Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6900,2,Mod(1,6900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6900.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: | \(55.0967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.175557.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 8x^{2} + 3x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.15613\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6900.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.22855 | 1.22028 | 0.610138 | − | 0.792295i | \(-0.291114\pi\) | ||||
0.610138 | + | 0.792295i | \(0.291114\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.15613 | 0.650098 | 0.325049 | − | 0.945697i | \(-0.394619\pi\) | ||||
0.325049 | + | 0.945697i | \(0.394619\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.08372 | 0.855270 | 0.427635 | − | 0.903952i | \(-0.359347\pi\) | ||||
0.427635 | + | 0.903952i | \(0.359347\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.11730 | −1.24113 | −0.620564 | − | 0.784156i | \(-0.713096\pi\) | ||||
−0.620564 | + | 0.784156i | \(0.713096\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.80504 | −0.414104 | −0.207052 | − | 0.978330i | \(-0.566387\pi\) | ||||
−0.207052 | + | 0.978330i | \(0.566387\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.22855 | −0.704526 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.18972 | 1.33510 | 0.667548 | − | 0.744566i | \(-0.267344\pi\) | ||||
0.667548 | + | 0.744566i | \(0.267344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50408 | −0.270141 | −0.135070 | − | 0.990836i | \(-0.543126\pi\) | ||||
−0.135070 | + | 0.990836i | \(0.543126\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.15613 | −0.375334 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.1173 | 1.82767 | 0.913837 | − | 0.406082i | \(-0.133105\pi\) | ||||
0.913837 | + | 0.406082i | \(0.133105\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.08372 | −0.493790 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.38468 | −0.997119 | −0.498560 | − | 0.866855i | \(-0.666137\pi\) | ||||
−0.498560 | + | 0.866855i | \(0.666137\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.16744 | 0.788027 | 0.394013 | − | 0.919105i | \(-0.371086\pi\) | ||||
0.394013 | + | 0.919105i | \(0.371086\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.19496 | 0.174303 | 0.0871515 | − | 0.996195i | \(-0.472224\pi\) | ||||
0.0871515 | + | 0.996195i | \(0.472224\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.42351 | 0.489072 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.11730 | 0.716566 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.57649 | 0.353909 | 0.176954 | − | 0.984219i | \(-0.443376\pi\) | ||||
0.176954 | + | 0.984219i | \(0.443376\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.80504 | 0.239083 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.34585 | 1.21673 | 0.608363 | − | 0.793659i | \(-0.291827\pi\) | ||||
0.608363 | + | 0.793659i | \(0.291827\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.96117 | −1.01932 | −0.509662 | − | 0.860375i | \(-0.670229\pi\) | ||||
−0.509662 | + | 0.860375i | \(0.670229\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.22855 | 0.406759 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.30096 | 0.647615 | 0.323808 | − | 0.946123i | \(-0.395037\pi\) | ||||
0.323808 | + | 0.946123i | \(0.395037\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.966415 | −0.114692 | −0.0573462 | − | 0.998354i | \(-0.518264\pi\) | ||||
−0.0573462 | + | 0.998354i | \(0.518264\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.23985 | −0.496237 | −0.248119 | − | 0.968730i | \(-0.579812\pi\) | ||||
−0.248119 | + | 0.968730i | \(0.579812\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.96117 | 0.793299 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.53767 | 0.848054 | 0.424027 | − | 0.905650i | \(-0.360616\pi\) | ||||
0.424027 | + | 0.905650i | \(0.360616\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.1622 | −1.55450 | −0.777251 | − | 0.629190i | \(-0.783387\pi\) | ||||
−0.777251 | + | 0.629190i | \(0.783387\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.18972 | −0.770819 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.81949 | 1.04086 | 0.520432 | − | 0.853903i | \(-0.325771\pi\) | ||||
0.520432 | + | 0.853903i | \(0.325771\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.95593 | 1.04366 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.50408 | 0.155966 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.4183 | 1.66702 | 0.833511 | − | 0.552503i | \(-0.186327\pi\) | ||||
0.833511 | + | 0.552503i | \(0.186327\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.15613 | 0.216699 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.8386 | −1.17799 | −0.588994 | − | 0.808138i | \(-0.700476\pi\) | ||||
−0.588994 | + | 0.808138i | \(0.700476\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.57964 | 0.549778 | 0.274889 | − | 0.961476i | \(-0.411359\pi\) | ||||
0.274889 | + | 0.961476i | \(0.411359\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.19496 | −0.115521 | −0.0577606 | − | 0.998330i | \(-0.518396\pi\) | ||||
−0.0577606 | + | 0.998330i | \(0.518396\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.27553 | 0.122174 | 0.0610870 | − | 0.998132i | \(-0.480543\pi\) | ||||
0.0610870 | + | 0.998132i | \(0.480543\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.1173 | −1.05521 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.39598 | −0.225395 | −0.112698 | − | 0.993629i | \(-0.535949\pi\) | ||||
−0.112698 | + | 0.993629i | \(0.535949\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.08372 | 0.285090 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.5214 | −1.51452 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.35109 | −0.577372 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.38468 | 0.575687 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.85517 | 0.342091 | 0.171046 | − | 0.985263i | \(-0.445285\pi\) | ||||
0.171046 | + | 0.985263i | \(0.445285\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.16744 | −0.454968 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.19496 | −0.628627 | −0.314313 | − | 0.949319i | \(-0.601774\pi\) | ||||
−0.314313 | + | 0.949319i | \(0.601774\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.82765 | −0.505321 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.0898 | 1.37464 | 0.687321 | − | 0.726353i | \(-0.258786\pi\) | ||||
0.687321 | + | 0.726353i | \(0.258786\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.26423 | 0.192049 | 0.0960247 | − | 0.995379i | \(-0.469387\pi\) | ||||
0.0960247 | + | 0.995379i | \(0.469387\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.19496 | −0.100634 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.64891 | 0.556010 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.42351 | −0.282366 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.79688 | −0.311052 | −0.155526 | − | 0.987832i | \(-0.549707\pi\) | ||||
−0.155526 | + | 0.987832i | \(0.549707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.90006 | −0.805656 | −0.402828 | − | 0.915276i | \(-0.631973\pi\) | ||||
−0.402828 | + | 0.915276i | \(0.631973\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.11730 | −0.413710 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.84993 | −0.227449 | −0.113725 | − | 0.993512i | \(-0.536278\pi\) | ||||
−0.113725 | + | 0.993512i | \(0.536278\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.57649 | −0.204329 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.22855 | 0.254445 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.7998 | 1.08088 | 0.540442 | − | 0.841381i | \(-0.318257\pi\) | ||||
0.540442 | + | 0.841381i | \(0.318257\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.4632 | −1.73825 | −0.869126 | − | 0.494592i | \(-0.835318\pi\) | ||||
−0.869126 | + | 0.494592i | \(0.835318\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.49068 | −0.268514 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.80504 | −0.138035 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.71349 | 0.510417 | 0.255209 | − | 0.966886i | \(-0.417856\pi\) | ||||
0.255209 | + | 0.966886i | \(0.417856\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.34585 | −0.702477 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.576494 | 0.0430892 | 0.0215446 | − | 0.999768i | \(-0.493142\pi\) | ||||
0.0215446 | + | 0.999768i | \(0.493142\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.53767 | −0.634600 | −0.317300 | − | 0.948325i | \(-0.602776\pi\) | ||||
−0.317300 | + | 0.948325i | \(0.602776\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.96117 | 0.588507 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.0336 | −0.806856 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.22855 | −0.234842 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.0724 | −0.728814 | −0.364407 | − | 0.931240i | \(-0.618728\pi\) | ||||
−0.364407 | + | 0.931240i | \(0.618728\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.267374 | 0.0192460 | 0.00962300 | − | 0.999954i | \(-0.496937\pi\) | ||||
0.00962300 | + | 0.999954i | \(0.496937\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.79980 | −0.199477 | −0.0997386 | − | 0.995014i | \(-0.531801\pi\) | ||||
−0.0997386 | + | 0.995014i | \(0.531801\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.1989 | −1.07742 | −0.538712 | − | 0.842490i | \(-0.681089\pi\) | ||||
−0.538712 | + | 0.842490i | \(0.681089\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.30096 | −0.373901 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 23.2123 | 1.62919 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.89190 | −0.269209 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.1766 | 1.66439 | 0.832194 | − | 0.554484i | \(-0.187084\pi\) | ||||
0.832194 | + | 0.554484i | \(0.187084\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.966415 | 0.0662177 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.85599 | −0.329646 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.23985 | 0.286503 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.7803 | −1.06150 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 29.5582 | 1.97936 | 0.989681 | − | 0.143288i | \(-0.0457675\pi\) | ||||
0.989681 | + | 0.143288i | \(0.0457675\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.58256 | 0.569644 | 0.284822 | − | 0.958580i | \(-0.408065\pi\) | ||||
0.284822 | + | 0.958580i | \(0.408065\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.97772 | 0.527183 | 0.263591 | − | 0.964634i | \(-0.415093\pi\) | ||||
0.263591 | + | 0.964634i | \(0.415093\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.96117 | −0.458011 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.9192 | 0.715340 | 0.357670 | − | 0.933848i | \(-0.383571\pi\) | ||||
0.357670 | + | 0.933848i | \(0.383571\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.53767 | −0.489624 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.54291 | 0.358541 | 0.179270 | − | 0.983800i | \(-0.442626\pi\) | ||||
0.179270 | + | 0.983800i | \(0.442626\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.92549 | −0.639357 | −0.319678 | − | 0.947526i | \(-0.603575\pi\) | ||||
−0.319678 | + | 0.947526i | \(0.603575\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.56623 | −0.354171 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.1622 | 0.897493 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.2764 | −1.53231 | −0.766155 | − | 0.642656i | \(-0.777832\pi\) | ||||
−0.766155 | + | 0.642656i | \(0.777832\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.15613 | 0.135555 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.98345 | 0.622751 | 0.311375 | − | 0.950287i | \(-0.399210\pi\) | ||||
0.311375 | + | 0.950287i | \(0.399210\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 35.8927 | 2.23027 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.18972 | 0.445032 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.66302 | 0.410860 | 0.205430 | − | 0.978672i | \(-0.434141\pi\) | ||||
0.205430 | + | 0.978672i | \(0.434141\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.81949 | −0.600943 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.7140 | −1.44587 | −0.722933 | − | 0.690918i | \(-0.757207\pi\) | ||||
−0.722933 | + | 0.690918i | \(0.757207\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.0315 | −0.852352 | −0.426176 | − | 0.904640i | \(-0.640140\pi\) | ||||
−0.426176 | + | 0.904640i | \(0.640140\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.95593 | −0.602560 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.6355 | 1.48020 | 0.740102 | − | 0.672495i | \(-0.234777\pi\) | ||||
0.740102 | + | 0.672495i | \(0.234777\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.50408 | −0.0900469 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.8090 | 1.30102 | 0.650508 | − | 0.759499i | \(-0.274556\pi\) | ||||
0.650508 | + | 0.759499i | \(0.274556\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.2795 | −1.08660 | −0.543302 | − | 0.839538i | \(-0.682826\pi\) | ||||
−0.543302 | + | 0.839538i | \(0.682826\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.6132 | −1.21676 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.18680 | 0.540400 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.4183 | −0.962456 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.5888 | 1.55334 | 0.776668 | − | 0.629910i | \(-0.216908\pi\) | ||||
0.776668 | + | 0.629910i | \(0.216908\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.15613 | −0.125111 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.08372 | 0.178336 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.6833 | 0.961610 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.8386 | 0.680111 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.3886 | 1.27779 | 0.638894 | − | 0.769295i | \(-0.279392\pi\) | ||||
0.638894 | + | 0.769295i | \(0.279392\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.57964 | −0.317415 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.35424 | −0.360316 | −0.180158 | − | 0.983638i | \(-0.557661\pi\) | ||||
−0.180158 | + | 0.983638i | \(0.557661\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.04489 | 0.454724 | 0.227362 | − | 0.973810i | \(-0.426990\pi\) | ||||
0.227362 | + | 0.973810i | \(0.426990\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.8397 | −1.00198 | −0.500988 | − | 0.865454i | \(-0.667030\pi\) | ||||
−0.500988 | + | 0.865454i | \(0.667030\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.5020 | 0.867944 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.19496 | 0.0666962 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.23693 | 0.513957 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.27553 | −0.0705372 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.85799 | 0.212698 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.9429 | 1.81070 | 0.905352 | − | 0.424663i | \(-0.139607\pi\) | ||||
0.905352 | + | 0.424663i | \(0.139607\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.1173 | 0.609225 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.7140 | 1.56415 | 0.782075 | − | 0.623184i | \(-0.214161\pi\) | ||||
0.782075 | + | 0.623184i | \(0.214161\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.39598 | 0.130132 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.24300 | −0.175618 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.5469 | −0.623473 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.5387 | 0.619430 | 0.309715 | − | 0.950829i | \(-0.399766\pi\) | ||||
0.309715 | + | 0.950829i | \(0.399766\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.5967 | 1.20957 | 0.604786 | − | 0.796388i | \(-0.293259\pi\) | ||||
0.604786 | + | 0.796388i | \(0.293259\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.08372 | −0.164597 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.8033 | 1.10725 | 0.553623 | − | 0.832767i | \(-0.313245\pi\) | ||||
0.553623 | + | 0.832767i | \(0.313245\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.5214 | 0.874408 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.2543 | 0.910647 | 0.455324 | − | 0.890326i | \(-0.349524\pi\) | ||||
0.455324 | + | 0.890326i | \(0.349524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.7418 | −0.828518 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.35109 | 0.333346 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.4020 | 1.11718 | 0.558589 | − | 0.829445i | \(-0.311343\pi\) | ||||
0.558589 | + | 0.829445i | \(0.311343\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.38468 | −0.332373 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.31833 | 0.431866 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.4017 | 1.36703 | 0.683514 | − | 0.729937i | \(-0.260451\pi\) | ||||
0.683514 | + | 0.729937i | \(0.260451\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.1711 | 1.14187 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0990 | −1.44335 | −0.721674 | − | 0.692233i | \(-0.756627\pi\) | ||||
−0.721674 | + | 0.692233i | \(0.756627\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.85517 | −0.197507 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.82126 | 0.195257 | 0.0976285 | − | 0.995223i | \(-0.468874\pi\) | ||||
0.0976285 | + | 0.995223i | \(0.468874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.16744 | 0.262676 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.50116 | −0.278920 | −0.139460 | − | 0.990228i | \(-0.544537\pi\) | ||||
−0.139460 | + | 0.990228i | \(0.544537\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.11730 | −0.258793 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.19496 | 0.362938 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.9987 | −1.00371 | −0.501853 | − | 0.864953i | \(-0.667348\pi\) | ||||
−0.501853 | + | 0.864953i | \(0.667348\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.82765 | 0.291747 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.2682 | 1.36171 | 0.680854 | − | 0.732419i | \(-0.261609\pi\) | ||||
0.680854 | + | 0.732419i | \(0.261609\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.63816 | −0.231043 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.9704 | 1.18817 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36.8090 | 1.82009 | 0.910044 | − | 0.414512i | \(-0.136048\pi\) | ||||
0.910044 | + | 0.414512i | \(0.136048\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.0898 | −0.793650 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.1735 | 1.48474 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.26423 | −0.110880 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.25082 | −0.451932 | −0.225966 | − | 0.974135i | \(-0.572554\pi\) | ||||
−0.225966 | + | 0.974135i | \(0.572554\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.90579 | −0.385305 | −0.192652 | − | 0.981267i | \(-0.561709\pi\) | ||||
−0.192652 | + | 0.981267i | \(0.561709\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.19496 | 0.0581010 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.7030 | −1.24386 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.64891 | −0.321012 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6684 | −0.562046 | −0.281023 | − | 0.959701i | \(-0.590674\pi\) | ||||
−0.281023 | + | 0.959701i | \(0.590674\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.88142 | −0.426814 | −0.213407 | − | 0.976963i | \(-0.568456\pi\) | ||||
−0.213407 | + | 0.976963i | \(0.568456\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.80504 | −0.0863467 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.4122 | 0.592402 | 0.296201 | − | 0.955126i | \(-0.404280\pi\) | ||||
0.296201 | + | 0.955126i | \(0.404280\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.42351 | 0.163024 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.05901 | −0.0503150 | −0.0251575 | − | 0.999683i | \(-0.508009\pi\) | ||||
−0.0251575 | + | 0.999683i | \(0.508009\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.79688 | 0.179586 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.69871 | 0.410517 | 0.205259 | − | 0.978708i | \(-0.434196\pi\) | ||||
0.205259 | + | 0.978708i | \(0.434196\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.7662 | −0.648226 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.90006 | 0.465146 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.1593 | 0.989789 | 0.494895 | − | 0.868953i | \(-0.335207\pi\) | ||||
0.494895 | + | 0.868953i | \(0.335207\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.11730 | 0.238855 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.96608 | 0.0915696 | 0.0457848 | − | 0.998951i | \(-0.485421\pi\) | ||||
0.0457848 | + | 0.998951i | \(0.485421\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.0375 | −1.58186 | −0.790930 | − | 0.611907i | \(-0.790403\pi\) | ||||
−0.790930 | + | 0.611907i | \(0.790403\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.1184 | −0.977241 | −0.488620 | − | 0.872497i | \(-0.662500\pi\) | ||||
−0.488620 | + | 0.872497i | \(0.662500\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.1144 | 0.790269 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.84993 | 0.131318 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.1417 | 0.512295 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.57649 | 0.117970 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.9446 | 0.591455 | 0.295727 | − | 0.955272i | \(-0.404438\pi\) | ||||
0.295727 | + | 0.955272i | \(0.404438\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.2826 | 1.56315 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.22855 | −0.146904 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.4663 | −1.38056 | −0.690280 | − | 0.723542i | \(-0.742513\pi\) | ||||
−0.690280 | + | 0.723542i | \(0.742513\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.7998 | −0.624048 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.2155 | −0.912312 | −0.456156 | − | 0.889900i | \(-0.650774\pi\) | ||||
−0.456156 | + | 0.889900i | \(0.650774\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −36.7920 | −1.65703 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.12012 | −0.139956 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.6468 | 1.46147 | 0.730736 | − | 0.682660i | \(-0.239177\pi\) | ||||
0.730736 | + | 0.682660i | \(0.239177\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.4632 | 1.00358 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.75595 | −0.434996 | −0.217498 | − | 0.976061i | \(-0.569790\pi\) | ||||
−0.217498 | + | 0.976061i | \(0.569790\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.49068 | 0.155026 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0375 | 0.622203 | 0.311102 | − | 0.950377i | \(-0.399302\pi\) | ||||
0.311102 | + | 0.950377i | \(0.399302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.6886 | −0.605546 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.80504 | 0.0796944 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.57649 | 0.113314 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.71349 | −0.294690 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.0103 | 1.70907 | 0.854535 | − | 0.519394i | \(-0.173842\pi\) | ||||
0.854535 | + | 0.519394i | \(0.173842\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.9935 | −1.74879 | −0.874396 | − | 0.485212i | \(-0.838742\pi\) | ||||
−0.874396 | + | 0.485212i | \(0.838742\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.69684 | 0.335279 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.34585 | 0.405575 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.6886 | −0.852806 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.576494 | −0.0248775 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.38153 | 0.317945 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.51539 | 0.237125 | 0.118562 | − | 0.992947i | \(-0.462171\pi\) | ||||
0.118562 | + | 0.992947i | \(0.462171\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.53767 | 0.366386 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.3211 | −1.12541 | −0.562705 | − | 0.826658i | \(-0.690239\pi\) | ||||
−0.562705 | + | 0.826658i | \(0.690239\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.96117 | −0.339775 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.9777 | −0.552870 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.3357 | 1.03486 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.3267 | 0.988385 | 0.494192 | − | 0.869353i | \(-0.335464\pi\) | ||||
0.494192 | + | 0.869353i | \(0.335464\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.9349 | 0.673976 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.0336 | 0.465838 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.3180 | 0.476997 | 0.238498 | − | 0.971143i | \(-0.423345\pi\) | ||||
0.238498 | + | 0.971143i | \(0.423345\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.22855 | 0.135586 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.8722 | 0.539631 | 0.269816 | − | 0.962912i | \(-0.413037\pi\) | ||||
0.269816 | + | 0.962912i | \(0.413037\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.9754 | −0.626701 | −0.313350 | − | 0.949638i | \(-0.601451\pi\) | ||||
−0.313350 | + | 0.949638i | \(0.601451\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.0724 | 0.420781 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.21409 | 0.258696 | 0.129348 | − | 0.991599i | \(-0.458712\pi\) | ||||
0.129348 | + | 0.991599i | \(0.458712\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.267374 | −0.0111117 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45.7233 | −1.89692 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.55526 | 0.230075 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.1040 | −1.53145 | −0.765723 | − | 0.643170i | \(-0.777619\pi\) | ||||
−0.765723 | + | 0.643170i | \(0.777619\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.71492 | 0.111867 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.79980 | 0.115168 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.2357 | −0.913109 | −0.456554 | − | 0.889695i | \(-0.650917\pi\) | ||||
−0.456554 | + | 0.889695i | \(0.650917\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.1989 | 0.622051 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.66254 | 0.149647 | 0.0748236 | − | 0.997197i | \(-0.476161\pi\) | ||||
0.0748236 | + | 0.997197i | \(0.476161\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.5440 | −0.430097 | −0.215048 | − | 0.976603i | \(-0.568991\pi\) | ||||
−0.215048 | + | 0.976603i | \(0.568991\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.30096 | 0.215872 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.7980 | 1.33123 | 0.665615 | − | 0.746295i | \(-0.268169\pi\) | ||||
0.665615 | + | 0.746295i | \(0.268169\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23.2123 | −0.940611 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.68492 | 0.149076 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.96713 | 0.160231 | 0.0801154 | − | 0.996786i | \(-0.474471\pi\) | ||||
0.0801154 | + | 0.996786i | \(0.474471\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.7705 | −1.44007 | −0.720033 | − | 0.693940i | \(-0.755873\pi\) | ||||
−0.720033 | + | 0.693940i | \(0.755873\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.9982 | 0.442056 | 0.221028 | − | 0.975267i | \(-0.429059\pi\) | ||||
0.221028 | + | 0.975267i | \(0.429059\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 31.7027 | 1.27014 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.89190 | 0.155428 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −56.8906 | −2.26838 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.7108 | 0.943913 | 0.471957 | − | 0.881622i | \(-0.343548\pi\) | ||||
0.471957 | + | 0.881622i | \(0.343548\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.1766 | −0.960935 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.5571 | 0.418289 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.966415 | −0.0382308 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.67676 | 0.184721 | 0.0923605 | − | 0.995726i | \(-0.470559\pi\) | ||||
0.0923605 | + | 0.995726i | \(0.470559\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.6578 | −0.420302 | −0.210151 | − | 0.977669i | \(-0.567396\pi\) | ||||
−0.210151 | + | 0.977669i | \(0.567396\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.04522 | 0.0804061 | 0.0402030 | − | 0.999192i | \(-0.487200\pi\) | ||||
0.0402030 | + | 0.999192i | \(0.487200\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.1509 | 0.790992 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.85599 | 0.190321 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.26246 | −0.166803 | −0.0834015 | − | 0.996516i | \(-0.526578\pi\) | ||||
−0.0834015 | + | 0.996516i | \(0.526578\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.23985 | −0.165412 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.6083 | −1.38710 | −0.693551 | − | 0.720407i | \(-0.743955\pi\) | ||||
−0.693551 | + | 0.720407i | \(0.743955\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.9517 | −1.43726 | −0.718628 | − | 0.695395i | \(-0.755230\pi\) | ||||
−0.718628 | + | 0.695395i | \(0.755230\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.7803 | 0.612857 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.18972 | 0.278387 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.5582 | −1.14279 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.1653 | −0.662661 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.9266 | 1.69325 | 0.846624 | − | 0.532192i | \(-0.178632\pi\) | ||||
0.846624 | + | 0.532192i | \(0.178632\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.5998 | 1.13761 | 0.568807 | − | 0.822471i | \(-0.307405\pi\) | ||||
0.568807 | + | 0.822471i | \(0.307405\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 53.0071 | 2.03423 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.58256 | −0.328884 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.39251 | −0.168075 | −0.0840373 | − | 0.996463i | \(-0.526781\pi\) | ||||
−0.0840373 | + | 0.996463i | \(0.526781\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.97772 | −0.304369 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.94518 | 0.302687 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.0170 | 0.723442 | 0.361721 | − | 0.932286i | \(-0.382189\pi\) | ||||
0.361721 | + | 0.932286i | \(0.382189\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.96117 | 0.264433 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.6723 | 1.23755 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.9192 | −0.413002 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.3745 | 1.18500 | 0.592500 | − | 0.805571i | \(-0.298141\pi\) | ||||
0.592500 | + | 0.805571i | \(0.298141\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.0672 | −0.756848 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −38.2215 | −1.43747 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.7828 | 0.480067 | 0.240033 | − | 0.970765i | \(-0.422842\pi\) | ||||
0.240033 | + | 0.970765i | \(0.422842\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.53767 | 0.282685 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.50408 | −0.0563283 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.54291 | −0.207004 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.6521 | −0.882073 | −0.441036 | − | 0.897489i | \(-0.645389\pi\) | ||||
−0.441036 | + | 0.897489i | \(0.645389\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.0141 | 0.670881 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.92549 | 0.369133 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.4031 | −1.31303 | −0.656514 | − | 0.754314i | \(-0.727970\pi\) | ||||
−0.656514 | + | 0.754314i | \(0.727970\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.4434 | −0.978043 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.65602 | 0.319717 | 0.159859 | − | 0.987140i | \(-0.448896\pi\) | ||||
0.159859 | + | 0.987140i | \(0.448896\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.4296 | 0.421014 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.3458 | 0.564506 | 0.282253 | − | 0.959340i | \(-0.408918\pi\) | ||||
0.282253 | + | 0.959340i | \(0.408918\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.56623 | 0.204481 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 54.1997 | 1.98840 | 0.994198 | − | 0.107567i | \(-0.0343059\pi\) | ||||
0.994198 | + | 0.107567i | \(0.0343059\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.1622 | −0.518168 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.85799 | −0.140968 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.4360 | 0.672738 | 0.336369 | − | 0.941730i | \(-0.390801\pi\) | ||||
0.336369 | + | 0.941730i | \(0.390801\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.2764 | 0.884680 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.9003 | 0.432523 | 0.216262 | − | 0.976335i | \(-0.430614\pi\) | ||||
0.216262 | + | 0.976335i | \(0.430614\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.15613 | −0.0782626 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.3359 | 1.02718 | 0.513588 | − | 0.858037i | \(-0.328316\pi\) | ||||
0.513588 | + | 0.858037i | \(0.328316\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.11812 | 0.149086 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.8200 | 1.04063 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.30096 | −0.119036 | −0.0595178 | − | 0.998227i | \(-0.518956\pi\) | ||||
−0.0595178 | + | 0.998227i | \(0.518956\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.98345 | −0.359545 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.8591 | −0.894121 | −0.447061 | − | 0.894504i | \(-0.647529\pi\) | ||||
−0.447061 | + | 0.894504i | \(0.647529\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −35.8927 | −1.28764 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.5246 | 0.412911 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.08372 | −0.0745613 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.18972 | −0.256940 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.40624 | −0.335296 | −0.167648 | − | 0.985847i | \(-0.553617\pi\) | ||||
−0.167648 | + | 0.985847i | \(0.553617\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.66302 | −0.237210 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.73554 | −0.275044 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.5500 | −0.871797 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −43.9319 | −1.55615 | −0.778074 | − | 0.628173i | \(-0.783803\pi\) | ||||
−0.778074 | + | 0.628173i | \(0.783803\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.11498 | −0.216332 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.81949 | 0.346955 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.14168 | −0.322603 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.7140 | 0.834772 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.0092 | −1.44181 | −0.720903 | − | 0.693035i | \(-0.756273\pi\) | ||||
−0.720903 | + | 0.693035i | \(0.756273\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.03860 | 0.212044 | 0.106022 | − | 0.994364i | \(-0.466189\pi\) | ||||
0.106022 | + | 0.994364i | \(0.466189\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.0315 | 0.492106 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.32743 | −0.326325 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.95593 | 0.347888 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.4073 | −0.921621 | −0.460810 | − | 0.887499i | \(-0.652441\pi\) | ||||
−0.460810 | + | 0.887499i | \(0.652441\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.4572 | 0.782809 | 0.391404 | − | 0.920219i | \(-0.371989\pi\) | ||||
0.391404 | + | 0.920219i | \(0.371989\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.7601 | −1.03486 | −0.517431 | − | 0.855725i | \(-0.673112\pi\) | ||||
−0.517431 | + | 0.855725i | \(0.673112\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.9164 | 0.795919 | 0.397959 | − | 0.917403i | \(-0.369718\pi\) | ||||
0.397959 | + | 0.917403i | \(0.369718\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.6355 | −0.854596 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.5191 | −0.607002 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.50408 | 0.0519886 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.5962 | −0.883679 | −0.441839 | − | 0.897094i | \(-0.645674\pi\) | ||||
−0.441839 | + | 0.897094i | \(0.645674\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.6920 | 0.782484 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.8090 | −0.751142 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.5048 | −0.704553 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.2795 | 0.627351 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.1173 | 0.381096 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.24768 | −0.111198 | −0.0555992 | − | 0.998453i | \(-0.517707\pi\) | ||||
−0.0555992 | + | 0.998453i | \(0.517707\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.6112 | 1.04566 | 0.522830 | − | 0.852437i | \(-0.324876\pi\) | ||||
0.522830 | + | 0.852437i | \(0.324876\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.4219 | −1.20858 | −0.604290 | − | 0.796765i | \(-0.706543\pi\) | ||||
−0.604290 | + | 0.796765i | \(0.706543\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.6132 | 0.702497 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.8640 | −0.948503 | −0.474252 | − | 0.880389i | \(-0.657281\pi\) | ||||
−0.474252 | + | 0.880389i | \(0.657281\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.18680 | −0.312000 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.2522 | 0.551318 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.3467 | 0.553886 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.4183 | 0.555674 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.42455 | −0.149407 | −0.0747033 | − | 0.997206i | \(-0.523801\pi\) | ||||
−0.0747033 | + | 0.997206i | \(0.523801\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.5888 | −0.896820 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.0506 | 1.28196 | 0.640979 | − | 0.767558i | \(-0.278529\pi\) | ||||
0.640979 | + | 0.767558i | \(0.278529\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.79489 | 0.295971 | 0.147986 | − | 0.988989i | \(-0.452721\pi\) | ||||
0.147986 | + | 0.988989i | \(0.452721\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.5637 | 1.32842 | 0.664209 | − | 0.747547i | \(-0.268768\pi\) | ||||
0.664209 | + | 0.747547i | \(0.268768\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.4466 | 0.417446 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.15613 | 0.0722332 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.15695 | −0.0721796 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.08372 | −0.102962 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.8139 | −0.360664 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.1847 | −0.439246 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.6833 | −0.555186 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.9138 | 0.528411 | 0.264205 | − | 0.964466i | \(-0.414890\pi\) | ||||
0.264205 | + | 0.964466i | \(0.414890\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.8386 | −0.392662 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.6216 | −0.915145 | −0.457572 | − | 0.889172i | \(-0.651281\pi\) | ||||
−0.457572 | + | 0.889172i | \(0.651281\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.5356 | −1.01058 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.2293 | −0.767098 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.2520 | 0.964934 | 0.482467 | − | 0.875914i | \(-0.339741\pi\) | ||||
0.482467 | + | 0.875914i | \(0.339741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.3886 | −0.737731 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.98015 | −0.0980929 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.57964 | 0.183259 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.9336 | 0.457148 | 0.228574 | − | 0.973527i | \(-0.426594\pi\) | ||||
0.228574 | + | 0.973527i | \(0.426594\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.17956 | −0.202527 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.35424 | 0.208028 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.4257 | 1.74534 | 0.872671 | − | 0.488309i | \(-0.162386\pi\) | ||||
0.872671 | + | 0.488309i | \(0.162386\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.04489 | −0.262535 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.10633 | −0.264259 | −0.132129 | − | 0.991232i | \(-0.542181\pi\) | ||||
−0.132129 | + | 0.991232i | \(0.542181\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.38468 | −0.207914 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.1241 | −1.43384 | −0.716920 | − | 0.697155i | \(-0.754449\pi\) | ||||
−0.716920 | + | 0.697155i | \(0.754449\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.0745 | −0.424417 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.8397 | 0.578491 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.2540 | −1.10959 | −0.554797 | − | 0.831985i | \(-0.687204\pi\) | ||||
−0.554797 | + | 0.831985i | \(0.687204\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.5020 | −0.501108 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 51.9466 | 1.67744 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.7377 | −0.927024 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.19496 | −0.0385071 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.0518 | −0.869926 | −0.434963 | − | 0.900448i | \(-0.643239\pi\) | ||||
−0.434963 | + | 0.900448i | \(0.643239\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.23693 | −0.296733 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.1202 | 0.324773 | 0.162387 | − | 0.986727i | \(-0.448081\pi\) | ||||
0.162387 | + | 0.986727i | \(0.448081\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.31017 | 0.234353 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.9387 | −0.957823 | −0.478911 | − | 0.877863i | \(-0.658968\pi\) | ||||
−0.478911 | + | 0.877863i | \(0.658968\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.1721 | 0.676664 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.27553 | 0.0407247 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.54373 | 0.176817 | 0.0884087 | − | 0.996084i | \(-0.471822\pi\) | ||||
0.0884087 | + | 0.996084i | \(0.471822\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.85799 | −0.122801 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.16744 | 0.164315 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.1517 | −0.926035 | −0.463017 | − | 0.886349i | \(-0.653233\pi\) | ||||
−0.463017 | + | 0.886349i | \(0.653233\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32.9429 | −1.04541 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.5419 | 1.47400 | 0.736998 | − | 0.675895i | \(-0.236243\pi\) | ||||
0.736998 | + | 0.675895i | \(0.236243\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.1173 | −0.351736 |
(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 | 6900.2.a.ba.1.3 | ✓ | 4 | |
5.2 | odd | 4 | 6900.2.f.s.6349.7 | 8 | |||
5.3 | odd | 4 | 6900.2.f.s.6349.2 | 8 | |||
5.4 | even | 2 | 6900.2.a.bb.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6900.2.a.ba.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
6900.2.a.bb.1.2 | yes | 4 | 5.4 | even | 2 | ||
6900.2.f.s.6349.2 | 8 | 5.3 | odd | 4 | |||
6900.2.f.s.6349.7 | 8 | 5.2 | odd | 4 |