Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(1,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, 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("855.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.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: | \(6.82720937282\) |
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: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 855.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.311108 | 0.219986 | 0.109993 | − | 0.993932i | \(-0.464917\pi\) | ||||
0.109993 | + | 0.993932i | \(0.464917\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.90321 | −0.951606 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.59210 | −1.35769 | −0.678844 | − | 0.734283i | \(-0.737519\pi\) | ||||
−0.678844 | + | 0.734283i | \(0.737519\pi\) | |||||||
\(8\) | −1.21432 | −0.429327 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.311108 | −0.0983809 | ||||||||
\(11\) | −3.11753 | −0.939971 | −0.469986 | − | 0.882674i | \(-0.655741\pi\) | ||||
−0.469986 | + | 0.882674i | \(0.655741\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.64296 | 1.28773 | 0.643863 | − | 0.765141i | \(-0.277331\pi\) | ||||
0.643863 | + | 0.765141i | \(0.277331\pi\) | |||||||
\(14\) | −1.11753 | −0.298673 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.42864 | 0.857160 | ||||||||
\(17\) | 7.52543 | 1.82518 | 0.912592 | − | 0.408871i | \(-0.134077\pi\) | ||||
0.912592 | + | 0.408871i | \(0.134077\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 1.90321 | 0.425571 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.969888 | −0.206781 | ||||||||
\(23\) | 5.52543 | 1.15213 | 0.576066 | − | 0.817403i | \(-0.304587\pi\) | ||||
0.576066 | + | 0.817403i | \(0.304587\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.44446 | 0.283282 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.83654 | 1.29198 | ||||||||
\(29\) | 8.16839 | 1.51683 | 0.758416 | − | 0.651771i | \(-0.225974\pi\) | ||||
0.758416 | + | 0.651771i | \(0.225974\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.95407 | −0.710171 | −0.355086 | − | 0.934834i | \(-0.615548\pi\) | ||||
−0.355086 | + | 0.934834i | \(0.615548\pi\) | |||||||
\(32\) | 3.49532 | 0.617890 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.34122 | 0.401516 | ||||||||
\(35\) | 3.59210 | 0.607176 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.83654 | −1.45272 | −0.726359 | − | 0.687316i | \(-0.758789\pi\) | ||||
−0.726359 | + | 0.687316i | \(0.758789\pi\) | |||||||
\(38\) | 0.311108 | 0.0504684 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.21432 | 0.192001 | ||||||||
\(41\) | 7.87310 | 1.22957 | 0.614786 | − | 0.788694i | \(-0.289242\pi\) | ||||
0.614786 | + | 0.788694i | \(0.289242\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.45875 | −0.832452 | −0.416226 | − | 0.909261i | \(-0.636647\pi\) | ||||
−0.416226 | + | 0.909261i | \(0.636647\pi\) | |||||||
\(44\) | 5.93332 | 0.894482 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.71900 | 0.253453 | ||||||||
\(47\) | −9.13828 | −1.33295 | −0.666477 | − | 0.745525i | \(-0.732199\pi\) | ||||
−0.666477 | + | 0.745525i | \(0.732199\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.90321 | 0.843316 | ||||||||
\(50\) | 0.311108 | 0.0439973 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.83654 | −1.22541 | ||||||||
\(53\) | 5.03657 | 0.691825 | 0.345913 | − | 0.938267i | \(-0.387569\pi\) | ||||
0.345913 | + | 0.938267i | \(0.387569\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.11753 | 0.420368 | ||||||||
\(56\) | 4.36196 | 0.582892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.54125 | 0.333682 | ||||||||
\(59\) | −6.42864 | −0.836938 | −0.418469 | − | 0.908231i | \(-0.637433\pi\) | ||||
−0.418469 | + | 0.908231i | \(0.637433\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.280996 | −0.0359779 | −0.0179889 | − | 0.999838i | \(-0.505726\pi\) | ||||
−0.0179889 | + | 0.999838i | \(0.505726\pi\) | |||||||
\(62\) | −1.23014 | −0.156228 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.76986 | −0.721232 | ||||||||
\(65\) | −4.64296 | −0.575888 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.67307 | 0.448737 | 0.224369 | − | 0.974504i | \(-0.427968\pi\) | ||||
0.224369 | + | 0.974504i | \(0.427968\pi\) | |||||||
\(68\) | −14.3225 | −1.73686 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.11753 | 0.133571 | ||||||||
\(71\) | 3.37778 | 0.400869 | 0.200435 | − | 0.979707i | \(-0.435765\pi\) | ||||
0.200435 | + | 0.979707i | \(0.435765\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.18421 | 0.372683 | 0.186342 | − | 0.982485i | \(-0.440337\pi\) | ||||
0.186342 | + | 0.982485i | \(0.440337\pi\) | |||||||
\(74\) | −2.74912 | −0.319578 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.90321 | −0.218313 | ||||||||
\(77\) | 11.1985 | 1.27619 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9906 | 1.46156 | 0.730780 | − | 0.682613i | \(-0.239156\pi\) | ||||
0.730780 | + | 0.682613i | \(0.239156\pi\) | |||||||
\(80\) | −3.42864 | −0.383334 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.44938 | 0.270489 | ||||||||
\(83\) | 8.57628 | 0.941369 | 0.470685 | − | 0.882302i | \(-0.344007\pi\) | ||||
0.470685 | + | 0.882302i | \(0.344007\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.52543 | −0.816247 | ||||||||
\(86\) | −1.69826 | −0.183128 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.78568 | 0.403555 | ||||||||
\(89\) | 17.7397 | 1.88041 | 0.940205 | − | 0.340610i | \(-0.110634\pi\) | ||||
0.940205 | + | 0.340610i | \(0.110634\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.6780 | −1.74833 | ||||||||
\(92\) | −10.5161 | −1.09638 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.84299 | −0.293232 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.26517 | −0.737667 | −0.368833 | − | 0.929496i | \(-0.620243\pi\) | ||||
−0.368833 | + | 0.929496i | \(0.620243\pi\) | |||||||
\(98\) | 1.83654 | 0.185518 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.90321 | −0.190321 | ||||||||
\(101\) | −10.7239 | −1.06707 | −0.533535 | − | 0.845778i | \(-0.679137\pi\) | ||||
−0.533535 | + | 0.845778i | \(0.679137\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.24443 | 0.516749 | 0.258375 | − | 0.966045i | \(-0.416813\pi\) | ||||
0.258375 | + | 0.966045i | \(0.416813\pi\) | |||||||
\(104\) | −5.63804 | −0.552855 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.56691 | 0.152192 | ||||||||
\(107\) | 6.23506 | 0.602766 | 0.301383 | − | 0.953503i | \(-0.402552\pi\) | ||||
0.301383 | + | 0.953503i | \(0.402552\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.74620 | 0.933517 | 0.466758 | − | 0.884385i | \(-0.345422\pi\) | ||||
0.466758 | + | 0.884385i | \(0.345422\pi\) | |||||||
\(110\) | 0.969888 | 0.0924752 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.3160 | −1.16376 | ||||||||
\(113\) | 17.8938 | 1.68331 | 0.841656 | − | 0.540015i | \(-0.181581\pi\) | ||||
0.841656 | + | 0.540015i | \(0.181581\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.52543 | −0.515249 | ||||||||
\(116\) | −15.5462 | −1.44343 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.00000 | −0.184115 | ||||||||
\(119\) | −27.0321 | −2.47803 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.28100 | −0.116454 | ||||||||
\(122\) | −0.0874201 | −0.00791465 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.52543 | 0.675803 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.86665 | −0.520581 | −0.260290 | − | 0.965530i | \(-0.583818\pi\) | ||||
−0.260290 | + | 0.965530i | \(0.583818\pi\) | |||||||
\(128\) | −8.78568 | −0.776552 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.44446 | −0.126688 | ||||||||
\(131\) | 9.25088 | 0.808254 | 0.404127 | − | 0.914703i | \(-0.367575\pi\) | ||||
0.404127 | + | 0.914703i | \(0.367575\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.59210 | −0.311475 | ||||||||
\(134\) | 1.14272 | 0.0987161 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.13828 | −0.783601 | ||||||||
\(137\) | −9.09234 | −0.776811 | −0.388406 | − | 0.921489i | \(-0.626974\pi\) | ||||
−0.388406 | + | 0.921489i | \(0.626974\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.4795 | 1.65223 | 0.826115 | − | 0.563502i | \(-0.190546\pi\) | ||||
0.826115 | + | 0.563502i | \(0.190546\pi\) | |||||||
\(140\) | −6.83654 | −0.577793 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.05086 | 0.0881858 | ||||||||
\(143\) | −14.4746 | −1.21042 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.16839 | −0.678348 | ||||||||
\(146\) | 0.990632 | 0.0819853 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 16.8178 | 1.38241 | ||||||||
\(149\) | 16.8573 | 1.38100 | 0.690501 | − | 0.723331i | \(-0.257390\pi\) | ||||
0.690501 | + | 0.723331i | \(0.257390\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.4844 | 1.82976 | 0.914878 | − | 0.403731i | \(-0.132287\pi\) | ||||
0.914878 | + | 0.403731i | \(0.132287\pi\) | |||||||
\(152\) | −1.21432 | −0.0984943 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.48394 | 0.280744 | ||||||||
\(155\) | 3.95407 | 0.317598 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.387152 | −0.0308981 | −0.0154491 | − | 0.999881i | \(-0.504918\pi\) | ||||
−0.0154491 | + | 0.999881i | \(0.504918\pi\) | |||||||
\(158\) | 4.04149 | 0.321523 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.49532 | −0.276329 | ||||||||
\(161\) | −19.8479 | −1.56423 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.3067 | −1.35556 | −0.677781 | − | 0.735264i | \(-0.737058\pi\) | ||||
−0.677781 | + | 0.735264i | \(0.737058\pi\) | |||||||
\(164\) | −14.9842 | −1.17007 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.66815 | 0.207088 | ||||||||
\(167\) | 6.81135 | 0.527078 | 0.263539 | − | 0.964649i | \(-0.415110\pi\) | ||||
0.263539 | + | 0.964649i | \(0.415110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.55707 | 0.658236 | ||||||||
\(170\) | −2.34122 | −0.179563 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.3892 | 0.792166 | ||||||||
\(173\) | −14.8430 | −1.12849 | −0.564246 | − | 0.825607i | \(-0.690833\pi\) | ||||
−0.564246 | + | 0.825607i | \(0.690833\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.59210 | −0.271538 | ||||||||
\(176\) | −10.6889 | −0.805706 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.51897 | 0.413665 | ||||||||
\(179\) | 6.72393 | 0.502570 | 0.251285 | − | 0.967913i | \(-0.419147\pi\) | ||||
0.251285 | + | 0.967913i | \(0.419147\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.32693 | −0.321618 | −0.160809 | − | 0.986986i | \(-0.551410\pi\) | ||||
−0.160809 | + | 0.986986i | \(0.551410\pi\) | |||||||
\(182\) | −5.18865 | −0.384609 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.70964 | −0.494641 | ||||||||
\(185\) | 8.83654 | 0.649675 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.4608 | −1.71562 | ||||||||
\(188\) | 17.3921 | 1.26845 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.311108 | −0.0225701 | ||||||||
\(191\) | −17.3526 | −1.25559 | −0.627795 | − | 0.778379i | \(-0.716042\pi\) | ||||
−0.627795 | + | 0.778379i | \(0.716042\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.56046 | 0.544214 | 0.272107 | − | 0.962267i | \(-0.412280\pi\) | ||||
0.272107 | + | 0.962267i | \(0.412280\pi\) | |||||||
\(194\) | −2.26025 | −0.162277 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.2351 | −0.802505 | ||||||||
\(197\) | 12.9447 | 0.922272 | 0.461136 | − | 0.887330i | \(-0.347442\pi\) | ||||
0.461136 | + | 0.887330i | \(0.347442\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.133353 | −0.00945315 | −0.00472658 | − | 0.999989i | \(-0.501505\pi\) | ||||
−0.00472658 | + | 0.999989i | \(0.501505\pi\) | |||||||
\(200\) | −1.21432 | −0.0858654 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.33630 | −0.234741 | ||||||||
\(203\) | −29.3417 | −2.05938 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.87310 | −0.549881 | ||||||||
\(206\) | 1.63158 | 0.113678 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 15.9190 | 1.10379 | ||||||||
\(209\) | −3.11753 | −0.215644 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.3368 | 1.95078 | 0.975392 | − | 0.220478i | \(-0.0707617\pi\) | ||||
0.975392 | + | 0.220478i | \(0.0707617\pi\) | |||||||
\(212\) | −9.58565 | −0.658345 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.93978 | 0.132600 | ||||||||
\(215\) | 5.45875 | 0.372284 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.2034 | 0.964191 | ||||||||
\(218\) | 3.03212 | 0.205361 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.93332 | −0.400025 | ||||||||
\(221\) | 34.9403 | 2.35034 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | −12.5555 | −0.838902 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.56691 | 0.370306 | ||||||||
\(227\) | 0.709636 | 0.0471002 | 0.0235501 | − | 0.999723i | \(-0.492503\pi\) | ||||
0.0235501 | + | 0.999723i | \(0.492503\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.4242 | −1.74616 | −0.873080 | − | 0.487577i | \(-0.837881\pi\) | ||||
−0.873080 | + | 0.487577i | \(0.837881\pi\) | |||||||
\(230\) | −1.71900 | −0.113348 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.91903 | −0.651216 | ||||||||
\(233\) | −17.5210 | −1.14784 | −0.573919 | − | 0.818912i | \(-0.694578\pi\) | ||||
−0.573919 | + | 0.818912i | \(0.694578\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.13828 | 0.596115 | ||||||||
\(236\) | 12.2351 | 0.796435 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.40990 | −0.545133 | ||||||||
\(239\) | −2.49532 | −0.161409 | −0.0807043 | − | 0.996738i | \(-0.525717\pi\) | ||||
−0.0807043 | + | 0.996738i | \(0.525717\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.85728 | −0.184054 | −0.0920268 | − | 0.995757i | \(-0.529335\pi\) | ||||
−0.0920268 | + | 0.995757i | \(0.529335\pi\) | |||||||
\(242\) | −0.398528 | −0.0256183 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.534795 | 0.0342368 | ||||||||
\(245\) | −5.90321 | −0.377142 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.64296 | 0.295424 | ||||||||
\(248\) | 4.80150 | 0.304896 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.311108 | −0.0196762 | ||||||||
\(251\) | 14.9240 | 0.941992 | 0.470996 | − | 0.882135i | \(-0.343895\pi\) | ||||
0.470996 | + | 0.882135i | \(0.343895\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.2257 | −1.08297 | ||||||||
\(254\) | −1.82516 | −0.114521 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.80642 | 0.550401 | ||||||||
\(257\) | −23.4750 | −1.46433 | −0.732167 | − | 0.681126i | \(-0.761491\pi\) | ||||
−0.732167 | + | 0.681126i | \(0.761491\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31.7418 | 1.97234 | ||||||||
\(260\) | 8.83654 | 0.548019 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.87802 | 0.177805 | ||||||||
\(263\) | 16.3225 | 1.00649 | 0.503244 | − | 0.864145i | \(-0.332140\pi\) | ||||
0.503244 | + | 0.864145i | \(0.332140\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.03657 | −0.309394 | ||||||||
\(266\) | −1.11753 | −0.0685203 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.99063 | −0.427021 | ||||||||
\(269\) | −15.5877 | −0.950396 | −0.475198 | − | 0.879879i | \(-0.657624\pi\) | ||||
−0.475198 | + | 0.879879i | \(0.657624\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.3082 | 1.23363 | 0.616817 | − | 0.787106i | \(-0.288422\pi\) | ||||
0.616817 | + | 0.787106i | \(0.288422\pi\) | |||||||
\(272\) | 25.8020 | 1.56447 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.82870 | −0.170888 | ||||||||
\(275\) | −3.11753 | −0.187994 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.1338 | −1.75048 | −0.875241 | − | 0.483687i | \(-0.839297\pi\) | ||||
−0.875241 | + | 0.483687i | \(0.839297\pi\) | |||||||
\(278\) | 6.06022 | 0.363468 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.36196 | −0.260677 | ||||||||
\(281\) | −18.3017 | −1.09179 | −0.545895 | − | 0.837854i | \(-0.683810\pi\) | ||||
−0.545895 | + | 0.837854i | \(0.683810\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.39853 | −0.558684 | −0.279342 | − | 0.960192i | \(-0.590116\pi\) | ||||
−0.279342 | + | 0.960192i | \(0.590116\pi\) | |||||||
\(284\) | −6.42864 | −0.381470 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.50315 | −0.266277 | ||||||||
\(287\) | −28.2810 | −1.66937 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 39.6321 | 2.33130 | ||||||||
\(290\) | −2.54125 | −0.149227 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.06022 | −0.354648 | ||||||||
\(293\) | −0.811346 | −0.0473993 | −0.0236997 | − | 0.999719i | \(-0.507545\pi\) | ||||
−0.0236997 | + | 0.999719i | \(0.507545\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.42864 | 0.374290 | ||||||||
\(296\) | 10.7304 | 0.623691 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.24443 | 0.303802 | ||||||||
\(299\) | 25.6543 | 1.48363 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.6084 | 1.13021 | ||||||||
\(302\) | 6.99508 | 0.402521 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.42864 | 0.196646 | ||||||||
\(305\) | 0.280996 | 0.0160898 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.6035 | −1.17590 | −0.587951 | − | 0.808896i | \(-0.700065\pi\) | ||||
−0.587951 | + | 0.808896i | \(0.700065\pi\) | |||||||
\(308\) | −21.3131 | −1.21443 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.23014 | 0.0698673 | ||||||||
\(311\) | −4.43509 | −0.251491 | −0.125746 | − | 0.992063i | \(-0.540132\pi\) | ||||
−0.125746 | + | 0.992063i | \(0.540132\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.2953 | −0.694971 | −0.347485 | − | 0.937685i | \(-0.612964\pi\) | ||||
−0.347485 | + | 0.937685i | \(0.612964\pi\) | |||||||
\(314\) | −0.120446 | −0.00679717 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.7239 | −1.39083 | ||||||||
\(317\) | −0.220773 | −0.0123999 | −0.00619993 | − | 0.999981i | \(-0.501974\pi\) | ||||
−0.00619993 | + | 0.999981i | \(0.501974\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.4652 | −1.42578 | ||||||||
\(320\) | 5.76986 | 0.322545 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.17484 | −0.344110 | ||||||||
\(323\) | 7.52543 | 0.418726 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.64296 | 0.257545 | ||||||||
\(326\) | −5.38424 | −0.298205 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.56046 | −0.527888 | ||||||||
\(329\) | 32.8256 | 1.80974 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.6681 | 0.586374 | 0.293187 | − | 0.956055i | \(-0.405284\pi\) | ||||
0.293187 | + | 0.956055i | \(0.405284\pi\) | |||||||
\(332\) | −16.3225 | −0.895813 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.11906 | 0.115950 | ||||||||
\(335\) | −3.67307 | −0.200681 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.02074 | −0.436918 | −0.218459 | − | 0.975846i | \(-0.570103\pi\) | ||||
−0.218459 | + | 0.975846i | \(0.570103\pi\) | |||||||
\(338\) | 2.66217 | 0.144803 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.3225 | 0.776746 | ||||||||
\(341\) | 12.3269 | 0.667541 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.93978 | 0.212728 | ||||||||
\(344\) | 6.62867 | 0.357394 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.61777 | −0.248253 | ||||||||
\(347\) | −7.06515 | −0.379277 | −0.189638 | − | 0.981854i | \(-0.560732\pi\) | ||||
−0.189638 | + | 0.981854i | \(0.560732\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.6731 | 1.05308 | 0.526538 | − | 0.850152i | \(-0.323490\pi\) | ||||
0.526538 | + | 0.850152i | \(0.323490\pi\) | |||||||
\(350\) | −1.11753 | −0.0597346 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.8968 | −0.580799 | ||||||||
\(353\) | 5.61285 | 0.298742 | 0.149371 | − | 0.988781i | \(-0.452275\pi\) | ||||
0.149371 | + | 0.988781i | \(0.452275\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.37778 | −0.179274 | ||||||||
\(356\) | −33.7625 | −1.78941 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.09187 | 0.110559 | ||||||||
\(359\) | −10.0065 | −0.528120 | −0.264060 | − | 0.964506i | \(-0.585062\pi\) | ||||
−0.264060 | + | 0.964506i | \(0.585062\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −1.34614 | −0.0707516 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 31.7418 | 1.66372 | ||||||||
\(365\) | −3.18421 | −0.166669 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.25581 | 0.430950 | 0.215475 | − | 0.976509i | \(-0.430870\pi\) | ||||
0.215475 | + | 0.976509i | \(0.430870\pi\) | |||||||
\(368\) | 18.9447 | 0.987561 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.74912 | 0.142920 | ||||||||
\(371\) | −18.0919 | −0.939283 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.71609 | 0.347746 | 0.173873 | − | 0.984768i | \(-0.444372\pi\) | ||||
0.173873 | + | 0.984768i | \(0.444372\pi\) | |||||||
\(374\) | −7.29883 | −0.377413 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.0968 | 0.572273 | ||||||||
\(377\) | 37.9255 | 1.95326 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.7003 | −1.83380 | −0.916900 | − | 0.399117i | \(-0.869317\pi\) | ||||
−0.916900 | + | 0.399117i | \(0.869317\pi\) | |||||||
\(380\) | 1.90321 | 0.0976327 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.39853 | −0.276213 | ||||||||
\(383\) | −1.53972 | −0.0786759 | −0.0393379 | − | 0.999226i | \(-0.512525\pi\) | ||||
−0.0393379 | + | 0.999226i | \(0.512525\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.1985 | −0.570728 | ||||||||
\(386\) | 2.35212 | 0.119720 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.8272 | 0.701968 | ||||||||
\(389\) | −15.5111 | −0.786446 | −0.393223 | − | 0.919443i | \(-0.628640\pi\) | ||||
−0.393223 | + | 0.919443i | \(0.628640\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.5812 | 2.10285 | ||||||||
\(392\) | −7.16839 | −0.362058 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.02720 | 0.202887 | ||||||||
\(395\) | −12.9906 | −0.653630 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.78415 | −0.240110 | −0.120055 | − | 0.992767i | \(-0.538307\pi\) | ||||
−0.120055 | + | 0.992767i | \(0.538307\pi\) | |||||||
\(398\) | −0.0414872 | −0.00207956 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.42864 | 0.171432 | ||||||||
\(401\) | −3.57781 | −0.178668 | −0.0893338 | − | 0.996002i | \(-0.528474\pi\) | ||||
−0.0893338 | + | 0.996002i | \(0.528474\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.3586 | −0.914506 | ||||||||
\(404\) | 20.4099 | 1.01543 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.12843 | −0.453036 | ||||||||
\(407\) | 27.5482 | 1.36551 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.8385 | −0.832612 | −0.416306 | − | 0.909224i | \(-0.636676\pi\) | ||||
−0.416306 | + | 0.909224i | \(0.636676\pi\) | |||||||
\(410\) | −2.44938 | −0.120966 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.98126 | −0.491742 | ||||||||
\(413\) | 23.0923 | 1.13630 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.57628 | −0.420993 | ||||||||
\(416\) | 16.2286 | 0.795673 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.969888 | −0.0474388 | ||||||||
\(419\) | 13.4445 | 0.656805 | 0.328402 | − | 0.944538i | \(-0.393490\pi\) | ||||
0.328402 | + | 0.944538i | \(0.393490\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.74620 | −0.0851046 | −0.0425523 | − | 0.999094i | \(-0.513549\pi\) | ||||
−0.0425523 | + | 0.999094i | \(0.513549\pi\) | |||||||
\(422\) | 8.81579 | 0.429146 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.11600 | −0.297019 | ||||||||
\(425\) | 7.52543 | 0.365037 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.00937 | 0.0488467 | ||||||||
\(428\) | −11.8666 | −0.573596 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.69826 | 0.0818974 | ||||||||
\(431\) | 22.1432 | 1.06660 | 0.533300 | − | 0.845926i | \(-0.320952\pi\) | ||||
0.533300 | + | 0.845926i | \(0.320952\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.3892 | 1.74875 | 0.874376 | − | 0.485250i | \(-0.161271\pi\) | ||||
0.874376 | + | 0.485250i | \(0.161271\pi\) | |||||||
\(434\) | 4.41880 | 0.212109 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.5491 | −0.888340 | ||||||||
\(437\) | 5.52543 | 0.264317 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.63158 | −0.0778712 | −0.0389356 | − | 0.999242i | \(-0.512397\pi\) | ||||
−0.0389356 | + | 0.999242i | \(0.512397\pi\) | |||||||
\(440\) | −3.78568 | −0.180475 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.8702 | 0.517042 | ||||||||
\(443\) | −5.68736 | −0.270215 | −0.135107 | − | 0.990831i | \(-0.543138\pi\) | ||||
−0.135107 | + | 0.990831i | \(0.543138\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.7397 | −0.840945 | ||||||||
\(446\) | −1.24443 | −0.0589255 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 20.7259 | 0.979208 | ||||||||
\(449\) | 35.0988 | 1.65641 | 0.828207 | − | 0.560422i | \(-0.189361\pi\) | ||||
0.828207 | + | 0.560422i | \(0.189361\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.5446 | −1.15576 | ||||||||
\(452\) | −34.0558 | −1.60185 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.220773 | 0.0103614 | ||||||||
\(455\) | 16.6780 | 0.781876 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.6450 | 1.15284 | 0.576421 | − | 0.817153i | \(-0.304449\pi\) | ||||
0.576421 | + | 0.817153i | \(0.304449\pi\) | |||||||
\(458\) | −8.22077 | −0.384132 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.5161 | 0.490314 | ||||||||
\(461\) | 20.4701 | 0.953389 | 0.476694 | − | 0.879069i | \(-0.341835\pi\) | ||||
0.476694 | + | 0.879069i | \(0.341835\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.6113 | −1.23673 | −0.618366 | − | 0.785890i | \(-0.712205\pi\) | ||||
−0.618366 | + | 0.785890i | \(0.712205\pi\) | |||||||
\(464\) | 28.0065 | 1.30017 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.45091 | −0.252509 | ||||||||
\(467\) | 35.9353 | 1.66289 | 0.831444 | − | 0.555608i | \(-0.187514\pi\) | ||||
0.831444 | + | 0.555608i | \(0.187514\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.1941 | −0.609245 | ||||||||
\(470\) | 2.84299 | 0.131137 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.80642 | 0.359320 | ||||||||
\(473\) | 17.0178 | 0.782481 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 51.4479 | 2.35811 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.776312 | −0.0355077 | ||||||||
\(479\) | −17.1461 | −0.783426 | −0.391713 | − | 0.920087i | \(-0.628117\pi\) | ||||
−0.391713 | + | 0.920087i | \(0.628117\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.0277 | −1.87070 | ||||||||
\(482\) | −0.888922 | −0.0404893 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.43801 | 0.110819 | ||||||||
\(485\) | 7.26517 | 0.329895 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.5941 | −1.06915 | −0.534576 | − | 0.845121i | \(-0.679529\pi\) | ||||
−0.534576 | + | 0.845121i | \(0.679529\pi\) | |||||||
\(488\) | 0.341219 | 0.0154463 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.83654 | −0.0829662 | ||||||||
\(491\) | 33.4859 | 1.51120 | 0.755600 | − | 0.655033i | \(-0.227345\pi\) | ||||
0.755600 | + | 0.655033i | \(0.227345\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 61.4706 | 2.76850 | ||||||||
\(494\) | 1.44446 | 0.0649894 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.5571 | −0.608730 | ||||||||
\(497\) | −12.1334 | −0.544255 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.7052 | −1.01642 | −0.508212 | − | 0.861232i | \(-0.669693\pi\) | ||||
−0.508212 | + | 0.861232i | \(0.669693\pi\) | |||||||
\(500\) | 1.90321 | 0.0851142 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.64296 | 0.207225 | ||||||||
\(503\) | 7.07805 | 0.315595 | 0.157797 | − | 0.987472i | \(-0.449561\pi\) | ||||
0.157797 | + | 0.987472i | \(0.449561\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.7239 | 0.477208 | ||||||||
\(506\) | −5.35905 | −0.238239 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.1655 | 0.495388 | ||||||||
\(509\) | −25.9748 | −1.15131 | −0.575657 | − | 0.817692i | \(-0.695253\pi\) | ||||
−0.575657 | + | 0.817692i | \(0.695253\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.4380 | −0.505988 | ||||||||
\(512\) | 20.3111 | 0.897633 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.30327 | −0.322133 | ||||||||
\(515\) | −5.24443 | −0.231097 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.4889 | 1.25294 | ||||||||
\(518\) | 9.87511 | 0.433887 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.63804 | 0.247244 | ||||||||
\(521\) | 12.7491 | 0.558549 | 0.279274 | − | 0.960211i | \(-0.409906\pi\) | ||||
0.279274 | + | 0.960211i | \(0.409906\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.4479 | 1.37512 | 0.687559 | − | 0.726128i | \(-0.258682\pi\) | ||||
0.687559 | + | 0.726128i | \(0.258682\pi\) | |||||||
\(524\) | −17.6064 | −0.769139 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.07805 | 0.221414 | ||||||||
\(527\) | −29.7560 | −1.29619 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.53035 | 0.327407 | ||||||||
\(530\) | −1.56691 | −0.0680624 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.83654 | 0.296401 | ||||||||
\(533\) | 36.5545 | 1.58335 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.23506 | −0.269565 | ||||||||
\(536\) | −4.46028 | −0.192655 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.84944 | −0.209074 | ||||||||
\(539\) | −18.4035 | −0.792693 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.4889 | 0.880885 | 0.440443 | − | 0.897781i | \(-0.354822\pi\) | ||||
0.440443 | + | 0.897781i | \(0.354822\pi\) | |||||||
\(542\) | 6.31804 | 0.271383 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 26.3037 | 1.12776 | ||||||||
\(545\) | −9.74620 | −0.417481 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.2065 | 0.607425 | 0.303713 | − | 0.952764i | \(-0.401774\pi\) | ||||
0.303713 | + | 0.952764i | \(0.401774\pi\) | |||||||
\(548\) | 17.3047 | 0.739218 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.969888 | −0.0413562 | ||||||||
\(551\) | 8.16839 | 0.347985 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −46.6637 | −1.98434 | ||||||||
\(554\) | −9.06376 | −0.385082 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −37.0736 | −1.57227 | ||||||||
\(557\) | −24.5303 | −1.03938 | −0.519692 | − | 0.854354i | \(-0.673953\pi\) | ||||
−0.519692 | + | 0.854354i | \(0.673953\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.3448 | −1.07197 | ||||||||
\(560\) | 12.3160 | 0.520447 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.69381 | −0.240179 | ||||||||
\(563\) | −20.2306 | −0.852619 | −0.426309 | − | 0.904577i | \(-0.640187\pi\) | ||||
−0.426309 | + | 0.904577i | \(0.640187\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.8938 | −0.752800 | ||||||||
\(566\) | −2.92396 | −0.122903 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.10171 | −0.172104 | ||||||||
\(569\) | 8.64740 | 0.362518 | 0.181259 | − | 0.983435i | \(-0.441983\pi\) | ||||
0.181259 | + | 0.983435i | \(0.441983\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.33630 | 0.390712 | 0.195356 | − | 0.980732i | \(-0.437414\pi\) | ||||
0.195356 | + | 0.980732i | \(0.437414\pi\) | |||||||
\(572\) | 27.5482 | 1.15185 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.79844 | −0.367240 | ||||||||
\(575\) | 5.52543 | 0.230426 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.5718 | 1.10620 | 0.553100 | − | 0.833115i | \(-0.313445\pi\) | ||||
0.553100 | + | 0.833115i | \(0.313445\pi\) | |||||||
\(578\) | 12.3298 | 0.512854 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 15.5462 | 0.645520 | ||||||||
\(581\) | −30.8069 | −1.27809 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.7017 | −0.650296 | ||||||||
\(584\) | −3.86665 | −0.160003 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.252416 | −0.0104272 | ||||||||
\(587\) | −20.8845 | −0.861995 | −0.430997 | − | 0.902353i | \(-0.641838\pi\) | ||||
−0.430997 | + | 0.902353i | \(0.641838\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.95407 | −0.162924 | ||||||||
\(590\) | 2.00000 | 0.0823387 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −30.2973 | −1.24521 | ||||||||
\(593\) | 14.4286 | 0.592513 | 0.296257 | − | 0.955108i | \(-0.404262\pi\) | ||||
0.296257 | + | 0.955108i | \(0.404262\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.0321 | 1.10821 | ||||||||
\(596\) | −32.0830 | −1.31417 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.98126 | 0.326378 | ||||||||
\(599\) | −46.3497 | −1.89380 | −0.946898 | − | 0.321533i | \(-0.895802\pi\) | ||||
−0.946898 | + | 0.321533i | \(0.895802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.0415 | −0.735928 | −0.367964 | − | 0.929840i | \(-0.619945\pi\) | ||||
−0.367964 | + | 0.929840i | \(0.619945\pi\) | |||||||
\(602\) | 6.10033 | 0.248631 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −42.7926 | −1.74121 | ||||||||
\(605\) | 1.28100 | 0.0520799 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.87601 | 0.197911 | 0.0989557 | − | 0.995092i | \(-0.468450\pi\) | ||||
0.0989557 | + | 0.995092i | \(0.468450\pi\) | |||||||
\(608\) | 3.49532 | 0.141754 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.0874201 | 0.00353954 | ||||||||
\(611\) | −42.4286 | −1.71648 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.8064 | −0.719195 | −0.359597 | − | 0.933108i | \(-0.617086\pi\) | ||||
−0.359597 | + | 0.933108i | \(0.617086\pi\) | |||||||
\(614\) | −6.40990 | −0.258683 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.5986 | −0.547901 | ||||||||
\(617\) | −0.595019 | −0.0239545 | −0.0119773 | − | 0.999928i | \(-0.503813\pi\) | ||||
−0.0119773 | + | 0.999928i | \(0.503813\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.3783 | 0.819071 | 0.409536 | − | 0.912294i | \(-0.365691\pi\) | ||||
0.409536 | + | 0.912294i | \(0.365691\pi\) | |||||||
\(620\) | −7.52543 | −0.302228 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.37979 | −0.0553246 | ||||||||
\(623\) | −63.7230 | −2.55301 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −3.82516 | −0.152884 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.736833 | 0.0294028 | ||||||||
\(629\) | −66.4987 | −2.65148 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.50177 | −0.0995939 | −0.0497969 | − | 0.998759i | \(-0.515857\pi\) | ||||
−0.0497969 | + | 0.998759i | \(0.515857\pi\) | |||||||
\(632\) | −15.7748 | −0.627487 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.0686843 | −0.00272780 | ||||||||
\(635\) | 5.86665 | 0.232811 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.4084 | 1.08596 | ||||||||
\(638\) | −7.92242 | −0.313652 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.78568 | 0.347285 | ||||||||
\(641\) | 33.6479 | 1.32901 | 0.664506 | − | 0.747283i | \(-0.268642\pi\) | ||||
0.664506 | + | 0.747283i | \(0.268642\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.2242 | 0.718691 | 0.359345 | − | 0.933205i | \(-0.383000\pi\) | ||||
0.359345 | + | 0.933205i | \(0.383000\pi\) | |||||||
\(644\) | 37.7748 | 1.48853 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.34122 | 0.0921140 | ||||||||
\(647\) | −26.7195 | −1.05045 | −0.525226 | − | 0.850963i | \(-0.676019\pi\) | ||||
−0.525226 | + | 0.850963i | \(0.676019\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.0415 | 0.786697 | ||||||||
\(650\) | 1.44446 | 0.0566564 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32.9382 | 1.28996 | ||||||||
\(653\) | −43.9037 | −1.71808 | −0.859042 | − | 0.511905i | \(-0.828940\pi\) | ||||
−0.859042 | + | 0.511905i | \(0.828940\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.25088 | −0.361462 | ||||||||
\(656\) | 26.9940 | 1.05394 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10.2123 | 0.398117 | ||||||||
\(659\) | 15.3274 | 0.597071 | 0.298535 | − | 0.954399i | \(-0.403502\pi\) | ||||
0.298535 | + | 0.954399i | \(0.403502\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.1526 | 0.900530 | 0.450265 | − | 0.892895i | \(-0.351329\pi\) | ||||
0.450265 | + | 0.892895i | \(0.351329\pi\) | |||||||
\(662\) | 3.31894 | 0.128994 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.4143 | −0.404155 | ||||||||
\(665\) | 3.59210 | 0.139296 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 45.1338 | 1.74759 | ||||||||
\(668\) | −12.9634 | −0.501570 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.14272 | −0.0441472 | ||||||||
\(671\) | 0.876015 | 0.0338182 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.97926 | 0.153389 | 0.0766945 | − | 0.997055i | \(-0.475563\pi\) | ||||
0.0766945 | + | 0.997055i | \(0.475563\pi\) | |||||||
\(674\) | −2.49532 | −0.0961160 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.2859 | −0.626381 | ||||||||
\(677\) | 21.4652 | 0.824975 | 0.412487 | − | 0.910963i | \(-0.364660\pi\) | ||||
0.412487 | + | 0.910963i | \(0.364660\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.0973 | 1.00152 | ||||||||
\(680\) | 9.13828 | 0.350437 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.83500 | 0.146850 | ||||||||
\(683\) | −16.5205 | −0.632140 | −0.316070 | − | 0.948736i | \(-0.602363\pi\) | ||||
−0.316070 | + | 0.948736i | \(0.602363\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.09234 | 0.347401 | ||||||||
\(686\) | 1.22570 | 0.0467973 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.7161 | −0.713544 | ||||||||
\(689\) | 23.3846 | 0.890881 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.2543 | −1.18897 | −0.594484 | − | 0.804107i | \(-0.702644\pi\) | ||||
−0.594484 | + | 0.804107i | \(0.702644\pi\) | |||||||
\(692\) | 28.2494 | 1.07388 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.19802 | −0.0834358 | ||||||||
\(695\) | −19.4795 | −0.738899 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 59.2484 | 2.24419 | ||||||||
\(698\) | 6.12045 | 0.231662 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.83654 | 0.258397 | ||||||||
\(701\) | −11.3176 | −0.427458 | −0.213729 | − | 0.976893i | \(-0.568561\pi\) | ||||
−0.213729 | + | 0.976893i | \(0.568561\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.83654 | −0.333276 | ||||||||
\(704\) | 17.9877 | 0.677938 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.74620 | 0.0657191 | ||||||||
\(707\) | 38.5215 | 1.44875 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.3131 | 0.650208 | 0.325104 | − | 0.945678i | \(-0.394601\pi\) | ||||
0.325104 | + | 0.945678i | \(0.394601\pi\) | |||||||
\(710\) | −1.05086 | −0.0394379 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −21.5417 | −0.807310 | ||||||||
\(713\) | −21.8479 | −0.818211 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.4746 | 0.541318 | ||||||||
\(716\) | −12.7971 | −0.478248 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.11309 | −0.116179 | ||||||||
\(719\) | 21.1175 | 0.787551 | 0.393776 | − | 0.919207i | \(-0.371169\pi\) | ||||
0.393776 | + | 0.919207i | \(0.371169\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.8385 | −0.701584 | ||||||||
\(722\) | 0.311108 | 0.0115782 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.23506 | 0.306054 | ||||||||
\(725\) | 8.16839 | 0.303366 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.1220 | 0.709195 | 0.354597 | − | 0.935019i | \(-0.384618\pi\) | ||||
0.354597 | + | 0.935019i | \(0.384618\pi\) | |||||||
\(728\) | 20.2524 | 0.750604 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.990632 | −0.0366649 | ||||||||
\(731\) | −41.0794 | −1.51938 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.1842 | −1.00407 | −0.502036 | − | 0.864847i | \(-0.667415\pi\) | ||||
−0.502036 | + | 0.864847i | \(0.667415\pi\) | |||||||
\(734\) | 2.56845 | 0.0948031 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.3131 | 0.711891 | ||||||||
\(737\) | −11.4509 | −0.421800 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.9684 | −0.955261 | −0.477631 | − | 0.878561i | \(-0.658504\pi\) | ||||
−0.477631 | + | 0.878561i | \(0.658504\pi\) | |||||||
\(740\) | −16.8178 | −0.618235 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.62852 | −0.206630 | ||||||||
\(743\) | −0.866170 | −0.0317767 | −0.0158884 | − | 0.999874i | \(-0.505058\pi\) | ||||
−0.0158884 | + | 0.999874i | \(0.505058\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.8573 | −0.617603 | ||||||||
\(746\) | 2.08943 | 0.0764994 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 44.6508 | 1.63259 | ||||||||
\(749\) | −22.3970 | −0.818368 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.01429 | −0.219465 | −0.109732 | − | 0.993961i | \(-0.534999\pi\) | ||||
−0.109732 | + | 0.993961i | \(0.534999\pi\) | |||||||
\(752\) | −31.3319 | −1.14256 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.7989 | 0.429691 | ||||||||
\(755\) | −22.4844 | −0.818292 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.7560 | −1.59034 | −0.795170 | − | 0.606386i | \(-0.792619\pi\) | ||||
−0.795170 | + | 0.606386i | \(0.792619\pi\) | |||||||
\(758\) | −11.1066 | −0.403411 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.21432 | 0.0440480 | ||||||||
\(761\) | 7.68598 | 0.278616 | 0.139308 | − | 0.990249i | \(-0.455512\pi\) | ||||
0.139308 | + | 0.990249i | \(0.455512\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.0094 | −1.26742 | ||||||||
\(764\) | 33.0257 | 1.19483 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.479018 | −0.0173076 | ||||||||
\(767\) | −29.8479 | −1.07775 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.2444 | −1.12670 | −0.563352 | − | 0.826217i | \(-0.690488\pi\) | ||||
−0.563352 | + | 0.826217i | \(0.690488\pi\) | |||||||
\(770\) | −3.48394 | −0.125552 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.3892 | −0.517877 | ||||||||
\(773\) | 38.0687 | 1.36924 | 0.684618 | − | 0.728902i | \(-0.259969\pi\) | ||||
0.684618 | + | 0.728902i | \(0.259969\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.95407 | −0.142034 | ||||||||
\(776\) | 8.82225 | 0.316700 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.82564 | −0.173007 | ||||||||
\(779\) | 7.87310 | 0.282083 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.5303 | −0.376806 | ||||||||
\(782\) | 12.9362 | 0.462599 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20.2400 | 0.722857 | ||||||||
\(785\) | 0.387152 | 0.0138181 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.5111 | 0.695497 | 0.347748 | − | 0.937588i | \(-0.386946\pi\) | ||||
0.347748 | + | 0.937588i | \(0.386946\pi\) | |||||||
\(788\) | −24.6365 | −0.877639 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.04149 | −0.143790 | ||||||||
\(791\) | −64.2766 | −2.28541 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.30465 | −0.0463296 | ||||||||
\(794\) | −1.48839 | −0.0528208 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.253799 | 0.00899567 | ||||||||
\(797\) | −13.4938 | −0.477974 | −0.238987 | − | 0.971023i | \(-0.576815\pi\) | ||||
−0.238987 | + | 0.971023i | \(0.576815\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −68.7694 | −2.43289 | ||||||||
\(800\) | 3.49532 | 0.123578 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.11309 | −0.0393044 | ||||||||
\(803\) | −9.92687 | −0.350312 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.8479 | 0.699547 | ||||||||
\(806\) | −5.71150 | −0.201179 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.0223 | 0.458122 | ||||||||
\(809\) | 39.8163 | 1.39987 | 0.699933 | − | 0.714209i | \(-0.253213\pi\) | ||||
0.699933 | + | 0.714209i | \(0.253213\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.5496 | 1.24831 | 0.624157 | − | 0.781299i | \(-0.285443\pi\) | ||||
0.624157 | + | 0.781299i | \(0.285443\pi\) | |||||||
\(812\) | 55.8435 | 1.95972 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.57045 | 0.300394 | ||||||||
\(815\) | 17.3067 | 0.606226 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.45875 | −0.190978 | ||||||||
\(818\) | −5.23860 | −0.183163 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.9842 | 0.523270 | ||||||||
\(821\) | 15.9684 | 0.557300 | 0.278650 | − | 0.960393i | \(-0.410113\pi\) | ||||
0.278650 | + | 0.960393i | \(0.410113\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.4400 | −1.09593 | −0.547965 | − | 0.836501i | \(-0.684597\pi\) | ||||
−0.547965 | + | 0.836501i | \(0.684597\pi\) | |||||||
\(824\) | −6.36842 | −0.221854 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.18421 | 0.249971 | ||||||||
\(827\) | −53.0593 | −1.84505 | −0.922527 | − | 0.385933i | \(-0.873879\pi\) | ||||
−0.922527 | + | 0.385933i | \(0.873879\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.1526 | −1.08197 | −0.540987 | − | 0.841031i | \(-0.681949\pi\) | ||||
−0.540987 | + | 0.841031i | \(0.681949\pi\) | |||||||
\(830\) | −2.66815 | −0.0926128 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −26.7892 | −0.928749 | ||||||||
\(833\) | 44.4242 | 1.53921 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.81135 | −0.235716 | ||||||||
\(836\) | 5.93332 | 0.205208 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.18268 | 0.144488 | ||||||||
\(839\) | 23.6642 | 0.816978 | 0.408489 | − | 0.912763i | \(-0.366056\pi\) | ||||
0.408489 | + | 0.912763i | \(0.366056\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.7225 | 1.30078 | ||||||||
\(842\) | −0.543257 | −0.0187219 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −53.9309 | −1.85638 | ||||||||
\(845\) | −8.55707 | −0.294372 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.60147 | 0.158108 | ||||||||
\(848\) | 17.2686 | 0.593005 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.34122 | 0.0803032 | ||||||||
\(851\) | −48.8256 | −1.67372 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.7560 | −1.36122 | −0.680611 | − | 0.732645i | \(-0.738285\pi\) | ||||
−0.680611 | + | 0.732645i | \(0.738285\pi\) | |||||||
\(854\) | 0.314022 | 0.0107456 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.57136 | −0.258784 | ||||||||
\(857\) | −42.3640 | −1.44713 | −0.723563 | − | 0.690259i | \(-0.757497\pi\) | ||||
−0.723563 | + | 0.690259i | \(0.757497\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0638 | 0.377491 | 0.188745 | − | 0.982026i | \(-0.439558\pi\) | ||||
0.188745 | + | 0.982026i | \(0.439558\pi\) | |||||||
\(860\) | −10.3892 | −0.354267 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.88892 | 0.234638 | ||||||||
\(863\) | −29.7649 | −1.01321 | −0.506605 | − | 0.862178i | \(-0.669100\pi\) | ||||
−0.506605 | + | 0.862178i | \(0.669100\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.8430 | 0.504677 | ||||||||
\(866\) | 11.3210 | 0.384702 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −27.0321 | −0.917530 | ||||||||
\(869\) | −40.4987 | −1.37382 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.0539 | 0.577850 | ||||||||
\(872\) | −11.8350 | −0.400784 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.71900 | 0.0581462 | ||||||||
\(875\) | 3.59210 | 0.121435 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.24644 | −0.109624 | −0.0548122 | − | 0.998497i | \(-0.517456\pi\) | ||||
−0.0548122 | + | 0.998497i | \(0.517456\pi\) | |||||||
\(878\) | −0.507598 | −0.0171306 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.6889 | 0.360322 | ||||||||
\(881\) | 30.3269 | 1.02174 | 0.510870 | − | 0.859658i | \(-0.329323\pi\) | ||||
0.510870 | + | 0.859658i | \(0.329323\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.92840 | −0.165854 | −0.0829270 | − | 0.996556i | \(-0.526427\pi\) | ||||
−0.0829270 | + | 0.996556i | \(0.526427\pi\) | |||||||
\(884\) | −66.4987 | −2.23659 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.76938 | −0.0594436 | ||||||||
\(887\) | −8.08297 | −0.271400 | −0.135700 | − | 0.990750i | \(-0.543328\pi\) | ||||
−0.135700 | + | 0.990750i | \(0.543328\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.0736 | 0.706786 | ||||||||
\(890\) | −5.51897 | −0.184996 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.61285 | 0.254897 | ||||||||
\(893\) | −9.13828 | −0.305801 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.72393 | −0.224756 | ||||||||
\(896\) | 31.5591 | 1.05431 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.9195 | 0.364389 | ||||||||
\(899\) | −32.2983 | −1.07721 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.9023 | 1.26271 | ||||||||
\(902\) | −7.63603 | −0.254252 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21.7288 | −0.722691 | ||||||||
\(905\) | 4.32693 | 0.143832 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.1427 | 0.436397 | 0.218198 | − | 0.975904i | \(-0.429982\pi\) | ||||
0.218198 | + | 0.975904i | \(0.429982\pi\) | |||||||
\(908\) | −1.35059 | −0.0448208 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.18865 | 0.172002 | ||||||||
\(911\) | −6.83854 | −0.226571 | −0.113286 | − | 0.993562i | \(-0.536137\pi\) | ||||
−0.113286 | + | 0.993562i | \(0.536137\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.7368 | −0.884860 | ||||||||
\(914\) | 7.66724 | 0.253610 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 50.2908 | 1.66166 | ||||||||
\(917\) | −33.2301 | −1.09736 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.9398 | −1.11957 | −0.559785 | − | 0.828638i | \(-0.689116\pi\) | ||||
−0.559785 | + | 0.828638i | \(0.689116\pi\) | |||||||
\(920\) | 6.70964 | 0.221210 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.36842 | 0.209733 | ||||||||
\(923\) | 15.6829 | 0.516209 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.83654 | −0.290543 | ||||||||
\(926\) | −8.27899 | −0.272064 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 28.5511 | 0.937236 | ||||||||
\(929\) | 41.5714 | 1.36391 | 0.681956 | − | 0.731393i | \(-0.261130\pi\) | ||||
0.681956 | + | 0.731393i | \(0.261130\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.90321 | 0.193470 | ||||||||
\(932\) | 33.3461 | 1.09229 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.1798 | 0.365813 | ||||||||
\(935\) | 23.4608 | 0.767249 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.2538 | −0.857674 | −0.428837 | − | 0.903382i | \(-0.641077\pi\) | ||||
−0.428837 | + | 0.903382i | \(0.641077\pi\) | |||||||
\(938\) | −4.10477 | −0.134026 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −17.3921 | −0.567267 | ||||||||
\(941\) | −45.8642 | −1.49513 | −0.747565 | − | 0.664188i | \(-0.768777\pi\) | ||||
−0.747565 | + | 0.664188i | \(0.768777\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.5022 | 1.41663 | ||||||||
\(944\) | −22.0415 | −0.717389 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.29438 | 0.172135 | ||||||||
\(947\) | 19.6271 | 0.637796 | 0.318898 | − | 0.947789i | \(-0.396687\pi\) | ||||
0.318898 | + | 0.947789i | \(0.396687\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.7841 | 0.479914 | ||||||||
\(950\) | 0.311108 | 0.0100937 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 32.8256 | 1.06388 | ||||||||
\(953\) | −16.2079 | −0.525024 | −0.262512 | − | 0.964929i | \(-0.584551\pi\) | ||||
−0.262512 | + | 0.964929i | \(0.584551\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.3526 | 0.561517 | ||||||||
\(956\) | 4.74912 | 0.153597 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.33429 | −0.172343 | ||||||||
\(959\) | 32.6606 | 1.05467 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.3654 | −0.495657 | ||||||||
\(962\) | −12.7640 | −0.411529 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.43801 | 0.175146 | ||||||||
\(965\) | −7.56046 | −0.243380 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.8499 | 1.28149 | 0.640743 | − | 0.767755i | \(-0.278626\pi\) | ||||
0.640743 | + | 0.767755i | \(0.278626\pi\) | |||||||
\(968\) | 1.55554 | 0.0499969 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.26025 | 0.0725723 | ||||||||
\(971\) | −19.3907 | −0.622277 | −0.311138 | − | 0.950365i | \(-0.600710\pi\) | ||||
−0.311138 | + | 0.950365i | \(0.600710\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −69.9724 | −2.24321 | ||||||||
\(974\) | −7.34031 | −0.235199 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.963435 | −0.0308388 | ||||||||
\(977\) | 10.7096 | 0.342632 | 0.171316 | − | 0.985216i | \(-0.445198\pi\) | ||||
0.171316 | + | 0.985216i | \(0.445198\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −55.3042 | −1.76753 | ||||||||
\(980\) | 11.2351 | 0.358891 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.4177 | 0.332443 | ||||||||
\(983\) | 47.9639 | 1.52981 | 0.764906 | − | 0.644142i | \(-0.222786\pi\) | ||||
0.764906 | + | 0.644142i | \(0.222786\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.9447 | −0.412452 | ||||||||
\(986\) | 19.1240 | 0.609032 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.83654 | −0.281128 | ||||||||
\(989\) | −30.1619 | −0.959094 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.81627 | 0.121228 | 0.0606139 | − | 0.998161i | \(-0.480694\pi\) | ||||
0.0606139 | + | 0.998161i | \(0.480694\pi\) | |||||||
\(992\) | −13.8207 | −0.438808 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.77478 | −0.119729 | ||||||||
\(995\) | 0.133353 | 0.00422758 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.8894 | 1.19997 | 0.599985 | − | 0.800012i | \(-0.295173\pi\) | ||||
0.599985 | + | 0.800012i | \(0.295173\pi\) | |||||||
\(998\) | −7.06376 | −0.223599 | ||||||||
\(999\) | 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 | 855.2.a.k.1.2 | yes | 3 | |
3.2 | odd | 2 | 855.2.a.j.1.2 | ✓ | 3 | ||
5.4 | even | 2 | 4275.2.a.bc.1.2 | 3 | |||
15.14 | odd | 2 | 4275.2.a.bl.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
855.2.a.j.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
855.2.a.k.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
4275.2.a.bc.1.2 | 3 | 5.4 | even | 2 | |||
4275.2.a.bl.1.2 | 3 | 15.14 | odd | 2 |