Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.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: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.596587 | −0.421851 | −0.210925 | − | 0.977502i | \(-0.567648\pi\) | ||||
−0.210925 | + | 0.977502i | \(0.567648\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.64408 | −0.822042 | ||||||||
\(5\) | 4.06129 | 1.81627 | 0.908133 | − | 0.418682i | \(-0.137508\pi\) | ||||
0.908133 | + | 0.418682i | \(0.137508\pi\) | |||||||
\(6\) | 0.596587 | 0.243556 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.17401 | 0.768630 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.42291 | −0.766193 | ||||||||
\(11\) | −0.0366506 | −0.0110506 | −0.00552529 | − | 0.999985i | \(-0.501759\pi\) | ||||
−0.00552529 | + | 0.999985i | \(0.501759\pi\) | |||||||
\(12\) | 1.64408 | 0.474606 | ||||||||
\(13\) | 5.73847 | 1.59157 | 0.795783 | − | 0.605582i | \(-0.207060\pi\) | ||||
0.795783 | + | 0.605582i | \(0.207060\pi\) | |||||||
\(14\) | 0.596587 | 0.159445 | ||||||||
\(15\) | −4.06129 | −1.04862 | ||||||||
\(16\) | 1.99118 | 0.497795 | ||||||||
\(17\) | 3.28922 | 0.797753 | 0.398877 | − | 0.917005i | \(-0.369400\pi\) | ||||
0.398877 | + | 0.917005i | \(0.369400\pi\) | |||||||
\(18\) | −0.596587 | −0.140617 | ||||||||
\(19\) | −0.844005 | −0.193628 | −0.0968140 | − | 0.995302i | \(-0.530865\pi\) | ||||
−0.0968140 | + | 0.995302i | \(0.530865\pi\) | |||||||
\(20\) | −6.67711 | −1.49305 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0.0218653 | 0.00466170 | ||||||||
\(23\) | −2.13704 | −0.445603 | −0.222801 | − | 0.974864i | \(-0.571520\pi\) | ||||
−0.222801 | + | 0.974864i | \(0.571520\pi\) | |||||||
\(24\) | −2.17401 | −0.443769 | ||||||||
\(25\) | 11.4941 | 2.29882 | ||||||||
\(26\) | −3.42350 | −0.671403 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.64408 | 0.310703 | ||||||||
\(29\) | 7.14777 | 1.32731 | 0.663653 | − | 0.748040i | \(-0.269005\pi\) | ||||
0.663653 | + | 0.748040i | \(0.269005\pi\) | |||||||
\(30\) | 2.42291 | 0.442362 | ||||||||
\(31\) | 6.50937 | 1.16912 | 0.584559 | − | 0.811351i | \(-0.301267\pi\) | ||||
0.584559 | + | 0.811351i | \(0.301267\pi\) | |||||||
\(32\) | −5.53594 | −0.978625 | ||||||||
\(33\) | 0.0366506 | 0.00638006 | ||||||||
\(34\) | −1.96231 | −0.336533 | ||||||||
\(35\) | −4.06129 | −0.686484 | ||||||||
\(36\) | −1.64408 | −0.274014 | ||||||||
\(37\) | −10.4102 | −1.71143 | −0.855716 | − | 0.517446i | \(-0.826883\pi\) | ||||
−0.855716 | + | 0.517446i | \(0.826883\pi\) | |||||||
\(38\) | 0.503522 | 0.0816821 | ||||||||
\(39\) | −5.73847 | −0.918891 | ||||||||
\(40\) | 8.82930 | 1.39604 | ||||||||
\(41\) | 10.9305 | 1.70706 | 0.853531 | − | 0.521042i | \(-0.174456\pi\) | ||||
0.853531 | + | 0.521042i | \(0.174456\pi\) | |||||||
\(42\) | −0.596587 | −0.0920554 | ||||||||
\(43\) | −4.01763 | −0.612683 | −0.306342 | − | 0.951922i | \(-0.599105\pi\) | ||||
−0.306342 | + | 0.951922i | \(0.599105\pi\) | |||||||
\(44\) | 0.0602567 | 0.00908404 | ||||||||
\(45\) | 4.06129 | 0.605422 | ||||||||
\(46\) | 1.27493 | 0.187978 | ||||||||
\(47\) | 1.96344 | 0.286397 | 0.143198 | − | 0.989694i | \(-0.454261\pi\) | ||||
0.143198 | + | 0.989694i | \(0.454261\pi\) | |||||||
\(48\) | −1.99118 | −0.287402 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −6.85723 | −0.969759 | ||||||||
\(51\) | −3.28922 | −0.460583 | ||||||||
\(52\) | −9.43453 | −1.30833 | ||||||||
\(53\) | 11.2481 | 1.54505 | 0.772524 | − | 0.634985i | \(-0.218994\pi\) | ||||
0.772524 | + | 0.634985i | \(0.218994\pi\) | |||||||
\(54\) | 0.596587 | 0.0811852 | ||||||||
\(55\) | −0.148849 | −0.0200708 | ||||||||
\(56\) | −2.17401 | −0.290515 | ||||||||
\(57\) | 0.844005 | 0.111791 | ||||||||
\(58\) | −4.26426 | −0.559925 | ||||||||
\(59\) | −2.72011 | −0.354128 | −0.177064 | − | 0.984199i | \(-0.556660\pi\) | ||||
−0.177064 | + | 0.984199i | \(0.556660\pi\) | |||||||
\(60\) | 6.67711 | 0.862011 | ||||||||
\(61\) | −5.24229 | −0.671207 | −0.335603 | − | 0.942003i | \(-0.608940\pi\) | ||||
−0.335603 | + | 0.942003i | \(0.608940\pi\) | |||||||
\(62\) | −3.88341 | −0.493193 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −0.679692 | −0.0849615 | ||||||||
\(65\) | 23.3056 | 2.89071 | ||||||||
\(66\) | −0.0218653 | −0.00269143 | ||||||||
\(67\) | −5.39696 | −0.659343 | −0.329672 | − | 0.944096i | \(-0.606938\pi\) | ||||
−0.329672 | + | 0.944096i | \(0.606938\pi\) | |||||||
\(68\) | −5.40776 | −0.655787 | ||||||||
\(69\) | 2.13704 | 0.257269 | ||||||||
\(70\) | 2.42291 | 0.289594 | ||||||||
\(71\) | −11.4633 | −1.36044 | −0.680222 | − | 0.733006i | \(-0.738116\pi\) | ||||
−0.680222 | + | 0.733006i | \(0.738116\pi\) | |||||||
\(72\) | 2.17401 | 0.256210 | ||||||||
\(73\) | −5.56933 | −0.651841 | −0.325920 | − | 0.945397i | \(-0.605674\pi\) | ||||
−0.325920 | + | 0.945397i | \(0.605674\pi\) | |||||||
\(74\) | 6.21061 | 0.721968 | ||||||||
\(75\) | −11.4941 | −1.32722 | ||||||||
\(76\) | 1.38761 | 0.159170 | ||||||||
\(77\) | 0.0366506 | 0.00417673 | ||||||||
\(78\) | 3.42350 | 0.387635 | ||||||||
\(79\) | 3.28461 | 0.369547 | 0.184774 | − | 0.982781i | \(-0.440845\pi\) | ||||
0.184774 | + | 0.982781i | \(0.440845\pi\) | |||||||
\(80\) | 8.08677 | 0.904128 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.52101 | −0.720126 | ||||||||
\(83\) | 12.0518 | 1.32286 | 0.661430 | − | 0.750007i | \(-0.269950\pi\) | ||||
0.661430 | + | 0.750007i | \(0.269950\pi\) | |||||||
\(84\) | −1.64408 | −0.179384 | ||||||||
\(85\) | 13.3585 | 1.44893 | ||||||||
\(86\) | 2.39687 | 0.258461 | ||||||||
\(87\) | −7.14777 | −0.766321 | ||||||||
\(88\) | −0.0796790 | −0.00849381 | ||||||||
\(89\) | −9.93837 | −1.05347 | −0.526733 | − | 0.850031i | \(-0.676583\pi\) | ||||
−0.526733 | + | 0.850031i | \(0.676583\pi\) | |||||||
\(90\) | −2.42291 | −0.255398 | ||||||||
\(91\) | −5.73847 | −0.601555 | ||||||||
\(92\) | 3.51347 | 0.366304 | ||||||||
\(93\) | −6.50937 | −0.674991 | ||||||||
\(94\) | −1.17136 | −0.120817 | ||||||||
\(95\) | −3.42775 | −0.351680 | ||||||||
\(96\) | 5.53594 | 0.565009 | ||||||||
\(97\) | 12.7465 | 1.29422 | 0.647108 | − | 0.762398i | \(-0.275978\pi\) | ||||
0.647108 | + | 0.762398i | \(0.275978\pi\) | |||||||
\(98\) | −0.596587 | −0.0602644 | ||||||||
\(99\) | −0.0366506 | −0.00368353 | ||||||||
\(100\) | −18.8973 | −1.88973 | ||||||||
\(101\) | 8.42052 | 0.837873 | 0.418936 | − | 0.908016i | \(-0.362403\pi\) | ||||
0.418936 | + | 0.908016i | \(0.362403\pi\) | |||||||
\(102\) | 1.96231 | 0.194297 | ||||||||
\(103\) | −8.41991 | −0.829638 | −0.414819 | − | 0.909904i | \(-0.636155\pi\) | ||||
−0.414819 | + | 0.909904i | \(0.636155\pi\) | |||||||
\(104\) | 12.4755 | 1.22332 | ||||||||
\(105\) | 4.06129 | 0.396342 | ||||||||
\(106\) | −6.71048 | −0.651780 | ||||||||
\(107\) | −3.52936 | −0.341196 | −0.170598 | − | 0.985341i | \(-0.554570\pi\) | ||||
−0.170598 | + | 0.985341i | \(0.554570\pi\) | |||||||
\(108\) | 1.64408 | 0.158202 | ||||||||
\(109\) | −4.43885 | −0.425165 | −0.212582 | − | 0.977143i | \(-0.568187\pi\) | ||||
−0.212582 | + | 0.977143i | \(0.568187\pi\) | |||||||
\(110\) | 0.0888014 | 0.00846688 | ||||||||
\(111\) | 10.4102 | 0.988095 | ||||||||
\(112\) | −1.99118 | −0.188149 | ||||||||
\(113\) | −13.4260 | −1.26301 | −0.631505 | − | 0.775372i | \(-0.717562\pi\) | ||||
−0.631505 | + | 0.775372i | \(0.717562\pi\) | |||||||
\(114\) | −0.503522 | −0.0471592 | ||||||||
\(115\) | −8.67913 | −0.809333 | ||||||||
\(116\) | −11.7515 | −1.09110 | ||||||||
\(117\) | 5.73847 | 0.530522 | ||||||||
\(118\) | 1.62278 | 0.149389 | ||||||||
\(119\) | −3.28922 | −0.301522 | ||||||||
\(120\) | −8.82930 | −0.806002 | ||||||||
\(121\) | −10.9987 | −0.999878 | ||||||||
\(122\) | 3.12748 | 0.283149 | ||||||||
\(123\) | −10.9305 | −0.985573 | ||||||||
\(124\) | −10.7020 | −0.961064 | ||||||||
\(125\) | 26.3745 | 2.35900 | ||||||||
\(126\) | 0.596587 | 0.0531482 | ||||||||
\(127\) | 1.64452 | 0.145928 | 0.0729638 | − | 0.997335i | \(-0.476754\pi\) | ||||
0.0729638 | + | 0.997335i | \(0.476754\pi\) | |||||||
\(128\) | 11.4774 | 1.01447 | ||||||||
\(129\) | 4.01763 | 0.353733 | ||||||||
\(130\) | −13.9038 | −1.21945 | ||||||||
\(131\) | 20.1631 | 1.76166 | 0.880830 | − | 0.473432i | \(-0.156985\pi\) | ||||
0.880830 | + | 0.473432i | \(0.156985\pi\) | |||||||
\(132\) | −0.0602567 | −0.00524468 | ||||||||
\(133\) | 0.844005 | 0.0731845 | ||||||||
\(134\) | 3.21975 | 0.278144 | ||||||||
\(135\) | −4.06129 | −0.349540 | ||||||||
\(136\) | 7.15081 | 0.613177 | ||||||||
\(137\) | −7.27768 | −0.621775 | −0.310887 | − | 0.950447i | \(-0.600626\pi\) | ||||
−0.310887 | + | 0.950447i | \(0.600626\pi\) | |||||||
\(138\) | −1.27493 | −0.108529 | ||||||||
\(139\) | −12.5015 | −1.06036 | −0.530181 | − | 0.847884i | \(-0.677876\pi\) | ||||
−0.530181 | + | 0.847884i | \(0.677876\pi\) | |||||||
\(140\) | 6.67711 | 0.564319 | ||||||||
\(141\) | −1.96344 | −0.165351 | ||||||||
\(142\) | 6.83885 | 0.573904 | ||||||||
\(143\) | −0.210319 | −0.0175877 | ||||||||
\(144\) | 1.99118 | 0.165932 | ||||||||
\(145\) | 29.0292 | 2.41074 | ||||||||
\(146\) | 3.32259 | 0.274980 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 17.1153 | 1.40687 | ||||||||
\(149\) | −17.4040 | −1.42579 | −0.712896 | − | 0.701270i | \(-0.752617\pi\) | ||||
−0.712896 | + | 0.701270i | \(0.752617\pi\) | |||||||
\(150\) | 6.85723 | 0.559891 | ||||||||
\(151\) | −12.6550 | −1.02985 | −0.514924 | − | 0.857236i | \(-0.672180\pi\) | ||||
−0.514924 | + | 0.857236i | \(0.672180\pi\) | |||||||
\(152\) | −1.83488 | −0.148828 | ||||||||
\(153\) | 3.28922 | 0.265918 | ||||||||
\(154\) | −0.0218653 | −0.00176196 | ||||||||
\(155\) | 26.4365 | 2.12343 | ||||||||
\(156\) | 9.43453 | 0.755367 | ||||||||
\(157\) | −8.35868 | −0.667095 | −0.333548 | − | 0.942733i | \(-0.608246\pi\) | ||||
−0.333548 | + | 0.942733i | \(0.608246\pi\) | |||||||
\(158\) | −1.95955 | −0.155894 | ||||||||
\(159\) | −11.2481 | −0.892034 | ||||||||
\(160\) | −22.4831 | −1.77744 | ||||||||
\(161\) | 2.13704 | 0.168422 | ||||||||
\(162\) | −0.596587 | −0.0468723 | ||||||||
\(163\) | −14.3097 | −1.12082 | −0.560410 | − | 0.828216i | \(-0.689356\pi\) | ||||
−0.560410 | + | 0.828216i | \(0.689356\pi\) | |||||||
\(164\) | −17.9707 | −1.40328 | ||||||||
\(165\) | 0.148849 | 0.0115879 | ||||||||
\(166\) | −7.18997 | −0.558050 | ||||||||
\(167\) | 8.50396 | 0.658056 | 0.329028 | − | 0.944320i | \(-0.393279\pi\) | ||||
0.329028 | + | 0.944320i | \(0.393279\pi\) | |||||||
\(168\) | 2.17401 | 0.167729 | ||||||||
\(169\) | 19.9300 | 1.53308 | ||||||||
\(170\) | −7.96950 | −0.611233 | ||||||||
\(171\) | −0.844005 | −0.0645427 | ||||||||
\(172\) | 6.60533 | 0.503651 | ||||||||
\(173\) | 8.94722 | 0.680245 | 0.340122 | − | 0.940381i | \(-0.389532\pi\) | ||||
0.340122 | + | 0.940381i | \(0.389532\pi\) | |||||||
\(174\) | 4.26426 | 0.323273 | ||||||||
\(175\) | −11.4941 | −0.868873 | ||||||||
\(176\) | −0.0729780 | −0.00550093 | ||||||||
\(177\) | 2.72011 | 0.204456 | ||||||||
\(178\) | 5.92910 | 0.444405 | ||||||||
\(179\) | 15.6746 | 1.17157 | 0.585786 | − | 0.810466i | \(-0.300786\pi\) | ||||
0.585786 | + | 0.810466i | \(0.300786\pi\) | |||||||
\(180\) | −6.67711 | −0.497682 | ||||||||
\(181\) | 23.4932 | 1.74624 | 0.873119 | − | 0.487507i | \(-0.162093\pi\) | ||||
0.873119 | + | 0.487507i | \(0.162093\pi\) | |||||||
\(182\) | 3.42350 | 0.253766 | ||||||||
\(183\) | 5.24229 | 0.387521 | ||||||||
\(184\) | −4.64594 | −0.342504 | ||||||||
\(185\) | −42.2790 | −3.10841 | ||||||||
\(186\) | 3.88341 | 0.284745 | ||||||||
\(187\) | −0.120552 | −0.00881564 | ||||||||
\(188\) | −3.22806 | −0.235430 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 2.04495 | 0.148356 | ||||||||
\(191\) | 1.00000 | 0.0723575 | ||||||||
\(192\) | 0.679692 | 0.0490526 | ||||||||
\(193\) | 13.5056 | 0.972155 | 0.486077 | − | 0.873916i | \(-0.338427\pi\) | ||||
0.486077 | + | 0.873916i | \(0.338427\pi\) | |||||||
\(194\) | −7.60442 | −0.545966 | ||||||||
\(195\) | −23.3056 | −1.66895 | ||||||||
\(196\) | −1.64408 | −0.117435 | ||||||||
\(197\) | −7.82429 | −0.557457 | −0.278729 | − | 0.960370i | \(-0.589913\pi\) | ||||
−0.278729 | + | 0.960370i | \(0.589913\pi\) | |||||||
\(198\) | 0.0218653 | 0.00155390 | ||||||||
\(199\) | 24.9482 | 1.76853 | 0.884266 | − | 0.466984i | \(-0.154659\pi\) | ||||
0.884266 | + | 0.466984i | \(0.154659\pi\) | |||||||
\(200\) | 24.9883 | 1.76694 | ||||||||
\(201\) | 5.39696 | 0.380672 | ||||||||
\(202\) | −5.02357 | −0.353457 | ||||||||
\(203\) | −7.14777 | −0.501675 | ||||||||
\(204\) | 5.40776 | 0.378619 | ||||||||
\(205\) | 44.3921 | 3.10048 | ||||||||
\(206\) | 5.02321 | 0.349983 | ||||||||
\(207\) | −2.13704 | −0.148534 | ||||||||
\(208\) | 11.4263 | 0.792273 | ||||||||
\(209\) | 0.0309333 | 0.00213970 | ||||||||
\(210\) | −2.42291 | −0.167197 | ||||||||
\(211\) | 8.87133 | 0.610728 | 0.305364 | − | 0.952236i | \(-0.401222\pi\) | ||||
0.305364 | + | 0.952236i | \(0.401222\pi\) | |||||||
\(212\) | −18.4929 | −1.27009 | ||||||||
\(213\) | 11.4633 | 0.785452 | ||||||||
\(214\) | 2.10557 | 0.143934 | ||||||||
\(215\) | −16.3168 | −1.11280 | ||||||||
\(216\) | −2.17401 | −0.147923 | ||||||||
\(217\) | −6.50937 | −0.441885 | ||||||||
\(218\) | 2.64816 | 0.179356 | ||||||||
\(219\) | 5.56933 | 0.376341 | ||||||||
\(220\) | 0.244720 | 0.0164990 | ||||||||
\(221\) | 18.8751 | 1.26968 | ||||||||
\(222\) | −6.21061 | −0.416829 | ||||||||
\(223\) | 4.09068 | 0.273932 | 0.136966 | − | 0.990576i | \(-0.456265\pi\) | ||||
0.136966 | + | 0.990576i | \(0.456265\pi\) | |||||||
\(224\) | 5.53594 | 0.369885 | ||||||||
\(225\) | 11.4941 | 0.766274 | ||||||||
\(226\) | 8.00976 | 0.532801 | ||||||||
\(227\) | −11.2615 | −0.747451 | −0.373725 | − | 0.927539i | \(-0.621920\pi\) | ||||
−0.373725 | + | 0.927539i | \(0.621920\pi\) | |||||||
\(228\) | −1.38761 | −0.0918970 | ||||||||
\(229\) | −13.8576 | −0.915737 | −0.457868 | − | 0.889020i | \(-0.651387\pi\) | ||||
−0.457868 | + | 0.889020i | \(0.651387\pi\) | |||||||
\(230\) | 5.17786 | 0.341418 | ||||||||
\(231\) | −0.0366506 | −0.00241143 | ||||||||
\(232\) | 15.5393 | 1.02021 | ||||||||
\(233\) | −2.61287 | −0.171175 | −0.0855873 | − | 0.996331i | \(-0.527277\pi\) | ||||
−0.0855873 | + | 0.996331i | \(0.527277\pi\) | |||||||
\(234\) | −3.42350 | −0.223801 | ||||||||
\(235\) | 7.97410 | 0.520173 | ||||||||
\(236\) | 4.47209 | 0.291108 | ||||||||
\(237\) | −3.28461 | −0.213358 | ||||||||
\(238\) | 1.96231 | 0.127197 | ||||||||
\(239\) | 2.39576 | 0.154969 | 0.0774845 | − | 0.996994i | \(-0.475311\pi\) | ||||
0.0774845 | + | 0.996994i | \(0.475311\pi\) | |||||||
\(240\) | −8.08677 | −0.521999 | ||||||||
\(241\) | 1.09133 | 0.0702989 | 0.0351495 | − | 0.999382i | \(-0.488809\pi\) | ||||
0.0351495 | + | 0.999382i | \(0.488809\pi\) | |||||||
\(242\) | 6.56166 | 0.421799 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 8.61877 | 0.551760 | ||||||||
\(245\) | 4.06129 | 0.259467 | ||||||||
\(246\) | 6.52101 | 0.415765 | ||||||||
\(247\) | −4.84330 | −0.308172 | ||||||||
\(248\) | 14.1515 | 0.898619 | ||||||||
\(249\) | −12.0518 | −0.763754 | ||||||||
\(250\) | −15.7347 | −0.995147 | ||||||||
\(251\) | 26.5495 | 1.67579 | 0.837896 | − | 0.545830i | \(-0.183786\pi\) | ||||
0.837896 | + | 0.545830i | \(0.183786\pi\) | |||||||
\(252\) | 1.64408 | 0.103568 | ||||||||
\(253\) | 0.0783237 | 0.00492417 | ||||||||
\(254\) | −0.981100 | −0.0615597 | ||||||||
\(255\) | −13.3585 | −0.836541 | ||||||||
\(256\) | −5.48787 | −0.342992 | ||||||||
\(257\) | −27.5507 | −1.71856 | −0.859281 | − | 0.511503i | \(-0.829089\pi\) | ||||
−0.859281 | + | 0.511503i | \(0.829089\pi\) | |||||||
\(258\) | −2.39687 | −0.149222 | ||||||||
\(259\) | 10.4102 | 0.646860 | ||||||||
\(260\) | −38.3164 | −2.37628 | ||||||||
\(261\) | 7.14777 | 0.442436 | ||||||||
\(262\) | −12.0291 | −0.743158 | ||||||||
\(263\) | −3.07677 | −0.189722 | −0.0948609 | − | 0.995491i | \(-0.530241\pi\) | ||||
−0.0948609 | + | 0.995491i | \(0.530241\pi\) | |||||||
\(264\) | 0.0796790 | 0.00490390 | ||||||||
\(265\) | 45.6819 | 2.80622 | ||||||||
\(266\) | −0.503522 | −0.0308729 | ||||||||
\(267\) | 9.93837 | 0.608218 | ||||||||
\(268\) | 8.87305 | 0.542008 | ||||||||
\(269\) | −6.88448 | −0.419754 | −0.209877 | − | 0.977728i | \(-0.567306\pi\) | ||||
−0.209877 | + | 0.977728i | \(0.567306\pi\) | |||||||
\(270\) | 2.42291 | 0.147454 | ||||||||
\(271\) | 12.8477 | 0.780442 | 0.390221 | − | 0.920721i | \(-0.372399\pi\) | ||||
0.390221 | + | 0.920721i | \(0.372399\pi\) | |||||||
\(272\) | 6.54943 | 0.397118 | ||||||||
\(273\) | 5.73847 | 0.347308 | ||||||||
\(274\) | 4.34177 | 0.262296 | ||||||||
\(275\) | −0.421266 | −0.0254033 | ||||||||
\(276\) | −3.51347 | −0.211486 | ||||||||
\(277\) | −5.36962 | −0.322629 | −0.161314 | − | 0.986903i | \(-0.551573\pi\) | ||||
−0.161314 | + | 0.986903i | \(0.551573\pi\) | |||||||
\(278\) | 7.45823 | 0.447315 | ||||||||
\(279\) | 6.50937 | 0.389706 | ||||||||
\(280\) | −8.82930 | −0.527652 | ||||||||
\(281\) | −10.8067 | −0.644672 | −0.322336 | − | 0.946625i | \(-0.604468\pi\) | ||||
−0.322336 | + | 0.946625i | \(0.604468\pi\) | |||||||
\(282\) | 1.17136 | 0.0697535 | ||||||||
\(283\) | 8.30846 | 0.493887 | 0.246943 | − | 0.969030i | \(-0.420574\pi\) | ||||
0.246943 | + | 0.969030i | \(0.420574\pi\) | |||||||
\(284\) | 18.8466 | 1.11834 | ||||||||
\(285\) | 3.42775 | 0.203042 | ||||||||
\(286\) | 0.125473 | 0.00741939 | ||||||||
\(287\) | −10.9305 | −0.645209 | ||||||||
\(288\) | −5.53594 | −0.326208 | ||||||||
\(289\) | −6.18102 | −0.363590 | ||||||||
\(290\) | −17.3184 | −1.01697 | ||||||||
\(291\) | −12.7465 | −0.747216 | ||||||||
\(292\) | 9.15645 | 0.535841 | ||||||||
\(293\) | 30.6949 | 1.79321 | 0.896607 | − | 0.442827i | \(-0.146024\pi\) | ||||
0.896607 | + | 0.442827i | \(0.146024\pi\) | |||||||
\(294\) | 0.596587 | 0.0347937 | ||||||||
\(295\) | −11.0472 | −0.643191 | ||||||||
\(296\) | −22.6320 | −1.31546 | ||||||||
\(297\) | 0.0366506 | 0.00212669 | ||||||||
\(298\) | 10.3830 | 0.601471 | ||||||||
\(299\) | −12.2633 | −0.709206 | ||||||||
\(300\) | 18.8973 | 1.09103 | ||||||||
\(301\) | 4.01763 | 0.231572 | ||||||||
\(302\) | 7.54980 | 0.434442 | ||||||||
\(303\) | −8.42052 | −0.483746 | ||||||||
\(304\) | −1.68057 | −0.0963870 | ||||||||
\(305\) | −21.2905 | −1.21909 | ||||||||
\(306\) | −1.96231 | −0.112178 | ||||||||
\(307\) | 29.7647 | 1.69876 | 0.849381 | − | 0.527780i | \(-0.176976\pi\) | ||||
0.849381 | + | 0.527780i | \(0.176976\pi\) | |||||||
\(308\) | −0.0602567 | −0.00343345 | ||||||||
\(309\) | 8.41991 | 0.478992 | ||||||||
\(310\) | −15.7717 | −0.895770 | ||||||||
\(311\) | −8.78746 | −0.498291 | −0.249146 | − | 0.968466i | \(-0.580150\pi\) | ||||
−0.249146 | + | 0.968466i | \(0.580150\pi\) | |||||||
\(312\) | −12.4755 | −0.706287 | ||||||||
\(313\) | 23.8210 | 1.34644 | 0.673222 | − | 0.739440i | \(-0.264910\pi\) | ||||
0.673222 | + | 0.739440i | \(0.264910\pi\) | |||||||
\(314\) | 4.98668 | 0.281414 | ||||||||
\(315\) | −4.06129 | −0.228828 | ||||||||
\(316\) | −5.40017 | −0.303783 | ||||||||
\(317\) | −11.5055 | −0.646215 | −0.323107 | − | 0.946362i | \(-0.604728\pi\) | ||||
−0.323107 | + | 0.946362i | \(0.604728\pi\) | |||||||
\(318\) | 6.71048 | 0.376305 | ||||||||
\(319\) | −0.261970 | −0.0146675 | ||||||||
\(320\) | −2.76043 | −0.154313 | ||||||||
\(321\) | 3.52936 | 0.196990 | ||||||||
\(322\) | −1.27493 | −0.0710489 | ||||||||
\(323\) | −2.77612 | −0.154467 | ||||||||
\(324\) | −1.64408 | −0.0913380 | ||||||||
\(325\) | 65.9586 | 3.65872 | ||||||||
\(326\) | 8.53696 | 0.472818 | ||||||||
\(327\) | 4.43885 | 0.245469 | ||||||||
\(328\) | 23.7631 | 1.31210 | ||||||||
\(329\) | −1.96344 | −0.108248 | ||||||||
\(330\) | −0.0888014 | −0.00488835 | ||||||||
\(331\) | −33.5885 | −1.84619 | −0.923096 | − | 0.384569i | \(-0.874350\pi\) | ||||
−0.923096 | + | 0.384569i | \(0.874350\pi\) | |||||||
\(332\) | −19.8142 | −1.08745 | ||||||||
\(333\) | −10.4102 | −0.570477 | ||||||||
\(334\) | −5.07335 | −0.277601 | ||||||||
\(335\) | −21.9186 | −1.19754 | ||||||||
\(336\) | 1.99118 | 0.108628 | ||||||||
\(337\) | −2.20891 | −0.120327 | −0.0601635 | − | 0.998189i | \(-0.519162\pi\) | ||||
−0.0601635 | + | 0.998189i | \(0.519162\pi\) | |||||||
\(338\) | −11.8900 | −0.646731 | ||||||||
\(339\) | 13.4260 | 0.729199 | ||||||||
\(340\) | −21.9625 | −1.19108 | ||||||||
\(341\) | −0.238573 | −0.0129194 | ||||||||
\(342\) | 0.503522 | 0.0272274 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −8.73439 | −0.470927 | ||||||||
\(345\) | 8.67913 | 0.467269 | ||||||||
\(346\) | −5.33780 | −0.286962 | ||||||||
\(347\) | 28.3669 | 1.52281 | 0.761406 | − | 0.648275i | \(-0.224509\pi\) | ||||
0.761406 | + | 0.648275i | \(0.224509\pi\) | |||||||
\(348\) | 11.7515 | 0.629948 | ||||||||
\(349\) | −2.59706 | −0.139018 | −0.0695088 | − | 0.997581i | \(-0.522143\pi\) | ||||
−0.0695088 | + | 0.997581i | \(0.522143\pi\) | |||||||
\(350\) | 6.85723 | 0.366534 | ||||||||
\(351\) | −5.73847 | −0.306297 | ||||||||
\(352\) | 0.202896 | 0.0108144 | ||||||||
\(353\) | −13.2413 | −0.704763 | −0.352382 | − | 0.935856i | \(-0.614628\pi\) | ||||
−0.352382 | + | 0.935856i | \(0.614628\pi\) | |||||||
\(354\) | −1.62278 | −0.0862499 | ||||||||
\(355\) | −46.5558 | −2.47093 | ||||||||
\(356\) | 16.3395 | 0.865993 | ||||||||
\(357\) | 3.28922 | 0.174084 | ||||||||
\(358\) | −9.35124 | −0.494228 | ||||||||
\(359\) | 33.1025 | 1.74708 | 0.873541 | − | 0.486751i | \(-0.161818\pi\) | ||||
0.873541 | + | 0.486751i | \(0.161818\pi\) | |||||||
\(360\) | 8.82930 | 0.465345 | ||||||||
\(361\) | −18.2877 | −0.962508 | ||||||||
\(362\) | −14.0158 | −0.736652 | ||||||||
\(363\) | 10.9987 | 0.577280 | ||||||||
\(364\) | 9.43453 | 0.494504 | ||||||||
\(365\) | −22.6187 | −1.18392 | ||||||||
\(366\) | −3.12748 | −0.163476 | ||||||||
\(367\) | 16.0319 | 0.836857 | 0.418429 | − | 0.908250i | \(-0.362581\pi\) | ||||
0.418429 | + | 0.908250i | \(0.362581\pi\) | |||||||
\(368\) | −4.25522 | −0.221819 | ||||||||
\(369\) | 10.9305 | 0.569021 | ||||||||
\(370\) | 25.2231 | 1.31129 | ||||||||
\(371\) | −11.2481 | −0.583973 | ||||||||
\(372\) | 10.7020 | 0.554871 | ||||||||
\(373\) | 19.2805 | 0.998307 | 0.499153 | − | 0.866514i | \(-0.333644\pi\) | ||||
0.499153 | + | 0.866514i | \(0.333644\pi\) | |||||||
\(374\) | 0.0719198 | 0.00371888 | ||||||||
\(375\) | −26.3745 | −1.36197 | ||||||||
\(376\) | 4.26854 | 0.220133 | ||||||||
\(377\) | 41.0172 | 2.11250 | ||||||||
\(378\) | −0.596587 | −0.0306851 | ||||||||
\(379\) | 18.7562 | 0.963442 | 0.481721 | − | 0.876325i | \(-0.340012\pi\) | ||||
0.481721 | + | 0.876325i | \(0.340012\pi\) | |||||||
\(380\) | 5.63551 | 0.289096 | ||||||||
\(381\) | −1.64452 | −0.0842514 | ||||||||
\(382\) | −0.596587 | −0.0305240 | ||||||||
\(383\) | 16.0788 | 0.821589 | 0.410794 | − | 0.911728i | \(-0.365251\pi\) | ||||
0.410794 | + | 0.911728i | \(0.365251\pi\) | |||||||
\(384\) | −11.4774 | −0.585702 | ||||||||
\(385\) | 0.148849 | 0.00758605 | ||||||||
\(386\) | −8.05727 | −0.410104 | ||||||||
\(387\) | −4.01763 | −0.204228 | ||||||||
\(388\) | −20.9564 | −1.06390 | ||||||||
\(389\) | −19.8417 | −1.00602 | −0.503008 | − | 0.864282i | \(-0.667773\pi\) | ||||
−0.503008 | + | 0.864282i | \(0.667773\pi\) | |||||||
\(390\) | 13.9038 | 0.704047 | ||||||||
\(391\) | −7.02918 | −0.355481 | ||||||||
\(392\) | 2.17401 | 0.109804 | ||||||||
\(393\) | −20.1631 | −1.01710 | ||||||||
\(394\) | 4.66787 | 0.235164 | ||||||||
\(395\) | 13.3398 | 0.671196 | ||||||||
\(396\) | 0.0602567 | 0.00302801 | ||||||||
\(397\) | 11.3893 | 0.571613 | 0.285807 | − | 0.958287i | \(-0.407739\pi\) | ||||
0.285807 | + | 0.958287i | \(0.407739\pi\) | |||||||
\(398\) | −14.8838 | −0.746056 | ||||||||
\(399\) | −0.844005 | −0.0422531 | ||||||||
\(400\) | 22.8868 | 1.14434 | ||||||||
\(401\) | 38.1159 | 1.90342 | 0.951708 | − | 0.307005i | \(-0.0993267\pi\) | ||||
0.951708 | + | 0.307005i | \(0.0993267\pi\) | |||||||
\(402\) | −3.21975 | −0.160587 | ||||||||
\(403\) | 37.3539 | 1.86073 | ||||||||
\(404\) | −13.8440 | −0.688767 | ||||||||
\(405\) | 4.06129 | 0.201807 | ||||||||
\(406\) | 4.26426 | 0.211632 | ||||||||
\(407\) | 0.381542 | 0.0189123 | ||||||||
\(408\) | −7.15081 | −0.354018 | ||||||||
\(409\) | 29.2086 | 1.44427 | 0.722136 | − | 0.691752i | \(-0.243161\pi\) | ||||
0.722136 | + | 0.691752i | \(0.243161\pi\) | |||||||
\(410\) | −26.4838 | −1.30794 | ||||||||
\(411\) | 7.27768 | 0.358982 | ||||||||
\(412\) | 13.8430 | 0.681997 | ||||||||
\(413\) | 2.72011 | 0.133848 | ||||||||
\(414\) | 1.27493 | 0.0626593 | ||||||||
\(415\) | 48.9460 | 2.40267 | ||||||||
\(416\) | −31.7678 | −1.55755 | ||||||||
\(417\) | 12.5015 | 0.612201 | ||||||||
\(418\) | −0.0184544 | −0.000902635 0 | ||||||||
\(419\) | −1.82071 | −0.0889475 | −0.0444737 | − | 0.999011i | \(-0.514161\pi\) | ||||
−0.0444737 | + | 0.999011i | \(0.514161\pi\) | |||||||
\(420\) | −6.67711 | −0.325809 | ||||||||
\(421\) | 5.80427 | 0.282883 | 0.141441 | − | 0.989947i | \(-0.454826\pi\) | ||||
0.141441 | + | 0.989947i | \(0.454826\pi\) | |||||||
\(422\) | −5.29252 | −0.257636 | ||||||||
\(423\) | 1.96344 | 0.0954656 | ||||||||
\(424\) | 24.4536 | 1.18757 | ||||||||
\(425\) | 37.8067 | 1.83389 | ||||||||
\(426\) | −6.83885 | −0.331344 | ||||||||
\(427\) | 5.24229 | 0.253692 | ||||||||
\(428\) | 5.80257 | 0.280478 | ||||||||
\(429\) | 0.210319 | 0.0101543 | ||||||||
\(430\) | 9.73438 | 0.469434 | ||||||||
\(431\) | −4.95352 | −0.238603 | −0.119301 | − | 0.992858i | \(-0.538065\pi\) | ||||
−0.119301 | + | 0.992858i | \(0.538065\pi\) | |||||||
\(432\) | −1.99118 | −0.0958007 | ||||||||
\(433\) | 26.1195 | 1.25522 | 0.627612 | − | 0.778526i | \(-0.284032\pi\) | ||||
0.627612 | + | 0.778526i | \(0.284032\pi\) | |||||||
\(434\) | 3.88341 | 0.186410 | ||||||||
\(435\) | −29.0292 | −1.39184 | ||||||||
\(436\) | 7.29785 | 0.349503 | ||||||||
\(437\) | 1.80367 | 0.0862812 | ||||||||
\(438\) | −3.32259 | −0.158760 | ||||||||
\(439\) | 23.2695 | 1.11059 | 0.555295 | − | 0.831653i | \(-0.312605\pi\) | ||||
0.555295 | + | 0.831653i | \(0.312605\pi\) | |||||||
\(440\) | −0.323600 | −0.0154270 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −11.2606 | −0.535614 | ||||||||
\(443\) | 9.99727 | 0.474985 | 0.237492 | − | 0.971389i | \(-0.423675\pi\) | ||||
0.237492 | + | 0.971389i | \(0.423675\pi\) | |||||||
\(444\) | −17.1153 | −0.812256 | ||||||||
\(445\) | −40.3626 | −1.91337 | ||||||||
\(446\) | −2.44044 | −0.115558 | ||||||||
\(447\) | 17.4040 | 0.823181 | ||||||||
\(448\) | 0.679692 | 0.0321124 | ||||||||
\(449\) | −21.8543 | −1.03137 | −0.515684 | − | 0.856779i | \(-0.672462\pi\) | ||||
−0.515684 | + | 0.856779i | \(0.672462\pi\) | |||||||
\(450\) | −6.85723 | −0.323253 | ||||||||
\(451\) | −0.400611 | −0.0188640 | ||||||||
\(452\) | 22.0734 | 1.03825 | ||||||||
\(453\) | 12.6550 | 0.594583 | ||||||||
\(454\) | 6.71845 | 0.315313 | ||||||||
\(455\) | −23.3056 | −1.09258 | ||||||||
\(456\) | 1.83488 | 0.0859260 | ||||||||
\(457\) | 10.1375 | 0.474211 | 0.237105 | − | 0.971484i | \(-0.423801\pi\) | ||||
0.237105 | + | 0.971484i | \(0.423801\pi\) | |||||||
\(458\) | 8.26727 | 0.386304 | ||||||||
\(459\) | −3.28922 | −0.153528 | ||||||||
\(460\) | 14.2692 | 0.665306 | ||||||||
\(461\) | 26.8464 | 1.25036 | 0.625181 | − | 0.780480i | \(-0.285025\pi\) | ||||
0.625181 | + | 0.780480i | \(0.285025\pi\) | |||||||
\(462\) | 0.0218653 | 0.00101727 | ||||||||
\(463\) | −22.8400 | −1.06146 | −0.530731 | − | 0.847540i | \(-0.678083\pi\) | ||||
−0.530731 | + | 0.847540i | \(0.678083\pi\) | |||||||
\(464\) | 14.2325 | 0.660727 | ||||||||
\(465\) | −26.4365 | −1.22596 | ||||||||
\(466\) | 1.55880 | 0.0722101 | ||||||||
\(467\) | 2.83717 | 0.131289 | 0.0656443 | − | 0.997843i | \(-0.479090\pi\) | ||||
0.0656443 | + | 0.997843i | \(0.479090\pi\) | |||||||
\(468\) | −9.43453 | −0.436111 | ||||||||
\(469\) | 5.39696 | 0.249208 | ||||||||
\(470\) | −4.75724 | −0.219435 | ||||||||
\(471\) | 8.35868 | 0.385147 | ||||||||
\(472\) | −5.91356 | −0.272194 | ||||||||
\(473\) | 0.147249 | 0.00677051 | ||||||||
\(474\) | 1.95955 | 0.0900053 | ||||||||
\(475\) | −9.70108 | −0.445116 | ||||||||
\(476\) | 5.40776 | 0.247864 | ||||||||
\(477\) | 11.2481 | 0.515016 | ||||||||
\(478\) | −1.42928 | −0.0653738 | ||||||||
\(479\) | −6.85478 | −0.313203 | −0.156601 | − | 0.987662i | \(-0.550054\pi\) | ||||
−0.156601 | + | 0.987662i | \(0.550054\pi\) | |||||||
\(480\) | 22.4831 | 1.02621 | ||||||||
\(481\) | −59.7388 | −2.72385 | ||||||||
\(482\) | −0.651075 | −0.0296557 | ||||||||
\(483\) | −2.13704 | −0.0972385 | ||||||||
\(484\) | 18.0827 | 0.821942 | ||||||||
\(485\) | 51.7675 | 2.35064 | ||||||||
\(486\) | 0.596587 | 0.0270617 | ||||||||
\(487\) | 31.0590 | 1.40742 | 0.703709 | − | 0.710488i | \(-0.251526\pi\) | ||||
0.703709 | + | 0.710488i | \(0.251526\pi\) | |||||||
\(488\) | −11.3968 | −0.515910 | ||||||||
\(489\) | 14.3097 | 0.647105 | ||||||||
\(490\) | −2.42291 | −0.109456 | ||||||||
\(491\) | −1.64485 | −0.0742310 | −0.0371155 | − | 0.999311i | \(-0.511817\pi\) | ||||
−0.0371155 | + | 0.999311i | \(0.511817\pi\) | |||||||
\(492\) | 17.9707 | 0.810182 | ||||||||
\(493\) | 23.5106 | 1.05886 | ||||||||
\(494\) | 2.88945 | 0.130002 | ||||||||
\(495\) | −0.148849 | −0.00669026 | ||||||||
\(496\) | 12.9613 | 0.581981 | ||||||||
\(497\) | 11.4633 | 0.514199 | ||||||||
\(498\) | 7.18997 | 0.322190 | ||||||||
\(499\) | −33.7150 | −1.50929 | −0.754646 | − | 0.656133i | \(-0.772191\pi\) | ||||
−0.754646 | + | 0.656133i | \(0.772191\pi\) | |||||||
\(500\) | −43.3618 | −1.93920 | ||||||||
\(501\) | −8.50396 | −0.379929 | ||||||||
\(502\) | −15.8391 | −0.706934 | ||||||||
\(503\) | −15.5582 | −0.693705 | −0.346852 | − | 0.937920i | \(-0.612750\pi\) | ||||
−0.346852 | + | 0.937920i | \(0.612750\pi\) | |||||||
\(504\) | −2.17401 | −0.0968382 | ||||||||
\(505\) | 34.1982 | 1.52180 | ||||||||
\(506\) | −0.0467269 | −0.00207726 | ||||||||
\(507\) | −19.9300 | −0.885124 | ||||||||
\(508\) | −2.70373 | −0.119959 | ||||||||
\(509\) | 4.26687 | 0.189126 | 0.0945628 | − | 0.995519i | \(-0.469855\pi\) | ||||
0.0945628 | + | 0.995519i | \(0.469855\pi\) | |||||||
\(510\) | 7.96950 | 0.352895 | ||||||||
\(511\) | 5.56933 | 0.246373 | ||||||||
\(512\) | −19.6808 | −0.869775 | ||||||||
\(513\) | 0.844005 | 0.0372637 | ||||||||
\(514\) | 16.4364 | 0.724977 | ||||||||
\(515\) | −34.1957 | −1.50684 | ||||||||
\(516\) | −6.60533 | −0.290783 | ||||||||
\(517\) | −0.0719612 | −0.00316485 | ||||||||
\(518\) | −6.21061 | −0.272878 | ||||||||
\(519\) | −8.94722 | −0.392739 | ||||||||
\(520\) | 50.6667 | 2.22188 | ||||||||
\(521\) | −30.6461 | −1.34263 | −0.671314 | − | 0.741173i | \(-0.734270\pi\) | ||||
−0.671314 | + | 0.741173i | \(0.734270\pi\) | |||||||
\(522\) | −4.26426 | −0.186642 | ||||||||
\(523\) | 3.94602 | 0.172547 | 0.0862737 | − | 0.996271i | \(-0.472504\pi\) | ||||
0.0862737 | + | 0.996271i | \(0.472504\pi\) | |||||||
\(524\) | −33.1499 | −1.44816 | ||||||||
\(525\) | 11.4941 | 0.501644 | ||||||||
\(526\) | 1.83556 | 0.0800343 | ||||||||
\(527\) | 21.4108 | 0.932668 | ||||||||
\(528\) | 0.0729780 | 0.00317596 | ||||||||
\(529\) | −18.4331 | −0.801438 | ||||||||
\(530\) | −27.2532 | −1.18381 | ||||||||
\(531\) | −2.72011 | −0.118043 | ||||||||
\(532\) | −1.38761 | −0.0601607 | ||||||||
\(533\) | 62.7245 | 2.71690 | ||||||||
\(534\) | −5.92910 | −0.256577 | ||||||||
\(535\) | −14.3338 | −0.619703 | ||||||||
\(536\) | −11.7331 | −0.506791 | ||||||||
\(537\) | −15.6746 | −0.676407 | ||||||||
\(538\) | 4.10719 | 0.177074 | ||||||||
\(539\) | −0.0366506 | −0.00157865 | ||||||||
\(540\) | 6.67711 | 0.287337 | ||||||||
\(541\) | −43.0110 | −1.84919 | −0.924595 | − | 0.380952i | \(-0.875596\pi\) | ||||
−0.924595 | + | 0.380952i | \(0.875596\pi\) | |||||||
\(542\) | −7.66477 | −0.329230 | ||||||||
\(543\) | −23.4932 | −1.00819 | ||||||||
\(544\) | −18.2089 | −0.780701 | ||||||||
\(545\) | −18.0275 | −0.772212 | ||||||||
\(546\) | −3.42350 | −0.146512 | ||||||||
\(547\) | −24.6409 | −1.05357 | −0.526784 | − | 0.849999i | \(-0.676602\pi\) | ||||
−0.526784 | + | 0.849999i | \(0.676602\pi\) | |||||||
\(548\) | 11.9651 | 0.511125 | ||||||||
\(549\) | −5.24229 | −0.223736 | ||||||||
\(550\) | 0.251322 | 0.0107164 | ||||||||
\(551\) | −6.03275 | −0.257004 | ||||||||
\(552\) | 4.64594 | 0.197745 | ||||||||
\(553\) | −3.28461 | −0.139676 | ||||||||
\(554\) | 3.20344 | 0.136101 | ||||||||
\(555\) | 42.2790 | 1.79464 | ||||||||
\(556\) | 20.5535 | 0.871663 | ||||||||
\(557\) | −20.6836 | −0.876391 | −0.438196 | − | 0.898880i | \(-0.644382\pi\) | ||||
−0.438196 | + | 0.898880i | \(0.644382\pi\) | |||||||
\(558\) | −3.88341 | −0.164398 | ||||||||
\(559\) | −23.0551 | −0.975125 | ||||||||
\(560\) | −8.08677 | −0.341728 | ||||||||
\(561\) | 0.120552 | 0.00508971 | ||||||||
\(562\) | 6.44712 | 0.271955 | ||||||||
\(563\) | −31.0927 | −1.31040 | −0.655201 | − | 0.755455i | \(-0.727416\pi\) | ||||
−0.655201 | + | 0.755455i | \(0.727416\pi\) | |||||||
\(564\) | 3.22806 | 0.135926 | ||||||||
\(565\) | −54.5268 | −2.29396 | ||||||||
\(566\) | −4.95672 | −0.208346 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −24.9214 | −1.04568 | ||||||||
\(569\) | 2.11572 | 0.0886956 | 0.0443478 | − | 0.999016i | \(-0.485879\pi\) | ||||
0.0443478 | + | 0.999016i | \(0.485879\pi\) | |||||||
\(570\) | −2.04495 | −0.0856536 | ||||||||
\(571\) | 25.8638 | 1.08236 | 0.541182 | − | 0.840905i | \(-0.317977\pi\) | ||||
0.541182 | + | 0.840905i | \(0.317977\pi\) | |||||||
\(572\) | 0.345781 | 0.0144578 | ||||||||
\(573\) | −1.00000 | −0.0417756 | ||||||||
\(574\) | 6.52101 | 0.272182 | ||||||||
\(575\) | −24.5633 | −1.02436 | ||||||||
\(576\) | −0.679692 | −0.0283205 | ||||||||
\(577\) | 15.1456 | 0.630519 | 0.315259 | − | 0.949006i | \(-0.397909\pi\) | ||||
0.315259 | + | 0.949006i | \(0.397909\pi\) | |||||||
\(578\) | 3.68752 | 0.153381 | ||||||||
\(579\) | −13.5056 | −0.561274 | ||||||||
\(580\) | −47.7264 | −1.98173 | ||||||||
\(581\) | −12.0518 | −0.499994 | ||||||||
\(582\) | 7.60442 | 0.315214 | ||||||||
\(583\) | −0.412251 | −0.0170737 | ||||||||
\(584\) | −12.1078 | −0.501024 | ||||||||
\(585\) | 23.3056 | 0.963568 | ||||||||
\(586\) | −18.3122 | −0.756469 | ||||||||
\(587\) | −39.2402 | −1.61961 | −0.809807 | − | 0.586696i | \(-0.800428\pi\) | ||||
−0.809807 | + | 0.586696i | \(0.800428\pi\) | |||||||
\(588\) | 1.64408 | 0.0678009 | ||||||||
\(589\) | −5.49394 | −0.226374 | ||||||||
\(590\) | 6.59060 | 0.271331 | ||||||||
\(591\) | 7.82429 | 0.321848 | ||||||||
\(592\) | −20.7286 | −0.851942 | ||||||||
\(593\) | −0.156852 | −0.00644115 | −0.00322057 | − | 0.999995i | \(-0.501025\pi\) | ||||
−0.00322057 | + | 0.999995i | \(0.501025\pi\) | |||||||
\(594\) | −0.0218653 | −0.000897144 0 | ||||||||
\(595\) | −13.3585 | −0.547645 | ||||||||
\(596\) | 28.6136 | 1.17206 | ||||||||
\(597\) | −24.9482 | −1.02106 | ||||||||
\(598\) | 7.31613 | 0.299179 | ||||||||
\(599\) | −28.8827 | −1.18011 | −0.590057 | − | 0.807362i | \(-0.700895\pi\) | ||||
−0.590057 | + | 0.807362i | \(0.700895\pi\) | |||||||
\(600\) | −24.9883 | −1.02014 | ||||||||
\(601\) | −14.1337 | −0.576526 | −0.288263 | − | 0.957551i | \(-0.593078\pi\) | ||||
−0.288263 | + | 0.957551i | \(0.593078\pi\) | |||||||
\(602\) | −2.39687 | −0.0976890 | ||||||||
\(603\) | −5.39696 | −0.219781 | ||||||||
\(604\) | 20.8058 | 0.846578 | ||||||||
\(605\) | −44.6688 | −1.81604 | ||||||||
\(606\) | 5.02357 | 0.204069 | ||||||||
\(607\) | −43.0094 | −1.74570 | −0.872850 | − | 0.487989i | \(-0.837731\pi\) | ||||
−0.872850 | + | 0.487989i | \(0.837731\pi\) | |||||||
\(608\) | 4.67236 | 0.189489 | ||||||||
\(609\) | 7.14777 | 0.289642 | ||||||||
\(610\) | 12.7016 | 0.514274 | ||||||||
\(611\) | 11.2671 | 0.455819 | ||||||||
\(612\) | −5.40776 | −0.218596 | ||||||||
\(613\) | −16.3540 | −0.660532 | −0.330266 | − | 0.943888i | \(-0.607138\pi\) | ||||
−0.330266 | + | 0.943888i | \(0.607138\pi\) | |||||||
\(614\) | −17.7572 | −0.716624 | ||||||||
\(615\) | −44.3921 | −1.79006 | ||||||||
\(616\) | 0.0796790 | 0.00321036 | ||||||||
\(617\) | −33.4102 | −1.34504 | −0.672522 | − | 0.740077i | \(-0.734789\pi\) | ||||
−0.672522 | + | 0.740077i | \(0.734789\pi\) | |||||||
\(618\) | −5.02321 | −0.202063 | ||||||||
\(619\) | 35.9494 | 1.44493 | 0.722464 | − | 0.691409i | \(-0.243010\pi\) | ||||
0.722464 | + | 0.691409i | \(0.243010\pi\) | |||||||
\(620\) | −43.4638 | −1.74555 | ||||||||
\(621\) | 2.13704 | 0.0857563 | ||||||||
\(622\) | 5.24248 | 0.210204 | ||||||||
\(623\) | 9.93837 | 0.398172 | ||||||||
\(624\) | −11.4263 | −0.457419 | ||||||||
\(625\) | 49.6439 | 1.98576 | ||||||||
\(626\) | −14.2113 | −0.567999 | ||||||||
\(627\) | −0.0309333 | −0.00123536 | ||||||||
\(628\) | 13.7424 | 0.548380 | ||||||||
\(629\) | −34.2415 | −1.36530 | ||||||||
\(630\) | 2.42291 | 0.0965312 | ||||||||
\(631\) | −26.5993 | −1.05890 | −0.529452 | − | 0.848340i | \(-0.677602\pi\) | ||||
−0.529452 | + | 0.848340i | \(0.677602\pi\) | |||||||
\(632\) | 7.14078 | 0.284045 | ||||||||
\(633\) | −8.87133 | −0.352604 | ||||||||
\(634\) | 6.86405 | 0.272606 | ||||||||
\(635\) | 6.67888 | 0.265043 | ||||||||
\(636\) | 18.4929 | 0.733290 | ||||||||
\(637\) | 5.73847 | 0.227366 | ||||||||
\(638\) | 0.156288 | 0.00618750 | ||||||||
\(639\) | −11.4633 | −0.453481 | ||||||||
\(640\) | 46.6130 | 1.84254 | ||||||||
\(641\) | 34.1004 | 1.34688 | 0.673442 | − | 0.739240i | \(-0.264815\pi\) | ||||
0.673442 | + | 0.739240i | \(0.264815\pi\) | |||||||
\(642\) | −2.10557 | −0.0831003 | ||||||||
\(643\) | 8.80594 | 0.347272 | 0.173636 | − | 0.984810i | \(-0.444448\pi\) | ||||
0.173636 | + | 0.984810i | \(0.444448\pi\) | |||||||
\(644\) | −3.51347 | −0.138450 | ||||||||
\(645\) | 16.3168 | 0.642473 | ||||||||
\(646\) | 1.65620 | 0.0651622 | ||||||||
\(647\) | 10.6708 | 0.419513 | 0.209757 | − | 0.977754i | \(-0.432733\pi\) | ||||
0.209757 | + | 0.977754i | \(0.432733\pi\) | |||||||
\(648\) | 2.17401 | 0.0854033 | ||||||||
\(649\) | 0.0996938 | 0.00391332 | ||||||||
\(650\) | −39.3500 | −1.54343 | ||||||||
\(651\) | 6.50937 | 0.255123 | ||||||||
\(652\) | 23.5263 | 0.921360 | ||||||||
\(653\) | −26.1605 | −1.02374 | −0.511870 | − | 0.859063i | \(-0.671047\pi\) | ||||
−0.511870 | + | 0.859063i | \(0.671047\pi\) | |||||||
\(654\) | −2.64816 | −0.103551 | ||||||||
\(655\) | 81.8884 | 3.19964 | ||||||||
\(656\) | 21.7647 | 0.849767 | ||||||||
\(657\) | −5.56933 | −0.217280 | ||||||||
\(658\) | 1.17136 | 0.0456644 | ||||||||
\(659\) | −37.8063 | −1.47272 | −0.736362 | − | 0.676588i | \(-0.763458\pi\) | ||||
−0.736362 | + | 0.676588i | \(0.763458\pi\) | |||||||
\(660\) | −0.244720 | −0.00952572 | ||||||||
\(661\) | 13.3380 | 0.518790 | 0.259395 | − | 0.965771i | \(-0.416477\pi\) | ||||
0.259395 | + | 0.965771i | \(0.416477\pi\) | |||||||
\(662\) | 20.0385 | 0.778817 | ||||||||
\(663\) | −18.8751 | −0.733048 | ||||||||
\(664\) | 26.2008 | 1.01679 | ||||||||
\(665\) | 3.42775 | 0.132922 | ||||||||
\(666\) | 6.21061 | 0.240656 | ||||||||
\(667\) | −15.2750 | −0.591452 | ||||||||
\(668\) | −13.9812 | −0.540950 | ||||||||
\(669\) | −4.09068 | −0.158155 | ||||||||
\(670\) | 13.0764 | 0.505184 | ||||||||
\(671\) | 0.192133 | 0.00741723 | ||||||||
\(672\) | −5.53594 | −0.213553 | ||||||||
\(673\) | −29.9320 | −1.15379 | −0.576897 | − | 0.816817i | \(-0.695736\pi\) | ||||
−0.576897 | + | 0.816817i | \(0.695736\pi\) | |||||||
\(674\) | 1.31781 | 0.0507600 | ||||||||
\(675\) | −11.4941 | −0.442408 | ||||||||
\(676\) | −32.7667 | −1.26026 | ||||||||
\(677\) | 20.5821 | 0.791034 | 0.395517 | − | 0.918459i | \(-0.370565\pi\) | ||||
0.395517 | + | 0.918459i | \(0.370565\pi\) | |||||||
\(678\) | −8.00976 | −0.307613 | ||||||||
\(679\) | −12.7465 | −0.489168 | ||||||||
\(680\) | 29.0415 | 1.11369 | ||||||||
\(681\) | 11.2615 | 0.431541 | ||||||||
\(682\) | 0.142329 | 0.00545007 | ||||||||
\(683\) | 3.86925 | 0.148053 | 0.0740264 | − | 0.997256i | \(-0.476415\pi\) | ||||
0.0740264 | + | 0.997256i | \(0.476415\pi\) | |||||||
\(684\) | 1.38761 | 0.0530568 | ||||||||
\(685\) | −29.5568 | −1.12931 | ||||||||
\(686\) | 0.596587 | 0.0227778 | ||||||||
\(687\) | 13.8576 | 0.528701 | ||||||||
\(688\) | −7.99983 | −0.304991 | ||||||||
\(689\) | 64.5470 | 2.45905 | ||||||||
\(690\) | −5.17786 | −0.197118 | ||||||||
\(691\) | −38.8416 | −1.47761 | −0.738803 | − | 0.673922i | \(-0.764608\pi\) | ||||
−0.738803 | + | 0.673922i | \(0.764608\pi\) | |||||||
\(692\) | −14.7100 | −0.559190 | ||||||||
\(693\) | 0.0366506 | 0.00139224 | ||||||||
\(694\) | −16.9233 | −0.642399 | ||||||||
\(695\) | −50.7722 | −1.92590 | ||||||||
\(696\) | −15.5393 | −0.589017 | ||||||||
\(697\) | 35.9529 | 1.36181 | ||||||||
\(698\) | 1.54937 | 0.0586447 | ||||||||
\(699\) | 2.61287 | 0.0988277 | ||||||||
\(700\) | 18.8973 | 0.714250 | ||||||||
\(701\) | −29.6266 | −1.11898 | −0.559490 | − | 0.828837i | \(-0.689003\pi\) | ||||
−0.559490 | + | 0.828837i | \(0.689003\pi\) | |||||||
\(702\) | 3.42350 | 0.129212 | ||||||||
\(703\) | 8.78628 | 0.331381 | ||||||||
\(704\) | 0.0249111 | 0.000938874 0 | ||||||||
\(705\) | −7.97410 | −0.300322 | ||||||||
\(706\) | 7.89958 | 0.297305 | ||||||||
\(707\) | −8.42052 | −0.316686 | ||||||||
\(708\) | −4.47209 | −0.168071 | ||||||||
\(709\) | 28.9486 | 1.08719 | 0.543593 | − | 0.839349i | \(-0.317064\pi\) | ||||
0.543593 | + | 0.839349i | \(0.317064\pi\) | |||||||
\(710\) | 27.7746 | 1.04236 | ||||||||
\(711\) | 3.28461 | 0.123182 | ||||||||
\(712\) | −21.6061 | −0.809725 | ||||||||
\(713\) | −13.9108 | −0.520962 | ||||||||
\(714\) | −1.96231 | −0.0734375 | ||||||||
\(715\) | −0.854166 | −0.0319440 | ||||||||
\(716\) | −25.7703 | −0.963081 | ||||||||
\(717\) | −2.39576 | −0.0894714 | ||||||||
\(718\) | −19.7485 | −0.737008 | ||||||||
\(719\) | 18.1650 | 0.677439 | 0.338720 | − | 0.940887i | \(-0.390006\pi\) | ||||
0.338720 | + | 0.940887i | \(0.390006\pi\) | |||||||
\(720\) | 8.08677 | 0.301376 | ||||||||
\(721\) | 8.41991 | 0.313574 | ||||||||
\(722\) | 10.9102 | 0.406035 | ||||||||
\(723\) | −1.09133 | −0.0405871 | ||||||||
\(724\) | −38.6249 | −1.43548 | ||||||||
\(725\) | 82.1572 | 3.05124 | ||||||||
\(726\) | −6.56166 | −0.243526 | ||||||||
\(727\) | 6.28106 | 0.232952 | 0.116476 | − | 0.993194i | \(-0.462840\pi\) | ||||
0.116476 | + | 0.993194i | \(0.462840\pi\) | |||||||
\(728\) | −12.4755 | −0.462373 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 13.4940 | 0.499436 | ||||||||
\(731\) | −13.2149 | −0.488770 | ||||||||
\(732\) | −8.61877 | −0.318559 | ||||||||
\(733\) | −4.43301 | −0.163737 | −0.0818685 | − | 0.996643i | \(-0.526089\pi\) | ||||
−0.0818685 | + | 0.996643i | \(0.526089\pi\) | |||||||
\(734\) | −9.56441 | −0.353029 | ||||||||
\(735\) | −4.06129 | −0.149803 | ||||||||
\(736\) | 11.8305 | 0.436078 | ||||||||
\(737\) | 0.197802 | 0.00728613 | ||||||||
\(738\) | −6.52101 | −0.240042 | ||||||||
\(739\) | 41.9437 | 1.54292 | 0.771462 | − | 0.636276i | \(-0.219526\pi\) | ||||
0.771462 | + | 0.636276i | \(0.219526\pi\) | |||||||
\(740\) | 69.5102 | 2.55525 | ||||||||
\(741\) | 4.84330 | 0.177923 | ||||||||
\(742\) | 6.71048 | 0.246350 | ||||||||
\(743\) | 17.6244 | 0.646575 | 0.323287 | − | 0.946301i | \(-0.395212\pi\) | ||||
0.323287 | + | 0.946301i | \(0.395212\pi\) | |||||||
\(744\) | −14.1515 | −0.518818 | ||||||||
\(745\) | −70.6828 | −2.58962 | ||||||||
\(746\) | −11.5025 | −0.421136 | ||||||||
\(747\) | 12.0518 | 0.440954 | ||||||||
\(748\) | 0.198198 | 0.00724683 | ||||||||
\(749\) | 3.52936 | 0.128960 | ||||||||
\(750\) | 15.7347 | 0.574549 | ||||||||
\(751\) | 12.1380 | 0.442921 | 0.221461 | − | 0.975169i | \(-0.428918\pi\) | ||||
0.221461 | + | 0.975169i | \(0.428918\pi\) | |||||||
\(752\) | 3.90956 | 0.142567 | ||||||||
\(753\) | −26.5495 | −0.967519 | ||||||||
\(754\) | −24.4704 | −0.891158 | ||||||||
\(755\) | −51.3956 | −1.87048 | ||||||||
\(756\) | −1.64408 | −0.0597948 | ||||||||
\(757\) | −30.4617 | −1.10715 | −0.553575 | − | 0.832800i | \(-0.686737\pi\) | ||||
−0.553575 | + | 0.832800i | \(0.686737\pi\) | |||||||
\(758\) | −11.1897 | −0.406429 | ||||||||
\(759\) | −0.0783237 | −0.00284297 | ||||||||
\(760\) | −7.45197 | −0.270312 | ||||||||
\(761\) | −12.7952 | −0.463824 | −0.231912 | − | 0.972737i | \(-0.574498\pi\) | ||||
−0.231912 | + | 0.972737i | \(0.574498\pi\) | |||||||
\(762\) | 0.981100 | 0.0355415 | ||||||||
\(763\) | 4.43885 | 0.160697 | ||||||||
\(764\) | −1.64408 | −0.0594809 | ||||||||
\(765\) | 13.3585 | 0.482977 | ||||||||
\(766\) | −9.59241 | −0.346588 | ||||||||
\(767\) | −15.6093 | −0.563618 | ||||||||
\(768\) | 5.48787 | 0.198026 | ||||||||
\(769\) | −7.30174 | −0.263307 | −0.131654 | − | 0.991296i | \(-0.542029\pi\) | ||||
−0.131654 | + | 0.991296i | \(0.542029\pi\) | |||||||
\(770\) | −0.0888014 | −0.00320018 | ||||||||
\(771\) | 27.5507 | 0.992213 | ||||||||
\(772\) | −22.2044 | −0.799152 | ||||||||
\(773\) | −39.0629 | −1.40500 | −0.702498 | − | 0.711685i | \(-0.747932\pi\) | ||||
−0.702498 | + | 0.711685i | \(0.747932\pi\) | |||||||
\(774\) | 2.39687 | 0.0861536 | ||||||||
\(775\) | 74.8194 | 2.68759 | ||||||||
\(776\) | 27.7112 | 0.994773 | ||||||||
\(777\) | −10.4102 | −0.373465 | ||||||||
\(778\) | 11.8373 | 0.424388 | ||||||||
\(779\) | −9.22542 | −0.330535 | ||||||||
\(780\) | 38.3164 | 1.37195 | ||||||||
\(781\) | 0.420137 | 0.0150337 | ||||||||
\(782\) | 4.19352 | 0.149960 | ||||||||
\(783\) | −7.14777 | −0.255440 | ||||||||
\(784\) | 1.99118 | 0.0711136 | ||||||||
\(785\) | −33.9470 | −1.21162 | ||||||||
\(786\) | 12.0291 | 0.429062 | ||||||||
\(787\) | −38.1559 | −1.36011 | −0.680056 | − | 0.733160i | \(-0.738045\pi\) | ||||
−0.680056 | + | 0.733160i | \(0.738045\pi\) | |||||||
\(788\) | 12.8638 | 0.458253 | ||||||||
\(789\) | 3.07677 | 0.109536 | ||||||||
\(790\) | −7.95833 | −0.283145 | ||||||||
\(791\) | 13.4260 | 0.477373 | ||||||||
\(792\) | −0.0796790 | −0.00283127 | ||||||||
\(793\) | −30.0827 | −1.06827 | ||||||||
\(794\) | −6.79471 | −0.241135 | ||||||||
\(795\) | −45.6819 | −1.62017 | ||||||||
\(796\) | −41.0169 | −1.45381 | ||||||||
\(797\) | −48.3879 | −1.71399 | −0.856994 | − | 0.515327i | \(-0.827670\pi\) | ||||
−0.856994 | + | 0.515327i | \(0.827670\pi\) | |||||||
\(798\) | 0.503522 | 0.0178245 | ||||||||
\(799\) | 6.45818 | 0.228474 | ||||||||
\(800\) | −63.6306 | −2.24968 | ||||||||
\(801\) | −9.93837 | −0.351155 | ||||||||
\(802\) | −22.7394 | −0.802957 | ||||||||
\(803\) | 0.204120 | 0.00720322 | ||||||||
\(804\) | −8.87305 | −0.312928 | ||||||||
\(805\) | 8.67913 | 0.305899 | ||||||||
\(806\) | −22.2848 | −0.784949 | ||||||||
\(807\) | 6.88448 | 0.242345 | ||||||||
\(808\) | 18.3063 | 0.644014 | ||||||||
\(809\) | −9.39155 | −0.330189 | −0.165095 | − | 0.986278i | \(-0.552793\pi\) | ||||
−0.165095 | + | 0.986278i | \(0.552793\pi\) | |||||||
\(810\) | −2.42291 | −0.0851325 | ||||||||
\(811\) | 9.09656 | 0.319423 | 0.159712 | − | 0.987164i | \(-0.448944\pi\) | ||||
0.159712 | + | 0.987164i | \(0.448944\pi\) | |||||||
\(812\) | 11.7515 | 0.412398 | ||||||||
\(813\) | −12.8477 | −0.450589 | ||||||||
\(814\) | −0.227623 | −0.00797817 | ||||||||
\(815\) | −58.1157 | −2.03571 | ||||||||
\(816\) | −6.54943 | −0.229276 | ||||||||
\(817\) | 3.39090 | 0.118633 | ||||||||
\(818\) | −17.4255 | −0.609267 | ||||||||
\(819\) | −5.73847 | −0.200518 | ||||||||
\(820\) | −72.9844 | −2.54872 | ||||||||
\(821\) | −8.81763 | −0.307737 | −0.153869 | − | 0.988091i | \(-0.549173\pi\) | ||||
−0.153869 | + | 0.988091i | \(0.549173\pi\) | |||||||
\(822\) | −4.34177 | −0.151437 | ||||||||
\(823\) | 42.8775 | 1.49462 | 0.747308 | − | 0.664477i | \(-0.231346\pi\) | ||||
0.747308 | + | 0.664477i | \(0.231346\pi\) | |||||||
\(824\) | −18.3050 | −0.637685 | ||||||||
\(825\) | 0.421266 | 0.0146666 | ||||||||
\(826\) | −1.62278 | −0.0564638 | ||||||||
\(827\) | 9.82786 | 0.341748 | 0.170874 | − | 0.985293i | \(-0.445341\pi\) | ||||
0.170874 | + | 0.985293i | \(0.445341\pi\) | |||||||
\(828\) | 3.51347 | 0.122101 | ||||||||
\(829\) | −2.90732 | −0.100975 | −0.0504876 | − | 0.998725i | \(-0.516078\pi\) | ||||
−0.0504876 | + | 0.998725i | \(0.516078\pi\) | |||||||
\(830\) | −29.2006 | −1.01357 | ||||||||
\(831\) | 5.36962 | 0.186270 | ||||||||
\(832\) | −3.90039 | −0.135222 | ||||||||
\(833\) | 3.28922 | 0.113965 | ||||||||
\(834\) | −7.45823 | −0.258257 | ||||||||
\(835\) | 34.5371 | 1.19520 | ||||||||
\(836\) | −0.0508570 | −0.00175892 | ||||||||
\(837\) | −6.50937 | −0.224997 | ||||||||
\(838\) | 1.08621 | 0.0375226 | ||||||||
\(839\) | −2.75261 | −0.0950308 | −0.0475154 | − | 0.998871i | \(-0.515130\pi\) | ||||
−0.0475154 | + | 0.998871i | \(0.515130\pi\) | |||||||
\(840\) | 8.82930 | 0.304640 | ||||||||
\(841\) | 22.0906 | 0.761743 | ||||||||
\(842\) | −3.46275 | −0.119334 | ||||||||
\(843\) | 10.8067 | 0.372202 | ||||||||
\(844\) | −14.5852 | −0.502044 | ||||||||
\(845\) | 80.9417 | 2.78448 | ||||||||
\(846\) | −1.17136 | −0.0402722 | ||||||||
\(847\) | 10.9987 | 0.377918 | ||||||||
\(848\) | 22.3970 | 0.769118 | ||||||||
\(849\) | −8.30846 | −0.285146 | ||||||||
\(850\) | −22.5550 | −0.773629 | ||||||||
\(851\) | 22.2470 | 0.762618 | ||||||||
\(852\) | −18.8466 | −0.645675 | ||||||||
\(853\) | −35.9223 | −1.22996 | −0.614979 | − | 0.788544i | \(-0.710835\pi\) | ||||
−0.614979 | + | 0.788544i | \(0.710835\pi\) | |||||||
\(854\) | −3.12748 | −0.107020 | ||||||||
\(855\) | −3.42775 | −0.117227 | ||||||||
\(856\) | −7.67288 | −0.262254 | ||||||||
\(857\) | −17.6768 | −0.603828 | −0.301914 | − | 0.953335i | \(-0.597625\pi\) | ||||
−0.301914 | + | 0.953335i | \(0.597625\pi\) | |||||||
\(858\) | −0.125473 | −0.00428359 | ||||||||
\(859\) | −4.86891 | −0.166125 | −0.0830625 | − | 0.996544i | \(-0.526470\pi\) | ||||
−0.0830625 | + | 0.996544i | \(0.526470\pi\) | |||||||
\(860\) | 26.8262 | 0.914765 | ||||||||
\(861\) | 10.9305 | 0.372512 | ||||||||
\(862\) | 2.95521 | 0.100655 | ||||||||
\(863\) | 52.0150 | 1.77061 | 0.885305 | − | 0.465011i | \(-0.153950\pi\) | ||||
0.885305 | + | 0.465011i | \(0.153950\pi\) | |||||||
\(864\) | 5.53594 | 0.188336 | ||||||||
\(865\) | 36.3373 | 1.23550 | ||||||||
\(866\) | −15.5826 | −0.529517 | ||||||||
\(867\) | 6.18102 | 0.209919 | ||||||||
\(868\) | 10.7020 | 0.363248 | ||||||||
\(869\) | −0.120383 | −0.00408371 | ||||||||
\(870\) | 17.3184 | 0.587150 | ||||||||
\(871\) | −30.9703 | −1.04939 | ||||||||
\(872\) | −9.65012 | −0.326794 | ||||||||
\(873\) | 12.7465 | 0.431405 | ||||||||
\(874\) | −1.07605 | −0.0363978 | ||||||||
\(875\) | −26.3745 | −0.891620 | ||||||||
\(876\) | −9.15645 | −0.309368 | ||||||||
\(877\) | 6.39599 | 0.215977 | 0.107989 | − | 0.994152i | \(-0.465559\pi\) | ||||
0.107989 | + | 0.994152i | \(0.465559\pi\) | |||||||
\(878\) | −13.8823 | −0.468503 | ||||||||
\(879\) | −30.6949 | −1.03531 | ||||||||
\(880\) | −0.296385 | −0.00999114 | ||||||||
\(881\) | 44.6292 | 1.50359 | 0.751797 | − | 0.659394i | \(-0.229187\pi\) | ||||
0.751797 | + | 0.659394i | \(0.229187\pi\) | |||||||
\(882\) | −0.596587 | −0.0200881 | ||||||||
\(883\) | −2.45544 | −0.0826320 | −0.0413160 | − | 0.999146i | \(-0.513155\pi\) | ||||
−0.0413160 | + | 0.999146i | \(0.513155\pi\) | |||||||
\(884\) | −31.0322 | −1.04373 | ||||||||
\(885\) | 11.0472 | 0.371347 | ||||||||
\(886\) | −5.96424 | −0.200373 | ||||||||
\(887\) | −7.52473 | −0.252656 | −0.126328 | − | 0.991989i | \(-0.540319\pi\) | ||||
−0.126328 | + | 0.991989i | \(0.540319\pi\) | |||||||
\(888\) | 22.6320 | 0.759479 | ||||||||
\(889\) | −1.64452 | −0.0551555 | ||||||||
\(890\) | 24.0798 | 0.807157 | ||||||||
\(891\) | −0.0366506 | −0.00122784 | ||||||||
\(892\) | −6.72542 | −0.225184 | ||||||||
\(893\) | −1.65715 | −0.0554544 | ||||||||
\(894\) | −10.3830 | −0.347259 | ||||||||
\(895\) | 63.6590 | 2.12789 | ||||||||
\(896\) | −11.4774 | −0.383432 | ||||||||
\(897\) | 12.2633 | 0.409460 | ||||||||
\(898\) | 13.0380 | 0.435084 | ||||||||
\(899\) | 46.5275 | 1.55178 | ||||||||
\(900\) | −18.8973 | −0.629909 | ||||||||
\(901\) | 36.9976 | 1.23257 | ||||||||
\(902\) | 0.238999 | 0.00795781 | ||||||||
\(903\) | −4.01763 | −0.133698 | ||||||||
\(904\) | −29.1882 | −0.970787 | ||||||||
\(905\) | 95.4129 | 3.17163 | ||||||||
\(906\) | −7.54980 | −0.250825 | ||||||||
\(907\) | 27.8467 | 0.924636 | 0.462318 | − | 0.886714i | \(-0.347018\pi\) | ||||
0.462318 | + | 0.886714i | \(0.347018\pi\) | |||||||
\(908\) | 18.5148 | 0.614436 | ||||||||
\(909\) | 8.42052 | 0.279291 | ||||||||
\(910\) | 13.9038 | 0.460907 | ||||||||
\(911\) | −30.2050 | −1.00074 | −0.500369 | − | 0.865812i | \(-0.666802\pi\) | ||||
−0.500369 | + | 0.865812i | \(0.666802\pi\) | |||||||
\(912\) | 1.68057 | 0.0556491 | ||||||||
\(913\) | −0.441707 | −0.0146184 | ||||||||
\(914\) | −6.04788 | −0.200046 | ||||||||
\(915\) | 21.2905 | 0.703842 | ||||||||
\(916\) | 22.7831 | 0.752774 | ||||||||
\(917\) | −20.1631 | −0.665845 | ||||||||
\(918\) | 1.96231 | 0.0647658 | ||||||||
\(919\) | −1.03564 | −0.0341627 | −0.0170813 | − | 0.999854i | \(-0.505437\pi\) | ||||
−0.0170813 | + | 0.999854i | \(0.505437\pi\) | |||||||
\(920\) | −18.8685 | −0.622077 | ||||||||
\(921\) | −29.7647 | −0.980781 | ||||||||
\(922\) | −16.0162 | −0.527466 | ||||||||
\(923\) | −65.7818 | −2.16523 | ||||||||
\(924\) | 0.0602567 | 0.00198230 | ||||||||
\(925\) | −119.656 | −3.93427 | ||||||||
\(926\) | 13.6260 | 0.447779 | ||||||||
\(927\) | −8.41991 | −0.276546 | ||||||||
\(928\) | −39.5696 | −1.29894 | ||||||||
\(929\) | −4.20876 | −0.138085 | −0.0690424 | − | 0.997614i | \(-0.521994\pi\) | ||||
−0.0690424 | + | 0.997614i | \(0.521994\pi\) | |||||||
\(930\) | 15.7717 | 0.517173 | ||||||||
\(931\) | −0.844005 | −0.0276611 | ||||||||
\(932\) | 4.29577 | 0.140713 | ||||||||
\(933\) | 8.78746 | 0.287689 | ||||||||
\(934\) | −1.69262 | −0.0553842 | ||||||||
\(935\) | −0.489597 | −0.0160115 | ||||||||
\(936\) | 12.4755 | 0.407775 | ||||||||
\(937\) | −47.6812 | −1.55768 | −0.778838 | − | 0.627225i | \(-0.784190\pi\) | ||||
−0.778838 | + | 0.627225i | \(0.784190\pi\) | |||||||
\(938\) | −3.21975 | −0.105129 | ||||||||
\(939\) | −23.8210 | −0.777370 | ||||||||
\(940\) | −13.1101 | −0.427604 | ||||||||
\(941\) | 10.4356 | 0.340191 | 0.170096 | − | 0.985428i | \(-0.445592\pi\) | ||||
0.170096 | + | 0.985428i | \(0.445592\pi\) | |||||||
\(942\) | −4.98668 | −0.162475 | ||||||||
\(943\) | −23.3589 | −0.760672 | ||||||||
\(944\) | −5.41623 | −0.176283 | ||||||||
\(945\) | 4.06129 | 0.132114 | ||||||||
\(946\) | −0.0878467 | −0.00285614 | ||||||||
\(947\) | 36.3005 | 1.17961 | 0.589803 | − | 0.807547i | \(-0.299205\pi\) | ||||
0.589803 | + | 0.807547i | \(0.299205\pi\) | |||||||
\(948\) | 5.40017 | 0.175389 | ||||||||
\(949\) | −31.9594 | −1.03745 | ||||||||
\(950\) | 5.78754 | 0.187772 | ||||||||
\(951\) | 11.5055 | 0.373092 | ||||||||
\(952\) | −7.15081 | −0.231759 | ||||||||
\(953\) | 37.0334 | 1.19963 | 0.599815 | − | 0.800138i | \(-0.295241\pi\) | ||||
0.599815 | + | 0.800138i | \(0.295241\pi\) | |||||||
\(954\) | −6.71048 | −0.217260 | ||||||||
\(955\) | 4.06129 | 0.131420 | ||||||||
\(956\) | −3.93883 | −0.127391 | ||||||||
\(957\) | 0.261970 | 0.00846829 | ||||||||
\(958\) | 4.08947 | 0.132125 | ||||||||
\(959\) | 7.27768 | 0.235009 | ||||||||
\(960\) | 2.76043 | 0.0890925 | ||||||||
\(961\) | 11.3720 | 0.366837 | ||||||||
\(962\) | 35.6394 | 1.14906 | ||||||||
\(963\) | −3.52936 | −0.113732 | ||||||||
\(964\) | −1.79424 | −0.0577887 | ||||||||
\(965\) | 54.8502 | 1.76569 | ||||||||
\(966\) | 1.27493 | 0.0410201 | ||||||||
\(967\) | −41.1212 | −1.32237 | −0.661185 | − | 0.750223i | \(-0.729946\pi\) | ||||
−0.661185 | + | 0.750223i | \(0.729946\pi\) | |||||||
\(968\) | −23.9112 | −0.768536 | ||||||||
\(969\) | 2.77612 | 0.0891818 | ||||||||
\(970\) | −30.8838 | −0.991619 | ||||||||
\(971\) | −27.8410 | −0.893460 | −0.446730 | − | 0.894669i | \(-0.647411\pi\) | ||||
−0.446730 | + | 0.894669i | \(0.647411\pi\) | |||||||
\(972\) | 1.64408 | 0.0527340 | ||||||||
\(973\) | 12.5015 | 0.400780 | ||||||||
\(974\) | −18.5294 | −0.593720 | ||||||||
\(975\) | −65.9586 | −2.11236 | ||||||||
\(976\) | −10.4384 | −0.334123 | ||||||||
\(977\) | 31.0538 | 0.993499 | 0.496750 | − | 0.867894i | \(-0.334527\pi\) | ||||
0.496750 | + | 0.867894i | \(0.334527\pi\) | |||||||
\(978\) | −8.53696 | −0.272982 | ||||||||
\(979\) | 0.364248 | 0.0116414 | ||||||||
\(980\) | −6.67711 | −0.213292 | ||||||||
\(981\) | −4.43885 | −0.141722 | ||||||||
\(982\) | 0.981295 | 0.0313144 | ||||||||
\(983\) | −16.0732 | −0.512655 | −0.256327 | − | 0.966590i | \(-0.582513\pi\) | ||||
−0.256327 | + | 0.966590i | \(0.582513\pi\) | |||||||
\(984\) | −23.7631 | −0.757541 | ||||||||
\(985\) | −31.7767 | −1.01249 | ||||||||
\(986\) | −14.0261 | −0.446682 | ||||||||
\(987\) | 1.96344 | 0.0624969 | ||||||||
\(988\) | 7.96279 | 0.253330 | ||||||||
\(989\) | 8.58583 | 0.273013 | ||||||||
\(990\) | 0.0888014 | 0.00282229 | ||||||||
\(991\) | −35.6406 | −1.13216 | −0.566080 | − | 0.824350i | \(-0.691541\pi\) | ||||
−0.566080 | + | 0.824350i | \(0.691541\pi\) | |||||||
\(992\) | −36.0355 | −1.14413 | ||||||||
\(993\) | 33.5885 | 1.06590 | ||||||||
\(994\) | −6.83885 | −0.216915 | ||||||||
\(995\) | 101.322 | 3.21212 | ||||||||
\(996\) | 19.8142 | 0.627838 | ||||||||
\(997\) | 28.8499 | 0.913684 | 0.456842 | − | 0.889548i | \(-0.348980\pi\) | ||||
0.456842 | + | 0.889548i | \(0.348980\pi\) | |||||||
\(998\) | 20.1139 | 0.636696 | ||||||||
\(999\) | 10.4102 | 0.329365 |
(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 | 4011.2.a.j.1.12 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.j.1.12 | ✓ | 26 | 1.1 | even | 1 | trivial |