Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2925,2,Mod(1,2925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2925, 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("2925.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2925.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(23.3562425912\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 195) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.81361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2925.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.289169 | −0.204473 | −0.102237 | − | 0.994760i | \(-0.532600\pi\) | ||||
−0.102237 | + | 0.994760i | \(0.532600\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.91638 | −0.958191 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.91638 | −1.85822 | −0.929109 | − | 0.369807i | \(-0.879424\pi\) | ||||
−0.929109 | + | 0.369807i | \(0.879424\pi\) | |||||||
\(8\) | 1.13249 | 0.400397 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.91638 | −1.48234 | −0.741172 | − | 0.671315i | \(-0.765730\pi\) | ||||
−0.741172 | + | 0.671315i | \(0.765730\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 1.42166 | 0.379955 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.50528 | 0.876320 | ||||||||
\(17\) | −4.33804 | −1.05213 | −0.526065 | − | 0.850444i | \(-0.676333\pi\) | ||||
−0.526065 | + | 0.850444i | \(0.676333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.57834 | 0.591511 | 0.295756 | − | 0.955264i | \(-0.404429\pi\) | ||||
0.295756 | + | 0.955264i | \(0.404429\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.42166 | 0.303100 | ||||||||
\(23\) | −6.33804 | −1.32157 | −0.660787 | − | 0.750574i | \(-0.729777\pi\) | ||||
−0.660787 | + | 0.750574i | \(0.729777\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.289169 | 0.0567106 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.42166 | 1.78053 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.42166 | 0.255338 | 0.127669 | − | 0.991817i | \(-0.459250\pi\) | ||||
0.127669 | + | 0.991817i | \(0.459250\pi\) | |||||||
\(32\) | −3.27861 | −0.579581 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.25443 | 0.215132 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.49472 | −1.56092 | −0.780461 | − | 0.625204i | \(-0.785016\pi\) | ||||
−0.780461 | + | 0.625204i | \(0.785016\pi\) | |||||||
\(38\) | −0.745574 | −0.120948 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.33804 | −0.677489 | −0.338744 | − | 0.940878i | \(-0.610002\pi\) | ||||
−0.338744 | + | 0.940878i | \(0.610002\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.15667 | 0.176391 | 0.0881956 | − | 0.996103i | \(-0.471890\pi\) | ||||
0.0881956 | + | 0.996103i | \(0.471890\pi\) | |||||||
\(44\) | 9.42166 | 1.42037 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.83276 | 0.270226 | ||||||||
\(47\) | −5.42166 | −0.790831 | −0.395415 | − | 0.918502i | \(-0.629399\pi\) | ||||
−0.395415 | + | 0.918502i | \(0.629399\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.1708 | 2.45297 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.91638 | 0.265754 | ||||||||
\(53\) | −0.338044 | −0.0464340 | −0.0232170 | − | 0.999730i | \(-0.507391\pi\) | ||||
−0.0232170 | + | 0.999730i | \(0.507391\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.56777 | −0.744025 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.73501 | 0.227818 | ||||||||
\(59\) | 11.2544 | 1.46520 | 0.732601 | − | 0.680659i | \(-0.238306\pi\) | ||||
0.732601 | + | 0.680659i | \(0.238306\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.1708 | −1.30224 | −0.651119 | − | 0.758975i | \(-0.725700\pi\) | ||||
−0.651119 | + | 0.758975i | \(0.725700\pi\) | |||||||
\(62\) | −0.411100 | −0.0522098 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.06249 | −0.757812 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.25443 | 0.886269 | 0.443135 | − | 0.896455i | \(-0.353866\pi\) | ||||
0.443135 | + | 0.896455i | \(0.353866\pi\) | |||||||
\(68\) | 8.31335 | 1.00814 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.916382 | −0.108754 | −0.0543772 | − | 0.998520i | \(-0.517317\pi\) | ||||
−0.0543772 | + | 0.998520i | \(0.517317\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.15667 | 0.369461 | 0.184730 | − | 0.982789i | \(-0.440859\pi\) | ||||
0.184730 | + | 0.982789i | \(0.440859\pi\) | |||||||
\(74\) | 2.74557 | 0.319166 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.94108 | −0.566780 | ||||||||
\(77\) | 24.1708 | 2.75452 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.49472 | −0.393187 | −0.196593 | − | 0.980485i | \(-0.562988\pi\) | ||||
−0.196593 | + | 0.980485i | \(0.562988\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.25443 | 0.138528 | ||||||||
\(83\) | 11.2544 | 1.23533 | 0.617667 | − | 0.786440i | \(-0.288078\pi\) | ||||
0.617667 | + | 0.786440i | \(0.288078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.334474 | −0.0360672 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.56777 | −0.593527 | ||||||||
\(89\) | 0.338044 | 0.0358326 | 0.0179163 | − | 0.999839i | \(-0.494297\pi\) | ||||
0.0179163 | + | 0.999839i | \(0.494297\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.91638 | 0.515377 | ||||||||
\(92\) | 12.1461 | 1.26632 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.56777 | 0.161704 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3380 | 1.25274 | 0.626369 | − | 0.779526i | \(-0.284540\pi\) | ||||
0.626369 | + | 0.779526i | \(0.284540\pi\) | |||||||
\(98\) | −4.96526 | −0.501567 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.6761 | −1.06231 | −0.531155 | − | 0.847274i | \(-0.678242\pi\) | ||||
−0.531155 | + | 0.847274i | \(0.678242\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.5089 | 1.42960 | 0.714800 | − | 0.699329i | \(-0.246518\pi\) | ||||
0.714800 | + | 0.699329i | \(0.246518\pi\) | |||||||
\(104\) | −1.13249 | −0.111050 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0977518 | 0.00949450 | ||||||||
\(107\) | 4.17081 | 0.403207 | 0.201604 | − | 0.979467i | \(-0.435385\pi\) | ||||
0.201604 | + | 0.979467i | \(0.435385\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.83276 | −0.367112 | −0.183556 | − | 0.983009i | \(-0.558761\pi\) | ||||
−0.183556 | + | 0.983009i | \(0.558761\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −17.2333 | −1.62839 | ||||||||
\(113\) | −0.843326 | −0.0793334 | −0.0396667 | − | 0.999213i | \(-0.512630\pi\) | ||||
−0.0396667 | + | 0.999213i | \(0.512630\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 11.4983 | 1.06759 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.25443 | −0.299594 | ||||||||
\(119\) | 21.3275 | 1.95509 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.1708 | 1.19735 | ||||||||
\(122\) | 2.94108 | 0.266273 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.72445 | −0.244663 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.83276 | −0.162631 | −0.0813157 | − | 0.996688i | \(-0.525912\pi\) | ||||
−0.0813157 | + | 0.996688i | \(0.525912\pi\) | |||||||
\(128\) | 8.31029 | 0.734533 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.83276 | −0.509611 | −0.254805 | − | 0.966992i | \(-0.582011\pi\) | ||||
−0.254805 | + | 0.966992i | \(0.582011\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.6761 | −1.09916 | ||||||||
\(134\) | −2.09775 | −0.181218 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.91281 | −0.421270 | ||||||||
\(137\) | −16.5089 | −1.41045 | −0.705223 | − | 0.708985i | \(-0.749153\pi\) | ||||
−0.705223 | + | 0.708985i | \(0.749153\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.49472 | 0.635694 | 0.317847 | − | 0.948142i | \(-0.397040\pi\) | ||||
0.317847 | + | 0.948142i | \(0.397040\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.264989 | 0.0222374 | ||||||||
\(143\) | 4.91638 | 0.411128 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.912811 | −0.0755448 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 18.1955 | 1.49566 | ||||||||
\(149\) | −20.4842 | −1.67813 | −0.839064 | − | 0.544033i | \(-0.816897\pi\) | ||||
−0.839064 | + | 0.544033i | \(0.816897\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.4111 | −1.33552 | −0.667758 | − | 0.744378i | \(-0.732746\pi\) | ||||
−0.667758 | + | 0.744378i | \(0.732746\pi\) | |||||||
\(152\) | 2.91995 | 0.236839 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.98944 | −0.563225 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.6655 | 1.72910 | 0.864549 | − | 0.502549i | \(-0.167604\pi\) | ||||
0.864549 | + | 0.502549i | \(0.167604\pi\) | |||||||
\(158\) | 1.01056 | 0.0803961 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 31.1602 | 2.45577 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.07306 | −0.475678 | −0.237839 | − | 0.971305i | \(-0.576439\pi\) | ||||
−0.237839 | + | 0.971305i | \(0.576439\pi\) | |||||||
\(164\) | 8.31335 | 0.649163 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.25443 | −0.252592 | ||||||||
\(167\) | −0.745574 | −0.0576942 | −0.0288471 | − | 0.999584i | \(-0.509184\pi\) | ||||
−0.0288471 | + | 0.999584i | \(0.509184\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.21663 | −0.169016 | ||||||||
\(173\) | 0.843326 | 0.0641169 | 0.0320584 | − | 0.999486i | \(-0.489794\pi\) | ||||
0.0320584 | + | 0.999486i | \(0.489794\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −17.2333 | −1.29901 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.0977518 | −0.00732681 | ||||||||
\(179\) | 18.9894 | 1.41934 | 0.709669 | − | 0.704536i | \(-0.248845\pi\) | ||||
0.709669 | + | 0.704536i | \(0.248845\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4947 | 1.30037 | 0.650186 | − | 0.759775i | \(-0.274691\pi\) | ||||
0.650186 | + | 0.759775i | \(0.274691\pi\) | |||||||
\(182\) | −1.42166 | −0.105381 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.17780 | −0.529154 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.3275 | 1.55962 | ||||||||
\(188\) | 10.3900 | 0.757767 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.5089 | 1.62868 | 0.814342 | − | 0.580386i | \(-0.197098\pi\) | ||||
0.814342 | + | 0.580386i | \(0.197098\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.65139 | −0.190851 | −0.0954257 | − | 0.995437i | \(-0.530421\pi\) | ||||
−0.0954257 | + | 0.995437i | \(0.530421\pi\) | |||||||
\(194\) | −3.56777 | −0.256151 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −32.9058 | −2.35042 | ||||||||
\(197\) | −12.9894 | −0.925459 | −0.462730 | − | 0.886500i | \(-0.653130\pi\) | ||||
−0.462730 | + | 0.886500i | \(0.653130\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.84333 | −0.201558 | −0.100779 | − | 0.994909i | \(-0.532134\pi\) | ||||
−0.100779 | + | 0.994909i | \(0.532134\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.08719 | 0.217214 | ||||||||
\(203\) | 29.4983 | 2.07037 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.19550 | −0.292315 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.50528 | −0.243048 | ||||||||
\(209\) | −12.6761 | −0.876823 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.31335 | 0.434629 | 0.217314 | − | 0.976102i | \(-0.430270\pi\) | ||||
0.217314 | + | 0.976102i | \(0.430270\pi\) | |||||||
\(212\) | 0.647822 | 0.0444926 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.20607 | −0.0824450 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.98944 | −0.474474 | ||||||||
\(218\) | 1.10831 | 0.0750645 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.33804 | 0.291808 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.2544 | −1.28937 | −0.644686 | − | 0.764448i | \(-0.723012\pi\) | ||||
−0.644686 | + | 0.764448i | \(0.723012\pi\) | |||||||
\(224\) | 16.1189 | 1.07699 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.243863 | 0.0162215 | ||||||||
\(227\) | −13.0872 | −0.868627 | −0.434314 | − | 0.900762i | \(-0.643009\pi\) | ||||
−0.434314 | + | 0.900762i | \(0.643009\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.5089 | −1.61959 | −0.809795 | − | 0.586713i | \(-0.800422\pi\) | ||||
−0.809795 | + | 0.586713i | \(0.800422\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.79497 | −0.446111 | ||||||||
\(233\) | 8.33804 | 0.546243 | 0.273122 | − | 0.961979i | \(-0.411944\pi\) | ||||
0.273122 | + | 0.961979i | \(0.411944\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −21.5678 | −1.40394 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.16724 | −0.399763 | ||||||||
\(239\) | −8.91638 | −0.576753 | −0.288376 | − | 0.957517i | \(-0.593115\pi\) | ||||
−0.288376 | + | 0.957517i | \(0.593115\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.00000 | −0.386494 | −0.193247 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193247 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(242\) | −3.80858 | −0.244825 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 19.4911 | 1.24779 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.57834 | −0.164056 | ||||||||
\(248\) | 1.61003 | 0.102237 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.31335 | 0.398495 | 0.199248 | − | 0.979949i | \(-0.436150\pi\) | ||||
0.199248 | + | 0.979949i | \(0.436150\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.1602 | 1.95903 | ||||||||
\(254\) | 0.529977 | 0.0332537 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.72191 | 0.607619 | ||||||||
\(257\) | −11.1567 | −0.695934 | −0.347967 | − | 0.937507i | \(-0.613128\pi\) | ||||
−0.347967 | + | 0.937507i | \(0.613128\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 46.6797 | 2.90053 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.68665 | 0.104202 | ||||||||
\(263\) | 8.00000 | 0.493301 | 0.246651 | − | 0.969104i | \(-0.420670\pi\) | ||||
0.246651 | + | 0.969104i | \(0.420670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.66553 | 0.224748 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.9022 | −0.849215 | ||||||||
\(269\) | −18.6761 | −1.13870 | −0.569351 | − | 0.822095i | \(-0.692805\pi\) | ||||
−0.569351 | + | 0.822095i | \(0.692805\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.57834 | 0.399606 | 0.199803 | − | 0.979836i | \(-0.435970\pi\) | ||||
0.199803 | + | 0.979836i | \(0.435970\pi\) | |||||||
\(272\) | −15.2061 | −0.922003 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.77384 | 0.288398 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.6655 | −1.54209 | −0.771046 | − | 0.636779i | \(-0.780266\pi\) | ||||
−0.771046 | + | 0.636779i | \(0.780266\pi\) | |||||||
\(278\) | −2.16724 | −0.129982 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.15667 | −0.188311 | −0.0941557 | − | 0.995557i | \(-0.530015\pi\) | ||||
−0.0941557 | + | 0.995557i | \(0.530015\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.47002 | 0.206271 | 0.103136 | − | 0.994667i | \(-0.467112\pi\) | ||||
0.103136 | + | 0.994667i | \(0.467112\pi\) | |||||||
\(284\) | 1.75614 | 0.104208 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.42166 | −0.0840647 | ||||||||
\(287\) | 21.3275 | 1.25892 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.81863 | 0.106978 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.04939 | −0.354014 | ||||||||
\(293\) | 28.6550 | 1.67404 | 0.837020 | − | 0.547172i | \(-0.184296\pi\) | ||||
0.837020 | + | 0.547172i | \(0.184296\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −10.7527 | −0.624989 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.92337 | 0.343132 | ||||||||
\(299\) | 6.33804 | 0.366539 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.68665 | −0.327773 | ||||||||
\(302\) | 4.74557 | 0.273077 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.03780 | 0.518353 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.92694 | 0.109977 | 0.0549883 | − | 0.998487i | \(-0.482488\pi\) | ||||
0.0549883 | + | 0.998487i | \(0.482488\pi\) | |||||||
\(308\) | −46.3205 | −2.63935 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.9789 | 1.69995 | 0.849973 | − | 0.526826i | \(-0.176618\pi\) | ||||
0.849973 | + | 0.526826i | \(0.176618\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.3133 | 0.922085 | 0.461042 | − | 0.887378i | \(-0.347476\pi\) | ||||
0.461042 | + | 0.887378i | \(0.347476\pi\) | |||||||
\(314\) | −6.26499 | −0.353554 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.69721 | 0.376748 | ||||||||
\(317\) | 30.6761 | 1.72294 | 0.861470 | − | 0.507808i | \(-0.169544\pi\) | ||||
0.861470 | + | 0.507808i | \(0.169544\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 29.4983 | 1.65159 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.01056 | −0.502139 | ||||||||
\(323\) | −11.1849 | −0.622347 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.75614 | 0.0972634 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.91281 | −0.271265 | ||||||||
\(329\) | 26.6550 | 1.46954 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0978 | −0.555023 | −0.277511 | − | 0.960722i | \(-0.589510\pi\) | ||||
−0.277511 | + | 0.960722i | \(0.589510\pi\) | |||||||
\(332\) | −21.5678 | −1.18369 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.215597 | 0.0117969 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.32391 | 0.0721180 | 0.0360590 | − | 0.999350i | \(-0.488520\pi\) | ||||
0.0360590 | + | 0.999350i | \(0.488520\pi\) | |||||||
\(338\) | −0.289169 | −0.0157287 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.98944 | −0.378499 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −50.0036 | −2.69994 | ||||||||
\(344\) | 1.30993 | 0.0706265 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.243863 | −0.0131102 | ||||||||
\(347\) | −7.49472 | −0.402338 | −0.201169 | − | 0.979557i | \(-0.564474\pi\) | ||||
−0.201169 | + | 0.979557i | \(0.564474\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.1461 | −1.18545 | −0.592727 | − | 0.805403i | \(-0.701949\pi\) | ||||
−0.592727 | + | 0.805403i | \(0.701949\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.1189 | 0.859139 | ||||||||
\(353\) | 4.50885 | 0.239982 | 0.119991 | − | 0.992775i | \(-0.461713\pi\) | ||||
0.119991 | + | 0.992775i | \(0.461713\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.647822 | −0.0343345 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.49115 | −0.290216 | ||||||||
\(359\) | 20.4111 | 1.07726 | 0.538628 | − | 0.842543i | \(-0.318943\pi\) | ||||
0.538628 | + | 0.842543i | \(0.318943\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3522 | −0.650115 | ||||||||
\(362\) | −5.05892 | −0.265891 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.42166 | −0.493829 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.3133 | 0.538352 | 0.269176 | − | 0.963091i | \(-0.413249\pi\) | ||||
0.269176 | + | 0.963091i | \(0.413249\pi\) | |||||||
\(368\) | −22.2166 | −1.15812 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.66196 | 0.0862844 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.6761 | −0.967011 | −0.483506 | − | 0.875341i | \(-0.660637\pi\) | ||||
−0.483506 | + | 0.875341i | \(0.660637\pi\) | |||||||
\(374\) | −6.16724 | −0.318900 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.14000 | −0.316646 | ||||||||
\(377\) | 6.00000 | 0.309016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.7527 | −1.47693 | −0.738464 | − | 0.674293i | \(-0.764448\pi\) | ||||
−0.738464 | + | 0.674293i | \(0.764448\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.50885 | −0.333022 | ||||||||
\(383\) | −14.2439 | −0.727827 | −0.363914 | − | 0.931433i | \(-0.618560\pi\) | ||||
−0.363914 | + | 0.931433i | \(0.618560\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.766699 | 0.0390240 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −23.6444 | −1.20036 | ||||||||
\(389\) | −34.6761 | −1.75815 | −0.879074 | − | 0.476686i | \(-0.841838\pi\) | ||||
−0.879074 | + | 0.476686i | \(0.841838\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.4947 | 1.39047 | ||||||||
\(392\) | 19.4458 | 0.982163 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.75614 | 0.189231 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.18137 | −0.360423 | −0.180211 | − | 0.983628i | \(-0.557678\pi\) | ||||
−0.180211 | + | 0.983628i | \(0.557678\pi\) | |||||||
\(398\) | 0.822200 | 0.0412132 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.8610 | −1.89069 | −0.945345 | − | 0.326072i | \(-0.894275\pi\) | ||||
−0.945345 | + | 0.326072i | \(0.894275\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.42166 | −0.0708181 | ||||||||
\(404\) | 20.4595 | 1.01790 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.52998 | −0.423336 | ||||||||
\(407\) | 46.6797 | 2.31382 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.0000 | −0.692255 | −0.346128 | − | 0.938187i | \(-0.612504\pi\) | ||||
−0.346128 | + | 0.938187i | \(0.612504\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −27.8045 | −1.36983 | ||||||||
\(413\) | −55.3311 | −2.72266 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.27861 | 0.160747 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.66553 | 0.179287 | ||||||||
\(419\) | 33.4983 | 1.63650 | 0.818249 | − | 0.574864i | \(-0.194945\pi\) | ||||
0.818249 | + | 0.574864i | \(0.194945\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.5194 | 0.658896 | 0.329448 | − | 0.944174i | \(-0.393137\pi\) | ||||
0.329448 | + | 0.944174i | \(0.393137\pi\) | |||||||
\(422\) | −1.82562 | −0.0888699 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.382833 | −0.0185920 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 50.0036 | 2.41984 | ||||||||
\(428\) | −7.99286 | −0.386349 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.4111 | −0.597822 | −0.298911 | − | 0.954281i | \(-0.596623\pi\) | ||||
−0.298911 | + | 0.954281i | \(0.596623\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.3239 | 0.832534 | 0.416267 | − | 0.909242i | \(-0.363338\pi\) | ||||
0.416267 | + | 0.909242i | \(0.363338\pi\) | |||||||
\(434\) | 2.02113 | 0.0970171 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.34504 | 0.351763 | ||||||||
\(437\) | −16.3416 | −0.781725 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.651393 | 0.0310893 | 0.0155446 | − | 0.999879i | \(-0.495052\pi\) | ||||
0.0155446 | + | 0.999879i | \(0.495052\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.25443 | −0.0596670 | ||||||||
\(443\) | −8.84690 | −0.420329 | −0.210164 | − | 0.977666i | \(-0.567400\pi\) | ||||
−0.210164 | + | 0.977666i | \(0.567400\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.56777 | 0.263642 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 29.8055 | 1.40818 | ||||||||
\(449\) | −4.33804 | −0.204725 | −0.102362 | − | 0.994747i | \(-0.532640\pi\) | ||||
−0.102362 | + | 0.994747i | \(0.532640\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.3275 | 1.00427 | ||||||||
\(452\) | 1.61613 | 0.0760166 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.78440 | 0.177611 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.3275 | −0.716989 | −0.358495 | − | 0.933532i | \(-0.616710\pi\) | ||||
−0.358495 | + | 0.933532i | \(0.616710\pi\) | |||||||
\(458\) | 7.08719 | 0.331163 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.8575 | 0.552257 | 0.276128 | − | 0.961121i | \(-0.410948\pi\) | ||||
0.276128 | + | 0.961121i | \(0.410948\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.4147 | 1.22759 | 0.613797 | − | 0.789464i | \(-0.289641\pi\) | ||||
0.613797 | + | 0.789464i | \(0.289641\pi\) | |||||||
\(464\) | −21.0317 | −0.976372 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.41110 | −0.111692 | ||||||||
\(467\) | −33.6691 | −1.55802 | −0.779010 | − | 0.627012i | \(-0.784278\pi\) | ||||
−0.779010 | + | 0.627012i | \(0.784278\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −35.6655 | −1.64688 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.7456 | 0.586663 | ||||||||
\(473\) | −5.68665 | −0.261473 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −40.8716 | −1.87335 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.57834 | 0.117930 | ||||||||
\(479\) | −10.7491 | −0.491141 | −0.245570 | − | 0.969379i | \(-0.578975\pi\) | ||||
−0.245570 | + | 0.969379i | \(0.578975\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.49472 | 0.432922 | ||||||||
\(482\) | 1.73501 | 0.0790276 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −25.2403 | −1.14729 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.7491 | −1.03086 | −0.515431 | − | 0.856931i | \(-0.672368\pi\) | ||||
−0.515431 | + | 0.856931i | \(0.672368\pi\) | |||||||
\(488\) | −11.5184 | −0.521413 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.6867 | 0.798187 | 0.399094 | − | 0.916910i | \(-0.369325\pi\) | ||||
0.399094 | + | 0.916910i | \(0.369325\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.0283 | 1.17225 | ||||||||
\(494\) | 0.745574 | 0.0335450 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.98333 | 0.223758 | ||||||||
\(497\) | 4.50528 | 0.202089 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.9305 | 0.892212 | 0.446106 | − | 0.894980i | \(-0.352810\pi\) | ||||
0.446106 | + | 0.894980i | \(0.352810\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.82562 | −0.0814815 | ||||||||
\(503\) | 33.3522 | 1.48710 | 0.743550 | − | 0.668680i | \(-0.233140\pi\) | ||||
0.743550 | + | 0.668680i | \(0.233140\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.01056 | −0.400568 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.51227 | 0.155832 | ||||||||
\(509\) | −13.8363 | −0.613285 | −0.306642 | − | 0.951825i | \(-0.599206\pi\) | ||||
−0.306642 | + | 0.951825i | \(0.599206\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.5194 | −0.686538 | ||||||||
\(512\) | −19.4319 | −0.858775 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.22616 | 0.142300 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.6550 | 1.17228 | ||||||||
\(518\) | −13.4983 | −0.593081 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.3522 | 1.02308 | 0.511539 | − | 0.859260i | \(-0.329076\pi\) | ||||
0.511539 | + | 0.859260i | \(0.329076\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00000 | 0.174908 | 0.0874539 | − | 0.996169i | \(-0.472127\pi\) | ||||
0.0874539 | + | 0.996169i | \(0.472127\pi\) | |||||||
\(524\) | 11.1778 | 0.488304 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.31335 | −0.100867 | ||||||||
\(527\) | −6.16724 | −0.268649 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.1708 | 0.746557 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 24.2922 | 1.05320 | ||||||||
\(533\) | 4.33804 | 0.187902 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.21560 | 0.354860 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.40054 | 0.232834 | ||||||||
\(539\) | −84.4182 | −3.63615 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.1744 | 0.695391 | 0.347695 | − | 0.937608i | \(-0.386964\pi\) | ||||
0.347695 | + | 0.937608i | \(0.386964\pi\) | |||||||
\(542\) | −1.90225 | −0.0817086 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 14.2227 | 0.609795 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.68665 | −0.414171 | −0.207086 | − | 0.978323i | \(-0.566398\pi\) | ||||
−0.207086 | + | 0.978323i | \(0.566398\pi\) | |||||||
\(548\) | 31.6373 | 1.35148 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.4700 | −0.659045 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.1814 | 0.730626 | ||||||||
\(554\) | 7.42166 | 0.315316 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.3627 | −0.609116 | ||||||||
\(557\) | 0.647822 | 0.0274491 | 0.0137246 | − | 0.999906i | \(-0.495631\pi\) | ||||
0.0137246 | + | 0.999906i | \(0.495631\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.15667 | −0.0489221 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.912811 | 0.0385046 | ||||||||
\(563\) | −16.3169 | −0.687676 | −0.343838 | − | 0.939029i | \(-0.611727\pi\) | ||||
−0.343838 | + | 0.939029i | \(0.611727\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.00342 | −0.0421769 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.03780 | −0.0435450 | ||||||||
\(569\) | −44.6550 | −1.87203 | −0.936017 | − | 0.351956i | \(-0.885517\pi\) | ||||
−0.936017 | + | 0.351956i | \(0.885517\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.67252 | −0.279236 | −0.139618 | − | 0.990205i | \(-0.544587\pi\) | ||||
−0.139618 | + | 0.990205i | \(0.544587\pi\) | |||||||
\(572\) | −9.42166 | −0.393940 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.16724 | −0.257415 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.3275 | −0.638091 | −0.319046 | − | 0.947739i | \(-0.603362\pi\) | ||||
−0.319046 | + | 0.947739i | \(0.603362\pi\) | |||||||
\(578\) | −0.525891 | −0.0218742 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −55.3311 | −2.29552 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.66196 | 0.0688312 | ||||||||
\(584\) | 3.57492 | 0.147931 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.28611 | −0.342296 | ||||||||
\(587\) | 12.2650 | 0.506230 | 0.253115 | − | 0.967436i | \(-0.418545\pi\) | ||||
0.253115 | + | 0.967436i | \(0.418545\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.66553 | 0.151035 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −33.2817 | −1.36787 | ||||||||
\(593\) | −5.85389 | −0.240390 | −0.120195 | − | 0.992750i | \(-0.538352\pi\) | ||||
−0.120195 | + | 0.992750i | \(0.538352\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 39.2555 | 1.60797 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.83276 | −0.0749473 | ||||||||
\(599\) | −27.1355 | −1.10873 | −0.554364 | − | 0.832274i | \(-0.687039\pi\) | ||||
−0.554364 | + | 0.832274i | \(0.687039\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.1708 | 1.39386 | 0.696928 | − | 0.717141i | \(-0.254550\pi\) | ||||
0.696928 | + | 0.717141i | \(0.254550\pi\) | |||||||
\(602\) | 1.64440 | 0.0670208 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 31.4499 | 1.27968 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.3133 | −0.418606 | −0.209303 | − | 0.977851i | \(-0.567119\pi\) | ||||
−0.209303 | + | 0.977851i | \(0.567119\pi\) | |||||||
\(608\) | −8.45335 | −0.342829 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.42166 | 0.219337 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.484156 | −0.0195549 | −0.00977744 | − | 0.999952i | \(-0.503112\pi\) | ||||
−0.00977744 | + | 0.999952i | \(0.503112\pi\) | |||||||
\(614\) | −0.557212 | −0.0224872 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 27.3733 | 1.10290 | ||||||||
\(617\) | −7.15667 | −0.288117 | −0.144058 | − | 0.989569i | \(-0.546015\pi\) | ||||
−0.144058 | + | 0.989569i | \(0.546015\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.42166 | 0.217915 | 0.108958 | − | 0.994046i | \(-0.465249\pi\) | ||||
0.108958 | + | 0.994046i | \(0.465249\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.66895 | −0.347593 | ||||||||
\(623\) | −1.66196 | −0.0665848 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.71731 | −0.188542 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −41.5194 | −1.65681 | ||||||||
\(629\) | 41.1885 | 1.64229 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.7244 | −0.426934 | −0.213467 | − | 0.976950i | \(-0.568476\pi\) | ||||
−0.213467 | + | 0.976950i | \(0.568476\pi\) | |||||||
\(632\) | −3.95775 | −0.157431 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.87056 | −0.352295 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.1708 | −0.680332 | ||||||||
\(638\) | −8.52998 | −0.337705 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.362741 | 0.0143274 | 0.00716370 | − | 0.999974i | \(-0.497720\pi\) | ||||
0.00716370 | + | 0.999974i | \(0.497720\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.39697 | 0.370580 | 0.185290 | − | 0.982684i | \(-0.440678\pi\) | ||||
0.185290 | + | 0.982684i | \(0.440678\pi\) | |||||||
\(644\) | −59.7149 | −2.35310 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.23433 | 0.127253 | ||||||||
\(647\) | 18.0036 | 0.707793 | 0.353897 | − | 0.935285i | \(-0.384856\pi\) | ||||
0.353897 | + | 0.935285i | \(0.384856\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −55.3311 | −2.17193 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.6383 | 0.455791 | ||||||||
\(653\) | −34.8222 | −1.36270 | −0.681349 | − | 0.731959i | \(-0.738606\pi\) | ||||
−0.681349 | + | 0.731959i | \(0.738606\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −15.2061 | −0.593697 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.70778 | −0.300480 | ||||||||
\(659\) | −11.4700 | −0.446809 | −0.223404 | − | 0.974726i | \(-0.571717\pi\) | ||||
−0.223404 | + | 0.974726i | \(0.571717\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.1672 | 0.473251 | 0.236625 | − | 0.971601i | \(-0.423959\pi\) | ||||
0.236625 | + | 0.971601i | \(0.423959\pi\) | |||||||
\(662\) | 2.91995 | 0.113487 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.7456 | 0.494624 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.0283 | 1.47246 | ||||||||
\(668\) | 1.42880 | 0.0552821 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 50.0036 | 1.93037 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.9789 | 1.07851 | 0.539253 | − | 0.842144i | \(-0.318707\pi\) | ||||
0.539253 | + | 0.842144i | \(0.318707\pi\) | |||||||
\(674\) | −0.382833 | −0.0147462 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.91638 | −0.0737070 | ||||||||
\(677\) | 22.9930 | 0.883693 | 0.441847 | − | 0.897091i | \(-0.354324\pi\) | ||||
0.441847 | + | 0.897091i | \(0.354324\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −60.6585 | −2.32786 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.02113 | 0.0773929 | ||||||||
\(683\) | −28.6066 | −1.09460 | −0.547301 | − | 0.836936i | \(-0.684345\pi\) | ||||
−0.547301 | + | 0.836936i | \(0.684345\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14.4595 | 0.552065 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.05447 | 0.154575 | ||||||||
\(689\) | 0.338044 | 0.0128785 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.4005 | −0.738031 | −0.369016 | − | 0.929423i | \(-0.620305\pi\) | ||||
−0.369016 | + | 0.929423i | \(0.620305\pi\) | |||||||
\(692\) | −1.61613 | −0.0614362 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.16724 | 0.0822672 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.8186 | 0.712806 | ||||||||
\(698\) | 6.40396 | 0.242393 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.9683 | 1.47181 | 0.735906 | − | 0.677083i | \(-0.236756\pi\) | ||||
0.735906 | + | 0.677083i | \(0.236756\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.4806 | −0.923303 | ||||||||
\(704\) | 29.8055 | 1.12334 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.30382 | −0.0490698 | ||||||||
\(707\) | 52.4877 | 1.97400 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.5194 | −0.657955 | −0.328978 | − | 0.944338i | \(-0.606704\pi\) | ||||
−0.328978 | + | 0.944338i | \(0.606704\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.382833 | 0.0143473 | ||||||||
\(713\) | −9.01056 | −0.337448 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −36.3910 | −1.36000 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.90225 | −0.220270 | ||||||||
\(719\) | 4.33447 | 0.161649 | 0.0808243 | − | 0.996728i | \(-0.474245\pi\) | ||||
0.0808243 | + | 0.996728i | \(0.474245\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −71.3311 | −2.65651 | ||||||||
\(722\) | 3.57186 | 0.132931 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −33.5266 | −1.24600 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.1672 | −0.822137 | −0.411069 | − | 0.911604i | \(-0.634844\pi\) | ||||
−0.411069 | + | 0.911604i | \(0.634844\pi\) | |||||||
\(728\) | 5.56777 | 0.206355 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.01770 | −0.185586 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.83976 | 0.104889 | 0.0524444 | − | 0.998624i | \(-0.483299\pi\) | ||||
0.0524444 | + | 0.998624i | \(0.483299\pi\) | |||||||
\(734\) | −2.98230 | −0.110079 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.7799 | 0.765959 | ||||||||
\(737\) | −35.6655 | −1.31376 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.9305 | −1.61601 | −0.808005 | − | 0.589176i | \(-0.799453\pi\) | ||||
−0.808005 | + | 0.589176i | \(0.799453\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.480585 | −0.0176428 | ||||||||
\(743\) | 41.0872 | 1.50734 | 0.753671 | − | 0.657251i | \(-0.228281\pi\) | ||||
0.753671 | + | 0.657251i | \(0.228281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.40054 | 0.197728 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −40.8716 | −1.49441 | ||||||||
\(749\) | −20.5053 | −0.749247 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.6902 | 0.864468 | 0.432234 | − | 0.901761i | \(-0.357725\pi\) | ||||
0.432234 | + | 0.901761i | \(0.357725\pi\) | |||||||
\(752\) | −19.0045 | −0.693021 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.73501 | −0.0631854 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.32391 | −0.338883 | −0.169442 | − | 0.985540i | \(-0.554196\pi\) | ||||
−0.169442 | + | 0.985540i | \(0.554196\pi\) | |||||||
\(758\) | 8.31438 | 0.301992 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.8222 | 1.55230 | 0.776152 | − | 0.630546i | \(-0.217169\pi\) | ||||
0.776152 | + | 0.630546i | \(0.217169\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.8433 | 0.682174 | ||||||||
\(764\) | −43.1355 | −1.56059 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.11888 | 0.148821 | ||||||||
\(767\) | −11.2544 | −0.406374 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.3239 | −0.624716 | −0.312358 | − | 0.949964i | \(-0.601119\pi\) | ||||
−0.312358 | + | 0.949964i | \(0.601119\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.08108 | 0.182872 | ||||||||
\(773\) | −11.6373 | −0.418563 | −0.209282 | − | 0.977855i | \(-0.567113\pi\) | ||||
−0.209282 | + | 0.977855i | \(0.567113\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 13.9728 | 0.501593 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.0272 | 0.359494 | ||||||||
\(779\) | −11.1849 | −0.400742 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.50528 | 0.161212 | ||||||||
\(782\) | −7.95061 | −0.284313 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 60.1885 | 2.14959 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.9411 | −0.746469 | −0.373234 | − | 0.927737i | \(-0.621751\pi\) | ||||
−0.373234 | + | 0.927737i | \(0.621751\pi\) | |||||||
\(788\) | 24.8927 | 0.886766 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.14611 | 0.147419 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.1708 | 0.361176 | ||||||||
\(794\) | 2.07663 | 0.0736967 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.44890 | 0.193131 | ||||||||
\(797\) | 20.3380 | 0.720410 | 0.360205 | − | 0.932873i | \(-0.382707\pi\) | ||||
0.360205 | + | 0.932873i | \(0.382707\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.5194 | 0.832057 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.9482 | 0.386595 | ||||||||
\(803\) | −15.5194 | −0.547668 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.411100 | 0.0144804 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.0906 | −0.425346 | ||||||||
\(809\) | −7.68665 | −0.270248 | −0.135124 | − | 0.990829i | \(-0.543143\pi\) | ||||
−0.135124 | + | 0.990829i | \(0.543143\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.4111 | −1.55948 | −0.779742 | − | 0.626101i | \(-0.784650\pi\) | ||||
−0.779742 | + | 0.626101i | \(0.784650\pi\) | |||||||
\(812\) | −56.5300 | −1.98381 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13.4983 | −0.473115 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.98230 | 0.104337 | ||||||||
\(818\) | 4.04836 | 0.141548 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.4630 | 1.62157 | 0.810785 | − | 0.585343i | \(-0.199040\pi\) | ||||
0.810785 | + | 0.585343i | \(0.199040\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −46.5089 | −1.62120 | −0.810598 | − | 0.585603i | \(-0.800858\pi\) | ||||
−0.810598 | + | 0.585603i | \(0.800858\pi\) | |||||||
\(824\) | 16.4312 | 0.572408 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.0000 | 0.556711 | ||||||||
\(827\) | 39.4005 | 1.37009 | 0.685045 | − | 0.728500i | \(-0.259782\pi\) | ||||
0.685045 | + | 0.728500i | \(0.259782\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.6444 | 1.65476 | 0.827379 | − | 0.561644i | \(-0.189831\pi\) | ||||
0.827379 | + | 0.561644i | \(0.189831\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.06249 | 0.210179 | ||||||||
\(833\) | −74.4877 | −2.58085 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 24.2922 | 0.840164 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.68665 | −0.334620 | ||||||||
\(839\) | 39.9058 | 1.37770 | 0.688851 | − | 0.724903i | \(-0.258115\pi\) | ||||
0.688851 | + | 0.724903i | \(0.258115\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −3.90939 | −0.134726 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.0988 | −0.416457 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −64.7527 | −2.22493 | ||||||||
\(848\) | −1.18494 | −0.0406910 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 60.1779 | 2.06287 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.5019 | −1.01012 | −0.505062 | − | 0.863083i | \(-0.668530\pi\) | ||||
−0.505062 | + | 0.863083i | \(0.668530\pi\) | |||||||
\(854\) | −14.4595 | −0.494793 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.72342 | 0.161443 | ||||||||
\(857\) | 8.33804 | 0.284822 | 0.142411 | − | 0.989808i | \(-0.454515\pi\) | ||||
0.142411 | + | 0.989808i | \(0.454515\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.17081 | −0.142306 | −0.0711531 | − | 0.997465i | \(-0.522668\pi\) | ||||
−0.0711531 | + | 0.997465i | \(0.522668\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.58890 | 0.122238 | ||||||||
\(863\) | −3.93051 | −0.133796 | −0.0668981 | − | 0.997760i | \(-0.521310\pi\) | ||||
−0.0668981 | + | 0.997760i | \(0.521310\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.00953 | −0.170231 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.3944 | 0.454637 | ||||||||
\(869\) | 17.1814 | 0.582838 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.25443 | −0.245807 | ||||||||
\(872\) | −4.34058 | −0.146991 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.72548 | 0.159842 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.0177 | 0.777253 | 0.388626 | − | 0.921395i | \(-0.372950\pi\) | ||||
0.388626 | + | 0.921395i | \(0.372950\pi\) | |||||||
\(878\) | −0.188362 | −0.00635692 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.3522 | 0.517228 | 0.258614 | − | 0.965981i | \(-0.416734\pi\) | ||||
0.258614 | + | 0.965981i | \(0.416734\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.8011 | −1.44037 | −0.720185 | − | 0.693782i | \(-0.755943\pi\) | ||||
−0.720185 | + | 0.693782i | \(0.755943\pi\) | |||||||
\(884\) | −8.31335 | −0.279608 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.55824 | 0.0859459 | ||||||||
\(887\) | −53.1885 | −1.78590 | −0.892948 | − | 0.450160i | \(-0.851367\pi\) | ||||
−0.892948 | + | 0.450160i | \(0.851367\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.01056 | 0.302205 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 36.8988 | 1.23546 | ||||||||
\(893\) | −13.9789 | −0.467785 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −40.8566 | −1.36492 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.25443 | 0.0418607 | ||||||||
\(899\) | −8.52998 | −0.284491 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.46645 | 0.0488546 | ||||||||
\(902\) | −6.16724 | −0.205347 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.955062 | −0.0317649 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.8116 | −0.392199 | −0.196099 | − | 0.980584i | \(-0.562828\pi\) | ||||
−0.196099 | + | 0.980584i | \(0.562828\pi\) | |||||||
\(908\) | 25.0800 | 0.832311 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.1955 | −1.46426 | −0.732131 | − | 0.681164i | \(-0.761474\pi\) | ||||
−0.732131 | + | 0.681164i | \(0.761474\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −55.3311 | −1.83119 | ||||||||
\(914\) | 4.43223 | 0.146605 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 46.9683 | 1.55188 | ||||||||
\(917\) | 28.6761 | 0.946968 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.2096 | 1.82120 | 0.910599 | − | 0.413291i | \(-0.135621\pi\) | ||||
0.910599 | + | 0.413291i | \(0.135621\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.42880 | −0.112922 | ||||||||
\(923\) | 0.916382 | 0.0301631 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.63829 | −0.251010 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 19.6716 | 0.645753 | ||||||||
\(929\) | −22.9930 | −0.754376 | −0.377188 | − | 0.926137i | \(-0.623109\pi\) | ||||
−0.377188 | + | 0.926137i | \(0.623109\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 44.2721 | 1.45096 | ||||||||
\(932\) | −15.9789 | −0.523405 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.73604 | 0.318573 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.97887 | −0.260658 | −0.130329 | − | 0.991471i | \(-0.541603\pi\) | ||||
−0.130329 | + | 0.991471i | \(0.541603\pi\) | |||||||
\(938\) | 10.3133 | 0.336743 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.5019 | −1.35292 | −0.676461 | − | 0.736478i | \(-0.736487\pi\) | ||||
−0.676461 | + | 0.736478i | \(0.736487\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.4947 | 0.895351 | ||||||||
\(944\) | 39.4499 | 1.28399 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.64440 | 0.0534641 | ||||||||
\(947\) | 47.4499 | 1.54192 | 0.770958 | − | 0.636886i | \(-0.219778\pi\) | ||||
0.770958 | + | 0.636886i | \(0.219778\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.15667 | −0.102470 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 24.1533 | 0.782811 | ||||||||
\(953\) | 30.3663 | 0.983661 | 0.491831 | − | 0.870691i | \(-0.336328\pi\) | ||||
0.491831 | + | 0.870691i | \(0.336328\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 17.0872 | 0.552639 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.10831 | 0.100425 | ||||||||
\(959\) | 81.1638 | 2.62092 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.9789 | −0.934802 | ||||||||
\(962\) | −2.74557 | −0.0885209 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.4983 | 0.370335 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.0943 | 1.32150 | 0.660752 | − | 0.750604i | \(-0.270237\pi\) | ||||
0.660752 | + | 0.750604i | \(0.270237\pi\) | |||||||
\(968\) | 14.9159 | 0.479414 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.1744 | −1.22507 | −0.612537 | − | 0.790442i | \(-0.709851\pi\) | ||||
−0.612537 | + | 0.790442i | \(0.709851\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36.8469 | −1.18126 | ||||||||
\(974\) | 6.57834 | 0.210784 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −35.6515 | −1.14118 | ||||||||
\(977\) | −10.4806 | −0.335304 | −0.167652 | − | 0.985846i | \(-0.553618\pi\) | ||||
−0.167652 | + | 0.985846i | \(0.553618\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.66196 | −0.0531163 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.11442 | −0.163208 | ||||||||
\(983\) | −0.0766264 | −0.00244400 | −0.00122200 | − | 0.999999i | \(-0.500389\pi\) | ||||
−0.00122200 | + | 0.999999i | \(0.500389\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.52656 | −0.239694 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.94108 | 0.157197 | ||||||||
\(989\) | −7.33105 | −0.233114 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.8575 | −0.440197 | −0.220098 | − | 0.975478i | \(-0.570638\pi\) | ||||
−0.220098 | + | 0.975478i | \(0.570638\pi\) | |||||||
\(992\) | −4.66107 | −0.147989 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.30279 | −0.0413219 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.3416 | 0.327522 | 0.163761 | − | 0.986500i | \(-0.447637\pi\) | ||||
0.163761 | + | 0.986500i | \(0.447637\pi\) | |||||||
\(998\) | −5.76328 | −0.182433 | ||||||||
\(999\) | 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 | 2925.2.a.bh.1.2 | 3 | ||
3.2 | odd | 2 | 975.2.a.o.1.2 | 3 | |||
5.2 | odd | 4 | 2925.2.c.w.2224.3 | 6 | |||
5.3 | odd | 4 | 2925.2.c.w.2224.4 | 6 | |||
5.4 | even | 2 | 585.2.a.n.1.2 | 3 | |||
15.2 | even | 4 | 975.2.c.i.274.4 | 6 | |||
15.8 | even | 4 | 975.2.c.i.274.3 | 6 | |||
15.14 | odd | 2 | 195.2.a.e.1.2 | ✓ | 3 | ||
20.19 | odd | 2 | 9360.2.a.dd.1.1 | 3 | |||
60.59 | even | 2 | 3120.2.a.bj.1.1 | 3 | |||
65.64 | even | 2 | 7605.2.a.bx.1.2 | 3 | |||
105.104 | even | 2 | 9555.2.a.bq.1.2 | 3 | |||
195.194 | odd | 2 | 2535.2.a.bc.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.a.e.1.2 | ✓ | 3 | 15.14 | odd | 2 | ||
585.2.a.n.1.2 | 3 | 5.4 | even | 2 | |||
975.2.a.o.1.2 | 3 | 3.2 | odd | 2 | |||
975.2.c.i.274.3 | 6 | 15.8 | even | 4 | |||
975.2.c.i.274.4 | 6 | 15.2 | even | 4 | |||
2535.2.a.bc.1.2 | 3 | 195.194 | odd | 2 | |||
2925.2.a.bh.1.2 | 3 | 1.1 | even | 1 | trivial | ||
2925.2.c.w.2224.3 | 6 | 5.2 | odd | 4 | |||
2925.2.c.w.2224.4 | 6 | 5.3 | odd | 4 | |||
3120.2.a.bj.1.1 | 3 | 60.59 | even | 2 | |||
7605.2.a.bx.1.2 | 3 | 65.64 | even | 2 | |||
9360.2.a.dd.1.1 | 3 | 20.19 | odd | 2 | |||
9555.2.a.bq.1.2 | 3 | 105.104 | even | 2 |