Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [644,2,Mod(1,644)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(644, 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("644.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 644 = 2^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 644.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: | \(5.14236589017\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.6963152.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 10x^{3} + 10x^{2} + 29x + 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.435854\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 644.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.43585 | 0.828991 | 0.414495 | − | 0.910051i | \(-0.363958\pi\) | ||||
0.414495 | + | 0.910051i | \(0.363958\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.34236 | 1.04753 | 0.523767 | − | 0.851862i | \(-0.324526\pi\) | ||||
0.523767 | + | 0.851862i | \(0.324526\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.938323 | −0.312774 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.38507 | 1.62366 | 0.811830 | − | 0.583894i | \(-0.198472\pi\) | ||||
0.811830 | + | 0.583894i | \(0.198472\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.32339 | −1.47644 | −0.738222 | − | 0.674558i | \(-0.764334\pi\) | ||||
−0.738222 | + | 0.674558i | \(0.764334\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.36328 | 0.868396 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.88754 | 1.91301 | 0.956505 | − | 0.291717i | \(-0.0942265\pi\) | ||||
0.956505 | + | 0.291717i | \(0.0942265\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.06364 | 1.39109 | 0.695547 | − | 0.718480i | \(-0.255162\pi\) | ||||
0.695547 | + | 0.718480i | \(0.255162\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.43585 | −0.313329 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.486637 | 0.0973275 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65486 | −1.08828 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.87468 | 0.348120 | 0.174060 | − | 0.984735i | \(-0.444311\pi\) | ||||
0.174060 | + | 0.984735i | \(0.444311\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.83096 | −1.04727 | −0.523635 | − | 0.851942i | \(-0.675425\pi\) | ||||
−0.523635 | + | 0.851942i | \(0.675425\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.73218 | 1.34600 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.34236 | −0.395931 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.19193 | 0.195952 | 0.0979762 | − | 0.995189i | \(-0.468763\pi\) | ||||
0.0979762 | + | 0.995189i | \(0.468763\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.64362 | −1.22396 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.45169 | 1.00758 | 0.503792 | − | 0.863825i | \(-0.331938\pi\) | ||||
0.503792 | + | 0.863825i | \(0.331938\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.93535 | −1.05763 | −0.528815 | − | 0.848737i | \(-0.677364\pi\) | ||||
−0.528815 | + | 0.848737i | \(0.677364\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.19789 | −0.327642 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.8577 | −1.58376 | −0.791878 | − | 0.610679i | \(-0.790896\pi\) | ||||
−0.791878 | + | 0.610679i | \(0.790896\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.3254 | 1.58587 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.94029 | 1.09068 | 0.545341 | − | 0.838214i | \(-0.316400\pi\) | ||||
0.545341 | + | 0.838214i | \(0.316400\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.6138 | 1.70084 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.70650 | 1.15320 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.69561 | −0.350938 | −0.175469 | − | 0.984485i | \(-0.556144\pi\) | ||||
−0.175469 | + | 0.984485i | \(0.556144\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.27771 | −0.419667 | −0.209834 | − | 0.977737i | \(-0.567292\pi\) | ||||
−0.209834 | + | 0.977737i | \(0.567292\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.938323 | 0.118218 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.4693 | −1.54663 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.82865 | −0.223405 | −0.111702 | − | 0.993742i | \(-0.535630\pi\) | ||||
−0.111702 | + | 0.993742i | \(0.535630\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.43585 | −0.172857 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.30161 | 0.866541 | 0.433271 | − | 0.901264i | \(-0.357359\pi\) | ||||
0.433271 | + | 0.901264i | \(0.357359\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.51039 | −0.879024 | −0.439512 | − | 0.898237i | \(-0.644849\pi\) | ||||
−0.439512 | + | 0.898237i | \(0.644849\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.698740 | 0.0806836 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.38507 | −0.613686 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.49158 | −0.280324 | −0.140162 | − | 0.990129i | \(-0.544762\pi\) | ||||
−0.140162 | + | 0.990129i | \(0.544762\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.30458 | −0.589398 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.8120 | −1.84536 | −0.922678 | − | 0.385571i | \(-0.874004\pi\) | ||||
−0.922678 | + | 0.385571i | \(0.874004\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.4754 | 2.00394 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.69177 | 0.288588 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.2665 | 1.40624 | 0.703121 | − | 0.711070i | \(-0.251789\pi\) | ||||
0.703121 | + | 0.711070i | \(0.251789\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.32339 | 0.558043 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.37240 | −0.868178 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.2032 | 1.45722 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.9624 | 1.21460 | 0.607300 | − | 0.794473i | \(-0.292253\pi\) | ||||
0.607300 | + | 0.794473i | \(0.292253\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.05294 | −0.507839 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.4918 | −1.44199 | −0.720993 | − | 0.692943i | \(-0.756314\pi\) | ||||
−0.720993 | + | 0.692943i | \(0.756314\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.55642 | 0.744556 | 0.372278 | − | 0.928121i | \(-0.378577\pi\) | ||||
0.372278 | + | 0.928121i | \(0.378577\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.36328 | −0.328223 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.9353 | −1.05716 | −0.528580 | − | 0.848883i | \(-0.677275\pi\) | ||||
−0.528580 | + | 0.848883i | \(0.677275\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.6250 | −1.20926 | −0.604628 | − | 0.796508i | \(-0.706678\pi\) | ||||
−0.604628 | + | 0.796508i | \(0.706678\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.71144 | 0.162443 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.15008 | −0.296335 | −0.148167 | − | 0.988962i | \(-0.547337\pi\) | ||||
−0.148167 | + | 0.988962i | \(0.547337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.34236 | −0.218426 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.99506 | 0.461794 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.88754 | −0.723050 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.9990 | 1.63627 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.26368 | 0.835278 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.5719 | −0.945580 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.25975 | −0.821670 | −0.410835 | − | 0.911710i | \(-0.634763\pi\) | ||||
−0.410835 | + | 0.911710i | \(0.634763\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.95815 | −0.876766 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.02289 | 0.438852 | 0.219426 | − | 0.975629i | \(-0.429582\pi\) | ||||
0.219426 | + | 0.975629i | \(0.429582\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.06364 | −0.525784 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.2457 | −1.14001 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.7114 | −1.34232 | −0.671159 | − | 0.741313i | \(-0.734203\pi\) | ||||
−0.671159 | + | 0.741313i | \(0.734203\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.0569290 | −0.00482865 | −0.00241433 | − | 0.999997i | \(-0.500769\pi\) | ||||
−0.00241433 | + | 0.999997i | \(0.500769\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.5900 | −1.31292 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −28.6669 | −2.39724 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.39118 | 0.364667 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.43585 | 0.118427 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.55642 | 0.127507 | 0.0637536 | − | 0.997966i | \(-0.479693\pi\) | ||||
0.0637536 | + | 0.997966i | \(0.479693\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.44675 | −0.280492 | −0.140246 | − | 0.990117i | \(-0.544789\pi\) | ||||
−0.140246 | + | 0.990117i | \(0.544789\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.40106 | −0.598340 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.6582 | −1.09705 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.0366 | 1.59910 | 0.799548 | − | 0.600603i | \(-0.205073\pi\) | ||||
0.799548 | + | 0.600603i | \(0.205073\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.4011 | 0.904165 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.4556 | −1.60221 | −0.801104 | − | 0.598526i | \(-0.795753\pi\) | ||||
−0.801104 | + | 0.598526i | \(0.795753\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 18.1115 | 1.40998 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.3044 | 1.41644 | 0.708220 | − | 0.705992i | \(-0.249499\pi\) | ||||
0.708220 | + | 0.705992i | \(0.249499\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.3385 | 1.17989 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.68965 | −0.435099 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.0636396 | 0.00483843 | 0.00241922 | − | 0.999997i | \(-0.499230\pi\) | ||||
0.00241922 | + | 0.999997i | \(0.499230\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.486637 | −0.0367863 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.87050 | −0.290925 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.0500 | −0.751169 | −0.375585 | − | 0.926788i | \(-0.622558\pi\) | ||||
−0.375585 | + | 0.926788i | \(0.622558\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.138173 | −0.0102703 | −0.00513516 | − | 0.999987i | \(-0.501635\pi\) | ||||
−0.00513516 | + | 0.999987i | \(0.501635\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.70631 | −0.347900 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.79193 | 0.205267 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 42.4750 | 3.10608 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.65486 | 0.411330 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.55149 | −0.618764 | −0.309382 | − | 0.950938i | \(-0.600122\pi\) | ||||
−0.309382 | + | 0.950938i | \(0.600122\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.3765 | −1.75466 | −0.877330 | − | 0.479887i | \(-0.840678\pi\) | ||||
−0.877330 | + | 0.479887i | \(0.840678\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −17.9041 | −1.28214 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.5421 | 1.53481 | 0.767404 | − | 0.641164i | \(-0.221548\pi\) | ||||
0.767404 | + | 0.641164i | \(0.221548\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.51951 | 0.462156 | 0.231078 | − | 0.972935i | \(-0.425775\pi\) | ||||
0.231078 | + | 0.972935i | \(0.425775\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.62567 | −0.185201 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.87468 | −0.131577 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.1122 | 1.05548 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.938323 | 0.0652180 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 32.6531 | 2.25866 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.2352 | −1.25536 | −0.627681 | − | 0.778471i | \(-0.715996\pi\) | ||||
−0.627681 | + | 0.778471i | \(0.715996\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.4840 | 0.718355 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.2451 | −1.10790 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.83096 | 0.395831 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.7838 | −0.728703 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −41.9885 | −2.82445 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.8496 | −1.32923 | −0.664614 | − | 0.747187i | \(-0.731404\pi\) | ||||
−0.664614 | + | 0.747187i | \(0.731404\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.456623 | −0.0304415 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.579223 | −0.0384444 | −0.0192222 | − | 0.999815i | \(-0.506119\pi\) | ||||
−0.0192222 | + | 0.999815i | \(0.506119\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.6538 | 0.968347 | 0.484174 | − | 0.874972i | \(-0.339120\pi\) | ||||
0.484174 | + | 0.874972i | \(0.339120\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.73218 | −0.508740 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.5953 | 0.956170 | 0.478085 | − | 0.878314i | \(-0.341331\pi\) | ||||
0.478085 | + | 0.878314i | \(0.341331\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.4326 | −1.65904 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.57754 | −0.232386 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.9435 | −0.837243 | −0.418621 | − | 0.908161i | \(-0.637487\pi\) | ||||
−0.418621 | + | 0.908161i | \(0.637487\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.24075 | 0.0799239 | 0.0399619 | − | 0.999201i | \(-0.487276\pi\) | ||||
0.0399619 | + | 0.999201i | \(0.487276\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.34797 | 0.599672 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.34236 | 0.149648 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −32.2791 | −2.05387 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −24.1396 | −1.52978 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.8766 | 1.25460 | 0.627301 | − | 0.778777i | \(-0.284159\pi\) | ||||
0.627301 | + | 0.778777i | \(0.284159\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.38507 | −0.338557 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 26.5280 | 1.66125 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.85803 | 0.303036 | 0.151518 | − | 0.988455i | \(-0.451584\pi\) | ||||
0.151518 | + | 0.988455i | \(0.451584\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.19193 | −0.0740630 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.75906 | −0.108883 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.5760 | 0.713806 | 0.356903 | − | 0.934141i | \(-0.383833\pi\) | ||||
0.356903 | + | 0.934141i | \(0.383833\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.5990 | 1.14253 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.0487 | 1.16576 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.38805 | −0.267544 | −0.133772 | − | 0.991012i | \(-0.542709\pi\) | ||||
−0.133772 | + | 0.991012i | \(0.542709\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.44396 | −0.0877145 | −0.0438572 | − | 0.999038i | \(-0.513965\pi\) | ||||
−0.0438572 | + | 0.999038i | \(0.513965\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.64362 | 0.462613 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.62058 | 0.158027 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.281027 | 0.0168853 | 0.00844263 | − | 0.999964i | \(-0.497313\pi\) | ||||
0.00844263 | + | 0.999964i | \(0.497313\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.47132 | 0.327559 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.5185 | −1.16438 | −0.582188 | − | 0.813054i | \(-0.697803\pi\) | ||||
−0.582188 | + | 0.813054i | \(0.697803\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.3097 | 1.62339 | 0.811697 | − | 0.584079i | \(-0.198544\pi\) | ||||
0.811697 | + | 0.584079i | \(0.198544\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 20.3937 | 1.20802 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.45169 | −0.380831 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 45.2133 | 2.65960 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.1763 | 1.00689 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.8180 | 1.21620 | 0.608100 | − | 0.793860i | \(-0.291932\pi\) | ||||
0.608100 | + | 0.793860i | \(0.291932\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.31408 | −0.367620 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −30.4518 | −1.76699 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.32339 | 0.307860 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.93535 | 0.399747 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −20.8081 | −1.19539 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.67756 | −0.439616 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.1772 | 1.03742 | 0.518712 | − | 0.854949i | \(-0.326412\pi\) | ||||
0.518712 | + | 0.854949i | \(0.326412\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.8499 | 0.617230 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.6176 | −0.715478 | −0.357739 | − | 0.933822i | \(-0.616452\pi\) | ||||
−0.357739 | + | 0.933822i | \(0.616452\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.2510 | −1.08813 | −0.544066 | − | 0.839042i | \(-0.683116\pi\) | ||||
−0.544066 | + | 0.839042i | \(0.683116\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.19789 | 0.123837 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.9197 | 0.613312 | 0.306656 | − | 0.951820i | \(-0.400790\pi\) | ||||
0.306656 | + | 0.951820i | \(0.400790\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.0953 | 0.565228 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.7016 | −0.876376 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 47.8272 | 2.66118 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.59056 | −0.143699 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.1277 | −1.00246 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.8577 | 0.598603 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.1364 | 1.82134 | 0.910671 | − | 0.413133i | \(-0.135566\pi\) | ||||
0.910671 | + | 0.413133i | \(0.135566\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.11842 | −0.0612888 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.28335 | −0.234024 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 35.6458 | 1.94175 | 0.970875 | − | 0.239588i | \(-0.0770125\pi\) | ||||
0.970875 | + | 0.239588i | \(0.0770125\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.52305 | −0.245659 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31.4001 | −1.70041 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.36328 | −0.181073 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.117783 | −0.00632293 | −0.00316146 | − | 0.999995i | \(-0.501006\pi\) | ||||
−0.00316146 | + | 0.999995i | \(0.501006\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7083 | −0.680258 | −0.340129 | − | 0.940379i | \(-0.610471\pi\) | ||||
−0.340129 | + | 0.940379i | \(0.610471\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 30.1030 | 1.60678 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.4791 | −0.823870 | −0.411935 | − | 0.911213i | \(-0.635147\pi\) | ||||
−0.411935 | + | 0.911213i | \(0.635147\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.1030 | 0.907731 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.3254 | −0.599401 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.66806 | 0.404705 | 0.202352 | − | 0.979313i | \(-0.435141\pi\) | ||||
0.202352 | + | 0.979313i | \(0.435141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.7677 | 0.935143 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.8439 | 1.35645 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.5920 | −0.920808 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.1079 | 0.527628 | 0.263814 | − | 0.964574i | \(-0.415019\pi\) | ||||
0.263814 | + | 0.964574i | \(0.415019\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.05376 | −0.315146 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.94029 | −0.412239 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.8437 | −1.49347 | −0.746734 | − | 0.665123i | \(-0.768379\pi\) | ||||
−0.746734 | + | 0.665123i | \(0.768379\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.1797 | −0.783877 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.97968 | −0.513980 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.2020 | 1.39727 | 0.698636 | − | 0.715477i | \(-0.253790\pi\) | ||||
0.698636 | + | 0.715477i | \(0.253790\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.2957 | −0.681157 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.6517 | 1.00416 | 0.502078 | − | 0.864822i | \(-0.332569\pi\) | ||||
0.502078 | + | 0.864822i | \(0.332569\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.6138 | −0.642857 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.50760 | 0.330800 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.9990 | 0.659075 | 0.329537 | − | 0.944143i | \(-0.393107\pi\) | ||||
0.329537 | + | 0.944143i | \(0.393107\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.88754 | −0.398890 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.21214 | 0.363804 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.83616 | −0.293649 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.2637 | 1.36832 | 0.684162 | − | 0.729330i | \(-0.260168\pi\) | ||||
0.684162 | + | 0.729330i | \(0.260168\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.70650 | −0.435870 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.3543 | 0.517069 | 0.258535 | − | 0.966002i | \(-0.416760\pi\) | ||||
0.258535 | + | 0.966002i | \(0.416760\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.0405 | 1.54624 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.4252 | −0.617414 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.41863 | 0.318160 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.4338 | 0.713707 | 0.356853 | − | 0.934160i | \(-0.383850\pi\) | ||||
0.356853 | + | 0.934160i | \(0.383850\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.5593 | −1.11277 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.69561 | 0.132642 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −39.3797 | −1.93307 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.0817417 | −0.00400291 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.7780 | 1.89443 | 0.947214 | − | 0.320601i | \(-0.103885\pi\) | ||||
0.947214 | + | 0.320601i | \(0.103885\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.3097 | 1.62342 | 0.811708 | − | 0.584063i | \(-0.198538\pi\) | ||||
0.811708 | + | 0.584063i | \(0.198538\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.1880 | 0.495358 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.83837 | 0.186188 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.27771 | 0.158619 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −41.1614 | −1.98729 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.967325 | −0.0465944 | −0.0232972 | − | 0.999729i | \(-0.507416\pi\) | ||||
−0.0232972 | + | 0.999729i | \(0.507416\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.4173 | 0.548679 | 0.274340 | − | 0.961633i | \(-0.411541\pi\) | ||||
0.274340 | + | 0.961633i | \(0.411541\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.30509 | 0.302306 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.06364 | −0.290063 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.3789 | −0.495357 | −0.247678 | − | 0.968842i | \(-0.579668\pi\) | ||||
−0.247678 | + | 0.968842i | \(0.579668\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.938323 | −0.0446820 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.2218 | −1.10330 | −0.551651 | − | 0.834075i | \(-0.686002\pi\) | ||||
−0.551651 | + | 0.834075i | \(0.686002\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 31.0748 | 1.47309 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.23480 | 0.105702 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.6505 | −0.502629 | −0.251314 | − | 0.967905i | \(-0.580863\pi\) | ||||
−0.251314 | + | 0.967905i | \(0.580863\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.7428 | 1.63597 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.94903 | −0.232526 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.4693 | 0.584569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.379938 | 0.0177727 | 0.00888637 | − | 0.999961i | \(-0.497171\pi\) | ||||
0.00888637 | + | 0.999961i | \(0.497171\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −44.6029 | −2.08189 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.3880 | −0.763267 | −0.381634 | − | 0.924314i | \(-0.624638\pi\) | ||||
−0.381634 | + | 0.924314i | \(0.624638\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.2349 | −1.68398 | −0.841989 | − | 0.539495i | \(-0.818615\pi\) | ||||
−0.841989 | + | 0.539495i | \(0.818615\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.6112 | −0.909446 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.1603 | 0.794083 | 0.397041 | − | 0.917801i | \(-0.370037\pi\) | ||||
0.397041 | + | 0.917801i | \(0.370037\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.82865 | 0.0844391 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28.7696 | 1.32564 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −37.3473 | −1.71723 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.95079 | 0.135392 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.45055 | −0.341137 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.8299 | −0.768976 | −0.384488 | − | 0.923130i | \(-0.625622\pi\) | ||||
−0.384488 | + | 0.923130i | \(0.625622\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.34512 | −0.289313 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.43585 | 0.0653336 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.0203 | 1.27233 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.9276 | −1.22021 | −0.610103 | − | 0.792322i | \(-0.708872\pi\) | ||||
−0.610103 | + | 0.792322i | \(0.708872\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −29.3713 | −1.32821 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.3432 | −0.963203 | −0.481602 | − | 0.876390i | \(-0.659945\pi\) | ||||
−0.481602 | + | 0.876390i | \(0.659945\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.7866 | 0.665957 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.8358 | −0.531979 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.30161 | −0.327522 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.5203 | −0.873847 | −0.436923 | − | 0.899499i | \(-0.643932\pi\) | ||||
−0.436923 | + | 0.899499i | \(0.643932\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26.2825 | 1.17422 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.02673 | 0.224131 | 0.112065 | − | 0.993701i | \(-0.464253\pi\) | ||||
0.112065 | + | 0.993701i | \(0.464253\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.9449 | −1.51053 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.0239 | 0.978115 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.5354 | −0.466973 | −0.233486 | − | 0.972360i | \(-0.575013\pi\) | ||||
−0.233486 | + | 0.972360i | \(0.575013\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.51039 | 0.332240 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −34.2890 | −1.51390 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.6998 | 0.779948 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −58.4694 | −2.57148 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.0913772 | 0.00401101 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.8559 | 0.475606 | 0.237803 | − | 0.971313i | \(-0.423573\pi\) | ||||
0.237803 | + | 0.971313i | \(0.423573\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.5175 | 0.722259 | 0.361130 | − | 0.932516i | \(-0.382391\pi\) | ||||
0.361130 | + | 0.932516i | \(0.382391\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.698740 | −0.0304955 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −45.9919 | −2.00344 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.52935 | 0.109764 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.3449 | −1.48764 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.6145 | −1.10741 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.4303 | −0.622712 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.38507 | 0.231951 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.0983 | −0.477152 | −0.238576 | − | 0.971124i | \(-0.576681\pi\) | ||||
−0.238576 | + | 0.971124i | \(0.576681\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.198396 | −0.00851400 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −29.5723 | −1.26674 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.70757 | −0.158524 | −0.0792621 | − | 0.996854i | \(-0.525256\pi\) | ||||
−0.0792621 | + | 0.996854i | \(0.525256\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.07555 | 0.131261 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.3674 | 0.484268 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.49158 | 0.105953 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.00880 | 0.170164 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.5792 | −0.617741 | −0.308871 | − | 0.951104i | \(-0.599951\pi\) | ||||
−0.308871 | + | 0.951104i | \(0.599951\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.9196 | 1.56153 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 60.9878 | 2.57491 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.2872 | −0.644280 | −0.322140 | − | 0.946692i | \(-0.604402\pi\) | ||||
−0.322140 | + | 0.946692i | \(0.604402\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.37861 | −0.310420 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.30458 | 0.222771 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.3853 | 0.728828 | 0.364414 | − | 0.931237i | \(-0.381269\pi\) | ||||
0.364414 | + | 0.931237i | \(0.381269\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.96802 | −0.249754 | −0.124877 | − | 0.992172i | \(-0.539854\pi\) | ||||
−0.124877 | + | 0.992172i | \(0.539854\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.2787 | −0.512949 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.486637 | −0.0202942 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.1611 | −0.922579 | −0.461289 | − | 0.887250i | \(-0.652613\pi\) | ||||
−0.461289 | + | 0.887250i | \(0.652613\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −35.0011 | −1.45460 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.8120 | 0.697479 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 42.7590 | 1.77090 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.7002 | 0.483745 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.96131 | 0.411147 | 0.205574 | − | 0.978642i | \(-0.434094\pi\) | ||||
0.205574 | + | 0.978642i | \(0.434094\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.3568 | −1.45685 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.9312 | 1.27234 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.77014 | 0.360147 | 0.180073 | − | 0.983653i | \(-0.442367\pi\) | ||||
0.180073 | + | 0.983653i | \(0.442367\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.4754 | −0.757419 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.36106 | 0.383123 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.3276 | 0.462832 | 0.231416 | − | 0.972855i | \(-0.425664\pi\) | ||||
0.231416 | + | 0.972855i | \(0.425664\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.77090 | 0.235400 | 0.117700 | − | 0.993049i | \(-0.462448\pi\) | ||||
0.117700 | + | 0.993049i | \(0.462448\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.71586 | 0.0698753 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 42.1601 | 1.71405 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.19400 | 0.0484630 | 0.0242315 | − | 0.999706i | \(-0.492286\pi\) | ||||
0.0242315 | + | 0.999706i | \(0.492286\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.69177 | −0.109076 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 57.7997 | 2.33833 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.3622 | −1.71099 | −0.855496 | − | 0.517810i | \(-0.826747\pi\) | ||||
−0.855496 | + | 0.517810i | \(0.826747\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 21.6988 | 0.874982 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.9063 | 1.36502 | 0.682508 | − | 0.730878i | \(-0.260889\pi\) | ||||
0.682508 | + | 0.730878i | \(0.260889\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.6830 | 1.11267 | 0.556337 | − | 0.830957i | \(-0.312206\pi\) | ||||
0.556337 | + | 0.830957i | \(0.312206\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.65486 | 0.226922 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.2665 | −0.531510 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.1964 | −1.08785 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 46.8851 | 1.87241 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.40141 | 0.374859 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.801923 | −0.0319240 | −0.0159620 | − | 0.999873i | \(-0.505081\pi\) | ||||
−0.0159620 | + | 0.999873i | \(0.505081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.1831 | −1.04068 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.6897 | −0.860728 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.32339 | −0.210921 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.85126 | −0.271032 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.1287 | 0.755538 | 0.377769 | − | 0.925900i | \(-0.376691\pi\) | ||||
0.377769 | + | 0.925900i | \(0.376691\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.8827 | −1.73056 | −0.865282 | − | 0.501286i | \(-0.832861\pi\) | ||||
−0.865282 | + | 0.501286i | \(0.832861\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.3255 | −0.918442 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.0032 | 1.61200 | 0.806001 | − | 0.591914i | \(-0.201627\pi\) | ||||
0.806001 | + | 0.591914i | \(0.201627\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.5160 | −0.569804 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.37240 | 0.328140 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.1744 | 1.37648 | 0.688240 | − | 0.725483i | \(-0.258383\pi\) | ||||
0.688240 | + | 0.725483i | \(0.258383\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.7654 | 0.459712 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.04717 | 0.274936 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.7839 | −0.965445 | −0.482723 | − | 0.875773i | \(-0.660352\pi\) | ||||
−0.482723 | + | 0.875773i | \(0.660352\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.4545 | 1.61239 | 0.806197 | − | 0.591648i | \(-0.201522\pi\) | ||||
0.806197 | + | 0.591648i | \(0.201522\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −60.2893 | −2.34144 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.2032 | −0.550777 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.87468 | −0.0725880 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −28.5011 | −1.10192 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.6507 | −0.681397 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.0660 | −1.39024 | −0.695121 | − | 0.718893i | \(-0.744649\pi\) | ||||
−0.695121 | + | 0.718893i | \(0.744649\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.75187 | −0.105919 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.41266 | 0.131159 | 0.0655795 | − | 0.997847i | \(-0.479110\pi\) | ||||
0.0655795 | + | 0.997847i | \(0.479110\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.9624 | −0.459076 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.831679 | −0.0318700 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.2314 | −0.927188 | −0.463594 | − | 0.886048i | \(-0.653440\pi\) | ||||
−0.463594 | + | 0.886048i | \(0.653440\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.8018 | −1.40612 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.0407 | 0.802751 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −42.2693 | −1.61033 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.37573 | 0.280586 | 0.140293 | − | 0.990110i | \(-0.455196\pi\) | ||||
0.140293 | + | 0.990110i | \(0.455196\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.05294 | 0.191945 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.133348 | −0.00505818 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 50.8879 | 1.92752 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.9567 | 0.792656 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.25950 | 0.123109 | 0.0615547 | − | 0.998104i | \(-0.480394\pi\) | ||||
0.0615547 | + | 0.998104i | \(0.480394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.22744 | 0.272588 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −36.5175 | −1.37533 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.4918 | 0.545019 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 43.0749 | 1.61771 | 0.808856 | − | 0.588006i | \(-0.200087\pi\) | ||||
0.808856 | + | 0.588006i | \(0.200087\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.33790 | 0.0876782 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.83096 | 0.218371 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −67.1480 | −2.51119 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.5849 | −0.694066 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.219003 | 0.00816744 | 0.00408372 | − | 0.999992i | \(-0.498700\pi\) | ||||
0.00408372 | + | 0.999992i | \(0.498700\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.55642 | −0.281416 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.78154 | 0.0662562 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.912291 | 0.0338816 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.7045 | −0.842062 | −0.421031 | − | 0.907046i | \(-0.638332\pi\) | ||||
−0.421031 | + | 0.907046i | \(0.638332\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.3361 | 1.08652 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −54.7028 | −2.02326 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.9129 | 0.661628 | 0.330814 | − | 0.943696i | \(-0.392677\pi\) | ||||
0.330814 | + | 0.943696i | \(0.392677\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.36328 | 0.124057 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.84740 | −0.362734 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.3452 | −0.417339 | −0.208670 | − | 0.977986i | \(-0.566913\pi\) | ||||
−0.208670 | + | 0.977986i | \(0.566913\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −46.3481 | −1.70264 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.31548 | 0.341752 | 0.170876 | − | 0.985293i | \(-0.445340\pi\) | ||||
0.170876 | + | 0.985293i | \(0.445340\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.64570 | 0.133568 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.7751 | 0.577180 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.9353 | 0.399569 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.43047 | 0.198161 | 0.0990803 | − | 0.995079i | \(-0.468410\pi\) | ||||
0.0990803 | + | 0.995079i | \(0.468410\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.5400 | 1.04005 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.07351 | −0.293825 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.50823 | −0.345582 | −0.172791 | − | 0.984958i | \(-0.555279\pi\) | ||||
−0.172791 | + | 0.984958i | \(0.555279\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.73218 | −0.280660 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.6974 | 0.786529 | 0.393265 | − | 0.919425i | \(-0.371346\pi\) | ||||
0.393265 | + | 0.919425i | \(0.371346\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.6250 | 0.457056 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17.3359 | −0.626782 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.3498 | 0.518141 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.7850 | −0.388916 | −0.194458 | − | 0.980911i | \(-0.562295\pi\) | ||||
−0.194458 | + | 0.980911i | \(0.562295\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.97542 | 0.251214 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.1118 | −0.903210 | −0.451605 | − | 0.892218i | \(-0.649148\pi\) | ||||
−0.451605 | + | 0.892218i | \(0.649148\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.83756 | −0.101928 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.71144 | −0.0613976 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 39.1207 | 1.40164 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.3197 | 1.40697 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.6011 | −0.378851 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46.9329 | 1.67511 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.64538 | 0.0586516 | 0.0293258 | − | 0.999570i | \(-0.490664\pi\) | ||||
0.0293258 | + | 0.999570i | \(0.490664\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.6214 | 0.591739 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.15008 | 0.112004 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.4485 | 0.619615 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 26.7054 | 0.947144 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0243 | 0.425923 | 0.212962 | − | 0.977061i | \(-0.431689\pi\) | ||||
0.212962 | + | 0.977061i | \(0.431689\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −85.6404 | −3.02974 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.4482 | −0.439837 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −40.4440 | −1.42724 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.34236 | 0.0825572 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.30059 | −0.221791 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.4285 | 0.401803 | 0.200901 | − | 0.979611i | \(-0.435613\pi\) | ||||
0.200901 | + | 0.979611i | \(0.435613\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.2552 | 0.851714 | 0.425857 | − | 0.904790i | \(-0.359973\pi\) | ||||
0.425857 | + | 0.904790i | \(0.359973\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.07332 | −0.0727145 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −47.9143 | −1.67837 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −42.0535 | −1.47126 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.99506 | −0.174542 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.1394 | 0.563268 | 0.281634 | − | 0.959522i | \(-0.409124\pi\) | ||||
0.281634 | + | 0.959522i | \(0.409124\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.72512 | −0.199565 | −0.0997825 | − | 0.995009i | \(-0.531815\pi\) | ||||
−0.0997825 | + | 0.995009i | \(0.531815\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.76277 | 0.131003 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.6141 | −0.960237 | −0.480118 | − | 0.877204i | \(-0.659406\pi\) | ||||
−0.480118 | + | 0.877204i | \(0.659406\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.3694 | 0.950580 | 0.475290 | − | 0.879829i | \(-0.342343\pi\) | ||||
0.475290 | + | 0.879829i | \(0.342343\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.403514 | 0.0139977 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.88754 | 0.273287 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 42.8755 | 1.48377 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.9732 | 1.13972 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.24538 | 0.319186 | 0.159593 | − | 0.987183i | \(-0.448982\pi\) | ||||
0.159593 | + | 0.987183i | \(0.448982\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.4856 | −0.878813 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.0257 | −0.965257 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 35.9283 | 1.23597 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.9990 | −0.618453 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 39.2128 | 1.34578 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.19193 | −0.0408589 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.3601 | 1.65582 | 0.827910 | − | 0.560862i | \(-0.189530\pi\) | ||||
0.827910 | + | 0.560862i | \(0.189530\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.3272 | −0.455781 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.42104 | −0.0485416 | −0.0242708 | − | 0.999705i | \(-0.507726\pi\) | ||||
−0.0242708 | + | 0.999705i | \(0.507726\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.68890 | −0.262342 | −0.131171 | − | 0.991360i | \(-0.541874\pi\) | ||||
−0.131171 | + | 0.991360i | \(0.541874\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.26368 | −0.315705 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.91806 | 0.0652916 | 0.0326458 | − | 0.999467i | \(-0.489607\pi\) | ||||
0.0326458 | + | 0.999467i | \(0.489607\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.149067 | 0.00506842 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 64.9197 | 2.20479 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.4173 | −0.455151 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.73461 | 0.329845 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.2246 | −0.379896 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.5719 | 0.357396 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.2136 | −0.615029 | −0.307515 | − | 0.951543i | \(-0.599497\pi\) | ||||
−0.307515 | + | 0.951543i | \(0.599497\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 29.8916 | 1.00822 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.2662 | −1.42399 | −0.711993 | − | 0.702187i | \(-0.752207\pi\) | ||||
−0.711993 | + | 0.702187i | \(0.752207\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.1758 | 0.578011 | 0.289006 | − | 0.957327i | \(-0.406675\pi\) | ||||
0.289006 | + | 0.957327i | \(0.406675\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.06609 | −0.304753 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.8742 | 0.398696 | 0.199348 | − | 0.979929i | \(-0.436118\pi\) | ||||
0.199348 | + | 0.979929i | \(0.436118\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.25975 | 0.310562 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.5655 | −0.956982 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −65.8371 | −2.20315 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.5406 | −0.786875 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.64362 | 0.255213 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.9312 | −0.364576 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 62.6293 | 2.08649 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.95815 | 0.331386 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.323651 | −0.0107585 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.7923 | 0.557579 | 0.278790 | − | 0.960352i | \(-0.410067\pi\) | ||||
0.278790 | + | 0.960352i | \(0.410067\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.5980 | 0.451016 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.6355 | 1.41258 | 0.706288 | − | 0.707925i | \(-0.250368\pi\) | ||||
0.706288 | + | 0.707925i | \(0.250368\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −90.5338 | −2.99623 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.0239 | −0.364437 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.02289 | −0.165870 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.9742 | −0.658887 | −0.329444 | − | 0.944175i | \(-0.606861\pi\) | ||||
−0.329444 | + | 0.944175i | \(0.606861\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.0997 | 0.860016 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −38.8693 | −1.27940 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.580038 | 0.0190715 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.09036 | −0.232878 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.02222 | 0.197583 | 0.0987914 | − | 0.995108i | \(-0.468502\pi\) | ||||
0.0987914 | + | 0.995108i | \(0.468502\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.06364 | 0.198728 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.1170 | −0.593125 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 99.4915 | 3.25372 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.6553 | −0.805452 | −0.402726 | − | 0.915320i | \(-0.631937\pi\) | ||||
−0.402726 | + | 0.915320i | \(0.631937\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.6417 | −0.902051 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.1049 | 1.63337 | 0.816686 | − | 0.577082i | \(-0.195809\pi\) | ||||
0.816686 | + | 0.577082i | \(0.195809\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.45169 | −0.210096 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.2457 | 0.430883 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.9519 | 0.648351 | 0.324175 | − | 0.945997i | \(-0.394913\pi\) | ||||
0.324175 | + | 0.945997i | \(0.394913\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.9807 | 1.29783 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.6791 | 0.508430 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.2873 | −1.30503 | −0.652517 | − | 0.757774i | \(-0.726287\pi\) | ||||
−0.652517 | + | 0.757774i | \(0.726287\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.0306 | −0.648176 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.4954 | 0.468569 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.7114 | 0.507349 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00006 | 0.0967762 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.2609 | 0.330652 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −57.0985 | −1.83807 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.2689 | −1.00554 | −0.502771 | − | 0.864420i | \(-0.667686\pi\) | ||||
−0.502771 | + | 0.864420i | \(0.667686\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 68.6729 | 2.20609 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.5037 | −1.36401 | −0.682005 | − | 0.731347i | \(-0.738892\pi\) | ||||
−0.682005 | + | 0.731347i | \(0.738892\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.0569290 | 0.00182506 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.71967 | −0.119125 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.2556 | −1.06394 | −0.531971 | − | 0.846762i | \(-0.678549\pi\) | ||||
−0.531971 | + | 0.846762i | \(0.678549\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 71.4409 | 2.28326 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.8463 | 0.378224 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.5016 | 1.48317 | 0.741586 | − | 0.670858i | \(-0.234074\pi\) | ||||
0.741586 | + | 0.670858i | \(0.234074\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 50.4592 | 1.60776 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.5900 | 0.496237 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.93535 | 0.220531 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.1965 | −0.990991 | −0.495496 | − | 0.868610i | \(-0.665014\pi\) | ||||
−0.495496 | + | 0.868610i | \(0.665014\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 47.5790 | 1.50988 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.2710 | 0.484124 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.37962 | 0.233715 | 0.116857 | − | 0.993149i | \(-0.462718\pi\) | ||||
0.116857 | + | 0.993149i | \(0.462718\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.74020 | −0.213251 |
(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 | 644.2.a.d.1.3 | ✓ | 5 | |
3.2 | odd | 2 | 5796.2.a.t.1.2 | 5 | |||
4.3 | odd | 2 | 2576.2.a.bb.1.3 | 5 | |||
7.6 | odd | 2 | 4508.2.a.f.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
644.2.a.d.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
2576.2.a.bb.1.3 | 5 | 4.3 | odd | 2 | |||
4508.2.a.f.1.3 | 5 | 7.6 | odd | 2 | |||
5796.2.a.t.1.2 | 5 | 3.2 | odd | 2 |