Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [152,2,Mod(1,152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(152, 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("152.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 152 = 2^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 152.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: | \(1.21372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.961.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 10x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.786802\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 152.1 |
$q$-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 | ||||||||
\(3\) | 0.786802 | 0.454260 | 0.227130 | − | 0.973864i | \(-0.427066\pi\) | ||||
0.227130 | + | 0.973864i | \(0.427066\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.29707 | 1.47449 | 0.737247 | − | 0.675623i | \(-0.236125\pi\) | ||||
0.737247 | + | 0.675623i | \(0.236125\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.08387 | −0.787630 | −0.393815 | − | 0.919190i | \(-0.628845\pi\) | ||||
−0.393815 | + | 0.919190i | \(0.628845\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.38094 | −0.793648 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.29707 | 0.391081 | 0.195541 | − | 0.980696i | \(-0.437354\pi\) | ||||
0.195541 | + | 0.980696i | \(0.437354\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.21320 | 0.336481 | 0.168240 | − | 0.985746i | \(-0.446192\pi\) | ||||
0.168240 | + | 0.985746i | \(0.446192\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.59414 | 0.669804 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.08387 | 0.990485 | 0.495242 | − | 0.868755i | \(-0.335079\pi\) | ||||
0.495242 | + | 0.868755i | \(0.335079\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.63959 | −0.357789 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.95455 | −1.86715 | −0.933576 | − | 0.358379i | \(-0.883329\pi\) | ||||
−0.933576 | + | 0.358379i | \(0.883329\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.87067 | 1.17413 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.23374 | −0.814783 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.38094 | −1.74200 | −0.870999 | − | 0.491285i | \(-0.836527\pi\) | ||||
−0.870999 | + | 0.491285i | \(0.836527\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.02054 | 0.177653 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.87067 | −1.16136 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.954547 | 0.152850 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.57360 | 0.558103 | 0.279052 | − | 0.960276i | \(-0.409980\pi\) | ||||
0.279052 | + | 0.960276i | \(0.409980\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.72347 | 1.17782 | 0.588909 | − | 0.808199i | \(-0.299558\pi\) | ||||
0.588909 | + | 0.808199i | \(0.299558\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.85014 | −1.17023 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.46482 | 1.38059 | 0.690293 | − | 0.723530i | \(-0.257482\pi\) | ||||
0.690293 | + | 0.723530i | \(0.257482\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.65748 | −0.379639 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.21320 | 0.449938 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.9751 | −1.64490 | −0.822452 | − | 0.568834i | \(-0.807395\pi\) | ||||
−0.822452 | + | 0.568834i | \(0.807395\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.27653 | 0.576648 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.786802 | −0.104214 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.21320 | −0.939078 | −0.469539 | − | 0.882912i | \(-0.655580\pi\) | ||||
−0.469539 | + | 0.882912i | \(0.655580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.87067 | 0.623626 | 0.311813 | − | 0.950144i | \(-0.399064\pi\) | ||||
0.311813 | + | 0.950144i | \(0.399064\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.96158 | 0.625100 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3809 | 1.39040 | 0.695202 | − | 0.718815i | \(-0.255315\pi\) | ||||
0.695202 | + | 0.718815i | \(0.255315\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.04545 | −0.848173 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.02054 | −1.07054 | −0.535270 | − | 0.844681i | \(-0.679790\pi\) | ||||
−0.535270 | + | 0.844681i | \(0.679790\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.65748 | 0.662157 | 0.331079 | − | 0.943603i | \(-0.392587\pi\) | ||||
0.331079 | + | 0.943603i | \(0.392587\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.61906 | 0.533363 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.70293 | −0.308027 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.57360 | 1.07711 | 0.538557 | − | 0.842589i | \(-0.318970\pi\) | ||||
0.538557 | + | 0.842589i | \(0.318970\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.81172 | 0.423524 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.7619 | 1.18127 | 0.590635 | − | 0.806939i | \(-0.298877\pi\) | ||||
0.590635 | + | 0.806939i | \(0.298877\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.4648 | 1.46046 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.38094 | −0.791320 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.0205 | 1.16817 | 0.584087 | − | 0.811691i | \(-0.301453\pi\) | ||||
0.584087 | + | 0.811691i | \(0.301453\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.52815 | −0.265022 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.29707 | −0.338272 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.59414 | −0.872603 | −0.436301 | − | 0.899801i | \(-0.643712\pi\) | ||||
−0.436301 | + | 0.899801i | \(0.643712\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.08825 | −0.310381 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.14721 | 0.910181 | 0.455091 | − | 0.890445i | \(-0.349607\pi\) | ||||
0.455091 | + | 0.890445i | \(0.349607\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.3560 | 1.71014 | 0.855070 | − | 0.518512i | \(-0.173514\pi\) | ||||
0.855070 | + | 0.518512i | \(0.173514\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.40586 | −0.527558 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.786802 | −0.0760630 | −0.0380315 | − | 0.999277i | \(-0.512109\pi\) | ||||
−0.0380315 | + | 0.999277i | \(0.512109\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.5487 | −1.29773 | −0.648864 | − | 0.760904i | \(-0.724756\pi\) | ||||
−0.648864 | + | 0.760904i | \(0.724756\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.57360 | −0.149360 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.14721 | −0.107920 | −0.0539601 | − | 0.998543i | \(-0.517184\pi\) | ||||
−0.0539601 | + | 0.998543i | \(0.517184\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −29.5238 | −2.75311 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.88856 | −0.267047 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.51027 | −0.780135 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.31761 | −0.847055 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.81172 | 0.253524 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.87067 | 0.256761 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.02054 | −0.0905581 | −0.0452790 | − | 0.998974i | \(-0.514418\pi\) | ||||
−0.0452790 | + | 0.998974i | \(0.514418\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.07684 | 0.535036 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.72347 | −0.674802 | −0.337401 | − | 0.941361i | \(-0.609548\pi\) | ||||
−0.337401 | + | 0.941361i | \(0.609548\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.08387 | 0.180695 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.9589 | −1.20139 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.2311 | 1.30128 | 0.650639 | − | 0.759387i | \(-0.274501\pi\) | ||||
0.650639 | + | 0.759387i | \(0.274501\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.0590 | 1.36210 | 0.681051 | − | 0.732236i | \(-0.261523\pi\) | ||||
0.681051 | + | 0.732236i | \(0.261523\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.44693 | 0.627145 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.57360 | 0.131591 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −30.9296 | −2.56857 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.09091 | −0.172455 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.10879 | −0.172759 | −0.0863793 | − | 0.996262i | \(-0.527530\pi\) | ||||
−0.0863793 | + | 0.996262i | \(0.527530\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.3560 | 1.41241 | 0.706207 | − | 0.708006i | \(-0.250405\pi\) | ||||
0.706207 | + | 0.708006i | \(0.250405\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.72347 | −0.786096 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.42202 | −0.747215 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.6601 | 1.47062 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.852793 | −0.0667959 | −0.0333979 | − | 0.999442i | \(-0.510633\pi\) | ||||
−0.0333979 | + | 0.999442i | \(0.510633\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.36478 | 0.261948 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.5941 | −1.43886 | −0.719429 | − | 0.694566i | \(-0.755596\pi\) | ||||
−0.719429 | + | 0.694566i | \(0.755596\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5282 | −0.886781 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.38094 | 0.182075 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.85279 | 0.216894 | 0.108447 | − | 0.994102i | \(-0.465412\pi\) | ||||
0.108447 | + | 0.994102i | \(0.465412\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.2337 | −0.924783 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.67536 | −0.426586 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −26.0768 | −1.94907 | −0.974537 | − | 0.224226i | \(-0.928015\pi\) | ||||
−0.974537 | + | 0.224226i | \(0.928015\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.18828 | 0.236983 | 0.118492 | − | 0.992955i | \(-0.462194\pi\) | ||||
0.118492 | + | 0.992955i | \(0.462194\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.83226 | 0.283288 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.59414 | −0.484811 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.29707 | 0.387360 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.82256 | 0.641747 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.95720 | 0.575763 | 0.287881 | − | 0.957666i | \(-0.407049\pi\) | ||||
0.287881 | + | 0.957666i | \(0.407049\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.9296 | 1.50655 | 0.753274 | − | 0.657707i | \(-0.228473\pi\) | ||||
0.753274 | + | 0.657707i | \(0.228473\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.14721 | 0.225376 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.57360 | −0.254609 | −0.127304 | − | 0.991864i | \(-0.540632\pi\) | ||||
−0.127304 | + | 0.991864i | \(0.540632\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.4194 | −1.87282 | −0.936409 | − | 0.350909i | \(-0.885873\pi\) | ||||
−0.936409 | + | 0.350909i | \(0.885873\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.95455 | 0.631605 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19.5487 | 1.37205 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.7824 | 0.822920 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 21.3203 | 1.48186 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.29707 | −0.0897202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.5487 | −1.62116 | −0.810579 | − | 0.585629i | \(-0.800848\pi\) | ||||
−0.810579 | + | 0.585629i | \(0.800848\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.09738 | −0.486304 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.4648 | 1.73669 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.45131 | 0.300792 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.95455 | 0.333279 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.02054 | 0.0683402 | 0.0341701 | − | 0.999416i | \(-0.489121\pi\) | ||||
0.0341701 | + | 0.999416i | \(0.489121\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.9777 | −0.931849 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.04545 | 0.202134 | 0.101067 | − | 0.994880i | \(-0.467774\pi\) | ||||
0.101067 | + | 0.994880i | \(0.467774\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.01788 | −0.265509 | −0.132755 | − | 0.991149i | \(-0.542382\pi\) | ||||
−0.132755 | + | 0.991149i | \(0.542382\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.12667 | −0.139925 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.2062 | 1.65131 | 0.825655 | − | 0.564175i | \(-0.190806\pi\) | ||||
0.825655 | + | 0.564175i | \(0.190806\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 31.2062 | 2.03567 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.53253 | 0.489290 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.93667 | −0.448696 | −0.224348 | − | 0.974509i | \(-0.572025\pi\) | ||||
−0.224348 | + | 0.974509i | \(0.572025\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.761886 | 0.0490774 | 0.0245387 | − | 0.999699i | \(-0.492188\pi\) | ||||
0.0245387 | + | 0.999699i | \(0.492188\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.7003 | 1.00717 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.76189 | −0.559776 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.21320 | −0.0771940 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.46747 | 0.536604 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.14986 | −0.388176 | −0.194088 | − | 0.980984i | \(-0.562175\pi\) | ||||
−0.194088 | + | 0.980984i | \(0.562175\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.6147 | −0.730209 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.5941 | 0.663431 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.3560 | −1.45691 | −0.728454 | − | 0.685094i | \(-0.759761\pi\) | ||||
−0.728454 | + | 0.685094i | \(0.759761\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.16774 | 0.258971 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.3355 | 1.38253 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.2765 | 0.757003 | 0.378502 | − | 0.925601i | \(-0.376439\pi\) | ||||
0.378502 | + | 0.925601i | \(0.376439\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −39.4827 | −2.42540 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.67098 | 0.530655 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.74135 | −0.471998 | −0.235999 | − | 0.971753i | \(-0.575836\pi\) | ||||
−0.235999 | + | 0.971753i | \(0.575836\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.954547 | −0.0579846 | −0.0289923 | − | 0.999580i | \(-0.509230\pi\) | ||||
−0.0289923 | + | 0.999580i | \(0.509230\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.98915 | −0.120389 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.61468 | 0.459182 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.0384 | 1.02374 | 0.511870 | − | 0.859063i | \(-0.328953\pi\) | ||||
0.511870 | + | 0.859063i | \(0.328953\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.0974 | −0.781324 | −0.390662 | − | 0.920534i | \(-0.627754\pi\) | ||||
−0.390662 | + | 0.920534i | \(0.627754\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.29707 | 0.0771028 | 0.0385514 | − | 0.999257i | \(-0.487726\pi\) | ||||
0.0385514 | + | 0.999257i | \(0.487726\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.59414 | −0.153664 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.44693 | −0.439579 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.321987 | −0.0189404 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.76189 | −0.396389 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.5487 | −1.25889 | −0.629444 | − | 0.777046i | \(-0.716717\pi\) | ||||
−0.629444 | + | 0.777046i | \(0.716717\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.7824 | −1.38467 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.49145 | −0.318646 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.8636 | −0.628260 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0947 | −0.927684 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.19704 | 0.413459 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.0590 | 0.919533 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.18828 | −0.524403 | −0.262201 | − | 0.965013i | \(-0.584449\pi\) | ||||
−0.262201 | + | 0.965013i | \(0.584449\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.6558 | 0.776849 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.48973 | −0.424704 | −0.212352 | − | 0.977193i | \(-0.568112\pi\) | ||||
−0.212352 | + | 0.977193i | \(0.568112\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.76626 | −0.552022 | −0.276011 | − | 0.961154i | \(-0.589013\pi\) | ||||
−0.276011 | + | 0.961154i | \(0.589013\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 16.3587 | 0.921707 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.7164 | 0.770392 | 0.385196 | − | 0.922835i | \(-0.374134\pi\) | ||||
0.385196 | + | 0.922835i | \(0.374134\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.1677 | −0.681263 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.619057 | −0.0345524 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.08387 | −0.227233 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.12229 | 0.395074 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.6601 | −0.589507 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.7235 | −1.08739 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.5282 | −0.798539 | −0.399270 | − | 0.916834i | \(-0.630736\pi\) | ||||
−0.399270 | + | 0.916834i | \(0.630736\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.76189 | 0.260950 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 37.5238 | 2.05014 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.31495 | 0.507418 | 0.253709 | − | 0.967281i | \(-0.418349\pi\) | ||||
0.253709 | + | 0.967281i | \(0.418349\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.902625 | −0.0490238 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1249 | 1.08665 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −23.2294 | −1.25063 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.29707 | −0.499093 | −0.249546 | − | 0.968363i | \(-0.580282\pi\) | ||||
−0.249546 | + | 0.968363i | \(0.580282\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0590 | −0.752559 | −0.376279 | − | 0.926506i | \(-0.622797\pi\) | ||||
−0.376279 | + | 0.926506i | \(0.622797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.13636 | −0.274159 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.4783 | −1.08995 | −0.544975 | − | 0.838452i | \(-0.683461\pi\) | ||||
−0.544975 | + | 0.838452i | \(0.683461\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −29.7413 | −1.57851 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.69589 | −0.354384 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.9724 | 1.00133 | 0.500663 | − | 0.865642i | \(-0.333090\pi\) | ||||
0.500663 | + | 0.865642i | \(0.333090\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.33111 | −0.384784 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.6531 | 0.976348 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.85279 | −0.253314 | −0.126657 | − | 0.991947i | \(-0.540425\pi\) | ||||
−0.126657 | + | 0.991947i | \(0.540425\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.50855 | −0.442937 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.9545 | 1.29558 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.1071 | −0.626880 | −0.313440 | − | 0.949608i | \(-0.601481\pi\) | ||||
−0.313440 | + | 0.949608i | \(0.601481\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.25865 | 0.116636 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.3809 | −0.586148 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.02492 | −0.104013 | −0.0520065 | − | 0.998647i | \(-0.516562\pi\) | ||||
−0.0520065 | + | 0.998647i | \(0.516562\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.802961 | −0.0411369 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.23811 | −0.0632647 | −0.0316323 | − | 0.999500i | \(-0.510071\pi\) | ||||
−0.0316323 | + | 0.999500i | \(0.510071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.91175 | −0.454185 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.3891 | −0.934772 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.8707 | 0.652569 | 0.326285 | − | 0.945272i | \(-0.394203\pi\) | ||||
0.326285 | + | 0.945272i | \(0.394203\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.5692 | −1.84939 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.07684 | −0.306536 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 31.5648 | 1.58820 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.3739 | 0.871971 | 0.435986 | − | 0.899954i | \(-0.356400\pi\) | ||||
0.435986 | + | 0.899954i | \(0.356400\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.63959 | 0.0820824 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.0205 | 0.949840 | 0.474920 | − | 0.880029i | \(-0.342477\pi\) | ||||
0.474920 | + | 0.880029i | \(0.342477\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.5675 | 0.624484 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.59414 | −0.128587 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.4622 | 1.01179 | 0.505894 | − | 0.862595i | \(-0.331163\pi\) | ||||
0.505894 | + | 0.862595i | \(0.331163\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.9838 | 0.591119 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.0314 | 0.739646 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 35.4827 | 1.74178 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.6352 | 0.618749 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.14721 | −0.349164 | −0.174582 | − | 0.984643i | \(-0.555857\pi\) | ||||
−0.174582 | + | 0.984643i | \(0.555857\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.3604 | 0.602409 | 0.301205 | − | 0.953560i | \(-0.402611\pi\) | ||||
0.301205 | + | 0.953560i | \(0.402611\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.5352 | −1.09570 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.9751 | 1.16296 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.1499 | −0.491186 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.23811 | 0.0597767 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.90909 | −0.0919578 | −0.0459789 | − | 0.998942i | \(-0.514641\pi\) | ||||
−0.0459789 | + | 0.998942i | \(0.514641\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.04107 | 0.194202 | 0.0971008 | − | 0.995275i | \(-0.469043\pi\) | ||||
0.0971008 | + | 0.995275i | \(0.469043\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −24.3355 | −1.16680 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.95455 | 0.428354 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0768 | 0.671851 | 0.335925 | − | 0.941889i | \(-0.390951\pi\) | ||||
0.335925 | + | 0.941889i | \(0.390951\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.32730 | 0.301300 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.6736 | −0.934723 | −0.467361 | − | 0.884066i | \(-0.654795\pi\) | ||||
−0.467361 | + | 0.884066i | \(0.654795\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 36.3355 | 1.72247 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.65920 | −0.0784774 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.5531 | 0.498030 | 0.249015 | − | 0.968500i | \(-0.419893\pi\) | ||||
0.249015 | + | 0.968500i | \(0.419893\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.63522 | 0.218264 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.6558 | 0.641603 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.33549 | −0.390774 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.72785 | 0.127603 | 0.0638016 | − | 0.997963i | \(-0.479678\pi\) | ||||
0.0638016 | + | 0.997963i | \(0.479678\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.2900 | −0.807030 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.1153 | −1.63548 | −0.817740 | − | 0.575587i | \(-0.804773\pi\) | ||||
−0.817740 | + | 0.575587i | \(0.804773\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.1293 | 0.796067 | 0.398034 | − | 0.917371i | \(-0.369693\pi\) | ||||
0.398034 | + | 0.917371i | \(0.369693\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.7029 | 0.680370 | 0.340185 | − | 0.940358i | \(-0.389510\pi\) | ||||
0.340185 | + | 0.940358i | \(0.389510\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.7164 | −1.09512 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.0152 | 0.507555 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.0179 | 0.460623 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.87067 | −0.269365 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.5120 | 1.30547 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.0411 | 0.458788 | 0.229394 | − | 0.973334i | \(-0.426326\pi\) | ||||
0.229394 | + | 0.973334i | \(0.426326\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.42640 | −0.110634 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.6818 | 0.668046 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −28.3355 | −1.28665 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.6504 | −1.07170 | −0.535852 | − | 0.844312i | \(-0.680009\pi\) | ||||
−0.535852 | + | 0.844312i | \(0.680009\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.670979 | −0.0303427 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.3766 | −1.73191 | −0.865955 | − | 0.500122i | \(-0.833289\pi\) | ||||
−0.865955 | + | 0.500122i | \(0.833289\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38.3106 | −1.72542 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.1822 | −0.457655 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.7976 | 0.843190 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.3176 | 0.461880 | 0.230940 | − | 0.972968i | \(-0.425820\pi\) | ||||
0.230940 | + | 0.972968i | \(0.425820\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.6299 | −0.653616 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.4372 | −0.911252 | −0.455626 | − | 0.890171i | \(-0.650584\pi\) | ||||
−0.455626 | + | 0.890171i | \(0.650584\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.1590 | 1.34206 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.07037 | −0.402829 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.4059 | −0.682853 | −0.341426 | − | 0.939909i | \(-0.610910\pi\) | ||||
−0.341426 | + | 0.939909i | \(0.610910\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.7895 | −0.521535 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.23374 | 0.186924 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 57.2240 | 2.52159 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.2765 | 0.539921 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.24458 | 0.0985262 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.0270 | 1.57837 | 0.789186 | − | 0.614154i | \(-0.210503\pi\) | ||||
0.789186 | + | 0.614154i | \(0.210503\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 44.7370 | 1.95621 | 0.978106 | − | 0.208109i | \(-0.0667310\pi\) | ||||
0.978106 | + | 0.208109i | \(0.0667310\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.62553 | −0.420092 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 57.1839 | 2.48626 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.1742 | 0.745297 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.33549 | 0.187791 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.59414 | −0.112154 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.5173 | −0.885387 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.44693 | −0.148470 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.5059 | −1.61250 | −0.806252 | − | 0.591572i | \(-0.798507\pi\) | ||||
−0.806252 | + | 0.591572i | \(0.798507\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.50855 | 0.107652 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −44.6710 | −1.91349 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.5968 | −0.494939 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.38094 | 0.399642 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.9502 | −0.848367 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.18828 | −0.220230 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.3381 | −1.41258 | −0.706291 | − | 0.707921i | \(-0.749633\pi\) | ||||
−0.706291 | + | 0.707921i | \(0.749633\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.37010 | 0.396313 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.16774 | 0.175962 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.44693 | 0.145271 | 0.0726355 | − | 0.997359i | \(-0.476859\pi\) | ||||
0.0726355 | + | 0.997359i | \(0.476859\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.78242 | −0.159128 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.94313 | −0.333580 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.0205 | 1.13276 | 0.566380 | − | 0.824144i | \(-0.308343\pi\) | ||||
0.566380 | + | 0.824144i | \(0.308343\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.70559 | −0.238771 | −0.119386 | − | 0.992848i | \(-0.538092\pi\) | ||||
−0.119386 | + | 0.992848i | \(0.538092\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.26074 | 0.261546 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −52.5692 | −2.19229 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.34252 | 0.264043 | 0.132021 | − | 0.991247i | \(-0.457853\pi\) | ||||
0.132021 | + | 0.991247i | \(0.457853\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.4675 | 0.684365 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.4264 | −0.930404 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.5325 | −0.643292 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.52377 | −0.393759 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.5827 | −1.55121 | −0.775603 | − | 0.631222i | \(-0.782554\pi\) | ||||
−0.775603 | + | 0.631222i | \(0.782554\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.81172 | −0.115659 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.48270 | −0.389408 | −0.194704 | − | 0.980862i | \(-0.562375\pi\) | ||||
−0.194704 | + | 0.980862i | \(0.562375\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.0590 | −1.15031 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.7868 | −0.850747 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.6710 | 1.00803 | 0.504014 | − | 0.863695i | \(-0.331856\pi\) | ||||
0.504014 | + | 0.863695i | \(0.331856\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.4329 | 1.69008 | 0.845041 | − | 0.534702i | \(-0.179576\pi\) | ||||
0.845041 | + | 0.534702i | \(0.179576\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −27.0974 | −1.10349 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.7208 | −1.24898 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.32026 | 0.215943 | 0.107971 | − | 0.994154i | \(-0.465564\pi\) | ||||
0.107971 | + | 0.994154i | \(0.465564\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.3809 | 0.623267 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.4827 | 0.464540 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.2472 | −1.10051 | −0.550253 | − | 0.834998i | \(-0.685469\pi\) | ||||
−0.550253 | + | 0.834998i | \(0.685469\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.27043 | 0.373820 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.9117 | −1.24446 | −0.622230 | − | 0.782834i | \(-0.713773\pi\) | ||||
−0.622230 | + | 0.782834i | \(0.713773\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.2857 | −0.976123 | −0.488061 | − | 0.872809i | \(-0.662296\pi\) | ||||
−0.488061 | + | 0.872809i | \(0.662296\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 37.9112 | 1.52132 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.9654 | −0.920089 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.8886 | −0.795542 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.02054 | −0.0407563 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.16774 | −0.325669 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.9117 | 0.991721 | 0.495861 | − | 0.868402i | \(-0.334853\pi\) | ||||
0.495861 | + | 0.868402i | \(0.334853\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.5282 | −0.736428 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.36478 | −0.133527 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.22405 | −0.127741 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.4774 | 0.849632 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.25865 | 0.168207 | 0.0841033 | − | 0.996457i | \(-0.473197\pi\) | ||||
0.0841033 | + | 0.996457i | \(0.473197\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.9323 | −0.549436 | −0.274718 | − | 0.961525i | \(-0.588584\pi\) | ||||
−0.274718 | + | 0.961525i | \(0.588584\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20.0358 | 0.788907 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.58064 | 0.219398 | 0.109699 | − | 0.993965i | \(-0.465011\pi\) | ||||
0.109699 | + | 0.993965i | \(0.465011\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.35603 | −0.367256 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.77330 | −0.0693945 | −0.0346973 | − | 0.999398i | \(-0.511047\pi\) | ||||
−0.0346973 | + | 0.999398i | \(0.511047\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.4648 | −0.994993 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.4701 | −0.525520 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.12229 | −0.0437183 | −0.0218591 | − | 0.999761i | \(-0.506959\pi\) | ||||
−0.0218591 | + | 0.999761i | \(0.506959\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.9340 | 0.853134 | 0.426567 | − | 0.904456i | \(-0.359723\pi\) | ||||
0.426567 | + | 0.904456i | \(0.359723\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.89825 | 0.151395 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.87067 | 0.266433 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 84.0021 | 3.25257 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.802961 | 0.0310443 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.31761 | 0.243889 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.24458 | −0.317805 | −0.158903 | − | 0.987294i | \(-0.550796\pi\) | ||||
−0.158903 | + | 0.987294i | \(0.550796\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −24.8549 | −0.956665 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.76626 | −0.221616 | −0.110808 | − | 0.993842i | \(-0.535344\pi\) | ||||
−0.110808 | + | 0.993842i | \(0.535344\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.9091 | 0.687288 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.39617 | 0.0918214 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 50.2179 | 1.91873 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.16128 | −0.120610 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.5282 | −0.553478 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.0384 | 0.876423 | 0.438211 | − | 0.898872i | \(-0.355612\pi\) | ||||
0.438211 | + | 0.898872i | \(0.355612\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.43552 | 0.244465 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 52.9475 | 2.00841 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.5941 | 0.552793 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.8323 | 0.750125 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.90909 | −0.147644 | −0.0738222 | − | 0.997271i | \(-0.523520\pi\) | ||||
−0.0738222 | + | 0.997271i | \(0.523520\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.00000 | 0.0754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 24.5531 | 0.924722 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.0616 | −0.716886 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.0411 | −0.452212 | −0.226106 | − | 0.974103i | \(-0.572600\pi\) | ||||
−0.226106 | + | 0.974103i | \(0.572600\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.7942 | −0.854849 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.18828 | 0.194031 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.45778 | −0.203825 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.2927 | 1.20431 | 0.602157 | − | 0.798378i | \(-0.294308\pi\) | ||||
0.602157 | + | 0.798378i | \(0.294308\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.1677 | −1.34696 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.599453 | 0.0222939 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −55.0725 | −2.04534 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.1812 | 1.52733 | 0.763664 | − | 0.645614i | \(-0.223398\pi\) | ||||
0.763664 | + | 0.645614i | \(0.223398\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.917850 | 0.0339945 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.5417 | 1.16661 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.27919 | 0.0472479 | 0.0236240 | − | 0.999721i | \(-0.492480\pi\) | ||||
0.0236240 | + | 0.999721i | \(0.492480\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.89387 | −0.254284 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.7619 | 0.543761 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.3534 | 1.11657 | 0.558283 | − | 0.829650i | \(-0.311460\pi\) | ||||
0.558283 | + | 0.829650i | \(0.311460\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.954547 | −0.0350661 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.4827 | −0.714751 | −0.357375 | − | 0.933961i | \(-0.616328\pi\) | ||||
−0.357375 | + | 0.933961i | \(0.616328\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.95282 | −0.254732 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −25.6234 | −0.937512 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.63959 | 0.0599095 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.6710 | −1.77603 | −0.888015 | − | 0.459815i | \(-0.847916\pi\) | ||||
−0.888015 | + | 0.459815i | \(0.847916\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.83872 | −0.176333 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 57.2240 | 2.08260 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.7235 | 1.51647 | 0.758233 | − | 0.651984i | \(-0.226063\pi\) | ||||
0.758233 | + | 0.651984i | \(0.226063\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.13845 | −0.331705 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.10441 | −0.330035 | −0.165017 | − | 0.986291i | \(-0.552768\pi\) | ||||
−0.165017 | + | 0.986291i | \(0.552768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.2337 | 1.02213 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −32.0590 | −1.15909 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.75104 | −0.315982 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.14548 | 0.257673 | 0.128836 | − | 0.991666i | \(-0.458876\pi\) | ||||
0.128836 | + | 0.991666i | \(0.458876\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.3766 | −0.661816 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.9956 | −1.04290 | −0.521450 | − | 0.853282i | \(-0.674609\pi\) | ||||
−0.521450 | + | 0.853282i | \(0.674609\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.27919 | 0.117640 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.57360 | −0.128038 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.7003 | −0.418669 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 39.7164 | 1.41935 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46.1590 | 1.64748 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.3311 | −0.831664 | −0.415832 | − | 0.909441i | \(-0.636510\pi\) | ||||
−0.415832 | + | 0.909441i | \(0.636510\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.65920 | 0.343877 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.39063 | 0.0850011 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.90909 | 0.209838 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −31.0651 | −1.10176 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.2543 | 0.682021 | 0.341011 | − | 0.940059i | \(-0.389231\pi\) | ||||
0.341011 | + | 0.940059i | \(0.389231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.6531 | 1.36745 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −26.2393 | −0.927119 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.33815 | 0.258958 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 61.5238 | 2.16843 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.09091 | −0.214410 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.9983 | 0.984367 | 0.492184 | − | 0.870491i | \(-0.336199\pi\) | ||||
0.492184 | + | 0.870491i | \(0.336199\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.4631 | −1.66665 | −0.833327 | − | 0.552780i | \(-0.813567\pi\) | ||||
−0.833327 | + | 0.552780i | \(0.813567\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.751039 | −0.0263401 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.81172 | −0.0984902 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.72347 | −0.270210 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.01938 | 0.210334 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.14455 | 0.0748454 | 0.0374227 | − | 0.999300i | \(-0.488085\pi\) | ||||
0.0374227 | + | 0.999300i | \(0.488085\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.8458 | −1.14493 | −0.572466 | − | 0.819929i | \(-0.694013\pi\) | ||||
−0.572466 | + | 0.819929i | \(0.694013\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.99124 | 0.208588 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.6103 | 0.925331 | 0.462665 | − | 0.886533i | \(-0.346893\pi\) | ||||
0.462665 | + | 0.886533i | \(0.346893\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.6871 | 1.76044 | 0.880219 | − | 0.474569i | \(-0.157396\pi\) | ||||
0.880219 | + | 0.474569i | \(0.157396\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.4059 | 0.465044 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.8528 | −0.376027 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −61.3062 | −2.12159 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.2651 | −1.76987 | −0.884934 | − | 0.465716i | \(-0.845797\pi\) | ||||
−0.884934 | + | 0.465716i | \(0.845797\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.0021 | 2.03455 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.3050 | −0.354924 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −38.0091 | −1.30755 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.4167 | 0.667166 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.02054 | 0.0350248 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.9091 | 0.613916 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.95893 | −0.272508 | −0.136254 | − | 0.990674i | \(-0.543506\pi\) | ||||
−0.136254 | + | 0.990674i | \(0.543506\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.85014 | 0.268469 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.09091 | −0.139743 | −0.0698714 | − | 0.997556i | \(-0.522259\pi\) | ||||
−0.0698714 | + | 0.997556i | \(0.522259\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.3328 | −0.454910 | −0.227455 | − | 0.973789i | \(-0.573041\pi\) | ||||
−0.227455 | + | 0.973789i | \(0.573041\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.85926 | −0.199683 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.1677 | −0.686518 | −0.343259 | − | 0.939241i | \(-0.611531\pi\) | ||||
−0.343259 | + | 0.939241i | \(0.611531\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.40586 | 0.319809 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.253340 | −0.00860386 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.4176 | 0.421240 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.8073 | 0.467844 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.4622 | 0.692539 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.98212 | −0.202233 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.8572 | 0.805599 | 0.402800 | − | 0.915288i | \(-0.368037\pi\) | ||||
0.402800 | + | 0.915288i | \(0.368037\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.9545 | −0.571863 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.9182 | −1.61441 | −0.807203 | − | 0.590274i | \(-0.799020\pi\) | ||||
−0.807203 | + | 0.590274i | \(0.799020\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.5622 | −0.961194 | −0.480597 | − | 0.876942i | \(-0.659580\pi\) | ||||
−0.480597 | + | 0.876942i | \(0.659580\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.7121 | −0.628999 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.3150 | 1.58868 | 0.794340 | − | 0.607473i | \(-0.207817\pi\) | ||||
0.794340 | + | 0.607473i | \(0.207817\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.12667 | 0.0713262 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.94407 | 0.165632 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.46482 | −0.316728 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −85.9772 | −2.87390 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.54753 | −0.285394 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.9047 | −1.62925 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.6634 | −0.421410 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.5120 | 0.349430 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.8982 | −0.527893 | −0.263946 | − | 0.964537i | \(-0.585024\pi\) | ||||
−0.263946 | + | 0.964537i | \(0.585024\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21.7790 | −0.722363 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.2997 | −0.672560 | −0.336280 | − | 0.941762i | \(-0.609169\pi\) | ||||
−0.336280 | + | 0.941762i | \(0.609169\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.9589 | 0.461973 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.6352 | 0.417707 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.0947 | 0.531494 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.6191 | 1.07600 | 0.538002 | − | 0.842944i | \(-0.319179\pi\) | ||||
0.538002 | + | 0.842944i | \(0.319179\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.22936 | −0.238215 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.9437 | −0.360216 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.7413 | −0.386053 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −41.3237 | −1.35725 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 53.4631 | 1.75407 | 0.877034 | − | 0.480429i | \(-0.159519\pi\) | ||||
0.877034 | + | 0.480429i | \(0.159519\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.65748 | 0.0870953 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.89293 | −0.192926 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.4648 | 0.571161 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.0135 | −1.40519 | −0.702595 | − | 0.711590i | \(-0.747975\pi\) | ||||
−0.702595 | + | 0.711590i | \(0.747975\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.68411 | −0.250762 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.3311 | 0.825771 | 0.412885 | − | 0.910783i | \(-0.364521\pi\) | ||||
0.412885 | + | 0.910783i | \(0.364521\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.0000 | −1.04206 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 29.0886 | 0.946253 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.6710 | 0.411751 | 0.205876 | − | 0.978578i | \(-0.433996\pi\) | ||||
0.205876 | + | 0.978578i | \(0.433996\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.86364 | 0.222803 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.7921 | 0.349958 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.2240 | −1.01145 | −0.505723 | − | 0.862696i | \(-0.668774\pi\) | ||||
−0.505723 | + | 0.862696i | \(0.668774\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.2355 | 0.848959 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.57360 | −0.309471 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −31.7396 | −1.02493 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.87333 | 0.0603672 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 69.0065 | 2.22140 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.29441 | 0.202415 | 0.101207 | − | 0.994865i | \(-0.467729\pi\) | ||||
0.101207 | + | 0.994865i | \(0.467729\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.21320 | −0.103223 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.0000 | 0.641831 | 0.320915 | − | 0.947108i | \(-0.396010\pi\) | ||||
0.320915 | + | 0.947108i | \(0.396010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.4648 | −1.07283 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.60383 | 0.179466 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.1677 | −1.09312 | −0.546561 | − | 0.837419i | \(-0.684064\pi\) | ||||
−0.546561 | + | 0.837419i | \(0.684064\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.2944 | 0.456851 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 32.2587 | 1.02994 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.4264 | 0.970451 | 0.485226 | − | 0.874389i | \(-0.338737\pi\) | ||||
0.485226 | + | 0.874389i | \(0.338737\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.7824 | −0.375419 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.5185 | −0.493958 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −69.1601 | −2.19916 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.1179 | −0.766131 | −0.383065 | − | 0.923721i | \(-0.625132\pi\) | ||||
−0.383065 | + | 0.923721i | \(0.625132\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.4308 | −0.362745 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −87.1065 | −2.76146 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.9323 | 0.504581 | 0.252290 | − | 0.967652i | \(-0.418816\pi\) | ||||
0.252290 | + | 0.967652i | \(0.418816\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.46747 | 0.267899 |
(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 | 152.2.a.c.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 1368.2.a.n.1.1 | 3 | |||
4.3 | odd | 2 | 304.2.a.g.1.2 | 3 | |||
5.2 | odd | 4 | 3800.2.d.j.3649.3 | 6 | |||
5.3 | odd | 4 | 3800.2.d.j.3649.4 | 6 | |||
5.4 | even | 2 | 3800.2.a.r.1.2 | 3 | |||
7.6 | odd | 2 | 7448.2.a.bf.1.2 | 3 | |||
8.3 | odd | 2 | 1216.2.a.v.1.2 | 3 | |||
8.5 | even | 2 | 1216.2.a.u.1.2 | 3 | |||
12.11 | even | 2 | 2736.2.a.bd.1.1 | 3 | |||
19.18 | odd | 2 | 2888.2.a.o.1.2 | 3 | |||
20.19 | odd | 2 | 7600.2.a.bv.1.2 | 3 | |||
76.75 | even | 2 | 5776.2.a.bp.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.a.c.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
304.2.a.g.1.2 | 3 | 4.3 | odd | 2 | |||
1216.2.a.u.1.2 | 3 | 8.5 | even | 2 | |||
1216.2.a.v.1.2 | 3 | 8.3 | odd | 2 | |||
1368.2.a.n.1.1 | 3 | 3.2 | odd | 2 | |||
2736.2.a.bd.1.1 | 3 | 12.11 | even | 2 | |||
2888.2.a.o.1.2 | 3 | 19.18 | odd | 2 | |||
3800.2.a.r.1.2 | 3 | 5.4 | even | 2 | |||
3800.2.d.j.3649.3 | 6 | 5.2 | odd | 4 | |||
3800.2.d.j.3649.4 | 6 | 5.3 | odd | 4 | |||
5776.2.a.bp.1.2 | 3 | 76.75 | even | 2 | |||
7448.2.a.bf.1.2 | 3 | 7.6 | odd | 2 | |||
7600.2.a.bv.1.2 | 3 | 20.19 | odd | 2 |