Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, 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("1575.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(12.5764383184\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 175) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | −0.437016 | −0.218508 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.236068 | 0.0711772 | 0.0355886 | − | 0.999367i | \(-0.488669\pi\) | ||||
0.0355886 | + | 0.999367i | \(0.488669\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.23607 | −0.342824 | −0.171412 | − | 0.985199i | \(-0.554833\pi\) | ||||
−0.171412 | + | 0.985199i | \(0.554833\pi\) | |||||||
\(14\) | 0.618034 | 0.165177 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | 2.47214 | 0.599581 | 0.299791 | − | 0.954005i | \(-0.403083\pi\) | ||||
0.299791 | + | 0.954005i | \(0.403083\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.47214 | −1.02598 | −0.512989 | − | 0.858395i | \(-0.671462\pi\) | ||||
−0.512989 | + | 0.858395i | \(0.671462\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.145898 | −0.0311056 | ||||||||
\(23\) | 6.23607 | 1.30031 | 0.650155 | − | 0.759802i | \(-0.274704\pi\) | ||||
0.650155 | + | 0.759802i | \(0.274704\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.763932 | 0.149819 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.61803 | 0.305780 | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.70820 | 0.666013 | 0.333007 | − | 0.942925i | \(-0.391937\pi\) | ||||
0.333007 | + | 0.942925i | \(0.391937\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.52786 | −0.262027 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | −0.493197 | −0.246598 | − | 0.969118i | \(-0.579313\pi\) | ||||
−0.246598 | + | 0.969118i | \(0.579313\pi\) | |||||||
\(38\) | 2.76393 | 0.448369 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.76393 | −0.744001 | −0.372001 | − | 0.928232i | \(-0.621328\pi\) | ||||
−0.372001 | + | 0.928232i | \(0.621328\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.76393 | −0.268997 | −0.134499 | − | 0.990914i | \(-0.542942\pi\) | ||||
−0.134499 | + | 0.990914i | \(0.542942\pi\) | |||||||
\(44\) | −0.381966 | −0.0575835 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.85410 | −0.568256 | ||||||||
\(47\) | −2.00000 | −0.291730 | −0.145865 | − | 0.989305i | \(-0.546597\pi\) | ||||
−0.145865 | + | 0.989305i | \(0.546597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 8.47214 | 1.16374 | 0.581869 | − | 0.813283i | \(-0.302322\pi\) | ||||
0.581869 | + | 0.813283i | \(0.302322\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.23607 | −0.298807 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.09017 | 0.405759 | ||||||||
\(59\) | −11.7082 | −1.52428 | −0.762139 | − | 0.647413i | \(-0.775851\pi\) | ||||
−0.762139 | + | 0.647413i | \(0.775851\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.70820 | −1.24301 | −0.621504 | − | 0.783411i | \(-0.713478\pi\) | ||||
−0.621504 | + | 0.783411i | \(0.713478\pi\) | |||||||
\(62\) | −2.29180 | −0.291058 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.23607 | 0.517518 | 0.258759 | − | 0.965942i | \(-0.416686\pi\) | ||||
0.258759 | + | 0.965942i | \(0.416686\pi\) | |||||||
\(68\) | −4.00000 | −0.485071 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.70820 | −1.03347 | −0.516737 | − | 0.856144i | \(-0.672853\pi\) | ||||
−0.516737 | + | 0.856144i | \(0.672853\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.76393 | 1.02574 | 0.512870 | − | 0.858466i | \(-0.328582\pi\) | ||||
0.512870 | + | 0.858466i | \(0.328582\pi\) | |||||||
\(74\) | 1.85410 | 0.215535 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.23607 | 0.830034 | ||||||||
\(77\) | −0.236068 | −0.0269024 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.1803 | −1.25789 | −0.628943 | − | 0.777451i | \(-0.716512\pi\) | ||||
−0.628943 | + | 0.777451i | \(0.716512\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.94427 | 0.325140 | ||||||||
\(83\) | −7.70820 | −0.846085 | −0.423043 | − | 0.906110i | \(-0.639038\pi\) | ||||
−0.423043 | + | 0.906110i | \(0.639038\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.09017 | 0.117556 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.527864 | 0.0562705 | ||||||||
\(89\) | −17.2361 | −1.82702 | −0.913510 | − | 0.406817i | \(-0.866639\pi\) | ||||
−0.913510 | + | 0.406817i | \(0.866639\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.23607 | 0.129575 | ||||||||
\(92\) | −10.0902 | −1.05197 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.23607 | 0.127491 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.23607 | −0.531642 | −0.265821 | − | 0.964022i | \(-0.585643\pi\) | ||||
−0.265821 | + | 0.964022i | \(0.585643\pi\) | |||||||
\(98\) | −0.618034 | −0.0624309 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.76393 | −0.474029 | −0.237014 | − | 0.971506i | \(-0.576169\pi\) | ||||
−0.237014 | + | 0.971506i | \(0.576169\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.47214 | −0.834784 | −0.417392 | − | 0.908726i | \(-0.637056\pi\) | ||||
−0.417392 | + | 0.908726i | \(0.637056\pi\) | |||||||
\(104\) | −2.76393 | −0.271026 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.23607 | −0.508572 | ||||||||
\(107\) | 8.00000 | 0.773389 | 0.386695 | − | 0.922208i | \(-0.373617\pi\) | ||||
0.386695 | + | 0.922208i | \(0.373617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.41641 | 0.806146 | 0.403073 | − | 0.915168i | \(-0.367942\pi\) | ||||
0.403073 | + | 0.915168i | \(0.367942\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.85410 | −0.175196 | ||||||||
\(113\) | −14.4164 | −1.35618 | −0.678091 | − | 0.734978i | \(-0.737192\pi\) | ||||
−0.678091 | + | 0.734978i | \(0.737192\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.09017 | 0.751153 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.23607 | 0.666134 | ||||||||
\(119\) | −2.47214 | −0.226620 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9443 | −0.994934 | ||||||||
\(122\) | 6.00000 | 0.543214 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.00000 | −0.538816 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.6525 | −1.21146 | −0.605731 | − | 0.795670i | \(-0.707119\pi\) | ||||
−0.605731 | + | 0.795670i | \(0.707119\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.9443 | 1.48043 | 0.740214 | − | 0.672371i | \(-0.234724\pi\) | ||||
0.740214 | + | 0.672371i | \(0.234724\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.47214 | 0.387783 | ||||||||
\(134\) | −2.61803 | −0.226164 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.52786 | 0.474010 | ||||||||
\(137\) | −10.9443 | −0.935032 | −0.467516 | − | 0.883985i | \(-0.654851\pi\) | ||||
−0.467516 | + | 0.883985i | \(0.654851\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.6525 | 0.903531 | 0.451766 | − | 0.892137i | \(-0.350794\pi\) | ||||
0.451766 | + | 0.892137i | \(0.350794\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.38197 | 0.451645 | ||||||||
\(143\) | −0.291796 | −0.0244012 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.41641 | −0.448265 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.85410 | 0.399005 | ||||||||
\(149\) | −3.94427 | −0.323127 | −0.161564 | − | 0.986862i | \(-0.551654\pi\) | ||||
−0.161564 | + | 0.986862i | \(0.551654\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.2361 | −1.64679 | −0.823394 | − | 0.567470i | \(-0.807922\pi\) | ||||
−0.823394 | + | 0.567470i | \(0.807922\pi\) | |||||||
\(152\) | −10.0000 | −0.811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.145898 | 0.0117568 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.763932 | −0.0609684 | −0.0304842 | − | 0.999535i | \(-0.509705\pi\) | ||||
−0.0304842 | + | 0.999535i | \(0.509705\pi\) | |||||||
\(158\) | 6.90983 | 0.549717 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.23607 | −0.491471 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.52786 | 0.119672 | 0.0598358 | − | 0.998208i | \(-0.480942\pi\) | ||||
0.0598358 | + | 0.998208i | \(0.480942\pi\) | |||||||
\(164\) | 7.70820 | 0.601910 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.76393 | 0.369753 | ||||||||
\(167\) | 5.23607 | 0.405179 | 0.202590 | − | 0.979264i | \(-0.435064\pi\) | ||||
0.202590 | + | 0.979264i | \(0.435064\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.85410 | 0.217623 | ||||||||
\(173\) | −11.5279 | −0.876447 | −0.438224 | − | 0.898866i | \(-0.644392\pi\) | ||||
−0.438224 | + | 0.898866i | \(0.644392\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.437694 | 0.0329924 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.6525 | 0.798437 | ||||||||
\(179\) | 23.4164 | 1.75022 | 0.875112 | − | 0.483920i | \(-0.160787\pi\) | ||||
0.875112 | + | 0.483920i | \(0.160787\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.18034 | 0.608040 | 0.304020 | − | 0.952666i | \(-0.401671\pi\) | ||||
0.304020 | + | 0.952666i | \(0.401671\pi\) | |||||||
\(182\) | −0.763932 | −0.0566264 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.9443 | 1.02799 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.583592 | 0.0426765 | ||||||||
\(188\) | 3.23607 | 0.236015 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.47214 | −0.468307 | −0.234154 | − | 0.972200i | \(-0.575232\pi\) | ||||
−0.234154 | + | 0.972200i | \(0.575232\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.4164 | −0.893753 | −0.446876 | − | 0.894596i | \(-0.647464\pi\) | ||||
−0.446876 | + | 0.894596i | \(0.647464\pi\) | |||||||
\(194\) | 3.23607 | 0.232336 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.61803 | −0.115574 | ||||||||
\(197\) | −1.47214 | −0.104885 | −0.0524427 | − | 0.998624i | \(-0.516701\pi\) | ||||
−0.0524427 | + | 0.998624i | \(0.516701\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.23607 | 0.512951 | 0.256476 | − | 0.966551i | \(-0.417439\pi\) | ||||
0.256476 | + | 0.966551i | \(0.417439\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.94427 | 0.207158 | ||||||||
\(203\) | 5.00000 | 0.350931 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.23607 | 0.364814 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.29180 | −0.158907 | ||||||||
\(209\) | −1.05573 | −0.0730262 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | −13.7082 | −0.941483 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.94427 | −0.337983 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.70820 | −0.251729 | ||||||||
\(218\) | −5.20163 | −0.352299 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.05573 | −0.205551 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.1803 | −1.35138 | −0.675688 | − | 0.737188i | \(-0.736153\pi\) | ||||
−0.675688 | + | 0.737188i | \(0.736153\pi\) | |||||||
\(224\) | 5.61803 | 0.375371 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.90983 | 0.592673 | ||||||||
\(227\) | 21.4164 | 1.42146 | 0.710728 | − | 0.703466i | \(-0.248365\pi\) | ||||
0.710728 | + | 0.703466i | \(0.248365\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.47214 | −0.295527 | −0.147764 | − | 0.989023i | \(-0.547207\pi\) | ||||
−0.147764 | + | 0.989023i | \(0.547207\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.1803 | −0.734025 | ||||||||
\(233\) | 7.94427 | 0.520447 | 0.260223 | − | 0.965548i | \(-0.416204\pi\) | ||||
0.260223 | + | 0.965548i | \(0.416204\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 18.9443 | 1.23317 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.52786 | 0.0990367 | ||||||||
\(239\) | 5.52786 | 0.357568 | 0.178784 | − | 0.983888i | \(-0.442784\pi\) | ||||
0.178784 | + | 0.983888i | \(0.442784\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.52786 | −0.227250 | −0.113625 | − | 0.993524i | \(-0.536246\pi\) | ||||
−0.113625 | + | 0.993524i | \(0.536246\pi\) | |||||||
\(242\) | 6.76393 | 0.434802 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 15.7082 | 1.00561 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.52786 | 0.351730 | ||||||||
\(248\) | 8.29180 | 0.526530 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.47214 | −0.408518 | −0.204259 | − | 0.978917i | \(-0.565478\pi\) | ||||
−0.204259 | + | 0.978917i | \(0.565478\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.47214 | 0.0925524 | ||||||||
\(254\) | 8.43769 | 0.529428 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | −12.6525 | −0.789240 | −0.394620 | − | 0.918844i | \(-0.629124\pi\) | ||||
−0.394620 | + | 0.918844i | \(0.629124\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.00000 | 0.186411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.4721 | −0.646971 | ||||||||
\(263\) | 16.2361 | 1.00116 | 0.500579 | − | 0.865691i | \(-0.333120\pi\) | ||||
0.500579 | + | 0.865691i | \(0.333120\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.76393 | −0.169468 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.85410 | −0.418681 | ||||||||
\(269\) | 11.7082 | 0.713862 | 0.356931 | − | 0.934131i | \(-0.383823\pi\) | ||||
0.356931 | + | 0.934131i | \(0.383823\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.7082 | 1.44017 | 0.720085 | − | 0.693885i | \(-0.244103\pi\) | ||||
0.720085 | + | 0.693885i | \(0.244103\pi\) | |||||||
\(272\) | 4.58359 | 0.277921 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.76393 | 0.408624 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.8885 | 1.19499 | 0.597493 | − | 0.801874i | \(-0.296163\pi\) | ||||
0.597493 | + | 0.801874i | \(0.296163\pi\) | |||||||
\(278\) | −6.58359 | −0.394858 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.3607 | 0.916341 | 0.458171 | − | 0.888864i | \(-0.348505\pi\) | ||||
0.458171 | + | 0.888864i | \(0.348505\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.4164 | −1.03530 | −0.517649 | − | 0.855593i | \(-0.673193\pi\) | ||||
−0.517649 | + | 0.855593i | \(0.673193\pi\) | |||||||
\(284\) | 14.0902 | 0.836098 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.180340 | 0.0106637 | ||||||||
\(287\) | 4.76393 | 0.281206 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8885 | −0.640503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.1803 | −0.829842 | ||||||||
\(293\) | −31.1246 | −1.81832 | −0.909160 | − | 0.416448i | \(-0.863275\pi\) | ||||
−0.909160 | + | 0.416448i | \(0.863275\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.70820 | −0.389906 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.43769 | 0.141212 | ||||||||
\(299\) | −7.70820 | −0.445777 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.76393 | 0.101671 | ||||||||
\(302\) | 12.5066 | 0.719673 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.29180 | −0.475567 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.58359 | −0.261599 | −0.130800 | − | 0.991409i | \(-0.541754\pi\) | ||||
−0.130800 | + | 0.991409i | \(0.541754\pi\) | |||||||
\(308\) | 0.381966 | 0.0217645 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.3607 | −1.38137 | −0.690684 | − | 0.723157i | \(-0.742690\pi\) | ||||
−0.690684 | + | 0.723157i | \(0.742690\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.5279 | −1.10378 | −0.551890 | − | 0.833917i | \(-0.686093\pi\) | ||||
−0.551890 | + | 0.833917i | \(0.686093\pi\) | |||||||
\(314\) | 0.472136 | 0.0266442 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 18.0902 | 1.01765 | ||||||||
\(317\) | 25.3607 | 1.42440 | 0.712199 | − | 0.701978i | \(-0.247699\pi\) | ||||
0.712199 | + | 0.701978i | \(0.247699\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.18034 | −0.0660863 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.85410 | 0.214781 | ||||||||
\(323\) | −11.0557 | −0.615157 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.944272 | −0.0522984 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.6525 | −0.588185 | ||||||||
\(329\) | 2.00000 | 0.110264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.7082 | −1.35809 | −0.679043 | − | 0.734099i | \(-0.737605\pi\) | ||||
−0.679043 | + | 0.734099i | \(0.737605\pi\) | |||||||
\(332\) | 12.4721 | 0.684497 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.23607 | −0.177070 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.4721 | 0.897294 | 0.448647 | − | 0.893709i | \(-0.351906\pi\) | ||||
0.448647 | + | 0.893709i | \(0.351906\pi\) | |||||||
\(338\) | 7.09017 | 0.385654 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.875388 | 0.0474049 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −3.94427 | −0.212661 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.12461 | 0.383022 | ||||||||
\(347\) | 20.2361 | 1.08633 | 0.543165 | − | 0.839626i | \(-0.317226\pi\) | ||||
0.543165 | + | 0.839626i | \(0.317226\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.47214 | 0.239388 | 0.119694 | − | 0.992811i | \(-0.461809\pi\) | ||||
0.119694 | + | 0.992811i | \(0.461809\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.32624 | −0.0706887 | ||||||||
\(353\) | −2.18034 | −0.116048 | −0.0580239 | − | 0.998315i | \(-0.518480\pi\) | ||||
−0.0580239 | + | 0.998315i | \(0.518480\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 27.8885 | 1.47809 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.4721 | −0.764876 | ||||||||
\(359\) | 30.1246 | 1.58992 | 0.794958 | − | 0.606664i | \(-0.207493\pi\) | ||||
0.794958 | + | 0.606664i | \(0.207493\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −5.05573 | −0.265723 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 37.1246 | 1.93789 | 0.968944 | − | 0.247278i | \(-0.0795362\pi\) | ||||
0.968944 | + | 0.247278i | \(0.0795362\pi\) | |||||||
\(368\) | 11.5623 | 0.602727 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.47214 | −0.439851 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 37.8328 | 1.95891 | 0.979454 | − | 0.201665i | \(-0.0646354\pi\) | ||||
0.979454 | + | 0.201665i | \(0.0646354\pi\) | |||||||
\(374\) | −0.360680 | −0.0186503 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.47214 | −0.230633 | ||||||||
\(377\) | 6.18034 | 0.318304 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.1803 | −0.574295 | −0.287148 | − | 0.957886i | \(-0.592707\pi\) | ||||
−0.287148 | + | 0.957886i | \(0.592707\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.00000 | 0.204658 | ||||||||
\(383\) | −33.2361 | −1.69828 | −0.849142 | − | 0.528165i | \(-0.822880\pi\) | ||||
−0.849142 | + | 0.528165i | \(0.822880\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.67376 | 0.390584 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.47214 | 0.430108 | ||||||||
\(389\) | −2.88854 | −0.146455 | −0.0732275 | − | 0.997315i | \(-0.523330\pi\) | ||||
−0.0732275 | + | 0.997315i | \(0.523330\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.4164 | 0.779641 | ||||||||
\(392\) | 2.23607 | 0.112938 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.909830 | 0.0458366 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.05573 | −0.454494 | −0.227247 | − | 0.973837i | \(-0.572972\pi\) | ||||
−0.227247 | + | 0.973837i | \(0.572972\pi\) | |||||||
\(398\) | −4.47214 | −0.224168 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.52786 | −0.126236 | −0.0631178 | − | 0.998006i | \(-0.520104\pi\) | ||||
−0.0631178 | + | 0.998006i | \(0.520104\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.58359 | −0.228325 | ||||||||
\(404\) | 7.70820 | 0.383497 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.09017 | −0.153363 | ||||||||
\(407\) | −0.708204 | −0.0351044 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.4721 | 1.21007 | 0.605035 | − | 0.796199i | \(-0.293159\pi\) | ||||
0.605035 | + | 0.796199i | \(0.293159\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.7082 | 0.675355 | ||||||||
\(413\) | 11.7082 | 0.576123 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.94427 | 0.340471 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.652476 | 0.0319136 | ||||||||
\(419\) | 26.1803 | 1.27899 | 0.639497 | − | 0.768794i | \(-0.279143\pi\) | ||||
0.639497 | + | 0.768794i | \(0.279143\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0000 | −0.633581 | −0.316791 | − | 0.948495i | \(-0.602605\pi\) | ||||
−0.316791 | + | 0.948495i | \(0.602605\pi\) | |||||||
\(422\) | −7.41641 | −0.361025 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 18.9443 | 0.920015 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.70820 | 0.469813 | ||||||||
\(428\) | −12.9443 | −0.625685 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.5279 | −0.844288 | −0.422144 | − | 0.906529i | \(-0.638722\pi\) | ||||
−0.422144 | + | 0.906529i | \(0.638722\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.3607 | 1.36293 | 0.681464 | − | 0.731852i | \(-0.261344\pi\) | ||||
0.681464 | + | 0.731852i | \(0.261344\pi\) | |||||||
\(434\) | 2.29180 | 0.110010 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.6180 | −0.652186 | ||||||||
\(437\) | −27.8885 | −1.33409 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.29180 | −0.395746 | −0.197873 | − | 0.980228i | \(-0.563403\pi\) | ||||
−0.197873 | + | 0.980228i | \(0.563403\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.88854 | 0.0898289 | ||||||||
\(443\) | −19.4164 | −0.922501 | −0.461251 | − | 0.887270i | \(-0.652599\pi\) | ||||
−0.461251 | + | 0.887270i | \(0.652599\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.4721 | 0.590573 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.236068 | 0.0111532 | ||||||||
\(449\) | −20.5279 | −0.968770 | −0.484385 | − | 0.874855i | \(-0.660957\pi\) | ||||
−0.484385 | + | 0.874855i | \(0.660957\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.12461 | −0.0529559 | ||||||||
\(452\) | 23.3262 | 1.09717 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.2361 | −0.621199 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.5279 | 0.586029 | 0.293014 | − | 0.956108i | \(-0.405342\pi\) | ||||
0.293014 | + | 0.956108i | \(0.405342\pi\) | |||||||
\(458\) | 2.76393 | 0.129150 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.1803 | 0.660444 | 0.330222 | − | 0.943903i | \(-0.392876\pi\) | ||||
0.330222 | + | 0.943903i | \(0.392876\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.8885 | 0.645455 | 0.322728 | − | 0.946492i | \(-0.395400\pi\) | ||||
0.322728 | + | 0.946492i | \(0.395400\pi\) | |||||||
\(464\) | −9.27051 | −0.430373 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.90983 | −0.227443 | ||||||||
\(467\) | 6.94427 | 0.321343 | 0.160671 | − | 0.987008i | \(-0.448634\pi\) | ||||
0.160671 | + | 0.987008i | \(0.448634\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.23607 | −0.195603 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −26.1803 | −1.20505 | ||||||||
\(473\) | −0.416408 | −0.0191465 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.41641 | −0.156263 | ||||||||
\(479\) | 26.1803 | 1.19621 | 0.598105 | − | 0.801418i | \(-0.295921\pi\) | ||||
0.598105 | + | 0.801418i | \(0.295921\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.70820 | 0.169080 | ||||||||
\(482\) | 2.18034 | 0.0993118 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.7082 | 0.804918 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.76393 | −0.261189 | −0.130594 | − | 0.991436i | \(-0.541689\pi\) | ||||
−0.130594 | + | 0.991436i | \(0.541689\pi\) | |||||||
\(488\) | −21.7082 | −0.982684 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.76393 | 0.260123 | 0.130061 | − | 0.991506i | \(-0.458483\pi\) | ||||
0.130061 | + | 0.991506i | \(0.458483\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.3607 | −0.556697 | ||||||||
\(494\) | −3.41641 | −0.153711 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.87539 | 0.308714 | ||||||||
\(497\) | 8.70820 | 0.390616 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.0557 | 0.494922 | 0.247461 | − | 0.968898i | \(-0.420404\pi\) | ||||
0.247461 | + | 0.968898i | \(0.420404\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.00000 | 0.178529 | ||||||||
\(503\) | −8.11146 | −0.361672 | −0.180836 | − | 0.983513i | \(-0.557880\pi\) | ||||
−0.180836 | + | 0.983513i | \(0.557880\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.909830 | −0.0404469 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22.0902 | 0.980093 | ||||||||
\(509\) | −40.6525 | −1.80189 | −0.900945 | − | 0.433934i | \(-0.857125\pi\) | ||||
−0.900945 | + | 0.433934i | \(0.857125\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.76393 | −0.387694 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.81966 | 0.344910 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.472136 | −0.0207645 | ||||||||
\(518\) | −1.85410 | −0.0814646 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.0000 | −0.963837 | −0.481919 | − | 0.876216i | \(-0.660060\pi\) | ||||
−0.481919 | + | 0.876216i | \(0.660060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.3607 | −0.715403 | −0.357701 | − | 0.933836i | \(-0.616439\pi\) | ||||
−0.357701 | + | 0.933836i | \(0.616439\pi\) | |||||||
\(524\) | −27.4164 | −1.19769 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.0344 | −0.437522 | ||||||||
\(527\) | 9.16718 | 0.399329 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.8885 | 0.690806 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.23607 | −0.313723 | ||||||||
\(533\) | 5.88854 | 0.255061 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.47214 | 0.409134 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.23607 | −0.311969 | ||||||||
\(539\) | 0.236068 | 0.0101682 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.9443 | 0.685498 | 0.342749 | − | 0.939427i | \(-0.388642\pi\) | ||||
0.342749 | + | 0.939427i | \(0.388642\pi\) | |||||||
\(542\) | −14.6525 | −0.629378 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13.8885 | −0.595466 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.76393 | 0.417476 | 0.208738 | − | 0.977972i | \(-0.433064\pi\) | ||||
0.208738 | + | 0.977972i | \(0.433064\pi\) | |||||||
\(548\) | 17.7082 | 0.756457 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.3607 | 0.952597 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.1803 | 0.475436 | ||||||||
\(554\) | −12.2918 | −0.522228 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.2361 | −0.730972 | ||||||||
\(557\) | −9.11146 | −0.386065 | −0.193032 | − | 0.981192i | \(-0.561832\pi\) | ||||
−0.193032 | + | 0.981192i | \(0.561832\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.18034 | 0.0922186 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.49342 | −0.400456 | ||||||||
\(563\) | 17.4164 | 0.734014 | 0.367007 | − | 0.930218i | \(-0.380382\pi\) | ||||
0.367007 | + | 0.930218i | \(0.380382\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.7639 | 0.452442 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19.4721 | −0.817033 | ||||||||
\(569\) | 3.94427 | 0.165352 | 0.0826762 | − | 0.996576i | \(-0.473653\pi\) | ||||
0.0826762 | + | 0.996576i | \(0.473653\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.5967 | 1.53153 | 0.765763 | − | 0.643123i | \(-0.222362\pi\) | ||||
0.765763 | + | 0.643123i | \(0.222362\pi\) | |||||||
\(572\) | 0.472136 | 0.0197410 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.94427 | −0.122892 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 6.72949 | 0.279910 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.70820 | 0.319790 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.00000 | 0.0828315 | ||||||||
\(584\) | 19.5967 | 0.810919 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.2361 | 0.794635 | ||||||||
\(587\) | −24.7639 | −1.02212 | −0.511058 | − | 0.859546i | \(-0.670746\pi\) | ||||
−0.511058 | + | 0.859546i | \(0.670746\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.5836 | −0.683315 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.56231 | −0.228609 | ||||||||
\(593\) | −37.3050 | −1.53193 | −0.765965 | − | 0.642882i | \(-0.777739\pi\) | ||||
−0.765965 | + | 0.642882i | \(0.777739\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.38197 | 0.261416 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.76393 | 0.194812 | ||||||||
\(599\) | 11.1803 | 0.456816 | 0.228408 | − | 0.973565i | \(-0.426648\pi\) | ||||
0.228408 | + | 0.973565i | \(0.426648\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.9443 | −1.50699 | −0.753494 | − | 0.657455i | \(-0.771633\pi\) | ||||
−0.753494 | + | 0.657455i | \(0.771633\pi\) | |||||||
\(602\) | −1.09017 | −0.0444320 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 32.7426 | 1.33228 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.12461 | 0.289179 | 0.144590 | − | 0.989492i | \(-0.453814\pi\) | ||||
0.144590 | + | 0.989492i | \(0.453814\pi\) | |||||||
\(608\) | 25.1246 | 1.01894 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.47214 | 0.100012 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.4164 | 1.79396 | 0.896981 | − | 0.442069i | \(-0.145755\pi\) | ||||
0.896981 | + | 0.442069i | \(0.145755\pi\) | |||||||
\(614\) | 2.83282 | 0.114323 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.527864 | −0.0212682 | ||||||||
\(617\) | −5.94427 | −0.239307 | −0.119654 | − | 0.992816i | \(-0.538178\pi\) | ||||
−0.119654 | + | 0.992816i | \(0.538178\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.7082 | −0.470592 | −0.235296 | − | 0.971924i | \(-0.575606\pi\) | ||||
−0.235296 | + | 0.971924i | \(0.575606\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.0557 | 0.603680 | ||||||||
\(623\) | 17.2361 | 0.690548 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.0689 | 0.482370 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.23607 | 0.0493245 | ||||||||
\(629\) | −7.41641 | −0.295712 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.6525 | 1.10083 | 0.550414 | − | 0.834892i | \(-0.314470\pi\) | ||||
0.550414 | + | 0.834892i | \(0.314470\pi\) | |||||||
\(632\) | −25.0000 | −0.994447 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.6738 | −0.622485 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.23607 | −0.0489748 | ||||||||
\(638\) | 0.729490 | 0.0288808 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.8328 | −1.73129 | −0.865646 | − | 0.500656i | \(-0.833092\pi\) | ||||
−0.865646 | + | 0.500656i | \(0.833092\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.4721 | −0.728470 | −0.364235 | − | 0.931307i | \(-0.618669\pi\) | ||||
−0.364235 | + | 0.931307i | \(0.618669\pi\) | |||||||
\(644\) | 10.0902 | 0.397608 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.83282 | 0.268834 | ||||||||
\(647\) | −19.8885 | −0.781899 | −0.390950 | − | 0.920412i | \(-0.627853\pi\) | ||||
−0.390950 | + | 0.920412i | \(0.627853\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.76393 | −0.108494 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.47214 | −0.0968163 | ||||||||
\(653\) | 25.0557 | 0.980506 | 0.490253 | − | 0.871580i | \(-0.336904\pi\) | ||||
0.490253 | + | 0.871580i | \(0.336904\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.83282 | −0.344864 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.23607 | −0.0481869 | ||||||||
\(659\) | −17.8885 | −0.696839 | −0.348419 | − | 0.937339i | \(-0.613281\pi\) | ||||
−0.348419 | + | 0.937339i | \(0.613281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.7214 | −1.66167 | −0.830834 | − | 0.556520i | \(-0.812136\pi\) | ||||
−0.830834 | + | 0.556520i | \(0.812136\pi\) | |||||||
\(662\) | 15.2705 | 0.593505 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17.2361 | −0.668889 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.1803 | −1.20731 | ||||||||
\(668\) | −8.47214 | −0.327797 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.29180 | −0.0884738 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.5279 | −0.752744 | −0.376372 | − | 0.926469i | \(-0.622829\pi\) | ||||
−0.376372 | + | 0.926469i | \(0.622829\pi\) | |||||||
\(674\) | −10.1803 | −0.392132 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.5623 | 0.713935 | ||||||||
\(677\) | −14.3607 | −0.551926 | −0.275963 | − | 0.961168i | \(-0.588997\pi\) | ||||
−0.275963 | + | 0.961168i | \(0.588997\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.23607 | 0.200942 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.541020 | −0.0207167 | ||||||||
\(683\) | 14.1246 | 0.540463 | 0.270232 | − | 0.962795i | \(-0.412900\pi\) | ||||
0.270232 | + | 0.962795i | \(0.412900\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.618034 | 0.0235966 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.27051 | −0.124687 | ||||||||
\(689\) | −10.4721 | −0.398957 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.18034 | −0.159028 | −0.0795138 | − | 0.996834i | \(-0.525337\pi\) | ||||
−0.0795138 | + | 0.996834i | \(0.525337\pi\) | |||||||
\(692\) | 18.6525 | 0.709061 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.5066 | −0.474743 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.7771 | −0.446089 | ||||||||
\(698\) | −2.76393 | −0.104616 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.0557 | 1.09742 | 0.548710 | − | 0.836013i | \(-0.315119\pi\) | ||||
0.548710 | + | 0.836013i | \(0.315119\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.4164 | 0.506009 | ||||||||
\(704\) | −0.0557281 | −0.00210033 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.34752 | 0.0507147 | ||||||||
\(707\) | 4.76393 | 0.179166 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.1115 | −0.454855 | −0.227428 | − | 0.973795i | \(-0.573032\pi\) | ||||
−0.227428 | + | 0.973795i | \(0.573032\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −38.5410 | −1.44439 | ||||||||
\(713\) | 23.1246 | 0.866024 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −37.8885 | −1.41596 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.6180 | −0.694819 | ||||||||
\(719\) | −16.1803 | −0.603425 | −0.301712 | − | 0.953399i | \(-0.597558\pi\) | ||||
−0.301712 | + | 0.953399i | \(0.597558\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.47214 | 0.315519 | ||||||||
\(722\) | −0.618034 | −0.0230008 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.2361 | −0.491915 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.05573 | 0.113331 | 0.0566653 | − | 0.998393i | \(-0.481953\pi\) | ||||
0.0566653 | + | 0.998393i | \(0.481953\pi\) | |||||||
\(728\) | 2.76393 | 0.102438 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.36068 | −0.161286 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.00000 | −0.147743 | −0.0738717 | − | 0.997268i | \(-0.523536\pi\) | ||||
−0.0738717 | + | 0.997268i | \(0.523536\pi\) | |||||||
\(734\) | −22.9443 | −0.846889 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −35.0344 | −1.29139 | ||||||||
\(737\) | 1.00000 | 0.0368355 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.6525 | 0.943642 | 0.471821 | − | 0.881694i | \(-0.343597\pi\) | ||||
0.471821 | + | 0.881694i | \(0.343597\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.23607 | 0.192222 | ||||||||
\(743\) | −10.4721 | −0.384185 | −0.192093 | − | 0.981377i | \(-0.561527\pi\) | ||||
−0.192093 | + | 0.981377i | \(0.561527\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −23.3820 | −0.856075 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.944272 | −0.0345260 | ||||||||
\(749\) | −8.00000 | −0.292314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.05573 | 0.111505 | 0.0557526 | − | 0.998445i | \(-0.482244\pi\) | ||||
0.0557526 | + | 0.998445i | \(0.482244\pi\) | |||||||
\(752\) | −3.70820 | −0.135224 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.81966 | −0.139104 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.5836 | −0.711778 | −0.355889 | − | 0.934528i | \(-0.615822\pi\) | ||||
−0.355889 | + | 0.934528i | \(0.615822\pi\) | |||||||
\(758\) | 6.90983 | 0.250976 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.7771 | −1.00692 | −0.503459 | − | 0.864019i | \(-0.667940\pi\) | ||||
−0.503459 | + | 0.864019i | \(0.667940\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.41641 | −0.304694 | ||||||||
\(764\) | 10.4721 | 0.378869 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.5410 | 0.742177 | ||||||||
\(767\) | 14.4721 | 0.522559 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.0132 | −1.55109 | −0.775547 | − | 0.631290i | \(-0.782526\pi\) | ||||
−0.775547 | + | 0.631290i | \(0.782526\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20.0902 | 0.723061 | ||||||||
\(773\) | 50.1803 | 1.80486 | 0.902431 | − | 0.430835i | \(-0.141781\pi\) | ||||
0.902431 | + | 0.430835i | \(0.141781\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −11.7082 | −0.420300 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.78522 | 0.0640032 | ||||||||
\(779\) | 21.3050 | 0.763329 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.05573 | −0.0735597 | ||||||||
\(782\) | −9.52786 | −0.340716 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.85410 | 0.0662179 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.7639 | −1.45308 | −0.726539 | − | 0.687126i | \(-0.758872\pi\) | ||||
−0.726539 | + | 0.687126i | \(0.758872\pi\) | |||||||
\(788\) | 2.38197 | 0.0848540 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.4164 | 0.512588 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.0000 | 0.426132 | ||||||||
\(794\) | 5.59675 | 0.198621 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.7082 | −0.414986 | ||||||||
\(797\) | −35.4164 | −1.25451 | −0.627257 | − | 0.778813i | \(-0.715822\pi\) | ||||
−0.627257 | + | 0.778813i | \(0.715822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.94427 | −0.174916 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.56231 | 0.0551669 | ||||||||
\(803\) | 2.06888 | 0.0730093 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.83282 | 0.0997817 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.6525 | −0.374753 | ||||||||
\(809\) | −29.4721 | −1.03619 | −0.518093 | − | 0.855325i | \(-0.673358\pi\) | ||||
−0.518093 | + | 0.855325i | \(0.673358\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.7214 | −1.50015 | −0.750075 | − | 0.661353i | \(-0.769983\pi\) | ||||
−0.750075 | + | 0.661353i | \(0.769983\pi\) | |||||||
\(812\) | −8.09017 | −0.283909 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.437694 | 0.0153412 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.88854 | 0.275985 | ||||||||
\(818\) | −15.1246 | −0.528820 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.8328 | −1.00627 | −0.503136 | − | 0.864207i | \(-0.667821\pi\) | ||||
−0.503136 | + | 0.864207i | \(0.667821\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.6525 | 1.10334 | 0.551668 | − | 0.834064i | \(-0.313992\pi\) | ||||
0.551668 | + | 0.834064i | \(0.313992\pi\) | |||||||
\(824\) | −18.9443 | −0.659955 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.23607 | −0.251775 | ||||||||
\(827\) | 41.5410 | 1.44452 | 0.722261 | − | 0.691620i | \(-0.243103\pi\) | ||||
0.722261 | + | 0.691620i | \(0.243103\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.63932 | −0.265325 | −0.132662 | − | 0.991161i | \(-0.542353\pi\) | ||||
−0.132662 | + | 0.991161i | \(0.542353\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.291796 | 0.0101162 | ||||||||
\(833\) | 2.47214 | 0.0856544 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.70820 | 0.0590795 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.1803 | −0.558941 | ||||||||
\(839\) | 30.6525 | 1.05824 | 0.529120 | − | 0.848547i | \(-0.322522\pi\) | ||||
0.529120 | + | 0.848547i | \(0.322522\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 8.03444 | 0.276885 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −19.4164 | −0.668340 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9443 | 0.376050 | ||||||||
\(848\) | 15.7082 | 0.539422 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.7082 | −0.641309 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.4164 | −0.938720 | −0.469360 | − | 0.883007i | \(-0.655515\pi\) | ||||
−0.469360 | + | 0.883007i | \(0.655515\pi\) | |||||||
\(854\) | −6.00000 | −0.205316 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.8885 | 0.611418 | ||||||||
\(857\) | −15.8197 | −0.540389 | −0.270195 | − | 0.962806i | \(-0.587088\pi\) | ||||
−0.270195 | + | 0.962806i | \(0.587088\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.3607 | 0.762937 | 0.381468 | − | 0.924382i | \(-0.375419\pi\) | ||||
0.381468 | + | 0.924382i | \(0.375419\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.8328 | 0.368967 | ||||||||
\(863\) | 18.3475 | 0.624557 | 0.312278 | − | 0.949991i | \(-0.398908\pi\) | ||||
0.312278 | + | 0.949991i | \(0.398908\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.5279 | −0.595621 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.00000 | 0.203653 | ||||||||
\(869\) | −2.63932 | −0.0895328 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.23607 | −0.177417 | ||||||||
\(872\) | 18.8197 | 0.637314 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 17.2361 | 0.583019 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.3607 | −1.02521 | −0.512604 | − | 0.858625i | \(-0.671319\pi\) | ||||
−0.512604 | + | 0.858625i | \(0.671319\pi\) | |||||||
\(878\) | 5.12461 | 0.172947 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.81966 | −0.196069 | −0.0980347 | − | 0.995183i | \(-0.531256\pi\) | ||||
−0.0980347 | + | 0.995183i | \(0.531256\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.40325 | 0.0472232 | 0.0236116 | − | 0.999721i | \(-0.492483\pi\) | ||||
0.0236116 | + | 0.999721i | \(0.492483\pi\) | |||||||
\(884\) | 4.94427 | 0.166294 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0000 | 0.403148 | ||||||||
\(887\) | −21.3475 | −0.716780 | −0.358390 | − | 0.933572i | \(-0.616674\pi\) | ||||
−0.358390 | + | 0.933572i | \(0.616674\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.6525 | 0.457889 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 32.6525 | 1.09329 | ||||||||
\(893\) | 8.94427 | 0.299309 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −11.3820 | −0.380245 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.6869 | 0.423368 | ||||||||
\(899\) | −18.5410 | −0.618378 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.9443 | 0.697755 | ||||||||
\(902\) | 0.695048 | 0.0231426 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −32.2361 | −1.07216 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.8328 | −1.15660 | −0.578302 | − | 0.815823i | \(-0.696285\pi\) | ||||
−0.578302 | + | 0.815823i | \(0.696285\pi\) | |||||||
\(908\) | −34.6525 | −1.14998 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.819660 | −0.0271566 | −0.0135783 | − | 0.999908i | \(-0.504322\pi\) | ||||
−0.0135783 | + | 0.999908i | \(0.504322\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.81966 | −0.0602220 | ||||||||
\(914\) | −7.74265 | −0.256104 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.23607 | 0.239086 | ||||||||
\(917\) | −16.9443 | −0.559549 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.7639 | −0.915848 | −0.457924 | − | 0.888991i | \(-0.651407\pi\) | ||||
−0.457924 | + | 0.888991i | \(0.651407\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.76393 | −0.288625 | ||||||||
\(923\) | 10.7639 | 0.354299 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.58359 | −0.282074 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 28.0902 | 0.922105 | ||||||||
\(929\) | −38.2918 | −1.25631 | −0.628157 | − | 0.778087i | \(-0.716190\pi\) | ||||
−0.628157 | + | 0.778087i | \(0.716190\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.47214 | −0.146568 | ||||||||
\(932\) | −12.8541 | −0.421050 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.29180 | −0.140432 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.2361 | −1.15111 | −0.575556 | − | 0.817762i | \(-0.695214\pi\) | ||||
−0.575556 | + | 0.817762i | \(0.695214\pi\) | |||||||
\(938\) | 2.61803 | 0.0854818 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.23607 | 0.170691 | 0.0853455 | − | 0.996351i | \(-0.472801\pi\) | ||||
0.0853455 | + | 0.996351i | \(0.472801\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.7082 | −0.967432 | ||||||||
\(944\) | −21.7082 | −0.706542 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.257354 | 0.00836731 | ||||||||
\(947\) | 34.8328 | 1.13191 | 0.565957 | − | 0.824435i | \(-0.308507\pi\) | ||||
0.565957 | + | 0.824435i | \(0.308507\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.8328 | −0.351648 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.52786 | −0.179159 | ||||||||
\(953\) | 3.47214 | 0.112474 | 0.0562368 | − | 0.998417i | \(-0.482090\pi\) | ||||
0.0562368 | + | 0.998417i | \(0.482090\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8.94427 | −0.289278 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.1803 | −0.522763 | ||||||||
\(959\) | 10.9443 | 0.353409 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.2492 | −0.556427 | ||||||||
\(962\) | −2.29180 | −0.0738905 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.70820 | 0.183849 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.1115 | 0.453794 | 0.226897 | − | 0.973919i | \(-0.427142\pi\) | ||||
0.226897 | + | 0.973919i | \(0.427142\pi\) | |||||||
\(968\) | −24.4721 | −0.786564 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0000 | 0.577647 | 0.288824 | − | 0.957382i | \(-0.406736\pi\) | ||||
0.288824 | + | 0.957382i | \(0.406736\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.6525 | −0.341503 | ||||||||
\(974\) | 3.56231 | 0.114144 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.0000 | −0.576166 | ||||||||
\(977\) | −11.4721 | −0.367026 | −0.183513 | − | 0.983017i | \(-0.558747\pi\) | ||||
−0.183513 | + | 0.983017i | \(0.558747\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.06888 | −0.130042 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.56231 | −0.113678 | ||||||||
\(983\) | −34.5410 | −1.10169 | −0.550844 | − | 0.834608i | \(-0.685694\pi\) | ||||
−0.550844 | + | 0.834608i | \(0.685694\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.63932 | 0.243286 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.94427 | −0.284555 | ||||||||
\(989\) | −11.0000 | −0.349780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.1803 | 0.418687 | 0.209344 | − | 0.977842i | \(-0.432867\pi\) | ||||
0.209344 | + | 0.977842i | \(0.432867\pi\) | |||||||
\(992\) | −20.8328 | −0.661443 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.38197 | −0.170706 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.4164 | 1.43835 | 0.719176 | − | 0.694828i | \(-0.244519\pi\) | ||||
0.719176 | + | 0.694828i | \(0.244519\pi\) | |||||||
\(998\) | −6.83282 | −0.216289 | ||||||||
\(999\) | 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 | 1575.2.a.s.1.1 | 2 | ||
3.2 | odd | 2 | 175.2.a.d.1.2 | ✓ | 2 | ||
5.2 | odd | 4 | 1575.2.d.k.1324.2 | 4 | |||
5.3 | odd | 4 | 1575.2.d.k.1324.3 | 4 | |||
5.4 | even | 2 | 1575.2.a.n.1.2 | 2 | |||
12.11 | even | 2 | 2800.2.a.bh.1.1 | 2 | |||
15.2 | even | 4 | 175.2.b.c.99.3 | 4 | |||
15.8 | even | 4 | 175.2.b.c.99.2 | 4 | |||
15.14 | odd | 2 | 175.2.a.e.1.1 | yes | 2 | ||
21.20 | even | 2 | 1225.2.a.n.1.2 | 2 | |||
60.23 | odd | 4 | 2800.2.g.s.449.1 | 4 | |||
60.47 | odd | 4 | 2800.2.g.s.449.4 | 4 | |||
60.59 | even | 2 | 2800.2.a.bp.1.2 | 2 | |||
105.62 | odd | 4 | 1225.2.b.k.99.3 | 4 | |||
105.83 | odd | 4 | 1225.2.b.k.99.2 | 4 | |||
105.104 | even | 2 | 1225.2.a.u.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.2.a.d.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
175.2.a.e.1.1 | yes | 2 | 15.14 | odd | 2 | ||
175.2.b.c.99.2 | 4 | 15.8 | even | 4 | |||
175.2.b.c.99.3 | 4 | 15.2 | even | 4 | |||
1225.2.a.n.1.2 | 2 | 21.20 | even | 2 | |||
1225.2.a.u.1.1 | 2 | 105.104 | even | 2 | |||
1225.2.b.k.99.2 | 4 | 105.83 | odd | 4 | |||
1225.2.b.k.99.3 | 4 | 105.62 | odd | 4 | |||
1575.2.a.n.1.2 | 2 | 5.4 | even | 2 | |||
1575.2.a.s.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1575.2.d.k.1324.2 | 4 | 5.2 | odd | 4 | |||
1575.2.d.k.1324.3 | 4 | 5.3 | odd | 4 | |||
2800.2.a.bh.1.1 | 2 | 12.11 | even | 2 | |||
2800.2.a.bp.1.2 | 2 | 60.59 | even | 2 | |||
2800.2.g.s.449.1 | 4 | 60.23 | odd | 4 | |||
2800.2.g.s.449.4 | 4 | 60.47 | odd | 4 |