Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8010,2,Mod(1,8010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8010, 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("8010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8010 = 2 \cdot 3^{2} \cdot 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8010.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: | \(63.9601720190\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 24x^{5} + 34x^{4} + 111x^{3} - 127x^{2} - 20x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2670) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.68936\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8010.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.07548 | −1.91835 | −0.959175 | − | 0.282813i | \(-0.908732\pi\) | ||||
−0.959175 | + | 0.282813i | \(0.908732\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.99647 | −0.601959 | −0.300979 | − | 0.953631i | \(-0.597314\pi\) | ||||
−0.300979 | + | 0.953631i | \(0.597314\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.82627 | −1.61592 | −0.807959 | − | 0.589239i | \(-0.799428\pi\) | ||||
−0.807959 | + | 0.589239i | \(0.799428\pi\) | |||||||
\(14\) | −5.07548 | −1.35648 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.54221 | 1.10165 | 0.550824 | − | 0.834622i | \(-0.314314\pi\) | ||||
0.550824 | + | 0.834622i | \(0.314314\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.38225 | −1.69360 | −0.846802 | − | 0.531908i | \(-0.821475\pi\) | ||||
−0.846802 | + | 0.531908i | \(0.821475\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.99647 | −0.425649 | ||||||||
\(23\) | 1.23986 | 0.258530 | 0.129265 | − | 0.991610i | \(-0.458738\pi\) | ||||
0.129265 | + | 0.991610i | \(0.458738\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.82627 | −1.14263 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.07548 | −0.959175 | ||||||||
\(29\) | −2.25904 | −0.419494 | −0.209747 | − | 0.977756i | \(-0.567264\pi\) | ||||
−0.209747 | + | 0.977756i | \(0.567264\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.32468 | −0.417525 | −0.208763 | − | 0.977966i | \(-0.566944\pi\) | ||||
−0.208763 | + | 0.977966i | \(0.566944\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.54221 | 0.778982 | ||||||||
\(35\) | −5.07548 | −0.857912 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.84545 | 1.45418 | 0.727092 | − | 0.686541i | \(-0.240872\pi\) | ||||
0.727092 | + | 0.686541i | \(0.240872\pi\) | |||||||
\(38\) | −7.38225 | −1.19756 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 10.3743 | 1.62019 | 0.810096 | − | 0.586297i | \(-0.199415\pi\) | ||||
0.810096 | + | 0.586297i | \(0.199415\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.6712 | −1.77985 | −0.889923 | − | 0.456112i | \(-0.849242\pi\) | ||||
−0.889923 | + | 0.456112i | \(0.849242\pi\) | |||||||
\(44\) | −1.99647 | −0.300979 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.23986 | 0.182808 | ||||||||
\(47\) | 4.79584 | 0.699545 | 0.349773 | − | 0.936835i | \(-0.386259\pi\) | ||||
0.349773 | + | 0.936835i | \(0.386259\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.7605 | 2.68007 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.82627 | −0.807959 | ||||||||
\(53\) | 10.0857 | 1.38538 | 0.692690 | − | 0.721236i | \(-0.256425\pi\) | ||||
0.692690 | + | 0.721236i | \(0.256425\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.99647 | −0.269204 | ||||||||
\(56\) | −5.07548 | −0.678239 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.25904 | −0.296627 | ||||||||
\(59\) | 3.00090 | 0.390684 | 0.195342 | − | 0.980735i | \(-0.437418\pi\) | ||||
0.195342 | + | 0.980735i | \(0.437418\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.57657 | 0.714007 | 0.357003 | − | 0.934103i | \(-0.383798\pi\) | ||||
0.357003 | + | 0.934103i | \(0.383798\pi\) | |||||||
\(62\) | −2.32468 | −0.295235 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.82627 | −0.722660 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6279 | 1.29841 | 0.649204 | − | 0.760614i | \(-0.275102\pi\) | ||||
0.649204 | + | 0.760614i | \(0.275102\pi\) | |||||||
\(68\) | 4.54221 | 0.550824 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.07548 | −0.606636 | ||||||||
\(71\) | 8.65205 | 1.02681 | 0.513405 | − | 0.858147i | \(-0.328384\pi\) | ||||
0.513405 | + | 0.858147i | \(0.328384\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.77313 | 0.207530 | 0.103765 | − | 0.994602i | \(-0.466911\pi\) | ||||
0.103765 | + | 0.994602i | \(0.466911\pi\) | |||||||
\(74\) | 8.84545 | 1.02826 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.38225 | −0.846802 | ||||||||
\(77\) | 10.1330 | 1.15477 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.85479 | −0.771224 | −0.385612 | − | 0.922661i | \(-0.626010\pi\) | ||||
−0.385612 | + | 0.922661i | \(0.626010\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.3743 | 1.14565 | ||||||||
\(83\) | −9.44789 | −1.03704 | −0.518520 | − | 0.855065i | \(-0.673517\pi\) | ||||
−0.518520 | + | 0.855065i | \(0.673517\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.54221 | 0.492672 | ||||||||
\(86\) | −11.6712 | −1.25854 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.99647 | −0.212825 | ||||||||
\(89\) | −1.00000 | −0.106000 | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 29.5711 | 3.09990 | ||||||||
\(92\) | 1.23986 | 0.129265 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.79584 | 0.494653 | ||||||||
\(95\) | −7.38225 | −0.757403 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.47973 | 0.454848 | 0.227424 | − | 0.973796i | \(-0.426970\pi\) | ||||
0.227424 | + | 0.973796i | \(0.426970\pi\) | |||||||
\(98\) | 18.7605 | 1.89509 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 16.4984 | 1.64165 | 0.820826 | − | 0.571178i | \(-0.193514\pi\) | ||||
0.820826 | + | 0.571178i | \(0.193514\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.536798 | −0.0528923 | −0.0264461 | − | 0.999650i | \(-0.508419\pi\) | ||||
−0.0264461 | + | 0.999650i | \(0.508419\pi\) | |||||||
\(104\) | −5.82627 | −0.571313 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.0857 | 0.979611 | ||||||||
\(107\) | −2.47267 | −0.239042 | −0.119521 | − | 0.992832i | \(-0.538136\pi\) | ||||
−0.119521 | + | 0.992832i | \(0.538136\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.49891 | 0.718265 | 0.359133 | − | 0.933287i | \(-0.383073\pi\) | ||||
0.359133 | + | 0.933287i | \(0.383073\pi\) | |||||||
\(110\) | −1.99647 | −0.190356 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.07548 | −0.479588 | ||||||||
\(113\) | 2.99204 | 0.281468 | 0.140734 | − | 0.990047i | \(-0.455054\pi\) | ||||
0.140734 | + | 0.990047i | \(0.455054\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.23986 | 0.115618 | ||||||||
\(116\) | −2.25904 | −0.209747 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.00090 | 0.276255 | ||||||||
\(119\) | −23.0539 | −2.11335 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.01410 | −0.637646 | ||||||||
\(122\) | 5.57657 | 0.504879 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.32468 | −0.208763 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.46370 | 0.573561 | 0.286780 | − | 0.957996i | \(-0.407415\pi\) | ||||
0.286780 | + | 0.957996i | \(0.407415\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.82627 | −0.510998 | ||||||||
\(131\) | −4.56974 | −0.399260 | −0.199630 | − | 0.979871i | \(-0.563974\pi\) | ||||
−0.199630 | + | 0.979871i | \(0.563974\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 37.4684 | 3.24893 | ||||||||
\(134\) | 10.6279 | 0.918113 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.54221 | 0.389491 | ||||||||
\(137\) | −2.99910 | −0.256230 | −0.128115 | − | 0.991759i | \(-0.540893\pi\) | ||||
−0.128115 | + | 0.991759i | \(0.540893\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.1580 | 0.861591 | 0.430796 | − | 0.902449i | \(-0.358233\pi\) | ||||
0.430796 | + | 0.902449i | \(0.358233\pi\) | |||||||
\(140\) | −5.07548 | −0.428956 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.65205 | 0.726064 | ||||||||
\(143\) | 11.6320 | 0.972715 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.25904 | −0.187603 | ||||||||
\(146\) | 1.77313 | 0.146746 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.84545 | 0.727092 | ||||||||
\(149\) | −0.741455 | −0.0607424 | −0.0303712 | − | 0.999539i | \(-0.509669\pi\) | ||||
−0.0303712 | + | 0.999539i | \(0.509669\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.81921 | −0.310803 | −0.155402 | − | 0.987851i | \(-0.549667\pi\) | ||||
−0.155402 | + | 0.987851i | \(0.549667\pi\) | |||||||
\(152\) | −7.38225 | −0.598779 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.1330 | 0.816544 | ||||||||
\(155\) | −2.32468 | −0.186723 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.38315 | −0.349813 | −0.174907 | − | 0.984585i | \(-0.555962\pi\) | ||||
−0.174907 | + | 0.984585i | \(0.555962\pi\) | |||||||
\(158\) | −6.85479 | −0.545338 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −6.29291 | −0.495950 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.7716 | −1.15700 | −0.578499 | − | 0.815683i | \(-0.696361\pi\) | ||||
−0.578499 | + | 0.815683i | \(0.696361\pi\) | |||||||
\(164\) | 10.3743 | 0.810096 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.44789 | −0.733298 | ||||||||
\(167\) | −1.77037 | −0.136996 | −0.0684978 | − | 0.997651i | \(-0.521821\pi\) | ||||
−0.0684978 | + | 0.997651i | \(0.521821\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.9455 | 1.61119 | ||||||||
\(170\) | 4.54221 | 0.348371 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.6712 | −0.889923 | ||||||||
\(173\) | −6.06704 | −0.461268 | −0.230634 | − | 0.973041i | \(-0.574080\pi\) | ||||
−0.230634 | + | 0.973041i | \(0.574080\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.07548 | −0.383670 | ||||||||
\(176\) | −1.99647 | −0.150490 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.00000 | −0.0749532 | ||||||||
\(179\) | 20.5547 | 1.53633 | 0.768165 | − | 0.640252i | \(-0.221170\pi\) | ||||
0.768165 | + | 0.640252i | \(0.221170\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.5112 | −1.89623 | −0.948116 | − | 0.317924i | \(-0.897014\pi\) | ||||
−0.948116 | + | 0.317924i | \(0.897014\pi\) | |||||||
\(182\) | 29.5711 | 2.19196 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.23986 | 0.0914041 | ||||||||
\(185\) | 8.84545 | 0.650330 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.06839 | −0.663146 | ||||||||
\(188\) | 4.79584 | 0.349773 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.38225 | −0.535565 | ||||||||
\(191\) | −12.6042 | −0.912008 | −0.456004 | − | 0.889978i | \(-0.650720\pi\) | ||||
−0.456004 | + | 0.889978i | \(0.650720\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.2363 | 1.45664 | 0.728319 | − | 0.685238i | \(-0.240302\pi\) | ||||
0.728319 | + | 0.685238i | \(0.240302\pi\) | |||||||
\(194\) | 4.47973 | 0.321626 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.7605 | 1.34003 | ||||||||
\(197\) | −23.2562 | −1.65694 | −0.828470 | − | 0.560034i | \(-0.810788\pi\) | ||||
−0.828470 | + | 0.560034i | \(0.810788\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.9954 | 1.41744 | 0.708719 | − | 0.705491i | \(-0.249273\pi\) | ||||
0.708719 | + | 0.705491i | \(0.249273\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.4984 | 1.16082 | ||||||||
\(203\) | 11.4657 | 0.804736 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.3743 | 0.724572 | ||||||||
\(206\) | −0.536798 | −0.0374005 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.82627 | −0.403979 | ||||||||
\(209\) | 14.7384 | 1.01948 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.5992 | −1.07389 | −0.536947 | − | 0.843616i | \(-0.680422\pi\) | ||||
−0.536947 | + | 0.843616i | \(0.680422\pi\) | |||||||
\(212\) | 10.0857 | 0.692690 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.47267 | −0.169028 | ||||||||
\(215\) | −11.6712 | −0.795971 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.7989 | 0.800960 | ||||||||
\(218\) | 7.49891 | 0.507890 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.99647 | −0.134602 | ||||||||
\(221\) | −26.4641 | −1.78017 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.08392 | 0.139549 | 0.0697747 | − | 0.997563i | \(-0.477772\pi\) | ||||
0.0697747 | + | 0.997563i | \(0.477772\pi\) | |||||||
\(224\) | −5.07548 | −0.339120 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.99204 | 0.199028 | ||||||||
\(227\) | 16.2848 | 1.08086 | 0.540429 | − | 0.841390i | \(-0.318262\pi\) | ||||
0.540429 | + | 0.841390i | \(0.318262\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.1214 | 1.06533 | 0.532667 | − | 0.846325i | \(-0.321190\pi\) | ||||
0.532667 | + | 0.846325i | \(0.321190\pi\) | |||||||
\(230\) | 1.23986 | 0.0817543 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.25904 | −0.148313 | ||||||||
\(233\) | −18.2358 | −1.19467 | −0.597334 | − | 0.801992i | \(-0.703773\pi\) | ||||
−0.597334 | + | 0.801992i | \(0.703773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.79584 | 0.312846 | ||||||||
\(236\) | 3.00090 | 0.195342 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −23.0539 | −1.49436 | ||||||||
\(239\) | 11.6735 | 0.755096 | 0.377548 | − | 0.925990i | \(-0.376767\pi\) | ||||
0.377548 | + | 0.925990i | \(0.376767\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.66417 | −0.107198 | −0.0535992 | − | 0.998563i | \(-0.517069\pi\) | ||||
−0.0535992 | + | 0.998563i | \(0.517069\pi\) | |||||||
\(242\) | −7.01410 | −0.450884 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.57657 | 0.357003 | ||||||||
\(245\) | 18.7605 | 1.19856 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 43.0110 | 2.73672 | ||||||||
\(248\) | −2.32468 | −0.147617 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −9.80102 | −0.618635 | −0.309317 | − | 0.950959i | \(-0.600101\pi\) | ||||
−0.309317 | + | 0.950959i | \(0.600101\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.47535 | −0.155624 | ||||||||
\(254\) | 6.46370 | 0.405569 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.6966 | −0.916750 | −0.458375 | − | 0.888759i | \(-0.651568\pi\) | ||||
−0.458375 | + | 0.888759i | \(0.651568\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −44.8949 | −2.78963 | ||||||||
\(260\) | −5.82627 | −0.361330 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.56974 | −0.282320 | ||||||||
\(263\) | 22.0723 | 1.36103 | 0.680517 | − | 0.732733i | \(-0.261755\pi\) | ||||
0.680517 | + | 0.732733i | \(0.261755\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0857 | 0.619561 | ||||||||
\(266\) | 37.4684 | 2.29734 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.6279 | 0.649204 | ||||||||
\(269\) | 16.0973 | 0.981467 | 0.490733 | − | 0.871310i | \(-0.336729\pi\) | ||||
0.490733 | + | 0.871310i | \(0.336729\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.89944 | 0.540602 | 0.270301 | − | 0.962776i | \(-0.412877\pi\) | ||||
0.270301 | + | 0.962776i | \(0.412877\pi\) | |||||||
\(272\) | 4.54221 | 0.275412 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.99910 | −0.181182 | ||||||||
\(275\) | −1.99647 | −0.120392 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.86117 | 0.171911 | 0.0859554 | − | 0.996299i | \(-0.472606\pi\) | ||||
0.0859554 | + | 0.996299i | \(0.472606\pi\) | |||||||
\(278\) | 10.1580 | 0.609237 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.07548 | −0.303318 | ||||||||
\(281\) | −9.20148 | −0.548914 | −0.274457 | − | 0.961599i | \(-0.588498\pi\) | ||||
−0.274457 | + | 0.961599i | \(0.588498\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.7789 | 0.759626 | 0.379813 | − | 0.925063i | \(-0.375988\pi\) | ||||
0.379813 | + | 0.925063i | \(0.375988\pi\) | |||||||
\(284\) | 8.65205 | 0.513405 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.6320 | 0.687814 | ||||||||
\(287\) | −52.6545 | −3.10810 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.63165 | 0.213627 | ||||||||
\(290\) | −2.25904 | −0.132656 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.77313 | 0.103765 | ||||||||
\(293\) | 1.01175 | 0.0591072 | 0.0295536 | − | 0.999563i | \(-0.490591\pi\) | ||||
0.0295536 | + | 0.999563i | \(0.490591\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00090 | 0.174719 | ||||||||
\(296\) | 8.84545 | 0.514131 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.741455 | −0.0429513 | ||||||||
\(299\) | −7.22379 | −0.417763 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 59.2370 | 3.41437 | ||||||||
\(302\) | −3.81921 | −0.219771 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.38225 | −0.423401 | ||||||||
\(305\) | 5.57657 | 0.319313 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.8807 | 0.620995 | 0.310497 | − | 0.950574i | \(-0.399504\pi\) | ||||
0.310497 | + | 0.950574i | \(0.399504\pi\) | |||||||
\(308\) | 10.1330 | 0.577384 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.32468 | −0.132033 | ||||||||
\(311\) | 24.2777 | 1.37666 | 0.688331 | − | 0.725396i | \(-0.258344\pi\) | ||||
0.688331 | + | 0.725396i | \(0.258344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.58691 | 0.428837 | 0.214419 | − | 0.976742i | \(-0.431214\pi\) | ||||
0.214419 | + | 0.976742i | \(0.431214\pi\) | |||||||
\(314\) | −4.38315 | −0.247355 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.85479 | −0.385612 | ||||||||
\(317\) | −27.8079 | −1.56185 | −0.780923 | − | 0.624627i | \(-0.785251\pi\) | ||||
−0.780923 | + | 0.624627i | \(0.785251\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.51011 | 0.252518 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.29291 | −0.350690 | ||||||||
\(323\) | −33.5317 | −1.86575 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.82627 | −0.323183 | ||||||||
\(326\) | −14.7716 | −0.818121 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.3743 | 0.572824 | ||||||||
\(329\) | −24.3412 | −1.34197 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.340397 | −0.0187099 | −0.00935496 | − | 0.999956i | \(-0.502978\pi\) | ||||
−0.00935496 | + | 0.999956i | \(0.502978\pi\) | |||||||
\(332\) | −9.44789 | −0.518520 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.77037 | −0.0968706 | ||||||||
\(335\) | 10.6279 | 0.580666 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.55121 | 0.0845000 | 0.0422500 | − | 0.999107i | \(-0.486547\pi\) | ||||
0.0422500 | + | 0.999107i | \(0.486547\pi\) | |||||||
\(338\) | 20.9455 | 1.13928 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.54221 | 0.246336 | ||||||||
\(341\) | 4.64116 | 0.251333 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −59.6900 | −3.22296 | ||||||||
\(344\) | −11.6712 | −0.629270 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.06704 | −0.326166 | ||||||||
\(347\) | −16.7549 | −0.899450 | −0.449725 | − | 0.893167i | \(-0.648478\pi\) | ||||
−0.449725 | + | 0.893167i | \(0.648478\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.9284 | −1.38791 | −0.693957 | − | 0.720016i | \(-0.744134\pi\) | ||||
−0.693957 | + | 0.720016i | \(0.744134\pi\) | |||||||
\(350\) | −5.07548 | −0.271296 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.99647 | −0.106412 | ||||||||
\(353\) | −21.3394 | −1.13578 | −0.567890 | − | 0.823105i | \(-0.692240\pi\) | ||||
−0.567890 | + | 0.823105i | \(0.692240\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.65205 | 0.459203 | ||||||||
\(356\) | −1.00000 | −0.0529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.5547 | 1.08635 | ||||||||
\(359\) | 34.3005 | 1.81031 | 0.905156 | − | 0.425081i | \(-0.139754\pi\) | ||||
0.905156 | + | 0.425081i | \(0.139754\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 35.4976 | 1.86829 | ||||||||
\(362\) | −25.5112 | −1.34084 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 29.5711 | 1.54995 | ||||||||
\(365\) | 1.77313 | 0.0928101 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.1434 | −0.581681 | −0.290840 | − | 0.956772i | \(-0.593935\pi\) | ||||
−0.290840 | + | 0.956772i | \(0.593935\pi\) | |||||||
\(368\) | 1.23986 | 0.0646324 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.84545 | 0.459853 | ||||||||
\(371\) | −51.1898 | −2.65764 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.5452 | −1.84046 | −0.920230 | − | 0.391378i | \(-0.871999\pi\) | ||||
−0.920230 | + | 0.391378i | \(0.871999\pi\) | |||||||
\(374\) | −9.06839 | −0.468915 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.79584 | 0.247327 | ||||||||
\(377\) | 13.1618 | 0.677867 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.7720 | 1.47792 | 0.738960 | − | 0.673749i | \(-0.235317\pi\) | ||||
0.738960 | + | 0.673749i | \(0.235317\pi\) | |||||||
\(380\) | −7.38225 | −0.378701 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.6042 | −0.644887 | ||||||||
\(383\) | 34.0955 | 1.74220 | 0.871100 | − | 0.491106i | \(-0.163407\pi\) | ||||
0.871100 | + | 0.491106i | \(0.163407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.1330 | 0.516428 | ||||||||
\(386\) | 20.2363 | 1.03000 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.47973 | 0.227424 | ||||||||
\(389\) | −36.0768 | −1.82917 | −0.914584 | − | 0.404395i | \(-0.867482\pi\) | ||||
−0.914584 | + | 0.404395i | \(0.867482\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.63172 | 0.284809 | ||||||||
\(392\) | 18.7605 | 0.947547 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.2562 | −1.17163 | ||||||||
\(395\) | −6.85479 | −0.344902 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.6401 | −1.43741 | −0.718703 | − | 0.695318i | \(-0.755264\pi\) | ||||
−0.718703 | + | 0.695318i | \(0.755264\pi\) | |||||||
\(398\) | 19.9954 | 1.00228 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 0.299964 | 0.0149795 | 0.00748974 | − | 0.999972i | \(-0.497616\pi\) | ||||
0.00748974 | + | 0.999972i | \(0.497616\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.5442 | 0.674686 | ||||||||
\(404\) | 16.4984 | 0.820826 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.4657 | 0.569034 | ||||||||
\(407\) | −17.6597 | −0.875358 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.7289 | 0.827191 | 0.413595 | − | 0.910461i | \(-0.364273\pi\) | ||||
0.413595 | + | 0.910461i | \(0.364273\pi\) | |||||||
\(410\) | 10.3743 | 0.512350 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.536798 | −0.0264461 | ||||||||
\(413\) | −15.2310 | −0.749468 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.44789 | −0.463779 | ||||||||
\(416\) | −5.82627 | −0.285657 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.7384 | 0.720881 | ||||||||
\(419\) | 16.8301 | 0.822206 | 0.411103 | − | 0.911589i | \(-0.365144\pi\) | ||||
0.411103 | + | 0.911589i | \(0.365144\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.3008 | 1.28182 | 0.640911 | − | 0.767615i | \(-0.278557\pi\) | ||||
0.640911 | + | 0.767615i | \(0.278557\pi\) | |||||||
\(422\) | −15.5992 | −0.759358 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.0857 | 0.489806 | ||||||||
\(425\) | 4.54221 | 0.220329 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.3038 | −1.36971 | ||||||||
\(428\) | −2.47267 | −0.119521 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.6712 | −0.562836 | ||||||||
\(431\) | 18.2075 | 0.877025 | 0.438512 | − | 0.898725i | \(-0.355506\pi\) | ||||
0.438512 | + | 0.898725i | \(0.355506\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.5844 | −0.893110 | −0.446555 | − | 0.894756i | \(-0.647349\pi\) | ||||
−0.446555 | + | 0.894756i | \(0.647349\pi\) | |||||||
\(434\) | 11.7989 | 0.566364 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.49891 | 0.359133 | ||||||||
\(437\) | −9.15299 | −0.437847 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.7898 | 1.46952 | 0.734759 | − | 0.678328i | \(-0.237295\pi\) | ||||
0.734759 | + | 0.678328i | \(0.237295\pi\) | |||||||
\(440\) | −1.99647 | −0.0951780 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −26.4641 | −1.25877 | ||||||||
\(443\) | 1.82123 | 0.0865293 | 0.0432646 | − | 0.999064i | \(-0.486224\pi\) | ||||
0.0432646 | + | 0.999064i | \(0.486224\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.00000 | −0.0474045 | ||||||||
\(446\) | 2.08392 | 0.0986764 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.07548 | −0.239794 | ||||||||
\(449\) | −15.6167 | −0.736997 | −0.368498 | − | 0.929628i | \(-0.620128\pi\) | ||||
−0.368498 | + | 0.929628i | \(0.620128\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.7120 | −0.975289 | ||||||||
\(452\) | 2.99204 | 0.140734 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.2848 | 0.764282 | ||||||||
\(455\) | 29.5711 | 1.38632 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 41.5922 | 1.94560 | 0.972799 | − | 0.231649i | \(-0.0744121\pi\) | ||||
0.972799 | + | 0.231649i | \(0.0744121\pi\) | |||||||
\(458\) | 16.1214 | 0.753305 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.23986 | 0.0578090 | ||||||||
\(461\) | 10.9806 | 0.511417 | 0.255708 | − | 0.966754i | \(-0.417691\pi\) | ||||
0.255708 | + | 0.966754i | \(0.417691\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.8145 | −1.71091 | −0.855457 | − | 0.517874i | \(-0.826724\pi\) | ||||
−0.855457 | + | 0.517874i | \(0.826724\pi\) | |||||||
\(464\) | −2.25904 | −0.104873 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −18.2358 | −0.844758 | ||||||||
\(467\) | 32.3762 | 1.49819 | 0.749096 | − | 0.662462i | \(-0.230488\pi\) | ||||
0.749096 | + | 0.662462i | \(0.230488\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −53.9418 | −2.49080 | ||||||||
\(470\) | 4.79584 | 0.221216 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.00090 | 0.138128 | ||||||||
\(473\) | 23.3013 | 1.07139 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.38225 | −0.338721 | ||||||||
\(476\) | −23.0539 | −1.05667 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.6735 | 0.533934 | ||||||||
\(479\) | 0.901550 | 0.0411929 | 0.0205964 | − | 0.999788i | \(-0.493443\pi\) | ||||
0.0205964 | + | 0.999788i | \(0.493443\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −51.5360 | −2.34984 | ||||||||
\(482\) | −1.66417 | −0.0758007 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.01410 | −0.318823 | ||||||||
\(485\) | 4.47973 | 0.203414 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −42.0001 | −1.90320 | −0.951602 | − | 0.307333i | \(-0.900564\pi\) | ||||
−0.951602 | + | 0.307333i | \(0.900564\pi\) | |||||||
\(488\) | 5.57657 | 0.252439 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 18.7605 | 0.847512 | ||||||||
\(491\) | 19.7629 | 0.891885 | 0.445943 | − | 0.895061i | \(-0.352868\pi\) | ||||
0.445943 | + | 0.895061i | \(0.352868\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2610 | −0.462134 | ||||||||
\(494\) | 43.0110 | 1.93516 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.32468 | −0.104381 | ||||||||
\(497\) | −43.9133 | −1.96978 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.29093 | −0.415919 | −0.207959 | − | 0.978137i | \(-0.566682\pi\) | ||||
−0.207959 | + | 0.978137i | \(0.566682\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.80102 | −0.437441 | ||||||||
\(503\) | 16.3646 | 0.729661 | 0.364830 | − | 0.931074i | \(-0.381127\pi\) | ||||
0.364830 | + | 0.931074i | \(0.381127\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.4984 | 0.734169 | ||||||||
\(506\) | −2.47535 | −0.110043 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.46370 | 0.286780 | ||||||||
\(509\) | 6.05293 | 0.268292 | 0.134146 | − | 0.990962i | \(-0.457171\pi\) | ||||
0.134146 | + | 0.990962i | \(0.457171\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.99950 | −0.398115 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.6966 | −0.648240 | ||||||||
\(515\) | −0.536798 | −0.0236542 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.57476 | −0.421097 | ||||||||
\(518\) | −44.8949 | −1.97257 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.82627 | −0.255499 | ||||||||
\(521\) | 25.2209 | 1.10495 | 0.552475 | − | 0.833530i | \(-0.313684\pi\) | ||||
0.552475 | + | 0.833530i | \(0.313684\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −44.2331 | −1.93418 | −0.967090 | − | 0.254434i | \(-0.918111\pi\) | ||||
−0.967090 | + | 0.254434i | \(0.918111\pi\) | |||||||
\(524\) | −4.56974 | −0.199630 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.0723 | 0.962396 | ||||||||
\(527\) | −10.5592 | −0.459966 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.4627 | −0.933162 | ||||||||
\(530\) | 10.0857 | 0.438096 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 37.4684 | 1.62446 | ||||||||
\(533\) | −60.4435 | −2.61810 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.47267 | −0.106903 | ||||||||
\(536\) | 10.6279 | 0.459056 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.0973 | 0.694002 | ||||||||
\(539\) | −37.4547 | −1.61329 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.6888 | −0.545536 | −0.272768 | − | 0.962080i | \(-0.587939\pi\) | ||||
−0.272768 | + | 0.962080i | \(0.587939\pi\) | |||||||
\(542\) | 8.89944 | 0.382263 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.54221 | 0.194746 | ||||||||
\(545\) | 7.49891 | 0.321218 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.1619 | 0.904819 | 0.452409 | − | 0.891810i | \(-0.350565\pi\) | ||||
0.452409 | + | 0.891810i | \(0.350565\pi\) | |||||||
\(548\) | −2.99910 | −0.128115 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.99647 | −0.0851298 | ||||||||
\(551\) | 16.6768 | 0.710456 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 34.7913 | 1.47948 | ||||||||
\(554\) | 2.86117 | 0.121559 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.1580 | 0.430796 | ||||||||
\(557\) | 36.4757 | 1.54553 | 0.772763 | − | 0.634694i | \(-0.218874\pi\) | ||||
0.772763 | + | 0.634694i | \(0.218874\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 67.9997 | 2.87608 | ||||||||
\(560\) | −5.07548 | −0.214478 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.20148 | −0.388141 | ||||||||
\(563\) | −26.1875 | −1.10367 | −0.551836 | − | 0.833953i | \(-0.686072\pi\) | ||||
−0.551836 | + | 0.833953i | \(0.686072\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.99204 | 0.125876 | ||||||||
\(566\) | 12.7789 | 0.537136 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.65205 | 0.363032 | ||||||||
\(569\) | 29.5139 | 1.23729 | 0.618643 | − | 0.785672i | \(-0.287683\pi\) | ||||
0.618643 | + | 0.785672i | \(0.287683\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.8378 | −0.913883 | −0.456941 | − | 0.889497i | \(-0.651055\pi\) | ||||
−0.456941 | + | 0.889497i | \(0.651055\pi\) | |||||||
\(572\) | 11.6320 | 0.486358 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −52.6545 | −2.19776 | ||||||||
\(575\) | 1.23986 | 0.0517059 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.2920 | 0.803138 | 0.401569 | − | 0.915829i | \(-0.368465\pi\) | ||||
0.401569 | + | 0.915829i | \(0.368465\pi\) | |||||||
\(578\) | 3.63165 | 0.151057 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.25904 | −0.0938017 | ||||||||
\(581\) | 47.9525 | 1.98941 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.1358 | −0.833941 | ||||||||
\(584\) | 1.77313 | 0.0733728 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.01175 | 0.0417951 | ||||||||
\(587\) | −21.4839 | −0.886734 | −0.443367 | − | 0.896340i | \(-0.646216\pi\) | ||||
−0.443367 | + | 0.896340i | \(0.646216\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.1614 | 0.707122 | ||||||||
\(590\) | 3.00090 | 0.123545 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.84545 | 0.363546 | ||||||||
\(593\) | 35.9315 | 1.47553 | 0.737766 | − | 0.675057i | \(-0.235881\pi\) | ||||
0.737766 | + | 0.675057i | \(0.235881\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.0539 | −0.945117 | ||||||||
\(596\) | −0.741455 | −0.0303712 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.22379 | −0.295403 | ||||||||
\(599\) | 29.7968 | 1.21746 | 0.608732 | − | 0.793376i | \(-0.291678\pi\) | ||||
0.608732 | + | 0.793376i | \(0.291678\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.4573 | 1.24238 | 0.621190 | − | 0.783660i | \(-0.286649\pi\) | ||||
0.621190 | + | 0.783660i | \(0.286649\pi\) | |||||||
\(602\) | 59.2370 | 2.41432 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.81921 | −0.155402 | ||||||||
\(605\) | −7.01410 | −0.285164 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.6738 | −1.04207 | −0.521033 | − | 0.853537i | \(-0.674453\pi\) | ||||
−0.521033 | + | 0.853537i | \(0.674453\pi\) | |||||||
\(608\) | −7.38225 | −0.299390 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.57657 | 0.225789 | ||||||||
\(611\) | −27.9419 | −1.13041 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.04363 | 0.0825416 | 0.0412708 | − | 0.999148i | \(-0.486859\pi\) | ||||
0.0412708 | + | 0.999148i | \(0.486859\pi\) | |||||||
\(614\) | 10.8807 | 0.439110 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.1330 | 0.408272 | ||||||||
\(617\) | 18.1550 | 0.730894 | 0.365447 | − | 0.930832i | \(-0.380916\pi\) | ||||
0.365447 | + | 0.930832i | \(0.380916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.644800 | −0.0259167 | −0.0129584 | − | 0.999916i | \(-0.504125\pi\) | ||||
−0.0129584 | + | 0.999916i | \(0.504125\pi\) | |||||||
\(620\) | −2.32468 | −0.0933615 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.2777 | 0.973447 | ||||||||
\(623\) | 5.07548 | 0.203345 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.58691 | 0.303234 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.38315 | −0.174907 | ||||||||
\(629\) | 40.1779 | 1.60200 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.4511 | 0.654907 | 0.327453 | − | 0.944867i | \(-0.393810\pi\) | ||||
0.327453 | + | 0.944867i | \(0.393810\pi\) | |||||||
\(632\) | −6.85479 | −0.272669 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −27.8079 | −1.10439 | ||||||||
\(635\) | 6.46370 | 0.256504 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −109.304 | −4.33077 | ||||||||
\(638\) | 4.51011 | 0.178557 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −23.1359 | −0.913812 | −0.456906 | − | 0.889515i | \(-0.651042\pi\) | ||||
−0.456906 | + | 0.889515i | \(0.651042\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.6516 | −1.09047 | −0.545236 | − | 0.838283i | \(-0.683560\pi\) | ||||
−0.545236 | + | 0.838283i | \(0.683560\pi\) | |||||||
\(644\) | −6.29291 | −0.247975 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −33.5317 | −1.31929 | ||||||||
\(647\) | 23.9588 | 0.941918 | 0.470959 | − | 0.882155i | \(-0.343908\pi\) | ||||
0.470959 | + | 0.882155i | \(0.343908\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.99121 | −0.235176 | ||||||||
\(650\) | −5.82627 | −0.228525 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.7716 | −0.578499 | ||||||||
\(653\) | 47.2481 | 1.84896 | 0.924480 | − | 0.381229i | \(-0.124499\pi\) | ||||
0.924480 | + | 0.381229i | \(0.124499\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.56974 | −0.178555 | ||||||||
\(656\) | 10.3743 | 0.405048 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −24.3412 | −0.948918 | ||||||||
\(659\) | 35.5901 | 1.38639 | 0.693196 | − | 0.720749i | \(-0.256202\pi\) | ||||
0.693196 | + | 0.720749i | \(0.256202\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.5722 | 0.683479 | 0.341739 | − | 0.939795i | \(-0.388984\pi\) | ||||
0.341739 | + | 0.939795i | \(0.388984\pi\) | |||||||
\(662\) | −0.340397 | −0.0132299 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.44789 | −0.366649 | ||||||||
\(665\) | 37.4684 | 1.45296 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.80091 | −0.108452 | ||||||||
\(668\) | −1.77037 | −0.0684978 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.6279 | 0.410593 | ||||||||
\(671\) | −11.1335 | −0.429802 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.5686 | −1.13978 | −0.569892 | − | 0.821719i | \(-0.693015\pi\) | ||||
−0.569892 | + | 0.821719i | \(0.693015\pi\) | |||||||
\(674\) | 1.55121 | 0.0597505 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.9455 | 0.805594 | ||||||||
\(677\) | 13.6656 | 0.525213 | 0.262607 | − | 0.964903i | \(-0.415418\pi\) | ||||
0.262607 | + | 0.964903i | \(0.415418\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.7368 | −0.872557 | ||||||||
\(680\) | 4.54221 | 0.174186 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.64116 | 0.177719 | ||||||||
\(683\) | −6.12490 | −0.234363 | −0.117181 | − | 0.993111i | \(-0.537386\pi\) | ||||
−0.117181 | + | 0.993111i | \(0.537386\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.99910 | −0.114590 | ||||||||
\(686\) | −59.6900 | −2.27897 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11.6712 | −0.444961 | ||||||||
\(689\) | −58.7621 | −2.23866 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.5414 | 0.705348 | 0.352674 | − | 0.935746i | \(-0.385272\pi\) | ||||
0.352674 | + | 0.935746i | \(0.385272\pi\) | |||||||
\(692\) | −6.06704 | −0.230634 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.7549 | −0.636008 | ||||||||
\(695\) | 10.1580 | 0.385315 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 47.1222 | 1.78488 | ||||||||
\(698\) | −25.9284 | −0.981403 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.07548 | −0.191835 | ||||||||
\(701\) | 3.09528 | 0.116907 | 0.0584536 | − | 0.998290i | \(-0.481383\pi\) | ||||
0.0584536 | + | 0.998290i | \(0.481383\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −65.2993 | −2.46281 | ||||||||
\(704\) | −1.99647 | −0.0752448 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.3394 | −0.803118 | ||||||||
\(707\) | −83.7372 | −3.14926 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.6815 | 0.626486 | 0.313243 | − | 0.949673i | \(-0.398585\pi\) | ||||
0.313243 | + | 0.949673i | \(0.398585\pi\) | |||||||
\(710\) | 8.65205 | 0.324706 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.00000 | −0.0374766 | ||||||||
\(713\) | −2.88229 | −0.107943 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.6320 | 0.435012 | ||||||||
\(716\) | 20.5547 | 0.768165 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 34.3005 | 1.28008 | ||||||||
\(719\) | 38.5013 | 1.43586 | 0.717928 | − | 0.696118i | \(-0.245091\pi\) | ||||
0.717928 | + | 0.696118i | \(0.245091\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.72451 | 0.101466 | ||||||||
\(722\) | 35.4976 | 1.32108 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −25.5112 | −0.948116 | ||||||||
\(725\) | −2.25904 | −0.0838987 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.8143 | 1.84751 | 0.923755 | − | 0.382983i | \(-0.125103\pi\) | ||||
0.923755 | + | 0.382983i | \(0.125103\pi\) | |||||||
\(728\) | 29.5711 | 1.09598 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.77313 | 0.0656266 | ||||||||
\(731\) | −53.0131 | −1.96076 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.99504 | 0.184496 | 0.0922480 | − | 0.995736i | \(-0.470595\pi\) | ||||
0.0922480 | + | 0.995736i | \(0.470595\pi\) | |||||||
\(734\) | −11.1434 | −0.411310 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.23986 | 0.0457020 | ||||||||
\(737\) | −21.2183 | −0.781588 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.9949 | 0.882667 | 0.441333 | − | 0.897343i | \(-0.354506\pi\) | ||||
0.441333 | + | 0.897343i | \(0.354506\pi\) | |||||||
\(740\) | 8.84545 | 0.325165 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −51.1898 | −1.87924 | ||||||||
\(743\) | −19.3354 | −0.709347 | −0.354674 | − | 0.934990i | \(-0.615408\pi\) | ||||
−0.354674 | + | 0.934990i | \(0.615408\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.741455 | −0.0271648 | ||||||||
\(746\) | −35.5452 | −1.30140 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.06839 | −0.331573 | ||||||||
\(749\) | 12.5500 | 0.458567 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.8005 | 1.08744 | 0.543718 | − | 0.839268i | \(-0.317016\pi\) | ||||
0.543718 | + | 0.839268i | \(0.317016\pi\) | |||||||
\(752\) | 4.79584 | 0.174886 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.1618 | 0.479324 | ||||||||
\(755\) | −3.81921 | −0.138995 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.7274 | 0.753349 | 0.376675 | − | 0.926346i | \(-0.377068\pi\) | ||||
0.376675 | + | 0.926346i | \(0.377068\pi\) | |||||||
\(758\) | 28.7720 | 1.04505 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.38225 | −0.267782 | ||||||||
\(761\) | 19.5659 | 0.709265 | 0.354632 | − | 0.935006i | \(-0.384606\pi\) | ||||
0.354632 | + | 0.935006i | \(0.384606\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.0605 | −1.37788 | ||||||||
\(764\) | −12.6042 | −0.456004 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.0955 | 1.23192 | ||||||||
\(767\) | −17.4841 | −0.631313 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.6008 | 1.13955 | 0.569777 | − | 0.821799i | \(-0.307030\pi\) | ||||
0.569777 | + | 0.821799i | \(0.307030\pi\) | |||||||
\(770\) | 10.1330 | 0.365170 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20.2363 | 0.728319 | ||||||||
\(773\) | 10.1917 | 0.366568 | 0.183284 | − | 0.983060i | \(-0.441327\pi\) | ||||
0.183284 | + | 0.983060i | \(0.441327\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.32468 | −0.0835050 | ||||||||
\(776\) | 4.47973 | 0.160813 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −36.0768 | −1.29342 | ||||||||
\(779\) | −76.5856 | −2.74396 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.2736 | −0.618097 | ||||||||
\(782\) | 5.63172 | 0.201390 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 18.7605 | 0.670017 | ||||||||
\(785\) | −4.38315 | −0.156441 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.1985 | −0.719999 | −0.359999 | − | 0.932953i | \(-0.617223\pi\) | ||||
−0.359999 | + | 0.932953i | \(0.617223\pi\) | |||||||
\(788\) | −23.2562 | −0.828470 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.85479 | −0.243883 | ||||||||
\(791\) | −15.1860 | −0.539954 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.4906 | −1.15378 | ||||||||
\(794\) | −28.6401 | −1.01640 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.9954 | 0.708719 | ||||||||
\(797\) | 21.4681 | 0.760440 | 0.380220 | − | 0.924896i | \(-0.375848\pi\) | ||||
0.380220 | + | 0.924896i | \(0.375848\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.7837 | 0.770652 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.299964 | 0.0105921 | ||||||||
\(803\) | −3.54001 | −0.124924 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.29291 | −0.221796 | ||||||||
\(806\) | 13.5442 | 0.477075 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.4984 | 0.580412 | ||||||||
\(809\) | −11.9849 | −0.421366 | −0.210683 | − | 0.977554i | \(-0.567569\pi\) | ||||
−0.210683 | + | 0.977554i | \(0.567569\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.0621 | 1.02051 | 0.510254 | − | 0.860023i | \(-0.329551\pi\) | ||||
0.510254 | + | 0.860023i | \(0.329551\pi\) | |||||||
\(812\) | 11.4657 | 0.402368 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.6597 | −0.618972 | ||||||||
\(815\) | −14.7716 | −0.517425 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 86.1599 | 3.01435 | ||||||||
\(818\) | 16.7289 | 0.584912 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.3743 | 0.362286 | ||||||||
\(821\) | −21.7919 | −0.760544 | −0.380272 | − | 0.924875i | \(-0.624170\pi\) | ||||
−0.380272 | + | 0.924875i | \(0.624170\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.9556 | 0.869898 | 0.434949 | − | 0.900455i | \(-0.356766\pi\) | ||||
0.434949 | + | 0.900455i | \(0.356766\pi\) | |||||||
\(824\) | −0.536798 | −0.0187002 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.2310 | −0.529954 | ||||||||
\(827\) | 32.2356 | 1.12094 | 0.560471 | − | 0.828174i | \(-0.310620\pi\) | ||||
0.560471 | + | 0.828174i | \(0.310620\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.997690 | 0.0346512 | 0.0173256 | − | 0.999850i | \(-0.494485\pi\) | ||||
0.0173256 | + | 0.999850i | \(0.494485\pi\) | |||||||
\(830\) | −9.44789 | −0.327941 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.82627 | −0.201990 | ||||||||
\(833\) | 85.2140 | 2.95249 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.77037 | −0.0612663 | ||||||||
\(836\) | 14.7384 | 0.509740 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.8301 | 0.581387 | ||||||||
\(839\) | −33.1776 | −1.14542 | −0.572709 | − | 0.819759i | \(-0.694107\pi\) | ||||
−0.572709 | + | 0.819759i | \(0.694107\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.8967 | −0.824025 | ||||||||
\(842\) | 26.3008 | 0.906385 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15.5992 | −0.536947 | ||||||||
\(845\) | 20.9455 | 0.720545 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35.5999 | 1.22323 | ||||||||
\(848\) | 10.0857 | 0.346345 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.54221 | 0.155796 | ||||||||
\(851\) | 10.9672 | 0.375950 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.71562 | 0.332657 | 0.166328 | − | 0.986070i | \(-0.446809\pi\) | ||||
0.166328 | + | 0.986070i | \(0.446809\pi\) | |||||||
\(854\) | −28.3038 | −0.968534 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.47267 | −0.0845142 | ||||||||
\(857\) | −20.3458 | −0.695001 | −0.347500 | − | 0.937680i | \(-0.612969\pi\) | ||||
−0.347500 | + | 0.937680i | \(0.612969\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.1046 | −1.26599 | −0.632996 | − | 0.774155i | \(-0.718175\pi\) | ||||
−0.632996 | + | 0.774155i | \(0.718175\pi\) | |||||||
\(860\) | −11.6712 | −0.397985 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.2075 | 0.620150 | ||||||||
\(863\) | −21.3660 | −0.727306 | −0.363653 | − | 0.931534i | \(-0.618471\pi\) | ||||
−0.363653 | + | 0.931534i | \(0.618471\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.06704 | −0.206285 | ||||||||
\(866\) | −18.5844 | −0.631524 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.7989 | 0.400480 | ||||||||
\(869\) | 13.6854 | 0.464245 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −61.9212 | −2.09812 | ||||||||
\(872\) | 7.49891 | 0.253945 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.15299 | −0.309605 | ||||||||
\(875\) | −5.07548 | −0.171582 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.9356 | −0.470571 | −0.235285 | − | 0.971926i | \(-0.575603\pi\) | ||||
−0.235285 | + | 0.971926i | \(0.575603\pi\) | |||||||
\(878\) | 30.7898 | 1.03911 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.99647 | −0.0673010 | ||||||||
\(881\) | −18.3276 | −0.617474 | −0.308737 | − | 0.951147i | \(-0.599906\pi\) | ||||
−0.308737 | + | 0.951147i | \(0.599906\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.2023 | 0.444293 | 0.222147 | − | 0.975013i | \(-0.428694\pi\) | ||||
0.222147 | + | 0.975013i | \(0.428694\pi\) | |||||||
\(884\) | −26.4641 | −0.890085 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.82123 | 0.0611854 | ||||||||
\(887\) | 7.40324 | 0.248577 | 0.124288 | − | 0.992246i | \(-0.460335\pi\) | ||||
0.124288 | + | 0.992246i | \(0.460335\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.8064 | −1.10029 | ||||||||
\(890\) | −1.00000 | −0.0335201 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.08392 | 0.0697747 | ||||||||
\(893\) | −35.4041 | −1.18475 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.5547 | 0.687068 | ||||||||
\(896\) | −5.07548 | −0.169560 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.6167 | −0.521135 | ||||||||
\(899\) | 5.25156 | 0.175149 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45.8114 | 1.52620 | ||||||||
\(902\) | −20.7120 | −0.689633 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.99204 | 0.0995139 | ||||||||
\(905\) | −25.5112 | −0.848021 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.5955 | 1.01591 | 0.507954 | − | 0.861384i | \(-0.330402\pi\) | ||||
0.507954 | + | 0.861384i | \(0.330402\pi\) | |||||||
\(908\) | 16.2848 | 0.540429 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 29.5711 | 0.980273 | ||||||||
\(911\) | −34.5117 | −1.14342 | −0.571711 | − | 0.820455i | \(-0.693720\pi\) | ||||
−0.571711 | + | 0.820455i | \(0.693720\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.8624 | 0.624255 | ||||||||
\(914\) | 41.5922 | 1.37575 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.1214 | 0.532667 | ||||||||
\(917\) | 23.1936 | 0.765921 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.15305 | 0.104010 | 0.0520048 | − | 0.998647i | \(-0.483439\pi\) | ||||
0.0520048 | + | 0.998647i | \(0.483439\pi\) | |||||||
\(920\) | 1.23986 | 0.0408771 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.9806 | 0.361626 | ||||||||
\(923\) | −50.4092 | −1.65924 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.84545 | 0.290837 | ||||||||
\(926\) | −36.8145 | −1.20980 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.25904 | −0.0741567 | ||||||||
\(929\) | −37.5164 | −1.23087 | −0.615436 | − | 0.788187i | \(-0.711020\pi\) | ||||
−0.615436 | + | 0.788187i | \(0.711020\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −138.494 | −4.53897 | ||||||||
\(932\) | −18.2358 | −0.597334 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 32.3762 | 1.05938 | ||||||||
\(935\) | −9.06839 | −0.296568 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.8150 | −1.36604 | −0.683018 | − | 0.730401i | \(-0.739333\pi\) | ||||
−0.683018 | + | 0.730401i | \(0.739333\pi\) | |||||||
\(938\) | −53.9418 | −1.76126 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.79584 | 0.156423 | ||||||||
\(941\) | 28.9525 | 0.943824 | 0.471912 | − | 0.881646i | \(-0.343564\pi\) | ||||
0.471912 | + | 0.881646i | \(0.343564\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.8627 | 0.418868 | ||||||||
\(944\) | 3.00090 | 0.0976709 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.3013 | 0.757589 | ||||||||
\(947\) | −46.7288 | −1.51848 | −0.759241 | − | 0.650809i | \(-0.774430\pi\) | ||||
−0.759241 | + | 0.650809i | \(0.774430\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.3308 | −0.335351 | ||||||||
\(950\) | −7.38225 | −0.239512 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −23.0539 | −0.747180 | ||||||||
\(953\) | −1.34233 | −0.0434823 | −0.0217411 | − | 0.999764i | \(-0.506921\pi\) | ||||
−0.0217411 | + | 0.999764i | \(0.506921\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.6042 | −0.407862 | ||||||||
\(956\) | 11.6735 | 0.377548 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.901550 | 0.0291278 | ||||||||
\(959\) | 15.2219 | 0.491540 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.5959 | −0.825673 | ||||||||
\(962\) | −51.5360 | −1.66159 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.66417 | −0.0535992 | ||||||||
\(965\) | 20.2363 | 0.651429 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.9277 | 1.34830 | 0.674152 | − | 0.738593i | \(-0.264509\pi\) | ||||
0.674152 | + | 0.738593i | \(0.264509\pi\) | |||||||
\(968\) | −7.01410 | −0.225442 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.47973 | 0.143835 | ||||||||
\(971\) | −12.4573 | −0.399775 | −0.199887 | − | 0.979819i | \(-0.564058\pi\) | ||||
−0.199887 | + | 0.979819i | \(0.564058\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51.5568 | −1.65283 | ||||||||
\(974\) | −42.0001 | −1.34577 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.57657 | 0.178502 | ||||||||
\(977\) | −7.40272 | −0.236834 | −0.118417 | − | 0.992964i | \(-0.537782\pi\) | ||||
−0.118417 | + | 0.992964i | \(0.537782\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.99647 | 0.0638075 | ||||||||
\(980\) | 18.7605 | 0.599281 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.7629 | 0.630658 | ||||||||
\(983\) | 55.2136 | 1.76104 | 0.880521 | − | 0.474008i | \(-0.157193\pi\) | ||||
0.880521 | + | 0.474008i | \(0.157193\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.2562 | −0.741006 | ||||||||
\(986\) | −10.2610 | −0.326778 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 43.0110 | 1.36836 | ||||||||
\(989\) | −14.4707 | −0.460143 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.5854 | −0.526853 | −0.263426 | − | 0.964680i | \(-0.584853\pi\) | ||||
−0.263426 | + | 0.964680i | \(0.584853\pi\) | |||||||
\(992\) | −2.32468 | −0.0738087 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −43.9133 | −1.39284 | ||||||||
\(995\) | 19.9954 | 0.633898 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.2925 | 0.674341 | 0.337171 | − | 0.941444i | \(-0.390530\pi\) | ||||
0.337171 | + | 0.941444i | \(0.390530\pi\) | |||||||
\(998\) | −9.29093 | −0.294099 | ||||||||
\(999\) | 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 | 8010.2.a.bn.1.1 | 7 | ||
3.2 | odd | 2 | 2670.2.a.t.1.1 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2670.2.a.t.1.1 | ✓ | 7 | 3.2 | odd | 2 | ||
8010.2.a.bn.1.1 | 7 | 1.1 | even | 1 | trivial |