Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 29 x^{10} + 76 x^{9} + 320 x^{8} - 724 x^{7} - 1643 x^{6} + 3265 x^{5} + 3921 x^{4} + \cdots + 423 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.15566\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.15566 | −0.964042 | −0.482021 | − | 0.876160i | \(-0.660097\pi\) | ||||
−0.482021 | + | 0.876160i | \(0.660097\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.96511 | −1.49867 | −0.749334 | − | 0.662192i | \(-0.769626\pi\) | ||||
−0.749334 | + | 0.662192i | \(0.769626\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.15566 | 0.681680 | ||||||||
\(11\) | 1.12390 | 0.338869 | 0.169435 | − | 0.985541i | \(-0.445806\pi\) | ||||
0.169435 | + | 0.985541i | \(0.445806\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.24395 | 0.899710 | 0.449855 | − | 0.893102i | \(-0.351476\pi\) | ||||
0.449855 | + | 0.893102i | \(0.351476\pi\) | |||||||
\(14\) | 3.96511 | 1.05972 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.0965560 | 0.0234183 | 0.0117091 | − | 0.999931i | \(-0.496273\pi\) | ||||
0.0117091 | + | 0.999931i | \(0.496273\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.93839 | −0.674113 | −0.337056 | − | 0.941485i | \(-0.609431\pi\) | ||||
−0.337056 | + | 0.941485i | \(0.609431\pi\) | |||||||
\(20\) | −2.15566 | −0.482021 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.12390 | −0.239617 | ||||||||
\(23\) | −6.32576 | −1.31901 | −0.659506 | − | 0.751699i | \(-0.729235\pi\) | ||||
−0.659506 | + | 0.751699i | \(0.729235\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.353119 | −0.0706237 | ||||||||
\(26\) | −3.24395 | −0.636191 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.96511 | −0.749334 | ||||||||
\(29\) | 3.71653 | 0.690142 | 0.345071 | − | 0.938577i | \(-0.387855\pi\) | ||||
0.345071 | + | 0.938577i | \(0.387855\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.97900 | 1.43307 | 0.716536 | − | 0.697550i | \(-0.245727\pi\) | ||||
0.716536 | + | 0.697550i | \(0.245727\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.0965560 | −0.0165592 | ||||||||
\(35\) | 8.54743 | 1.44478 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.52602 | −0.250876 | −0.125438 | − | 0.992101i | \(-0.540034\pi\) | ||||
−0.125438 | + | 0.992101i | \(0.540034\pi\) | |||||||
\(38\) | 2.93839 | 0.476670 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.15566 | 0.340840 | ||||||||
\(41\) | −4.49469 | −0.701952 | −0.350976 | − | 0.936384i | \(-0.614150\pi\) | ||||
−0.350976 | + | 0.936384i | \(0.614150\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.35768 | 1.12204 | 0.561018 | − | 0.827804i | \(-0.310410\pi\) | ||||
0.561018 | + | 0.827804i | \(0.310410\pi\) | |||||||
\(44\) | 1.12390 | 0.169435 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.32576 | 0.932683 | ||||||||
\(47\) | 0.857841 | 0.125129 | 0.0625645 | − | 0.998041i | \(-0.480072\pi\) | ||||
0.0625645 | + | 0.998041i | \(0.480072\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.72206 | 1.24601 | ||||||||
\(50\) | 0.353119 | 0.0499385 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.24395 | 0.449855 | ||||||||
\(53\) | 6.36279 | 0.873997 | 0.436998 | − | 0.899462i | \(-0.356042\pi\) | ||||
0.436998 | + | 0.899462i | \(0.356042\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.42275 | −0.326684 | ||||||||
\(56\) | 3.96511 | 0.529859 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.71653 | −0.488004 | ||||||||
\(59\) | 1.21347 | 0.157981 | 0.0789905 | − | 0.996875i | \(-0.474830\pi\) | ||||
0.0789905 | + | 0.996875i | \(0.474830\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.66519 | −0.469279 | −0.234640 | − | 0.972082i | \(-0.575391\pi\) | ||||
−0.234640 | + | 0.972082i | \(0.575391\pi\) | |||||||
\(62\) | −7.97900 | −1.01333 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.99286 | −0.867358 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.51851 | 1.16287 | 0.581436 | − | 0.813592i | \(-0.302491\pi\) | ||||
0.581436 | + | 0.813592i | \(0.302491\pi\) | |||||||
\(68\) | 0.0965560 | 0.0117091 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.54743 | −1.02161 | ||||||||
\(71\) | −8.51164 | −1.01015 | −0.505073 | − | 0.863077i | \(-0.668534\pi\) | ||||
−0.505073 | + | 0.863077i | \(0.668534\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.49546 | 0.526154 | 0.263077 | − | 0.964775i | \(-0.415263\pi\) | ||||
0.263077 | + | 0.964775i | \(0.415263\pi\) | |||||||
\(74\) | 1.52602 | 0.177396 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.93839 | −0.337056 | ||||||||
\(77\) | −4.45639 | −0.507852 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.19969 | 0.585011 | 0.292505 | − | 0.956264i | \(-0.405511\pi\) | ||||
0.292505 | + | 0.956264i | \(0.405511\pi\) | |||||||
\(80\) | −2.15566 | −0.241010 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.49469 | 0.496355 | ||||||||
\(83\) | −2.22728 | −0.244475 | −0.122238 | − | 0.992501i | \(-0.539007\pi\) | ||||
−0.122238 | + | 0.992501i | \(0.539007\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.208142 | −0.0225762 | ||||||||
\(86\) | −7.35768 | −0.793399 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.12390 | −0.119808 | ||||||||
\(89\) | −2.10826 | −0.223475 | −0.111738 | − | 0.993738i | \(-0.535642\pi\) | ||||
−0.111738 | + | 0.993738i | \(0.535642\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.8626 | −1.34837 | ||||||||
\(92\) | −6.32576 | −0.659506 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.857841 | −0.0884795 | ||||||||
\(95\) | 6.33417 | 0.649873 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.31013 | 0.133024 | 0.0665119 | − | 0.997786i | \(-0.478813\pi\) | ||||
0.0665119 | + | 0.997786i | \(0.478813\pi\) | |||||||
\(98\) | −8.72206 | −0.881061 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.353119 | −0.0353119 | ||||||||
\(101\) | −2.81738 | −0.280340 | −0.140170 | − | 0.990127i | \(-0.544765\pi\) | ||||
−0.140170 | + | 0.990127i | \(0.544765\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.7823 | 1.45654 | 0.728270 | − | 0.685291i | \(-0.240325\pi\) | ||||
0.728270 | + | 0.685291i | \(0.240325\pi\) | |||||||
\(104\) | −3.24395 | −0.318095 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.36279 | −0.618009 | ||||||||
\(107\) | −9.77733 | −0.945210 | −0.472605 | − | 0.881274i | \(-0.656686\pi\) | ||||
−0.472605 | + | 0.881274i | \(0.656686\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.16298 | −0.686089 | −0.343044 | − | 0.939319i | \(-0.611458\pi\) | ||||
−0.343044 | + | 0.939319i | \(0.611458\pi\) | |||||||
\(110\) | 2.42275 | 0.231000 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.96511 | −0.374667 | ||||||||
\(113\) | 16.4629 | 1.54870 | 0.774350 | − | 0.632757i | \(-0.218077\pi\) | ||||
0.774350 | + | 0.632757i | \(0.218077\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.6362 | 1.27158 | ||||||||
\(116\) | 3.71653 | 0.345071 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.21347 | −0.111709 | ||||||||
\(119\) | −0.382854 | −0.0350962 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.73685 | −0.885168 | ||||||||
\(122\) | 3.66519 | 0.331831 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.97900 | 0.716536 | ||||||||
\(125\) | 11.5395 | 1.03213 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.84668 | −0.430073 | −0.215036 | − | 0.976606i | \(-0.568987\pi\) | ||||
−0.215036 | + | 0.976606i | \(0.568987\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.99286 | 0.613315 | ||||||||
\(131\) | −14.9599 | −1.30705 | −0.653526 | − | 0.756904i | \(-0.726711\pi\) | ||||
−0.653526 | + | 0.756904i | \(0.726711\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.6510 | 1.01027 | ||||||||
\(134\) | −9.51851 | −0.822274 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.0965560 | −0.00827960 | ||||||||
\(137\) | −5.99201 | −0.511932 | −0.255966 | − | 0.966686i | \(-0.582394\pi\) | ||||
−0.255966 | + | 0.966686i | \(0.582394\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.3257 | 1.29991 | 0.649955 | − | 0.759972i | \(-0.274788\pi\) | ||||
0.649955 | + | 0.759972i | \(0.274788\pi\) | |||||||
\(140\) | 8.54743 | 0.722390 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.51164 | 0.714281 | ||||||||
\(143\) | 3.64588 | 0.304884 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.01158 | −0.665326 | ||||||||
\(146\) | −4.49546 | −0.372047 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.52602 | −0.125438 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2736 | 1.08019 | 0.540094 | − | 0.841605i | \(-0.318389\pi\) | ||||
0.540094 | + | 0.841605i | \(0.318389\pi\) | |||||||
\(152\) | 2.93839 | 0.238335 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.45639 | 0.359106 | ||||||||
\(155\) | −17.2000 | −1.38154 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.5100 | 1.23783 | 0.618917 | − | 0.785456i | \(-0.287572\pi\) | ||||
0.618917 | + | 0.785456i | \(0.287572\pi\) | |||||||
\(158\) | −5.19969 | −0.413665 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.15566 | 0.170420 | ||||||||
\(161\) | 25.0823 | 1.97676 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0464 | 0.786897 | 0.393449 | − | 0.919347i | \(-0.371282\pi\) | ||||
0.393449 | + | 0.919347i | \(0.371282\pi\) | |||||||
\(164\) | −4.49469 | −0.350976 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.22728 | 0.172870 | ||||||||
\(167\) | 5.45389 | 0.422034 | 0.211017 | − | 0.977482i | \(-0.432322\pi\) | ||||
0.211017 | + | 0.977482i | \(0.432322\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.47679 | −0.190522 | ||||||||
\(170\) | 0.208142 | 0.0159638 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.35768 | 0.561018 | ||||||||
\(173\) | −18.8846 | −1.43577 | −0.717885 | − | 0.696162i | \(-0.754890\pi\) | ||||
−0.717885 | + | 0.696162i | \(0.754890\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.40015 | 0.105842 | ||||||||
\(176\) | 1.12390 | 0.0847173 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.10826 | 0.158021 | ||||||||
\(179\) | −1.75154 | −0.130916 | −0.0654579 | − | 0.997855i | \(-0.520851\pi\) | ||||
−0.0654579 | + | 0.997855i | \(0.520851\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.2991 | −1.58315 | −0.791576 | − | 0.611070i | \(-0.790739\pi\) | ||||
−0.791576 | + | 0.611070i | \(0.790739\pi\) | |||||||
\(182\) | 12.8626 | 0.953440 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.32576 | 0.466341 | ||||||||
\(185\) | 3.28958 | 0.241855 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.108519 | 0.00793572 | ||||||||
\(188\) | 0.857841 | 0.0625645 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.33417 | −0.459529 | ||||||||
\(191\) | 14.5648 | 1.05387 | 0.526937 | − | 0.849904i | \(-0.323340\pi\) | ||||
0.526937 | + | 0.849904i | \(0.323340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.5204 | 0.901238 | 0.450619 | − | 0.892716i | \(-0.351203\pi\) | ||||
0.450619 | + | 0.892716i | \(0.351203\pi\) | |||||||
\(194\) | −1.31013 | −0.0940620 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.72206 | 0.623004 | ||||||||
\(197\) | −12.2475 | −0.872598 | −0.436299 | − | 0.899802i | \(-0.643711\pi\) | ||||
−0.436299 | + | 0.899802i | \(0.643711\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.23542 | −0.0875766 | −0.0437883 | − | 0.999041i | \(-0.513943\pi\) | ||||
−0.0437883 | + | 0.999041i | \(0.513943\pi\) | |||||||
\(200\) | 0.353119 | 0.0249693 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.81738 | 0.198230 | ||||||||
\(203\) | −14.7364 | −1.03429 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.68902 | 0.676711 | ||||||||
\(206\) | −14.7823 | −1.02993 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.24395 | 0.224927 | ||||||||
\(209\) | −3.30246 | −0.228436 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.32672 | −0.297864 | −0.148932 | − | 0.988847i | \(-0.547584\pi\) | ||||
−0.148932 | + | 0.988847i | \(0.547584\pi\) | |||||||
\(212\) | 6.36279 | 0.436998 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.77733 | 0.668365 | ||||||||
\(215\) | −15.8607 | −1.08169 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −31.6376 | −2.14770 | ||||||||
\(218\) | 7.16298 | 0.485138 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.42275 | −0.163342 | ||||||||
\(221\) | 0.313223 | 0.0210696 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.7666 | 0.854913 | 0.427457 | − | 0.904036i | \(-0.359410\pi\) | ||||
0.427457 | + | 0.904036i | \(0.359410\pi\) | |||||||
\(224\) | 3.96511 | 0.264930 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.4629 | −1.09510 | ||||||||
\(227\) | 22.7865 | 1.51239 | 0.756197 | − | 0.654344i | \(-0.227055\pi\) | ||||
0.756197 | + | 0.654344i | \(0.227055\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.6307 | 0.702494 | 0.351247 | − | 0.936283i | \(-0.385758\pi\) | ||||
0.351247 | + | 0.936283i | \(0.385758\pi\) | |||||||
\(230\) | −13.6362 | −0.899145 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.71653 | −0.244002 | ||||||||
\(233\) | −25.2615 | −1.65493 | −0.827467 | − | 0.561515i | \(-0.810219\pi\) | ||||
−0.827467 | + | 0.561515i | \(0.810219\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.84922 | −0.120630 | ||||||||
\(236\) | 1.21347 | 0.0789905 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.382854 | 0.0248168 | ||||||||
\(239\) | 4.22269 | 0.273143 | 0.136571 | − | 0.990630i | \(-0.456392\pi\) | ||||
0.136571 | + | 0.990630i | \(0.456392\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.9213 | −0.767916 | −0.383958 | − | 0.923351i | \(-0.625439\pi\) | ||||
−0.383958 | + | 0.923351i | \(0.625439\pi\) | |||||||
\(242\) | 9.73685 | 0.625908 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.66519 | −0.234640 | ||||||||
\(245\) | −18.8018 | −1.20120 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.53199 | −0.606506 | ||||||||
\(248\) | −7.97900 | −0.506667 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.5395 | −0.729823 | ||||||||
\(251\) | −17.8818 | −1.12869 | −0.564345 | − | 0.825539i | \(-0.690871\pi\) | ||||
−0.564345 | + | 0.825539i | \(0.690871\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.10953 | −0.446972 | ||||||||
\(254\) | 4.84668 | 0.304107 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.387919 | −0.0241977 | −0.0120989 | − | 0.999927i | \(-0.503851\pi\) | ||||
−0.0120989 | + | 0.999927i | \(0.503851\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.05083 | 0.375980 | ||||||||
\(260\) | −6.99286 | −0.433679 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.9599 | 0.924226 | ||||||||
\(263\) | 4.34002 | 0.267617 | 0.133809 | − | 0.991007i | \(-0.457279\pi\) | ||||
0.133809 | + | 0.991007i | \(0.457279\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.7160 | −0.842569 | ||||||||
\(266\) | −11.6510 | −0.714370 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.51851 | 0.581436 | ||||||||
\(269\) | −28.7658 | −1.75388 | −0.876941 | − | 0.480599i | \(-0.840419\pi\) | ||||
−0.876941 | + | 0.480599i | \(0.840419\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.2160 | 1.16729 | 0.583644 | − | 0.812010i | \(-0.301627\pi\) | ||||
0.583644 | + | 0.812010i | \(0.301627\pi\) | |||||||
\(272\) | 0.0965560 | 0.00585456 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.99201 | 0.361991 | ||||||||
\(275\) | −0.396871 | −0.0239322 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.5206 | 0.812376 | 0.406188 | − | 0.913789i | \(-0.366858\pi\) | ||||
0.406188 | + | 0.913789i | \(0.366858\pi\) | |||||||
\(278\) | −15.3257 | −0.919176 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.54743 | −0.510807 | ||||||||
\(281\) | −23.6498 | −1.41083 | −0.705415 | − | 0.708794i | \(-0.749240\pi\) | ||||
−0.705415 | + | 0.708794i | \(0.749240\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.5799 | −1.63945 | −0.819726 | − | 0.572756i | \(-0.805874\pi\) | ||||
−0.819726 | + | 0.572756i | \(0.805874\pi\) | |||||||
\(284\) | −8.51164 | −0.505073 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.64588 | −0.215585 | ||||||||
\(287\) | 17.8219 | 1.05199 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9907 | −0.999452 | ||||||||
\(290\) | 8.01158 | 0.470456 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.49546 | 0.263077 | ||||||||
\(293\) | −20.8470 | −1.21789 | −0.608946 | − | 0.793211i | \(-0.708408\pi\) | ||||
−0.608946 | + | 0.793211i | \(0.708408\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.61584 | −0.152300 | ||||||||
\(296\) | 1.52602 | 0.0886981 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | −20.5205 | −1.18673 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −29.1740 | −1.68156 | ||||||||
\(302\) | −13.2736 | −0.763809 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.93839 | −0.168528 | ||||||||
\(305\) | 7.90091 | 0.452405 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.77284 | −0.101181 | −0.0505906 | − | 0.998719i | \(-0.516110\pi\) | ||||
−0.0505906 | + | 0.998719i | \(0.516110\pi\) | |||||||
\(308\) | −4.45639 | −0.253926 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 17.2000 | 0.976897 | ||||||||
\(311\) | −15.0758 | −0.854867 | −0.427434 | − | 0.904047i | \(-0.640582\pi\) | ||||
−0.427434 | + | 0.904047i | \(0.640582\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.21243 | −0.407670 | −0.203835 | − | 0.979005i | \(-0.565341\pi\) | ||||
−0.203835 | + | 0.979005i | \(0.565341\pi\) | |||||||
\(314\) | −15.5100 | −0.875281 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.19969 | 0.292505 | ||||||||
\(317\) | 21.3367 | 1.19839 | 0.599193 | − | 0.800604i | \(-0.295488\pi\) | ||||
0.599193 | + | 0.800604i | \(0.295488\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.17701 | 0.233868 | ||||||||
\(320\) | −2.15566 | −0.120505 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −25.0823 | −1.39778 | ||||||||
\(323\) | −0.283719 | −0.0157865 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.14550 | −0.0635409 | ||||||||
\(326\) | −10.0464 | −0.556420 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.49469 | 0.248177 | ||||||||
\(329\) | −3.40143 | −0.187527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.74660 | −0.370827 | −0.185413 | − | 0.982661i | \(-0.559362\pi\) | ||||
−0.185413 | + | 0.982661i | \(0.559362\pi\) | |||||||
\(332\) | −2.22728 | −0.122238 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.45389 | −0.298423 | ||||||||
\(335\) | −20.5187 | −1.12106 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.3557 | −1.70806 | −0.854028 | − | 0.520227i | \(-0.825847\pi\) | ||||
−0.854028 | + | 0.520227i | \(0.825847\pi\) | |||||||
\(338\) | 2.47679 | 0.134719 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.208142 | −0.0112881 | ||||||||
\(341\) | 8.96761 | 0.485623 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.82814 | −0.368685 | ||||||||
\(344\) | −7.35768 | −0.396699 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.8846 | 1.01524 | ||||||||
\(347\) | −11.2623 | −0.604591 | −0.302296 | − | 0.953214i | \(-0.597753\pi\) | ||||
−0.302296 | + | 0.953214i | \(0.597753\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.9957 | −1.55210 | −0.776051 | − | 0.630670i | \(-0.782780\pi\) | ||||
−0.776051 | + | 0.630670i | \(0.782780\pi\) | |||||||
\(350\) | −1.40015 | −0.0748413 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.12390 | −0.0599041 | ||||||||
\(353\) | 28.4759 | 1.51562 | 0.757808 | − | 0.652477i | \(-0.226270\pi\) | ||||
0.757808 | + | 0.652477i | \(0.226270\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.3482 | 0.973823 | ||||||||
\(356\) | −2.10826 | −0.111738 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.75154 | 0.0925715 | ||||||||
\(359\) | −6.75847 | −0.356698 | −0.178349 | − | 0.983967i | \(-0.557076\pi\) | ||||
−0.178349 | + | 0.983967i | \(0.557076\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.3659 | −0.545572 | ||||||||
\(362\) | 21.2991 | 1.11946 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.8626 | −0.674184 | ||||||||
\(365\) | −9.69070 | −0.507234 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.7374 | −1.29128 | −0.645642 | − | 0.763640i | \(-0.723410\pi\) | ||||
−0.645642 | + | 0.763640i | \(0.723410\pi\) | |||||||
\(368\) | −6.32576 | −0.329753 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.28958 | −0.171017 | ||||||||
\(371\) | −25.2291 | −1.30983 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.52425 | 0.493147 | 0.246573 | − | 0.969124i | \(-0.420695\pi\) | ||||
0.246573 | + | 0.969124i | \(0.420695\pi\) | |||||||
\(374\) | −0.108519 | −0.00561140 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.857841 | −0.0442398 | ||||||||
\(377\) | 12.0562 | 0.620928 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.76673 | −0.347583 | −0.173792 | − | 0.984782i | \(-0.555602\pi\) | ||||
−0.173792 | + | 0.984782i | \(0.555602\pi\) | |||||||
\(380\) | 6.33417 | 0.324936 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.5648 | −0.745202 | ||||||||
\(383\) | 19.4512 | 0.993910 | 0.496955 | − | 0.867776i | \(-0.334451\pi\) | ||||
0.496955 | + | 0.867776i | \(0.334451\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.60647 | 0.489591 | ||||||||
\(386\) | −12.5204 | −0.637271 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.31013 | 0.0665119 | ||||||||
\(389\) | 11.3920 | 0.577596 | 0.288798 | − | 0.957390i | \(-0.406744\pi\) | ||||
0.288798 | + | 0.957390i | \(0.406744\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.610790 | −0.0308890 | ||||||||
\(392\) | −8.72206 | −0.440530 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.2475 | 0.617020 | ||||||||
\(395\) | −11.2088 | −0.563975 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.0348 | −1.05571 | −0.527853 | − | 0.849336i | \(-0.677003\pi\) | ||||
−0.527853 | + | 0.849336i | \(0.677003\pi\) | |||||||
\(398\) | 1.23542 | 0.0619260 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.353119 | −0.0176559 | ||||||||
\(401\) | 1.42155 | 0.0709886 | 0.0354943 | − | 0.999370i | \(-0.488699\pi\) | ||||
0.0354943 | + | 0.999370i | \(0.488699\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.8835 | 1.28935 | ||||||||
\(404\) | −2.81738 | −0.140170 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14.7364 | 0.731357 | ||||||||
\(407\) | −1.71510 | −0.0850141 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.5108 | −1.01419 | −0.507096 | − | 0.861890i | \(-0.669281\pi\) | ||||
−0.507096 | + | 0.861890i | \(0.669281\pi\) | |||||||
\(410\) | −9.68902 | −0.478507 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.7823 | 0.728270 | ||||||||
\(413\) | −4.81155 | −0.236761 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.80126 | 0.235685 | ||||||||
\(416\) | −3.24395 | −0.159048 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.30246 | 0.161529 | ||||||||
\(419\) | −22.5840 | −1.10330 | −0.551650 | − | 0.834075i | \(-0.686002\pi\) | ||||
−0.551650 | + | 0.834075i | \(0.686002\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.44910 | −0.460521 | −0.230260 | − | 0.973129i | \(-0.573958\pi\) | ||||
−0.230260 | + | 0.973129i | \(0.573958\pi\) | |||||||
\(422\) | 4.32672 | 0.210621 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.36279 | −0.309004 | ||||||||
\(425\) | −0.0340957 | −0.00165388 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.5329 | 0.703294 | ||||||||
\(428\) | −9.77733 | −0.472605 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.8607 | 0.764870 | ||||||||
\(431\) | 0.748219 | 0.0360404 | 0.0180202 | − | 0.999838i | \(-0.494264\pi\) | ||||
0.0180202 | + | 0.999838i | \(0.494264\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.18287 | 0.345187 | 0.172593 | − | 0.984993i | \(-0.444785\pi\) | ||||
0.172593 | + | 0.984993i | \(0.444785\pi\) | |||||||
\(434\) | 31.6376 | 1.51865 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.16298 | −0.343044 | ||||||||
\(437\) | 18.5875 | 0.889163 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.06995 | −0.146521 | −0.0732604 | − | 0.997313i | \(-0.523340\pi\) | ||||
−0.0732604 | + | 0.997313i | \(0.523340\pi\) | |||||||
\(440\) | 2.42275 | 0.115500 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.313223 | −0.0148985 | ||||||||
\(443\) | −11.1300 | −0.528802 | −0.264401 | − | 0.964413i | \(-0.585174\pi\) | ||||
−0.264401 | + | 0.964413i | \(0.585174\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.54470 | 0.215440 | ||||||||
\(446\) | −12.7666 | −0.604515 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.96511 | −0.187334 | ||||||||
\(449\) | −9.93204 | −0.468722 | −0.234361 | − | 0.972150i | \(-0.575300\pi\) | ||||
−0.234361 | + | 0.972150i | \(0.575300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.05158 | −0.237870 | ||||||||
\(452\) | 16.4629 | 0.774350 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −22.7865 | −1.06942 | ||||||||
\(455\) | 27.7274 | 1.29988 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.3761 | −0.672485 | −0.336243 | − | 0.941775i | \(-0.609156\pi\) | ||||
−0.336243 | + | 0.941775i | \(0.609156\pi\) | |||||||
\(458\) | −10.6307 | −0.496738 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13.6362 | 0.635791 | ||||||||
\(461\) | 3.63676 | 0.169381 | 0.0846905 | − | 0.996407i | \(-0.473010\pi\) | ||||
0.0846905 | + | 0.996407i | \(0.473010\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.9033 | 1.43620 | 0.718098 | − | 0.695942i | \(-0.245013\pi\) | ||||
0.718098 | + | 0.695942i | \(0.245013\pi\) | |||||||
\(464\) | 3.71653 | 0.172536 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.2615 | 1.17021 | ||||||||
\(467\) | −26.0997 | −1.20775 | −0.603875 | − | 0.797079i | \(-0.706378\pi\) | ||||
−0.603875 | + | 0.797079i | \(0.706378\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −37.7419 | −1.74276 | ||||||||
\(470\) | 1.84922 | 0.0852980 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.21347 | −0.0558547 | ||||||||
\(473\) | 8.26930 | 0.380223 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.03760 | 0.0476083 | ||||||||
\(476\) | −0.382854 | −0.0175481 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.22269 | −0.193141 | ||||||||
\(479\) | −0.185023 | −0.00845390 | −0.00422695 | − | 0.999991i | \(-0.501345\pi\) | ||||
−0.00422695 | + | 0.999991i | \(0.501345\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.95033 | −0.225716 | ||||||||
\(482\) | 11.9213 | 0.542999 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.73685 | −0.442584 | ||||||||
\(485\) | −2.82420 | −0.128240 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.9888 | 0.588581 | 0.294290 | − | 0.955716i | \(-0.404917\pi\) | ||||
0.294290 | + | 0.955716i | \(0.404917\pi\) | |||||||
\(488\) | 3.66519 | 0.165915 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 18.8018 | 0.849379 | ||||||||
\(491\) | −10.9945 | −0.496176 | −0.248088 | − | 0.968738i | \(-0.579802\pi\) | ||||
−0.248088 | + | 0.968738i | \(0.579802\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.358853 | 0.0161619 | ||||||||
\(494\) | 9.53199 | 0.428864 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.97900 | 0.358268 | ||||||||
\(497\) | 33.7496 | 1.51387 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.7533 | −1.01858 | −0.509288 | − | 0.860596i | \(-0.670091\pi\) | ||||
−0.509288 | + | 0.860596i | \(0.670091\pi\) | |||||||
\(500\) | 11.5395 | 0.516063 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 17.8818 | 0.798104 | ||||||||
\(503\) | 14.6114 | 0.651489 | 0.325745 | − | 0.945458i | \(-0.394385\pi\) | ||||
0.325745 | + | 0.945458i | \(0.394385\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.07333 | 0.270260 | ||||||||
\(506\) | 7.10953 | 0.316057 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.84668 | −0.215036 | ||||||||
\(509\) | −1.36980 | −0.0607152 | −0.0303576 | − | 0.999539i | \(-0.509665\pi\) | ||||
−0.0303576 | + | 0.999539i | \(0.509665\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.8250 | −0.788530 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.387919 | 0.0171104 | ||||||||
\(515\) | −31.8656 | −1.40416 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.964129 | 0.0424023 | ||||||||
\(518\) | −6.05083 | −0.265858 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.99286 | 0.306657 | ||||||||
\(521\) | −15.9176 | −0.697361 | −0.348681 | − | 0.937242i | \(-0.613370\pi\) | ||||
−0.348681 | + | 0.937242i | \(0.613370\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.99278 | 0.262046 | 0.131023 | − | 0.991379i | \(-0.458174\pi\) | ||||
0.131023 | + | 0.991379i | \(0.458174\pi\) | |||||||
\(524\) | −14.9599 | −0.653526 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.34002 | −0.189234 | ||||||||
\(527\) | 0.770420 | 0.0335600 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.0153 | 0.739794 | ||||||||
\(530\) | 13.7160 | 0.595786 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.6510 | 0.505136 | ||||||||
\(533\) | −14.5805 | −0.631553 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.0766 | 0.911222 | ||||||||
\(536\) | −9.51851 | −0.411137 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 28.7658 | 1.24018 | ||||||||
\(539\) | 9.80273 | 0.422234 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.03756 | −0.345562 | −0.172781 | − | 0.984960i | \(-0.555275\pi\) | ||||
−0.172781 | + | 0.984960i | \(0.555275\pi\) | |||||||
\(542\) | −19.2160 | −0.825397 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.0965560 | −0.00413980 | ||||||||
\(545\) | 15.4410 | 0.661418 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.19273 | 0.307539 | 0.153769 | − | 0.988107i | \(-0.450859\pi\) | ||||
0.153769 | + | 0.988107i | \(0.450859\pi\) | |||||||
\(548\) | −5.99201 | −0.255966 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.396871 | 0.0169226 | ||||||||
\(551\) | −10.9206 | −0.465233 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.6173 | −0.876737 | ||||||||
\(554\) | −13.5206 | −0.574437 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.3257 | 0.649955 | ||||||||
\(557\) | −2.40926 | −0.102084 | −0.0510418 | − | 0.998697i | \(-0.516254\pi\) | ||||
−0.0510418 | + | 0.998697i | \(0.516254\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.8679 | 1.00951 | ||||||||
\(560\) | 8.54743 | 0.361195 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.6498 | 0.997608 | ||||||||
\(563\) | −3.49642 | −0.147357 | −0.0736783 | − | 0.997282i | \(-0.523474\pi\) | ||||
−0.0736783 | + | 0.997282i | \(0.523474\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −35.4885 | −1.49301 | ||||||||
\(566\) | 27.5799 | 1.15927 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.51164 | 0.357141 | ||||||||
\(569\) | −0.242490 | −0.0101657 | −0.00508285 | − | 0.999987i | \(-0.501618\pi\) | ||||
−0.00508285 | + | 0.999987i | \(0.501618\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.3859 | 1.56455 | 0.782275 | − | 0.622933i | \(-0.214059\pi\) | ||||
0.782275 | + | 0.622933i | \(0.214059\pi\) | |||||||
\(572\) | 3.64588 | 0.152442 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −17.8219 | −0.743872 | ||||||||
\(575\) | 2.23374 | 0.0931536 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.9303 | 0.996233 | 0.498116 | − | 0.867110i | \(-0.334025\pi\) | ||||
0.498116 | + | 0.867110i | \(0.334025\pi\) | |||||||
\(578\) | 16.9907 | 0.706719 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.01158 | −0.332663 | ||||||||
\(581\) | 8.83139 | 0.366388 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.15115 | 0.296170 | ||||||||
\(584\) | −4.49546 | −0.186023 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.8470 | 0.861180 | ||||||||
\(587\) | 14.4272 | 0.595474 | 0.297737 | − | 0.954648i | \(-0.403768\pi\) | ||||
0.297737 | + | 0.954648i | \(0.403768\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.4454 | −0.966051 | ||||||||
\(590\) | 2.61584 | 0.107693 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.52602 | −0.0627190 | ||||||||
\(593\) | −11.9471 | −0.490607 | −0.245303 | − | 0.969446i | \(-0.578888\pi\) | ||||
−0.245303 | + | 0.969446i | \(0.578888\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.825305 | 0.0338342 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 20.5205 | 0.839144 | ||||||||
\(599\) | 23.7388 | 0.969943 | 0.484972 | − | 0.874530i | \(-0.338830\pi\) | ||||
0.484972 | + | 0.874530i | \(0.338830\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.5580 | 1.40965 | 0.704825 | − | 0.709381i | \(-0.251025\pi\) | ||||
0.704825 | + | 0.709381i | \(0.251025\pi\) | |||||||
\(602\) | 29.1740 | 1.18904 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.2736 | 0.540094 | ||||||||
\(605\) | 20.9894 | 0.853339 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.4660 | −1.11481 | −0.557406 | − | 0.830240i | \(-0.688203\pi\) | ||||
−0.557406 | + | 0.830240i | \(0.688203\pi\) | |||||||
\(608\) | 2.93839 | 0.119167 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.90091 | −0.319898 | ||||||||
\(611\) | 2.78279 | 0.112580 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.22930 | 0.170820 | 0.0854100 | − | 0.996346i | \(-0.472780\pi\) | ||||
0.0854100 | + | 0.996346i | \(0.472780\pi\) | |||||||
\(614\) | 1.77284 | 0.0715459 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.45639 | 0.179553 | ||||||||
\(617\) | 26.3829 | 1.06214 | 0.531068 | − | 0.847329i | \(-0.321791\pi\) | ||||
0.531068 | + | 0.847329i | \(0.321791\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.92730 | 0.117658 | 0.0588291 | − | 0.998268i | \(-0.481263\pi\) | ||||
0.0588291 | + | 0.998268i | \(0.481263\pi\) | |||||||
\(620\) | −17.2000 | −0.690770 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.0758 | 0.604483 | ||||||||
\(623\) | 8.35949 | 0.334916 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.1097 | −0.924389 | ||||||||
\(626\) | 7.21243 | 0.288267 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.5100 | 0.618917 | ||||||||
\(629\) | −0.147346 | −0.00587508 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.4077 | −1.17070 | −0.585351 | − | 0.810780i | \(-0.699043\pi\) | ||||
−0.585351 | + | 0.810780i | \(0.699043\pi\) | |||||||
\(632\) | −5.19969 | −0.206833 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.3367 | −0.847387 | ||||||||
\(635\) | 10.4478 | 0.414608 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.2939 | 1.12105 | ||||||||
\(638\) | −4.17701 | −0.165369 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.15566 | 0.0852100 | ||||||||
\(641\) | −12.4149 | −0.490359 | −0.245180 | − | 0.969478i | \(-0.578847\pi\) | ||||
−0.245180 | + | 0.969478i | \(0.578847\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.5602 | −1.36292 | −0.681460 | − | 0.731855i | \(-0.738655\pi\) | ||||
−0.681460 | + | 0.731855i | \(0.738655\pi\) | |||||||
\(644\) | 25.0823 | 0.988381 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.283719 | 0.0111628 | ||||||||
\(647\) | 30.5414 | 1.20071 | 0.600353 | − | 0.799735i | \(-0.295027\pi\) | ||||
0.600353 | + | 0.799735i | \(0.295027\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.36383 | 0.0535349 | ||||||||
\(650\) | 1.14550 | 0.0449302 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.0464 | 0.393449 | ||||||||
\(653\) | 21.3686 | 0.836219 | 0.418109 | − | 0.908397i | \(-0.362693\pi\) | ||||
0.418109 | + | 0.908397i | \(0.362693\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.2485 | 1.26005 | ||||||||
\(656\) | −4.49469 | −0.175488 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.40143 | 0.132602 | ||||||||
\(659\) | −14.2126 | −0.553645 | −0.276823 | − | 0.960921i | \(-0.589281\pi\) | ||||
−0.276823 | + | 0.960921i | \(0.589281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.0789 | −0.780980 | −0.390490 | − | 0.920607i | \(-0.627694\pi\) | ||||
−0.390490 | + | 0.920607i | \(0.627694\pi\) | |||||||
\(662\) | 6.74660 | 0.262214 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.22728 | 0.0864351 | ||||||||
\(665\) | −25.1157 | −0.973944 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.5099 | −0.910306 | ||||||||
\(668\) | 5.45389 | 0.211017 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 20.5187 | 0.792707 | ||||||||
\(671\) | −4.11931 | −0.159024 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.4010 | −0.979138 | −0.489569 | − | 0.871964i | \(-0.662846\pi\) | ||||
−0.489569 | + | 0.871964i | \(0.662846\pi\) | |||||||
\(674\) | 31.3557 | 1.20778 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.47679 | −0.0952611 | ||||||||
\(677\) | 31.5694 | 1.21331 | 0.606654 | − | 0.794966i | \(-0.292511\pi\) | ||||
0.606654 | + | 0.794966i | \(0.292511\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.19481 | −0.199358 | ||||||||
\(680\) | 0.208142 | 0.00798188 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.96761 | −0.343388 | ||||||||
\(683\) | −16.5155 | −0.631949 | −0.315975 | − | 0.948768i | \(-0.602331\pi\) | ||||
−0.315975 | + | 0.948768i | \(0.602331\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9168 | 0.493524 | ||||||||
\(686\) | 6.82814 | 0.260700 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.35768 | 0.280509 | ||||||||
\(689\) | 20.6406 | 0.786343 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.08327 | −0.155335 | −0.0776675 | − | 0.996979i | \(-0.524747\pi\) | ||||
−0.0776675 | + | 0.996979i | \(0.524747\pi\) | |||||||
\(692\) | −18.8846 | −0.717885 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.2623 | 0.427511 | ||||||||
\(695\) | −33.0371 | −1.25317 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.433989 | −0.0164385 | ||||||||
\(698\) | 28.9957 | 1.09750 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.40015 | 0.0529208 | ||||||||
\(701\) | 16.7314 | 0.631935 | 0.315967 | − | 0.948770i | \(-0.397671\pi\) | ||||
0.315967 | + | 0.948770i | \(0.397671\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.48404 | 0.169119 | ||||||||
\(704\) | 1.12390 | 0.0423586 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −28.4759 | −1.07170 | ||||||||
\(707\) | 11.1712 | 0.420137 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.1120 | −1.16844 | −0.584218 | − | 0.811597i | \(-0.698599\pi\) | ||||
−0.584218 | + | 0.811597i | \(0.698599\pi\) | |||||||
\(710\) | −18.3482 | −0.688597 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.10826 | 0.0790105 | ||||||||
\(713\) | −50.4733 | −1.89024 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.85929 | −0.293921 | ||||||||
\(716\) | −1.75154 | −0.0654579 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.75847 | 0.252224 | ||||||||
\(719\) | −21.1950 | −0.790439 | −0.395220 | − | 0.918587i | \(-0.629332\pi\) | ||||
−0.395220 | + | 0.918587i | \(0.629332\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −58.6132 | −2.18287 | ||||||||
\(722\) | 10.3659 | 0.385778 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −21.2991 | −0.791576 | ||||||||
\(725\) | −1.31238 | −0.0487404 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.3725 | −1.53442 | −0.767211 | − | 0.641394i | \(-0.778356\pi\) | ||||
−0.767211 | + | 0.641394i | \(0.778356\pi\) | |||||||
\(728\) | 12.8626 | 0.476720 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.69070 | 0.358669 | ||||||||
\(731\) | 0.710428 | 0.0262761 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.61119 | −0.354997 | −0.177499 | − | 0.984121i | \(-0.556801\pi\) | ||||
−0.177499 | + | 0.984121i | \(0.556801\pi\) | |||||||
\(734\) | 24.7374 | 0.913076 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.32576 | 0.233171 | ||||||||
\(737\) | 10.6979 | 0.394061 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.1643 | −1.47747 | −0.738733 | − | 0.673998i | \(-0.764576\pi\) | ||||
−0.738733 | + | 0.673998i | \(0.764576\pi\) | |||||||
\(740\) | 3.28958 | 0.120927 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 25.2291 | 0.926191 | ||||||||
\(743\) | −23.2162 | −0.851719 | −0.425860 | − | 0.904789i | \(-0.640028\pi\) | ||||
−0.425860 | + | 0.904789i | \(0.640028\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.15566 | 0.0789774 | ||||||||
\(746\) | −9.52425 | −0.348707 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.108519 | 0.00396786 | ||||||||
\(749\) | 38.7681 | 1.41656 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.6393 | −1.00857 | −0.504286 | − | 0.863537i | \(-0.668244\pi\) | ||||
−0.504286 | + | 0.863537i | \(0.668244\pi\) | |||||||
\(752\) | 0.857841 | 0.0312822 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.0562 | −0.439062 | ||||||||
\(755\) | −28.6134 | −1.04135 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.9761 | −1.12585 | −0.562923 | − | 0.826510i | \(-0.690323\pi\) | ||||
−0.562923 | + | 0.826510i | \(0.690323\pi\) | |||||||
\(758\) | 6.76673 | 0.245779 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.33417 | −0.229765 | ||||||||
\(761\) | 36.0461 | 1.30667 | 0.653336 | − | 0.757068i | \(-0.273369\pi\) | ||||
0.653336 | + | 0.757068i | \(0.273369\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.4020 | 1.02822 | ||||||||
\(764\) | 14.5648 | 0.526937 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.4512 | −0.702800 | ||||||||
\(767\) | 3.93645 | 0.142137 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 53.8427 | 1.94162 | 0.970810 | − | 0.239852i | \(-0.0770988\pi\) | ||||
0.970810 | + | 0.239852i | \(0.0770988\pi\) | |||||||
\(770\) | −9.60647 | −0.346193 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.5204 | 0.450619 | ||||||||
\(773\) | −33.1205 | −1.19126 | −0.595631 | − | 0.803259i | \(-0.703098\pi\) | ||||
−0.595631 | + | 0.803259i | \(0.703098\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.81753 | −0.101209 | ||||||||
\(776\) | −1.31013 | −0.0470310 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.3920 | −0.408422 | ||||||||
\(779\) | 13.2071 | 0.473195 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.56625 | −0.342307 | ||||||||
\(782\) | 0.610790 | 0.0218418 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.72206 | 0.311502 | ||||||||
\(785\) | −33.4344 | −1.19332 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.52820 | −0.232705 | −0.116353 | − | 0.993208i | \(-0.537120\pi\) | ||||
−0.116353 | + | 0.993208i | \(0.537120\pi\) | |||||||
\(788\) | −12.2475 | −0.436299 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.2088 | 0.398790 | ||||||||
\(791\) | −65.2772 | −2.32099 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.8897 | −0.422215 | ||||||||
\(794\) | 21.0348 | 0.746497 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.23542 | −0.0437883 | ||||||||
\(797\) | 5.21140 | 0.184597 | 0.0922987 | − | 0.995731i | \(-0.470579\pi\) | ||||
0.0922987 | + | 0.995731i | \(0.470579\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.0828297 | 0.00293030 | ||||||||
\(800\) | 0.353119 | 0.0124846 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.42155 | −0.0501965 | ||||||||
\(803\) | 5.05245 | 0.178297 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −54.0690 | −1.90568 | ||||||||
\(806\) | −25.8835 | −0.911707 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.81738 | 0.0991152 | ||||||||
\(809\) | −43.9427 | −1.54494 | −0.772471 | − | 0.635050i | \(-0.780979\pi\) | ||||
−0.772471 | + | 0.635050i | \(0.780979\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.1938 | 0.779331 | 0.389666 | − | 0.920956i | \(-0.372591\pi\) | ||||
0.389666 | + | 0.920956i | \(0.372591\pi\) | |||||||
\(812\) | −14.7364 | −0.517147 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.71510 | 0.0601141 | ||||||||
\(815\) | −21.6567 | −0.758602 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.6197 | −0.756378 | ||||||||
\(818\) | 20.5108 | 0.717142 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.68902 | 0.338355 | ||||||||
\(821\) | −17.1951 | −0.600114 | −0.300057 | − | 0.953921i | \(-0.597006\pi\) | ||||
−0.300057 | + | 0.953921i | \(0.597006\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −56.2378 | −1.96033 | −0.980163 | − | 0.198194i | \(-0.936492\pi\) | ||||
−0.980163 | + | 0.198194i | \(0.936492\pi\) | |||||||
\(824\) | −14.7823 | −0.514964 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.81155 | 0.167415 | ||||||||
\(827\) | 15.4087 | 0.535812 | 0.267906 | − | 0.963445i | \(-0.413668\pi\) | ||||
0.267906 | + | 0.963445i | \(0.413668\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.0979 | 1.18427 | 0.592134 | − | 0.805839i | \(-0.298286\pi\) | ||||
0.592134 | + | 0.805839i | \(0.298286\pi\) | |||||||
\(830\) | −4.80126 | −0.166654 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.24395 | 0.112464 | ||||||||
\(833\) | 0.842167 | 0.0291793 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.7567 | −0.406859 | ||||||||
\(836\) | −3.30246 | −0.114218 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.5840 | 0.780151 | ||||||||
\(839\) | 39.6777 | 1.36983 | 0.684913 | − | 0.728625i | \(-0.259840\pi\) | ||||
0.684913 | + | 0.728625i | \(0.259840\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.1874 | −0.523704 | ||||||||
\(842\) | 9.44910 | 0.325637 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.32672 | −0.148932 | ||||||||
\(845\) | 5.33912 | 0.183671 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38.6076 | 1.32657 | ||||||||
\(848\) | 6.36279 | 0.218499 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.0340957 | 0.00116947 | ||||||||
\(851\) | 9.65323 | 0.330909 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.6846 | 0.639749 | 0.319874 | − | 0.947460i | \(-0.396359\pi\) | ||||
0.319874 | + | 0.947460i | \(0.396359\pi\) | |||||||
\(854\) | −14.5329 | −0.497304 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.77733 | 0.334182 | ||||||||
\(857\) | −29.4136 | −1.00475 | −0.502375 | − | 0.864650i | \(-0.667540\pi\) | ||||
−0.502375 | + | 0.864650i | \(0.667540\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.3033 | −0.556262 | −0.278131 | − | 0.960543i | \(-0.589715\pi\) | ||||
−0.278131 | + | 0.960543i | \(0.589715\pi\) | |||||||
\(860\) | −15.8607 | −0.540844 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.748219 | −0.0254844 | ||||||||
\(863\) | −33.2394 | −1.13148 | −0.565741 | − | 0.824583i | \(-0.691410\pi\) | ||||
−0.565741 | + | 0.824583i | \(0.691410\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.7088 | 1.38414 | ||||||||
\(866\) | −7.18287 | −0.244084 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −31.6376 | −1.07385 | ||||||||
\(869\) | 5.84394 | 0.198242 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.8776 | 1.04625 | ||||||||
\(872\) | 7.16298 | 0.242569 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −18.5875 | −0.628733 | ||||||||
\(875\) | −45.7554 | −1.54681 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.3313 | 1.56450 | 0.782248 | − | 0.622967i | \(-0.214073\pi\) | ||||
0.782248 | + | 0.622967i | \(0.214073\pi\) | |||||||
\(878\) | 3.06995 | 0.103606 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.42275 | −0.0816710 | ||||||||
\(881\) | −49.6464 | −1.67263 | −0.836314 | − | 0.548250i | \(-0.815294\pi\) | ||||
−0.836314 | + | 0.548250i | \(0.815294\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.0836456 | 0.00281490 | 0.00140745 | − | 0.999999i | \(-0.499552\pi\) | ||||
0.00140745 | + | 0.999999i | \(0.499552\pi\) | |||||||
\(884\) | 0.313223 | 0.0105348 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.1300 | 0.373920 | ||||||||
\(887\) | −56.8653 | −1.90935 | −0.954674 | − | 0.297653i | \(-0.903796\pi\) | ||||
−0.954674 | + | 0.297653i | \(0.903796\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.2176 | 0.644537 | ||||||||
\(890\) | −4.54470 | −0.152339 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.7666 | 0.427457 | ||||||||
\(893\) | −2.52067 | −0.0843510 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.77572 | 0.126208 | ||||||||
\(896\) | 3.96511 | 0.132465 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.93204 | 0.331436 | ||||||||
\(899\) | 29.6542 | 0.989023 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.614365 | 0.0204675 | ||||||||
\(902\) | 5.05158 | 0.168199 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.4629 | −0.547548 | ||||||||
\(905\) | 45.9138 | 1.52623 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.8216 | −0.691369 | −0.345684 | − | 0.938351i | \(-0.612353\pi\) | ||||
−0.345684 | + | 0.938351i | \(0.612353\pi\) | |||||||
\(908\) | 22.7865 | 0.756197 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −27.7274 | −0.919155 | ||||||||
\(911\) | −4.26897 | −0.141437 | −0.0707187 | − | 0.997496i | \(-0.522529\pi\) | ||||
−0.0707187 | + | 0.997496i | \(0.522529\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.50324 | −0.0828452 | ||||||||
\(914\) | 14.3761 | 0.475519 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.6307 | 0.351247 | ||||||||
\(917\) | 59.3176 | 1.95884 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.02565 | −0.297729 | −0.148864 | − | 0.988858i | \(-0.547562\pi\) | ||||
−0.148864 | + | 0.988858i | \(0.547562\pi\) | |||||||
\(920\) | −13.6362 | −0.449572 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.63676 | −0.119770 | ||||||||
\(923\) | −27.6113 | −0.908838 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.538866 | 0.0177178 | ||||||||
\(926\) | −30.9033 | −1.01554 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.71653 | −0.122001 | ||||||||
\(929\) | −53.2021 | −1.74550 | −0.872752 | − | 0.488164i | \(-0.837667\pi\) | ||||
−0.872752 | + | 0.488164i | \(0.837667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.6288 | −0.839950 | ||||||||
\(932\) | −25.2615 | −0.827467 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 26.0997 | 0.854009 | ||||||||
\(935\) | −0.233931 | −0.00765037 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.0840 | −0.558109 | −0.279055 | − | 0.960275i | \(-0.590021\pi\) | ||||
−0.279055 | + | 0.960275i | \(0.590021\pi\) | |||||||
\(938\) | 37.7419 | 1.23232 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.84922 | −0.0603148 | ||||||||
\(941\) | 26.6781 | 0.869681 | 0.434841 | − | 0.900507i | \(-0.356805\pi\) | ||||
0.434841 | + | 0.900507i | \(0.356805\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.4323 | 0.925883 | ||||||||
\(944\) | 1.21347 | 0.0394952 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.26930 | −0.268858 | ||||||||
\(947\) | 6.14436 | 0.199665 | 0.0998324 | − | 0.995004i | \(-0.468169\pi\) | ||||
0.0998324 | + | 0.995004i | \(0.468169\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.5830 | 0.473386 | ||||||||
\(950\) | −1.03760 | −0.0336642 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.382854 | 0.0124084 | ||||||||
\(953\) | −0.723083 | −0.0234230 | −0.0117115 | − | 0.999931i | \(-0.503728\pi\) | ||||
−0.0117115 | + | 0.999931i | \(0.503728\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31.3969 | −1.01598 | ||||||||
\(956\) | 4.22269 | 0.136571 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.185023 | 0.00597781 | ||||||||
\(959\) | 23.7589 | 0.767216 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32.6645 | 1.05369 | ||||||||
\(962\) | 4.95033 | 0.159605 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.9213 | −0.383958 | ||||||||
\(965\) | −26.9897 | −0.868831 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.6165 | 1.08103 | 0.540517 | − | 0.841333i | \(-0.318229\pi\) | ||||
0.540517 | + | 0.841333i | \(0.318229\pi\) | |||||||
\(968\) | 9.73685 | 0.312954 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.82420 | 0.0906796 | ||||||||
\(971\) | 24.5850 | 0.788969 | 0.394484 | − | 0.918903i | \(-0.370923\pi\) | ||||
0.394484 | + | 0.918903i | \(0.370923\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −60.7681 | −1.94814 | ||||||||
\(974\) | −12.9888 | −0.416189 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.66519 | −0.117320 | ||||||||
\(977\) | 11.1003 | 0.355130 | 0.177565 | − | 0.984109i | \(-0.443178\pi\) | ||||
0.177565 | + | 0.984109i | \(0.443178\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.36948 | −0.0757289 | ||||||||
\(980\) | −18.8018 | −0.600602 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.9945 | 0.350849 | ||||||||
\(983\) | 17.7913 | 0.567453 | 0.283726 | − | 0.958905i | \(-0.408429\pi\) | ||||
0.283726 | + | 0.958905i | \(0.408429\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.4015 | 0.841221 | ||||||||
\(986\) | −0.358853 | −0.0114282 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.53199 | −0.303253 | ||||||||
\(989\) | −46.5429 | −1.47998 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.64208 | −0.147461 | −0.0737303 | − | 0.997278i | \(-0.523490\pi\) | ||||
−0.0737303 | + | 0.997278i | \(0.523490\pi\) | |||||||
\(992\) | −7.97900 | −0.253334 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −33.7496 | −1.07047 | ||||||||
\(995\) | 2.66315 | 0.0844275 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.0802 | −0.762628 | −0.381314 | − | 0.924446i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924446i | \(0.624528\pi\) | |||||||
\(998\) | 22.7533 | 0.720242 | ||||||||
\(999\) | 0 | 0 |
(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 | 8046.2.a.j.1.3 | ✓ | 12 | |
3.2 | odd | 2 | 8046.2.a.o.1.10 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.j.1.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8046.2.a.o.1.10 | yes | 12 | 3.2 | odd | 2 |