Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, 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("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-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 | ||||||||
\(3\) | −1.68125 | −0.970668 | −0.485334 | − | 0.874329i | \(-0.661302\pi\) | ||||
−0.485334 | + | 0.874329i | \(0.661302\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.32036 | −1.48491 | −0.742456 | − | 0.669895i | \(-0.766339\pi\) | ||||
−0.742456 | + | 0.669895i | \(0.766339\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.49635 | 1.32150 | 0.660749 | − | 0.750607i | \(-0.270239\pi\) | ||||
0.660749 | + | 0.750607i | \(0.270239\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.173410 | −0.0578034 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.26661 | 0.381896 | 0.190948 | − | 0.981600i | \(-0.438844\pi\) | ||||
0.190948 | + | 0.981600i | \(0.438844\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.98312 | −0.550018 | −0.275009 | − | 0.961442i | \(-0.588681\pi\) | ||||
−0.275009 | + | 0.961442i | \(0.588681\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.58235 | 1.44136 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.03307 | −0.250556 | −0.125278 | − | 0.992122i | \(-0.539982\pi\) | ||||
−0.125278 | + | 0.992122i | \(0.539982\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.87823 | −1.28274 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.45830 | −1.34665 | −0.673325 | − | 0.739347i | \(-0.735134\pi\) | ||||
−0.673325 | + | 0.739347i | \(0.735134\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.02481 | 1.20496 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.33528 | 1.02678 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.24328 | 0.973653 | 0.486826 | − | 0.873499i | \(-0.338154\pi\) | ||||
0.486826 | + | 0.873499i | \(0.338154\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.427070 | −0.0767041 | −0.0383520 | − | 0.999264i | \(-0.512211\pi\) | ||||
−0.0383520 | + | 0.999264i | \(0.512211\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.12948 | −0.370694 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.6092 | −1.96231 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.20179 | 1.34837 | 0.674183 | − | 0.738564i | \(-0.264496\pi\) | ||||
0.674183 | + | 0.738564i | \(0.264496\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.33411 | 0.533885 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.4681 | −1.94719 | −0.973593 | − | 0.228289i | \(-0.926687\pi\) | ||||
−0.973593 | + | 0.228289i | \(0.926687\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.70973 | −0.718227 | −0.359114 | − | 0.933294i | \(-0.616921\pi\) | ||||
−0.359114 | + | 0.933294i | \(0.616921\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.575785 | 0.0858330 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.04823 | 1.31982 | 0.659910 | − | 0.751345i | \(-0.270594\pi\) | ||||
0.659910 | + | 0.751345i | \(0.270594\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.22450 | 0.746357 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.73684 | 0.243206 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.909060 | 0.124869 | 0.0624345 | − | 0.998049i | \(-0.480114\pi\) | ||||
0.0624345 | + | 0.998049i | \(0.480114\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.20559 | −0.567082 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.68125 | −0.222687 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.3555 | −1.34818 | −0.674088 | − | 0.738651i | \(-0.735463\pi\) | ||||
−0.674088 | + | 0.738651i | \(0.735463\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.1296 | 1.93714 | 0.968572 | − | 0.248732i | \(-0.0800139\pi\) | ||||
0.968572 | + | 0.248732i | \(0.0800139\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.606304 | −0.0763871 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.58467 | 0.816728 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.76031 | −0.459395 | −0.229698 | − | 0.973262i | \(-0.573774\pi\) | ||||
−0.229698 | + | 0.973262i | \(0.573774\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.8580 | 1.30715 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.33012 | 0.632569 | 0.316284 | − | 0.948664i | \(-0.397565\pi\) | ||||
0.316284 | + | 0.948664i | \(0.397565\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.75154 | 0.673167 | 0.336584 | − | 0.941654i | \(-0.390729\pi\) | ||||
0.336584 | + | 0.941654i | \(0.390729\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.1292 | −1.16962 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.42851 | 0.504675 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.44970 | −0.938855 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.11305 | −0.890523 | −0.445261 | − | 0.895401i | \(-0.646889\pi\) | ||||
−0.445261 | + | 0.895401i | \(0.646889\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.43016 | 0.372053 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.81525 | −0.945094 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.12521 | −0.225271 | −0.112636 | − | 0.993636i | \(-0.535929\pi\) | ||||
−0.112636 | + | 0.993636i | \(0.535929\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.93369 | −0.726848 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.718010 | 0.0744542 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.32036 | −0.340662 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.4726 | 1.46947 | 0.734734 | − | 0.678355i | \(-0.237307\pi\) | ||||
0.734734 | + | 0.678355i | \(0.237307\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.219643 | −0.0220749 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.5493 | 1.84572 | 0.922861 | − | 0.385134i | \(-0.125845\pi\) | ||||
0.922861 | + | 0.385134i | \(0.125845\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.132652 | −0.0130706 | −0.00653528 | − | 0.999979i | \(-0.502080\pi\) | ||||
−0.00653528 | + | 0.999979i | \(0.502080\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 19.5179 | 1.90475 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.807610 | −0.0780746 | −0.0390373 | − | 0.999238i | \(-0.512429\pi\) | ||||
−0.0390373 | + | 0.999238i | \(0.512429\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.29642 | 0.411522 | 0.205761 | − | 0.978602i | \(-0.434033\pi\) | ||||
0.205761 | + | 0.978602i | \(0.434033\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.7892 | −1.30882 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.2214 | −1.43191 | −0.715956 | − | 0.698145i | \(-0.754009\pi\) | ||||
−0.715956 | + | 0.698145i | \(0.754009\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21.4439 | 1.99965 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.343893 | 0.0317930 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.61197 | −0.331109 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.39571 | −0.854155 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.9619 | 1.89007 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.40273 | −0.304350 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.371561 | 0.0329707 | 0.0164853 | − | 0.999864i | \(-0.494752\pi\) | ||||
0.0164853 | + | 0.999864i | \(0.494752\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.91822 | 0.697160 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.99094 | 0.436060 | 0.218030 | − | 0.975942i | \(-0.430037\pi\) | ||||
0.218030 | + | 0.975942i | \(0.430037\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.49635 | 0.303172 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.7151 | −1.52467 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.2861 | −1.04967 | −0.524837 | − | 0.851203i | \(-0.675874\pi\) | ||||
−0.524837 | + | 0.851203i | \(0.675874\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.3930 | 0.881520 | 0.440760 | − | 0.897625i | \(-0.354709\pi\) | ||||
0.440760 | + | 0.897625i | \(0.354709\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.2123 | −1.28111 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.51183 | −0.210050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.4096 | −1.44579 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.78367 | −0.724465 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.52981 | 0.453020 | 0.226510 | − | 0.974009i | \(-0.427268\pi\) | ||||
0.226510 | + | 0.974009i | \(0.427268\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.05849 | −0.167517 | −0.0837586 | − | 0.996486i | \(-0.526692\pi\) | ||||
−0.0837586 | + | 0.996486i | \(0.526692\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.179145 | 0.0144830 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.41803 | 0.113899 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.42056 | −0.352799 | −0.176400 | − | 0.984319i | \(-0.556445\pi\) | ||||
−0.176400 | + | 0.984319i | \(0.556445\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.52835 | −0.121206 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.5805 | −1.77959 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.01264 | −0.392620 | −0.196310 | − | 0.980542i | \(-0.562896\pi\) | ||||
−0.196310 | + | 0.980542i | \(0.562896\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.07064 | 0.550448 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.8475 | 1.84538 | 0.922689 | − | 0.385544i | \(-0.125986\pi\) | ||||
0.922689 | + | 0.385544i | \(0.125986\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.06724 | −0.697480 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.173410 | −0.0132610 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.06203 | −0.612945 | −0.306472 | − | 0.951880i | \(-0.599149\pi\) | ||||
−0.306472 | + | 0.951880i | \(0.599149\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.0649 | 1.59235 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.4102 | 1.30863 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.39075 | −0.253436 | −0.126718 | − | 0.991939i | \(-0.540444\pi\) | ||||
−0.126718 | + | 0.991939i | \(0.540444\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.58804 | 0.415356 | 0.207678 | − | 0.978197i | \(-0.433409\pi\) | ||||
0.207678 | + | 0.978197i | \(0.433409\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −25.4366 | −1.88032 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −27.2329 | −2.00220 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.30849 | −0.0956863 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.6540 | 1.35688 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.7560 | −1.06770 | −0.533852 | − | 0.845578i | \(-0.679256\pi\) | ||||
−0.533852 | + | 0.845578i | \(0.679256\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.77834 | −0.559897 | −0.279949 | − | 0.960015i | \(-0.590317\pi\) | ||||
−0.279949 | + | 0.960015i | \(0.590317\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.0705 | −0.792772 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.6711 | −1.04527 | −0.522636 | − | 0.852556i | \(-0.675051\pi\) | ||||
−0.522636 | + | 0.852556i | \(0.675051\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.33881 | 0.165794 | 0.0828969 | − | 0.996558i | \(-0.473583\pi\) | ||||
0.0828969 | + | 0.996558i | \(0.473583\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.32201 | 0.445920 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.3324 | 1.28668 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 41.3985 | 2.89140 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.11994 | 0.0778410 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.26661 | 0.0876130 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.5048 | 1.34277 | 0.671384 | − | 0.741110i | \(-0.265700\pi\) | ||||
0.671384 | + | 0.741110i | \(0.265700\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.96125 | −0.614014 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.6380 | 1.06650 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.49319 | −0.101364 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.66976 | −0.653422 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.04870 | 0.137810 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.8667 | −1.59823 | −0.799116 | − | 0.601177i | \(-0.794699\pi\) | ||||
−0.799116 | + | 0.601177i | \(0.794699\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.04476 | −0.0696509 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.8376 | 1.31666 | 0.658332 | − | 0.752727i | \(-0.271262\pi\) | ||||
0.658332 | + | 0.752727i | \(0.271262\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.8457 | −0.914949 | −0.457474 | − | 0.889223i | \(-0.651246\pi\) | ||||
−0.457474 | + | 0.889223i | \(0.651246\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.44541 | −0.489872 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.6041 | 1.34982 | 0.674911 | − | 0.737899i | \(-0.264182\pi\) | ||||
0.674911 | + | 0.737899i | \(0.264182\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.0434 | −1.95982 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.68125 | 0.109209 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.1289 | −1.49608 | −0.748042 | − | 0.663651i | \(-0.769006\pi\) | ||||
−0.748042 | + | 0.663651i | \(0.769006\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.9271 | −1.28362 | −0.641810 | − | 0.766863i | \(-0.721816\pi\) | ||||
−0.641810 | + | 0.766863i | \(0.721816\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.79983 | −0.115459 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.3472 | −1.10827 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.98312 | −0.126183 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.6400 | 0.864402 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.8450 | −1.69444 | −0.847220 | − | 0.531242i | \(-0.821725\pi\) | ||||
−0.847220 | + | 0.531242i | \(0.821725\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.18013 | −0.514280 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.76694 | −0.361140 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.7548 | 1.16989 | 0.584946 | − | 0.811072i | \(-0.301116\pi\) | ||||
0.584946 | + | 0.811072i | \(0.301116\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.6764 | 1.78186 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.909239 | −0.0562805 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.4425 | −1.32220 | −0.661101 | − | 0.750297i | \(-0.729910\pi\) | ||||
−0.661101 | + | 0.750297i | \(0.729910\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.01841 | −0.185419 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.57299 | 0.218664 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.0706 | −1.58955 | −0.794776 | − | 0.606903i | \(-0.792412\pi\) | ||||
−0.794776 | + | 0.606903i | \(0.792412\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.8688 | −0.842470 | −0.421235 | − | 0.906952i | \(-0.638403\pi\) | ||||
−0.421235 | + | 0.906952i | \(0.638403\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.6572 | 0.705528 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.63106 | 0.460170 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.24715 | −0.435439 | −0.217719 | − | 0.976011i | \(-0.569862\pi\) | ||||
−0.217719 | + | 0.976011i | \(0.569862\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.0740584 | 0.00443376 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.8410 | −0.944993 | −0.472496 | − | 0.881333i | \(-0.656647\pi\) | ||||
−0.472496 | + | 0.881333i | \(0.656647\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.3513 | −1.09087 | −0.545436 | − | 0.838153i | \(-0.683636\pi\) | ||||
−0.545436 | + | 0.838153i | \(0.683636\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.58235 | 0.330670 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −43.5928 | −2.57320 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9328 | −0.937222 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.3320 | −1.42637 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.0088 | −0.643143 | −0.321572 | − | 0.946885i | \(-0.604211\pi\) | ||||
−0.321572 | + | 0.946885i | \(0.604211\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34.3841 | 2.00192 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.75771 | 0.392122 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.8076 | 0.740682 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.4669 | −0.949136 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −31.1859 | −1.79158 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −50.2357 | −2.87649 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0621 | 1.14500 | 0.572502 | − | 0.819903i | \(-0.305973\pi\) | ||||
0.572502 | + | 0.819903i | \(0.305973\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.223020 | 0.0126872 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.1654 | 1.82393 | 0.911965 | − | 0.410268i | \(-0.134565\pi\) | ||||
0.911965 | + | 0.410268i | \(0.134565\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.4898 | −1.44077 | −0.720385 | − | 0.693574i | \(-0.756035\pi\) | ||||
−0.720385 | + | 0.693574i | \(0.756035\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.01315 | 0.113428 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.3911 | −1.03295 | −0.516475 | − | 0.856302i | \(-0.672756\pi\) | ||||
−0.516475 | + | 0.856302i | \(0.672756\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.64117 | 0.371834 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.35779 | 0.0757846 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.03307 | −0.0574814 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.9479 | −0.662751 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.22334 | −0.399452 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 31.6358 | 1.74414 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.1213 | −1.54569 | −0.772844 | − | 0.634596i | \(-0.781166\pi\) | ||||
−0.772844 | + | 0.634596i | \(0.781166\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.42228 | −0.0779402 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.4856 | 0.682161 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.794119 | 0.0432584 | 0.0216292 | − | 0.999766i | \(-0.493115\pi\) | ||||
0.0216292 | + | 0.999766i | \(0.493115\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 25.5910 | 1.38991 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.540930 | −0.0292930 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.20779 | −0.335189 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −36.0525 | −1.94100 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.7652 | 0.792635 | 0.396317 | − | 0.918114i | \(-0.370288\pi\) | ||||
0.396317 | + | 0.918114i | \(0.370288\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.21238 | 0.386070 | 0.193035 | − | 0.981192i | \(-0.438167\pi\) | ||||
0.193035 | + | 0.981192i | \(0.438167\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.5805 | −0.564746 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.3047 | 1.29361 | 0.646804 | − | 0.762656i | \(-0.276105\pi\) | ||||
0.646804 | + | 0.762656i | \(0.276105\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.6979 | −0.939309 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.07261 | 0.321397 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.46627 | 0.0773870 | 0.0386935 | − | 0.999251i | \(-0.487680\pi\) | ||||
0.0386935 | + | 0.999251i | \(0.487680\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.7965 | 0.829101 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.0972 | −0.999593 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.999961 | 0.0521975 | 0.0260988 | − | 0.999659i | \(-0.491692\pi\) | ||||
0.0260988 | + | 0.999659i | \(0.491692\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.16209 | 0.112554 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.17840 | 0.165014 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.61737 | −0.497968 | −0.248984 | − | 0.968508i | \(-0.580097\pi\) | ||||
−0.248984 | + | 0.968508i | \(0.580097\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.72083 | 0.295422 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.3980 | −0.535527 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.63781 | −0.0841289 | −0.0420645 | − | 0.999115i | \(-0.513393\pi\) | ||||
−0.0420645 | + | 0.999115i | \(0.513393\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.624685 | −0.0320036 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.0318 | −1.58565 | −0.792825 | − | 0.609449i | \(-0.791391\pi\) | ||||
−0.792825 | + | 0.609449i | \(0.791391\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.7042 | −0.749398 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.816716 | 0.0415160 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.5350 | −1.24398 | −0.621988 | − | 0.783027i | \(-0.713675\pi\) | ||||
−0.621988 | + | 0.783027i | \(0.713675\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.67186 | 0.337411 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.39100 | −0.423270 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.32036 | 0.167066 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.9648 | −0.901627 | −0.450813 | − | 0.892618i | \(-0.648866\pi\) | ||||
−0.450813 | + | 0.892618i | \(0.648866\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.87823 | −0.294280 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.2471 | −1.66028 | −0.830140 | − | 0.557555i | \(-0.811740\pi\) | ||||
−0.830140 | + | 0.557555i | \(0.811740\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.846931 | 0.0421886 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 28.0561 | 1.39412 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.3884 | 0.514936 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.24436 | −0.407657 | −0.203829 | − | 0.979007i | \(-0.565339\pi\) | ||||
−0.203829 | + | 0.979007i | \(0.565339\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.6560 | 1.01888 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −36.2066 | −1.78161 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.9383 | 1.32235 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.4731 | −0.855663 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.3445 | −0.603068 | −0.301534 | − | 0.953455i | \(-0.597499\pi\) | ||||
−0.301534 | + | 0.953455i | \(0.597499\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.8527 | −1.06504 | −0.532518 | − | 0.846419i | \(-0.678754\pi\) | ||||
−0.532518 | + | 0.846419i | \(0.678754\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.56906 | −0.0762901 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.22403 | −0.301910 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 52.8984 | 2.55993 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.22301 | 0.203889 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.0252 | −1.39809 | −0.699047 | − | 0.715076i | \(-0.746392\pi\) | ||||
−0.699047 | + | 0.715076i | \(0.746392\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.2078 | 1.30753 | 0.653763 | − | 0.756700i | \(-0.273190\pi\) | ||||
0.653763 | + | 0.756700i | \(0.273190\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 29.2698 | 1.40338 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.45830 | −0.308943 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.5741 | −1.26831 | −0.634156 | − | 0.773206i | \(-0.718652\pi\) | ||||
−0.634156 | + | 0.773206i | \(0.718652\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.905982 | −0.0431420 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.8090 | 1.46378 | 0.731890 | − | 0.681423i | \(-0.238638\pi\) | ||||
0.731890 | + | 0.681423i | \(0.238638\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.05645 | 0.334508 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.29698 | −0.439732 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.9251 | 0.515587 | 0.257793 | − | 0.966200i | \(-0.417005\pi\) | ||||
0.257793 | + | 0.966200i | \(0.417005\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.7922 | −0.743623 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.46082 | 0.162604 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.0224 | 1.07930 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.3313 | 0.670388 | 0.335194 | − | 0.942149i | \(-0.391198\pi\) | ||||
0.335194 | + | 0.942149i | \(0.391198\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.51171 | −0.257265 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.6189 | 1.14661 | 0.573307 | − | 0.819340i | \(-0.305660\pi\) | ||||
0.573307 | + | 0.819340i | \(0.305660\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.6334 | −0.773020 | −0.386510 | − | 0.922285i | \(-0.626320\pi\) | ||||
−0.386510 | + | 0.922285i | \(0.626320\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.38405 | −0.110558 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.8559 | −1.47412 | −0.737059 | − | 0.675829i | \(-0.763786\pi\) | ||||
−0.737059 | + | 0.675829i | \(0.763786\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.1474 | −0.607090 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.43206 | 0.342451 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.96538 | −0.274288 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.02481 | 0.276437 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.157640 | −0.00721786 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.7382 | 0.490643 | 0.245321 | − | 0.969442i | \(-0.421106\pi\) | ||||
0.245321 | + | 0.969442i | \(0.421106\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.2651 | −0.741626 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 37.9634 | 1.72740 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −48.0542 | −2.18203 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.9175 | 0.540035 | 0.270018 | − | 0.962855i | \(-0.412970\pi\) | ||||
0.270018 | + | 0.962855i | \(0.412970\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.42748 | 0.381104 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.7813 | 1.43427 | 0.717134 | − | 0.696935i | \(-0.245454\pi\) | ||||
0.717134 | + | 0.696935i | \(0.245454\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.41666 | −0.243954 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.729293 | 0.0327793 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.6360 | 0.835938 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.8203 | 0.618681 | 0.309341 | − | 0.950951i | \(-0.399892\pi\) | ||||
0.309341 | + | 0.950951i | \(0.399892\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −40.0936 | −1.79125 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.7226 | −1.01315 | −0.506575 | − | 0.862196i | \(-0.669089\pi\) | ||||
−0.506575 | + | 0.862196i | \(0.669089\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −61.5903 | −2.74073 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.2443 | 0.677021 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.6081 | 0.824789 | 0.412395 | − | 0.911005i | \(-0.364692\pi\) | ||||
0.412395 | + | 0.911005i | \(0.364692\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.1094 | 0.889589 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.33528 | 0.235559 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.440452 | 0.0194086 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.4605 | 0.504034 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.5543 | 0.594966 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.63400 | 0.246830 | 0.123415 | − | 0.992355i | \(-0.460615\pi\) | ||||
0.123415 | + | 0.992355i | \(0.460615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.0347 | −0.569969 | −0.284985 | − | 0.958532i | \(-0.591989\pi\) | ||||
−0.284985 | + | 0.958532i | \(0.591989\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −35.4152 | −1.54565 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.441192 | 0.0192186 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.7097 | 0.813464 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.79576 | 0.0779292 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.7257 | 1.07099 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.68156 | 0.115934 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.70068 | 0.246003 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.61738 | 0.285031 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.0611 | 0.604535 | 0.302267 | − | 0.953223i | \(-0.402256\pi\) | ||||
0.302267 | + | 0.953223i | \(0.402256\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.39487 | −0.403173 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.2657 | −0.611074 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.59072 | −0.324556 | −0.162278 | − | 0.986745i | \(-0.551884\pi\) | ||||
−0.162278 | + | 0.986745i | \(0.551884\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.62363 | −0.111974 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.24328 | 0.223371 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.49635 | −0.148680 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 45.7853 | 1.94348 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.3102 | −0.818201 | −0.409100 | − | 0.912489i | \(-0.634157\pi\) | ||||
−0.409100 | + | 0.912489i | \(0.634157\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.33996 | 0.395038 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.19989 | 0.0928796 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.2777 | −0.475299 | −0.237649 | − | 0.971351i | \(-0.576377\pi\) | ||||
−0.237649 | + | 0.971351i | \(0.576377\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 50.5407 | 2.12626 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −29.5431 | −1.24070 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.6778 | 0.615327 | 0.307663 | − | 0.951495i | \(-0.400453\pi\) | ||||
0.307663 | + | 0.951495i | \(0.400453\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.2476 | 0.972883 | 0.486441 | − | 0.873713i | \(-0.338295\pi\) | ||||
0.486441 | + | 0.873713i | \(0.338295\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.8084 | 1.03639 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.9100 | −1.62266 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.79889 | −0.116519 | −0.0582596 | − | 0.998301i | \(-0.518555\pi\) | ||||
−0.0582596 | + | 0.998301i | \(0.518555\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.0773 | 0.543475 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.3661 | −1.17682 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.15142 | 0.0476870 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.14185 | −0.0472097 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.4760 | 1.83572 | 0.917860 | − | 0.396905i | \(-0.129916\pi\) | ||||
0.917860 | + | 0.396905i | \(0.129916\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.427070 | −0.0175971 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.6657 | 1.01461 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.2530 | −1.40660 | −0.703300 | − | 0.710893i | \(-0.748291\pi\) | ||||
−0.703300 | + | 0.710893i | \(0.748291\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.9931 | 0.491667 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.93211 | −0.160931 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −40.6935 | −1.66269 | −0.831346 | − | 0.555755i | \(-0.812429\pi\) | ||||
−0.831346 | + | 0.555755i | \(0.812429\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.4266 | 1.15954 | 0.579772 | − | 0.814778i | \(-0.303141\pi\) | ||||
0.579772 | + | 0.814778i | \(0.303141\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.652077 | 0.0265546 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 31.1972 | 1.26834 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.1611 | −0.534191 | −0.267095 | − | 0.963670i | \(-0.586064\pi\) | ||||
−0.267095 | + | 0.963670i | \(0.586064\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −30.8212 | −1.24894 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.9437 | −0.725925 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.6195 | −0.671257 | −0.335628 | − | 0.941995i | \(-0.608949\pi\) | ||||
−0.335628 | + | 0.941995i | \(0.608949\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −69.6012 | −2.80659 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.4142 | −1.70753 | −0.853765 | − | 0.520658i | \(-0.825687\pi\) | ||||
−0.853765 | + | 0.520658i | \(0.825687\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.6570 | −1.03124 | −0.515622 | − | 0.856816i | \(-0.672439\pi\) | ||||
−0.515622 | + | 0.856816i | \(0.672439\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −34.4569 | −1.38271 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.43047 | −0.297696 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.8257 | −0.753029 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.12948 | −0.0850431 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.47301 | −0.337841 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.9840 | 0.477077 | 0.238538 | − | 0.971133i | \(-0.423332\pi\) | ||||
0.238538 | + | 0.971133i | \(0.423332\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −32.7924 | −1.30338 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.23372 | −0.0489586 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.3608 | −0.410510 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.924298 | −0.0365647 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.7830 | −1.49234 | −0.746170 | − | 0.665756i | \(-0.768109\pi\) | ||||
−0.746170 | + | 0.665756i | \(0.768109\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.0679 | 0.712528 | 0.356264 | − | 0.934385i | \(-0.384050\pi\) | ||||
0.356264 | + | 0.934385i | \(0.384050\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −26.2914 | −1.03522 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.8721 | 0.584681 | 0.292341 | − | 0.956314i | \(-0.405566\pi\) | ||||
0.292341 | + | 0.956314i | \(0.405566\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.1164 | −0.514863 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.51042 | 0.0983911 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.0504 | 0.823766 | 0.411883 | − | 0.911237i | \(-0.364871\pi\) | ||||
0.411883 | + | 0.911237i | \(0.364871\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.5717 | −0.647511 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.997377 | −0.0389114 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.7380 | −0.963657 | −0.481829 | − | 0.876265i | \(-0.660027\pi\) | ||||
−0.481829 | + | 0.876265i | \(0.660027\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.5182 | 1.10923 | 0.554615 | − | 0.832107i | \(-0.312866\pi\) | ||||
0.554615 | + | 0.832107i | \(0.312866\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.44436 | −0.133768 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.6092 | −0.450184 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −33.8627 | −1.31117 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 40.1258 | 1.55135 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.1632 | 0.739788 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.05670 | 0.349110 | 0.174555 | − | 0.984647i | \(-0.444151\pi\) | ||||
0.174555 | + | 0.984647i | \(0.444151\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 32.1441 | 1.23723 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.32881 | −0.166370 | −0.0831848 | − | 0.996534i | \(-0.526509\pi\) | ||||
−0.0831848 | + | 0.996534i | \(0.526509\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 50.6013 | 1.94190 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.3518 | −1.27804 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.08891 | −0.0799299 | −0.0399650 | − | 0.999201i | \(-0.512725\pi\) | ||||
−0.0399650 | + | 0.999201i | \(0.512725\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.7944 | 1.55867 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.2780 | 0.888111 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.80277 | −0.0686802 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.9220 | 0.681785 | 0.340892 | − | 0.940102i | \(-0.389271\pi\) | ||||
0.340892 | + | 0.940102i | \(0.389271\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.767949 | −0.0291720 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34.5084 | −1.30898 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.8804 | 0.487879 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −34.6406 | −1.31023 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.2178 | −1.02800 | −0.514002 | − | 0.857789i | \(-0.671838\pi\) | ||||
−0.514002 | + | 0.857789i | \(0.671838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.20179 | 0.309337 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 50.5104 | 1.90233 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 64.8548 | 2.43912 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.0913 | −0.604321 | −0.302160 | − | 0.953257i | \(-0.597708\pi\) | ||||
−0.302160 | + | 0.953257i | \(0.597708\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.173410 | 0.00650340 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.75815 | 0.103294 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.34019 | 0.311905 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 38.8854 | 1.45220 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.17704 | 0.342246 | 0.171123 | − | 0.985250i | \(-0.445260\pi\) | ||||
0.171123 | + | 0.985250i | \(0.445260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.463797 | −0.0172727 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 33.5024 | 1.24597 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 31.5898 | 1.17321 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.6531 | 1.47065 | 0.735326 | − | 0.677713i | \(-0.237029\pi\) | ||||
0.735326 | + | 0.677713i | \(0.237029\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.3751 | 1.05093 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.86547 | 0.179956 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.2952 | 0.823493 | 0.411746 | − | 0.911298i | \(-0.364919\pi\) | ||||
0.411746 | + | 0.911298i | \(0.364919\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 29.1650 | 1.07577 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.76284 | −0.175441 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.5829 | 0.499656 | 0.249828 | − | 0.968290i | \(-0.419626\pi\) | ||||
0.249828 | + | 0.968290i | \(0.419626\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.33411 | 0.122482 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.05890 | 0.295653 | 0.147826 | − | 0.989013i | \(-0.452772\pi\) | ||||
0.147826 | + | 0.989013i | \(0.452772\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.3610 | −0.672694 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.40689 | 0.0514753 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.82369 | −0.103175 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.5015 | 0.894072 | 0.447036 | − | 0.894516i | \(-0.352480\pi\) | ||||
0.447036 | + | 0.894516i | \(0.352480\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 45.1330 | 1.64474 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.83492 | 0.248748 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.28504 | −0.337471 | −0.168735 | − | 0.985661i | \(-0.553968\pi\) | ||||
−0.168735 | + | 0.985661i | \(0.553968\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.7528 | 0.499195 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.08497 | −0.0393303 | −0.0196651 | − | 0.999807i | \(-0.506260\pi\) | ||||
−0.0196651 | + | 0.999807i | \(0.506260\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.0218 | 0.543826 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.594825 | −0.0215059 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.5363 | 0.741521 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.3327 | −1.38231 | −0.691156 | − | 0.722705i | \(-0.742898\pi\) | ||||
−0.691156 | + | 0.722705i | \(0.742898\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.5314 | −1.13558 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.9782 | 0.754532 | 0.377266 | − | 0.926105i | \(-0.376864\pi\) | ||||
0.377266 | + | 0.926105i | \(0.376864\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.57302 | −0.0924255 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −48.2121 | −1.72960 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.4681 | −0.446715 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.75117 | 0.241576 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.9744 | 0.999723 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.6779 | 0.523876 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.0647 | 1.07169 | 0.535846 | − | 0.844316i | \(-0.319993\pi\) | ||||
0.535846 | + | 0.844316i | \(0.319993\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 36.0501 | 1.28342 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −53.2195 | −1.89227 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.0038 | −1.06546 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.07469 | 0.179981 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.5740 | 0.657925 | 0.328963 | − | 0.944343i | \(-0.393301\pi\) | ||||
0.328963 | + | 0.944343i | \(0.393301\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.34743 | −0.330688 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.368533 | 0.0130215 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.28494 | 0.257080 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 74.9755 | 2.64254 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 43.8311 | 1.54293 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.15637 | 0.286763 | 0.143381 | − | 0.989668i | \(-0.454202\pi\) | ||||
0.143381 | + | 0.989668i | \(0.454202\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.4763 | 0.719022 | 0.359511 | − | 0.933141i | \(-0.382944\pi\) | ||||
0.359511 | + | 0.933141i | \(0.382944\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.3169 | 0.817759 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.6438 | 0.583006 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.70973 | −0.164773 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.20237 | 0.0420143 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.2547 | 1.05590 | 0.527949 | − | 0.849276i | \(-0.322961\pi\) | ||||
0.527949 | + | 0.849276i | \(0.322961\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.4332 | 1.54884 | 0.774422 | − | 0.632669i | \(-0.218041\pi\) | ||||
0.774422 | + | 0.632669i | \(0.218041\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.8297 | −0.446673 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.4952 | −0.538820 | −0.269410 | − | 0.963026i | \(-0.586829\pi\) | ||||
−0.269410 | + | 0.963026i | \(0.586829\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.5222 | 0.747499 | 0.373749 | − | 0.927530i | \(-0.378072\pi\) | ||||
0.373749 | + | 0.927530i | \(0.378072\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.1842 | 0.422667 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.39726 | −0.187004 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −79.1825 | −2.74022 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.27854 | −0.0787579 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.6891 | −0.541649 | −0.270825 | − | 0.962629i | \(-0.587296\pi\) | ||||
−0.270825 | + | 0.962629i | \(0.587296\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.50801 | −0.0520004 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26.6326 | 0.917274 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.1065 | 1.03570 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32.8507 | −1.12876 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.8531 | 1.05887 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −52.9697 | −1.81578 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.9636 | 1.19713 | 0.598565 | − | 0.801074i | \(-0.295738\pi\) | ||||
0.598565 | + | 0.801074i | \(0.295738\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.575785 | 0.0196914 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.8079 | −0.642466 | −0.321233 | − | 0.947000i | \(-0.604097\pi\) | ||||
−0.321233 | + | 0.947000i | \(0.604097\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.2523 | −0.349803 | −0.174901 | − | 0.984586i | \(-0.555961\pi\) | ||||
−0.174901 | + | 0.984586i | \(0.555961\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 73.2903 | 2.49773 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.0872 | −1.12630 | −0.563151 | − | 0.826354i | \(-0.690411\pi\) | ||||
−0.563151 | + | 0.826354i | \(0.690411\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.7689 | 0.910169 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.7869 | 0.909731 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.26661 | −0.0429667 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.45715 | 0.252676 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.50970 | −0.0849403 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.8972 | −0.402197 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.9270 | 0.436514 | 0.218257 | − | 0.975891i | \(-0.429963\pi\) | ||||
0.218257 | + | 0.975891i | \(0.429963\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.5086 | 0.624279 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.1846 | 1.75814 | 0.879072 | − | 0.476689i | \(-0.158163\pi\) | ||||
0.879072 | + | 0.476689i | \(0.158163\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.5787 | 1.33193 | 0.665965 | − | 0.745983i | \(-0.268020\pi\) | ||||
0.665965 | + | 0.745983i | \(0.268020\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −57.8082 | −1.94320 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.1055 | −1.07800 | −0.538998 | − | 0.842307i | \(-0.681197\pi\) | ||||
−0.538998 | + | 0.842307i | \(0.681197\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.29911 | 0.0435707 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.7024 | −0.358545 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.04823 | 0.302787 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.2585 | 0.376331 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.5327 | −0.718956 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.23925 | −0.0746831 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.939120 | −0.0312866 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.6849 | 0.921296 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.5543 | −0.616766 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.4698 | −1.34378 | −0.671889 | − | 0.740651i | \(-0.734517\pi\) | ||||
−0.671889 | + | 0.740651i | \(0.734517\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.21664 | −0.106689 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.5309 | 0.448297 | 0.224149 | − | 0.974555i | \(-0.428040\pi\) | ||||
0.224149 | + | 0.974555i | \(0.428040\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.2760 | −0.340087 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 84.4586 | 2.79211 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.4501 | 0.576253 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.0076 | 1.31973 | 0.659864 | − | 0.751385i | \(-0.270614\pi\) | ||||
0.659864 | + | 0.751385i | \(0.270614\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.7293 | −1.11142 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.5703 | −0.347924 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 49.4142 | 1.62473 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.0230032 | 0.000755523 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.3525 | −0.470889 | −0.235444 | − | 0.971888i | \(-0.575655\pi\) | ||||
−0.235444 | + | 0.971888i | \(0.575655\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.22450 | 0.171226 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −54.0779 | −1.77043 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.34466 | 0.142086 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.23488 | −0.105679 | −0.0528394 | − | 0.998603i | \(-0.516827\pi\) | ||||
−0.0528394 | + | 0.998603i | \(0.516827\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.8547 | 1.39851 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47.5835 | −1.55118 | −0.775589 | − | 0.631238i | \(-0.782547\pi\) | ||||
−0.775589 | + | 0.631238i | \(0.782547\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 80.5226 | 2.62218 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −61.9382 | −2.01485 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.9219 | −0.419905 | −0.209953 | − | 0.977712i | \(-0.567331\pi\) | ||||
−0.209953 | + | 0.977712i | \(0.567331\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.4060 | −0.370254 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.9200 | 1.00265 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.1361 | −1.72125 | −0.860624 | − | 0.509241i | \(-0.829926\pi\) | ||||
−0.860624 | + | 0.509241i | \(0.829926\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.9951 | 1.58545 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.1654 | −0.360928 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −42.9566 | −1.38714 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8176 | −0.994116 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.140048 | 0.00451298 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.8269 | 0.831398 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.1088 | −0.710972 | −0.355486 | − | 0.934682i | \(-0.615685\pi\) | ||||
−0.355486 | + | 0.934682i | \(0.615685\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.73684 | 0.0557954 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.955264 | −0.0306559 | −0.0153279 | − | 0.999883i | \(-0.504879\pi\) | ||||
−0.0153279 | + | 0.999883i | \(0.504879\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.3375 | 1.16493 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20.0874 | 0.643311 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.5005 | 0.655868 | 0.327934 | − | 0.944701i | \(-0.393648\pi\) | ||||
0.327934 | + | 0.944701i | \(0.393648\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.69180 | −0.0860303 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.745044 | −0.0237874 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.5967 | −1.23104 | −0.615522 | − | 0.788120i | \(-0.711055\pi\) | ||||
−0.615522 | + | 0.788120i | \(0.711055\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48.7133 | 1.55213 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −53.1876 | −1.69298 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.4169 | 0.967200 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.8674 | −0.980535 | −0.490267 | − | 0.871572i | \(-0.663101\pi\) | ||||
−0.490267 | + | 0.871572i | \(0.663101\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 47.2789 | 1.50035 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.76569 | −0.246189 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.75663 | 0.182314 | 0.0911571 | − | 0.995837i | \(-0.470943\pi\) | ||||
0.0911571 | + | 0.995837i | \(0.470943\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 43.7589 | 1.38447 |
(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 | 6004.2.a.g.1.8 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.g.1.8 | ✓ | 27 | 1.1 | even | 1 | trivial |