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: | \(0\) |
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 | 1.10 | ||
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 | \(-0.339903\pi\) | ||||
0.482021 | + | 0.876160i | \(0.339903\pi\) | |||||||
\(6\) | 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 | \(-0.554194\pi\) | ||||
−0.169435 | + | 0.985541i | \(0.554194\pi\) | |||||||
\(12\) | 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 | \(-0.503727\pi\) | ||||
−0.0117091 | + | 0.999931i | \(0.503727\pi\) | |||||||
\(18\) | 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 | \(-0.270765\pi\) | ||||
0.659506 | + | 0.751699i | \(0.270765\pi\) | |||||||
\(24\) | 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 | \(-0.612145\pi\) | ||||
−0.345071 | + | 0.938577i | \(0.612145\pi\) | |||||||
\(30\) | 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 | \(-0.385850\pi\) | ||||
0.350976 | + | 0.936384i | \(0.385850\pi\) | |||||||
\(42\) | 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 | \(-0.519928\pi\) | ||||
−0.0625645 | + | 0.998041i | \(0.519928\pi\) | |||||||
\(48\) | 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 | \(-0.643958\pi\) | ||||
−0.436998 | + | 0.899462i | \(0.643958\pi\) | |||||||
\(54\) | 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 | \(-0.525170\pi\) | ||||
−0.0789905 | + | 0.996875i | \(0.525170\pi\) | |||||||
\(60\) | 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 | \(-0.331466\pi\) | ||||
0.505073 | + | 0.863077i | \(0.331466\pi\) | |||||||
\(72\) | 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 | \(-0.460993\pi\) | ||||
0.122238 | + | 0.992501i | \(0.460993\pi\) | |||||||
\(84\) | 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 | \(-0.464358\pi\) | ||||
0.111738 | + | 0.993738i | \(0.464358\pi\) | |||||||
\(90\) | 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 | \(-0.455235\pi\) | ||||
0.140170 | + | 0.990127i | \(0.455235\pi\) | |||||||
\(102\) | 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 | \(-0.343314\pi\) | ||||
0.472605 | + | 0.881274i | \(0.343314\pi\) | |||||||
\(108\) | 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 | \(-0.781923\pi\) | ||||
−0.774350 | + | 0.632757i | \(0.781923\pi\) | |||||||
\(114\) | 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 | \(-0.273289\pi\) | ||||
0.653526 | + | 0.756904i | \(0.273289\pi\) | |||||||
\(132\) | 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 | \(-0.417606\pi\) | ||||
0.255966 | + | 0.966686i | \(0.417606\pi\) | |||||||
\(138\) | 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 | \(-0.567678\pi\) | ||||
−0.211017 | + | 0.977482i | \(0.567678\pi\) | |||||||
\(168\) | 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 | \(-0.245110\pi\) | ||||
0.717885 | + | 0.696162i | \(0.245110\pi\) | |||||||
\(174\) | 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 | \(-0.479149\pi\) | ||||
0.0654579 | + | 0.997855i | \(0.479149\pi\) | |||||||
\(180\) | 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 | \(-0.676660\pi\) | ||||
−0.526937 | + | 0.849904i | \(0.676660\pi\) | |||||||
\(192\) | 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 | \(-0.356289\pi\) | ||||
0.436299 | + | 0.899802i | \(0.356289\pi\) | |||||||
\(198\) | 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 | \(-0.772945\pi\) | ||||
−0.756197 | + | 0.654344i | \(0.772945\pi\) | |||||||
\(228\) | 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 | \(-0.189781\pi\) | ||||
0.827467 | + | 0.561515i | \(0.189781\pi\) | |||||||
\(234\) | 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 | \(-0.543608\pi\) | ||||
−0.136571 | + | 0.990630i | \(0.543608\pi\) | |||||||
\(240\) | 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 | \(-0.309129\pi\) | ||||
0.564345 | + | 0.825539i | \(0.309129\pi\) | |||||||
\(252\) | 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 | \(-0.496149\pi\) | ||||
0.0120989 | + | 0.999927i | \(0.496149\pi\) | |||||||
\(258\) | 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 | \(-0.542721\pi\) | ||||
−0.133809 | + | 0.991007i | \(0.542721\pi\) | |||||||
\(264\) | 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 | \(-0.159581\pi\) | ||||
0.876941 | + | 0.480599i | \(0.159581\pi\) | |||||||
\(270\) | 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 | \(-0.250760\pi\) | ||||
0.705415 | + | 0.708794i | \(0.250760\pi\) | |||||||
\(282\) | 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 | \(-0.291592\pi\) | ||||
0.608946 | + | 0.793211i | \(0.291592\pi\) | |||||||
\(294\) | 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 | \(-0.359418\pi\) | ||||
0.427434 | + | 0.904047i | \(0.359418\pi\) | |||||||
\(312\) | 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 | \(-0.704512\pi\) | ||||
−0.599193 | + | 0.800604i | \(0.704512\pi\) | |||||||
\(318\) | 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 | \(-0.402247\pi\) | ||||
0.302296 | + | 0.953214i | \(0.402247\pi\) | |||||||
\(348\) | 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 | \(-0.773730\pi\) | ||||
−0.757808 | + | 0.652477i | \(0.773730\pi\) | |||||||
\(354\) | 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 | \(-0.442924\pi\) | ||||
0.178349 | + | 0.983967i | \(0.442924\pi\) | |||||||
\(360\) | 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 | \(-0.665549\pi\) | ||||
−0.496955 | + | 0.867776i | \(0.665549\pi\) | |||||||
\(384\) | 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 | \(-0.593256\pi\) | ||||
−0.288798 | + | 0.957390i | \(0.593256\pi\) | |||||||
\(390\) | 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 | \(-0.511301\pi\) | ||||
−0.0354943 | + | 0.999370i | \(0.511301\pi\) | |||||||
\(402\) | 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 | \(-0.313998\pi\) | ||||
0.551650 | + | 0.834075i | \(0.313998\pi\) | |||||||
\(420\) | 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 | \(-0.505736\pi\) | ||||
−0.0180202 | + | 0.999838i | \(0.505736\pi\) | |||||||
\(432\) | 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 | \(-0.414826\pi\) | ||||
0.264401 | + | 0.964413i | \(0.414826\pi\) | |||||||
\(444\) | 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 | \(-0.424700\pi\) | ||||
0.234361 | + | 0.972150i | \(0.424700\pi\) | |||||||
\(450\) | 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 | \(-0.526990\pi\) | ||||
−0.0846905 | + | 0.996407i | \(0.526990\pi\) | |||||||
\(462\) | 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 | \(-0.293622\pi\) | ||||
0.603875 | + | 0.797079i | \(0.293622\pi\) | |||||||
\(468\) | 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 | \(-0.498655\pi\) | ||||
0.00422695 | + | 0.999991i | \(0.498655\pi\) | |||||||
\(480\) | 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 | \(-0.420198\pi\) | ||||
0.248088 | + | 0.968738i | \(0.420198\pi\) | |||||||
\(492\) | 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 | \(-0.605615\pi\) | ||||
−0.325745 | + | 0.945458i | \(0.605615\pi\) | |||||||
\(504\) | 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 | \(-0.490335\pi\) | ||||
0.0303576 | + | 0.999539i | \(0.490335\pi\) | |||||||
\(510\) | 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 | \(-0.386630\pi\) | ||||
0.348681 | + | 0.937242i | \(0.386630\pi\) | |||||||
\(522\) | 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 | \(-0.483746\pi\) | ||||
0.0510418 | + | 0.998697i | \(0.483746\pi\) | |||||||
\(558\) | 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 | \(-0.476526\pi\) | ||||
0.0736783 | + | 0.997282i | \(0.476526\pi\) | |||||||
\(564\) | 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 | \(-0.498382\pi\) | ||||
0.00508285 | + | 0.999987i | \(0.498382\pi\) | |||||||
\(570\) | 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 | \(-0.596232\pi\) | ||||
−0.297737 | + | 0.954648i | \(0.596232\pi\) | |||||||
\(588\) | 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 | \(-0.421112\pi\) | ||||
0.245303 | + | 0.969446i | \(0.421112\pi\) | |||||||
\(594\) | 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 | \(-0.661170\pi\) | ||||
−0.484972 | + | 0.874530i | \(0.661170\pi\) | |||||||
\(600\) | 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 | \(-0.678209\pi\) | ||||
−0.531068 | + | 0.847329i | \(0.678209\pi\) | |||||||
\(618\) | 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 | \(-0.421153\pi\) | ||||
0.245180 | + | 0.969478i | \(0.421153\pi\) | |||||||
\(642\) | 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 | \(-0.704973\pi\) | ||||
−0.600353 | + | 0.799735i | \(0.704973\pi\) | |||||||
\(648\) | 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 | \(-0.637307\pi\) | ||||
−0.418109 | + | 0.908397i | \(0.637307\pi\) | |||||||
\(654\) | 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 | \(-0.410719\pi\) | ||||
0.276823 | + | 0.960921i | \(0.410719\pi\) | |||||||
\(660\) | 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 | \(-0.707489\pi\) | ||||
−0.606654 | + | 0.794966i | \(0.707489\pi\) | |||||||
\(678\) | 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 | \(-0.397669\pi\) | ||||
0.315975 | + | 0.948768i | \(0.397669\pi\) | |||||||
\(684\) | 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 | \(-0.602329\pi\) | ||||
−0.315967 | + | 0.948770i | \(0.602329\pi\) | |||||||
\(702\) | 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 | \(-0.370668\pi\) | ||||
0.395220 | + | 0.918587i | \(0.370668\pi\) | |||||||
\(720\) | 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 | \(-0.359972\pi\) | ||||
0.425860 | + | 0.904789i | \(0.359972\pi\) | |||||||
\(744\) | 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 | \(-0.726631\pi\) | ||||
−0.653336 | + | 0.757068i | \(0.726631\pi\) | |||||||
\(762\) | 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 | \(-0.296902\pi\) | ||||
0.595631 | + | 0.803259i | \(0.296902\pi\) | |||||||
\(774\) | 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 | \(-0.529421\pi\) | ||||
−0.0922987 | + | 0.995731i | \(0.529421\pi\) | |||||||
\(798\) | 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 | \(-0.219021\pi\) | ||||
0.772471 | + | 0.635050i | \(0.219021\pi\) | |||||||
\(810\) | 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 | \(-0.402994\pi\) | ||||
0.300057 | + | 0.953921i | \(0.402994\pi\) | |||||||
\(822\) | 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 | \(-0.586332\pi\) | ||||
−0.267906 | + | 0.963445i | \(0.586332\pi\) | |||||||
\(828\) | 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 | \(-0.740160\pi\) | ||||
−0.684913 | + | 0.728625i | \(0.740160\pi\) | |||||||
\(840\) | 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 | \(-0.332460\pi\) | ||||
0.502375 | + | 0.864650i | \(0.332460\pi\) | |||||||
\(858\) | 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 | \(-0.308590\pi\) | ||||
0.565741 | + | 0.824583i | \(0.308590\pi\) | |||||||
\(864\) | 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 | \(-0.184706\pi\) | ||||
0.836314 | + | 0.548250i | \(0.184706\pi\) | |||||||
\(882\) | 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 | \(-0.0962039\pi\) | ||||
0.954674 | + | 0.297653i | \(0.0962039\pi\) | |||||||
\(888\) | 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 | \(-0.477471\pi\) | ||||
0.0707187 | + | 0.997496i | \(0.477471\pi\) | |||||||
\(912\) | 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 | \(-0.162333\pi\) | ||||
0.872752 | + | 0.488164i | \(0.162333\pi\) | |||||||
\(930\) | 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 | \(-0.643195\pi\) | ||||
−0.434841 | + | 0.900507i | \(0.643195\pi\) | |||||||
\(942\) | 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 | \(-0.531831\pi\) | ||||
−0.0998324 | + | 0.995004i | \(0.531831\pi\) | |||||||
\(948\) | 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 | \(-0.496272\pi\) | ||||
0.0117115 | + | 0.999931i | \(0.496272\pi\) | |||||||
\(954\) | 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 | \(-0.629077\pi\) | ||||
−0.394484 | + | 0.918903i | \(0.629077\pi\) | |||||||
\(972\) | 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 | \(-0.556822\pi\) | ||||
−0.177565 | + | 0.984109i | \(0.556822\pi\) | |||||||
\(978\) | 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 | \(-0.591571\pi\) | ||||
−0.283726 | + | 0.958905i | \(0.591571\pi\) | |||||||
\(984\) | 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.o.1.10 | yes | 12 | |
3.2 | odd | 2 | 8046.2.a.j.1.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.j.1.3 | ✓ | 12 | 3.2 | odd | 2 | ||
8046.2.a.o.1.10 | yes | 12 | 1.1 | even | 1 | trivial |