Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 11 x^{16} + 123 x^{15} - 35 x^{14} - 982 x^{13} + 988 x^{12} + 3872 x^{11} - 5421 x^{10} - 7882 x^{9} + 13376 x^{8} + 7948 x^{7} - 15795 x^{6} - 3858 x^{5} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Root | \(2.77035\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.77035 | 1.95893 | 0.979466 | − | 0.201609i | \(-0.0646170\pi\) | ||||
0.979466 | + | 0.201609i | \(0.0646170\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.67483 | 2.83742 | ||||||||
\(5\) | 3.69380 | 1.65192 | 0.825958 | − | 0.563731i | \(-0.190635\pi\) | ||||
0.825958 | + | 0.563731i | \(0.190635\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 10.1806 | 3.59937 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 10.2331 | 3.23599 | ||||||||
\(11\) | 5.84456 | 1.76220 | 0.881101 | − | 0.472929i | \(-0.156803\pi\) | ||||
0.881101 | + | 0.472929i | \(0.156803\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.83862 | −1.89669 | −0.948346 | − | 0.317238i | \(-0.897244\pi\) | ||||
−0.948346 | + | 0.317238i | \(0.897244\pi\) | |||||||
\(14\) | 2.77035 | 0.740407 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.8540 | 4.21351 | ||||||||
\(17\) | −2.91249 | −0.706383 | −0.353191 | − | 0.935551i | \(-0.614904\pi\) | ||||
−0.353191 | + | 0.935551i | \(0.614904\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.728183 | −0.167057 | −0.0835283 | − | 0.996505i | \(-0.526619\pi\) | ||||
−0.0835283 | + | 0.996505i | \(0.526619\pi\) | |||||||
\(20\) | 20.9617 | 4.68717 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 16.1915 | 3.45203 | ||||||||
\(23\) | −8.42541 | −1.75682 | −0.878410 | − | 0.477908i | \(-0.841395\pi\) | ||||
−0.878410 | + | 0.477908i | \(0.841395\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.64414 | 1.72883 | ||||||||
\(26\) | −18.9454 | −3.71549 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.67483 | 1.07244 | ||||||||
\(29\) | −5.16908 | −0.959874 | −0.479937 | − | 0.877303i | \(-0.659341\pi\) | ||||
−0.479937 | + | 0.877303i | \(0.659341\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.147299 | −0.0264556 | −0.0132278 | − | 0.999913i | \(-0.504211\pi\) | ||||
−0.0132278 | + | 0.999913i | \(0.504211\pi\) | |||||||
\(32\) | 26.3305 | 4.65461 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.06861 | −1.38376 | ||||||||
\(35\) | 3.69380 | 0.624366 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.220660 | 0.0362762 | 0.0181381 | − | 0.999835i | \(-0.494226\pi\) | ||||
0.0181381 | + | 0.999835i | \(0.494226\pi\) | |||||||
\(38\) | −2.01732 | −0.327253 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 37.6049 | 5.94586 | ||||||||
\(41\) | −6.63743 | −1.03659 | −0.518296 | − | 0.855201i | \(-0.673433\pi\) | ||||
−0.518296 | + | 0.855201i | \(0.673433\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.26302 | 0.345107 | 0.172554 | − | 0.985000i | \(-0.444798\pi\) | ||||
0.172554 | + | 0.985000i | \(0.444798\pi\) | |||||||
\(44\) | 33.1669 | 5.00010 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −23.3413 | −3.44149 | ||||||||
\(47\) | 2.62826 | 0.383371 | 0.191685 | − | 0.981456i | \(-0.438605\pi\) | ||||
0.191685 | + | 0.981456i | \(0.438605\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 23.9473 | 3.38666 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −38.8080 | −5.38170 | ||||||||
\(53\) | 12.8622 | 1.76676 | 0.883379 | − | 0.468659i | \(-0.155263\pi\) | ||||
0.883379 | + | 0.468659i | \(0.155263\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 21.5886 | 2.91101 | ||||||||
\(56\) | 10.1806 | 1.36043 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −14.3202 | −1.88033 | ||||||||
\(59\) | −5.14980 | −0.670447 | −0.335223 | − | 0.942139i | \(-0.608812\pi\) | ||||
−0.335223 | + | 0.942139i | \(0.608812\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8107 | 1.38417 | 0.692086 | − | 0.721815i | \(-0.256692\pi\) | ||||
0.692086 | + | 0.721815i | \(0.256692\pi\) | |||||||
\(62\) | −0.408069 | −0.0518248 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 39.2364 | 4.90456 | ||||||||
\(65\) | −25.2605 | −3.13318 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.61979 | 0.320059 | 0.160029 | − | 0.987112i | \(-0.448841\pi\) | ||||
0.160029 | + | 0.987112i | \(0.448841\pi\) | |||||||
\(68\) | −16.5279 | −2.00430 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 10.2331 | 1.22309 | ||||||||
\(71\) | 3.60167 | 0.427440 | 0.213720 | − | 0.976895i | \(-0.431442\pi\) | ||||
0.213720 | + | 0.976895i | \(0.431442\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.18425 | −0.723811 | −0.361906 | − | 0.932215i | \(-0.617874\pi\) | ||||
−0.361906 | + | 0.932215i | \(0.617874\pi\) | |||||||
\(74\) | 0.611304 | 0.0710626 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.13231 | −0.474009 | ||||||||
\(77\) | 5.84456 | 0.666050 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.74021 | 0.420807 | 0.210403 | − | 0.977615i | \(-0.432522\pi\) | ||||
0.210403 | + | 0.977615i | \(0.432522\pi\) | |||||||
\(80\) | 62.2554 | 6.96037 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −18.3880 | −2.03061 | ||||||||
\(83\) | −5.02267 | −0.551310 | −0.275655 | − | 0.961257i | \(-0.588895\pi\) | ||||
−0.275655 | + | 0.961257i | \(0.588895\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.7582 | −1.16689 | ||||||||
\(86\) | 6.26936 | 0.676042 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 59.5009 | 6.34282 | ||||||||
\(89\) | −9.91415 | −1.05090 | −0.525449 | − | 0.850825i | \(-0.676103\pi\) | ||||
−0.525449 | + | 0.850825i | \(0.676103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.83862 | −0.716882 | ||||||||
\(92\) | −47.8128 | −4.98483 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.28119 | 0.750998 | ||||||||
\(95\) | −2.68976 | −0.275964 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.08019 | −0.312745 | −0.156373 | − | 0.987698i | \(-0.549980\pi\) | ||||
−0.156373 | + | 0.987698i | \(0.549980\pi\) | |||||||
\(98\) | 2.77035 | 0.279847 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 49.0541 | 4.90541 | ||||||||
\(101\) | 6.71801 | 0.668467 | 0.334233 | − | 0.942490i | \(-0.391523\pi\) | ||||
0.334233 | + | 0.942490i | \(0.391523\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.9532 | −1.57192 | −0.785958 | − | 0.618280i | \(-0.787830\pi\) | ||||
−0.785958 | + | 0.618280i | \(0.787830\pi\) | |||||||
\(104\) | −69.6210 | −6.82690 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 35.6328 | 3.46096 | ||||||||
\(107\) | −17.3101 | −1.67343 | −0.836714 | − | 0.547640i | \(-0.815526\pi\) | ||||
−0.836714 | + | 0.547640i | \(0.815526\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.73388 | −0.357641 | −0.178820 | − | 0.983882i | \(-0.557228\pi\) | ||||
−0.178820 | + | 0.983882i | \(0.557228\pi\) | |||||||
\(110\) | 59.8080 | 5.70247 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 16.8540 | 1.59256 | ||||||||
\(113\) | 5.36995 | 0.505162 | 0.252581 | − | 0.967576i | \(-0.418721\pi\) | ||||
0.252581 | + | 0.967576i | \(0.418721\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −31.1218 | −2.90212 | ||||||||
\(116\) | −29.3337 | −2.72356 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −14.2667 | −1.31336 | ||||||||
\(119\) | −2.91249 | −0.266988 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.1589 | 2.10535 | ||||||||
\(122\) | 29.9495 | 2.71150 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.835896 | −0.0750657 | ||||||||
\(125\) | 13.4607 | 1.20396 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 56.0377 | 4.95308 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −69.9803 | −6.13768 | ||||||||
\(131\) | 18.6600 | 1.63033 | 0.815166 | − | 0.579227i | \(-0.196646\pi\) | ||||
0.815166 | + | 0.579227i | \(0.196646\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.728183 | −0.0631415 | ||||||||
\(134\) | 7.25774 | 0.626974 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −29.6508 | −2.54253 | ||||||||
\(137\) | −10.2323 | −0.874203 | −0.437101 | − | 0.899412i | \(-0.643995\pi\) | ||||
−0.437101 | + | 0.899412i | \(0.643995\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.06275 | 0.514236 | 0.257118 | − | 0.966380i | \(-0.417227\pi\) | ||||
0.257118 | + | 0.966380i | \(0.417227\pi\) | |||||||
\(140\) | 20.9617 | 1.77159 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.97789 | 0.837326 | ||||||||
\(143\) | −39.9687 | −3.34235 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.0935 | −1.58563 | ||||||||
\(146\) | −17.1325 | −1.41790 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.25221 | 0.102931 | ||||||||
\(149\) | −3.78097 | −0.309749 | −0.154874 | − | 0.987934i | \(-0.549497\pi\) | ||||
−0.154874 | + | 0.987934i | \(0.549497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.80071 | −0.716192 | −0.358096 | − | 0.933685i | \(-0.616574\pi\) | ||||
−0.358096 | + | 0.933685i | \(0.616574\pi\) | |||||||
\(152\) | −7.41331 | −0.601299 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 16.1915 | 1.30475 | ||||||||
\(155\) | −0.544092 | −0.0437025 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.06816 | −0.165057 | −0.0825287 | − | 0.996589i | \(-0.526300\pi\) | ||||
−0.0825287 | + | 0.996589i | \(0.526300\pi\) | |||||||
\(158\) | 10.3617 | 0.824332 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 97.2594 | 7.68903 | ||||||||
\(161\) | −8.42541 | −0.664016 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.55816 | −0.435349 | −0.217674 | − | 0.976021i | \(-0.569847\pi\) | ||||
−0.217674 | + | 0.976021i | \(0.569847\pi\) | |||||||
\(164\) | −37.6663 | −2.94124 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.9145 | −1.07998 | ||||||||
\(167\) | 4.47087 | 0.345966 | 0.172983 | − | 0.984925i | \(-0.444659\pi\) | ||||
0.172983 | + | 0.984925i | \(0.444659\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.7667 | 2.59744 | ||||||||
\(170\) | −29.8038 | −2.28585 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.8423 | 0.979213 | ||||||||
\(173\) | 6.66702 | 0.506884 | 0.253442 | − | 0.967351i | \(-0.418437\pi\) | ||||
0.253442 | + | 0.967351i | \(0.418437\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.64414 | 0.653436 | ||||||||
\(176\) | 98.5045 | 7.42506 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −27.4657 | −2.05864 | ||||||||
\(179\) | −23.8805 | −1.78491 | −0.892457 | − | 0.451132i | \(-0.851020\pi\) | ||||
−0.892457 | + | 0.451132i | \(0.851020\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.67808 | 0.347719 | 0.173860 | − | 0.984770i | \(-0.444376\pi\) | ||||
0.173860 | + | 0.984770i | \(0.444376\pi\) | |||||||
\(182\) | −18.9454 | −1.40432 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −85.7755 | −6.32345 | ||||||||
\(185\) | 0.815072 | 0.0599253 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.0222 | −1.24479 | ||||||||
\(188\) | 14.9149 | 1.08778 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.45157 | −0.540594 | ||||||||
\(191\) | −20.6313 | −1.49283 | −0.746414 | − | 0.665482i | \(-0.768226\pi\) | ||||
−0.746414 | + | 0.665482i | \(0.768226\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.649615 | −0.0467603 | −0.0233802 | − | 0.999727i | \(-0.507443\pi\) | ||||
−0.0233802 | + | 0.999727i | \(0.507443\pi\) | |||||||
\(194\) | −8.53319 | −0.612647 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.67483 | 0.405345 | ||||||||
\(197\) | −10.5454 | −0.751330 | −0.375665 | − | 0.926755i | \(-0.622586\pi\) | ||||
−0.375665 | + | 0.926755i | \(0.622586\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.2177 | −1.36231 | −0.681155 | − | 0.732139i | \(-0.738522\pi\) | ||||
−0.681155 | + | 0.732139i | \(0.738522\pi\) | |||||||
\(200\) | 88.0022 | 6.22270 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18.6112 | 1.30948 | ||||||||
\(203\) | −5.16908 | −0.362798 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.5173 | −1.71236 | ||||||||
\(206\) | −44.1959 | −3.07928 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −115.258 | −7.99173 | ||||||||
\(209\) | −4.25591 | −0.294387 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.801027 | −0.0551450 | −0.0275725 | − | 0.999620i | \(-0.508778\pi\) | ||||
−0.0275725 | + | 0.999620i | \(0.508778\pi\) | |||||||
\(212\) | 72.9908 | 5.01303 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −47.9549 | −3.27813 | ||||||||
\(215\) | 8.35914 | 0.570089 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.147299 | −0.00999929 | ||||||||
\(218\) | −10.3442 | −0.700594 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 122.512 | 8.25975 | ||||||||
\(221\) | 19.9174 | 1.33979 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.6856 | −1.78700 | −0.893498 | − | 0.449066i | \(-0.851757\pi\) | ||||
−0.893498 | + | 0.449066i | \(0.851757\pi\) | |||||||
\(224\) | 26.3305 | 1.75928 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.8766 | 0.989579 | ||||||||
\(227\) | 5.62346 | 0.373242 | 0.186621 | − | 0.982432i | \(-0.440246\pi\) | ||||
0.186621 | + | 0.982432i | \(0.440246\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 30.0812 | 1.98782 | 0.993912 | − | 0.110179i | \(-0.0351426\pi\) | ||||
0.993912 | + | 0.110179i | \(0.0351426\pi\) | |||||||
\(230\) | −86.2182 | −5.68506 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −52.6242 | −3.45495 | ||||||||
\(233\) | 25.0722 | 1.64254 | 0.821269 | − | 0.570542i | \(-0.193267\pi\) | ||||
0.821269 | + | 0.570542i | \(0.193267\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.70826 | 0.633297 | ||||||||
\(236\) | −29.2243 | −1.90234 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.06861 | −0.523011 | ||||||||
\(239\) | 5.11449 | 0.330829 | 0.165414 | − | 0.986224i | \(-0.447104\pi\) | ||||
0.165414 | + | 0.986224i | \(0.447104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.2167 | −1.10902 | −0.554511 | − | 0.832176i | \(-0.687095\pi\) | ||||
−0.554511 | + | 0.832176i | \(0.687095\pi\) | |||||||
\(242\) | 64.1582 | 4.12425 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 61.3491 | 3.92747 | ||||||||
\(245\) | 3.69380 | 0.235988 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.97977 | 0.316855 | ||||||||
\(248\) | −1.49958 | −0.0952237 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 37.2909 | 2.35848 | ||||||||
\(251\) | 6.60961 | 0.417195 | 0.208597 | − | 0.978002i | \(-0.433110\pi\) | ||||
0.208597 | + | 0.978002i | \(0.433110\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −49.2428 | −3.09587 | ||||||||
\(254\) | 2.77035 | 0.173827 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 76.7711 | 4.79820 | ||||||||
\(257\) | 8.00894 | 0.499584 | 0.249792 | − | 0.968299i | \(-0.419638\pi\) | ||||
0.249792 | + | 0.968299i | \(0.419638\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.220660 | 0.0137111 | ||||||||
\(260\) | −143.349 | −8.89012 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 51.6947 | 3.19371 | ||||||||
\(263\) | −2.81053 | −0.173305 | −0.0866523 | − | 0.996239i | \(-0.527617\pi\) | ||||
−0.0866523 | + | 0.996239i | \(0.527617\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 47.5104 | 2.91854 | ||||||||
\(266\) | −2.01732 | −0.123690 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.8669 | 0.908140 | ||||||||
\(269\) | 16.8965 | 1.03020 | 0.515099 | − | 0.857131i | \(-0.327755\pi\) | ||||
0.515099 | + | 0.857131i | \(0.327755\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.61690 | −0.280457 | −0.140228 | − | 0.990119i | \(-0.544784\pi\) | ||||
−0.140228 | + | 0.990119i | \(0.544784\pi\) | |||||||
\(272\) | −49.0872 | −2.97635 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −28.3470 | −1.71250 | ||||||||
\(275\) | 50.5212 | 3.04654 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.56502 | 0.514622 | 0.257311 | − | 0.966329i | \(-0.417163\pi\) | ||||
0.257311 | + | 0.966329i | \(0.417163\pi\) | |||||||
\(278\) | 16.7959 | 1.00735 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 37.6049 | 2.24733 | ||||||||
\(281\) | 9.85734 | 0.588040 | 0.294020 | − | 0.955799i | \(-0.405007\pi\) | ||||
0.294020 | + | 0.955799i | \(0.405007\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.8460 | −0.882505 | −0.441253 | − | 0.897383i | \(-0.645466\pi\) | ||||
−0.441253 | + | 0.897383i | \(0.645466\pi\) | |||||||
\(284\) | 20.4389 | 1.21282 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −110.727 | −6.54744 | ||||||||
\(287\) | −6.63743 | −0.391795 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.51740 | −0.501023 | ||||||||
\(290\) | −52.8958 | −3.10615 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −35.0946 | −2.05375 | ||||||||
\(293\) | 22.3075 | 1.30322 | 0.651609 | − | 0.758555i | \(-0.274094\pi\) | ||||
0.651609 | + | 0.758555i | \(0.274094\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.0223 | −1.10752 | ||||||||
\(296\) | 2.24644 | 0.130572 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.4746 | −0.606777 | ||||||||
\(299\) | 57.6182 | 3.33215 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.26302 | 0.130438 | ||||||||
\(302\) | −24.3810 | −1.40297 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.2728 | −0.703895 | ||||||||
\(305\) | 39.9327 | 2.28654 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.4884 | 1.22641 | 0.613205 | − | 0.789924i | \(-0.289880\pi\) | ||||
0.613205 | + | 0.789924i | \(0.289880\pi\) | |||||||
\(308\) | 33.1669 | 1.88986 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.50732 | −0.0856103 | ||||||||
\(311\) | 2.66770 | 0.151272 | 0.0756358 | − | 0.997136i | \(-0.475901\pi\) | ||||
0.0756358 | + | 0.997136i | \(0.475901\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.03542 | −0.228095 | −0.114048 | − | 0.993475i | \(-0.536382\pi\) | ||||
−0.114048 | + | 0.993475i | \(0.536382\pi\) | |||||||
\(314\) | −5.72953 | −0.323336 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21.2251 | 1.19400 | ||||||||
\(317\) | −27.9402 | −1.56928 | −0.784639 | − | 0.619953i | \(-0.787152\pi\) | ||||
−0.784639 | + | 0.619953i | \(0.787152\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.2110 | −1.69149 | ||||||||
\(320\) | 144.932 | 8.10192 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −23.3413 | −1.30076 | ||||||||
\(323\) | 2.12083 | 0.118006 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −59.1140 | −3.27905 | ||||||||
\(326\) | −15.3980 | −0.852819 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −67.5727 | −3.73108 | ||||||||
\(329\) | 2.62826 | 0.144901 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.9479 | 1.53616 | 0.768079 | − | 0.640355i | \(-0.221213\pi\) | ||||
0.768079 | + | 0.640355i | \(0.221213\pi\) | |||||||
\(332\) | −28.5028 | −1.56429 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.3859 | 0.677724 | ||||||||
\(335\) | 9.67699 | 0.528711 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.7508 | 0.640108 | 0.320054 | − | 0.947399i | \(-0.396299\pi\) | ||||
0.320054 | + | 0.947399i | \(0.396299\pi\) | |||||||
\(338\) | 93.5456 | 5.08821 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −61.0507 | −3.31094 | ||||||||
\(341\) | −0.860897 | −0.0466202 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 23.0388 | 1.24217 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.4700 | 0.992952 | ||||||||
\(347\) | 32.9383 | 1.76822 | 0.884110 | − | 0.467279i | \(-0.154766\pi\) | ||||
0.884110 | + | 0.467279i | \(0.154766\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.7484 | 1.43181 | 0.715903 | − | 0.698199i | \(-0.246015\pi\) | ||||
0.715903 | + | 0.698199i | \(0.246015\pi\) | |||||||
\(350\) | 23.9473 | 1.28004 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 153.890 | 8.20236 | ||||||||
\(353\) | −21.2637 | −1.13175 | −0.565875 | − | 0.824491i | \(-0.691462\pi\) | ||||
−0.565875 | + | 0.824491i | \(0.691462\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.3039 | 0.706095 | ||||||||
\(356\) | −56.2611 | −2.98183 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −66.1574 | −3.49653 | ||||||||
\(359\) | 20.8707 | 1.10152 | 0.550758 | − | 0.834665i | \(-0.314339\pi\) | ||||
0.550758 | + | 0.834665i | \(0.314339\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4697 | −0.972092 | ||||||||
\(362\) | 12.9599 | 0.681158 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −38.8080 | −2.03409 | ||||||||
\(365\) | −22.8434 | −1.19568 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.11925 | 0.476021 | 0.238010 | − | 0.971263i | \(-0.423505\pi\) | ||||
0.238010 | + | 0.971263i | \(0.423505\pi\) | |||||||
\(368\) | −142.002 | −7.40238 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.25803 | 0.117390 | ||||||||
\(371\) | 12.8622 | 0.667772 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.2620 | −0.945572 | −0.472786 | − | 0.881177i | \(-0.656752\pi\) | ||||
−0.472786 | + | 0.881177i | \(0.656752\pi\) | |||||||
\(374\) | −47.1575 | −2.43846 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 26.7572 | 1.37989 | ||||||||
\(377\) | 35.3494 | 1.82059 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.4251 | −0.792332 | −0.396166 | − | 0.918179i | \(-0.629659\pi\) | ||||
−0.396166 | + | 0.918179i | \(0.629659\pi\) | |||||||
\(380\) | −15.2639 | −0.783023 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −57.1559 | −2.92435 | ||||||||
\(383\) | 1.07843 | 0.0551054 | 0.0275527 | − | 0.999620i | \(-0.491229\pi\) | ||||
0.0275527 | + | 0.999620i | \(0.491229\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.5886 | 1.10026 | ||||||||
\(386\) | −1.79966 | −0.0916003 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −17.4795 | −0.887389 | ||||||||
\(389\) | 9.69935 | 0.491776 | 0.245888 | − | 0.969298i | \(-0.420920\pi\) | ||||
0.245888 | + | 0.969298i | \(0.420920\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.5389 | 1.24099 | ||||||||
\(392\) | 10.1806 | 0.514196 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −29.2145 | −1.47181 | ||||||||
\(395\) | 13.8156 | 0.695138 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.4990 | −0.677495 | −0.338747 | − | 0.940877i | \(-0.610003\pi\) | ||||
−0.338747 | + | 0.940877i | \(0.610003\pi\) | |||||||
\(398\) | −53.2398 | −2.66867 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 145.689 | 7.28444 | ||||||||
\(401\) | −12.9871 | −0.648547 | −0.324273 | − | 0.945963i | \(-0.605120\pi\) | ||||
−0.324273 | + | 0.945963i | \(0.605120\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.00732 | 0.0501782 | ||||||||
\(404\) | 38.1236 | 1.89672 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.3202 | −0.710698 | ||||||||
\(407\) | 1.28966 | 0.0639260 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.0022 | −1.38462 | −0.692310 | − | 0.721600i | \(-0.743407\pi\) | ||||
−0.692310 | + | 0.721600i | \(0.743407\pi\) | |||||||
\(410\) | −67.9215 | −3.35440 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −90.5317 | −4.46018 | ||||||||
\(413\) | −5.14980 | −0.253405 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.5527 | −0.910718 | ||||||||
\(416\) | −180.064 | −8.82836 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.7904 | −0.576685 | ||||||||
\(419\) | 17.9029 | 0.874612 | 0.437306 | − | 0.899313i | \(-0.355933\pi\) | ||||
0.437306 | + | 0.899313i | \(0.355933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.02171 | −0.244743 | −0.122372 | − | 0.992484i | \(-0.539050\pi\) | ||||
−0.122372 | + | 0.992484i | \(0.539050\pi\) | |||||||
\(422\) | −2.21912 | −0.108025 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 130.944 | 6.35922 | ||||||||
\(425\) | −25.1760 | −1.22121 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.8107 | 0.523168 | ||||||||
\(428\) | −98.2317 | −4.74821 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 23.1577 | 1.11677 | ||||||||
\(431\) | 9.87050 | 0.475445 | 0.237723 | − | 0.971333i | \(-0.423599\pi\) | ||||
0.237723 | + | 0.971333i | \(0.423599\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.6320 | −0.991511 | −0.495756 | − | 0.868462i | \(-0.665109\pi\) | ||||
−0.495756 | + | 0.868462i | \(0.665109\pi\) | |||||||
\(434\) | −0.408069 | −0.0195879 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −21.1891 | −1.01478 | ||||||||
\(437\) | 6.13524 | 0.293488 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.5226 | 0.597671 | 0.298836 | − | 0.954305i | \(-0.403402\pi\) | ||||
0.298836 | + | 0.954305i | \(0.403402\pi\) | |||||||
\(440\) | 219.784 | 10.4778 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 55.1782 | 2.62456 | ||||||||
\(443\) | −17.5570 | −0.834157 | −0.417079 | − | 0.908870i | \(-0.636946\pi\) | ||||
−0.417079 | + | 0.908870i | \(0.636946\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −36.6209 | −1.73600 | ||||||||
\(446\) | −73.9283 | −3.50061 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 39.2364 | 1.85375 | ||||||||
\(449\) | −15.1729 | −0.716052 | −0.358026 | − | 0.933712i | \(-0.616550\pi\) | ||||
−0.358026 | + | 0.933712i | \(0.616550\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −38.7928 | −1.82668 | ||||||||
\(452\) | 30.4735 | 1.43336 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.5789 | 0.731156 | ||||||||
\(455\) | −25.2605 | −1.18423 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.72959 | 0.408353 | 0.204176 | − | 0.978934i | \(-0.434548\pi\) | ||||
0.204176 | + | 0.978934i | \(0.434548\pi\) | |||||||
\(458\) | 83.3355 | 3.89401 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −176.611 | −8.23452 | ||||||||
\(461\) | −39.0180 | −1.81725 | −0.908625 | − | 0.417613i | \(-0.862867\pi\) | ||||
−0.908625 | + | 0.417613i | \(0.862867\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.1406 | 1.07544 | 0.537718 | − | 0.843125i | \(-0.319287\pi\) | ||||
0.537718 | + | 0.843125i | \(0.319287\pi\) | |||||||
\(464\) | −87.1199 | −4.04444 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 69.4589 | 3.21762 | ||||||||
\(467\) | 5.76547 | 0.266794 | 0.133397 | − | 0.991063i | \(-0.457411\pi\) | ||||
0.133397 | + | 0.991063i | \(0.457411\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.61979 | 0.120971 | ||||||||
\(470\) | 26.8953 | 1.24059 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −52.4279 | −2.41319 | ||||||||
\(473\) | 13.2264 | 0.608149 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.29452 | −0.288812 | ||||||||
\(476\) | −16.5279 | −0.757555 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.1689 | 0.648071 | ||||||||
\(479\) | −18.8928 | −0.863233 | −0.431616 | − | 0.902057i | \(-0.642057\pi\) | ||||
−0.431616 | + | 0.902057i | \(0.642057\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.50901 | −0.0688048 | ||||||||
\(482\) | −47.6961 | −2.17250 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 131.423 | 5.97377 | ||||||||
\(485\) | −11.3776 | −0.516629 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.2365 | −0.509174 | −0.254587 | − | 0.967050i | \(-0.581940\pi\) | ||||
−0.254587 | + | 0.967050i | \(0.581940\pi\) | |||||||
\(488\) | 110.059 | 4.98215 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.2331 | 0.462285 | ||||||||
\(491\) | 28.7501 | 1.29747 | 0.648736 | − | 0.761014i | \(-0.275298\pi\) | ||||
0.648736 | + | 0.761014i | \(0.275298\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.0549 | 0.678039 | ||||||||
\(494\) | 13.7957 | 0.620697 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.48258 | −0.111471 | ||||||||
\(497\) | 3.60167 | 0.161557 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.34025 | 0.239063 | 0.119531 | − | 0.992830i | \(-0.461861\pi\) | ||||
0.119531 | + | 0.992830i | \(0.461861\pi\) | |||||||
\(500\) | 76.3874 | 3.41615 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.3109 | 0.817257 | ||||||||
\(503\) | 22.5608 | 1.00593 | 0.502967 | − | 0.864306i | \(-0.332242\pi\) | ||||
0.502967 | + | 0.864306i | \(0.332242\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.8150 | 1.10425 | ||||||||
\(506\) | −136.420 | −6.06460 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.67483 | 0.251780 | ||||||||
\(509\) | 6.47857 | 0.287158 | 0.143579 | − | 0.989639i | \(-0.454139\pi\) | ||||
0.143579 | + | 0.989639i | \(0.454139\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.18425 | −0.273575 | ||||||||
\(512\) | 100.607 | 4.44626 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.1876 | 0.978652 | ||||||||
\(515\) | −58.9279 | −2.59667 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.3610 | 0.675577 | ||||||||
\(518\) | 0.611304 | 0.0268591 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −257.166 | −11.2775 | ||||||||
\(521\) | 23.6416 | 1.03576 | 0.517878 | − | 0.855454i | \(-0.326722\pi\) | ||||
0.517878 | + | 0.855454i | \(0.326722\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.6939 | 0.948609 | 0.474304 | − | 0.880361i | \(-0.342700\pi\) | ||||
0.474304 | + | 0.880361i | \(0.342700\pi\) | |||||||
\(524\) | 105.892 | 4.62593 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.78614 | −0.339492 | ||||||||
\(527\) | 0.429006 | 0.0186878 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 47.9876 | 2.08642 | ||||||||
\(530\) | 131.620 | 5.71722 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.13231 | −0.179159 | ||||||||
\(533\) | 45.3908 | 1.96610 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −63.9399 | −2.76436 | ||||||||
\(536\) | 26.6710 | 1.15201 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 46.8092 | 2.01809 | ||||||||
\(539\) | 5.84456 | 0.251743 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.9628 | −0.600306 | −0.300153 | − | 0.953891i | \(-0.597038\pi\) | ||||
−0.300153 | + | 0.953891i | \(0.597038\pi\) | |||||||
\(542\) | −12.7904 | −0.549396 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −76.6872 | −3.28794 | ||||||||
\(545\) | −13.7922 | −0.590793 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.1167 | −1.15943 | −0.579714 | − | 0.814820i | \(-0.696836\pi\) | ||||
−0.579714 | + | 0.814820i | \(0.696836\pi\) | |||||||
\(548\) | −58.0665 | −2.48048 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 139.961 | 5.96797 | ||||||||
\(551\) | 3.76404 | 0.160353 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.74021 | 0.159050 | ||||||||
\(554\) | 23.7281 | 1.00811 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 34.4051 | 1.45910 | ||||||||
\(557\) | −9.65775 | −0.409212 | −0.204606 | − | 0.978844i | \(-0.565591\pi\) | ||||
−0.204606 | + | 0.978844i | \(0.565591\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.4759 | −0.654562 | ||||||||
\(560\) | 62.2554 | 2.63077 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.3083 | 1.15193 | ||||||||
\(563\) | 12.9538 | 0.545939 | 0.272970 | − | 0.962023i | \(-0.411994\pi\) | ||||
0.272970 | + | 0.962023i | \(0.411994\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.8355 | 0.834486 | ||||||||
\(566\) | −41.1287 | −1.72877 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 36.6671 | 1.53852 | ||||||||
\(569\) | 6.56268 | 0.275122 | 0.137561 | − | 0.990493i | \(-0.456074\pi\) | ||||
0.137561 | + | 0.990493i | \(0.456074\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.3502 | 1.77230 | 0.886150 | − | 0.463398i | \(-0.153370\pi\) | ||||
0.886150 | + | 0.463398i | \(0.153370\pi\) | |||||||
\(572\) | −226.816 | −9.48364 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −18.3880 | −0.767500 | ||||||||
\(575\) | −72.8305 | −3.03724 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.112165 | 0.00466947 | 0.00233474 | − | 0.999997i | \(-0.499257\pi\) | ||||
0.00233474 | + | 0.999997i | \(0.499257\pi\) | |||||||
\(578\) | −23.5962 | −0.981471 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −108.353 | −4.49910 | ||||||||
\(581\) | −5.02267 | −0.208375 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 75.1739 | 3.11338 | ||||||||
\(584\) | −62.9591 | −2.60527 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 61.7995 | 2.55292 | ||||||||
\(587\) | −7.07831 | −0.292153 | −0.146076 | − | 0.989273i | \(-0.546665\pi\) | ||||
−0.146076 | + | 0.989273i | \(0.546665\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.107260 | 0.00441959 | ||||||||
\(590\) | −52.6985 | −2.16956 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.71901 | 0.152850 | ||||||||
\(593\) | −20.3183 | −0.834374 | −0.417187 | − | 0.908821i | \(-0.636984\pi\) | ||||
−0.417187 | + | 0.908821i | \(0.636984\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.7582 | −0.441041 | ||||||||
\(596\) | −21.4563 | −0.878886 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 159.622 | 6.52745 | ||||||||
\(599\) | −15.2665 | −0.623772 | −0.311886 | − | 0.950119i | \(-0.600961\pi\) | ||||
−0.311886 | + | 0.950119i | \(0.600961\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.2328 | −0.866104 | −0.433052 | − | 0.901369i | \(-0.642563\pi\) | ||||
−0.433052 | + | 0.901369i | \(0.642563\pi\) | |||||||
\(602\) | 6.26936 | 0.255520 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −49.9426 | −2.03213 | ||||||||
\(605\) | 85.5443 | 3.47787 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.3036 | 1.43293 | 0.716465 | − | 0.697623i | \(-0.245759\pi\) | ||||
0.716465 | + | 0.697623i | \(0.245759\pi\) | |||||||
\(608\) | −19.1734 | −0.777583 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 110.627 | 4.47917 | ||||||||
\(611\) | −17.9737 | −0.727136 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.9099 | −1.61195 | −0.805974 | − | 0.591951i | \(-0.798358\pi\) | ||||
−0.805974 | + | 0.591951i | \(0.798358\pi\) | |||||||
\(614\) | 59.5304 | 2.40245 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 59.5009 | 2.39736 | ||||||||
\(617\) | 32.7641 | 1.31903 | 0.659516 | − | 0.751690i | \(-0.270761\pi\) | ||||
0.659516 | + | 0.751690i | \(0.270761\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.3437 | −0.536327 | −0.268164 | − | 0.963373i | \(-0.586417\pi\) | ||||
−0.268164 | + | 0.963373i | \(0.586417\pi\) | |||||||
\(620\) | −3.08763 | −0.124002 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.39047 | 0.296331 | ||||||||
\(623\) | −9.91415 | −0.397202 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.50050 | 0.260020 | ||||||||
\(626\) | −11.1795 | −0.446823 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.7365 | −0.468336 | ||||||||
\(629\) | −0.642669 | −0.0256249 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.08019 | 0.281858 | 0.140929 | − | 0.990020i | \(-0.454991\pi\) | ||||
0.140929 | + | 0.990020i | \(0.454991\pi\) | |||||||
\(632\) | 38.0775 | 1.51464 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −77.4041 | −3.07411 | ||||||||
\(635\) | 3.69380 | 0.146584 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.83862 | −0.270956 | ||||||||
\(638\) | −83.6951 | −3.31352 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 206.992 | 8.18208 | ||||||||
\(641\) | −3.09638 | −0.122300 | −0.0611499 | − | 0.998129i | \(-0.519477\pi\) | ||||
−0.0611499 | + | 0.998129i | \(0.519477\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.9201 | 0.470083 | 0.235041 | − | 0.971985i | \(-0.424477\pi\) | ||||
0.235041 | + | 0.971985i | \(0.424477\pi\) | |||||||
\(644\) | −47.8128 | −1.88409 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.87543 | 0.231166 | ||||||||
\(647\) | 3.56438 | 0.140130 | 0.0700652 | − | 0.997542i | \(-0.477679\pi\) | ||||
0.0700652 | + | 0.997542i | \(0.477679\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.0983 | −1.18146 | ||||||||
\(650\) | −163.766 | −6.42345 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −31.5416 | −1.23527 | ||||||||
\(653\) | 7.64872 | 0.299318 | 0.149659 | − | 0.988738i | \(-0.452182\pi\) | ||||
0.149659 | + | 0.988738i | \(0.452182\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 68.9263 | 2.69317 | ||||||||
\(656\) | −111.867 | −4.36769 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.28119 | 0.283850 | ||||||||
\(659\) | 13.2146 | 0.514768 | 0.257384 | − | 0.966309i | \(-0.417140\pi\) | ||||
0.257384 | + | 0.966309i | \(0.417140\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.55692 | −0.0605572 | −0.0302786 | − | 0.999541i | \(-0.509639\pi\) | ||||
−0.0302786 | + | 0.999541i | \(0.509639\pi\) | |||||||
\(662\) | 77.4256 | 3.00923 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −51.1336 | −1.98437 | ||||||||
\(665\) | −2.68976 | −0.104304 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 43.5517 | 1.68633 | ||||||||
\(668\) | 25.3714 | 0.981649 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 26.8086 | 1.03571 | ||||||||
\(671\) | 63.1840 | 2.43919 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.3157 | −1.43842 | −0.719208 | − | 0.694795i | \(-0.755495\pi\) | ||||
−0.719208 | + | 0.694795i | \(0.755495\pi\) | |||||||
\(674\) | 32.5539 | 1.25393 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 191.620 | 7.37001 | ||||||||
\(677\) | 5.28980 | 0.203303 | 0.101652 | − | 0.994820i | \(-0.467587\pi\) | ||||
0.101652 | + | 0.994820i | \(0.467587\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.08019 | −0.118207 | ||||||||
\(680\) | −109.524 | −4.20006 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.38498 | −0.0913258 | ||||||||
\(683\) | 23.9694 | 0.917163 | 0.458581 | − | 0.888652i | \(-0.348358\pi\) | ||||
0.458581 | + | 0.888652i | \(0.348358\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.7960 | −1.44411 | ||||||||
\(686\) | 2.77035 | 0.105772 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 38.1411 | 1.45411 | ||||||||
\(689\) | −87.9597 | −3.35100 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.7326 | 1.58758 | 0.793791 | − | 0.608191i | \(-0.208104\pi\) | ||||
0.793791 | + | 0.608191i | \(0.208104\pi\) | |||||||
\(692\) | 37.8342 | 1.43824 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 91.2505 | 3.46382 | ||||||||
\(695\) | 22.3946 | 0.849475 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.3314 | 0.732231 | ||||||||
\(698\) | 74.1023 | 2.80481 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 49.0541 | 1.85407 | ||||||||
\(701\) | 37.9876 | 1.43477 | 0.717385 | − | 0.696677i | \(-0.245339\pi\) | ||||
0.717385 | + | 0.696677i | \(0.245339\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.160680 | −0.00606018 | ||||||||
\(704\) | 229.320 | 8.64282 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −58.9078 | −2.21702 | ||||||||
\(707\) | 6.71801 | 0.252657 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.4515 | 1.18118 | 0.590592 | − | 0.806970i | \(-0.298894\pi\) | ||||
0.590592 | + | 0.806970i | \(0.298894\pi\) | |||||||
\(710\) | 36.8563 | 1.38319 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −100.932 | −3.78257 | ||||||||
\(713\) | 1.24105 | 0.0464778 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −147.636 | −5.52129 | ||||||||
\(716\) | −135.518 | −5.06455 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 57.8192 | 2.15779 | ||||||||
\(719\) | −41.6021 | −1.55150 | −0.775748 | − | 0.631043i | \(-0.782627\pi\) | ||||
−0.775748 | + | 0.631043i | \(0.782627\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.9532 | −0.594128 | ||||||||
\(722\) | −51.1676 | −1.90426 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 26.5473 | 0.986624 | ||||||||
\(725\) | −44.6823 | −1.65946 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.5582 | 0.984990 | 0.492495 | − | 0.870315i | \(-0.336085\pi\) | ||||
0.492495 | + | 0.870315i | \(0.336085\pi\) | |||||||
\(728\) | −69.6210 | −2.58033 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −63.2841 | −2.34225 | ||||||||
\(731\) | −6.59103 | −0.243778 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.8971 | −1.17815 | −0.589073 | − | 0.808080i | \(-0.700507\pi\) | ||||
−0.589073 | + | 0.808080i | \(0.700507\pi\) | |||||||
\(734\) | 25.2635 | 0.932493 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −221.845 | −8.17731 | ||||||||
\(737\) | 15.3116 | 0.564008 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.69965 | 0.320022 | 0.160011 | − | 0.987115i | \(-0.448847\pi\) | ||||
0.160011 | + | 0.987115i | \(0.448847\pi\) | |||||||
\(740\) | 4.62539 | 0.170033 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 35.6328 | 1.30812 | ||||||||
\(743\) | −12.8619 | −0.471857 | −0.235928 | − | 0.971770i | \(-0.575813\pi\) | ||||
−0.235928 | + | 0.971770i | \(0.575813\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.9661 | −0.511679 | ||||||||
\(746\) | −50.5922 | −1.85231 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −96.5983 | −3.53198 | ||||||||
\(749\) | −17.3101 | −0.632496 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.2868 | 1.25114 | 0.625571 | − | 0.780167i | \(-0.284866\pi\) | ||||
0.625571 | + | 0.780167i | \(0.284866\pi\) | |||||||
\(752\) | 44.2968 | 1.61534 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 97.9301 | 3.56640 | ||||||||
\(755\) | −32.5080 | −1.18309 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.4358 | 1.76043 | 0.880215 | − | 0.474576i | \(-0.157399\pi\) | ||||
0.880215 | + | 0.474576i | \(0.157399\pi\) | |||||||
\(758\) | −42.7328 | −1.55212 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −27.3833 | −0.993296 | ||||||||
\(761\) | 1.81753 | 0.0658853 | 0.0329427 | − | 0.999457i | \(-0.489512\pi\) | ||||
0.0329427 | + | 0.999457i | \(0.489512\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.73388 | −0.135176 | ||||||||
\(764\) | −117.079 | −4.23577 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.98764 | 0.107948 | ||||||||
\(767\) | 35.2175 | 1.27163 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.2880 | −0.479179 | −0.239590 | − | 0.970874i | \(-0.577013\pi\) | ||||
−0.239590 | + | 0.970874i | \(0.577013\pi\) | |||||||
\(770\) | 59.8080 | 2.15533 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.68646 | −0.132678 | ||||||||
\(773\) | 7.17442 | 0.258046 | 0.129023 | − | 0.991642i | \(-0.458816\pi\) | ||||
0.129023 | + | 0.991642i | \(0.458816\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.27327 | −0.0457373 | ||||||||
\(776\) | −31.3580 | −1.12569 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26.8706 | 0.963357 | ||||||||
\(779\) | 4.83326 | 0.173170 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.0502 | 0.753235 | ||||||||
\(782\) | 67.9814 | 2.43101 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 16.8540 | 0.601930 | ||||||||
\(785\) | −7.63938 | −0.272661 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.0658 | 0.857852 | 0.428926 | − | 0.903340i | \(-0.358892\pi\) | ||||
0.428926 | + | 0.903340i | \(0.358892\pi\) | |||||||
\(788\) | −59.8435 | −2.13184 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 38.2740 | 1.36173 | ||||||||
\(791\) | 5.36995 | 0.190933 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −73.9305 | −2.62535 | ||||||||
\(794\) | −37.3969 | −1.32717 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −109.057 | −3.86544 | ||||||||
\(797\) | −22.2703 | −0.788853 | −0.394427 | − | 0.918927i | \(-0.629057\pi\) | ||||
−0.394427 | + | 0.918927i | \(0.629057\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.65478 | −0.270807 | ||||||||
\(800\) | 227.604 | 8.04702 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −35.9789 | −1.27046 | ||||||||
\(803\) | −36.1442 | −1.27550 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.1218 | −1.09690 | ||||||||
\(806\) | 2.79063 | 0.0982957 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 68.3931 | 2.40606 | ||||||||
\(809\) | 14.4820 | 0.509159 | 0.254580 | − | 0.967052i | \(-0.418063\pi\) | ||||
0.254580 | + | 0.967052i | \(0.418063\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.3208 | −1.17005 | −0.585026 | − | 0.811014i | \(-0.698916\pi\) | ||||
−0.585026 | + | 0.811014i | \(0.698916\pi\) | |||||||
\(812\) | −29.3337 | −1.02941 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.57280 | 0.125227 | ||||||||
\(815\) | −20.5307 | −0.719160 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.64789 | −0.0576525 | ||||||||
\(818\) | −77.5758 | −2.71238 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −139.132 | −4.85869 | ||||||||
\(821\) | 29.5966 | 1.03293 | 0.516464 | − | 0.856309i | \(-0.327248\pi\) | ||||
0.516464 | + | 0.856309i | \(0.327248\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.04541 | −0.175872 | −0.0879359 | − | 0.996126i | \(-0.528027\pi\) | ||||
−0.0879359 | + | 0.996126i | \(0.528027\pi\) | |||||||
\(824\) | −162.413 | −5.65791 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.2667 | −0.496404 | ||||||||
\(827\) | 4.98336 | 0.173289 | 0.0866443 | − | 0.996239i | \(-0.472386\pi\) | ||||
0.0866443 | + | 0.996239i | \(0.472386\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.2886 | −0.565728 | −0.282864 | − | 0.959160i | \(-0.591285\pi\) | ||||
−0.282864 | + | 0.959160i | \(0.591285\pi\) | |||||||
\(830\) | −51.3975 | −1.78403 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −268.323 | −9.30243 | ||||||||
\(833\) | −2.91249 | −0.100912 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.5145 | 0.571507 | ||||||||
\(836\) | −24.1516 | −0.835299 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 49.5972 | 1.71331 | ||||||||
\(839\) | 17.4021 | 0.600787 | 0.300393 | − | 0.953815i | \(-0.402882\pi\) | ||||
0.300393 | + | 0.953815i | \(0.402882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.28059 | −0.0786410 | ||||||||
\(842\) | −13.9119 | −0.479435 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.54569 | −0.156469 | ||||||||
\(845\) | 124.727 | 4.29075 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.1589 | 0.795749 | ||||||||
\(848\) | 216.780 | 7.44426 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −69.7463 | −2.39228 | ||||||||
\(851\) | −1.85915 | −0.0637308 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.2893 | −0.420777 | −0.210389 | − | 0.977618i | \(-0.567473\pi\) | ||||
−0.210389 | + | 0.977618i | \(0.567473\pi\) | |||||||
\(854\) | 29.9495 | 1.02485 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −176.226 | −6.02329 | ||||||||
\(857\) | −6.88542 | −0.235202 | −0.117601 | − | 0.993061i | \(-0.537520\pi\) | ||||
−0.117601 | + | 0.993061i | \(0.537520\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.4083 | −0.901039 | −0.450520 | − | 0.892767i | \(-0.648761\pi\) | ||||
−0.450520 | + | 0.892767i | \(0.648761\pi\) | |||||||
\(860\) | 47.4367 | 1.61758 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.3447 | 0.931365 | ||||||||
\(863\) | 15.6362 | 0.532261 | 0.266131 | − | 0.963937i | \(-0.414255\pi\) | ||||
0.266131 | + | 0.963937i | \(0.414255\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.6266 | 0.837331 | ||||||||
\(866\) | −57.1579 | −1.94230 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.835896 | −0.0283722 | ||||||||
\(869\) | 21.8599 | 0.741546 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.9158 | −0.607053 | ||||||||
\(872\) | −38.0130 | −1.28728 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16.9968 | 0.574924 | ||||||||
\(875\) | 13.4607 | 0.455056 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.24374 | −0.143301 | −0.0716504 | − | 0.997430i | \(-0.522827\pi\) | ||||
−0.0716504 | + | 0.997430i | \(0.522827\pi\) | |||||||
\(878\) | 34.6920 | 1.17080 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 363.856 | 12.2656 | ||||||||
\(881\) | −15.7838 | −0.531768 | −0.265884 | − | 0.964005i | \(-0.585664\pi\) | ||||
−0.265884 | + | 0.964005i | \(0.585664\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.4214 | 1.12472 | 0.562360 | − | 0.826892i | \(-0.309893\pi\) | ||||
0.562360 | + | 0.826892i | \(0.309893\pi\) | |||||||
\(884\) | 113.028 | 3.80154 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −48.6390 | −1.63406 | ||||||||
\(887\) | 7.62418 | 0.255995 | 0.127998 | − | 0.991774i | \(-0.459145\pi\) | ||||
0.127998 | + | 0.991774i | \(0.459145\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −101.453 | −3.40070 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −151.436 | −5.07045 | ||||||||
\(893\) | −1.91385 | −0.0640447 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −88.2099 | −2.94853 | ||||||||
\(896\) | 56.0377 | 1.87209 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −42.0342 | −1.40270 | ||||||||
\(899\) | 0.761400 | 0.0253941 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.4610 | −1.24801 | ||||||||
\(902\) | −107.470 | −3.57835 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 54.6691 | 1.81827 | ||||||||
\(905\) | 17.2799 | 0.574403 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.2359 | −0.738331 | −0.369165 | − | 0.929364i | \(-0.620356\pi\) | ||||
−0.369165 | + | 0.929364i | \(0.620356\pi\) | |||||||
\(908\) | 31.9122 | 1.05904 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −69.9803 | −2.31983 | ||||||||
\(911\) | −7.49497 | −0.248319 | −0.124160 | − | 0.992262i | \(-0.539624\pi\) | ||||
−0.124160 | + | 0.992262i | \(0.539624\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.3553 | −0.971519 | ||||||||
\(914\) | 24.1840 | 0.799936 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 170.706 | 5.64028 | ||||||||
\(917\) | 18.6600 | 0.616208 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.1185 | −1.38936 | −0.694680 | − | 0.719319i | \(-0.744454\pi\) | ||||
−0.694680 | + | 0.719319i | \(0.744454\pi\) | |||||||
\(920\) | −316.837 | −10.4458 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −108.093 | −3.55987 | ||||||||
\(923\) | −24.6305 | −0.810722 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.90741 | 0.0627153 | ||||||||
\(926\) | 64.1076 | 2.10671 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −136.104 | −4.46784 | ||||||||
\(929\) | −15.2870 | −0.501549 | −0.250775 | − | 0.968046i | \(-0.580685\pi\) | ||||
−0.250775 | + | 0.968046i | \(0.580685\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.728183 | −0.0238652 | ||||||||
\(932\) | 142.281 | 4.66056 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15.9724 | 0.522632 | ||||||||
\(935\) | −62.8767 | −2.05629 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.6073 | 0.346526 | 0.173263 | − | 0.984876i | \(-0.444569\pi\) | ||||
0.173263 | + | 0.984876i | \(0.444569\pi\) | |||||||
\(938\) | 7.25774 | 0.236974 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 55.0927 | 1.79693 | ||||||||
\(941\) | 40.6002 | 1.32353 | 0.661764 | − | 0.749713i | \(-0.269808\pi\) | ||||
0.661764 | + | 0.749713i | \(0.269808\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 55.9231 | 1.82111 | ||||||||
\(944\) | −86.7950 | −2.82494 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 36.6416 | 1.19132 | ||||||||
\(947\) | −42.6979 | −1.38749 | −0.693747 | − | 0.720219i | \(-0.744041\pi\) | ||||
−0.693747 | + | 0.720219i | \(0.744041\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.2917 | 1.37285 | ||||||||
\(950\) | −17.4380 | −0.565764 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −29.6508 | −0.960988 | ||||||||
\(953\) | 29.4085 | 0.952636 | 0.476318 | − | 0.879273i | \(-0.341971\pi\) | ||||
0.476318 | + | 0.879273i | \(0.341971\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −76.2078 | −2.46603 | ||||||||
\(956\) | 29.0238 | 0.938698 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −52.3395 | −1.69101 | ||||||||
\(959\) | −10.2323 | −0.330418 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9783 | −0.999300 | ||||||||
\(962\) | −4.18047 | −0.134784 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −97.7016 | −3.14676 | ||||||||
\(965\) | −2.39955 | −0.0772441 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.9006 | −1.21880 | −0.609400 | − | 0.792863i | \(-0.708590\pi\) | ||||
−0.609400 | + | 0.792863i | \(0.708590\pi\) | |||||||
\(968\) | 235.771 | 7.57795 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −31.5199 | −1.01204 | ||||||||
\(971\) | 18.8576 | 0.605170 | 0.302585 | − | 0.953122i | \(-0.402150\pi\) | ||||
0.302585 | + | 0.953122i | \(0.402150\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.06275 | 0.194363 | ||||||||
\(974\) | −31.1290 | −0.997438 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 182.205 | 5.83223 | ||||||||
\(977\) | −1.39022 | −0.0444772 | −0.0222386 | − | 0.999753i | \(-0.507079\pi\) | ||||
−0.0222386 | + | 0.999753i | \(0.507079\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −57.9439 | −1.85189 | ||||||||
\(980\) | 20.9617 | 0.669596 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 79.6477 | 2.54166 | ||||||||
\(983\) | −8.63107 | −0.275288 | −0.137644 | − | 0.990482i | \(-0.543953\pi\) | ||||
−0.137644 | + | 0.990482i | \(0.543953\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −38.9527 | −1.24114 | ||||||||
\(986\) | 41.7073 | 1.32823 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 28.2593 | 0.899049 | ||||||||
\(989\) | −19.0669 | −0.606292 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.1925 | −1.40382 | −0.701911 | − | 0.712264i | \(-0.747670\pi\) | ||||
−0.701911 | + | 0.712264i | \(0.747670\pi\) | |||||||
\(992\) | −3.87844 | −0.123141 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.97789 | 0.316479 | ||||||||
\(995\) | −70.9865 | −2.25042 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.2697 | 0.990320 | 0.495160 | − | 0.868802i | \(-0.335109\pi\) | ||||
0.495160 | + | 0.868802i | \(0.335109\pi\) | |||||||
\(998\) | 14.7944 | 0.468308 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.u.1.18 | 18 | ||
3.2 | odd | 2 | 2667.2.a.p.1.1 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.p.1.1 | ✓ | 18 | 3.2 | odd | 2 | ||
8001.2.a.u.1.18 | 18 | 1.1 | even | 1 | trivial |