Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2476334663\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 29 x^{10} + 76 x^{9} + 320 x^{8} - 724 x^{7} - 1643 x^{6} + 3265 x^{5} + 3921 x^{4} + \cdots + 423 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.0737297\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.0737297 | 0.0329729 | 0.0164865 | − | 0.999864i | \(-0.494752\pi\) | ||||
0.0164865 | + | 0.999864i | \(0.494752\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82077 | 1.06615 | 0.533076 | − | 0.846067i | \(-0.321036\pi\) | ||||
0.533076 | + | 0.846067i | \(0.321036\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.0737297 | −0.0233154 | ||||||||
\(11\) | −0.846877 | −0.255343 | −0.127672 | − | 0.991817i | \(-0.540750\pi\) | ||||
−0.127672 | + | 0.991817i | \(0.540750\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.61317 | 1.83416 | 0.917081 | − | 0.398701i | \(-0.130539\pi\) | ||||
0.917081 | + | 0.398701i | \(0.130539\pi\) | |||||||
\(14\) | −2.82077 | −0.753883 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.99097 | 0.725418 | 0.362709 | − | 0.931903i | \(-0.381852\pi\) | ||||
0.362709 | + | 0.931903i | \(0.381852\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.47691 | −1.02707 | −0.513537 | − | 0.858067i | \(-0.671665\pi\) | ||||
−0.513537 | + | 0.858067i | \(0.671665\pi\) | |||||||
\(20\) | 0.0737297 | 0.0164865 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.846877 | 0.180555 | ||||||||
\(23\) | −3.02516 | −0.630789 | −0.315394 | − | 0.948961i | \(-0.602137\pi\) | ||||
−0.315394 | + | 0.948961i | \(0.602137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99456 | −0.998913 | ||||||||
\(26\) | −6.61317 | −1.29695 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.82077 | 0.533076 | ||||||||
\(29\) | −7.80750 | −1.44982 | −0.724908 | − | 0.688846i | \(-0.758118\pi\) | ||||
−0.724908 | + | 0.688846i | \(0.758118\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.54086 | 1.53398 | 0.766992 | − | 0.641657i | \(-0.221753\pi\) | ||||
0.766992 | + | 0.641657i | \(0.221753\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.99097 | −0.512948 | ||||||||
\(35\) | 0.207975 | 0.0351541 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.28035 | −0.703685 | −0.351842 | − | 0.936059i | \(-0.614445\pi\) | ||||
−0.351842 | + | 0.936059i | \(0.614445\pi\) | |||||||
\(38\) | 4.47691 | 0.726251 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.0737297 | −0.0116577 | ||||||||
\(41\) | −4.12319 | −0.643933 | −0.321967 | − | 0.946751i | \(-0.604344\pi\) | ||||
−0.321967 | + | 0.946751i | \(0.604344\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.9934 | −1.67648 | −0.838242 | − | 0.545298i | \(-0.816417\pi\) | ||||
−0.838242 | + | 0.545298i | \(0.816417\pi\) | |||||||
\(44\) | −0.846877 | −0.127672 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.02516 | 0.446035 | ||||||||
\(47\) | −3.07244 | −0.448162 | −0.224081 | − | 0.974571i | \(-0.571938\pi\) | ||||
−0.224081 | + | 0.974571i | \(0.571938\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.956763 | 0.136680 | ||||||||
\(50\) | 4.99456 | 0.706338 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.61317 | 0.917081 | ||||||||
\(53\) | −5.55611 | −0.763190 | −0.381595 | − | 0.924330i | \(-0.624625\pi\) | ||||
−0.381595 | + | 0.924330i | \(0.624625\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0624400 | −0.00841940 | ||||||||
\(56\) | −2.82077 | −0.376942 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.80750 | 1.02517 | ||||||||
\(59\) | −13.5281 | −1.76120 | −0.880602 | − | 0.473858i | \(-0.842861\pi\) | ||||
−0.880602 | + | 0.473858i | \(0.842861\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.57187 | −0.329294 | −0.164647 | − | 0.986353i | \(-0.552649\pi\) | ||||
−0.164647 | + | 0.986353i | \(0.552649\pi\) | |||||||
\(62\) | −8.54086 | −1.08469 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.487586 | 0.0604777 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.662125 | −0.0808914 | −0.0404457 | − | 0.999182i | \(-0.512878\pi\) | ||||
−0.0404457 | + | 0.999182i | \(0.512878\pi\) | |||||||
\(68\) | 2.99097 | 0.362709 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.207975 | −0.0248577 | ||||||||
\(71\) | −10.6685 | −1.26612 | −0.633062 | − | 0.774101i | \(-0.718202\pi\) | ||||
−0.633062 | + | 0.774101i | \(0.718202\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.88447 | 0.688725 | 0.344363 | − | 0.938837i | \(-0.388095\pi\) | ||||
0.344363 | + | 0.938837i | \(0.388095\pi\) | |||||||
\(74\) | 4.28035 | 0.497580 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.47691 | −0.513537 | ||||||||
\(77\) | −2.38885 | −0.272235 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.96274 | −0.895878 | −0.447939 | − | 0.894064i | \(-0.647842\pi\) | ||||
−0.447939 | + | 0.894064i | \(0.647842\pi\) | |||||||
\(80\) | 0.0737297 | 0.00824323 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.12319 | 0.455330 | ||||||||
\(83\) | −1.58303 | −0.173761 | −0.0868803 | − | 0.996219i | \(-0.527690\pi\) | ||||
−0.0868803 | + | 0.996219i | \(0.527690\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.220523 | 0.0239191 | ||||||||
\(86\) | 10.9934 | 1.18545 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.846877 | 0.0902774 | ||||||||
\(89\) | −5.09852 | −0.540442 | −0.270221 | − | 0.962798i | \(-0.587097\pi\) | ||||
−0.270221 | + | 0.962798i | \(0.587097\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.6542 | 1.95550 | ||||||||
\(92\) | −3.02516 | −0.315394 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.07244 | 0.316898 | ||||||||
\(95\) | −0.330081 | −0.0338656 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.6060 | −1.17841 | −0.589206 | − | 0.807983i | \(-0.700560\pi\) | ||||
−0.589206 | + | 0.807983i | \(0.700560\pi\) | |||||||
\(98\) | −0.956763 | −0.0966477 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.99456 | −0.499456 | ||||||||
\(101\) | −0.530840 | −0.0528205 | −0.0264103 | − | 0.999651i | \(-0.508408\pi\) | ||||
−0.0264103 | + | 0.999651i | \(0.508408\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.3632 | −1.02111 | −0.510556 | − | 0.859844i | \(-0.670560\pi\) | ||||
−0.510556 | + | 0.859844i | \(0.670560\pi\) | |||||||
\(104\) | −6.61317 | −0.648474 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.55611 | 0.539657 | ||||||||
\(107\) | 17.9925 | 1.73940 | 0.869701 | − | 0.493579i | \(-0.164311\pi\) | ||||
0.869701 | + | 0.493579i | \(0.164311\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.56786 | −0.245957 | −0.122978 | − | 0.992409i | \(-0.539245\pi\) | ||||
−0.122978 | + | 0.992409i | \(0.539245\pi\) | |||||||
\(110\) | 0.0624400 | 0.00595342 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.82077 | 0.266538 | ||||||||
\(113\) | −18.5242 | −1.74261 | −0.871305 | − | 0.490741i | \(-0.836726\pi\) | ||||
−0.871305 | + | 0.490741i | \(0.836726\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.223044 | −0.0207989 | ||||||||
\(116\) | −7.80750 | −0.724908 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.5281 | 1.24536 | ||||||||
\(119\) | 8.43686 | 0.773405 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2828 | −0.934800 | ||||||||
\(122\) | 2.57187 | 0.232846 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.54086 | 0.766992 | ||||||||
\(125\) | −0.736896 | −0.0659100 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.61735 | −0.853402 | −0.426701 | − | 0.904393i | \(-0.640324\pi\) | ||||
−0.426701 | + | 0.904393i | \(0.640324\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.487586 | −0.0427642 | ||||||||
\(131\) | 11.3291 | 0.989826 | 0.494913 | − | 0.868943i | \(-0.335200\pi\) | ||||
0.494913 | + | 0.868943i | \(0.335200\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.6284 | −1.09502 | ||||||||
\(134\) | 0.662125 | 0.0571989 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.99097 | −0.256474 | ||||||||
\(137\) | 11.1716 | 0.954455 | 0.477227 | − | 0.878780i | \(-0.341642\pi\) | ||||
0.477227 | + | 0.878780i | \(0.341642\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.5964 | 1.91660 | 0.958300 | − | 0.285764i | \(-0.0922475\pi\) | ||||
0.958300 | + | 0.285764i | \(0.0922475\pi\) | |||||||
\(140\) | 0.207975 | 0.0175771 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.6685 | 0.895285 | ||||||||
\(143\) | −5.60054 | −0.468341 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.575644 | −0.0478046 | ||||||||
\(146\) | −5.88447 | −0.487002 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.28035 | −0.351842 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.1615 | 1.72210 | 0.861051 | − | 0.508519i | \(-0.169807\pi\) | ||||
0.861051 | + | 0.508519i | \(0.169807\pi\) | |||||||
\(152\) | 4.47691 | 0.363126 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.38885 | 0.192499 | ||||||||
\(155\) | 0.629715 | 0.0505799 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.31978 | −0.264947 | −0.132474 | − | 0.991187i | \(-0.542292\pi\) | ||||
−0.132474 | + | 0.991187i | \(0.542292\pi\) | |||||||
\(158\) | 7.96274 | 0.633482 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.0737297 | −0.00582884 | ||||||||
\(161\) | −8.53328 | −0.672517 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.5398 | −0.825544 | −0.412772 | − | 0.910834i | \(-0.635439\pi\) | ||||
−0.412772 | + | 0.910834i | \(0.635439\pi\) | |||||||
\(164\) | −4.12319 | −0.321967 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.58303 | 0.122867 | ||||||||
\(167\) | 5.76356 | 0.445997 | 0.222999 | − | 0.974819i | \(-0.428415\pi\) | ||||
0.222999 | + | 0.974819i | \(0.428415\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.7340 | 2.36415 | ||||||||
\(170\) | −0.220523 | −0.0169134 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.9934 | −0.838242 | ||||||||
\(173\) | −14.7159 | −1.11883 | −0.559416 | − | 0.828887i | \(-0.688975\pi\) | ||||
−0.559416 | + | 0.828887i | \(0.688975\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.0885 | −1.06499 | ||||||||
\(176\) | −0.846877 | −0.0638358 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.09852 | 0.382150 | ||||||||
\(179\) | −13.1718 | −0.984507 | −0.492253 | − | 0.870452i | \(-0.663827\pi\) | ||||
−0.492253 | + | 0.870452i | \(0.663827\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.62996 | −0.269813 | −0.134906 | − | 0.990858i | \(-0.543073\pi\) | ||||
−0.134906 | + | 0.990858i | \(0.543073\pi\) | |||||||
\(182\) | −18.6542 | −1.38274 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.02516 | 0.223018 | ||||||||
\(185\) | −0.315589 | −0.0232025 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.53299 | −0.185230 | ||||||||
\(188\) | −3.07244 | −0.224081 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.330081 | 0.0239466 | ||||||||
\(191\) | 8.47963 | 0.613564 | 0.306782 | − | 0.951780i | \(-0.400748\pi\) | ||||
0.306782 | + | 0.951780i | \(0.400748\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.8965 | −1.28822 | −0.644108 | − | 0.764934i | \(-0.722771\pi\) | ||||
−0.644108 | + | 0.764934i | \(0.722771\pi\) | |||||||
\(194\) | 11.6060 | 0.833264 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.956763 | 0.0683402 | ||||||||
\(197\) | 20.6524 | 1.47142 | 0.735710 | − | 0.677297i | \(-0.236849\pi\) | ||||
0.735710 | + | 0.677297i | \(0.236849\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.3635 | 1.51442 | 0.757210 | − | 0.653171i | \(-0.226562\pi\) | ||||
0.757210 | + | 0.653171i | \(0.226562\pi\) | |||||||
\(200\) | 4.99456 | 0.353169 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.530840 | 0.0373497 | ||||||||
\(203\) | −22.0232 | −1.54572 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.304001 | −0.0212324 | ||||||||
\(206\) | 10.3632 | 0.722036 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.61317 | 0.458541 | ||||||||
\(209\) | 3.79140 | 0.262256 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.8145 | 1.63946 | 0.819729 | − | 0.572752i | \(-0.194124\pi\) | ||||
0.819729 | + | 0.572752i | \(0.194124\pi\) | |||||||
\(212\) | −5.55611 | −0.381595 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −17.9925 | −1.22994 | ||||||||
\(215\) | −0.810543 | −0.0552786 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.0918 | 1.63546 | ||||||||
\(218\) | 2.56786 | 0.173918 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.0624400 | −0.00420970 | ||||||||
\(221\) | 19.7798 | 1.33053 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.4209 | −0.831765 | −0.415883 | − | 0.909418i | \(-0.636527\pi\) | ||||
−0.415883 | + | 0.909418i | \(0.636527\pi\) | |||||||
\(224\) | −2.82077 | −0.188471 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.5242 | 1.23221 | ||||||||
\(227\) | −14.9424 | −0.991759 | −0.495879 | − | 0.868391i | \(-0.665154\pi\) | ||||
−0.495879 | + | 0.868391i | \(0.665154\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.02872 | 0.398389 | 0.199194 | − | 0.979960i | \(-0.436167\pi\) | ||||
0.199194 | + | 0.979960i | \(0.436167\pi\) | |||||||
\(230\) | 0.223044 | 0.0147071 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.80750 | 0.512587 | ||||||||
\(233\) | −15.1492 | −0.992460 | −0.496230 | − | 0.868191i | \(-0.665283\pi\) | ||||
−0.496230 | + | 0.868191i | \(0.665283\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.226530 | −0.0147772 | ||||||||
\(236\) | −13.5281 | −0.880602 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.43686 | −0.546880 | ||||||||
\(239\) | 20.3706 | 1.31767 | 0.658833 | − | 0.752289i | \(-0.271050\pi\) | ||||
0.658833 | + | 0.752289i | \(0.271050\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.15656 | −0.460994 | −0.230497 | − | 0.973073i | \(-0.574035\pi\) | ||||
−0.230497 | + | 0.973073i | \(0.574035\pi\) | |||||||
\(242\) | 10.2828 | 0.661003 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.57187 | −0.164647 | ||||||||
\(245\) | 0.0705418 | 0.00450675 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29.6066 | −1.88382 | ||||||||
\(248\) | −8.54086 | −0.542345 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.736896 | 0.0466054 | ||||||||
\(251\) | −13.4244 | −0.847343 | −0.423671 | − | 0.905816i | \(-0.639259\pi\) | ||||
−0.423671 | + | 0.905816i | \(0.639259\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.56194 | 0.161068 | ||||||||
\(254\) | 9.61735 | 0.603446 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.8316 | −1.17468 | −0.587340 | − | 0.809340i | \(-0.699825\pi\) | ||||
−0.587340 | + | 0.809340i | \(0.699825\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.0739 | −0.750235 | ||||||||
\(260\) | 0.487586 | 0.0302388 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.3291 | −0.699912 | ||||||||
\(263\) | −2.43969 | −0.150437 | −0.0752187 | − | 0.997167i | \(-0.523966\pi\) | ||||
−0.0752187 | + | 0.997167i | \(0.523966\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.409650 | −0.0251646 | ||||||||
\(266\) | 12.6284 | 0.774295 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.662125 | −0.0404457 | ||||||||
\(269\) | 19.1312 | 1.16645 | 0.583225 | − | 0.812311i | \(-0.301791\pi\) | ||||
0.583225 | + | 0.812311i | \(0.301791\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.8732 | −1.75392 | −0.876962 | − | 0.480560i | \(-0.840433\pi\) | ||||
−0.876962 | + | 0.480560i | \(0.840433\pi\) | |||||||
\(272\) | 2.99097 | 0.181354 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.1716 | −0.674902 | ||||||||
\(275\) | 4.22978 | 0.255065 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.8577 | 1.19313 | 0.596567 | − | 0.802563i | \(-0.296531\pi\) | ||||
0.596567 | + | 0.802563i | \(0.296531\pi\) | |||||||
\(278\) | −22.5964 | −1.35524 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.207975 | −0.0124289 | ||||||||
\(281\) | −16.1625 | −0.964174 | −0.482087 | − | 0.876123i | \(-0.660121\pi\) | ||||
−0.482087 | + | 0.876123i | \(0.660121\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.3573 | 0.853453 | 0.426727 | − | 0.904381i | \(-0.359667\pi\) | ||||
0.426727 | + | 0.904381i | \(0.359667\pi\) | |||||||
\(284\) | −10.6685 | −0.633062 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.60054 | 0.331167 | ||||||||
\(287\) | −11.6306 | −0.686531 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.05408 | −0.473769 | ||||||||
\(290\) | 0.575644 | 0.0338030 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.88447 | 0.344363 | ||||||||
\(293\) | 8.57843 | 0.501157 | 0.250579 | − | 0.968096i | \(-0.419379\pi\) | ||||
0.250579 | + | 0.968096i | \(0.419379\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.997419 | −0.0580720 | ||||||||
\(296\) | 4.28035 | 0.248790 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | −20.0059 | −1.15697 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.0100 | −1.78739 | ||||||||
\(302\) | −21.1615 | −1.21771 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.47691 | −0.256769 | ||||||||
\(305\) | −0.189623 | −0.0108578 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.96009 | −0.397233 | −0.198617 | − | 0.980077i | \(-0.563645\pi\) | ||||
−0.198617 | + | 0.980077i | \(0.563645\pi\) | |||||||
\(308\) | −2.38885 | −0.136117 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.629715 | −0.0357654 | ||||||||
\(311\) | 27.5601 | 1.56279 | 0.781395 | − | 0.624036i | \(-0.214508\pi\) | ||||
0.781395 | + | 0.624036i | \(0.214508\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.0236 | −0.679615 | −0.339807 | − | 0.940495i | \(-0.610362\pi\) | ||||
−0.339807 | + | 0.940495i | \(0.610362\pi\) | |||||||
\(314\) | 3.31978 | 0.187346 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.96274 | −0.447939 | ||||||||
\(317\) | 26.5999 | 1.49400 | 0.747001 | − | 0.664823i | \(-0.231493\pi\) | ||||
0.747001 | + | 0.664823i | \(0.231493\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.61199 | 0.370200 | ||||||||
\(320\) | 0.0737297 | 0.00412161 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.53328 | 0.475541 | ||||||||
\(323\) | −13.3903 | −0.745058 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −33.0299 | −1.83217 | ||||||||
\(326\) | 10.5398 | 0.583748 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.12319 | 0.227665 | ||||||||
\(329\) | −8.66667 | −0.477809 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.9022 | 1.36875 | 0.684373 | − | 0.729132i | \(-0.260076\pi\) | ||||
0.684373 | + | 0.729132i | \(0.260076\pi\) | |||||||
\(332\) | −1.58303 | −0.0868803 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.76356 | −0.315368 | ||||||||
\(335\) | −0.0488182 | −0.00266723 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.9366 | 1.03154 | 0.515771 | − | 0.856727i | \(-0.327506\pi\) | ||||
0.515771 | + | 0.856727i | \(0.327506\pi\) | |||||||
\(338\) | −30.7340 | −1.67171 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.220523 | 0.0119596 | ||||||||
\(341\) | −7.23306 | −0.391692 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0466 | −0.920430 | ||||||||
\(344\) | 10.9934 | 0.592727 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.7159 | 0.791134 | ||||||||
\(347\) | 23.5737 | 1.26550 | 0.632751 | − | 0.774356i | \(-0.281926\pi\) | ||||
0.632751 | + | 0.774356i | \(0.281926\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.1375 | 1.34558 | 0.672790 | − | 0.739833i | \(-0.265096\pi\) | ||||
0.672790 | + | 0.739833i | \(0.265096\pi\) | |||||||
\(350\) | 14.0885 | 0.753064 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.846877 | 0.0451387 | ||||||||
\(353\) | 9.49147 | 0.505180 | 0.252590 | − | 0.967573i | \(-0.418718\pi\) | ||||
0.252590 | + | 0.967573i | \(0.418718\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.786588 | −0.0417478 | ||||||||
\(356\) | −5.09852 | −0.270221 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.1718 | 0.696152 | ||||||||
\(359\) | −16.0817 | −0.848761 | −0.424381 | − | 0.905484i | \(-0.639508\pi\) | ||||
−0.424381 | + | 0.905484i | \(0.639508\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.04277 | 0.0548824 | ||||||||
\(362\) | 3.62996 | 0.190787 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 18.6542 | 0.977748 | ||||||||
\(365\) | 0.433860 | 0.0227093 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.0566 | 1.46454 | 0.732271 | − | 0.681013i | \(-0.238460\pi\) | ||||
0.732271 | + | 0.681013i | \(0.238460\pi\) | |||||||
\(368\) | −3.02516 | −0.157697 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.315589 | 0.0164067 | ||||||||
\(371\) | −15.6725 | −0.813677 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.06289 | 0.365703 | 0.182851 | − | 0.983141i | \(-0.441467\pi\) | ||||
0.182851 | + | 0.983141i | \(0.441467\pi\) | |||||||
\(374\) | 2.53299 | 0.130978 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.07244 | 0.158449 | ||||||||
\(377\) | −51.6323 | −2.65920 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.1458 | 1.44575 | 0.722876 | − | 0.690978i | \(-0.242820\pi\) | ||||
0.722876 | + | 0.690978i | \(0.242820\pi\) | |||||||
\(380\) | −0.330081 | −0.0169328 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.47963 | −0.433855 | ||||||||
\(383\) | −37.3687 | −1.90945 | −0.954726 | − | 0.297486i | \(-0.903852\pi\) | ||||
−0.954726 | + | 0.297486i | \(0.903852\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.176129 | −0.00897637 | ||||||||
\(386\) | 17.8965 | 0.910907 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.6060 | −0.589206 | ||||||||
\(389\) | −35.1791 | −1.78365 | −0.891826 | − | 0.452379i | \(-0.850576\pi\) | ||||
−0.891826 | + | 0.452379i | \(0.850576\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.04816 | −0.457585 | ||||||||
\(392\) | −0.956763 | −0.0483238 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.6524 | −1.04045 | ||||||||
\(395\) | −0.587090 | −0.0295397 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.0007 | −0.903430 | −0.451715 | − | 0.892162i | \(-0.649188\pi\) | ||||
−0.451715 | + | 0.892162i | \(0.649188\pi\) | |||||||
\(398\) | −21.3635 | −1.07086 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.99456 | −0.249728 | ||||||||
\(401\) | 7.81326 | 0.390175 | 0.195088 | − | 0.980786i | \(-0.437501\pi\) | ||||
0.195088 | + | 0.980786i | \(0.437501\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 56.4821 | 2.81357 | ||||||||
\(404\) | −0.530840 | −0.0264103 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.0232 | 1.09299 | ||||||||
\(407\) | 3.62493 | 0.179681 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.56848 | 0.275344 | 0.137672 | − | 0.990478i | \(-0.456038\pi\) | ||||
0.137672 | + | 0.990478i | \(0.456038\pi\) | |||||||
\(410\) | 0.304001 | 0.0150135 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.3632 | −0.510556 | ||||||||
\(413\) | −38.1596 | −1.87771 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.116717 | −0.00572939 | ||||||||
\(416\) | −6.61317 | −0.324237 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.79140 | −0.185443 | ||||||||
\(419\) | 16.2733 | 0.795003 | 0.397502 | − | 0.917601i | \(-0.369877\pi\) | ||||
0.397502 | + | 0.917601i | \(0.369877\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.69362 | −0.423701 | −0.211851 | − | 0.977302i | \(-0.567949\pi\) | ||||
−0.211851 | + | 0.977302i | \(0.567949\pi\) | |||||||
\(422\) | −23.8145 | −1.15927 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.55611 | 0.269829 | ||||||||
\(425\) | −14.9386 | −0.724629 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.25467 | −0.351078 | ||||||||
\(428\) | 17.9925 | 0.869701 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.810543 | 0.0390879 | ||||||||
\(431\) | −17.6996 | −0.852561 | −0.426281 | − | 0.904591i | \(-0.640176\pi\) | ||||
−0.426281 | + | 0.904591i | \(0.640176\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.4256 | 0.885478 | 0.442739 | − | 0.896650i | \(-0.354007\pi\) | ||||
0.442739 | + | 0.896650i | \(0.354007\pi\) | |||||||
\(434\) | −24.0918 | −1.15645 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.56786 | −0.122978 | ||||||||
\(437\) | 13.5434 | 0.647867 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.35941 | −0.398973 | −0.199486 | − | 0.979901i | \(-0.563927\pi\) | ||||
−0.199486 | + | 0.979901i | \(0.563927\pi\) | |||||||
\(440\) | 0.0624400 | 0.00297671 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19.7798 | −0.940829 | ||||||||
\(443\) | 32.2101 | 1.53035 | 0.765173 | − | 0.643824i | \(-0.222653\pi\) | ||||
0.765173 | + | 0.643824i | \(0.222653\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.375912 | −0.0178200 | ||||||||
\(446\) | 12.4209 | 0.588147 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.82077 | 0.133269 | ||||||||
\(449\) | 16.0870 | 0.759191 | 0.379595 | − | 0.925153i | \(-0.376063\pi\) | ||||
0.379595 | + | 0.925153i | \(0.376063\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.49183 | 0.164424 | ||||||||
\(452\) | −18.5242 | −0.871305 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.9424 | 0.701279 | ||||||||
\(455\) | 1.37537 | 0.0644784 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.2568 | 1.46213 | 0.731065 | − | 0.682308i | \(-0.239024\pi\) | ||||
0.731065 | + | 0.682308i | \(0.239024\pi\) | |||||||
\(458\) | −6.02872 | −0.281704 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.223044 | −0.0103995 | ||||||||
\(461\) | −19.0181 | −0.885763 | −0.442881 | − | 0.896580i | \(-0.646044\pi\) | ||||
−0.442881 | + | 0.896580i | \(0.646044\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0685 | 0.514395 | 0.257198 | − | 0.966359i | \(-0.417201\pi\) | ||||
0.257198 | + | 0.966359i | \(0.417201\pi\) | |||||||
\(464\) | −7.80750 | −0.362454 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.1492 | 0.701775 | ||||||||
\(467\) | 19.8084 | 0.916624 | 0.458312 | − | 0.888791i | \(-0.348454\pi\) | ||||
0.458312 | + | 0.888791i | \(0.348454\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.86770 | −0.0862426 | ||||||||
\(470\) | 0.226530 | 0.0104491 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.5281 | 0.622679 | ||||||||
\(473\) | 9.31010 | 0.428079 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.3602 | 1.02596 | ||||||||
\(476\) | 8.43686 | 0.386703 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.3706 | −0.931731 | ||||||||
\(479\) | 5.02223 | 0.229472 | 0.114736 | − | 0.993396i | \(-0.463398\pi\) | ||||
0.114736 | + | 0.993396i | \(0.463398\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.3066 | −1.29067 | ||||||||
\(482\) | 7.15656 | 0.325972 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.2828 | −0.467400 | ||||||||
\(485\) | −0.855708 | −0.0388557 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.9240 | −0.902842 | −0.451421 | − | 0.892311i | \(-0.649083\pi\) | ||||
−0.451421 | + | 0.892311i | \(0.649083\pi\) | |||||||
\(488\) | 2.57187 | 0.116423 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.0705418 | −0.00318675 | ||||||||
\(491\) | −13.0304 | −0.588054 | −0.294027 | − | 0.955797i | \(-0.594996\pi\) | ||||
−0.294027 | + | 0.955797i | \(0.594996\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.3520 | −1.05172 | ||||||||
\(494\) | 29.6066 | 1.33206 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.54086 | 0.383496 | ||||||||
\(497\) | −30.0936 | −1.34988 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.3213 | 1.22307 | 0.611535 | − | 0.791218i | \(-0.290552\pi\) | ||||
0.611535 | + | 0.791218i | \(0.290552\pi\) | |||||||
\(500\) | −0.736896 | −0.0329550 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.4244 | 0.599162 | ||||||||
\(503\) | −39.0248 | −1.74003 | −0.870016 | − | 0.493024i | \(-0.835892\pi\) | ||||
−0.870016 | + | 0.493024i | \(0.835892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.0391386 | −0.00174165 | ||||||||
\(506\) | −2.56194 | −0.113892 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.61735 | −0.426701 | ||||||||
\(509\) | −30.4449 | −1.34945 | −0.674724 | − | 0.738070i | \(-0.735737\pi\) | ||||
−0.674724 | + | 0.738070i | \(0.735737\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.5988 | 0.734286 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.8316 | 0.830625 | ||||||||
\(515\) | −0.764072 | −0.0336690 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.60198 | 0.114435 | ||||||||
\(518\) | 12.0739 | 0.530496 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.487586 | −0.0213821 | ||||||||
\(521\) | 26.0464 | 1.14111 | 0.570557 | − | 0.821258i | \(-0.306728\pi\) | ||||
0.570557 | + | 0.821258i | \(0.306728\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.50636 | −0.109596 | −0.0547978 | − | 0.998497i | \(-0.517451\pi\) | ||||
−0.0547978 | + | 0.998497i | \(0.517451\pi\) | |||||||
\(524\) | 11.3291 | 0.494913 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.43969 | 0.106375 | ||||||||
\(527\) | 25.5455 | 1.11278 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.8484 | −0.602105 | ||||||||
\(530\) | 0.409650 | 0.0177941 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.6284 | −0.547509 | ||||||||
\(533\) | −27.2673 | −1.18108 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.32658 | 0.0573532 | ||||||||
\(536\) | 0.662125 | 0.0285994 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19.1312 | −0.824805 | ||||||||
\(539\) | −0.810261 | −0.0349004 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.1124 | −0.563746 | −0.281873 | − | 0.959452i | \(-0.590956\pi\) | ||||
−0.281873 | + | 0.959452i | \(0.590956\pi\) | |||||||
\(542\) | 28.8732 | 1.24021 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.99097 | −0.128237 | ||||||||
\(545\) | −0.189328 | −0.00810991 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.1933 | −1.41924 | −0.709622 | − | 0.704583i | \(-0.751134\pi\) | ||||
−0.709622 | + | 0.704583i | \(0.751134\pi\) | |||||||
\(548\) | 11.1716 | 0.477227 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.22978 | −0.180359 | ||||||||
\(551\) | 34.9535 | 1.48907 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.4611 | −0.955143 | ||||||||
\(554\) | −19.8577 | −0.843673 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.5964 | 0.958300 | ||||||||
\(557\) | 3.66313 | 0.155212 | 0.0776060 | − | 0.996984i | \(-0.475272\pi\) | ||||
0.0776060 | + | 0.996984i | \(0.475272\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −72.7015 | −3.07495 | ||||||||
\(560\) | 0.207975 | 0.00878853 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.1625 | 0.681774 | ||||||||
\(563\) | 44.6936 | 1.88361 | 0.941805 | − | 0.336160i | \(-0.109128\pi\) | ||||
0.941805 | + | 0.336160i | \(0.109128\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.36578 | −0.0574589 | ||||||||
\(566\) | −14.3573 | −0.603482 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.6685 | 0.447642 | ||||||||
\(569\) | 28.3965 | 1.19044 | 0.595222 | − | 0.803561i | \(-0.297064\pi\) | ||||
0.595222 | + | 0.803561i | \(0.297064\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.1958 | 0.594075 | 0.297038 | − | 0.954866i | \(-0.404001\pi\) | ||||
0.297038 | + | 0.954866i | \(0.404001\pi\) | |||||||
\(572\) | −5.60054 | −0.234170 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.6306 | 0.485451 | ||||||||
\(575\) | 15.1093 | 0.630103 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.95543 | −0.289558 | −0.144779 | − | 0.989464i | \(-0.546247\pi\) | ||||
−0.144779 | + | 0.989464i | \(0.546247\pi\) | |||||||
\(578\) | 8.05408 | 0.335006 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.575644 | −0.0239023 | ||||||||
\(581\) | −4.46538 | −0.185255 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.70534 | 0.194875 | ||||||||
\(584\) | −5.88447 | −0.243501 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.57843 | −0.354372 | ||||||||
\(587\) | 20.2969 | 0.837744 | 0.418872 | − | 0.908045i | \(-0.362426\pi\) | ||||
0.418872 | + | 0.908045i | \(0.362426\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −38.2367 | −1.57552 | ||||||||
\(590\) | 0.997419 | 0.0410631 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.28035 | −0.175921 | ||||||||
\(593\) | 37.4732 | 1.53884 | 0.769419 | − | 0.638744i | \(-0.220546\pi\) | ||||
0.769419 | + | 0.638744i | \(0.220546\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.622047 | 0.0255014 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 20.0059 | 0.818101 | ||||||||
\(599\) | −10.4893 | −0.428580 | −0.214290 | − | 0.976770i | \(-0.568744\pi\) | ||||
−0.214290 | + | 0.976770i | \(0.568744\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.305383 | 0.0124568 | 0.00622841 | − | 0.999981i | \(-0.498017\pi\) | ||||
0.00622841 | + | 0.999981i | \(0.498017\pi\) | |||||||
\(602\) | 31.0100 | 1.26387 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 21.1615 | 0.861051 | ||||||||
\(605\) | −0.758147 | −0.0308231 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.6928 | −0.434006 | −0.217003 | − | 0.976171i | \(-0.569628\pi\) | ||||
−0.217003 | + | 0.976171i | \(0.569628\pi\) | |||||||
\(608\) | 4.47691 | 0.181563 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.189623 | 0.00767762 | ||||||||
\(611\) | −20.3186 | −0.822002 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.270765 | 0.0109361 | 0.00546805 | − | 0.999985i | \(-0.498259\pi\) | ||||
0.00546805 | + | 0.999985i | \(0.498259\pi\) | |||||||
\(614\) | 6.96009 | 0.280886 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.38885 | 0.0962494 | ||||||||
\(617\) | −17.7655 | −0.715213 | −0.357606 | − | 0.933872i | \(-0.616407\pi\) | ||||
−0.357606 | + | 0.933872i | \(0.616407\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.99701 | 0.241040 | 0.120520 | − | 0.992711i | \(-0.461544\pi\) | ||||
0.120520 | + | 0.992711i | \(0.461544\pi\) | |||||||
\(620\) | 0.629715 | 0.0252900 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −27.5601 | −1.10506 | ||||||||
\(623\) | −14.3818 | −0.576194 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9185 | 0.996740 | ||||||||
\(626\) | 12.0236 | 0.480560 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.31978 | −0.132474 | ||||||||
\(629\) | −12.8024 | −0.510465 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.9808 | −1.63142 | −0.815710 | − | 0.578461i | \(-0.803654\pi\) | ||||
−0.815710 | + | 0.578461i | \(0.803654\pi\) | |||||||
\(632\) | 7.96274 | 0.316741 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −26.5999 | −1.05642 | ||||||||
\(635\) | −0.709084 | −0.0281392 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.32723 | 0.250694 | ||||||||
\(638\) | −6.61199 | −0.261771 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.0737297 | −0.00291442 | ||||||||
\(641\) | −29.3792 | −1.16041 | −0.580204 | − | 0.814472i | \(-0.697027\pi\) | ||||
−0.580204 | + | 0.814472i | \(0.697027\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.8828 | −0.626357 | −0.313179 | − | 0.949694i | \(-0.601394\pi\) | ||||
−0.313179 | + | 0.949694i | \(0.601394\pi\) | |||||||
\(644\) | −8.53328 | −0.336258 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.3903 | 0.526836 | ||||||||
\(647\) | −30.4711 | −1.19794 | −0.598972 | − | 0.800770i | \(-0.704424\pi\) | ||||
−0.598972 | + | 0.800770i | \(0.704424\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.4566 | 0.449711 | ||||||||
\(650\) | 33.0299 | 1.29554 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.5398 | −0.412772 | ||||||||
\(653\) | 24.3418 | 0.952566 | 0.476283 | − | 0.879292i | \(-0.341984\pi\) | ||||
0.476283 | + | 0.879292i | \(0.341984\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.835289 | 0.0326374 | ||||||||
\(656\) | −4.12319 | −0.160983 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.66667 | 0.337862 | ||||||||
\(659\) | 6.33161 | 0.246645 | 0.123322 | − | 0.992367i | \(-0.460645\pi\) | ||||
0.123322 | + | 0.992367i | \(0.460645\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.5389 | −0.993348 | −0.496674 | − | 0.867937i | \(-0.665445\pi\) | ||||
−0.496674 | + | 0.867937i | \(0.665445\pi\) | |||||||
\(662\) | −24.9022 | −0.967850 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.58303 | 0.0614337 | ||||||||
\(665\) | −0.931085 | −0.0361059 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.6189 | 0.914528 | ||||||||
\(668\) | 5.76356 | 0.222999 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.0488182 | 0.00188601 | ||||||||
\(671\) | 2.17806 | 0.0840830 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.9146 | −1.07603 | −0.538014 | − | 0.842936i | \(-0.680825\pi\) | ||||
−0.538014 | + | 0.842936i | \(0.680825\pi\) | |||||||
\(674\) | −18.9366 | −0.729410 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 30.7340 | 1.18208 | ||||||||
\(677\) | 45.8343 | 1.76155 | 0.880777 | − | 0.473531i | \(-0.157021\pi\) | ||||
0.880777 | + | 0.473531i | \(0.157021\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.7380 | −1.25637 | ||||||||
\(680\) | −0.220523 | −0.00845669 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.23306 | 0.276968 | ||||||||
\(683\) | −3.67086 | −0.140461 | −0.0702307 | − | 0.997531i | \(-0.522374\pi\) | ||||
−0.0702307 | + | 0.997531i | \(0.522374\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.823679 | 0.0314712 | ||||||||
\(686\) | 17.0466 | 0.650842 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.9934 | −0.419121 | ||||||||
\(689\) | −36.7435 | −1.39981 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.86087 | −0.108833 | −0.0544164 | − | 0.998518i | \(-0.517330\pi\) | ||||
−0.0544164 | + | 0.998518i | \(0.517330\pi\) | |||||||
\(692\) | −14.7159 | −0.559416 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −23.5737 | −0.894844 | ||||||||
\(695\) | 1.66602 | 0.0631959 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.3323 | −0.467121 | ||||||||
\(698\) | −25.1375 | −0.951469 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14.0885 | −0.532497 | ||||||||
\(701\) | −14.6876 | −0.554745 | −0.277372 | − | 0.960762i | \(-0.589464\pi\) | ||||
−0.277372 | + | 0.960762i | \(0.589464\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.1627 | 0.722737 | ||||||||
\(704\) | −0.846877 | −0.0319179 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.49147 | −0.357216 | ||||||||
\(707\) | −1.49738 | −0.0563147 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.9566 | −0.899708 | −0.449854 | − | 0.893102i | \(-0.648524\pi\) | ||||
−0.449854 | + | 0.893102i | \(0.648524\pi\) | |||||||
\(710\) | 0.786588 | 0.0295201 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.09852 | 0.191075 | ||||||||
\(713\) | −25.8374 | −0.967620 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.412926 | −0.0154425 | ||||||||
\(716\) | −13.1718 | −0.492253 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.0817 | 0.600165 | ||||||||
\(719\) | −41.3366 | −1.54159 | −0.770797 | − | 0.637081i | \(-0.780142\pi\) | ||||
−0.770797 | + | 0.637081i | \(0.780142\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.2321 | −1.08866 | ||||||||
\(722\) | −1.04277 | −0.0388077 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.62996 | −0.134906 | ||||||||
\(725\) | 38.9950 | 1.44824 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.7090 | −1.80652 | −0.903258 | − | 0.429098i | \(-0.858832\pi\) | ||||
−0.903258 | + | 0.429098i | \(0.858832\pi\) | |||||||
\(728\) | −18.6542 | −0.691372 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.433860 | −0.0160579 | ||||||||
\(731\) | −32.8811 | −1.21615 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.7973 | 0.472680 | 0.236340 | − | 0.971670i | \(-0.424052\pi\) | ||||
0.236340 | + | 0.971670i | \(0.424052\pi\) | |||||||
\(734\) | −28.0566 | −1.03559 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.02516 | 0.111509 | ||||||||
\(737\) | 0.560738 | 0.0206551 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.8730 | 0.473541 | 0.236770 | − | 0.971566i | \(-0.423911\pi\) | ||||
0.236770 | + | 0.971566i | \(0.423911\pi\) | |||||||
\(740\) | −0.315589 | −0.0116013 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15.6725 | 0.575357 | ||||||||
\(743\) | 39.5383 | 1.45052 | 0.725259 | − | 0.688476i | \(-0.241720\pi\) | ||||
0.725259 | + | 0.688476i | \(0.241720\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.0737297 | −0.00270125 | ||||||||
\(746\) | −7.06289 | −0.258591 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.53299 | −0.0926152 | ||||||||
\(749\) | 50.7528 | 1.85447 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.92207 | 0.325571 | 0.162786 | − | 0.986661i | \(-0.447952\pi\) | ||||
0.162786 | + | 0.986661i | \(0.447952\pi\) | |||||||
\(752\) | −3.07244 | −0.112040 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 51.6323 | 1.88034 | ||||||||
\(755\) | 1.56023 | 0.0567827 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.3899 | −1.43165 | −0.715824 | − | 0.698280i | \(-0.753949\pi\) | ||||
−0.715824 | + | 0.698280i | \(0.753949\pi\) | |||||||
\(758\) | −28.1458 | −1.02230 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.330081 | 0.0119733 | ||||||||
\(761\) | −38.3367 | −1.38970 | −0.694852 | − | 0.719153i | \(-0.744530\pi\) | ||||
−0.694852 | + | 0.719153i | \(0.744530\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.24336 | −0.262227 | ||||||||
\(764\) | 8.47963 | 0.306782 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37.3687 | 1.35019 | ||||||||
\(767\) | −89.4633 | −3.23033 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.25167 | −0.297563 | −0.148781 | − | 0.988870i | \(-0.547535\pi\) | ||||
−0.148781 | + | 0.988870i | \(0.547535\pi\) | |||||||
\(770\) | 0.176129 | 0.00634725 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.8965 | −0.644108 | ||||||||
\(773\) | −0.822376 | −0.0295788 | −0.0147894 | − | 0.999891i | \(-0.504708\pi\) | ||||
−0.0147894 | + | 0.999891i | \(0.504708\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.6579 | −1.53232 | ||||||||
\(776\) | 11.6060 | 0.416632 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 35.1791 | 1.26123 | ||||||||
\(779\) | 18.4592 | 0.661368 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.03495 | 0.323296 | ||||||||
\(782\) | 9.04816 | 0.323562 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.956763 | 0.0341701 | ||||||||
\(785\) | −0.244766 | −0.00873608 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.6214 | −0.770718 | −0.385359 | − | 0.922767i | \(-0.625922\pi\) | ||||
−0.385359 | + | 0.922767i | \(0.625922\pi\) | |||||||
\(788\) | 20.6524 | 0.735710 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.587090 | 0.0208877 | ||||||||
\(791\) | −52.2526 | −1.85789 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.0082 | −0.603979 | ||||||||
\(794\) | 18.0007 | 0.638822 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.3635 | 0.757210 | ||||||||
\(797\) | −3.98465 | −0.141144 | −0.0705718 | − | 0.997507i | \(-0.522482\pi\) | ||||
−0.0705718 | + | 0.997507i | \(0.522482\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.18960 | −0.325105 | ||||||||
\(800\) | 4.99456 | 0.176585 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.81326 | −0.275896 | ||||||||
\(803\) | −4.98342 | −0.175861 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.629156 | −0.0221748 | ||||||||
\(806\) | −56.4821 | −1.98950 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.530840 | 0.0186749 | ||||||||
\(809\) | 15.7371 | 0.553287 | 0.276643 | − | 0.960973i | \(-0.410778\pi\) | ||||
0.276643 | + | 0.960973i | \(0.410778\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.23071 | 0.0432160 | 0.0216080 | − | 0.999767i | \(-0.493121\pi\) | ||||
0.0216080 | + | 0.999767i | \(0.493121\pi\) | |||||||
\(812\) | −22.0232 | −0.772862 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.62493 | −0.127054 | ||||||||
\(815\) | −0.777099 | −0.0272206 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 49.2167 | 1.72188 | ||||||||
\(818\) | −5.56848 | −0.194697 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.304001 | −0.0106162 | ||||||||
\(821\) | 17.9576 | 0.626724 | 0.313362 | − | 0.949634i | \(-0.398545\pi\) | ||||
0.313362 | + | 0.949634i | \(0.398545\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.1046 | −0.561370 | −0.280685 | − | 0.959800i | \(-0.590562\pi\) | ||||
−0.280685 | + | 0.959800i | \(0.590562\pi\) | |||||||
\(824\) | 10.3632 | 0.361018 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 38.1596 | 1.32774 | ||||||||
\(827\) | −36.7883 | −1.27926 | −0.639628 | − | 0.768685i | \(-0.720912\pi\) | ||||
−0.639628 | + | 0.768685i | \(0.720912\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −54.8626 | −1.90546 | −0.952729 | − | 0.303821i | \(-0.901738\pi\) | ||||
−0.952729 | + | 0.303821i | \(0.901738\pi\) | |||||||
\(830\) | 0.116717 | 0.00405129 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.61317 | 0.229270 | ||||||||
\(833\) | 2.86165 | 0.0991504 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.424945 | 0.0147058 | ||||||||
\(836\) | 3.79140 | 0.131128 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.2733 | −0.562152 | ||||||||
\(839\) | 42.0659 | 1.45228 | 0.726138 | − | 0.687549i | \(-0.241313\pi\) | ||||
0.726138 | + | 0.687549i | \(0.241313\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.9570 | 1.10197 | ||||||||
\(842\) | 8.69362 | 0.299602 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 23.8145 | 0.819729 | ||||||||
\(845\) | 2.26600 | 0.0779529 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.0054 | −0.996639 | ||||||||
\(848\) | −5.55611 | −0.190798 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 14.9386 | 0.512390 | ||||||||
\(851\) | 12.9487 | 0.443876 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.1030 | −0.791032 | −0.395516 | − | 0.918459i | \(-0.629434\pi\) | ||||
−0.395516 | + | 0.918459i | \(0.629434\pi\) | |||||||
\(854\) | 7.25467 | 0.248250 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.9925 | −0.614972 | ||||||||
\(857\) | −13.1296 | −0.448498 | −0.224249 | − | 0.974532i | \(-0.571993\pi\) | ||||
−0.224249 | + | 0.974532i | \(0.571993\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.7488 | −0.946776 | −0.473388 | − | 0.880854i | \(-0.656969\pi\) | ||||
−0.473388 | + | 0.880854i | \(0.656969\pi\) | |||||||
\(860\) | −0.810543 | −0.0276393 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.6996 | 0.602852 | ||||||||
\(863\) | −13.4467 | −0.457731 | −0.228866 | − | 0.973458i | \(-0.573502\pi\) | ||||
−0.228866 | + | 0.973458i | \(0.573502\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.08500 | −0.0368911 | ||||||||
\(866\) | −18.4256 | −0.626128 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 24.0918 | 0.817730 | ||||||||
\(869\) | 6.74346 | 0.228756 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.37874 | −0.148368 | ||||||||
\(872\) | 2.56786 | 0.0869588 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.5434 | −0.458111 | ||||||||
\(875\) | −2.07862 | −0.0702701 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.0581 | 1.75788 | 0.878939 | − | 0.476933i | \(-0.158252\pi\) | ||||
0.878939 | + | 0.476933i | \(0.158252\pi\) | |||||||
\(878\) | 8.35941 | 0.282116 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.0624400 | −0.00210485 | ||||||||
\(881\) | 32.5420 | 1.09637 | 0.548184 | − | 0.836358i | \(-0.315319\pi\) | ||||
0.548184 | + | 0.836358i | \(0.315319\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.00628 | 0.134822 | 0.0674111 | − | 0.997725i | \(-0.478526\pi\) | ||||
0.0674111 | + | 0.997725i | \(0.478526\pi\) | |||||||
\(884\) | 19.7798 | 0.665267 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.2101 | −1.08212 | ||||||||
\(887\) | 34.9539 | 1.17364 | 0.586818 | − | 0.809719i | \(-0.300380\pi\) | ||||
0.586818 | + | 0.809719i | \(0.300380\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.1284 | −0.909857 | ||||||||
\(890\) | 0.375912 | 0.0126006 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.4209 | −0.415883 | ||||||||
\(893\) | 13.7551 | 0.460296 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.971153 | −0.0324621 | ||||||||
\(896\) | −2.82077 | −0.0942354 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.0870 | −0.536829 | ||||||||
\(899\) | −66.6827 | −2.22399 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.6182 | −0.553632 | ||||||||
\(902\) | −3.49183 | −0.116265 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.5242 | 0.616106 | ||||||||
\(905\) | −0.267636 | −0.00889652 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.9878 | 0.398049 | 0.199024 | − | 0.979995i | \(-0.436223\pi\) | ||||
0.199024 | + | 0.979995i | \(0.436223\pi\) | |||||||
\(908\) | −14.9424 | −0.495879 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.37537 | −0.0455931 | ||||||||
\(911\) | 27.0943 | 0.897675 | 0.448838 | − | 0.893613i | \(-0.351838\pi\) | ||||
0.448838 | + | 0.893613i | \(0.351838\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.34064 | 0.0443686 | ||||||||
\(914\) | −31.2568 | −1.03388 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.02872 | 0.199194 | ||||||||
\(917\) | 31.9567 | 1.05530 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.1911 | 1.16085 | 0.580424 | − | 0.814314i | \(-0.302887\pi\) | ||||
0.580424 | + | 0.814314i | \(0.302887\pi\) | |||||||
\(920\) | 0.223044 | 0.00735354 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 19.0181 | 0.626329 | ||||||||
\(923\) | −70.5529 | −2.32228 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.3785 | 0.702920 | ||||||||
\(926\) | −11.0685 | −0.363732 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.80750 | 0.256294 | ||||||||
\(929\) | −7.64764 | −0.250911 | −0.125455 | − | 0.992099i | \(-0.540039\pi\) | ||||
−0.125455 | + | 0.992099i | \(0.540039\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.28335 | −0.140381 | ||||||||
\(932\) | −15.1492 | −0.496230 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19.8084 | −0.648151 | ||||||||
\(935\) | −0.186756 | −0.00610758 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.21281 | −0.0396209 | −0.0198104 | − | 0.999804i | \(-0.506306\pi\) | ||||
−0.0198104 | + | 0.999804i | \(0.506306\pi\) | |||||||
\(938\) | 1.86770 | 0.0609827 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.226530 | −0.00738860 | ||||||||
\(941\) | −12.2619 | −0.399726 | −0.199863 | − | 0.979824i | \(-0.564050\pi\) | ||||
−0.199863 | + | 0.979824i | \(0.564050\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.4733 | 0.406186 | ||||||||
\(944\) | −13.5281 | −0.440301 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.31010 | −0.302697 | ||||||||
\(947\) | −17.5657 | −0.570808 | −0.285404 | − | 0.958407i | \(-0.592128\pi\) | ||||
−0.285404 | + | 0.958407i | \(0.592128\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38.9150 | 1.26323 | ||||||||
\(950\) | −22.3602 | −0.725462 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.43686 | −0.273440 | ||||||||
\(953\) | 26.6383 | 0.862898 | 0.431449 | − | 0.902137i | \(-0.358002\pi\) | ||||
0.431449 | + | 0.902137i | \(0.358002\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.625200 | 0.0202310 | ||||||||
\(956\) | 20.3706 | 0.658833 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.02223 | −0.162261 | ||||||||
\(959\) | 31.5126 | 1.01759 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.9463 | 1.35311 | ||||||||
\(962\) | 28.3066 | 0.912643 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.15656 | −0.230497 | ||||||||
\(965\) | −1.31950 | −0.0424763 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.0542 | −1.06295 | −0.531475 | − | 0.847074i | \(-0.678362\pi\) | ||||
−0.531475 | + | 0.847074i | \(0.678362\pi\) | |||||||
\(968\) | 10.2828 | 0.330502 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.855708 | 0.0274751 | ||||||||
\(971\) | 26.2117 | 0.841172 | 0.420586 | − | 0.907253i | \(-0.361824\pi\) | ||||
0.420586 | + | 0.907253i | \(0.361824\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 63.7393 | 2.04339 | ||||||||
\(974\) | 19.9240 | 0.638406 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.57187 | −0.0823236 | ||||||||
\(977\) | −4.11029 | −0.131500 | −0.0657498 | − | 0.997836i | \(-0.520944\pi\) | ||||
−0.0657498 | + | 0.997836i | \(0.520944\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.31782 | 0.137998 | ||||||||
\(980\) | 0.0705418 | 0.00225338 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.0304 | 0.415817 | ||||||||
\(983\) | −2.85827 | −0.0911647 | −0.0455823 | − | 0.998961i | \(-0.514514\pi\) | ||||
−0.0455823 | + | 0.998961i | \(0.514514\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.52269 | 0.0485170 | ||||||||
\(986\) | 23.3520 | 0.743680 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −29.6066 | −0.941911 | ||||||||
\(989\) | 33.2569 | 1.05751 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.01338 | −0.191021 | −0.0955106 | − | 0.995428i | \(-0.530448\pi\) | ||||
−0.0955106 | + | 0.995428i | \(0.530448\pi\) | |||||||
\(992\) | −8.54086 | −0.271173 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 30.0936 | 0.954510 | ||||||||
\(995\) | 1.57513 | 0.0499349 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.1427 | 0.764608 | 0.382304 | − | 0.924037i | \(-0.375131\pi\) | ||||
0.382304 | + | 0.924037i | \(0.375131\pi\) | |||||||
\(998\) | −27.3213 | −0.864841 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8046.2.a.j.1.7 | ✓ | 12 | |
3.2 | odd | 2 | 8046.2.a.o.1.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.j.1.7 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8046.2.a.o.1.6 | yes | 12 | 3.2 | odd | 2 |