Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6013,2,Mod(1,6013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6013, 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("6013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6013 = 7 \cdot 859 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6013.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: | \(48.0140467354\) |
Analytic rank: | \(0\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64232 | −1.86840 | −0.934201 | − | 0.356747i | \(-0.883886\pi\) | ||||
−0.934201 | + | 0.356747i | \(0.883886\pi\) | |||||||
\(3\) | 0.320634 | 0.185118 | 0.0925590 | − | 0.995707i | \(-0.470495\pi\) | ||||
0.0925590 | + | 0.995707i | \(0.470495\pi\) | |||||||
\(4\) | 4.98185 | 2.49093 | ||||||||
\(5\) | 3.17576 | 1.42024 | 0.710121 | − | 0.704080i | \(-0.248640\pi\) | ||||
0.710121 | + | 0.704080i | \(0.248640\pi\) | |||||||
\(6\) | −0.847217 | −0.345875 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −7.87900 | −2.78565 | ||||||||
\(9\) | −2.89719 | −0.965731 | ||||||||
\(10\) | −8.39136 | −2.65358 | ||||||||
\(11\) | −2.25492 | −0.679884 | −0.339942 | − | 0.940446i | \(-0.610407\pi\) | ||||
−0.339942 | + | 0.940446i | \(0.610407\pi\) | |||||||
\(12\) | 1.59735 | 0.461115 | ||||||||
\(13\) | −4.14521 | −1.14967 | −0.574837 | − | 0.818268i | \(-0.694935\pi\) | ||||
−0.574837 | + | 0.818268i | \(0.694935\pi\) | |||||||
\(14\) | −2.64232 | −0.706189 | ||||||||
\(15\) | 1.01826 | 0.262912 | ||||||||
\(16\) | 10.8551 | 2.71378 | ||||||||
\(17\) | −4.34057 | −1.05274 | −0.526371 | − | 0.850255i | \(-0.676448\pi\) | ||||
−0.526371 | + | 0.850255i | \(0.676448\pi\) | |||||||
\(18\) | 7.65531 | 1.80437 | ||||||||
\(19\) | −3.45874 | −0.793489 | −0.396744 | − | 0.917929i | \(-0.629860\pi\) | ||||
−0.396744 | + | 0.917929i | \(0.629860\pi\) | |||||||
\(20\) | 15.8211 | 3.53772 | ||||||||
\(21\) | 0.320634 | 0.0699680 | ||||||||
\(22\) | 5.95822 | 1.27030 | ||||||||
\(23\) | −0.0874563 | −0.0182359 | −0.00911795 | − | 0.999958i | \(-0.502902\pi\) | ||||
−0.00911795 | + | 0.999958i | \(0.502902\pi\) | |||||||
\(24\) | −2.52627 | −0.515674 | ||||||||
\(25\) | 5.08544 | 1.01709 | ||||||||
\(26\) | 10.9530 | 2.14805 | ||||||||
\(27\) | −1.89084 | −0.363892 | ||||||||
\(28\) | 4.98185 | 0.941481 | ||||||||
\(29\) | 8.08271 | 1.50092 | 0.750461 | − | 0.660915i | \(-0.229832\pi\) | ||||
0.750461 | + | 0.660915i | \(0.229832\pi\) | |||||||
\(30\) | −2.69056 | −0.491226 | ||||||||
\(31\) | −1.22874 | −0.220689 | −0.110345 | − | 0.993893i | \(-0.535195\pi\) | ||||
−0.110345 | + | 0.993893i | \(0.535195\pi\) | |||||||
\(32\) | −12.9247 | −2.28479 | ||||||||
\(33\) | −0.723004 | −0.125859 | ||||||||
\(34\) | 11.4692 | 1.96695 | ||||||||
\(35\) | 3.17576 | 0.536801 | ||||||||
\(36\) | −14.4334 | −2.40556 | ||||||||
\(37\) | 2.47866 | 0.407490 | 0.203745 | − | 0.979024i | \(-0.434689\pi\) | ||||
0.203745 | + | 0.979024i | \(0.434689\pi\) | |||||||
\(38\) | 9.13908 | 1.48256 | ||||||||
\(39\) | −1.32909 | −0.212825 | ||||||||
\(40\) | −25.0218 | −3.95629 | ||||||||
\(41\) | 0.513039 | 0.0801232 | 0.0400616 | − | 0.999197i | \(-0.487245\pi\) | ||||
0.0400616 | + | 0.999197i | \(0.487245\pi\) | |||||||
\(42\) | −0.847217 | −0.130728 | ||||||||
\(43\) | 1.83803 | 0.280297 | 0.140149 | − | 0.990130i | \(-0.455242\pi\) | ||||
0.140149 | + | 0.990130i | \(0.455242\pi\) | |||||||
\(44\) | −11.2337 | −1.69354 | ||||||||
\(45\) | −9.20079 | −1.37157 | ||||||||
\(46\) | 0.231087 | 0.0340720 | ||||||||
\(47\) | 3.62406 | 0.528623 | 0.264312 | − | 0.964437i | \(-0.414855\pi\) | ||||
0.264312 | + | 0.964437i | \(0.414855\pi\) | |||||||
\(48\) | 3.48052 | 0.502370 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −13.4373 | −1.90033 | ||||||||
\(51\) | −1.39173 | −0.194882 | ||||||||
\(52\) | −20.6508 | −2.86375 | ||||||||
\(53\) | 0.723055 | 0.0993193 | 0.0496596 | − | 0.998766i | \(-0.484186\pi\) | ||||
0.0496596 | + | 0.998766i | \(0.484186\pi\) | |||||||
\(54\) | 4.99620 | 0.679897 | ||||||||
\(55\) | −7.16108 | −0.965600 | ||||||||
\(56\) | −7.87900 | −1.05288 | ||||||||
\(57\) | −1.10899 | −0.146889 | ||||||||
\(58\) | −21.3571 | −2.80433 | ||||||||
\(59\) | −6.53732 | −0.851086 | −0.425543 | − | 0.904938i | \(-0.639917\pi\) | ||||
−0.425543 | + | 0.904938i | \(0.639917\pi\) | |||||||
\(60\) | 5.07280 | 0.654895 | ||||||||
\(61\) | −0.324330 | −0.0415261 | −0.0207631 | − | 0.999784i | \(-0.506610\pi\) | ||||
−0.0207631 | + | 0.999784i | \(0.506610\pi\) | |||||||
\(62\) | 3.24673 | 0.412336 | ||||||||
\(63\) | −2.89719 | −0.365012 | ||||||||
\(64\) | 12.4410 | 1.55512 | ||||||||
\(65\) | −13.1642 | −1.63282 | ||||||||
\(66\) | 1.91041 | 0.235155 | ||||||||
\(67\) | 7.47223 | 0.912879 | 0.456439 | − | 0.889755i | \(-0.349125\pi\) | ||||
0.456439 | + | 0.889755i | \(0.349125\pi\) | |||||||
\(68\) | −21.6241 | −2.62230 | ||||||||
\(69\) | −0.0280415 | −0.00337579 | ||||||||
\(70\) | −8.39136 | −1.00296 | ||||||||
\(71\) | −6.11028 | −0.725156 | −0.362578 | − | 0.931953i | \(-0.618103\pi\) | ||||
−0.362578 | + | 0.931953i | \(0.618103\pi\) | |||||||
\(72\) | 22.8270 | 2.69019 | ||||||||
\(73\) | −1.38985 | −0.162670 | −0.0813349 | − | 0.996687i | \(-0.525918\pi\) | ||||
−0.0813349 | + | 0.996687i | \(0.525918\pi\) | |||||||
\(74\) | −6.54942 | −0.761355 | ||||||||
\(75\) | 1.63056 | 0.188281 | ||||||||
\(76\) | −17.2309 | −1.97652 | ||||||||
\(77\) | −2.25492 | −0.256972 | ||||||||
\(78\) | 3.51189 | 0.397643 | ||||||||
\(79\) | 4.31579 | 0.485565 | 0.242782 | − | 0.970081i | \(-0.421940\pi\) | ||||
0.242782 | + | 0.970081i | \(0.421940\pi\) | |||||||
\(80\) | 34.4733 | 3.85423 | ||||||||
\(81\) | 8.08531 | 0.898368 | ||||||||
\(82\) | −1.35561 | −0.149702 | ||||||||
\(83\) | 16.0073 | 1.75703 | 0.878515 | − | 0.477715i | \(-0.158535\pi\) | ||||
0.878515 | + | 0.477715i | \(0.158535\pi\) | |||||||
\(84\) | 1.59735 | 0.174285 | ||||||||
\(85\) | −13.7846 | −1.49515 | ||||||||
\(86\) | −4.85667 | −0.523708 | ||||||||
\(87\) | 2.59159 | 0.277848 | ||||||||
\(88\) | 17.7665 | 1.89392 | ||||||||
\(89\) | 0.168935 | 0.0179071 | 0.00895355 | − | 0.999960i | \(-0.497150\pi\) | ||||
0.00895355 | + | 0.999960i | \(0.497150\pi\) | |||||||
\(90\) | 24.3114 | 2.56265 | ||||||||
\(91\) | −4.14521 | −0.434536 | ||||||||
\(92\) | −0.435694 | −0.0454243 | ||||||||
\(93\) | −0.393977 | −0.0408535 | ||||||||
\(94\) | −9.57591 | −0.987680 | ||||||||
\(95\) | −10.9841 | −1.12695 | ||||||||
\(96\) | −4.14410 | −0.422956 | ||||||||
\(97\) | 4.41054 | 0.447822 | 0.223911 | − | 0.974610i | \(-0.428117\pi\) | ||||
0.223911 | + | 0.974610i | \(0.428117\pi\) | |||||||
\(98\) | −2.64232 | −0.266915 | ||||||||
\(99\) | 6.53294 | 0.656585 | ||||||||
\(100\) | 25.3349 | 2.53349 | ||||||||
\(101\) | 14.1880 | 1.41176 | 0.705881 | − | 0.708331i | \(-0.250552\pi\) | ||||
0.705881 | + | 0.708331i | \(0.250552\pi\) | |||||||
\(102\) | 3.67740 | 0.364117 | ||||||||
\(103\) | 8.06600 | 0.794766 | 0.397383 | − | 0.917653i | \(-0.369918\pi\) | ||||
0.397383 | + | 0.917653i | \(0.369918\pi\) | |||||||
\(104\) | 32.6601 | 3.20259 | ||||||||
\(105\) | 1.01826 | 0.0993716 | ||||||||
\(106\) | −1.91054 | −0.185568 | ||||||||
\(107\) | −3.05395 | −0.295236 | −0.147618 | − | 0.989044i | \(-0.547161\pi\) | ||||
−0.147618 | + | 0.989044i | \(0.547161\pi\) | |||||||
\(108\) | −9.41988 | −0.906429 | ||||||||
\(109\) | −10.6433 | −1.01945 | −0.509724 | − | 0.860338i | \(-0.670252\pi\) | ||||
−0.509724 | + | 0.860338i | \(0.670252\pi\) | |||||||
\(110\) | 18.9219 | 1.80413 | ||||||||
\(111\) | 0.794744 | 0.0754337 | ||||||||
\(112\) | 10.8551 | 1.02571 | ||||||||
\(113\) | −4.99844 | −0.470214 | −0.235107 | − | 0.971969i | \(-0.575544\pi\) | ||||
−0.235107 | + | 0.971969i | \(0.575544\pi\) | |||||||
\(114\) | 2.93030 | 0.274448 | ||||||||
\(115\) | −0.277740 | −0.0258994 | ||||||||
\(116\) | 40.2669 | 3.73868 | ||||||||
\(117\) | 12.0095 | 1.11028 | ||||||||
\(118\) | 17.2737 | 1.59017 | ||||||||
\(119\) | −4.34057 | −0.397899 | ||||||||
\(120\) | −8.02283 | −0.732381 | ||||||||
\(121\) | −5.91533 | −0.537758 | ||||||||
\(122\) | 0.856982 | 0.0775875 | ||||||||
\(123\) | 0.164498 | 0.0148323 | ||||||||
\(124\) | −6.12142 | −0.549720 | ||||||||
\(125\) | 0.271324 | 0.0242680 | ||||||||
\(126\) | 7.65531 | 0.681989 | ||||||||
\(127\) | 6.43874 | 0.571346 | 0.285673 | − | 0.958327i | \(-0.407783\pi\) | ||||
0.285673 | + | 0.958327i | \(0.407783\pi\) | |||||||
\(128\) | −7.02359 | −0.620803 | ||||||||
\(129\) | 0.589335 | 0.0518881 | ||||||||
\(130\) | 34.7840 | 3.05076 | ||||||||
\(131\) | 7.45692 | 0.651514 | 0.325757 | − | 0.945454i | \(-0.394381\pi\) | ||||
0.325757 | + | 0.945454i | \(0.394381\pi\) | |||||||
\(132\) | −3.60190 | −0.313505 | ||||||||
\(133\) | −3.45874 | −0.299910 | ||||||||
\(134\) | −19.7440 | −1.70562 | ||||||||
\(135\) | −6.00485 | −0.516815 | ||||||||
\(136\) | 34.1993 | 2.93257 | ||||||||
\(137\) | 18.5423 | 1.58418 | 0.792088 | − | 0.610407i | \(-0.208994\pi\) | ||||
0.792088 | + | 0.610407i | \(0.208994\pi\) | |||||||
\(138\) | 0.0740945 | 0.00630734 | ||||||||
\(139\) | −12.4252 | −1.05390 | −0.526948 | − | 0.849898i | \(-0.676664\pi\) | ||||
−0.526948 | + | 0.849898i | \(0.676664\pi\) | |||||||
\(140\) | 15.8211 | 1.33713 | ||||||||
\(141\) | 1.16200 | 0.0978577 | ||||||||
\(142\) | 16.1453 | 1.35488 | ||||||||
\(143\) | 9.34712 | 0.781645 | ||||||||
\(144\) | −31.4494 | −2.62079 | ||||||||
\(145\) | 25.6687 | 2.13167 | ||||||||
\(146\) | 3.67243 | 0.303933 | ||||||||
\(147\) | 0.320634 | 0.0264454 | ||||||||
\(148\) | 12.3483 | 1.01503 | ||||||||
\(149\) | 16.0116 | 1.31172 | 0.655860 | − | 0.754882i | \(-0.272306\pi\) | ||||
0.655860 | + | 0.754882i | \(0.272306\pi\) | |||||||
\(150\) | −4.30847 | −0.351785 | ||||||||
\(151\) | 3.72561 | 0.303185 | 0.151593 | − | 0.988443i | \(-0.451560\pi\) | ||||
0.151593 | + | 0.988443i | \(0.451560\pi\) | |||||||
\(152\) | 27.2514 | 2.21038 | ||||||||
\(153\) | 12.5755 | 1.01667 | ||||||||
\(154\) | 5.95822 | 0.480127 | ||||||||
\(155\) | −3.90219 | −0.313432 | ||||||||
\(156\) | −6.62135 | −0.530132 | ||||||||
\(157\) | −13.5703 | −1.08303 | −0.541515 | − | 0.840691i | \(-0.682149\pi\) | ||||
−0.541515 | + | 0.840691i | \(0.682149\pi\) | |||||||
\(158\) | −11.4037 | −0.907230 | ||||||||
\(159\) | 0.231836 | 0.0183858 | ||||||||
\(160\) | −41.0458 | −3.24495 | ||||||||
\(161\) | −0.0874563 | −0.00689252 | ||||||||
\(162\) | −21.3640 | −1.67851 | ||||||||
\(163\) | 7.25112 | 0.567952 | 0.283976 | − | 0.958831i | \(-0.408346\pi\) | ||||
0.283976 | + | 0.958831i | \(0.408346\pi\) | |||||||
\(164\) | 2.55588 | 0.199581 | ||||||||
\(165\) | −2.29609 | −0.178750 | ||||||||
\(166\) | −42.2964 | −3.28284 | ||||||||
\(167\) | 13.2017 | 1.02158 | 0.510788 | − | 0.859706i | \(-0.329354\pi\) | ||||
0.510788 | + | 0.859706i | \(0.329354\pi\) | |||||||
\(168\) | −2.52627 | −0.194906 | ||||||||
\(169\) | 4.18276 | 0.321751 | ||||||||
\(170\) | 36.4233 | 2.79354 | ||||||||
\(171\) | 10.0206 | 0.766297 | ||||||||
\(172\) | 9.15680 | 0.698200 | ||||||||
\(173\) | 12.3773 | 0.941030 | 0.470515 | − | 0.882392i | \(-0.344068\pi\) | ||||
0.470515 | + | 0.882392i | \(0.344068\pi\) | |||||||
\(174\) | −6.84781 | −0.519131 | ||||||||
\(175\) | 5.08544 | 0.384423 | ||||||||
\(176\) | −24.4775 | −1.84506 | ||||||||
\(177\) | −2.09609 | −0.157551 | ||||||||
\(178\) | −0.446381 | −0.0334577 | ||||||||
\(179\) | 19.9556 | 1.49155 | 0.745776 | − | 0.666197i | \(-0.232079\pi\) | ||||
0.745776 | + | 0.666197i | \(0.232079\pi\) | |||||||
\(180\) | −45.8369 | −3.41648 | ||||||||
\(181\) | −0.979065 | −0.0727734 | −0.0363867 | − | 0.999338i | \(-0.511585\pi\) | ||||
−0.0363867 | + | 0.999338i | \(0.511585\pi\) | |||||||
\(182\) | 10.9530 | 0.811888 | ||||||||
\(183\) | −0.103991 | −0.00768724 | ||||||||
\(184\) | 0.689068 | 0.0507988 | ||||||||
\(185\) | 7.87164 | 0.578734 | ||||||||
\(186\) | 1.04101 | 0.0763308 | ||||||||
\(187\) | 9.78763 | 0.715743 | ||||||||
\(188\) | 18.0545 | 1.31676 | ||||||||
\(189\) | −1.89084 | −0.137538 | ||||||||
\(190\) | 29.0235 | 2.10559 | ||||||||
\(191\) | 7.02299 | 0.508166 | 0.254083 | − | 0.967182i | \(-0.418226\pi\) | ||||
0.254083 | + | 0.967182i | \(0.418226\pi\) | |||||||
\(192\) | 3.98900 | 0.287881 | ||||||||
\(193\) | 16.0737 | 1.15701 | 0.578506 | − | 0.815678i | \(-0.303636\pi\) | ||||
0.578506 | + | 0.815678i | \(0.303636\pi\) | |||||||
\(194\) | −11.6540 | −0.836712 | ||||||||
\(195\) | −4.22088 | −0.302264 | ||||||||
\(196\) | 4.98185 | 0.355846 | ||||||||
\(197\) | −8.03130 | −0.572207 | −0.286103 | − | 0.958199i | \(-0.592360\pi\) | ||||
−0.286103 | + | 0.958199i | \(0.592360\pi\) | |||||||
\(198\) | −17.2621 | −1.22677 | ||||||||
\(199\) | 21.6683 | 1.53603 | 0.768013 | − | 0.640434i | \(-0.221246\pi\) | ||||
0.768013 | + | 0.640434i | \(0.221246\pi\) | |||||||
\(200\) | −40.0682 | −2.83325 | ||||||||
\(201\) | 2.39585 | 0.168990 | ||||||||
\(202\) | −37.4893 | −2.63774 | ||||||||
\(203\) | 8.08271 | 0.567295 | ||||||||
\(204\) | −6.93341 | −0.485435 | ||||||||
\(205\) | 1.62929 | 0.113794 | ||||||||
\(206\) | −21.3129 | −1.48494 | ||||||||
\(207\) | 0.253378 | 0.0176110 | ||||||||
\(208\) | −44.9968 | −3.11997 | ||||||||
\(209\) | 7.79918 | 0.539480 | ||||||||
\(210\) | −2.69056 | −0.185666 | ||||||||
\(211\) | −20.5592 | −1.41535 | −0.707677 | − | 0.706536i | \(-0.750257\pi\) | ||||
−0.707677 | + | 0.706536i | \(0.750257\pi\) | |||||||
\(212\) | 3.60215 | 0.247397 | ||||||||
\(213\) | −1.95916 | −0.134240 | ||||||||
\(214\) | 8.06951 | 0.551620 | ||||||||
\(215\) | 5.83715 | 0.398090 | ||||||||
\(216\) | 14.8979 | 1.01368 | ||||||||
\(217\) | −1.22874 | −0.0834126 | ||||||||
\(218\) | 28.1231 | 1.90474 | ||||||||
\(219\) | −0.445633 | −0.0301131 | ||||||||
\(220\) | −35.6754 | −2.40524 | ||||||||
\(221\) | 17.9926 | 1.21031 | ||||||||
\(222\) | −2.09997 | −0.140941 | ||||||||
\(223\) | 22.4438 | 1.50295 | 0.751475 | − | 0.659762i | \(-0.229343\pi\) | ||||
0.751475 | + | 0.659762i | \(0.229343\pi\) | |||||||
\(224\) | −12.9247 | −0.863569 | ||||||||
\(225\) | −14.7335 | −0.982233 | ||||||||
\(226\) | 13.2075 | 0.878549 | ||||||||
\(227\) | 10.4453 | 0.693277 | 0.346638 | − | 0.937999i | \(-0.387323\pi\) | ||||
0.346638 | + | 0.937999i | \(0.387323\pi\) | |||||||
\(228\) | −5.52481 | −0.365890 | ||||||||
\(229\) | 15.2443 | 1.00737 | 0.503686 | − | 0.863887i | \(-0.331977\pi\) | ||||
0.503686 | + | 0.863887i | \(0.331977\pi\) | |||||||
\(230\) | 0.733878 | 0.0483905 | ||||||||
\(231\) | −0.723004 | −0.0475702 | ||||||||
\(232\) | −63.6837 | −4.18104 | ||||||||
\(233\) | −25.4580 | −1.66781 | −0.833905 | − | 0.551907i | \(-0.813900\pi\) | ||||
−0.833905 | + | 0.551907i | \(0.813900\pi\) | |||||||
\(234\) | −31.7329 | −2.07444 | ||||||||
\(235\) | 11.5091 | 0.750773 | ||||||||
\(236\) | −32.5679 | −2.11999 | ||||||||
\(237\) | 1.38379 | 0.0898868 | ||||||||
\(238\) | 11.4692 | 0.743436 | ||||||||
\(239\) | −24.1092 | −1.55950 | −0.779749 | − | 0.626093i | \(-0.784653\pi\) | ||||
−0.779749 | + | 0.626093i | \(0.784653\pi\) | |||||||
\(240\) | 11.0533 | 0.713487 | ||||||||
\(241\) | −20.0411 | −1.29096 | −0.645482 | − | 0.763776i | \(-0.723343\pi\) | ||||
−0.645482 | + | 0.763776i | \(0.723343\pi\) | |||||||
\(242\) | 15.6302 | 1.00475 | ||||||||
\(243\) | 8.26495 | 0.530197 | ||||||||
\(244\) | −1.61576 | −0.103439 | ||||||||
\(245\) | 3.17576 | 0.202892 | ||||||||
\(246\) | −0.434655 | −0.0277126 | ||||||||
\(247\) | 14.3372 | 0.912253 | ||||||||
\(248\) | 9.68128 | 0.614762 | ||||||||
\(249\) | 5.13248 | 0.325258 | ||||||||
\(250\) | −0.716925 | −0.0453423 | ||||||||
\(251\) | 21.6054 | 1.36372 | 0.681861 | − | 0.731481i | \(-0.261171\pi\) | ||||
0.681861 | + | 0.731481i | \(0.261171\pi\) | |||||||
\(252\) | −14.4334 | −0.909218 | ||||||||
\(253\) | 0.197207 | 0.0123983 | ||||||||
\(254\) | −17.0132 | −1.06750 | ||||||||
\(255\) | −4.41981 | −0.276779 | ||||||||
\(256\) | −6.32340 | −0.395212 | ||||||||
\(257\) | 23.0018 | 1.43482 | 0.717408 | − | 0.696654i | \(-0.245329\pi\) | ||||
0.717408 | + | 0.696654i | \(0.245329\pi\) | |||||||
\(258\) | −1.55721 | −0.0969478 | ||||||||
\(259\) | 2.47866 | 0.154017 | ||||||||
\(260\) | −65.5820 | −4.06722 | ||||||||
\(261\) | −23.4172 | −1.44949 | ||||||||
\(262\) | −19.7036 | −1.21729 | ||||||||
\(263\) | −2.20155 | −0.135754 | −0.0678768 | − | 0.997694i | \(-0.521622\pi\) | ||||
−0.0678768 | + | 0.997694i | \(0.521622\pi\) | |||||||
\(264\) | 5.69655 | 0.350598 | ||||||||
\(265\) | 2.29625 | 0.141057 | ||||||||
\(266\) | 9.13908 | 0.560353 | ||||||||
\(267\) | 0.0541664 | 0.00331493 | ||||||||
\(268\) | 37.2256 | 2.27391 | ||||||||
\(269\) | 18.5627 | 1.13178 | 0.565892 | − | 0.824479i | \(-0.308532\pi\) | ||||
0.565892 | + | 0.824479i | \(0.308532\pi\) | |||||||
\(270\) | 15.8667 | 0.965618 | ||||||||
\(271\) | −14.7983 | −0.898930 | −0.449465 | − | 0.893298i | \(-0.648385\pi\) | ||||
−0.449465 | + | 0.893298i | \(0.648385\pi\) | |||||||
\(272\) | −47.1174 | −2.85691 | ||||||||
\(273\) | −1.32909 | −0.0804405 | ||||||||
\(274\) | −48.9947 | −2.95988 | ||||||||
\(275\) | −11.4673 | −0.691501 | ||||||||
\(276\) | −0.139698 | −0.00840885 | ||||||||
\(277\) | −12.6694 | −0.761232 | −0.380616 | − | 0.924733i | \(-0.624288\pi\) | ||||
−0.380616 | + | 0.924733i | \(0.624288\pi\) | |||||||
\(278\) | 32.8314 | 1.96910 | ||||||||
\(279\) | 3.55991 | 0.213126 | ||||||||
\(280\) | −25.0218 | −1.49534 | ||||||||
\(281\) | −4.86512 | −0.290229 | −0.145114 | − | 0.989415i | \(-0.546355\pi\) | ||||
−0.145114 | + | 0.989415i | \(0.546355\pi\) | |||||||
\(282\) | −3.07036 | −0.182837 | ||||||||
\(283\) | −5.17506 | −0.307625 | −0.153813 | − | 0.988100i | \(-0.549155\pi\) | ||||
−0.153813 | + | 0.988100i | \(0.549155\pi\) | |||||||
\(284\) | −30.4405 | −1.80631 | ||||||||
\(285\) | −3.52188 | −0.208618 | ||||||||
\(286\) | −24.6981 | −1.46043 | ||||||||
\(287\) | 0.513039 | 0.0302837 | ||||||||
\(288\) | 37.4454 | 2.20649 | ||||||||
\(289\) | 1.84053 | 0.108266 | ||||||||
\(290\) | −67.8250 | −3.98282 | ||||||||
\(291\) | 1.41417 | 0.0829000 | ||||||||
\(292\) | −6.92403 | −0.405198 | ||||||||
\(293\) | −7.98020 | −0.466208 | −0.233104 | − | 0.972452i | \(-0.574888\pi\) | ||||
−0.233104 | + | 0.972452i | \(0.574888\pi\) | |||||||
\(294\) | −0.847217 | −0.0494107 | ||||||||
\(295\) | −20.7609 | −1.20875 | ||||||||
\(296\) | −19.5294 | −1.13512 | ||||||||
\(297\) | 4.26369 | 0.247405 | ||||||||
\(298\) | −42.3077 | −2.45082 | ||||||||
\(299\) | 0.362525 | 0.0209653 | ||||||||
\(300\) | 8.12322 | 0.468994 | ||||||||
\(301\) | 1.83803 | 0.105942 | ||||||||
\(302\) | −9.84424 | −0.566472 | ||||||||
\(303\) | 4.54916 | 0.261342 | ||||||||
\(304\) | −37.5450 | −2.15336 | ||||||||
\(305\) | −1.02999 | −0.0589772 | ||||||||
\(306\) | −33.2284 | −1.89954 | ||||||||
\(307\) | −13.5611 | −0.773973 | −0.386986 | − | 0.922085i | \(-0.626484\pi\) | ||||
−0.386986 | + | 0.922085i | \(0.626484\pi\) | |||||||
\(308\) | −11.2337 | −0.640098 | ||||||||
\(309\) | 2.58623 | 0.147126 | ||||||||
\(310\) | 10.3108 | 0.585617 | ||||||||
\(311\) | −9.64570 | −0.546957 | −0.273479 | − | 0.961878i | \(-0.588174\pi\) | ||||
−0.273479 | + | 0.961878i | \(0.588174\pi\) | |||||||
\(312\) | 10.4719 | 0.592857 | ||||||||
\(313\) | 10.3211 | 0.583384 | 0.291692 | − | 0.956512i | \(-0.405782\pi\) | ||||
0.291692 | + | 0.956512i | \(0.405782\pi\) | |||||||
\(314\) | 35.8572 | 2.02354 | ||||||||
\(315\) | −9.20079 | −0.518406 | ||||||||
\(316\) | 21.5006 | 1.20951 | ||||||||
\(317\) | 4.47127 | 0.251132 | 0.125566 | − | 0.992085i | \(-0.459925\pi\) | ||||
0.125566 | + | 0.992085i | \(0.459925\pi\) | |||||||
\(318\) | −0.612585 | −0.0343520 | ||||||||
\(319\) | −18.2259 | −1.02045 | ||||||||
\(320\) | 39.5095 | 2.20865 | ||||||||
\(321\) | −0.979199 | −0.0546536 | ||||||||
\(322\) | 0.231087 | 0.0128780 | ||||||||
\(323\) | 15.0129 | 0.835339 | ||||||||
\(324\) | 40.2798 | 2.23777 | ||||||||
\(325\) | −21.0802 | −1.16932 | ||||||||
\(326\) | −19.1598 | −1.06116 | ||||||||
\(327\) | −3.41262 | −0.188718 | ||||||||
\(328\) | −4.04223 | −0.223195 | ||||||||
\(329\) | 3.62406 | 0.199801 | ||||||||
\(330\) | 6.06699 | 0.333977 | ||||||||
\(331\) | 13.1757 | 0.724201 | 0.362100 | − | 0.932139i | \(-0.382060\pi\) | ||||
0.362100 | + | 0.932139i | \(0.382060\pi\) | |||||||
\(332\) | 79.7460 | 4.37663 | ||||||||
\(333\) | −7.18117 | −0.393526 | ||||||||
\(334\) | −34.8831 | −1.90872 | ||||||||
\(335\) | 23.7300 | 1.29651 | ||||||||
\(336\) | 3.48052 | 0.189878 | ||||||||
\(337\) | 7.32420 | 0.398975 | 0.199487 | − | 0.979900i | \(-0.436072\pi\) | ||||
0.199487 | + | 0.979900i | \(0.436072\pi\) | |||||||
\(338\) | −11.0522 | −0.601159 | ||||||||
\(339\) | −1.60267 | −0.0870451 | ||||||||
\(340\) | −68.6728 | −3.72430 | ||||||||
\(341\) | 2.77072 | 0.150043 | ||||||||
\(342\) | −26.4777 | −1.43175 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −14.4819 | −0.780809 | ||||||||
\(345\) | −0.0890529 | −0.00479445 | ||||||||
\(346\) | −32.7048 | −1.75822 | ||||||||
\(347\) | −27.5390 | −1.47837 | −0.739186 | − | 0.673501i | \(-0.764790\pi\) | ||||
−0.739186 | + | 0.673501i | \(0.764790\pi\) | |||||||
\(348\) | 12.9109 | 0.692098 | ||||||||
\(349\) | 26.4658 | 1.41668 | 0.708341 | − | 0.705870i | \(-0.249444\pi\) | ||||
0.708341 | + | 0.705870i | \(0.249444\pi\) | |||||||
\(350\) | −13.4373 | −0.718256 | ||||||||
\(351\) | 7.83793 | 0.418358 | ||||||||
\(352\) | 29.1442 | 1.55339 | ||||||||
\(353\) | 5.00160 | 0.266208 | 0.133104 | − | 0.991102i | \(-0.457506\pi\) | ||||
0.133104 | + | 0.991102i | \(0.457506\pi\) | |||||||
\(354\) | 5.53853 | 0.294369 | ||||||||
\(355\) | −19.4048 | −1.02990 | ||||||||
\(356\) | 0.841610 | 0.0446053 | ||||||||
\(357\) | −1.39173 | −0.0736583 | ||||||||
\(358\) | −52.7291 | −2.78682 | ||||||||
\(359\) | 25.4529 | 1.34335 | 0.671677 | − | 0.740844i | \(-0.265574\pi\) | ||||
0.671677 | + | 0.740844i | \(0.265574\pi\) | |||||||
\(360\) | 72.4930 | 3.82072 | ||||||||
\(361\) | −7.03714 | −0.370376 | ||||||||
\(362\) | 2.58700 | 0.135970 | ||||||||
\(363\) | −1.89666 | −0.0995486 | ||||||||
\(364\) | −20.6508 | −1.08240 | ||||||||
\(365\) | −4.41383 | −0.231030 | ||||||||
\(366\) | 0.274778 | 0.0143629 | ||||||||
\(367\) | −3.59788 | −0.187808 | −0.0939040 | − | 0.995581i | \(-0.529935\pi\) | ||||
−0.0939040 | + | 0.995581i | \(0.529935\pi\) | |||||||
\(368\) | −0.949350 | −0.0494883 | ||||||||
\(369\) | −1.48637 | −0.0773775 | ||||||||
\(370\) | −20.7994 | −1.08131 | ||||||||
\(371\) | 0.723055 | 0.0375392 | ||||||||
\(372\) | −1.96273 | −0.101763 | ||||||||
\(373\) | 3.59247 | 0.186011 | 0.0930054 | − | 0.995666i | \(-0.470353\pi\) | ||||
0.0930054 | + | 0.995666i | \(0.470353\pi\) | |||||||
\(374\) | −25.8621 | −1.33730 | ||||||||
\(375\) | 0.0869958 | 0.00449244 | ||||||||
\(376\) | −28.5539 | −1.47256 | ||||||||
\(377\) | −33.5045 | −1.72557 | ||||||||
\(378\) | 4.99620 | 0.256977 | ||||||||
\(379\) | 1.68973 | 0.0867954 | 0.0433977 | − | 0.999058i | \(-0.486182\pi\) | ||||
0.0433977 | + | 0.999058i | \(0.486182\pi\) | |||||||
\(380\) | −54.7212 | −2.80714 | ||||||||
\(381\) | 2.06448 | 0.105766 | ||||||||
\(382\) | −18.5570 | −0.949458 | ||||||||
\(383\) | 10.7477 | 0.549181 | 0.274590 | − | 0.961561i | \(-0.411458\pi\) | ||||
0.274590 | + | 0.961561i | \(0.411458\pi\) | |||||||
\(384\) | −2.25200 | −0.114922 | ||||||||
\(385\) | −7.16108 | −0.364962 | ||||||||
\(386\) | −42.4719 | −2.16176 | ||||||||
\(387\) | −5.32514 | −0.270692 | ||||||||
\(388\) | 21.9726 | 1.11549 | ||||||||
\(389\) | 16.3811 | 0.830555 | 0.415278 | − | 0.909695i | \(-0.363684\pi\) | ||||
0.415278 | + | 0.909695i | \(0.363684\pi\) | |||||||
\(390\) | 11.1529 | 0.564750 | ||||||||
\(391\) | 0.379610 | 0.0191977 | ||||||||
\(392\) | −7.87900 | −0.397950 | ||||||||
\(393\) | 2.39094 | 0.120607 | ||||||||
\(394\) | 21.2213 | 1.06911 | ||||||||
\(395\) | 13.7059 | 0.689619 | ||||||||
\(396\) | 32.5461 | 1.63551 | ||||||||
\(397\) | −16.5515 | −0.830695 | −0.415347 | − | 0.909663i | \(-0.636340\pi\) | ||||
−0.415347 | + | 0.909663i | \(0.636340\pi\) | |||||||
\(398\) | −57.2546 | −2.86991 | ||||||||
\(399\) | −1.10899 | −0.0555188 | ||||||||
\(400\) | 55.2031 | 2.76015 | ||||||||
\(401\) | 21.4851 | 1.07292 | 0.536458 | − | 0.843927i | \(-0.319762\pi\) | ||||
0.536458 | + | 0.843927i | \(0.319762\pi\) | |||||||
\(402\) | −6.33060 | −0.315742 | ||||||||
\(403\) | 5.09340 | 0.253720 | ||||||||
\(404\) | 70.6826 | 3.51659 | ||||||||
\(405\) | 25.6770 | 1.27590 | ||||||||
\(406\) | −21.3571 | −1.05994 | ||||||||
\(407\) | −5.58919 | −0.277046 | ||||||||
\(408\) | 10.9655 | 0.542871 | ||||||||
\(409\) | −15.9226 | −0.787321 | −0.393661 | − | 0.919256i | \(-0.628791\pi\) | ||||
−0.393661 | + | 0.919256i | \(0.628791\pi\) | |||||||
\(410\) | −4.30510 | −0.212614 | ||||||||
\(411\) | 5.94529 | 0.293259 | ||||||||
\(412\) | 40.1836 | 1.97970 | ||||||||
\(413\) | −6.53732 | −0.321680 | ||||||||
\(414\) | −0.669505 | −0.0329044 | ||||||||
\(415\) | 50.8353 | 2.49541 | ||||||||
\(416\) | 53.5757 | 2.62676 | ||||||||
\(417\) | −3.98395 | −0.195095 | ||||||||
\(418\) | −20.6079 | −1.00797 | ||||||||
\(419\) | −2.24045 | −0.109453 | −0.0547266 | − | 0.998501i | \(-0.517429\pi\) | ||||
−0.0547266 | + | 0.998501i | \(0.517429\pi\) | |||||||
\(420\) | 5.07280 | 0.247527 | ||||||||
\(421\) | 5.19408 | 0.253144 | 0.126572 | − | 0.991957i | \(-0.459603\pi\) | ||||
0.126572 | + | 0.991957i | \(0.459603\pi\) | |||||||
\(422\) | 54.3239 | 2.64445 | ||||||||
\(423\) | −10.4996 | −0.510508 | ||||||||
\(424\) | −5.69695 | −0.276668 | ||||||||
\(425\) | −22.0737 | −1.07073 | ||||||||
\(426\) | 5.17673 | 0.250813 | ||||||||
\(427\) | −0.324330 | −0.0156954 | ||||||||
\(428\) | −15.2143 | −0.735412 | ||||||||
\(429\) | 2.99700 | 0.144697 | ||||||||
\(430\) | −15.4236 | −0.743792 | ||||||||
\(431\) | 10.7555 | 0.518076 | 0.259038 | − | 0.965867i | \(-0.416594\pi\) | ||||
0.259038 | + | 0.965867i | \(0.416594\pi\) | |||||||
\(432\) | −20.5253 | −0.987525 | ||||||||
\(433\) | 2.38804 | 0.114762 | 0.0573810 | − | 0.998352i | \(-0.481725\pi\) | ||||
0.0573810 | + | 0.998352i | \(0.481725\pi\) | |||||||
\(434\) | 3.24673 | 0.155848 | ||||||||
\(435\) | 8.23027 | 0.394611 | ||||||||
\(436\) | −53.0236 | −2.53937 | ||||||||
\(437\) | 0.302488 | 0.0144700 | ||||||||
\(438\) | 1.17751 | 0.0562634 | ||||||||
\(439\) | 13.5279 | 0.645650 | 0.322825 | − | 0.946459i | \(-0.395368\pi\) | ||||
0.322825 | + | 0.946459i | \(0.395368\pi\) | |||||||
\(440\) | 56.4222 | 2.68982 | ||||||||
\(441\) | −2.89719 | −0.137962 | ||||||||
\(442\) | −47.5421 | −2.26135 | ||||||||
\(443\) | 15.3217 | 0.727956 | 0.363978 | − | 0.931408i | \(-0.381418\pi\) | ||||
0.363978 | + | 0.931408i | \(0.381418\pi\) | |||||||
\(444\) | 3.95929 | 0.187900 | ||||||||
\(445\) | 0.536498 | 0.0254324 | ||||||||
\(446\) | −59.3037 | −2.80811 | ||||||||
\(447\) | 5.13386 | 0.242823 | ||||||||
\(448\) | 12.4410 | 0.587781 | ||||||||
\(449\) | −12.1618 | −0.573951 | −0.286976 | − | 0.957938i | \(-0.592650\pi\) | ||||
−0.286976 | + | 0.957938i | \(0.592650\pi\) | |||||||
\(450\) | 38.9306 | 1.83521 | ||||||||
\(451\) | −1.15686 | −0.0544745 | ||||||||
\(452\) | −24.9015 | −1.17127 | ||||||||
\(453\) | 1.19456 | 0.0561251 | ||||||||
\(454\) | −27.5997 | −1.29532 | ||||||||
\(455\) | −13.1642 | −0.617146 | ||||||||
\(456\) | 8.73772 | 0.409181 | ||||||||
\(457\) | −11.4311 | −0.534724 | −0.267362 | − | 0.963596i | \(-0.586152\pi\) | ||||
−0.267362 | + | 0.963596i | \(0.586152\pi\) | |||||||
\(458\) | −40.2803 | −1.88218 | ||||||||
\(459\) | 8.20732 | 0.383085 | ||||||||
\(460\) | −1.38366 | −0.0645135 | ||||||||
\(461\) | 0.207894 | 0.00968258 | 0.00484129 | − | 0.999988i | \(-0.498459\pi\) | ||||
0.00484129 | + | 0.999988i | \(0.498459\pi\) | |||||||
\(462\) | 1.91041 | 0.0888802 | ||||||||
\(463\) | 13.3184 | 0.618958 | 0.309479 | − | 0.950906i | \(-0.399845\pi\) | ||||
0.309479 | + | 0.950906i | \(0.399845\pi\) | |||||||
\(464\) | 87.7389 | 4.07318 | ||||||||
\(465\) | −1.25118 | −0.0580219 | ||||||||
\(466\) | 67.2682 | 3.11614 | ||||||||
\(467\) | 39.7135 | 1.83772 | 0.918862 | − | 0.394580i | \(-0.129110\pi\) | ||||
0.918862 | + | 0.394580i | \(0.129110\pi\) | |||||||
\(468\) | 59.8294 | 2.76562 | ||||||||
\(469\) | 7.47223 | 0.345036 | ||||||||
\(470\) | −30.4108 | −1.40274 | ||||||||
\(471\) | −4.35111 | −0.200489 | ||||||||
\(472\) | 51.5075 | 2.37083 | ||||||||
\(473\) | −4.14462 | −0.190570 | ||||||||
\(474\) | −3.65641 | −0.167945 | ||||||||
\(475\) | −17.5892 | −0.807047 | ||||||||
\(476\) | −21.6241 | −0.991137 | ||||||||
\(477\) | −2.09483 | −0.0959157 | ||||||||
\(478\) | 63.7043 | 2.91377 | ||||||||
\(479\) | −27.5611 | −1.25930 | −0.629649 | − | 0.776880i | \(-0.716801\pi\) | ||||
−0.629649 | + | 0.776880i | \(0.716801\pi\) | |||||||
\(480\) | −13.1607 | −0.600700 | ||||||||
\(481\) | −10.2746 | −0.468481 | ||||||||
\(482\) | 52.9551 | 2.41204 | ||||||||
\(483\) | −0.0280415 | −0.00127593 | ||||||||
\(484\) | −29.4693 | −1.33951 | ||||||||
\(485\) | 14.0068 | 0.636016 | ||||||||
\(486\) | −21.8386 | −0.990620 | ||||||||
\(487\) | 24.9500 | 1.13059 | 0.565296 | − | 0.824888i | \(-0.308762\pi\) | ||||
0.565296 | + | 0.824888i | \(0.308762\pi\) | |||||||
\(488\) | 2.55539 | 0.115677 | ||||||||
\(489\) | 2.32495 | 0.105138 | ||||||||
\(490\) | −8.39136 | −0.379083 | ||||||||
\(491\) | −3.63544 | −0.164065 | −0.0820326 | − | 0.996630i | \(-0.526141\pi\) | ||||
−0.0820326 | + | 0.996630i | \(0.526141\pi\) | |||||||
\(492\) | 0.819503 | 0.0369460 | ||||||||
\(493\) | −35.0836 | −1.58008 | ||||||||
\(494\) | −37.8834 | −1.70446 | ||||||||
\(495\) | 20.7470 | 0.932510 | ||||||||
\(496\) | −13.3382 | −0.598902 | ||||||||
\(497\) | −6.11028 | −0.274083 | ||||||||
\(498\) | −13.5617 | −0.607713 | ||||||||
\(499\) | −39.5693 | −1.77137 | −0.885683 | − | 0.464290i | \(-0.846310\pi\) | ||||
−0.885683 | + | 0.464290i | \(0.846310\pi\) | |||||||
\(500\) | 1.35170 | 0.0604497 | ||||||||
\(501\) | 4.23291 | 0.189112 | ||||||||
\(502\) | −57.0884 | −2.54798 | ||||||||
\(503\) | 2.80048 | 0.124867 | 0.0624336 | − | 0.998049i | \(-0.480114\pi\) | ||||
0.0624336 | + | 0.998049i | \(0.480114\pi\) | |||||||
\(504\) | 22.8270 | 1.01679 | ||||||||
\(505\) | 45.0577 | 2.00504 | ||||||||
\(506\) | −0.521084 | −0.0231650 | ||||||||
\(507\) | 1.34113 | 0.0595618 | ||||||||
\(508\) | 32.0768 | 1.42318 | ||||||||
\(509\) | 14.0930 | 0.624662 | 0.312331 | − | 0.949973i | \(-0.398890\pi\) | ||||
0.312331 | + | 0.949973i | \(0.398890\pi\) | |||||||
\(510\) | 11.6785 | 0.517134 | ||||||||
\(511\) | −1.38985 | −0.0614834 | ||||||||
\(512\) | 30.7556 | 1.35922 | ||||||||
\(513\) | 6.53992 | 0.288744 | ||||||||
\(514\) | −60.7782 | −2.68081 | ||||||||
\(515\) | 25.6156 | 1.12876 | ||||||||
\(516\) | 2.93598 | 0.129249 | ||||||||
\(517\) | −8.17196 | −0.359402 | ||||||||
\(518\) | −6.54942 | −0.287765 | ||||||||
\(519\) | 3.96859 | 0.174202 | ||||||||
\(520\) | 103.721 | 4.54845 | ||||||||
\(521\) | 37.2880 | 1.63362 | 0.816809 | − | 0.576908i | \(-0.195741\pi\) | ||||
0.816809 | + | 0.576908i | \(0.195741\pi\) | |||||||
\(522\) | 61.8757 | 2.70822 | ||||||||
\(523\) | −25.1252 | −1.09865 | −0.549325 | − | 0.835609i | \(-0.685115\pi\) | ||||
−0.549325 | + | 0.835609i | \(0.685115\pi\) | |||||||
\(524\) | 37.1492 | 1.62287 | ||||||||
\(525\) | 1.63056 | 0.0711636 | ||||||||
\(526\) | 5.81720 | 0.253642 | ||||||||
\(527\) | 5.33345 | 0.232329 | ||||||||
\(528\) | −7.84830 | −0.341554 | ||||||||
\(529\) | −22.9924 | −0.999667 | ||||||||
\(530\) | −6.06742 | −0.263552 | ||||||||
\(531\) | 18.9399 | 0.821921 | ||||||||
\(532\) | −17.2309 | −0.747055 | ||||||||
\(533\) | −2.12665 | −0.0921156 | ||||||||
\(534\) | −0.143125 | −0.00619362 | ||||||||
\(535\) | −9.69860 | −0.419307 | ||||||||
\(536\) | −58.8737 | −2.54296 | ||||||||
\(537\) | 6.39844 | 0.276113 | ||||||||
\(538\) | −49.0485 | −2.11463 | ||||||||
\(539\) | −2.25492 | −0.0971263 | ||||||||
\(540\) | −29.9153 | −1.28735 | ||||||||
\(541\) | −2.79764 | −0.120280 | −0.0601400 | − | 0.998190i | \(-0.519155\pi\) | ||||
−0.0601400 | + | 0.998190i | \(0.519155\pi\) | |||||||
\(542\) | 39.1017 | 1.67956 | ||||||||
\(543\) | −0.313922 | −0.0134717 | ||||||||
\(544\) | 56.1006 | 2.40529 | ||||||||
\(545\) | −33.8007 | −1.44786 | ||||||||
\(546\) | 3.51189 | 0.150295 | ||||||||
\(547\) | 1.01710 | 0.0434878 | 0.0217439 | − | 0.999764i | \(-0.493078\pi\) | ||||
0.0217439 | + | 0.999764i | \(0.493078\pi\) | |||||||
\(548\) | 92.3749 | 3.94606 | ||||||||
\(549\) | 0.939646 | 0.0401031 | ||||||||
\(550\) | 30.3001 | 1.29200 | ||||||||
\(551\) | −27.9560 | −1.19096 | ||||||||
\(552\) | 0.220939 | 0.00940377 | ||||||||
\(553\) | 4.31579 | 0.183526 | ||||||||
\(554\) | 33.4767 | 1.42229 | ||||||||
\(555\) | 2.52391 | 0.107134 | ||||||||
\(556\) | −61.9007 | −2.62517 | ||||||||
\(557\) | 11.3077 | 0.479121 | 0.239560 | − | 0.970881i | \(-0.422997\pi\) | ||||
0.239560 | + | 0.970881i | \(0.422997\pi\) | |||||||
\(558\) | −9.40642 | −0.398206 | ||||||||
\(559\) | −7.61903 | −0.322251 | ||||||||
\(560\) | 34.4733 | 1.45676 | ||||||||
\(561\) | 3.13825 | 0.132497 | ||||||||
\(562\) | 12.8552 | 0.542264 | ||||||||
\(563\) | −38.2528 | −1.61217 | −0.806083 | − | 0.591803i | \(-0.798416\pi\) | ||||
−0.806083 | + | 0.591803i | \(0.798416\pi\) | |||||||
\(564\) | 5.78889 | 0.243756 | ||||||||
\(565\) | −15.8738 | −0.667818 | ||||||||
\(566\) | 13.6742 | 0.574768 | ||||||||
\(567\) | 8.08531 | 0.339551 | ||||||||
\(568\) | 48.1429 | 2.02003 | ||||||||
\(569\) | 23.1702 | 0.971346 | 0.485673 | − | 0.874141i | \(-0.338575\pi\) | ||||
0.485673 | + | 0.874141i | \(0.338575\pi\) | |||||||
\(570\) | 9.30592 | 0.389782 | ||||||||
\(571\) | 12.5117 | 0.523598 | 0.261799 | − | 0.965122i | \(-0.415684\pi\) | ||||
0.261799 | + | 0.965122i | \(0.415684\pi\) | |||||||
\(572\) | 46.5659 | 1.94702 | ||||||||
\(573\) | 2.25181 | 0.0940706 | ||||||||
\(574\) | −1.35561 | −0.0565822 | ||||||||
\(575\) | −0.444754 | −0.0185475 | ||||||||
\(576\) | −36.0439 | −1.50183 | ||||||||
\(577\) | 18.0570 | 0.751721 | 0.375860 | − | 0.926676i | \(-0.377347\pi\) | ||||
0.375860 | + | 0.926676i | \(0.377347\pi\) | |||||||
\(578\) | −4.86326 | −0.202285 | ||||||||
\(579\) | 5.15378 | 0.214184 | ||||||||
\(580\) | 127.878 | 5.30984 | ||||||||
\(581\) | 16.0073 | 0.664095 | ||||||||
\(582\) | −3.73668 | −0.154890 | ||||||||
\(583\) | −1.63043 | −0.0675256 | ||||||||
\(584\) | 10.9506 | 0.453141 | ||||||||
\(585\) | 38.1392 | 1.57686 | ||||||||
\(586\) | 21.0862 | 0.871064 | ||||||||
\(587\) | −28.2171 | −1.16464 | −0.582322 | − | 0.812958i | \(-0.697856\pi\) | ||||
−0.582322 | + | 0.812958i | \(0.697856\pi\) | |||||||
\(588\) | 1.59735 | 0.0658736 | ||||||||
\(589\) | 4.24990 | 0.175114 | ||||||||
\(590\) | 54.8570 | 2.25843 | ||||||||
\(591\) | −2.57511 | −0.105926 | ||||||||
\(592\) | 26.9062 | 1.10584 | ||||||||
\(593\) | 15.5471 | 0.638442 | 0.319221 | − | 0.947680i | \(-0.396579\pi\) | ||||
0.319221 | + | 0.947680i | \(0.396579\pi\) | |||||||
\(594\) | −11.2660 | −0.462251 | ||||||||
\(595\) | −13.7846 | −0.565113 | ||||||||
\(596\) | 79.7674 | 3.26740 | ||||||||
\(597\) | 6.94760 | 0.284346 | ||||||||
\(598\) | −0.957906 | −0.0391717 | ||||||||
\(599\) | −23.3398 | −0.953638 | −0.476819 | − | 0.879002i | \(-0.658210\pi\) | ||||
−0.476819 | + | 0.879002i | \(0.658210\pi\) | |||||||
\(600\) | −12.8472 | −0.524485 | ||||||||
\(601\) | −7.53645 | −0.307418 | −0.153709 | − | 0.988116i | \(-0.549122\pi\) | ||||
−0.153709 | + | 0.988116i | \(0.549122\pi\) | |||||||
\(602\) | −4.85667 | −0.197943 | ||||||||
\(603\) | −21.6485 | −0.881596 | ||||||||
\(604\) | 18.5604 | 0.755212 | ||||||||
\(605\) | −18.7857 | −0.763746 | ||||||||
\(606\) | −12.0203 | −0.488293 | ||||||||
\(607\) | 31.0866 | 1.26177 | 0.630883 | − | 0.775878i | \(-0.282693\pi\) | ||||
0.630883 | + | 0.775878i | \(0.282693\pi\) | |||||||
\(608\) | 44.7032 | 1.81295 | ||||||||
\(609\) | 2.59159 | 0.105017 | ||||||||
\(610\) | 2.72157 | 0.110193 | ||||||||
\(611\) | −15.0225 | −0.607744 | ||||||||
\(612\) | 62.6491 | 2.53244 | ||||||||
\(613\) | −2.93536 | −0.118558 | −0.0592790 | − | 0.998241i | \(-0.518880\pi\) | ||||
−0.0592790 | + | 0.998241i | \(0.518880\pi\) | |||||||
\(614\) | 35.8328 | 1.44609 | ||||||||
\(615\) | 0.522405 | 0.0210654 | ||||||||
\(616\) | 17.7665 | 0.715833 | ||||||||
\(617\) | 42.2244 | 1.69989 | 0.849944 | − | 0.526873i | \(-0.176636\pi\) | ||||
0.849944 | + | 0.526873i | \(0.176636\pi\) | |||||||
\(618\) | −6.83365 | −0.274890 | ||||||||
\(619\) | −23.9597 | −0.963020 | −0.481510 | − | 0.876440i | \(-0.659912\pi\) | ||||
−0.481510 | + | 0.876440i | \(0.659912\pi\) | |||||||
\(620\) | −19.4401 | −0.780735 | ||||||||
\(621\) | 0.165366 | 0.00663591 | ||||||||
\(622\) | 25.4870 | 1.02194 | ||||||||
\(623\) | 0.168935 | 0.00676825 | ||||||||
\(624\) | −14.4275 | −0.577562 | ||||||||
\(625\) | −24.5655 | −0.982621 | ||||||||
\(626\) | −27.2717 | −1.09000 | ||||||||
\(627\) | 2.50068 | 0.0998675 | ||||||||
\(628\) | −67.6054 | −2.69775 | ||||||||
\(629\) | −10.7588 | −0.428982 | ||||||||
\(630\) | 24.3114 | 0.968590 | ||||||||
\(631\) | 21.9157 | 0.872449 | 0.436224 | − | 0.899838i | \(-0.356315\pi\) | ||||
0.436224 | + | 0.899838i | \(0.356315\pi\) | |||||||
\(632\) | −34.0041 | −1.35261 | ||||||||
\(633\) | −6.59197 | −0.262007 | ||||||||
\(634\) | −11.8145 | −0.469215 | ||||||||
\(635\) | 20.4479 | 0.811449 | ||||||||
\(636\) | 1.15497 | 0.0457976 | ||||||||
\(637\) | −4.14521 | −0.164239 | ||||||||
\(638\) | 48.1586 | 1.90662 | ||||||||
\(639\) | 17.7027 | 0.700306 | ||||||||
\(640\) | −22.3052 | −0.881691 | ||||||||
\(641\) | 2.78360 | 0.109945 | 0.0549727 | − | 0.998488i | \(-0.482493\pi\) | ||||
0.0549727 | + | 0.998488i | \(0.482493\pi\) | |||||||
\(642\) | 2.58736 | 0.102115 | ||||||||
\(643\) | −1.77914 | −0.0701625 | −0.0350812 | − | 0.999384i | \(-0.511169\pi\) | ||||
−0.0350812 | + | 0.999384i | \(0.511169\pi\) | |||||||
\(644\) | −0.435694 | −0.0171688 | ||||||||
\(645\) | 1.87159 | 0.0736937 | ||||||||
\(646\) | −39.6688 | −1.56075 | ||||||||
\(647\) | 10.0738 | 0.396041 | 0.198021 | − | 0.980198i | \(-0.436549\pi\) | ||||
0.198021 | + | 0.980198i | \(0.436549\pi\) | |||||||
\(648\) | −63.7042 | −2.50254 | ||||||||
\(649\) | 14.7411 | 0.578640 | ||||||||
\(650\) | 55.7006 | 2.18476 | ||||||||
\(651\) | −0.393977 | −0.0154412 | ||||||||
\(652\) | 36.1240 | 1.41472 | ||||||||
\(653\) | 10.7235 | 0.419643 | 0.209821 | − | 0.977740i | \(-0.432712\pi\) | ||||
0.209821 | + | 0.977740i | \(0.432712\pi\) | |||||||
\(654\) | 9.01723 | 0.352601 | ||||||||
\(655\) | 23.6814 | 0.925307 | ||||||||
\(656\) | 5.56910 | 0.217437 | ||||||||
\(657\) | 4.02667 | 0.157095 | ||||||||
\(658\) | −9.57591 | −0.373308 | ||||||||
\(659\) | 16.0478 | 0.625135 | 0.312568 | − | 0.949896i | \(-0.398811\pi\) | ||||
0.312568 | + | 0.949896i | \(0.398811\pi\) | |||||||
\(660\) | −11.4388 | −0.445253 | ||||||||
\(661\) | −46.2532 | −1.79904 | −0.899520 | − | 0.436879i | \(-0.856084\pi\) | ||||
−0.899520 | + | 0.436879i | \(0.856084\pi\) | |||||||
\(662\) | −34.8143 | −1.35310 | ||||||||
\(663\) | 5.76902 | 0.224050 | ||||||||
\(664\) | −126.122 | −4.89447 | ||||||||
\(665\) | −10.9841 | −0.425945 | ||||||||
\(666\) | 18.9749 | 0.735264 | ||||||||
\(667\) | −0.706884 | −0.0273707 | ||||||||
\(668\) | 65.7688 | 2.54467 | ||||||||
\(669\) | 7.19625 | 0.278223 | ||||||||
\(670\) | −62.7022 | −2.42240 | ||||||||
\(671\) | 0.731337 | 0.0282330 | ||||||||
\(672\) | −4.14410 | −0.159862 | ||||||||
\(673\) | 12.6888 | 0.489118 | 0.244559 | − | 0.969634i | \(-0.421357\pi\) | ||||
0.244559 | + | 0.969634i | \(0.421357\pi\) | |||||||
\(674\) | −19.3529 | −0.745445 | ||||||||
\(675\) | −9.61575 | −0.370110 | ||||||||
\(676\) | 20.8379 | 0.801457 | ||||||||
\(677\) | 35.3157 | 1.35729 | 0.678646 | − | 0.734466i | \(-0.262567\pi\) | ||||
0.678646 | + | 0.734466i | \(0.262567\pi\) | |||||||
\(678\) | 4.23477 | 0.162635 | ||||||||
\(679\) | 4.41054 | 0.169261 | ||||||||
\(680\) | 108.609 | 4.16496 | ||||||||
\(681\) | 3.34911 | 0.128338 | ||||||||
\(682\) | −7.32113 | −0.280341 | ||||||||
\(683\) | −35.6799 | −1.36525 | −0.682627 | − | 0.730767i | \(-0.739163\pi\) | ||||
−0.682627 | + | 0.730767i | \(0.739163\pi\) | |||||||
\(684\) | 49.9213 | 1.90879 | ||||||||
\(685\) | 58.8858 | 2.24991 | ||||||||
\(686\) | −2.64232 | −0.100884 | ||||||||
\(687\) | 4.88784 | 0.186483 | ||||||||
\(688\) | 19.9521 | 0.760666 | ||||||||
\(689\) | −2.99722 | −0.114185 | ||||||||
\(690\) | 0.235306 | 0.00895795 | ||||||||
\(691\) | −27.7905 | −1.05720 | −0.528599 | − | 0.848871i | \(-0.677283\pi\) | ||||
−0.528599 | + | 0.848871i | \(0.677283\pi\) | |||||||
\(692\) | 61.6619 | 2.34403 | ||||||||
\(693\) | 6.53294 | 0.248166 | ||||||||
\(694\) | 72.7669 | 2.76219 | ||||||||
\(695\) | −39.4595 | −1.49679 | ||||||||
\(696\) | −20.4191 | −0.773986 | ||||||||
\(697\) | −2.22688 | −0.0843491 | ||||||||
\(698\) | −69.9311 | −2.64693 | ||||||||
\(699\) | −8.16271 | −0.308742 | ||||||||
\(700\) | 25.3349 | 0.957569 | ||||||||
\(701\) | −23.7986 | −0.898860 | −0.449430 | − | 0.893316i | \(-0.648373\pi\) | ||||
−0.449430 | + | 0.893316i | \(0.648373\pi\) | |||||||
\(702\) | −20.7103 | −0.781660 | ||||||||
\(703\) | −8.57305 | −0.323339 | ||||||||
\(704\) | −28.0534 | −1.05730 | ||||||||
\(705\) | 3.69022 | 0.138982 | ||||||||
\(706\) | −13.2158 | −0.497384 | ||||||||
\(707\) | 14.1880 | 0.533596 | ||||||||
\(708\) | −10.4424 | −0.392449 | ||||||||
\(709\) | 2.40624 | 0.0903683 | 0.0451842 | − | 0.998979i | \(-0.485613\pi\) | ||||
0.0451842 | + | 0.998979i | \(0.485613\pi\) | |||||||
\(710\) | 51.2736 | 1.92426 | ||||||||
\(711\) | −12.5037 | −0.468925 | ||||||||
\(712\) | −1.33104 | −0.0498829 | ||||||||
\(713\) | 0.107461 | 0.00402446 | ||||||||
\(714\) | 3.67740 | 0.137623 | ||||||||
\(715\) | 29.6842 | 1.11013 | ||||||||
\(716\) | 99.4158 | 3.71534 | ||||||||
\(717\) | −7.73024 | −0.288691 | ||||||||
\(718\) | −67.2548 | −2.50993 | ||||||||
\(719\) | −2.49024 | −0.0928703 | −0.0464352 | − | 0.998921i | \(-0.514786\pi\) | ||||
−0.0464352 | + | 0.998921i | \(0.514786\pi\) | |||||||
\(720\) | −99.8757 | −3.72215 | ||||||||
\(721\) | 8.06600 | 0.300393 | ||||||||
\(722\) | 18.5944 | 0.692011 | ||||||||
\(723\) | −6.42587 | −0.238981 | ||||||||
\(724\) | −4.87756 | −0.181273 | ||||||||
\(725\) | 41.1041 | 1.52657 | ||||||||
\(726\) | 5.01157 | 0.185997 | ||||||||
\(727\) | 20.1483 | 0.747261 | 0.373630 | − | 0.927578i | \(-0.378113\pi\) | ||||
0.373630 | + | 0.927578i | \(0.378113\pi\) | |||||||
\(728\) | 32.6601 | 1.21046 | ||||||||
\(729\) | −21.6059 | −0.800219 | ||||||||
\(730\) | 11.6628 | 0.431658 | ||||||||
\(731\) | −7.97810 | −0.295081 | ||||||||
\(732\) | −0.518068 | −0.0191483 | ||||||||
\(733\) | 32.3164 | 1.19363 | 0.596817 | − | 0.802378i | \(-0.296432\pi\) | ||||
0.596817 | + | 0.802378i | \(0.296432\pi\) | |||||||
\(734\) | 9.50676 | 0.350901 | ||||||||
\(735\) | 1.01826 | 0.0375589 | ||||||||
\(736\) | 1.13035 | 0.0416652 | ||||||||
\(737\) | −16.8493 | −0.620652 | ||||||||
\(738\) | 3.92747 | 0.144572 | ||||||||
\(739\) | −5.43566 | −0.199954 | −0.0999771 | − | 0.994990i | \(-0.531877\pi\) | ||||
−0.0999771 | + | 0.994990i | \(0.531877\pi\) | |||||||
\(740\) | 39.2153 | 1.44158 | ||||||||
\(741\) | 4.59699 | 0.168875 | ||||||||
\(742\) | −1.91054 | −0.0701382 | ||||||||
\(743\) | −4.12811 | −0.151446 | −0.0757229 | − | 0.997129i | \(-0.524126\pi\) | ||||
−0.0757229 | + | 0.997129i | \(0.524126\pi\) | |||||||
\(744\) | 3.10415 | 0.113803 | ||||||||
\(745\) | 50.8489 | 1.86296 | ||||||||
\(746\) | −9.49244 | −0.347543 | ||||||||
\(747\) | −46.3763 | −1.69682 | ||||||||
\(748\) | 48.7605 | 1.78286 | ||||||||
\(749\) | −3.05395 | −0.111589 | ||||||||
\(750\) | −0.229871 | −0.00839369 | ||||||||
\(751\) | 29.8530 | 1.08935 | 0.544676 | − | 0.838647i | \(-0.316653\pi\) | ||||
0.544676 | + | 0.838647i | \(0.316653\pi\) | |||||||
\(752\) | 39.3396 | 1.43457 | ||||||||
\(753\) | 6.92743 | 0.252450 | ||||||||
\(754\) | 88.5297 | 3.22406 | ||||||||
\(755\) | 11.8316 | 0.430597 | ||||||||
\(756\) | −9.41988 | −0.342598 | ||||||||
\(757\) | −4.74385 | −0.172418 | −0.0862090 | − | 0.996277i | \(-0.527475\pi\) | ||||
−0.0862090 | + | 0.996277i | \(0.527475\pi\) | |||||||
\(758\) | −4.46479 | −0.162169 | ||||||||
\(759\) | 0.0632313 | 0.00229515 | ||||||||
\(760\) | 86.5438 | 3.13927 | ||||||||
\(761\) | −3.31318 | −0.120103 | −0.0600513 | − | 0.998195i | \(-0.519126\pi\) | ||||
−0.0600513 | + | 0.998195i | \(0.519126\pi\) | |||||||
\(762\) | −5.45501 | −0.197614 | ||||||||
\(763\) | −10.6433 | −0.385315 | ||||||||
\(764\) | 34.9875 | 1.26580 | ||||||||
\(765\) | 39.9366 | 1.44391 | ||||||||
\(766\) | −28.3988 | −1.02609 | ||||||||
\(767\) | 27.0985 | 0.978472 | ||||||||
\(768\) | −2.02750 | −0.0731609 | ||||||||
\(769\) | −5.16827 | −0.186373 | −0.0931863 | − | 0.995649i | \(-0.529705\pi\) | ||||
−0.0931863 | + | 0.995649i | \(0.529705\pi\) | |||||||
\(770\) | 18.9219 | 0.681897 | ||||||||
\(771\) | 7.37517 | 0.265610 | ||||||||
\(772\) | 80.0768 | 2.88203 | ||||||||
\(773\) | 43.4416 | 1.56249 | 0.781243 | − | 0.624228i | \(-0.214586\pi\) | ||||
0.781243 | + | 0.624228i | \(0.214586\pi\) | |||||||
\(774\) | 14.0707 | 0.505761 | ||||||||
\(775\) | −6.24870 | −0.224460 | ||||||||
\(776\) | −34.7506 | −1.24747 | ||||||||
\(777\) | 0.794744 | 0.0285113 | ||||||||
\(778\) | −43.2841 | −1.55181 | ||||||||
\(779\) | −1.77447 | −0.0635768 | ||||||||
\(780\) | −21.0278 | −0.752916 | ||||||||
\(781\) | 13.7782 | 0.493022 | ||||||||
\(782\) | −1.00305 | −0.0358690 | ||||||||
\(783\) | −15.2831 | −0.546174 | ||||||||
\(784\) | 10.8551 | 0.387683 | ||||||||
\(785\) | −43.0961 | −1.53817 | ||||||||
\(786\) | −6.31763 | −0.225342 | ||||||||
\(787\) | 2.28367 | 0.0814040 | 0.0407020 | − | 0.999171i | \(-0.487041\pi\) | ||||
0.0407020 | + | 0.999171i | \(0.487041\pi\) | |||||||
\(788\) | −40.0107 | −1.42532 | ||||||||
\(789\) | −0.705892 | −0.0251304 | ||||||||
\(790\) | −36.2154 | −1.28849 | ||||||||
\(791\) | −4.99844 | −0.177724 | ||||||||
\(792\) | −51.4731 | −1.82902 | ||||||||
\(793\) | 1.34441 | 0.0477415 | ||||||||
\(794\) | 43.7343 | 1.55207 | ||||||||
\(795\) | 0.736255 | 0.0261123 | ||||||||
\(796\) | 107.948 | 3.82613 | ||||||||
\(797\) | −36.6606 | −1.29859 | −0.649293 | − | 0.760539i | \(-0.724935\pi\) | ||||
−0.649293 | + | 0.760539i | \(0.724935\pi\) | |||||||
\(798\) | 2.93030 | 0.103732 | ||||||||
\(799\) | −15.7305 | −0.556504 | ||||||||
\(800\) | −65.7278 | −2.32383 | ||||||||
\(801\) | −0.489438 | −0.0172935 | ||||||||
\(802\) | −56.7705 | −2.00464 | ||||||||
\(803\) | 3.13400 | 0.110597 | ||||||||
\(804\) | 11.9358 | 0.420942 | ||||||||
\(805\) | −0.277740 | −0.00978905 | ||||||||
\(806\) | −13.4584 | −0.474052 | ||||||||
\(807\) | 5.95182 | 0.209514 | ||||||||
\(808\) | −111.787 | −3.93267 | ||||||||
\(809\) | −46.7473 | −1.64355 | −0.821774 | − | 0.569814i | \(-0.807015\pi\) | ||||
−0.821774 | + | 0.569814i | \(0.807015\pi\) | |||||||
\(810\) | −67.8468 | −2.38389 | ||||||||
\(811\) | −43.6072 | −1.53126 | −0.765628 | − | 0.643284i | \(-0.777571\pi\) | ||||
−0.765628 | + | 0.643284i | \(0.777571\pi\) | |||||||
\(812\) | 40.2669 | 1.41309 | ||||||||
\(813\) | −4.74482 | −0.166408 | ||||||||
\(814\) | 14.7684 | 0.517633 | ||||||||
\(815\) | 23.0278 | 0.806629 | ||||||||
\(816\) | −15.1074 | −0.528866 | ||||||||
\(817\) | −6.35727 | −0.222413 | ||||||||
\(818\) | 42.0726 | 1.47103 | ||||||||
\(819\) | 12.0095 | 0.419645 | ||||||||
\(820\) | 8.11686 | 0.283453 | ||||||||
\(821\) | 22.3921 | 0.781489 | 0.390745 | − | 0.920499i | \(-0.372218\pi\) | ||||
0.390745 | + | 0.920499i | \(0.372218\pi\) | |||||||
\(822\) | −15.7093 | −0.547926 | ||||||||
\(823\) | 11.4757 | 0.400019 | 0.200010 | − | 0.979794i | \(-0.435903\pi\) | ||||
0.200010 | + | 0.979794i | \(0.435903\pi\) | |||||||
\(824\) | −63.5520 | −2.21394 | ||||||||
\(825\) | −3.67679 | −0.128009 | ||||||||
\(826\) | 17.2737 | 0.601028 | ||||||||
\(827\) | 21.5012 | 0.747670 | 0.373835 | − | 0.927495i | \(-0.378043\pi\) | ||||
0.373835 | + | 0.927495i | \(0.378043\pi\) | |||||||
\(828\) | 1.26229 | 0.0438676 | ||||||||
\(829\) | −10.1045 | −0.350945 | −0.175472 | − | 0.984484i | \(-0.556145\pi\) | ||||
−0.175472 | + | 0.984484i | \(0.556145\pi\) | |||||||
\(830\) | −134.323 | −4.66242 | ||||||||
\(831\) | −4.06225 | −0.140918 | ||||||||
\(832\) | −51.5704 | −1.78788 | ||||||||
\(833\) | −4.34057 | −0.150392 | ||||||||
\(834\) | 10.5269 | 0.364516 | ||||||||
\(835\) | 41.9253 | 1.45089 | ||||||||
\(836\) | 38.8543 | 1.34380 | ||||||||
\(837\) | 2.32336 | 0.0803070 | ||||||||
\(838\) | 5.91999 | 0.204503 | ||||||||
\(839\) | −18.7556 | −0.647514 | −0.323757 | − | 0.946140i | \(-0.604946\pi\) | ||||
−0.323757 | + | 0.946140i | \(0.604946\pi\) | |||||||
\(840\) | −8.02283 | −0.276814 | ||||||||
\(841\) | 36.3302 | 1.25277 | ||||||||
\(842\) | −13.7244 | −0.472975 | ||||||||
\(843\) | −1.55992 | −0.0537265 | ||||||||
\(844\) | −102.423 | −3.52554 | ||||||||
\(845\) | 13.2834 | 0.456964 | ||||||||
\(846\) | 27.7433 | 0.953834 | ||||||||
\(847\) | −5.91533 | −0.203253 | ||||||||
\(848\) | 7.84886 | 0.269531 | ||||||||
\(849\) | −1.65930 | −0.0569470 | ||||||||
\(850\) | 58.3257 | 2.00056 | ||||||||
\(851\) | −0.216775 | −0.00743095 | ||||||||
\(852\) | −9.76025 | −0.334381 | ||||||||
\(853\) | 36.4910 | 1.24943 | 0.624713 | − | 0.780854i | \(-0.285216\pi\) | ||||
0.624713 | + | 0.780854i | \(0.285216\pi\) | |||||||
\(854\) | 0.856982 | 0.0293253 | ||||||||
\(855\) | 31.8231 | 1.08833 | ||||||||
\(856\) | 24.0621 | 0.822424 | ||||||||
\(857\) | −25.8429 | −0.882777 | −0.441388 | − | 0.897316i | \(-0.645514\pi\) | ||||
−0.441388 | + | 0.897316i | \(0.645514\pi\) | |||||||
\(858\) | −7.91904 | −0.270351 | ||||||||
\(859\) | −1.00000 | −0.0341196 | ||||||||
\(860\) | 29.0798 | 0.991612 | ||||||||
\(861\) | 0.164498 | 0.00560606 | ||||||||
\(862\) | −28.4196 | −0.967974 | ||||||||
\(863\) | 6.51288 | 0.221701 | 0.110851 | − | 0.993837i | \(-0.464643\pi\) | ||||
0.110851 | + | 0.993837i | \(0.464643\pi\) | |||||||
\(864\) | 24.4386 | 0.831417 | ||||||||
\(865\) | 39.3073 | 1.33649 | ||||||||
\(866\) | −6.30997 | −0.214421 | ||||||||
\(867\) | 0.590135 | 0.0200420 | ||||||||
\(868\) | −6.12142 | −0.207775 | ||||||||
\(869\) | −9.73177 | −0.330128 | ||||||||
\(870\) | −21.7470 | −0.737292 | ||||||||
\(871\) | −30.9740 | −1.04951 | ||||||||
\(872\) | 83.8589 | 2.83982 | ||||||||
\(873\) | −12.7782 | −0.432476 | ||||||||
\(874\) | −0.799271 | −0.0270357 | ||||||||
\(875\) | 0.271324 | 0.00917244 | ||||||||
\(876\) | −2.22008 | −0.0750095 | ||||||||
\(877\) | −23.5377 | −0.794813 | −0.397407 | − | 0.917643i | \(-0.630090\pi\) | ||||
−0.397407 | + | 0.917643i | \(0.630090\pi\) | |||||||
\(878\) | −35.7449 | −1.20633 | ||||||||
\(879\) | −2.55872 | −0.0863036 | ||||||||
\(880\) | −77.7345 | −2.62043 | ||||||||
\(881\) | −56.5228 | −1.90430 | −0.952152 | − | 0.305626i | \(-0.901134\pi\) | ||||
−0.952152 | + | 0.305626i | \(0.901134\pi\) | |||||||
\(882\) | 7.65531 | 0.257768 | ||||||||
\(883\) | 7.00314 | 0.235674 | 0.117837 | − | 0.993033i | \(-0.462404\pi\) | ||||
0.117837 | + | 0.993033i | \(0.462404\pi\) | |||||||
\(884\) | 89.6362 | 3.01479 | ||||||||
\(885\) | −6.65666 | −0.223761 | ||||||||
\(886\) | −40.4848 | −1.36011 | ||||||||
\(887\) | 14.8868 | 0.499849 | 0.249925 | − | 0.968265i | \(-0.419594\pi\) | ||||
0.249925 | + | 0.968265i | \(0.419594\pi\) | |||||||
\(888\) | −6.26179 | −0.210132 | ||||||||
\(889\) | 6.43874 | 0.215948 | ||||||||
\(890\) | −1.41760 | −0.0475180 | ||||||||
\(891\) | −18.2317 | −0.610786 | ||||||||
\(892\) | 111.812 | 3.74373 | ||||||||
\(893\) | −12.5347 | −0.419456 | ||||||||
\(894\) | −13.5653 | −0.453691 | ||||||||
\(895\) | 63.3742 | 2.11836 | ||||||||
\(896\) | −7.02359 | −0.234642 | ||||||||
\(897\) | 0.116238 | 0.00388106 | ||||||||
\(898\) | 32.1354 | 1.07237 | ||||||||
\(899\) | −9.93159 | −0.331237 | ||||||||
\(900\) | −73.4001 | −2.44667 | ||||||||
\(901\) | −3.13847 | −0.104558 | ||||||||
\(902\) | 3.05680 | 0.101780 | ||||||||
\(903\) | 0.589335 | 0.0196119 | ||||||||
\(904\) | 39.3827 | 1.30985 | ||||||||
\(905\) | −3.10927 | −0.103356 | ||||||||
\(906\) | −3.15640 | −0.104864 | ||||||||
\(907\) | 34.0339 | 1.13008 | 0.565039 | − | 0.825065i | \(-0.308861\pi\) | ||||
0.565039 | + | 0.825065i | \(0.308861\pi\) | |||||||
\(908\) | 52.0368 | 1.72690 | ||||||||
\(909\) | −41.1055 | −1.36338 | ||||||||
\(910\) | 34.7840 | 1.15308 | ||||||||
\(911\) | 40.8576 | 1.35367 | 0.676836 | − | 0.736134i | \(-0.263350\pi\) | ||||
0.676836 | + | 0.736134i | \(0.263350\pi\) | |||||||
\(912\) | −12.0382 | −0.398625 | ||||||||
\(913\) | −36.0952 | −1.19458 | ||||||||
\(914\) | 30.2046 | 0.999079 | ||||||||
\(915\) | −0.330250 | −0.0109177 | ||||||||
\(916\) | 75.9449 | 2.50929 | ||||||||
\(917\) | 7.45692 | 0.246249 | ||||||||
\(918\) | −21.6864 | −0.715756 | ||||||||
\(919\) | −31.7728 | −1.04809 | −0.524045 | − | 0.851691i | \(-0.675578\pi\) | ||||
−0.524045 | + | 0.851691i | \(0.675578\pi\) | |||||||
\(920\) | 2.18831 | 0.0721466 | ||||||||
\(921\) | −4.34815 | −0.143276 | ||||||||
\(922\) | −0.549322 | −0.0180909 | ||||||||
\(923\) | 25.3284 | 0.833694 | ||||||||
\(924\) | −3.60190 | −0.118494 | ||||||||
\(925\) | 12.6051 | 0.414453 | ||||||||
\(926\) | −35.1914 | −1.15646 | ||||||||
\(927\) | −23.3688 | −0.767531 | ||||||||
\(928\) | −104.467 | −3.42929 | ||||||||
\(929\) | 44.8537 | 1.47160 | 0.735802 | − | 0.677197i | \(-0.236806\pi\) | ||||
0.735802 | + | 0.677197i | \(0.236806\pi\) | |||||||
\(930\) | 3.30601 | 0.108408 | ||||||||
\(931\) | −3.45874 | −0.113356 | ||||||||
\(932\) | −126.828 | −4.15439 | ||||||||
\(933\) | −3.09274 | −0.101252 | ||||||||
\(934\) | −104.936 | −3.43360 | ||||||||
\(935\) | 31.0832 | 1.01653 | ||||||||
\(936\) | −94.6226 | −3.09284 | ||||||||
\(937\) | −36.9287 | −1.20641 | −0.603204 | − | 0.797587i | \(-0.706110\pi\) | ||||
−0.603204 | + | 0.797587i | \(0.706110\pi\) | |||||||
\(938\) | −19.7440 | −0.644665 | ||||||||
\(939\) | 3.30930 | 0.107995 | ||||||||
\(940\) | 57.3367 | 1.87012 | ||||||||
\(941\) | −38.0152 | −1.23926 | −0.619630 | − | 0.784894i | \(-0.712717\pi\) | ||||
−0.619630 | + | 0.784894i | \(0.712717\pi\) | |||||||
\(942\) | 11.4970 | 0.374593 | ||||||||
\(943\) | −0.0448685 | −0.00146112 | ||||||||
\(944\) | −70.9634 | −2.30966 | ||||||||
\(945\) | −6.00485 | −0.195338 | ||||||||
\(946\) | 10.9514 | 0.356061 | ||||||||
\(947\) | 5.88590 | 0.191266 | 0.0956331 | − | 0.995417i | \(-0.469512\pi\) | ||||
0.0956331 | + | 0.995417i | \(0.469512\pi\) | |||||||
\(948\) | 6.89383 | 0.223901 | ||||||||
\(949\) | 5.76122 | 0.187017 | ||||||||
\(950\) | 46.4762 | 1.50789 | ||||||||
\(951\) | 1.43364 | 0.0464890 | ||||||||
\(952\) | 34.1993 | 1.10841 | ||||||||
\(953\) | −1.04219 | −0.0337600 | −0.0168800 | − | 0.999858i | \(-0.505373\pi\) | ||||
−0.0168800 | + | 0.999858i | \(0.505373\pi\) | |||||||
\(954\) | 5.53521 | 0.179209 | ||||||||
\(955\) | 22.3033 | 0.721718 | ||||||||
\(956\) | −120.109 | −3.88459 | ||||||||
\(957\) | −5.84383 | −0.188904 | ||||||||
\(958\) | 72.8251 | 2.35287 | ||||||||
\(959\) | 18.5423 | 0.598762 | ||||||||
\(960\) | 12.6681 | 0.408861 | ||||||||
\(961\) | −29.4902 | −0.951296 | ||||||||
\(962\) | 27.1487 | 0.875310 | ||||||||
\(963\) | 8.84788 | 0.285119 | ||||||||
\(964\) | −99.8420 | −3.21569 | ||||||||
\(965\) | 51.0462 | 1.64324 | ||||||||
\(966\) | 0.0740945 | 0.00238395 | ||||||||
\(967\) | 28.1286 | 0.904553 | 0.452277 | − | 0.891878i | \(-0.350612\pi\) | ||||
0.452277 | + | 0.891878i | \(0.350612\pi\) | |||||||
\(968\) | 46.6069 | 1.49800 | ||||||||
\(969\) | 4.81364 | 0.154636 | ||||||||
\(970\) | −37.0104 | −1.18833 | ||||||||
\(971\) | 29.8038 | 0.956451 | 0.478225 | − | 0.878237i | \(-0.341280\pi\) | ||||
0.478225 | + | 0.878237i | \(0.341280\pi\) | |||||||
\(972\) | 41.1747 | 1.32068 | ||||||||
\(973\) | −12.4252 | −0.398335 | ||||||||
\(974\) | −65.9259 | −2.11240 | ||||||||
\(975\) | −6.75902 | −0.216462 | ||||||||
\(976\) | −3.52064 | −0.112693 | ||||||||
\(977\) | 5.27992 | 0.168920 | 0.0844599 | − | 0.996427i | \(-0.473084\pi\) | ||||
0.0844599 | + | 0.996427i | \(0.473084\pi\) | |||||||
\(978\) | −6.14327 | −0.196440 | ||||||||
\(979\) | −0.380936 | −0.0121748 | ||||||||
\(980\) | 15.8211 | 0.505388 | ||||||||
\(981\) | 30.8358 | 0.984513 | ||||||||
\(982\) | 9.60600 | 0.306540 | ||||||||
\(983\) | −3.92318 | −0.125130 | −0.0625651 | − | 0.998041i | \(-0.519928\pi\) | ||||
−0.0625651 | + | 0.998041i | \(0.519928\pi\) | |||||||
\(984\) | −1.29608 | −0.0413174 | ||||||||
\(985\) | −25.5055 | −0.812672 | ||||||||
\(986\) | 92.7019 | 2.95223 | ||||||||
\(987\) | 1.16200 | 0.0369867 | ||||||||
\(988\) | 71.4257 | 2.27235 | ||||||||
\(989\) | −0.160748 | −0.00511147 | ||||||||
\(990\) | −54.8203 | −1.74230 | ||||||||
\(991\) | −41.8517 | −1.32946 | −0.664732 | − | 0.747082i | \(-0.731454\pi\) | ||||
−0.664732 | + | 0.747082i | \(0.731454\pi\) | |||||||
\(992\) | 15.8812 | 0.504228 | ||||||||
\(993\) | 4.22457 | 0.134063 | ||||||||
\(994\) | 16.1453 | 0.512098 | ||||||||
\(995\) | 68.8133 | 2.18153 | ||||||||
\(996\) | 25.5693 | 0.810193 | ||||||||
\(997\) | −18.4242 | −0.583502 | −0.291751 | − | 0.956494i | \(-0.594238\pi\) | ||||
−0.291751 | + | 0.956494i | \(0.594238\pi\) | |||||||
\(998\) | 104.555 | 3.30962 | ||||||||
\(999\) | −4.68676 | −0.148282 |
(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 | 6013.2.a.e.1.4 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6013.2.a.e.1.4 | ✓ | 109 | 1.1 | even | 1 | trivial |