Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2800,2,Mod(1,2800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2800.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: | \(22.3581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.76156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.76156 | −1.01704 | −0.508518 | − | 0.861052i | \(-0.669806\pi\) | ||||
−0.508518 | + | 0.861052i | \(0.669806\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.103084 | 0.0343612 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.626198 | 0.188806 | 0.0944029 | − | 0.995534i | \(-0.469906\pi\) | ||||
0.0944029 | + | 0.995534i | \(0.469906\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.49084 | 1.52288 | 0.761442 | − | 0.648233i | \(-0.224492\pi\) | ||||
0.761442 | + | 0.648233i | \(0.224492\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.896916 | 0.217534 | 0.108767 | − | 0.994067i | \(-0.465310\pi\) | ||||
0.108767 | + | 0.994067i | \(0.465310\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.38776 | −1.46545 | −0.732726 | − | 0.680524i | \(-0.761752\pi\) | ||||
−0.732726 | + | 0.680524i | \(0.761752\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.76156 | 0.384403 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.72928 | 0.777609 | 0.388805 | − | 0.921320i | \(-0.372888\pi\) | ||||
0.388805 | + | 0.921320i | \(0.372888\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.10308 | 0.982089 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.87859 | −1.46302 | −0.731509 | − | 0.681832i | \(-0.761184\pi\) | ||||
−0.731509 | + | 0.681832i | \(0.761184\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.52311 | −1.35119 | −0.675596 | − | 0.737272i | \(-0.736113\pi\) | ||||
−0.675596 | + | 0.737272i | \(0.736113\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.10308 | −0.192022 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.67243 | −1.54883 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.72928 | 1.20711 | 0.603556 | − | 0.797321i | \(-0.293750\pi\) | ||||
0.603556 | + | 0.797321i | \(0.293750\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.72928 | −0.263713 | −0.131856 | − | 0.991269i | \(-0.542094\pi\) | ||||
−0.131856 | + | 0.991269i | \(0.542094\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.87859 | −0.857481 | −0.428741 | − | 0.903428i | \(-0.641043\pi\) | ||||
−0.428741 | + | 0.903428i | \(0.641043\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.57997 | −0.221240 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.77551 | −0.930688 | −0.465344 | − | 0.885130i | \(-0.654069\pi\) | ||||
−0.465344 | + | 0.885130i | \(0.654069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.2524 | 1.49042 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.593923 | 0.0773221 | 0.0386611 | − | 0.999252i | \(-0.487691\pi\) | ||||
0.0386611 | + | 0.999252i | \(0.487691\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.13536 | 0.913589 | 0.456795 | − | 0.889572i | \(-0.348997\pi\) | ||||
0.456795 | + | 0.889572i | \(0.348997\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.103084 | −0.0129873 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.79383 | 0.707829 | 0.353915 | − | 0.935278i | \(-0.384850\pi\) | ||||
0.353915 | + | 0.935278i | \(0.384850\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.56934 | −0.790856 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.52311 | −0.655473 | −0.327737 | − | 0.944769i | \(-0.606286\pi\) | ||||
−0.327737 | + | 0.944769i | \(0.606286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.72928 | −0.436479 | −0.218240 | − | 0.975895i | \(-0.570031\pi\) | ||||
−0.218240 | + | 0.975895i | \(0.570031\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.626198 | −0.0713619 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.67243 | 0.638198 | 0.319099 | − | 0.947721i | \(-0.396620\pi\) | ||||
0.319099 | + | 0.947721i | \(0.396620\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.29862 | −1.03318 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.4340 | 1.91363 | 0.956814 | − | 0.290700i | \(-0.0938882\pi\) | ||||
0.956814 | + | 0.290700i | \(0.0938882\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.8786 | 1.48794 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.2986 | 1.51565 | 0.757826 | − | 0.652457i | \(-0.226262\pi\) | ||||
0.757826 | + | 0.652457i | \(0.226262\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.49084 | −0.575596 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.2524 | 1.37421 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.1493 | −1.03051 | −0.515253 | − | 0.857038i | \(-0.672302\pi\) | ||||
−0.515253 | + | 0.857038i | \(0.672302\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0645508 | 0.00648760 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.64015 | 0.959231 | 0.479615 | − | 0.877479i | \(-0.340776\pi\) | ||||
0.479615 | + | 0.877479i | \(0.340776\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.626198 | 0.0617011 | 0.0308506 | − | 0.999524i | \(-0.490178\pi\) | ||||
0.0308506 | + | 0.999524i | \(0.490178\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.9248 | 1.81267 | 0.906335 | − | 0.422561i | \(-0.138869\pi\) | ||||
0.906335 | + | 0.422561i | \(0.138869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.5693 | −1.00320 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.04623 | −0.0984209 | −0.0492105 | − | 0.998788i | \(-0.515671\pi\) | ||||
−0.0492105 | + | 0.998788i | \(0.515671\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.566016 | 0.0523282 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.896916 | −0.0822202 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6079 | −0.964352 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.6156 | −1.22767 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.2803 | 1.88832 | 0.944161 | − | 0.329485i | \(-0.106875\pi\) | ||||
0.944161 | + | 0.329485i | \(0.106875\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.04623 | 0.268205 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.91087 | 0.865917 | 0.432958 | − | 0.901414i | \(-0.357470\pi\) | ||||
0.432958 | + | 0.901414i | \(0.357470\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.38776 | 0.553889 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.45856 | 0.295485 | 0.147743 | − | 0.989026i | \(-0.452799\pi\) | ||||
0.147743 | + | 0.989026i | \(0.452799\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.4157 | 1.73163 | 0.865817 | − | 0.500361i | \(-0.166799\pi\) | ||||
0.865817 | + | 0.500361i | \(0.166799\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.3555 | 0.872089 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.43835 | 0.287530 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.76156 | −0.145291 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.0462 | −1.39648 | −0.698241 | − | 0.715863i | \(-0.746033\pi\) | ||||
−0.698241 | + | 0.715863i | \(0.746033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.89692 | −0.235748 | −0.117874 | − | 0.993029i | \(-0.537608\pi\) | ||||
−0.117874 | + | 0.993029i | \(0.537608\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.0924575 | 0.00747474 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.1170 | 0.807427 | 0.403714 | − | 0.914885i | \(-0.367719\pi\) | ||||
0.403714 | + | 0.914885i | \(0.367719\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.9354 | 0.946543 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.72928 | −0.293909 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.476886 | −0.0373526 | −0.0186763 | − | 0.999826i | \(-0.505945\pi\) | ||||
−0.0186763 | + | 0.999826i | \(0.505945\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.1676 | 1.01894 | 0.509471 | − | 0.860488i | \(-0.329841\pi\) | ||||
0.509471 | + | 0.860488i | \(0.329841\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.1493 | 1.31918 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.658473 | −0.0503547 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.9677 | 1.06195 | 0.530973 | − | 0.847389i | \(-0.321826\pi\) | ||||
0.530973 | + | 0.847389i | \(0.321826\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.04623 | −0.0786394 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.45856 | −0.557479 | −0.278740 | − | 0.960367i | \(-0.589917\pi\) | ||||
−0.278740 | + | 0.960367i | \(0.589917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.1170 | −1.04931 | −0.524656 | − | 0.851315i | \(-0.675806\pi\) | ||||
−0.524656 | + | 0.851315i | \(0.675806\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.5693 | −0.929153 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.561647 | 0.0410717 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.10308 | −0.371195 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.42003 | 0.609252 | 0.304626 | − | 0.952472i | \(-0.401469\pi\) | ||||
0.304626 | + | 0.952472i | \(0.401469\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.2986 | −1.60509 | −0.802545 | − | 0.596591i | \(-0.796521\pi\) | ||||
−0.802545 | + | 0.596591i | \(0.796521\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.3632 | 1.87830 | 0.939149 | − | 0.343509i | \(-0.111616\pi\) | ||||
0.939149 | + | 0.343509i | \(0.111616\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.4402 | −1.59075 | −0.795373 | − | 0.606120i | \(-0.792725\pi\) | ||||
−0.795373 | + | 0.606120i | \(0.792725\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.2062 | −0.719888 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.87859 | 0.552969 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.384428 | 0.0267196 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.1955 | 1.04610 | 0.523052 | − | 0.852301i | \(-0.324793\pi\) | ||||
0.523052 | + | 0.852301i | \(0.324793\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.72928 | 0.666639 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.52311 | 0.510702 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.56934 | 0.443915 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.92482 | 0.331279 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.89692 | 0.461852 | 0.230926 | − | 0.972971i | \(-0.425825\pi\) | ||||
0.230926 | + | 0.972971i | \(0.425825\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.77988 | 0.184507 | 0.0922535 | − | 0.995736i | \(-0.470593\pi\) | ||||
0.0922535 | + | 0.995736i | \(0.470593\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.6585 | 1.23299 | 0.616493 | − | 0.787360i | \(-0.288553\pi\) | ||||
0.616493 | + | 0.787360i | \(0.288553\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.10308 | 0.0725776 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.0462 | −0.723663 | −0.361831 | − | 0.932244i | \(-0.617848\pi\) | ||||
−0.361831 | + | 0.932244i | \(0.617848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.99230 | −0.649070 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.1493 | 1.30335 | 0.651675 | − | 0.758498i | \(-0.274066\pi\) | ||||
0.651675 | + | 0.758498i | \(0.274066\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.72928 | 0.240224 | 0.120112 | − | 0.992760i | \(-0.461675\pi\) | ||||
0.120112 | + | 0.992760i | \(0.461675\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.07081 | 0.0686924 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −35.0741 | −2.23171 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −30.7110 | −1.94623 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.4985 | 1.35698 | 0.678488 | − | 0.734612i | \(-0.262636\pi\) | ||||
0.678488 | + | 0.734612i | \(0.262636\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.33527 | 0.146817 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.27072 | 0.266400 | 0.133200 | − | 0.991089i | \(-0.457475\pi\) | ||||
0.133200 | + | 0.991089i | \(0.457475\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.00000 | −0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.812155 | −0.0502711 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.4586 | 0.706565 | 0.353283 | − | 0.935517i | \(-0.385065\pi\) | ||||
0.353283 | + | 0.935517i | \(0.385065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −25.1878 | −1.54147 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.07081 | −0.431115 | −0.215557 | − | 0.976491i | \(-0.569157\pi\) | ||||
−0.215557 | + | 0.976491i | \(0.569157\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.0096 | −1.03326 | −0.516629 | − | 0.856209i | \(-0.672813\pi\) | ||||
−0.516629 | + | 0.856209i | \(0.672813\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.67243 | 0.585402 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7755 | −1.12811 | −0.564056 | − | 0.825737i | \(-0.690760\pi\) | ||||
−0.564056 | + | 0.825737i | \(0.690760\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.775511 | −0.0464286 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.59829 | −0.274311 | −0.137156 | − | 0.990550i | \(-0.543796\pi\) | ||||
−0.137156 | + | 0.990550i | \(0.543796\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.5833 | 0.807443 | 0.403722 | − | 0.914882i | \(-0.367716\pi\) | ||||
0.403722 | + | 0.914882i | \(0.367716\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.72928 | −0.456245 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1955 | −0.952679 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.8786 | 1.04806 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.8261 | 0.690889 | 0.345444 | − | 0.938439i | \(-0.387728\pi\) | ||||
0.345444 | + | 0.938439i | \(0.387728\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.19554 | 0.185424 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.4769 | 1.18421 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.72928 | 0.0996741 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.9817 | −0.975572 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.9860 | 1.19774 | 0.598868 | − | 0.800847i | \(-0.295617\pi\) | ||||
0.598868 | + | 0.800847i | \(0.295617\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.10308 | −0.0627522 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.5048 | 1.27613 | 0.638065 | − | 0.769983i | \(-0.279735\pi\) | ||||
0.638065 | + | 0.769983i | \(0.279735\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.4846 | −0.705670 | −0.352835 | − | 0.935686i | \(-0.614782\pi\) | ||||
−0.352835 | + | 0.935686i | \(0.614782\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.5231 | 1.43352 | 0.716760 | − | 0.697319i | \(-0.245624\pi\) | ||||
0.716760 | + | 0.697319i | \(0.245624\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.93356 | −0.276226 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.72928 | −0.318786 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −33.3372 | −1.84355 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.87859 | 0.324097 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.68305 | 0.147474 | 0.0737370 | − | 0.997278i | \(-0.476507\pi\) | ||||
0.0737370 | + | 0.997278i | \(0.476507\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.618502 | 0.0338937 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.5048 | 0.681179 | 0.340590 | − | 0.940212i | \(-0.389373\pi\) | ||||
0.340590 | + | 0.940212i | \(0.389373\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.84299 | 0.100098 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.71096 | −0.255113 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.9450 | 1.55385 | 0.776925 | − | 0.629593i | \(-0.216778\pi\) | ||||
0.776925 | + | 0.629593i | \(0.216778\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.1449 | 1.72068 | 0.860340 | − | 0.509721i | \(-0.170251\pi\) | ||||
0.860340 | + | 0.509721i | \(0.170251\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.0202 | 1.49561 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.17722 | 0.435229 | 0.217615 | − | 0.976035i | \(-0.430172\pi\) | ||||
0.217615 | + | 0.976035i | \(0.430172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.57997 | 0.0836208 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.5048 | −0.976646 | −0.488323 | − | 0.872663i | \(-0.662391\pi\) | ||||
−0.488323 | + | 0.872663i | \(0.662391\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.8034 | 1.14755 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.6864 | 0.980781 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.4942 | 1.43518 | 0.717592 | − | 0.696464i | \(-0.245244\pi\) | ||||
0.717592 | + | 0.696464i | \(0.245244\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.796763 | 0.0414778 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.77551 | 0.351767 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.06455 | 0.314011 | 0.157005 | − | 0.987598i | \(-0.449816\pi\) | ||||
0.157005 | + | 0.987598i | \(0.449816\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −43.2601 | −2.22801 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.72928 | 0.294293 | 0.147147 | − | 0.989115i | \(-0.452991\pi\) | ||||
0.147147 | + | 0.989115i | \(0.452991\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −37.4865 | −1.92049 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.72928 | 0.0883622 | 0.0441811 | − | 0.999024i | \(-0.485932\pi\) | ||||
0.0441811 | + | 0.999024i | \(0.485932\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.178261 | −0.00906150 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −36.7187 | −1.86171 | −0.930855 | − | 0.365389i | \(-0.880936\pi\) | ||||
−0.930855 | + | 0.365389i | \(0.880936\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.34485 | 0.169157 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.4586 | −0.880668 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.03228 | −0.101997 | −0.0509985 | − | 0.998699i | \(-0.516240\pi\) | ||||
−0.0509985 | + | 0.998699i | \(0.516240\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.2524 | −0.563324 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.64452 | −0.0821234 | −0.0410617 | − | 0.999157i | \(-0.513074\pi\) | ||||
−0.0410617 | + | 0.999157i | \(0.513074\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −41.3082 | −2.05771 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.75719 | 0.186237 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.98168 | −0.246328 | −0.123164 | − | 0.992386i | \(-0.539304\pi\) | ||||
−0.123164 | + | 0.992386i | \(0.539304\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.09246 | −0.300519 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.593923 | −0.0292250 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −35.9634 | −1.76113 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.9205 | −1.11974 | −0.559869 | − | 0.828581i | \(-0.689148\pi\) | ||||
−0.559869 | + | 0.828581i | \(0.689148\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.9527 | −1.02117 | −0.510587 | − | 0.859826i | \(-0.670572\pi\) | ||||
−0.510587 | + | 0.859826i | \(0.670572\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.605987 | −0.0294641 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.13536 | −0.345304 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.05685 | −0.292428 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.1589 | −1.59721 | −0.798604 | − | 0.601857i | \(-0.794428\pi\) | ||||
−0.798604 | + | 0.601857i | \(0.794428\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.5414 | −0.891045 | −0.445522 | − | 0.895271i | \(-0.646982\pi\) | ||||
−0.445522 | + | 0.895271i | \(0.646982\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.8217 | −1.13955 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.8401 | 0.994642 | 0.497321 | − | 0.867567i | \(-0.334317\pi\) | ||||
0.497321 | + | 0.867567i | \(0.334317\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.103084 | 0.00490875 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.5510 | −0.833874 | −0.416937 | − | 0.908935i | \(-0.636896\pi\) | ||||
−0.416937 | + | 0.908935i | \(0.636896\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 30.0279 | 1.42027 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.1955 | −0.622736 | −0.311368 | − | 0.950289i | \(-0.600787\pi\) | ||||
−0.311368 | + | 0.950289i | \(0.600787\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.84006 | 0.227910 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.10308 | 0.239764 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.1020 | −1.36134 | −0.680668 | − | 0.732592i | \(-0.738310\pi\) | ||||
−0.680668 | + | 0.732592i | \(0.738310\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.57704 | 0.213638 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.8280 | −0.876907 | −0.438454 | − | 0.898754i | \(-0.644474\pi\) | ||||
−0.438454 | + | 0.898754i | \(0.644474\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0925 | 0.654932 | 0.327466 | − | 0.944863i | \(-0.393805\pi\) | ||||
0.327466 | + | 0.944863i | \(0.393805\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.2663 | 0.567619 | 0.283809 | − | 0.958881i | \(-0.408402\pi\) | ||||
0.283809 | + | 0.958881i | \(0.408402\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.79383 | −0.267534 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.8217 | −0.821182 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.08287 | −0.0497905 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.698445 | −0.0319796 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.1570 | 0.646850 | 0.323425 | − | 0.946254i | \(-0.395166\pi\) | ||||
0.323425 | + | 0.946254i | \(0.395166\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.9450 | 1.50216 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.56934 | 0.298915 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.2341 | −1.37004 | −0.685018 | − | 0.728526i | \(-0.740206\pi\) | ||||
−0.685018 | + | 0.728526i | \(0.740206\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.840061 | 0.0379889 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.9065 | −1.80096 | −0.900478 | − | 0.434902i | \(-0.856783\pi\) | ||||
−0.900478 | + | 0.434902i | \(0.856783\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.06644 | −0.318256 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.52311 | 0.247746 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.3246 | −1.22322 | −0.611610 | − | 0.791160i | \(-0.709478\pi\) | ||||
−0.611610 | + | 0.791160i | \(0.709478\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.1955 | −1.03630 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.40171 | −0.0624991 | −0.0312495 | − | 0.999512i | \(-0.509949\pi\) | ||||
−0.0312495 | + | 0.999512i | \(0.509949\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −30.2095 | −1.34165 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.6585 | 0.827022 | 0.413511 | − | 0.910499i | \(-0.364302\pi\) | ||||
0.413511 | + | 0.910499i | \(0.364302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.72928 | 0.164974 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −32.5972 | −1.43920 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.68116 | −0.161897 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.6049 | −1.08004 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.02791 | −0.176466 | −0.0882329 | − | 0.996100i | \(-0.528122\pi\) | ||||
−0.0882329 | + | 0.996100i | \(0.528122\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.4436 | −1.68102 | −0.840510 | − | 0.541796i | \(-0.817744\pi\) | ||||
−0.840510 | + | 0.541796i | \(0.817744\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.74760 | −0.293930 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.09246 | −0.395324 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.0612237 | 0.00265688 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.4402 | 1.83829 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.1387 | 0.566976 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.626198 | 0.0269723 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.4846 | 0.536754 | 0.268377 | − | 0.963314i | \(-0.413513\pi\) | ||||
0.268377 | + | 0.963314i | \(0.413513\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.8680 | 1.06719 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.7851 | −1.61557 | −0.807787 | − | 0.589474i | \(-0.799335\pi\) | ||||
−0.807787 | + | 0.589474i | \(0.799335\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.735539 | 0.0313921 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 50.3265 | 2.14398 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.67243 | −0.241216 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.93545 | 0.0820076 | 0.0410038 | − | 0.999159i | \(-0.486944\pi\) | ||||
0.0410038 | + | 0.999159i | \(0.486944\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.49521 | −0.401604 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.989374 | −0.0417714 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.8463 | 1.25787 | 0.628936 | − | 0.777457i | \(-0.283491\pi\) | ||||
0.628936 | + | 0.777457i | \(0.283491\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.29862 | 0.390506 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.3449 | 0.643290 | 0.321645 | − | 0.946860i | \(-0.395764\pi\) | ||||
0.321645 | + | 0.946860i | \(0.395764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.8217 | −1.49909 | −0.749547 | − | 0.661952i | \(-0.769728\pi\) | ||||
−0.749547 | + | 0.661952i | \(0.769728\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.8324 | −0.619631 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.92482 | 0.121762 | 0.0608810 | − | 0.998145i | \(-0.480609\pi\) | ||||
0.0608810 | + | 0.998145i | \(0.480609\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 39.2803 | 1.63243 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.4340 | −0.723284 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.24281 | −0.175719 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.5756 | −0.807972 | −0.403986 | − | 0.914765i | \(-0.632375\pi\) | ||||
−0.403986 | + | 0.914765i | \(0.632375\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 48.0558 | 1.98011 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −46.4402 | −1.91030 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.00770 | 0.328837 | 0.164418 | − | 0.986391i | \(-0.447425\pi\) | ||||
0.164418 | + | 0.986391i | \(0.447425\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 39.5298 | 1.61785 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.3005 | 1.19719 | 0.598593 | − | 0.801053i | \(-0.295727\pi\) | ||||
0.598593 | + | 0.801053i | \(0.295727\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.3449 | 0.870675 | 0.435337 | − | 0.900267i | \(-0.356629\pi\) | ||||
0.435337 | + | 0.900267i | \(0.356629\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.597250 | 0.0243219 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.53081 | −0.386844 | −0.193422 | − | 0.981116i | \(-0.561959\pi\) | ||||
−0.193422 | + | 0.981116i | \(0.561959\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.8786 | −0.562389 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.2784 | −1.30584 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.75719 | −0.394089 | −0.197045 | − | 0.980395i | \(-0.563134\pi\) | ||||
−0.197045 | + | 0.980395i | \(0.563134\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.9267 | −1.52687 | −0.763436 | − | 0.645884i | \(-0.776489\pi\) | ||||
−0.763436 | + | 0.645884i | \(0.776489\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −41.9109 | −1.68454 | −0.842270 | − | 0.539056i | \(-0.818781\pi\) | ||||
−0.842270 | + | 0.539056i | \(0.818781\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19.0308 | 0.763681 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.2986 | −0.572862 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.04623 | 0.281399 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.38150 | 0.214574 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.42003 | 0.335196 | 0.167598 | − | 0.985855i | \(-0.446399\pi\) | ||||
0.167598 | + | 0.985855i | \(0.446399\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.7678 | −1.06393 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.49084 | 0.217555 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.569343 | −0.0225229 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.07707 | −0.0820392 | −0.0410196 | − | 0.999158i | \(-0.513061\pi\) | ||||
−0.0410196 | + | 0.999158i | \(0.513061\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.2480 | 1.07456 | 0.537279 | − | 0.843405i | \(-0.319452\pi\) | ||||
0.537279 | + | 0.843405i | \(0.319452\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.3632 | −0.486047 | −0.243023 | − | 0.970020i | \(-0.578139\pi\) | ||||
−0.243023 | + | 0.970020i | \(0.578139\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.371913 | 0.0145989 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.2524 | −0.519402 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.3449 | 1.46142 | 0.730709 | − | 0.682690i | \(-0.239190\pi\) | ||||
0.730709 | + | 0.682690i | \(0.239190\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.384428 | −0.0149980 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.1772 | 0.552266 | 0.276133 | − | 0.961119i | \(-0.410947\pi\) | ||||
0.276133 | + | 0.961119i | \(0.410947\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.76925 | −0.0688160 | −0.0344080 | − | 0.999408i | \(-0.510955\pi\) | ||||
−0.0344080 | + | 0.999408i | \(0.510955\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.67536 | −0.336923 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.3815 | −1.13766 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.1493 | −0.469720 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.46815 | 0.172491 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.05581 | 0.156340 | 0.0781701 | − | 0.996940i | \(-0.475092\pi\) | ||||
0.0781701 | + | 0.996940i | \(0.475092\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.37713 | −0.360392 | −0.180196 | − | 0.983631i | \(-0.557673\pi\) | ||||
−0.180196 | + | 0.983631i | \(0.557673\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.1493 | 0.389495 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.89692 | −0.187650 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.49521 | 0.210268 | 0.105134 | − | 0.994458i | \(-0.466473\pi\) | ||||
0.105134 | + | 0.994458i | \(0.466473\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −32.8680 | −1.25399 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −37.2032 | −1.41733 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.03416 | 0.115425 | 0.0577125 | − | 0.998333i | \(-0.481619\pi\) | ||||
0.0577125 | + | 0.998333i | \(0.481619\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0645508 | −0.00245208 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.93252 | 0.262588 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.4586 | 0.735990 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.2234 | 1.33037 | 0.665186 | − | 0.746678i | \(-0.268352\pi\) | ||||
0.665186 | + | 0.746678i | \(0.268352\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −38.3265 | −1.44551 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.64015 | −0.362555 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.7187 | 1.07855 | 0.539276 | − | 0.842129i | \(-0.318698\pi\) | ||||
0.539276 | + | 0.842129i | \(0.318698\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.584735 | 0.0219293 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.0558 | −1.05070 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −35.4942 | −1.32555 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.60599 | 0.320949 | 0.160475 | − | 0.987040i | \(-0.448698\pi\) | ||||
0.160475 | + | 0.987040i | \(0.448698\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.626198 | −0.0233208 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.56934 | −0.244316 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.2803 | 0.566715 | 0.283358 | − | 0.959014i | \(-0.408552\pi\) | ||||
0.283358 | + | 0.959014i | \(0.408552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.0096 | 0.963318 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.55102 | −0.0573666 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.0235 | −1.69992 | −0.849959 | − | 0.526849i | \(-0.823373\pi\) | ||||
−0.849959 | + | 0.526849i | \(0.823373\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.62809 | 0.133642 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.3467 | −1.70489 | −0.852446 | − | 0.522815i | \(-0.824882\pi\) | ||||
−0.852446 | + | 0.522815i | \(0.824882\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 61.7851 | 2.26973 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.7755 | −0.395315 | −0.197658 | − | 0.980271i | \(-0.563333\pi\) | ||||
−0.197658 | + | 0.980271i | \(0.563333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.79716 | 0.0657546 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.76781 | −0.100999 | −0.0504995 | − | 0.998724i | \(-0.516081\pi\) | ||||
−0.0504995 | + | 0.998724i | \(0.516081\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −37.8709 | −1.38009 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.8401 | 0.539371 | 0.269686 | − | 0.962948i | \(-0.413080\pi\) | ||||
0.269686 | + | 0.962948i | \(0.413080\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.11371 | −0.149318 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.3169 | 1.13524 | 0.567619 | − | 0.823291i | \(-0.307865\pi\) | ||||
0.567619 | + | 0.823291i | \(0.307865\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.9248 | −0.685125 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.26113 | 0.117753 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.92586 | 0.321875 | 0.160937 | − | 0.986965i | \(-0.448548\pi\) | ||||
0.160937 | + | 0.986965i | \(0.448548\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.52311 | −0.270938 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.7711 | 1.32257 | 0.661283 | − | 0.750136i | \(-0.270012\pi\) | ||||
0.661283 | + | 0.750136i | \(0.270012\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.5693 | 0.379173 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −49.3728 | −1.76896 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.45856 | −0.123757 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −40.2051 | −1.43681 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.53707 | −0.233021 | −0.116511 | − | 0.993189i | \(-0.537171\pi\) | ||||
−0.116511 | + | 0.993189i | \(0.537171\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.1849 | −0.718602 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.04623 | 0.0371996 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.1791 | 1.39129 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.82611 | 0.277215 | 0.138607 | − | 0.990347i | \(-0.455737\pi\) | ||||
0.138607 | + | 0.990347i | \(0.455737\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.27261 | −0.186531 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.47396 | 0.0520796 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.33527 | −0.0824099 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.4556 | 0.438459 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.4113 | 1.35047 | 0.675235 | − | 0.737603i | \(-0.264042\pi\) | ||||
0.675235 | + | 0.737603i | \(0.264042\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.64015 | −0.268282 | −0.134141 | − | 0.990962i | \(-0.542828\pi\) | ||||
−0.134141 | + | 0.990962i | \(0.542828\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.9634 | 1.05086 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.0462 | 0.386459 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.566016 | −0.0197782 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.56165 | 0.0894021 | 0.0447011 | − | 0.999000i | \(-0.485766\pi\) | ||||
0.0447011 | + | 0.999000i | \(0.485766\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.784248 | −0.0273372 | −0.0136686 | − | 0.999907i | \(-0.504351\pi\) | ||||
−0.0136686 | + | 0.999907i | \(0.504351\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.28904 | −0.253465 | −0.126732 | − | 0.991937i | \(-0.540449\pi\) | ||||
−0.126732 | + | 0.991937i | \(0.540449\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0708 | −0.384505 | −0.192253 | − | 0.981345i | \(-0.561579\pi\) | ||||
−0.192253 | + | 0.981345i | \(0.561579\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.0741 | 1.14733 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.896916 | 0.0310763 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −38.3911 | −1.32699 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.55976 | 0.191944 | 0.0959721 | − | 0.995384i | \(-0.469404\pi\) | ||||
0.0959721 | + | 0.995384i | \(0.469404\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.0722 | 1.14042 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.10015 | 0.278984 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.6079 | 0.364491 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.9278 | −0.821198 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.3757 | 0.767029 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.0804 | 0.550582 | 0.275291 | − | 0.961361i | \(-0.411226\pi\) | ||||
0.275291 | + | 0.961361i | \(0.411226\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.58767 | 0.0542336 | 0.0271168 | − | 0.999632i | \(-0.491367\pi\) | ||||
0.0271168 | + | 0.999632i | \(0.491367\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.94171 | −0.168609 | −0.0843044 | − | 0.996440i | \(-0.526867\pi\) | ||||
−0.0843044 | + | 0.996440i | \(0.526867\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.6156 | 0.464017 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.6647 | 1.28212 | 0.641061 | − | 0.767490i | \(-0.278494\pi\) | ||||
0.641061 | + | 0.767490i | \(0.278494\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.5294 | 0.968908 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.55206 | 0.120495 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.8130 | 1.07794 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.04623 | −0.0354095 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.66473 | −0.123749 | −0.0618746 | − | 0.998084i | \(-0.519708\pi\) | ||||
−0.0618746 | + | 0.998084i | \(0.519708\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.8324 | −0.702658 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.4373 | −1.46344 | −0.731720 | − | 0.681605i | \(-0.761282\pi\) | ||||
−0.731720 | + | 0.681605i | \(0.761282\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.3853 | 1.59464 | 0.797321 | − | 0.603556i | \(-0.206250\pi\) | ||||
0.797321 | + | 0.603556i | \(0.206250\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.3169 | −0.715753 | −0.357877 | − | 0.933769i | \(-0.616499\pi\) | ||||
−0.357877 | + | 0.933769i | \(0.616499\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.2803 | −0.713718 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.82278 | −0.195071 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 37.5510 | 1.25660 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −36.0712 | −1.20438 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 59.2716 | 1.97682 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.07707 | −0.202456 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.04623 | −0.101372 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.9325 | 0.628644 | 0.314322 | − | 0.949316i | \(-0.398223\pi\) | ||||
0.314322 | + | 0.949316i | \(0.398223\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.993743 | 0.0329604 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.6705 | 0.419794 | 0.209897 | − | 0.977724i | \(-0.432687\pi\) | ||||
0.209897 | + | 0.977724i | \(0.432687\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.9171 | 0.361304 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.91087 | −0.327286 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.8690 | −0.754379 | −0.377190 | − | 0.926136i | \(-0.623109\pi\) | ||||
−0.377190 | + | 0.926136i | \(0.623109\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36.9681 | −1.21814 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.3265 | −0.998210 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.0645508 | 0.00212013 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.4190 | 1.65419 | 0.827097 | − | 0.562060i | \(-0.189991\pi\) | ||||
0.827097 | + | 0.562060i | \(0.189991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.38776 | −0.209350 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −39.6435 | −1.29787 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.9344 | −1.56595 | −0.782974 | − | 0.622054i | \(-0.786298\pi\) | ||||
−0.782974 | + | 0.622054i | \(0.786298\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.9923 | 0.717692 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 59.9667 | 1.95486 | 0.977429 | − | 0.211264i | \(-0.0677580\pi\) | ||||
0.977429 | + | 0.211264i | \(0.0677580\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.8247 | 0.938660 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.5231 | 0.894381 | 0.447191 | − | 0.894439i | \(-0.352425\pi\) | ||||
0.447191 | + | 0.894439i | \(0.352425\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.4769 | −0.664708 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −44.9604 | −1.45794 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.840061 | 0.0272123 | 0.0136061 | − | 0.999907i | \(-0.495669\pi\) | ||||
0.0136061 | + | 0.999907i | \(0.495669\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.69075 | 0.280932 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.45856 | −0.111683 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.5972 | 0.825718 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.8988 | −1.02580 | −0.512898 | − | 0.858449i | \(-0.671428\pi\) | ||||
−0.512898 | + | 0.858449i | \(0.671428\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.0925 | 0.324216 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.4157 | −0.911902 | −0.455951 | − | 0.890005i | \(-0.650701\pi\) | ||||
−0.455951 | + | 0.890005i | \(0.650701\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.4157 | −0.654496 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.55102 | 0.305564 | 0.152782 | − | 0.988260i | \(-0.451177\pi\) | ||||
0.152782 | + | 0.988260i | \(0.451177\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.95377 | 0.286164 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.95084 | 0.0622856 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.0443400 | 0.00141423 | 0.000707113 | − | 1.00000i | \(-0.499775\pi\) | ||||
0.000707113 | 1.00000i | \(0.499775\pi\) | ||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.3555 | −0.329619 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.44898 | −0.205066 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.9913 | 0.444447 | 0.222224 | − | 0.974996i | \(-0.428669\pi\) | ||||
0.222224 | + | 0.974996i | \(0.428669\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.72635 | −0.149986 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.0419 | −0.603062 | −0.301531 | − | 0.953456i | \(-0.597498\pi\) | ||||
−0.301531 | + | 0.953456i | \(0.597498\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 30.6185 | 0.968727 |
(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 | 2800.2.a.br.1.1 | 3 | ||
4.3 | odd | 2 | 1400.2.a.s.1.3 | 3 | |||
5.2 | odd | 4 | 560.2.g.f.449.5 | 6 | |||
5.3 | odd | 4 | 560.2.g.f.449.2 | 6 | |||
5.4 | even | 2 | 2800.2.a.bq.1.3 | 3 | |||
15.2 | even | 4 | 5040.2.t.y.1009.4 | 6 | |||
15.8 | even | 4 | 5040.2.t.y.1009.3 | 6 | |||
20.3 | even | 4 | 280.2.g.b.169.5 | yes | 6 | ||
20.7 | even | 4 | 280.2.g.b.169.2 | ✓ | 6 | ||
20.19 | odd | 2 | 1400.2.a.t.1.1 | 3 | |||
28.27 | even | 2 | 9800.2.a.cg.1.1 | 3 | |||
40.3 | even | 4 | 2240.2.g.l.449.2 | 6 | |||
40.13 | odd | 4 | 2240.2.g.m.449.5 | 6 | |||
40.27 | even | 4 | 2240.2.g.l.449.5 | 6 | |||
40.37 | odd | 4 | 2240.2.g.m.449.2 | 6 | |||
60.23 | odd | 4 | 2520.2.t.g.1009.3 | 6 | |||
60.47 | odd | 4 | 2520.2.t.g.1009.4 | 6 | |||
140.27 | odd | 4 | 1960.2.g.c.1569.5 | 6 | |||
140.83 | odd | 4 | 1960.2.g.c.1569.2 | 6 | |||
140.139 | even | 2 | 9800.2.a.cd.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.g.b.169.2 | ✓ | 6 | 20.7 | even | 4 | ||
280.2.g.b.169.5 | yes | 6 | 20.3 | even | 4 | ||
560.2.g.f.449.2 | 6 | 5.3 | odd | 4 | |||
560.2.g.f.449.5 | 6 | 5.2 | odd | 4 | |||
1400.2.a.s.1.3 | 3 | 4.3 | odd | 2 | |||
1400.2.a.t.1.1 | 3 | 20.19 | odd | 2 | |||
1960.2.g.c.1569.2 | 6 | 140.83 | odd | 4 | |||
1960.2.g.c.1569.5 | 6 | 140.27 | odd | 4 | |||
2240.2.g.l.449.2 | 6 | 40.3 | even | 4 | |||
2240.2.g.l.449.5 | 6 | 40.27 | even | 4 | |||
2240.2.g.m.449.2 | 6 | 40.37 | odd | 4 | |||
2240.2.g.m.449.5 | 6 | 40.13 | odd | 4 | |||
2520.2.t.g.1009.3 | 6 | 60.23 | odd | 4 | |||
2520.2.t.g.1009.4 | 6 | 60.47 | odd | 4 | |||
2800.2.a.bq.1.3 | 3 | 5.4 | even | 2 | |||
2800.2.a.br.1.1 | 3 | 1.1 | even | 1 | trivial | ||
5040.2.t.y.1009.3 | 6 | 15.8 | even | 4 | |||
5040.2.t.y.1009.4 | 6 | 15.2 | even | 4 | |||
9800.2.a.cd.1.3 | 3 | 140.139 | even | 2 | |||
9800.2.a.cg.1.1 | 3 | 28.27 | even | 2 |