Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, 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("5070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.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: | \(40.4841538248\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −3.04892 | −1.15238 | −0.576191 | − | 0.817315i | \(-0.695462\pi\) | ||||
−0.576191 | + | 0.817315i | \(0.695462\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.13706 | −0.342837 | −0.171419 | − | 0.985198i | \(-0.554835\pi\) | ||||
−0.171419 | + | 0.985198i | \(0.554835\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.04892 | 0.814857 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.69202 | 0.652911 | 0.326456 | − | 0.945213i | \(-0.394146\pi\) | ||||
0.326456 | + | 0.945213i | \(0.394146\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.55496 | −0.356732 | −0.178366 | − | 0.983964i | \(-0.557081\pi\) | ||||
−0.178366 | + | 0.983964i | \(0.557081\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 3.04892 | 0.665328 | ||||||||
\(22\) | 1.13706 | 0.242423 | ||||||||
\(23\) | 5.40581 | 1.12719 | 0.563595 | − | 0.826051i | \(-0.309418\pi\) | ||||
0.563595 | + | 0.826051i | \(0.309418\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.04892 | −0.576191 | ||||||||
\(29\) | −6.15883 | −1.14367 | −0.571833 | − | 0.820370i | \(-0.693768\pi\) | ||||
−0.571833 | + | 0.820370i | \(0.693768\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 0.246980 | 0.0443588 | 0.0221794 | − | 0.999754i | \(-0.492939\pi\) | ||||
0.0221794 | + | 0.999754i | \(0.492939\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.13706 | 0.197937 | ||||||||
\(34\) | −2.69202 | −0.461678 | ||||||||
\(35\) | 3.04892 | 0.515361 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.554958 | 0.0912346 | 0.0456173 | − | 0.998959i | \(-0.485475\pi\) | ||||
0.0456173 | + | 0.998959i | \(0.485475\pi\) | |||||||
\(38\) | 1.55496 | 0.252248 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −8.26875 | −1.29136 | −0.645681 | − | 0.763607i | \(-0.723426\pi\) | ||||
−0.645681 | + | 0.763607i | \(0.723426\pi\) | |||||||
\(42\) | −3.04892 | −0.470458 | ||||||||
\(43\) | 2.03923 | 0.310979 | 0.155490 | − | 0.987838i | \(-0.450304\pi\) | ||||
0.155490 | + | 0.987838i | \(0.450304\pi\) | |||||||
\(44\) | −1.13706 | −0.171419 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −5.40581 | −0.797044 | ||||||||
\(47\) | 6.70171 | 0.977545 | 0.488772 | − | 0.872411i | \(-0.337445\pi\) | ||||
0.488772 | + | 0.872411i | \(0.337445\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 2.29590 | 0.327985 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −2.69202 | −0.376958 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.77479 | 0.793229 | 0.396614 | − | 0.917985i | \(-0.370185\pi\) | ||||
0.396614 | + | 0.917985i | \(0.370185\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.13706 | 0.153322 | ||||||||
\(56\) | 3.04892 | 0.407429 | ||||||||
\(57\) | 1.55496 | 0.205959 | ||||||||
\(58\) | 6.15883 | 0.808694 | ||||||||
\(59\) | −1.36898 | −0.178226 | −0.0891128 | − | 0.996022i | \(-0.528403\pi\) | ||||
−0.0891128 | + | 0.996022i | \(0.528403\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 10.9487 | 1.40184 | 0.700918 | − | 0.713242i | \(-0.252774\pi\) | ||||
0.700918 | + | 0.713242i | \(0.252774\pi\) | |||||||
\(62\) | −0.246980 | −0.0313664 | ||||||||
\(63\) | −3.04892 | −0.384127 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.13706 | −0.139963 | ||||||||
\(67\) | 2.47219 | 0.302026 | 0.151013 | − | 0.988532i | \(-0.451746\pi\) | ||||
0.151013 | + | 0.988532i | \(0.451746\pi\) | |||||||
\(68\) | 2.69202 | 0.326456 | ||||||||
\(69\) | −5.40581 | −0.650783 | ||||||||
\(70\) | −3.04892 | −0.364415 | ||||||||
\(71\) | 8.57002 | 1.01707 | 0.508537 | − | 0.861040i | \(-0.330186\pi\) | ||||
0.508537 | + | 0.861040i | \(0.330186\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 14.8334 | 1.73612 | 0.868059 | − | 0.496461i | \(-0.165368\pi\) | ||||
0.868059 | + | 0.496461i | \(0.165368\pi\) | |||||||
\(74\) | −0.554958 | −0.0645126 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −1.55496 | −0.178366 | ||||||||
\(77\) | 3.46681 | 0.395080 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.33513 | 0.600249 | 0.300124 | − | 0.953900i | \(-0.402972\pi\) | ||||
0.300124 | + | 0.953900i | \(0.402972\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.26875 | 0.913131 | ||||||||
\(83\) | 5.45473 | 0.598734 | 0.299367 | − | 0.954138i | \(-0.403224\pi\) | ||||
0.299367 | + | 0.954138i | \(0.403224\pi\) | |||||||
\(84\) | 3.04892 | 0.332664 | ||||||||
\(85\) | −2.69202 | −0.291991 | ||||||||
\(86\) | −2.03923 | −0.219896 | ||||||||
\(87\) | 6.15883 | 0.660296 | ||||||||
\(88\) | 1.13706 | 0.121211 | ||||||||
\(89\) | −16.8877 | −1.79009 | −0.895046 | − | 0.445974i | \(-0.852857\pi\) | ||||
−0.895046 | + | 0.445974i | \(0.852857\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.40581 | 0.563595 | ||||||||
\(93\) | −0.246980 | −0.0256106 | ||||||||
\(94\) | −6.70171 | −0.691229 | ||||||||
\(95\) | 1.55496 | 0.159535 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −1.93900 | −0.196876 | −0.0984379 | − | 0.995143i | \(-0.531385\pi\) | ||||
−0.0984379 | + | 0.995143i | \(0.531385\pi\) | |||||||
\(98\) | −2.29590 | −0.231921 | ||||||||
\(99\) | −1.13706 | −0.114279 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −14.4940 | −1.44220 | −0.721101 | − | 0.692830i | \(-0.756364\pi\) | ||||
−0.721101 | + | 0.692830i | \(0.756364\pi\) | |||||||
\(102\) | 2.69202 | 0.266550 | ||||||||
\(103\) | −16.1836 | −1.59462 | −0.797308 | − | 0.603572i | \(-0.793743\pi\) | ||||
−0.797308 | + | 0.603572i | \(0.793743\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.04892 | −0.297544 | ||||||||
\(106\) | −5.77479 | −0.560897 | ||||||||
\(107\) | 4.92931 | 0.476535 | 0.238267 | − | 0.971200i | \(-0.423421\pi\) | ||||
0.238267 | + | 0.971200i | \(0.423421\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −0.801938 | −0.0768117 | −0.0384059 | − | 0.999262i | \(-0.512228\pi\) | ||||
−0.0384059 | + | 0.999262i | \(0.512228\pi\) | |||||||
\(110\) | −1.13706 | −0.108415 | ||||||||
\(111\) | −0.554958 | −0.0526743 | ||||||||
\(112\) | −3.04892 | −0.288096 | ||||||||
\(113\) | −11.5211 | −1.08381 | −0.541907 | − | 0.840438i | \(-0.682298\pi\) | ||||
−0.541907 | + | 0.840438i | \(0.682298\pi\) | |||||||
\(114\) | −1.55496 | −0.145635 | ||||||||
\(115\) | −5.40581 | −0.504095 | ||||||||
\(116\) | −6.15883 | −0.571833 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.36898 | 0.126025 | ||||||||
\(119\) | −8.20775 | −0.752403 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −9.70709 | −0.882462 | ||||||||
\(122\) | −10.9487 | −0.991248 | ||||||||
\(123\) | 8.26875 | 0.745568 | ||||||||
\(124\) | 0.246980 | 0.0221794 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.04892 | 0.271619 | ||||||||
\(127\) | 6.22521 | 0.552398 | 0.276199 | − | 0.961100i | \(-0.410925\pi\) | ||||
0.276199 | + | 0.961100i | \(0.410925\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.03923 | −0.179544 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.34481 | 0.292238 | 0.146119 | − | 0.989267i | \(-0.453322\pi\) | ||||
0.146119 | + | 0.989267i | \(0.453322\pi\) | |||||||
\(132\) | 1.13706 | 0.0989687 | ||||||||
\(133\) | 4.74094 | 0.411092 | ||||||||
\(134\) | −2.47219 | −0.213565 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −2.69202 | −0.230839 | ||||||||
\(137\) | 9.53079 | 0.814271 | 0.407135 | − | 0.913368i | \(-0.366528\pi\) | ||||
0.407135 | + | 0.913368i | \(0.366528\pi\) | |||||||
\(138\) | 5.40581 | 0.460173 | ||||||||
\(139\) | 18.7017 | 1.58626 | 0.793129 | − | 0.609053i | \(-0.208451\pi\) | ||||
0.793129 | + | 0.609053i | \(0.208451\pi\) | |||||||
\(140\) | 3.04892 | 0.257681 | ||||||||
\(141\) | −6.70171 | −0.564386 | ||||||||
\(142\) | −8.57002 | −0.719180 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 6.15883 | 0.511463 | ||||||||
\(146\) | −14.8334 | −1.22762 | ||||||||
\(147\) | −2.29590 | −0.189362 | ||||||||
\(148\) | 0.554958 | 0.0456173 | ||||||||
\(149\) | −16.4209 | −1.34525 | −0.672625 | − | 0.739983i | \(-0.734833\pi\) | ||||
−0.672625 | + | 0.739983i | \(0.734833\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 9.26636 | 0.754085 | 0.377043 | − | 0.926196i | \(-0.376941\pi\) | ||||
0.377043 | + | 0.926196i | \(0.376941\pi\) | |||||||
\(152\) | 1.55496 | 0.126124 | ||||||||
\(153\) | 2.69202 | 0.217637 | ||||||||
\(154\) | −3.46681 | −0.279364 | ||||||||
\(155\) | −0.246980 | −0.0198379 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.0761 | 1.36282 | 0.681409 | − | 0.731903i | \(-0.261367\pi\) | ||||
0.681409 | + | 0.731903i | \(0.261367\pi\) | |||||||
\(158\) | −5.33513 | −0.424440 | ||||||||
\(159\) | −5.77479 | −0.457971 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −16.4819 | −1.29895 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 9.61894 | 0.753414 | 0.376707 | − | 0.926333i | \(-0.377056\pi\) | ||||
0.376707 | + | 0.926333i | \(0.377056\pi\) | |||||||
\(164\) | −8.26875 | −0.645681 | ||||||||
\(165\) | −1.13706 | −0.0885203 | ||||||||
\(166\) | −5.45473 | −0.423369 | ||||||||
\(167\) | −21.8509 | −1.69087 | −0.845435 | − | 0.534078i | \(-0.820659\pi\) | ||||
−0.845435 | + | 0.534078i | \(0.820659\pi\) | |||||||
\(168\) | −3.04892 | −0.235229 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.69202 | 0.206469 | ||||||||
\(171\) | −1.55496 | −0.118911 | ||||||||
\(172\) | 2.03923 | 0.155490 | ||||||||
\(173\) | 16.6853 | 1.26856 | 0.634281 | − | 0.773103i | \(-0.281296\pi\) | ||||
0.634281 | + | 0.773103i | \(0.281296\pi\) | |||||||
\(174\) | −6.15883 | −0.466900 | ||||||||
\(175\) | −3.04892 | −0.230476 | ||||||||
\(176\) | −1.13706 | −0.0857094 | ||||||||
\(177\) | 1.36898 | 0.102899 | ||||||||
\(178\) | 16.8877 | 1.26579 | ||||||||
\(179\) | −3.94438 | −0.294817 | −0.147408 | − | 0.989076i | \(-0.547093\pi\) | ||||
−0.147408 | + | 0.989076i | \(0.547093\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | −20.5308 | −1.52604 | −0.763021 | − | 0.646374i | \(-0.776285\pi\) | ||||
−0.763021 | + | 0.646374i | \(0.776285\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.9487 | −0.809350 | ||||||||
\(184\) | −5.40581 | −0.398522 | ||||||||
\(185\) | −0.554958 | −0.0408013 | ||||||||
\(186\) | 0.246980 | 0.0181094 | ||||||||
\(187\) | −3.06100 | −0.223842 | ||||||||
\(188\) | 6.70171 | 0.488772 | ||||||||
\(189\) | 3.04892 | 0.221776 | ||||||||
\(190\) | −1.55496 | −0.112809 | ||||||||
\(191\) | −6.66487 | −0.482253 | −0.241127 | − | 0.970494i | \(-0.577517\pi\) | ||||
−0.241127 | + | 0.970494i | \(0.577517\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −16.6558 | −1.19891 | −0.599455 | − | 0.800409i | \(-0.704616\pi\) | ||||
−0.599455 | + | 0.800409i | \(0.704616\pi\) | |||||||
\(194\) | 1.93900 | 0.139212 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.29590 | 0.163993 | ||||||||
\(197\) | −19.4494 | −1.38571 | −0.692855 | − | 0.721077i | \(-0.743647\pi\) | ||||
−0.692855 | + | 0.721077i | \(0.743647\pi\) | |||||||
\(198\) | 1.13706 | 0.0808076 | ||||||||
\(199\) | −21.6558 | −1.53514 | −0.767569 | − | 0.640967i | \(-0.778534\pi\) | ||||
−0.767569 | + | 0.640967i | \(0.778534\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −2.47219 | −0.174375 | ||||||||
\(202\) | 14.4940 | 1.01979 | ||||||||
\(203\) | 18.7778 | 1.31794 | ||||||||
\(204\) | −2.69202 | −0.188479 | ||||||||
\(205\) | 8.26875 | 0.577515 | ||||||||
\(206\) | 16.1836 | 1.12756 | ||||||||
\(207\) | 5.40581 | 0.375730 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.76809 | 0.122301 | ||||||||
\(210\) | 3.04892 | 0.210395 | ||||||||
\(211\) | 12.1521 | 0.836587 | 0.418294 | − | 0.908312i | \(-0.362628\pi\) | ||||
0.418294 | + | 0.908312i | \(0.362628\pi\) | |||||||
\(212\) | 5.77479 | 0.396614 | ||||||||
\(213\) | −8.57002 | −0.587208 | ||||||||
\(214\) | −4.92931 | −0.336961 | ||||||||
\(215\) | −2.03923 | −0.139074 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −0.753020 | −0.0511184 | ||||||||
\(218\) | 0.801938 | 0.0543141 | ||||||||
\(219\) | −14.8334 | −1.00235 | ||||||||
\(220\) | 1.13706 | 0.0766608 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.554958 | 0.0372464 | ||||||||
\(223\) | −1.11960 | −0.0749743 | −0.0374871 | − | 0.999297i | \(-0.511935\pi\) | ||||
−0.0374871 | + | 0.999297i | \(0.511935\pi\) | |||||||
\(224\) | 3.04892 | 0.203714 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 11.5211 | 0.766373 | ||||||||
\(227\) | −4.06638 | −0.269895 | −0.134947 | − | 0.990853i | \(-0.543087\pi\) | ||||
−0.134947 | + | 0.990853i | \(0.543087\pi\) | |||||||
\(228\) | 1.55496 | 0.102980 | ||||||||
\(229\) | 16.5187 | 1.09159 | 0.545794 | − | 0.837920i | \(-0.316228\pi\) | ||||
0.545794 | + | 0.837920i | \(0.316228\pi\) | |||||||
\(230\) | 5.40581 | 0.356449 | ||||||||
\(231\) | −3.46681 | −0.228099 | ||||||||
\(232\) | 6.15883 | 0.404347 | ||||||||
\(233\) | −6.16421 | −0.403831 | −0.201915 | − | 0.979403i | \(-0.564717\pi\) | ||||
−0.201915 | + | 0.979403i | \(0.564717\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.70171 | −0.437171 | ||||||||
\(236\) | −1.36898 | −0.0891128 | ||||||||
\(237\) | −5.33513 | −0.346554 | ||||||||
\(238\) | 8.20775 | 0.532029 | ||||||||
\(239\) | −18.1793 | −1.17592 | −0.587960 | − | 0.808890i | \(-0.700069\pi\) | ||||
−0.587960 | + | 0.808890i | \(0.700069\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 9.21744 | 0.593747 | 0.296874 | − | 0.954917i | \(-0.404056\pi\) | ||||
0.296874 | + | 0.954917i | \(0.404056\pi\) | |||||||
\(242\) | 9.70709 | 0.623995 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 10.9487 | 0.700918 | ||||||||
\(245\) | −2.29590 | −0.146679 | ||||||||
\(246\) | −8.26875 | −0.527196 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.246980 | −0.0156832 | ||||||||
\(249\) | −5.45473 | −0.345680 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 17.2054 | 1.08599 | 0.542996 | − | 0.839735i | \(-0.317290\pi\) | ||||
0.542996 | + | 0.839735i | \(0.317290\pi\) | |||||||
\(252\) | −3.04892 | −0.192064 | ||||||||
\(253\) | −6.14675 | −0.386443 | ||||||||
\(254\) | −6.22521 | −0.390604 | ||||||||
\(255\) | 2.69202 | 0.168581 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.5157 | −1.21736 | −0.608679 | − | 0.793417i | \(-0.708300\pi\) | ||||
−0.608679 | + | 0.793417i | \(0.708300\pi\) | |||||||
\(258\) | 2.03923 | 0.126957 | ||||||||
\(259\) | −1.69202 | −0.105137 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.15883 | −0.381222 | ||||||||
\(262\) | −3.34481 | −0.206643 | ||||||||
\(263\) | 12.8834 | 0.794423 | 0.397212 | − | 0.917727i | \(-0.369978\pi\) | ||||
0.397212 | + | 0.917727i | \(0.369978\pi\) | |||||||
\(264\) | −1.13706 | −0.0699814 | ||||||||
\(265\) | −5.77479 | −0.354743 | ||||||||
\(266\) | −4.74094 | −0.290686 | ||||||||
\(267\) | 16.8877 | 1.03351 | ||||||||
\(268\) | 2.47219 | 0.151013 | ||||||||
\(269\) | −30.9138 | −1.88485 | −0.942423 | − | 0.334423i | \(-0.891459\pi\) | ||||
−0.942423 | + | 0.334423i | \(0.891459\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −7.24027 | −0.439815 | −0.219908 | − | 0.975521i | \(-0.570576\pi\) | ||||
−0.219908 | + | 0.975521i | \(0.570576\pi\) | |||||||
\(272\) | 2.69202 | 0.163228 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.53079 | −0.575776 | ||||||||
\(275\) | −1.13706 | −0.0685675 | ||||||||
\(276\) | −5.40581 | −0.325392 | ||||||||
\(277\) | 12.2446 | 0.735706 | 0.367853 | − | 0.929884i | \(-0.380093\pi\) | ||||
0.367853 | + | 0.929884i | \(0.380093\pi\) | |||||||
\(278\) | −18.7017 | −1.12165 | ||||||||
\(279\) | 0.246980 | 0.0147863 | ||||||||
\(280\) | −3.04892 | −0.182208 | ||||||||
\(281\) | 2.74632 | 0.163831 | 0.0819157 | − | 0.996639i | \(-0.473896\pi\) | ||||
0.0819157 | + | 0.996639i | \(0.473896\pi\) | |||||||
\(282\) | 6.70171 | 0.399081 | ||||||||
\(283\) | 14.9312 | 0.887570 | 0.443785 | − | 0.896133i | \(-0.353635\pi\) | ||||
0.443785 | + | 0.896133i | \(0.353635\pi\) | |||||||
\(284\) | 8.57002 | 0.508537 | ||||||||
\(285\) | −1.55496 | −0.0921078 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 25.2107 | 1.48814 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −9.75302 | −0.573707 | ||||||||
\(290\) | −6.15883 | −0.361659 | ||||||||
\(291\) | 1.93900 | 0.113666 | ||||||||
\(292\) | 14.8334 | 0.868059 | ||||||||
\(293\) | −18.5810 | −1.08552 | −0.542758 | − | 0.839889i | \(-0.682620\pi\) | ||||
−0.542758 | + | 0.839889i | \(0.682620\pi\) | |||||||
\(294\) | 2.29590 | 0.133899 | ||||||||
\(295\) | 1.36898 | 0.0797049 | ||||||||
\(296\) | −0.554958 | −0.0322563 | ||||||||
\(297\) | 1.13706 | 0.0659791 | ||||||||
\(298\) | 16.4209 | 0.951236 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −6.21744 | −0.358367 | ||||||||
\(302\) | −9.26636 | −0.533219 | ||||||||
\(303\) | 14.4940 | 0.832656 | ||||||||
\(304\) | −1.55496 | −0.0891830 | ||||||||
\(305\) | −10.9487 | −0.626920 | ||||||||
\(306\) | −2.69202 | −0.153893 | ||||||||
\(307\) | −32.4359 | −1.85122 | −0.925609 | − | 0.378482i | \(-0.876446\pi\) | ||||
−0.925609 | + | 0.378482i | \(0.876446\pi\) | |||||||
\(308\) | 3.46681 | 0.197540 | ||||||||
\(309\) | 16.1836 | 0.920652 | ||||||||
\(310\) | 0.246980 | 0.0140275 | ||||||||
\(311\) | −21.2771 | −1.20651 | −0.603257 | − | 0.797547i | \(-0.706131\pi\) | ||||
−0.603257 | + | 0.797547i | \(0.706131\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.7060 | −1.05733 | −0.528663 | − | 0.848832i | \(-0.677307\pi\) | ||||
−0.528663 | + | 0.848832i | \(0.677307\pi\) | |||||||
\(314\) | −17.0761 | −0.963658 | ||||||||
\(315\) | 3.04892 | 0.171787 | ||||||||
\(316\) | 5.33513 | 0.300124 | ||||||||
\(317\) | −17.4776 | −0.981638 | −0.490819 | − | 0.871262i | \(-0.663302\pi\) | ||||
−0.490819 | + | 0.871262i | \(0.663302\pi\) | |||||||
\(318\) | 5.77479 | 0.323834 | ||||||||
\(319\) | 7.00298 | 0.392092 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −4.92931 | −0.275127 | ||||||||
\(322\) | 16.4819 | 0.918499 | ||||||||
\(323\) | −4.18598 | −0.232914 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.61894 | −0.532744 | ||||||||
\(327\) | 0.801938 | 0.0443473 | ||||||||
\(328\) | 8.26875 | 0.456565 | ||||||||
\(329\) | −20.4330 | −1.12651 | ||||||||
\(330\) | 1.13706 | 0.0625933 | ||||||||
\(331\) | 23.1890 | 1.27458 | 0.637290 | − | 0.770624i | \(-0.280055\pi\) | ||||
0.637290 | + | 0.770624i | \(0.280055\pi\) | |||||||
\(332\) | 5.45473 | 0.299367 | ||||||||
\(333\) | 0.554958 | 0.0304115 | ||||||||
\(334\) | 21.8509 | 1.19563 | ||||||||
\(335\) | −2.47219 | −0.135070 | ||||||||
\(336\) | 3.04892 | 0.166332 | ||||||||
\(337\) | −26.1400 | −1.42394 | −0.711970 | − | 0.702210i | \(-0.752197\pi\) | ||||
−0.711970 | + | 0.702210i | \(0.752197\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.5211 | 0.625741 | ||||||||
\(340\) | −2.69202 | −0.145995 | ||||||||
\(341\) | −0.280831 | −0.0152079 | ||||||||
\(342\) | 1.55496 | 0.0840825 | ||||||||
\(343\) | 14.3424 | 0.774418 | ||||||||
\(344\) | −2.03923 | −0.109948 | ||||||||
\(345\) | 5.40581 | 0.291039 | ||||||||
\(346\) | −16.6853 | −0.897008 | ||||||||
\(347\) | 15.2959 | 0.821127 | 0.410563 | − | 0.911832i | \(-0.365332\pi\) | ||||
0.410563 | + | 0.911832i | \(0.365332\pi\) | |||||||
\(348\) | 6.15883 | 0.330148 | ||||||||
\(349\) | 19.2107 | 1.02833 | 0.514164 | − | 0.857692i | \(-0.328102\pi\) | ||||
0.514164 | + | 0.857692i | \(0.328102\pi\) | |||||||
\(350\) | 3.04892 | 0.162971 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.13706 | 0.0606057 | ||||||||
\(353\) | 5.35450 | 0.284991 | 0.142496 | − | 0.989795i | \(-0.454487\pi\) | ||||
0.142496 | + | 0.989795i | \(0.454487\pi\) | |||||||
\(354\) | −1.36898 | −0.0727603 | ||||||||
\(355\) | −8.57002 | −0.454850 | ||||||||
\(356\) | −16.8877 | −0.895046 | ||||||||
\(357\) | 8.20775 | 0.434400 | ||||||||
\(358\) | 3.94438 | 0.208467 | ||||||||
\(359\) | −8.49934 | −0.448578 | −0.224289 | − | 0.974523i | \(-0.572006\pi\) | ||||
−0.224289 | + | 0.974523i | \(0.572006\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −16.5821 | −0.872742 | ||||||||
\(362\) | 20.5308 | 1.07907 | ||||||||
\(363\) | 9.70709 | 0.509490 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.8334 | −0.776415 | ||||||||
\(366\) | 10.9487 | 0.572297 | ||||||||
\(367\) | 4.76032 | 0.248486 | 0.124243 | − | 0.992252i | \(-0.460350\pi\) | ||||
0.124243 | + | 0.992252i | \(0.460350\pi\) | |||||||
\(368\) | 5.40581 | 0.281797 | ||||||||
\(369\) | −8.26875 | −0.430454 | ||||||||
\(370\) | 0.554958 | 0.0288509 | ||||||||
\(371\) | −17.6069 | −0.914103 | ||||||||
\(372\) | −0.246980 | −0.0128053 | ||||||||
\(373\) | −20.2064 | −1.04625 | −0.523124 | − | 0.852256i | \(-0.675234\pi\) | ||||
−0.523124 | + | 0.852256i | \(0.675234\pi\) | |||||||
\(374\) | 3.06100 | 0.158280 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −6.70171 | −0.345614 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −3.04892 | −0.156819 | ||||||||
\(379\) | −24.4088 | −1.25380 | −0.626898 | − | 0.779101i | \(-0.715676\pi\) | ||||
−0.626898 | + | 0.779101i | \(0.715676\pi\) | |||||||
\(380\) | 1.55496 | 0.0797677 | ||||||||
\(381\) | −6.22521 | −0.318927 | ||||||||
\(382\) | 6.66487 | 0.341005 | ||||||||
\(383\) | −32.0237 | −1.63633 | −0.818167 | − | 0.574981i | \(-0.805010\pi\) | ||||
−0.818167 | + | 0.574981i | \(0.805010\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −3.46681 | −0.176685 | ||||||||
\(386\) | 16.6558 | 0.847757 | ||||||||
\(387\) | 2.03923 | 0.103660 | ||||||||
\(388\) | −1.93900 | −0.0984379 | ||||||||
\(389\) | 21.1879 | 1.07427 | 0.537135 | − | 0.843497i | \(-0.319507\pi\) | ||||
0.537135 | + | 0.843497i | \(0.319507\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.5526 | 0.735955 | ||||||||
\(392\) | −2.29590 | −0.115960 | ||||||||
\(393\) | −3.34481 | −0.168724 | ||||||||
\(394\) | 19.4494 | 0.979844 | ||||||||
\(395\) | −5.33513 | −0.268439 | ||||||||
\(396\) | −1.13706 | −0.0571396 | ||||||||
\(397\) | −10.9608 | −0.550105 | −0.275053 | − | 0.961429i | \(-0.588695\pi\) | ||||
−0.275053 | + | 0.961429i | \(0.588695\pi\) | |||||||
\(398\) | 21.6558 | 1.08551 | ||||||||
\(399\) | −4.74094 | −0.237344 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 29.2301 | 1.45968 | 0.729841 | − | 0.683617i | \(-0.239594\pi\) | ||||
0.729841 | + | 0.683617i | \(0.239594\pi\) | |||||||
\(402\) | 2.47219 | 0.123302 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.4940 | −0.721101 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −18.7778 | −0.931925 | ||||||||
\(407\) | −0.631023 | −0.0312786 | ||||||||
\(408\) | 2.69202 | 0.133275 | ||||||||
\(409\) | −36.3163 | −1.79573 | −0.897864 | − | 0.440274i | \(-0.854881\pi\) | ||||
−0.897864 | + | 0.440274i | \(0.854881\pi\) | |||||||
\(410\) | −8.26875 | −0.408364 | ||||||||
\(411\) | −9.53079 | −0.470119 | ||||||||
\(412\) | −16.1836 | −0.797308 | ||||||||
\(413\) | 4.17390 | 0.205384 | ||||||||
\(414\) | −5.40581 | −0.265681 | ||||||||
\(415\) | −5.45473 | −0.267762 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.7017 | −0.915827 | ||||||||
\(418\) | −1.76809 | −0.0864799 | ||||||||
\(419\) | 11.0382 | 0.539250 | 0.269625 | − | 0.962965i | \(-0.413100\pi\) | ||||
0.269625 | + | 0.962965i | \(0.413100\pi\) | |||||||
\(420\) | −3.04892 | −0.148772 | ||||||||
\(421\) | −4.58642 | −0.223528 | −0.111764 | − | 0.993735i | \(-0.535650\pi\) | ||||
−0.111764 | + | 0.993735i | \(0.535650\pi\) | |||||||
\(422\) | −12.1521 | −0.591556 | ||||||||
\(423\) | 6.70171 | 0.325848 | ||||||||
\(424\) | −5.77479 | −0.280449 | ||||||||
\(425\) | 2.69202 | 0.130582 | ||||||||
\(426\) | 8.57002 | 0.415219 | ||||||||
\(427\) | −33.3817 | −1.61545 | ||||||||
\(428\) | 4.92931 | 0.238267 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.03923 | 0.0983403 | ||||||||
\(431\) | −19.3642 | −0.932740 | −0.466370 | − | 0.884590i | \(-0.654439\pi\) | ||||
−0.466370 | + | 0.884590i | \(0.654439\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 4.41119 | 0.211988 | 0.105994 | − | 0.994367i | \(-0.466198\pi\) | ||||
0.105994 | + | 0.994367i | \(0.466198\pi\) | |||||||
\(434\) | 0.753020 | 0.0361461 | ||||||||
\(435\) | −6.15883 | −0.295293 | ||||||||
\(436\) | −0.801938 | −0.0384059 | ||||||||
\(437\) | −8.40581 | −0.402105 | ||||||||
\(438\) | 14.8334 | 0.708767 | ||||||||
\(439\) | 39.5260 | 1.88647 | 0.943237 | − | 0.332121i | \(-0.107764\pi\) | ||||
0.943237 | + | 0.332121i | \(0.107764\pi\) | |||||||
\(440\) | −1.13706 | −0.0542074 | ||||||||
\(441\) | 2.29590 | 0.109328 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.16182 | −0.340268 | −0.170134 | − | 0.985421i | \(-0.554420\pi\) | ||||
−0.170134 | + | 0.985421i | \(0.554420\pi\) | |||||||
\(444\) | −0.554958 | −0.0263371 | ||||||||
\(445\) | 16.8877 | 0.800553 | ||||||||
\(446\) | 1.11960 | 0.0530148 | ||||||||
\(447\) | 16.4209 | 0.776681 | ||||||||
\(448\) | −3.04892 | −0.144048 | ||||||||
\(449\) | 4.46011 | 0.210485 | 0.105243 | − | 0.994447i | \(-0.466438\pi\) | ||||
0.105243 | + | 0.994447i | \(0.466438\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 9.40209 | 0.442727 | ||||||||
\(452\) | −11.5211 | −0.541907 | ||||||||
\(453\) | −9.26636 | −0.435371 | ||||||||
\(454\) | 4.06638 | 0.190844 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.55496 | −0.0728176 | ||||||||
\(457\) | 8.04593 | 0.376373 | 0.188186 | − | 0.982133i | \(-0.439739\pi\) | ||||
0.188186 | + | 0.982133i | \(0.439739\pi\) | |||||||
\(458\) | −16.5187 | −0.771869 | ||||||||
\(459\) | −2.69202 | −0.125653 | ||||||||
\(460\) | −5.40581 | −0.252047 | ||||||||
\(461\) | −4.00538 | −0.186549 | −0.0932745 | − | 0.995640i | \(-0.529733\pi\) | ||||
−0.0932745 | + | 0.995640i | \(0.529733\pi\) | |||||||
\(462\) | 3.46681 | 0.161291 | ||||||||
\(463\) | 37.6142 | 1.74808 | 0.874039 | − | 0.485856i | \(-0.161492\pi\) | ||||
0.874039 | + | 0.485856i | \(0.161492\pi\) | |||||||
\(464\) | −6.15883 | −0.285917 | ||||||||
\(465\) | 0.246980 | 0.0114534 | ||||||||
\(466\) | 6.16421 | 0.285552 | ||||||||
\(467\) | −32.8079 | −1.51817 | −0.759084 | − | 0.650992i | \(-0.774353\pi\) | ||||
−0.759084 | + | 0.650992i | \(0.774353\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.53750 | −0.348049 | ||||||||
\(470\) | 6.70171 | 0.309127 | ||||||||
\(471\) | −17.0761 | −0.786824 | ||||||||
\(472\) | 1.36898 | 0.0630123 | ||||||||
\(473\) | −2.31873 | −0.106615 | ||||||||
\(474\) | 5.33513 | 0.245050 | ||||||||
\(475\) | −1.55496 | −0.0713464 | ||||||||
\(476\) | −8.20775 | −0.376202 | ||||||||
\(477\) | 5.77479 | 0.264410 | ||||||||
\(478\) | 18.1793 | 0.831501 | ||||||||
\(479\) | 9.88530 | 0.451671 | 0.225835 | − | 0.974165i | \(-0.427489\pi\) | ||||
0.225835 | + | 0.974165i | \(0.427489\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −9.21744 | −0.419843 | ||||||||
\(483\) | 16.4819 | 0.749951 | ||||||||
\(484\) | −9.70709 | −0.441231 | ||||||||
\(485\) | 1.93900 | 0.0880455 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −20.2610 | −0.918113 | −0.459056 | − | 0.888407i | \(-0.651812\pi\) | ||||
−0.459056 | + | 0.888407i | \(0.651812\pi\) | |||||||
\(488\) | −10.9487 | −0.495624 | ||||||||
\(489\) | −9.61894 | −0.434984 | ||||||||
\(490\) | 2.29590 | 0.103718 | ||||||||
\(491\) | −22.4940 | −1.01514 | −0.507569 | − | 0.861611i | \(-0.669456\pi\) | ||||
−0.507569 | + | 0.861611i | \(0.669456\pi\) | |||||||
\(492\) | 8.26875 | 0.372784 | ||||||||
\(493\) | −16.5797 | −0.746713 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.13706 | 0.0511072 | ||||||||
\(496\) | 0.246980 | 0.0110897 | ||||||||
\(497\) | −26.1293 | −1.17206 | ||||||||
\(498\) | 5.45473 | 0.244432 | ||||||||
\(499\) | 15.2728 | 0.683704 | 0.341852 | − | 0.939754i | \(-0.388946\pi\) | ||||
0.341852 | + | 0.939754i | \(0.388946\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 21.8509 | 0.976224 | ||||||||
\(502\) | −17.2054 | −0.767913 | ||||||||
\(503\) | −2.95838 | −0.131908 | −0.0659538 | − | 0.997823i | \(-0.521009\pi\) | ||||
−0.0659538 | + | 0.997823i | \(0.521009\pi\) | |||||||
\(504\) | 3.04892 | 0.135810 | ||||||||
\(505\) | 14.4940 | 0.644973 | ||||||||
\(506\) | 6.14675 | 0.273256 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.22521 | 0.276199 | ||||||||
\(509\) | 4.34614 | 0.192639 | 0.0963197 | − | 0.995350i | \(-0.469293\pi\) | ||||
0.0963197 | + | 0.995350i | \(0.469293\pi\) | |||||||
\(510\) | −2.69202 | −0.119205 | ||||||||
\(511\) | −45.2258 | −2.00067 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.55496 | 0.0686531 | ||||||||
\(514\) | 19.5157 | 0.860802 | ||||||||
\(515\) | 16.1836 | 0.713134 | ||||||||
\(516\) | −2.03923 | −0.0897720 | ||||||||
\(517\) | −7.62027 | −0.335139 | ||||||||
\(518\) | 1.69202 | 0.0743432 | ||||||||
\(519\) | −16.6853 | −0.732404 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.13228 | 0.400092 | 0.200046 | − | 0.979786i | \(-0.435891\pi\) | ||||
0.200046 | + | 0.979786i | \(0.435891\pi\) | |||||||
\(522\) | 6.15883 | 0.269565 | ||||||||
\(523\) | 10.2828 | 0.449633 | 0.224817 | − | 0.974401i | \(-0.427822\pi\) | ||||
0.224817 | + | 0.974401i | \(0.427822\pi\) | |||||||
\(524\) | 3.34481 | 0.146119 | ||||||||
\(525\) | 3.04892 | 0.133066 | ||||||||
\(526\) | −12.8834 | −0.561742 | ||||||||
\(527\) | 0.664874 | 0.0289624 | ||||||||
\(528\) | 1.13706 | 0.0494843 | ||||||||
\(529\) | 6.22282 | 0.270557 | ||||||||
\(530\) | 5.77479 | 0.250841 | ||||||||
\(531\) | −1.36898 | −0.0594086 | ||||||||
\(532\) | 4.74094 | 0.205546 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −16.8877 | −0.730802 | ||||||||
\(535\) | −4.92931 | −0.213113 | ||||||||
\(536\) | −2.47219 | −0.106782 | ||||||||
\(537\) | 3.94438 | 0.170212 | ||||||||
\(538\) | 30.9138 | 1.33279 | ||||||||
\(539\) | −2.61058 | −0.112446 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −1.47517 | −0.0634226 | −0.0317113 | − | 0.999497i | \(-0.510096\pi\) | ||||
−0.0317113 | + | 0.999497i | \(0.510096\pi\) | |||||||
\(542\) | 7.24027 | 0.310996 | ||||||||
\(543\) | 20.5308 | 0.881061 | ||||||||
\(544\) | −2.69202 | −0.115419 | ||||||||
\(545\) | 0.801938 | 0.0343512 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.82908 | −0.206477 | −0.103238 | − | 0.994657i | \(-0.532920\pi\) | ||||
−0.103238 | + | 0.994657i | \(0.532920\pi\) | |||||||
\(548\) | 9.53079 | 0.407135 | ||||||||
\(549\) | 10.9487 | 0.467279 | ||||||||
\(550\) | 1.13706 | 0.0484845 | ||||||||
\(551\) | 9.57673 | 0.407982 | ||||||||
\(552\) | 5.40581 | 0.230087 | ||||||||
\(553\) | −16.2664 | −0.691716 | ||||||||
\(554\) | −12.2446 | −0.520223 | ||||||||
\(555\) | 0.554958 | 0.0235567 | ||||||||
\(556\) | 18.7017 | 0.793129 | ||||||||
\(557\) | −3.26145 | −0.138192 | −0.0690961 | − | 0.997610i | \(-0.522012\pi\) | ||||
−0.0690961 | + | 0.997610i | \(0.522012\pi\) | |||||||
\(558\) | −0.246980 | −0.0104555 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.04892 | 0.128840 | ||||||||
\(561\) | 3.06100 | 0.129235 | ||||||||
\(562\) | −2.74632 | −0.115846 | ||||||||
\(563\) | 18.1551 | 0.765147 | 0.382573 | − | 0.923925i | \(-0.375038\pi\) | ||||
0.382573 | + | 0.923925i | \(0.375038\pi\) | |||||||
\(564\) | −6.70171 | −0.282193 | ||||||||
\(565\) | 11.5211 | 0.484697 | ||||||||
\(566\) | −14.9312 | −0.627606 | ||||||||
\(567\) | −3.04892 | −0.128042 | ||||||||
\(568\) | −8.57002 | −0.359590 | ||||||||
\(569\) | −39.2669 | −1.64616 | −0.823078 | − | 0.567928i | \(-0.807745\pi\) | ||||
−0.823078 | + | 0.567928i | \(0.807745\pi\) | |||||||
\(570\) | 1.55496 | 0.0651300 | ||||||||
\(571\) | −36.8649 | −1.54275 | −0.771373 | − | 0.636383i | \(-0.780430\pi\) | ||||
−0.771373 | + | 0.636383i | \(0.780430\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.66487 | 0.278429 | ||||||||
\(574\) | −25.2107 | −1.05228 | ||||||||
\(575\) | 5.40581 | 0.225438 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 20.3043 | 0.845277 | 0.422639 | − | 0.906298i | \(-0.361104\pi\) | ||||
0.422639 | + | 0.906298i | \(0.361104\pi\) | |||||||
\(578\) | 9.75302 | 0.405672 | ||||||||
\(579\) | 16.6558 | 0.692190 | ||||||||
\(580\) | 6.15883 | 0.255732 | ||||||||
\(581\) | −16.6310 | −0.689971 | ||||||||
\(582\) | −1.93900 | −0.0803742 | ||||||||
\(583\) | −6.56630 | −0.271948 | ||||||||
\(584\) | −14.8334 | −0.613810 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.5810 | 0.767576 | ||||||||
\(587\) | −24.5472 | −1.01317 | −0.506585 | − | 0.862190i | \(-0.669093\pi\) | ||||
−0.506585 | + | 0.862190i | \(0.669093\pi\) | |||||||
\(588\) | −2.29590 | −0.0946812 | ||||||||
\(589\) | −0.384043 | −0.0158242 | ||||||||
\(590\) | −1.36898 | −0.0563599 | ||||||||
\(591\) | 19.4494 | 0.800040 | ||||||||
\(592\) | 0.554958 | 0.0228086 | ||||||||
\(593\) | 24.0844 | 0.989029 | 0.494514 | − | 0.869169i | \(-0.335346\pi\) | ||||
0.494514 | + | 0.869169i | \(0.335346\pi\) | |||||||
\(594\) | −1.13706 | −0.0466543 | ||||||||
\(595\) | 8.20775 | 0.336485 | ||||||||
\(596\) | −16.4209 | −0.672625 | ||||||||
\(597\) | 21.6558 | 0.886312 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.84415 | 0.0753499 | 0.0376750 | − | 0.999290i | \(-0.488005\pi\) | ||||
0.0376750 | + | 0.999290i | \(0.488005\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −15.6770 | −0.639476 | −0.319738 | − | 0.947506i | \(-0.603595\pi\) | ||||
−0.319738 | + | 0.947506i | \(0.603595\pi\) | |||||||
\(602\) | 6.21744 | 0.253404 | ||||||||
\(603\) | 2.47219 | 0.100675 | ||||||||
\(604\) | 9.26636 | 0.377043 | ||||||||
\(605\) | 9.70709 | 0.394649 | ||||||||
\(606\) | −14.4940 | −0.588777 | ||||||||
\(607\) | −29.6866 | −1.20494 | −0.602472 | − | 0.798140i | \(-0.705817\pi\) | ||||
−0.602472 | + | 0.798140i | \(0.705817\pi\) | |||||||
\(608\) | 1.55496 | 0.0630619 | ||||||||
\(609\) | −18.7778 | −0.760914 | ||||||||
\(610\) | 10.9487 | 0.443299 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.69202 | 0.108819 | ||||||||
\(613\) | 42.5163 | 1.71722 | 0.858609 | − | 0.512631i | \(-0.171329\pi\) | ||||
0.858609 | + | 0.512631i | \(0.171329\pi\) | |||||||
\(614\) | 32.4359 | 1.30901 | ||||||||
\(615\) | −8.26875 | −0.333428 | ||||||||
\(616\) | −3.46681 | −0.139682 | ||||||||
\(617\) | −27.3666 | −1.10174 | −0.550869 | − | 0.834592i | \(-0.685703\pi\) | ||||
−0.550869 | + | 0.834592i | \(0.685703\pi\) | |||||||
\(618\) | −16.1836 | −0.650999 | ||||||||
\(619\) | −27.9420 | −1.12308 | −0.561542 | − | 0.827449i | \(-0.689792\pi\) | ||||
−0.561542 | + | 0.827449i | \(0.689792\pi\) | |||||||
\(620\) | −0.246980 | −0.00991894 | ||||||||
\(621\) | −5.40581 | −0.216928 | ||||||||
\(622\) | 21.2771 | 0.853134 | ||||||||
\(623\) | 51.4892 | 2.06287 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 18.7060 | 0.747643 | ||||||||
\(627\) | −1.76809 | −0.0706105 | ||||||||
\(628\) | 17.0761 | 0.681409 | ||||||||
\(629\) | 1.49396 | 0.0595681 | ||||||||
\(630\) | −3.04892 | −0.121472 | ||||||||
\(631\) | −7.43594 | −0.296020 | −0.148010 | − | 0.988986i | \(-0.547287\pi\) | ||||
−0.148010 | + | 0.988986i | \(0.547287\pi\) | |||||||
\(632\) | −5.33513 | −0.212220 | ||||||||
\(633\) | −12.1521 | −0.483004 | ||||||||
\(634\) | 17.4776 | 0.694123 | ||||||||
\(635\) | −6.22521 | −0.247040 | ||||||||
\(636\) | −5.77479 | −0.228985 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.00298 | −0.277251 | ||||||||
\(639\) | 8.57002 | 0.339025 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −24.9444 | −0.985244 | −0.492622 | − | 0.870243i | \(-0.663961\pi\) | ||||
−0.492622 | + | 0.870243i | \(0.663961\pi\) | |||||||
\(642\) | 4.92931 | 0.194544 | ||||||||
\(643\) | −30.1661 | −1.18964 | −0.594818 | − | 0.803860i | \(-0.702776\pi\) | ||||
−0.594818 | + | 0.803860i | \(0.702776\pi\) | |||||||
\(644\) | −16.4819 | −0.649477 | ||||||||
\(645\) | 2.03923 | 0.0802946 | ||||||||
\(646\) | 4.18598 | 0.164695 | ||||||||
\(647\) | −44.4053 | −1.74575 | −0.872877 | − | 0.487940i | \(-0.837748\pi\) | ||||
−0.872877 | + | 0.487940i | \(0.837748\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 1.55661 | 0.0611024 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.753020 | 0.0295132 | ||||||||
\(652\) | 9.61894 | 0.376707 | ||||||||
\(653\) | −29.2573 | −1.14493 | −0.572463 | − | 0.819931i | \(-0.694012\pi\) | ||||
−0.572463 | + | 0.819931i | \(0.694012\pi\) | |||||||
\(654\) | −0.801938 | −0.0313582 | ||||||||
\(655\) | −3.34481 | −0.130693 | ||||||||
\(656\) | −8.26875 | −0.322840 | ||||||||
\(657\) | 14.8334 | 0.578706 | ||||||||
\(658\) | 20.4330 | 0.796560 | ||||||||
\(659\) | −11.4808 | −0.447229 | −0.223614 | − | 0.974678i | \(-0.571786\pi\) | ||||
−0.223614 | + | 0.974678i | \(0.571786\pi\) | |||||||
\(660\) | −1.13706 | −0.0442601 | ||||||||
\(661\) | −26.1129 | −1.01567 | −0.507837 | − | 0.861453i | \(-0.669555\pi\) | ||||
−0.507837 | + | 0.861453i | \(0.669555\pi\) | |||||||
\(662\) | −23.1890 | −0.901265 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.45473 | −0.211685 | ||||||||
\(665\) | −4.74094 | −0.183846 | ||||||||
\(666\) | −0.554958 | −0.0215042 | ||||||||
\(667\) | −33.2935 | −1.28913 | ||||||||
\(668\) | −21.8509 | −0.845435 | ||||||||
\(669\) | 1.11960 | 0.0432864 | ||||||||
\(670\) | 2.47219 | 0.0955090 | ||||||||
\(671\) | −12.4494 | −0.480602 | ||||||||
\(672\) | −3.04892 | −0.117615 | ||||||||
\(673\) | −12.4190 | −0.478716 | −0.239358 | − | 0.970931i | \(-0.576937\pi\) | ||||
−0.239358 | + | 0.970931i | \(0.576937\pi\) | |||||||
\(674\) | 26.1400 | 1.00688 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.7646 | 0.490585 | 0.245292 | − | 0.969449i | \(-0.421116\pi\) | ||||
0.245292 | + | 0.969449i | \(0.421116\pi\) | |||||||
\(678\) | −11.5211 | −0.442465 | ||||||||
\(679\) | 5.91185 | 0.226876 | ||||||||
\(680\) | 2.69202 | 0.103234 | ||||||||
\(681\) | 4.06638 | 0.155824 | ||||||||
\(682\) | 0.280831 | 0.0107536 | ||||||||
\(683\) | −31.6142 | −1.20968 | −0.604841 | − | 0.796346i | \(-0.706763\pi\) | ||||
−0.604841 | + | 0.796346i | \(0.706763\pi\) | |||||||
\(684\) | −1.55496 | −0.0594553 | ||||||||
\(685\) | −9.53079 | −0.364153 | ||||||||
\(686\) | −14.3424 | −0.547596 | ||||||||
\(687\) | −16.5187 | −0.630228 | ||||||||
\(688\) | 2.03923 | 0.0777449 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −5.40581 | −0.205796 | ||||||||
\(691\) | −2.06962 | −0.0787322 | −0.0393661 | − | 0.999225i | \(-0.512534\pi\) | ||||
−0.0393661 | + | 0.999225i | \(0.512534\pi\) | |||||||
\(692\) | 16.6853 | 0.634281 | ||||||||
\(693\) | 3.46681 | 0.131693 | ||||||||
\(694\) | −15.2959 | −0.580624 | ||||||||
\(695\) | −18.7017 | −0.709396 | ||||||||
\(696\) | −6.15883 | −0.233450 | ||||||||
\(697\) | −22.2597 | −0.843144 | ||||||||
\(698\) | −19.2107 | −0.727137 | ||||||||
\(699\) | 6.16421 | 0.233152 | ||||||||
\(700\) | −3.04892 | −0.115238 | ||||||||
\(701\) | −23.0030 | −0.868811 | −0.434405 | − | 0.900717i | \(-0.643041\pi\) | ||||
−0.434405 | + | 0.900717i | \(0.643041\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.862937 | −0.0325463 | ||||||||
\(704\) | −1.13706 | −0.0428547 | ||||||||
\(705\) | 6.70171 | 0.252401 | ||||||||
\(706\) | −5.35450 | −0.201519 | ||||||||
\(707\) | 44.1909 | 1.66197 | ||||||||
\(708\) | 1.36898 | 0.0514493 | ||||||||
\(709\) | 32.4373 | 1.21821 | 0.609104 | − | 0.793091i | \(-0.291529\pi\) | ||||
0.609104 | + | 0.793091i | \(0.291529\pi\) | |||||||
\(710\) | 8.57002 | 0.321627 | ||||||||
\(711\) | 5.33513 | 0.200083 | ||||||||
\(712\) | 16.8877 | 0.632893 | ||||||||
\(713\) | 1.33513 | 0.0500008 | ||||||||
\(714\) | −8.20775 | −0.307167 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.94438 | −0.147408 | ||||||||
\(717\) | 18.1793 | 0.678917 | ||||||||
\(718\) | 8.49934 | 0.317192 | ||||||||
\(719\) | −13.7845 | −0.514074 | −0.257037 | − | 0.966402i | \(-0.582746\pi\) | ||||
−0.257037 | + | 0.966402i | \(0.582746\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 49.3424 | 1.83761 | ||||||||
\(722\) | 16.5821 | 0.617122 | ||||||||
\(723\) | −9.21744 | −0.342800 | ||||||||
\(724\) | −20.5308 | −0.763021 | ||||||||
\(725\) | −6.15883 | −0.228733 | ||||||||
\(726\) | −9.70709 | −0.360264 | ||||||||
\(727\) | 4.64848 | 0.172403 | 0.0862013 | − | 0.996278i | \(-0.472527\pi\) | ||||
0.0862013 | + | 0.996278i | \(0.472527\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.8334 | 0.549009 | ||||||||
\(731\) | 5.48965 | 0.203042 | ||||||||
\(732\) | −10.9487 | −0.404675 | ||||||||
\(733\) | 27.4717 | 1.01469 | 0.507345 | − | 0.861743i | \(-0.330627\pi\) | ||||
0.507345 | + | 0.861743i | \(0.330627\pi\) | |||||||
\(734\) | −4.76032 | −0.175706 | ||||||||
\(735\) | 2.29590 | 0.0846854 | ||||||||
\(736\) | −5.40581 | −0.199261 | ||||||||
\(737\) | −2.81104 | −0.103546 | ||||||||
\(738\) | 8.26875 | 0.304377 | ||||||||
\(739\) | 48.0170 | 1.76633 | 0.883167 | − | 0.469059i | \(-0.155407\pi\) | ||||
0.883167 | + | 0.469059i | \(0.155407\pi\) | |||||||
\(740\) | −0.554958 | −0.0204007 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17.6069 | 0.646368 | ||||||||
\(743\) | 23.6517 | 0.867698 | 0.433849 | − | 0.900986i | \(-0.357155\pi\) | ||||
0.433849 | + | 0.900986i | \(0.357155\pi\) | |||||||
\(744\) | 0.246980 | 0.00905471 | ||||||||
\(745\) | 16.4209 | 0.601614 | ||||||||
\(746\) | 20.2064 | 0.739810 | ||||||||
\(747\) | 5.45473 | 0.199578 | ||||||||
\(748\) | −3.06100 | −0.111921 | ||||||||
\(749\) | −15.0291 | −0.549150 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −39.5133 | −1.44186 | −0.720931 | − | 0.693007i | \(-0.756286\pi\) | ||||
−0.720931 | + | 0.693007i | \(0.756286\pi\) | |||||||
\(752\) | 6.70171 | 0.244386 | ||||||||
\(753\) | −17.2054 | −0.626998 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.26636 | −0.337237 | ||||||||
\(756\) | 3.04892 | 0.110888 | ||||||||
\(757\) | −11.2239 | −0.407939 | −0.203969 | − | 0.978977i | \(-0.565384\pi\) | ||||
−0.203969 | + | 0.978977i | \(0.565384\pi\) | |||||||
\(758\) | 24.4088 | 0.886567 | ||||||||
\(759\) | 6.14675 | 0.223113 | ||||||||
\(760\) | −1.55496 | −0.0564043 | ||||||||
\(761\) | 5.80864 | 0.210563 | 0.105282 | − | 0.994442i | \(-0.466426\pi\) | ||||
0.105282 | + | 0.994442i | \(0.466426\pi\) | |||||||
\(762\) | 6.22521 | 0.225516 | ||||||||
\(763\) | 2.44504 | 0.0885165 | ||||||||
\(764\) | −6.66487 | −0.241127 | ||||||||
\(765\) | −2.69202 | −0.0973302 | ||||||||
\(766\) | 32.0237 | 1.15706 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 31.8316 | 1.14788 | 0.573938 | − | 0.818899i | \(-0.305415\pi\) | ||||
0.573938 | + | 0.818899i | \(0.305415\pi\) | |||||||
\(770\) | 3.46681 | 0.124935 | ||||||||
\(771\) | 19.5157 | 0.702842 | ||||||||
\(772\) | −16.6558 | −0.599455 | ||||||||
\(773\) | −39.7434 | −1.42947 | −0.714736 | − | 0.699394i | \(-0.753453\pi\) | ||||
−0.714736 | + | 0.699394i | \(0.753453\pi\) | |||||||
\(774\) | −2.03923 | −0.0732986 | ||||||||
\(775\) | 0.246980 | 0.00887177 | ||||||||
\(776\) | 1.93900 | 0.0696061 | ||||||||
\(777\) | 1.69202 | 0.0607009 | ||||||||
\(778\) | −21.1879 | −0.759623 | ||||||||
\(779\) | 12.8576 | 0.460670 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.74466 | −0.348691 | ||||||||
\(782\) | −14.5526 | −0.520399 | ||||||||
\(783\) | 6.15883 | 0.220099 | ||||||||
\(784\) | 2.29590 | 0.0819963 | ||||||||
\(785\) | −17.0761 | −0.609471 | ||||||||
\(786\) | 3.34481 | 0.119306 | ||||||||
\(787\) | −19.3183 | −0.688622 | −0.344311 | − | 0.938856i | \(-0.611887\pi\) | ||||
−0.344311 | + | 0.938856i | \(0.611887\pi\) | |||||||
\(788\) | −19.4494 | −0.692855 | ||||||||
\(789\) | −12.8834 | −0.458660 | ||||||||
\(790\) | 5.33513 | 0.189815 | ||||||||
\(791\) | 35.1269 | 1.24897 | ||||||||
\(792\) | 1.13706 | 0.0404038 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 10.9608 | 0.388983 | ||||||||
\(795\) | 5.77479 | 0.204811 | ||||||||
\(796\) | −21.6558 | −0.767569 | ||||||||
\(797\) | 29.4946 | 1.04475 | 0.522375 | − | 0.852716i | \(-0.325046\pi\) | ||||
0.522375 | + | 0.852716i | \(0.325046\pi\) | |||||||
\(798\) | 4.74094 | 0.167827 | ||||||||
\(799\) | 18.0411 | 0.638250 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −16.8877 | −0.596697 | ||||||||
\(802\) | −29.2301 | −1.03215 | ||||||||
\(803\) | −16.8665 | −0.595206 | ||||||||
\(804\) | −2.47219 | −0.0871874 | ||||||||
\(805\) | 16.4819 | 0.580910 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.9138 | 1.08822 | ||||||||
\(808\) | 14.4940 | 0.509896 | ||||||||
\(809\) | 14.0901 | 0.495380 | 0.247690 | − | 0.968839i | \(-0.420329\pi\) | ||||
0.247690 | + | 0.968839i | \(0.420329\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 45.5060 | 1.59793 | 0.798967 | − | 0.601375i | \(-0.205380\pi\) | ||||
0.798967 | + | 0.601375i | \(0.205380\pi\) | |||||||
\(812\) | 18.7778 | 0.658971 | ||||||||
\(813\) | 7.24027 | 0.253928 | ||||||||
\(814\) | 0.631023 | 0.0221173 | ||||||||
\(815\) | −9.61894 | −0.336937 | ||||||||
\(816\) | −2.69202 | −0.0942396 | ||||||||
\(817\) | −3.17092 | −0.110936 | ||||||||
\(818\) | 36.3163 | 1.26977 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.26875 | 0.288757 | ||||||||
\(821\) | 14.6853 | 0.512521 | 0.256261 | − | 0.966608i | \(-0.417509\pi\) | ||||
0.256261 | + | 0.966608i | \(0.417509\pi\) | |||||||
\(822\) | 9.53079 | 0.332425 | ||||||||
\(823\) | −32.0551 | −1.11737 | −0.558686 | − | 0.829379i | \(-0.688694\pi\) | ||||
−0.558686 | + | 0.829379i | \(0.688694\pi\) | |||||||
\(824\) | 16.1836 | 0.563782 | ||||||||
\(825\) | 1.13706 | 0.0395875 | ||||||||
\(826\) | −4.17390 | −0.145229 | ||||||||
\(827\) | −8.09352 | −0.281439 | −0.140720 | − | 0.990049i | \(-0.544942\pi\) | ||||
−0.140720 | + | 0.990049i | \(0.544942\pi\) | |||||||
\(828\) | 5.40581 | 0.187865 | ||||||||
\(829\) | −23.8708 | −0.829068 | −0.414534 | − | 0.910034i | \(-0.636055\pi\) | ||||
−0.414534 | + | 0.910034i | \(0.636055\pi\) | |||||||
\(830\) | 5.45473 | 0.189336 | ||||||||
\(831\) | −12.2446 | −0.424760 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.18060 | 0.214145 | ||||||||
\(834\) | 18.7017 | 0.647587 | ||||||||
\(835\) | 21.8509 | 0.756180 | ||||||||
\(836\) | 1.76809 | 0.0611505 | ||||||||
\(837\) | −0.246980 | −0.00853686 | ||||||||
\(838\) | −11.0382 | −0.381307 | ||||||||
\(839\) | 17.5569 | 0.606131 | 0.303065 | − | 0.952970i | \(-0.401990\pi\) | ||||
0.303065 | + | 0.952970i | \(0.401990\pi\) | |||||||
\(840\) | 3.04892 | 0.105198 | ||||||||
\(841\) | 8.93123 | 0.307973 | ||||||||
\(842\) | 4.58642 | 0.158058 | ||||||||
\(843\) | −2.74632 | −0.0945881 | ||||||||
\(844\) | 12.1521 | 0.418294 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.70171 | −0.230410 | ||||||||
\(847\) | 29.5961 | 1.01693 | ||||||||
\(848\) | 5.77479 | 0.198307 | ||||||||
\(849\) | −14.9312 | −0.512439 | ||||||||
\(850\) | −2.69202 | −0.0923356 | ||||||||
\(851\) | 3.00000 | 0.102839 | ||||||||
\(852\) | −8.57002 | −0.293604 | ||||||||
\(853\) | 40.2892 | 1.37948 | 0.689738 | − | 0.724059i | \(-0.257726\pi\) | ||||
0.689738 | + | 0.724059i | \(0.257726\pi\) | |||||||
\(854\) | 33.3817 | 1.14230 | ||||||||
\(855\) | 1.55496 | 0.0531784 | ||||||||
\(856\) | −4.92931 | −0.168480 | ||||||||
\(857\) | 44.5913 | 1.52321 | 0.761605 | − | 0.648041i | \(-0.224412\pi\) | ||||
0.761605 | + | 0.648041i | \(0.224412\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.6467 | −1.38685 | −0.693423 | − | 0.720530i | \(-0.743898\pi\) | ||||
−0.693423 | + | 0.720530i | \(0.743898\pi\) | |||||||
\(860\) | −2.03923 | −0.0695371 | ||||||||
\(861\) | −25.2107 | −0.859180 | ||||||||
\(862\) | 19.3642 | 0.659547 | ||||||||
\(863\) | 31.9748 | 1.08843 | 0.544217 | − | 0.838945i | \(-0.316827\pi\) | ||||
0.544217 | + | 0.838945i | \(0.316827\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −16.6853 | −0.567318 | ||||||||
\(866\) | −4.41119 | −0.149898 | ||||||||
\(867\) | 9.75302 | 0.331230 | ||||||||
\(868\) | −0.753020 | −0.0255592 | ||||||||
\(869\) | −6.06638 | −0.205788 | ||||||||
\(870\) | 6.15883 | 0.208804 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.801938 | 0.0271570 | ||||||||
\(873\) | −1.93900 | −0.0656252 | ||||||||
\(874\) | 8.40581 | 0.284331 | ||||||||
\(875\) | 3.04892 | 0.103072 | ||||||||
\(876\) | −14.8334 | −0.501174 | ||||||||
\(877\) | 39.2476 | 1.32530 | 0.662648 | − | 0.748931i | \(-0.269433\pi\) | ||||
0.662648 | + | 0.748931i | \(0.269433\pi\) | |||||||
\(878\) | −39.5260 | −1.33394 | ||||||||
\(879\) | 18.5810 | 0.626723 | ||||||||
\(880\) | 1.13706 | 0.0383304 | ||||||||
\(881\) | −24.3153 | −0.819202 | −0.409601 | − | 0.912265i | \(-0.634332\pi\) | ||||
−0.409601 | + | 0.912265i | \(0.634332\pi\) | |||||||
\(882\) | −2.29590 | −0.0773069 | ||||||||
\(883\) | 51.8756 | 1.74575 | 0.872877 | − | 0.487941i | \(-0.162252\pi\) | ||||
0.872877 | + | 0.487941i | \(0.162252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.36898 | −0.0460177 | ||||||||
\(886\) | 7.16182 | 0.240606 | ||||||||
\(887\) | −13.4383 | −0.451215 | −0.225608 | − | 0.974218i | \(-0.572437\pi\) | ||||
−0.225608 | + | 0.974218i | \(0.572437\pi\) | |||||||
\(888\) | 0.554958 | 0.0186232 | ||||||||
\(889\) | −18.9801 | −0.636574 | ||||||||
\(890\) | −16.8877 | −0.566077 | ||||||||
\(891\) | −1.13706 | −0.0380931 | ||||||||
\(892\) | −1.11960 | −0.0374871 | ||||||||
\(893\) | −10.4209 | −0.348721 | ||||||||
\(894\) | −16.4209 | −0.549196 | ||||||||
\(895\) | 3.94438 | 0.131846 | ||||||||
\(896\) | 3.04892 | 0.101857 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.46011 | −0.148836 | ||||||||
\(899\) | −1.52111 | −0.0507317 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 15.5459 | 0.517908 | ||||||||
\(902\) | −9.40209 | −0.313055 | ||||||||
\(903\) | 6.21744 | 0.206903 | ||||||||
\(904\) | 11.5211 | 0.383186 | ||||||||
\(905\) | 20.5308 | 0.682467 | ||||||||
\(906\) | 9.26636 | 0.307854 | ||||||||
\(907\) | −6.58881 | −0.218778 | −0.109389 | − | 0.993999i | \(-0.534889\pi\) | ||||
−0.109389 | + | 0.993999i | \(0.534889\pi\) | |||||||
\(908\) | −4.06638 | −0.134947 | ||||||||
\(909\) | −14.4940 | −0.480734 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.2646 | 1.69847 | 0.849235 | − | 0.528015i | \(-0.177063\pi\) | ||||
0.849235 | + | 0.528015i | \(0.177063\pi\) | |||||||
\(912\) | 1.55496 | 0.0514898 | ||||||||
\(913\) | −6.20237 | −0.205269 | ||||||||
\(914\) | −8.04593 | −0.266136 | ||||||||
\(915\) | 10.9487 | 0.361953 | ||||||||
\(916\) | 16.5187 | 0.545794 | ||||||||
\(917\) | −10.1981 | −0.336770 | ||||||||
\(918\) | 2.69202 | 0.0888499 | ||||||||
\(919\) | 50.7066 | 1.67266 | 0.836328 | − | 0.548229i | \(-0.184698\pi\) | ||||
0.836328 | + | 0.548229i | \(0.184698\pi\) | |||||||
\(920\) | 5.40581 | 0.178224 | ||||||||
\(921\) | 32.4359 | 1.06880 | ||||||||
\(922\) | 4.00538 | 0.131910 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.46681 | −0.114050 | ||||||||
\(925\) | 0.554958 | 0.0182469 | ||||||||
\(926\) | −37.6142 | −1.23608 | ||||||||
\(927\) | −16.1836 | −0.531539 | ||||||||
\(928\) | 6.15883 | 0.202174 | ||||||||
\(929\) | 18.2903 | 0.600084 | 0.300042 | − | 0.953926i | \(-0.402999\pi\) | ||||
0.300042 | + | 0.953926i | \(0.402999\pi\) | |||||||
\(930\) | −0.246980 | −0.00809878 | ||||||||
\(931\) | −3.57002 | −0.117003 | ||||||||
\(932\) | −6.16421 | −0.201915 | ||||||||
\(933\) | 21.2771 | 0.696581 | ||||||||
\(934\) | 32.8079 | 1.07351 | ||||||||
\(935\) | 3.06100 | 0.100105 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −59.6679 | −1.94926 | −0.974632 | − | 0.223814i | \(-0.928149\pi\) | ||||
−0.974632 | + | 0.223814i | \(0.928149\pi\) | |||||||
\(938\) | 7.53750 | 0.246108 | ||||||||
\(939\) | 18.7060 | 0.610448 | ||||||||
\(940\) | −6.70171 | −0.218586 | ||||||||
\(941\) | 36.2513 | 1.18176 | 0.590879 | − | 0.806760i | \(-0.298781\pi\) | ||||
0.590879 | + | 0.806760i | \(0.298781\pi\) | |||||||
\(942\) | 17.0761 | 0.556368 | ||||||||
\(943\) | −44.6993 | −1.45561 | ||||||||
\(944\) | −1.36898 | −0.0445564 | ||||||||
\(945\) | −3.04892 | −0.0991813 | ||||||||
\(946\) | 2.31873 | 0.0753885 | ||||||||
\(947\) | −7.02475 | −0.228274 | −0.114137 | − | 0.993465i | \(-0.536410\pi\) | ||||
−0.114137 | + | 0.993465i | \(0.536410\pi\) | |||||||
\(948\) | −5.33513 | −0.173277 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.55496 | 0.0504495 | ||||||||
\(951\) | 17.4776 | 0.566749 | ||||||||
\(952\) | 8.20775 | 0.266015 | ||||||||
\(953\) | 12.5730 | 0.407280 | 0.203640 | − | 0.979046i | \(-0.434723\pi\) | ||||
0.203640 | + | 0.979046i | \(0.434723\pi\) | |||||||
\(954\) | −5.77479 | −0.186966 | ||||||||
\(955\) | 6.66487 | 0.215670 | ||||||||
\(956\) | −18.1793 | −0.587960 | ||||||||
\(957\) | −7.00298 | −0.226374 | ||||||||
\(958\) | −9.88530 | −0.319379 | ||||||||
\(959\) | −29.0586 | −0.938351 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −30.9390 | −0.998032 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.92931 | 0.158845 | ||||||||
\(964\) | 9.21744 | 0.296874 | ||||||||
\(965\) | 16.6558 | 0.536168 | ||||||||
\(966\) | −16.4819 | −0.530296 | ||||||||
\(967\) | 23.1371 | 0.744038 | 0.372019 | − | 0.928225i | \(-0.378666\pi\) | ||||
0.372019 | + | 0.928225i | \(0.378666\pi\) | |||||||
\(968\) | 9.70709 | 0.311998 | ||||||||
\(969\) | 4.18598 | 0.134473 | ||||||||
\(970\) | −1.93900 | −0.0622576 | ||||||||
\(971\) | −26.5394 | −0.851690 | −0.425845 | − | 0.904796i | \(-0.640023\pi\) | ||||
−0.425845 | + | 0.904796i | \(0.640023\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −57.0200 | −1.82798 | ||||||||
\(974\) | 20.2610 | 0.649204 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.9487 | 0.350459 | ||||||||
\(977\) | −19.5670 | −0.626005 | −0.313003 | − | 0.949752i | \(-0.601335\pi\) | ||||
−0.313003 | + | 0.949752i | \(0.601335\pi\) | |||||||
\(978\) | 9.61894 | 0.307580 | ||||||||
\(979\) | 19.2024 | 0.613711 | ||||||||
\(980\) | −2.29590 | −0.0733397 | ||||||||
\(981\) | −0.801938 | −0.0256039 | ||||||||
\(982\) | 22.4940 | 0.717811 | ||||||||
\(983\) | 8.82610 | 0.281509 | 0.140754 | − | 0.990045i | \(-0.455047\pi\) | ||||
0.140754 | + | 0.990045i | \(0.455047\pi\) | |||||||
\(984\) | −8.26875 | −0.263598 | ||||||||
\(985\) | 19.4494 | 0.619708 | ||||||||
\(986\) | 16.5797 | 0.528006 | ||||||||
\(987\) | 20.4330 | 0.650388 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.0237 | 0.350533 | ||||||||
\(990\) | −1.13706 | −0.0361382 | ||||||||
\(991\) | 0.601483 | 0.0191067 | 0.00955336 | − | 0.999954i | \(-0.496959\pi\) | ||||
0.00955336 | + | 0.999954i | \(0.496959\pi\) | |||||||
\(992\) | −0.246980 | −0.00784161 | ||||||||
\(993\) | −23.1890 | −0.735880 | ||||||||
\(994\) | 26.1293 | 0.828771 | ||||||||
\(995\) | 21.6558 | 0.686534 | ||||||||
\(996\) | −5.45473 | −0.172840 | ||||||||
\(997\) | 13.4101 | 0.424703 | 0.212351 | − | 0.977193i | \(-0.431888\pi\) | ||||
0.212351 | + | 0.977193i | \(0.431888\pi\) | |||||||
\(998\) | −15.2728 | −0.483452 | ||||||||
\(999\) | −0.554958 | −0.0175581 |
(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 | 5070.2.a.bj.1.1 | ✓ | 3 | |
13.5 | odd | 4 | 5070.2.b.t.1351.4 | 6 | |||
13.8 | odd | 4 | 5070.2.b.t.1351.3 | 6 | |||
13.12 | even | 2 | 5070.2.a.bu.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bj.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
5070.2.a.bu.1.3 | yes | 3 | 13.12 | even | 2 | ||
5070.2.b.t.1351.3 | 6 | 13.8 | odd | 4 | |||
5070.2.b.t.1351.4 | 6 | 13.5 | odd | 4 |