Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2280,2,Mod(1,2280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("2280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2280.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: | \(18.2058916609\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2280.1 |
$q$-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 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.41421 | −1.29045 | −0.645226 | − | 0.763992i | \(-0.723237\pi\) | ||||
−0.645226 | + | 0.763992i | \(0.723237\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.41421 | −0.426401 | −0.213201 | − | 0.977008i | \(-0.568389\pi\) | ||||
−0.213201 | + | 0.977008i | \(0.568389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24264 | 1.17670 | 0.588348 | − | 0.808608i | \(-0.299778\pi\) | ||||
0.588348 | + | 0.808608i | \(0.299778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.82843 | 0.685994 | 0.342997 | − | 0.939336i | \(-0.388558\pi\) | ||||
0.342997 | + | 0.939336i | \(0.388558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.41421 | −0.745042 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.82843 | −1.00680 | −0.503398 | − | 0.864054i | \(-0.667917\pi\) | ||||
−0.503398 | + | 0.864054i | \(0.667917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.24264 | 0.416448 | 0.208224 | − | 0.978081i | \(-0.433232\pi\) | ||||
0.208224 | + | 0.978081i | \(0.433232\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.82843 | −1.58563 | −0.792816 | − | 0.609461i | \(-0.791386\pi\) | ||||
−0.792816 | + | 0.609461i | \(0.791386\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.41421 | −0.246183 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.41421 | 0.577107 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.07107 | −1.16248 | −0.581238 | − | 0.813733i | \(-0.697432\pi\) | ||||
−0.581238 | + | 0.813733i | \(0.697432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.24264 | 0.679366 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.24264 | 0.350242 | 0.175121 | − | 0.984547i | \(-0.443968\pi\) | ||||
0.175121 | + | 0.984547i | \(0.443968\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.75736 | −0.267995 | −0.133997 | − | 0.990982i | \(-0.542781\pi\) | ||||
−0.133997 | + | 0.990982i | \(0.542781\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.82843 | 0.704298 | 0.352149 | − | 0.935944i | \(-0.385451\pi\) | ||||
0.352149 | + | 0.935944i | \(0.385451\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.65685 | 0.665265 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.82843 | 0.396059 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.4853 | −1.71499 | −0.857493 | − | 0.514496i | \(-0.827979\pi\) | ||||
−0.857493 | + | 0.514496i | \(0.827979\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.41421 | 0.190693 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.82843 | −0.368230 | −0.184115 | − | 0.982905i | \(-0.558942\pi\) | ||||
−0.184115 | + | 0.982905i | \(0.558942\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.00000 | −1.02430 | −0.512148 | − | 0.858898i | \(-0.671150\pi\) | ||||
−0.512148 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.41421 | −0.430150 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.24264 | −0.526235 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.3137 | −1.38219 | −0.691095 | − | 0.722764i | \(-0.742871\pi\) | ||||
−0.691095 | + | 0.722764i | \(0.742871\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.82843 | −0.581274 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.17157 | −0.613753 | −0.306876 | − | 0.951749i | \(-0.599284\pi\) | ||||
−0.306876 | + | 0.951749i | \(0.599284\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.65685 | −0.428002 | −0.214001 | − | 0.976833i | \(-0.568650\pi\) | ||||
−0.214001 | + | 0.976833i | \(0.568650\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.82843 | 0.550250 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.34315 | −0.263624 | −0.131812 | − | 0.991275i | \(-0.542080\pi\) | ||||
−0.131812 | + | 0.991275i | \(0.542080\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.82843 | −0.306786 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.24264 | 0.240436 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.5563 | −1.43697 | −0.718485 | − | 0.695542i | \(-0.755164\pi\) | ||||
−0.718485 | + | 0.695542i | \(0.755164\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.4853 | −1.51847 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.82843 | −0.915465 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.89949 | 1.00514 | 0.502571 | − | 0.864536i | \(-0.332388\pi\) | ||||
0.502571 | + | 0.864536i | \(0.332388\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.41421 | −0.142134 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.8284 | −1.27648 | −0.638238 | − | 0.769839i | \(-0.720336\pi\) | ||||
−0.638238 | + | 0.769839i | \(0.720336\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.41421 | 0.333193 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.6569 | 1.32026 | 0.660129 | − | 0.751152i | \(-0.270502\pi\) | ||||
0.660129 | + | 0.751152i | \(0.270502\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.1421 | 1.16301 | 0.581503 | − | 0.813544i | \(-0.302465\pi\) | ||||
0.581503 | + | 0.813544i | \(0.302465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.07107 | −0.671156 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.65685 | 0.908440 | 0.454220 | − | 0.890889i | \(-0.349918\pi\) | ||||
0.454220 | + | 0.890889i | \(0.349918\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.82843 | 0.450253 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.24264 | 0.392232 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.65685 | −0.885242 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.24264 | 0.202212 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.9706 | 1.50589 | 0.752947 | − | 0.658081i | \(-0.228632\pi\) | ||||
0.752947 | + | 0.658081i | \(0.228632\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.75736 | −0.154727 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.92893 | 0.430643 | 0.215321 | − | 0.976543i | \(-0.430920\pi\) | ||||
0.215321 | + | 0.976543i | \(0.430920\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.41421 | 0.296050 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.9706 | −1.27902 | −0.639511 | − | 0.768782i | \(-0.720863\pi\) | ||||
−0.639511 | + | 0.768782i | \(0.720863\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.4853 | −1.05899 | −0.529494 | − | 0.848314i | \(-0.677618\pi\) | ||||
−0.529494 | + | 0.848314i | \(0.677618\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.82843 | 0.406627 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.00000 | −0.501745 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.24264 | −0.186241 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.65685 | 0.384091 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.6569 | 0.954967 | 0.477483 | − | 0.878641i | \(-0.341549\pi\) | ||||
0.477483 | + | 0.878641i | \(0.341549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1716 | −0.909130 | −0.454565 | − | 0.890714i | \(-0.650205\pi\) | ||||
−0.454565 | + | 0.890714i | \(0.650205\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.82843 | 0.228665 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.82843 | 0.709116 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.14214 | −0.649813 | −0.324907 | − | 0.945746i | \(-0.605333\pi\) | ||||
−0.324907 | + | 0.945746i | \(0.605333\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.4853 | −0.990147 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.4853 | 1.29922 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.100505 | −0.00787216 | −0.00393608 | − | 0.999992i | \(-0.501253\pi\) | ||||
−0.00393608 | + | 0.999992i | \(0.501253\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.41421 | 0.110096 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.6569 | 1.21156 | 0.605782 | − | 0.795631i | \(-0.292860\pi\) | ||||
0.605782 | + | 0.795631i | \(0.292860\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.6569 | 1.03831 | 0.519156 | − | 0.854680i | \(-0.326246\pi\) | ||||
0.519156 | + | 0.854680i | \(0.326246\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.41421 | −0.258090 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.82843 | −0.212598 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.7990 | 1.77882 | 0.889410 | − | 0.457110i | \(-0.151116\pi\) | ||||
0.889410 | + | 0.457110i | \(0.151116\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.82843 | 0.358894 | 0.179447 | − | 0.983768i | \(-0.442569\pi\) | ||||
0.179447 | + | 0.983768i | \(0.442569\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.00000 | −0.591377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.07107 | 0.519875 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | −0.292509 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.41421 | −0.248347 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.4142 | 0.970618 | 0.485309 | − | 0.874343i | \(-0.338707\pi\) | ||||
0.485309 | + | 0.874343i | \(0.338707\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.0711 | 1.66069 | 0.830346 | − | 0.557248i | \(-0.188143\pi\) | ||||
0.830346 | + | 0.557248i | \(0.188143\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.24264 | −0.303822 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.48528 | 0.604551 | 0.302276 | − | 0.953221i | \(-0.402254\pi\) | ||||
0.302276 | + | 0.953221i | \(0.402254\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.1421 | −1.00251 | −0.501255 | − | 0.865300i | \(-0.667128\pi\) | ||||
−0.501255 | + | 0.865300i | \(0.667128\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.3137 | −0.798007 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.65685 | −0.537406 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.24264 | −0.156633 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.82843 | −0.335599 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.41421 | 0.0978232 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.17157 | −0.354350 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.75736 | 0.119851 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30.1421 | 2.04618 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.65685 | −0.247107 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.3137 | −1.82906 | −0.914531 | − | 0.404517i | \(-0.867440\pi\) | ||||
−0.914531 | + | 0.404517i | \(0.867440\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.31371 | −0.352683 | −0.176342 | − | 0.984329i | \(-0.556426\pi\) | ||||
−0.176342 | + | 0.984329i | \(0.556426\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.6274 | −1.23093 | −0.615467 | − | 0.788163i | \(-0.711033\pi\) | ||||
−0.615467 | + | 0.788163i | \(0.711033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.82843 | 0.317687 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.65685 | 0.501617 | 0.250809 | − | 0.968037i | \(-0.419304\pi\) | ||||
0.250809 | + | 0.968037i | \(0.419304\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.82843 | −0.314972 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.34315 | −0.152204 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.2426 | −0.791911 | −0.395955 | − | 0.918270i | \(-0.629586\pi\) | ||||
−0.395955 | + | 0.918270i | \(0.629586\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.9706 | −0.964339 | −0.482169 | − | 0.876078i | \(-0.660151\pi\) | ||||
−0.482169 | + | 0.876078i | \(0.660151\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.65685 | −0.297516 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.24264 | −0.269953 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.7279 | 1.56081 | 0.780406 | − | 0.625273i | \(-0.215012\pi\) | ||||
0.780406 | + | 0.625273i | \(0.215012\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.82843 | 0.429300 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.82843 | −0.177123 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.6569 | 1.10140 | 0.550702 | − | 0.834702i | \(-0.314360\pi\) | ||||
0.550702 | + | 0.834702i | \(0.314360\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.1421 | 1.50012 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.24264 | 0.138816 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.6569 | −1.21209 | −0.606047 | − | 0.795429i | \(-0.707246\pi\) | ||||
−0.606047 | + | 0.795429i | \(0.707246\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.4853 | 0.766965 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.5563 | −0.829635 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.10051 | 0.250012 | 0.125006 | − | 0.992156i | \(-0.460105\pi\) | ||||
0.125006 | + | 0.992156i | \(0.460105\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.14214 | 0.130125 | 0.0650627 | − | 0.997881i | \(-0.479275\pi\) | ||||
0.0650627 | + | 0.997881i | \(0.479275\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.4853 | −0.876689 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.41421 | −0.0852803 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.31371 | −0.319270 | −0.159635 | − | 0.987176i | \(-0.551032\pi\) | ||||
−0.159635 | + | 0.987176i | \(0.551032\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.82843 | −0.528544 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.2426 | 0.849645 | 0.424822 | − | 0.905277i | \(-0.360337\pi\) | ||||
0.424822 | + | 0.905277i | \(0.360337\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.10051 | −0.243750 | −0.121875 | − | 0.992545i | \(-0.538891\pi\) | ||||
−0.121875 | + | 0.992545i | \(0.538891\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00000 | 0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.65685 | −0.451970 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.89949 | 0.580319 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.00000 | 0.233682 | 0.116841 | − | 0.993151i | \(-0.462723\pi\) | ||||
0.116841 | + | 0.993151i | \(0.462723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.82843 | 0.164677 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.41421 | −0.0820610 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.4853 | −1.18469 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | 0.345834 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.8284 | −0.736974 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.00000 | 0.458079 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.17157 | 0.0668652 | 0.0334326 | − | 0.999441i | \(-0.489356\pi\) | ||||
0.0334326 | + | 0.999441i | \(0.489356\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.41421 | −0.533831 | −0.266916 | − | 0.963720i | \(-0.586004\pi\) | ||||
−0.266916 | + | 0.963720i | \(0.586004\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.7990 | 1.68434 | 0.842169 | − | 0.539213i | \(-0.181278\pi\) | ||||
0.842169 | + | 0.539213i | \(0.181278\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.41421 | 0.192369 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.48528 | 0.476581 | 0.238290 | − | 0.971194i | \(-0.423413\pi\) | ||||
0.238290 | + | 0.971194i | \(0.423413\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.17157 | −0.177574 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.6569 | 0.762251 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.82843 | −0.157378 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.24264 | 0.235339 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.1421 | 0.671462 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.4853 | −0.908863 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8284 | −0.705114 | −0.352557 | − | 0.935790i | \(-0.614688\pi\) | ||||
−0.352557 | + | 0.935790i | \(0.614688\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.07107 | −0.387492 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.3137 | 0.618134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.89949 | −0.103472 | −0.0517360 | − | 0.998661i | \(-0.516475\pi\) | ||||
−0.0517360 | + | 0.998661i | \(0.516475\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.65685 | 0.524488 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.4853 | 0.676116 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.82843 | 0.259954 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.343146 | 0.0184210 | 0.00921051 | − | 0.999958i | \(-0.497068\pi\) | ||||
0.00921051 | + | 0.999958i | \(0.497068\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0000 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.24264 | 0.226455 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.0000 | 0.745145 | 0.372572 | − | 0.928003i | \(-0.378476\pi\) | ||||
0.372572 | + | 0.928003i | \(0.378476\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.17157 | 0.274479 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.65685 | −0.511095 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.0416 | 1.05776 | 0.528878 | − | 0.848698i | \(-0.322613\pi\) | ||||
0.528878 | + | 0.848698i | \(0.322613\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.00000 | −0.472377 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.65685 | 0.191408 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.07107 | −0.264708 | −0.132354 | − | 0.991203i | \(-0.542254\pi\) | ||||
−0.132354 | + | 0.991203i | \(0.542254\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.24264 | 0.116747 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 42.6274 | 2.21311 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.0416 | −1.45194 | −0.725970 | − | 0.687726i | \(-0.758609\pi\) | ||||
−0.725970 | + | 0.687726i | \(0.758609\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.51472 | 0.490033 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.4853 | −0.538593 | −0.269296 | − | 0.963057i | \(-0.586791\pi\) | ||||
−0.269296 | + | 0.963057i | \(0.586791\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.9706 | 0.869428 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.3137 | −1.19127 | −0.595637 | − | 0.803253i | \(-0.703100\pi\) | ||||
−0.595637 | + | 0.803253i | \(0.703100\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.82843 | −0.246079 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.75736 | −0.0893316 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.6569 | −1.19945 | −0.599725 | − | 0.800206i | \(-0.704723\pi\) | ||||
−0.599725 | + | 0.800206i | \(0.704723\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.6569 | −0.690657 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.92893 | 0.248632 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.34315 | 0.117896 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.0000 | 1.30490 | 0.652451 | − | 0.757831i | \(-0.273741\pi\) | ||||
0.652451 | + | 0.757831i | \(0.273741\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.41421 | 0.170924 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.2132 | −0.559961 | −0.279980 | − | 0.960006i | \(-0.590328\pi\) | ||||
−0.279980 | + | 0.960006i | \(0.590328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.4558 | −1.86581 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.0000 | 0.495682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.1421 | −1.78711 | −0.893557 | − | 0.448950i | \(-0.851798\pi\) | ||||
−0.893557 | + | 0.448950i | \(0.851798\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.9706 | −0.738443 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.65685 | 0.475183 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.4853 | −0.611407 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.2426 | 1.37974 | 0.689872 | − | 0.723932i | \(-0.257667\pi\) | ||||
0.689872 | + | 0.723932i | \(0.257667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.3137 | 1.23371 | 0.616857 | − | 0.787075i | \(-0.288406\pi\) | ||||
0.616857 | + | 0.787075i | \(0.288406\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.82843 | 0.234766 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.82843 | 0.137199 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.3137 | 1.32180 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.00000 | −0.289683 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.1421 | −1.64457 | −0.822284 | − | 0.569077i | \(-0.807301\pi\) | ||||
−0.822284 | + | 0.569077i | \(0.807301\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.7574 | 0.565023 | 0.282511 | − | 0.959264i | \(-0.408833\pi\) | ||||
0.282511 | + | 0.959264i | \(0.408833\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.24264 | −0.107526 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.82843 | 0.230975 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.68629 | −0.223664 | −0.111832 | − | 0.993727i | \(-0.535672\pi\) | ||||
−0.111832 | + | 0.993727i | \(0.535672\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.65685 | 0.221755 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.14214 | 0.196799 | 0.0983994 | − | 0.995147i | \(-0.468628\pi\) | ||||
0.0983994 | + | 0.995147i | \(0.468628\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.5563 | 0.642633 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.6569 | 0.551350 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.5269 | 1.25188 | 0.625941 | − | 0.779870i | \(-0.284715\pi\) | ||||
0.625941 | + | 0.779870i | \(0.284715\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.17157 | −0.149344 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.1716 | −0.524886 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.4853 | 0.679080 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.1421 | 0.942209 | 0.471105 | − | 0.882077i | \(-0.343855\pi\) | ||||
0.471105 | + | 0.882077i | \(0.343855\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.82843 | 0.132020 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.6274 | −0.960715 | −0.480357 | − | 0.877073i | \(-0.659493\pi\) | ||||
−0.480357 | + | 0.877073i | \(0.659493\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.7574 | −1.19705 | −0.598523 | − | 0.801106i | \(-0.704245\pi\) | ||||
−0.598523 | + | 0.801106i | \(0.704245\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.82843 | 0.409409 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.1421 | −0.932067 | −0.466033 | − | 0.884767i | \(-0.654317\pi\) | ||||
−0.466033 | + | 0.884767i | \(0.654317\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 38.6274 | 1.78365 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.14214 | −0.375170 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.48528 | 0.114273 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.4853 | −0.571662 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.61522 | 0.0738015 | 0.0369007 | − | 0.999319i | \(-0.488251\pi\) | ||||
0.0369007 | + | 0.999319i | \(0.488251\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.0000 | −1.36788 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.4853 | 0.750106 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.89949 | −0.449513 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.8284 | 0.853197 | 0.426599 | − | 0.904441i | \(-0.359712\pi\) | ||||
0.426599 | + | 0.904441i | \(0.359712\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.100505 | −0.00454500 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.7574 | 1.43319 | 0.716595 | − | 0.697490i | \(-0.245700\pi\) | ||||
0.716595 | + | 0.697490i | \(0.245700\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.34315 | 0.285681 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.41421 | 0.0635642 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.6569 | 0.792018 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.8284 | 0.663812 | 0.331906 | − | 0.943313i | \(-0.392308\pi\) | ||||
0.331906 | + | 0.943313i | \(0.392308\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.6569 | 0.699497 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −26.2843 | −1.17196 | −0.585979 | − | 0.810326i | \(-0.699290\pi\) | ||||
−0.585979 | + | 0.810326i | \(0.699290\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.8284 | 0.570858 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000 | 0.222058 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.0711 | 0.579365 | 0.289682 | − | 0.957123i | \(-0.406450\pi\) | ||||
0.289682 | + | 0.957123i | \(0.406450\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.4853 | 0.552316 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | 0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.82843 | −0.300314 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.6569 | 0.599469 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.3848 | −0.893073 | −0.446537 | − | 0.894765i | \(-0.647343\pi\) | ||||
−0.446537 | + | 0.894765i | \(0.647343\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.1421 | 1.66784 | 0.833920 | − | 0.551886i | \(-0.186092\pi\) | ||||
0.833920 | + | 0.551886i | \(0.186092\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.41421 | −0.149008 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.9706 | −1.08773 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.313708 | 0.0136395 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.82843 | −0.122743 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.51472 | 0.412128 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.6569 | −0.590437 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.7990 | 1.02700 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.58579 | −0.283670 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.6863 | 0.803386 | 0.401693 | − | 0.915774i | \(-0.368422\pi\) | ||||
0.401693 | + | 0.915774i | \(0.368422\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.82843 | 0.207208 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.1421 | −0.520112 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.4853 | 1.21794 | 0.608971 | − | 0.793192i | \(-0.291582\pi\) | ||||
0.608971 | + | 0.793192i | \(0.291582\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.00000 | −0.341432 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.24264 | −0.0955397 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | 0.340195 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.07107 | 0.300150 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.9706 | 0.464838 | 0.232419 | − | 0.972616i | \(-0.425336\pi\) | ||||
0.232419 | + | 0.972616i | \(0.425336\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.45584 | −0.315349 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.3137 | 1.40401 | 0.702003 | − | 0.712174i | \(-0.252289\pi\) | ||||
0.702003 | + | 0.712174i | \(0.252289\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.65685 | −0.406267 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.41421 | −0.143383 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.10051 | −0.171902 | −0.0859511 | − | 0.996299i | \(-0.527393\pi\) | ||||
−0.0859511 | + | 0.996299i | \(0.527393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.485281 | 0.0203084 | 0.0101542 | − | 0.999948i | \(-0.496768\pi\) | ||||
0.0101542 | + | 0.999948i | \(0.496768\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.4142 | 0.560387 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.82843 | −0.201359 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.51472 | 0.0630586 | 0.0315293 | − | 0.999503i | \(-0.489962\pi\) | ||||
0.0315293 | + | 0.999503i | \(0.489962\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 23.0711 | 0.958801 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.4853 | 0.849873 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.6569 | 0.731272 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.24264 | −0.175412 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.17157 | 0.296002 | 0.148001 | − | 0.988987i | \(-0.452716\pi\) | ||||
0.148001 | + | 0.988987i | \(0.452716\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.82843 | 0.363769 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.48528 | 0.349038 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.3137 | −0.875249 | −0.437625 | − | 0.899158i | \(-0.644180\pi\) | ||||
−0.437625 | + | 0.899158i | \(0.644180\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.65685 | 0.395892 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.1421 | −0.578799 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.9706 | −0.693398 | −0.346699 | − | 0.937976i | \(-0.612698\pi\) | ||||
−0.346699 | + | 0.937976i | \(0.612698\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.1421 | −1.63743 | −0.818716 | − | 0.574199i | \(-0.805314\pi\) | ||||
−0.818716 | + | 0.574199i | \(0.805314\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.3137 | −0.460730 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.00000 | 0.365902 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.1421 | 1.38579 | 0.692893 | − | 0.721040i | \(-0.256336\pi\) | ||||
0.692893 | + | 0.721040i | \(0.256336\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.65685 | −0.310271 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.4853 | 0.828746 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.142136 | 0.00574080 | 0.00287040 | − | 0.999996i | \(-0.499086\pi\) | ||||
0.00287040 | + | 0.999996i | \(0.499086\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.24264 | −0.0904320 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.1127 | −1.25255 | −0.626275 | − | 0.779602i | \(-0.715421\pi\) | ||||
−0.626275 | + | 0.779602i | \(0.715421\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.17157 | −0.207863 | −0.103932 | − | 0.994584i | \(-0.533142\pi\) | ||||
−0.103932 | + | 0.994584i | \(0.533142\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.82843 | −0.193758 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 46.2843 | 1.85434 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.41421 | 0.0564782 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.0000 | −0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.97056 | 0.357112 | 0.178556 | − | 0.983930i | \(-0.442857\pi\) | ||||
0.178556 | + | 0.983930i | \(0.442857\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0000 | −0.476957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.9706 | −0.673456 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.7574 | 0.782815 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.17157 | −0.204584 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.2426 | −1.35250 | −0.676251 | − | 0.736671i | \(-0.736397\pi\) | ||||
−0.676251 | + | 0.736671i | \(0.736397\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.75736 | 0.0693035 | 0.0346517 | − | 0.999399i | \(-0.488968\pi\) | ||||
0.0346517 | + | 0.999399i | \(0.488968\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.75736 | 0.0691960 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.3431 | 0.799772 | 0.399886 | − | 0.916565i | \(-0.369050\pi\) | ||||
0.399886 | + | 0.916565i | \(0.369050\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.00000 | 0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 30.1421 | 1.18136 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.4853 | −0.488587 | −0.244293 | − | 0.969701i | \(-0.578556\pi\) | ||||
−0.244293 | + | 0.969701i | \(0.578556\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.92893 | −0.192589 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.65685 | −0.142667 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.34315 | −0.247094 | −0.123547 | − | 0.992339i | \(-0.539427\pi\) | ||||
−0.123547 | + | 0.992339i | \(0.539427\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.1127 | 0.976771 | 0.488385 | − | 0.872628i | \(-0.337586\pi\) | ||||
0.488385 | + | 0.872628i | \(0.337586\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.0000 | 0.466041 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.41421 | −0.132398 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.8284 | −0.419278 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.3137 | −1.05601 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.3137 | 0.436761 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.8995 | −1.15254 | −0.576270 | − | 0.817259i | \(-0.695492\pi\) | ||||
−0.576270 | + | 0.817259i | \(0.695492\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.7990 | 1.52960 | 0.764800 | − | 0.644268i | \(-0.222838\pi\) | ||||
0.764800 | + | 0.644268i | \(0.222838\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33.7990 | −1.29709 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.31371 | −0.203622 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.6863 | −0.791539 | −0.395769 | − | 0.918350i | \(-0.629522\pi\) | ||||
−0.395769 | + | 0.918350i | \(0.629522\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.9706 | 0.571996 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.6274 | −0.710680 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −52.9706 | −2.01802 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.1127 | −1.18358 | −0.591791 | − | 0.806091i | \(-0.701579\pi\) | ||||
−0.591791 | + | 0.806091i | \(0.701579\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.82843 | 0.183417 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.4853 | 0.473594 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.34315 | 0.240264 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.65685 | 0.289609 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.343146 | 0.0129604 | 0.00648022 | − | 0.999979i | \(-0.497937\pi\) | ||||
0.00648022 | + | 0.999979i | \(0.497937\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.07107 | 0.266690 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.82843 | −0.181849 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 43.7990 | 1.64723 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.3431 | −0.688891 | −0.344446 | − | 0.938806i | \(-0.611933\pi\) | ||||
−0.344446 | + | 0.938806i | \(0.611933\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.34315 | −0.0878748 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 42.6274 | 1.59641 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | 0.224387 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.2426 | −0.457210 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 46.3848 | 1.72986 | 0.864930 | − | 0.501892i | \(-0.167363\pi\) | ||||
0.864930 | + | 0.501892i | \(0.167363\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.3137 | 1.01722 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.9706 | −0.556761 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.24264 | 0.0832896 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.38478 | 0.310974 | 0.155487 | − | 0.987838i | \(-0.450305\pi\) | ||||
0.155487 | + | 0.987838i | \(0.450305\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.97056 | −0.183843 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0000 | 0.960332 | 0.480166 | − | 0.877178i | \(-0.340576\pi\) | ||||
0.480166 | + | 0.877178i | \(0.340576\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.65685 | −0.171771 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0000 | 0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.68629 | 0.319530 | 0.159765 | − | 0.987155i | \(-0.448926\pi\) | ||||
0.159765 | + | 0.987155i | \(0.448926\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.24264 | −0.155857 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.9411 | 1.68542 | 0.842708 | − | 0.538371i | \(-0.180960\pi\) | ||||
0.842708 | + | 0.538371i | \(0.180960\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.6569 | −0.427074 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.00000 | −0.219529 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −46.6274 | −1.70373 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.142136 | −0.00518660 | −0.00259330 | − | 0.999997i | \(-0.500825\pi\) | ||||
−0.00259330 | + | 0.999997i | \(0.500825\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.7279 | 0.901136 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.1716 | 0.406575 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.7696 | 1.69987 | 0.849934 | − | 0.526889i | \(-0.176642\pi\) | ||||
0.849934 | + | 0.526889i | \(0.176642\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.82843 | 0.247856 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.9706 | 0.542682 | 0.271341 | − | 0.962483i | \(-0.412533\pi\) | ||||
0.271341 | + | 0.962483i | \(0.412533\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −41.4558 | −1.50080 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.82843 | −0.102262 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0000 | −0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.6569 | −0.708844 | −0.354422 | − | 0.935086i | \(-0.615322\pi\) | ||||
−0.354422 | + | 0.935086i | \(0.615322\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.6569 | 0.635896 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.4853 | 0.880674 | 0.440337 | − | 0.897832i | \(-0.354859\pi\) | ||||
0.440337 | + | 0.897832i | \(0.354859\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.82843 | −0.317126 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.1421 | 0.866094 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.24264 | −0.0803509 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.31371 | 0.261705 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.24264 | 0.0801454 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.14214 | 0.290605 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.48528 | −0.302468 | −0.151234 | − | 0.988498i | \(-0.548325\pi\) | ||||
−0.151234 | + | 0.988498i | \(0.548325\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.6569 | −0.699803 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.9706 | −1.17230 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.9411 | −1.20528 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.4853 | 0.442807 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.9706 | −1.45125 | −0.725626 | − | 0.688089i | \(-0.758450\pi\) | ||||
−0.725626 | + | 0.688089i | \(0.758450\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.6569 | 0.483145 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.5563 | −0.478990 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.17157 | 0.182501 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.4853 | −0.581030 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.10051 | 0.144345 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.68629 | 0.0944450 | 0.0472225 | − | 0.998884i | \(-0.484963\pi\) | ||||
0.0472225 | + | 0.998884i | \(0.484963\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.2843 | −1.69549 | −0.847745 | − | 0.530404i | \(-0.822040\pi\) | ||||
−0.847745 | + | 0.530404i | \(0.822040\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.14214 | 0.0751280 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.100505 | 0.00352054 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.75736 | 0.0614822 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.4853 | −0.506157 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.4853 | −0.784742 | −0.392371 | − | 0.919807i | \(-0.628345\pi\) | ||||
−0.392371 | + | 0.919807i | \(0.628345\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.2132 | 0.669730 | 0.334865 | − | 0.942266i | \(-0.391309\pi\) | ||||
0.334865 | + | 0.942266i | \(0.391309\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.41421 | −0.0492366 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.0000 | 0.904109 | 0.452054 | − | 0.891990i | \(-0.350691\pi\) | ||||
0.452054 | + | 0.891990i | \(0.350691\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.79899 | −0.0624815 | −0.0312408 | − | 0.999512i | \(-0.509946\pi\) | ||||
−0.0312408 | + | 0.999512i | \(0.509946\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.31371 | −0.184331 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.1716 | 0.456368 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.6569 | −0.541828 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.82843 | −0.305155 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.5147 | −0.811818 | −0.405909 | − | 0.913913i | \(-0.633045\pi\) | ||||
−0.405909 | + | 0.913913i | \(0.633045\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.9706 | −0.826571 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.2426 | 0.490543 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.00000 | −0.172005 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.7279 | 1.05582 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.10051 | −0.140729 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.1421 | 1.17038 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.4558 | −1.62486 | −0.812429 | − | 0.583061i | \(-0.801855\pi\) | ||||
−0.812429 | + | 0.583061i | \(0.801855\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.0833 | 1.50586 | 0.752928 | − | 0.658103i | \(-0.228641\pi\) | ||||
0.752928 | + | 0.658103i | \(0.228641\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.9411 | 1.70397 | 0.851985 | − | 0.523567i | \(-0.175399\pi\) | ||||
0.851985 | + | 0.523567i | \(0.175399\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.65685 | −0.260945 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.0000 | −1.22545 | −0.612727 | − | 0.790295i | \(-0.709928\pi\) | ||||
−0.612727 | + | 0.790295i | \(0.709928\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.6569 | −0.464347 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.00000 | −0.305656 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.31371 | 0.112410 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.0000 | −1.62642 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.89949 | 0.335047 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.41421 | 0.115421 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.4142 | 1.26339 | 0.631694 | − | 0.775218i | \(-0.282360\pi\) | ||||
0.631694 | + | 0.775218i | \(0.282360\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.00000 | 0.134917 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.1127 | 1.11560 | 0.557798 | − | 0.829977i | \(-0.311647\pi\) | ||||
0.557798 | + | 0.829977i | \(0.311647\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.27208 | 0.312030 | 0.156015 | − | 0.987755i | \(-0.450135\pi\) | ||||
0.156015 | + | 0.987755i | \(0.450135\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.82843 | 0.0950765 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.9706 | 0.569816 | 0.284908 | − | 0.958555i | \(-0.408037\pi\) | ||||
0.284908 | + | 0.958555i | \(0.408037\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −57.9411 | −1.94328 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.41421 | −0.0473779 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.82843 | −0.161577 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.7990 | −0.795512 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.4853 | −0.683984 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.7990 | −0.660333 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −35.3137 | −1.17647 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.00000 | 0.199667 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.82843 | −0.160502 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.8579 | −0.460143 | −0.230071 | − | 0.973174i | \(-0.573896\pi\) | ||||
−0.230071 | + | 0.973174i | \(0.573896\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.8284 | −0.425492 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.0000 | −0.662630 | −0.331315 | − | 0.943520i | \(-0.607492\pi\) | ||||
−0.331315 | + | 0.943520i | \(0.607492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.48528 | 0.280822 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.00000 | 0.264472 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.8284 | −0.555724 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.6569 | −0.582446 | −0.291223 | − | 0.956655i | \(-0.594062\pi\) | ||||
−0.291223 | + | 0.956655i | \(0.594062\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.17157 | 0.0386046 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21.9411 | −0.722201 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.07107 | −0.232495 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.00000 | −0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.8284 | −0.814594 | −0.407297 | − | 0.913296i | \(-0.633529\pi\) | ||||
−0.407297 | + | 0.913296i | \(0.633529\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.65685 | −0.152622 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.41421 | −0.308208 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.00000 | 0.130814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.1127 | −0.428373 | −0.214187 | − | 0.976793i | \(-0.568710\pi\) | ||||
−0.214187 | + | 0.976793i | \(0.568710\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.7990 | 0.972453 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.0416 | 0.718537 | 0.359268 | − | 0.933234i | \(-0.383026\pi\) | ||||
0.359268 | + | 0.933234i | \(0.383026\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.8284 | −0.352622 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.41421 | 0.111064 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.3137 | 0.822585 | 0.411292 | − | 0.911503i | \(-0.365077\pi\) | ||||
0.411292 | + | 0.911503i | \(0.365077\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.5147 | −0.503629 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.48528 | 0.275154 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.9411 | −0.710743 | −0.355371 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355371 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.4142 | −0.434074 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.17157 | −0.102522 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 51.1127 | 1.65052 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.9411 | 1.51423 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.6569 | 0.440086 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.0711 | −0.742684 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.89949 | −0.254031 | −0.127015 | − | 0.991901i | \(-0.540540\pi\) | ||||
−0.127015 | + | 0.991901i | \(0.540540\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.82843 | −0.0908622 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.686292 | 0.0220241 | 0.0110121 | − | 0.999939i | \(-0.496495\pi\) | ||||
0.0110121 | + | 0.999939i | \(0.496495\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.6274 | 1.36657 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.24264 | 0.135873 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.2010 | −0.646288 | −0.323144 | − | 0.946350i | \(-0.604740\pi\) | ||||
−0.323144 | + | 0.946350i | \(0.604740\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.1716 | 0.612726 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.1421 | 0.387669 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.5980 | 0.688869 | 0.344434 | − | 0.938810i | \(-0.388071\pi\) | ||||
0.344434 | + | 0.938810i | \(0.388071\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.48528 | −0.270364 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.4853 | −0.524732 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.48528 | 0.269816 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.0294 | −0.477426 | −0.238713 | − | 0.971090i | \(-0.576725\pi\) | ||||
−0.238713 | + | 0.971090i | \(0.576725\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.8284 | −0.407098 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.1421 | 0.448336 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.7990 | 1.57715 | 0.788575 | − | 0.614939i | \(-0.210819\pi\) | ||||
0.788575 | + | 0.614939i | \(0.210819\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.07107 | −0.223719 |
(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 | 2280.2.a.o.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 6840.2.a.x.1.1 | 2 | |||
4.3 | odd | 2 | 4560.2.a.bg.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.o.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4560.2.a.bg.1.2 | 2 | 4.3 | odd | 2 | |||
6840.2.a.x.1.1 | 2 | 3.2 | odd | 2 |