Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 22x^{8} - 16x^{7} + 146x^{6} + 200x^{5} - 206x^{4} - 440x^{3} - 124x^{2} + 72x + 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{41}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 1960) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.609577\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.35056 | −0.779746 | −0.389873 | − | 0.920869i | \(-0.627481\pi\) | ||||
−0.389873 | + | 0.920869i | \(0.627481\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.17599 | −0.391995 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.15296 | 0.950654 | 0.475327 | − | 0.879809i | \(-0.342330\pi\) | ||||
0.475327 | + | 0.879809i | \(0.342330\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.17296 | 0.325322 | 0.162661 | − | 0.986682i | \(-0.447992\pi\) | ||||
0.162661 | + | 0.986682i | \(0.447992\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.07395 | 0.503006 | 0.251503 | − | 0.967857i | \(-0.419075\pi\) | ||||
0.251503 | + | 0.967857i | \(0.419075\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.92745 | −0.442186 | −0.221093 | − | 0.975253i | \(-0.570962\pi\) | ||||
−0.221093 | + | 0.975253i | \(0.570962\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.51311 | 0.941049 | 0.470524 | − | 0.882387i | \(-0.344065\pi\) | ||||
0.470524 | + | 0.882387i | \(0.344065\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.63992 | 1.08540 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.97293 | −1.29484 | −0.647420 | − | 0.762134i | \(-0.724152\pi\) | ||||
−0.647420 | + | 0.762134i | \(0.724152\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.07731 | −0.552701 | −0.276351 | − | 0.961057i | \(-0.589125\pi\) | ||||
−0.276351 | + | 0.961057i | \(0.589125\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.25827 | −0.741269 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.4901 | −1.88896 | −0.944480 | − | 0.328570i | \(-0.893433\pi\) | ||||
−0.944480 | + | 0.328570i | \(0.893433\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.58416 | −0.253669 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.79587 | 0.436641 | 0.218321 | − | 0.975877i | \(-0.429942\pi\) | ||||
0.218321 | + | 0.975877i | \(0.429942\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.22814 | −0.492286 | −0.246143 | − | 0.969234i | \(-0.579163\pi\) | ||||
−0.246143 | + | 0.969234i | \(0.579163\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.89635 | −0.276611 | −0.138306 | − | 0.990390i | \(-0.544166\pi\) | ||||
−0.138306 | + | 0.990390i | \(0.544166\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.80099 | −0.392217 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.64710 | −0.913050 | −0.456525 | − | 0.889711i | \(-0.650906\pi\) | ||||
−0.456525 | + | 0.889711i | \(0.650906\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.60313 | 0.344793 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.93376 | 1.03289 | 0.516444 | − | 0.856321i | \(-0.327255\pi\) | ||||
0.516444 | + | 0.856321i | \(0.327255\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.15581 | 1.04424 | 0.522122 | − | 0.852871i | \(-0.325140\pi\) | ||||
0.522122 | + | 0.852871i | \(0.325140\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.63580 | −1.05503 | −0.527515 | − | 0.849545i | \(-0.676876\pi\) | ||||
−0.527515 | + | 0.849545i | \(0.676876\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.09523 | −0.733780 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.84298 | −0.337400 | −0.168700 | − | 0.985667i | \(-0.553957\pi\) | ||||
−0.168700 | + | 0.985667i | \(0.553957\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.35195 | 0.626399 | 0.313199 | − | 0.949687i | \(-0.398599\pi\) | ||||
0.313199 | + | 0.949687i | \(0.398599\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.5300 | 1.74726 | 0.873631 | − | 0.486588i | \(-0.161759\pi\) | ||||
0.873631 | + | 0.486588i | \(0.161759\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.08910 | −0.454344 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −18.0496 | −1.98120 | −0.990599 | − | 0.136795i | \(-0.956320\pi\) | ||||
−0.990599 | + | 0.136795i | \(0.956320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.41736 | 1.00965 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.01829 | −0.213938 | −0.106969 | − | 0.994262i | \(-0.534115\pi\) | ||||
−0.106969 | + | 0.994262i | \(0.534115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.15609 | 0.430967 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00968 | 0.711725 | 0.355862 | − | 0.934538i | \(-0.384187\pi\) | ||||
0.355862 | + | 0.934538i | \(0.384187\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.70784 | −0.372652 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.5026 | 1.54257 | 0.771283 | − | 0.636493i | \(-0.219615\pi\) | ||||
0.771283 | + | 0.636493i | \(0.219615\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.6990 | −1.64540 | −0.822702 | − | 0.568473i | \(-0.807534\pi\) | ||||
−0.822702 | + | 0.568473i | \(0.807534\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.3403 | −1.48300 | −0.741499 | − | 0.670954i | \(-0.765885\pi\) | ||||
−0.741499 | + | 0.670954i | \(0.765885\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.8272 | 1.51597 | 0.757986 | − | 0.652271i | \(-0.226183\pi\) | ||||
0.757986 | + | 0.652271i | \(0.226183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.5181 | 1.47291 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.41897 | −0.321630 | −0.160815 | − | 0.986985i | \(-0.551412\pi\) | ||||
−0.160815 | + | 0.986985i | \(0.551412\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.37939 | −0.127525 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.05882 | −0.0962564 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.77599 | −0.340469 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.64710 | 0.234893 | 0.117446 | − | 0.993079i | \(-0.462529\pi\) | ||||
0.117446 | + | 0.993079i | \(0.462529\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.35979 | 0.383858 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.2514 | −1.15778 | −0.578891 | − | 0.815405i | \(-0.696514\pi\) | ||||
−0.578891 | + | 0.815405i | \(0.696514\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.6830 | 1.08358 | 0.541790 | − | 0.840514i | \(-0.317747\pi\) | ||||
0.541790 | + | 0.840514i | \(0.317747\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.7452 | 1.67477 | 0.837384 | − | 0.546614i | \(-0.184084\pi\) | ||||
0.837384 | + | 0.546614i | \(0.184084\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.56114 | 0.215687 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.69832 | 0.309269 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.78563 | 0.719747 | 0.359874 | − | 0.933001i | \(-0.382820\pi\) | ||||
0.359874 | + | 0.933001i | \(0.382820\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5874 | 0.942966 | 0.471483 | − | 0.881875i | \(-0.343719\pi\) | ||||
0.471483 | + | 0.881875i | \(0.343719\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.43893 | −0.197176 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.5528 | 1.24125 | 0.620624 | − | 0.784109i | \(-0.286880\pi\) | ||||
0.620624 | + | 0.784109i | \(0.286880\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.97732 | 0.711947 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.68390 | 0.288545 | 0.144273 | − | 0.989538i | \(-0.453916\pi\) | ||||
0.144273 | + | 0.989538i | \(0.453916\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.8528 | −1.38149 | −0.690745 | − | 0.723098i | \(-0.742717\pi\) | ||||
−0.690745 | + | 0.723098i | \(0.742717\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6242 | −0.894166 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.26665 | 0.173335 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.8551 | 1.35749 | 0.678747 | − | 0.734372i | \(-0.262523\pi\) | ||||
0.678747 | + | 0.734372i | \(0.262523\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.7150 | −0.805390 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.3059 | −1.36825 | −0.684125 | − | 0.729365i | \(-0.739816\pi\) | ||||
−0.684125 | + | 0.729365i | \(0.739816\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.8779 | −0.808550 | −0.404275 | − | 0.914637i | \(-0.632476\pi\) | ||||
−0.404275 | + | 0.914637i | \(0.632476\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.0149 | −0.814246 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.53908 | 0.478185 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.74438 | −0.632721 | −0.316360 | − | 0.948639i | \(-0.602461\pi\) | ||||
−0.316360 | + | 0.948639i | \(0.602461\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.57691 | −0.113508 | −0.0567541 | − | 0.998388i | \(-0.518075\pi\) | ||||
−0.0567541 | + | 0.998388i | \(0.518075\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.873188 | −0.0622121 | −0.0311060 | − | 0.999516i | \(-0.509903\pi\) | ||||
−0.0311060 | + | 0.999516i | \(0.509903\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.33192 | −0.236194 | −0.118097 | − | 0.993002i | \(-0.537679\pi\) | ||||
−0.118097 | + | 0.993002i | \(0.537679\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.6632 | 0.822657 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.30736 | −0.368887 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.07716 | −0.420366 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.2354 | −0.773476 | −0.386738 | − | 0.922190i | \(-0.626398\pi\) | ||||
−0.386738 | + | 0.922190i | \(0.626398\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.83962 | 0.263087 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.22814 | −0.488432 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.43267 | 0.163639 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.21315 | 0.148204 | 0.0741018 | − | 0.997251i | \(-0.476391\pi\) | ||||
0.0741018 | + | 0.997251i | \(0.476391\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.1760 | 1.47187 | 0.735937 | − | 0.677050i | \(-0.236742\pi\) | ||||
0.735937 | + | 0.677050i | \(0.236742\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.55568 | −0.102802 | −0.0514012 | − | 0.998678i | \(-0.516369\pi\) | ||||
−0.0514012 | + | 0.998678i | \(0.516369\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.0467 | −1.44433 | −0.722163 | − | 0.691723i | \(-0.756852\pi\) | ||||
−0.722163 | + | 0.691723i | \(0.756852\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −20.9742 | −1.36242 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.7710 | −1.34357 | −0.671783 | − | 0.740748i | \(-0.734471\pi\) | ||||
−0.671783 | + | 0.740748i | \(0.734471\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.25118 | −0.145011 | −0.0725057 | − | 0.997368i | \(-0.523100\pi\) | ||||
−0.0725057 | + | 0.997368i | \(0.523100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.3972 | −0.731130 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.26083 | −0.143853 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 24.3770 | 1.54483 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.6537 | −1.17741 | −0.588704 | − | 0.808349i | \(-0.700362\pi\) | ||||
−0.588704 | + | 0.808349i | \(0.700362\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.2297 | 0.894612 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.2112 | −1.38550 | −0.692748 | − | 0.721180i | \(-0.743600\pi\) | ||||
−0.692748 | + | 0.721180i | \(0.743600\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.20007 | 0.507571 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.20626 | −0.321032 | −0.160516 | − | 0.987033i | \(-0.551316\pi\) | ||||
−0.160516 | + | 0.987033i | \(0.551316\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.72582 | 0.166817 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.3802 | 0.632890 | 0.316445 | − | 0.948611i | \(-0.397511\pi\) | ||||
0.316445 | + | 0.948611i | \(0.397511\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.53627 | 0.457796 | 0.228898 | − | 0.973450i | \(-0.426488\pi\) | ||||
0.228898 | + | 0.973450i | \(0.426488\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.0370 | −1.74467 | −0.872333 | − | 0.488913i | \(-0.837394\pi\) | ||||
−0.872333 | + | 0.488913i | \(0.837394\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.61887 | 0.216656 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.34677 | −0.0803416 | −0.0401708 | − | 0.999193i | \(-0.512790\pi\) | ||||
−0.0401708 | + | 0.999193i | \(0.512790\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.50433 | 0.148867 | 0.0744335 | − | 0.997226i | \(-0.476285\pi\) | ||||
0.0744335 | + | 0.997226i | \(0.476285\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.6987 | −0.746985 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.46699 | −0.554965 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.13770 | 0.183306 | 0.0916531 | − | 0.995791i | \(-0.470785\pi\) | ||||
0.0916531 | + | 0.995791i | \(0.470785\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.7825 | 1.03184 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.29372 | 0.306144 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −20.9372 | −1.20281 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.3702 | −0.820150 | −0.410075 | − | 0.912052i | \(-0.634497\pi\) | ||||
−0.410075 | + | 0.912052i | \(0.634497\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.5530 | 1.28300 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.3522 | −1.04066 | −0.520329 | − | 0.853966i | \(-0.674191\pi\) | ||||
−0.520329 | + | 0.853966i | \(0.674191\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.81933 | 0.102835 | 0.0514174 | − | 0.998677i | \(-0.483626\pi\) | ||||
0.0514174 | + | 0.998677i | \(0.483626\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −32.2865 | −1.81339 | −0.906696 | − | 0.421785i | \(-0.861404\pi\) | ||||
−0.906696 | + | 0.421785i | \(0.861404\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.9854 | −1.23094 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.7179 | 1.15636 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.99742 | −0.222422 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.3756 | −1.18207 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.6482 | 1.02500 | 0.512500 | − | 0.858687i | \(-0.328720\pi\) | ||||
0.512500 | + | 0.858687i | \(0.328720\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.5122 | 0.740463 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.1300 | −1.25997 | −0.629986 | − | 0.776606i | \(-0.716939\pi\) | ||||
−0.629986 | + | 0.776606i | \(0.716939\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.61752 | 0.250790 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.70264 | −0.525428 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0936 | −0.810269 | −0.405134 | − | 0.914257i | \(-0.632775\pi\) | ||||
−0.405134 | + | 0.914257i | \(0.632775\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.8618 | −0.742005 | −0.371003 | − | 0.928632i | \(-0.620986\pi\) | ||||
−0.371003 | + | 0.928632i | \(0.620986\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.61543 | 0.353106 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.7238 | 1.47559 | 0.737795 | − | 0.675025i | \(-0.235867\pi\) | ||||
0.737795 | + | 0.675025i | \(0.235867\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.949322 | −0.0501033 | −0.0250516 | − | 0.999686i | \(-0.507975\pi\) | ||||
−0.0250516 | + | 0.999686i | \(0.507975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2850 | −0.804471 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.43000 | 0.0750556 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.5483 | 1.17701 | 0.588506 | − | 0.808493i | \(-0.299716\pi\) | ||||
0.588506 | + | 0.808493i | \(0.299716\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.28790 | −0.171161 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.6314 | −1.48248 | −0.741239 | − | 0.671241i | \(-0.765761\pi\) | ||||
−0.741239 | + | 0.671241i | \(0.765761\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.17900 | −0.421240 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.4263 | 0.638296 | 0.319148 | − | 0.947705i | \(-0.396603\pi\) | ||||
0.319148 | + | 0.947705i | \(0.396603\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.57507 | −0.183157 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.8845 | 1.42483 | 0.712415 | − | 0.701758i | \(-0.247601\pi\) | ||||
0.712415 | + | 0.701758i | \(0.247601\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.79624 | 0.192974 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.5167 | 0.837428 | 0.418714 | − | 0.908118i | \(-0.362481\pi\) | ||||
0.418714 | + | 0.908118i | \(0.362481\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.35995 | 0.473353 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.8968 | 0.902776 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.4055 | −1.32525 | −0.662626 | − | 0.748951i | \(-0.730558\pi\) | ||||
−0.662626 | + | 0.748951i | \(0.730558\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.4738 | 1.22216 | 0.611082 | − | 0.791567i | \(-0.290735\pi\) | ||||
0.611082 | + | 0.791567i | \(0.290735\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.60958 | −0.179806 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −36.2278 | −1.79575 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.8212 | 0.782309 | 0.391154 | − | 0.920325i | \(-0.372076\pi\) | ||||
0.391154 | + | 0.920325i | \(0.372076\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.1291 | −0.844917 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.6671 | −1.30590 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.8828 | 1.45987 | 0.729934 | − | 0.683517i | \(-0.239551\pi\) | ||||
0.729934 | + | 0.683517i | \(0.239551\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.4027 | 0.799418 | 0.399709 | − | 0.916642i | \(-0.369111\pi\) | ||||
0.399709 | + | 0.916642i | \(0.369111\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.23008 | 0.108430 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.99480 | −0.241151 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.52681 | 0.266217 | 0.133109 | − | 0.991101i | \(-0.457504\pi\) | ||||
0.133109 | + | 0.991101i | \(0.457504\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.1912 | 1.16255 | 0.581277 | − | 0.813706i | \(-0.302553\pi\) | ||||
0.581277 | + | 0.813706i | \(0.302553\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.69878 | −0.416119 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.7223 | −1.08447 | −0.542237 | − | 0.840225i | \(-0.682423\pi\) | ||||
−0.542237 | + | 0.840225i | \(0.682423\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.9115 | 0.613445 | 0.306722 | − | 0.951799i | \(-0.400768\pi\) | ||||
0.306722 | + | 0.951799i | \(0.400768\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.8655 | −0.561220 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.3152 | 1.57224 | 0.786121 | − | 0.618072i | \(-0.212086\pi\) | ||||
0.786121 | + | 0.618072i | \(0.212086\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.81527 | 0.415095 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.6494 | −0.735274 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.35310 | 0.390742 | 0.195371 | − | 0.980729i | \(-0.437409\pi\) | ||||
0.195371 | + | 0.980729i | \(0.437409\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.6969 | 0.545964 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.8066 | −1.15536 | −0.577680 | − | 0.816263i | \(-0.696042\pi\) | ||||
−0.577680 | + | 0.816263i | \(0.696042\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.65975 | −0.216557 | −0.108278 | − | 0.994121i | \(-0.534534\pi\) | ||||
−0.108278 | + | 0.994121i | \(0.534534\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.9637 | −1.71048 | −0.855239 | − | 0.518234i | \(-0.826590\pi\) | ||||
−0.855239 | + | 0.518234i | \(0.826590\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.0050 | −0.967858 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.1782 | −0.467994 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.81690 | 0.357911 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.3295 | −1.24872 | −0.624359 | − | 0.781137i | \(-0.714640\pi\) | ||||
−0.624359 | + | 0.781137i | \(0.714640\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.4775 | −0.614520 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.7613 | −1.62050 | −0.810249 | − | 0.586086i | \(-0.800668\pi\) | ||||
−0.810249 | + | 0.586086i | \(0.800668\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.97533 | −0.224992 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.5187 | −1.33216 | −0.666080 | − | 0.745880i | \(-0.732029\pi\) | ||||
−0.666080 | + | 0.745880i | \(0.732029\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.4615 | −0.651312 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −42.6555 | −1.90952 | −0.954761 | − | 0.297375i | \(-0.903889\pi\) | ||||
−0.954761 | + | 0.297375i | \(0.903889\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.1113 | 1.07721 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.52860 | 0.246508 | 0.123254 | − | 0.992375i | \(-0.460667\pi\) | ||||
0.123254 | + | 0.992375i | \(0.460667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.6991 | 0.697222 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.9285 | 1.06061 | 0.530306 | − | 0.847806i | \(-0.322077\pi\) | ||||
0.530306 | + | 0.847806i | \(0.322077\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.8706 | −0.479950 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.97913 | −0.262962 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.1143 | −1.05850 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.18778 | −0.183470 | −0.0917350 | − | 0.995783i | \(-0.529241\pi\) | ||||
−0.0917350 | + | 0.995783i | \(0.529241\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.6134 | −1.33863 | −0.669316 | − | 0.742978i | \(-0.733413\pi\) | ||||
−0.669316 | + | 0.742978i | \(0.733413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.38218 | −0.278012 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.63182 | −0.114427 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.33000 | −0.404887 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.27945 | 0.142049 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.7233 | 1.06689 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.76740 | −0.247960 | −0.123980 | − | 0.992285i | \(-0.539566\pi\) | ||||
−0.123980 | + | 0.992285i | \(0.539566\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.6913 | 0.630464 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.49973 | 0.192395 | 0.0961974 | − | 0.995362i | \(-0.469332\pi\) | ||||
0.0961974 | + | 0.995362i | \(0.469332\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.59113 | −0.409339 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.4399 | 0.572560 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.58126 | 0.194114 | 0.0970571 | − | 0.995279i | \(-0.469057\pi\) | ||||
0.0970571 | + | 0.995279i | \(0.469057\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.78649 | −0.160151 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.83142 | −0.372863 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.3871 | 0.606345 | 0.303172 | − | 0.952936i | \(-0.401954\pi\) | ||||
0.303172 | + | 0.952936i | \(0.401954\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.8927 | 0.959712 | 0.479856 | − | 0.877347i | \(-0.340689\pi\) | ||||
0.479856 | + | 0.877347i | \(0.340689\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.0662 | −1.84411 | −0.922057 | − | 0.387054i | \(-0.873493\pi\) | ||||
−0.922057 | + | 0.387054i | \(0.873493\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.8098 | 0.493362 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.8358 | 1.70002 | 0.850009 | − | 0.526768i | \(-0.176596\pi\) | ||||
0.850009 | + | 0.526768i | \(0.176596\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.12971 | 0.0885077 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.9581 | −0.867995 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.9756 | −0.453012 | −0.226506 | − | 0.974010i | \(-0.572730\pi\) | ||||
−0.226506 | + | 0.974010i | \(0.572730\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.93135 | 0.244397 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.17929 | 0.0485097 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.4526 | 0.716690 | 0.358345 | − | 0.933589i | \(-0.383341\pi\) | ||||
0.358345 | + | 0.933589i | \(0.383341\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.49996 | 0.184171 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.7673 | −1.46141 | −0.730706 | − | 0.682693i | \(-0.760809\pi\) | ||||
−0.730706 | + | 0.682693i | \(0.760809\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.7828 | −1.70436 | −0.852179 | − | 0.523251i | \(-0.824719\pi\) | ||||
−0.852179 | + | 0.523251i | \(0.824719\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.1556 | 0.413567 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.0829 | −0.815139 | −0.407569 | − | 0.913174i | \(-0.633624\pi\) | ||||
−0.407569 | + | 0.913174i | \(0.633624\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.22435 | −0.0899877 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.9238 | −0.441207 | −0.220603 | − | 0.975364i | \(-0.570803\pi\) | ||||
−0.220603 | + | 0.975364i | \(0.570803\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.2723 | −0.614838 | −0.307419 | − | 0.951574i | \(-0.599465\pi\) | ||||
−0.307419 | + | 0.951574i | \(0.599465\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −46.4570 | −1.86727 | −0.933633 | − | 0.358232i | \(-0.883380\pi\) | ||||
−0.933633 | + | 0.358232i | \(0.883380\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.4536 | 1.02142 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.20758 | 0.327779 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23.8298 | −0.950158 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.98975 | 0.357876 | 0.178938 | − | 0.983860i | \(-0.442734\pi\) | ||||
0.178938 | + | 0.983860i | \(0.442734\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.1741 | 0.603115 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.34331 | 0.132259 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.0396 | 1.42348 | 0.711739 | − | 0.702444i | \(-0.247908\pi\) | ||||
0.711739 | + | 0.702444i | \(0.247908\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.95563 | −0.155995 | −0.0779974 | − | 0.996954i | \(-0.524853\pi\) | ||||
−0.0779974 | + | 0.996954i | \(0.524853\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.2626 | −0.835920 | −0.417960 | − | 0.908465i | \(-0.637255\pi\) | ||||
−0.417960 | + | 0.908465i | \(0.637255\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.0149 | 0.981919 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.2373 | −0.557148 | −0.278574 | − | 0.960415i | \(-0.589862\pi\) | ||||
−0.278574 | + | 0.960415i | \(0.589862\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.29382 | −0.245545 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.2364 | 0.476663 | 0.238332 | − | 0.971184i | \(-0.423399\pi\) | ||||
0.238332 | + | 0.971184i | \(0.423399\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.6555 | 0.453347 | 0.226673 | − | 0.973971i | \(-0.427215\pi\) | ||||
0.226673 | + | 0.973971i | \(0.427215\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.28546 | −0.127597 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.4696 | −1.21851 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.98899 | −0.115561 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.7150 | 0.992716 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.6866 | −1.29852 | −0.649261 | − | 0.760565i | \(-0.724922\pi\) | ||||
−0.649261 | + | 0.760565i | \(0.724922\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.4835 | −0.748812 | −0.374406 | − | 0.927265i | \(-0.622153\pi\) | ||||
−0.374406 | + | 0.927265i | \(0.622153\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −29.9500 | −1.14769 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.6882 | −1.59516 | −0.797578 | − | 0.603216i | \(-0.793886\pi\) | ||||
−0.797578 | + | 0.603216i | \(0.793886\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.10104 | 0.0801597 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.79682 | −0.297035 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.7762 | −1.05665 | −0.528327 | − | 0.849041i | \(-0.677181\pi\) | ||||
−0.528327 | + | 0.849041i | \(0.677181\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.79848 | 0.219633 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.7754 | 1.12621 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.71304 | 0.253548 | 0.126774 | − | 0.991932i | \(-0.459538\pi\) | ||||
0.126774 | + | 0.991932i | \(0.459538\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.1465 | 0.835272 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.18729 | 0.307480 | 0.153740 | − | 0.988111i | \(-0.450868\pi\) | ||||
0.153740 | + | 0.988111i | \(0.450868\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.2631 | −0.684919 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.8882 | −0.520119 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28.0525 | 1.04764 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.3339 | −0.832915 | −0.416458 | − | 0.909155i | \(-0.636729\pi\) | ||||
−0.416458 | + | 0.909155i | \(0.636729\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.04036 | 0.113072 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.48235 | −0.314593 | −0.157296 | − | 0.987551i | \(-0.550278\pi\) | ||||
−0.157296 | + | 0.987551i | \(0.550278\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.6599 | 1.02444 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.69498 | −0.247623 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.6227 | −1.24188 | −0.620942 | − | 0.783857i | \(-0.713250\pi\) | ||||
−0.620942 | + | 0.783857i | \(0.713250\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27.2284 | −1.00297 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.18450 | −0.0435727 | −0.0217863 | − | 0.999763i | \(-0.506935\pi\) | ||||
−0.0217863 | + | 0.999763i | \(0.506935\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.05338 | 0.112169 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.8482 | 1.75538 | 0.877690 | − | 0.479228i | \(-0.159083\pi\) | ||||
0.877690 | + | 0.479228i | \(0.159083\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.2261 | 0.776621 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.0164 | 1.05882 | 0.529412 | − | 0.848365i | \(-0.322413\pi\) | ||||
0.529412 | + | 0.848365i | \(0.322413\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.1929 | 0.918080 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.7722 | 1.59093 | 0.795464 | − | 0.606001i | \(-0.207227\pi\) | ||||
0.795464 | + | 0.606001i | \(0.207227\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.2180 | −0.697571 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.6484 | −0.639753 | −0.319877 | − | 0.947459i | \(-0.603642\pi\) | ||||
−0.319877 | + | 0.947459i | \(0.603642\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.30602 | 0.336021 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.3759 | −1.60024 | −0.800118 | − | 0.599842i | \(-0.795230\pi\) | ||||
−0.800118 | + | 0.599842i | \(0.795230\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.9976 | 1.08034 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.1494 | 0.544886 | 0.272443 | − | 0.962172i | \(-0.412168\pi\) | ||||
0.272443 | + | 0.962172i | \(0.412168\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.38888 | −0.193077 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.96383 | −0.320751 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −39.3268 | −1.40542 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.99429 | 0.106735 | 0.0533674 | − | 0.998575i | \(-0.483005\pi\) | ||||
0.0533674 | + | 0.998575i | \(0.483005\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.03137 | 0.250323 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.56648 | 0.339716 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.26106 | −0.328044 | −0.164022 | − | 0.986457i | \(-0.552447\pi\) | ||||
−0.164022 | + | 0.986457i | \(0.552447\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.93293 | −0.139137 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.37348 | 0.0838627 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.8745 | 0.595489 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.0190 | −0.493494 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.4860 | −0.579617 | −0.289809 | − | 0.957085i | \(-0.593592\pi\) | ||||
−0.289809 | + | 0.957085i | \(0.593592\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.6119 | 0.618437 | 0.309218 | − | 0.950991i | \(-0.399933\pi\) | ||||
0.309218 | + | 0.950991i | \(0.399933\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.1782 | −0.356965 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.22205 | 0.217682 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.527484 | 0.0184093 | 0.00920465 | − | 0.999958i | \(-0.497070\pi\) | ||||
0.00920465 | + | 0.999958i | \(0.497070\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.36367 | 0.152108 | 0.0760540 | − | 0.997104i | \(-0.475768\pi\) | ||||
0.0760540 | + | 0.997104i | \(0.475768\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.38579 | −0.256829 | −0.128415 | − | 0.991721i | \(-0.540989\pi\) | ||||
−0.128415 | + | 0.991721i | \(0.540989\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.2988 | 1.33017 | 0.665087 | − | 0.746766i | \(-0.268395\pi\) | ||||
0.665087 | + | 0.746766i | \(0.268395\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 39.2163 | 1.36040 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.3558 | −0.599904 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.9391 | −0.377660 | −0.188830 | − | 0.982010i | \(-0.560470\pi\) | ||||
−0.188830 | + | 0.982010i | \(0.560470\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.6217 | 0.676610 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.81890 | 0.0626461 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.38225 | −0.116078 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −51.8561 | −1.77760 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.9925 | −0.855726 | −0.427863 | − | 0.903844i | \(-0.640733\pi\) | ||||
−0.427863 | + | 0.903844i | \(0.640733\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.5504 | 1.21438 | 0.607189 | − | 0.794557i | \(-0.292297\pi\) | ||||
0.607189 | + | 0.794557i | \(0.292297\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.2283 | −1.23609 | −0.618047 | − | 0.786141i | \(-0.712076\pi\) | ||||
−0.618047 | + | 0.786141i | \(0.712076\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.6846 | 0.601992 | 0.300996 | − | 0.953625i | \(-0.402681\pi\) | ||||
0.300996 | + | 0.953625i | \(0.402681\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.1504 | 0.582459 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48.9656 | 1.66104 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.1295 | −0.343225 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.24329 | −0.278993 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.54026 | −0.288384 | −0.144192 | − | 0.989550i | \(-0.546058\pi\) | ||||
−0.144192 | + | 0.989550i | \(0.546058\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.23765 | −0.142932 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.40485 | 0.316857 | 0.158429 | − | 0.987370i | \(-0.449357\pi\) | ||||
0.158429 | + | 0.987370i | \(0.449357\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.5005 | −1.56487 | −0.782433 | − | 0.622735i | \(-0.786021\pi\) | ||||
−0.782433 | + | 0.622735i | \(0.786021\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.76370 | 0.227103 | 0.113551 | − | 0.993532i | \(-0.463777\pi\) | ||||
0.113551 | + | 0.993532i | \(0.463777\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.8928 | −0.431924 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.65511 | 0.122314 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.14949 | −0.238715 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.4579 | 0.715659 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.7857 | −0.459270 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.8793 | 0.494060 | 0.247030 | − | 0.969008i | \(-0.420545\pi\) | ||||
0.247030 | + | 0.969008i | \(0.420545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.2308 | −0.604679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.6643 | 1.01595 | 0.507977 | − | 0.861371i | \(-0.330394\pi\) | ||||
0.507977 | + | 0.861371i | \(0.330394\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −56.9097 | −1.88343 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.2241 | 0.568170 | 0.284085 | − | 0.958799i | \(-0.408310\pi\) | ||||
0.284085 | + | 0.958799i | \(0.408310\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.4078 | 0.639509 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.33472 | −0.109764 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.6378 | 0.644991 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.3768 | 0.865395 | 0.432698 | − | 0.901539i | \(-0.357562\pi\) | ||||
0.432698 | + | 0.901539i | \(0.357562\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.7858 | 0.811450 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.8347 | 0.778647 | 0.389323 | − | 0.921101i | \(-0.372709\pi\) | ||||
0.389323 | + | 0.921101i | \(0.372709\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.45712 | −0.0801851 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53.7553 | −1.75237 | −0.876186 | − | 0.481974i | \(-0.839920\pi\) | ||||
−0.876186 | + | 0.481974i | \(0.839920\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.6181 | 0.410901 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.4187 | −1.24844 | −0.624220 | − | 0.781249i | \(-0.714583\pi\) | ||||
−0.624220 | + | 0.781249i | \(0.714583\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.27765 | 0.203781 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 43.6049 | 1.41399 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.3480 | −0.367598 | −0.183799 | − | 0.982964i | \(-0.558839\pi\) | ||||
−0.183799 | + | 0.982964i | \(0.558839\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29.6926 | 0.959825 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.5302 | −0.694521 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.0399 | 0.581329 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.9509 | 0.577262 | 0.288631 | − | 0.957440i | \(-0.406800\pi\) | ||||
0.288631 | + | 0.957440i | \(0.406800\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.39876 | 0.173433 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.44215 | 0.0462807 | 0.0231404 | − | 0.999732i | \(-0.492634\pi\) | ||||
0.0231404 | + | 0.999732i | \(0.492634\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.2856 | 0.744973 | 0.372487 | − | 0.928038i | \(-0.378505\pi\) | ||||
0.372487 | + | 0.928038i | \(0.378505\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.36359 | −0.203381 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.6126 | −0.594254 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.99917 | 0.223239 | 0.111619 | − | 0.993751i | \(-0.464396\pi\) | ||||
0.111619 | + | 0.993751i | \(0.464396\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.5689 | −0.463265 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.9589 | 1.49170 | 0.745850 | − | 0.666114i | \(-0.232044\pi\) | ||||
0.745850 | + | 0.666114i | \(0.232044\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.1856 | −0.799240 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.9501 | −1.26523 | −0.632616 | − | 0.774465i | \(-0.718019\pi\) | ||||
−0.632616 | + | 0.774465i | \(0.718019\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −64.8032 | −2.05028 |
(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 | 9800.2.a.db.1.3 | 10 | ||
5.2 | odd | 4 | 1960.2.g.g.1569.16 | yes | 20 | ||
5.3 | odd | 4 | 1960.2.g.g.1569.6 | yes | 20 | ||
5.4 | even | 2 | 9800.2.a.dc.1.8 | 10 | |||
7.6 | odd | 2 | inner | 9800.2.a.db.1.8 | 10 | ||
35.13 | even | 4 | 1960.2.g.g.1569.15 | yes | 20 | ||
35.27 | even | 4 | 1960.2.g.g.1569.5 | ✓ | 20 | ||
35.34 | odd | 2 | 9800.2.a.dc.1.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.g.g.1569.5 | ✓ | 20 | 35.27 | even | 4 | ||
1960.2.g.g.1569.6 | yes | 20 | 5.3 | odd | 4 | ||
1960.2.g.g.1569.15 | yes | 20 | 35.13 | even | 4 | ||
1960.2.g.g.1569.16 | yes | 20 | 5.2 | odd | 4 | ||
9800.2.a.db.1.3 | 10 | 1.1 | even | 1 | trivial | ||
9800.2.a.db.1.8 | 10 | 7.6 | odd | 2 | inner | ||
9800.2.a.dc.1.3 | 10 | 35.34 | odd | 2 | |||
9800.2.a.dc.1.8 | 10 | 5.4 | even | 2 |