Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.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: | \(48.2456129013\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 3 x^{12} - 40 x^{11} + 123 x^{10} + 537 x^{9} - 1707 x^{8} - 2914 x^{7} + 9639 x^{6} + 6938 x^{5} - 22200 x^{4} - 9466 x^{3} + 16812 x^{2} + 9304 x + 1200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(4.22619\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.22619 | 1.89001 | 0.945004 | − | 0.327059i | \(-0.106058\pi\) | ||||
0.945004 | + | 0.327059i | \(0.106058\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.162672 | 0.0614841 | 0.0307420 | − | 0.999527i | \(-0.490213\pi\) | ||||
0.0307420 | + | 0.999527i | \(0.490213\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.22619 | 1.33644 | ||||||||
\(11\) | 4.28864 | 1.29307 | 0.646537 | − | 0.762882i | \(-0.276216\pi\) | ||||
0.646537 | + | 0.762882i | \(0.276216\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.72968 | −0.479726 | −0.239863 | − | 0.970807i | \(-0.577103\pi\) | ||||
−0.239863 | + | 0.970807i | \(0.577103\pi\) | |||||||
\(14\) | 0.162672 | 0.0434758 | ||||||||
\(15\) | 4.22619 | 1.09120 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.372560 | −0.0903590 | −0.0451795 | − | 0.998979i | \(-0.514386\pi\) | ||||
−0.0451795 | + | 0.998979i | \(0.514386\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 4.22619 | 0.945004 | ||||||||
\(21\) | 0.162672 | 0.0354979 | ||||||||
\(22\) | 4.28864 | 0.914342 | ||||||||
\(23\) | −3.58563 | −0.747656 | −0.373828 | − | 0.927498i | \(-0.621955\pi\) | ||||
−0.373828 | + | 0.927498i | \(0.621955\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 12.8606 | 2.57213 | ||||||||
\(26\) | −1.72968 | −0.339218 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.162672 | 0.0307420 | ||||||||
\(29\) | 9.28951 | 1.72502 | 0.862510 | − | 0.506040i | \(-0.168891\pi\) | ||||
0.862510 | + | 0.506040i | \(0.168891\pi\) | |||||||
\(30\) | 4.22619 | 0.771592 | ||||||||
\(31\) | −4.13779 | −0.743169 | −0.371585 | − | 0.928399i | \(-0.621185\pi\) | ||||
−0.371585 | + | 0.928399i | \(0.621185\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.28864 | 0.746557 | ||||||||
\(34\) | −0.372560 | −0.0638935 | ||||||||
\(35\) | 0.687480 | 0.116205 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.48845 | 0.244699 | 0.122349 | − | 0.992487i | \(-0.460957\pi\) | ||||
0.122349 | + | 0.992487i | \(0.460957\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −1.72968 | −0.276970 | ||||||||
\(40\) | 4.22619 | 0.668219 | ||||||||
\(41\) | −2.88605 | −0.450725 | −0.225363 | − | 0.974275i | \(-0.572357\pi\) | ||||
−0.225363 | + | 0.974275i | \(0.572357\pi\) | |||||||
\(42\) | 0.162672 | 0.0251008 | ||||||||
\(43\) | −7.90481 | −1.20547 | −0.602736 | − | 0.797941i | \(-0.705923\pi\) | ||||
−0.602736 | + | 0.797941i | \(0.705923\pi\) | |||||||
\(44\) | 4.28864 | 0.646537 | ||||||||
\(45\) | 4.22619 | 0.630003 | ||||||||
\(46\) | −3.58563 | −0.528673 | ||||||||
\(47\) | −7.12704 | −1.03959 | −0.519793 | − | 0.854292i | \(-0.673991\pi\) | ||||
−0.519793 | + | 0.854292i | \(0.673991\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.97354 | −0.996220 | ||||||||
\(50\) | 12.8606 | 1.81877 | ||||||||
\(51\) | −0.372560 | −0.0521688 | ||||||||
\(52\) | −1.72968 | −0.239863 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 18.1246 | 2.44392 | ||||||||
\(56\) | 0.162672 | 0.0217379 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 9.28951 | 1.21977 | ||||||||
\(59\) | −4.09719 | −0.533409 | −0.266704 | − | 0.963778i | \(-0.585935\pi\) | ||||
−0.266704 | + | 0.963778i | \(0.585935\pi\) | |||||||
\(60\) | 4.22619 | 0.545598 | ||||||||
\(61\) | −12.6996 | −1.62602 | −0.813011 | − | 0.582248i | \(-0.802173\pi\) | ||||
−0.813011 | + | 0.582248i | \(0.802173\pi\) | |||||||
\(62\) | −4.13779 | −0.525500 | ||||||||
\(63\) | 0.162672 | 0.0204947 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.30994 | −0.906686 | ||||||||
\(66\) | 4.28864 | 0.527896 | ||||||||
\(67\) | −12.5390 | −1.53188 | −0.765940 | − | 0.642913i | \(-0.777726\pi\) | ||||
−0.765940 | + | 0.642913i | \(0.777726\pi\) | |||||||
\(68\) | −0.372560 | −0.0451795 | ||||||||
\(69\) | −3.58563 | −0.431660 | ||||||||
\(70\) | 0.687480 | 0.0821696 | ||||||||
\(71\) | 16.1640 | 1.91832 | 0.959159 | − | 0.282866i | \(-0.0912852\pi\) | ||||
0.959159 | + | 0.282866i | \(0.0912852\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 15.0565 | 1.76223 | 0.881117 | − | 0.472899i | \(-0.156792\pi\) | ||||
0.881117 | + | 0.472899i | \(0.156792\pi\) | |||||||
\(74\) | 1.48845 | 0.173028 | ||||||||
\(75\) | 12.8606 | 1.48502 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0.697641 | 0.0795035 | ||||||||
\(78\) | −1.72968 | −0.195847 | ||||||||
\(79\) | −7.40316 | −0.832921 | −0.416461 | − | 0.909154i | \(-0.636730\pi\) | ||||
−0.416461 | + | 0.909154i | \(0.636730\pi\) | |||||||
\(80\) | 4.22619 | 0.472502 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.88605 | −0.318711 | ||||||||
\(83\) | −8.64039 | −0.948406 | −0.474203 | − | 0.880416i | \(-0.657264\pi\) | ||||
−0.474203 | + | 0.880416i | \(0.657264\pi\) | |||||||
\(84\) | 0.162672 | 0.0177489 | ||||||||
\(85\) | −1.57451 | −0.170779 | ||||||||
\(86\) | −7.90481 | −0.852397 | ||||||||
\(87\) | 9.28951 | 0.995941 | ||||||||
\(88\) | 4.28864 | 0.457171 | ||||||||
\(89\) | 3.54113 | 0.375359 | 0.187679 | − | 0.982230i | \(-0.439903\pi\) | ||||
0.187679 | + | 0.982230i | \(0.439903\pi\) | |||||||
\(90\) | 4.22619 | 0.445479 | ||||||||
\(91\) | −0.281369 | −0.0294955 | ||||||||
\(92\) | −3.58563 | −0.373828 | ||||||||
\(93\) | −4.13779 | −0.429069 | ||||||||
\(94\) | −7.12704 | −0.735098 | ||||||||
\(95\) | 4.22619 | 0.433597 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 7.12709 | 0.723647 | 0.361823 | − | 0.932247i | \(-0.382154\pi\) | ||||
0.361823 | + | 0.932247i | \(0.382154\pi\) | |||||||
\(98\) | −6.97354 | −0.704434 | ||||||||
\(99\) | 4.28864 | 0.431025 | ||||||||
\(100\) | 12.8606 | 1.28606 | ||||||||
\(101\) | −0.0690802 | −0.00687374 | −0.00343687 | − | 0.999994i | \(-0.501094\pi\) | ||||
−0.00343687 | + | 0.999994i | \(0.501094\pi\) | |||||||
\(102\) | −0.372560 | −0.0368889 | ||||||||
\(103\) | −8.84739 | −0.871760 | −0.435880 | − | 0.900005i | \(-0.643563\pi\) | ||||
−0.435880 | + | 0.900005i | \(0.643563\pi\) | |||||||
\(104\) | −1.72968 | −0.169609 | ||||||||
\(105\) | 0.687480 | 0.0670912 | ||||||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | 5.16527 | 0.499345 | 0.249673 | − | 0.968330i | \(-0.419677\pi\) | ||||
0.249673 | + | 0.968330i | \(0.419677\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −7.17230 | −0.686982 | −0.343491 | − | 0.939156i | \(-0.611610\pi\) | ||||
−0.343491 | + | 0.939156i | \(0.611610\pi\) | |||||||
\(110\) | 18.1246 | 1.72811 | ||||||||
\(111\) | 1.48845 | 0.141277 | ||||||||
\(112\) | 0.162672 | 0.0153710 | ||||||||
\(113\) | 18.3107 | 1.72253 | 0.861265 | − | 0.508157i | \(-0.169673\pi\) | ||||
0.861265 | + | 0.508157i | \(0.169673\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | −15.1536 | −1.41308 | ||||||||
\(116\) | 9.28951 | 0.862510 | ||||||||
\(117\) | −1.72968 | −0.159909 | ||||||||
\(118\) | −4.09719 | −0.377177 | ||||||||
\(119\) | −0.0606049 | −0.00555564 | ||||||||
\(120\) | 4.22619 | 0.385796 | ||||||||
\(121\) | 7.39247 | 0.672043 | ||||||||
\(122\) | −12.6996 | −1.14977 | ||||||||
\(123\) | −2.88605 | −0.260226 | ||||||||
\(124\) | −4.13779 | −0.371585 | ||||||||
\(125\) | 33.2205 | 2.97134 | ||||||||
\(126\) | 0.162672 | 0.0144919 | ||||||||
\(127\) | 7.32539 | 0.650024 | 0.325012 | − | 0.945710i | \(-0.394632\pi\) | ||||
0.325012 | + | 0.945710i | \(0.394632\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.90481 | −0.695980 | ||||||||
\(130\) | −7.30994 | −0.641124 | ||||||||
\(131\) | 1.88204 | 0.164435 | 0.0822173 | − | 0.996614i | \(-0.473800\pi\) | ||||
0.0822173 | + | 0.996614i | \(0.473800\pi\) | |||||||
\(132\) | 4.28864 | 0.373279 | ||||||||
\(133\) | 0.162672 | 0.0141054 | ||||||||
\(134\) | −12.5390 | −1.08320 | ||||||||
\(135\) | 4.22619 | 0.363732 | ||||||||
\(136\) | −0.372560 | −0.0319467 | ||||||||
\(137\) | −13.4413 | −1.14837 | −0.574183 | − | 0.818727i | \(-0.694680\pi\) | ||||
−0.574183 | + | 0.818727i | \(0.694680\pi\) | |||||||
\(138\) | −3.58563 | −0.305229 | ||||||||
\(139\) | 1.73787 | 0.147404 | 0.0737020 | − | 0.997280i | \(-0.476519\pi\) | ||||
0.0737020 | + | 0.997280i | \(0.476519\pi\) | |||||||
\(140\) | 0.687480 | 0.0581027 | ||||||||
\(141\) | −7.12704 | −0.600205 | ||||||||
\(142\) | 16.1640 | 1.35646 | ||||||||
\(143\) | −7.41797 | −0.620322 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 39.2592 | 3.26030 | ||||||||
\(146\) | 15.0565 | 1.24609 | ||||||||
\(147\) | −6.97354 | −0.575168 | ||||||||
\(148\) | 1.48845 | 0.122349 | ||||||||
\(149\) | −10.0368 | −0.822243 | −0.411121 | − | 0.911581i | \(-0.634863\pi\) | ||||
−0.411121 | + | 0.911581i | \(0.634863\pi\) | |||||||
\(150\) | 12.8606 | 1.05007 | ||||||||
\(151\) | −4.42076 | −0.359756 | −0.179878 | − | 0.983689i | \(-0.557570\pi\) | ||||
−0.179878 | + | 0.983689i | \(0.557570\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −0.372560 | −0.0301197 | ||||||||
\(154\) | 0.697641 | 0.0562175 | ||||||||
\(155\) | −17.4871 | −1.40460 | ||||||||
\(156\) | −1.72968 | −0.138485 | ||||||||
\(157\) | −10.0984 | −0.805939 | −0.402969 | − | 0.915213i | \(-0.632022\pi\) | ||||
−0.402969 | + | 0.915213i | \(0.632022\pi\) | |||||||
\(158\) | −7.40316 | −0.588964 | ||||||||
\(159\) | −1.00000 | −0.0793052 | ||||||||
\(160\) | 4.22619 | 0.334109 | ||||||||
\(161\) | −0.583281 | −0.0459690 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −7.51964 | −0.588984 | −0.294492 | − | 0.955654i | \(-0.595150\pi\) | ||||
−0.294492 | + | 0.955654i | \(0.595150\pi\) | |||||||
\(164\) | −2.88605 | −0.225363 | ||||||||
\(165\) | 18.1246 | 1.41100 | ||||||||
\(166\) | −8.64039 | −0.670624 | ||||||||
\(167\) | 12.4136 | 0.960594 | 0.480297 | − | 0.877106i | \(-0.340529\pi\) | ||||
0.480297 | + | 0.877106i | \(0.340529\pi\) | |||||||
\(168\) | 0.162672 | 0.0125504 | ||||||||
\(169\) | −10.0082 | −0.769863 | ||||||||
\(170\) | −1.57451 | −0.120759 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | −7.90481 | −0.602736 | ||||||||
\(173\) | 7.13359 | 0.542357 | 0.271178 | − | 0.962529i | \(-0.412587\pi\) | ||||
0.271178 | + | 0.962529i | \(0.412587\pi\) | |||||||
\(174\) | 9.28951 | 0.704236 | ||||||||
\(175\) | 2.09206 | 0.158145 | ||||||||
\(176\) | 4.28864 | 0.323269 | ||||||||
\(177\) | −4.09719 | −0.307964 | ||||||||
\(178\) | 3.54113 | 0.265419 | ||||||||
\(179\) | 16.6540 | 1.24477 | 0.622387 | − | 0.782709i | \(-0.286163\pi\) | ||||
0.622387 | + | 0.782709i | \(0.286163\pi\) | |||||||
\(180\) | 4.22619 | 0.315001 | ||||||||
\(181\) | −15.5258 | −1.15403 | −0.577014 | − | 0.816735i | \(-0.695782\pi\) | ||||
−0.577014 | + | 0.816735i | \(0.695782\pi\) | |||||||
\(182\) | −0.281369 | −0.0208565 | ||||||||
\(183\) | −12.6996 | −0.938784 | ||||||||
\(184\) | −3.58563 | −0.264336 | ||||||||
\(185\) | 6.29045 | 0.462483 | ||||||||
\(186\) | −4.13779 | −0.303398 | ||||||||
\(187\) | −1.59778 | −0.116841 | ||||||||
\(188\) | −7.12704 | −0.519793 | ||||||||
\(189\) | 0.162672 | 0.0118326 | ||||||||
\(190\) | 4.22619 | 0.306600 | ||||||||
\(191\) | −11.7620 | −0.851068 | −0.425534 | − | 0.904943i | \(-0.639914\pi\) | ||||
−0.425534 | + | 0.904943i | \(0.639914\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −19.5836 | −1.40966 | −0.704828 | − | 0.709378i | \(-0.748976\pi\) | ||||
−0.704828 | + | 0.709378i | \(0.748976\pi\) | |||||||
\(194\) | 7.12709 | 0.511696 | ||||||||
\(195\) | −7.30994 | −0.523475 | ||||||||
\(196\) | −6.97354 | −0.498110 | ||||||||
\(197\) | 11.7158 | 0.834716 | 0.417358 | − | 0.908742i | \(-0.362956\pi\) | ||||
0.417358 | + | 0.908742i | \(0.362956\pi\) | |||||||
\(198\) | 4.28864 | 0.304781 | ||||||||
\(199\) | −3.78323 | −0.268186 | −0.134093 | − | 0.990969i | \(-0.542812\pi\) | ||||
−0.134093 | + | 0.990969i | \(0.542812\pi\) | |||||||
\(200\) | 12.8606 | 0.909385 | ||||||||
\(201\) | −12.5390 | −0.884431 | ||||||||
\(202\) | −0.0690802 | −0.00486047 | ||||||||
\(203\) | 1.51114 | 0.106061 | ||||||||
\(204\) | −0.372560 | −0.0260844 | ||||||||
\(205\) | −12.1970 | −0.851874 | ||||||||
\(206\) | −8.84739 | −0.616427 | ||||||||
\(207\) | −3.58563 | −0.249219 | ||||||||
\(208\) | −1.72968 | −0.119932 | ||||||||
\(209\) | 4.28864 | 0.296652 | ||||||||
\(210\) | 0.687480 | 0.0474407 | ||||||||
\(211\) | −21.0364 | −1.44820 | −0.724102 | − | 0.689693i | \(-0.757746\pi\) | ||||
−0.724102 | + | 0.689693i | \(0.757746\pi\) | |||||||
\(212\) | −1.00000 | −0.0686803 | ||||||||
\(213\) | 16.1640 | 1.10754 | ||||||||
\(214\) | 5.16527 | 0.353091 | ||||||||
\(215\) | −33.4072 | −2.27835 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −0.673101 | −0.0456931 | ||||||||
\(218\) | −7.17230 | −0.485770 | ||||||||
\(219\) | 15.0565 | 1.01743 | ||||||||
\(220\) | 18.1246 | 1.22196 | ||||||||
\(221\) | 0.644408 | 0.0433476 | ||||||||
\(222\) | 1.48845 | 0.0998979 | ||||||||
\(223\) | 9.18604 | 0.615142 | 0.307571 | − | 0.951525i | \(-0.400484\pi\) | ||||
0.307571 | + | 0.951525i | \(0.400484\pi\) | |||||||
\(224\) | 0.162672 | 0.0108690 | ||||||||
\(225\) | 12.8606 | 0.857376 | ||||||||
\(226\) | 18.3107 | 1.21801 | ||||||||
\(227\) | 8.29125 | 0.550309 | 0.275155 | − | 0.961400i | \(-0.411271\pi\) | ||||
0.275155 | + | 0.961400i | \(0.411271\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 6.24366 | 0.412593 | 0.206296 | − | 0.978490i | \(-0.433859\pi\) | ||||
0.206296 | + | 0.978490i | \(0.433859\pi\) | |||||||
\(230\) | −15.1536 | −0.999196 | ||||||||
\(231\) | 0.697641 | 0.0459014 | ||||||||
\(232\) | 9.28951 | 0.609887 | ||||||||
\(233\) | 3.39537 | 0.222438 | 0.111219 | − | 0.993796i | \(-0.464524\pi\) | ||||
0.111219 | + | 0.993796i | \(0.464524\pi\) | |||||||
\(234\) | −1.72968 | −0.113073 | ||||||||
\(235\) | −30.1202 | −1.96482 | ||||||||
\(236\) | −4.09719 | −0.266704 | ||||||||
\(237\) | −7.40316 | −0.480887 | ||||||||
\(238\) | −0.0606049 | −0.00392843 | ||||||||
\(239\) | 22.0413 | 1.42574 | 0.712868 | − | 0.701298i | \(-0.247396\pi\) | ||||
0.712868 | + | 0.701298i | \(0.247396\pi\) | |||||||
\(240\) | 4.22619 | 0.272799 | ||||||||
\(241\) | −15.7486 | −1.01446 | −0.507229 | − | 0.861812i | \(-0.669330\pi\) | ||||
−0.507229 | + | 0.861812i | \(0.669330\pi\) | |||||||
\(242\) | 7.39247 | 0.475206 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −12.6996 | −0.813011 | ||||||||
\(245\) | −29.4715 | −1.88286 | ||||||||
\(246\) | −2.88605 | −0.184008 | ||||||||
\(247\) | −1.72968 | −0.110057 | ||||||||
\(248\) | −4.13779 | −0.262750 | ||||||||
\(249\) | −8.64039 | −0.547562 | ||||||||
\(250\) | 33.2205 | 2.10105 | ||||||||
\(251\) | −0.454889 | −0.0287123 | −0.0143562 | − | 0.999897i | \(-0.504570\pi\) | ||||
−0.0143562 | + | 0.999897i | \(0.504570\pi\) | |||||||
\(252\) | 0.162672 | 0.0102473 | ||||||||
\(253\) | −15.3775 | −0.966776 | ||||||||
\(254\) | 7.32539 | 0.459636 | ||||||||
\(255\) | −1.57451 | −0.0985995 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.38596 | −0.273589 | −0.136794 | − | 0.990599i | \(-0.543680\pi\) | ||||
−0.136794 | + | 0.990599i | \(0.543680\pi\) | |||||||
\(258\) | −7.90481 | −0.492132 | ||||||||
\(259\) | 0.242128 | 0.0150451 | ||||||||
\(260\) | −7.30994 | −0.453343 | ||||||||
\(261\) | 9.28951 | 0.575007 | ||||||||
\(262\) | 1.88204 | 0.116273 | ||||||||
\(263\) | −4.09165 | −0.252302 | −0.126151 | − | 0.992011i | \(-0.540262\pi\) | ||||
−0.126151 | + | 0.992011i | \(0.540262\pi\) | |||||||
\(264\) | 4.28864 | 0.263948 | ||||||||
\(265\) | −4.22619 | −0.259613 | ||||||||
\(266\) | 0.162672 | 0.00997404 | ||||||||
\(267\) | 3.54113 | 0.216713 | ||||||||
\(268\) | −12.5390 | −0.765940 | ||||||||
\(269\) | −20.0849 | −1.22460 | −0.612298 | − | 0.790627i | \(-0.709755\pi\) | ||||
−0.612298 | + | 0.790627i | \(0.709755\pi\) | |||||||
\(270\) | 4.22619 | 0.257197 | ||||||||
\(271\) | 18.2974 | 1.11149 | 0.555745 | − | 0.831353i | \(-0.312433\pi\) | ||||
0.555745 | + | 0.831353i | \(0.312433\pi\) | |||||||
\(272\) | −0.372560 | −0.0225898 | ||||||||
\(273\) | −0.281369 | −0.0170292 | ||||||||
\(274\) | −13.4413 | −0.812018 | ||||||||
\(275\) | 55.1547 | 3.32596 | ||||||||
\(276\) | −3.58563 | −0.215830 | ||||||||
\(277\) | 2.76894 | 0.166370 | 0.0831849 | − | 0.996534i | \(-0.473491\pi\) | ||||
0.0831849 | + | 0.996534i | \(0.473491\pi\) | |||||||
\(278\) | 1.73787 | 0.104230 | ||||||||
\(279\) | −4.13779 | −0.247723 | ||||||||
\(280\) | 0.687480 | 0.0410848 | ||||||||
\(281\) | 10.5622 | 0.630091 | 0.315045 | − | 0.949077i | \(-0.397980\pi\) | ||||
0.315045 | + | 0.949077i | \(0.397980\pi\) | |||||||
\(282\) | −7.12704 | −0.424409 | ||||||||
\(283\) | 7.76833 | 0.461780 | 0.230890 | − | 0.972980i | \(-0.425836\pi\) | ||||
0.230890 | + | 0.972980i | \(0.425836\pi\) | |||||||
\(284\) | 16.1640 | 0.959159 | ||||||||
\(285\) | 4.22619 | 0.250338 | ||||||||
\(286\) | −7.41797 | −0.438634 | ||||||||
\(287\) | −0.469479 | −0.0277124 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.8612 | −0.991835 | ||||||||
\(290\) | 39.2592 | 2.30538 | ||||||||
\(291\) | 7.12709 | 0.417798 | ||||||||
\(292\) | 15.0565 | 0.881117 | ||||||||
\(293\) | 23.0341 | 1.34567 | 0.672834 | − | 0.739794i | \(-0.265077\pi\) | ||||
0.672834 | + | 0.739794i | \(0.265077\pi\) | |||||||
\(294\) | −6.97354 | −0.406705 | ||||||||
\(295\) | −17.3155 | −1.00815 | ||||||||
\(296\) | 1.48845 | 0.0865141 | ||||||||
\(297\) | 4.28864 | 0.248852 | ||||||||
\(298\) | −10.0368 | −0.581414 | ||||||||
\(299\) | 6.20199 | 0.358670 | ||||||||
\(300\) | 12.8606 | 0.742510 | ||||||||
\(301\) | −1.28589 | −0.0741174 | ||||||||
\(302\) | −4.42076 | −0.254386 | ||||||||
\(303\) | −0.0690802 | −0.00396856 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −53.6710 | −3.07319 | ||||||||
\(306\) | −0.372560 | −0.0212978 | ||||||||
\(307\) | 1.13527 | 0.0647935 | 0.0323967 | − | 0.999475i | \(-0.489686\pi\) | ||||
0.0323967 | + | 0.999475i | \(0.489686\pi\) | |||||||
\(308\) | 0.697641 | 0.0397518 | ||||||||
\(309\) | −8.84739 | −0.503311 | ||||||||
\(310\) | −17.4871 | −0.993199 | ||||||||
\(311\) | 11.1763 | 0.633752 | 0.316876 | − | 0.948467i | \(-0.397366\pi\) | ||||
0.316876 | + | 0.948467i | \(0.397366\pi\) | |||||||
\(312\) | −1.72968 | −0.0979237 | ||||||||
\(313\) | 30.5985 | 1.72953 | 0.864765 | − | 0.502176i | \(-0.167467\pi\) | ||||
0.864765 | + | 0.502176i | \(0.167467\pi\) | |||||||
\(314\) | −10.0984 | −0.569885 | ||||||||
\(315\) | 0.687480 | 0.0387351 | ||||||||
\(316\) | −7.40316 | −0.416461 | ||||||||
\(317\) | 30.7369 | 1.72636 | 0.863179 | − | 0.504899i | \(-0.168470\pi\) | ||||
0.863179 | + | 0.504899i | \(0.168470\pi\) | |||||||
\(318\) | −1.00000 | −0.0560772 | ||||||||
\(319\) | 39.8394 | 2.23058 | ||||||||
\(320\) | 4.22619 | 0.236251 | ||||||||
\(321\) | 5.16527 | 0.288297 | ||||||||
\(322\) | −0.583281 | −0.0325050 | ||||||||
\(323\) | −0.372560 | −0.0207298 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −22.2448 | −1.23392 | ||||||||
\(326\) | −7.51964 | −0.416474 | ||||||||
\(327\) | −7.17230 | −0.396629 | ||||||||
\(328\) | −2.88605 | −0.159355 | ||||||||
\(329\) | −1.15937 | −0.0639180 | ||||||||
\(330\) | 18.1246 | 0.997727 | ||||||||
\(331\) | −21.4262 | −1.17769 | −0.588844 | − | 0.808246i | \(-0.700417\pi\) | ||||
−0.588844 | + | 0.808246i | \(0.700417\pi\) | |||||||
\(332\) | −8.64039 | −0.474203 | ||||||||
\(333\) | 1.48845 | 0.0815663 | ||||||||
\(334\) | 12.4136 | 0.679243 | ||||||||
\(335\) | −52.9920 | −2.89526 | ||||||||
\(336\) | 0.162672 | 0.00887446 | ||||||||
\(337\) | 9.17522 | 0.499806 | 0.249903 | − | 0.968271i | \(-0.419601\pi\) | ||||
0.249903 | + | 0.968271i | \(0.419601\pi\) | |||||||
\(338\) | −10.0082 | −0.544375 | ||||||||
\(339\) | 18.3107 | 0.994503 | ||||||||
\(340\) | −1.57451 | −0.0853896 | ||||||||
\(341\) | −17.7455 | −0.960974 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | −2.27310 | −0.122736 | ||||||||
\(344\) | −7.90481 | −0.426199 | ||||||||
\(345\) | −15.1536 | −0.815840 | ||||||||
\(346\) | 7.13359 | 0.383504 | ||||||||
\(347\) | −36.7735 | −1.97410 | −0.987052 | − | 0.160402i | \(-0.948721\pi\) | ||||
−0.987052 | + | 0.160402i | \(0.948721\pi\) | |||||||
\(348\) | 9.28951 | 0.497970 | ||||||||
\(349\) | −10.8254 | −0.579471 | −0.289736 | − | 0.957107i | \(-0.593567\pi\) | ||||
−0.289736 | + | 0.957107i | \(0.593567\pi\) | |||||||
\(350\) | 2.09206 | 0.111825 | ||||||||
\(351\) | −1.72968 | −0.0923233 | ||||||||
\(352\) | 4.28864 | 0.228586 | ||||||||
\(353\) | −6.44252 | −0.342901 | −0.171450 | − | 0.985193i | \(-0.554845\pi\) | ||||
−0.171450 | + | 0.985193i | \(0.554845\pi\) | |||||||
\(354\) | −4.09719 | −0.217763 | ||||||||
\(355\) | 68.3122 | 3.62564 | ||||||||
\(356\) | 3.54113 | 0.187679 | ||||||||
\(357\) | −0.0606049 | −0.00320755 | ||||||||
\(358\) | 16.6540 | 0.880189 | ||||||||
\(359\) | 21.0901 | 1.11309 | 0.556546 | − | 0.830817i | \(-0.312126\pi\) | ||||
0.556546 | + | 0.830817i | \(0.312126\pi\) | |||||||
\(360\) | 4.22619 | 0.222740 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −15.5258 | −0.816021 | ||||||||
\(363\) | 7.39247 | 0.388004 | ||||||||
\(364\) | −0.281369 | −0.0147478 | ||||||||
\(365\) | 63.6317 | 3.33064 | ||||||||
\(366\) | −12.6996 | −0.663821 | ||||||||
\(367\) | 20.9199 | 1.09201 | 0.546004 | − | 0.837782i | \(-0.316148\pi\) | ||||
0.546004 | + | 0.837782i | \(0.316148\pi\) | |||||||
\(368\) | −3.58563 | −0.186914 | ||||||||
\(369\) | −2.88605 | −0.150242 | ||||||||
\(370\) | 6.29045 | 0.327025 | ||||||||
\(371\) | −0.162672 | −0.00844549 | ||||||||
\(372\) | −4.13779 | −0.214535 | ||||||||
\(373\) | 22.1666 | 1.14774 | 0.573870 | − | 0.818946i | \(-0.305441\pi\) | ||||
0.573870 | + | 0.818946i | \(0.305441\pi\) | |||||||
\(374\) | −1.59778 | −0.0826191 | ||||||||
\(375\) | 33.2205 | 1.71550 | ||||||||
\(376\) | −7.12704 | −0.367549 | ||||||||
\(377\) | −16.0679 | −0.827537 | ||||||||
\(378\) | 0.162672 | 0.00836693 | ||||||||
\(379\) | 21.5553 | 1.10722 | 0.553612 | − | 0.832775i | \(-0.313249\pi\) | ||||
0.553612 | + | 0.832775i | \(0.313249\pi\) | |||||||
\(380\) | 4.22619 | 0.216799 | ||||||||
\(381\) | 7.32539 | 0.375291 | ||||||||
\(382\) | −11.7620 | −0.601796 | ||||||||
\(383\) | 8.53506 | 0.436121 | 0.218061 | − | 0.975935i | \(-0.430027\pi\) | ||||
0.218061 | + | 0.975935i | \(0.430027\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 2.94836 | 0.150262 | ||||||||
\(386\) | −19.5836 | −0.996777 | ||||||||
\(387\) | −7.90481 | −0.401824 | ||||||||
\(388\) | 7.12709 | 0.361823 | ||||||||
\(389\) | −27.8908 | −1.41412 | −0.707060 | − | 0.707154i | \(-0.749979\pi\) | ||||
−0.707060 | + | 0.707154i | \(0.749979\pi\) | |||||||
\(390\) | −7.30994 | −0.370153 | ||||||||
\(391\) | 1.33586 | 0.0675575 | ||||||||
\(392\) | −6.97354 | −0.352217 | ||||||||
\(393\) | 1.88204 | 0.0949364 | ||||||||
\(394\) | 11.7158 | 0.590233 | ||||||||
\(395\) | −31.2871 | −1.57423 | ||||||||
\(396\) | 4.28864 | 0.215512 | ||||||||
\(397\) | 25.2537 | 1.26745 | 0.633724 | − | 0.773559i | \(-0.281526\pi\) | ||||
0.633724 | + | 0.773559i | \(0.281526\pi\) | |||||||
\(398\) | −3.78323 | −0.189636 | ||||||||
\(399\) | 0.162672 | 0.00814377 | ||||||||
\(400\) | 12.8606 | 0.643032 | ||||||||
\(401\) | −33.6898 | −1.68239 | −0.841194 | − | 0.540733i | \(-0.818147\pi\) | ||||
−0.841194 | + | 0.540733i | \(0.818147\pi\) | |||||||
\(402\) | −12.5390 | −0.625387 | ||||||||
\(403\) | 7.15704 | 0.356518 | ||||||||
\(404\) | −0.0690802 | −0.00343687 | ||||||||
\(405\) | 4.22619 | 0.210001 | ||||||||
\(406\) | 1.51114 | 0.0749966 | ||||||||
\(407\) | 6.38341 | 0.316414 | ||||||||
\(408\) | −0.372560 | −0.0184445 | ||||||||
\(409\) | 0.180224 | 0.00891152 | 0.00445576 | − | 0.999990i | \(-0.498582\pi\) | ||||
0.00445576 | + | 0.999990i | \(0.498582\pi\) | |||||||
\(410\) | −12.1970 | −0.602366 | ||||||||
\(411\) | −13.4413 | −0.663010 | ||||||||
\(412\) | −8.84739 | −0.435880 | ||||||||
\(413\) | −0.666496 | −0.0327961 | ||||||||
\(414\) | −3.58563 | −0.176224 | ||||||||
\(415\) | −36.5159 | −1.79249 | ||||||||
\(416\) | −1.72968 | −0.0848044 | ||||||||
\(417\) | 1.73787 | 0.0851037 | ||||||||
\(418\) | 4.28864 | 0.209764 | ||||||||
\(419\) | 21.5428 | 1.05244 | 0.526218 | − | 0.850350i | \(-0.323610\pi\) | ||||
0.526218 | + | 0.850350i | \(0.323610\pi\) | |||||||
\(420\) | 0.687480 | 0.0335456 | ||||||||
\(421\) | −18.3236 | −0.893040 | −0.446520 | − | 0.894774i | \(-0.647337\pi\) | ||||
−0.446520 | + | 0.894774i | \(0.647337\pi\) | |||||||
\(422\) | −21.0364 | −1.02403 | ||||||||
\(423\) | −7.12704 | −0.346528 | ||||||||
\(424\) | −1.00000 | −0.0485643 | ||||||||
\(425\) | −4.79136 | −0.232415 | ||||||||
\(426\) | 16.1640 | 0.783150 | ||||||||
\(427\) | −2.06587 | −0.0999745 | ||||||||
\(428\) | 5.16527 | 0.249673 | ||||||||
\(429\) | −7.41797 | −0.358143 | ||||||||
\(430\) | −33.4072 | −1.61104 | ||||||||
\(431\) | −5.20265 | −0.250603 | −0.125301 | − | 0.992119i | \(-0.539990\pi\) | ||||
−0.125301 | + | 0.992119i | \(0.539990\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 16.4447 | 0.790284 | 0.395142 | − | 0.918620i | \(-0.370695\pi\) | ||||
0.395142 | + | 0.918620i | \(0.370695\pi\) | |||||||
\(434\) | −0.673101 | −0.0323099 | ||||||||
\(435\) | 39.2592 | 1.88234 | ||||||||
\(436\) | −7.17230 | −0.343491 | ||||||||
\(437\) | −3.58563 | −0.171524 | ||||||||
\(438\) | 15.0565 | 0.719429 | ||||||||
\(439\) | −20.4949 | −0.978168 | −0.489084 | − | 0.872237i | \(-0.662669\pi\) | ||||
−0.489084 | + | 0.872237i | \(0.662669\pi\) | |||||||
\(440\) | 18.1246 | 0.864057 | ||||||||
\(441\) | −6.97354 | −0.332073 | ||||||||
\(442\) | 0.644408 | 0.0306514 | ||||||||
\(443\) | −10.2245 | −0.485779 | −0.242889 | − | 0.970054i | \(-0.578095\pi\) | ||||
−0.242889 | + | 0.970054i | \(0.578095\pi\) | |||||||
\(444\) | 1.48845 | 0.0706385 | ||||||||
\(445\) | 14.9655 | 0.709431 | ||||||||
\(446\) | 9.18604 | 0.434971 | ||||||||
\(447\) | −10.0368 | −0.474722 | ||||||||
\(448\) | 0.162672 | 0.00768551 | ||||||||
\(449\) | 3.69271 | 0.174270 | 0.0871349 | − | 0.996197i | \(-0.472229\pi\) | ||||
0.0871349 | + | 0.996197i | \(0.472229\pi\) | |||||||
\(450\) | 12.8606 | 0.606257 | ||||||||
\(451\) | −12.3772 | −0.582822 | ||||||||
\(452\) | 18.3107 | 0.861265 | ||||||||
\(453\) | −4.42076 | −0.207705 | ||||||||
\(454\) | 8.29125 | 0.389128 | ||||||||
\(455\) | −1.18912 | −0.0557468 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | −21.8596 | −1.02255 | −0.511275 | − | 0.859417i | \(-0.670827\pi\) | ||||
−0.511275 | + | 0.859417i | \(0.670827\pi\) | |||||||
\(458\) | 6.24366 | 0.291747 | ||||||||
\(459\) | −0.372560 | −0.0173896 | ||||||||
\(460\) | −15.1536 | −0.706538 | ||||||||
\(461\) | 5.50751 | 0.256510 | 0.128255 | − | 0.991741i | \(-0.459062\pi\) | ||||
0.128255 | + | 0.991741i | \(0.459062\pi\) | |||||||
\(462\) | 0.697641 | 0.0324572 | ||||||||
\(463\) | −6.95025 | −0.323005 | −0.161503 | − | 0.986872i | \(-0.551634\pi\) | ||||
−0.161503 | + | 0.986872i | \(0.551634\pi\) | |||||||
\(464\) | 9.28951 | 0.431255 | ||||||||
\(465\) | −17.4871 | −0.810944 | ||||||||
\(466\) | 3.39537 | 0.157288 | ||||||||
\(467\) | 16.6192 | 0.769045 | 0.384523 | − | 0.923116i | \(-0.374366\pi\) | ||||
0.384523 | + | 0.923116i | \(0.374366\pi\) | |||||||
\(468\) | −1.72968 | −0.0799543 | ||||||||
\(469\) | −2.03973 | −0.0941862 | ||||||||
\(470\) | −30.1202 | −1.38934 | ||||||||
\(471\) | −10.0984 | −0.465309 | ||||||||
\(472\) | −4.09719 | −0.188588 | ||||||||
\(473\) | −33.9009 | −1.55877 | ||||||||
\(474\) | −7.40316 | −0.340039 | ||||||||
\(475\) | 12.8606 | 0.590087 | ||||||||
\(476\) | −0.0606049 | −0.00277782 | ||||||||
\(477\) | −1.00000 | −0.0457869 | ||||||||
\(478\) | 22.0413 | 1.00815 | ||||||||
\(479\) | 10.4381 | 0.476931 | 0.238465 | − | 0.971151i | \(-0.423356\pi\) | ||||
0.238465 | + | 0.971151i | \(0.423356\pi\) | |||||||
\(480\) | 4.22619 | 0.192898 | ||||||||
\(481\) | −2.57453 | −0.117388 | ||||||||
\(482\) | −15.7486 | −0.717330 | ||||||||
\(483\) | −0.583281 | −0.0265402 | ||||||||
\(484\) | 7.39247 | 0.336021 | ||||||||
\(485\) | 30.1204 | 1.36770 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −2.99753 | −0.135831 | −0.0679156 | − | 0.997691i | \(-0.521635\pi\) | ||||
−0.0679156 | + | 0.997691i | \(0.521635\pi\) | |||||||
\(488\) | −12.6996 | −0.574886 | ||||||||
\(489\) | −7.51964 | −0.340050 | ||||||||
\(490\) | −29.4715 | −1.33139 | ||||||||
\(491\) | −25.7095 | −1.16025 | −0.580127 | − | 0.814526i | \(-0.696997\pi\) | ||||
−0.580127 | + | 0.814526i | \(0.696997\pi\) | |||||||
\(492\) | −2.88605 | −0.130113 | ||||||||
\(493\) | −3.46090 | −0.155871 | ||||||||
\(494\) | −1.72968 | −0.0778218 | ||||||||
\(495\) | 18.1246 | 0.814640 | ||||||||
\(496\) | −4.13779 | −0.185792 | ||||||||
\(497\) | 2.62943 | 0.117946 | ||||||||
\(498\) | −8.64039 | −0.387185 | ||||||||
\(499\) | −38.6690 | −1.73106 | −0.865532 | − | 0.500854i | \(-0.833019\pi\) | ||||
−0.865532 | + | 0.500854i | \(0.833019\pi\) | |||||||
\(500\) | 33.2205 | 1.48567 | ||||||||
\(501\) | 12.4136 | 0.554599 | ||||||||
\(502\) | −0.454889 | −0.0203027 | ||||||||
\(503\) | 4.67451 | 0.208426 | 0.104213 | − | 0.994555i | \(-0.466768\pi\) | ||||
0.104213 | + | 0.994555i | \(0.466768\pi\) | |||||||
\(504\) | 0.162672 | 0.00724597 | ||||||||
\(505\) | −0.291946 | −0.0129914 | ||||||||
\(506\) | −15.3775 | −0.683614 | ||||||||
\(507\) | −10.0082 | −0.444481 | ||||||||
\(508\) | 7.32539 | 0.325012 | ||||||||
\(509\) | 36.4649 | 1.61628 | 0.808139 | − | 0.588992i | \(-0.200475\pi\) | ||||
0.808139 | + | 0.588992i | \(0.200475\pi\) | |||||||
\(510\) | −1.57451 | −0.0697204 | ||||||||
\(511\) | 2.44927 | 0.108349 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −4.38596 | −0.193456 | ||||||||
\(515\) | −37.3907 | −1.64763 | ||||||||
\(516\) | −7.90481 | −0.347990 | ||||||||
\(517\) | −30.5653 | −1.34426 | ||||||||
\(518\) | 0.242128 | 0.0106385 | ||||||||
\(519\) | 7.13359 | 0.313130 | ||||||||
\(520\) | −7.30994 | −0.320562 | ||||||||
\(521\) | 28.4787 | 1.24767 | 0.623837 | − | 0.781555i | \(-0.285573\pi\) | ||||
0.623837 | + | 0.781555i | \(0.285573\pi\) | |||||||
\(522\) | 9.28951 | 0.406591 | ||||||||
\(523\) | 28.3933 | 1.24155 | 0.620775 | − | 0.783988i | \(-0.286818\pi\) | ||||
0.620775 | + | 0.783988i | \(0.286818\pi\) | |||||||
\(524\) | 1.88204 | 0.0822173 | ||||||||
\(525\) | 2.09206 | 0.0913051 | ||||||||
\(526\) | −4.09165 | −0.178404 | ||||||||
\(527\) | 1.54158 | 0.0671521 | ||||||||
\(528\) | 4.28864 | 0.186639 | ||||||||
\(529\) | −10.1432 | −0.441010 | ||||||||
\(530\) | −4.22619 | −0.183574 | ||||||||
\(531\) | −4.09719 | −0.177803 | ||||||||
\(532\) | 0.162672 | 0.00705271 | ||||||||
\(533\) | 4.99193 | 0.216225 | ||||||||
\(534\) | 3.54113 | 0.153240 | ||||||||
\(535\) | 21.8294 | 0.943767 | ||||||||
\(536\) | −12.5390 | −0.541601 | ||||||||
\(537\) | 16.6540 | 0.718671 | ||||||||
\(538\) | −20.0849 | −0.865920 | ||||||||
\(539\) | −29.9070 | −1.28819 | ||||||||
\(540\) | 4.22619 | 0.181866 | ||||||||
\(541\) | −22.3005 | −0.958772 | −0.479386 | − | 0.877604i | \(-0.659141\pi\) | ||||
−0.479386 | + | 0.877604i | \(0.659141\pi\) | |||||||
\(542\) | 18.2974 | 0.785941 | ||||||||
\(543\) | −15.5258 | −0.666278 | ||||||||
\(544\) | −0.372560 | −0.0159734 | ||||||||
\(545\) | −30.3115 | −1.29840 | ||||||||
\(546\) | −0.281369 | −0.0120415 | ||||||||
\(547\) | −9.02108 | −0.385713 | −0.192857 | − | 0.981227i | \(-0.561775\pi\) | ||||
−0.192857 | + | 0.981227i | \(0.561775\pi\) | |||||||
\(548\) | −13.4413 | −0.574183 | ||||||||
\(549\) | −12.6996 | −0.542007 | ||||||||
\(550\) | 55.1547 | 2.35181 | ||||||||
\(551\) | 9.28951 | 0.395747 | ||||||||
\(552\) | −3.58563 | −0.152615 | ||||||||
\(553\) | −1.20428 | −0.0512114 | ||||||||
\(554\) | 2.76894 | 0.117641 | ||||||||
\(555\) | 6.29045 | 0.267015 | ||||||||
\(556\) | 1.73787 | 0.0737020 | ||||||||
\(557\) | 3.68994 | 0.156348 | 0.0781739 | − | 0.996940i | \(-0.475091\pi\) | ||||
0.0781739 | + | 0.996940i | \(0.475091\pi\) | |||||||
\(558\) | −4.13779 | −0.175167 | ||||||||
\(559\) | 13.6728 | 0.578296 | ||||||||
\(560\) | 0.687480 | 0.0290514 | ||||||||
\(561\) | −1.59778 | −0.0674582 | ||||||||
\(562\) | 10.5622 | 0.445542 | ||||||||
\(563\) | 33.8671 | 1.42733 | 0.713663 | − | 0.700489i | \(-0.247035\pi\) | ||||
0.713663 | + | 0.700489i | \(0.247035\pi\) | |||||||
\(564\) | −7.12704 | −0.300102 | ||||||||
\(565\) | 77.3846 | 3.25559 | ||||||||
\(566\) | 7.76833 | 0.326527 | ||||||||
\(567\) | 0.162672 | 0.00683157 | ||||||||
\(568\) | 16.1640 | 0.678228 | ||||||||
\(569\) | −42.4617 | −1.78009 | −0.890043 | − | 0.455877i | \(-0.849326\pi\) | ||||
−0.890043 | + | 0.455877i | \(0.849326\pi\) | |||||||
\(570\) | 4.22619 | 0.177015 | ||||||||
\(571\) | 23.2265 | 0.972000 | 0.486000 | − | 0.873959i | \(-0.338455\pi\) | ||||
0.486000 | + | 0.873959i | \(0.338455\pi\) | |||||||
\(572\) | −7.41797 | −0.310161 | ||||||||
\(573\) | −11.7620 | −0.491364 | ||||||||
\(574\) | −0.469479 | −0.0195957 | ||||||||
\(575\) | −46.1136 | −1.92307 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 25.6241 | 1.06675 | 0.533373 | − | 0.845880i | \(-0.320924\pi\) | ||||
0.533373 | + | 0.845880i | \(0.320924\pi\) | |||||||
\(578\) | −16.8612 | −0.701333 | ||||||||
\(579\) | −19.5836 | −0.813865 | ||||||||
\(580\) | 39.2592 | 1.63015 | ||||||||
\(581\) | −1.40555 | −0.0583119 | ||||||||
\(582\) | 7.12709 | 0.295428 | ||||||||
\(583\) | −4.28864 | −0.177617 | ||||||||
\(584\) | 15.0565 | 0.623044 | ||||||||
\(585\) | −7.30994 | −0.302229 | ||||||||
\(586\) | 23.0341 | 0.951530 | ||||||||
\(587\) | −4.55310 | −0.187927 | −0.0939633 | − | 0.995576i | \(-0.529954\pi\) | ||||
−0.0939633 | + | 0.995576i | \(0.529954\pi\) | |||||||
\(588\) | −6.97354 | −0.287584 | ||||||||
\(589\) | −4.13779 | −0.170495 | ||||||||
\(590\) | −17.3155 | −0.712867 | ||||||||
\(591\) | 11.7158 | 0.481923 | ||||||||
\(592\) | 1.48845 | 0.0611747 | ||||||||
\(593\) | 13.5703 | 0.557266 | 0.278633 | − | 0.960398i | \(-0.410119\pi\) | ||||
0.278633 | + | 0.960398i | \(0.410119\pi\) | |||||||
\(594\) | 4.28864 | 0.175965 | ||||||||
\(595\) | −0.256128 | −0.0105002 | ||||||||
\(596\) | −10.0368 | −0.411121 | ||||||||
\(597\) | −3.78323 | −0.154837 | ||||||||
\(598\) | 6.20199 | 0.253618 | ||||||||
\(599\) | −18.3926 | −0.751501 | −0.375750 | − | 0.926721i | \(-0.622615\pi\) | ||||
−0.375750 | + | 0.926721i | \(0.622615\pi\) | |||||||
\(600\) | 12.8606 | 0.525034 | ||||||||
\(601\) | 38.3615 | 1.56480 | 0.782398 | − | 0.622778i | \(-0.213996\pi\) | ||||
0.782398 | + | 0.622778i | \(0.213996\pi\) | |||||||
\(602\) | −1.28589 | −0.0524089 | ||||||||
\(603\) | −12.5390 | −0.510626 | ||||||||
\(604\) | −4.42076 | −0.179878 | ||||||||
\(605\) | 31.2419 | 1.27017 | ||||||||
\(606\) | −0.0690802 | −0.00280619 | ||||||||
\(607\) | −17.7781 | −0.721590 | −0.360795 | − | 0.932645i | \(-0.617495\pi\) | ||||
−0.360795 | + | 0.932645i | \(0.617495\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 1.51114 | 0.0612345 | ||||||||
\(610\) | −53.6710 | −2.17308 | ||||||||
\(611\) | 12.3275 | 0.498716 | ||||||||
\(612\) | −0.372560 | −0.0150598 | ||||||||
\(613\) | 25.1389 | 1.01535 | 0.507676 | − | 0.861548i | \(-0.330505\pi\) | ||||
0.507676 | + | 0.861548i | \(0.330505\pi\) | |||||||
\(614\) | 1.13527 | 0.0458159 | ||||||||
\(615\) | −12.1970 | −0.491830 | ||||||||
\(616\) | 0.697641 | 0.0281087 | ||||||||
\(617\) | 34.4086 | 1.38524 | 0.692618 | − | 0.721304i | \(-0.256457\pi\) | ||||
0.692618 | + | 0.721304i | \(0.256457\pi\) | |||||||
\(618\) | −8.84739 | −0.355894 | ||||||||
\(619\) | −18.2421 | −0.733211 | −0.366605 | − | 0.930377i | \(-0.619480\pi\) | ||||
−0.366605 | + | 0.930377i | \(0.619480\pi\) | |||||||
\(620\) | −17.4871 | −0.702298 | ||||||||
\(621\) | −3.58563 | −0.143887 | ||||||||
\(622\) | 11.1763 | 0.448130 | ||||||||
\(623\) | 0.576041 | 0.0230786 | ||||||||
\(624\) | −1.72968 | −0.0692425 | ||||||||
\(625\) | 76.0930 | 3.04372 | ||||||||
\(626\) | 30.5985 | 1.22296 | ||||||||
\(627\) | 4.28864 | 0.171272 | ||||||||
\(628\) | −10.0984 | −0.402969 | ||||||||
\(629\) | −0.554535 | −0.0221108 | ||||||||
\(630\) | 0.687480 | 0.0273899 | ||||||||
\(631\) | −42.5170 | −1.69258 | −0.846288 | − | 0.532725i | \(-0.821168\pi\) | ||||
−0.846288 | + | 0.532725i | \(0.821168\pi\) | |||||||
\(632\) | −7.40316 | −0.294482 | ||||||||
\(633\) | −21.0364 | −0.836121 | ||||||||
\(634\) | 30.7369 | 1.22072 | ||||||||
\(635\) | 30.9585 | 1.22855 | ||||||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | 12.0620 | 0.477913 | ||||||||
\(638\) | 39.8394 | 1.57726 | ||||||||
\(639\) | 16.1640 | 0.639440 | ||||||||
\(640\) | 4.22619 | 0.167055 | ||||||||
\(641\) | 31.0360 | 1.22585 | 0.612923 | − | 0.790142i | \(-0.289993\pi\) | ||||
0.612923 | + | 0.790142i | \(0.289993\pi\) | |||||||
\(642\) | 5.16527 | 0.203857 | ||||||||
\(643\) | −9.87265 | −0.389339 | −0.194670 | − | 0.980869i | \(-0.562363\pi\) | ||||
−0.194670 | + | 0.980869i | \(0.562363\pi\) | |||||||
\(644\) | −0.583281 | −0.0229845 | ||||||||
\(645\) | −33.4072 | −1.31541 | ||||||||
\(646\) | −0.372560 | −0.0146582 | ||||||||
\(647\) | −39.8754 | −1.56766 | −0.783831 | − | 0.620974i | \(-0.786737\pi\) | ||||
−0.783831 | + | 0.620974i | \(0.786737\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −17.5714 | −0.689737 | ||||||||
\(650\) | −22.2448 | −0.872511 | ||||||||
\(651\) | −0.673101 | −0.0263809 | ||||||||
\(652\) | −7.51964 | −0.294492 | ||||||||
\(653\) | −8.50568 | −0.332853 | −0.166427 | − | 0.986054i | \(-0.553223\pi\) | ||||
−0.166427 | + | 0.986054i | \(0.553223\pi\) | |||||||
\(654\) | −7.17230 | −0.280459 | ||||||||
\(655\) | 7.95385 | 0.310783 | ||||||||
\(656\) | −2.88605 | −0.112681 | ||||||||
\(657\) | 15.0565 | 0.587411 | ||||||||
\(658\) | −1.15937 | −0.0451968 | ||||||||
\(659\) | −35.5319 | −1.38413 | −0.692063 | − | 0.721837i | \(-0.743298\pi\) | ||||
−0.692063 | + | 0.721837i | \(0.743298\pi\) | |||||||
\(660\) | 18.1246 | 0.705499 | ||||||||
\(661\) | −4.96815 | −0.193239 | −0.0966193 | − | 0.995321i | \(-0.530803\pi\) | ||||
−0.0966193 | + | 0.995321i | \(0.530803\pi\) | |||||||
\(662\) | −21.4262 | −0.832752 | ||||||||
\(663\) | 0.644408 | 0.0250267 | ||||||||
\(664\) | −8.64039 | −0.335312 | ||||||||
\(665\) | 0.687480 | 0.0266593 | ||||||||
\(666\) | 1.48845 | 0.0576761 | ||||||||
\(667\) | −33.3088 | −1.28972 | ||||||||
\(668\) | 12.4136 | 0.480297 | ||||||||
\(669\) | 9.18604 | 0.355153 | ||||||||
\(670\) | −52.9920 | −2.04726 | ||||||||
\(671\) | −54.4642 | −2.10257 | ||||||||
\(672\) | 0.162672 | 0.00627519 | ||||||||
\(673\) | 33.1654 | 1.27843 | 0.639216 | − | 0.769027i | \(-0.279259\pi\) | ||||
0.639216 | + | 0.769027i | \(0.279259\pi\) | |||||||
\(674\) | 9.17522 | 0.353416 | ||||||||
\(675\) | 12.8606 | 0.495006 | ||||||||
\(676\) | −10.0082 | −0.384931 | ||||||||
\(677\) | −31.8766 | −1.22512 | −0.612558 | − | 0.790426i | \(-0.709859\pi\) | ||||
−0.612558 | + | 0.790426i | \(0.709859\pi\) | |||||||
\(678\) | 18.3107 | 0.703220 | ||||||||
\(679\) | 1.15938 | 0.0444928 | ||||||||
\(680\) | −1.57451 | −0.0603796 | ||||||||
\(681\) | 8.29125 | 0.317721 | ||||||||
\(682\) | −17.7455 | −0.679511 | ||||||||
\(683\) | −49.5338 | −1.89536 | −0.947680 | − | 0.319222i | \(-0.896578\pi\) | ||||
−0.947680 | + | 0.319222i | \(0.896578\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | −56.8054 | −2.17042 | ||||||||
\(686\) | −2.27310 | −0.0867873 | ||||||||
\(687\) | 6.24366 | 0.238211 | ||||||||
\(688\) | −7.90481 | −0.301368 | ||||||||
\(689\) | 1.72968 | 0.0658954 | ||||||||
\(690\) | −15.1536 | −0.576886 | ||||||||
\(691\) | 27.6975 | 1.05366 | 0.526831 | − | 0.849970i | \(-0.323380\pi\) | ||||
0.526831 | + | 0.849970i | \(0.323380\pi\) | |||||||
\(692\) | 7.13359 | 0.271178 | ||||||||
\(693\) | 0.697641 | 0.0265012 | ||||||||
\(694\) | −36.7735 | −1.39590 | ||||||||
\(695\) | 7.34455 | 0.278595 | ||||||||
\(696\) | 9.28951 | 0.352118 | ||||||||
\(697\) | 1.07523 | 0.0407271 | ||||||||
\(698\) | −10.8254 | −0.409748 | ||||||||
\(699\) | 3.39537 | 0.128425 | ||||||||
\(700\) | 2.09206 | 0.0790725 | ||||||||
\(701\) | −9.39265 | −0.354756 | −0.177378 | − | 0.984143i | \(-0.556761\pi\) | ||||
−0.177378 | + | 0.984143i | \(0.556761\pi\) | |||||||
\(702\) | −1.72968 | −0.0652824 | ||||||||
\(703\) | 1.48845 | 0.0561378 | ||||||||
\(704\) | 4.28864 | 0.161634 | ||||||||
\(705\) | −30.1202 | −1.13439 | ||||||||
\(706\) | −6.44252 | −0.242467 | ||||||||
\(707\) | −0.0112374 | −0.000422626 0 | ||||||||
\(708\) | −4.09719 | −0.153982 | ||||||||
\(709\) | 9.57952 | 0.359766 | 0.179883 | − | 0.983688i | \(-0.442428\pi\) | ||||
0.179883 | + | 0.983688i | \(0.442428\pi\) | |||||||
\(710\) | 68.3122 | 2.56371 | ||||||||
\(711\) | −7.40316 | −0.277640 | ||||||||
\(712\) | 3.54113 | 0.132709 | ||||||||
\(713\) | 14.8366 | 0.555635 | ||||||||
\(714\) | −0.0606049 | −0.00226808 | ||||||||
\(715\) | −31.3497 | −1.17241 | ||||||||
\(716\) | 16.6540 | 0.622387 | ||||||||
\(717\) | 22.0413 | 0.823149 | ||||||||
\(718\) | 21.0901 | 0.787075 | ||||||||
\(719\) | −28.7626 | −1.07266 | −0.536331 | − | 0.844008i | \(-0.680190\pi\) | ||||
−0.536331 | + | 0.844008i | \(0.680190\pi\) | |||||||
\(720\) | 4.22619 | 0.157501 | ||||||||
\(721\) | −1.43922 | −0.0535993 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −15.7486 | −0.585697 | ||||||||
\(724\) | −15.5258 | −0.577014 | ||||||||
\(725\) | 119.469 | 4.43697 | ||||||||
\(726\) | 7.39247 | 0.274360 | ||||||||
\(727\) | −2.79135 | −0.103525 | −0.0517626 | − | 0.998659i | \(-0.516484\pi\) | ||||
−0.0517626 | + | 0.998659i | \(0.516484\pi\) | |||||||
\(728\) | −0.281369 | −0.0104282 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 63.6317 | 2.35511 | ||||||||
\(731\) | 2.94501 | 0.108925 | ||||||||
\(732\) | −12.6996 | −0.469392 | ||||||||
\(733\) | 26.9353 | 0.994877 | 0.497439 | − | 0.867499i | \(-0.334274\pi\) | ||||
0.497439 | + | 0.867499i | \(0.334274\pi\) | |||||||
\(734\) | 20.9199 | 0.772167 | ||||||||
\(735\) | −29.4715 | −1.08707 | ||||||||
\(736\) | −3.58563 | −0.132168 | ||||||||
\(737\) | −53.7752 | −1.98083 | ||||||||
\(738\) | −2.88605 | −0.106237 | ||||||||
\(739\) | −3.07320 | −0.113049 | −0.0565247 | − | 0.998401i | \(-0.518002\pi\) | ||||
−0.0565247 | + | 0.998401i | \(0.518002\pi\) | |||||||
\(740\) | 6.29045 | 0.231241 | ||||||||
\(741\) | −1.72968 | −0.0635413 | ||||||||
\(742\) | −0.162672 | −0.00597186 | ||||||||
\(743\) | 31.8045 | 1.16680 | 0.583398 | − | 0.812187i | \(-0.301723\pi\) | ||||
0.583398 | + | 0.812187i | \(0.301723\pi\) | |||||||
\(744\) | −4.13779 | −0.151699 | ||||||||
\(745\) | −42.4172 | −1.55405 | ||||||||
\(746\) | 22.1666 | 0.811575 | ||||||||
\(747\) | −8.64039 | −0.316135 | ||||||||
\(748\) | −1.59778 | −0.0584205 | ||||||||
\(749\) | 0.840243 | 0.0307018 | ||||||||
\(750\) | 33.2205 | 1.21304 | ||||||||
\(751\) | −30.9245 | −1.12845 | −0.564225 | − | 0.825621i | \(-0.690825\pi\) | ||||
−0.564225 | + | 0.825621i | \(0.690825\pi\) | |||||||
\(752\) | −7.12704 | −0.259896 | ||||||||
\(753\) | −0.454889 | −0.0165771 | ||||||||
\(754\) | −16.0679 | −0.585157 | ||||||||
\(755\) | −18.6830 | −0.679942 | ||||||||
\(756\) | 0.162672 | 0.00591631 | ||||||||
\(757\) | 44.3179 | 1.61076 | 0.805380 | − | 0.592758i | \(-0.201961\pi\) | ||||
0.805380 | + | 0.592758i | \(0.201961\pi\) | |||||||
\(758\) | 21.5553 | 0.782926 | ||||||||
\(759\) | −15.3775 | −0.558168 | ||||||||
\(760\) | 4.22619 | 0.153300 | ||||||||
\(761\) | −13.3572 | −0.484197 | −0.242099 | − | 0.970252i | \(-0.577836\pi\) | ||||
−0.242099 | + | 0.970252i | \(0.577836\pi\) | |||||||
\(762\) | 7.32539 | 0.265371 | ||||||||
\(763\) | −1.16673 | −0.0422385 | ||||||||
\(764\) | −11.7620 | −0.425534 | ||||||||
\(765\) | −1.57451 | −0.0569264 | ||||||||
\(766\) | 8.53506 | 0.308384 | ||||||||
\(767\) | 7.08681 | 0.255890 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −13.6384 | −0.491814 | −0.245907 | − | 0.969293i | \(-0.579086\pi\) | ||||
−0.245907 | + | 0.969293i | \(0.579086\pi\) | |||||||
\(770\) | 2.94836 | 0.106251 | ||||||||
\(771\) | −4.38596 | −0.157956 | ||||||||
\(772\) | −19.5836 | −0.704828 | ||||||||
\(773\) | 42.9885 | 1.54619 | 0.773094 | − | 0.634292i | \(-0.218708\pi\) | ||||
0.773094 | + | 0.634292i | \(0.218708\pi\) | |||||||
\(774\) | −7.90481 | −0.284132 | ||||||||
\(775\) | −53.2147 | −1.91153 | ||||||||
\(776\) | 7.12709 | 0.255848 | ||||||||
\(777\) | 0.242128 | 0.00868629 | ||||||||
\(778\) | −27.8908 | −0.999934 | ||||||||
\(779\) | −2.88605 | −0.103403 | ||||||||
\(780\) | −7.30994 | −0.261738 | ||||||||
\(781\) | 69.3218 | 2.48053 | ||||||||
\(782\) | 1.33586 | 0.0477704 | ||||||||
\(783\) | 9.28951 | 0.331980 | ||||||||
\(784\) | −6.97354 | −0.249055 | ||||||||
\(785\) | −42.6776 | −1.52323 | ||||||||
\(786\) | 1.88204 | 0.0671302 | ||||||||
\(787\) | 26.3867 | 0.940583 | 0.470292 | − | 0.882511i | \(-0.344149\pi\) | ||||
0.470292 | + | 0.882511i | \(0.344149\pi\) | |||||||
\(788\) | 11.7158 | 0.417358 | ||||||||
\(789\) | −4.09165 | −0.145666 | ||||||||
\(790\) | −31.2871 | −1.11315 | ||||||||
\(791\) | 2.97864 | 0.105908 | ||||||||
\(792\) | 4.28864 | 0.152390 | ||||||||
\(793\) | 21.9663 | 0.780045 | ||||||||
\(794\) | 25.2537 | 0.896221 | ||||||||
\(795\) | −4.22619 | −0.149887 | ||||||||
\(796\) | −3.78323 | −0.134093 | ||||||||
\(797\) | 4.93861 | 0.174935 | 0.0874673 | − | 0.996167i | \(-0.472123\pi\) | ||||
0.0874673 | + | 0.996167i | \(0.472123\pi\) | |||||||
\(798\) | 0.162672 | 0.00575851 | ||||||||
\(799\) | 2.65525 | 0.0939359 | ||||||||
\(800\) | 12.8606 | 0.454692 | ||||||||
\(801\) | 3.54113 | 0.125120 | ||||||||
\(802\) | −33.6898 | −1.18963 | ||||||||
\(803\) | 64.5721 | 2.27870 | ||||||||
\(804\) | −12.5390 | −0.442215 | ||||||||
\(805\) | −2.46505 | −0.0868817 | ||||||||
\(806\) | 7.15704 | 0.252096 | ||||||||
\(807\) | −20.0849 | −0.707021 | ||||||||
\(808\) | −0.0690802 | −0.00243023 | ||||||||
\(809\) | −26.5144 | −0.932195 | −0.466098 | − | 0.884733i | \(-0.654340\pi\) | ||||
−0.466098 | + | 0.884733i | \(0.654340\pi\) | |||||||
\(810\) | 4.22619 | 0.148493 | ||||||||
\(811\) | −20.2594 | −0.711403 | −0.355701 | − | 0.934600i | \(-0.615758\pi\) | ||||
−0.355701 | + | 0.934600i | \(0.615758\pi\) | |||||||
\(812\) | 1.51114 | 0.0530306 | ||||||||
\(813\) | 18.2974 | 0.641719 | ||||||||
\(814\) | 6.38341 | 0.223738 | ||||||||
\(815\) | −31.7794 | −1.11318 | ||||||||
\(816\) | −0.372560 | −0.0130422 | ||||||||
\(817\) | −7.90481 | −0.276554 | ||||||||
\(818\) | 0.180224 | 0.00630140 | ||||||||
\(819\) | −0.281369 | −0.00983184 | ||||||||
\(820\) | −12.1970 | −0.425937 | ||||||||
\(821\) | 55.1772 | 1.92570 | 0.962849 | − | 0.270039i | \(-0.0870367\pi\) | ||||
0.962849 | + | 0.270039i | \(0.0870367\pi\) | |||||||
\(822\) | −13.4413 | −0.468819 | ||||||||
\(823\) | −6.23221 | −0.217241 | −0.108621 | − | 0.994083i | \(-0.534643\pi\) | ||||
−0.108621 | + | 0.994083i | \(0.534643\pi\) | |||||||
\(824\) | −8.84739 | −0.308214 | ||||||||
\(825\) | 55.1547 | 1.92024 | ||||||||
\(826\) | −0.666496 | −0.0231904 | ||||||||
\(827\) | −14.7224 | −0.511949 | −0.255974 | − | 0.966684i | \(-0.582396\pi\) | ||||
−0.255974 | + | 0.966684i | \(0.582396\pi\) | |||||||
\(828\) | −3.58563 | −0.124609 | ||||||||
\(829\) | 52.6306 | 1.82793 | 0.913967 | − | 0.405787i | \(-0.133003\pi\) | ||||
0.913967 | + | 0.405787i | \(0.133003\pi\) | |||||||
\(830\) | −36.5159 | −1.26748 | ||||||||
\(831\) | 2.76894 | 0.0960536 | ||||||||
\(832\) | −1.72968 | −0.0599658 | ||||||||
\(833\) | 2.59806 | 0.0900175 | ||||||||
\(834\) | 1.73787 | 0.0601774 | ||||||||
\(835\) | 52.4622 | 1.81553 | ||||||||
\(836\) | 4.28864 | 0.148326 | ||||||||
\(837\) | −4.13779 | −0.143023 | ||||||||
\(838\) | 21.5428 | 0.744185 | ||||||||
\(839\) | −8.28142 | −0.285906 | −0.142953 | − | 0.989729i | \(-0.545660\pi\) | ||||
−0.142953 | + | 0.989729i | \(0.545660\pi\) | |||||||
\(840\) | 0.687480 | 0.0237203 | ||||||||
\(841\) | 57.2951 | 1.97569 | ||||||||
\(842\) | −18.3236 | −0.631474 | ||||||||
\(843\) | 10.5622 | 0.363783 | ||||||||
\(844\) | −21.0364 | −0.724102 | ||||||||
\(845\) | −42.2966 | −1.45505 | ||||||||
\(846\) | −7.12704 | −0.245033 | ||||||||
\(847\) | 1.20254 | 0.0413199 | ||||||||
\(848\) | −1.00000 | −0.0343401 | ||||||||
\(849\) | 7.76833 | 0.266609 | ||||||||
\(850\) | −4.79136 | −0.164342 | ||||||||
\(851\) | −5.33702 | −0.182951 | ||||||||
\(852\) | 16.1640 | 0.553771 | ||||||||
\(853\) | −41.0831 | −1.40666 | −0.703329 | − | 0.710864i | \(-0.748304\pi\) | ||||
−0.703329 | + | 0.710864i | \(0.748304\pi\) | |||||||
\(854\) | −2.06587 | −0.0706926 | ||||||||
\(855\) | 4.22619 | 0.144532 | ||||||||
\(856\) | 5.16527 | 0.176545 | ||||||||
\(857\) | 45.8851 | 1.56740 | 0.783702 | − | 0.621137i | \(-0.213329\pi\) | ||||
0.783702 | + | 0.621137i | \(0.213329\pi\) | |||||||
\(858\) | −7.41797 | −0.253245 | ||||||||
\(859\) | −28.0686 | −0.957689 | −0.478844 | − | 0.877900i | \(-0.658944\pi\) | ||||
−0.478844 | + | 0.877900i | \(0.658944\pi\) | |||||||
\(860\) | −33.4072 | −1.13918 | ||||||||
\(861\) | −0.469479 | −0.0159998 | ||||||||
\(862\) | −5.20265 | −0.177203 | ||||||||
\(863\) | −0.920314 | −0.0313278 | −0.0156639 | − | 0.999877i | \(-0.504986\pi\) | ||||
−0.0156639 | + | 0.999877i | \(0.504986\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 30.1479 | 1.02506 | ||||||||
\(866\) | 16.4447 | 0.558815 | ||||||||
\(867\) | −16.8612 | −0.572636 | ||||||||
\(868\) | −0.673101 | −0.0228465 | ||||||||
\(869\) | −31.7495 | −1.07703 | ||||||||
\(870\) | 39.2592 | 1.33101 | ||||||||
\(871\) | 21.6884 | 0.734882 | ||||||||
\(872\) | −7.17230 | −0.242885 | ||||||||
\(873\) | 7.12709 | 0.241216 | ||||||||
\(874\) | −3.58563 | −0.121286 | ||||||||
\(875\) | 5.40404 | 0.182690 | ||||||||
\(876\) | 15.0565 | 0.508713 | ||||||||
\(877\) | 15.8758 | 0.536088 | 0.268044 | − | 0.963407i | \(-0.413623\pi\) | ||||
0.268044 | + | 0.963407i | \(0.413623\pi\) | |||||||
\(878\) | −20.4949 | −0.691669 | ||||||||
\(879\) | 23.0341 | 0.776921 | ||||||||
\(880\) | 18.1246 | 0.610980 | ||||||||
\(881\) | 29.1007 | 0.980426 | 0.490213 | − | 0.871603i | \(-0.336919\pi\) | ||||
0.490213 | + | 0.871603i | \(0.336919\pi\) | |||||||
\(882\) | −6.97354 | −0.234811 | ||||||||
\(883\) | 43.2015 | 1.45385 | 0.726923 | − | 0.686719i | \(-0.240950\pi\) | ||||
0.726923 | + | 0.686719i | \(0.240950\pi\) | |||||||
\(884\) | 0.644408 | 0.0216738 | ||||||||
\(885\) | −17.3155 | −0.582054 | ||||||||
\(886\) | −10.2245 | −0.343498 | ||||||||
\(887\) | 51.9922 | 1.74573 | 0.872863 | − | 0.487965i | \(-0.162260\pi\) | ||||
0.872863 | + | 0.487965i | \(0.162260\pi\) | |||||||
\(888\) | 1.48845 | 0.0499489 | ||||||||
\(889\) | 1.19163 | 0.0399661 | ||||||||
\(890\) | 14.9655 | 0.501643 | ||||||||
\(891\) | 4.28864 | 0.143675 | ||||||||
\(892\) | 9.18604 | 0.307571 | ||||||||
\(893\) | −7.12704 | −0.238497 | ||||||||
\(894\) | −10.0368 | −0.335679 | ||||||||
\(895\) | 70.3827 | 2.35263 | ||||||||
\(896\) | 0.162672 | 0.00543448 | ||||||||
\(897\) | 6.20199 | 0.207078 | ||||||||
\(898\) | 3.69271 | 0.123227 | ||||||||
\(899\) | −38.4381 | −1.28198 | ||||||||
\(900\) | 12.8606 | 0.428688 | ||||||||
\(901\) | 0.372560 | 0.0124118 | ||||||||
\(902\) | −12.3772 | −0.412117 | ||||||||
\(903\) | −1.28589 | −0.0427917 | ||||||||
\(904\) | 18.3107 | 0.609006 | ||||||||
\(905\) | −65.6151 | −2.18112 | ||||||||
\(906\) | −4.42076 | −0.146870 | ||||||||
\(907\) | −40.6484 | −1.34971 | −0.674853 | − | 0.737952i | \(-0.735793\pi\) | ||||
−0.674853 | + | 0.737952i | \(0.735793\pi\) | |||||||
\(908\) | 8.29125 | 0.275155 | ||||||||
\(909\) | −0.0690802 | −0.00229125 | ||||||||
\(910\) | −1.18912 | −0.0394189 | ||||||||
\(911\) | −14.4664 | −0.479292 | −0.239646 | − | 0.970860i | \(-0.577031\pi\) | ||||
−0.239646 | + | 0.970860i | \(0.577031\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −37.0555 | −1.22636 | ||||||||
\(914\) | −21.8596 | −0.723052 | ||||||||
\(915\) | −53.6710 | −1.77431 | ||||||||
\(916\) | 6.24366 | 0.206296 | ||||||||
\(917\) | 0.306155 | 0.0101101 | ||||||||
\(918\) | −0.372560 | −0.0122963 | ||||||||
\(919\) | 27.3628 | 0.902616 | 0.451308 | − | 0.892368i | \(-0.350958\pi\) | ||||
0.451308 | + | 0.892368i | \(0.350958\pi\) | |||||||
\(920\) | −15.1536 | −0.499598 | ||||||||
\(921\) | 1.13527 | 0.0374085 | ||||||||
\(922\) | 5.50751 | 0.181380 | ||||||||
\(923\) | −27.9586 | −0.920268 | ||||||||
\(924\) | 0.697641 | 0.0229507 | ||||||||
\(925\) | 19.1424 | 0.629397 | ||||||||
\(926\) | −6.95025 | −0.228399 | ||||||||
\(927\) | −8.84739 | −0.290587 | ||||||||
\(928\) | 9.28951 | 0.304943 | ||||||||
\(929\) | −41.5793 | −1.36417 | −0.682087 | − | 0.731271i | \(-0.738927\pi\) | ||||
−0.682087 | + | 0.731271i | \(0.738927\pi\) | |||||||
\(930\) | −17.4871 | −0.573424 | ||||||||
\(931\) | −6.97354 | −0.228548 | ||||||||
\(932\) | 3.39537 | 0.111219 | ||||||||
\(933\) | 11.1763 | 0.365897 | ||||||||
\(934\) | 16.6192 | 0.543797 | ||||||||
\(935\) | −6.75250 | −0.220830 | ||||||||
\(936\) | −1.72968 | −0.0565363 | ||||||||
\(937\) | 35.9521 | 1.17450 | 0.587252 | − | 0.809404i | \(-0.300210\pi\) | ||||
0.587252 | + | 0.809404i | \(0.300210\pi\) | |||||||
\(938\) | −2.03973 | −0.0665997 | ||||||||
\(939\) | 30.5985 | 0.998545 | ||||||||
\(940\) | −30.1202 | −0.982412 | ||||||||
\(941\) | 23.6335 | 0.770430 | 0.385215 | − | 0.922827i | \(-0.374127\pi\) | ||||
0.385215 | + | 0.922827i | \(0.374127\pi\) | |||||||
\(942\) | −10.0984 | −0.329023 | ||||||||
\(943\) | 10.3483 | 0.336988 | ||||||||
\(944\) | −4.09719 | −0.133352 | ||||||||
\(945\) | 0.687480 | 0.0223637 | ||||||||
\(946\) | −33.9009 | −1.10221 | ||||||||
\(947\) | −31.8694 | −1.03562 | −0.517808 | − | 0.855497i | \(-0.673252\pi\) | ||||
−0.517808 | + | 0.855497i | \(0.673252\pi\) | |||||||
\(948\) | −7.40316 | −0.240444 | ||||||||
\(949\) | −26.0429 | −0.845389 | ||||||||
\(950\) | 12.8606 | 0.417254 | ||||||||
\(951\) | 30.7369 | 0.996713 | ||||||||
\(952\) | −0.0606049 | −0.00196422 | ||||||||
\(953\) | 22.8148 | 0.739045 | 0.369523 | − | 0.929222i | \(-0.379521\pi\) | ||||
0.369523 | + | 0.929222i | \(0.379521\pi\) | |||||||
\(954\) | −1.00000 | −0.0323762 | ||||||||
\(955\) | −49.7083 | −1.60852 | ||||||||
\(956\) | 22.0413 | 0.712868 | ||||||||
\(957\) | 39.8394 | 1.28783 | ||||||||
\(958\) | 10.4381 | 0.337241 | ||||||||
\(959\) | −2.18652 | −0.0706063 | ||||||||
\(960\) | 4.22619 | 0.136400 | ||||||||
\(961\) | −13.8787 | −0.447699 | ||||||||
\(962\) | −2.57453 | −0.0830061 | ||||||||
\(963\) | 5.16527 | 0.166448 | ||||||||
\(964\) | −15.7486 | −0.507229 | ||||||||
\(965\) | −82.7638 | −2.66426 | ||||||||
\(966\) | −0.583281 | −0.0187668 | ||||||||
\(967\) | −3.88653 | −0.124983 | −0.0624913 | − | 0.998046i | \(-0.519905\pi\) | ||||
−0.0624913 | + | 0.998046i | \(0.519905\pi\) | |||||||
\(968\) | 7.39247 | 0.237603 | ||||||||
\(969\) | −0.372560 | −0.0119683 | ||||||||
\(970\) | 30.1204 | 0.967109 | ||||||||
\(971\) | −42.7227 | −1.37104 | −0.685519 | − | 0.728055i | \(-0.740425\pi\) | ||||
−0.685519 | + | 0.728055i | \(0.740425\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0.282702 | 0.00906300 | ||||||||
\(974\) | −2.99753 | −0.0960471 | ||||||||
\(975\) | −22.2448 | −0.712402 | ||||||||
\(976\) | −12.6996 | −0.406506 | ||||||||
\(977\) | −10.0421 | −0.321277 | −0.160638 | − | 0.987013i | \(-0.551355\pi\) | ||||
−0.160638 | + | 0.987013i | \(0.551355\pi\) | |||||||
\(978\) | −7.51964 | −0.240452 | ||||||||
\(979\) | 15.1866 | 0.485367 | ||||||||
\(980\) | −29.4715 | −0.941431 | ||||||||
\(981\) | −7.17230 | −0.228994 | ||||||||
\(982\) | −25.7095 | −0.820424 | ||||||||
\(983\) | −23.5438 | −0.750930 | −0.375465 | − | 0.926837i | \(-0.622517\pi\) | ||||
−0.375465 | + | 0.926837i | \(0.622517\pi\) | |||||||
\(984\) | −2.88605 | −0.0920039 | ||||||||
\(985\) | 49.5131 | 1.57762 | ||||||||
\(986\) | −3.46090 | −0.110218 | ||||||||
\(987\) | −1.15937 | −0.0369031 | ||||||||
\(988\) | −1.72968 | −0.0550284 | ||||||||
\(989\) | 28.3438 | 0.901279 | ||||||||
\(990\) | 18.1246 | 0.576038 | ||||||||
\(991\) | −5.93370 | −0.188490 | −0.0942451 | − | 0.995549i | \(-0.530044\pi\) | ||||
−0.0942451 | + | 0.995549i | \(0.530044\pi\) | |||||||
\(992\) | −4.13779 | −0.131375 | ||||||||
\(993\) | −21.4262 | −0.679939 | ||||||||
\(994\) | 2.62943 | 0.0834005 | ||||||||
\(995\) | −15.9886 | −0.506874 | ||||||||
\(996\) | −8.64039 | −0.273781 | ||||||||
\(997\) | −28.3726 | −0.898571 | −0.449285 | − | 0.893388i | \(-0.648321\pi\) | ||||
−0.449285 | + | 0.893388i | \(0.648321\pi\) | |||||||
\(998\) | −38.6690 | −1.22405 | ||||||||
\(999\) | 1.48845 | 0.0470923 |
(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 | 6042.2.a.bh.1.13 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.bh.1.13 | ✓ | 13 | 1.1 | even | 1 | trivial |