Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2898,2,Mod(1,2898)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2898, 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("2898.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2898.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: | \(23.1406465058\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2898.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.41421 | 1.52688 | 0.763441 | − | 0.645877i | \(-0.223508\pi\) | ||||
0.763441 | + | 0.645877i | \(0.223508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.41421 | −1.07967 | ||||||||
\(11\) | −4.24264 | −1.27920 | −0.639602 | − | 0.768706i | \(-0.720901\pi\) | ||||
−0.639602 | + | 0.768706i | \(0.720901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.828427 | 0.229764 | 0.114882 | − | 0.993379i | \(-0.463351\pi\) | ||||
0.114882 | + | 0.993379i | \(0.463351\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.828427 | 0.200923 | 0.100462 | − | 0.994941i | \(-0.467968\pi\) | ||||
0.100462 | + | 0.994941i | \(0.467968\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.07107 | −1.62221 | −0.811107 | − | 0.584898i | \(-0.801135\pi\) | ||||
−0.811107 | + | 0.584898i | \(0.801135\pi\) | |||||||
\(20\) | 3.41421 | 0.763441 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.24264 | 0.904534 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.65685 | 1.33137 | ||||||||
\(26\) | −0.828427 | −0.162468 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.828427 | 0.148790 | 0.0743950 | − | 0.997229i | \(-0.476297\pi\) | ||||
0.0743950 | + | 0.997229i | \(0.476297\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.828427 | −0.142074 | ||||||||
\(35\) | −3.41421 | −0.577107 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.2426 | −1.68388 | −0.841940 | − | 0.539571i | \(-0.818586\pi\) | ||||
−0.841940 | + | 0.539571i | \(0.818586\pi\) | |||||||
\(38\) | 7.07107 | 1.14708 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.41421 | −0.539835 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.58579 | −1.00432 | −0.502162 | − | 0.864774i | \(-0.667462\pi\) | ||||
−0.502162 | + | 0.864774i | \(0.667462\pi\) | |||||||
\(44\) | −4.24264 | −0.639602 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 3.17157 | 0.462621 | 0.231311 | − | 0.972880i | \(-0.425699\pi\) | ||||
0.231311 | + | 0.972880i | \(0.425699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −6.65685 | −0.941421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.828427 | 0.114882 | ||||||||
\(53\) | 1.75736 | 0.241392 | 0.120696 | − | 0.992690i | \(-0.461487\pi\) | ||||
0.120696 | + | 0.992690i | \(0.461487\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.4853 | −1.95319 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | −2.82843 | −0.368230 | −0.184115 | − | 0.982905i | \(-0.558942\pi\) | ||||
−0.184115 | + | 0.982905i | \(0.558942\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.75736 | −0.737154 | −0.368577 | − | 0.929597i | \(-0.620155\pi\) | ||||
−0.368577 | + | 0.929597i | \(0.620155\pi\) | |||||||
\(62\) | −0.828427 | −0.105210 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.82843 | 0.350823 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.75736 | −0.459034 | −0.229517 | − | 0.973305i | \(-0.573715\pi\) | ||||
−0.229517 | + | 0.973305i | \(0.573715\pi\) | |||||||
\(68\) | 0.828427 | 0.100462 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.41421 | 0.408077 | ||||||||
\(71\) | −12.8284 | −1.52245 | −0.761227 | − | 0.648485i | \(-0.775403\pi\) | ||||
−0.761227 | + | 0.648485i | \(0.775403\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0000 | −1.40449 | −0.702247 | − | 0.711934i | \(-0.747820\pi\) | ||||
−0.702247 | + | 0.711934i | \(0.747820\pi\) | |||||||
\(74\) | 10.2426 | 1.19068 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.07107 | −0.811107 | ||||||||
\(77\) | 4.24264 | 0.483494 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3137 | −1.27289 | −0.636446 | − | 0.771321i | \(-0.719596\pi\) | ||||
−0.636446 | + | 0.771321i | \(0.719596\pi\) | |||||||
\(80\) | 3.41421 | 0.381721 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.00000 | −0.220863 | ||||||||
\(83\) | 6.58579 | 0.722884 | 0.361442 | − | 0.932395i | \(-0.382285\pi\) | ||||
0.361442 | + | 0.932395i | \(0.382285\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.82843 | 0.306786 | ||||||||
\(86\) | 6.58579 | 0.710164 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.24264 | 0.452267 | ||||||||
\(89\) | 3.65685 | 0.387626 | 0.193813 | − | 0.981039i | \(-0.437915\pi\) | ||||
0.193813 | + | 0.981039i | \(0.437915\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.828427 | −0.0868428 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.17157 | −0.327123 | ||||||||
\(95\) | −24.1421 | −2.47693 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.17157 | −0.322024 | −0.161012 | − | 0.986952i | \(-0.551476\pi\) | ||||
−0.161012 | + | 0.986952i | \(0.551476\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.65685 | 0.665685 | ||||||||
\(101\) | 7.65685 | 0.761885 | 0.380943 | − | 0.924599i | \(-0.375599\pi\) | ||||
0.380943 | + | 0.924599i | \(0.375599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.48528 | 0.441948 | 0.220974 | − | 0.975280i | \(-0.429076\pi\) | ||||
0.220974 | + | 0.975280i | \(0.429076\pi\) | |||||||
\(104\) | −0.828427 | −0.0812340 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.75736 | −0.170690 | ||||||||
\(107\) | 18.3848 | 1.77732 | 0.888662 | − | 0.458563i | \(-0.151636\pi\) | ||||
0.888662 | + | 0.458563i | \(0.151636\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.4142 | 1.47641 | 0.738207 | − | 0.674574i | \(-0.235673\pi\) | ||||
0.738207 | + | 0.674574i | \(0.235673\pi\) | |||||||
\(110\) | 14.4853 | 1.38112 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −9.31371 | −0.876160 | −0.438080 | − | 0.898936i | \(-0.644341\pi\) | ||||
−0.438080 | + | 0.898936i | \(0.644341\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.41421 | −0.318377 | ||||||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.82843 | 0.260378 | ||||||||
\(119\) | −0.828427 | −0.0759418 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 5.75736 | 0.521247 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.828427 | 0.0743950 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.9706 | −1.50589 | −0.752947 | − | 0.658081i | \(-0.771368\pi\) | ||||
−0.752947 | + | 0.658081i | \(0.771368\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.82843 | −0.248069 | ||||||||
\(131\) | 9.17157 | 0.801324 | 0.400662 | − | 0.916226i | \(-0.368780\pi\) | ||||
0.400662 | + | 0.916226i | \(0.368780\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.07107 | 0.613139 | ||||||||
\(134\) | 3.75736 | 0.324586 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.828427 | −0.0710370 | ||||||||
\(137\) | 18.4853 | 1.57930 | 0.789652 | − | 0.613555i | \(-0.210261\pi\) | ||||
0.789652 | + | 0.613555i | \(0.210261\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.4853 | −1.73754 | −0.868769 | − | 0.495217i | \(-0.835089\pi\) | ||||
−0.868769 | + | 0.495217i | \(0.835089\pi\) | |||||||
\(140\) | −3.41421 | −0.288554 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.8284 | 1.07654 | ||||||||
\(143\) | −3.51472 | −0.293916 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.82843 | −0.567070 | ||||||||
\(146\) | 12.0000 | 0.993127 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.2426 | −0.841940 | ||||||||
\(149\) | 2.72792 | 0.223480 | 0.111740 | − | 0.993737i | \(-0.464358\pi\) | ||||
0.111740 | + | 0.993737i | \(0.464358\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.17157 | 0.583614 | 0.291807 | − | 0.956477i | \(-0.405743\pi\) | ||||
0.291807 | + | 0.956477i | \(0.405743\pi\) | |||||||
\(152\) | 7.07107 | 0.573539 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.24264 | −0.341882 | ||||||||
\(155\) | 2.82843 | 0.227185 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.41421 | 0.591719 | 0.295859 | − | 0.955232i | \(-0.404394\pi\) | ||||
0.295859 | + | 0.955232i | \(0.404394\pi\) | |||||||
\(158\) | 11.3137 | 0.900070 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.41421 | −0.269917 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.17157 | −0.405069 | −0.202534 | − | 0.979275i | \(-0.564918\pi\) | ||||
−0.202534 | + | 0.979275i | \(0.564918\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.58579 | −0.511156 | ||||||||
\(167\) | 8.14214 | 0.630057 | 0.315029 | − | 0.949082i | \(-0.397986\pi\) | ||||
0.315029 | + | 0.949082i | \(0.397986\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3137 | −0.947208 | ||||||||
\(170\) | −2.82843 | −0.216930 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.58579 | −0.502162 | ||||||||
\(173\) | 8.14214 | 0.619035 | 0.309518 | − | 0.950894i | \(-0.399832\pi\) | ||||
0.309518 | + | 0.950894i | \(0.399832\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.65685 | −0.503211 | ||||||||
\(176\) | −4.24264 | −0.319801 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.65685 | −0.274093 | ||||||||
\(179\) | −1.17157 | −0.0875675 | −0.0437837 | − | 0.999041i | \(-0.513941\pi\) | ||||
−0.0437837 | + | 0.999041i | \(0.513941\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.3848 | 1.51519 | 0.757594 | − | 0.652726i | \(-0.226375\pi\) | ||||
0.757594 | + | 0.652726i | \(0.226375\pi\) | |||||||
\(182\) | 0.828427 | 0.0614071 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −34.9706 | −2.57109 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.51472 | −0.257022 | ||||||||
\(188\) | 3.17157 | 0.231311 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 24.1421 | 1.75145 | ||||||||
\(191\) | −2.82843 | −0.204658 | −0.102329 | − | 0.994751i | \(-0.532629\pi\) | ||||
−0.102329 | + | 0.994751i | \(0.532629\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.65685 | −0.551152 | −0.275576 | − | 0.961279i | \(-0.588869\pi\) | ||||
−0.275576 | + | 0.961279i | \(0.588869\pi\) | |||||||
\(194\) | 3.17157 | 0.227706 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −19.6569 | −1.40049 | −0.700246 | − | 0.713901i | \(-0.746927\pi\) | ||||
−0.700246 | + | 0.713901i | \(0.746927\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | −6.65685 | −0.470711 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.65685 | −0.538734 | ||||||||
\(203\) | 2.00000 | 0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.82843 | 0.476918 | ||||||||
\(206\) | −4.48528 | −0.312504 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.828427 | 0.0574411 | ||||||||
\(209\) | 30.0000 | 2.07514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.65685 | −0.664805 | −0.332403 | − | 0.943138i | \(-0.607859\pi\) | ||||
−0.332403 | + | 0.943138i | \(0.607859\pi\) | |||||||
\(212\) | 1.75736 | 0.120696 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.3848 | −1.25676 | ||||||||
\(215\) | −22.4853 | −1.53348 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.828427 | −0.0562373 | ||||||||
\(218\) | −15.4142 | −1.04398 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −14.4853 | −0.976597 | ||||||||
\(221\) | 0.686292 | 0.0461650 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.1421 | 1.88454 | 0.942268 | − | 0.334859i | \(-0.108689\pi\) | ||||
0.942268 | + | 0.334859i | \(0.108689\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.31371 | 0.619539 | ||||||||
\(227\) | −3.75736 | −0.249385 | −0.124692 | − | 0.992195i | \(-0.539794\pi\) | ||||
−0.124692 | + | 0.992195i | \(0.539794\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.3848 | 1.34706 | 0.673532 | − | 0.739158i | \(-0.264776\pi\) | ||||
0.673532 | + | 0.739158i | \(0.264776\pi\) | |||||||
\(230\) | 3.41421 | 0.225127 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.00000 | 0.131306 | ||||||||
\(233\) | −22.6274 | −1.48237 | −0.741186 | − | 0.671300i | \(-0.765736\pi\) | ||||
−0.741186 | + | 0.671300i | \(0.765736\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.8284 | 0.706369 | ||||||||
\(236\) | −2.82843 | −0.184115 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.828427 | 0.0536990 | ||||||||
\(239\) | −10.3431 | −0.669042 | −0.334521 | − | 0.942388i | \(-0.608575\pi\) | ||||
−0.334521 | + | 0.942388i | \(0.608575\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.48528 | 0.417754 | 0.208877 | − | 0.977942i | \(-0.433019\pi\) | ||||
0.208877 | + | 0.977942i | \(0.433019\pi\) | |||||||
\(242\) | −7.00000 | −0.449977 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.75736 | −0.368577 | ||||||||
\(245\) | 3.41421 | 0.218126 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.85786 | −0.372727 | ||||||||
\(248\) | −0.828427 | −0.0526052 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.65685 | −0.357771 | ||||||||
\(251\) | −18.3848 | −1.16044 | −0.580218 | − | 0.814461i | \(-0.697033\pi\) | ||||
−0.580218 | + | 0.814461i | \(0.697033\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.24264 | 0.266733 | ||||||||
\(254\) | 16.9706 | 1.06483 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −29.3137 | −1.82854 | −0.914269 | − | 0.405107i | \(-0.867234\pi\) | ||||
−0.914269 | + | 0.405107i | \(0.867234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.2426 | 0.636447 | ||||||||
\(260\) | 2.82843 | 0.175412 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.17157 | −0.566622 | ||||||||
\(263\) | −12.0000 | −0.739952 | −0.369976 | − | 0.929041i | \(-0.620634\pi\) | ||||
−0.369976 | + | 0.929041i | \(0.620634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | −7.07107 | −0.433555 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.75736 | −0.229517 | ||||||||
\(269\) | −13.7990 | −0.841339 | −0.420670 | − | 0.907214i | \(-0.638205\pi\) | ||||
−0.420670 | + | 0.907214i | \(0.638205\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.3431 | −0.628301 | −0.314151 | − | 0.949373i | \(-0.601720\pi\) | ||||
−0.314151 | + | 0.949373i | \(0.601720\pi\) | |||||||
\(272\) | 0.828427 | 0.0502308 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.4853 | −1.11674 | ||||||||
\(275\) | −28.2426 | −1.70310 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.828427 | −0.0497754 | −0.0248877 | − | 0.999690i | \(-0.507923\pi\) | ||||
−0.0248877 | + | 0.999690i | \(0.507923\pi\) | |||||||
\(278\) | 20.4853 | 1.22863 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.41421 | 0.204038 | ||||||||
\(281\) | −18.9706 | −1.13169 | −0.565844 | − | 0.824512i | \(-0.691450\pi\) | ||||
−0.565844 | + | 0.824512i | \(0.691450\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.41421 | 0.0840663 | 0.0420331 | − | 0.999116i | \(-0.486616\pi\) | ||||
0.0420331 | + | 0.999116i | \(0.486616\pi\) | |||||||
\(284\) | −12.8284 | −0.761227 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.51472 | 0.207830 | ||||||||
\(287\) | −2.00000 | −0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3137 | −0.959630 | ||||||||
\(290\) | 6.82843 | 0.400979 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.0000 | −0.702247 | ||||||||
\(293\) | 27.2132 | 1.58981 | 0.794906 | − | 0.606732i | \(-0.207520\pi\) | ||||
0.794906 | + | 0.606732i | \(0.207520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.65685 | −0.562244 | ||||||||
\(296\) | 10.2426 | 0.595341 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.72792 | −0.158024 | ||||||||
\(299\) | −0.828427 | −0.0479092 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.58579 | 0.379598 | ||||||||
\(302\) | −7.17157 | −0.412678 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.07107 | −0.405554 | ||||||||
\(305\) | −19.6569 | −1.12555 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.3137 | 0.645707 | 0.322854 | − | 0.946449i | \(-0.395358\pi\) | ||||
0.322854 | + | 0.946449i | \(0.395358\pi\) | |||||||
\(308\) | 4.24264 | 0.241747 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.82843 | −0.160644 | ||||||||
\(311\) | 0.970563 | 0.0550356 | 0.0275178 | − | 0.999621i | \(-0.491240\pi\) | ||||
0.0275178 | + | 0.999621i | \(0.491240\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.7990 | −0.779965 | −0.389983 | − | 0.920822i | \(-0.627519\pi\) | ||||
−0.389983 | + | 0.920822i | \(0.627519\pi\) | |||||||
\(314\) | −7.41421 | −0.418408 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.3137 | −0.636446 | ||||||||
\(317\) | −6.97056 | −0.391506 | −0.195753 | − | 0.980653i | \(-0.562715\pi\) | ||||
−0.195753 | + | 0.980653i | \(0.562715\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.48528 | 0.475085 | ||||||||
\(320\) | 3.41421 | 0.190860 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.00000 | −0.0557278 | ||||||||
\(323\) | −5.85786 | −0.325940 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.51472 | 0.305902 | ||||||||
\(326\) | 5.17157 | 0.286427 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.00000 | −0.110432 | ||||||||
\(329\) | −3.17157 | −0.174854 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.6274 | −1.02386 | −0.511928 | − | 0.859029i | \(-0.671068\pi\) | ||||
−0.511928 | + | 0.859029i | \(0.671068\pi\) | |||||||
\(332\) | 6.58579 | 0.361442 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.14214 | −0.445518 | ||||||||
\(335\) | −12.8284 | −0.700892 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.6569 | −1.28867 | −0.644335 | − | 0.764743i | \(-0.722866\pi\) | ||||
−0.644335 | + | 0.764743i | \(0.722866\pi\) | |||||||
\(338\) | 12.3137 | 0.669777 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.82843 | 0.153393 | ||||||||
\(341\) | −3.51472 | −0.190333 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 6.58579 | 0.355082 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.14214 | −0.437724 | ||||||||
\(347\) | 15.7990 | 0.848134 | 0.424067 | − | 0.905631i | \(-0.360602\pi\) | ||||
0.424067 | + | 0.905631i | \(0.360602\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.6569 | −1.26632 | −0.633161 | − | 0.774020i | \(-0.718243\pi\) | ||||
−0.633161 | + | 0.774020i | \(0.718243\pi\) | |||||||
\(350\) | 6.65685 | 0.355824 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.24264 | 0.226134 | ||||||||
\(353\) | −3.31371 | −0.176371 | −0.0881855 | − | 0.996104i | \(-0.528107\pi\) | ||||
−0.0881855 | + | 0.996104i | \(0.528107\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −43.7990 | −2.32461 | ||||||||
\(356\) | 3.65685 | 0.193813 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.17157 | 0.0619196 | ||||||||
\(359\) | −15.5147 | −0.818836 | −0.409418 | − | 0.912347i | \(-0.634268\pi\) | ||||
−0.409418 | + | 0.912347i | \(0.634268\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.0000 | 1.63158 | ||||||||
\(362\) | −20.3848 | −1.07140 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.828427 | −0.0434214 | ||||||||
\(365\) | −40.9706 | −2.14450 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.3137 | 1.63456 | 0.817281 | − | 0.576239i | \(-0.195480\pi\) | ||||
0.817281 | + | 0.576239i | \(0.195480\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 34.9706 | 1.81803 | ||||||||
\(371\) | −1.75736 | −0.0912375 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.7574 | −0.712329 | −0.356165 | − | 0.934423i | \(-0.615916\pi\) | ||||
−0.356165 | + | 0.934423i | \(0.615916\pi\) | |||||||
\(374\) | 3.51472 | 0.181742 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.17157 | −0.163561 | ||||||||
\(377\) | −1.65685 | −0.0853323 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.5269 | 1.67080 | 0.835398 | − | 0.549646i | \(-0.185237\pi\) | ||||
0.835398 | + | 0.549646i | \(0.185237\pi\) | |||||||
\(380\) | −24.1421 | −1.23847 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.82843 | 0.144715 | ||||||||
\(383\) | −20.0000 | −1.02195 | −0.510976 | − | 0.859595i | \(-0.670716\pi\) | ||||
−0.510976 | + | 0.859595i | \(0.670716\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.4853 | 0.738238 | ||||||||
\(386\) | 7.65685 | 0.389724 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.17157 | −0.161012 | ||||||||
\(389\) | 31.6985 | 1.60718 | 0.803588 | − | 0.595185i | \(-0.202921\pi\) | ||||
0.803588 | + | 0.595185i | \(0.202921\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.828427 | −0.0418954 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.6569 | 0.990298 | ||||||||
\(395\) | −38.6274 | −1.94356 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.17157 | 0.359931 | 0.179965 | − | 0.983673i | \(-0.442401\pi\) | ||||
0.179965 | + | 0.983673i | \(0.442401\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.65685 | 0.332843 | ||||||||
\(401\) | −4.82843 | −0.241120 | −0.120560 | − | 0.992706i | \(-0.538469\pi\) | ||||
−0.120560 | + | 0.992706i | \(0.538469\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.686292 | 0.0341866 | ||||||||
\(404\) | 7.65685 | 0.380943 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.00000 | −0.0992583 | ||||||||
\(407\) | 43.4558 | 2.15403 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.31371 | −0.262746 | −0.131373 | − | 0.991333i | \(-0.541939\pi\) | ||||
−0.131373 | + | 0.991333i | \(0.541939\pi\) | |||||||
\(410\) | −6.82843 | −0.337232 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.48528 | 0.220974 | ||||||||
\(413\) | 2.82843 | 0.139178 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.4853 | 1.10376 | ||||||||
\(416\) | −0.828427 | −0.0406170 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −30.0000 | −1.46735 | ||||||||
\(419\) | 39.5563 | 1.93245 | 0.966227 | − | 0.257692i | \(-0.0829621\pi\) | ||||
0.966227 | + | 0.257692i | \(0.0829621\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.10051 | −0.394794 | −0.197397 | − | 0.980324i | \(-0.563249\pi\) | ||||
−0.197397 | + | 0.980324i | \(0.563249\pi\) | |||||||
\(422\) | 9.65685 | 0.470088 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.75736 | −0.0853449 | ||||||||
\(425\) | 5.51472 | 0.267503 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.75736 | 0.278618 | ||||||||
\(428\) | 18.3848 | 0.888662 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 22.4853 | 1.08434 | ||||||||
\(431\) | 38.8284 | 1.87030 | 0.935150 | − | 0.354253i | \(-0.115265\pi\) | ||||
0.935150 | + | 0.354253i | \(0.115265\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.14214 | 0.391286 | 0.195643 | − | 0.980675i | \(-0.437321\pi\) | ||||
0.195643 | + | 0.980675i | \(0.437321\pi\) | |||||||
\(434\) | 0.828427 | 0.0397658 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.4142 | 0.738207 | ||||||||
\(437\) | 7.07107 | 0.338255 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.6569 | −0.651806 | −0.325903 | − | 0.945403i | \(-0.605668\pi\) | ||||
−0.325903 | + | 0.945403i | \(0.605668\pi\) | |||||||
\(440\) | 14.4853 | 0.690559 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.686292 | −0.0326436 | ||||||||
\(443\) | −28.4853 | −1.35338 | −0.676688 | − | 0.736270i | \(-0.736586\pi\) | ||||
−0.676688 | + | 0.736270i | \(0.736586\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.4853 | 0.591859 | ||||||||
\(446\) | −28.1421 | −1.33257 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 30.9706 | 1.46159 | 0.730796 | − | 0.682596i | \(-0.239149\pi\) | ||||
0.730796 | + | 0.682596i | \(0.239149\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.48528 | −0.399556 | ||||||||
\(452\) | −9.31371 | −0.438080 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.75736 | 0.176342 | ||||||||
\(455\) | −2.82843 | −0.132599 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.8284 | 0.974313 | 0.487156 | − | 0.873315i | \(-0.338034\pi\) | ||||
0.487156 | + | 0.873315i | \(0.338034\pi\) | |||||||
\(458\) | −20.3848 | −0.952518 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.41421 | −0.159189 | ||||||||
\(461\) | 3.17157 | 0.147715 | 0.0738574 | − | 0.997269i | \(-0.476469\pi\) | ||||
0.0738574 | + | 0.997269i | \(0.476469\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.3137 | 1.26938 | 0.634688 | − | 0.772769i | \(-0.281129\pi\) | ||||
0.634688 | + | 0.772769i | \(0.281129\pi\) | |||||||
\(464\) | −2.00000 | −0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.6274 | 1.04819 | ||||||||
\(467\) | 9.41421 | 0.435638 | 0.217819 | − | 0.975989i | \(-0.430106\pi\) | ||||
0.217819 | + | 0.975989i | \(0.430106\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.75736 | 0.173499 | ||||||||
\(470\) | −10.8284 | −0.499478 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.82843 | 0.130189 | ||||||||
\(473\) | 27.9411 | 1.28473 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −47.0711 | −2.15977 | ||||||||
\(476\) | −0.828427 | −0.0379709 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.3431 | 0.473084 | ||||||||
\(479\) | 8.97056 | 0.409875 | 0.204938 | − | 0.978775i | \(-0.434301\pi\) | ||||
0.204938 | + | 0.978775i | \(0.434301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.48528 | −0.386896 | ||||||||
\(482\) | −6.48528 | −0.295396 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | −10.8284 | −0.491694 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(488\) | 5.75736 | 0.260623 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.41421 | −0.154238 | ||||||||
\(491\) | −18.1421 | −0.818743 | −0.409372 | − | 0.912368i | \(-0.634252\pi\) | ||||
−0.409372 | + | 0.912368i | \(0.634252\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.65685 | −0.0746210 | ||||||||
\(494\) | 5.85786 | 0.263558 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.828427 | 0.0371975 | ||||||||
\(497\) | 12.8284 | 0.575434 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.1421 | 1.17028 | 0.585141 | − | 0.810931i | \(-0.301039\pi\) | ||||
0.585141 | + | 0.810931i | \(0.301039\pi\) | |||||||
\(500\) | 5.65685 | 0.252982 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.3848 | 0.820553 | ||||||||
\(503\) | −44.7696 | −1.99618 | −0.998088 | − | 0.0618114i | \(-0.980312\pi\) | ||||
−0.998088 | + | 0.0618114i | \(0.980312\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.1421 | 1.16331 | ||||||||
\(506\) | −4.24264 | −0.188608 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.9706 | −0.752947 | ||||||||
\(509\) | 29.1127 | 1.29040 | 0.645199 | − | 0.764015i | \(-0.276775\pi\) | ||||
0.645199 | + | 0.764015i | \(0.276775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | 0.530849 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 29.3137 | 1.29297 | ||||||||
\(515\) | 15.3137 | 0.674803 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.4558 | −0.591787 | ||||||||
\(518\) | −10.2426 | −0.450036 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.82843 | −0.124035 | ||||||||
\(521\) | 5.51472 | 0.241604 | 0.120802 | − | 0.992677i | \(-0.461453\pi\) | ||||
0.120802 | + | 0.992677i | \(0.461453\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.7574 | −0.863929 | −0.431965 | − | 0.901891i | \(-0.642179\pi\) | ||||
−0.431965 | + | 0.901891i | \(0.642179\pi\) | |||||||
\(524\) | 9.17157 | 0.400662 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0000 | 0.523225 | ||||||||
\(527\) | 0.686292 | 0.0298953 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −6.00000 | −0.260623 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.07107 | 0.306570 | ||||||||
\(533\) | 1.65685 | 0.0717663 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 62.7696 | 2.71376 | ||||||||
\(536\) | 3.75736 | 0.162293 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.7990 | 0.594917 | ||||||||
\(539\) | −4.24264 | −0.182743 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.17157 | 0.308330 | 0.154165 | − | 0.988045i | \(-0.450731\pi\) | ||||
0.154165 | + | 0.988045i | \(0.450731\pi\) | |||||||
\(542\) | 10.3431 | 0.444276 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.828427 | −0.0355185 | ||||||||
\(545\) | 52.6274 | 2.25431 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.6274 | −0.967478 | −0.483739 | − | 0.875212i | \(-0.660722\pi\) | ||||
−0.483739 | + | 0.875212i | \(0.660722\pi\) | |||||||
\(548\) | 18.4853 | 0.789652 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 28.2426 | 1.20427 | ||||||||
\(551\) | 14.1421 | 0.602475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.3137 | 0.481108 | ||||||||
\(554\) | 0.828427 | 0.0351965 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.4853 | −0.868769 | ||||||||
\(557\) | 1.27208 | 0.0538997 | 0.0269498 | − | 0.999637i | \(-0.491421\pi\) | ||||
0.0269498 | + | 0.999637i | \(0.491421\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.45584 | −0.230758 | ||||||||
\(560\) | −3.41421 | −0.144277 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.9706 | 0.800225 | ||||||||
\(563\) | −13.2132 | −0.556870 | −0.278435 | − | 0.960455i | \(-0.589816\pi\) | ||||
−0.278435 | + | 0.960455i | \(0.589816\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −31.7990 | −1.33779 | ||||||||
\(566\) | −1.41421 | −0.0594438 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.8284 | 0.538269 | ||||||||
\(569\) | 13.5147 | 0.566566 | 0.283283 | − | 0.959036i | \(-0.408576\pi\) | ||||
0.283283 | + | 0.959036i | \(0.408576\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.0711 | 0.965494 | 0.482747 | − | 0.875760i | \(-0.339639\pi\) | ||||
0.482747 | + | 0.875760i | \(0.339639\pi\) | |||||||
\(572\) | −3.51472 | −0.146958 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.00000 | 0.0834784 | ||||||||
\(575\) | −6.65685 | −0.277610 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.9411 | −0.913421 | −0.456711 | − | 0.889615i | \(-0.650972\pi\) | ||||
−0.456711 | + | 0.889615i | \(0.650972\pi\) | |||||||
\(578\) | 16.3137 | 0.678561 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.82843 | −0.283535 | ||||||||
\(581\) | −6.58579 | −0.273224 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.45584 | −0.308790 | ||||||||
\(584\) | 12.0000 | 0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.2132 | −1.12417 | ||||||||
\(587\) | −25.4558 | −1.05068 | −0.525338 | − | 0.850894i | \(-0.676061\pi\) | ||||
−0.525338 | + | 0.850894i | \(0.676061\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.85786 | −0.241369 | ||||||||
\(590\) | 9.65685 | 0.397566 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.2426 | −0.420970 | ||||||||
\(593\) | −14.0000 | −0.574911 | −0.287456 | − | 0.957794i | \(-0.592809\pi\) | ||||
−0.287456 | + | 0.957794i | \(0.592809\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.82843 | −0.115954 | ||||||||
\(596\) | 2.72792 | 0.111740 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.828427 | 0.0338769 | ||||||||
\(599\) | −33.9411 | −1.38680 | −0.693398 | − | 0.720554i | \(-0.743887\pi\) | ||||
−0.693398 | + | 0.720554i | \(0.743887\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.6274 | −0.433501 | −0.216751 | − | 0.976227i | \(-0.569546\pi\) | ||||
−0.216751 | + | 0.976227i | \(0.569546\pi\) | |||||||
\(602\) | −6.58579 | −0.268417 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.17157 | 0.291807 | ||||||||
\(605\) | 23.8995 | 0.971653 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.8284 | −1.33246 | −0.666232 | − | 0.745744i | \(-0.732094\pi\) | ||||
−0.666232 | + | 0.745744i | \(0.732094\pi\) | |||||||
\(608\) | 7.07107 | 0.286770 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 19.6569 | 0.795883 | ||||||||
\(611\) | 2.62742 | 0.106294 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.6985 | −1.76497 | −0.882483 | − | 0.470345i | \(-0.844129\pi\) | ||||
−0.882483 | + | 0.470345i | \(0.844129\pi\) | |||||||
\(614\) | −11.3137 | −0.456584 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.24264 | −0.170941 | ||||||||
\(617\) | 35.6569 | 1.43549 | 0.717745 | − | 0.696306i | \(-0.245174\pi\) | ||||
0.717745 | + | 0.696306i | \(0.245174\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.8701 | 0.758452 | 0.379226 | − | 0.925304i | \(-0.376190\pi\) | ||||
0.379226 | + | 0.925304i | \(0.376190\pi\) | |||||||
\(620\) | 2.82843 | 0.113592 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.970563 | −0.0389160 | ||||||||
\(623\) | −3.65685 | −0.146509 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 13.7990 | 0.551519 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.41421 | 0.295859 | ||||||||
\(629\) | −8.48528 | −0.338330 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.1716 | 1.00206 | 0.501032 | − | 0.865429i | \(-0.332954\pi\) | ||||
0.501032 | + | 0.865429i | \(0.332954\pi\) | |||||||
\(632\) | 11.3137 | 0.450035 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.97056 | 0.276836 | ||||||||
\(635\) | −57.9411 | −2.29932 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.828427 | 0.0328235 | ||||||||
\(638\) | −8.48528 | −0.335936 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.41421 | −0.134959 | ||||||||
\(641\) | 11.8579 | 0.468357 | 0.234179 | − | 0.972194i | \(-0.424760\pi\) | ||||
0.234179 | + | 0.972194i | \(0.424760\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.6985 | −0.540216 | −0.270108 | − | 0.962830i | \(-0.587059\pi\) | ||||
−0.270108 | + | 0.962830i | \(0.587059\pi\) | |||||||
\(644\) | 1.00000 | 0.0394055 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.85786 | 0.230475 | ||||||||
\(647\) | 47.5980 | 1.87127 | 0.935635 | − | 0.352969i | \(-0.114828\pi\) | ||||
0.935635 | + | 0.352969i | \(0.114828\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.0000 | 0.471041 | ||||||||
\(650\) | −5.51472 | −0.216305 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.17157 | −0.202534 | ||||||||
\(653\) | −25.1127 | −0.982736 | −0.491368 | − | 0.870952i | \(-0.663503\pi\) | ||||
−0.491368 | + | 0.870952i | \(0.663503\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.3137 | 1.22353 | ||||||||
\(656\) | 2.00000 | 0.0780869 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.17157 | 0.123641 | ||||||||
\(659\) | −12.7279 | −0.495809 | −0.247905 | − | 0.968784i | \(-0.579742\pi\) | ||||
−0.247905 | + | 0.968784i | \(0.579742\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.2426 | −0.398393 | −0.199196 | − | 0.979960i | \(-0.563833\pi\) | ||||
−0.199196 | + | 0.979960i | \(0.563833\pi\) | |||||||
\(662\) | 18.6274 | 0.723975 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.58579 | −0.255578 | ||||||||
\(665\) | 24.1421 | 0.936192 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.00000 | 0.0774403 | ||||||||
\(668\) | 8.14214 | 0.315029 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.8284 | 0.495605 | ||||||||
\(671\) | 24.4264 | 0.942971 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.0000 | −0.616755 | −0.308377 | − | 0.951264i | \(-0.599786\pi\) | ||||
−0.308377 | + | 0.951264i | \(0.599786\pi\) | |||||||
\(674\) | 23.6569 | 0.911228 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.3137 | −0.473604 | ||||||||
\(677\) | 28.5858 | 1.09864 | 0.549321 | − | 0.835612i | \(-0.314887\pi\) | ||||
0.549321 | + | 0.835612i | \(0.314887\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.17157 | 0.121714 | ||||||||
\(680\) | −2.82843 | −0.108465 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.51472 | 0.134586 | ||||||||
\(683\) | 15.0294 | 0.575085 | 0.287543 | − | 0.957768i | \(-0.407162\pi\) | ||||
0.287543 | + | 0.957768i | \(0.407162\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 63.1127 | 2.41141 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.58579 | −0.251081 | ||||||||
\(689\) | 1.45584 | 0.0554632 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.1421 | 1.29883 | 0.649414 | − | 0.760435i | \(-0.275014\pi\) | ||||
0.649414 | + | 0.760435i | \(0.275014\pi\) | |||||||
\(692\) | 8.14214 | 0.309518 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.7990 | −0.599721 | ||||||||
\(695\) | −69.9411 | −2.65302 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.65685 | 0.0627578 | ||||||||
\(698\) | 23.6569 | 0.895425 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.65685 | −0.251605 | ||||||||
\(701\) | 25.0711 | 0.946921 | 0.473461 | − | 0.880815i | \(-0.343005\pi\) | ||||
0.473461 | + | 0.880815i | \(0.343005\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 72.4264 | 2.73161 | ||||||||
\(704\) | −4.24264 | −0.159901 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.31371 | 0.124713 | ||||||||
\(707\) | −7.65685 | −0.287966 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.2721 | 0.949113 | 0.474556 | − | 0.880225i | \(-0.342608\pi\) | ||||
0.474556 | + | 0.880225i | \(0.342608\pi\) | |||||||
\(710\) | 43.7990 | 1.64375 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.65685 | −0.137046 | ||||||||
\(713\) | −0.828427 | −0.0310248 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | −0.448775 | ||||||||
\(716\) | −1.17157 | −0.0437837 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.5147 | 0.579004 | ||||||||
\(719\) | −24.9706 | −0.931245 | −0.465622 | − | 0.884983i | \(-0.654170\pi\) | ||||
−0.465622 | + | 0.884983i | \(0.654170\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.48528 | −0.167041 | ||||||||
\(722\) | −31.0000 | −1.15370 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20.3848 | 0.757594 | ||||||||
\(725\) | −13.3137 | −0.494459 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.2843 | −1.34571 | −0.672855 | − | 0.739775i | \(-0.734932\pi\) | ||||
−0.672855 | + | 0.739775i | \(0.734932\pi\) | |||||||
\(728\) | 0.828427 | 0.0307036 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 40.9706 | 1.51639 | ||||||||
\(731\) | −5.45584 | −0.201792 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.1005 | −0.742429 | −0.371215 | − | 0.928547i | \(-0.621059\pi\) | ||||
−0.371215 | + | 0.928547i | \(0.621059\pi\) | |||||||
\(734\) | −31.3137 | −1.15581 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 15.9411 | 0.587199 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.85786 | 0.215485 | 0.107743 | − | 0.994179i | \(-0.465638\pi\) | ||||
0.107743 | + | 0.994179i | \(0.465638\pi\) | |||||||
\(740\) | −34.9706 | −1.28554 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.75736 | 0.0645147 | ||||||||
\(743\) | 42.6274 | 1.56385 | 0.781924 | − | 0.623374i | \(-0.214238\pi\) | ||||
0.781924 | + | 0.623374i | \(0.214238\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.31371 | 0.341228 | ||||||||
\(746\) | 13.7574 | 0.503693 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.51472 | −0.128511 | ||||||||
\(749\) | −18.3848 | −0.671765 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.1127 | 0.843394 | 0.421697 | − | 0.906737i | \(-0.361435\pi\) | ||||
0.421697 | + | 0.906737i | \(0.361435\pi\) | |||||||
\(752\) | 3.17157 | 0.115655 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.65685 | 0.0603391 | ||||||||
\(755\) | 24.4853 | 0.891111 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.07107 | 0.184311 | 0.0921555 | − | 0.995745i | \(-0.470624\pi\) | ||||
0.0921555 | + | 0.995745i | \(0.470624\pi\) | |||||||
\(758\) | −32.5269 | −1.18143 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 24.1421 | 0.875727 | ||||||||
\(761\) | −25.6569 | −0.930060 | −0.465030 | − | 0.885295i | \(-0.653957\pi\) | ||||
−0.465030 | + | 0.885295i | \(0.653957\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.4142 | −0.558032 | ||||||||
\(764\) | −2.82843 | −0.102329 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.0000 | 0.722629 | ||||||||
\(767\) | −2.34315 | −0.0846061 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.79899 | 0.209117 | 0.104558 | − | 0.994519i | \(-0.466657\pi\) | ||||
0.104558 | + | 0.994519i | \(0.466657\pi\) | |||||||
\(770\) | −14.4853 | −0.522013 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.65685 | −0.275576 | ||||||||
\(773\) | −5.07107 | −0.182394 | −0.0911968 | − | 0.995833i | \(-0.529069\pi\) | ||||
−0.0911968 | + | 0.995833i | \(0.529069\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.51472 | 0.198095 | ||||||||
\(776\) | 3.17157 | 0.113853 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.6985 | −1.13645 | ||||||||
\(779\) | −14.1421 | −0.506695 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 54.4264 | 1.94753 | ||||||||
\(782\) | 0.828427 | 0.0296245 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 25.3137 | 0.903485 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.1005 | 0.502629 | 0.251314 | − | 0.967906i | \(-0.419137\pi\) | ||||
0.251314 | + | 0.967906i | \(0.419137\pi\) | |||||||
\(788\) | −19.6569 | −0.700246 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 38.6274 | 1.37430 | ||||||||
\(791\) | 9.31371 | 0.331157 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.76955 | −0.169372 | ||||||||
\(794\) | −7.17157 | −0.254510 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.87006 | −0.172506 | −0.0862531 | − | 0.996273i | \(-0.527489\pi\) | ||||
−0.0862531 | + | 0.996273i | \(0.527489\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.62742 | 0.0929513 | ||||||||
\(800\) | −6.65685 | −0.235355 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.82843 | 0.170498 | ||||||||
\(803\) | 50.9117 | 1.79663 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.41421 | 0.120335 | ||||||||
\(806\) | −0.686292 | −0.0241736 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.65685 | −0.269367 | ||||||||
\(809\) | 33.9411 | 1.19331 | 0.596653 | − | 0.802499i | \(-0.296497\pi\) | ||||
0.596653 | + | 0.802499i | \(0.296497\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.82843 | −0.0993195 | −0.0496598 | − | 0.998766i | \(-0.515814\pi\) | ||||
−0.0496598 | + | 0.998766i | \(0.515814\pi\) | |||||||
\(812\) | 2.00000 | 0.0701862 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −43.4558 | −1.52313 | ||||||||
\(815\) | −17.6569 | −0.618493 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.5685 | 1.62923 | ||||||||
\(818\) | 5.31371 | 0.185789 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.82843 | 0.238459 | ||||||||
\(821\) | 25.1127 | 0.876439 | 0.438220 | − | 0.898868i | \(-0.355609\pi\) | ||||
0.438220 | + | 0.898868i | \(0.355609\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.51472 | 0.192231 | 0.0961155 | − | 0.995370i | \(-0.469358\pi\) | ||||
0.0961155 | + | 0.995370i | \(0.469358\pi\) | |||||||
\(824\) | −4.48528 | −0.156252 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.82843 | −0.0984136 | ||||||||
\(827\) | −5.21320 | −0.181281 | −0.0906404 | − | 0.995884i | \(-0.528891\pi\) | ||||
−0.0906404 | + | 0.995884i | \(0.528891\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.6274 | 1.27212 | 0.636061 | − | 0.771638i | \(-0.280562\pi\) | ||||
0.636061 | + | 0.771638i | \(0.280562\pi\) | |||||||
\(830\) | −22.4853 | −0.780476 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.828427 | 0.0287205 | ||||||||
\(833\) | 0.828427 | 0.0287033 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.7990 | 0.962024 | ||||||||
\(836\) | 30.0000 | 1.03757 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −39.5563 | −1.36645 | ||||||||
\(839\) | −0.686292 | −0.0236934 | −0.0118467 | − | 0.999930i | \(-0.503771\pi\) | ||||
−0.0118467 | + | 0.999930i | \(0.503771\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 8.10051 | 0.279162 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.65685 | −0.332403 | ||||||||
\(845\) | −42.0416 | −1.44628 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.00000 | −0.240523 | ||||||||
\(848\) | 1.75736 | 0.0603480 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.51472 | −0.189153 | ||||||||
\(851\) | 10.2426 | 0.351113 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.5147 | −0.599693 | −0.299846 | − | 0.953988i | \(-0.596935\pi\) | ||||
−0.299846 | + | 0.953988i | \(0.596935\pi\) | |||||||
\(854\) | −5.75736 | −0.197013 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.3848 | −0.628379 | ||||||||
\(857\) | −12.6863 | −0.433355 | −0.216678 | − | 0.976243i | \(-0.569522\pi\) | ||||
−0.216678 | + | 0.976243i | \(0.569522\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.5980 | 1.21459 | 0.607294 | − | 0.794477i | \(-0.292255\pi\) | ||||
0.607294 | + | 0.794477i | \(0.292255\pi\) | |||||||
\(860\) | −22.4853 | −0.766742 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −38.8284 | −1.32250 | ||||||||
\(863\) | 8.97056 | 0.305362 | 0.152681 | − | 0.988276i | \(-0.451209\pi\) | ||||
0.152681 | + | 0.988276i | \(0.451209\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27.7990 | 0.945194 | ||||||||
\(866\) | −8.14214 | −0.276681 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.828427 | −0.0281186 | ||||||||
\(869\) | 48.0000 | 1.62829 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.11270 | −0.105470 | ||||||||
\(872\) | −15.4142 | −0.521991 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.07107 | −0.239182 | ||||||||
\(875\) | −5.65685 | −0.191237 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.82843 | 0.298115 | 0.149057 | − | 0.988829i | \(-0.452376\pi\) | ||||
0.149057 | + | 0.988829i | \(0.452376\pi\) | |||||||
\(878\) | 13.6569 | 0.460897 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −14.4853 | −0.488299 | ||||||||
\(881\) | −9.31371 | −0.313787 | −0.156893 | − | 0.987616i | \(-0.550148\pi\) | ||||
−0.156893 | + | 0.987616i | \(0.550148\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.9411 | −1.14221 | −0.571105 | − | 0.820877i | \(-0.693485\pi\) | ||||
−0.571105 | + | 0.820877i | \(0.693485\pi\) | |||||||
\(884\) | 0.686292 | 0.0230825 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.4853 | 0.956982 | ||||||||
\(887\) | −40.1421 | −1.34784 | −0.673921 | − | 0.738804i | \(-0.735391\pi\) | ||||
−0.673921 | + | 0.738804i | \(0.735391\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.9706 | 0.569174 | ||||||||
\(890\) | −12.4853 | −0.418508 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 28.1421 | 0.942268 | ||||||||
\(893\) | −22.4264 | −0.750471 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.00000 | −0.133705 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30.9706 | −1.03350 | ||||||||
\(899\) | −1.65685 | −0.0552592 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.45584 | 0.0485012 | ||||||||
\(902\) | 8.48528 | 0.282529 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.31371 | 0.309769 | ||||||||
\(905\) | 69.5980 | 2.31352 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.0122 | −1.36179 | −0.680894 | − | 0.732382i | \(-0.738408\pi\) | ||||
−0.680894 | + | 0.732382i | \(0.738408\pi\) | |||||||
\(908\) | −3.75736 | −0.124692 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.82843 | 0.0937614 | ||||||||
\(911\) | 42.1421 | 1.39623 | 0.698116 | − | 0.715985i | \(-0.254022\pi\) | ||||
0.698116 | + | 0.715985i | \(0.254022\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.9411 | −0.924716 | ||||||||
\(914\) | −20.8284 | −0.688943 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.3848 | 0.673532 | ||||||||
\(917\) | −9.17157 | −0.302872 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.6274 | 1.80199 | 0.900996 | − | 0.433827i | \(-0.142837\pi\) | ||||
0.900996 | + | 0.433827i | \(0.142837\pi\) | |||||||
\(920\) | 3.41421 | 0.112563 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.17157 | −0.104450 | ||||||||
\(923\) | −10.6274 | −0.349806 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −68.1838 | −2.24187 | ||||||||
\(926\) | −27.3137 | −0.897584 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.00000 | 0.0656532 | ||||||||
\(929\) | −10.0000 | −0.328089 | −0.164045 | − | 0.986453i | \(-0.552454\pi\) | ||||
−0.164045 | + | 0.986453i | \(0.552454\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.07107 | −0.231745 | ||||||||
\(932\) | −22.6274 | −0.741186 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.41421 | −0.308042 | ||||||||
\(935\) | −12.0000 | −0.392442 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.2843 | −1.64272 | −0.821358 | − | 0.570413i | \(-0.806783\pi\) | ||||
−0.821358 | + | 0.570413i | \(0.806783\pi\) | |||||||
\(938\) | −3.75736 | −0.122682 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.8284 | 0.353184 | ||||||||
\(941\) | 7.89949 | 0.257516 | 0.128758 | − | 0.991676i | \(-0.458901\pi\) | ||||
0.128758 | + | 0.991676i | \(0.458901\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.00000 | −0.0651290 | ||||||||
\(944\) | −2.82843 | −0.0920575 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.9411 | −0.908444 | ||||||||
\(947\) | −19.5147 | −0.634143 | −0.317072 | − | 0.948402i | \(-0.602700\pi\) | ||||
−0.317072 | + | 0.948402i | \(0.602700\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.94113 | −0.322703 | ||||||||
\(950\) | 47.0711 | 1.52719 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.828427 | 0.0268495 | ||||||||
\(953\) | −11.1716 | −0.361883 | −0.180941 | − | 0.983494i | \(-0.557914\pi\) | ||||
−0.180941 | + | 0.983494i | \(0.557914\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.65685 | −0.312488 | ||||||||
\(956\) | −10.3431 | −0.334521 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.97056 | −0.289826 | ||||||||
\(959\) | −18.4853 | −0.596921 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3137 | −0.977862 | ||||||||
\(962\) | 8.48528 | 0.273576 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.48528 | 0.208877 | ||||||||
\(965\) | −26.1421 | −0.841545 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.8284 | 0.541166 | 0.270583 | − | 0.962697i | \(-0.412784\pi\) | ||||
0.270583 | + | 0.962697i | \(0.412784\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.8284 | 0.347680 | ||||||||
\(971\) | 32.5269 | 1.04384 | 0.521919 | − | 0.852995i | \(-0.325216\pi\) | ||||
0.521919 | + | 0.852995i | \(0.325216\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.4853 | 0.656728 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.75736 | −0.184289 | ||||||||
\(977\) | −9.11270 | −0.291541 | −0.145771 | − | 0.989318i | \(-0.546566\pi\) | ||||
−0.145771 | + | 0.989318i | \(0.546566\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.5147 | −0.495853 | ||||||||
\(980\) | 3.41421 | 0.109063 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.1421 | 0.578939 | ||||||||
\(983\) | 38.1421 | 1.21655 | 0.608273 | − | 0.793728i | \(-0.291863\pi\) | ||||
0.608273 | + | 0.793728i | \(0.291863\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −67.1127 | −2.13839 | ||||||||
\(986\) | 1.65685 | 0.0527650 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.85786 | −0.186363 | ||||||||
\(989\) | 6.58579 | 0.209416 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.1421 | 1.27516 | 0.637578 | − | 0.770385i | \(-0.279936\pi\) | ||||
0.637578 | + | 0.770385i | \(0.279936\pi\) | |||||||
\(992\) | −0.828427 | −0.0263026 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.8284 | −0.406893 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.9706 | −0.474122 | −0.237061 | − | 0.971495i | \(-0.576184\pi\) | ||||
−0.237061 | + | 0.971495i | \(0.576184\pi\) | |||||||
\(998\) | −26.1421 | −0.827515 | ||||||||
\(999\) | 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 | 2898.2.a.y.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 2898.2.a.z.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2898.2.a.y.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2898.2.a.z.1.1 | yes | 2 | 3.2 | odd | 2 |