Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 35 x^{18} + 154 x^{17} + 460 x^{16} - 2392 x^{15} - 2591 x^{14} + 19157 x^{13} + \cdots + 104 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(2.32194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-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 | ||||||||
\(3\) | 2.32194 | 1.34057 | 0.670287 | − | 0.742102i | \(-0.266171\pi\) | ||||
0.670287 | + | 0.742102i | \(0.266171\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.32194 | −0.947929 | ||||||||
\(7\) | 1.00226 | 0.378820 | 0.189410 | − | 0.981898i | \(-0.439343\pi\) | ||||
0.189410 | + | 0.981898i | \(0.439343\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.39142 | 0.797139 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −0.100439 | −0.0302834 | −0.0151417 | − | 0.999885i | \(-0.504820\pi\) | ||||
−0.0151417 | + | 0.999885i | \(0.504820\pi\) | |||||||
\(12\) | 2.32194 | 0.670287 | ||||||||
\(13\) | 4.75377 | 1.31846 | 0.659230 | − | 0.751942i | \(-0.270882\pi\) | ||||
0.659230 | + | 0.751942i | \(0.270882\pi\) | |||||||
\(14\) | −1.00226 | −0.267866 | ||||||||
\(15\) | 2.32194 | 0.599523 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.59968 | 1.84319 | 0.921597 | − | 0.388149i | \(-0.126885\pi\) | ||||
0.921597 | + | 0.388149i | \(0.126885\pi\) | |||||||
\(18\) | −2.39142 | −0.563663 | ||||||||
\(19\) | 6.05061 | 1.38811 | 0.694053 | − | 0.719924i | \(-0.255823\pi\) | ||||
0.694053 | + | 0.719924i | \(0.255823\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 2.32720 | 0.507836 | ||||||||
\(22\) | 0.100439 | 0.0214136 | ||||||||
\(23\) | −5.89368 | −1.22892 | −0.614459 | − | 0.788949i | \(-0.710626\pi\) | ||||
−0.614459 | + | 0.788949i | \(0.710626\pi\) | |||||||
\(24\) | −2.32194 | −0.473965 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.75377 | −0.932292 | ||||||||
\(27\) | −1.41309 | −0.271950 | ||||||||
\(28\) | 1.00226 | 0.189410 | ||||||||
\(29\) | −3.17341 | −0.589288 | −0.294644 | − | 0.955607i | \(-0.595201\pi\) | ||||
−0.294644 | + | 0.955607i | \(0.595201\pi\) | |||||||
\(30\) | −2.32194 | −0.423927 | ||||||||
\(31\) | 3.07263 | 0.551862 | 0.275931 | − | 0.961178i | \(-0.411014\pi\) | ||||
0.275931 | + | 0.961178i | \(0.411014\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.233213 | −0.0405971 | ||||||||
\(34\) | −7.59968 | −1.30333 | ||||||||
\(35\) | 1.00226 | 0.169413 | ||||||||
\(36\) | 2.39142 | 0.398570 | ||||||||
\(37\) | 12.0629 | 1.98313 | 0.991564 | − | 0.129618i | \(-0.0413752\pi\) | ||||
0.991564 | + | 0.129618i | \(0.0413752\pi\) | |||||||
\(38\) | −6.05061 | −0.981539 | ||||||||
\(39\) | 11.0380 | 1.76749 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −2.81396 | −0.439466 | −0.219733 | − | 0.975560i | \(-0.570519\pi\) | ||||
−0.219733 | + | 0.975560i | \(0.570519\pi\) | |||||||
\(42\) | −2.32720 | −0.359094 | ||||||||
\(43\) | 11.9210 | 1.81793 | 0.908967 | − | 0.416869i | \(-0.136873\pi\) | ||||
0.908967 | + | 0.416869i | \(0.136873\pi\) | |||||||
\(44\) | −0.100439 | −0.0151417 | ||||||||
\(45\) | 2.39142 | 0.356492 | ||||||||
\(46\) | 5.89368 | 0.868976 | ||||||||
\(47\) | −11.1479 | −1.62609 | −0.813047 | − | 0.582198i | \(-0.802193\pi\) | ||||
−0.813047 | + | 0.582198i | \(0.802193\pi\) | |||||||
\(48\) | 2.32194 | 0.335144 | ||||||||
\(49\) | −5.99547 | −0.856496 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 17.6460 | 2.47094 | ||||||||
\(52\) | 4.75377 | 0.659230 | ||||||||
\(53\) | −12.5149 | −1.71906 | −0.859528 | − | 0.511088i | \(-0.829242\pi\) | ||||
−0.859528 | + | 0.511088i | \(0.829242\pi\) | |||||||
\(54\) | 1.41309 | 0.192298 | ||||||||
\(55\) | −0.100439 | −0.0135431 | ||||||||
\(56\) | −1.00226 | −0.133933 | ||||||||
\(57\) | 14.0492 | 1.86086 | ||||||||
\(58\) | 3.17341 | 0.416689 | ||||||||
\(59\) | −8.79853 | −1.14547 | −0.572735 | − | 0.819740i | \(-0.694118\pi\) | ||||
−0.572735 | + | 0.819740i | \(0.694118\pi\) | |||||||
\(60\) | 2.32194 | 0.299762 | ||||||||
\(61\) | −9.57495 | −1.22595 | −0.612974 | − | 0.790103i | \(-0.710027\pi\) | ||||
−0.612974 | + | 0.790103i | \(0.710027\pi\) | |||||||
\(62\) | −3.07263 | −0.390225 | ||||||||
\(63\) | 2.39683 | 0.301972 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.75377 | 0.589633 | ||||||||
\(66\) | 0.233213 | 0.0287065 | ||||||||
\(67\) | −16.1207 | −1.96946 | −0.984729 | − | 0.174092i | \(-0.944301\pi\) | ||||
−0.984729 | + | 0.174092i | \(0.944301\pi\) | |||||||
\(68\) | 7.59968 | 0.921597 | ||||||||
\(69\) | −13.6848 | −1.64746 | ||||||||
\(70\) | −1.00226 | −0.119793 | ||||||||
\(71\) | 3.80916 | 0.452064 | 0.226032 | − | 0.974120i | \(-0.427425\pi\) | ||||
0.226032 | + | 0.974120i | \(0.427425\pi\) | |||||||
\(72\) | −2.39142 | −0.281831 | ||||||||
\(73\) | −1.60086 | −0.187367 | −0.0936835 | − | 0.995602i | \(-0.529864\pi\) | ||||
−0.0936835 | + | 0.995602i | \(0.529864\pi\) | |||||||
\(74\) | −12.0629 | −1.40228 | ||||||||
\(75\) | 2.32194 | 0.268115 | ||||||||
\(76\) | 6.05061 | 0.694053 | ||||||||
\(77\) | −0.100666 | −0.0114719 | ||||||||
\(78\) | −11.0380 | −1.24981 | ||||||||
\(79\) | 0.972634 | 0.109430 | 0.0547149 | − | 0.998502i | \(-0.482575\pi\) | ||||
0.0547149 | + | 0.998502i | \(0.482575\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −10.4554 | −1.16171 | ||||||||
\(82\) | 2.81396 | 0.310749 | ||||||||
\(83\) | 6.67734 | 0.732934 | 0.366467 | − | 0.930431i | \(-0.380567\pi\) | ||||
0.366467 | + | 0.930431i | \(0.380567\pi\) | |||||||
\(84\) | 2.32720 | 0.253918 | ||||||||
\(85\) | 7.59968 | 0.824301 | ||||||||
\(86\) | −11.9210 | −1.28547 | ||||||||
\(87\) | −7.36848 | −0.789984 | ||||||||
\(88\) | 0.100439 | 0.0107068 | ||||||||
\(89\) | −6.50261 | −0.689275 | −0.344638 | − | 0.938736i | \(-0.611998\pi\) | ||||
−0.344638 | + | 0.938736i | \(0.611998\pi\) | |||||||
\(90\) | −2.39142 | −0.252078 | ||||||||
\(91\) | 4.76453 | 0.499458 | ||||||||
\(92\) | −5.89368 | −0.614459 | ||||||||
\(93\) | 7.13448 | 0.739811 | ||||||||
\(94\) | 11.1479 | 1.14982 | ||||||||
\(95\) | 6.05061 | 0.620780 | ||||||||
\(96\) | −2.32194 | −0.236982 | ||||||||
\(97\) | −1.29416 | −0.131402 | −0.0657010 | − | 0.997839i | \(-0.520928\pi\) | ||||
−0.0657010 | + | 0.997839i | \(0.520928\pi\) | |||||||
\(98\) | 5.99547 | 0.605634 | ||||||||
\(99\) | −0.240191 | −0.0241401 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 3.73268 | 0.371416 | 0.185708 | − | 0.982605i | \(-0.440542\pi\) | ||||
0.185708 | + | 0.982605i | \(0.440542\pi\) | |||||||
\(102\) | −17.6460 | −1.74722 | ||||||||
\(103\) | 4.88703 | 0.481534 | 0.240767 | − | 0.970583i | \(-0.422601\pi\) | ||||
0.240767 | + | 0.970583i | \(0.422601\pi\) | |||||||
\(104\) | −4.75377 | −0.466146 | ||||||||
\(105\) | 2.32720 | 0.227111 | ||||||||
\(106\) | 12.5149 | 1.21556 | ||||||||
\(107\) | 18.5605 | 1.79431 | 0.897157 | − | 0.441713i | \(-0.145629\pi\) | ||||
0.897157 | + | 0.441713i | \(0.145629\pi\) | |||||||
\(108\) | −1.41309 | −0.135975 | ||||||||
\(109\) | 1.07320 | 0.102794 | 0.0513971 | − | 0.998678i | \(-0.483633\pi\) | ||||
0.0513971 | + | 0.998678i | \(0.483633\pi\) | |||||||
\(110\) | 0.100439 | 0.00957645 | ||||||||
\(111\) | 28.0094 | 2.65853 | ||||||||
\(112\) | 1.00226 | 0.0947049 | ||||||||
\(113\) | 12.8704 | 1.21075 | 0.605375 | − | 0.795940i | \(-0.293023\pi\) | ||||
0.605375 | + | 0.795940i | \(0.293023\pi\) | |||||||
\(114\) | −14.0492 | −1.31583 | ||||||||
\(115\) | −5.89368 | −0.549589 | ||||||||
\(116\) | −3.17341 | −0.294644 | ||||||||
\(117\) | 11.3683 | 1.05100 | ||||||||
\(118\) | 8.79853 | 0.809970 | ||||||||
\(119\) | 7.61687 | 0.698238 | ||||||||
\(120\) | −2.32194 | −0.211963 | ||||||||
\(121\) | −10.9899 | −0.999083 | ||||||||
\(122\) | 9.57495 | 0.866876 | ||||||||
\(123\) | −6.53384 | −0.589137 | ||||||||
\(124\) | 3.07263 | 0.275931 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.39683 | −0.213526 | ||||||||
\(127\) | −4.80638 | −0.426497 | −0.213249 | − | 0.976998i | \(-0.568404\pi\) | ||||
−0.213249 | + | 0.976998i | \(0.568404\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 27.6798 | 2.43707 | ||||||||
\(130\) | −4.75377 | −0.416933 | ||||||||
\(131\) | 9.97336 | 0.871377 | 0.435688 | − | 0.900098i | \(-0.356505\pi\) | ||||
0.435688 | + | 0.900098i | \(0.356505\pi\) | |||||||
\(132\) | −0.233213 | −0.0202986 | ||||||||
\(133\) | 6.06430 | 0.525841 | ||||||||
\(134\) | 16.1207 | 1.39262 | ||||||||
\(135\) | −1.41309 | −0.121620 | ||||||||
\(136\) | −7.59968 | −0.651667 | ||||||||
\(137\) | 13.8007 | 1.17907 | 0.589535 | − | 0.807743i | \(-0.299311\pi\) | ||||
0.589535 | + | 0.807743i | \(0.299311\pi\) | |||||||
\(138\) | 13.6848 | 1.16493 | ||||||||
\(139\) | 16.5925 | 1.40735 | 0.703677 | − | 0.710520i | \(-0.251540\pi\) | ||||
0.703677 | + | 0.710520i | \(0.251540\pi\) | |||||||
\(140\) | 1.00226 | 0.0847066 | ||||||||
\(141\) | −25.8849 | −2.17990 | ||||||||
\(142\) | −3.80916 | −0.319658 | ||||||||
\(143\) | −0.477463 | −0.0399274 | ||||||||
\(144\) | 2.39142 | 0.199285 | ||||||||
\(145\) | −3.17341 | −0.263538 | ||||||||
\(146\) | 1.60086 | 0.132489 | ||||||||
\(147\) | −13.9211 | −1.14820 | ||||||||
\(148\) | 12.0629 | 0.991564 | ||||||||
\(149\) | −5.94886 | −0.487350 | −0.243675 | − | 0.969857i | \(-0.578353\pi\) | ||||
−0.243675 | + | 0.969857i | \(0.578353\pi\) | |||||||
\(150\) | −2.32194 | −0.189586 | ||||||||
\(151\) | 10.8154 | 0.880146 | 0.440073 | − | 0.897962i | \(-0.354953\pi\) | ||||
0.440073 | + | 0.897962i | \(0.354953\pi\) | |||||||
\(152\) | −6.05061 | −0.490769 | ||||||||
\(153\) | 18.1740 | 1.46928 | ||||||||
\(154\) | 0.100666 | 0.00811189 | ||||||||
\(155\) | 3.07263 | 0.246800 | ||||||||
\(156\) | 11.0380 | 0.883746 | ||||||||
\(157\) | −14.2912 | −1.14056 | −0.570281 | − | 0.821450i | \(-0.693166\pi\) | ||||
−0.570281 | + | 0.821450i | \(0.693166\pi\) | |||||||
\(158\) | −0.972634 | −0.0773786 | ||||||||
\(159\) | −29.0589 | −2.30452 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −5.90701 | −0.465538 | ||||||||
\(162\) | 10.4554 | 0.821452 | ||||||||
\(163\) | 16.1635 | 1.26602 | 0.633012 | − | 0.774142i | \(-0.281818\pi\) | ||||
0.633012 | + | 0.774142i | \(0.281818\pi\) | |||||||
\(164\) | −2.81396 | −0.219733 | ||||||||
\(165\) | −0.233213 | −0.0181556 | ||||||||
\(166\) | −6.67734 | −0.518262 | ||||||||
\(167\) | 12.5864 | 0.973969 | 0.486984 | − | 0.873411i | \(-0.338097\pi\) | ||||
0.486984 | + | 0.873411i | \(0.338097\pi\) | |||||||
\(168\) | −2.32720 | −0.179547 | ||||||||
\(169\) | 9.59836 | 0.738335 | ||||||||
\(170\) | −7.59968 | −0.582869 | ||||||||
\(171\) | 14.4695 | 1.10651 | ||||||||
\(172\) | 11.9210 | 0.908967 | ||||||||
\(173\) | −3.63810 | −0.276599 | −0.138300 | − | 0.990390i | \(-0.544164\pi\) | ||||
−0.138300 | + | 0.990390i | \(0.544164\pi\) | |||||||
\(174\) | 7.36848 | 0.558603 | ||||||||
\(175\) | 1.00226 | 0.0757639 | ||||||||
\(176\) | −0.100439 | −0.00757085 | ||||||||
\(177\) | −20.4297 | −1.53559 | ||||||||
\(178\) | 6.50261 | 0.487391 | ||||||||
\(179\) | 8.57072 | 0.640606 | 0.320303 | − | 0.947315i | \(-0.396215\pi\) | ||||
0.320303 | + | 0.947315i | \(0.396215\pi\) | |||||||
\(180\) | 2.39142 | 0.178246 | ||||||||
\(181\) | −10.8974 | −0.809995 | −0.404997 | − | 0.914318i | \(-0.632728\pi\) | ||||
−0.404997 | + | 0.914318i | \(0.632728\pi\) | |||||||
\(182\) | −4.76453 | −0.353170 | ||||||||
\(183\) | −22.2325 | −1.64347 | ||||||||
\(184\) | 5.89368 | 0.434488 | ||||||||
\(185\) | 12.0629 | 0.886882 | ||||||||
\(186\) | −7.13448 | −0.523126 | ||||||||
\(187\) | −0.763302 | −0.0558181 | ||||||||
\(188\) | −11.1479 | −0.813047 | ||||||||
\(189\) | −1.41629 | −0.103020 | ||||||||
\(190\) | −6.05061 | −0.438957 | ||||||||
\(191\) | 13.3672 | 0.967213 | 0.483607 | − | 0.875286i | \(-0.339327\pi\) | ||||
0.483607 | + | 0.875286i | \(0.339327\pi\) | |||||||
\(192\) | 2.32194 | 0.167572 | ||||||||
\(193\) | −5.68441 | −0.409173 | −0.204586 | − | 0.978849i | \(-0.565585\pi\) | ||||
−0.204586 | + | 0.978849i | \(0.565585\pi\) | |||||||
\(194\) | 1.29416 | 0.0929152 | ||||||||
\(195\) | 11.0380 | 0.790447 | ||||||||
\(196\) | −5.99547 | −0.428248 | ||||||||
\(197\) | −8.45322 | −0.602267 | −0.301133 | − | 0.953582i | \(-0.597365\pi\) | ||||
−0.301133 | + | 0.953582i | \(0.597365\pi\) | |||||||
\(198\) | 0.240191 | 0.0170696 | ||||||||
\(199\) | −2.85955 | −0.202708 | −0.101354 | − | 0.994850i | \(-0.532317\pi\) | ||||
−0.101354 | + | 0.994850i | \(0.532317\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −37.4314 | −2.64021 | ||||||||
\(202\) | −3.73268 | −0.262631 | ||||||||
\(203\) | −3.18059 | −0.223234 | ||||||||
\(204\) | 17.6460 | 1.23547 | ||||||||
\(205\) | −2.81396 | −0.196535 | ||||||||
\(206\) | −4.88703 | −0.340496 | ||||||||
\(207\) | −14.0943 | −0.979618 | ||||||||
\(208\) | 4.75377 | 0.329615 | ||||||||
\(209\) | −0.607715 | −0.0420365 | ||||||||
\(210\) | −2.32720 | −0.160592 | ||||||||
\(211\) | −0.857110 | −0.0590059 | −0.0295029 | − | 0.999565i | \(-0.509392\pi\) | ||||
−0.0295029 | + | 0.999565i | \(0.509392\pi\) | |||||||
\(212\) | −12.5149 | −0.859528 | ||||||||
\(213\) | 8.84465 | 0.606026 | ||||||||
\(214\) | −18.5605 | −1.26877 | ||||||||
\(215\) | 11.9210 | 0.813004 | ||||||||
\(216\) | 1.41309 | 0.0961488 | ||||||||
\(217\) | 3.07959 | 0.209056 | ||||||||
\(218\) | −1.07320 | −0.0726864 | ||||||||
\(219\) | −3.71712 | −0.251179 | ||||||||
\(220\) | −0.100439 | −0.00677157 | ||||||||
\(221\) | 36.1272 | 2.43018 | ||||||||
\(222\) | −28.0094 | −1.87986 | ||||||||
\(223\) | −0.534205 | −0.0357730 | −0.0178865 | − | 0.999840i | \(-0.505694\pi\) | ||||
−0.0178865 | + | 0.999840i | \(0.505694\pi\) | |||||||
\(224\) | −1.00226 | −0.0669665 | ||||||||
\(225\) | 2.39142 | 0.159428 | ||||||||
\(226\) | −12.8704 | −0.856130 | ||||||||
\(227\) | −27.1656 | −1.80304 | −0.901522 | − | 0.432732i | \(-0.857549\pi\) | ||||
−0.901522 | + | 0.432732i | \(0.857549\pi\) | |||||||
\(228\) | 14.0492 | 0.930429 | ||||||||
\(229\) | −2.31059 | −0.152688 | −0.0763442 | − | 0.997082i | \(-0.524325\pi\) | ||||
−0.0763442 | + | 0.997082i | \(0.524325\pi\) | |||||||
\(230\) | 5.89368 | 0.388618 | ||||||||
\(231\) | −0.233740 | −0.0153790 | ||||||||
\(232\) | 3.17341 | 0.208345 | ||||||||
\(233\) | 24.6839 | 1.61709 | 0.808547 | − | 0.588431i | \(-0.200254\pi\) | ||||
0.808547 | + | 0.588431i | \(0.200254\pi\) | |||||||
\(234\) | −11.3683 | −0.743166 | ||||||||
\(235\) | −11.1479 | −0.727212 | ||||||||
\(236\) | −8.79853 | −0.572735 | ||||||||
\(237\) | 2.25840 | 0.146699 | ||||||||
\(238\) | −7.61687 | −0.493729 | ||||||||
\(239\) | −26.2464 | −1.69774 | −0.848870 | − | 0.528602i | \(-0.822717\pi\) | ||||
−0.848870 | + | 0.528602i | \(0.822717\pi\) | |||||||
\(240\) | 2.32194 | 0.149881 | ||||||||
\(241\) | −6.72237 | −0.433026 | −0.216513 | − | 0.976280i | \(-0.569468\pi\) | ||||
−0.216513 | + | 0.976280i | \(0.569468\pi\) | |||||||
\(242\) | 10.9899 | 0.706458 | ||||||||
\(243\) | −20.0375 | −1.28541 | ||||||||
\(244\) | −9.57495 | −0.612974 | ||||||||
\(245\) | −5.99547 | −0.383037 | ||||||||
\(246\) | 6.53384 | 0.416583 | ||||||||
\(247\) | 28.7632 | 1.83016 | ||||||||
\(248\) | −3.07263 | −0.195113 | ||||||||
\(249\) | 15.5044 | 0.982552 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −20.8752 | −1.31763 | −0.658815 | − | 0.752305i | \(-0.728942\pi\) | ||||
−0.658815 | + | 0.752305i | \(0.728942\pi\) | |||||||
\(252\) | 2.39683 | 0.150986 | ||||||||
\(253\) | 0.591953 | 0.0372158 | ||||||||
\(254\) | 4.80638 | 0.301579 | ||||||||
\(255\) | 17.6460 | 1.10504 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.9835 | −0.997023 | −0.498512 | − | 0.866883i | \(-0.666120\pi\) | ||||
−0.498512 | + | 0.866883i | \(0.666120\pi\) | |||||||
\(258\) | −27.6798 | −1.72327 | ||||||||
\(259\) | 12.0902 | 0.751248 | ||||||||
\(260\) | 4.75377 | 0.294816 | ||||||||
\(261\) | −7.58896 | −0.469745 | ||||||||
\(262\) | −9.97336 | −0.616157 | ||||||||
\(263\) | 13.6444 | 0.841348 | 0.420674 | − | 0.907212i | \(-0.361794\pi\) | ||||
0.420674 | + | 0.907212i | \(0.361794\pi\) | |||||||
\(264\) | 0.233213 | 0.0143533 | ||||||||
\(265\) | −12.5149 | −0.768785 | ||||||||
\(266\) | −6.06430 | −0.371826 | ||||||||
\(267\) | −15.0987 | −0.924025 | ||||||||
\(268\) | −16.1207 | −0.984729 | ||||||||
\(269\) | 30.5624 | 1.86342 | 0.931712 | − | 0.363197i | \(-0.118315\pi\) | ||||
0.931712 | + | 0.363197i | \(0.118315\pi\) | |||||||
\(270\) | 1.41309 | 0.0859981 | ||||||||
\(271\) | 19.2016 | 1.16641 | 0.583207 | − | 0.812323i | \(-0.301798\pi\) | ||||
0.583207 | + | 0.812323i | \(0.301798\pi\) | |||||||
\(272\) | 7.59968 | 0.460798 | ||||||||
\(273\) | 11.0630 | 0.669561 | ||||||||
\(274\) | −13.8007 | −0.833728 | ||||||||
\(275\) | −0.100439 | −0.00605668 | ||||||||
\(276\) | −13.6848 | −0.823728 | ||||||||
\(277\) | −26.1073 | −1.56864 | −0.784318 | − | 0.620359i | \(-0.786987\pi\) | ||||
−0.784318 | + | 0.620359i | \(0.786987\pi\) | |||||||
\(278\) | −16.5925 | −0.995150 | ||||||||
\(279\) | 7.34795 | 0.439911 | ||||||||
\(280\) | −1.00226 | −0.0598966 | ||||||||
\(281\) | −6.76306 | −0.403450 | −0.201725 | − | 0.979442i | \(-0.564655\pi\) | ||||
−0.201725 | + | 0.979442i | \(0.564655\pi\) | |||||||
\(282\) | 25.8849 | 1.54142 | ||||||||
\(283\) | 3.11151 | 0.184960 | 0.0924799 | − | 0.995715i | \(-0.470521\pi\) | ||||
0.0924799 | + | 0.995715i | \(0.470521\pi\) | |||||||
\(284\) | 3.80916 | 0.226032 | ||||||||
\(285\) | 14.0492 | 0.832201 | ||||||||
\(286\) | 0.477463 | 0.0282330 | ||||||||
\(287\) | −2.82032 | −0.166478 | ||||||||
\(288\) | −2.39142 | −0.140916 | ||||||||
\(289\) | 40.7551 | 2.39736 | ||||||||
\(290\) | 3.17341 | 0.186349 | ||||||||
\(291\) | −3.00496 | −0.176154 | ||||||||
\(292\) | −1.60086 | −0.0936835 | ||||||||
\(293\) | −21.8787 | −1.27817 | −0.639084 | − | 0.769137i | \(-0.720686\pi\) | ||||
−0.639084 | + | 0.769137i | \(0.720686\pi\) | |||||||
\(294\) | 13.9211 | 0.811897 | ||||||||
\(295\) | −8.79853 | −0.512270 | ||||||||
\(296\) | −12.0629 | −0.701142 | ||||||||
\(297\) | 0.141929 | 0.00823556 | ||||||||
\(298\) | 5.94886 | 0.344608 | ||||||||
\(299\) | −28.0172 | −1.62028 | ||||||||
\(300\) | 2.32194 | 0.134057 | ||||||||
\(301\) | 11.9480 | 0.688669 | ||||||||
\(302\) | −10.8154 | −0.622357 | ||||||||
\(303\) | 8.66708 | 0.497911 | ||||||||
\(304\) | 6.05061 | 0.347026 | ||||||||
\(305\) | −9.57495 | −0.548260 | ||||||||
\(306\) | −18.1740 | −1.03894 | ||||||||
\(307\) | −13.1852 | −0.752520 | −0.376260 | − | 0.926514i | \(-0.622790\pi\) | ||||
−0.376260 | + | 0.926514i | \(0.622790\pi\) | |||||||
\(308\) | −0.100666 | −0.00573597 | ||||||||
\(309\) | 11.3474 | 0.645532 | ||||||||
\(310\) | −3.07263 | −0.174514 | ||||||||
\(311\) | 8.53085 | 0.483740 | 0.241870 | − | 0.970309i | \(-0.422239\pi\) | ||||
0.241870 | + | 0.970309i | \(0.422239\pi\) | |||||||
\(312\) | −11.0380 | −0.624903 | ||||||||
\(313\) | 3.83262 | 0.216633 | 0.108316 | − | 0.994116i | \(-0.465454\pi\) | ||||
0.108316 | + | 0.994116i | \(0.465454\pi\) | |||||||
\(314\) | 14.2912 | 0.806499 | ||||||||
\(315\) | 2.39683 | 0.135046 | ||||||||
\(316\) | 0.972634 | 0.0547149 | ||||||||
\(317\) | −13.0704 | −0.734104 | −0.367052 | − | 0.930200i | \(-0.619633\pi\) | ||||
−0.367052 | + | 0.930200i | \(0.619633\pi\) | |||||||
\(318\) | 29.0589 | 1.62954 | ||||||||
\(319\) | 0.318733 | 0.0178456 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 43.0965 | 2.40541 | ||||||||
\(322\) | 5.90701 | 0.329185 | ||||||||
\(323\) | 45.9827 | 2.55855 | ||||||||
\(324\) | −10.4554 | −0.580854 | ||||||||
\(325\) | 4.75377 | 0.263692 | ||||||||
\(326\) | −16.1635 | −0.895215 | ||||||||
\(327\) | 2.49191 | 0.137803 | ||||||||
\(328\) | 2.81396 | 0.155375 | ||||||||
\(329\) | −11.1732 | −0.615996 | ||||||||
\(330\) | 0.233213 | 0.0128379 | ||||||||
\(331\) | −0.415964 | −0.0228635 | −0.0114317 | − | 0.999935i | \(-0.503639\pi\) | ||||
−0.0114317 | + | 0.999935i | \(0.503639\pi\) | |||||||
\(332\) | 6.67734 | 0.366467 | ||||||||
\(333\) | 28.8474 | 1.58083 | ||||||||
\(334\) | −12.5864 | −0.688700 | ||||||||
\(335\) | −16.1207 | −0.880769 | ||||||||
\(336\) | 2.32720 | 0.126959 | ||||||||
\(337\) | 5.96765 | 0.325079 | 0.162539 | − | 0.986702i | \(-0.448032\pi\) | ||||
0.162539 | + | 0.986702i | \(0.448032\pi\) | |||||||
\(338\) | −9.59836 | −0.522082 | ||||||||
\(339\) | 29.8844 | 1.62310 | ||||||||
\(340\) | 7.59968 | 0.412151 | ||||||||
\(341\) | −0.308611 | −0.0167122 | ||||||||
\(342\) | −14.4695 | −0.782423 | ||||||||
\(343\) | −13.0249 | −0.703277 | ||||||||
\(344\) | −11.9210 | −0.642736 | ||||||||
\(345\) | −13.6848 | −0.736764 | ||||||||
\(346\) | 3.63810 | 0.195585 | ||||||||
\(347\) | 0.723471 | 0.0388379 | 0.0194190 | − | 0.999811i | \(-0.493818\pi\) | ||||
0.0194190 | + | 0.999811i | \(0.493818\pi\) | |||||||
\(348\) | −7.36848 | −0.394992 | ||||||||
\(349\) | 25.6014 | 1.37041 | 0.685205 | − | 0.728350i | \(-0.259713\pi\) | ||||
0.685205 | + | 0.728350i | \(0.259713\pi\) | |||||||
\(350\) | −1.00226 | −0.0535732 | ||||||||
\(351\) | −6.71752 | −0.358555 | ||||||||
\(352\) | 0.100439 | 0.00535340 | ||||||||
\(353\) | −16.8800 | −0.898434 | −0.449217 | − | 0.893423i | \(-0.648297\pi\) | ||||
−0.449217 | + | 0.893423i | \(0.648297\pi\) | |||||||
\(354\) | 20.4297 | 1.08583 | ||||||||
\(355\) | 3.80916 | 0.202169 | ||||||||
\(356\) | −6.50261 | −0.344638 | ||||||||
\(357\) | 17.6859 | 0.936039 | ||||||||
\(358\) | −8.57072 | −0.452977 | ||||||||
\(359\) | −11.0961 | −0.585627 | −0.292814 | − | 0.956170i | \(-0.594592\pi\) | ||||
−0.292814 | + | 0.956170i | \(0.594592\pi\) | |||||||
\(360\) | −2.39142 | −0.126039 | ||||||||
\(361\) | 17.6099 | 0.926836 | ||||||||
\(362\) | 10.8974 | 0.572753 | ||||||||
\(363\) | −25.5179 | −1.33934 | ||||||||
\(364\) | 4.76453 | 0.249729 | ||||||||
\(365\) | −1.60086 | −0.0837931 | ||||||||
\(366\) | 22.2325 | 1.16211 | ||||||||
\(367\) | −28.0345 | −1.46339 | −0.731694 | − | 0.681634i | \(-0.761270\pi\) | ||||
−0.731694 | + | 0.681634i | \(0.761270\pi\) | |||||||
\(368\) | −5.89368 | −0.307229 | ||||||||
\(369\) | −6.72935 | −0.350316 | ||||||||
\(370\) | −12.0629 | −0.627120 | ||||||||
\(371\) | −12.5432 | −0.651212 | ||||||||
\(372\) | 7.13448 | 0.369906 | ||||||||
\(373\) | 18.7554 | 0.971116 | 0.485558 | − | 0.874204i | \(-0.338616\pi\) | ||||
0.485558 | + | 0.874204i | \(0.338616\pi\) | |||||||
\(374\) | 0.763302 | 0.0394694 | ||||||||
\(375\) | 2.32194 | 0.119905 | ||||||||
\(376\) | 11.1479 | 0.574911 | ||||||||
\(377\) | −15.0857 | −0.776952 | ||||||||
\(378\) | 1.41629 | 0.0728461 | ||||||||
\(379\) | 29.1260 | 1.49610 | 0.748052 | − | 0.663640i | \(-0.230989\pi\) | ||||
0.748052 | + | 0.663640i | \(0.230989\pi\) | |||||||
\(380\) | 6.05061 | 0.310390 | ||||||||
\(381\) | −11.1601 | −0.571751 | ||||||||
\(382\) | −13.3672 | −0.683923 | ||||||||
\(383\) | 14.1299 | 0.722005 | 0.361003 | − | 0.932565i | \(-0.382435\pi\) | ||||
0.361003 | + | 0.932565i | \(0.382435\pi\) | |||||||
\(384\) | −2.32194 | −0.118491 | ||||||||
\(385\) | −0.100666 | −0.00513041 | ||||||||
\(386\) | 5.68441 | 0.289329 | ||||||||
\(387\) | 28.5081 | 1.44915 | ||||||||
\(388\) | −1.29416 | −0.0657010 | ||||||||
\(389\) | −21.3146 | −1.08070 | −0.540348 | − | 0.841442i | \(-0.681707\pi\) | ||||
−0.540348 | + | 0.841442i | \(0.681707\pi\) | |||||||
\(390\) | −11.0380 | −0.558930 | ||||||||
\(391\) | −44.7901 | −2.26513 | ||||||||
\(392\) | 5.99547 | 0.302817 | ||||||||
\(393\) | 23.1576 | 1.16815 | ||||||||
\(394\) | 8.45322 | 0.425867 | ||||||||
\(395\) | 0.972634 | 0.0489385 | ||||||||
\(396\) | −0.240191 | −0.0120700 | ||||||||
\(397\) | −20.1305 | −1.01032 | −0.505162 | − | 0.863025i | \(-0.668567\pi\) | ||||
−0.505162 | + | 0.863025i | \(0.668567\pi\) | |||||||
\(398\) | 2.85955 | 0.143336 | ||||||||
\(399\) | 14.0810 | 0.704930 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 37.4314 | 1.86691 | ||||||||
\(403\) | 14.6066 | 0.727607 | ||||||||
\(404\) | 3.73268 | 0.185708 | ||||||||
\(405\) | −10.4554 | −0.519532 | ||||||||
\(406\) | 3.18059 | 0.157850 | ||||||||
\(407\) | −1.21158 | −0.0600558 | ||||||||
\(408\) | −17.6460 | −0.873608 | ||||||||
\(409\) | −21.2779 | −1.05213 | −0.526063 | − | 0.850446i | \(-0.676332\pi\) | ||||
−0.526063 | + | 0.850446i | \(0.676332\pi\) | |||||||
\(410\) | 2.81396 | 0.138971 | ||||||||
\(411\) | 32.0443 | 1.58063 | ||||||||
\(412\) | 4.88703 | 0.240767 | ||||||||
\(413\) | −8.81843 | −0.433927 | ||||||||
\(414\) | 14.0943 | 0.692695 | ||||||||
\(415\) | 6.67734 | 0.327778 | ||||||||
\(416\) | −4.75377 | −0.233073 | ||||||||
\(417\) | 38.5268 | 1.88666 | ||||||||
\(418\) | 0.607715 | 0.0297243 | ||||||||
\(419\) | −30.0402 | −1.46756 | −0.733779 | − | 0.679388i | \(-0.762245\pi\) | ||||
−0.733779 | + | 0.679388i | \(0.762245\pi\) | |||||||
\(420\) | 2.32720 | 0.113556 | ||||||||
\(421\) | −15.3414 | −0.747694 | −0.373847 | − | 0.927490i | \(-0.621962\pi\) | ||||
−0.373847 | + | 0.927490i | \(0.621962\pi\) | |||||||
\(422\) | 0.857110 | 0.0417235 | ||||||||
\(423\) | −26.6594 | −1.29622 | ||||||||
\(424\) | 12.5149 | 0.607778 | ||||||||
\(425\) | 7.59968 | 0.368639 | ||||||||
\(426\) | −8.84465 | −0.428525 | ||||||||
\(427\) | −9.59662 | −0.464413 | ||||||||
\(428\) | 18.5605 | 0.897157 | ||||||||
\(429\) | −1.10864 | −0.0535257 | ||||||||
\(430\) | −11.9210 | −0.574881 | ||||||||
\(431\) | 4.94001 | 0.237952 | 0.118976 | − | 0.992897i | \(-0.462039\pi\) | ||||
0.118976 | + | 0.992897i | \(0.462039\pi\) | |||||||
\(432\) | −1.41309 | −0.0679874 | ||||||||
\(433\) | 12.5278 | 0.602048 | 0.301024 | − | 0.953617i | \(-0.402672\pi\) | ||||
0.301024 | + | 0.953617i | \(0.402672\pi\) | |||||||
\(434\) | −3.07959 | −0.147825 | ||||||||
\(435\) | −7.36848 | −0.353292 | ||||||||
\(436\) | 1.07320 | 0.0513971 | ||||||||
\(437\) | −35.6604 | −1.70587 | ||||||||
\(438\) | 3.71712 | 0.177611 | ||||||||
\(439\) | 6.65174 | 0.317470 | 0.158735 | − | 0.987321i | \(-0.449258\pi\) | ||||
0.158735 | + | 0.987321i | \(0.449258\pi\) | |||||||
\(440\) | 0.100439 | 0.00478822 | ||||||||
\(441\) | −14.3377 | −0.682746 | ||||||||
\(442\) | −36.1272 | −1.71839 | ||||||||
\(443\) | −0.682149 | −0.0324099 | −0.0162049 | − | 0.999869i | \(-0.505158\pi\) | ||||
−0.0162049 | + | 0.999869i | \(0.505158\pi\) | |||||||
\(444\) | 28.0094 | 1.32927 | ||||||||
\(445\) | −6.50261 | −0.308253 | ||||||||
\(446\) | 0.534205 | 0.0252954 | ||||||||
\(447\) | −13.8129 | −0.653328 | ||||||||
\(448\) | 1.00226 | 0.0473524 | ||||||||
\(449\) | 0.981671 | 0.0463279 | 0.0231640 | − | 0.999732i | \(-0.492626\pi\) | ||||
0.0231640 | + | 0.999732i | \(0.492626\pi\) | |||||||
\(450\) | −2.39142 | −0.112733 | ||||||||
\(451\) | 0.282630 | 0.0133085 | ||||||||
\(452\) | 12.8704 | 0.605375 | ||||||||
\(453\) | 25.1128 | 1.17990 | ||||||||
\(454\) | 27.1656 | 1.27495 | ||||||||
\(455\) | 4.76453 | 0.223365 | ||||||||
\(456\) | −14.0492 | −0.657913 | ||||||||
\(457\) | 5.68196 | 0.265791 | 0.132895 | − | 0.991130i | \(-0.457573\pi\) | ||||
0.132895 | + | 0.991130i | \(0.457573\pi\) | |||||||
\(458\) | 2.31059 | 0.107967 | ||||||||
\(459\) | −10.7390 | −0.501256 | ||||||||
\(460\) | −5.89368 | −0.274794 | ||||||||
\(461\) | −11.8077 | −0.549938 | −0.274969 | − | 0.961453i | \(-0.588668\pi\) | ||||
−0.274969 | + | 0.961453i | \(0.588668\pi\) | |||||||
\(462\) | 0.233740 | 0.0108746 | ||||||||
\(463\) | −25.4495 | −1.18274 | −0.591369 | − | 0.806401i | \(-0.701412\pi\) | ||||
−0.591369 | + | 0.806401i | \(0.701412\pi\) | |||||||
\(464\) | −3.17341 | −0.147322 | ||||||||
\(465\) | 7.13448 | 0.330854 | ||||||||
\(466\) | −24.6839 | −1.14346 | ||||||||
\(467\) | −27.5015 | −1.27262 | −0.636309 | − | 0.771434i | \(-0.719540\pi\) | ||||
−0.636309 | + | 0.771434i | \(0.719540\pi\) | |||||||
\(468\) | 11.3683 | 0.525498 | ||||||||
\(469\) | −16.1572 | −0.746069 | ||||||||
\(470\) | 11.1479 | 0.514216 | ||||||||
\(471\) | −33.1834 | −1.52901 | ||||||||
\(472\) | 8.79853 | 0.404985 | ||||||||
\(473\) | −1.19733 | −0.0550532 | ||||||||
\(474\) | −2.25840 | −0.103732 | ||||||||
\(475\) | 6.05061 | 0.277621 | ||||||||
\(476\) | 7.61687 | 0.349119 | ||||||||
\(477\) | −29.9284 | −1.37033 | ||||||||
\(478\) | 26.2464 | 1.20048 | ||||||||
\(479\) | 34.2537 | 1.56509 | 0.782545 | − | 0.622594i | \(-0.213921\pi\) | ||||
0.782545 | + | 0.622594i | \(0.213921\pi\) | |||||||
\(480\) | −2.32194 | −0.105982 | ||||||||
\(481\) | 57.3443 | 2.61467 | ||||||||
\(482\) | 6.72237 | 0.306196 | ||||||||
\(483\) | −13.7157 | −0.624088 | ||||||||
\(484\) | −10.9899 | −0.499541 | ||||||||
\(485\) | −1.29416 | −0.0587647 | ||||||||
\(486\) | 20.0375 | 0.908920 | ||||||||
\(487\) | 8.39120 | 0.380242 | 0.190121 | − | 0.981761i | \(-0.439112\pi\) | ||||
0.190121 | + | 0.981761i | \(0.439112\pi\) | |||||||
\(488\) | 9.57495 | 0.433438 | ||||||||
\(489\) | 37.5308 | 1.69720 | ||||||||
\(490\) | 5.99547 | 0.270848 | ||||||||
\(491\) | −29.7272 | −1.34157 | −0.670785 | − | 0.741652i | \(-0.734043\pi\) | ||||
−0.670785 | + | 0.741652i | \(0.734043\pi\) | |||||||
\(492\) | −6.53384 | −0.294568 | ||||||||
\(493\) | −24.1169 | −1.08617 | ||||||||
\(494\) | −28.7632 | −1.29412 | ||||||||
\(495\) | −0.240191 | −0.0107958 | ||||||||
\(496\) | 3.07263 | 0.137965 | ||||||||
\(497\) | 3.81778 | 0.171251 | ||||||||
\(498\) | −15.5044 | −0.694769 | ||||||||
\(499\) | 14.3645 | 0.643043 | 0.321522 | − | 0.946902i | \(-0.395806\pi\) | ||||
0.321522 | + | 0.946902i | \(0.395806\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 29.2250 | 1.30568 | ||||||||
\(502\) | 20.8752 | 0.931705 | ||||||||
\(503\) | −29.1101 | −1.29795 | −0.648977 | − | 0.760808i | \(-0.724803\pi\) | ||||
−0.648977 | + | 0.760808i | \(0.724803\pi\) | |||||||
\(504\) | −2.39683 | −0.106763 | ||||||||
\(505\) | 3.73268 | 0.166102 | ||||||||
\(506\) | −0.591953 | −0.0263155 | ||||||||
\(507\) | 22.2868 | 0.989793 | ||||||||
\(508\) | −4.80638 | −0.213249 | ||||||||
\(509\) | 15.7303 | 0.697235 | 0.348617 | − | 0.937265i | \(-0.386651\pi\) | ||||
0.348617 | + | 0.937265i | \(0.386651\pi\) | |||||||
\(510\) | −17.6460 | −0.781379 | ||||||||
\(511\) | −1.60449 | −0.0709783 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −8.55007 | −0.377495 | ||||||||
\(514\) | 15.9835 | 0.705002 | ||||||||
\(515\) | 4.88703 | 0.215348 | ||||||||
\(516\) | 27.6798 | 1.21854 | ||||||||
\(517\) | 1.11968 | 0.0492437 | ||||||||
\(518\) | −12.0902 | −0.531212 | ||||||||
\(519\) | −8.44746 | −0.370802 | ||||||||
\(520\) | −4.75377 | −0.208467 | ||||||||
\(521\) | −2.02577 | −0.0887505 | −0.0443752 | − | 0.999015i | \(-0.514130\pi\) | ||||
−0.0443752 | + | 0.999015i | \(0.514130\pi\) | |||||||
\(522\) | 7.58896 | 0.332160 | ||||||||
\(523\) | 26.3225 | 1.15100 | 0.575501 | − | 0.817801i | \(-0.304807\pi\) | ||||
0.575501 | + | 0.817801i | \(0.304807\pi\) | |||||||
\(524\) | 9.97336 | 0.435688 | ||||||||
\(525\) | 2.32720 | 0.101567 | ||||||||
\(526\) | −13.6444 | −0.594923 | ||||||||
\(527\) | 23.3510 | 1.01719 | ||||||||
\(528\) | −0.233213 | −0.0101493 | ||||||||
\(529\) | 11.7355 | 0.510238 | ||||||||
\(530\) | 12.5149 | 0.543613 | ||||||||
\(531\) | −21.0410 | −0.913100 | ||||||||
\(532\) | 6.06430 | 0.262921 | ||||||||
\(533\) | −13.3769 | −0.579418 | ||||||||
\(534\) | 15.0987 | 0.653384 | ||||||||
\(535\) | 18.5605 | 0.802441 | ||||||||
\(536\) | 16.1207 | 0.696309 | ||||||||
\(537\) | 19.9007 | 0.858779 | ||||||||
\(538\) | −30.5624 | −1.31764 | ||||||||
\(539\) | 0.602177 | 0.0259376 | ||||||||
\(540\) | −1.41309 | −0.0608098 | ||||||||
\(541\) | 14.0303 | 0.603211 | 0.301606 | − | 0.953433i | \(-0.402477\pi\) | ||||
0.301606 | + | 0.953433i | \(0.402477\pi\) | |||||||
\(542\) | −19.2016 | −0.824779 | ||||||||
\(543\) | −25.3031 | −1.08586 | ||||||||
\(544\) | −7.59968 | −0.325834 | ||||||||
\(545\) | 1.07320 | 0.0459709 | ||||||||
\(546\) | −11.0630 | −0.473451 | ||||||||
\(547\) | 7.93761 | 0.339388 | 0.169694 | − | 0.985497i | \(-0.445722\pi\) | ||||
0.169694 | + | 0.985497i | \(0.445722\pi\) | |||||||
\(548\) | 13.8007 | 0.589535 | ||||||||
\(549\) | −22.8977 | −0.977251 | ||||||||
\(550\) | 0.100439 | 0.00428272 | ||||||||
\(551\) | −19.2011 | −0.817994 | ||||||||
\(552\) | 13.6848 | 0.582463 | ||||||||
\(553\) | 0.974834 | 0.0414542 | ||||||||
\(554\) | 26.1073 | 1.10919 | ||||||||
\(555\) | 28.0094 | 1.18893 | ||||||||
\(556\) | 16.5925 | 0.703677 | ||||||||
\(557\) | 21.4580 | 0.909206 | 0.454603 | − | 0.890694i | \(-0.349781\pi\) | ||||
0.454603 | + | 0.890694i | \(0.349781\pi\) | |||||||
\(558\) | −7.34795 | −0.311064 | ||||||||
\(559\) | 56.6697 | 2.39687 | ||||||||
\(560\) | 1.00226 | 0.0423533 | ||||||||
\(561\) | −1.77234 | −0.0748284 | ||||||||
\(562\) | 6.76306 | 0.285283 | ||||||||
\(563\) | −21.5501 | −0.908228 | −0.454114 | − | 0.890944i | \(-0.650044\pi\) | ||||
−0.454114 | + | 0.890944i | \(0.650044\pi\) | |||||||
\(564\) | −25.8849 | −1.08995 | ||||||||
\(565\) | 12.8704 | 0.541464 | ||||||||
\(566\) | −3.11151 | −0.130786 | ||||||||
\(567\) | −10.4790 | −0.440078 | ||||||||
\(568\) | −3.80916 | −0.159829 | ||||||||
\(569\) | −33.7226 | −1.41372 | −0.706862 | − | 0.707351i | \(-0.749890\pi\) | ||||
−0.706862 | + | 0.707351i | \(0.749890\pi\) | |||||||
\(570\) | −14.0492 | −0.588455 | ||||||||
\(571\) | 34.6770 | 1.45119 | 0.725593 | − | 0.688124i | \(-0.241565\pi\) | ||||
0.725593 | + | 0.688124i | \(0.241565\pi\) | |||||||
\(572\) | −0.477463 | −0.0199637 | ||||||||
\(573\) | 31.0378 | 1.29662 | ||||||||
\(574\) | 2.82032 | 0.117718 | ||||||||
\(575\) | −5.89368 | −0.245783 | ||||||||
\(576\) | 2.39142 | 0.0996424 | ||||||||
\(577\) | −40.1546 | −1.67166 | −0.835828 | − | 0.548991i | \(-0.815012\pi\) | ||||
−0.835828 | + | 0.548991i | \(0.815012\pi\) | |||||||
\(578\) | −40.7551 | −1.69519 | ||||||||
\(579\) | −13.1989 | −0.548526 | ||||||||
\(580\) | −3.17341 | −0.131769 | ||||||||
\(581\) | 6.69245 | 0.277650 | ||||||||
\(582\) | 3.00496 | 0.124560 | ||||||||
\(583\) | 1.25698 | 0.0520589 | ||||||||
\(584\) | 1.60086 | 0.0662443 | ||||||||
\(585\) | 11.3683 | 0.470020 | ||||||||
\(586\) | 21.8787 | 0.903802 | ||||||||
\(587\) | −20.4847 | −0.845496 | −0.422748 | − | 0.906247i | \(-0.638934\pi\) | ||||
−0.422748 | + | 0.906247i | \(0.638934\pi\) | |||||||
\(588\) | −13.9211 | −0.574098 | ||||||||
\(589\) | 18.5913 | 0.766042 | ||||||||
\(590\) | 8.79853 | 0.362230 | ||||||||
\(591\) | −19.6279 | −0.807383 | ||||||||
\(592\) | 12.0629 | 0.495782 | ||||||||
\(593\) | 1.05997 | 0.0435278 | 0.0217639 | − | 0.999763i | \(-0.493072\pi\) | ||||
0.0217639 | + | 0.999763i | \(0.493072\pi\) | |||||||
\(594\) | −0.141929 | −0.00582342 | ||||||||
\(595\) | 7.61687 | 0.312261 | ||||||||
\(596\) | −5.94886 | −0.243675 | ||||||||
\(597\) | −6.63971 | −0.271745 | ||||||||
\(598\) | 28.0172 | 1.14571 | ||||||||
\(599\) | 27.5563 | 1.12592 | 0.562961 | − | 0.826484i | \(-0.309662\pi\) | ||||
0.562961 | + | 0.826484i | \(0.309662\pi\) | |||||||
\(600\) | −2.32194 | −0.0947929 | ||||||||
\(601\) | −31.0102 | −1.26493 | −0.632466 | − | 0.774588i | \(-0.717957\pi\) | ||||
−0.632466 | + | 0.774588i | \(0.717957\pi\) | |||||||
\(602\) | −11.9480 | −0.486962 | ||||||||
\(603\) | −38.5514 | −1.56993 | ||||||||
\(604\) | 10.8154 | 0.440073 | ||||||||
\(605\) | −10.9899 | −0.446803 | ||||||||
\(606\) | −8.66708 | −0.352076 | ||||||||
\(607\) | −15.3837 | −0.624404 | −0.312202 | − | 0.950016i | \(-0.601066\pi\) | ||||
−0.312202 | + | 0.950016i | \(0.601066\pi\) | |||||||
\(608\) | −6.05061 | −0.245385 | ||||||||
\(609\) | −7.38515 | −0.299261 | ||||||||
\(610\) | 9.57495 | 0.387679 | ||||||||
\(611\) | −52.9948 | −2.14394 | ||||||||
\(612\) | 18.1740 | 0.734641 | ||||||||
\(613\) | 10.3396 | 0.417613 | 0.208806 | − | 0.977957i | \(-0.433042\pi\) | ||||
0.208806 | + | 0.977957i | \(0.433042\pi\) | |||||||
\(614\) | 13.1852 | 0.532112 | ||||||||
\(615\) | −6.53384 | −0.263470 | ||||||||
\(616\) | 0.100666 | 0.00405594 | ||||||||
\(617\) | 27.0342 | 1.08835 | 0.544177 | − | 0.838970i | \(-0.316842\pi\) | ||||
0.544177 | + | 0.838970i | \(0.316842\pi\) | |||||||
\(618\) | −11.3474 | −0.456460 | ||||||||
\(619\) | 33.7618 | 1.35700 | 0.678500 | − | 0.734601i | \(-0.262630\pi\) | ||||
0.678500 | + | 0.734601i | \(0.262630\pi\) | |||||||
\(620\) | 3.07263 | 0.123400 | ||||||||
\(621\) | 8.32832 | 0.334204 | ||||||||
\(622\) | −8.53085 | −0.342056 | ||||||||
\(623\) | −6.51732 | −0.261111 | ||||||||
\(624\) | 11.0380 | 0.441873 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −3.83262 | −0.153182 | ||||||||
\(627\) | −1.41108 | −0.0563531 | ||||||||
\(628\) | −14.2912 | −0.570281 | ||||||||
\(629\) | 91.6742 | 3.65529 | ||||||||
\(630\) | −2.39683 | −0.0954919 | ||||||||
\(631\) | −6.33945 | −0.252369 | −0.126185 | − | 0.992007i | \(-0.540273\pi\) | ||||
−0.126185 | + | 0.992007i | \(0.540273\pi\) | |||||||
\(632\) | −0.972634 | −0.0386893 | ||||||||
\(633\) | −1.99016 | −0.0791018 | ||||||||
\(634\) | 13.0704 | 0.519090 | ||||||||
\(635\) | −4.80638 | −0.190735 | ||||||||
\(636\) | −29.0589 | −1.15226 | ||||||||
\(637\) | −28.5011 | −1.12925 | ||||||||
\(638\) | −0.318733 | −0.0126188 | ||||||||
\(639\) | 9.10930 | 0.360358 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 26.4011 | 1.04278 | 0.521390 | − | 0.853318i | \(-0.325414\pi\) | ||||
0.521390 | + | 0.853318i | \(0.325414\pi\) | |||||||
\(642\) | −43.0965 | −1.70088 | ||||||||
\(643\) | 27.7479 | 1.09427 | 0.547135 | − | 0.837044i | \(-0.315718\pi\) | ||||
0.547135 | + | 0.837044i | \(0.315718\pi\) | |||||||
\(644\) | −5.90701 | −0.232769 | ||||||||
\(645\) | 27.6798 | 1.08989 | ||||||||
\(646\) | −45.9827 | −1.80917 | ||||||||
\(647\) | 26.1088 | 1.02644 | 0.513221 | − | 0.858257i | \(-0.328452\pi\) | ||||
0.513221 | + | 0.858257i | \(0.328452\pi\) | |||||||
\(648\) | 10.4554 | 0.410726 | ||||||||
\(649\) | 0.883712 | 0.0346887 | ||||||||
\(650\) | −4.75377 | −0.186458 | ||||||||
\(651\) | 7.15062 | 0.280255 | ||||||||
\(652\) | 16.1635 | 0.633012 | ||||||||
\(653\) | −9.52959 | −0.372922 | −0.186461 | − | 0.982462i | \(-0.559702\pi\) | ||||
−0.186461 | + | 0.982462i | \(0.559702\pi\) | |||||||
\(654\) | −2.49191 | −0.0974415 | ||||||||
\(655\) | 9.97336 | 0.389692 | ||||||||
\(656\) | −2.81396 | −0.109867 | ||||||||
\(657\) | −3.82834 | −0.149358 | ||||||||
\(658\) | 11.1732 | 0.435575 | ||||||||
\(659\) | −28.6371 | −1.11554 | −0.557771 | − | 0.829995i | \(-0.688343\pi\) | ||||
−0.557771 | + | 0.829995i | \(0.688343\pi\) | |||||||
\(660\) | −0.233213 | −0.00907780 | ||||||||
\(661\) | −9.75905 | −0.379583 | −0.189792 | − | 0.981824i | \(-0.560781\pi\) | ||||
−0.189792 | + | 0.981824i | \(0.560781\pi\) | |||||||
\(662\) | 0.415964 | 0.0161669 | ||||||||
\(663\) | 83.8852 | 3.25783 | ||||||||
\(664\) | −6.67734 | −0.259131 | ||||||||
\(665\) | 6.06430 | 0.235163 | ||||||||
\(666\) | −28.8474 | −1.11782 | ||||||||
\(667\) | 18.7031 | 0.724186 | ||||||||
\(668\) | 12.5864 | 0.486984 | ||||||||
\(669\) | −1.24039 | −0.0479564 | ||||||||
\(670\) | 16.1207 | 0.622798 | ||||||||
\(671\) | 0.961695 | 0.0371258 | ||||||||
\(672\) | −2.32720 | −0.0897735 | ||||||||
\(673\) | 28.3981 | 1.09467 | 0.547333 | − | 0.836915i | \(-0.315643\pi\) | ||||
0.547333 | + | 0.836915i | \(0.315643\pi\) | |||||||
\(674\) | −5.96765 | −0.229865 | ||||||||
\(675\) | −1.41309 | −0.0543899 | ||||||||
\(676\) | 9.59836 | 0.369168 | ||||||||
\(677\) | −7.26635 | −0.279269 | −0.139634 | − | 0.990203i | \(-0.544593\pi\) | ||||
−0.139634 | + | 0.990203i | \(0.544593\pi\) | |||||||
\(678\) | −29.8844 | −1.14771 | ||||||||
\(679\) | −1.29709 | −0.0497776 | ||||||||
\(680\) | −7.59968 | −0.291434 | ||||||||
\(681\) | −63.0770 | −2.41712 | ||||||||
\(682\) | 0.308611 | 0.0118173 | ||||||||
\(683\) | 2.05562 | 0.0786561 | 0.0393281 | − | 0.999226i | \(-0.487478\pi\) | ||||
0.0393281 | + | 0.999226i | \(0.487478\pi\) | |||||||
\(684\) | 14.4695 | 0.553257 | ||||||||
\(685\) | 13.8007 | 0.527296 | ||||||||
\(686\) | 13.0249 | 0.497292 | ||||||||
\(687\) | −5.36507 | −0.204690 | ||||||||
\(688\) | 11.9210 | 0.454483 | ||||||||
\(689\) | −59.4931 | −2.26651 | ||||||||
\(690\) | 13.6848 | 0.520971 | ||||||||
\(691\) | −7.03333 | −0.267561 | −0.133780 | − | 0.991011i | \(-0.542712\pi\) | ||||
−0.133780 | + | 0.991011i | \(0.542712\pi\) | |||||||
\(692\) | −3.63810 | −0.138300 | ||||||||
\(693\) | −0.240734 | −0.00914474 | ||||||||
\(694\) | −0.723471 | −0.0274626 | ||||||||
\(695\) | 16.5925 | 0.629388 | ||||||||
\(696\) | 7.36848 | 0.279302 | ||||||||
\(697\) | −21.3852 | −0.810021 | ||||||||
\(698\) | −25.6014 | −0.969026 | ||||||||
\(699\) | 57.3146 | 2.16784 | ||||||||
\(700\) | 1.00226 | 0.0378820 | ||||||||
\(701\) | −2.50129 | −0.0944726 | −0.0472363 | − | 0.998884i | \(-0.515041\pi\) | ||||
−0.0472363 | + | 0.998884i | \(0.515041\pi\) | |||||||
\(702\) | 6.71752 | 0.253536 | ||||||||
\(703\) | 72.9879 | 2.75279 | ||||||||
\(704\) | −0.100439 | −0.00378542 | ||||||||
\(705\) | −25.8849 | −0.974881 | ||||||||
\(706\) | 16.8800 | 0.635289 | ||||||||
\(707\) | 3.74113 | 0.140700 | ||||||||
\(708\) | −20.4297 | −0.767794 | ||||||||
\(709\) | −29.9271 | −1.12394 | −0.561968 | − | 0.827159i | \(-0.689956\pi\) | ||||
−0.561968 | + | 0.827159i | \(0.689956\pi\) | |||||||
\(710\) | −3.80916 | −0.142955 | ||||||||
\(711\) | 2.32597 | 0.0872308 | ||||||||
\(712\) | 6.50261 | 0.243696 | ||||||||
\(713\) | −18.1091 | −0.678192 | ||||||||
\(714\) | −17.6859 | −0.661880 | ||||||||
\(715\) | −0.477463 | −0.0178561 | ||||||||
\(716\) | 8.57072 | 0.320303 | ||||||||
\(717\) | −60.9427 | −2.27595 | ||||||||
\(718\) | 11.0961 | 0.414101 | ||||||||
\(719\) | −0.794209 | −0.0296190 | −0.0148095 | − | 0.999890i | \(-0.504714\pi\) | ||||
−0.0148095 | + | 0.999890i | \(0.504714\pi\) | |||||||
\(720\) | 2.39142 | 0.0891229 | ||||||||
\(721\) | 4.89809 | 0.182414 | ||||||||
\(722\) | −17.6099 | −0.655372 | ||||||||
\(723\) | −15.6090 | −0.580504 | ||||||||
\(724\) | −10.8974 | −0.404997 | ||||||||
\(725\) | −3.17341 | −0.117858 | ||||||||
\(726\) | 25.5179 | 0.947060 | ||||||||
\(727\) | −7.62985 | −0.282976 | −0.141488 | − | 0.989940i | \(-0.545189\pi\) | ||||
−0.141488 | + | 0.989940i | \(0.545189\pi\) | |||||||
\(728\) | −4.76453 | −0.176585 | ||||||||
\(729\) | −15.1598 | −0.561474 | ||||||||
\(730\) | 1.60086 | 0.0592507 | ||||||||
\(731\) | 90.5957 | 3.35080 | ||||||||
\(732\) | −22.2325 | −0.821737 | ||||||||
\(733\) | −27.4248 | −1.01296 | −0.506480 | − | 0.862252i | \(-0.669053\pi\) | ||||
−0.506480 | + | 0.862252i | \(0.669053\pi\) | |||||||
\(734\) | 28.0345 | 1.03477 | ||||||||
\(735\) | −13.9211 | −0.513489 | ||||||||
\(736\) | 5.89368 | 0.217244 | ||||||||
\(737\) | 1.61914 | 0.0596419 | ||||||||
\(738\) | 6.72935 | 0.247711 | ||||||||
\(739\) | 15.7748 | 0.580287 | 0.290143 | − | 0.956983i | \(-0.406297\pi\) | ||||
0.290143 | + | 0.956983i | \(0.406297\pi\) | |||||||
\(740\) | 12.0629 | 0.443441 | ||||||||
\(741\) | 66.7866 | 2.45347 | ||||||||
\(742\) | 12.5432 | 0.460477 | ||||||||
\(743\) | −42.3587 | −1.55399 | −0.776995 | − | 0.629507i | \(-0.783257\pi\) | ||||
−0.776995 | + | 0.629507i | \(0.783257\pi\) | |||||||
\(744\) | −7.13448 | −0.261563 | ||||||||
\(745\) | −5.94886 | −0.217949 | ||||||||
\(746\) | −18.7554 | −0.686683 | ||||||||
\(747\) | 15.9683 | 0.584250 | ||||||||
\(748\) | −0.763302 | −0.0279091 | ||||||||
\(749\) | 18.6025 | 0.679721 | ||||||||
\(750\) | −2.32194 | −0.0847854 | ||||||||
\(751\) | 13.4053 | 0.489166 | 0.244583 | − | 0.969628i | \(-0.421349\pi\) | ||||
0.244583 | + | 0.969628i | \(0.421349\pi\) | |||||||
\(752\) | −11.1479 | −0.406524 | ||||||||
\(753\) | −48.4710 | −1.76638 | ||||||||
\(754\) | 15.0857 | 0.549388 | ||||||||
\(755\) | 10.8154 | 0.393613 | ||||||||
\(756\) | −1.41629 | −0.0515099 | ||||||||
\(757\) | −52.0482 | −1.89172 | −0.945861 | − | 0.324571i | \(-0.894780\pi\) | ||||
−0.945861 | + | 0.324571i | \(0.894780\pi\) | |||||||
\(758\) | −29.1260 | −1.05791 | ||||||||
\(759\) | 1.37448 | 0.0498905 | ||||||||
\(760\) | −6.05061 | −0.219479 | ||||||||
\(761\) | 23.8009 | 0.862783 | 0.431391 | − | 0.902165i | \(-0.358023\pi\) | ||||
0.431391 | + | 0.902165i | \(0.358023\pi\) | |||||||
\(762\) | 11.1601 | 0.404289 | ||||||||
\(763\) | 1.07563 | 0.0389404 | ||||||||
\(764\) | 13.3672 | 0.483607 | ||||||||
\(765\) | 18.1740 | 0.657083 | ||||||||
\(766\) | −14.1299 | −0.510535 | ||||||||
\(767\) | −41.8262 | −1.51026 | ||||||||
\(768\) | 2.32194 | 0.0837859 | ||||||||
\(769\) | −26.3676 | −0.950840 | −0.475420 | − | 0.879759i | \(-0.657704\pi\) | ||||
−0.475420 | + | 0.879759i | \(0.657704\pi\) | |||||||
\(770\) | 0.100666 | 0.00362775 | ||||||||
\(771\) | −37.1128 | −1.33658 | ||||||||
\(772\) | −5.68441 | −0.204586 | ||||||||
\(773\) | 47.6275 | 1.71304 | 0.856522 | − | 0.516111i | \(-0.172621\pi\) | ||||
0.856522 | + | 0.516111i | \(0.172621\pi\) | |||||||
\(774\) | −28.5081 | −1.02470 | ||||||||
\(775\) | 3.07263 | 0.110372 | ||||||||
\(776\) | 1.29416 | 0.0464576 | ||||||||
\(777\) | 28.0727 | 1.00710 | ||||||||
\(778\) | 21.3146 | 0.764167 | ||||||||
\(779\) | −17.0262 | −0.610025 | ||||||||
\(780\) | 11.0380 | 0.395223 | ||||||||
\(781\) | −0.382587 | −0.0136900 | ||||||||
\(782\) | 44.7901 | 1.60169 | ||||||||
\(783\) | 4.48432 | 0.160257 | ||||||||
\(784\) | −5.99547 | −0.214124 | ||||||||
\(785\) | −14.2912 | −0.510075 | ||||||||
\(786\) | −23.1576 | −0.826004 | ||||||||
\(787\) | −18.8524 | −0.672016 | −0.336008 | − | 0.941859i | \(-0.609077\pi\) | ||||
−0.336008 | + | 0.941859i | \(0.609077\pi\) | |||||||
\(788\) | −8.45322 | −0.301133 | ||||||||
\(789\) | 31.6814 | 1.12789 | ||||||||
\(790\) | −0.972634 | −0.0346048 | ||||||||
\(791\) | 12.8996 | 0.458656 | ||||||||
\(792\) | 0.240191 | 0.00853481 | ||||||||
\(793\) | −45.5172 | −1.61636 | ||||||||
\(794\) | 20.1305 | 0.714406 | ||||||||
\(795\) | −29.0589 | −1.03061 | ||||||||
\(796\) | −2.85955 | −0.101354 | ||||||||
\(797\) | −18.0476 | −0.639280 | −0.319640 | − | 0.947539i | \(-0.603562\pi\) | ||||
−0.319640 | + | 0.947539i | \(0.603562\pi\) | |||||||
\(798\) | −14.0810 | −0.498460 | ||||||||
\(799\) | −84.7208 | −2.99721 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −15.5505 | −0.549449 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | 0.160789 | 0.00567411 | ||||||||
\(804\) | −37.4314 | −1.32010 | ||||||||
\(805\) | −5.90701 | −0.208195 | ||||||||
\(806\) | −14.6066 | −0.514496 | ||||||||
\(807\) | 70.9642 | 2.49806 | ||||||||
\(808\) | −3.73268 | −0.131315 | ||||||||
\(809\) | 22.7074 | 0.798350 | 0.399175 | − | 0.916875i | \(-0.369297\pi\) | ||||
0.399175 | + | 0.916875i | \(0.369297\pi\) | |||||||
\(810\) | 10.4554 | 0.367364 | ||||||||
\(811\) | −11.3067 | −0.397031 | −0.198515 | − | 0.980098i | \(-0.563612\pi\) | ||||
−0.198515 | + | 0.980098i | \(0.563612\pi\) | |||||||
\(812\) | −3.18059 | −0.111617 | ||||||||
\(813\) | 44.5850 | 1.56367 | ||||||||
\(814\) | 1.21158 | 0.0424659 | ||||||||
\(815\) | 16.1635 | 0.566183 | ||||||||
\(816\) | 17.6460 | 0.617734 | ||||||||
\(817\) | 72.1292 | 2.52348 | ||||||||
\(818\) | 21.2779 | 0.743965 | ||||||||
\(819\) | 11.3940 | 0.398138 | ||||||||
\(820\) | −2.81396 | −0.0982676 | ||||||||
\(821\) | 41.5267 | 1.44929 | 0.724646 | − | 0.689122i | \(-0.242003\pi\) | ||||
0.724646 | + | 0.689122i | \(0.242003\pi\) | |||||||
\(822\) | −32.0443 | −1.11767 | ||||||||
\(823\) | −18.0149 | −0.627961 | −0.313980 | − | 0.949429i | \(-0.601663\pi\) | ||||
−0.313980 | + | 0.949429i | \(0.601663\pi\) | |||||||
\(824\) | −4.88703 | −0.170248 | ||||||||
\(825\) | −0.233213 | −0.00811943 | ||||||||
\(826\) | 8.81843 | 0.306832 | ||||||||
\(827\) | −34.0812 | −1.18512 | −0.592560 | − | 0.805526i | \(-0.701883\pi\) | ||||
−0.592560 | + | 0.805526i | \(0.701883\pi\) | |||||||
\(828\) | −14.0943 | −0.489809 | ||||||||
\(829\) | 2.27683 | 0.0790777 | 0.0395389 | − | 0.999218i | \(-0.487411\pi\) | ||||
0.0395389 | + | 0.999218i | \(0.487411\pi\) | |||||||
\(830\) | −6.67734 | −0.231774 | ||||||||
\(831\) | −60.6197 | −2.10287 | ||||||||
\(832\) | 4.75377 | 0.164807 | ||||||||
\(833\) | −45.5637 | −1.57869 | ||||||||
\(834\) | −38.5268 | −1.33407 | ||||||||
\(835\) | 12.5864 | 0.435572 | ||||||||
\(836\) | −0.607715 | −0.0210183 | ||||||||
\(837\) | −4.34192 | −0.150079 | ||||||||
\(838\) | 30.0402 | 1.03772 | ||||||||
\(839\) | 51.5922 | 1.78116 | 0.890580 | − | 0.454828i | \(-0.150299\pi\) | ||||
0.890580 | + | 0.454828i | \(0.150299\pi\) | |||||||
\(840\) | −2.32720 | −0.0802959 | ||||||||
\(841\) | −18.9295 | −0.652740 | ||||||||
\(842\) | 15.3414 | 0.528700 | ||||||||
\(843\) | −15.7034 | −0.540855 | ||||||||
\(844\) | −0.857110 | −0.0295029 | ||||||||
\(845\) | 9.59836 | 0.330194 | ||||||||
\(846\) | 26.6594 | 0.916569 | ||||||||
\(847\) | −11.0148 | −0.378472 | ||||||||
\(848\) | −12.5149 | −0.429764 | ||||||||
\(849\) | 7.22474 | 0.247952 | ||||||||
\(850\) | −7.59968 | −0.260667 | ||||||||
\(851\) | −71.0949 | −2.43710 | ||||||||
\(852\) | 8.84465 | 0.303013 | ||||||||
\(853\) | −7.16454 | −0.245309 | −0.122655 | − | 0.992449i | \(-0.539141\pi\) | ||||
−0.122655 | + | 0.992449i | \(0.539141\pi\) | |||||||
\(854\) | 9.59662 | 0.328389 | ||||||||
\(855\) | 14.4695 | 0.494848 | ||||||||
\(856\) | −18.5605 | −0.634386 | ||||||||
\(857\) | 7.41856 | 0.253413 | 0.126707 | − | 0.991940i | \(-0.459559\pi\) | ||||
0.126707 | + | 0.991940i | \(0.459559\pi\) | |||||||
\(858\) | 1.10864 | 0.0378484 | ||||||||
\(859\) | −39.6370 | −1.35240 | −0.676198 | − | 0.736720i | \(-0.736374\pi\) | ||||
−0.676198 | + | 0.736720i | \(0.736374\pi\) | |||||||
\(860\) | 11.9210 | 0.406502 | ||||||||
\(861\) | −6.54863 | −0.223177 | ||||||||
\(862\) | −4.94001 | −0.168257 | ||||||||
\(863\) | −46.1052 | −1.56944 | −0.784719 | − | 0.619851i | \(-0.787193\pi\) | ||||
−0.784719 | + | 0.619851i | \(0.787193\pi\) | |||||||
\(864\) | 1.41309 | 0.0480744 | ||||||||
\(865\) | −3.63810 | −0.123699 | ||||||||
\(866\) | −12.5278 | −0.425712 | ||||||||
\(867\) | 94.6311 | 3.21384 | ||||||||
\(868\) | 3.07959 | 0.104528 | ||||||||
\(869\) | −0.0976900 | −0.00331391 | ||||||||
\(870\) | 7.36848 | 0.249815 | ||||||||
\(871\) | −76.6342 | −2.59665 | ||||||||
\(872\) | −1.07320 | −0.0363432 | ||||||||
\(873\) | −3.09488 | −0.104746 | ||||||||
\(874\) | 35.6604 | 1.20623 | ||||||||
\(875\) | 1.00226 | 0.0338827 | ||||||||
\(876\) | −3.71712 | −0.125590 | ||||||||
\(877\) | −42.2024 | −1.42507 | −0.712537 | − | 0.701634i | \(-0.752454\pi\) | ||||
−0.712537 | + | 0.701634i | \(0.752454\pi\) | |||||||
\(878\) | −6.65174 | −0.224485 | ||||||||
\(879\) | −50.8011 | −1.71348 | ||||||||
\(880\) | −0.100439 | −0.00338579 | ||||||||
\(881\) | −4.27447 | −0.144010 | −0.0720052 | − | 0.997404i | \(-0.522940\pi\) | ||||
−0.0720052 | + | 0.997404i | \(0.522940\pi\) | |||||||
\(882\) | 14.3377 | 0.482775 | ||||||||
\(883\) | −12.2112 | −0.410939 | −0.205470 | − | 0.978663i | \(-0.565872\pi\) | ||||
−0.205470 | + | 0.978663i | \(0.565872\pi\) | |||||||
\(884\) | 36.1272 | 1.21509 | ||||||||
\(885\) | −20.4297 | −0.686736 | ||||||||
\(886\) | 0.682149 | 0.0229172 | ||||||||
\(887\) | −16.8673 | −0.566349 | −0.283175 | − | 0.959068i | \(-0.591388\pi\) | ||||
−0.283175 | + | 0.959068i | \(0.591388\pi\) | |||||||
\(888\) | −28.0094 | −0.939932 | ||||||||
\(889\) | −4.81725 | −0.161566 | ||||||||
\(890\) | 6.50261 | 0.217968 | ||||||||
\(891\) | 1.05012 | 0.0351805 | ||||||||
\(892\) | −0.534205 | −0.0178865 | ||||||||
\(893\) | −67.4519 | −2.25719 | ||||||||
\(894\) | 13.8129 | 0.461973 | ||||||||
\(895\) | 8.57072 | 0.286488 | ||||||||
\(896\) | −1.00226 | −0.0334832 | ||||||||
\(897\) | −65.0544 | −2.17210 | ||||||||
\(898\) | −0.981671 | −0.0327588 | ||||||||
\(899\) | −9.75074 | −0.325205 | ||||||||
\(900\) | 2.39142 | 0.0797139 | ||||||||
\(901\) | −95.1094 | −3.16855 | ||||||||
\(902\) | −0.282630 | −0.00941055 | ||||||||
\(903\) | 27.7425 | 0.923211 | ||||||||
\(904\) | −12.8704 | −0.428065 | ||||||||
\(905\) | −10.8974 | −0.362241 | ||||||||
\(906\) | −25.1128 | −0.834316 | ||||||||
\(907\) | 26.1590 | 0.868594 | 0.434297 | − | 0.900770i | \(-0.356997\pi\) | ||||
0.434297 | + | 0.900770i | \(0.356997\pi\) | |||||||
\(908\) | −27.1656 | −0.901522 | ||||||||
\(909\) | 8.92641 | 0.296070 | ||||||||
\(910\) | −4.76453 | −0.157943 | ||||||||
\(911\) | −43.3376 | −1.43584 | −0.717920 | − | 0.696126i | \(-0.754905\pi\) | ||||
−0.717920 | + | 0.696126i | \(0.754905\pi\) | |||||||
\(912\) | 14.0492 | 0.465215 | ||||||||
\(913\) | −0.670663 | −0.0221957 | ||||||||
\(914\) | −5.68196 | −0.187943 | ||||||||
\(915\) | −22.2325 | −0.734984 | ||||||||
\(916\) | −2.31059 | −0.0763442 | ||||||||
\(917\) | 9.99593 | 0.330095 | ||||||||
\(918\) | 10.7390 | 0.354441 | ||||||||
\(919\) | 33.9230 | 1.11902 | 0.559509 | − | 0.828824i | \(-0.310990\pi\) | ||||
0.559509 | + | 0.828824i | \(0.310990\pi\) | |||||||
\(920\) | 5.89368 | 0.194309 | ||||||||
\(921\) | −30.6153 | −1.00881 | ||||||||
\(922\) | 11.8077 | 0.388865 | ||||||||
\(923\) | 18.1079 | 0.596028 | ||||||||
\(924\) | −0.233740 | −0.00768949 | ||||||||
\(925\) | 12.0629 | 0.396626 | ||||||||
\(926\) | 25.4495 | 0.836323 | ||||||||
\(927\) | 11.6869 | 0.383850 | ||||||||
\(928\) | 3.17341 | 0.104172 | ||||||||
\(929\) | 50.7657 | 1.66557 | 0.832785 | − | 0.553597i | \(-0.186745\pi\) | ||||
0.832785 | + | 0.553597i | \(0.186745\pi\) | |||||||
\(930\) | −7.13448 | −0.233949 | ||||||||
\(931\) | −36.2763 | −1.18891 | ||||||||
\(932\) | 24.6839 | 0.808547 | ||||||||
\(933\) | 19.8081 | 0.648489 | ||||||||
\(934\) | 27.5015 | 0.899877 | ||||||||
\(935\) | −0.763302 | −0.0249626 | ||||||||
\(936\) | −11.3683 | −0.371583 | ||||||||
\(937\) | −39.6993 | −1.29692 | −0.648459 | − | 0.761250i | \(-0.724586\pi\) | ||||
−0.648459 | + | 0.761250i | \(0.724586\pi\) | |||||||
\(938\) | 16.1572 | 0.527551 | ||||||||
\(939\) | 8.89913 | 0.290412 | ||||||||
\(940\) | −11.1479 | −0.363606 | ||||||||
\(941\) | −3.68999 | −0.120290 | −0.0601451 | − | 0.998190i | \(-0.519156\pi\) | ||||
−0.0601451 | + | 0.998190i | \(0.519156\pi\) | |||||||
\(942\) | 33.1834 | 1.08117 | ||||||||
\(943\) | 16.5846 | 0.540068 | ||||||||
\(944\) | −8.79853 | −0.286368 | ||||||||
\(945\) | −1.41629 | −0.0460719 | ||||||||
\(946\) | 1.19733 | 0.0389285 | ||||||||
\(947\) | −35.9431 | −1.16799 | −0.583997 | − | 0.811756i | \(-0.698512\pi\) | ||||
−0.583997 | + | 0.811756i | \(0.698512\pi\) | |||||||
\(948\) | 2.25840 | 0.0733494 | ||||||||
\(949\) | −7.61015 | −0.247036 | ||||||||
\(950\) | −6.05061 | −0.196308 | ||||||||
\(951\) | −30.3486 | −0.984121 | ||||||||
\(952\) | −7.61687 | −0.246864 | ||||||||
\(953\) | −5.14347 | −0.166613 | −0.0833067 | − | 0.996524i | \(-0.526548\pi\) | ||||
−0.0833067 | + | 0.996524i | \(0.526548\pi\) | |||||||
\(954\) | 29.9284 | 0.968968 | ||||||||
\(955\) | 13.3672 | 0.432551 | ||||||||
\(956\) | −26.2464 | −0.848870 | ||||||||
\(957\) | 0.740080 | 0.0239234 | ||||||||
\(958\) | −34.2537 | −1.10669 | ||||||||
\(959\) | 13.8319 | 0.446655 | ||||||||
\(960\) | 2.32194 | 0.0749404 | ||||||||
\(961\) | −21.5589 | −0.695449 | ||||||||
\(962\) | −57.3443 | −1.84885 | ||||||||
\(963\) | 44.3860 | 1.43032 | ||||||||
\(964\) | −6.72237 | −0.216513 | ||||||||
\(965\) | −5.68441 | −0.182988 | ||||||||
\(966\) | 13.7157 | 0.441297 | ||||||||
\(967\) | 44.2132 | 1.42180 | 0.710900 | − | 0.703293i | \(-0.248288\pi\) | ||||
0.710900 | + | 0.703293i | \(0.248288\pi\) | |||||||
\(968\) | 10.9899 | 0.353229 | ||||||||
\(969\) | 106.769 | 3.42992 | ||||||||
\(970\) | 1.29416 | 0.0415529 | ||||||||
\(971\) | −12.5271 | −0.402012 | −0.201006 | − | 0.979590i | \(-0.564421\pi\) | ||||
−0.201006 | + | 0.979590i | \(0.564421\pi\) | |||||||
\(972\) | −20.0375 | −0.642703 | ||||||||
\(973\) | 16.6300 | 0.533134 | ||||||||
\(974\) | −8.39120 | −0.268871 | ||||||||
\(975\) | 11.0380 | 0.353499 | ||||||||
\(976\) | −9.57495 | −0.306487 | ||||||||
\(977\) | 11.3444 | 0.362941 | 0.181470 | − | 0.983396i | \(-0.441914\pi\) | ||||
0.181470 | + | 0.983396i | \(0.441914\pi\) | |||||||
\(978\) | −37.5308 | −1.20010 | ||||||||
\(979\) | 0.653114 | 0.0208736 | ||||||||
\(980\) | −5.99547 | −0.191518 | ||||||||
\(981\) | 2.56648 | 0.0819412 | ||||||||
\(982\) | 29.7272 | 0.948634 | ||||||||
\(983\) | 36.1645 | 1.15347 | 0.576734 | − | 0.816932i | \(-0.304327\pi\) | ||||
0.576734 | + | 0.816932i | \(0.304327\pi\) | |||||||
\(984\) | 6.53384 | 0.208291 | ||||||||
\(985\) | −8.45322 | −0.269342 | ||||||||
\(986\) | 24.1169 | 0.768039 | ||||||||
\(987\) | −25.9434 | −0.825789 | ||||||||
\(988\) | 28.7632 | 0.915080 | ||||||||
\(989\) | −70.2585 | −2.23409 | ||||||||
\(990\) | 0.240191 | 0.00763376 | ||||||||
\(991\) | −47.3693 | −1.50474 | −0.752368 | − | 0.658743i | \(-0.771088\pi\) | ||||
−0.752368 | + | 0.658743i | \(0.771088\pi\) | |||||||
\(992\) | −3.07263 | −0.0975563 | ||||||||
\(993\) | −0.965846 | −0.0306502 | ||||||||
\(994\) | −3.81778 | −0.121093 | ||||||||
\(995\) | −2.85955 | −0.0906538 | ||||||||
\(996\) | 15.5044 | 0.491276 | ||||||||
\(997\) | 37.6526 | 1.19247 | 0.596235 | − | 0.802810i | \(-0.296663\pi\) | ||||
0.596235 | + | 0.802810i | \(0.296663\pi\) | |||||||
\(998\) | −14.3645 | −0.454700 | ||||||||
\(999\) | −17.0460 | −0.539311 |
(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 | 4010.2.a.m.1.16 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.m.1.16 | ✓ | 20 | 1.1 | even | 1 | trivial |