Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 31 x^{10} + 131 x^{9} + 309 x^{8} - 1453 x^{7} - 1072 x^{6} + 6350 x^{5} + \cdots + 3008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(3.59055\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.59055 | 1.60574 | 0.802872 | − | 0.596151i | \(-0.203304\pi\) | ||||
0.802872 | + | 0.596151i | \(0.203304\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.10828 | 1.55279 | 0.776393 | − | 0.630250i | \(-0.217047\pi\) | ||||
0.776393 | + | 0.630250i | \(0.217047\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.62131 | 0.488842 | 0.244421 | − | 0.969669i | \(-0.421402\pi\) | ||||
0.244421 | + | 0.969669i | \(0.421402\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.55250 | 1.53999 | 0.769993 | − | 0.638052i | \(-0.220260\pi\) | ||||
0.769993 | + | 0.638052i | \(0.220260\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.59055 | 0.927077 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.51714 | −1.33810 | −0.669051 | − | 0.743216i | \(-0.733299\pi\) | ||||
−0.669051 | + | 0.743216i | \(0.733299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.688902 | −0.158045 | −0.0790225 | − | 0.996873i | \(-0.525180\pi\) | ||||
−0.0790225 | + | 0.996873i | \(0.525180\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.10828 | 0.896501 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.57662 | −0.954291 | −0.477145 | − | 0.878824i | \(-0.658329\pi\) | ||||
−0.477145 | + | 0.878824i | \(0.658329\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.89208 | 1.57842 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.57239 | 0.663376 | 0.331688 | − | 0.943389i | \(-0.392382\pi\) | ||||
0.331688 | + | 0.943389i | \(0.392382\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.18724 | 1.29087 | 0.645433 | − | 0.763817i | \(-0.276677\pi\) | ||||
0.645433 | + | 0.763817i | \(0.276677\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.62131 | 0.282233 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.7510 | 2.49338 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0764 | −1.65655 | −0.828273 | − | 0.560325i | \(-0.810676\pi\) | ||||
−0.828273 | + | 0.560325i | \(0.810676\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.55250 | 0.889111 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.17469 | −1.43285 | −0.716423 | − | 0.697666i | \(-0.754222\pi\) | ||||
−0.716423 | + | 0.697666i | \(0.754222\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.89063 | 0.440817 | 0.220408 | − | 0.975408i | \(-0.429261\pi\) | ||||
0.220408 | + | 0.975408i | \(0.429261\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.59055 | 0.535248 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.70322 | −0.831901 | −0.415950 | − | 0.909387i | \(-0.636551\pi\) | ||||
−0.415950 | + | 0.909387i | \(0.636551\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.87799 | 1.41114 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.51714 | −0.772554 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.787842 | −0.108218 | −0.0541092 | − | 0.998535i | \(-0.517232\pi\) | ||||
−0.0541092 | + | 0.998535i | \(0.517232\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.82139 | 0.784956 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.688902 | −0.0912473 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.75855 | −0.359132 | −0.179566 | − | 0.983746i | \(-0.557469\pi\) | ||||
−0.179566 | + | 0.983746i | \(0.557469\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.60053 | −0.204927 | −0.102464 | − | 0.994737i | \(-0.532673\pi\) | ||||
−0.102464 | + | 0.994737i | \(0.532673\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.10828 | 0.517595 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19.9365 | 2.47282 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.32502 | 0.894893 | 0.447447 | − | 0.894311i | \(-0.352333\pi\) | ||||
0.447447 | + | 0.894311i | \(0.352333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.57662 | −0.550960 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.98319 | −0.828752 | −0.414376 | − | 0.910106i | \(-0.636000\pi\) | ||||
−0.414376 | + | 0.910106i | \(0.636000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.181729 | 0.0212698 | 0.0106349 | − | 0.999943i | \(-0.496615\pi\) | ||||
0.0106349 | + | 0.999943i | \(0.496615\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.89208 | 0.911299 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.66079 | 0.759067 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.9222 | −1.56637 | −0.783184 | − | 0.621790i | \(-0.786406\pi\) | ||||
−0.783184 | + | 0.621790i | \(0.786406\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.82200 | 0.419519 | 0.209759 | − | 0.977753i | \(-0.432732\pi\) | ||||
0.209759 | + | 0.977753i | \(0.432732\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19.8096 | −2.14865 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.57239 | 0.383000 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.78217 | −0.718908 | −0.359454 | − | 0.933163i | \(-0.617037\pi\) | ||||
−0.359454 | + | 0.933163i | \(0.617037\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 22.8112 | 2.39127 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.18724 | 0.745282 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.47354 | −0.253780 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.41920 | −0.753306 | −0.376653 | − | 0.926354i | \(-0.622925\pi\) | ||||
−0.376653 | + | 0.926354i | \(0.622925\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.62131 | 0.162947 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −19.3734 | −1.92773 | −0.963863 | − | 0.266399i | \(-0.914166\pi\) | ||||
−0.963863 | + | 0.266399i | \(0.914166\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.04851 | −0.201846 | −0.100923 | − | 0.994894i | \(-0.532180\pi\) | ||||
−0.100923 | + | 0.994894i | \(0.532180\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.7510 | 1.43955 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.805768 | 0.0778965 | 0.0389482 | − | 0.999241i | \(-0.487599\pi\) | ||||
0.0389482 | + | 0.999241i | \(0.487599\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.62091 | 0.825733 | 0.412867 | − | 0.910791i | \(-0.364528\pi\) | ||||
0.412867 | + | 0.910791i | \(0.364528\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0764 | −0.956407 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.93599 | 0.464339 | 0.232169 | − | 0.972675i | \(-0.425418\pi\) | ||||
0.232169 | + | 0.972675i | \(0.425418\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.4326 | −1.53235 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.55250 | 0.513329 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −22.6660 | −2.07778 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.37136 | −0.761033 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.17469 | −0.827254 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.3842 | 0.928787 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.3106 | −1.09239 | −0.546196 | − | 0.837658i | \(-0.683925\pi\) | ||||
−0.546196 | + | 0.837658i | \(0.683925\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.89063 | 0.254506 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.4098 | 1.43373 | 0.716867 | − | 0.697210i | \(-0.245576\pi\) | ||||
0.716867 | + | 0.697210i | \(0.245576\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.83021 | −0.245410 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.59055 | 0.309026 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.2690 | −1.38996 | −0.694979 | − | 0.719030i | \(-0.744586\pi\) | ||||
−0.694979 | + | 0.719030i | \(0.744586\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.33754 | −0.452724 | −0.226362 | − | 0.974043i | \(-0.572683\pi\) | ||||
−0.226362 | + | 0.974043i | \(0.572683\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.70322 | −0.480298 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.00230 | 0.752810 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.8269 | 1.06521 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.87799 | 0.814723 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.27063 | −0.759480 | −0.379740 | − | 0.925093i | \(-0.623986\pi\) | ||||
−0.379740 | + | 0.925093i | \(0.623986\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.4894 | −1.66741 | −0.833703 | − | 0.552213i | \(-0.813784\pi\) | ||||
−0.833703 | + | 0.552213i | \(0.813784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.51714 | −0.446034 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.8062 | 2.07280 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.90511 | −0.311662 | −0.155831 | − | 0.987784i | \(-0.549805\pi\) | ||||
−0.155831 | + | 0.987784i | \(0.549805\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.787842 | −0.0624799 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.8020 | −1.48181 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.1543 | −1.03032 | −0.515161 | − | 0.857094i | \(-0.672268\pi\) | ||||
−0.515161 | + | 0.857094i | \(0.672268\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.82139 | 0.453195 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.8302 | 1.37156 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.688902 | −0.0526817 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.4082 | 0.867351 | 0.433676 | − | 0.901069i | \(-0.357216\pi\) | ||||
0.433676 | + | 0.901069i | \(0.357216\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 32.4229 | 2.45094 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.75855 | −0.207345 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.7878 | 1.47901 | 0.739503 | − | 0.673153i | \(-0.235060\pi\) | ||||
0.739503 | + | 0.673153i | \(0.235060\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.54242 | 0.411965 | 0.205982 | − | 0.978556i | \(-0.433961\pi\) | ||||
0.205982 | + | 0.978556i | \(0.433961\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.60053 | −0.118315 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −36.1798 | −2.65999 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.94497 | −0.654121 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.10828 | 0.298834 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.3823 | 1.25774 | 0.628871 | − | 0.777510i | \(-0.283517\pi\) | ||||
0.628871 | + | 0.777510i | \(0.283517\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.1587 | −0.731239 | −0.365619 | − | 0.930765i | \(-0.619143\pi\) | ||||
−0.365619 | + | 0.930765i | \(0.619143\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 19.9365 | 1.42769 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.6909 | 0.904193 | 0.452096 | − | 0.891969i | \(-0.350676\pi\) | ||||
0.452096 | + | 0.891969i | \(0.350676\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 27.3399 | 1.93808 | 0.969038 | − | 0.246913i | \(-0.0794161\pi\) | ||||
0.969038 | + | 0.246913i | \(0.0794161\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.32502 | 0.516667 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.6764 | 1.03008 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −32.9422 | −2.30078 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.57662 | −0.318097 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.11692 | −0.0772591 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.6413 | 1.21448 | 0.607239 | − | 0.794519i | \(-0.292277\pi\) | ||||
0.607239 | + | 0.794519i | \(0.292277\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.98319 | −0.478480 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.3790 | 0.707839 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 29.5272 | 2.00444 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.181729 | 0.0122801 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −30.6339 | −2.06066 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.6260 | 1.38122 | 0.690608 | − | 0.723229i | \(-0.257343\pi\) | ||||
0.690608 | + | 0.723229i | \(0.257343\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.89208 | 0.526138 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.16425 | −0.409135 | −0.204568 | − | 0.978852i | \(-0.565579\pi\) | ||||
−0.204568 | + | 0.978852i | \(0.565579\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.4392 | −1.28458 | −0.642289 | − | 0.766462i | \(-0.722015\pi\) | ||||
−0.642289 | + | 0.766462i | \(0.722015\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.66079 | 0.438248 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.8065 | 1.29757 | 0.648783 | − | 0.760973i | \(-0.275278\pi\) | ||||
0.648783 | + | 0.760973i | \(0.275278\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.4777 | −1.33582 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.9222 | −0.904343 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.11360 | 0.0720327 | 0.0360164 | − | 0.999351i | \(-0.488533\pi\) | ||||
0.0360164 | + | 0.999351i | \(0.488533\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.4165 | −1.70164 | −0.850820 | − | 0.525458i | \(-0.823894\pi\) | ||||
−0.850820 | + | 0.525458i | \(0.823894\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 35.4675 | 2.26593 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.82513 | −0.243387 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.82200 | 0.242209 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.81268 | 0.114415 | 0.0572077 | − | 0.998362i | \(-0.481780\pi\) | ||||
0.0572077 | + | 0.998362i | \(0.481780\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.42010 | −0.466498 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19.8096 | −1.24052 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.84493 | 0.115084 | 0.0575418 | − | 0.998343i | \(-0.481674\pi\) | ||||
0.0575418 | + | 0.998343i | \(0.481674\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −41.3966 | −2.57226 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.57239 | 0.221125 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.50485 | −0.462769 | −0.231384 | − | 0.972862i | \(-0.574326\pi\) | ||||
−0.231384 | + | 0.972862i | \(0.574326\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.82879 | −0.173771 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.78217 | −0.415062 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.31805 | −0.385218 | −0.192609 | − | 0.981276i | \(-0.561695\pi\) | ||||
−0.192609 | + | 0.981276i | \(0.561695\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.88653 | 0.539818 | 0.269909 | − | 0.962886i | \(-0.413006\pi\) | ||||
0.269909 | + | 0.962886i | \(0.413006\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 22.8112 | 1.38060 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.7955 | 0.771596 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.3868 | 1.82576 | 0.912882 | − | 0.408223i | \(-0.133851\pi\) | ||||
0.912882 | + | 0.408223i | \(0.133851\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.18724 | 0.430289 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.0587 | −0.898330 | −0.449165 | − | 0.893449i | \(-0.648278\pi\) | ||||
−0.449165 | + | 0.893449i | \(0.648278\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.8690 | 1.18109 | 0.590546 | − | 0.807004i | \(-0.298912\pi\) | ||||
0.590546 | + | 0.807004i | \(0.298912\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.47354 | −0.146520 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −37.6922 | −2.22490 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.4388 | 0.790517 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.41920 | −0.434921 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.68694 | 0.156973 | 0.0784864 | − | 0.996915i | \(-0.474991\pi\) | ||||
0.0784864 | + | 0.996915i | \(0.474991\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.90472 | −0.576675 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.62131 | 0.0940778 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −25.4117 | −1.46959 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.8755 | 0.684493 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.3734 | −1.11297 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.74680 | −0.329061 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.8605 | 1.19057 | 0.595284 | − | 0.803515i | \(-0.297039\pi\) | ||||
0.595284 | + | 0.803515i | \(0.297039\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.04851 | −0.116536 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.4158 | −0.590627 | −0.295313 | − | 0.955400i | \(-0.595424\pi\) | ||||
−0.295313 | + | 0.955400i | \(0.595424\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.9992 | 1.75218 | 0.876089 | − | 0.482149i | \(-0.160144\pi\) | ||||
0.876089 | + | 0.482149i | \(0.160144\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.7510 | 0.831125 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.8470 | −1.39555 | −0.697774 | − | 0.716318i | \(-0.745826\pi\) | ||||
−0.697774 | + | 0.716318i | \(0.745826\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.79194 | 0.324286 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.805768 | 0.0449736 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.80077 | 0.211480 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 43.8207 | 2.43074 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.62091 | 0.476737 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −23.4305 | −1.29176 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.7919 | −0.977930 | −0.488965 | − | 0.872303i | \(-0.662625\pi\) | ||||
−0.488965 | + | 0.872303i | \(0.662625\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.0764 | −0.552182 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.3009 | 1.43697 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.5764 | 1.66560 | 0.832802 | − | 0.553570i | \(-0.186735\pi\) | ||||
0.832802 | + | 0.553570i | \(0.186735\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.93599 | 0.268086 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.6527 | 0.631030 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.8236 | 0.638414 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.4326 | −0.884701 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.2533 | 0.926207 | 0.463104 | − | 0.886304i | \(-0.346736\pi\) | ||||
0.463104 | + | 0.886304i | \(0.346736\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.6088 | −0.567874 | −0.283937 | − | 0.958843i | \(-0.591641\pi\) | ||||
−0.283937 | + | 0.958843i | \(0.591641\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.55250 | 0.296370 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.8287 | −1.37472 | −0.687362 | − | 0.726315i | \(-0.741231\pi\) | ||||
−0.687362 | + | 0.726315i | \(0.741231\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.0735 | −1.33076 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22.6660 | −1.19961 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.5743 | −0.874759 | −0.437379 | − | 0.899277i | \(-0.644093\pi\) | ||||
−0.437379 | + | 0.899277i | \(0.644093\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5254 | −0.975022 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.37136 | −0.439383 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.652509 | 0.0341539 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.5959 | 1.33610 | 0.668049 | − | 0.744117i | \(-0.267130\pi\) | ||||
0.668049 | + | 0.744117i | \(0.267130\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.17469 | −0.477615 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.23668 | −0.168040 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.5687 | −1.22034 | −0.610170 | − | 0.792270i | \(-0.708899\pi\) | ||||
−0.610170 | + | 0.792270i | \(0.708899\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.3842 | 0.536236 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.8357 | 1.02159 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.7128 | 1.01258 | 0.506289 | − | 0.862364i | \(-0.331017\pi\) | ||||
0.506289 | + | 0.862364i | \(0.331017\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.3106 | −0.630693 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.8187 | −0.552811 | −0.276406 | − | 0.961041i | \(-0.589143\pi\) | ||||
−0.276406 | + | 0.961041i | \(0.589143\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 23.9159 | 1.21887 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.89063 | 0.146939 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 36.8399 | 1.86786 | 0.933929 | − | 0.357458i | \(-0.116356\pi\) | ||||
0.933929 | + | 0.357458i | \(0.116356\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.2498 | 1.27694 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.4098 | 0.827767 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −49.9883 | −2.51519 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.3928 | 1.47518 | 0.737591 | − | 0.675247i | \(-0.235963\pi\) | ||||
0.737591 | + | 0.675247i | \(0.235963\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.83021 | −0.141688 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.4047 | 1.36853 | 0.684263 | − | 0.729235i | \(-0.260124\pi\) | ||||
0.684263 | + | 0.729235i | \(0.260124\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 39.9071 | 1.98792 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.59055 | 0.178416 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.3369 | −0.809790 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.9808 | 1.68024 | 0.840120 | − | 0.542401i | \(-0.182484\pi\) | ||||
0.840120 | + | 0.542401i | \(0.182484\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.2690 | −0.802492 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.3329 | −0.557655 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.7231 | 0.673640 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.33754 | −0.261381 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.5038 | 0.757408 | 0.378704 | − | 0.925518i | \(-0.376370\pi\) | ||||
0.378704 | + | 0.925518i | \(0.376370\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.4215 | 1.04402 | 0.522010 | − | 0.852939i | \(-0.325182\pi\) | ||||
0.522010 | + | 0.852939i | \(0.325182\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.70322 | −0.277300 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −43.5417 | −2.11208 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.57545 | −0.318208 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.00230 | 0.434635 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.5013 | 1.46920 | 0.734598 | − | 0.678502i | \(-0.237371\pi\) | ||||
0.734598 | + | 0.678502i | \(0.237371\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.4355 | −1.31847 | −0.659234 | − | 0.751938i | \(-0.729119\pi\) | ||||
−0.659234 | + | 0.751938i | \(0.729119\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.8269 | 0.615000 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.15284 | 0.150821 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.281832 | −0.0134511 | −0.00672556 | − | 0.999977i | \(-0.502141\pi\) | ||||
−0.00672556 | + | 0.999977i | \(0.502141\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.87799 | 0.470380 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.9068 | −0.565708 | −0.282854 | − | 0.959163i | \(-0.591281\pi\) | ||||
−0.282854 | + | 0.959163i | \(0.591281\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.3517 | −1.15438 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.27063 | −0.438486 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.2052 | 0.859158 | 0.429579 | − | 0.903029i | \(-0.358662\pi\) | ||||
0.429579 | + | 0.903029i | \(0.358662\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.8750 | −0.700436 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.4894 | −0.962678 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 81.9050 | 3.83976 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.31943 | −0.435945 | −0.217972 | − | 0.975955i | \(-0.569944\pi\) | ||||
−0.217972 | + | 0.975955i | \(0.569944\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.51714 | −0.257518 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.0465 | −1.16653 | −0.583266 | − | 0.812281i | \(-0.698225\pi\) | ||||
−0.583266 | + | 0.812281i | \(0.698225\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.497940 | 0.0231412 | 0.0115706 | − | 0.999933i | \(-0.496317\pi\) | ||||
0.0115706 | + | 0.999933i | \(0.496317\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25.8062 | 1.19673 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.1274 | 1.02393 | 0.511966 | − | 0.859006i | \(-0.328917\pi\) | ||||
0.511966 | + | 0.859006i | \(0.328917\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.0932 | 1.38958 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.90511 | −0.179938 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.68659 | 0.215490 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.43687 | −0.249461 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.787842 | −0.0360728 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.8134 | 1.31652 | 0.658259 | − | 0.752792i | \(-0.271293\pi\) | ||||
0.658259 | + | 0.752792i | \(0.271293\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −55.9491 | −2.55106 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.8020 | −0.855523 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.6390 | −1.20962 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.03643 | 0.137594 | 0.0687968 | − | 0.997631i | \(-0.478084\pi\) | ||||
0.0687968 | + | 0.997631i | \(0.478084\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.1543 | −0.594856 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.6390 | 0.931425 | 0.465713 | − | 0.884936i | \(-0.345798\pi\) | ||||
0.465713 | + | 0.884936i | \(0.345798\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.7094 | −0.887665 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.82139 | 0.261652 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −28.6889 | −1.28687 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.8144 | 1.11084 | 0.555422 | − | 0.831568i | \(-0.312557\pi\) | ||||
0.555422 | + | 0.831568i | \(0.312557\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.0868793 | −0.00387375 | −0.00193688 | − | 0.999998i | \(-0.500617\pi\) | ||||
−0.00193688 | + | 0.999998i | \(0.500617\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −69.5613 | −3.09544 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.8302 | 0.791869 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.2337 | 1.56170 | 0.780852 | − | 0.624716i | \(-0.214785\pi\) | ||||
0.780852 | + | 0.624716i | \(0.214785\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.746596 | 0.0330274 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.688902 | −0.0304158 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.35530 | −0.324113 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.24667 | −0.406668 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.4082 | 0.500766 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.7270 | −0.864257 | −0.432129 | − | 0.901812i | \(-0.642237\pi\) | ||||
−0.432129 | + | 0.901812i | \(0.642237\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.8934 | 1.17597 | 0.587984 | − | 0.808872i | \(-0.299922\pi\) | ||||
0.587984 | + | 0.808872i | \(0.299922\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 32.4229 | 1.41505 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −39.6530 | −1.72731 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.05457 | −0.0893290 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.75855 | −0.119711 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −50.9425 | −2.20656 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.89315 | 0.125082 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.7878 | 0.853905 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.0153 | 0.689826 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.5773 | 0.712712 | 0.356356 | − | 0.934350i | \(-0.384019\pi\) | ||||
0.356356 | + | 0.934350i | \(0.384019\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.54242 | 0.237848 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.9538 | 1.32592 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.8486 | 1.01969 | 0.509846 | − | 0.860266i | \(-0.329702\pi\) | ||||
0.509846 | + | 0.860266i | \(0.329702\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.60053 | −0.0683091 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.46103 | −0.104843 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −57.1963 | −2.43223 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −36.1798 | −1.53575 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −35.7962 | −1.51673 | −0.758367 | − | 0.651828i | \(-0.774002\pi\) | ||||
−0.758367 | + | 0.651828i | \(0.774002\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0502 | 0.678851 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.94497 | −0.377657 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.8666 | −0.795131 | −0.397565 | − | 0.917574i | \(-0.630145\pi\) | ||||
−0.397565 | + | 0.917574i | \(0.630145\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.7229 | 0.745609 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.10828 | 0.172532 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.0694 | −0.841353 | −0.420677 | − | 0.907211i | \(-0.638207\pi\) | ||||
−0.420677 | + | 0.907211i | \(0.638207\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.5976 | 1.57341 | 0.786706 | − | 0.617328i | \(-0.211785\pi\) | ||||
0.786706 | + | 0.617328i | \(0.211785\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.3823 | 0.726158 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −36.1190 | −1.50627 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.4397 | −1.10070 | −0.550349 | − | 0.834934i | \(-0.685506\pi\) | ||||
−0.550349 | + | 0.834934i | \(0.685506\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.1587 | −0.422181 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.7018 | 0.651422 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.27733 | −0.0529017 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.9365 | 0.824275 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.6050 | −1.51085 | −0.755426 | − | 0.655234i | \(-0.772570\pi\) | ||||
−0.755426 | + | 0.655234i | \(0.772570\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.95130 | −0.204015 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.6909 | 0.522036 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.38597 | −0.385436 | −0.192718 | − | 0.981254i | \(-0.561730\pi\) | ||||
−0.192718 | + | 0.981254i | \(0.561730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −81.3833 | −3.33639 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 27.3399 | 1.11895 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.1060 | 1.63869 | 0.819344 | − | 0.573303i | \(-0.194338\pi\) | ||||
0.819344 | + | 0.573303i | \(0.194338\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.0025 | 1.26462 | 0.632309 | − | 0.774716i | \(-0.282107\pi\) | ||||
0.632309 | + | 0.774716i | \(0.282107\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.32502 | 0.298298 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.0578 | −1.22202 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.5512 | −0.834147 | −0.417074 | − | 0.908873i | \(-0.636944\pi\) | ||||
−0.417074 | + | 0.908873i | \(0.636944\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.6764 | 0.594717 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.6671 | −1.28112 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.7012 | 1.48235 | 0.741174 | − | 0.671313i | \(-0.234269\pi\) | ||||
0.741174 | + | 0.671313i | \(0.234269\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −32.9422 | −1.32836 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.21525 | −0.290475 | −0.145238 | − | 0.989397i | \(-0.546395\pi\) | ||||
−0.145238 | + | 0.989397i | \(0.546395\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.96526 | 0.0789904 | 0.0394952 | − | 0.999220i | \(-0.487425\pi\) | ||||
0.0394952 | + | 0.999220i | \(0.487425\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.57662 | −0.183653 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −27.8631 | −1.11631 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.17550 | −0.0870202 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.11692 | −0.0446056 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 55.5927 | 2.21663 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.5520 | −0.857970 | −0.428985 | − | 0.903312i | \(-0.641129\pi\) | ||||
−0.428985 | + | 0.903312i | \(0.641129\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.6413 | 0.701180 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −44.2020 | −1.75410 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 54.8475 | 2.17314 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.98319 | −0.276251 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.4228 | −0.648660 | −0.324330 | − | 0.945944i | \(-0.605139\pi\) | ||||
−0.324330 | + | 0.945944i | \(0.605139\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.24263 | 0.0490045 | 0.0245023 | − | 0.999700i | \(-0.492200\pi\) | ||||
0.0245023 | + | 0.999700i | \(0.492200\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.3790 | 0.408671 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.8033 | 1.28963 | 0.644816 | − | 0.764338i | \(-0.276934\pi\) | ||||
0.644816 | + | 0.764338i | \(0.276934\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.47245 | −0.175559 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.5272 | 1.15726 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.3674 | 0.405707 | 0.202854 | − | 0.979209i | \(-0.434978\pi\) | ||||
0.202854 | + | 0.979209i | \(0.434978\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 58.9204 | 2.30221 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.181729 | 0.00708994 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.4077 | −1.53511 | −0.767554 | − | 0.640984i | \(-0.778526\pi\) | ||||
−0.767554 | + | 0.640984i | \(0.778526\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.3055 | −1.17875 | −0.589374 | − | 0.807861i | \(-0.700625\pi\) | ||||
−0.589374 | + | 0.807861i | \(0.700625\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −30.6339 | −1.18972 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.1620 | −0.394066 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.3495 | −0.633053 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.6260 | 0.797445 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.59496 | −0.100177 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.8516 | −0.533940 | −0.266970 | − | 0.963705i | \(-0.586022\pi\) | ||||
−0.266970 | + | 0.963705i | \(0.586022\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.89208 | 0.303766 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.5715 | −0.982791 | −0.491396 | − | 0.870936i | \(-0.663513\pi\) | ||||
−0.491396 | + | 0.870936i | \(0.663513\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.4802 | −1.16972 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.16425 | −0.236214 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −44.9178 | −1.71873 | −0.859365 | − | 0.511362i | \(-0.829141\pi\) | ||||
−0.859365 | + | 0.511362i | \(0.829141\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −58.4148 | −2.23192 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.4392 | −0.741652 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.37449 | −0.166655 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.52688 | 0.248294 | 0.124147 | − | 0.992264i | \(-0.460381\pi\) | ||||
0.124147 | + | 0.992264i | \(0.460381\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.66079 | 0.253022 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.1647 | −0.726960 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 50.6180 | 1.91729 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.8065 | 0.749151 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.51986 | 0.208482 | 0.104241 | − | 0.994552i | \(-0.466759\pi\) | ||||
0.104241 | + | 0.994552i | \(0.466759\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.94164 | 0.261809 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −20.4777 | −0.771236 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −79.5914 | −2.99334 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.8699 | −1.64757 | −0.823785 | − | 0.566902i | \(-0.808142\pi\) | ||||
−0.823785 | + | 0.566902i | \(0.808142\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.9222 | −0.522123 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −32.8932 | −1.23186 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.3233 | 1.20882 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.11360 | 0.0415881 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.0080 | −0.596997 | −0.298499 | − | 0.954410i | \(-0.596486\pi\) | ||||
−0.298499 | + | 0.954410i | \(0.596486\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.41587 | −0.313423 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.4165 | −0.982442 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.1936 | 1.04708 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.8776 | 1.33063 | 0.665313 | − | 0.746565i | \(-0.268298\pi\) | ||||
0.665313 | + | 0.746565i | \(0.268298\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.9480 | −0.589857 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.6831 | −1.31798 | −0.658992 | − | 0.752150i | \(-0.729017\pi\) | ||||
−0.658992 | + | 0.752150i | \(0.729017\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 35.4675 | 1.30824 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.8761 | 0.437462 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.9496 | −1.35921 | −0.679607 | − | 0.733577i | \(-0.737850\pi\) | ||||
−0.679607 | + | 0.733577i | \(0.737850\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.82513 | −0.140520 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.8490 | −0.618131 | −0.309066 | − | 0.951041i | \(-0.600016\pi\) | ||||
−0.309066 | + | 0.951041i | \(0.600016\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33.2867 | −1.21953 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.82200 | 0.139840 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.31032 | 0.120957 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.5008 | 1.66035 | 0.830174 | − | 0.557505i | \(-0.188241\pi\) | ||||
0.830174 | + | 0.557505i | \(0.188241\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.81268 | 0.0660578 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −73.5684 | −2.67743 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.61208 | 0.131283 | 0.0656417 | − | 0.997843i | \(-0.479091\pi\) | ||||
0.0656417 | + | 0.997843i | \(0.479091\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.42010 | −0.269333 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.5545 | 1.14385 | 0.571924 | − | 0.820306i | \(-0.306197\pi\) | ||||
0.571924 | + | 0.820306i | \(0.306197\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.4171 | 1.28219 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19.8096 | −0.716217 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.3168 | −0.553059 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.4083 | 0.519577 | 0.259789 | − | 0.965665i | \(-0.416347\pi\) | ||||
0.259789 | + | 0.965665i | \(0.416347\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.84493 | 0.0664436 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.46104 | 0.232387 | 0.116194 | − | 0.993227i | \(-0.462931\pi\) | ||||
0.116194 | + | 0.993227i | \(0.462931\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 56.7222 | 2.03752 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −41.3966 | −1.48510 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.32047 | 0.226454 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.3219 | −0.405129 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.57239 | 0.127667 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.0215 | −0.500449 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.9998 | 0.570330 | 0.285165 | − | 0.958479i | \(-0.407952\pi\) | ||||
0.285165 | + | 0.958479i | \(0.407952\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.50485 | −0.267180 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.2784 | 0.721018 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.88696 | −0.315585 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.82879 | −0.100327 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.33123 | 0.0825765 | 0.0412883 | − | 0.999147i | \(-0.486854\pi\) | ||||
0.0412883 | + | 0.999147i | \(0.486854\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.4655 | 1.11317 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.78217 | −0.239636 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.294639 | 0.0103976 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −67.5097 | −2.37941 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.31805 | −0.222406 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.0736 | 0.565117 | 0.282558 | − | 0.959250i | \(-0.408817\pi\) | ||||
0.282558 | + | 0.959250i | \(0.408817\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.6082 | 1.35572 | 0.677859 | − | 0.735192i | \(-0.262908\pi\) | ||||
0.677859 | + | 0.735192i | \(0.262908\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.88653 | 0.311664 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −47.2311 | −1.65443 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.99136 | −0.0696689 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 22.8112 | 0.797089 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.49502 | −0.296478 | −0.148239 | − | 0.988952i | \(-0.547361\pi\) | ||||
−0.148239 | + | 0.988952i | \(0.547361\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.2987 | −0.707567 | −0.353783 | − | 0.935327i | \(-0.615105\pi\) | ||||
−0.353783 | + | 0.935327i | \(0.615105\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.7955 | 0.445481 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.6081 | 1.09912 | 0.549561 | − | 0.835454i | \(-0.314795\pi\) | ||||
0.549561 | + | 0.835454i | \(0.314795\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.2482 | 1.05056 | 0.525282 | − | 0.850928i | \(-0.323960\pi\) | ||||
0.525282 | + | 0.850928i | \(0.323960\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.3868 | 1.05411 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −54.4982 | −1.88825 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.59055 | 0.124256 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.18724 | 0.248427 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.0441 | −1.31343 | −0.656715 | − | 0.754139i | \(-0.728055\pi\) | ||||
−0.656715 | + | 0.754139i | \(0.728055\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.2380 | −0.559933 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.0587 | −0.518651 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 64.0204 | 2.20237 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.3919 | −1.18172 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.8690 | 0.681904 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 46.1157 | 1.58083 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.8978 | 0.510091 | 0.255045 | − | 0.966929i | \(-0.417910\pi\) | ||||
0.255045 | + | 0.966929i | \(0.417910\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.47354 | −0.0845933 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.2863 | 0.590487 | 0.295244 | − | 0.955422i | \(-0.404599\pi\) | ||||
0.295244 | + | 0.955422i | \(0.404599\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.45168 | 0.0836501 | 0.0418250 | − | 0.999125i | \(-0.486683\pi\) | ||||
0.0418250 | + | 0.999125i | \(0.486683\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −37.6922 | −1.28455 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.4142 | 0.831070 | 0.415535 | − | 0.909577i | \(-0.363594\pi\) | ||||
0.415535 | + | 0.909577i | \(0.363594\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.9618 | 1.39274 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.4388 | 0.456405 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.5721 | −0.765707 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.6721 | 1.37812 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.41920 | −0.251102 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 42.6611 | 1.44221 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.2565 | −0.717782 | −0.358891 | − | 0.933380i | \(-0.616845\pi\) | ||||
−0.358891 | + | 0.933380i | \(0.616845\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.68694 | 0.0906282 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.9501 | −0.773209 | −0.386605 | − | 0.922246i | \(-0.626352\pi\) | ||||
−0.386605 | + | 0.922246i | \(0.626352\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.97231 | 0.200984 | 0.100492 | − | 0.994938i | \(-0.467958\pi\) | ||||
0.100492 | + | 0.994938i | \(0.467958\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.90472 | −0.332943 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.82725 | −0.229237 | −0.114618 | − | 0.993410i | \(-0.536564\pi\) | ||||
−0.114618 | + | 0.993410i | \(0.536564\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −50.5755 | −1.69625 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.62131 | 0.0543158 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.92896 | 0.131478 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 71.0490 | 2.37491 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −25.4117 | −0.848471 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.6756 | 0.856329 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.34663 | 0.144807 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.8755 | 0.395192 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.9004 | 0.661510 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.0600 | 0.533263 | 0.266632 | − | 0.963798i | \(-0.414089\pi\) | ||||
0.266632 | + | 0.963798i | \(0.414089\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.3734 | −0.642575 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.0437 | 1.02852 | 0.514262 | − | 0.857633i | \(-0.328066\pi\) | ||||
0.514262 | + | 0.857633i | \(0.328066\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.19663 | 0.205079 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.74680 | −0.189983 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 67.4162 | 2.22628 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.2155 | −1.22762 | −0.613812 | − | 0.789452i | \(-0.710365\pi\) | ||||
−0.613812 | + | 0.789452i | \(0.710365\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.8605 | 0.687375 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −38.7741 | −1.27627 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −79.5235 | −2.61472 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.04851 | −0.0672820 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.11946 | −0.233582 | −0.116791 | − | 0.993157i | \(-0.537261\pi\) | ||||
−0.116791 | + | 0.993157i | \(0.537261\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.80497 | −0.223024 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.4158 | −0.340999 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −32.1174 | −1.05035 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.9767 | −0.489268 | −0.244634 | − | 0.969616i | \(-0.578668\pi\) | ||||
−0.244634 | + | 0.969616i | \(0.578668\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.9992 | 1.01162 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48.7595 | −1.58951 | −0.794756 | − | 0.606929i | \(-0.792401\pi\) | ||||
−0.794756 | + | 0.606929i | \(0.792401\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.9891 | 1.36735 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.7510 | 0.479850 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.6838 | −0.607142 | −0.303571 | − | 0.952809i | \(-0.598179\pi\) | ||||
−0.303571 | + | 0.952809i | \(0.598179\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.00905 | 0.0327552 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.8470 | −0.805720 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 57.8655 | 1.87445 | 0.937224 | − | 0.348729i | \(-0.113387\pi\) | ||||
0.937224 | + | 0.348729i | \(0.113387\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 62.4122 | 2.01961 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.79194 | 0.187227 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −66.8378 | −2.15831 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.6564 | 0.666335 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.805768 | 0.0259655 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −36.4753 | −1.17418 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.9913 | −0.449930 | −0.224965 | − | 0.974367i | \(-0.572227\pi\) | ||||
−0.224965 | + | 0.974367i | \(0.572227\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.80077 | 0.122098 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45.1729 | −1.44967 | −0.724833 | − | 0.688924i | \(-0.758083\pi\) | ||||
−0.724833 | + | 0.688924i | \(0.758083\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.9281 | −0.702984 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 43.8207 | 1.40339 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.49820 | 0.143910 | 0.0719550 | − | 0.997408i | \(-0.477076\pi\) | ||||
0.0719550 | + | 0.997408i | \(0.477076\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.9960 | −0.351433 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.62091 | 0.275244 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.41141 | 0.204492 | 0.102246 | − | 0.994759i | \(-0.467397\pi\) | ||||
0.102246 | + | 0.994759i | \(0.467397\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 45.5675 | 1.45190 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −23.4305 | −0.745800 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.2293 | −0.420667 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.9219 | −1.36346 | −0.681730 | − | 0.731604i | \(-0.738772\pi\) | ||||
−0.681730 | + | 0.731604i | \(0.738772\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.7919 | −0.564608 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 98.1655 | 3.11205 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.859857 | −0.0272319 | −0.0136160 | − | 0.999907i | \(-0.504334\pi\) | ||||
−0.0136160 | + | 0.999907i | \(0.504334\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.0764 | −0.318802 |
(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 | 4008.2.a.l.1.11 | ✓ | 12 | |
4.3 | odd | 2 | 8016.2.a.bf.1.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.l.1.11 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8016.2.a.bf.1.11 | 12 | 4.3 | odd | 2 |