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: | \( x^{12} - 5 x^{11} - 23 x^{10} + 142 x^{9} + 104 x^{8} - 1302 x^{7} + 607 x^{6} + 4323 x^{5} - 4461 x^{4} + \cdots - 553 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.33540\) 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 | ||||||||
\(5\) | 1.33540 | 0.597209 | 0.298605 | − | 0.954377i | \(-0.403479\pi\) | ||||
0.298605 | + | 0.954377i | \(0.403479\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.26685 | 0.856790 | 0.428395 | − | 0.903591i | \(-0.359079\pi\) | ||||
0.428395 | + | 0.903591i | \(0.359079\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.33540 | 0.422291 | ||||||||
\(11\) | 5.80942 | 1.75161 | 0.875803 | − | 0.482668i | \(-0.160332\pi\) | ||||
0.875803 | + | 0.482668i | \(0.160332\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.07946 | 0.576737 | 0.288369 | − | 0.957519i | \(-0.406887\pi\) | ||||
0.288369 | + | 0.957519i | \(0.406887\pi\) | |||||||
\(14\) | 2.26685 | 0.605842 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.11591 | −1.24079 | −0.620395 | − | 0.784289i | \(-0.713028\pi\) | ||||
−0.620395 | + | 0.784289i | \(0.713028\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.67108 | 1.98928 | 0.994641 | − | 0.103393i | \(-0.0329699\pi\) | ||||
0.994641 | + | 0.103393i | \(0.0329699\pi\) | |||||||
\(20\) | 1.33540 | 0.298605 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.80942 | 1.23857 | ||||||||
\(23\) | 3.21691 | 0.670771 | 0.335386 | − | 0.942081i | \(-0.391133\pi\) | ||||
0.335386 | + | 0.942081i | \(0.391133\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.21671 | −0.643341 | ||||||||
\(26\) | 2.07946 | 0.407815 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.26685 | 0.428395 | ||||||||
\(29\) | 3.55075 | 0.659357 | 0.329679 | − | 0.944093i | \(-0.393060\pi\) | ||||
0.329679 | + | 0.944093i | \(0.393060\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.87939 | −0.876364 | −0.438182 | − | 0.898886i | \(-0.644378\pi\) | ||||
−0.438182 | + | 0.898886i | \(0.644378\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.11591 | −0.877372 | ||||||||
\(35\) | 3.02716 | 0.511683 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.63624 | 0.762193 | 0.381096 | − | 0.924535i | \(-0.375547\pi\) | ||||
0.381096 | + | 0.924535i | \(0.375547\pi\) | |||||||
\(38\) | 8.67108 | 1.40663 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.33540 | 0.211145 | ||||||||
\(41\) | 8.09935 | 1.26491 | 0.632453 | − | 0.774599i | \(-0.282048\pi\) | ||||
0.632453 | + | 0.774599i | \(0.282048\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.14821 | −1.09009 | −0.545046 | − | 0.838406i | \(-0.683488\pi\) | ||||
−0.545046 | + | 0.838406i | \(0.683488\pi\) | |||||||
\(44\) | 5.80942 | 0.875803 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.21691 | 0.474307 | ||||||||
\(47\) | −4.49388 | −0.655500 | −0.327750 | − | 0.944764i | \(-0.606290\pi\) | ||||
−0.327750 | + | 0.944764i | \(0.606290\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.86137 | −0.265910 | ||||||||
\(50\) | −3.21671 | −0.454911 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.07946 | 0.288369 | ||||||||
\(53\) | 1.64247 | 0.225611 | 0.112805 | − | 0.993617i | \(-0.464016\pi\) | ||||
0.112805 | + | 0.993617i | \(0.464016\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.75790 | 1.04608 | ||||||||
\(56\) | 2.26685 | 0.302921 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.55075 | 0.466236 | ||||||||
\(59\) | 1.45742 | 0.189740 | 0.0948700 | − | 0.995490i | \(-0.469756\pi\) | ||||
0.0948700 | + | 0.995490i | \(0.469756\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.95663 | 0.378557 | 0.189279 | − | 0.981923i | \(-0.439385\pi\) | ||||
0.189279 | + | 0.981923i | \(0.439385\pi\) | |||||||
\(62\) | −4.87939 | −0.619683 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.77691 | 0.344433 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.2036 | −1.36874 | −0.684371 | − | 0.729134i | \(-0.739923\pi\) | ||||
−0.684371 | + | 0.729134i | \(0.739923\pi\) | |||||||
\(68\) | −5.11591 | −0.620395 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.02716 | 0.361814 | ||||||||
\(71\) | −6.47410 | −0.768334 | −0.384167 | − | 0.923264i | \(-0.625511\pi\) | ||||
−0.384167 | + | 0.923264i | \(0.625511\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.65611 | −0.427915 | −0.213958 | − | 0.976843i | \(-0.568635\pi\) | ||||
−0.213958 | + | 0.976843i | \(0.568635\pi\) | |||||||
\(74\) | 4.63624 | 0.538952 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.67108 | 0.994641 | ||||||||
\(77\) | 13.1691 | 1.50076 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.22676 | 0.475547 | 0.237774 | − | 0.971321i | \(-0.423582\pi\) | ||||
0.237774 | + | 0.971321i | \(0.423582\pi\) | |||||||
\(80\) | 1.33540 | 0.149302 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.09935 | 0.894423 | ||||||||
\(83\) | 0.157895 | 0.0173312 | 0.00866560 | − | 0.999962i | \(-0.497242\pi\) | ||||
0.00866560 | + | 0.999962i | \(0.497242\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.83179 | −0.741012 | ||||||||
\(86\) | −7.14821 | −0.770811 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.80942 | 0.619286 | ||||||||
\(89\) | −4.44985 | −0.471683 | −0.235842 | − | 0.971792i | \(-0.575785\pi\) | ||||
−0.235842 | + | 0.971792i | \(0.575785\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.71382 | 0.494143 | ||||||||
\(92\) | 3.21691 | 0.335386 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.49388 | −0.463509 | ||||||||
\(95\) | 11.5794 | 1.18802 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.30166 | 0.842906 | 0.421453 | − | 0.906850i | \(-0.361520\pi\) | ||||
0.421453 | + | 0.906850i | \(0.361520\pi\) | |||||||
\(98\) | −1.86137 | −0.188027 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.21671 | −0.321671 | ||||||||
\(101\) | 1.68201 | 0.167366 | 0.0836831 | − | 0.996492i | \(-0.473332\pi\) | ||||
0.0836831 | + | 0.996492i | \(0.473332\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.89775 | −0.384057 | −0.192028 | − | 0.981389i | \(-0.561507\pi\) | ||||
−0.192028 | + | 0.981389i | \(0.561507\pi\) | |||||||
\(104\) | 2.07946 | 0.203907 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.64247 | 0.159531 | ||||||||
\(107\) | −14.6552 | −1.41677 | −0.708385 | − | 0.705827i | \(-0.750576\pi\) | ||||
−0.708385 | + | 0.705827i | \(0.750576\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.4977 | −1.00549 | −0.502747 | − | 0.864434i | \(-0.667677\pi\) | ||||
−0.502747 | + | 0.864434i | \(0.667677\pi\) | |||||||
\(110\) | 7.75790 | 0.739687 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.26685 | 0.214198 | ||||||||
\(113\) | −13.8839 | −1.30609 | −0.653043 | − | 0.757321i | \(-0.726508\pi\) | ||||
−0.653043 | + | 0.757321i | \(0.726508\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.29586 | 0.400591 | ||||||||
\(116\) | 3.55075 | 0.329679 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.45742 | 0.134166 | ||||||||
\(119\) | −11.5970 | −1.06310 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.7494 | 2.06813 | ||||||||
\(122\) | 2.95663 | 0.267681 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.87939 | −0.438182 | ||||||||
\(125\) | −10.9726 | −0.981418 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.9253 | −1.67935 | −0.839676 | − | 0.543088i | \(-0.817255\pi\) | ||||
−0.839676 | + | 0.543088i | \(0.817255\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.77691 | 0.243551 | ||||||||
\(131\) | −7.87984 | −0.688465 | −0.344233 | − | 0.938884i | \(-0.611861\pi\) | ||||
−0.344233 | + | 0.938884i | \(0.611861\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.6561 | 1.70440 | ||||||||
\(134\) | −11.2036 | −0.967847 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.11591 | −0.438686 | ||||||||
\(137\) | 16.3169 | 1.39405 | 0.697025 | − | 0.717047i | \(-0.254507\pi\) | ||||
0.697025 | + | 0.717047i | \(0.254507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.4436 | 1.90364 | 0.951821 | − | 0.306654i | \(-0.0992094\pi\) | ||||
0.951821 | + | 0.306654i | \(0.0992094\pi\) | |||||||
\(140\) | 3.02716 | 0.255841 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.47410 | −0.543294 | ||||||||
\(143\) | 12.0804 | 1.01022 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.74167 | 0.393774 | ||||||||
\(146\) | −3.65611 | −0.302582 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.63624 | 0.381096 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.03910 | −0.0845608 | −0.0422804 | − | 0.999106i | \(-0.513462\pi\) | ||||
−0.0422804 | + | 0.999106i | \(0.513462\pi\) | |||||||
\(152\) | 8.67108 | 0.703317 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13.1691 | 1.06120 | ||||||||
\(155\) | −6.51594 | −0.523373 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.3346 | −0.904600 | −0.452300 | − | 0.891866i | \(-0.649396\pi\) | ||||
−0.452300 | + | 0.891866i | \(0.649396\pi\) | |||||||
\(158\) | 4.22676 | 0.336263 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.33540 | 0.105573 | ||||||||
\(161\) | 7.29226 | 0.574711 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.4023 | −0.971420 | −0.485710 | − | 0.874120i | \(-0.661439\pi\) | ||||
−0.485710 | + | 0.874120i | \(0.661439\pi\) | |||||||
\(164\) | 8.09935 | 0.632453 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.157895 | 0.0122550 | ||||||||
\(167\) | 7.40538 | 0.573046 | 0.286523 | − | 0.958073i | \(-0.407501\pi\) | ||||
0.286523 | + | 0.958073i | \(0.407501\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.67586 | −0.667374 | ||||||||
\(170\) | −6.83179 | −0.523974 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.14821 | −0.545046 | ||||||||
\(173\) | 4.62449 | 0.351594 | 0.175797 | − | 0.984426i | \(-0.443750\pi\) | ||||
0.175797 | + | 0.984426i | \(0.443750\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.29181 | −0.551209 | ||||||||
\(176\) | 5.80942 | 0.437902 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.44985 | −0.333530 | ||||||||
\(179\) | 11.2805 | 0.843141 | 0.421570 | − | 0.906796i | \(-0.361479\pi\) | ||||
0.421570 | + | 0.906796i | \(0.361479\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.51927 | −0.335915 | −0.167957 | − | 0.985794i | \(-0.553717\pi\) | ||||
−0.167957 | + | 0.985794i | \(0.553717\pi\) | |||||||
\(182\) | 4.71382 | 0.349412 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.21691 | 0.237154 | ||||||||
\(185\) | 6.19123 | 0.455188 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −29.7205 | −2.17338 | ||||||||
\(188\) | −4.49388 | −0.327750 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.5794 | 0.840055 | ||||||||
\(191\) | −5.82375 | −0.421392 | −0.210696 | − | 0.977552i | \(-0.567573\pi\) | ||||
−0.210696 | + | 0.977552i | \(0.567573\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.80698 | −0.561959 | −0.280979 | − | 0.959714i | \(-0.590659\pi\) | ||||
−0.280979 | + | 0.959714i | \(0.590659\pi\) | |||||||
\(194\) | 8.30166 | 0.596025 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.86137 | −0.132955 | ||||||||
\(197\) | −5.58618 | −0.397999 | −0.198999 | − | 0.980000i | \(-0.563769\pi\) | ||||
−0.198999 | + | 0.980000i | \(0.563769\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.7298 | −0.760613 | −0.380306 | − | 0.924861i | \(-0.624181\pi\) | ||||
−0.380306 | + | 0.924861i | \(0.624181\pi\) | |||||||
\(200\) | −3.21671 | −0.227456 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.68201 | 0.118346 | ||||||||
\(203\) | 8.04902 | 0.564931 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.8159 | 0.755413 | ||||||||
\(206\) | −3.89775 | −0.271569 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.07946 | 0.144184 | ||||||||
\(209\) | 50.3739 | 3.48444 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.18033 | 0.287786 | 0.143893 | − | 0.989593i | \(-0.454038\pi\) | ||||
0.143893 | + | 0.989593i | \(0.454038\pi\) | |||||||
\(212\) | 1.64247 | 0.112805 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.6552 | −1.00181 | ||||||||
\(215\) | −9.54572 | −0.651013 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.0609 | −0.750861 | ||||||||
\(218\) | −10.4977 | −0.710991 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.75790 | 0.523038 | ||||||||
\(221\) | −10.6383 | −0.715610 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.2349 | 0.819312 | 0.409656 | − | 0.912240i | \(-0.365649\pi\) | ||||
0.409656 | + | 0.912240i | \(0.365649\pi\) | |||||||
\(224\) | 2.26685 | 0.151461 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.8839 | −0.923542 | ||||||||
\(227\) | −10.8799 | −0.722124 | −0.361062 | − | 0.932542i | \(-0.617586\pi\) | ||||
−0.361062 | + | 0.932542i | \(0.617586\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.2384 | −1.66780 | −0.833900 | − | 0.551916i | \(-0.813897\pi\) | ||||
−0.833900 | + | 0.551916i | \(0.813897\pi\) | |||||||
\(230\) | 4.29586 | 0.283260 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.55075 | 0.233118 | ||||||||
\(233\) | 28.3597 | 1.85790 | 0.928952 | − | 0.370201i | \(-0.120711\pi\) | ||||
0.928952 | + | 0.370201i | \(0.120711\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00113 | −0.391471 | ||||||||
\(236\) | 1.45742 | 0.0948700 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11.5970 | −0.751724 | ||||||||
\(239\) | 7.12040 | 0.460580 | 0.230290 | − | 0.973122i | \(-0.426032\pi\) | ||||
0.230290 | + | 0.973122i | \(0.426032\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.08678 | −0.263253 | −0.131626 | − | 0.991299i | \(-0.542020\pi\) | ||||
−0.131626 | + | 0.991299i | \(0.542020\pi\) | |||||||
\(242\) | 22.7494 | 1.46239 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.95663 | 0.189279 | ||||||||
\(245\) | −2.48568 | −0.158804 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.0311 | 1.14729 | ||||||||
\(248\) | −4.87939 | −0.309842 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.9726 | −0.693968 | ||||||||
\(251\) | −13.6479 | −0.861447 | −0.430724 | − | 0.902484i | \(-0.641742\pi\) | ||||
−0.430724 | + | 0.902484i | \(0.641742\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.6884 | 1.17493 | ||||||||
\(254\) | −18.9253 | −1.18748 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.5964 | 1.03525 | 0.517627 | − | 0.855607i | \(-0.326816\pi\) | ||||
0.517627 | + | 0.855607i | \(0.326816\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.5097 | 0.653039 | ||||||||
\(260\) | 2.77691 | 0.172216 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.87984 | −0.486818 | ||||||||
\(263\) | −12.5008 | −0.770835 | −0.385417 | − | 0.922742i | \(-0.625943\pi\) | ||||
−0.385417 | + | 0.922742i | \(0.625943\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.19336 | 0.134737 | ||||||||
\(266\) | 19.6561 | 1.20519 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.2036 | −0.684371 | ||||||||
\(269\) | 20.6728 | 1.26044 | 0.630222 | − | 0.776415i | \(-0.282964\pi\) | ||||
0.630222 | + | 0.776415i | \(0.282964\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.2724 | 1.83891 | 0.919457 | − | 0.393190i | \(-0.128628\pi\) | ||||
0.919457 | + | 0.393190i | \(0.128628\pi\) | |||||||
\(272\) | −5.11591 | −0.310198 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.3169 | 0.985742 | ||||||||
\(275\) | −18.6872 | −1.12688 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.0407 | 0.903708 | 0.451854 | − | 0.892092i | \(-0.350763\pi\) | ||||
0.451854 | + | 0.892092i | \(0.350763\pi\) | |||||||
\(278\) | 22.4436 | 1.34608 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.02716 | 0.180907 | ||||||||
\(281\) | −13.3323 | −0.795337 | −0.397668 | − | 0.917529i | \(-0.630181\pi\) | ||||
−0.397668 | + | 0.917529i | \(0.630181\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.7754 | −0.937750 | −0.468875 | − | 0.883265i | \(-0.655340\pi\) | ||||
−0.468875 | + | 0.883265i | \(0.655340\pi\) | |||||||
\(284\) | −6.47410 | −0.384167 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.0804 | 0.714331 | ||||||||
\(287\) | 18.3600 | 1.08376 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.17256 | 0.539562 | ||||||||
\(290\) | 4.74167 | 0.278440 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.65611 | −0.213958 | ||||||||
\(293\) | 4.83921 | 0.282710 | 0.141355 | − | 0.989959i | \(-0.454854\pi\) | ||||
0.141355 | + | 0.989959i | \(0.454854\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.94624 | 0.113314 | ||||||||
\(296\) | 4.63624 | 0.269476 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | 6.68942 | 0.386859 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.2039 | −0.933980 | ||||||||
\(302\) | −1.03910 | −0.0597935 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.67108 | 0.497320 | ||||||||
\(305\) | 3.94828 | 0.226078 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.6584 | −1.06489 | −0.532446 | − | 0.846464i | \(-0.678727\pi\) | ||||
−0.532446 | + | 0.846464i | \(0.678727\pi\) | |||||||
\(308\) | 13.1691 | 0.750380 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.51594 | −0.370080 | ||||||||
\(311\) | 34.2651 | 1.94300 | 0.971498 | − | 0.237048i | \(-0.0761798\pi\) | ||||
0.971498 | + | 0.237048i | \(0.0761798\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.723019 | 0.0408674 | 0.0204337 | − | 0.999791i | \(-0.493495\pi\) | ||||
0.0204337 | + | 0.999791i | \(0.493495\pi\) | |||||||
\(314\) | −11.3346 | −0.639649 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.22676 | 0.237774 | ||||||||
\(317\) | 9.57951 | 0.538039 | 0.269019 | − | 0.963135i | \(-0.413300\pi\) | ||||
0.269019 | + | 0.963135i | \(0.413300\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.6278 | 1.15493 | ||||||||
\(320\) | 1.33540 | 0.0746511 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.29226 | 0.406382 | ||||||||
\(323\) | −44.3605 | −2.46828 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.68900 | −0.371039 | ||||||||
\(326\) | −12.4023 | −0.686897 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.09935 | 0.447212 | ||||||||
\(329\) | −10.1870 | −0.561626 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.6251 | 0.858831 | 0.429416 | − | 0.903107i | \(-0.358720\pi\) | ||||
0.429416 | + | 0.903107i | \(0.358720\pi\) | |||||||
\(332\) | 0.157895 | 0.00866560 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.40538 | 0.405205 | ||||||||
\(335\) | −14.9613 | −0.817426 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.12119 | −0.442390 | −0.221195 | − | 0.975230i | \(-0.570996\pi\) | ||||
−0.221195 | + | 0.975230i | \(0.570996\pi\) | |||||||
\(338\) | −8.67586 | −0.471905 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.83179 | −0.370506 | ||||||||
\(341\) | −28.3464 | −1.53505 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0874 | −1.08462 | ||||||||
\(344\) | −7.14821 | −0.385406 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.62449 | 0.248614 | ||||||||
\(347\) | 6.52384 | 0.350218 | 0.175109 | − | 0.984549i | \(-0.443972\pi\) | ||||
0.175109 | + | 0.984549i | \(0.443972\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.1926 | −1.02736 | −0.513678 | − | 0.857983i | \(-0.671717\pi\) | ||||
−0.513678 | + | 0.857983i | \(0.671717\pi\) | |||||||
\(350\) | −7.29181 | −0.389763 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.80942 | 0.309643 | ||||||||
\(353\) | 9.72044 | 0.517367 | 0.258683 | − | 0.965962i | \(-0.416711\pi\) | ||||
0.258683 | + | 0.965962i | \(0.416711\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.64551 | −0.458856 | ||||||||
\(356\) | −4.44985 | −0.235842 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.2805 | 0.596191 | ||||||||
\(359\) | 14.8797 | 0.785323 | 0.392661 | − | 0.919683i | \(-0.371554\pi\) | ||||
0.392661 | + | 0.919683i | \(0.371554\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 56.1876 | 2.95724 | ||||||||
\(362\) | −4.51927 | −0.237528 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.71382 | 0.247071 | ||||||||
\(365\) | −4.88237 | −0.255555 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −35.7769 | −1.86754 | −0.933769 | − | 0.357877i | \(-0.883501\pi\) | ||||
−0.933769 | + | 0.357877i | \(0.883501\pi\) | |||||||
\(368\) | 3.21691 | 0.167693 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.19123 | 0.321867 | ||||||||
\(371\) | 3.72325 | 0.193301 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.2864 | 1.72351 | 0.861753 | − | 0.507327i | \(-0.169367\pi\) | ||||
0.861753 | + | 0.507327i | \(0.169367\pi\) | |||||||
\(374\) | −29.7205 | −1.53681 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.49388 | −0.231754 | ||||||||
\(377\) | 7.38362 | 0.380276 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.08326 | −0.107010 | −0.0535048 | − | 0.998568i | \(-0.517039\pi\) | ||||
−0.0535048 | + | 0.998568i | \(0.517039\pi\) | |||||||
\(380\) | 11.5794 | 0.594008 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.82375 | −0.297969 | ||||||||
\(383\) | −18.2511 | −0.932590 | −0.466295 | − | 0.884629i | \(-0.654411\pi\) | ||||
−0.466295 | + | 0.884629i | \(0.654411\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.5860 | 0.896267 | ||||||||
\(386\) | −7.80698 | −0.397365 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.30166 | 0.421453 | ||||||||
\(389\) | −11.6927 | −0.592843 | −0.296422 | − | 0.955057i | \(-0.595793\pi\) | ||||
−0.296422 | + | 0.955057i | \(0.595793\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.4574 | −0.832287 | ||||||||
\(392\) | −1.86137 | −0.0940134 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.58618 | −0.281428 | ||||||||
\(395\) | 5.64441 | 0.284001 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.213966 | 0.0107386 | 0.00536932 | − | 0.999986i | \(-0.498291\pi\) | ||||
0.00536932 | + | 0.999986i | \(0.498291\pi\) | |||||||
\(398\) | −10.7298 | −0.537835 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.21671 | −0.160835 | ||||||||
\(401\) | 10.3209 | 0.515403 | 0.257701 | − | 0.966225i | \(-0.417035\pi\) | ||||
0.257701 | + | 0.966225i | \(0.417035\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.1465 | −0.505432 | ||||||||
\(404\) | 1.68201 | 0.0836831 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.04902 | 0.399466 | ||||||||
\(407\) | 26.9339 | 1.33506 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.211630 | 0.0104644 | 0.00523222 | − | 0.999986i | \(-0.498335\pi\) | ||||
0.00523222 | + | 0.999986i | \(0.498335\pi\) | |||||||
\(410\) | 10.8159 | 0.534158 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.89775 | −0.192028 | ||||||||
\(413\) | 3.30376 | 0.162567 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.210853 | 0.0103503 | ||||||||
\(416\) | 2.07946 | 0.101954 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 50.3739 | 2.46387 | ||||||||
\(419\) | 3.39484 | 0.165849 | 0.0829243 | − | 0.996556i | \(-0.473574\pi\) | ||||
0.0829243 | + | 0.996556i | \(0.473574\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.07013 | 0.247103 | 0.123552 | − | 0.992338i | \(-0.460572\pi\) | ||||
0.123552 | + | 0.992338i | \(0.460572\pi\) | |||||||
\(422\) | 4.18033 | 0.203495 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.64247 | 0.0797655 | ||||||||
\(425\) | 16.4564 | 0.798252 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.70225 | 0.324344 | ||||||||
\(428\) | −14.6552 | −0.708385 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.54572 | −0.460335 | ||||||||
\(431\) | −1.42121 | −0.0684573 | −0.0342287 | − | 0.999414i | \(-0.510897\pi\) | ||||
−0.0342287 | + | 0.999414i | \(0.510897\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.16167 | −0.392225 | −0.196112 | − | 0.980581i | \(-0.562832\pi\) | ||||
−0.196112 | + | 0.980581i | \(0.562832\pi\) | |||||||
\(434\) | −11.0609 | −0.530939 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.4977 | −0.502747 | ||||||||
\(437\) | 27.8940 | 1.33435 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.2959 | −1.15958 | −0.579791 | − | 0.814765i | \(-0.696866\pi\) | ||||
−0.579791 | + | 0.814765i | \(0.696866\pi\) | |||||||
\(440\) | 7.75790 | 0.369843 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.6383 | −0.506013 | ||||||||
\(443\) | 21.8590 | 1.03855 | 0.519277 | − | 0.854606i | \(-0.326201\pi\) | ||||
0.519277 | + | 0.854606i | \(0.326201\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.94233 | −0.281693 | ||||||||
\(446\) | 12.2349 | 0.579341 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.26685 | 0.107099 | ||||||||
\(449\) | 31.3083 | 1.47753 | 0.738765 | − | 0.673964i | \(-0.235410\pi\) | ||||
0.738765 | + | 0.673964i | \(0.235410\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 47.0525 | 2.21562 | ||||||||
\(452\) | −13.8839 | −0.653043 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.8799 | −0.510618 | ||||||||
\(455\) | 6.29484 | 0.295107 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.4776 | −1.05146 | −0.525729 | − | 0.850652i | \(-0.676207\pi\) | ||||
−0.525729 | + | 0.850652i | \(0.676207\pi\) | |||||||
\(458\) | −25.2384 | −1.17931 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.29586 | 0.200295 | ||||||||
\(461\) | −24.6409 | −1.14764 | −0.573820 | − | 0.818982i | \(-0.694539\pi\) | ||||
−0.573820 | + | 0.818982i | \(0.694539\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.3886 | −1.08696 | −0.543479 | − | 0.839423i | \(-0.682893\pi\) | ||||
−0.543479 | + | 0.839423i | \(0.682893\pi\) | |||||||
\(464\) | 3.55075 | 0.164839 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.3597 | 1.31374 | ||||||||
\(467\) | 30.4777 | 1.41034 | 0.705170 | − | 0.709038i | \(-0.250871\pi\) | ||||
0.705170 | + | 0.709038i | \(0.250871\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.3970 | −1.17273 | ||||||||
\(470\) | −6.00113 | −0.276812 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.45742 | 0.0670832 | ||||||||
\(473\) | −41.5270 | −1.90941 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.8923 | −1.27979 | ||||||||
\(476\) | −11.5970 | −0.531549 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.12040 | 0.325680 | ||||||||
\(479\) | 7.57443 | 0.346084 | 0.173042 | − | 0.984914i | \(-0.444640\pi\) | ||||
0.173042 | + | 0.984914i | \(0.444640\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.64085 | 0.439585 | ||||||||
\(482\) | −4.08678 | −0.186148 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.7494 | 1.03406 | ||||||||
\(485\) | 11.0860 | 0.503391 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.2731 | 1.82495 | 0.912474 | − | 0.409134i | \(-0.134169\pi\) | ||||
0.912474 | + | 0.409134i | \(0.134169\pi\) | |||||||
\(488\) | 2.95663 | 0.133840 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.48568 | −0.112291 | ||||||||
\(491\) | 15.3506 | 0.692765 | 0.346383 | − | 0.938093i | \(-0.387410\pi\) | ||||
0.346383 | + | 0.938093i | \(0.387410\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.1653 | −0.818124 | ||||||||
\(494\) | 18.0311 | 0.811258 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.87939 | −0.219091 | ||||||||
\(497\) | −14.6758 | −0.658302 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.3580 | 1.85144 | 0.925719 | − | 0.378212i | \(-0.123461\pi\) | ||||
0.925719 | + | 0.378212i | \(0.123461\pi\) | |||||||
\(500\) | −10.9726 | −0.490709 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.6479 | −0.609135 | ||||||||
\(503\) | −5.57208 | −0.248447 | −0.124223 | − | 0.992254i | \(-0.539644\pi\) | ||||
−0.124223 | + | 0.992254i | \(0.539644\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.24616 | 0.0999526 | ||||||||
\(506\) | 18.6884 | 0.830799 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.9253 | −0.839676 | ||||||||
\(509\) | 29.8590 | 1.32348 | 0.661740 | − | 0.749734i | \(-0.269818\pi\) | ||||
0.661740 | + | 0.749734i | \(0.269818\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.28787 | −0.366634 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.5964 | 0.732034 | ||||||||
\(515\) | −5.20506 | −0.229362 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.1069 | −1.14818 | ||||||||
\(518\) | 10.5097 | 0.461769 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.77691 | 0.121775 | ||||||||
\(521\) | −8.13727 | −0.356500 | −0.178250 | − | 0.983985i | \(-0.557044\pi\) | ||||
−0.178250 | + | 0.983985i | \(0.557044\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.53980 | −0.329692 | −0.164846 | − | 0.986319i | \(-0.552713\pi\) | ||||
−0.164846 | + | 0.986319i | \(0.552713\pi\) | |||||||
\(524\) | −7.87984 | −0.344233 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.5008 | −0.545062 | ||||||||
\(527\) | 24.9625 | 1.08738 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.6515 | −0.550066 | ||||||||
\(530\) | 2.19336 | 0.0952734 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 19.6561 | 0.852199 | ||||||||
\(533\) | 16.8422 | 0.729518 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.5705 | −0.846107 | ||||||||
\(536\) | −11.2036 | −0.483924 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.6728 | 0.891268 | ||||||||
\(539\) | −10.8135 | −0.465770 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.3168 | −1.08845 | −0.544227 | − | 0.838938i | \(-0.683177\pi\) | ||||
−0.544227 | + | 0.838938i | \(0.683177\pi\) | |||||||
\(542\) | 30.2724 | 1.30031 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.11591 | −0.219343 | ||||||||
\(545\) | −14.0186 | −0.600490 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.87966 | 0.422424 | 0.211212 | − | 0.977440i | \(-0.432259\pi\) | ||||
0.211212 | + | 0.977440i | \(0.432259\pi\) | |||||||
\(548\) | 16.3169 | 0.697025 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −18.6872 | −0.796825 | ||||||||
\(551\) | 30.7888 | 1.31165 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.58144 | 0.407444 | ||||||||
\(554\) | 15.0407 | 0.639018 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.4436 | 0.951821 | ||||||||
\(557\) | −23.0656 | −0.977320 | −0.488660 | − | 0.872474i | \(-0.662514\pi\) | ||||
−0.488660 | + | 0.872474i | \(0.662514\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.8644 | −0.628696 | ||||||||
\(560\) | 3.02716 | 0.127921 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.3323 | −0.562388 | ||||||||
\(563\) | 7.90993 | 0.333364 | 0.166682 | − | 0.986011i | \(-0.446695\pi\) | ||||
0.166682 | + | 0.986011i | \(0.446695\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.5405 | −0.780006 | ||||||||
\(566\) | −15.7754 | −0.663089 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.47410 | −0.271647 | ||||||||
\(569\) | −2.89792 | −0.121487 | −0.0607435 | − | 0.998153i | \(-0.519347\pi\) | ||||
−0.0607435 | + | 0.998153i | \(0.519347\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.6023 | 1.36436 | 0.682182 | − | 0.731183i | \(-0.261031\pi\) | ||||
0.682182 | + | 0.731183i | \(0.261031\pi\) | |||||||
\(572\) | 12.0804 | 0.505108 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.3600 | 0.766333 | ||||||||
\(575\) | −10.3478 | −0.431535 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.55957 | 0.148187 | 0.0740935 | − | 0.997251i | \(-0.476394\pi\) | ||||
0.0740935 | + | 0.997251i | \(0.476394\pi\) | |||||||
\(578\) | 9.17256 | 0.381528 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.74167 | 0.196887 | ||||||||
\(581\) | 0.357924 | 0.0148492 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.54182 | 0.395182 | ||||||||
\(584\) | −3.65611 | −0.151291 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.83921 | 0.199906 | ||||||||
\(587\) | 18.3174 | 0.756039 | 0.378019 | − | 0.925798i | \(-0.376605\pi\) | ||||
0.378019 | + | 0.925798i | \(0.376605\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.3096 | −1.74333 | ||||||||
\(590\) | 1.94624 | 0.0801254 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.63624 | 0.190548 | ||||||||
\(593\) | −6.58426 | −0.270383 | −0.135192 | − | 0.990819i | \(-0.543165\pi\) | ||||
−0.135192 | + | 0.990819i | \(0.543165\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.4867 | −0.634892 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.68942 | 0.273551 | ||||||||
\(599\) | 1.77773 | 0.0726360 | 0.0363180 | − | 0.999340i | \(-0.488437\pi\) | ||||
0.0363180 | + | 0.999340i | \(0.488437\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.8709 | 0.484222 | 0.242111 | − | 0.970249i | \(-0.422160\pi\) | ||||
0.242111 | + | 0.970249i | \(0.422160\pi\) | |||||||
\(602\) | −16.2039 | −0.660424 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.03910 | −0.0422804 | ||||||||
\(605\) | 30.3795 | 1.23510 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.55085 | −0.225302 | −0.112651 | − | 0.993635i | \(-0.535934\pi\) | ||||
−0.112651 | + | 0.993635i | \(0.535934\pi\) | |||||||
\(608\) | 8.67108 | 0.351659 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.94828 | 0.159861 | ||||||||
\(611\) | −9.34483 | −0.378051 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.5635 | 0.668993 | 0.334496 | − | 0.942397i | \(-0.391434\pi\) | ||||
0.334496 | + | 0.942397i | \(0.391434\pi\) | |||||||
\(614\) | −18.6584 | −0.752993 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.1691 | 0.530599 | ||||||||
\(617\) | 0.583822 | 0.0235038 | 0.0117519 | − | 0.999931i | \(-0.496259\pi\) | ||||
0.0117519 | + | 0.999931i | \(0.496259\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.5344 | −0.865539 | −0.432769 | − | 0.901505i | \(-0.642464\pi\) | ||||
−0.432769 | + | 0.901505i | \(0.642464\pi\) | |||||||
\(620\) | −6.51594 | −0.261686 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 34.2651 | 1.37391 | ||||||||
\(623\) | −10.0872 | −0.404134 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.43074 | 0.0572295 | ||||||||
\(626\) | 0.723019 | 0.0288976 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.3346 | −0.452300 | ||||||||
\(629\) | −23.7186 | −0.945722 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.665901 | 0.0265091 | 0.0132546 | − | 0.999912i | \(-0.495781\pi\) | ||||
0.0132546 | + | 0.999912i | \(0.495781\pi\) | |||||||
\(632\) | 4.22676 | 0.168131 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.57951 | 0.380451 | ||||||||
\(635\) | −25.2729 | −1.00292 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.87064 | −0.153360 | ||||||||
\(638\) | 20.6278 | 0.816662 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.33540 | 0.0527863 | ||||||||
\(641\) | 49.8567 | 1.96922 | 0.984611 | − | 0.174758i | \(-0.0559142\pi\) | ||||
0.984611 | + | 0.174758i | \(0.0559142\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.0304 | −1.46034 | −0.730169 | − | 0.683267i | \(-0.760559\pi\) | ||||
−0.730169 | + | 0.683267i | \(0.760559\pi\) | |||||||
\(644\) | 7.29226 | 0.287355 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −44.3605 | −1.74534 | ||||||||
\(647\) | 45.7407 | 1.79825 | 0.899126 | − | 0.437691i | \(-0.144203\pi\) | ||||
0.899126 | + | 0.437691i | \(0.144203\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.46677 | 0.332350 | ||||||||
\(650\) | −6.68900 | −0.262364 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.4023 | −0.485710 | ||||||||
\(653\) | 16.6391 | 0.651138 | 0.325569 | − | 0.945518i | \(-0.394444\pi\) | ||||
0.325569 | + | 0.945518i | \(0.394444\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.5227 | −0.411158 | ||||||||
\(656\) | 8.09935 | 0.316226 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.1870 | −0.397130 | ||||||||
\(659\) | −32.1205 | −1.25124 | −0.625619 | − | 0.780129i | \(-0.715154\pi\) | ||||
−0.625619 | + | 0.780129i | \(0.715154\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.5899 | −0.606377 | −0.303188 | − | 0.952931i | \(-0.598051\pi\) | ||||
−0.303188 | + | 0.952931i | \(0.598051\pi\) | |||||||
\(662\) | 15.6251 | 0.607285 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.157895 | 0.00612750 | ||||||||
\(665\) | 26.2487 | 1.01788 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.4224 | 0.442278 | ||||||||
\(668\) | 7.40538 | 0.286523 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.9613 | −0.578007 | ||||||||
\(671\) | 17.1763 | 0.663084 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.3356 | −1.47773 | −0.738865 | − | 0.673853i | \(-0.764638\pi\) | ||||
−0.738865 | + | 0.673853i | \(0.764638\pi\) | |||||||
\(674\) | −8.12119 | −0.312817 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.67586 | −0.333687 | ||||||||
\(677\) | −34.3362 | −1.31965 | −0.659823 | − | 0.751421i | \(-0.729369\pi\) | ||||
−0.659823 | + | 0.751421i | \(0.729369\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.8187 | 0.722194 | ||||||||
\(680\) | −6.83179 | −0.261987 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −28.3464 | −1.08544 | ||||||||
\(683\) | 8.44528 | 0.323150 | 0.161575 | − | 0.986860i | \(-0.448343\pi\) | ||||
0.161575 | + | 0.986860i | \(0.448343\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.7896 | 0.832539 | ||||||||
\(686\) | −20.0874 | −0.766942 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.14821 | −0.272523 | ||||||||
\(689\) | 3.41545 | 0.130118 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.3854 | −1.11787 | −0.558937 | − | 0.829210i | \(-0.688790\pi\) | ||||
−0.558937 | + | 0.829210i | \(0.688790\pi\) | |||||||
\(692\) | 4.62449 | 0.175797 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.52384 | 0.247641 | ||||||||
\(695\) | 29.9712 | 1.13687 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41.4355 | −1.56948 | ||||||||
\(698\) | −19.1926 | −0.726450 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.29181 | −0.275604 | ||||||||
\(701\) | 40.5189 | 1.53038 | 0.765189 | − | 0.643806i | \(-0.222645\pi\) | ||||
0.765189 | + | 0.643806i | \(0.222645\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.2012 | 1.51622 | ||||||||
\(704\) | 5.80942 | 0.218951 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.72044 | 0.365834 | ||||||||
\(707\) | 3.81287 | 0.143398 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.3299 | −1.10151 | −0.550753 | − | 0.834668i | \(-0.685659\pi\) | ||||
−0.550753 | + | 0.834668i | \(0.685659\pi\) | |||||||
\(710\) | −8.64551 | −0.324460 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.44985 | −0.166765 | ||||||||
\(713\) | −15.6965 | −0.587840 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.1322 | 0.603311 | ||||||||
\(716\) | 11.2805 | 0.421570 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.8797 | 0.555307 | ||||||||
\(719\) | 23.3369 | 0.870320 | 0.435160 | − | 0.900353i | \(-0.356692\pi\) | ||||
0.435160 | + | 0.900353i | \(0.356692\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.83563 | −0.329056 | ||||||||
\(722\) | 56.1876 | 2.09108 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.51927 | −0.167957 | ||||||||
\(725\) | −11.4217 | −0.424192 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.8362 | −0.735682 | −0.367841 | − | 0.929889i | \(-0.619903\pi\) | ||||
−0.367841 | + | 0.929889i | \(0.619903\pi\) | |||||||
\(728\) | 4.71382 | 0.174706 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.88237 | −0.180705 | ||||||||
\(731\) | 36.5696 | 1.35258 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.000758868 0 | 2.80294e−5 0 | 1.40147e−5 | − | 1.00000i | \(-0.499996\pi\) | ||||
1.40147e−5 | 1.00000i | \(0.499996\pi\) | ||||||||
\(734\) | −35.7769 | −1.32055 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.21691 | 0.118577 | ||||||||
\(737\) | −65.0867 | −2.39750 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.4783 | 0.863665 | 0.431832 | − | 0.901954i | \(-0.357867\pi\) | ||||
0.431832 | + | 0.901954i | \(0.357867\pi\) | |||||||
\(740\) | 6.19123 | 0.227594 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.72325 | 0.136685 | ||||||||
\(743\) | 25.1755 | 0.923601 | 0.461801 | − | 0.886984i | \(-0.347204\pi\) | ||||
0.461801 | + | 0.886984i | \(0.347204\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.33540 | −0.0489253 | ||||||||
\(746\) | 33.2864 | 1.21870 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −29.7205 | −1.08669 | ||||||||
\(749\) | −33.2211 | −1.21387 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.2907 | 0.922870 | 0.461435 | − | 0.887174i | \(-0.347335\pi\) | ||||
0.461435 | + | 0.887174i | \(0.347335\pi\) | |||||||
\(752\) | −4.49388 | −0.163875 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.38362 | 0.268896 | ||||||||
\(755\) | −1.38761 | −0.0505005 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.1046 | −0.367257 | −0.183628 | − | 0.982996i | \(-0.558784\pi\) | ||||
−0.183628 | + | 0.982996i | \(0.558784\pi\) | |||||||
\(758\) | −2.08326 | −0.0756672 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11.5794 | 0.420027 | ||||||||
\(761\) | −38.6287 | −1.40029 | −0.700145 | − | 0.714001i | \(-0.746881\pi\) | ||||
−0.700145 | + | 0.714001i | \(0.746881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.7967 | −0.861497 | ||||||||
\(764\) | −5.82375 | −0.210696 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.2511 | −0.659440 | ||||||||
\(767\) | 3.03064 | 0.109430 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.70976 | −0.314082 | −0.157041 | − | 0.987592i | \(-0.550195\pi\) | ||||
−0.157041 | + | 0.987592i | \(0.550195\pi\) | |||||||
\(770\) | 17.5860 | 0.633757 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.80698 | −0.280979 | ||||||||
\(773\) | −7.97472 | −0.286831 | −0.143415 | − | 0.989663i | \(-0.545808\pi\) | ||||
−0.143415 | + | 0.989663i | \(0.545808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.6956 | 0.563801 | ||||||||
\(776\) | 8.30166 | 0.298012 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.6927 | −0.419204 | ||||||||
\(779\) | 70.2300 | 2.51625 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.6108 | −1.34582 | ||||||||
\(782\) | −16.4574 | −0.588516 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.86137 | −0.0664775 | ||||||||
\(785\) | −15.1362 | −0.540235 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.5425 | −1.83729 | −0.918646 | − | 0.395082i | \(-0.870716\pi\) | ||||
−0.918646 | + | 0.395082i | \(0.870716\pi\) | |||||||
\(788\) | −5.58618 | −0.198999 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.64441 | 0.200819 | ||||||||
\(791\) | −31.4727 | −1.11904 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.14818 | 0.218328 | ||||||||
\(794\) | 0.213966 | 0.00759336 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.7298 | −0.380306 | ||||||||
\(797\) | −51.1112 | −1.81045 | −0.905225 | − | 0.424933i | \(-0.860298\pi\) | ||||
−0.905225 | + | 0.424933i | \(0.860298\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.9903 | 0.813339 | ||||||||
\(800\) | −3.21671 | −0.113728 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.3209 | 0.364445 | ||||||||
\(803\) | −21.2399 | −0.749539 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.73808 | 0.343222 | ||||||||
\(806\) | −10.1465 | −0.357394 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.68201 | 0.0591729 | ||||||||
\(809\) | −7.09891 | −0.249584 | −0.124792 | − | 0.992183i | \(-0.539826\pi\) | ||||
−0.124792 | + | 0.992183i | \(0.539826\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.1182 | −1.44386 | −0.721928 | − | 0.691968i | \(-0.756744\pi\) | ||||
−0.721928 | + | 0.691968i | \(0.756744\pi\) | |||||||
\(812\) | 8.04902 | 0.282465 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 26.9339 | 0.944031 | ||||||||
\(815\) | −16.5620 | −0.580140 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −61.9827 | −2.16850 | ||||||||
\(818\) | 0.211630 | 0.00739948 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.8159 | 0.377706 | ||||||||
\(821\) | 2.66641 | 0.0930585 | 0.0465293 | − | 0.998917i | \(-0.485184\pi\) | ||||
0.0465293 | + | 0.998917i | \(0.485184\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.8142 | 1.03926 | 0.519630 | − | 0.854392i | \(-0.326070\pi\) | ||||
0.519630 | + | 0.854392i | \(0.326070\pi\) | |||||||
\(824\) | −3.89775 | −0.135785 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.30376 | 0.114953 | ||||||||
\(827\) | −47.2228 | −1.64210 | −0.821049 | − | 0.570857i | \(-0.806611\pi\) | ||||
−0.821049 | + | 0.570857i | \(0.806611\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.3167 | −0.948747 | −0.474373 | − | 0.880324i | \(-0.657325\pi\) | ||||
−0.474373 | + | 0.880324i | \(0.657325\pi\) | |||||||
\(830\) | 0.210853 | 0.00731880 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.07946 | 0.0720922 | ||||||||
\(833\) | 9.52261 | 0.329939 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.88915 | 0.342228 | ||||||||
\(836\) | 50.3739 | 1.74222 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.39484 | 0.117273 | ||||||||
\(839\) | 7.28988 | 0.251675 | 0.125837 | − | 0.992051i | \(-0.459838\pi\) | ||||
0.125837 | + | 0.992051i | \(0.459838\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.3922 | −0.565248 | ||||||||
\(842\) | 5.07013 | 0.174728 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.18033 | 0.143893 | ||||||||
\(845\) | −11.5857 | −0.398562 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 51.5695 | 1.77195 | ||||||||
\(848\) | 1.64247 | 0.0564027 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16.4564 | 0.564450 | ||||||||
\(851\) | 14.9143 | 0.511257 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.7076 | 0.914452 | 0.457226 | − | 0.889351i | \(-0.348843\pi\) | ||||
0.457226 | + | 0.889351i | \(0.348843\pi\) | |||||||
\(854\) | 6.70225 | 0.229346 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.6552 | −0.500904 | ||||||||
\(857\) | −21.2306 | −0.725224 | −0.362612 | − | 0.931940i | \(-0.618115\pi\) | ||||
−0.362612 | + | 0.931940i | \(0.618115\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.7136 | 0.536141 | 0.268071 | − | 0.963399i | \(-0.413614\pi\) | ||||
0.268071 | + | 0.963399i | \(0.413614\pi\) | |||||||
\(860\) | −9.54572 | −0.325506 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.42121 | −0.0484066 | ||||||||
\(863\) | −55.9282 | −1.90382 | −0.951910 | − | 0.306378i | \(-0.900883\pi\) | ||||
−0.951910 | + | 0.306378i | \(0.900883\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.17555 | 0.209975 | ||||||||
\(866\) | −8.16167 | −0.277345 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.0609 | −0.375430 | ||||||||
\(869\) | 24.5550 | 0.832972 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.2975 | −0.789405 | ||||||||
\(872\) | −10.4977 | −0.355496 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 27.8940 | 0.943530 | ||||||||
\(875\) | −24.8733 | −0.840870 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −48.2782 | −1.63024 | −0.815120 | − | 0.579292i | \(-0.803329\pi\) | ||||
−0.815120 | + | 0.579292i | \(0.803329\pi\) | |||||||
\(878\) | −24.2959 | −0.819948 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.75790 | 0.261519 | ||||||||
\(881\) | −11.0099 | −0.370934 | −0.185467 | − | 0.982651i | \(-0.559380\pi\) | ||||
−0.185467 | + | 0.982651i | \(0.559380\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.0571 | 0.641321 | 0.320661 | − | 0.947194i | \(-0.396095\pi\) | ||||
0.320661 | + | 0.947194i | \(0.396095\pi\) | |||||||
\(884\) | −10.6383 | −0.357805 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.8590 | 0.734368 | ||||||||
\(887\) | 31.8567 | 1.06964 | 0.534822 | − | 0.844965i | \(-0.320379\pi\) | ||||
0.534822 | + | 0.844965i | \(0.320379\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −42.9010 | −1.43885 | ||||||||
\(890\) | −5.94233 | −0.199187 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.2349 | 0.409656 | ||||||||
\(893\) | −38.9668 | −1.30397 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.0639 | 0.503531 | ||||||||
\(896\) | 2.26685 | 0.0757303 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31.3083 | 1.04477 | ||||||||
\(899\) | −17.3255 | −0.577837 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.40275 | −0.279936 | ||||||||
\(902\) | 47.0525 | 1.56668 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.8839 | −0.461771 | ||||||||
\(905\) | −6.03503 | −0.200611 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.0250 | −0.897352 | −0.448676 | − | 0.893695i | \(-0.648104\pi\) | ||||
−0.448676 | + | 0.893695i | \(0.648104\pi\) | |||||||
\(908\) | −10.8799 | −0.361062 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.29484 | 0.208672 | ||||||||
\(911\) | 21.8821 | 0.724987 | 0.362493 | − | 0.931986i | \(-0.381926\pi\) | ||||
0.362493 | + | 0.931986i | \(0.381926\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.917277 | 0.0303574 | ||||||||
\(914\) | −22.4776 | −0.743493 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −25.2384 | −0.833900 | ||||||||
\(917\) | −17.8625 | −0.589870 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.5127 | 1.00652 | 0.503261 | − | 0.864134i | \(-0.332133\pi\) | ||||
0.503261 | + | 0.864134i | \(0.332133\pi\) | |||||||
\(920\) | 4.29586 | 0.141630 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −24.6409 | −0.811504 | ||||||||
\(923\) | −13.4626 | −0.443127 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.9134 | −0.490350 | ||||||||
\(926\) | −23.3886 | −0.768595 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.55075 | 0.116559 | ||||||||
\(929\) | −29.4298 | −0.965562 | −0.482781 | − | 0.875741i | \(-0.660373\pi\) | ||||
−0.482781 | + | 0.875741i | \(0.660373\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.1401 | −0.528970 | ||||||||
\(932\) | 28.3597 | 0.928952 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.4777 | 0.997261 | ||||||||
\(935\) | −39.6887 | −1.29796 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.9101 | 1.56515 | 0.782577 | − | 0.622554i | \(-0.213905\pi\) | ||||
0.782577 | + | 0.622554i | \(0.213905\pi\) | |||||||
\(938\) | −25.3970 | −0.829242 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.00113 | −0.195735 | ||||||||
\(941\) | 7.06453 | 0.230297 | 0.115149 | − | 0.993348i | \(-0.463266\pi\) | ||||
0.115149 | + | 0.993348i | \(0.463266\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.0548 | 0.848463 | ||||||||
\(944\) | 1.45742 | 0.0474350 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −41.5270 | −1.35016 | ||||||||
\(947\) | −42.3321 | −1.37561 | −0.687804 | − | 0.725896i | \(-0.741425\pi\) | ||||
−0.687804 | + | 0.725896i | \(0.741425\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.60272 | −0.246795 | ||||||||
\(950\) | −27.8923 | −0.904946 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.5970 | −0.375862 | ||||||||
\(953\) | 46.5984 | 1.50947 | 0.754735 | − | 0.656029i | \(-0.227765\pi\) | ||||
0.754735 | + | 0.656029i | \(0.227765\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.77704 | −0.251659 | ||||||||
\(956\) | 7.12040 | 0.230290 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.57443 | 0.244719 | ||||||||
\(959\) | 36.9881 | 1.19441 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.19156 | −0.231986 | ||||||||
\(962\) | 9.64085 | 0.310833 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.08678 | −0.131626 | ||||||||
\(965\) | −10.4254 | −0.335607 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.9542 | 1.18837 | 0.594184 | − | 0.804329i | \(-0.297475\pi\) | ||||
0.594184 | + | 0.804329i | \(0.297475\pi\) | |||||||
\(968\) | 22.7494 | 0.731193 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.0860 | 0.355951 | ||||||||
\(971\) | 13.4887 | 0.432872 | 0.216436 | − | 0.976297i | \(-0.430557\pi\) | ||||
0.216436 | + | 0.976297i | \(0.430557\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 50.8764 | 1.63102 | ||||||||
\(974\) | 40.2731 | 1.29043 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.95663 | 0.0946394 | ||||||||
\(977\) | 1.91216 | 0.0611755 | 0.0305878 | − | 0.999532i | \(-0.490262\pi\) | ||||
0.0305878 | + | 0.999532i | \(0.490262\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.8511 | −0.826203 | ||||||||
\(980\) | −2.48568 | −0.0794020 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.3506 | 0.489859 | ||||||||
\(983\) | 53.5309 | 1.70737 | 0.853686 | − | 0.520788i | \(-0.174362\pi\) | ||||
0.853686 | + | 0.520788i | \(0.174362\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.45979 | −0.237689 | ||||||||
\(986\) | −18.1653 | −0.578501 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.0311 | 0.573646 | ||||||||
\(989\) | −22.9951 | −0.731202 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.4059 | −0.552915 | −0.276458 | − | 0.961026i | \(-0.589161\pi\) | ||||
−0.276458 | + | 0.961026i | \(0.589161\pi\) | |||||||
\(992\) | −4.87939 | −0.154921 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −14.6758 | −0.465490 | ||||||||
\(995\) | −14.3285 | −0.454245 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.0850 | 1.87124 | 0.935620 | − | 0.353010i | \(-0.114842\pi\) | ||||
0.935620 | + | 0.353010i | \(0.114842\pi\) | |||||||
\(998\) | 41.3580 | 1.30916 | ||||||||
\(999\) | 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.p.1.8 | yes | 12 | |
3.2 | odd | 2 | 8046.2.a.i.1.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.i.1.5 | ✓ | 12 | 3.2 | odd | 2 | ||
8046.2.a.p.1.8 | yes | 12 | 1.1 | even | 1 | trivial |