Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3675,2,Mod(1,3675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3675.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3675.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: | \(29.3450227428\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.90321 | −1.34577 | −0.672887 | − | 0.739745i | \(-0.734946\pi\) | ||||
−0.672887 | + | 0.739745i | \(0.734946\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.62222 | 0.811108 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.90321 | −0.776983 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.719004 | 0.254206 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 1.62222 | 0.468293 | ||||||||
\(13\) | 6.42864 | 1.78298 | 0.891492 | − | 0.453037i | \(-0.149659\pi\) | ||||
0.891492 | + | 0.453037i | \(0.149659\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.61285 | −1.15321 | ||||||||
\(17\) | −4.42864 | −1.07410 | −0.537051 | − | 0.843550i | \(-0.680462\pi\) | ||||
−0.537051 | + | 0.843550i | \(0.680462\pi\) | |||||||
\(18\) | −1.90321 | −0.448591 | ||||||||
\(19\) | 2.42864 | 0.557168 | 0.278584 | − | 0.960412i | \(-0.410135\pi\) | ||||
0.278584 | + | 0.960412i | \(0.410135\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.80642 | −0.811532 | ||||||||
\(23\) | 1.37778 | 0.287288 | 0.143644 | − | 0.989629i | \(-0.454118\pi\) | ||||
0.143644 | + | 0.989629i | \(0.454118\pi\) | |||||||
\(24\) | 0.719004 | 0.146766 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −12.2351 | −2.39949 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.755569 | 0.140306 | 0.0701528 | − | 0.997536i | \(-0.477651\pi\) | ||||
0.0701528 | + | 0.997536i | \(0.477651\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.18421 | −0.931111 | −0.465556 | − | 0.885019i | \(-0.654145\pi\) | ||||
−0.465556 | + | 0.885019i | \(0.654145\pi\) | |||||||
\(32\) | 7.34122 | 1.29776 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 8.42864 | 1.44550 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.62222 | 0.270369 | ||||||||
\(37\) | 7.61285 | 1.25154 | 0.625772 | − | 0.780006i | \(-0.284784\pi\) | ||||
0.625772 | + | 0.780006i | \(0.284784\pi\) | |||||||
\(38\) | −4.62222 | −0.749822 | ||||||||
\(39\) | 6.42864 | 1.02941 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.23506 | 1.28610 | 0.643050 | − | 0.765824i | \(-0.277669\pi\) | ||||
0.643050 | + | 0.765824i | \(0.277669\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.1017 | 1.54050 | 0.770248 | − | 0.637744i | \(-0.220132\pi\) | ||||
0.770248 | + | 0.637744i | \(0.220132\pi\) | |||||||
\(44\) | 3.24443 | 0.489116 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.62222 | −0.386625 | ||||||||
\(47\) | −2.75557 | −0.401941 | −0.200971 | − | 0.979597i | \(-0.564410\pi\) | ||||
−0.200971 | + | 0.979597i | \(0.564410\pi\) | |||||||
\(48\) | −4.61285 | −0.665807 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.42864 | −0.620134 | ||||||||
\(52\) | 10.4286 | 1.44619 | ||||||||
\(53\) | 9.18421 | 1.26155 | 0.630774 | − | 0.775967i | \(-0.282737\pi\) | ||||
0.630774 | + | 0.775967i | \(0.282737\pi\) | |||||||
\(54\) | −1.90321 | −0.258994 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.42864 | 0.321681 | ||||||||
\(58\) | −1.43801 | −0.188820 | ||||||||
\(59\) | −14.1017 | −1.83589 | −0.917943 | − | 0.396712i | \(-0.870151\pi\) | ||||
−0.917943 | + | 0.396712i | \(0.870151\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.85728 | −0.877985 | −0.438992 | − | 0.898491i | \(-0.644664\pi\) | ||||
−0.438992 | + | 0.898491i | \(0.644664\pi\) | |||||||
\(62\) | 9.86665 | 1.25307 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.74620 | −0.593275 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.80642 | −0.468538 | ||||||||
\(67\) | 2.75557 | 0.336646 | 0.168323 | − | 0.985732i | \(-0.446165\pi\) | ||||
0.168323 | + | 0.985732i | \(0.446165\pi\) | |||||||
\(68\) | −7.18421 | −0.871213 | ||||||||
\(69\) | 1.37778 | 0.165866 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 0.719004 | 0.0847354 | ||||||||
\(73\) | 1.57136 | 0.183914 | 0.0919569 | − | 0.995763i | \(-0.470688\pi\) | ||||
0.0919569 | + | 0.995763i | \(0.470688\pi\) | |||||||
\(74\) | −14.4889 | −1.68430 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.93978 | 0.451923 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −12.2351 | −1.38535 | ||||||||
\(79\) | −4.85728 | −0.546487 | −0.273243 | − | 0.961945i | \(-0.588096\pi\) | ||||
−0.273243 | + | 0.961945i | \(0.588096\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −15.6731 | −1.73080 | ||||||||
\(83\) | −11.6128 | −1.27468 | −0.637338 | − | 0.770585i | \(-0.719964\pi\) | ||||
−0.637338 | + | 0.770585i | \(0.719964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −19.2257 | −2.07316 | ||||||||
\(87\) | 0.755569 | 0.0810055 | ||||||||
\(88\) | 1.43801 | 0.153292 | ||||||||
\(89\) | −4.62222 | −0.489954 | −0.244977 | − | 0.969529i | \(-0.578780\pi\) | ||||
−0.244977 | + | 0.969529i | \(0.578780\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.23506 | 0.233021 | ||||||||
\(93\) | −5.18421 | −0.537577 | ||||||||
\(94\) | 5.24443 | 0.540922 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.34122 | 0.749260 | ||||||||
\(97\) | 11.9398 | 1.21230 | 0.606150 | − | 0.795350i | \(-0.292713\pi\) | ||||
0.606150 | + | 0.795350i | \(0.292713\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.47949 | −0.147215 | −0.0736076 | − | 0.997287i | \(-0.523451\pi\) | ||||
−0.0736076 | + | 0.997287i | \(0.523451\pi\) | |||||||
\(102\) | 8.42864 | 0.834560 | ||||||||
\(103\) | 8.85728 | 0.872734 | 0.436367 | − | 0.899769i | \(-0.356265\pi\) | ||||
0.436367 | + | 0.899769i | \(0.356265\pi\) | |||||||
\(104\) | 4.62222 | 0.453246 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.4795 | −1.69776 | ||||||||
\(107\) | 1.76494 | 0.170623 | 0.0853114 | − | 0.996354i | \(-0.472811\pi\) | ||||
0.0853114 | + | 0.996354i | \(0.472811\pi\) | |||||||
\(108\) | 1.62222 | 0.156098 | ||||||||
\(109\) | 5.61285 | 0.537613 | 0.268807 | − | 0.963194i | \(-0.413371\pi\) | ||||
0.268807 | + | 0.963194i | \(0.413371\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.61285 | 0.722580 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.2859 | −1.06169 | −0.530845 | − | 0.847469i | \(-0.678125\pi\) | ||||
−0.530845 | + | 0.847469i | \(0.678125\pi\) | |||||||
\(114\) | −4.62222 | −0.432910 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.22570 | 0.113803 | ||||||||
\(117\) | 6.42864 | 0.594328 | ||||||||
\(118\) | 26.8385 | 2.47069 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 13.0509 | 1.18157 | ||||||||
\(123\) | 8.23506 | 0.742531 | ||||||||
\(124\) | −8.40990 | −0.755232 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.8573 | −1.14090 | −0.570450 | − | 0.821333i | \(-0.693231\pi\) | ||||
−0.570450 | + | 0.821333i | \(0.693231\pi\) | |||||||
\(128\) | −5.64941 | −0.499342 | ||||||||
\(129\) | 10.1017 | 0.889406 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.10171 | 0.183627 | 0.0918136 | − | 0.995776i | \(-0.470734\pi\) | ||||
0.0918136 | + | 0.995776i | \(0.470734\pi\) | |||||||
\(132\) | 3.24443 | 0.282391 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.24443 | −0.453050 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.18421 | −0.273044 | ||||||||
\(137\) | 15.9398 | 1.36183 | 0.680914 | − | 0.732364i | \(-0.261583\pi\) | ||||
0.680914 | + | 0.732364i | \(0.261583\pi\) | |||||||
\(138\) | −2.62222 | −0.223218 | ||||||||
\(139\) | −11.6731 | −0.990097 | −0.495048 | − | 0.868865i | \(-0.664850\pi\) | ||||
−0.495048 | + | 0.868865i | \(0.664850\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.75557 | −0.232061 | ||||||||
\(142\) | −3.80642 | −0.319428 | ||||||||
\(143\) | 12.8573 | 1.07518 | ||||||||
\(144\) | −4.61285 | −0.384404 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.99063 | −0.247506 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 12.3497 | 1.01514 | ||||||||
\(149\) | −21.2257 | −1.73888 | −0.869438 | − | 0.494041i | \(-0.835519\pi\) | ||||
−0.869438 | + | 0.494041i | \(0.835519\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.8573 | 1.37183 | 0.685913 | − | 0.727684i | \(-0.259403\pi\) | ||||
0.685913 | + | 0.727684i | \(0.259403\pi\) | |||||||
\(152\) | 1.74620 | 0.141636 | ||||||||
\(153\) | −4.42864 | −0.358034 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.4286 | 0.834959 | ||||||||
\(157\) | 10.4286 | 0.832296 | 0.416148 | − | 0.909297i | \(-0.363380\pi\) | ||||
0.416148 | + | 0.909297i | \(0.363380\pi\) | |||||||
\(158\) | 9.24443 | 0.735447 | ||||||||
\(159\) | 9.18421 | 0.728355 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.90321 | −0.149530 | ||||||||
\(163\) | 20.8573 | 1.63367 | 0.816834 | − | 0.576873i | \(-0.195727\pi\) | ||||
0.816834 | + | 0.576873i | \(0.195727\pi\) | |||||||
\(164\) | 13.3590 | 1.04317 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 22.1017 | 1.71543 | ||||||||
\(167\) | −15.3461 | −1.18752 | −0.593760 | − | 0.804642i | \(-0.702357\pi\) | ||||
−0.593760 | + | 0.804642i | \(0.702357\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.3274 | 2.17903 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.42864 | 0.185723 | ||||||||
\(172\) | 16.3872 | 1.24951 | ||||||||
\(173\) | −2.06022 | −0.156636 | −0.0783179 | − | 0.996928i | \(-0.524955\pi\) | ||||
−0.0783179 | + | 0.996928i | \(0.524955\pi\) | |||||||
\(174\) | −1.43801 | −0.109015 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.22570 | −0.695413 | ||||||||
\(177\) | −14.1017 | −1.05995 | ||||||||
\(178\) | 8.79706 | 0.659367 | ||||||||
\(179\) | 10.0000 | 0.747435 | 0.373718 | − | 0.927543i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.1017 | 0.899513 | 0.449757 | − | 0.893151i | \(-0.351511\pi\) | ||||
0.449757 | + | 0.893151i | \(0.351511\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.85728 | −0.506905 | ||||||||
\(184\) | 0.990632 | 0.0730304 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.86665 | 0.723458 | ||||||||
\(187\) | −8.85728 | −0.647708 | ||||||||
\(188\) | −4.47013 | −0.326017 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.488863 | 0.0353729 | 0.0176864 | − | 0.999844i | \(-0.494370\pi\) | ||||
0.0176864 | + | 0.999844i | \(0.494370\pi\) | |||||||
\(192\) | −4.74620 | −0.342528 | ||||||||
\(193\) | −22.9590 | −1.65262 | −0.826312 | − | 0.563212i | \(-0.809565\pi\) | ||||
−0.826312 | + | 0.563212i | \(0.809565\pi\) | |||||||
\(194\) | −22.7239 | −1.63148 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.18421 | −0.0843713 | −0.0421857 | − | 0.999110i | \(-0.513432\pi\) | ||||
−0.0421857 | + | 0.999110i | \(0.513432\pi\) | |||||||
\(198\) | −3.80642 | −0.270511 | ||||||||
\(199\) | −8.79706 | −0.623607 | −0.311803 | − | 0.950147i | \(-0.600933\pi\) | ||||
−0.311803 | + | 0.950147i | \(0.600933\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.75557 | 0.194363 | ||||||||
\(202\) | 2.81579 | 0.198118 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.18421 | −0.502995 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −16.8573 | −1.17450 | ||||||||
\(207\) | 1.37778 | 0.0957626 | ||||||||
\(208\) | −29.6543 | −2.05616 | ||||||||
\(209\) | 4.85728 | 0.335985 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.2257 | 1.59892 | 0.799461 | − | 0.600717i | \(-0.205118\pi\) | ||||
0.799461 | + | 0.600717i | \(0.205118\pi\) | |||||||
\(212\) | 14.8988 | 1.02325 | ||||||||
\(213\) | 2.00000 | 0.137038 | ||||||||
\(214\) | −3.35905 | −0.229620 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.719004 | 0.0489220 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.6824 | −0.723506 | ||||||||
\(219\) | 1.57136 | 0.106183 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.4701 | −1.91511 | ||||||||
\(222\) | −14.4889 | −0.972429 | ||||||||
\(223\) | 15.2257 | 1.01959 | 0.509794 | − | 0.860297i | \(-0.329722\pi\) | ||||
0.509794 | + | 0.860297i | \(0.329722\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.4795 | 1.42879 | ||||||||
\(227\) | 14.3684 | 0.953665 | 0.476833 | − | 0.878994i | \(-0.341785\pi\) | ||||
0.476833 | + | 0.878994i | \(0.341785\pi\) | |||||||
\(228\) | 3.93978 | 0.260918 | ||||||||
\(229\) | 5.61285 | 0.370907 | 0.185454 | − | 0.982653i | \(-0.440625\pi\) | ||||
0.185454 | + | 0.982653i | \(0.440625\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.543257 | 0.0356666 | ||||||||
\(233\) | 23.2859 | 1.52551 | 0.762756 | − | 0.646687i | \(-0.223846\pi\) | ||||
0.762756 | + | 0.646687i | \(0.223846\pi\) | |||||||
\(234\) | −12.2351 | −0.799831 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −22.8760 | −1.48910 | ||||||||
\(237\) | −4.85728 | −0.315514 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.48886 | −0.549099 | −0.274549 | − | 0.961573i | \(-0.588529\pi\) | ||||
−0.274549 | + | 0.961573i | \(0.588529\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.24443 | 0.466655 | 0.233327 | − | 0.972398i | \(-0.425039\pi\) | ||||
0.233327 | + | 0.972398i | \(0.425039\pi\) | |||||||
\(242\) | 13.3225 | 0.856402 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −11.1240 | −0.712140 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.6731 | −0.999278 | ||||||||
\(247\) | 15.6128 | 0.993422 | ||||||||
\(248\) | −3.72746 | −0.236694 | ||||||||
\(249\) | −11.6128 | −0.735934 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.6128 | −1.74291 | −0.871454 | − | 0.490478i | \(-0.836822\pi\) | ||||
−0.871454 | + | 0.490478i | \(0.836822\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.75557 | 0.173241 | ||||||||
\(254\) | 24.4701 | 1.53539 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.2444 | 1.26528 | ||||||||
\(257\) | 0.428639 | 0.0267378 | 0.0133689 | − | 0.999911i | \(-0.495744\pi\) | ||||
0.0133689 | + | 0.999911i | \(0.495744\pi\) | |||||||
\(258\) | −19.2257 | −1.19694 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.755569 | 0.0467685 | ||||||||
\(262\) | −4.00000 | −0.247121 | ||||||||
\(263\) | −9.37778 | −0.578259 | −0.289129 | − | 0.957290i | \(-0.593366\pi\) | ||||
−0.289129 | + | 0.957290i | \(0.593366\pi\) | |||||||
\(264\) | 1.43801 | 0.0885032 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.62222 | −0.282875 | ||||||||
\(268\) | 4.47013 | 0.273056 | ||||||||
\(269\) | −1.74620 | −0.106468 | −0.0532339 | − | 0.998582i | \(-0.516953\pi\) | ||||
−0.0532339 | + | 0.998582i | \(0.516953\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.69535 | 0.163731 | 0.0818653 | − | 0.996643i | \(-0.473912\pi\) | ||||
0.0818653 | + | 0.996643i | \(0.473912\pi\) | |||||||
\(272\) | 20.4286 | 1.23867 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −30.3368 | −1.83271 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.23506 | 0.134535 | ||||||||
\(277\) | −5.12399 | −0.307870 | −0.153935 | − | 0.988081i | \(-0.549195\pi\) | ||||
−0.153935 | + | 0.988081i | \(0.549195\pi\) | |||||||
\(278\) | 22.2163 | 1.33245 | ||||||||
\(279\) | −5.18421 | −0.310370 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.9813 | 1.43060 | 0.715301 | − | 0.698816i | \(-0.246290\pi\) | ||||
0.715301 | + | 0.698816i | \(0.246290\pi\) | |||||||
\(282\) | 5.24443 | 0.312301 | ||||||||
\(283\) | −2.36842 | −0.140788 | −0.0703939 | − | 0.997519i | \(-0.522426\pi\) | ||||
−0.0703939 | + | 0.997519i | \(0.522426\pi\) | |||||||
\(284\) | 3.24443 | 0.192522 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24.4701 | −1.44695 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 7.34122 | 0.432585 | ||||||||
\(289\) | 2.61285 | 0.153697 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.9398 | 0.699922 | ||||||||
\(292\) | 2.54909 | 0.149174 | ||||||||
\(293\) | −8.42864 | −0.492406 | −0.246203 | − | 0.969218i | \(-0.579183\pi\) | ||||
−0.246203 | + | 0.969218i | \(0.579183\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.47367 | 0.318150 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | 40.3970 | 2.34014 | ||||||||
\(299\) | 8.85728 | 0.512230 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −32.0830 | −1.84617 | ||||||||
\(303\) | −1.47949 | −0.0849947 | ||||||||
\(304\) | −11.2029 | −0.642533 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 8.42864 | 0.481833 | ||||||||
\(307\) | 22.5718 | 1.28824 | 0.644121 | − | 0.764923i | \(-0.277223\pi\) | ||||
0.644121 | + | 0.764923i | \(0.277223\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.85728 | 0.503873 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.0830 | 1.36562 | 0.682810 | − | 0.730596i | \(-0.260758\pi\) | ||||
0.682810 | + | 0.730596i | \(0.260758\pi\) | |||||||
\(312\) | 4.62222 | 0.261681 | ||||||||
\(313\) | −9.65433 | −0.545695 | −0.272848 | − | 0.962057i | \(-0.587965\pi\) | ||||
−0.272848 | + | 0.962057i | \(0.587965\pi\) | |||||||
\(314\) | −19.8479 | −1.12008 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.87955 | −0.443260 | ||||||||
\(317\) | −6.04149 | −0.339324 | −0.169662 | − | 0.985502i | \(-0.554268\pi\) | ||||
−0.169662 | + | 0.985502i | \(0.554268\pi\) | |||||||
\(318\) | −17.4795 | −0.980201 | ||||||||
\(319\) | 1.51114 | 0.0846075 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.76494 | 0.0985092 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.7556 | −0.598456 | ||||||||
\(324\) | 1.62222 | 0.0901231 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −39.6958 | −2.19855 | ||||||||
\(327\) | 5.61285 | 0.310391 | ||||||||
\(328\) | 5.92104 | 0.326935 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.5111 | 0.742639 | 0.371320 | − | 0.928505i | \(-0.378905\pi\) | ||||
0.371320 | + | 0.928505i | \(0.378905\pi\) | |||||||
\(332\) | −18.8385 | −1.03390 | ||||||||
\(333\) | 7.61285 | 0.417181 | ||||||||
\(334\) | 29.2070 | 1.59813 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.4889 | 0.571365 | 0.285682 | − | 0.958324i | \(-0.407780\pi\) | ||||
0.285682 | + | 0.958324i | \(0.407780\pi\) | |||||||
\(338\) | −53.9131 | −2.93248 | ||||||||
\(339\) | −11.2859 | −0.612967 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.3684 | −0.561481 | ||||||||
\(342\) | −4.62222 | −0.249941 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.26317 | 0.391604 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.92104 | 0.210796 | ||||||||
\(347\) | −16.7239 | −0.897787 | −0.448894 | − | 0.893585i | \(-0.648182\pi\) | ||||
−0.448894 | + | 0.893585i | \(0.648182\pi\) | |||||||
\(348\) | 1.22570 | 0.0657042 | ||||||||
\(349\) | 16.3684 | 0.876181 | 0.438091 | − | 0.898931i | \(-0.355655\pi\) | ||||
0.438091 | + | 0.898931i | \(0.355655\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.42864 | 0.343135 | ||||||||
\(352\) | 14.6824 | 0.782577 | ||||||||
\(353\) | −0.549086 | −0.0292249 | −0.0146124 | − | 0.999893i | \(-0.504651\pi\) | ||||
−0.0146124 | + | 0.999893i | \(0.504651\pi\) | |||||||
\(354\) | 26.8385 | 1.42645 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.49823 | −0.397405 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −19.0321 | −1.00588 | ||||||||
\(359\) | −0.285442 | −0.0150651 | −0.00753253 | − | 0.999972i | \(-0.502398\pi\) | ||||
−0.00753253 | + | 0.999972i | \(0.502398\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1017 | −0.689564 | ||||||||
\(362\) | −23.0321 | −1.21054 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 13.0509 | 0.682179 | ||||||||
\(367\) | −1.71456 | −0.0894992 | −0.0447496 | − | 0.998998i | \(-0.514249\pi\) | ||||
−0.0447496 | + | 0.998998i | \(0.514249\pi\) | |||||||
\(368\) | −6.35551 | −0.331304 | ||||||||
\(369\) | 8.23506 | 0.428700 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.40990 | −0.436033 | ||||||||
\(373\) | 16.0000 | 0.828449 | 0.414224 | − | 0.910175i | \(-0.364053\pi\) | ||||
0.414224 | + | 0.910175i | \(0.364053\pi\) | |||||||
\(374\) | 16.8573 | 0.871669 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.98126 | −0.102176 | ||||||||
\(377\) | 4.85728 | 0.250163 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.85728 | −0.249502 | −0.124751 | − | 0.992188i | \(-0.539813\pi\) | ||||
−0.124751 | + | 0.992188i | \(0.539813\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.8573 | −0.658698 | ||||||||
\(382\) | −0.930409 | −0.0476039 | ||||||||
\(383\) | 8.38715 | 0.428563 | 0.214282 | − | 0.976772i | \(-0.431259\pi\) | ||||
0.214282 | + | 0.976772i | \(0.431259\pi\) | |||||||
\(384\) | −5.64941 | −0.288295 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 43.6958 | 2.22406 | ||||||||
\(387\) | 10.1017 | 0.513499 | ||||||||
\(388\) | 19.3689 | 0.983307 | ||||||||
\(389\) | 8.95899 | 0.454239 | 0.227119 | − | 0.973867i | \(-0.427069\pi\) | ||||
0.227119 | + | 0.973867i | \(0.427069\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.10171 | −0.308577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.10171 | 0.106017 | ||||||||
\(394\) | 2.25380 | 0.113545 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.24443 | 0.163039 | ||||||||
\(397\) | 2.54909 | 0.127935 | 0.0639675 | − | 0.997952i | \(-0.479625\pi\) | ||||
0.0639675 | + | 0.997952i | \(0.479625\pi\) | |||||||
\(398\) | 16.7427 | 0.839234 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.958989 | 0.0478896 | 0.0239448 | − | 0.999713i | \(-0.492377\pi\) | ||||
0.0239448 | + | 0.999713i | \(0.492377\pi\) | |||||||
\(402\) | −5.24443 | −0.261568 | ||||||||
\(403\) | −33.3274 | −1.66016 | ||||||||
\(404\) | −2.40006 | −0.119407 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.2257 | 0.754710 | ||||||||
\(408\) | −3.18421 | −0.157642 | ||||||||
\(409\) | 31.9813 | 1.58137 | 0.790686 | − | 0.612222i | \(-0.209724\pi\) | ||||
0.790686 | + | 0.612222i | \(0.209724\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.9398 | 0.786251 | ||||||||
\(412\) | 14.3684 | 0.707881 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.62222 | −0.128875 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 47.1941 | 2.31388 | ||||||||
\(417\) | −11.6731 | −0.571633 | ||||||||
\(418\) | −9.24443 | −0.452160 | ||||||||
\(419\) | 0.470127 | 0.0229672 | 0.0114836 | − | 0.999934i | \(-0.496345\pi\) | ||||
0.0114836 | + | 0.999934i | \(0.496345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.6128 | −1.63819 | −0.819095 | − | 0.573658i | \(-0.805524\pi\) | ||||
−0.819095 | + | 0.573658i | \(0.805524\pi\) | |||||||
\(422\) | −44.2034 | −2.15179 | ||||||||
\(423\) | −2.75557 | −0.133980 | ||||||||
\(424\) | 6.60348 | 0.320693 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.80642 | −0.184422 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.86311 | 0.138394 | ||||||||
\(429\) | 12.8573 | 0.620755 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.7146 | 0.564270 | 0.282135 | − | 0.959375i | \(-0.408957\pi\) | ||||
0.282135 | + | 0.959375i | \(0.408957\pi\) | |||||||
\(432\) | −4.61285 | −0.221936 | ||||||||
\(433\) | 0.0602231 | 0.00289414 | 0.00144707 | − | 0.999999i | \(-0.499539\pi\) | ||||
0.00144707 | + | 0.999999i | \(0.499539\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.10525 | 0.436062 | ||||||||
\(437\) | 3.34614 | 0.160068 | ||||||||
\(438\) | −2.99063 | −0.142898 | ||||||||
\(439\) | 22.4286 | 1.07046 | 0.535230 | − | 0.844706i | \(-0.320225\pi\) | ||||
0.535230 | + | 0.844706i | \(0.320225\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 54.1847 | 2.57730 | ||||||||
\(443\) | −23.9496 | −1.13788 | −0.568940 | − | 0.822379i | \(-0.692647\pi\) | ||||
−0.568940 | + | 0.822379i | \(0.692647\pi\) | |||||||
\(444\) | 12.3497 | 0.586090 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −28.9777 | −1.37214 | ||||||||
\(447\) | −21.2257 | −1.00394 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.4291 | 1.38885 | 0.694423 | − | 0.719567i | \(-0.255660\pi\) | ||||
0.694423 | + | 0.719567i | \(0.255660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.4701 | 0.775548 | ||||||||
\(452\) | −18.3082 | −0.861145 | ||||||||
\(453\) | 16.8573 | 0.792024 | ||||||||
\(454\) | −27.3461 | −1.28342 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.74620 | 0.0817733 | ||||||||
\(457\) | −3.14272 | −0.147010 | −0.0735051 | − | 0.997295i | \(-0.523419\pi\) | ||||
−0.0735051 | + | 0.997295i | \(0.523419\pi\) | |||||||
\(458\) | −10.6824 | −0.499158 | ||||||||
\(459\) | −4.42864 | −0.206711 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.37778 | 0.157319 | 0.0786596 | − | 0.996902i | \(-0.474936\pi\) | ||||
0.0786596 | + | 0.996902i | \(0.474936\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.8573 | 0.969320 | 0.484660 | − | 0.874703i | \(-0.338943\pi\) | ||||
0.484660 | + | 0.874703i | \(0.338943\pi\) | |||||||
\(464\) | −3.48532 | −0.161802 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −44.3180 | −2.05299 | ||||||||
\(467\) | 14.3684 | 0.664891 | 0.332446 | − | 0.943122i | \(-0.392126\pi\) | ||||
0.332446 | + | 0.943122i | \(0.392126\pi\) | |||||||
\(468\) | 10.4286 | 0.482064 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.4286 | 0.480526 | ||||||||
\(472\) | −10.1392 | −0.466694 | ||||||||
\(473\) | 20.2034 | 0.928954 | ||||||||
\(474\) | 9.24443 | 0.424611 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.18421 | 0.420516 | ||||||||
\(478\) | 16.1561 | 0.738963 | ||||||||
\(479\) | −6.36842 | −0.290980 | −0.145490 | − | 0.989360i | \(-0.546476\pi\) | ||||
−0.145490 | + | 0.989360i | \(0.546476\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 48.9403 | 2.23148 | ||||||||
\(482\) | −13.7877 | −0.628012 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.3555 | −0.516160 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.90321 | −0.0863314 | ||||||||
\(487\) | 17.3274 | 0.785180 | 0.392590 | − | 0.919714i | \(-0.371579\pi\) | ||||
0.392590 | + | 0.919714i | \(0.371579\pi\) | |||||||
\(488\) | −4.93041 | −0.223189 | ||||||||
\(489\) | 20.8573 | 0.943199 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.00000 | 0.0902587 | 0.0451294 | − | 0.998981i | \(-0.485630\pi\) | ||||
0.0451294 | + | 0.998981i | \(0.485630\pi\) | |||||||
\(492\) | 13.3590 | 0.602272 | ||||||||
\(493\) | −3.34614 | −0.150703 | ||||||||
\(494\) | −29.7146 | −1.33692 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.9140 | 1.07377 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 22.1017 | 0.990401 | ||||||||
\(499\) | 23.3461 | 1.04512 | 0.522558 | − | 0.852603i | \(-0.324978\pi\) | ||||
0.522558 | + | 0.852603i | \(0.324978\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.3461 | −0.685615 | ||||||||
\(502\) | 52.5531 | 2.34556 | ||||||||
\(503\) | −0.387152 | −0.0172623 | −0.00863113 | − | 0.999963i | \(-0.502747\pi\) | ||||
−0.00863113 | + | 0.999963i | \(0.502747\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.24443 | −0.233143 | ||||||||
\(507\) | 28.3274 | 1.25806 | ||||||||
\(508\) | −20.8573 | −0.925392 | ||||||||
\(509\) | 29.9496 | 1.32749 | 0.663747 | − | 0.747957i | \(-0.268965\pi\) | ||||
0.663747 | + | 0.747957i | \(0.268965\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −27.2306 | −1.20343 | ||||||||
\(513\) | 2.42864 | 0.107227 | ||||||||
\(514\) | −0.815792 | −0.0359830 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 16.3872 | 0.721404 | ||||||||
\(517\) | −5.51114 | −0.242380 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.06022 | −0.0904338 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.5205 | 0.811398 | 0.405699 | − | 0.914007i | \(-0.367028\pi\) | ||||
0.405699 | + | 0.914007i | \(0.367028\pi\) | |||||||
\(522\) | −1.43801 | −0.0629399 | ||||||||
\(523\) | 4.00000 | 0.174908 | 0.0874539 | − | 0.996169i | \(-0.472127\pi\) | ||||
0.0874539 | + | 0.996169i | \(0.472127\pi\) | |||||||
\(524\) | 3.40943 | 0.148942 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.8479 | 0.778206 | ||||||||
\(527\) | 22.9590 | 1.00011 | ||||||||
\(528\) | −9.22570 | −0.401497 | ||||||||
\(529\) | −21.1017 | −0.917466 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.1017 | −0.611962 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 52.9403 | 2.29310 | ||||||||
\(534\) | 8.79706 | 0.380686 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.98126 | 0.0855776 | ||||||||
\(537\) | 10.0000 | 0.431532 | ||||||||
\(538\) | 3.32339 | 0.143282 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.5906 | 0.627298 | 0.313649 | − | 0.949539i | \(-0.398449\pi\) | ||||
0.313649 | + | 0.949539i | \(0.398449\pi\) | |||||||
\(542\) | −5.12981 | −0.220344 | ||||||||
\(543\) | 12.1017 | 0.519334 | ||||||||
\(544\) | −32.5116 | −1.39392 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.7556 | −0.801930 | −0.400965 | − | 0.916093i | \(-0.631325\pi\) | ||||
−0.400965 | + | 0.916093i | \(0.631325\pi\) | |||||||
\(548\) | 25.8578 | 1.10459 | ||||||||
\(549\) | −6.85728 | −0.292662 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.83500 | 0.0781738 | ||||||||
\(552\) | 0.990632 | 0.0421641 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.75203 | 0.414324 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.9362 | −0.803075 | ||||||||
\(557\) | 31.8765 | 1.35065 | 0.675325 | − | 0.737520i | \(-0.264003\pi\) | ||||
0.675325 | + | 0.737520i | \(0.264003\pi\) | |||||||
\(558\) | 9.86665 | 0.417688 | ||||||||
\(559\) | 64.9403 | 2.74668 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.85728 | −0.373955 | ||||||||
\(562\) | −45.6414 | −1.92527 | ||||||||
\(563\) | 2.01874 | 0.0850796 | 0.0425398 | − | 0.999095i | \(-0.486455\pi\) | ||||
0.0425398 | + | 0.999095i | \(0.486455\pi\) | |||||||
\(564\) | −4.47013 | −0.188226 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.50760 | 0.189468 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.43801 | 0.0603375 | ||||||||
\(569\) | −28.9590 | −1.21402 | −0.607012 | − | 0.794693i | \(-0.707632\pi\) | ||||
−0.607012 | + | 0.794693i | \(0.707632\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.97773 | 0.375706 | 0.187853 | − | 0.982197i | \(-0.439847\pi\) | ||||
0.187853 | + | 0.982197i | \(0.439847\pi\) | |||||||
\(572\) | 20.8573 | 0.872087 | ||||||||
\(573\) | 0.488863 | 0.0204225 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.74620 | −0.197758 | ||||||||
\(577\) | −28.6766 | −1.19382 | −0.596911 | − | 0.802307i | \(-0.703606\pi\) | ||||
−0.596911 | + | 0.802307i | \(0.703606\pi\) | |||||||
\(578\) | −4.97280 | −0.206841 | ||||||||
\(579\) | −22.9590 | −0.954143 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −22.7239 | −0.941937 | ||||||||
\(583\) | 18.3684 | 0.760742 | ||||||||
\(584\) | 1.12981 | 0.0467520 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.0415 | 0.662668 | ||||||||
\(587\) | −45.2070 | −1.86589 | −0.932945 | − | 0.360018i | \(-0.882771\pi\) | ||||
−0.932945 | + | 0.360018i | \(0.882771\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.5906 | −0.518786 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.18421 | −0.0487118 | ||||||||
\(592\) | −35.1169 | −1.44330 | ||||||||
\(593\) | 18.2636 | 0.749998 | 0.374999 | − | 0.927025i | \(-0.377643\pi\) | ||||
0.374999 | + | 0.927025i | \(0.377643\pi\) | |||||||
\(594\) | −3.80642 | −0.156179 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −34.4327 | −1.41042 | ||||||||
\(597\) | −8.79706 | −0.360040 | ||||||||
\(598\) | −16.8573 | −0.689345 | ||||||||
\(599\) | −22.7368 | −0.929002 | −0.464501 | − | 0.885573i | \(-0.653766\pi\) | ||||
−0.464501 | + | 0.885573i | \(0.653766\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.488863 | −0.0199411 | −0.00997056 | − | 0.999950i | \(-0.503174\pi\) | ||||
−0.00997056 | + | 0.999950i | \(0.503174\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.75557 | 0.112215 | ||||||||
\(604\) | 27.3461 | 1.11270 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.81579 | 0.114384 | ||||||||
\(607\) | −20.2034 | −0.820032 | −0.410016 | − | 0.912078i | \(-0.634477\pi\) | ||||
−0.410016 | + | 0.912078i | \(0.634477\pi\) | |||||||
\(608\) | 17.8292 | 0.723069 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.7146 | −0.716654 | ||||||||
\(612\) | −7.18421 | −0.290404 | ||||||||
\(613\) | −10.3684 | −0.418776 | −0.209388 | − | 0.977833i | \(-0.567147\pi\) | ||||
−0.209388 | + | 0.977833i | \(0.567147\pi\) | |||||||
\(614\) | −42.9590 | −1.73368 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.2859 | 1.58159 | 0.790796 | − | 0.612080i | \(-0.209667\pi\) | ||||
0.790796 | + | 0.612080i | \(0.209667\pi\) | |||||||
\(618\) | −16.8573 | −0.678099 | ||||||||
\(619\) | −42.8988 | −1.72425 | −0.862123 | − | 0.506698i | \(-0.830866\pi\) | ||||
−0.862123 | + | 0.506698i | \(0.830866\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.37778 | 0.0552886 | ||||||||
\(622\) | −45.8350 | −1.83782 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −29.6543 | −1.18712 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 18.3742 | 0.734383 | ||||||||
\(627\) | 4.85728 | 0.193981 | ||||||||
\(628\) | 16.9175 | 0.675082 | ||||||||
\(629\) | −33.7146 | −1.34429 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.3461 | 0.610920 | 0.305460 | − | 0.952205i | \(-0.401190\pi\) | ||||
0.305460 | + | 0.952205i | \(0.401190\pi\) | |||||||
\(632\) | −3.49240 | −0.138920 | ||||||||
\(633\) | 23.2257 | 0.923139 | ||||||||
\(634\) | 11.4982 | 0.456653 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14.8988 | 0.590775 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.87601 | −0.113863 | ||||||||
\(639\) | 2.00000 | 0.0791188 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.6735 | 1.21153 | 0.605766 | − | 0.795643i | \(-0.292867\pi\) | ||||
0.605766 | + | 0.795643i | \(0.292867\pi\) | |||||||
\(642\) | −3.35905 | −0.132571 | ||||||||
\(643\) | −49.0607 | −1.93477 | −0.967383 | − | 0.253320i | \(-0.918477\pi\) | ||||
−0.967383 | + | 0.253320i | \(0.918477\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.4701 | 0.805386 | ||||||||
\(647\) | −15.3461 | −0.603319 | −0.301660 | − | 0.953416i | \(-0.597541\pi\) | ||||
−0.301660 | + | 0.953416i | \(0.597541\pi\) | |||||||
\(648\) | 0.719004 | 0.0282451 | ||||||||
\(649\) | −28.2034 | −1.10708 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 33.8350 | 1.32508 | ||||||||
\(653\) | 19.4697 | 0.761906 | 0.380953 | − | 0.924594i | \(-0.375596\pi\) | ||||
0.380953 | + | 0.924594i | \(0.375596\pi\) | |||||||
\(654\) | −10.6824 | −0.417716 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −37.9871 | −1.48315 | ||||||||
\(657\) | 1.57136 | 0.0613046 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.9403 | 1.20526 | 0.602631 | − | 0.798020i | \(-0.294119\pi\) | ||||
0.602631 | + | 0.798020i | \(0.294119\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −47.7975 | −1.85911 | −0.929554 | − | 0.368685i | \(-0.879808\pi\) | ||||
−0.929554 | + | 0.368685i | \(0.879808\pi\) | |||||||
\(662\) | −25.7146 | −0.999425 | ||||||||
\(663\) | −28.4701 | −1.10569 | ||||||||
\(664\) | −8.34968 | −0.324030 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.4889 | −0.561432 | ||||||||
\(667\) | 1.04101 | 0.0403081 | ||||||||
\(668\) | −24.8948 | −0.963207 | ||||||||
\(669\) | 15.2257 | 0.588659 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.7146 | −0.529445 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.8163 | −1.07224 | −0.536119 | − | 0.844142i | \(-0.680110\pi\) | ||||
−0.536119 | + | 0.844142i | \(0.680110\pi\) | |||||||
\(674\) | −19.9625 | −0.768928 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 45.9532 | 1.76743 | ||||||||
\(677\) | −19.0005 | −0.730248 | −0.365124 | − | 0.930959i | \(-0.618973\pi\) | ||||
−0.365124 | + | 0.930959i | \(0.618973\pi\) | |||||||
\(678\) | 21.4795 | 0.824915 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.3684 | 0.550599 | ||||||||
\(682\) | 19.7333 | 0.755627 | ||||||||
\(683\) | −4.52051 | −0.172972 | −0.0864862 | − | 0.996253i | \(-0.527564\pi\) | ||||
−0.0864862 | + | 0.996253i | \(0.527564\pi\) | |||||||
\(684\) | 3.93978 | 0.150641 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.61285 | 0.214143 | ||||||||
\(688\) | −46.5977 | −1.77652 | ||||||||
\(689\) | 59.0420 | 2.24932 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.18421 | 0.0450494 | 0.0225247 | − | 0.999746i | \(-0.492830\pi\) | ||||
0.0225247 | + | 0.999746i | \(0.492830\pi\) | |||||||
\(692\) | −3.34213 | −0.127049 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31.8292 | 1.20822 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.543257 | 0.0205921 | ||||||||
\(697\) | −36.4701 | −1.38140 | ||||||||
\(698\) | −31.1526 | −1.17914 | ||||||||
\(699\) | 23.2859 | 0.880754 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.6735 | −1.00745 | −0.503723 | − | 0.863865i | \(-0.668037\pi\) | ||||
−0.503723 | + | 0.863865i | \(0.668037\pi\) | |||||||
\(702\) | −12.2351 | −0.461783 | ||||||||
\(703\) | 18.4889 | 0.697321 | ||||||||
\(704\) | −9.49240 | −0.357758 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.04503 | 0.0393301 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −22.8760 | −0.859733 | ||||||||
\(709\) | −18.2034 | −0.683644 | −0.341822 | − | 0.939765i | \(-0.611044\pi\) | ||||
−0.341822 | + | 0.939765i | \(0.611044\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.85728 | −0.182162 | ||||||||
\(712\) | −3.32339 | −0.124549 | ||||||||
\(713\) | −7.14272 | −0.267497 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.2222 | 0.606250 | ||||||||
\(717\) | −8.48886 | −0.317022 | ||||||||
\(718\) | 0.543257 | 0.0202742 | ||||||||
\(719\) | −4.85728 | −0.181146 | −0.0905730 | − | 0.995890i | \(-0.528870\pi\) | ||||
−0.0905730 | + | 0.995890i | \(0.528870\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 24.9353 | 0.927997 | ||||||||
\(723\) | 7.24443 | 0.269423 | ||||||||
\(724\) | 19.6316 | 0.729602 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13.3225 | 0.494444 | ||||||||
\(727\) | 21.0607 | 0.781098 | 0.390549 | − | 0.920582i | \(-0.372285\pi\) | ||||
0.390549 | + | 0.920582i | \(0.372285\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −44.7368 | −1.65465 | ||||||||
\(732\) | −11.1240 | −0.411154 | ||||||||
\(733\) | 9.45091 | 0.349077 | 0.174539 | − | 0.984650i | \(-0.444157\pi\) | ||||
0.174539 | + | 0.984650i | \(0.444157\pi\) | |||||||
\(734\) | 3.26317 | 0.120446 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.1146 | 0.372830 | ||||||||
\(737\) | 5.51114 | 0.203005 | ||||||||
\(738\) | −15.6731 | −0.576934 | ||||||||
\(739\) | −8.20342 | −0.301768 | −0.150884 | − | 0.988551i | \(-0.548212\pi\) | ||||
−0.150884 | + | 0.988551i | \(0.548212\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.6128 | 0.573552 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.33677 | −0.305847 | −0.152923 | − | 0.988238i | \(-0.548869\pi\) | ||||
−0.152923 | + | 0.988238i | \(0.548869\pi\) | |||||||
\(744\) | −3.72746 | −0.136655 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −30.4514 | −1.11490 | ||||||||
\(747\) | −11.6128 | −0.424892 | ||||||||
\(748\) | −14.3684 | −0.525361 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.9180 | −0.945760 | −0.472880 | − | 0.881127i | \(-0.656786\pi\) | ||||
−0.472880 | + | 0.881127i | \(0.656786\pi\) | |||||||
\(752\) | 12.7110 | 0.463523 | ||||||||
\(753\) | −27.6128 | −1.00627 | ||||||||
\(754\) | −9.24443 | −0.336662 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.94025 | −0.324939 | −0.162470 | − | 0.986714i | \(-0.551946\pi\) | ||||
−0.162470 | + | 0.986714i | \(0.551946\pi\) | |||||||
\(758\) | 9.24443 | 0.335773 | ||||||||
\(759\) | 2.75557 | 0.100021 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.825636 | 0.0299293 | 0.0149646 | − | 0.999888i | \(-0.495236\pi\) | ||||
0.0149646 | + | 0.999888i | \(0.495236\pi\) | |||||||
\(762\) | 24.4701 | 0.886459 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.793040 | 0.0286912 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.9625 | −0.576750 | ||||||||
\(767\) | −90.6548 | −3.27336 | ||||||||
\(768\) | 20.2444 | 0.730508 | ||||||||
\(769\) | −21.2257 | −0.765418 | −0.382709 | − | 0.923869i | \(-0.625009\pi\) | ||||
−0.382709 | + | 0.923869i | \(0.625009\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.428639 | 0.0154371 | ||||||||
\(772\) | −37.2444 | −1.34046 | ||||||||
\(773\) | 29.4893 | 1.06066 | 0.530329 | − | 0.847792i | \(-0.322068\pi\) | ||||
0.530329 | + | 0.847792i | \(0.322068\pi\) | |||||||
\(774\) | −19.2257 | −0.691053 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.58474 | 0.308174 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17.0509 | −0.611303 | ||||||||
\(779\) | 20.0000 | 0.716574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | 11.6128 | 0.415275 | ||||||||
\(783\) | 0.755569 | 0.0270018 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.00000 | −0.142675 | ||||||||
\(787\) | −34.4514 | −1.22806 | −0.614030 | − | 0.789283i | \(-0.710453\pi\) | ||||
−0.614030 | + | 0.789283i | \(0.710453\pi\) | |||||||
\(788\) | −1.92104 | −0.0684343 | ||||||||
\(789\) | −9.37778 | −0.333858 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.43801 | 0.0510974 | ||||||||
\(793\) | −44.0830 | −1.56543 | ||||||||
\(794\) | −4.85145 | −0.172172 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.2707 | −0.505812 | ||||||||
\(797\) | 18.9175 | 0.670092 | 0.335046 | − | 0.942202i | \(-0.391248\pi\) | ||||
0.335046 | + | 0.942202i | \(0.391248\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.2034 | 0.431726 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.62222 | −0.163318 | ||||||||
\(802\) | −1.82516 | −0.0644486 | ||||||||
\(803\) | 3.14272 | 0.110904 | ||||||||
\(804\) | 4.47013 | 0.157649 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 63.4291 | 2.23420 | ||||||||
\(807\) | −1.74620 | −0.0614692 | ||||||||
\(808\) | −1.06376 | −0.0374230 | ||||||||
\(809\) | 21.2257 | 0.746256 | 0.373128 | − | 0.927780i | \(-0.378285\pi\) | ||||
0.373128 | + | 0.927780i | \(0.378285\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.5081 | 0.755251 | 0.377625 | − | 0.925958i | \(-0.376741\pi\) | ||||
0.377625 | + | 0.925958i | \(0.376741\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.69535 | 0.0945299 | ||||||||
\(814\) | −28.9777 | −1.01567 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 20.4286 | 0.715145 | ||||||||
\(817\) | 24.5334 | 0.858315 | ||||||||
\(818\) | −60.8671 | −2.12817 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −46.2034 | −1.61251 | −0.806255 | − | 0.591568i | \(-0.798509\pi\) | ||||
−0.806255 | + | 0.591568i | \(0.798509\pi\) | |||||||
\(822\) | −30.3368 | −1.05812 | ||||||||
\(823\) | 17.8350 | 0.621689 | 0.310845 | − | 0.950461i | \(-0.399388\pi\) | ||||
0.310845 | + | 0.950461i | \(0.399388\pi\) | |||||||
\(824\) | 6.36842 | 0.221854 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.2128 | −1.22447 | −0.612234 | − | 0.790676i | \(-0.709729\pi\) | ||||
−0.612234 | + | 0.790676i | \(0.709729\pi\) | |||||||
\(828\) | 2.23506 | 0.0776738 | ||||||||
\(829\) | −14.3872 | −0.499686 | −0.249843 | − | 0.968286i | \(-0.580379\pi\) | ||||
−0.249843 | + | 0.968286i | \(0.580379\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.12399 | −0.177749 | ||||||||
\(832\) | −30.5116 | −1.05780 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 22.2163 | 0.769289 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.87955 | 0.272520 | ||||||||
\(837\) | −5.18421 | −0.179192 | ||||||||
\(838\) | −0.894751 | −0.0309087 | ||||||||
\(839\) | −1.51114 | −0.0521703 | −0.0260851 | − | 0.999660i | \(-0.508304\pi\) | ||||
−0.0260851 | + | 0.999660i | \(0.508304\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4291 | −0.980314 | ||||||||
\(842\) | 63.9724 | 2.20463 | ||||||||
\(843\) | 23.9813 | 0.825959 | ||||||||
\(844\) | 37.6771 | 1.29690 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.24443 | 0.180307 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −42.3654 | −1.45483 | ||||||||
\(849\) | −2.36842 | −0.0812838 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.4889 | 0.359554 | ||||||||
\(852\) | 3.24443 | 0.111152 | ||||||||
\(853\) | −15.4064 | −0.527504 | −0.263752 | − | 0.964591i | \(-0.584960\pi\) | ||||
−0.263752 | + | 0.964591i | \(0.584960\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.26900 | 0.0433734 | ||||||||
\(857\) | 19.8578 | 0.678328 | 0.339164 | − | 0.940727i | \(-0.389856\pi\) | ||||
0.339164 | + | 0.940727i | \(0.389856\pi\) | |||||||
\(858\) | −24.4701 | −0.835396 | ||||||||
\(859\) | −2.42864 | −0.0828641 | −0.0414321 | − | 0.999141i | \(-0.513192\pi\) | ||||
−0.0414321 | + | 0.999141i | \(0.513192\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.2953 | −0.759380 | ||||||||
\(863\) | 39.2958 | 1.33764 | 0.668822 | − | 0.743423i | \(-0.266799\pi\) | ||||
0.668822 | + | 0.743423i | \(0.266799\pi\) | |||||||
\(864\) | 7.34122 | 0.249753 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.114617 | −0.00389485 | ||||||||
\(867\) | 2.61285 | 0.0887370 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.71456 | −0.329544 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.7146 | 0.600235 | ||||||||
\(872\) | 4.03566 | 0.136665 | ||||||||
\(873\) | 11.9398 | 0.404100 | ||||||||
\(874\) | −6.36842 | −0.215415 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.54909 | 0.0861256 | ||||||||
\(877\) | 56.2864 | 1.90066 | 0.950328 | − | 0.311249i | \(-0.100747\pi\) | ||||
0.950328 | + | 0.311249i | \(0.100747\pi\) | |||||||
\(878\) | −42.6865 | −1.44060 | ||||||||
\(879\) | −8.42864 | −0.284291 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.33677 | 0.0787279 | 0.0393640 | − | 0.999225i | \(-0.487467\pi\) | ||||
0.0393640 | + | 0.999225i | \(0.487467\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.7146 | −1.13459 | −0.567293 | − | 0.823516i | \(-0.692009\pi\) | ||||
−0.567293 | + | 0.823516i | \(0.692009\pi\) | |||||||
\(884\) | −46.1847 | −1.55336 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 45.5812 | 1.53133 | ||||||||
\(887\) | 47.8992 | 1.60830 | 0.804150 | − | 0.594427i | \(-0.202621\pi\) | ||||
0.804150 | + | 0.594427i | \(0.202621\pi\) | |||||||
\(888\) | 5.47367 | 0.183684 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00000 | 0.0670025 | ||||||||
\(892\) | 24.6994 | 0.826996 | ||||||||
\(893\) | −6.69228 | −0.223949 | ||||||||
\(894\) | 40.3970 | 1.35108 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.85728 | 0.295736 | ||||||||
\(898\) | −56.0098 | −1.86907 | ||||||||
\(899\) | −3.91703 | −0.130640 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40.6735 | −1.35503 | ||||||||
\(902\) | −31.3461 | −1.04371 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.11462 | −0.269888 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −32.0830 | −1.06589 | ||||||||
\(907\) | −23.7591 | −0.788908 | −0.394454 | − | 0.918916i | \(-0.629066\pi\) | ||||
−0.394454 | + | 0.918916i | \(0.629066\pi\) | |||||||
\(908\) | 23.3087 | 0.773525 | ||||||||
\(909\) | −1.47949 | −0.0490717 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.9403 | 0.760045 | 0.380022 | − | 0.924977i | \(-0.375916\pi\) | ||||
0.380022 | + | 0.924977i | \(0.375916\pi\) | |||||||
\(912\) | −11.2029 | −0.370967 | ||||||||
\(913\) | −23.2257 | −0.768658 | ||||||||
\(914\) | 5.98126 | 0.197843 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.10525 | 0.300846 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 8.42864 | 0.278187 | ||||||||
\(919\) | 16.9777 | 0.560043 | 0.280022 | − | 0.959994i | \(-0.409658\pi\) | ||||
0.280022 | + | 0.959994i | \(0.409658\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.5718 | 0.743767 | ||||||||
\(922\) | −6.42864 | −0.211716 | ||||||||
\(923\) | 12.8573 | 0.423202 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −39.6958 | −1.30449 | ||||||||
\(927\) | 8.85728 | 0.290911 | ||||||||
\(928\) | 5.54680 | 0.182082 | ||||||||
\(929\) | −39.3403 | −1.29071 | −0.645357 | − | 0.763881i | \(-0.723291\pi\) | ||||
−0.645357 | + | 0.763881i | \(0.723291\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 37.7748 | 1.23735 | ||||||||
\(933\) | 24.0830 | 0.788441 | ||||||||
\(934\) | −27.3461 | −0.894793 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.62222 | 0.151082 | ||||||||
\(937\) | −17.7748 | −0.580677 | −0.290338 | − | 0.956924i | \(-0.593768\pi\) | ||||
−0.290338 | + | 0.956924i | \(0.593768\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.65433 | −0.315057 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.5812 | −1.15991 | −0.579957 | − | 0.814647i | \(-0.696931\pi\) | ||||
−0.579957 | + | 0.814647i | \(0.696931\pi\) | |||||||
\(942\) | −19.8479 | −0.646680 | ||||||||
\(943\) | 11.3461 | 0.369481 | ||||||||
\(944\) | 65.0490 | 2.11717 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.4514 | −1.25016 | ||||||||
\(947\) | −30.5018 | −0.991174 | −0.495587 | − | 0.868558i | \(-0.665047\pi\) | ||||
−0.495587 | + | 0.868558i | \(0.665047\pi\) | |||||||
\(948\) | −7.87955 | −0.255916 | ||||||||
\(949\) | 10.1017 | 0.327915 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.04149 | −0.195909 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.1655 | 1.65741 | 0.828706 | − | 0.559684i | \(-0.189077\pi\) | ||||
0.828706 | + | 0.559684i | \(0.189077\pi\) | |||||||
\(954\) | −17.4795 | −0.565920 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.7708 | −0.445378 | ||||||||
\(957\) | 1.51114 | 0.0488481 | ||||||||
\(958\) | 12.1204 | 0.391594 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.12399 | −0.133032 | ||||||||
\(962\) | −93.1437 | −3.00307 | ||||||||
\(963\) | 1.76494 | 0.0568743 | ||||||||
\(964\) | 11.7520 | 0.378507 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.8992 | −1.54034 | −0.770168 | − | 0.637841i | \(-0.779828\pi\) | ||||
−0.770168 | + | 0.637841i | \(0.779828\pi\) | |||||||
\(968\) | −5.03303 | −0.161768 | ||||||||
\(969\) | −10.7556 | −0.345519 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.6735 | −1.30528 | −0.652638 | − | 0.757670i | \(-0.726338\pi\) | ||||
−0.652638 | + | 0.757670i | \(0.726338\pi\) | |||||||
\(972\) | 1.62222 | 0.0520326 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −32.9777 | −1.05667 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 31.6316 | 1.01250 | ||||||||
\(977\) | 27.4893 | 0.879462 | 0.439731 | − | 0.898130i | \(-0.355074\pi\) | ||||
0.439731 | + | 0.898130i | \(0.355074\pi\) | |||||||
\(978\) | −39.6958 | −1.26933 | ||||||||
\(979\) | −9.24443 | −0.295453 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.61285 | 0.179204 | ||||||||
\(982\) | −3.80642 | −0.121468 | ||||||||
\(983\) | 24.0000 | 0.765481 | 0.382741 | − | 0.923856i | \(-0.374980\pi\) | ||||
0.382741 | + | 0.923856i | \(0.374980\pi\) | |||||||
\(984\) | 5.92104 | 0.188756 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.36842 | 0.202812 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 25.3274 | 0.805772 | ||||||||
\(989\) | 13.9180 | 0.442566 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.6923 | −1.10204 | −0.551018 | − | 0.834493i | \(-0.685761\pi\) | ||||
−0.551018 | + | 0.834493i | \(0.685761\pi\) | |||||||
\(992\) | −38.0584 | −1.20836 | ||||||||
\(993\) | 13.5111 | 0.428763 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −18.8385 | −0.596922 | ||||||||
\(997\) | −28.6766 | −0.908197 | −0.454099 | − | 0.890951i | \(-0.650039\pi\) | ||||
−0.454099 | + | 0.890951i | \(0.650039\pi\) | |||||||
\(998\) | −44.4327 | −1.40649 | ||||||||
\(999\) | 7.61285 | 0.240860 |
(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 | 3675.2.a.bj.1.1 | 3 | ||
5.2 | odd | 4 | 735.2.d.b.589.2 | 6 | |||
5.3 | odd | 4 | 735.2.d.b.589.5 | 6 | |||
5.4 | even | 2 | 3675.2.a.bi.1.3 | 3 | |||
7.6 | odd | 2 | 525.2.a.k.1.1 | 3 | |||
15.2 | even | 4 | 2205.2.d.l.1324.5 | 6 | |||
15.8 | even | 4 | 2205.2.d.l.1324.2 | 6 | |||
21.20 | even | 2 | 1575.2.a.w.1.3 | 3 | |||
28.27 | even | 2 | 8400.2.a.dj.1.1 | 3 | |||
35.2 | odd | 12 | 735.2.q.f.214.2 | 12 | |||
35.3 | even | 12 | 735.2.q.e.79.2 | 12 | |||
35.12 | even | 12 | 735.2.q.e.214.2 | 12 | |||
35.13 | even | 4 | 105.2.d.b.64.5 | yes | 6 | ||
35.17 | even | 12 | 735.2.q.e.79.5 | 12 | |||
35.18 | odd | 12 | 735.2.q.f.79.2 | 12 | |||
35.23 | odd | 12 | 735.2.q.f.214.5 | 12 | |||
35.27 | even | 4 | 105.2.d.b.64.2 | ✓ | 6 | ||
35.32 | odd | 12 | 735.2.q.f.79.5 | 12 | |||
35.33 | even | 12 | 735.2.q.e.214.5 | 12 | |||
35.34 | odd | 2 | 525.2.a.j.1.3 | 3 | |||
105.62 | odd | 4 | 315.2.d.e.64.5 | 6 | |||
105.83 | odd | 4 | 315.2.d.e.64.2 | 6 | |||
105.104 | even | 2 | 1575.2.a.x.1.1 | 3 | |||
140.27 | odd | 4 | 1680.2.t.k.1009.2 | 6 | |||
140.83 | odd | 4 | 1680.2.t.k.1009.5 | 6 | |||
140.139 | even | 2 | 8400.2.a.dg.1.3 | 3 | |||
420.83 | even | 4 | 5040.2.t.v.1009.3 | 6 | |||
420.167 | even | 4 | 5040.2.t.v.1009.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.d.b.64.2 | ✓ | 6 | 35.27 | even | 4 | ||
105.2.d.b.64.5 | yes | 6 | 35.13 | even | 4 | ||
315.2.d.e.64.2 | 6 | 105.83 | odd | 4 | |||
315.2.d.e.64.5 | 6 | 105.62 | odd | 4 | |||
525.2.a.j.1.3 | 3 | 35.34 | odd | 2 | |||
525.2.a.k.1.1 | 3 | 7.6 | odd | 2 | |||
735.2.d.b.589.2 | 6 | 5.2 | odd | 4 | |||
735.2.d.b.589.5 | 6 | 5.3 | odd | 4 | |||
735.2.q.e.79.2 | 12 | 35.3 | even | 12 | |||
735.2.q.e.79.5 | 12 | 35.17 | even | 12 | |||
735.2.q.e.214.2 | 12 | 35.12 | even | 12 | |||
735.2.q.e.214.5 | 12 | 35.33 | even | 12 | |||
735.2.q.f.79.2 | 12 | 35.18 | odd | 12 | |||
735.2.q.f.79.5 | 12 | 35.32 | odd | 12 | |||
735.2.q.f.214.2 | 12 | 35.2 | odd | 12 | |||
735.2.q.f.214.5 | 12 | 35.23 | odd | 12 | |||
1575.2.a.w.1.3 | 3 | 21.20 | even | 2 | |||
1575.2.a.x.1.1 | 3 | 105.104 | even | 2 | |||
1680.2.t.k.1009.2 | 6 | 140.27 | odd | 4 | |||
1680.2.t.k.1009.5 | 6 | 140.83 | odd | 4 | |||
2205.2.d.l.1324.2 | 6 | 15.8 | even | 4 | |||
2205.2.d.l.1324.5 | 6 | 15.2 | even | 4 | |||
3675.2.a.bi.1.3 | 3 | 5.4 | even | 2 | |||
3675.2.a.bj.1.1 | 3 | 1.1 | even | 1 | trivial | ||
5040.2.t.v.1009.3 | 6 | 420.83 | even | 4 | |||
5040.2.t.v.1009.4 | 6 | 420.167 | even | 4 | |||
8400.2.a.dg.1.3 | 3 | 140.139 | even | 2 | |||
8400.2.a.dj.1.1 | 3 | 28.27 | even | 2 |