Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, 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("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.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: | \(73.4623698596\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.143376304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 12x^{4} + 22x^{2} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 460) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.420790\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-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 | ||||||||
\(3\) | −1.73961 | −1.00436 | −0.502182 | − | 0.864762i | \(-0.667469\pi\) | ||||
−0.502182 | + | 0.864762i | \(0.667469\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.32224 | −1.25569 | −0.627844 | − | 0.778339i | \(-0.716062\pi\) | ||||
−0.627844 | + | 0.778339i | \(0.716062\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.0262434 | 0.00874780 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.77103 | −1.74003 | −0.870016 | − | 0.493024i | \(-0.835891\pi\) | ||||
−0.870016 | + | 0.493024i | \(0.835891\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.10197 | 0.305631 | 0.152816 | − | 0.988255i | \(-0.451166\pi\) | ||||
0.152816 | + | 0.988255i | \(0.451166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.893847 | 0.216790 | 0.108395 | − | 0.994108i | \(-0.465429\pi\) | ||||
0.108395 | + | 0.994108i | \(0.465429\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.42839 | −0.557111 | −0.278555 | − | 0.960420i | \(-0.589856\pi\) | ||||
−0.278555 | + | 0.960420i | \(0.589856\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.77940 | 1.26117 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.17318 | 0.995578 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.11268 | 0.763705 | 0.381853 | − | 0.924223i | \(-0.375286\pi\) | ||||
0.381853 | + | 0.924223i | \(0.375286\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.54624 | 1.71456 | 0.857278 | − | 0.514854i | \(-0.172154\pi\) | ||||
0.857278 | + | 0.514854i | \(0.172154\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.0393 | 1.74763 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.69904 | −1.26572 | −0.632858 | − | 0.774268i | \(-0.718118\pi\) | ||||
−0.632858 | + | 0.774268i | \(0.718118\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.91700 | −0.306965 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.00418347 | 0.000653348 0 | 0.000326674 | − | 1.00000i | \(-0.499896\pi\) | ||||
0.000326674 | 1.00000i | \(0.499896\pi\) | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.97045 | 1.52048 | 0.760240 | − | 0.649643i | \(-0.225081\pi\) | ||||
0.760240 | + | 0.649643i | \(0.225081\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.0079 | −1.45981 | −0.729903 | − | 0.683551i | \(-0.760435\pi\) | ||||
−0.729903 | + | 0.683551i | \(0.760435\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.03726 | 0.576751 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.55495 | −0.217736 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.25169 | 0.858735 | 0.429368 | − | 0.903130i | \(-0.358736\pi\) | ||||
0.429368 | + | 0.903130i | \(0.358736\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.22445 | 0.559542 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.7764 | 1.40297 | 0.701486 | − | 0.712684i | \(-0.252520\pi\) | ||||
0.701486 | + | 0.712684i | \(0.252520\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.5929 | 1.35628 | 0.678140 | − | 0.734932i | \(-0.262786\pi\) | ||||
0.678140 | + | 0.734932i | \(0.262786\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0871868 | −0.0109845 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.9529 | −1.33811 | −0.669055 | − | 0.743213i | \(-0.733301\pi\) | ||||
−0.669055 | + | 0.743213i | \(0.733301\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.73961 | 0.209424 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.9170 | 1.53296 | 0.766481 | − | 0.642267i | \(-0.222006\pi\) | ||||
0.766481 | + | 0.642267i | \(0.222006\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.89943 | 0.222311 | 0.111156 | − | 0.993803i | \(-0.464545\pi\) | ||||
0.111156 | + | 0.993803i | \(0.464545\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 19.1727 | 2.18494 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.216085 | 0.0243114 | 0.0121557 | − | 0.999926i | \(-0.496131\pi\) | ||||
0.0121557 | + | 0.999926i | \(0.496131\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.07804 | −1.00867 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.38967 | 0.591593 | 0.295796 | − | 0.955251i | \(-0.404415\pi\) | ||||
0.295796 | + | 0.955251i | \(0.404415\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.15446 | −0.767038 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00657 | 0.636696 | 0.318348 | − | 0.947974i | \(-0.396872\pi\) | ||||
0.318348 | + | 0.947974i | \(0.396872\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.66100 | −0.383777 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.6067 | −1.72204 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.08104 | 0.211297 | 0.105649 | − | 0.994404i | \(-0.466308\pi\) | ||||
0.105649 | + | 0.994404i | \(0.466308\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.151451 | −0.0152214 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.1576 | −1.30923 | −0.654617 | − | 0.755961i | \(-0.727170\pi\) | ||||
−0.654617 | + | 0.755961i | \(0.727170\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.0956 | −1.78301 | −0.891507 | − | 0.453008i | \(-0.850351\pi\) | ||||
−0.891507 | + | 0.453008i | \(0.850351\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.97263 | −0.674069 | −0.337035 | − | 0.941492i | \(-0.609424\pi\) | ||||
−0.337035 | + | 0.941492i | \(0.609424\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.2873 | 0.985344 | 0.492672 | − | 0.870215i | \(-0.336020\pi\) | ||||
0.492672 | + | 0.870215i | \(0.336020\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.3933 | 1.27124 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.53454 | −0.520646 | −0.260323 | − | 0.965522i | \(-0.583829\pi\) | ||||
−0.260323 | + | 0.965522i | \(0.583829\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0289194 | 0.00267360 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.96957 | −0.272220 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.3048 | 2.02771 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.00727760 | −0.000656199 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1580 | −0.990110 | −0.495055 | − | 0.868862i | \(-0.664852\pi\) | ||||
−0.495055 | + | 0.868862i | \(0.664852\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17.3447 | −1.52712 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.0421 | 1.31423 | 0.657117 | − | 0.753789i | \(-0.271776\pi\) | ||||
0.657117 | + | 0.753789i | \(0.271776\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.06769 | 0.699557 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.21231 | 0.189010 | 0.0945050 | − | 0.995524i | \(-0.469873\pi\) | ||||
0.0945050 | + | 0.995524i | \(0.469873\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.53729 | 0.554486 | 0.277243 | − | 0.960800i | \(-0.410579\pi\) | ||||
0.277243 | + | 0.960800i | \(0.410579\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.4099 | 1.46618 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.35950 | −0.531808 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.02326 | −0.579269 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.1844 | −0.916263 | −0.458131 | − | 0.888884i | \(-0.651481\pi\) | ||||
−0.458131 | + | 0.888884i | \(0.651481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.29176 | 0.105122 | 0.0525610 | − | 0.998618i | \(-0.483262\pi\) | ||||
0.0525610 | + | 0.998618i | \(0.483262\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.0234576 | 0.00189643 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0465 | 0.881609 | 0.440805 | − | 0.897603i | \(-0.354693\pi\) | ||||
0.440805 | + | 0.897603i | \(0.354693\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.8755 | −0.862483 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.32224 | 0.261829 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.04265 | −0.394971 | −0.197485 | − | 0.980306i | \(-0.563277\pi\) | ||||
−0.197485 | + | 0.980306i | \(0.563277\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.20759 | −0.0934465 | −0.0467232 | − | 0.998908i | \(-0.514878\pi\) | ||||
−0.0467232 | + | 0.998908i | \(0.514878\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7857 | −0.906590 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0637292 | −0.00487349 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.7392 | −1.19663 | −0.598313 | − | 0.801262i | \(-0.704162\pi\) | ||||
−0.598313 | + | 0.801262i | \(0.704162\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.7468 | −1.40909 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.61963 | −0.494774 | −0.247387 | − | 0.968917i | \(-0.579572\pi\) | ||||
−0.247387 | + | 0.968917i | \(0.579572\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0433 | −1.19249 | −0.596245 | − | 0.802803i | \(-0.703341\pi\) | ||||
−0.596245 | + | 0.802803i | \(0.703341\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.4275 | −1.36220 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.15842 | −0.377221 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −17.1865 | −1.25014 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.295590 | −0.0213881 | −0.0106941 | − | 0.999943i | \(-0.503404\pi\) | ||||
−0.0106941 | + | 0.999943i | \(0.503404\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.42564 | −0.102620 | −0.0513101 | − | 0.998683i | \(-0.516340\pi\) | ||||
−0.0513101 | + | 0.998683i | \(0.516340\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.60107 | −0.612801 | −0.306401 | − | 0.951903i | \(-0.599125\pi\) | ||||
−0.306401 | + | 0.951903i | \(0.599125\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.81515 | −0.270449 | −0.135224 | − | 0.990815i | \(-0.543176\pi\) | ||||
−0.135224 | + | 0.990815i | \(0.543176\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.0538 | 1.34395 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.6633 | −0.958975 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.0262434 | −0.00182404 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.0143 | 0.969390 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.32370 | −0.0911273 | −0.0455637 | − | 0.998961i | \(-0.514508\pi\) | ||||
−0.0455637 | + | 0.998961i | \(0.514508\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −22.4705 | −1.53965 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −31.7149 | −2.15295 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.30427 | −0.223282 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.984992 | 0.0662577 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.1286 | −1.68274 | −0.841368 | − | 0.540462i | \(-0.818249\pi\) | ||||
−0.841368 | + | 0.540462i | \(0.818249\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.8021 | 1.57980 | 0.789900 | − | 0.613236i | \(-0.210133\pi\) | ||||
0.789900 | + | 0.613236i | \(0.210133\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.789351 | −0.0521618 | −0.0260809 | − | 0.999660i | \(-0.508303\pi\) | ||||
−0.0260809 | + | 0.999660i | \(0.508303\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −33.3531 | −2.19447 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.8101 | −1.36331 | −0.681656 | − | 0.731672i | \(-0.738740\pi\) | ||||
−0.681656 | + | 0.731672i | \(0.738740\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.375903 | −0.0244175 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.2398 | 1.63262 | 0.816312 | − | 0.577611i | \(-0.196015\pi\) | ||||
0.816312 | + | 0.577611i | \(0.196015\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.27710 | 0.339928 | 0.169964 | − | 0.985450i | \(-0.445635\pi\) | ||||
0.169964 | + | 0.985450i | \(0.445635\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.272722 | 0.0174951 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.67601 | −0.170270 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.37592 | −0.594175 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.8439 | 0.684461 | 0.342230 | − | 0.939616i | \(-0.388818\pi\) | ||||
0.342230 | + | 0.939616i | \(0.388818\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.77103 | 0.362822 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.6238 | 1.16172 | 0.580859 | − | 0.814004i | \(-0.302717\pi\) | ||||
0.580859 | + | 0.814004i | \(0.302717\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25.5781 | 1.58934 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.107931 | 0.00668074 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.4370 | 1.19854 | 0.599269 | − | 0.800548i | \(-0.295458\pi\) | ||||
0.599269 | + | 0.800548i | \(0.295458\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.4491 | −0.639474 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.80493 | −0.231991 | −0.115995 | − | 0.993250i | \(-0.537006\pi\) | ||||
−0.115995 | + | 0.993250i | \(0.537006\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.2100 | 1.10618 | 0.553089 | − | 0.833122i | \(-0.313449\pi\) | ||||
0.553089 | + | 0.833122i | \(0.313449\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.36872 | 0.385452 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.7624 | 0.886988 | 0.443494 | − | 0.896277i | \(-0.353739\pi\) | ||||
0.443494 | + | 0.896277i | \(0.353739\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.250526 | 0.0149986 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.29738 | −0.375670 | −0.187835 | − | 0.982201i | \(-0.560147\pi\) | ||||
−0.187835 | + | 0.982201i | \(0.560147\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.4443 | −1.69084 | −0.845418 | − | 0.534105i | \(-0.820649\pi\) | ||||
−0.845418 | + | 0.534105i | \(0.820649\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0138985 | −0.000820401 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2010 | −0.953002 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.62020 | −0.212220 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.4907 | 0.846556 | 0.423278 | − | 0.906000i | \(-0.360879\pi\) | ||||
0.423278 | + | 0.906000i | \(0.360879\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −29.8546 | −1.73234 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.10197 | −0.0637285 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −33.1242 | −1.90925 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.8892 | 1.31495 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.4707 | 1.73905 | 0.869527 | − | 0.493885i | \(-0.164424\pi\) | ||||
0.869527 | + | 0.493885i | \(0.164424\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.4793 | 1.79080 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.9031 | −1.18531 | −0.592654 | − | 0.805457i | \(-0.701920\pi\) | ||||
−0.592654 | + | 0.805457i | \(0.701920\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.3614 | 0.811757 | 0.405878 | − | 0.913927i | \(-0.366966\pi\) | ||||
0.405878 | + | 0.913927i | \(0.366966\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33.6939 | 1.89244 | 0.946220 | − | 0.323525i | \(-0.104868\pi\) | ||||
0.946220 | + | 0.323525i | \(0.104868\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.7344 | −1.32887 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.1297 | 0.677011 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.17061 | −0.120776 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.8959 | −0.989644 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33.2487 | 1.83306 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.82292 | −0.539917 | −0.269958 | − | 0.962872i | \(-0.587010\pi\) | ||||
−0.269958 | + | 0.962872i | \(0.587010\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.202049 | −0.0110722 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.2410 | −0.721286 | −0.360643 | − | 0.932704i | \(-0.617443\pi\) | ||||
−0.360643 | + | 0.932704i | \(0.617443\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.62795 | 0.522918 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −55.0917 | −2.98338 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.84292 | 0.531468 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.15627 | 0.491534 | 0.245767 | − | 0.969329i | \(-0.420960\pi\) | ||||
0.245767 | + | 0.969329i | \(0.420960\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.7744 | 1.37967 | 0.689836 | − | 0.723966i | \(-0.257683\pi\) | ||||
0.689836 | + | 0.723966i | \(0.257683\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.70068 | 0.304280 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.40654 | −0.128087 | −0.0640436 | − | 0.997947i | \(-0.520400\pi\) | ||||
−0.0640436 | + | 0.997947i | \(0.520400\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.16590 | 0.273408 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.5236 | −1.13597 | −0.567985 | − | 0.823039i | \(-0.692277\pi\) | ||||
−0.567985 | + | 0.823039i | \(0.692277\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1029 | −0.689628 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −38.8016 | −2.03656 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.47203 | 0.337837 | 0.168919 | − | 0.985630i | \(-0.445972\pi\) | ||||
0.168919 | + | 0.985630i | \(0.445972\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.000109788 0 | 5.71536e−6 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.7696 | −1.07830 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.7866 | −1.43874 | −0.719368 | − | 0.694629i | \(-0.755569\pi\) | ||||
−0.719368 | + | 0.694629i | \(0.755569\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.53204 | 0.233412 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.63904 | −0.392391 | −0.196196 | − | 0.980565i | \(-0.562859\pi\) | ||||
−0.196196 | + | 0.980565i | \(0.562859\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.4105 | 0.994432 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.4206 | 0.992348 | 0.496174 | − | 0.868223i | \(-0.334738\pi\) | ||||
0.496174 | + | 0.868223i | \(0.334738\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.261659 | 0.0133009 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.1255 | −1.32461 | −0.662306 | − | 0.749233i | \(-0.730422\pi\) | ||||
−0.662306 | + | 0.749233i | \(0.730422\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.893847 | −0.0452038 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.1674 | −1.31997 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.5388 | −0.579117 | −0.289558 | − | 0.957160i | \(-0.593508\pi\) | ||||
−0.289558 | + | 0.957160i | \(0.593508\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.0346 | −0.702610 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.188549 | −0.00941568 | −0.00470784 | − | 0.999989i | \(-0.501499\pi\) | ||||
−0.00470784 | + | 0.999989i | \(0.501499\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.5197 | 0.524022 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.4314 | 2.20238 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.48327 | −0.419471 | −0.209735 | − | 0.977758i | \(-0.567260\pi\) | ||||
−0.209735 | + | 0.977758i | \(0.567260\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.84855 | −0.189835 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −35.8018 | −1.76169 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.3723 | −0.556906 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.15604 | 0.105329 | 0.0526647 | − | 0.998612i | \(-0.483229\pi\) | ||||
0.0526647 | + | 0.998612i | \(0.483229\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.01842 | 0.390794 | 0.195397 | − | 0.980724i | \(-0.437400\pi\) | ||||
0.195397 | + | 0.980724i | \(0.437400\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.262642 | −0.0127701 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −35.1921 | −1.70307 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.0630 | 0.534129 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.3343 | 0.738629 | 0.369315 | − | 0.929304i | \(-0.379592\pi\) | ||||
0.369315 | + | 0.929304i | \(0.379592\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.3093 | 0.783777 | 0.391888 | − | 0.920013i | \(-0.371822\pi\) | ||||
0.391888 | + | 0.920013i | \(0.371822\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.42839 | 0.116166 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.9534 | 1.14323 | 0.571617 | − | 0.820520i | \(-0.306316\pi\) | ||||
0.571617 | + | 0.820520i | \(0.306316\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.105951 | 0.00504531 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.2360 | 1.38905 | 0.694523 | − | 0.719471i | \(-0.255616\pi\) | ||||
0.694523 | + | 0.719471i | \(0.255616\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.4565 | 0.920262 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.2244 | −1.00164 | −0.500822 | − | 0.865550i | \(-0.666969\pi\) | ||||
−0.500822 | + | 0.865550i | \(0.666969\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0241429 | −0.00113685 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.24716 | −0.105581 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.5959 | −1.47799 | −0.738996 | − | 0.673710i | \(-0.764700\pi\) | ||||
−0.738996 | + | 0.673710i | \(0.764700\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.62403 | 0.215831 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.4858 | 0.767820 | 0.383910 | − | 0.923370i | \(-0.374577\pi\) | ||||
0.383910 | + | 0.923370i | \(0.374577\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.1555 | −1.40144 | −0.700722 | − | 0.713435i | \(-0.747139\pi\) | ||||
−0.700722 | + | 0.713435i | \(0.747139\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.89645 | 0.365404 | 0.182702 | − | 0.983168i | \(-0.441516\pi\) | ||||
0.182702 | + | 0.983168i | \(0.441516\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.3882 | 1.68025 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.2167 | −0.885457 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −57.5398 | −2.64568 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.164066 | 0.00751205 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.5234 | −1.80587 | −0.902935 | − | 0.429778i | \(-0.858592\pi\) | ||||
−0.902935 | + | 0.429778i | \(0.858592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.48411 | −0.386842 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.77940 | −0.262972 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.20444 | −0.145207 | −0.0726035 | − | 0.997361i | \(-0.523131\pi\) | ||||
−0.0726035 | + | 0.997361i | \(0.523131\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.77224 | 0.396695 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.8865 | −1.57441 | −0.787203 | − | 0.616694i | \(-0.788472\pi\) | ||||
−0.787203 | + | 0.616694i | \(0.788472\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.67611 | 0.165564 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −42.9132 | −1.92492 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.1594 | −1.48442 | −0.742210 | − | 0.670167i | \(-0.766222\pi\) | ||||
−0.742210 | + | 0.670167i | \(0.766222\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.10074 | 0.0938543 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.05945 | −0.314765 | −0.157383 | − | 0.987538i | \(-0.550306\pi\) | ||||
−0.157383 | + | 0.987538i | \(0.550306\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.5025 | 0.910546 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.6812 | 0.739382 | 0.369691 | − | 0.929155i | \(-0.379464\pi\) | ||||
0.369691 | + | 0.929155i | \(0.379464\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.31035 | −0.279154 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.5625 | −0.554648 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 57.7560 | 2.54011 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.3800 | 1.20185 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.9941 | −1.09501 | −0.547507 | − | 0.836801i | \(-0.684423\pi\) | ||||
−0.547507 | + | 0.836801i | \(0.684423\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.3283 | 0.626535 | 0.313267 | − | 0.949665i | \(-0.398576\pi\) | ||||
0.313267 | + | 0.949665i | \(0.398576\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.53289 | 0.371698 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.282810 | 0.0122729 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.00461005 | 0.000199683 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.5156 | 0.496934 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.2992 | −1.00357 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.0323 | 0.947244 | 0.473622 | − | 0.880728i | \(-0.342946\pi\) | ||||
0.473622 | + | 0.880728i | \(0.342946\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.9091 | 1.19769 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.5194 | −0.920104 | −0.460052 | − | 0.887892i | \(-0.652169\pi\) | ||||
−0.460052 | + | 0.887892i | \(0.652169\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.277993 | 0.0118645 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.98719 | −0.425468 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.717884 | −0.0305276 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.1923 | −0.897945 | −0.448972 | − | 0.893546i | \(-0.648210\pi\) | ||||
−0.448972 | + | 0.893546i | \(0.648210\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.9871 | 0.464706 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.97364 | 0.378867 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.6292 | −0.995851 | −0.497925 | − | 0.867220i | \(-0.665905\pi\) | ||||
−0.497925 | + | 0.867220i | \(0.665905\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 30.1594 | 1.26658 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.7490 | −1.41483 | −0.707415 | − | 0.706798i | \(-0.750139\pi\) | ||||
−0.707415 | + | 0.706798i | \(0.750139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.4667 | 1.06575 | 0.532874 | − | 0.846194i | \(-0.321112\pi\) | ||||
0.532874 | + | 0.846194i | \(0.321112\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.514211 | 0.0214815 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.7293 | −0.946234 | −0.473117 | − | 0.881000i | \(-0.656871\pi\) | ||||
−0.473117 | + | 0.881000i | \(0.656871\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.48006 | 0.103068 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.9057 | −0.742856 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.0787 | −1.49423 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.6609 | 1.47188 | 0.735941 | − | 0.677045i | \(-0.236740\pi\) | ||||
0.735941 | + | 0.677045i | \(0.236740\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.1820 | −0.955198 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.9625 | 0.615476 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.8412 | 0.855845 | 0.427922 | − | 0.903815i | \(-0.359246\pi\) | ||||
0.427922 | + | 0.903815i | \(0.359246\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.63687 | 0.271629 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.9952 | 0.449252 | 0.224626 | − | 0.974445i | \(-0.427884\pi\) | ||||
0.224626 | + | 0.974445i | \(0.427884\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.35032 | 0.0958714 | 0.0479357 | − | 0.998850i | \(-0.484736\pi\) | ||||
0.0479357 | + | 0.998850i | \(0.484736\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.287442 | −0.0117055 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.8412 | −1.29239 | −0.646197 | − | 0.763170i | \(-0.723642\pi\) | ||||
−0.646197 | + | 0.763170i | \(0.723642\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 23.7688 | 0.963160 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.0284 | −0.446162 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.0597 | 1.17371 | 0.586856 | − | 0.809692i | \(-0.300366\pi\) | ||||
0.586856 | + | 0.809692i | \(0.300366\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.9851 | −1.20715 | −0.603577 | − | 0.797304i | \(-0.706259\pi\) | ||||
−0.603577 | + | 0.797304i | \(0.706259\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.9204 | 0.680089 | 0.340045 | − | 0.940409i | \(-0.389558\pi\) | ||||
0.340045 | + | 0.940409i | \(0.389558\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.17318 | −0.207592 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.9553 | −0.799491 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −24.3794 | −0.973621 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.88177 | −0.274394 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.4522 | 0.814188 | 0.407094 | − | 0.913386i | \(-0.366542\pi\) | ||||
0.407094 | + | 0.913386i | \(0.366542\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.30272 | 0.0915250 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.44894 | 0.176273 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.338985 | 0.0134100 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.27686 | −0.326916 | −0.163458 | − | 0.986550i | \(-0.552265\pi\) | ||||
−0.163458 | + | 0.986550i | \(0.552265\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.627685 | −0.0247535 | −0.0123767 | − | 0.999923i | \(-0.503940\pi\) | ||||
−0.0123767 | + | 0.999923i | \(0.503940\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.3508 | −0.485561 | −0.242781 | − | 0.970081i | \(-0.578060\pi\) | ||||
−0.242781 | + | 0.970081i | \(0.578060\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −62.1911 | −2.44121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 55.1715 | 2.16234 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.3211 | −0.716959 | −0.358480 | − | 0.933538i | \(-0.616705\pi\) | ||||
−0.358480 | + | 0.933538i | \(0.616705\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.0498475 | 0.00194473 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.1896 | 1.52661 | 0.763306 | − | 0.646038i | \(-0.223575\pi\) | ||||
0.763306 | + | 0.646038i | \(0.223575\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.38565 | 0.365060 | 0.182530 | − | 0.983200i | \(-0.441571\pi\) | ||||
0.182530 | + | 0.983200i | \(0.441571\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.71350 | −0.0665469 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.11268 | −0.159244 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 43.7140 | 1.69008 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −61.1319 | −2.35997 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.05600 | 0.310536 | 0.155268 | − | 0.987872i | \(-0.450376\pi\) | ||||
0.155268 | + | 0.987872i | \(0.450376\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.9461 | −0.651293 | −0.325647 | − | 0.945492i | \(-0.605582\pi\) | ||||
−0.325647 | + | 0.945492i | \(0.605582\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.91370 | −0.265324 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −41.4063 | −1.58669 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.111363 | 0.00426119 | 0.00213059 | − | 0.999998i | \(-0.499322\pi\) | ||||
0.00213059 | + | 0.999998i | \(0.499322\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.37316 | 0.0523894 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.88917 | 0.262456 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.1718 | 1.45212 | 0.726062 | − | 0.687629i | \(-0.241348\pi\) | ||||
0.726062 | + | 0.687629i | \(0.241348\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.503158 | 0.0191134 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.00373938 | 0.000141639 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 36.2014 | 1.36926 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.7698 | 1.46431 | 0.732157 | − | 0.681136i | \(-0.238514\pi\) | ||||
0.732157 | + | 0.681136i | \(0.238514\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.6963 | 0.705144 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 43.7128 | 1.64399 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −47.4028 | −1.78025 | −0.890126 | − | 0.455715i | \(-0.849383\pi\) | ||||
−0.890126 | + | 0.455715i | \(0.849383\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.00567080 | 0.000212671 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.54624 | −0.357510 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −43.9073 | −1.63975 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.7370 | 0.661479 | 0.330740 | − | 0.943722i | \(-0.392702\pi\) | ||||
0.330740 | + | 0.943722i | \(0.392702\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 60.1179 | 2.23891 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.18010 | −0.341412 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.7341 | 1.88163 | 0.940813 | − | 0.338927i | \(-0.110064\pi\) | ||||
0.940813 | + | 0.338927i | \(0.110064\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.7597 | 0.991100 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.91206 | 0.329625 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.9970 | −0.701670 | −0.350835 | − | 0.936437i | \(-0.614102\pi\) | ||||
−0.350835 | + | 0.936437i | \(0.614102\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 63.2096 | 2.32835 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.6999 | 1.64431 | 0.822156 | − | 0.569263i | \(-0.192771\pi\) | ||||
0.822156 | + | 0.569263i | \(0.192771\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.65522 | 0.171014 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.9841 | −1.43019 | −0.715094 | − | 0.699029i | \(-0.753616\pi\) | ||||
−0.715094 | + | 0.699029i | \(0.753616\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.141443 | 0.00517513 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.1647 | 0.846421 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.97027 | −0.144877 | −0.0724386 | − | 0.997373i | \(-0.523078\pi\) | ||||
−0.0724386 | + | 0.997373i | \(0.523078\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.8641 | −0.687448 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.2885 | −0.846436 | −0.423218 | − | 0.906028i | \(-0.639100\pi\) | ||||
−0.423218 | + | 0.906028i | \(0.639100\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.0393 | −0.364405 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.62214 | 0.203802 | 0.101901 | − | 0.994795i | \(-0.467507\pi\) | ||||
0.101901 | + | 0.994795i | \(0.467507\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.1768 | −1.23728 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.8753 | 0.428792 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.0457 | −1.19166 | −0.595828 | − | 0.803112i | \(-0.703176\pi\) | ||||
−0.595828 | + | 0.803112i | \(0.703176\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32.3981 | −1.16679 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −46.8196 | −1.68398 | −0.841991 | − | 0.539491i | \(-0.818617\pi\) | ||||
−0.841991 | + | 0.539491i | \(0.818617\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −44.4958 | −1.59628 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.0101591 | −0.000363987 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −74.5442 | −2.66740 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.2756 | 0.760328 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.1470 | −1.25286 | −0.626428 | − | 0.779479i | \(-0.715484\pi\) | ||||
−0.626428 | + | 0.779479i | \(0.715484\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −33.8128 | −1.20377 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.3871 | 0.653769 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.6730 | 0.414522 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.8566 | 0.774200 | 0.387100 | − | 0.922038i | \(-0.373477\pi\) | ||||
0.387100 | + | 0.922038i | \(0.373477\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.94556 | −0.316471 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.157633 | 0.00556969 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.9617 | −0.386829 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.61909 | 0.233003 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.24801 | −0.0790357 | −0.0395178 | − | 0.999219i | \(-0.512582\pi\) | ||||
−0.0395178 | + | 0.999219i | \(0.512582\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.5155 | −1.03643 | −0.518215 | − | 0.855250i | \(-0.673403\pi\) | ||||
−0.518215 | + | 0.855250i | \(0.673403\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −31.6783 | −1.11101 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.2121 | −0.847076 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.0960772 | −0.00335721 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.1470 | −1.01724 | −0.508618 | − | 0.860992i | \(-0.669843\pi\) | ||||
−0.508618 | + | 0.860992i | \(0.669843\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.1354 | 0.457873 | 0.228936 | − | 0.973441i | \(-0.426475\pi\) | ||||
0.228936 | + | 0.973441i | \(0.426475\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −54.7619 | −1.90426 | −0.952129 | − | 0.305698i | \(-0.901110\pi\) | ||||
−0.952129 | + | 0.305698i | \(0.901110\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.3545 | −1.43630 | −0.718151 | − | 0.695887i | \(-0.755011\pi\) | ||||
−0.718151 | + | 0.695887i | \(0.755011\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.6809 | −0.890859 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.60869 | 0.125034 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 49.3844 | 1.70698 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.60909 | −0.297219 | −0.148609 | − | 0.988896i | \(-0.547480\pi\) | ||||
−0.148609 | + | 0.988896i | \(0.547480\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.0859 | −0.416755 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.9550 | 0.377310 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −74.1018 | −2.54617 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 49.4819 | 1.69822 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.69904 | 0.263920 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 53.2697 | 1.82392 | 0.911960 | − | 0.410280i | \(-0.134569\pi\) | ||||
0.911960 | + | 0.410280i | \(0.134569\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.3201 | 0.455005 | 0.227502 | − | 0.973778i | \(-0.426944\pi\) | ||||
0.227502 | + | 0.973778i | \(0.426944\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.3425 | −0.796434 | −0.398217 | − | 0.917291i | \(-0.630371\pi\) | ||||
−0.398217 | + | 0.917291i | \(0.630371\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0241779 | 0.000823981 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.8395 | −0.743426 | −0.371713 | − | 0.928348i | \(-0.621229\pi\) | ||||
−0.371713 | + | 0.928348i | \(0.621229\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.1835 | 0.957161 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.24703 | −0.0423026 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0698 | −0.408968 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.0546135 | 0.00184839 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.0903 | −0.982309 | −0.491155 | − | 0.871072i | \(-0.663425\pi\) | ||||
−0.491155 | + | 0.871072i | \(0.663425\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.2082 | −0.850251 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.7215 | −1.50671 | −0.753353 | − | 0.657616i | \(-0.771565\pi\) | ||||
−0.753353 | + | 0.657616i | \(0.771565\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.4889 | −0.655855 | −0.327927 | − | 0.944703i | \(-0.606350\pi\) | ||||
−0.327927 | + | 0.944703i | \(0.606350\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.0317 | 0.806906 | 0.403453 | − | 0.915000i | \(-0.367810\pi\) | ||||
0.403453 | + | 0.915000i | \(0.367810\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.0694 | 1.24327 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 52.3897 | 1.75512 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.3031 | 0.813274 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.91700 | 0.0640067 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 39.2606 | 1.30942 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.58806 | 0.186165 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 57.6232 | 1.91758 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.2777 | −0.540491 | −0.270245 | − | 0.962792i | \(-0.587105\pi\) | ||||
−0.270245 | + | 0.962792i | \(0.587105\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.345301 | −0.0114529 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.8128 | −0.788952 | −0.394476 | − | 0.918906i | \(-0.629074\pi\) | ||||
−0.394476 | + | 0.918906i | \(0.629074\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.1039 | −1.02939 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −49.9734 | −1.65027 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.0433 | −0.727141 | −0.363571 | − | 0.931567i | \(-0.618442\pi\) | ||||
−0.363571 | + | 0.931567i | \(0.618442\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −53.0071 | −1.74664 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.2341 | 0.468521 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.474890 | −0.0155974 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.19696 | −0.170507 | −0.0852534 | − | 0.996359i | \(-0.527170\pi\) | ||||
−0.0852534 | + | 0.996359i | \(0.527170\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.80404 | −0.321315 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.3633 | 1.19048 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.0029 | −0.947482 | −0.473741 | − | 0.880664i | \(-0.657097\pi\) | ||||
−0.473741 | + | 0.880664i | \(0.657097\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.9833 | −0.815300 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.2138 | 1.63692 | 0.818461 | − | 0.574562i | \(-0.194827\pi\) | ||||
0.818461 | + | 0.574562i | \(0.194827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.00418347 | −0.000136232 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.3661 | −0.596817 | −0.298408 | − | 0.954438i | \(-0.596456\pi\) | ||||
−0.298408 | + | 0.954438i | \(0.596456\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.09311 | 0.0679453 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −58.6143 | −1.90070 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.9542 | 1.13228 | 0.566139 | − | 0.824310i | \(-0.308437\pi\) | ||||
0.566139 | + | 0.824310i | \(0.308437\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 41.2886 | 1.33467 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.34980 | −0.237338 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.1308 | 1.93970 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.182985 | −0.00589662 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.3107 | −1.55357 | −0.776784 | − | 0.629767i | \(-0.783150\pi\) | ||||
−0.776784 | + | 0.629767i | \(0.783150\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.77602 | 0.121303 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.8815 | 0.477570 | 0.238785 | − | 0.971072i | \(-0.423251\pi\) | ||||
0.238785 | + | 0.971072i | \(0.423251\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.7184 | −0.696261 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.6833 | 0.597730 | 0.298865 | − | 0.954295i | \(-0.403392\pi\) | ||||
0.298865 | + | 0.954295i | \(0.403392\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.6641 | −1.10787 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.269974 | 0.00861959 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.4191 | −0.906428 | −0.453214 | − | 0.891402i | \(-0.649723\pi\) | ||||
−0.453214 | + | 0.891402i | \(0.649723\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −57.8398 | −1.84106 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.97045 | −0.317042 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.4942 | 0.905148 | 0.452574 | − | 0.891727i | \(-0.350506\pi\) | ||||
0.452574 | + | 0.891727i | \(0.350506\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.0881 | 0.542273 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.5435 | 0.840642 | 0.420321 | − | 0.907375i | \(-0.361917\pi\) | ||||
0.420321 | + | 0.907375i | \(0.361917\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −39.8285 | −1.26012 |
(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 | 9200.2.a.cx.1.3 | 6 | ||
4.3 | odd | 2 | 2300.2.a.o.1.4 | 6 | |||
5.2 | odd | 4 | 1840.2.e.f.369.9 | 12 | |||
5.3 | odd | 4 | 1840.2.e.f.369.4 | 12 | |||
5.4 | even | 2 | 9200.2.a.cy.1.4 | 6 | |||
20.3 | even | 4 | 460.2.c.a.369.9 | yes | 12 | ||
20.7 | even | 4 | 460.2.c.a.369.4 | ✓ | 12 | ||
20.19 | odd | 2 | 2300.2.a.n.1.3 | 6 | |||
60.23 | odd | 4 | 4140.2.f.b.829.1 | 12 | |||
60.47 | odd | 4 | 4140.2.f.b.829.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.c.a.369.4 | ✓ | 12 | 20.7 | even | 4 | ||
460.2.c.a.369.9 | yes | 12 | 20.3 | even | 4 | ||
1840.2.e.f.369.4 | 12 | 5.3 | odd | 4 | |||
1840.2.e.f.369.9 | 12 | 5.2 | odd | 4 | |||
2300.2.a.n.1.3 | 6 | 20.19 | odd | 2 | |||
2300.2.a.o.1.4 | 6 | 4.3 | odd | 2 | |||
4140.2.f.b.829.1 | 12 | 60.23 | odd | 4 | |||
4140.2.f.b.829.2 | 12 | 60.47 | odd | 4 | |||
9200.2.a.cx.1.3 | 6 | 1.1 | even | 1 | trivial | ||
9200.2.a.cy.1.4 | 6 | 5.4 | even | 2 |