Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + 678 x^{6} - 39390 x^{5} - 3280 x^{4} + 42456 x^{3} + 10816 x^{2} + \cdots - 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-1.50270\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.50270 | 0.672026 | 0.336013 | − | 0.941857i | \(-0.390921\pi\) | ||||
0.336013 | + | 0.941857i | \(0.390921\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.210711 | 0.0796411 | 0.0398206 | − | 0.999207i | \(-0.487321\pi\) | ||||
0.0398206 | + | 0.999207i | \(0.487321\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.50270 | −0.475194 | ||||||||
\(11\) | −5.97021 | −1.80009 | −0.900044 | − | 0.435800i | \(-0.856466\pi\) | ||||
−0.900044 | + | 0.435800i | \(0.856466\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −0.210711 | −0.0563148 | ||||||||
\(15\) | 1.50270 | 0.387994 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.33536 | 1.29401 | 0.647007 | − | 0.762484i | \(-0.276020\pi\) | ||||
0.647007 | + | 0.762484i | \(0.276020\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −3.08917 | −0.708705 | −0.354353 | − | 0.935112i | \(-0.615299\pi\) | ||||
−0.354353 | + | 0.935112i | \(0.615299\pi\) | |||||||
\(20\) | 1.50270 | 0.336013 | ||||||||
\(21\) | 0.210711 | 0.0459808 | ||||||||
\(22\) | 5.97021 | 1.27285 | ||||||||
\(23\) | −1.61839 | −0.337457 | −0.168729 | − | 0.985663i | \(-0.553966\pi\) | ||||
−0.168729 | + | 0.985663i | \(0.553966\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.74190 | −0.548381 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.210711 | 0.0398206 | ||||||||
\(29\) | 5.82084 | 1.08090 | 0.540451 | − | 0.841375i | \(-0.318254\pi\) | ||||
0.540451 | + | 0.841375i | \(0.318254\pi\) | |||||||
\(30\) | −1.50270 | −0.274353 | ||||||||
\(31\) | 1.12646 | 0.202318 | 0.101159 | − | 0.994870i | \(-0.467745\pi\) | ||||
0.101159 | + | 0.994870i | \(0.467745\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.97021 | −1.03928 | ||||||||
\(34\) | −5.33536 | −0.915007 | ||||||||
\(35\) | 0.316634 | 0.0535209 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.46916 | −0.734725 | −0.367363 | − | 0.930078i | \(-0.619739\pi\) | ||||
−0.367363 | + | 0.930078i | \(0.619739\pi\) | |||||||
\(38\) | 3.08917 | 0.501130 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −1.50270 | −0.237597 | ||||||||
\(41\) | −1.90597 | −0.297663 | −0.148832 | − | 0.988863i | \(-0.547551\pi\) | ||||
−0.148832 | + | 0.988863i | \(0.547551\pi\) | |||||||
\(42\) | −0.210711 | −0.0325134 | ||||||||
\(43\) | 3.41276 | 0.520441 | 0.260221 | − | 0.965549i | \(-0.416205\pi\) | ||||
0.260221 | + | 0.965549i | \(0.416205\pi\) | |||||||
\(44\) | −5.97021 | −0.900044 | ||||||||
\(45\) | 1.50270 | 0.224009 | ||||||||
\(46\) | 1.61839 | 0.238618 | ||||||||
\(47\) | −2.58248 | −0.376694 | −0.188347 | − | 0.982103i | \(-0.560313\pi\) | ||||
−0.188347 | + | 0.982103i | \(0.560313\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.95560 | −0.993657 | ||||||||
\(50\) | 2.74190 | 0.387764 | ||||||||
\(51\) | 5.33536 | 0.747100 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 3.85905 | 0.530082 | 0.265041 | − | 0.964237i | \(-0.414615\pi\) | ||||
0.265041 | + | 0.964237i | \(0.414615\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −8.97142 | −1.20971 | ||||||||
\(56\) | −0.210711 | −0.0281574 | ||||||||
\(57\) | −3.08917 | −0.409171 | ||||||||
\(58\) | −5.82084 | −0.764313 | ||||||||
\(59\) | −9.92780 | −1.29249 | −0.646245 | − | 0.763130i | \(-0.723661\pi\) | ||||
−0.646245 | + | 0.763130i | \(0.723661\pi\) | |||||||
\(60\) | 1.50270 | 0.193997 | ||||||||
\(61\) | 8.82911 | 1.13045 | 0.565226 | − | 0.824936i | \(-0.308789\pi\) | ||||
0.565226 | + | 0.824936i | \(0.308789\pi\) | |||||||
\(62\) | −1.12646 | −0.143061 | ||||||||
\(63\) | 0.210711 | 0.0265470 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.50270 | −0.186386 | ||||||||
\(66\) | 5.97021 | 0.734882 | ||||||||
\(67\) | 3.01531 | 0.368379 | 0.184190 | − | 0.982891i | \(-0.441034\pi\) | ||||
0.184190 | + | 0.982891i | \(0.441034\pi\) | |||||||
\(68\) | 5.33536 | 0.647007 | ||||||||
\(69\) | −1.61839 | −0.194831 | ||||||||
\(70\) | −0.316634 | −0.0378450 | ||||||||
\(71\) | −4.95796 | −0.588402 | −0.294201 | − | 0.955744i | \(-0.595053\pi\) | ||||
−0.294201 | + | 0.955744i | \(0.595053\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 9.33060 | 1.09206 | 0.546032 | − | 0.837764i | \(-0.316138\pi\) | ||||
0.546032 | + | 0.837764i | \(0.316138\pi\) | |||||||
\(74\) | 4.46916 | 0.519529 | ||||||||
\(75\) | −2.74190 | −0.316608 | ||||||||
\(76\) | −3.08917 | −0.354353 | ||||||||
\(77\) | −1.25799 | −0.143361 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −0.938893 | −0.105634 | −0.0528168 | − | 0.998604i | \(-0.516820\pi\) | ||||
−0.0528168 | + | 0.998604i | \(0.516820\pi\) | |||||||
\(80\) | 1.50270 | 0.168007 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.90597 | 0.210480 | ||||||||
\(83\) | 1.74572 | 0.191618 | 0.0958091 | − | 0.995400i | \(-0.469456\pi\) | ||||
0.0958091 | + | 0.995400i | \(0.469456\pi\) | |||||||
\(84\) | 0.210711 | 0.0229904 | ||||||||
\(85\) | 8.01742 | 0.869612 | ||||||||
\(86\) | −3.41276 | −0.368008 | ||||||||
\(87\) | 5.82084 | 0.624059 | ||||||||
\(88\) | 5.97021 | 0.636427 | ||||||||
\(89\) | −4.95336 | −0.525055 | −0.262527 | − | 0.964925i | \(-0.584556\pi\) | ||||
−0.262527 | + | 0.964925i | \(0.584556\pi\) | |||||||
\(90\) | −1.50270 | −0.158398 | ||||||||
\(91\) | −0.210711 | −0.0220885 | ||||||||
\(92\) | −1.61839 | −0.168729 | ||||||||
\(93\) | 1.12646 | 0.116809 | ||||||||
\(94\) | 2.58248 | 0.266363 | ||||||||
\(95\) | −4.64209 | −0.476268 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −10.7905 | −1.09561 | −0.547804 | − | 0.836607i | \(-0.684536\pi\) | ||||
−0.547804 | + | 0.836607i | \(0.684536\pi\) | |||||||
\(98\) | 6.95560 | 0.702622 | ||||||||
\(99\) | −5.97021 | −0.600029 | ||||||||
\(100\) | −2.74190 | −0.274190 | ||||||||
\(101\) | 0.162439 | 0.0161633 | 0.00808167 | − | 0.999967i | \(-0.497427\pi\) | ||||
0.00808167 | + | 0.999967i | \(0.497427\pi\) | |||||||
\(102\) | −5.33536 | −0.528279 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0.316634 | 0.0309003 | ||||||||
\(106\) | −3.85905 | −0.374824 | ||||||||
\(107\) | −1.59344 | −0.154043 | −0.0770216 | − | 0.997029i | \(-0.524541\pi\) | ||||
−0.0770216 | + | 0.997029i | \(0.524541\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 3.58061 | 0.342960 | 0.171480 | − | 0.985188i | \(-0.445145\pi\) | ||||
0.171480 | + | 0.985188i | \(0.445145\pi\) | |||||||
\(110\) | 8.97142 | 0.855391 | ||||||||
\(111\) | −4.46916 | −0.424194 | ||||||||
\(112\) | 0.210711 | 0.0199103 | ||||||||
\(113\) | −18.2195 | −1.71395 | −0.856974 | − | 0.515360i | \(-0.827658\pi\) | ||||
−0.856974 | + | 0.515360i | \(0.827658\pi\) | |||||||
\(114\) | 3.08917 | 0.289328 | ||||||||
\(115\) | −2.43195 | −0.226780 | ||||||||
\(116\) | 5.82084 | 0.540451 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 9.92780 | 0.913928 | ||||||||
\(119\) | 1.12422 | 0.103057 | ||||||||
\(120\) | −1.50270 | −0.137177 | ||||||||
\(121\) | 24.6434 | 2.24031 | ||||||||
\(122\) | −8.82911 | −0.799350 | ||||||||
\(123\) | −1.90597 | −0.171856 | ||||||||
\(124\) | 1.12646 | 0.101159 | ||||||||
\(125\) | −11.6337 | −1.04055 | ||||||||
\(126\) | −0.210711 | −0.0187716 | ||||||||
\(127\) | −17.8739 | −1.58605 | −0.793026 | − | 0.609188i | \(-0.791496\pi\) | ||||
−0.793026 | + | 0.609188i | \(0.791496\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 3.41276 | 0.300477 | ||||||||
\(130\) | 1.50270 | 0.131795 | ||||||||
\(131\) | −8.17659 | −0.714392 | −0.357196 | − | 0.934030i | \(-0.616267\pi\) | ||||
−0.357196 | + | 0.934030i | \(0.616267\pi\) | |||||||
\(132\) | −5.97021 | −0.519640 | ||||||||
\(133\) | −0.650922 | −0.0564421 | ||||||||
\(134\) | −3.01531 | −0.260483 | ||||||||
\(135\) | 1.50270 | 0.129331 | ||||||||
\(136\) | −5.33536 | −0.457503 | ||||||||
\(137\) | −4.87565 | −0.416555 | −0.208278 | − | 0.978070i | \(-0.566786\pi\) | ||||
−0.208278 | + | 0.978070i | \(0.566786\pi\) | |||||||
\(138\) | 1.61839 | 0.137766 | ||||||||
\(139\) | 10.4014 | 0.882236 | 0.441118 | − | 0.897449i | \(-0.354582\pi\) | ||||
0.441118 | + | 0.897449i | \(0.354582\pi\) | |||||||
\(140\) | 0.316634 | 0.0267605 | ||||||||
\(141\) | −2.58248 | −0.217484 | ||||||||
\(142\) | 4.95796 | 0.416063 | ||||||||
\(143\) | 5.97021 | 0.499254 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 8.74695 | 0.726394 | ||||||||
\(146\) | −9.33060 | −0.772206 | ||||||||
\(147\) | −6.95560 | −0.573688 | ||||||||
\(148\) | −4.46916 | −0.367363 | ||||||||
\(149\) | −7.01473 | −0.574669 | −0.287334 | − | 0.957830i | \(-0.592769\pi\) | ||||
−0.287334 | + | 0.957830i | \(0.592769\pi\) | |||||||
\(150\) | 2.74190 | 0.223876 | ||||||||
\(151\) | −9.45181 | −0.769178 | −0.384589 | − | 0.923088i | \(-0.625657\pi\) | ||||
−0.384589 | + | 0.923088i | \(0.625657\pi\) | |||||||
\(152\) | 3.08917 | 0.250565 | ||||||||
\(153\) | 5.33536 | 0.431338 | ||||||||
\(154\) | 1.25799 | 0.101371 | ||||||||
\(155\) | 1.69273 | 0.135963 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 7.64083 | 0.609805 | 0.304902 | − | 0.952384i | \(-0.401376\pi\) | ||||
0.304902 | + | 0.952384i | \(0.401376\pi\) | |||||||
\(158\) | 0.938893 | 0.0746943 | ||||||||
\(159\) | 3.85905 | 0.306043 | ||||||||
\(160\) | −1.50270 | −0.118799 | ||||||||
\(161\) | −0.341012 | −0.0268755 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −12.7215 | −0.996428 | −0.498214 | − | 0.867054i | \(-0.666011\pi\) | ||||
−0.498214 | + | 0.867054i | \(0.666011\pi\) | |||||||
\(164\) | −1.90597 | −0.148832 | ||||||||
\(165\) | −8.97142 | −0.698424 | ||||||||
\(166\) | −1.74572 | −0.135495 | ||||||||
\(167\) | −13.8412 | −1.07107 | −0.535533 | − | 0.844514i | \(-0.679889\pi\) | ||||
−0.535533 | + | 0.844514i | \(0.679889\pi\) | |||||||
\(168\) | −0.210711 | −0.0162567 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −8.01742 | −0.614908 | ||||||||
\(171\) | −3.08917 | −0.236235 | ||||||||
\(172\) | 3.41276 | 0.260221 | ||||||||
\(173\) | −18.4111 | −1.39977 | −0.699886 | − | 0.714254i | \(-0.746766\pi\) | ||||
−0.699886 | + | 0.714254i | \(0.746766\pi\) | |||||||
\(174\) | −5.82084 | −0.441276 | ||||||||
\(175\) | −0.577748 | −0.0436737 | ||||||||
\(176\) | −5.97021 | −0.450022 | ||||||||
\(177\) | −9.92780 | −0.746219 | ||||||||
\(178\) | 4.95336 | 0.371270 | ||||||||
\(179\) | −22.9519 | −1.71550 | −0.857752 | − | 0.514063i | \(-0.828140\pi\) | ||||
−0.857752 | + | 0.514063i | \(0.828140\pi\) | |||||||
\(180\) | 1.50270 | 0.112004 | ||||||||
\(181\) | −12.2315 | −0.909163 | −0.454582 | − | 0.890705i | \(-0.650211\pi\) | ||||
−0.454582 | + | 0.890705i | \(0.650211\pi\) | |||||||
\(182\) | 0.210711 | 0.0156189 | ||||||||
\(183\) | 8.82911 | 0.652666 | ||||||||
\(184\) | 1.61839 | 0.119309 | ||||||||
\(185\) | −6.71579 | −0.493754 | ||||||||
\(186\) | −1.12646 | −0.0825961 | ||||||||
\(187\) | −31.8532 | −2.32934 | ||||||||
\(188\) | −2.58248 | −0.188347 | ||||||||
\(189\) | 0.210711 | 0.0153269 | ||||||||
\(190\) | 4.64209 | 0.336773 | ||||||||
\(191\) | 16.9153 | 1.22395 | 0.611974 | − | 0.790878i | \(-0.290376\pi\) | ||||
0.611974 | + | 0.790878i | \(0.290376\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −10.5001 | −0.755816 | −0.377908 | − | 0.925843i | \(-0.623356\pi\) | ||||
−0.377908 | + | 0.925843i | \(0.623356\pi\) | |||||||
\(194\) | 10.7905 | 0.774712 | ||||||||
\(195\) | −1.50270 | −0.107610 | ||||||||
\(196\) | −6.95560 | −0.496829 | ||||||||
\(197\) | −8.88348 | −0.632922 | −0.316461 | − | 0.948606i | \(-0.602495\pi\) | ||||
−0.316461 | + | 0.948606i | \(0.602495\pi\) | |||||||
\(198\) | 5.97021 | 0.424285 | ||||||||
\(199\) | 10.5193 | 0.745691 | 0.372845 | − | 0.927893i | \(-0.378382\pi\) | ||||
0.372845 | + | 0.927893i | \(0.378382\pi\) | |||||||
\(200\) | 2.74190 | 0.193882 | ||||||||
\(201\) | 3.01531 | 0.212684 | ||||||||
\(202\) | −0.162439 | −0.0114292 | ||||||||
\(203\) | 1.22651 | 0.0860843 | ||||||||
\(204\) | 5.33536 | 0.373550 | ||||||||
\(205\) | −2.86410 | −0.200037 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | −1.61839 | −0.112486 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 18.4430 | 1.27573 | ||||||||
\(210\) | −0.316634 | −0.0218498 | ||||||||
\(211\) | 9.22779 | 0.635267 | 0.317633 | − | 0.948214i | \(-0.397112\pi\) | ||||
0.317633 | + | 0.948214i | \(0.397112\pi\) | |||||||
\(212\) | 3.85905 | 0.265041 | ||||||||
\(213\) | −4.95796 | −0.339714 | ||||||||
\(214\) | 1.59344 | 0.108925 | ||||||||
\(215\) | 5.12834 | 0.349750 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0.237357 | 0.0161129 | ||||||||
\(218\) | −3.58061 | −0.242509 | ||||||||
\(219\) | 9.33060 | 0.630504 | ||||||||
\(220\) | −8.97142 | −0.604853 | ||||||||
\(221\) | −5.33536 | −0.358895 | ||||||||
\(222\) | 4.46916 | 0.299950 | ||||||||
\(223\) | −3.58034 | −0.239757 | −0.119879 | − | 0.992789i | \(-0.538251\pi\) | ||||
−0.119879 | + | 0.992789i | \(0.538251\pi\) | |||||||
\(224\) | −0.210711 | −0.0140787 | ||||||||
\(225\) | −2.74190 | −0.182794 | ||||||||
\(226\) | 18.2195 | 1.21194 | ||||||||
\(227\) | −16.0110 | −1.06269 | −0.531345 | − | 0.847156i | \(-0.678313\pi\) | ||||
−0.531345 | + | 0.847156i | \(0.678313\pi\) | |||||||
\(228\) | −3.08917 | −0.204586 | ||||||||
\(229\) | 1.00564 | 0.0664544 | 0.0332272 | − | 0.999448i | \(-0.489422\pi\) | ||||
0.0332272 | + | 0.999448i | \(0.489422\pi\) | |||||||
\(230\) | 2.43195 | 0.160358 | ||||||||
\(231\) | −1.25799 | −0.0827695 | ||||||||
\(232\) | −5.82084 | −0.382157 | ||||||||
\(233\) | −5.94744 | −0.389630 | −0.194815 | − | 0.980840i | \(-0.562411\pi\) | ||||
−0.194815 | + | 0.980840i | \(0.562411\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −3.88068 | −0.253148 | ||||||||
\(236\) | −9.92780 | −0.646245 | ||||||||
\(237\) | −0.938893 | −0.0609876 | ||||||||
\(238\) | −1.12422 | −0.0728722 | ||||||||
\(239\) | 12.4367 | 0.804466 | 0.402233 | − | 0.915537i | \(-0.368234\pi\) | ||||
0.402233 | + | 0.915537i | \(0.368234\pi\) | |||||||
\(240\) | 1.50270 | 0.0969986 | ||||||||
\(241\) | 8.96181 | 0.577281 | 0.288641 | − | 0.957438i | \(-0.406797\pi\) | ||||
0.288641 | + | 0.957438i | \(0.406797\pi\) | |||||||
\(242\) | −24.6434 | −1.58414 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 8.82911 | 0.565226 | ||||||||
\(245\) | −10.4522 | −0.667764 | ||||||||
\(246\) | 1.90597 | 0.121521 | ||||||||
\(247\) | 3.08917 | 0.196559 | ||||||||
\(248\) | −1.12646 | −0.0715303 | ||||||||
\(249\) | 1.74572 | 0.110631 | ||||||||
\(250\) | 11.6337 | 0.735782 | ||||||||
\(251\) | −24.8961 | −1.57143 | −0.785714 | − | 0.618590i | \(-0.787704\pi\) | ||||
−0.785714 | + | 0.618590i | \(0.787704\pi\) | |||||||
\(252\) | 0.210711 | 0.0132735 | ||||||||
\(253\) | 9.66212 | 0.607453 | ||||||||
\(254\) | 17.8739 | 1.12151 | ||||||||
\(255\) | 8.01742 | 0.502071 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.94204 | −0.121141 | −0.0605706 | − | 0.998164i | \(-0.519292\pi\) | ||||
−0.0605706 | + | 0.998164i | \(0.519292\pi\) | |||||||
\(258\) | −3.41276 | −0.212469 | ||||||||
\(259\) | −0.941699 | −0.0585143 | ||||||||
\(260\) | −1.50270 | −0.0931932 | ||||||||
\(261\) | 5.82084 | 0.360301 | ||||||||
\(262\) | 8.17659 | 0.505151 | ||||||||
\(263\) | −26.4527 | −1.63114 | −0.815571 | − | 0.578657i | \(-0.803577\pi\) | ||||
−0.815571 | + | 0.578657i | \(0.803577\pi\) | |||||||
\(264\) | 5.97021 | 0.367441 | ||||||||
\(265\) | 5.79898 | 0.356229 | ||||||||
\(266\) | 0.650922 | 0.0399106 | ||||||||
\(267\) | −4.95336 | −0.303141 | ||||||||
\(268\) | 3.01531 | 0.184190 | ||||||||
\(269\) | 8.23376 | 0.502021 | 0.251011 | − | 0.967984i | \(-0.419237\pi\) | ||||
0.251011 | + | 0.967984i | \(0.419237\pi\) | |||||||
\(270\) | −1.50270 | −0.0914512 | ||||||||
\(271\) | −13.7981 | −0.838176 | −0.419088 | − | 0.907946i | \(-0.637650\pi\) | ||||
−0.419088 | + | 0.907946i | \(0.637650\pi\) | |||||||
\(272\) | 5.33536 | 0.323504 | ||||||||
\(273\) | −0.210711 | −0.0127528 | ||||||||
\(274\) | 4.87565 | 0.294549 | ||||||||
\(275\) | 16.3698 | 0.987134 | ||||||||
\(276\) | −1.61839 | −0.0974155 | ||||||||
\(277\) | 6.74113 | 0.405035 | 0.202517 | − | 0.979279i | \(-0.435088\pi\) | ||||
0.202517 | + | 0.979279i | \(0.435088\pi\) | |||||||
\(278\) | −10.4014 | −0.623835 | ||||||||
\(279\) | 1.12646 | 0.0674394 | ||||||||
\(280\) | −0.316634 | −0.0189225 | ||||||||
\(281\) | −5.37631 | −0.320724 | −0.160362 | − | 0.987058i | \(-0.551266\pi\) | ||||
−0.160362 | + | 0.987058i | \(0.551266\pi\) | |||||||
\(282\) | 2.58248 | 0.153785 | ||||||||
\(283\) | −31.3050 | −1.86089 | −0.930446 | − | 0.366429i | \(-0.880580\pi\) | ||||
−0.930446 | + | 0.366429i | \(0.880580\pi\) | |||||||
\(284\) | −4.95796 | −0.294201 | ||||||||
\(285\) | −4.64209 | −0.274974 | ||||||||
\(286\) | −5.97021 | −0.353026 | ||||||||
\(287\) | −0.401609 | −0.0237062 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 11.4661 | 0.674474 | ||||||||
\(290\) | −8.74695 | −0.513638 | ||||||||
\(291\) | −10.7905 | −0.632550 | ||||||||
\(292\) | 9.33060 | 0.546032 | ||||||||
\(293\) | 0.0967142 | 0.00565010 | 0.00282505 | − | 0.999996i | \(-0.499101\pi\) | ||||
0.00282505 | + | 0.999996i | \(0.499101\pi\) | |||||||
\(294\) | 6.95560 | 0.405659 | ||||||||
\(295\) | −14.9185 | −0.868587 | ||||||||
\(296\) | 4.46916 | 0.259765 | ||||||||
\(297\) | −5.97021 | −0.346427 | ||||||||
\(298\) | 7.01473 | 0.406352 | ||||||||
\(299\) | 1.61839 | 0.0935938 | ||||||||
\(300\) | −2.74190 | −0.158304 | ||||||||
\(301\) | 0.719105 | 0.0414485 | ||||||||
\(302\) | 9.45181 | 0.543891 | ||||||||
\(303\) | 0.162439 | 0.00933190 | ||||||||
\(304\) | −3.08917 | −0.177176 | ||||||||
\(305\) | 13.2675 | 0.759693 | ||||||||
\(306\) | −5.33536 | −0.305002 | ||||||||
\(307\) | 9.32491 | 0.532201 | 0.266100 | − | 0.963945i | \(-0.414265\pi\) | ||||
0.266100 | + | 0.963945i | \(0.414265\pi\) | |||||||
\(308\) | −1.25799 | −0.0716805 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −1.69273 | −0.0961405 | ||||||||
\(311\) | 15.1452 | 0.858807 | 0.429404 | − | 0.903113i | \(-0.358724\pi\) | ||||
0.429404 | + | 0.903113i | \(0.358724\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 20.6758 | 1.16867 | 0.584334 | − | 0.811513i | \(-0.301356\pi\) | ||||
0.584334 | + | 0.811513i | \(0.301356\pi\) | |||||||
\(314\) | −7.64083 | −0.431197 | ||||||||
\(315\) | 0.316634 | 0.0178403 | ||||||||
\(316\) | −0.938893 | −0.0528168 | ||||||||
\(317\) | −0.556614 | −0.0312625 | −0.0156313 | − | 0.999878i | \(-0.504976\pi\) | ||||
−0.0156313 | + | 0.999878i | \(0.504976\pi\) | |||||||
\(318\) | −3.85905 | −0.216405 | ||||||||
\(319\) | −34.7516 | −1.94572 | ||||||||
\(320\) | 1.50270 | 0.0840033 | ||||||||
\(321\) | −1.59344 | −0.0889369 | ||||||||
\(322\) | 0.341012 | 0.0190038 | ||||||||
\(323\) | −16.4819 | −0.917075 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 2.74190 | 0.152094 | ||||||||
\(326\) | 12.7215 | 0.704581 | ||||||||
\(327\) | 3.58061 | 0.198008 | ||||||||
\(328\) | 1.90597 | 0.105240 | ||||||||
\(329\) | −0.544156 | −0.0300003 | ||||||||
\(330\) | 8.97142 | 0.493860 | ||||||||
\(331\) | −11.8691 | −0.652387 | −0.326193 | − | 0.945303i | \(-0.605766\pi\) | ||||
−0.326193 | + | 0.945303i | \(0.605766\pi\) | |||||||
\(332\) | 1.74572 | 0.0958091 | ||||||||
\(333\) | −4.46916 | −0.244908 | ||||||||
\(334\) | 13.8412 | 0.757358 | ||||||||
\(335\) | 4.53110 | 0.247560 | ||||||||
\(336\) | 0.210711 | 0.0114952 | ||||||||
\(337\) | 12.4993 | 0.680881 | 0.340441 | − | 0.940266i | \(-0.389424\pi\) | ||||
0.340441 | + | 0.940266i | \(0.389424\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −18.2195 | −0.989548 | ||||||||
\(340\) | 8.01742 | 0.434806 | ||||||||
\(341\) | −6.72521 | −0.364191 | ||||||||
\(342\) | 3.08917 | 0.167043 | ||||||||
\(343\) | −2.94059 | −0.158777 | ||||||||
\(344\) | −3.41276 | −0.184004 | ||||||||
\(345\) | −2.43195 | −0.130932 | ||||||||
\(346\) | 18.4111 | 0.989789 | ||||||||
\(347\) | −5.29113 | −0.284042 | −0.142021 | − | 0.989864i | \(-0.545360\pi\) | ||||
−0.142021 | + | 0.989864i | \(0.545360\pi\) | |||||||
\(348\) | 5.82084 | 0.312030 | ||||||||
\(349\) | 12.9672 | 0.694120 | 0.347060 | − | 0.937843i | \(-0.387180\pi\) | ||||
0.347060 | + | 0.937843i | \(0.387180\pi\) | |||||||
\(350\) | 0.577748 | 0.0308820 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 5.97021 | 0.318213 | ||||||||
\(353\) | 10.7941 | 0.574514 | 0.287257 | − | 0.957854i | \(-0.407257\pi\) | ||||
0.287257 | + | 0.957854i | \(0.407257\pi\) | |||||||
\(354\) | 9.92780 | 0.527657 | ||||||||
\(355\) | −7.45031 | −0.395421 | ||||||||
\(356\) | −4.95336 | −0.262527 | ||||||||
\(357\) | 1.12422 | 0.0594999 | ||||||||
\(358\) | 22.9519 | 1.21304 | ||||||||
\(359\) | 36.9472 | 1.95000 | 0.974999 | − | 0.222207i | \(-0.0713262\pi\) | ||||
0.974999 | + | 0.222207i | \(0.0713262\pi\) | |||||||
\(360\) | −1.50270 | −0.0791990 | ||||||||
\(361\) | −9.45700 | −0.497737 | ||||||||
\(362\) | 12.2315 | 0.642876 | ||||||||
\(363\) | 24.6434 | 1.29345 | ||||||||
\(364\) | −0.210711 | −0.0110442 | ||||||||
\(365\) | 14.0211 | 0.733896 | ||||||||
\(366\) | −8.82911 | −0.461505 | ||||||||
\(367\) | 10.4460 | 0.545279 | 0.272640 | − | 0.962116i | \(-0.412103\pi\) | ||||
0.272640 | + | 0.962116i | \(0.412103\pi\) | |||||||
\(368\) | −1.61839 | −0.0843643 | ||||||||
\(369\) | −1.90597 | −0.0992211 | ||||||||
\(370\) | 6.71579 | 0.349137 | ||||||||
\(371\) | 0.813143 | 0.0422163 | ||||||||
\(372\) | 1.12646 | 0.0584043 | ||||||||
\(373\) | 29.3786 | 1.52117 | 0.760583 | − | 0.649240i | \(-0.224913\pi\) | ||||
0.760583 | + | 0.649240i | \(0.224913\pi\) | |||||||
\(374\) | 31.8532 | 1.64709 | ||||||||
\(375\) | −11.6337 | −0.600763 | ||||||||
\(376\) | 2.58248 | 0.133181 | ||||||||
\(377\) | −5.82084 | −0.299788 | ||||||||
\(378\) | −0.210711 | −0.0108378 | ||||||||
\(379\) | −23.7275 | −1.21880 | −0.609401 | − | 0.792862i | \(-0.708590\pi\) | ||||
−0.609401 | + | 0.792862i | \(0.708590\pi\) | |||||||
\(380\) | −4.64209 | −0.238134 | ||||||||
\(381\) | −17.8739 | −0.915708 | ||||||||
\(382\) | −16.9153 | −0.865462 | ||||||||
\(383\) | −29.9546 | −1.53061 | −0.765306 | − | 0.643667i | \(-0.777412\pi\) | ||||
−0.765306 | + | 0.643667i | \(0.777412\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −1.89037 | −0.0963423 | ||||||||
\(386\) | 10.5001 | 0.534442 | ||||||||
\(387\) | 3.41276 | 0.173480 | ||||||||
\(388\) | −10.7905 | −0.547804 | ||||||||
\(389\) | 1.59115 | 0.0806743 | 0.0403371 | − | 0.999186i | \(-0.487157\pi\) | ||||
0.0403371 | + | 0.999186i | \(0.487157\pi\) | |||||||
\(390\) | 1.50270 | 0.0760920 | ||||||||
\(391\) | −8.63468 | −0.436675 | ||||||||
\(392\) | 6.95560 | 0.351311 | ||||||||
\(393\) | −8.17659 | −0.412454 | ||||||||
\(394\) | 8.88348 | 0.447543 | ||||||||
\(395\) | −1.41087 | −0.0709886 | ||||||||
\(396\) | −5.97021 | −0.300015 | ||||||||
\(397\) | 24.9523 | 1.25232 | 0.626160 | − | 0.779695i | \(-0.284626\pi\) | ||||
0.626160 | + | 0.779695i | \(0.284626\pi\) | |||||||
\(398\) | −10.5193 | −0.527283 | ||||||||
\(399\) | −0.650922 | −0.0325868 | ||||||||
\(400\) | −2.74190 | −0.137095 | ||||||||
\(401\) | −17.1289 | −0.855378 | −0.427689 | − | 0.903926i | \(-0.640672\pi\) | ||||
−0.427689 | + | 0.903926i | \(0.640672\pi\) | |||||||
\(402\) | −3.01531 | −0.150390 | ||||||||
\(403\) | −1.12646 | −0.0561130 | ||||||||
\(404\) | 0.162439 | 0.00808167 | ||||||||
\(405\) | 1.50270 | 0.0746696 | ||||||||
\(406\) | −1.22651 | −0.0608708 | ||||||||
\(407\) | 26.6818 | 1.32257 | ||||||||
\(408\) | −5.33536 | −0.264140 | ||||||||
\(409\) | −14.3710 | −0.710600 | −0.355300 | − | 0.934752i | \(-0.615621\pi\) | ||||
−0.355300 | + | 0.934752i | \(0.615621\pi\) | |||||||
\(410\) | 2.86410 | 0.141448 | ||||||||
\(411\) | −4.87565 | −0.240498 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | −2.09189 | −0.102935 | ||||||||
\(414\) | 1.61839 | 0.0795395 | ||||||||
\(415\) | 2.62329 | 0.128772 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 10.4014 | 0.509359 | ||||||||
\(418\) | −18.4430 | −0.902078 | ||||||||
\(419\) | 2.17462 | 0.106237 | 0.0531187 | − | 0.998588i | \(-0.483084\pi\) | ||||
0.0531187 | + | 0.998588i | \(0.483084\pi\) | |||||||
\(420\) | 0.316634 | 0.0154502 | ||||||||
\(421\) | −12.9617 | −0.631714 | −0.315857 | − | 0.948807i | \(-0.602292\pi\) | ||||
−0.315857 | + | 0.948807i | \(0.602292\pi\) | |||||||
\(422\) | −9.22779 | −0.449202 | ||||||||
\(423\) | −2.58248 | −0.125565 | ||||||||
\(424\) | −3.85905 | −0.187412 | ||||||||
\(425\) | −14.6290 | −0.709613 | ||||||||
\(426\) | 4.95796 | 0.240214 | ||||||||
\(427\) | 1.86039 | 0.0900304 | ||||||||
\(428\) | −1.59344 | −0.0770216 | ||||||||
\(429\) | 5.97021 | 0.288245 | ||||||||
\(430\) | −5.12834 | −0.247311 | ||||||||
\(431\) | 35.9482 | 1.73157 | 0.865783 | − | 0.500420i | \(-0.166821\pi\) | ||||
0.865783 | + | 0.500420i | \(0.166821\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 40.0696 | 1.92562 | 0.962810 | − | 0.270179i | \(-0.0870828\pi\) | ||||
0.962810 | + | 0.270179i | \(0.0870828\pi\) | |||||||
\(434\) | −0.237357 | −0.0113935 | ||||||||
\(435\) | 8.74695 | 0.419384 | ||||||||
\(436\) | 3.58061 | 0.171480 | ||||||||
\(437\) | 4.99948 | 0.239158 | ||||||||
\(438\) | −9.33060 | −0.445833 | ||||||||
\(439\) | 11.9083 | 0.568352 | 0.284176 | − | 0.958772i | \(-0.408280\pi\) | ||||
0.284176 | + | 0.958772i | \(0.408280\pi\) | |||||||
\(440\) | 8.97142 | 0.427695 | ||||||||
\(441\) | −6.95560 | −0.331219 | ||||||||
\(442\) | 5.33536 | 0.253777 | ||||||||
\(443\) | 18.5916 | 0.883316 | 0.441658 | − | 0.897184i | \(-0.354390\pi\) | ||||
0.441658 | + | 0.897184i | \(0.354390\pi\) | |||||||
\(444\) | −4.46916 | −0.212097 | ||||||||
\(445\) | −7.44339 | −0.352850 | ||||||||
\(446\) | 3.58034 | 0.169534 | ||||||||
\(447\) | −7.01473 | −0.331785 | ||||||||
\(448\) | 0.210711 | 0.00995514 | ||||||||
\(449\) | 23.0858 | 1.08949 | 0.544744 | − | 0.838603i | \(-0.316627\pi\) | ||||
0.544744 | + | 0.838603i | \(0.316627\pi\) | |||||||
\(450\) | 2.74190 | 0.129255 | ||||||||
\(451\) | 11.3791 | 0.535820 | ||||||||
\(452\) | −18.2195 | −0.856974 | ||||||||
\(453\) | −9.45181 | −0.444085 | ||||||||
\(454\) | 16.0110 | 0.751435 | ||||||||
\(455\) | −0.316634 | −0.0148440 | ||||||||
\(456\) | 3.08917 | 0.144664 | ||||||||
\(457\) | 9.15541 | 0.428272 | 0.214136 | − | 0.976804i | \(-0.431306\pi\) | ||||
0.214136 | + | 0.976804i | \(0.431306\pi\) | |||||||
\(458\) | −1.00564 | −0.0469903 | ||||||||
\(459\) | 5.33536 | 0.249033 | ||||||||
\(460\) | −2.43195 | −0.113390 | ||||||||
\(461\) | 24.0754 | 1.12130 | 0.560652 | − | 0.828052i | \(-0.310551\pi\) | ||||
0.560652 | + | 0.828052i | \(0.310551\pi\) | |||||||
\(462\) | 1.25799 | 0.0585269 | ||||||||
\(463\) | −16.3129 | −0.758127 | −0.379063 | − | 0.925371i | \(-0.623754\pi\) | ||||
−0.379063 | + | 0.925371i | \(0.623754\pi\) | |||||||
\(464\) | 5.82084 | 0.270226 | ||||||||
\(465\) | 1.69273 | 0.0784984 | ||||||||
\(466\) | 5.94744 | 0.275510 | ||||||||
\(467\) | −11.2856 | −0.522234 | −0.261117 | − | 0.965307i | \(-0.584091\pi\) | ||||
−0.261117 | + | 0.965307i | \(0.584091\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 0.635359 | 0.0293381 | ||||||||
\(470\) | 3.88068 | 0.179003 | ||||||||
\(471\) | 7.64083 | 0.352071 | ||||||||
\(472\) | 9.92780 | 0.456964 | ||||||||
\(473\) | −20.3749 | −0.936840 | ||||||||
\(474\) | 0.938893 | 0.0431248 | ||||||||
\(475\) | 8.47022 | 0.388640 | ||||||||
\(476\) | 1.12422 | 0.0515284 | ||||||||
\(477\) | 3.85905 | 0.176694 | ||||||||
\(478\) | −12.4367 | −0.568843 | ||||||||
\(479\) | −14.2312 | −0.650238 | −0.325119 | − | 0.945673i | \(-0.605404\pi\) | ||||
−0.325119 | + | 0.945673i | \(0.605404\pi\) | |||||||
\(480\) | −1.50270 | −0.0685884 | ||||||||
\(481\) | 4.46916 | 0.203776 | ||||||||
\(482\) | −8.96181 | −0.408199 | ||||||||
\(483\) | −0.341012 | −0.0155166 | ||||||||
\(484\) | 24.6434 | 1.12016 | ||||||||
\(485\) | −16.2148 | −0.736277 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 28.6776 | 1.29951 | 0.649753 | − | 0.760145i | \(-0.274872\pi\) | ||||
0.649753 | + | 0.760145i | \(0.274872\pi\) | |||||||
\(488\) | −8.82911 | −0.399675 | ||||||||
\(489\) | −12.7215 | −0.575288 | ||||||||
\(490\) | 10.4522 | 0.472180 | ||||||||
\(491\) | −11.8787 | −0.536077 | −0.268039 | − | 0.963408i | \(-0.586375\pi\) | ||||
−0.268039 | + | 0.963408i | \(0.586375\pi\) | |||||||
\(492\) | −1.90597 | −0.0859280 | ||||||||
\(493\) | 31.0563 | 1.39870 | ||||||||
\(494\) | −3.08917 | −0.138989 | ||||||||
\(495\) | −8.97142 | −0.403235 | ||||||||
\(496\) | 1.12646 | 0.0505796 | ||||||||
\(497\) | −1.04469 | −0.0468610 | ||||||||
\(498\) | −1.74572 | −0.0782278 | ||||||||
\(499\) | −25.6731 | −1.14928 | −0.574642 | − | 0.818405i | \(-0.694859\pi\) | ||||
−0.574642 | + | 0.818405i | \(0.694859\pi\) | |||||||
\(500\) | −11.6337 | −0.520276 | ||||||||
\(501\) | −13.8412 | −0.618380 | ||||||||
\(502\) | 24.8961 | 1.11117 | ||||||||
\(503\) | −26.7132 | −1.19108 | −0.595541 | − | 0.803325i | \(-0.703062\pi\) | ||||
−0.595541 | + | 0.803325i | \(0.703062\pi\) | |||||||
\(504\) | −0.210711 | −0.00938580 | ||||||||
\(505\) | 0.244097 | 0.0108622 | ||||||||
\(506\) | −9.66212 | −0.429534 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −17.8739 | −0.793026 | ||||||||
\(509\) | 0.575983 | 0.0255300 | 0.0127650 | − | 0.999919i | \(-0.495937\pi\) | ||||
0.0127650 | + | 0.999919i | \(0.495937\pi\) | |||||||
\(510\) | −8.01742 | −0.355017 | ||||||||
\(511\) | 1.96606 | 0.0869732 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.08917 | −0.136390 | ||||||||
\(514\) | 1.94204 | 0.0856598 | ||||||||
\(515\) | 1.50270 | 0.0662167 | ||||||||
\(516\) | 3.41276 | 0.150238 | ||||||||
\(517\) | 15.4180 | 0.678081 | ||||||||
\(518\) | 0.941699 | 0.0413759 | ||||||||
\(519\) | −18.4111 | −0.808159 | ||||||||
\(520\) | 1.50270 | 0.0658976 | ||||||||
\(521\) | −30.9555 | −1.35618 | −0.678092 | − | 0.734977i | \(-0.737193\pi\) | ||||
−0.678092 | + | 0.734977i | \(0.737193\pi\) | |||||||
\(522\) | −5.82084 | −0.254771 | ||||||||
\(523\) | 3.58907 | 0.156939 | 0.0784695 | − | 0.996917i | \(-0.474997\pi\) | ||||
0.0784695 | + | 0.996917i | \(0.474997\pi\) | |||||||
\(524\) | −8.17659 | −0.357196 | ||||||||
\(525\) | −0.577748 | −0.0252150 | ||||||||
\(526\) | 26.4527 | 1.15339 | ||||||||
\(527\) | 6.01007 | 0.261803 | ||||||||
\(528\) | −5.97021 | −0.259820 | ||||||||
\(529\) | −20.3808 | −0.886123 | ||||||||
\(530\) | −5.79898 | −0.251892 | ||||||||
\(531\) | −9.92780 | −0.430830 | ||||||||
\(532\) | −0.650922 | −0.0282210 | ||||||||
\(533\) | 1.90597 | 0.0825569 | ||||||||
\(534\) | 4.95336 | 0.214353 | ||||||||
\(535\) | −2.39445 | −0.103521 | ||||||||
\(536\) | −3.01531 | −0.130242 | ||||||||
\(537\) | −22.9519 | −0.990447 | ||||||||
\(538\) | −8.23376 | −0.354983 | ||||||||
\(539\) | 41.5264 | 1.78867 | ||||||||
\(540\) | 1.50270 | 0.0646657 | ||||||||
\(541\) | 6.41437 | 0.275775 | 0.137888 | − | 0.990448i | \(-0.455969\pi\) | ||||
0.137888 | + | 0.990448i | \(0.455969\pi\) | |||||||
\(542\) | 13.7981 | 0.592680 | ||||||||
\(543\) | −12.2315 | −0.524906 | ||||||||
\(544\) | −5.33536 | −0.228752 | ||||||||
\(545\) | 5.38057 | 0.230478 | ||||||||
\(546\) | 0.210711 | 0.00901758 | ||||||||
\(547\) | 1.09095 | 0.0466455 | 0.0233228 | − | 0.999728i | \(-0.492575\pi\) | ||||
0.0233228 | + | 0.999728i | \(0.492575\pi\) | |||||||
\(548\) | −4.87565 | −0.208278 | ||||||||
\(549\) | 8.82911 | 0.376817 | ||||||||
\(550\) | −16.3698 | −0.698009 | ||||||||
\(551\) | −17.9816 | −0.766041 | ||||||||
\(552\) | 1.61839 | 0.0688832 | ||||||||
\(553\) | −0.197835 | −0.00841278 | ||||||||
\(554\) | −6.74113 | −0.286403 | ||||||||
\(555\) | −6.71579 | −0.285069 | ||||||||
\(556\) | 10.4014 | 0.441118 | ||||||||
\(557\) | 4.09704 | 0.173597 | 0.0867985 | − | 0.996226i | \(-0.472336\pi\) | ||||
0.0867985 | + | 0.996226i | \(0.472336\pi\) | |||||||
\(558\) | −1.12646 | −0.0476869 | ||||||||
\(559\) | −3.41276 | −0.144344 | ||||||||
\(560\) | 0.316634 | 0.0133802 | ||||||||
\(561\) | −31.8532 | −1.34484 | ||||||||
\(562\) | 5.37631 | 0.226786 | ||||||||
\(563\) | −26.0152 | −1.09641 | −0.548206 | − | 0.836343i | \(-0.684689\pi\) | ||||
−0.548206 | + | 0.836343i | \(0.684689\pi\) | |||||||
\(564\) | −2.58248 | −0.108742 | ||||||||
\(565\) | −27.3784 | −1.15182 | ||||||||
\(566\) | 31.3050 | 1.31585 | ||||||||
\(567\) | 0.210711 | 0.00884901 | ||||||||
\(568\) | 4.95796 | 0.208031 | ||||||||
\(569\) | −41.2205 | −1.72805 | −0.864026 | − | 0.503446i | \(-0.832065\pi\) | ||||
−0.864026 | + | 0.503446i | \(0.832065\pi\) | |||||||
\(570\) | 4.64209 | 0.194436 | ||||||||
\(571\) | −27.1897 | −1.13785 | −0.568927 | − | 0.822388i | \(-0.692641\pi\) | ||||
−0.568927 | + | 0.822388i | \(0.692641\pi\) | |||||||
\(572\) | 5.97021 | 0.249627 | ||||||||
\(573\) | 16.9153 | 0.706647 | ||||||||
\(574\) | 0.401609 | 0.0167628 | ||||||||
\(575\) | 4.43747 | 0.185055 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 15.5388 | 0.646890 | 0.323445 | − | 0.946247i | \(-0.395159\pi\) | ||||
0.323445 | + | 0.946247i | \(0.395159\pi\) | |||||||
\(578\) | −11.4661 | −0.476925 | ||||||||
\(579\) | −10.5001 | −0.436370 | ||||||||
\(580\) | 8.74695 | 0.363197 | ||||||||
\(581\) | 0.367843 | 0.0152607 | ||||||||
\(582\) | 10.7905 | 0.447280 | ||||||||
\(583\) | −23.0394 | −0.954193 | ||||||||
\(584\) | −9.33060 | −0.386103 | ||||||||
\(585\) | −1.50270 | −0.0621288 | ||||||||
\(586\) | −0.0967142 | −0.00399523 | ||||||||
\(587\) | 39.9662 | 1.64958 | 0.824791 | − | 0.565438i | \(-0.191293\pi\) | ||||
0.824791 | + | 0.565438i | \(0.191293\pi\) | |||||||
\(588\) | −6.95560 | −0.286844 | ||||||||
\(589\) | −3.47983 | −0.143384 | ||||||||
\(590\) | 14.9185 | 0.614183 | ||||||||
\(591\) | −8.88348 | −0.365418 | ||||||||
\(592\) | −4.46916 | −0.183681 | ||||||||
\(593\) | 13.3409 | 0.547846 | 0.273923 | − | 0.961752i | \(-0.411679\pi\) | ||||
0.273923 | + | 0.961752i | \(0.411679\pi\) | |||||||
\(594\) | 5.97021 | 0.244961 | ||||||||
\(595\) | 1.68936 | 0.0692568 | ||||||||
\(596\) | −7.01473 | −0.287334 | ||||||||
\(597\) | 10.5193 | 0.430525 | ||||||||
\(598\) | −1.61839 | −0.0661808 | ||||||||
\(599\) | −6.78375 | −0.277176 | −0.138588 | − | 0.990350i | \(-0.544256\pi\) | ||||
−0.138588 | + | 0.990350i | \(0.544256\pi\) | |||||||
\(600\) | 2.74190 | 0.111938 | ||||||||
\(601\) | −19.6675 | −0.802254 | −0.401127 | − | 0.916022i | \(-0.631381\pi\) | ||||
−0.401127 | + | 0.916022i | \(0.631381\pi\) | |||||||
\(602\) | −0.719105 | −0.0293085 | ||||||||
\(603\) | 3.01531 | 0.122793 | ||||||||
\(604\) | −9.45181 | −0.384589 | ||||||||
\(605\) | 37.0316 | 1.50555 | ||||||||
\(606\) | −0.162439 | −0.00659865 | ||||||||
\(607\) | −47.8269 | −1.94123 | −0.970617 | − | 0.240631i | \(-0.922646\pi\) | ||||
−0.970617 | + | 0.240631i | \(0.922646\pi\) | |||||||
\(608\) | 3.08917 | 0.125283 | ||||||||
\(609\) | 1.22651 | 0.0497008 | ||||||||
\(610\) | −13.2675 | −0.537184 | ||||||||
\(611\) | 2.58248 | 0.104476 | ||||||||
\(612\) | 5.33536 | 0.215669 | ||||||||
\(613\) | 4.52465 | 0.182749 | 0.0913744 | − | 0.995817i | \(-0.470874\pi\) | ||||
0.0913744 | + | 0.995817i | \(0.470874\pi\) | |||||||
\(614\) | −9.32491 | −0.376323 | ||||||||
\(615\) | −2.86410 | −0.115492 | ||||||||
\(616\) | 1.25799 | 0.0506857 | ||||||||
\(617\) | 31.8462 | 1.28208 | 0.641040 | − | 0.767508i | \(-0.278503\pi\) | ||||
0.641040 | + | 0.767508i | \(0.278503\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 25.0095 | 1.00522 | 0.502608 | − | 0.864515i | \(-0.332374\pi\) | ||||
0.502608 | + | 0.864515i | \(0.332374\pi\) | |||||||
\(620\) | 1.69273 | 0.0679816 | ||||||||
\(621\) | −1.61839 | −0.0649437 | ||||||||
\(622\) | −15.1452 | −0.607269 | ||||||||
\(623\) | −1.04372 | −0.0418160 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −3.77243 | −0.150897 | ||||||||
\(626\) | −20.6758 | −0.826373 | ||||||||
\(627\) | 18.4430 | 0.736544 | ||||||||
\(628\) | 7.64083 | 0.304902 | ||||||||
\(629\) | −23.8446 | −0.950745 | ||||||||
\(630\) | −0.316634 | −0.0126150 | ||||||||
\(631\) | 21.0089 | 0.836350 | 0.418175 | − | 0.908367i | \(-0.362670\pi\) | ||||
0.418175 | + | 0.908367i | \(0.362670\pi\) | |||||||
\(632\) | 0.938893 | 0.0373471 | ||||||||
\(633\) | 9.22779 | 0.366772 | ||||||||
\(634\) | 0.556614 | 0.0221060 | ||||||||
\(635\) | −26.8590 | −1.06587 | ||||||||
\(636\) | 3.85905 | 0.153021 | ||||||||
\(637\) | 6.95560 | 0.275591 | ||||||||
\(638\) | 34.7516 | 1.37583 | ||||||||
\(639\) | −4.95796 | −0.196134 | ||||||||
\(640\) | −1.50270 | −0.0593993 | ||||||||
\(641\) | 1.92961 | 0.0762149 | 0.0381075 | − | 0.999274i | \(-0.487867\pi\) | ||||
0.0381075 | + | 0.999274i | \(0.487867\pi\) | |||||||
\(642\) | 1.59344 | 0.0628879 | ||||||||
\(643\) | 19.5628 | 0.771481 | 0.385740 | − | 0.922607i | \(-0.373946\pi\) | ||||
0.385740 | + | 0.922607i | \(0.373946\pi\) | |||||||
\(644\) | −0.341012 | −0.0134377 | ||||||||
\(645\) | 5.12834 | 0.201928 | ||||||||
\(646\) | 16.4819 | 0.648470 | ||||||||
\(647\) | −18.5003 | −0.727320 | −0.363660 | − | 0.931532i | \(-0.618473\pi\) | ||||
−0.363660 | + | 0.931532i | \(0.618473\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 59.2711 | 2.32659 | ||||||||
\(650\) | −2.74190 | −0.107546 | ||||||||
\(651\) | 0.237357 | 0.00930276 | ||||||||
\(652\) | −12.7215 | −0.498214 | ||||||||
\(653\) | −0.532652 | −0.0208443 | −0.0104221 | − | 0.999946i | \(-0.503318\pi\) | ||||
−0.0104221 | + | 0.999946i | \(0.503318\pi\) | |||||||
\(654\) | −3.58061 | −0.140013 | ||||||||
\(655\) | −12.2869 | −0.480090 | ||||||||
\(656\) | −1.90597 | −0.0744158 | ||||||||
\(657\) | 9.33060 | 0.364021 | ||||||||
\(658\) | 0.544156 | 0.0212134 | ||||||||
\(659\) | 42.0313 | 1.63731 | 0.818654 | − | 0.574287i | \(-0.194720\pi\) | ||||
0.818654 | + | 0.574287i | \(0.194720\pi\) | |||||||
\(660\) | −8.97142 | −0.349212 | ||||||||
\(661\) | 22.7122 | 0.883401 | 0.441700 | − | 0.897163i | \(-0.354375\pi\) | ||||
0.441700 | + | 0.897163i | \(0.354375\pi\) | |||||||
\(662\) | 11.8691 | 0.461307 | ||||||||
\(663\) | −5.33536 | −0.207208 | ||||||||
\(664\) | −1.74572 | −0.0677473 | ||||||||
\(665\) | −0.978138 | −0.0379305 | ||||||||
\(666\) | 4.46916 | 0.173176 | ||||||||
\(667\) | −9.42037 | −0.364758 | ||||||||
\(668\) | −13.8412 | −0.535533 | ||||||||
\(669\) | −3.58034 | −0.138424 | ||||||||
\(670\) | −4.53110 | −0.175052 | ||||||||
\(671\) | −52.7117 | −2.03491 | ||||||||
\(672\) | −0.210711 | −0.00812834 | ||||||||
\(673\) | −1.45877 | −0.0562313 | −0.0281156 | − | 0.999605i | \(-0.508951\pi\) | ||||
−0.0281156 | + | 0.999605i | \(0.508951\pi\) | |||||||
\(674\) | −12.4993 | −0.481456 | ||||||||
\(675\) | −2.74190 | −0.105536 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −24.7516 | −0.951281 | −0.475641 | − | 0.879640i | \(-0.657784\pi\) | ||||
−0.475641 | + | 0.879640i | \(0.657784\pi\) | |||||||
\(678\) | 18.2195 | 0.699716 | ||||||||
\(679\) | −2.27367 | −0.0872554 | ||||||||
\(680\) | −8.01742 | −0.307454 | ||||||||
\(681\) | −16.0110 | −0.613544 | ||||||||
\(682\) | 6.72521 | 0.257522 | ||||||||
\(683\) | −37.0495 | −1.41766 | −0.708830 | − | 0.705380i | \(-0.750777\pi\) | ||||
−0.708830 | + | 0.705380i | \(0.750777\pi\) | |||||||
\(684\) | −3.08917 | −0.118118 | ||||||||
\(685\) | −7.32662 | −0.279936 | ||||||||
\(686\) | 2.94059 | 0.112272 | ||||||||
\(687\) | 1.00564 | 0.0383675 | ||||||||
\(688\) | 3.41276 | 0.130110 | ||||||||
\(689\) | −3.85905 | −0.147018 | ||||||||
\(690\) | 2.43195 | 0.0925826 | ||||||||
\(691\) | 31.9134 | 1.21404 | 0.607021 | − | 0.794685i | \(-0.292364\pi\) | ||||
0.607021 | + | 0.794685i | \(0.292364\pi\) | |||||||
\(692\) | −18.4111 | −0.699886 | ||||||||
\(693\) | −1.25799 | −0.0477870 | ||||||||
\(694\) | 5.29113 | 0.200848 | ||||||||
\(695\) | 15.6302 | 0.592886 | ||||||||
\(696\) | −5.82084 | −0.220638 | ||||||||
\(697\) | −10.1691 | −0.385181 | ||||||||
\(698\) | −12.9672 | −0.490817 | ||||||||
\(699\) | −5.94744 | −0.224953 | ||||||||
\(700\) | −0.577748 | −0.0218368 | ||||||||
\(701\) | −17.1796 | −0.648863 | −0.324431 | − | 0.945909i | \(-0.605173\pi\) | ||||
−0.324431 | + | 0.945909i | \(0.605173\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 13.8060 | 0.520703 | ||||||||
\(704\) | −5.97021 | −0.225011 | ||||||||
\(705\) | −3.88068 | −0.146155 | ||||||||
\(706\) | −10.7941 | −0.406243 | ||||||||
\(707\) | 0.0342277 | 0.00128727 | ||||||||
\(708\) | −9.92780 | −0.373110 | ||||||||
\(709\) | −44.2304 | −1.66111 | −0.830555 | − | 0.556937i | \(-0.811976\pi\) | ||||
−0.830555 | + | 0.556937i | \(0.811976\pi\) | |||||||
\(710\) | 7.45031 | 0.279605 | ||||||||
\(711\) | −0.938893 | −0.0352112 | ||||||||
\(712\) | 4.95336 | 0.185635 | ||||||||
\(713\) | −1.82305 | −0.0682738 | ||||||||
\(714\) | −1.12422 | −0.0420728 | ||||||||
\(715\) | 8.97142 | 0.335512 | ||||||||
\(716\) | −22.9519 | −0.857752 | ||||||||
\(717\) | 12.4367 | 0.464459 | ||||||||
\(718\) | −36.9472 | −1.37886 | ||||||||
\(719\) | 38.6635 | 1.44191 | 0.720954 | − | 0.692983i | \(-0.243704\pi\) | ||||
0.720954 | + | 0.692983i | \(0.243704\pi\) | |||||||
\(720\) | 1.50270 | 0.0560022 | ||||||||
\(721\) | 0.210711 | 0.00784727 | ||||||||
\(722\) | 9.45700 | 0.351953 | ||||||||
\(723\) | 8.96181 | 0.333293 | ||||||||
\(724\) | −12.2315 | −0.454582 | ||||||||
\(725\) | −15.9602 | −0.592746 | ||||||||
\(726\) | −24.6434 | −0.914604 | ||||||||
\(727\) | −23.5817 | −0.874598 | −0.437299 | − | 0.899316i | \(-0.644065\pi\) | ||||
−0.437299 | + | 0.899316i | \(0.644065\pi\) | |||||||
\(728\) | 0.210711 | 0.00780945 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −14.0211 | −0.518943 | ||||||||
\(731\) | 18.2083 | 0.673459 | ||||||||
\(732\) | 8.82911 | 0.326333 | ||||||||
\(733\) | −16.0518 | −0.592886 | −0.296443 | − | 0.955051i | \(-0.595801\pi\) | ||||
−0.296443 | + | 0.955051i | \(0.595801\pi\) | |||||||
\(734\) | −10.4460 | −0.385571 | ||||||||
\(735\) | −10.4522 | −0.385533 | ||||||||
\(736\) | 1.61839 | 0.0596546 | ||||||||
\(737\) | −18.0021 | −0.663115 | ||||||||
\(738\) | 1.90597 | 0.0701599 | ||||||||
\(739\) | −3.84802 | −0.141552 | −0.0707759 | − | 0.997492i | \(-0.522548\pi\) | ||||
−0.0707759 | + | 0.997492i | \(0.522548\pi\) | |||||||
\(740\) | −6.71579 | −0.246877 | ||||||||
\(741\) | 3.08917 | 0.113484 | ||||||||
\(742\) | −0.813143 | −0.0298514 | ||||||||
\(743\) | −41.7331 | −1.53104 | −0.765519 | − | 0.643413i | \(-0.777518\pi\) | ||||
−0.765519 | + | 0.643413i | \(0.777518\pi\) | |||||||
\(744\) | −1.12646 | −0.0412980 | ||||||||
\(745\) | −10.5410 | −0.386193 | ||||||||
\(746\) | −29.3786 | −1.07563 | ||||||||
\(747\) | 1.74572 | 0.0638727 | ||||||||
\(748\) | −31.8532 | −1.16467 | ||||||||
\(749\) | −0.335754 | −0.0122682 | ||||||||
\(750\) | 11.6337 | 0.424804 | ||||||||
\(751\) | 8.47303 | 0.309185 | 0.154593 | − | 0.987978i | \(-0.450594\pi\) | ||||
0.154593 | + | 0.987978i | \(0.450594\pi\) | |||||||
\(752\) | −2.58248 | −0.0941734 | ||||||||
\(753\) | −24.8961 | −0.907264 | ||||||||
\(754\) | 5.82084 | 0.211982 | ||||||||
\(755\) | −14.2032 | −0.516907 | ||||||||
\(756\) | 0.210711 | 0.00766347 | ||||||||
\(757\) | 20.7148 | 0.752894 | 0.376447 | − | 0.926438i | \(-0.377146\pi\) | ||||
0.376447 | + | 0.926438i | \(0.377146\pi\) | |||||||
\(758\) | 23.7275 | 0.861823 | ||||||||
\(759\) | 9.66212 | 0.350713 | ||||||||
\(760\) | 4.64209 | 0.168386 | ||||||||
\(761\) | −24.1299 | −0.874708 | −0.437354 | − | 0.899290i | \(-0.644084\pi\) | ||||
−0.437354 | + | 0.899290i | \(0.644084\pi\) | |||||||
\(762\) | 17.8739 | 0.647503 | ||||||||
\(763\) | 0.754472 | 0.0273137 | ||||||||
\(764\) | 16.9153 | 0.611974 | ||||||||
\(765\) | 8.01742 | 0.289871 | ||||||||
\(766\) | 29.9546 | 1.08231 | ||||||||
\(767\) | 9.92780 | 0.358472 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −13.0541 | −0.470742 | −0.235371 | − | 0.971906i | \(-0.575631\pi\) | ||||
−0.235371 | + | 0.971906i | \(0.575631\pi\) | |||||||
\(770\) | 1.89037 | 0.0681243 | ||||||||
\(771\) | −1.94204 | −0.0699410 | ||||||||
\(772\) | −10.5001 | −0.377908 | ||||||||
\(773\) | 34.6144 | 1.24499 | 0.622497 | − | 0.782622i | \(-0.286118\pi\) | ||||
0.622497 | + | 0.782622i | \(0.286118\pi\) | |||||||
\(774\) | −3.41276 | −0.122669 | ||||||||
\(775\) | −3.08865 | −0.110948 | ||||||||
\(776\) | 10.7905 | 0.387356 | ||||||||
\(777\) | −0.941699 | −0.0337833 | ||||||||
\(778\) | −1.59115 | −0.0570453 | ||||||||
\(779\) | 5.88789 | 0.210956 | ||||||||
\(780\) | −1.50270 | −0.0538051 | ||||||||
\(781\) | 29.6001 | 1.05917 | ||||||||
\(782\) | 8.63468 | 0.308776 | ||||||||
\(783\) | 5.82084 | 0.208020 | ||||||||
\(784\) | −6.95560 | −0.248414 | ||||||||
\(785\) | 11.4818 | 0.409805 | ||||||||
\(786\) | 8.17659 | 0.291649 | ||||||||
\(787\) | 17.9302 | 0.639141 | 0.319571 | − | 0.947563i | \(-0.396461\pi\) | ||||
0.319571 | + | 0.947563i | \(0.396461\pi\) | |||||||
\(788\) | −8.88348 | −0.316461 | ||||||||
\(789\) | −26.4527 | −0.941740 | ||||||||
\(790\) | 1.41087 | 0.0501965 | ||||||||
\(791\) | −3.83904 | −0.136501 | ||||||||
\(792\) | 5.97021 | 0.212142 | ||||||||
\(793\) | −8.82911 | −0.313531 | ||||||||
\(794\) | −24.9523 | −0.885524 | ||||||||
\(795\) | 5.79898 | 0.205669 | ||||||||
\(796\) | 10.5193 | 0.372845 | ||||||||
\(797\) | 26.2528 | 0.929922 | 0.464961 | − | 0.885331i | \(-0.346068\pi\) | ||||
0.464961 | + | 0.885331i | \(0.346068\pi\) | |||||||
\(798\) | 0.650922 | 0.0230424 | ||||||||
\(799\) | −13.7785 | −0.487447 | ||||||||
\(800\) | 2.74190 | 0.0969410 | ||||||||
\(801\) | −4.95336 | −0.175018 | ||||||||
\(802\) | 17.1289 | 0.604843 | ||||||||
\(803\) | −55.7057 | −1.96581 | ||||||||
\(804\) | 3.01531 | 0.106342 | ||||||||
\(805\) | −0.512437 | −0.0180610 | ||||||||
\(806\) | 1.12646 | 0.0396779 | ||||||||
\(807\) | 8.23376 | 0.289842 | ||||||||
\(808\) | −0.162439 | −0.00571460 | ||||||||
\(809\) | −23.2678 | −0.818054 | −0.409027 | − | 0.912522i | \(-0.634132\pi\) | ||||
−0.409027 | + | 0.912522i | \(0.634132\pi\) | |||||||
\(810\) | −1.50270 | −0.0527994 | ||||||||
\(811\) | 20.2770 | 0.712023 | 0.356012 | − | 0.934482i | \(-0.384136\pi\) | ||||
0.356012 | + | 0.934482i | \(0.384136\pi\) | |||||||
\(812\) | 1.22651 | 0.0430421 | ||||||||
\(813\) | −13.7981 | −0.483921 | ||||||||
\(814\) | −26.6818 | −0.935198 | ||||||||
\(815\) | −19.1166 | −0.669626 | ||||||||
\(816\) | 5.33536 | 0.186775 | ||||||||
\(817\) | −10.5426 | −0.368839 | ||||||||
\(818\) | 14.3710 | 0.502470 | ||||||||
\(819\) | −0.210711 | −0.00736282 | ||||||||
\(820\) | −2.86410 | −0.100019 | ||||||||
\(821\) | 22.7486 | 0.793933 | 0.396967 | − | 0.917833i | \(-0.370063\pi\) | ||||
0.396967 | + | 0.917833i | \(0.370063\pi\) | |||||||
\(822\) | 4.87565 | 0.170058 | ||||||||
\(823\) | 40.4001 | 1.40826 | 0.704130 | − | 0.710071i | \(-0.251337\pi\) | ||||
0.704130 | + | 0.710071i | \(0.251337\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 16.3698 | 0.569922 | ||||||||
\(826\) | 2.09189 | 0.0727863 | ||||||||
\(827\) | −40.6620 | −1.41396 | −0.706978 | − | 0.707235i | \(-0.749942\pi\) | ||||
−0.706978 | + | 0.707235i | \(0.749942\pi\) | |||||||
\(828\) | −1.61839 | −0.0562429 | ||||||||
\(829\) | 8.74279 | 0.303650 | 0.151825 | − | 0.988407i | \(-0.451485\pi\) | ||||
0.151825 | + | 0.988407i | \(0.451485\pi\) | |||||||
\(830\) | −2.62329 | −0.0910558 | ||||||||
\(831\) | 6.74113 | 0.233847 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −37.1106 | −1.28581 | ||||||||
\(834\) | −10.4014 | −0.360171 | ||||||||
\(835\) | −20.7992 | −0.719784 | ||||||||
\(836\) | 18.4430 | 0.637866 | ||||||||
\(837\) | 1.12646 | 0.0389362 | ||||||||
\(838\) | −2.17462 | −0.0751211 | ||||||||
\(839\) | 22.4549 | 0.775228 | 0.387614 | − | 0.921822i | \(-0.373299\pi\) | ||||
0.387614 | + | 0.921822i | \(0.373299\pi\) | |||||||
\(840\) | −0.316634 | −0.0109249 | ||||||||
\(841\) | 4.88214 | 0.168350 | ||||||||
\(842\) | 12.9617 | 0.446689 | ||||||||
\(843\) | −5.37631 | −0.185170 | ||||||||
\(844\) | 9.22779 | 0.317633 | ||||||||
\(845\) | 1.50270 | 0.0516943 | ||||||||
\(846\) | 2.58248 | 0.0887875 | ||||||||
\(847\) | 5.19264 | 0.178421 | ||||||||
\(848\) | 3.85905 | 0.132520 | ||||||||
\(849\) | −31.3050 | −1.07439 | ||||||||
\(850\) | 14.6290 | 0.501772 | ||||||||
\(851\) | 7.23283 | 0.247938 | ||||||||
\(852\) | −4.95796 | −0.169857 | ||||||||
\(853\) | −44.6610 | −1.52917 | −0.764583 | − | 0.644526i | \(-0.777055\pi\) | ||||
−0.764583 | + | 0.644526i | \(0.777055\pi\) | |||||||
\(854\) | −1.86039 | −0.0636611 | ||||||||
\(855\) | −4.64209 | −0.158756 | ||||||||
\(856\) | 1.59344 | 0.0544625 | ||||||||
\(857\) | 2.68975 | 0.0918802 | 0.0459401 | − | 0.998944i | \(-0.485372\pi\) | ||||
0.0459401 | + | 0.998944i | \(0.485372\pi\) | |||||||
\(858\) | −5.97021 | −0.203820 | ||||||||
\(859\) | 29.0991 | 0.992849 | 0.496424 | − | 0.868080i | \(-0.334646\pi\) | ||||
0.496424 | + | 0.868080i | \(0.334646\pi\) | |||||||
\(860\) | 5.12834 | 0.174875 | ||||||||
\(861\) | −0.401609 | −0.0136868 | ||||||||
\(862\) | −35.9482 | −1.22440 | ||||||||
\(863\) | −5.09589 | −0.173466 | −0.0867331 | − | 0.996232i | \(-0.527643\pi\) | ||||
−0.0867331 | + | 0.996232i | \(0.527643\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −27.6663 | −0.940684 | ||||||||
\(866\) | −40.0696 | −1.36162 | ||||||||
\(867\) | 11.4661 | 0.389408 | ||||||||
\(868\) | 0.237357 | 0.00805643 | ||||||||
\(869\) | 5.60539 | 0.190150 | ||||||||
\(870\) | −8.74695 | −0.296549 | ||||||||
\(871\) | −3.01531 | −0.102170 | ||||||||
\(872\) | −3.58061 | −0.121255 | ||||||||
\(873\) | −10.7905 | −0.365203 | ||||||||
\(874\) | −4.99948 | −0.169110 | ||||||||
\(875\) | −2.45135 | −0.0828708 | ||||||||
\(876\) | 9.33060 | 0.315252 | ||||||||
\(877\) | −4.48966 | −0.151605 | −0.0758025 | − | 0.997123i | \(-0.524152\pi\) | ||||
−0.0758025 | + | 0.997123i | \(0.524152\pi\) | |||||||
\(878\) | −11.9083 | −0.401886 | ||||||||
\(879\) | 0.0967142 | 0.00326209 | ||||||||
\(880\) | −8.97142 | −0.302426 | ||||||||
\(881\) | −22.8961 | −0.771391 | −0.385695 | − | 0.922626i | \(-0.626038\pi\) | ||||
−0.385695 | + | 0.922626i | \(0.626038\pi\) | |||||||
\(882\) | 6.95560 | 0.234207 | ||||||||
\(883\) | 5.50760 | 0.185345 | 0.0926727 | − | 0.995697i | \(-0.470459\pi\) | ||||
0.0926727 | + | 0.995697i | \(0.470459\pi\) | |||||||
\(884\) | −5.33536 | −0.179448 | ||||||||
\(885\) | −14.9185 | −0.501479 | ||||||||
\(886\) | −18.5916 | −0.624599 | ||||||||
\(887\) | 10.8054 | 0.362809 | 0.181404 | − | 0.983409i | \(-0.441936\pi\) | ||||
0.181404 | + | 0.983409i | \(0.441936\pi\) | |||||||
\(888\) | 4.46916 | 0.149975 | ||||||||
\(889\) | −3.76622 | −0.126315 | ||||||||
\(890\) | 7.44339 | 0.249503 | ||||||||
\(891\) | −5.97021 | −0.200010 | ||||||||
\(892\) | −3.58034 | −0.119879 | ||||||||
\(893\) | 7.97773 | 0.266965 | ||||||||
\(894\) | 7.01473 | 0.234608 | ||||||||
\(895\) | −34.4897 | −1.15286 | ||||||||
\(896\) | −0.210711 | −0.00703935 | ||||||||
\(897\) | 1.61839 | 0.0540364 | ||||||||
\(898\) | −23.0858 | −0.770384 | ||||||||
\(899\) | 6.55694 | 0.218686 | ||||||||
\(900\) | −2.74190 | −0.0913968 | ||||||||
\(901\) | 20.5894 | 0.685933 | ||||||||
\(902\) | −11.3791 | −0.378882 | ||||||||
\(903\) | 0.719105 | 0.0239303 | ||||||||
\(904\) | 18.2195 | 0.605972 | ||||||||
\(905\) | −18.3803 | −0.610982 | ||||||||
\(906\) | 9.45181 | 0.314015 | ||||||||
\(907\) | 4.33306 | 0.143877 | 0.0719385 | − | 0.997409i | \(-0.477081\pi\) | ||||
0.0719385 | + | 0.997409i | \(0.477081\pi\) | |||||||
\(908\) | −16.0110 | −0.531345 | ||||||||
\(909\) | 0.162439 | 0.00538778 | ||||||||
\(910\) | 0.316634 | 0.0104963 | ||||||||
\(911\) | 14.5252 | 0.481242 | 0.240621 | − | 0.970619i | \(-0.422649\pi\) | ||||
0.240621 | + | 0.970619i | \(0.422649\pi\) | |||||||
\(912\) | −3.08917 | −0.102293 | ||||||||
\(913\) | −10.4223 | −0.344929 | ||||||||
\(914\) | −9.15541 | −0.302834 | ||||||||
\(915\) | 13.2675 | 0.438609 | ||||||||
\(916\) | 1.00564 | 0.0332272 | ||||||||
\(917\) | −1.72289 | −0.0568949 | ||||||||
\(918\) | −5.33536 | −0.176093 | ||||||||
\(919\) | 46.0785 | 1.51999 | 0.759994 | − | 0.649930i | \(-0.225202\pi\) | ||||
0.759994 | + | 0.649930i | \(0.225202\pi\) | |||||||
\(920\) | 2.43195 | 0.0801789 | ||||||||
\(921\) | 9.32491 | 0.307266 | ||||||||
\(922\) | −24.0754 | −0.792881 | ||||||||
\(923\) | 4.95796 | 0.163193 | ||||||||
\(924\) | −1.25799 | −0.0413847 | ||||||||
\(925\) | 12.2540 | 0.402909 | ||||||||
\(926\) | 16.3129 | 0.536077 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | −5.82084 | −0.191078 | ||||||||
\(929\) | −13.9868 | −0.458892 | −0.229446 | − | 0.973321i | \(-0.573691\pi\) | ||||
−0.229446 | + | 0.973321i | \(0.573691\pi\) | |||||||
\(930\) | −1.69273 | −0.0555067 | ||||||||
\(931\) | 21.4871 | 0.704210 | ||||||||
\(932\) | −5.94744 | −0.194815 | ||||||||
\(933\) | 15.1452 | 0.495833 | ||||||||
\(934\) | 11.2856 | 0.369275 | ||||||||
\(935\) | −47.8657 | −1.56538 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | −35.6776 | −1.16554 | −0.582769 | − | 0.812638i | \(-0.698031\pi\) | ||||
−0.582769 | + | 0.812638i | \(0.698031\pi\) | |||||||
\(938\) | −0.635359 | −0.0207452 | ||||||||
\(939\) | 20.6758 | 0.674731 | ||||||||
\(940\) | −3.88068 | −0.126574 | ||||||||
\(941\) | −11.8984 | −0.387877 | −0.193938 | − | 0.981014i | \(-0.562126\pi\) | ||||
−0.193938 | + | 0.981014i | \(0.562126\pi\) | |||||||
\(942\) | −7.64083 | −0.248952 | ||||||||
\(943\) | 3.08461 | 0.100449 | ||||||||
\(944\) | −9.92780 | −0.323122 | ||||||||
\(945\) | 0.316634 | 0.0103001 | ||||||||
\(946\) | 20.3749 | 0.662446 | ||||||||
\(947\) | 44.4092 | 1.44310 | 0.721552 | − | 0.692360i | \(-0.243429\pi\) | ||||
0.721552 | + | 0.692360i | \(0.243429\pi\) | |||||||
\(948\) | −0.938893 | −0.0304938 | ||||||||
\(949\) | −9.33060 | −0.302884 | ||||||||
\(950\) | −8.47022 | −0.274810 | ||||||||
\(951\) | −0.556614 | −0.0180494 | ||||||||
\(952\) | −1.12422 | −0.0364361 | ||||||||
\(953\) | 30.5537 | 0.989731 | 0.494866 | − | 0.868969i | \(-0.335217\pi\) | ||||
0.494866 | + | 0.868969i | \(0.335217\pi\) | |||||||
\(954\) | −3.85905 | −0.124941 | ||||||||
\(955\) | 25.4186 | 0.822525 | ||||||||
\(956\) | 12.4367 | 0.402233 | ||||||||
\(957\) | −34.7516 | −1.12336 | ||||||||
\(958\) | 14.2312 | 0.459788 | ||||||||
\(959\) | −1.02735 | −0.0331749 | ||||||||
\(960\) | 1.50270 | 0.0484993 | ||||||||
\(961\) | −29.7311 | −0.959067 | ||||||||
\(962\) | −4.46916 | −0.144091 | ||||||||
\(963\) | −1.59344 | −0.0513478 | ||||||||
\(964\) | 8.96181 | 0.288641 | ||||||||
\(965\) | −15.7785 | −0.507928 | ||||||||
\(966\) | 0.341012 | 0.0109719 | ||||||||
\(967\) | 30.4137 | 0.978038 | 0.489019 | − | 0.872273i | \(-0.337355\pi\) | ||||
0.489019 | + | 0.872273i | \(0.337355\pi\) | |||||||
\(968\) | −24.6434 | −0.792070 | ||||||||
\(969\) | −16.4819 | −0.529474 | ||||||||
\(970\) | 16.2148 | 0.520626 | ||||||||
\(971\) | 22.7762 | 0.730922 | 0.365461 | − | 0.930827i | \(-0.380911\pi\) | ||||
0.365461 | + | 0.930827i | \(0.380911\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 2.19169 | 0.0702623 | ||||||||
\(974\) | −28.6776 | −0.918889 | ||||||||
\(975\) | 2.74190 | 0.0878112 | ||||||||
\(976\) | 8.82911 | 0.282613 | ||||||||
\(977\) | −38.1820 | −1.22155 | −0.610776 | − | 0.791804i | \(-0.709142\pi\) | ||||
−0.610776 | + | 0.791804i | \(0.709142\pi\) | |||||||
\(978\) | 12.7215 | 0.406790 | ||||||||
\(979\) | 29.5726 | 0.945144 | ||||||||
\(980\) | −10.4522 | −0.333882 | ||||||||
\(981\) | 3.58061 | 0.114320 | ||||||||
\(982\) | 11.8787 | 0.379064 | ||||||||
\(983\) | −32.1683 | −1.02601 | −0.513005 | − | 0.858386i | \(-0.671468\pi\) | ||||
−0.513005 | + | 0.858386i | \(0.671468\pi\) | |||||||
\(984\) | 1.90597 | 0.0607603 | ||||||||
\(985\) | −13.3492 | −0.425340 | ||||||||
\(986\) | −31.0563 | −0.989033 | ||||||||
\(987\) | −0.544156 | −0.0173207 | ||||||||
\(988\) | 3.08917 | 0.0982797 | ||||||||
\(989\) | −5.52317 | −0.175627 | ||||||||
\(990\) | 8.97142 | 0.285130 | ||||||||
\(991\) | −16.4259 | −0.521785 | −0.260892 | − | 0.965368i | \(-0.584017\pi\) | ||||
−0.260892 | + | 0.965368i | \(0.584017\pi\) | |||||||
\(992\) | −1.12646 | −0.0357652 | ||||||||
\(993\) | −11.8691 | −0.376656 | ||||||||
\(994\) | 1.04469 | 0.0331357 | ||||||||
\(995\) | 15.8073 | 0.501124 | ||||||||
\(996\) | 1.74572 | 0.0553154 | ||||||||
\(997\) | 10.6046 | 0.335851 | 0.167925 | − | 0.985800i | \(-0.446293\pi\) | ||||
0.167925 | + | 0.985800i | \(0.446293\pi\) | |||||||
\(998\) | 25.6731 | 0.812667 | ||||||||
\(999\) | −4.46916 | −0.141398 |
(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 | 8034.2.a.bb.1.11 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bb.1.11 | ✓ | 14 | 1.1 | even | 1 | trivial |