\(553\) | −9.39838 | −0.399660 | ||||||||
\(554\) | −17.7320 | −0.753360 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.3384 | −0.777720 | ||||||||
\(557\) | −36.7236 | −1.55603 | −0.778014 | − | 0.628246i | \(-0.783773\pi\) | ||||
−0.778014 | + | 0.628246i | \(0.783773\pi\) | |||||||
\(558\) | 18.0435 | 0.763844 | ||||||||
\(559\) | −39.8961 | −1.68742 | ||||||||
\(560\) | −0.350715 | −0.0148204 | ||||||||
\(561\) | 8.29847 | 0.350362 | ||||||||
\(562\) | 19.7493 | 0.833074 | ||||||||
\(563\) | −0.476912 | −0.0200995 | −0.0100497 | − | 0.999950i | \(-0.503199\pi\) | ||||
−0.0100497 | + | 0.999950i | \(0.503199\pi\) | |||||||
\(564\) | −33.2592 | −1.40047 | ||||||||
\(565\) | 3.20798 | 0.134961 | ||||||||
\(566\) | 24.3494 | 1.02348 | ||||||||
\(567\) | 4.43449 | 0.186231 | ||||||||
\(568\) | −0.312892 | −0.0131287 | ||||||||
\(569\) | −9.09812 | −0.381413 | −0.190706 | − | 0.981647i | \(-0.561078\pi\) | ||||
−0.190706 | + | 0.981647i | \(0.561078\pi\) | |||||||
\(570\) | −5.05916 | −0.211905 | ||||||||
\(571\) | 25.5966 | 1.07118 | 0.535592 | − | 0.844477i | \(-0.320089\pi\) | ||||
0.535592 | + | 0.844477i | \(0.320089\pi\) | |||||||
\(572\) | 34.7702 | 1.45381 | ||||||||
\(573\) | 30.5030 | 1.27428 | ||||||||
\(574\) | 1.11132 | 0.0463858 | ||||||||
\(575\) | 7.04087 | 0.293625 | ||||||||
\(576\) | 5.45490 | 0.227288 | ||||||||
\(577\) | −15.4291 | −0.642322 | −0.321161 | − | 0.947025i | \(-0.604073\pi\) | ||||
−0.321161 | + | 0.947025i | \(0.604073\pi\) | |||||||
\(578\) | 16.7273 | 0.695762 | ||||||||
\(579\) | −28.5815 | −1.18781 | ||||||||
\(580\) | −2.19988 | −0.0913449 | ||||||||
\(581\) | 9.55792 | 0.396530 | ||||||||
\(582\) | −2.70165 | −0.111987 | ||||||||
\(583\) | −0.504223 | −0.0208828 | ||||||||
\(584\) | −13.2325 | −0.547567 | ||||||||
\(585\) | 12.0538 | 0.498364 | ||||||||
\(586\) | 23.2486 | 0.960390 | ||||||||
\(587\) | −16.2385 | −0.670235 | −0.335118 | − | 0.942176i | \(-0.608776\pi\) | ||||
−0.335118 | + | 0.942176i | \(0.608776\pi\) | |||||||
\(588\) | −17.3889 | −0.717104 | ||||||||
\(589\) | 16.5714 | 0.682813 | ||||||||
\(590\) | −1.03847 | −0.0427531 | ||||||||
\(591\) | −35.0762 | −1.44284 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.0626 | −1.11133 | −0.555663 | − | 0.831407i | \(-0.687536\pi\) | ||||
−0.555663 | + | 0.831407i | \(0.687536\pi\) | |||||||
\(594\) | 39.0085 | 1.60054 | ||||||||
\(595\) | 0.183159 | 0.00750879 | ||||||||
\(596\) | 5.45291 | 0.223360 | ||||||||
\(597\) | 27.0416 | 1.10674 | ||||||||
\(598\) | −9.18118 | −0.375446 | ||||||||
\(599\) | −39.8486 | −1.62817 | −0.814085 | − | 0.580746i | \(-0.802761\pi\) | ||||
−0.814085 | + | 0.580746i | \(0.802761\pi\) | |||||||
\(600\) | 14.1879 | 0.579220 | ||||||||
\(601\) | 35.6736 | 1.45516 | 0.727578 | − | 0.686025i | \(-0.240646\pi\) | ||||
0.727578 | + | 0.686025i | \(0.240646\pi\) | |||||||
\(602\) | −6.33210 | −0.258077 | ||||||||
\(603\) | −6.35360 | −0.258739 | ||||||||
\(604\) | −15.5554 | −0.632939 | ||||||||
\(605\) | −6.55121 | −0.266345 | ||||||||
\(606\) | −24.8956 | −1.01131 | ||||||||
\(607\) | 12.7478 | 0.517417 | 0.258709 | − | 0.965955i | \(-0.416703\pi\) | ||||
0.258709 | + | 0.965955i | \(0.416703\pi\) | |||||||
\(608\) | 5.00984 | 0.203176 | ||||||||
\(609\) | 18.5997 | 0.753699 | ||||||||
\(610\) | −1.32522 | −0.0536568 | ||||||||
\(611\) | 72.7771 | 2.94425 | ||||||||
\(612\) | −2.84879 | −0.115156 | ||||||||
\(613\) | −4.09270 | −0.165303 | −0.0826513 | − | 0.996579i | \(-0.526339\pi\) | ||||
−0.0826513 | + | 0.996579i | \(0.526339\pi\) | |||||||
\(614\) | 10.6702 | 0.430613 | ||||||||
\(615\) | 1.11132 | 0.0448129 | ||||||||
\(616\) | 5.51855 | 0.222349 | ||||||||
\(617\) | 47.2712 | 1.90307 | 0.951534 | − | 0.307545i | \(-0.0995073\pi\) | ||||
0.951534 | + | 0.307545i | \(0.0995073\pi\) | |||||||
\(618\) | 14.4198 | 0.580050 | ||||||||
\(619\) | −21.0337 | −0.845416 | −0.422708 | − | 0.906266i | \(-0.638920\pi\) | ||||
−0.422708 | + | 0.906266i | \(0.638920\pi\) | |||||||
\(620\) | 1.14878 | 0.0461359 | ||||||||
\(621\) | −10.3003 | −0.413337 | ||||||||
\(622\) | 17.0201 | 0.682444 | ||||||||
\(623\) | 15.9230 | 0.637943 | ||||||||
\(624\) | −18.5008 | −0.740626 | ||||||||
\(625\) | 23.2053 | 0.928213 | ||||||||
\(626\) | 10.9104 | 0.436068 | ||||||||
\(627\) | 79.6065 | 3.17918 | ||||||||
\(628\) | −4.00822 | −0.159945 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.91312 | 0.0762205 | ||||||||
\(631\) | 32.7576 | 1.30406 | 0.652030 | − | 0.758193i | \(-0.273918\pi\) | ||||
0.652030 | + | 0.758193i | \(0.273918\pi\) | |||||||
\(632\) | 9.30676 | 0.370203 | ||||||||
\(633\) | −12.7941 | −0.508521 | ||||||||
\(634\) | 28.8403 | 1.14540 | ||||||||
\(635\) | −2.35172 | −0.0933252 | ||||||||
\(636\) | 0.268292 | 0.0106385 | ||||||||
\(637\) | 38.0499 | 1.50759 | ||||||||
\(638\) | 34.6153 | 1.37043 | ||||||||
\(639\) | 1.70680 | 0.0675198 | ||||||||
\(640\) | 0.347296 | 0.0137281 | ||||||||
\(641\) | 20.0323 | 0.791229 | 0.395614 | − | 0.918417i | \(-0.370532\pi\) | ||||
0.395614 | + | 0.918417i | \(0.370532\pi\) | |||||||
\(642\) | 10.3755 | 0.409490 | ||||||||
\(643\) | 13.3924 | 0.528143 | 0.264071 | − | 0.964503i | \(-0.414935\pi\) | ||||
0.264071 | + | 0.964503i | \(0.414935\pi\) | |||||||
\(644\) | −1.45719 | −0.0574213 | ||||||||
\(645\) | −6.33210 | −0.249326 | ||||||||
\(646\) | −2.61636 | −0.102939 | ||||||||
\(647\) | −14.7797 | −0.581049 | −0.290525 | − | 0.956867i | \(-0.593830\pi\) | ||||
−0.290525 | + | 0.956867i | \(0.593830\pi\) | |||||||
\(648\) | −4.39126 | −0.172505 | ||||||||
\(649\) | 16.3404 | 0.641419 | ||||||||
\(650\) | −31.0457 | −1.21771 | ||||||||
\(651\) | −9.71278 | −0.380674 | ||||||||
\(652\) | −4.69223 | −0.183762 | ||||||||
\(653\) | 27.1356 | 1.06190 | 0.530949 | − | 0.847404i | \(-0.321836\pi\) | ||||
0.530949 | + | 0.847404i | \(0.321836\pi\) | |||||||
\(654\) | −2.84576 | −0.111278 | ||||||||
\(655\) | −5.26101 | −0.205565 | ||||||||
\(656\) | −1.10049 | −0.0429669 | ||||||||
\(657\) | 72.1822 | 2.81610 | ||||||||
\(658\) | 11.5508 | 0.450297 | ||||||||
\(659\) | 31.6449 | 1.23271 | 0.616355 | − | 0.787468i | \(-0.288609\pi\) | ||||
0.616355 | + | 0.787468i | \(0.288609\pi\) | |||||||
\(660\) | 5.51855 | 0.214809 | ||||||||
\(661\) | −33.9896 | −1.32204 | −0.661022 | − | 0.750367i | \(-0.729877\pi\) | ||||
−0.661022 | + | 0.750367i | \(0.729877\pi\) | |||||||
\(662\) | 3.95955 | 0.153892 | ||||||||
\(663\) | 9.66196 | 0.375239 | ||||||||
\(664\) | −9.46475 | −0.367303 | ||||||||
\(665\) | 1.75703 | 0.0681347 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.14028 | −0.353913 | ||||||||
\(668\) | 0.776993 | 0.0300628 | ||||||||
\(669\) | 32.6571 | 1.26260 | ||||||||
\(670\) | −0.404514 | −0.0156277 | ||||||||
\(671\) | 20.8526 | 0.805004 | ||||||||
\(672\) | −2.93636 | −0.113272 | ||||||||
\(673\) | 39.6475 | 1.52830 | 0.764149 | − | 0.645039i | \(-0.223159\pi\) | ||||
0.764149 | + | 0.645039i | \(0.223159\pi\) | |||||||
\(674\) | 4.27678 | 0.164735 | ||||||||
\(675\) | −34.8300 | −1.34061 | ||||||||
\(676\) | 27.4831 | 1.05704 | ||||||||
\(677\) | 19.3061 | 0.741992 | 0.370996 | − | 0.928634i | \(-0.379016\pi\) | ||||
0.370996 | + | 0.928634i | \(0.379016\pi\) | |||||||
\(678\) | 26.8588 | 1.03151 | ||||||||
\(679\) | 0.938275 | 0.0360077 | ||||||||
\(680\) | −0.181374 | −0.00695536 | ||||||||
\(681\) | 44.0636 | 1.68852 | ||||||||
\(682\) | −18.0761 | −0.692170 | ||||||||
\(683\) | −2.02310 | −0.0774117 | −0.0387058 | − | 0.999251i | \(-0.512324\pi\) | ||||
−0.0387058 | + | 0.999251i | \(0.512324\pi\) | |||||||
\(684\) | −27.3282 | −1.04492 | ||||||||
\(685\) | 2.94567 | 0.112548 | ||||||||
\(686\) | 13.1080 | 0.500466 | ||||||||
\(687\) | −45.2493 | −1.72637 | ||||||||
\(688\) | 6.27037 | 0.239055 | ||||||||
\(689\) | −0.587070 | −0.0223656 | ||||||||
\(690\) | −1.45719 | −0.0554742 | ||||||||
\(691\) | −1.39530 | −0.0530798 | −0.0265399 | − | 0.999648i | \(-0.508449\pi\) | ||||
−0.0265399 | + | 0.999648i | \(0.508449\pi\) | |||||||
\(692\) | 10.7333 | 0.408021 | ||||||||
\(693\) | −30.1031 | −1.14352 | ||||||||
\(694\) | −10.1280 | −0.384455 | ||||||||
\(695\) | 6.36885 | 0.241584 | ||||||||
\(696\) | −18.4184 | −0.698148 | ||||||||
\(697\) | 0.574725 | 0.0217692 | ||||||||
\(698\) | 7.19087 | 0.272178 | ||||||||
\(699\) | 39.5077 | 1.49432 | ||||||||
\(700\) | −4.92742 | −0.186239 | ||||||||
\(701\) | 45.2003 | 1.70719 | 0.853596 | − | 0.520936i | \(-0.174417\pi\) | ||||
0.853596 | + | 0.520936i | \(0.174417\pi\) | |||||||
\(702\) | 45.4178 | 1.71418 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −5.46475 | −0.205960 | ||||||||
\(705\) | 11.5508 | 0.435028 | ||||||||
\(706\) | −34.0550 | −1.28168 | ||||||||
\(707\) | 8.64615 | 0.325172 | ||||||||
\(708\) | −8.69457 | −0.326762 | ||||||||
\(709\) | 28.5445 | 1.07201 | 0.536005 | − | 0.844215i | \(-0.319933\pi\) | ||||
0.536005 | + | 0.844215i | \(0.319933\pi\) | |||||||
\(710\) | 0.108666 | 0.00407817 | ||||||||
\(711\) | −50.7675 | −1.90393 | ||||||||
\(712\) | −15.7678 | −0.590924 | ||||||||
\(713\) | 4.77305 | 0.178752 | ||||||||
\(714\) | 1.53350 | 0.0573896 | ||||||||
\(715\) | −12.0756 | −0.451600 | ||||||||
\(716\) | 11.8976 | 0.444633 | ||||||||
\(717\) | 56.6847 | 2.11693 | ||||||||
\(718\) | −9.87953 | −0.368701 | ||||||||
\(719\) | −17.8740 | −0.666589 | −0.333294 | − | 0.942823i | \(-0.608160\pi\) | ||||
−0.333294 | + | 0.942823i | \(0.608160\pi\) | |||||||
\(720\) | −1.89447 | −0.0706027 | ||||||||
\(721\) | −5.00795 | −0.186506 | ||||||||
\(722\) | −6.09854 | −0.226964 | ||||||||
\(723\) | −4.19769 | −0.156114 | ||||||||
\(724\) | 4.38667 | 0.163029 | ||||||||
\(725\) | −30.9074 | −1.14787 | ||||||||
\(726\) | −54.8499 | −2.03567 | ||||||||
\(727\) | 17.4477 | 0.647099 | 0.323550 | − | 0.946211i | \(-0.395124\pi\) | ||||
0.323550 | + | 0.946211i | \(0.395124\pi\) | |||||||
\(728\) | 6.42527 | 0.238136 | ||||||||
\(729\) | −38.3140 | −1.41904 | ||||||||
\(730\) | 4.59561 | 0.170091 | ||||||||
\(731\) | −3.27466 | −0.121118 | ||||||||
\(732\) | −11.0954 | −0.410098 | ||||||||
\(733\) | −43.8731 | −1.62049 | −0.810244 | − | 0.586092i | \(-0.800666\pi\) | ||||
−0.810244 | + | 0.586092i | \(0.800666\pi\) | |||||||
\(734\) | 33.9039 | 1.25142 | ||||||||
\(735\) | 6.03909 | 0.222755 | ||||||||
\(736\) | 1.44298 | 0.0531891 | ||||||||
\(737\) | 6.36507 | 0.234460 | ||||||||
\(738\) | 6.00307 | 0.220976 | ||||||||
\(739\) | 39.5017 | 1.45309 | 0.726546 | − | 0.687118i | \(-0.241124\pi\) | ||||
0.726546 | + | 0.687118i | \(0.241124\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 92.6863 | 3.40492 | ||||||||
\(742\) | −0.0931767 | −0.00342062 | ||||||||
\(743\) | 19.8910 | 0.729730 | 0.364865 | − | 0.931060i | \(-0.381115\pi\) | ||||
0.364865 | + | 0.931060i | \(0.381115\pi\) | |||||||
\(744\) | 9.61810 | 0.352617 | ||||||||
\(745\) | −1.89378 | −0.0693826 | ||||||||
\(746\) | −31.3540 | −1.14795 | ||||||||
\(747\) | 51.6293 | 1.88902 | ||||||||
\(748\) | 2.85393 | 0.104350 | ||||||||
\(749\) | −3.60339 | −0.131665 | ||||||||
\(750\) | −9.97664 | −0.364296 | ||||||||
\(751\) | −33.2367 | −1.21283 | −0.606413 | − | 0.795150i | \(-0.707392\pi\) | ||||
−0.606413 | + | 0.795150i | \(0.707392\pi\) | |||||||
\(752\) | −11.4382 | −0.417108 | ||||||||
\(753\) | −29.2893 | −1.06736 | ||||||||
\(754\) | 40.3028 | 1.46774 | ||||||||
\(755\) | 5.40232 | 0.196611 | ||||||||
\(756\) | 7.20847 | 0.262170 | ||||||||
\(757\) | −43.4094 | −1.57774 | −0.788871 | − | 0.614558i | \(-0.789334\pi\) | ||||
−0.788871 | + | 0.614558i | \(0.789334\pi\) | |||||||
\(758\) | −10.6544 | −0.386986 | ||||||||
\(759\) | 22.9290 | 0.832271 | ||||||||
\(760\) | −1.73990 | −0.0631128 | ||||||||
\(761\) | 25.2861 | 0.916619 | 0.458309 | − | 0.888793i | \(-0.348455\pi\) | ||||
0.458309 | + | 0.888793i | \(0.348455\pi\) | |||||||
\(762\) | −19.6897 | −0.713284 | ||||||||
\(763\) | 0.988323 | 0.0357797 | ||||||||
\(764\) | 10.4903 | 0.379527 | ||||||||
\(765\) | 0.989375 | 0.0357709 | ||||||||
\(766\) | 19.4015 | 0.701006 | ||||||||
\(767\) | 19.0253 | 0.686963 | ||||||||
\(768\) | 2.90773 | 0.104924 | ||||||||
\(769\) | −27.7983 | −1.00243 | −0.501216 | − | 0.865322i | \(-0.667114\pi\) | ||||
−0.501216 | + | 0.865322i | \(0.667114\pi\) | |||||||
\(770\) | −1.91657 | −0.0690684 | ||||||||
\(771\) | 20.3105 | 0.731465 | ||||||||
\(772\) | −9.82949 | −0.353771 | ||||||||
\(773\) | −0.986707 | −0.0354894 | −0.0177447 | − | 0.999843i | \(-0.505649\pi\) | ||||
−0.0177447 | + | 0.999843i | \(0.505649\pi\) | |||||||
\(774\) | −34.2042 | −1.22945 | ||||||||
\(775\) | 16.1399 | 0.579761 | ||||||||
\(776\) | −0.929128 | −0.0333538 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.6990 | 0.670392 | ||||||||
\(779\) | 5.51328 | 0.197534 | ||||||||
\(780\) | 6.42527 | 0.230062 | ||||||||
\(781\) | −1.70988 | −0.0611842 | ||||||||
\(782\) | −0.753590 | −0.0269483 | ||||||||
\(783\) | 45.2154 | 1.61587 | ||||||||
\(784\) | −5.98021 | −0.213579 | ||||||||
\(785\) | 1.39204 | 0.0496841 | ||||||||
\(786\) | −44.0477 | −1.57113 | ||||||||
\(787\) | 25.7979 | 0.919597 | 0.459799 | − | 0.888023i | \(-0.347922\pi\) | ||||
0.459799 | + | 0.888023i | \(0.347922\pi\) | |||||||
\(788\) | −12.0631 | −0.429730 | ||||||||
\(789\) | 7.74283 | 0.275652 | ||||||||
\(790\) | −3.23220 | −0.114997 | ||||||||
\(791\) | −9.32796 | −0.331664 | ||||||||
\(792\) | 29.8097 | 1.05924 | ||||||||
\(793\) | 24.2787 | 0.862163 | ||||||||
\(794\) | 23.8632 | 0.846872 | ||||||||
\(795\) | −0.0931767 | −0.00330464 | ||||||||
\(796\) | 9.29990 | 0.329626 | ||||||||
\(797\) | −15.1068 | −0.535112 | −0.267556 | − | 0.963542i | \(-0.586216\pi\) | ||||
−0.267556 | + | 0.963542i | \(0.586216\pi\) | |||||||
\(798\) | 14.7107 | 0.520753 | ||||||||
\(799\) | 5.97353 | 0.211328 | ||||||||
\(800\) | 4.87939 | 0.172512 | ||||||||
\(801\) | 86.0119 | 3.03908 | ||||||||
\(802\) | 17.8350 | 0.629776 | ||||||||
\(803\) | −72.3125 | −2.55185 | ||||||||
\(804\) | −3.38678 | −0.119443 | ||||||||
\(805\) | 0.506077 | 0.0178369 | ||||||||
\(806\) | −21.0461 | −0.741318 | ||||||||
\(807\) | 7.02227 | 0.247196 | ||||||||
\(808\) | −8.56186 | −0.301205 | ||||||||
\(809\) | 42.6899 | 1.50090 | 0.750448 | − | 0.660929i | \(-0.229838\pi\) | ||||
0.750448 | + | 0.660929i | \(0.229838\pi\) | |||||||
\(810\) | 1.52507 | 0.0535855 | ||||||||
\(811\) | 20.4180 | 0.716974 | 0.358487 | − | 0.933535i | \(-0.383293\pi\) | ||||
0.358487 | + | 0.933535i | \(0.383293\pi\) | |||||||
\(812\) | 6.39665 | 0.224478 | ||||||||
\(813\) | −73.4219 | −2.57502 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.62960 | 0.0570822 | ||||||||
\(816\) | −1.51855 | −0.0531598 | ||||||||
\(817\) | −31.4136 | −1.09902 | ||||||||
\(818\) | −9.98668 | −0.349176 | ||||||||
\(819\) | −35.0492 | −1.22472 | ||||||||
\(820\) | 0.382196 | 0.0133469 | ||||||||
\(821\) | 13.4462 | 0.469275 | 0.234637 | − | 0.972083i | \(-0.424610\pi\) | ||||
0.234637 | + | 0.972083i | \(0.424610\pi\) | |||||||
\(822\) | 24.6626 | 0.860206 | ||||||||
\(823\) | −40.7832 | −1.42161 | −0.710807 | − | 0.703387i | \(-0.751670\pi\) | ||||
−0.710807 | + | 0.703387i | \(0.751670\pi\) | |||||||
\(824\) | 4.95913 | 0.172759 | ||||||||
\(825\) | 77.5335 | 2.69937 | ||||||||
\(826\) | 3.01959 | 0.105065 | ||||||||
\(827\) | 40.4427 | 1.40633 | 0.703165 | − | 0.711026i | \(-0.251769\pi\) | ||||
0.703165 | + | 0.711026i | \(0.251769\pi\) | |||||||
\(828\) | −7.87134 | −0.273548 | ||||||||
\(829\) | −2.65519 | −0.0922186 | −0.0461093 | − | 0.998936i | \(-0.514682\pi\) | ||||
−0.0461093 | + | 0.998936i | \(0.514682\pi\) | |||||||
\(830\) | 3.28707 | 0.114096 | ||||||||
\(831\) | 51.5598 | 1.78859 | ||||||||
\(832\) | −6.36263 | −0.220585 | ||||||||
\(833\) | 3.12313 | 0.108210 | ||||||||
\(834\) | 53.3231 | 1.84643 | ||||||||
\(835\) | −0.269847 | −0.00933844 | ||||||||
\(836\) | 27.3775 | 0.946872 | ||||||||
\(837\) | −23.6115 | −0.816133 | ||||||||
\(838\) | −36.0291 | −1.24460 | ||||||||
\(839\) | −43.1281 | −1.48895 | −0.744474 | − | 0.667651i | \(-0.767300\pi\) | ||||
−0.744474 | + | 0.667651i | \(0.767300\pi\) | |||||||
\(840\) | 1.01979 | 0.0351860 | ||||||||
\(841\) | 11.1232 | 0.383559 | ||||||||
\(842\) | 22.3336 | 0.769665 | ||||||||
\(843\) | −57.4257 | −1.97785 | ||||||||
\(844\) | −4.40004 | −0.151455 | ||||||||
\(845\) | −9.54479 | −0.328351 | ||||||||
\(846\) | 62.3943 | 2.14516 | ||||||||
\(847\) | 19.0492 | 0.654537 | ||||||||
\(848\) | 0.0922684 | 0.00316851 | ||||||||
\(849\) | −70.8015 | −2.42990 | ||||||||
\(850\) | −2.54823 | −0.0874036 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0.909807 | 0.0311695 | ||||||||
\(853\) | 44.9180 | 1.53796 | 0.768981 | − | 0.639271i | \(-0.220764\pi\) | ||||
0.768981 | + | 0.639271i | \(0.220764\pi\) | |||||||
\(854\) | 3.85340 | 0.131861 | ||||||||
\(855\) | 9.49099 | 0.324585 | ||||||||
\(856\) | 3.56826 | 0.121961 | ||||||||
\(857\) | 1.14287 | 0.0390395 | 0.0195198 | − | 0.999809i | \(-0.493786\pi\) | ||||
0.0195198 | + | 0.999809i | \(0.493786\pi\) | |||||||
\(858\) | −101.102 | −3.45158 | ||||||||
\(859\) | −20.6966 | −0.706160 | −0.353080 | − | 0.935593i | \(-0.614866\pi\) | ||||
−0.353080 | + | 0.935593i | \(0.614866\pi\) | |||||||
\(860\) | −2.17768 | −0.0742581 | ||||||||
\(861\) | −3.23143 | −0.110127 | ||||||||
\(862\) | 31.2560 | 1.06458 | ||||||||
\(863\) | −11.0475 | −0.376061 | −0.188030 | − | 0.982163i | \(-0.560210\pi\) | ||||
−0.188030 | + | 0.982163i | \(0.560210\pi\) | |||||||
\(864\) | −7.13820 | −0.242847 | ||||||||
\(865\) | −3.72765 | −0.126744 | ||||||||
\(866\) | −5.42187 | −0.184243 | ||||||||
\(867\) | −48.6384 | −1.65185 | ||||||||
\(868\) | −3.34033 | −0.113378 | ||||||||
\(869\) | 50.8591 | 1.72528 | ||||||||
\(870\) | 6.39665 | 0.216867 | ||||||||
\(871\) | 7.41088 | 0.251108 | ||||||||
\(872\) | −0.978688 | −0.0331426 | ||||||||
\(873\) | 5.06830 | 0.171536 | ||||||||
\(874\) | −7.22912 | −0.244529 | ||||||||
\(875\) | 3.46485 | 0.117133 | ||||||||
\(876\) | 38.4767 | 1.30001 | ||||||||
\(877\) | −12.3680 | −0.417638 | −0.208819 | − | 0.977954i | \(-0.566962\pi\) | ||||
−0.208819 | + | 0.977954i | \(0.566962\pi\) | |||||||
\(878\) | −15.4292 | −0.520712 | ||||||||
\(879\) | −67.6006 | −2.28011 | ||||||||
\(880\) | 1.89789 | 0.0639778 | ||||||||
\(881\) | 17.9831 | 0.605865 | 0.302933 | − | 0.953012i | \(-0.402034\pi\) | ||||
0.302933 | + | 0.953012i | \(0.402034\pi\) | |||||||
\(882\) | 32.6215 | 1.09842 | ||||||||
\(883\) | 10.7268 | 0.360986 | 0.180493 | − | 0.983576i | \(-0.442231\pi\) | ||||
0.180493 | + | 0.983576i | \(0.442231\pi\) | |||||||
\(884\) | 3.32285 | 0.111760 | ||||||||
\(885\) | 3.01959 | 0.101502 | ||||||||
\(886\) | 8.45523 | 0.284059 | ||||||||
\(887\) | −16.7444 | −0.562222 | −0.281111 | − | 0.959675i | \(-0.590703\pi\) | ||||
−0.281111 | + | 0.959675i | \(0.590703\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.83817 | 0.229345 | ||||||||
\(890\) | 5.47610 | 0.183559 | ||||||||
\(891\) | −23.9971 | −0.803934 | ||||||||
\(892\) | 11.2311 | 0.376046 | ||||||||
\(893\) | 57.3036 | 1.91759 | ||||||||
\(894\) | −15.8556 | −0.530291 | ||||||||
\(895\) | −4.13199 | −0.138117 | ||||||||
\(896\) | −1.00984 | −0.0337365 | ||||||||
\(897\) | 26.6964 | 0.891367 | ||||||||
\(898\) | 36.3945 | 1.21450 | ||||||||
\(899\) | −20.9524 | −0.698800 | ||||||||
\(900\) | −26.6166 | −0.887219 | ||||||||
\(901\) | −0.0481866 | −0.00160533 | ||||||||
\(902\) | −6.01390 | −0.200241 | ||||||||
\(903\) | 18.4120 | 0.612714 | ||||||||
\(904\) | 9.23702 | 0.307219 | ||||||||
\(905\) | −1.52348 | −0.0506421 | ||||||||
\(906\) | 45.2308 | 1.50269 | ||||||||
\(907\) | −43.3824 | −1.44049 | −0.720244 | − | 0.693721i | \(-0.755970\pi\) | ||||
−0.720244 | + | 0.693721i | \(0.755970\pi\) | |||||||
\(908\) | 15.1539 | 0.502901 | ||||||||
\(909\) | 46.7041 | 1.54908 | ||||||||
\(910\) | −2.23147 | −0.0739726 | ||||||||
\(911\) | −10.1061 | −0.334831 | −0.167416 | − | 0.985886i | \(-0.553542\pi\) | ||||
−0.167416 | + | 0.985886i | \(0.553542\pi\) | |||||||
\(912\) | −14.5673 | −0.482371 | ||||||||
\(913\) | −51.7225 | −1.71176 | ||||||||
\(914\) | 13.0415 | 0.431373 | ||||||||
\(915\) | 3.85340 | 0.127389 | ||||||||
\(916\) | −15.5617 | −0.514173 | ||||||||
\(917\) | 15.2976 | 0.505171 | ||||||||
\(918\) | 3.72788 | 0.123039 | ||||||||
\(919\) | −2.82736 | −0.0932661 | −0.0466330 | − | 0.998912i | \(-0.514849\pi\) | ||||
−0.0466330 | + | 0.998912i | \(0.514849\pi\) | |||||||
\(920\) | −0.501143 | −0.0165222 | ||||||||
\(921\) | −31.0260 | −1.02234 | ||||||||
\(922\) | 17.6483 | 0.581216 | ||||||||
\(923\) | −1.99082 | −0.0655286 | ||||||||
\(924\) | −16.0465 | −0.527889 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 26.4940 | 0.870646 | ||||||||
\(927\) | −27.0516 | −0.888490 | ||||||||
\(928\) | −6.33429 | −0.207933 | ||||||||
\(929\) | 33.4655 | 1.09797 | 0.548985 | − | 0.835833i | \(-0.315015\pi\) | ||||
0.548985 | + | 0.835833i | \(0.315015\pi\) | |||||||
\(930\) | −3.34033 | −0.109534 | ||||||||
\(931\) | 29.9599 | 0.981897 | ||||||||
\(932\) | 13.5871 | 0.445061 | ||||||||
\(933\) | −49.4899 | −1.62023 | ||||||||
\(934\) | −19.0975 | −0.624890 | ||||||||
\(935\) | −0.991161 | −0.0324144 | ||||||||
\(936\) | 34.7076 | 1.13445 | ||||||||
\(937\) | 46.0579 | 1.50465 | 0.752323 | − | 0.658794i | \(-0.228933\pi\) | ||||
0.752323 | + | 0.658794i | \(0.228933\pi\) | |||||||
\(938\) | 1.17622 | 0.0384048 | ||||||||
\(939\) | −31.7246 | −1.03529 | ||||||||
\(940\) | 3.97244 | 0.129567 | ||||||||
\(941\) | −17.5337 | −0.571583 | −0.285791 | − | 0.958292i | \(-0.592256\pi\) | ||||
−0.285791 | + | 0.958292i | \(0.592256\pi\) | |||||||
\(942\) | 11.6548 | 0.379735 | ||||||||
\(943\) | 1.58799 | 0.0517120 | ||||||||
\(944\) | −2.99016 | −0.0973213 | ||||||||
\(945\) | −2.50348 | −0.0814381 | ||||||||
\(946\) | 34.2660 | 1.11408 | ||||||||
\(947\) | −26.1918 | −0.851118 | −0.425559 | − | 0.904931i | \(-0.639923\pi\) | ||||
−0.425559 | + | 0.904931i | \(0.639923\pi\) | |||||||
\(948\) | −27.0616 | −0.878919 | ||||||||
\(949\) | −84.1938 | −2.73305 | ||||||||
\(950\) | −24.4450 | −0.793099 | ||||||||
\(951\) | −83.8599 | −2.71934 | ||||||||
\(952\) | 0.527386 | 0.0170927 | ||||||||
\(953\) | −25.9695 | −0.841235 | −0.420617 | − | 0.907238i | \(-0.638187\pi\) | ||||
−0.420617 | + | 0.907238i | \(0.638187\pi\) | |||||||
\(954\) | −0.503315 | −0.0162954 | ||||||||
\(955\) | −3.64325 | −0.117893 | ||||||||
\(956\) | 19.4945 | 0.630496 | ||||||||
\(957\) | −100.652 | −3.25362 | ||||||||
\(958\) | 19.1825 | 0.619759 | ||||||||
\(959\) | −8.56522 | −0.276586 | ||||||||
\(960\) | −1.00984 | −0.0325926 | ||||||||
\(961\) | −20.0587 | −0.647054 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.4645 | −0.627235 | ||||||||
\(964\) | −1.44363 | −0.0464962 | ||||||||
\(965\) | 3.41374 | 0.109892 | ||||||||
\(966\) | 4.23712 | 0.136327 | ||||||||
\(967\) | −33.7691 | −1.08594 | −0.542970 | − | 0.839752i | \(-0.682700\pi\) | ||||
−0.542970 | + | 0.839752i | \(0.682700\pi\) | |||||||
\(968\) | −18.8635 | −0.606295 | ||||||||
\(969\) | 7.60768 | 0.244394 | ||||||||
\(970\) | 0.322683 | 0.0103607 | ||||||||
\(971\) | −13.7944 | −0.442683 | −0.221342 | − | 0.975196i | \(-0.571044\pi\) | ||||
−0.221342 | + | 0.975196i | \(0.571044\pi\) | |||||||
\(972\) | −8.64599 | −0.277320 | ||||||||
\(973\) | −18.5189 | −0.593689 | ||||||||
\(974\) | −35.7577 | −1.14575 | ||||||||
\(975\) | 90.2727 | 2.89104 | ||||||||
\(976\) | −3.81583 | −0.122142 | ||||||||
\(977\) | 38.9852 | 1.24725 | 0.623624 | − | 0.781724i | \(-0.285660\pi\) | ||||
0.623624 | + | 0.781724i | \(0.285660\pi\) | |||||||
\(978\) | 13.6438 | 0.436279 | ||||||||
\(979\) | −86.1671 | −2.75391 | ||||||||
\(980\) | 2.07691 | 0.0663443 | ||||||||
\(981\) | 5.33865 | 0.170450 | ||||||||
\(982\) | −29.7732 | −0.950100 | ||||||||
\(983\) | 12.1963 | 0.389001 | 0.194501 | − | 0.980902i | \(-0.437691\pi\) | ||||
0.194501 | + | 0.980902i | \(0.437691\pi\) | |||||||
\(984\) | 3.19993 | 0.102010 | ||||||||
\(985\) | 4.18947 | 0.133488 | ||||||||
\(986\) | 3.30805 | 0.105350 | ||||||||
\(987\) | −33.5866 | −1.06907 | ||||||||
\(988\) | 31.8758 | 1.01410 | ||||||||
\(989\) | −9.04804 | −0.287711 | ||||||||
\(990\) | −10.3528 | −0.329033 | ||||||||
\(991\) | −26.4606 | −0.840549 | −0.420275 | − | 0.907397i | \(-0.638066\pi\) | ||||
−0.420275 | + | 0.907397i | \(0.638066\pi\) | |||||||
\(992\) | 3.30777 | 0.105022 | ||||||||
\(993\) | −11.5133 | −0.365364 | ||||||||
\(994\) | −0.315973 | −0.0100220 | ||||||||
\(995\) | −3.22982 | −0.102392 | ||||||||
\(996\) | 27.5209 | 0.872035 | ||||||||
\(997\) | 13.3432 | 0.422584 | 0.211292 | − | 0.977423i | \(-0.432233\pi\) | ||||
0.211292 | + | 0.977423i | \(0.432233\pi\) | |||||||
\(998\) | 24.8179 | 0.785597 | ||||||||
\(999\) | 0 | 0 |
(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 | 2738.2.a.q.1.6 | 6 | ||
37.3 | even | 18 | 74.2.f.b.9.2 | ✓ | 12 | ||
37.25 | even | 18 | 74.2.f.b.33.2 | yes | 12 | ||
37.36 | even | 2 | 2738.2.a.t.1.6 | 6 | |||
111.62 | odd | 18 | 666.2.x.g.181.2 | 12 | |||
111.77 | odd | 18 | 666.2.x.g.379.2 | 12 | |||
148.3 | odd | 18 | 592.2.bc.d.305.1 | 12 | |||
148.99 | odd | 18 | 592.2.bc.d.33.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.f.b.9.2 | ✓ | 12 | 37.3 | even | 18 | ||
74.2.f.b.33.2 | yes | 12 | 37.25 | even | 18 | ||
592.2.bc.d.33.1 | 12 | 148.99 | odd | 18 | |||
592.2.bc.d.305.1 | 12 | 148.3 | odd | 18 | |||
666.2.x.g.181.2 | 12 | 111.62 | odd | 18 | |||
666.2.x.g.379.2 | 12 | 111.77 | odd | 18 | |||
2738.2.a.q.1.6 | 6 | 1.1 | even | 1 | trivial | ||
2738.2.a.t.1.6 | 6 | 37.36 | even | 2 |