Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 30 x^{18} + 128 x^{17} + 348 x^{16} - 1644 x^{15} - 1934 x^{14} + 10948 x^{13} + 4748 x^{12} - 40524 x^{11} - 220 x^{10} + 82500 x^{9} - 21992 x^{8} - 84720 x^{7} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Root | \(3.29362\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 | ||||||||
\(3\) | 3.29362 | 1.90157 | 0.950785 | − | 0.309852i | \(-0.100280\pi\) | ||||
0.950785 | + | 0.309852i | \(0.100280\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.10165 | 1.38710 | 0.693551 | − | 0.720408i | \(-0.256045\pi\) | ||||
0.693551 | + | 0.720408i | \(0.256045\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.84790 | 2.61597 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.57618 | 1.07826 | 0.539129 | − | 0.842223i | \(-0.318754\pi\) | ||||
0.539129 | + | 0.842223i | \(0.318754\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.94081 | −0.815634 | −0.407817 | − | 0.913064i | \(-0.633710\pi\) | ||||
−0.407817 | + | 0.913064i | \(0.633710\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.2157 | 2.63767 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.836188 | 0.202805 | 0.101403 | − | 0.994845i | \(-0.467667\pi\) | ||||
0.101403 | + | 0.994845i | \(0.467667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.07491 | 0.246600 | 0.123300 | − | 0.992369i | \(-0.460652\pi\) | ||||
0.123300 | + | 0.992369i | \(0.460652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.90605 | −1.02298 | −0.511491 | − | 0.859288i | \(-0.670907\pi\) | ||||
−0.511491 | + | 0.859288i | \(0.670907\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.62026 | 0.924052 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 15.9671 | 3.07287 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.82134 | −0.709605 | −0.354803 | − | 0.934941i | \(-0.615452\pi\) | ||||
−0.354803 | + | 0.934941i | \(0.615452\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.16536 | 0.927726 | 0.463863 | − | 0.885907i | \(-0.346463\pi\) | ||||
0.463863 | + | 0.885907i | \(0.346463\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11.7785 | 2.05038 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.09614 | −1.00220 | −0.501100 | − | 0.865390i | \(-0.667071\pi\) | ||||
−0.501100 | + | 0.865390i | \(0.667071\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.68590 | −1.55099 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.59000 | 1.15746 | 0.578732 | − | 0.815518i | \(-0.303548\pi\) | ||||
0.578732 | + | 0.815518i | \(0.303548\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 24.3415 | 3.62861 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.2989 | −1.93984 | −0.969920 | − | 0.243425i | \(-0.921729\pi\) | ||||
−0.969920 | + | 0.243425i | \(0.921729\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.75408 | 0.385648 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.67058 | −0.504194 | −0.252097 | − | 0.967702i | \(-0.581120\pi\) | ||||
−0.252097 | + | 0.967702i | \(0.581120\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.0921 | 1.49565 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.54033 | 0.468928 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.05522 | 1.04870 | 0.524350 | − | 0.851503i | \(-0.324308\pi\) | ||||
0.524350 | + | 0.851503i | \(0.324308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.21710 | 0.796018 | 0.398009 | − | 0.917382i | \(-0.369701\pi\) | ||||
0.398009 | + | 0.917382i | \(0.369701\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.12138 | −1.13137 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.9460 | 1.33727 | 0.668634 | − | 0.743591i | \(-0.266879\pi\) | ||||
0.668634 | + | 0.743591i | \(0.266879\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.1586 | −1.94527 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9994 | 1.30538 | 0.652692 | − | 0.757624i | \(-0.273640\pi\) | ||||
0.652692 | + | 0.757624i | \(0.273640\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.78244 | 1.02791 | 0.513953 | − | 0.857818i | \(-0.328180\pi\) | ||||
0.513953 | + | 0.857818i | \(0.328180\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 15.2174 | 1.75715 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.46561 | −0.502420 | −0.251210 | − | 0.967933i | \(-0.580828\pi\) | ||||
−0.251210 | + | 0.967933i | \(0.580828\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.0458 | 3.22732 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.2702 | −1.23706 | −0.618531 | − | 0.785760i | \(-0.712272\pi\) | ||||
−0.618531 | + | 0.785760i | \(0.712272\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.59357 | 0.281312 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.5860 | −1.34936 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.02946 | 0.109122 | 0.0545611 | − | 0.998510i | \(-0.482624\pi\) | ||||
0.0545611 | + | 0.998510i | \(0.482624\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17.0127 | 1.76414 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.33399 | 0.342060 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.3000 | −1.24888 | −0.624440 | − | 0.781073i | \(-0.714673\pi\) | ||||
−0.624440 | + | 0.781073i | \(0.714673\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 28.0655 | 2.82069 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.02323 | −0.897845 | −0.448922 | − | 0.893571i | \(-0.648192\pi\) | ||||
−0.448922 | + | 0.893571i | \(0.648192\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.663227 | −0.0653497 | −0.0326749 | − | 0.999466i | \(-0.510403\pi\) | ||||
−0.0326749 | + | 0.999466i | \(0.510403\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.4968 | −1.40146 | −0.700731 | − | 0.713425i | \(-0.747143\pi\) | ||||
−0.700731 | + | 0.713425i | \(0.747143\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.4957 | −1.29265 | −0.646325 | − | 0.763063i | \(-0.723695\pi\) | ||||
−0.646325 | + | 0.763063i | \(0.723695\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.0783 | −1.90575 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.8171 | 1.67610 | 0.838048 | − | 0.545597i | \(-0.183697\pi\) | ||||
0.838048 | + | 0.545597i | \(0.183697\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.2169 | −1.41898 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −23.0792 | −2.13367 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.78904 | 0.162640 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.29362 | −0.296975 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.17782 | −0.105348 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.27006 | 0.201435 | 0.100718 | − | 0.994915i | \(-0.467886\pi\) | ||||
0.100718 | + | 0.994915i | \(0.467886\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24.9985 | 2.20100 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.1096 | 1.58224 | 0.791122 | − | 0.611659i | \(-0.209498\pi\) | ||||
0.791122 | + | 0.611659i | \(0.209498\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 49.5245 | 4.26239 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.326566 | −0.0279004 | −0.0139502 | − | 0.999903i | \(-0.504441\pi\) | ||||
−0.0139502 | + | 0.999903i | \(0.504441\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.3280 | 0.960825 | 0.480413 | − | 0.877043i | \(-0.340487\pi\) | ||||
0.480413 | + | 0.877043i | \(0.340487\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −43.8014 | −3.68874 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.5169 | −0.879464 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.8525 | −0.984295 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.35370 | 0.766285 | 0.383142 | − | 0.923689i | \(-0.374842\pi\) | ||||
0.383142 | + | 0.923689i | \(0.374842\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.3212 | 1.57234 | 0.786169 | − | 0.618012i | \(-0.212062\pi\) | ||||
0.786169 | + | 0.618012i | \(0.212062\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.56232 | 0.530532 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.0212 | 1.28685 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.85883 | 0.627203 | 0.313601 | − | 0.949555i | \(-0.398464\pi\) | ||||
0.313601 | + | 0.949555i | \(0.398464\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.0895 | −0.958759 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.46497 | 0.506375 | 0.253188 | − | 0.967417i | \(-0.418521\pi\) | ||||
0.253188 | + | 0.967417i | \(0.418521\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 36.5330 | 2.84409 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.8889 | −0.997370 | −0.498685 | − | 0.866783i | \(-0.666184\pi\) | ||||
−0.498685 | + | 0.866783i | \(0.666184\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.35163 | −0.334741 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.43575 | 0.645098 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.9211 | −1.21046 | −0.605231 | − | 0.796050i | \(-0.706919\pi\) | ||||
−0.605231 | + | 0.796050i | \(0.706919\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 26.5308 | 1.99418 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.17161 | −0.685518 | −0.342759 | − | 0.939423i | \(-0.611361\pi\) | ||||
−0.342759 | + | 0.939423i | \(0.611361\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.15105 | −0.382875 | −0.191437 | − | 0.981505i | \(-0.561315\pi\) | ||||
−0.191437 | + | 0.981505i | \(0.561315\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 20.4767 | 1.51368 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.9081 | −1.39015 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.99036 | 0.218676 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.35390 | 0.459752 | 0.229876 | − | 0.973220i | \(-0.426168\pi\) | ||||
0.229876 | + | 0.973220i | \(0.426168\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.0051 | −1.72793 | −0.863964 | − | 0.503553i | \(-0.832026\pi\) | ||||
−0.863964 | + | 0.503553i | \(0.832026\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −30.0423 | −2.15138 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.82514 | −0.343777 | −0.171889 | − | 0.985116i | \(-0.554987\pi\) | ||||
−0.171889 | + | 0.985116i | \(0.554987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.9592 | −1.41487 | −0.707434 | − | 0.706779i | \(-0.750147\pi\) | ||||
−0.707434 | + | 0.706779i | \(0.750147\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 36.0520 | 2.54291 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.10165 | −0.216629 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −38.5022 | −2.67609 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.84405 | 0.265899 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.8929 | −1.71370 | −0.856849 | − | 0.515568i | \(-0.827581\pi\) | ||||
−0.856849 | + | 0.515568i | \(0.827581\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 36.2276 | 2.48228 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23.5416 | 1.60552 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 28.9260 | 1.95464 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.45907 | −0.165415 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.5603 | −1.37682 | −0.688410 | − | 0.725321i | \(-0.741691\pi\) | ||||
−0.688410 | + | 0.725321i | \(0.741691\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 36.2593 | 2.41729 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.4532 | −1.15841 | −0.579205 | − | 0.815182i | \(-0.696637\pi\) | ||||
−0.579205 | + | 0.815182i | \(0.696637\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.71799 | 0.179610 | 0.0898051 | − | 0.995959i | \(-0.471376\pi\) | ||||
0.0898051 | + | 0.995959i | \(0.471376\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.5594 | −0.691770 | −0.345885 | − | 0.938277i | \(-0.612421\pi\) | ||||
−0.345885 | + | 0.938277i | \(0.612421\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −41.2485 | −2.69076 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.7080 | −0.955387 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −28.0324 | −1.81326 | −0.906632 | − | 0.421921i | \(-0.861356\pi\) | ||||
−0.906632 | + | 0.421921i | \(0.861356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.5604 | 1.25999 | 0.629997 | − | 0.776598i | \(-0.283056\pi\) | ||||
0.629997 | + | 0.776598i | \(0.283056\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 47.7645 | 3.06409 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.16110 | −0.201136 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −37.1196 | −2.35236 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.9605 | −1.13365 | −0.566827 | − | 0.823837i | \(-0.691829\pi\) | ||||
−0.566827 | + | 0.823837i | \(0.691829\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.5449 | −1.10304 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.54221 | 0.534934 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.2256 | 1.44877 | 0.724387 | − | 0.689394i | \(-0.242123\pi\) | ||||
0.724387 | + | 0.689394i | \(0.242123\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −29.9895 | −1.85630 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.2408 | 1.43309 | 0.716546 | − | 0.697540i | \(-0.245722\pi\) | ||||
0.716546 | + | 0.697540i | \(0.245722\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.3849 | −0.699368 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.39063 | 0.207503 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.7842 | 0.779468 | 0.389734 | − | 0.920927i | \(-0.372567\pi\) | ||||
0.389734 | + | 0.920927i | \(0.372567\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.118816 | −0.00721755 | −0.00360877 | − | 0.999993i | \(-0.501149\pi\) | ||||
−0.00360877 | + | 0.999993i | \(0.501149\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.5229 | 0.996366 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.92104 | 0.235592 | 0.117796 | − | 0.993038i | \(-0.462417\pi\) | ||||
0.117796 | + | 0.993038i | \(0.462417\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 40.5372 | 2.42690 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.3884 | 0.917995 | 0.458998 | − | 0.888437i | \(-0.348209\pi\) | ||||
0.458998 | + | 0.888437i | \(0.348209\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.04168 | 0.0619212 | 0.0309606 | − | 0.999521i | \(-0.490143\pi\) | ||||
0.0309606 | + | 0.999521i | \(0.490143\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.9809 | 0.650451 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3008 | −0.958870 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −40.5116 | −2.37483 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.376897 | 0.0220185 | 0.0110093 | − | 0.999939i | \(-0.496496\pi\) | ||||
0.0110093 | + | 0.999939i | \(0.496496\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.9845 | 1.45465 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 57.1012 | 3.31335 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.4278 | 0.834380 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −29.7190 | −1.70731 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.2833 | 1.10416 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.62744 | −0.0928830 | −0.0464415 | − | 0.998921i | \(-0.514788\pi\) | ||||
−0.0464415 | + | 0.998921i | \(0.514788\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.18442 | −0.124267 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.17325 | −0.406758 | −0.203379 | − | 0.979100i | \(-0.565192\pi\) | ||||
−0.203379 | + | 0.979100i | \(0.565192\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.50398 | −0.311103 | −0.155552 | − | 0.987828i | \(-0.549716\pi\) | ||||
−0.155552 | + | 0.987828i | \(0.549716\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.1090 | 1.63493 | 0.817464 | − | 0.575980i | \(-0.195380\pi\) | ||||
0.817464 | + | 0.575980i | \(0.195380\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.6658 | −0.765137 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −47.7470 | −2.66498 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.898823 | 0.0500119 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.5873 | −0.753689 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −44.4495 | −2.45806 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.1759 | 1.16393 | 0.581967 | − | 0.813212i | \(-0.302283\pi\) | ||||
0.581967 | + | 0.813212i | \(0.302283\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −47.8419 | −2.62172 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 33.9508 | 1.85493 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.192702 | −0.0104971 | −0.00524856 | − | 0.999986i | \(-0.501671\pi\) | ||||
−0.00524856 | + | 0.999986i | \(0.501671\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 58.6828 | 3.18721 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.4722 | 1.00033 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −50.1185 | −2.69829 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.8981 | −1.60501 | −0.802507 | − | 0.596643i | \(-0.796501\pi\) | ||||
−0.802507 | + | 0.596643i | \(0.796501\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.8946 | 1.01140 | 0.505701 | − | 0.862709i | \(-0.331234\pi\) | ||||
0.505701 | + | 0.862709i | \(0.331234\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −46.9563 | −2.50634 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.9608 | −1.75433 | −0.877164 | − | 0.480190i | \(-0.840568\pi\) | ||||
−0.877164 | + | 0.480190i | \(0.840568\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 34.1162 | 1.81070 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.47853 | −0.289146 | −0.144573 | − | 0.989494i | \(-0.546181\pi\) | ||||
−0.144573 | + | 0.989494i | \(0.546181\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.8446 | −0.939188 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.89241 | 0.309271 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 27.2401 | 1.42581 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.1999 | 1.10663 | 0.553314 | − | 0.832973i | \(-0.313363\pi\) | ||||
0.553314 | + | 0.832973i | \(0.313363\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.84790 | −0.408545 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.5756 | 0.599361 | 0.299681 | − | 0.954040i | \(-0.403120\pi\) | ||||
0.299681 | + | 0.954040i | \(0.403120\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.87929 | −0.200326 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.2378 | 0.578778 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.2015 | −1.60271 | −0.801357 | − | 0.598186i | \(-0.795888\pi\) | ||||
−0.801357 | + | 0.598186i | \(0.795888\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.47670 | 0.383043 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.4489 | 0.840498 | 0.420249 | − | 0.907409i | \(-0.361943\pi\) | ||||
0.420249 | + | 0.907409i | \(0.361943\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 59.5656 | 3.02789 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.5077 | 1.59751 | 0.798753 | − | 0.601659i | \(-0.205494\pi\) | ||||
0.798753 | + | 0.601659i | \(0.205494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.10238 | −0.207466 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 59.6461 | 3.00875 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.8508 | −0.696908 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.76668 | 0.0886671 | 0.0443335 | − | 0.999017i | \(-0.485884\pi\) | ||||
0.0443335 | + | 0.999017i | \(0.485884\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.0284 | −0.650609 | −0.325304 | − | 0.945609i | \(-0.605467\pi\) | ||||
−0.325304 | + | 0.945609i | \(0.605467\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.1903 | −0.756685 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 90.0902 | 4.47662 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.8009 | −1.08063 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.2624 | −0.952465 | −0.476232 | − | 0.879320i | \(-0.657998\pi\) | ||||
−0.476232 | + | 0.879320i | \(0.657998\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.07558 | −0.0530545 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −34.9562 | −1.71593 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 37.3100 | 1.82708 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.7472 | 1.69751 | 0.848757 | − | 0.528783i | \(-0.177351\pi\) | ||||
0.848757 | + | 0.528783i | \(0.177351\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.8518 | −1.74731 | −0.873654 | − | 0.486548i | \(-0.838256\pi\) | ||||
−0.873654 | + | 0.486548i | \(0.838256\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −104.368 | −5.07456 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.86341 | 0.187403 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −34.6385 | −1.67236 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.1395 | 1.54811 | 0.774053 | − | 0.633121i | \(-0.218226\pi\) | ||||
0.774053 | + | 0.633121i | \(0.218226\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.3202 | 0.784300 | 0.392150 | − | 0.919901i | \(-0.371731\pi\) | ||||
0.392150 | + | 0.919901i | \(0.371731\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −39.0375 | −1.87170 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.27354 | −0.252268 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.5846 | −1.93700 | −0.968498 | − | 0.249020i | \(-0.919892\pi\) | ||||
−0.968498 | + | 0.249020i | \(0.919892\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.64749 | −0.315832 | −0.157916 | − | 0.987453i | \(-0.550477\pi\) | ||||
−0.157916 | + | 0.987453i | \(0.550477\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.19302 | 0.151364 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 30.8075 | 1.45714 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.8140 | 1.83175 | 0.915873 | − | 0.401469i | \(-0.131500\pi\) | ||||
0.915873 | + | 0.401469i | \(0.131500\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.57618 | −0.168396 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 63.6366 | 2.98991 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.2024 | −1.45959 | −0.729794 | − | 0.683667i | \(-0.760384\pi\) | ||||
−0.729794 | + | 0.683667i | \(0.760384\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.3515 | 0.623195 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.0080 | 1.25789 | 0.628943 | − | 0.777451i | \(-0.283488\pi\) | ||||
0.628943 | + | 0.777451i | \(0.283488\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.4666 | 1.27648 | 0.638242 | − | 0.769836i | \(-0.279662\pi\) | ||||
0.638242 | + | 0.769836i | \(0.279662\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 52.7675 | 2.44704 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.74434 | −0.0807186 | −0.0403593 | − | 0.999185i | \(-0.512850\pi\) | ||||
−0.0403593 | + | 0.999185i | \(0.512850\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 25.8840 | 1.19267 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.1432 | 1.24805 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.96634 | 0.227872 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −28.8064 | −1.31895 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.1747 | −1.28733 | −0.643667 | − | 0.765306i | \(-0.722588\pi\) | ||||
−0.643667 | + | 0.765306i | \(0.722588\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.9276 | 0.817428 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −38.1505 | −1.73232 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.4673 | 0.791521 | 0.395760 | − | 0.918354i | \(-0.370481\pi\) | ||||
0.395760 | + | 0.918354i | \(0.370481\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.2931 | 0.962908 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.9428 | −1.39643 | −0.698215 | − | 0.715889i | \(-0.746022\pi\) | ||||
−0.698215 | + | 0.715889i | \(0.746022\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.19536 | −0.143912 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 87.0494 | 3.91258 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.3387 | 0.552357 | 0.276178 | − | 0.961106i | \(-0.410932\pi\) | ||||
0.276178 | + | 0.961106i | \(0.410932\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −42.4509 | −1.89657 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.9299 | −1.06698 | −0.533491 | − | 0.845806i | \(-0.679120\pi\) | ||||
−0.533491 | + | 0.845806i | \(0.679120\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.9869 | −1.24540 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.3326 | −0.636533 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.19945 | 0.230461 | 0.115231 | − | 0.993339i | \(-0.463239\pi\) | ||||
0.115231 | + | 0.993339i | \(0.463239\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.1632 | 0.757772 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.05710 | −0.0906467 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −47.5591 | −2.09165 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −52.4381 | −2.30178 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.2730 | 0.450069 | 0.225035 | − | 0.974351i | \(-0.427751\pi\) | ||||
0.225035 | + | 0.974351i | \(0.427751\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −42.6012 | −1.86282 | −0.931411 | − | 0.363968i | \(-0.881422\pi\) | ||||
−0.931411 | + | 0.363968i | \(0.881422\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.31921 | 0.188148 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.06935 | 0.0464935 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 63.2166 | 2.74337 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.94081 | 0.127381 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −44.9642 | −1.94397 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −30.2078 | −1.30356 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.5742 | 1.35748 | 0.678740 | − | 0.734379i | \(-0.262526\pi\) | ||||
0.678740 | + | 0.734379i | \(0.262526\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.9656 | −0.728063 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −41.8589 | −1.79304 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.7924 | 1.10280 | 0.551402 | − | 0.834239i | \(-0.314093\pi\) | ||||
0.551402 | + | 0.834239i | \(0.314093\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 48.7911 | 2.08236 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.10758 | −0.174989 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −62.2761 | −2.64347 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.3941 | −1.45732 | −0.728662 | − | 0.684874i | \(-0.759857\pi\) | ||||
−0.728662 | + | 0.684874i | \(0.759857\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.3208 | −0.944068 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.84908 | 0.415828 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.1609 | −0.596812 | −0.298406 | − | 0.954439i | \(-0.596455\pi\) | ||||
−0.298406 | + | 0.954439i | \(0.596455\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 55.2626 | 2.32492 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.0368 | 0.714221 | 0.357111 | − | 0.934062i | \(-0.383762\pi\) | ||||
0.357111 | + | 0.934062i | \(0.383762\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.0827 | −0.505646 | −0.252823 | − | 0.967513i | \(-0.581359\pi\) | ||||
−0.252823 | + | 0.967513i | \(0.581359\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.9273 | 0.874251 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.6672 | −0.945289 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.1332 | 1.00468 | 0.502338 | − | 0.864671i | \(-0.332473\pi\) | ||||
0.502338 | + | 0.864671i | \(0.332473\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −79.0637 | −3.28578 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.1267 | −0.543651 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −71.5837 | −2.95962 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.4115 | 0.429728 | 0.214864 | − | 0.976644i | \(-0.431069\pi\) | ||||
0.214864 | + | 0.976644i | \(0.431069\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.55228 | 0.228778 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.8922 | −0.653716 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.2660 | −0.544769 | −0.272384 | − | 0.962189i | \(-0.587812\pi\) | ||||
−0.272384 | + | 0.962189i | \(0.587812\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −65.7379 | −2.69047 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.2672 | −0.746376 | −0.373188 | − | 0.927756i | \(-0.621735\pi\) | ||||
−0.373188 | + | 0.927756i | \(0.621735\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.0344 | 0.654055 | 0.327028 | − | 0.945015i | \(-0.393953\pi\) | ||||
0.327028 | + | 0.945015i | \(0.393953\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 85.9033 | 3.49825 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.54898 | 0.225598 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.59212 | −0.145800 | −0.0728999 | − | 0.997339i | \(-0.523225\pi\) | ||||
−0.0728999 | + | 0.997339i | \(0.523225\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.1095 | 1.58220 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.2533 | −0.616076 | −0.308038 | − | 0.951374i | \(-0.599672\pi\) | ||||
−0.308038 | + | 0.951374i | \(0.599672\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.2157 | −0.411935 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.60446 | −0.145110 | −0.0725551 | − | 0.997364i | \(-0.523115\pi\) | ||||
−0.0725551 | + | 0.997364i | \(0.523115\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.29819 | 0.253145 | 0.126573 | − | 0.991957i | \(-0.459602\pi\) | ||||
0.126573 | + | 0.991957i | \(0.459602\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −78.3355 | −3.14350 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.7545 | −1.07018 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.6608 | 0.505625 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.09752 | −0.203251 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.0810 | −0.560556 | −0.280278 | − | 0.959919i | \(-0.590427\pi\) | ||||
−0.280278 | + | 0.959919i | \(0.590427\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −81.9876 | −3.25871 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.04094 | 0.279411 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 86.3218 | 3.41484 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −45.4067 | −1.79346 | −0.896728 | − | 0.442582i | \(-0.854063\pi\) | ||||
−0.896728 | + | 0.442582i | \(0.854063\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.1129 | 0.911482 | 0.455741 | − | 0.890112i | \(-0.349374\pi\) | ||||
0.455741 | + | 0.890112i | \(0.349374\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 77.5369 | 3.05301 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.334277 | 0.0131418 | 0.00657090 | − | 0.999978i | \(-0.497908\pi\) | ||||
0.00657090 | + | 0.999978i | \(0.497908\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.8069 | 1.13077 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.1516 | −1.21905 | −0.609527 | − | 0.792765i | \(-0.708641\pi\) | ||||
−0.609527 | + | 0.792765i | \(0.708641\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 56.1697 | 2.19473 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 68.9237 | 2.68897 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.50658 | −0.331369 | −0.165685 | − | 0.986179i | \(-0.552983\pi\) | ||||
−0.165685 | + | 0.986179i | \(0.552983\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.6835 | 1.15455 | 0.577277 | − | 0.816549i | \(-0.304115\pi\) | ||||
0.577277 | + | 0.816549i | \(0.304115\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.09923 | −0.314548 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.7477 | 0.725914 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −67.7178 | −2.61812 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.2334 | 0.858312 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.7554 | −0.954249 | −0.477125 | − | 0.878836i | \(-0.658321\pi\) | ||||
−0.477125 | + | 0.878836i | \(0.658321\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 73.7722 | 2.83950 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.8223 | 1.26146 | 0.630731 | − | 0.776002i | \(-0.282755\pi\) | ||||
0.630731 | + | 0.776002i | \(0.282755\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −57.4842 | −2.20280 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.40083 | −0.130129 | −0.0650647 | − | 0.997881i | \(-0.520725\pi\) | ||||
−0.0650647 | + | 0.997881i | \(0.520725\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.01289 | −0.0387007 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.95203 | 0.341541 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.7945 | 0.411238 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.5148 | 0.894544 | 0.447272 | − | 0.894398i | \(-0.352396\pi\) | ||||
0.447272 | + | 0.894398i | \(0.352396\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35.1354 | 1.33276 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.836188 | −0.0316729 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −34.7786 | −1.31545 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.44634 | −0.319014 | −0.159507 | − | 0.987197i | \(-0.550990\pi\) | ||||
−0.159507 | + | 0.987197i | \(0.550990\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.55278 | −0.247143 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −135.857 | −5.11666 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.30596 | 0.311937 | 0.155969 | − | 0.987762i | \(-0.450150\pi\) | ||||
0.155969 | + | 0.987762i | \(0.450150\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −35.0456 | −1.31431 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.3415 | −0.949048 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −32.6197 | −1.21991 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −92.3279 | −3.44805 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.5762 | −1.47594 | −0.737972 | − | 0.674832i | \(-0.764216\pi\) | ||||
−0.737972 | + | 0.674832i | \(0.764216\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 64.4243 | 2.39597 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.6556 | −0.655712 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.3315 | 1.19911 | 0.599554 | − | 0.800334i | \(-0.295345\pi\) | ||||
0.599554 | + | 0.800334i | \(0.295345\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 70.1803 | 2.59927 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.34667 | 0.234740 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.94991 | −0.293637 | −0.146818 | − | 0.989163i | \(-0.546903\pi\) | ||||
−0.146818 | + | 0.989163i | \(0.546903\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39.1449 | 1.44192 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.926861 | −0.0340951 | −0.0170476 | − | 0.999855i | \(-0.505427\pi\) | ||||
−0.0170476 | + | 0.999855i | \(0.505427\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.4114 | −0.382473 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −46.3280 | −1.69961 | −0.849804 | − | 0.527098i | \(-0.823280\pi\) | ||||
−0.849804 | + | 0.527098i | \(0.823280\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.0119 | 1.06291 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −88.4472 | −3.23611 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.1445 | 0.516139 | 0.258070 | − | 0.966126i | \(-0.416914\pi\) | ||||
0.258070 | + | 0.966126i | \(0.416914\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −59.1549 | −2.15572 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 59.9277 | 2.18099 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.9749 | −1.27118 | −0.635592 | − | 0.772025i | \(-0.719244\pi\) | ||||
−0.635592 | + | 0.772025i | \(0.719244\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −57.7862 | −2.09751 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.5723 | 1.18075 | 0.590373 | − | 0.807131i | \(-0.298981\pi\) | ||||
0.590373 | + | 0.807131i | \(0.298981\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20.3540 | 0.735902 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.6889 | −0.855356 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.66978 | 0.132335 | 0.0661677 | − | 0.997809i | \(-0.478923\pi\) | ||||
0.0661677 | + | 0.997809i | \(0.478923\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 76.4962 | 2.75494 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.3480 | −1.52315 | −0.761576 | − | 0.648076i | \(-0.775574\pi\) | ||||
−0.761576 | + | 0.648076i | \(0.775574\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.8653 | 0.857267 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.07491 | −0.0385125 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.3356 | 1.40754 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −61.0158 | −2.18053 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.3754 | 0.869994 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 54.1762 | 1.93117 | 0.965587 | − | 0.260080i | \(-0.0837491\pi\) | ||||
0.965587 | + | 0.260080i | \(0.0837491\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 76.5464 | 2.72512 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.2833 | −0.649259 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −37.4974 | −1.32990 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.4371 | 0.830186 | 0.415093 | − | 0.909779i | \(-0.363749\pi\) | ||||
0.415093 | + | 0.909779i | \(0.363749\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.1204 | −0.393410 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.07907 | 0.285460 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.4076 | 1.10835 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 42.1063 | 1.48221 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.01729 | 0.317031 | 0.158515 | − | 0.987356i | \(-0.449329\pi\) | ||||
0.158515 | + | 0.987356i | \(0.449329\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.4811 | −0.543614 | −0.271807 | − | 0.962352i | \(-0.587621\pi\) | ||||
−0.271807 | + | 0.962352i | \(0.587621\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.391334 | −0.0137247 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.0521 | 0.702394 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.15854 | 0.285431 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.58546 | −0.229834 | −0.114917 | − | 0.993375i | \(-0.536660\pi\) | ||||
−0.114917 | + | 0.993375i | \(0.536660\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.0408 | 0.872867 | 0.436433 | − | 0.899737i | \(-0.356241\pi\) | ||||
0.436433 | + | 0.899737i | \(0.356241\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 54.4200 | 1.89466 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.6075 | 0.577499 | 0.288749 | − | 0.957405i | \(-0.406761\pi\) | ||||
0.288749 | + | 0.957405i | \(0.406761\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.0905 | 1.53133 | 0.765664 | − | 0.643241i | \(-0.222411\pi\) | ||||
0.765664 | + | 0.643241i | \(0.222411\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.9144 | 0.447995 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −39.9768 | −1.38345 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 82.4759 | 2.85078 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.41164 | −0.117783 | −0.0588915 | − | 0.998264i | \(-0.518757\pi\) | ||||
−0.0588915 | + | 0.998264i | \(0.518757\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.3974 | −0.496461 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 50.6835 | 1.74563 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.4972 | −0.464319 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.43088 | 0.117748 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.9080 | 1.02523 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.9233 | −1.46967 | −0.734833 | − | 0.678248i | \(-0.762740\pi\) | ||||
−0.734833 | + | 0.678248i | \(0.762740\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 26.1648 | 0.894817 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.54303 | −0.189346 | −0.0946731 | − | 0.995508i | \(-0.530181\pi\) | ||||
−0.0946731 | + | 0.995508i | \(0.530181\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.55350 | −0.0530049 | −0.0265024 | − | 0.999649i | \(-0.508437\pi\) | ||||
−0.0265024 | + | 0.999649i | \(0.508437\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.7310 | 1.04610 | 0.523048 | − | 0.852303i | \(-0.324795\pi\) | ||||
0.523048 | + | 0.852303i | \(0.324795\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −49.3819 | −1.67904 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −53.6885 | −1.82336 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.9698 | −0.541738 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.1902 | −1.09072 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −96.5296 | −3.26703 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.0669 | 1.21789 | 0.608946 | − | 0.793212i | \(-0.291593\pi\) | ||||
0.608946 | + | 0.793212i | \(0.291593\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.24135 | 0.0418698 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.68973 | 0.292764 | 0.146382 | − | 0.989228i | \(-0.453237\pi\) | ||||
0.146382 | + | 0.989228i | \(0.453237\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.7617 | −1.20348 | −0.601738 | − | 0.798694i | \(-0.705525\pi\) | ||||
−0.601738 | + | 0.798694i | \(0.705525\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 82.2894 | 2.76613 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 50.8003 | 1.70571 | 0.852853 | − | 0.522150i | \(-0.174870\pi\) | ||||
0.852853 | + | 0.522150i | \(0.174870\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 103.873 | 3.47988 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.2950 | −0.478365 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28.4472 | −0.950884 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 47.5195 | 1.58663 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.7386 | −0.658319 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.06930 | −0.102253 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.9768 | −0.531086 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.0711 | 0.832471 | 0.416235 | − | 0.909257i | \(-0.363349\pi\) | ||||
0.416235 | + | 0.909257i | \(0.363349\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −70.8134 | −2.34873 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.2558 | 0.869894 | 0.434947 | − | 0.900456i | \(-0.356767\pi\) | ||||
0.434947 | + | 0.900456i | \(0.356767\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −40.3041 | −1.33387 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 63.5117 | 2.09963 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.3342 | 1.39647 | 0.698237 | − | 0.715866i | \(-0.253968\pi\) | ||||
0.698237 | + | 0.715866i | \(0.253968\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.36017 | −0.176624 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32.3470 | −1.06472 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.1658 | −0.926084 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.20494 | −0.170953 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.4915 | 1.13163 | 0.565814 | − | 0.824533i | \(-0.308562\pi\) | ||||
0.565814 | + | 0.824533i | \(0.308562\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.6259 | −0.773478 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.27505 | 0.303327 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.1040 | 0.852782 | 0.426391 | − | 0.904539i | \(-0.359785\pi\) | ||||
0.426391 | + | 0.904539i | \(0.359785\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.1280 | −0.591585 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.9381 | −0.421770 | −0.210885 | − | 0.977511i | \(-0.567634\pi\) | ||||
−0.210885 | + | 0.977511i | \(0.567634\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.90605 | 0.159763 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.6880 | −1.02972 | −0.514861 | − | 0.857274i | \(-0.672157\pi\) | ||||
−0.514861 | + | 0.857274i | \(0.672157\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.8275 | −0.838396 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 95.8740 | 3.10893 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.5326 | −0.405971 | −0.202986 | − | 0.979182i | \(-0.565064\pi\) | ||||
−0.202986 | + | 0.979182i | \(0.565064\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.7076 | 0.637723 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −45.0098 | −1.45496 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.31906 | −0.139325 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −113.770 | −3.66618 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −74.4557 | −2.39681 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.5778 | −1.78726 | −0.893630 | − | 0.448804i | \(-0.851850\pi\) | ||||
−0.893630 | + | 0.448804i | \(0.851850\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.96038 | 0.0951010 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.8504 | 0.572847 | 0.286424 | − | 0.958103i | \(-0.407534\pi\) | ||||
0.286424 | + | 0.958103i | \(0.407534\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −44.7514 | −1.43319 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.93281 | −0.285786 | −0.142893 | − | 0.989738i | \(-0.545640\pi\) | ||||
−0.142893 | + | 0.989738i | \(0.545640\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.68152 | 0.117662 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −105.913 | −3.38153 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.1246 | −1.05651 | −0.528256 | − | 0.849085i | \(-0.677154\pi\) | ||||
−0.528256 | + | 0.849085i | \(0.677154\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.9659 | −0.476854 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −37.2369 | −1.18407 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.7747 | 0.628164 | 0.314082 | − | 0.949396i | \(-0.398303\pi\) | ||||
0.314082 | + | 0.949396i | \(0.398303\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 69.7453 | 2.21330 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −61.9065 | −1.96257 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.706048 | −0.0223608 | −0.0111804 | − | 0.999937i | \(-0.503559\pi\) | ||||
−0.0111804 | + | 0.999937i | \(0.503559\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −97.3378 | −3.07963 |
(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 | 8036.2.a.t.1.20 | yes | 20 | |
7.6 | odd | 2 | 8036.2.a.s.1.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.s.1.1 | ✓ | 20 | 7.6 | odd | 2 | ||
8036.2.a.t.1.20 | yes | 20 | 1.1 | even | 1 | trivial |