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: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 49 x^{11} + 99 x^{10} + 901 x^{9} - 1879 x^{8} - 7582 x^{7} + 16968 x^{6} + 26911 x^{5} - 72240 x^{4} - 14532 x^{3} + 112850 x^{2} - 72184 x + 12144 \) |
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 | \(3.18209\) 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 | ||||||||
\(5\) | 3.18209 | 1.42307 | 0.711537 | − | 0.702648i | \(-0.247999\pi\) | ||||
0.711537 | + | 0.702648i | \(0.247999\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.39408 | −0.526912 | −0.263456 | − | 0.964671i | \(-0.584862\pi\) | ||||
−0.263456 | + | 0.964671i | \(0.584862\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.54587 | −0.767609 | −0.383805 | − | 0.923414i | \(-0.625386\pi\) | ||||
−0.383805 | + | 0.923414i | \(0.625386\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.18156 | 1.43711 | 0.718554 | − | 0.695471i | \(-0.244804\pi\) | ||||
0.718554 | + | 0.695471i | \(0.244804\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.18209 | 0.821612 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.90365 | −0.704238 | −0.352119 | − | 0.935955i | \(-0.614539\pi\) | ||||
−0.352119 | + | 0.935955i | \(0.614539\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.55969 | 1.50490 | 0.752448 | − | 0.658651i | \(-0.228873\pi\) | ||||
0.752448 | + | 0.658651i | \(0.228873\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.39408 | −0.304213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.68375 | 0.559601 | 0.279801 | − | 0.960058i | \(-0.409732\pi\) | ||||
0.279801 | + | 0.960058i | \(0.409732\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.12570 | 1.02514 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.50556 | −0.650965 | −0.325483 | − | 0.945548i | \(-0.605527\pi\) | ||||
−0.325483 | + | 0.945548i | \(0.605527\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.85751 | 1.23165 | 0.615823 | − | 0.787885i | \(-0.288824\pi\) | ||||
0.615823 | + | 0.787885i | \(0.288824\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.54587 | −0.443179 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.43609 | −0.749835 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.23682 | 0.696530 | 0.348265 | − | 0.937396i | \(-0.386771\pi\) | ||||
0.348265 | + | 0.937396i | \(0.386771\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.18156 | 0.829714 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.88971 | −0.295122 | −0.147561 | − | 0.989053i | \(-0.547142\pi\) | ||||
−0.147561 | + | 0.989053i | \(0.547142\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.49527 | −0.990520 | −0.495260 | − | 0.868745i | \(-0.664927\pi\) | ||||
−0.495260 | + | 0.868745i | \(0.664927\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.18209 | 0.474358 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.80101 | −1.13789 | −0.568947 | − | 0.822374i | \(-0.692649\pi\) | ||||
−0.568947 | + | 0.822374i | \(0.692649\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.05654 | −0.722364 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.90365 | −0.406592 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.5299 | 1.44640 | 0.723199 | − | 0.690639i | \(-0.242671\pi\) | ||||
0.723199 | + | 0.690639i | \(0.242671\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.10120 | −1.09237 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.55969 | 0.868852 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.200385 | 0.0260879 | 0.0130439 | − | 0.999915i | \(-0.495848\pi\) | ||||
0.0130439 | + | 0.999915i | \(0.495848\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.8595 | 1.51845 | 0.759226 | − | 0.650827i | \(-0.225578\pi\) | ||||
0.759226 | + | 0.650827i | \(0.225578\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.39408 | −0.175637 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.4882 | 2.04511 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.5383 | −1.53180 | −0.765901 | − | 0.642959i | \(-0.777707\pi\) | ||||
−0.765901 | + | 0.642959i | \(0.777707\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.68375 | 0.323086 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.92956 | −0.347674 | −0.173837 | − | 0.984774i | \(-0.555617\pi\) | ||||
−0.173837 | + | 0.984774i | \(0.555617\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.6356 | 1.71297 | 0.856487 | − | 0.516169i | \(-0.172642\pi\) | ||||
0.856487 | + | 0.516169i | \(0.172642\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.12570 | 0.591865 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.54915 | 0.404463 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.95847 | 0.220346 | 0.110173 | − | 0.993912i | \(-0.464860\pi\) | ||||
0.110173 | + | 0.993912i | \(0.464860\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.16521 | −0.347427 | −0.173714 | − | 0.984796i | \(-0.555577\pi\) | ||||
−0.173714 | + | 0.984796i | \(0.555577\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.23968 | −1.00218 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.50556 | −0.375835 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.01635 | 0.849732 | 0.424866 | − | 0.905256i | \(-0.360321\pi\) | ||||
0.424866 | + | 0.905256i | \(0.360321\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.22351 | −0.757230 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.85751 | 0.711091 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20.8735 | 2.14158 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.21764 | 0.225167 | 0.112584 | − | 0.993642i | \(-0.464087\pi\) | ||||
0.112584 | + | 0.993642i | \(0.464087\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.54587 | −0.255870 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.57057 | −0.156277 | −0.0781386 | − | 0.996943i | \(-0.524898\pi\) | ||||
−0.0781386 | + | 0.996943i | \(0.524898\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.64913 | 0.852224 | 0.426112 | − | 0.904670i | \(-0.359883\pi\) | ||||
0.426112 | + | 0.904670i | \(0.359883\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.43609 | −0.432918 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.32081 | 0.901077 | 0.450538 | − | 0.892757i | \(-0.351232\pi\) | ||||
0.450538 | + | 0.892757i | \(0.351232\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.99664 | −0.287026 | −0.143513 | − | 0.989648i | \(-0.545840\pi\) | ||||
−0.143513 | + | 0.989648i | \(0.545840\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.23682 | 0.402142 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.8938 | 1.30702 | 0.653508 | − | 0.756920i | \(-0.273297\pi\) | ||||
0.653508 | + | 0.756920i | \(0.273297\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.53995 | 0.796354 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.18156 | 0.479036 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.04792 | 0.371072 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.51854 | −0.410776 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.88971 | −0.170389 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.400003 | 0.0357773 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.49924 | −0.665450 | −0.332725 | − | 0.943024i | \(-0.607968\pi\) | ||||
−0.332725 | + | 0.943024i | \(0.607968\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.49527 | −0.571877 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.66672 | 0.145622 | 0.0728110 | − | 0.997346i | \(-0.476803\pi\) | ||||
0.0728110 | + | 0.997346i | \(0.476803\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.14473 | −0.792948 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.18209 | 0.273871 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.1564 | −0.953152 | −0.476576 | − | 0.879133i | \(-0.658122\pi\) | ||||
−0.476576 | + | 0.879133i | \(0.658122\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.80521 | −0.407573 | −0.203786 | − | 0.979015i | \(-0.565325\pi\) | ||||
−0.203786 | + | 0.979015i | \(0.565325\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.80101 | −0.656964 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.1916 | −1.10314 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.1550 | −0.926372 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.05654 | −0.417057 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.24977 | 0.348155 | 0.174077 | − | 0.984732i | \(-0.444306\pi\) | ||||
0.174077 | + | 0.984732i | \(0.444306\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8711 | 1.04743 | 0.523717 | − | 0.851892i | \(-0.324545\pi\) | ||||
0.523717 | + | 0.851892i | \(0.324545\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.90365 | −0.234746 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.8212 | 1.75272 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.92657 | 0.393183 | 0.196592 | − | 0.980485i | \(-0.437013\pi\) | ||||
0.196592 | + | 0.980485i | \(0.437013\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.5299 | 0.835079 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.74136 | −0.294861 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.4770 | −0.898945 | −0.449472 | − | 0.893294i | \(-0.648388\pi\) | ||||
−0.449472 | + | 0.893294i | \(0.648388\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.10120 | −0.630677 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.8486 | 1.06528 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.55969 | 0.501632 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.6626 | 1.11478 | 0.557390 | − | 0.830251i | \(-0.311803\pi\) | ||||
0.557390 | + | 0.830251i | \(0.311803\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.14564 | −0.540159 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.200385 | 0.0150618 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.5306 | −1.45979 | −0.729894 | − | 0.683560i | \(-0.760431\pi\) | ||||
−0.729894 | + | 0.683560i | \(0.760431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.281329 | 0.0209110 | 0.0104555 | − | 0.999945i | \(-0.496672\pi\) | ||||
0.0104555 | + | 0.999945i | \(0.496672\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.8595 | 0.876678 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.4820 | 0.991213 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.39232 | 0.540580 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.39408 | −0.101404 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.32165 | 0.167989 | 0.0839943 | − | 0.996466i | \(-0.473232\pi\) | ||||
0.0839943 | + | 0.996466i | \(0.473232\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.7761 | 1.63946 | 0.819729 | − | 0.572751i | \(-0.194124\pi\) | ||||
0.819729 | + | 0.572751i | \(0.194124\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.4882 | 1.18075 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.4276 | −0.742935 | −0.371467 | − | 0.928446i | \(-0.621145\pi\) | ||||
−0.371467 | + | 0.928446i | \(0.621145\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0417 | −1.13716 | −0.568582 | − | 0.822626i | \(-0.692508\pi\) | ||||
−0.568582 | + | 0.822626i | \(0.692508\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.5383 | −0.884386 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.88702 | 0.343002 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.01321 | −0.419981 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.68375 | 0.186534 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.7001 | −1.15517 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.5563 | 0.795569 | 0.397784 | − | 0.917479i | \(-0.369779\pi\) | ||||
0.397784 | + | 0.917479i | \(0.369779\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.92956 | −0.200730 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.6685 | −1.40958 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.55991 | −0.648969 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.6356 | 0.988985 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.0454 | −1.01207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.2536 | −0.686631 | −0.343316 | − | 0.939220i | \(-0.611550\pi\) | ||||
−0.343316 | + | 0.939220i | \(0.611550\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.12570 | 0.341714 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.3493 | −1.01877 | −0.509383 | − | 0.860540i | \(-0.670126\pi\) | ||||
−0.509383 | + | 0.860540i | \(0.670126\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.12046 | 0.602697 | 0.301349 | − | 0.953514i | \(-0.402563\pi\) | ||||
0.301349 | + | 0.953514i | \(0.402563\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.54915 | 0.233517 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.7291 | 1.88211 | 0.941053 | − | 0.338258i | \(-0.109838\pi\) | ||||
0.941053 | + | 0.338258i | \(0.109838\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.8235 | −1.61931 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.95847 | 0.127217 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.2277 | −0.855627 | −0.427814 | − | 0.903867i | \(-0.640716\pi\) | ||||
−0.427814 | + | 0.903867i | \(0.640716\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.0262 | −1.22558 | −0.612791 | − | 0.790245i | \(-0.709953\pi\) | ||||
−0.612791 | + | 0.790245i | \(0.709953\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.0904 | −1.02798 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.9895 | 2.16270 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.16521 | −0.200587 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.12412 | 0.134073 | 0.0670365 | − | 0.997751i | \(-0.478646\pi\) | ||||
0.0670365 | + | 0.997751i | \(0.478646\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.83249 | −0.429555 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.23968 | −0.578611 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.39914 | −0.149654 | −0.0748271 | − | 0.997197i | \(-0.523841\pi\) | ||||
−0.0748271 | + | 0.997197i | \(0.523841\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.90647 | −0.367010 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.50556 | −0.216988 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.69327 | −0.227737 | −0.113869 | − | 0.993496i | \(-0.536324\pi\) | ||||
−0.113869 | + | 0.993496i | \(0.536324\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.5072 | 2.05833 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.01635 | 0.490593 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.45323 | −0.332489 | −0.166245 | − | 0.986085i | \(-0.553164\pi\) | ||||
−0.166245 | + | 0.986085i | \(0.553164\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.6650 | 1.55904 | 0.779519 | − | 0.626378i | \(-0.215463\pi\) | ||||
0.779519 | + | 0.626378i | \(0.215463\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.22351 | −0.437187 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.0494 | −0.786908 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.5266 | −1.35349 | −0.676745 | − | 0.736217i | \(-0.736610\pi\) | ||||
−0.676745 | + | 0.736217i | \(0.736610\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.85751 | 0.410549 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.8370 | −0.646479 | −0.323239 | − | 0.946317i | \(-0.604772\pi\) | ||||
−0.323239 | + | 0.946317i | \(0.604772\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.38825 | 0.141967 | 0.0709834 | − | 0.997477i | \(-0.477386\pi\) | ||||
0.0709834 | + | 0.997477i | \(0.477386\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 20.8735 | 1.23644 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.63440 | 0.155504 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.56882 | −0.504048 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.21764 | 0.130000 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.2580 | −0.949800 | −0.474900 | − | 0.880040i | \(-0.657516\pi\) | ||||
−0.474900 | + | 0.880040i | \(0.657516\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.637642 | 0.0371250 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.54587 | −0.147726 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.9060 | 0.804207 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.05492 | 0.521917 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.57057 | −0.0902267 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 37.7380 | 2.16087 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.5390 | −0.601491 | −0.300746 | − | 0.953704i | \(-0.597235\pi\) | ||||
−0.300746 | + | 0.953704i | \(0.597235\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.64913 | 0.492032 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.52271 | 0.483279 | 0.241639 | − | 0.970366i | \(-0.422315\pi\) | ||||
0.241639 | + | 0.970366i | \(0.422315\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.5929 | −0.881362 | −0.440681 | − | 0.897664i | \(-0.645263\pi\) | ||||
−0.440681 | + | 0.897664i | \(0.645263\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.43609 | −0.249945 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.8386 | −1.05808 | −0.529042 | − | 0.848596i | \(-0.677448\pi\) | ||||
−0.529042 | + | 0.848596i | \(0.677448\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.92470 | 0.499687 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.32081 | 0.520237 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.0470 | −1.05981 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.5592 | 1.47324 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.99664 | −0.165714 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.8752 | 0.599571 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.3161 | −1.33653 | −0.668267 | − | 0.743921i | \(-0.732964\pi\) | ||||
−0.668267 | + | 0.743921i | \(0.732964\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.23682 | 0.232177 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −39.8981 | −2.17987 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.2241 | −0.556944 | −0.278472 | − | 0.960444i | \(-0.589828\pi\) | ||||
−0.278472 | + | 0.960444i | \(0.589828\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.8938 | 0.754606 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.4583 | −0.945423 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.8078 | 0.907534 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.53995 | 0.459775 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.09384 | 0.112403 | 0.0562017 | − | 0.998419i | \(-0.482101\pi\) | ||||
0.0562017 | + | 0.998419i | \(0.482101\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.7148 | 1.37648 | 0.688241 | − | 0.725482i | \(-0.258383\pi\) | ||||
0.688241 | + | 0.725482i | \(0.258383\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.18156 | 0.276571 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.3134 | 0.548929 | 0.274465 | − | 0.961597i | \(-0.411499\pi\) | ||||
0.274465 | + | 0.961597i | \(0.411499\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.32212 | −0.494767 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.04792 | 0.214238 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.07605 | 0.426237 | 0.213119 | − | 0.977026i | \(-0.431638\pi\) | ||||
0.213119 | + | 0.977026i | \(0.431638\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.0296 | 1.26471 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.51854 | −0.237162 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 46.5720 | 2.43769 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.0400 | 0.524082 | 0.262041 | − | 0.965057i | \(-0.415604\pi\) | ||||
0.262041 | + | 0.965057i | \(0.415604\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.88971 | −0.0983741 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.6796 | −0.762125 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.292570 | −0.0151487 | −0.00757435 | − | 0.999971i | \(-0.502411\pi\) | ||||
−0.00757435 | + | 0.999971i | \(0.502411\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.400003 | 0.0206561 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.1643 | −0.935507 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.65909 | −0.239321 | −0.119661 | − | 0.992815i | \(-0.538181\pi\) | ||||
−0.119661 | + | 0.992815i | \(0.538181\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.49924 | −0.384198 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.9662 | 0.560345 | 0.280173 | − | 0.959950i | \(-0.409608\pi\) | ||||
0.280173 | + | 0.959950i | \(0.409608\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.2937 | 0.575581 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.49527 | −0.330173 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −36.5417 | −1.85274 | −0.926370 | − | 0.376616i | \(-0.877088\pi\) | ||||
−0.926370 | + | 0.376616i | \(0.877088\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.79268 | −0.394093 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.66672 | 0.0840750 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.23204 | 0.313568 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.2781 | −0.566032 | −0.283016 | − | 0.959115i | \(-0.591335\pi\) | ||||
−0.283016 | + | 0.959115i | \(0.591335\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.14473 | −0.457809 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.3097 | 0.664655 | 0.332328 | − | 0.943164i | \(-0.392166\pi\) | ||||
0.332328 | + | 0.943164i | \(0.392166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.5326 | 1.77001 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.18209 | 0.158119 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.7864 | −0.534663 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.52181 | 0.124696 | 0.0623479 | − | 0.998054i | \(-0.480141\pi\) | ||||
0.0623479 | + | 0.998054i | \(0.480141\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.1564 | −0.550303 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.279352 | −0.0137460 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.0720 | −0.494415 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.80521 | −0.235312 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.84632 | −0.334465 | −0.167232 | − | 0.985917i | \(-0.553483\pi\) | ||||
−0.167232 | + | 0.985917i | \(0.553483\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.8171 | 1.45320 | 0.726599 | − | 0.687061i | \(-0.241100\pi\) | ||||
0.726599 | + | 0.687061i | \(0.241100\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.80101 | −0.379298 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.8832 | −0.721944 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.5331 | −0.800091 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.1916 | −0.636896 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.2712 | 0.591082 | 0.295541 | − | 0.955330i | \(-0.404500\pi\) | ||||
0.295541 | + | 0.955330i | \(0.404500\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.9314 | 1.39035 | 0.695177 | − | 0.718838i | \(-0.255326\pi\) | ||||
0.695177 | + | 0.718838i | \(0.255326\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.1550 | −0.534841 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.6046 | 0.842142 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.2562 | 0.537228 | 0.268614 | − | 0.963248i | \(-0.413434\pi\) | ||||
0.268614 | + | 0.963248i | \(0.413434\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.05654 | −0.240788 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.4501 | 0.876591 | 0.438296 | − | 0.898831i | \(-0.355582\pi\) | ||||
0.438296 | + | 0.898831i | \(0.355582\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.5088 | 1.20923 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.24977 | 0.201007 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.1633 | −1.28192 | −0.640958 | − | 0.767576i | \(-0.721463\pi\) | ||||
−0.640958 | + | 0.767576i | \(0.721463\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.81095 | 0.226539 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.8711 | 0.604736 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −22.9859 | −1.07759 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.2604 | 1.32197 | 0.660983 | − | 0.750401i | \(-0.270140\pi\) | ||||
0.660983 | + | 0.750401i | \(0.270140\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.90365 | −0.135531 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.9228 | −1.25392 | −0.626959 | − | 0.779052i | \(-0.715701\pi\) | ||||
−0.626959 | + | 0.779052i | \(0.715701\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.70108 | 0.404374 | 0.202187 | − | 0.979347i | \(-0.435195\pi\) | ||||
0.202187 | + | 0.979347i | \(0.435195\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 21.8212 | 1.01194 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.8472 | −1.28862 | −0.644308 | − | 0.764766i | \(-0.722855\pi\) | ||||
−0.644308 | + | 0.764766i | \(0.722855\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.4794 | 0.807125 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.92657 | 0.227005 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.5361 | 0.760332 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 33.6230 | 1.54273 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.5299 | 0.482133 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.9578 | −1.78003 | −0.890014 | − | 0.455933i | \(-0.849306\pi\) | ||||
−0.890014 | + | 0.455933i | \(0.849306\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.9534 | 1.00099 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.74136 | −0.170238 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.05674 | 0.320430 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.7195 | 0.757633 | 0.378816 | − | 0.925472i | \(-0.376331\pi\) | ||||
0.378816 | + | 0.925472i | \(0.376331\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.4770 | −0.519006 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.7073 | 0.483213 | 0.241607 | − | 0.970374i | \(-0.422326\pi\) | ||||
0.241607 | + | 0.970374i | \(0.422326\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.1789 | 0.458435 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.10120 | −0.364122 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.08403 | 0.183194 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.19869 | −0.187959 | −0.0939797 | − | 0.995574i | \(-0.529959\pi\) | ||||
−0.0939797 | + | 0.995574i | \(0.529959\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.6725 | −1.45680 | −0.728398 | − | 0.685154i | \(-0.759735\pi\) | ||||
−0.728398 | + | 0.685154i | \(0.759735\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.99769 | −0.222394 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.8486 | 0.615039 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.56268 | −0.157913 | −0.0789564 | − | 0.996878i | \(-0.525159\pi\) | ||||
−0.0789564 | + | 0.996878i | \(0.525159\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.4032 | −0.902586 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.55969 | 0.289617 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 27.5223 | 1.21278 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.8604 | 0.873458 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.6626 | 0.643619 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.09199 | −0.179273 | −0.0896367 | − | 0.995975i | \(-0.528571\pi\) | ||||
−0.0896367 | + | 0.995975i | \(0.528571\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.8494 | 0.561863 | 0.280932 | − | 0.959728i | \(-0.409357\pi\) | ||||
0.280932 | + | 0.959728i | \(0.409357\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.14564 | −0.311861 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.9118 | −0.867372 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.7975 | −0.686847 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.200385 | 0.00869596 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.79163 | −0.424123 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.6597 | 1.28230 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.5306 | −0.842809 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.8733 | 0.554493 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.8636 | −1.02597 | −0.512987 | − | 0.858396i | \(-0.671461\pi\) | ||||
−0.512987 | + | 0.858396i | \(0.671461\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.281329 | 0.0120730 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.53557 | −0.408459 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.1923 | −1.37645 | −0.688223 | − | 0.725500i | \(-0.741609\pi\) | ||||
−0.688223 | + | 0.725500i | \(0.741609\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.8595 | 0.506151 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.9954 | −0.979636 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.73027 | −0.116103 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.4820 | 0.572277 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.1486 | −0.430010 | −0.215005 | − | 0.976613i | \(-0.568977\pi\) | ||||
−0.215005 | + | 0.976613i | \(0.568977\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.6557 | −1.42348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.39232 | 0.312104 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.29505 | −0.223160 | −0.111580 | − | 0.993755i | \(-0.535591\pi\) | ||||
−0.111580 | + | 0.993755i | \(0.535591\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 44.2112 | 1.85998 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.39408 | −0.0585458 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.4824 | −0.774822 | −0.387411 | − | 0.921907i | \(-0.626631\pi\) | ||||
−0.387411 | + | 0.921907i | \(0.626631\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 46.1352 | 1.93070 | 0.965348 | − | 0.260966i | \(-0.0840409\pi\) | ||||
0.965348 | + | 0.260966i | \(0.0840409\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.32165 | 0.0969882 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.7561 | 0.573670 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.1408 | −0.547059 | −0.273529 | − | 0.961864i | \(-0.588191\pi\) | ||||
−0.273529 | + | 0.961864i | \(0.588191\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.7761 | 0.946542 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.41256 | 0.183064 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.8079 | −1.11027 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.4882 | 0.681704 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.0037 | 0.908189 | 0.454095 | − | 0.890954i | \(-0.349963\pi\) | ||||
0.454095 | + | 0.890954i | \(0.349963\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.9832 | 1.85350 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.4276 | −0.428934 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.1594 | −1.23850 | −0.619249 | − | 0.785195i | \(-0.712563\pi\) | ||||
−0.619249 | + | 0.785195i | \(0.712563\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.8808 | 0.528063 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.0417 | −0.656542 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.1500 | 0.659871 | 0.329935 | − | 0.944004i | \(-0.392973\pi\) | ||||
0.329935 | + | 0.944004i | \(0.392973\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.7075 | 1.33417 | 0.667083 | − | 0.744984i | \(-0.267543\pi\) | ||||
0.667083 | + | 0.744984i | \(0.267543\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.5383 | −0.510600 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.3784 | −0.584565 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.0158 | −1.50243 | −0.751213 | − | 0.660060i | \(-0.770531\pi\) | ||||
−0.751213 | + | 0.660060i | \(0.770531\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.88702 | 0.198032 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −40.4214 | −1.63528 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.4598 | −1.18987 | −0.594935 | − | 0.803774i | \(-0.702822\pi\) | ||||
−0.594935 | + | 0.803774i | \(0.702822\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.01321 | −0.242476 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.4634 | −1.18615 | −0.593075 | − | 0.805147i | \(-0.702086\pi\) | ||||
−0.593075 | + | 0.805147i | \(0.702086\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.7461 | −0.472117 | −0.236058 | − | 0.971739i | \(-0.575856\pi\) | ||||
−0.236058 | + | 0.971739i | \(0.575856\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.68375 | 0.107695 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.1754 | −0.447734 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.3557 | −0.974227 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.7001 | −0.666939 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.3023 | −0.490523 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.5462 | −1.33545 | −0.667727 | − | 0.744406i | \(-0.732733\pi\) | ||||
−0.667727 | + | 0.744406i | \(0.732733\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.5563 | 0.459322 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23.8633 | −0.946985 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.2008 | −1.03811 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.92956 | −0.115891 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.1843 | 0.994719 | 0.497360 | − | 0.867544i | \(-0.334303\pi\) | ||||
0.497360 | + | 0.867544i | \(0.334303\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.64113 | 0.0647197 | 0.0323599 | − | 0.999476i | \(-0.489698\pi\) | ||||
0.0323599 | + | 0.999476i | \(0.489698\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20.6685 | −0.813823 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.8963 | −1.60780 | −0.803900 | − | 0.594764i | \(-0.797245\pi\) | ||||
−0.803900 | + | 0.594764i | \(0.797245\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.510154 | −0.0200253 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.55991 | −0.374682 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.3875 | 0.836959 | 0.418479 | − | 0.908226i | \(-0.362563\pi\) | ||||
0.418479 | + | 0.908226i | \(0.362563\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.30366 | 0.207231 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.6356 | 0.570991 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.6553 | 1.15521 | 0.577604 | − | 0.816317i | \(-0.303988\pi\) | ||||
0.577604 | + | 0.816317i | \(0.303988\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.2127 | 0.786184 | 0.393092 | − | 0.919499i | \(-0.371405\pi\) | ||||
0.393092 | + | 0.919499i | \(0.371405\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.0454 | −0.584317 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −29.0994 | −1.12842 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.40805 | −0.364281 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.2536 | −0.396427 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.1927 | −1.16558 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.3275 | −1.01485 | −0.507425 | − | 0.861696i | \(-0.669403\pi\) | ||||
−0.507425 | + | 0.861696i | \(0.669403\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.12570 | 0.197288 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.0308 | −0.962013 | −0.481006 | − | 0.876717i | \(-0.659729\pi\) | ||||
−0.481006 | + | 0.876717i | \(0.659729\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.09157 | −0.118643 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.3493 | −0.588185 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 46.9156 | 1.79518 | 0.897589 | − | 0.440834i | \(-0.145317\pi\) | ||||
0.897589 | + | 0.440834i | \(0.145317\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −35.5005 | −1.35641 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.12046 | 0.347967 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 54.5616 | 2.07863 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.6225 | 1.12689 | 0.563447 | − | 0.826152i | \(-0.309475\pi\) | ||||
0.563447 | + | 0.826152i | \(0.309475\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.54915 | 0.134821 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.2906 | −0.580007 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.48704 | 0.207837 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.7291 | 1.08663 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −51.7652 | −1.95514 | −0.977572 | − | 0.210603i | \(-0.932457\pi\) | ||||
−0.977572 | + | 0.210603i | \(0.932457\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.7923 | 1.04821 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.8235 | −0.934908 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.18949 | 0.0823444 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.8216 | 1.00730 | 0.503652 | − | 0.863906i | \(-0.331989\pi\) | ||||
0.503652 | + | 0.863906i | \(0.331989\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.95847 | 0.0734485 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.4039 | 0.689230 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −41.9769 | −1.56985 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.2277 | −0.493996 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.1436 | 0.713934 | 0.356967 | − | 0.934117i | \(-0.383811\pi\) | ||||
0.356967 | + | 0.934117i | \(0.383811\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0576 | −0.449047 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.0262 | −0.707591 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.9684 | −0.667331 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.8740 | −0.959612 | −0.479806 | − | 0.877375i | \(-0.659293\pi\) | ||||
−0.479806 | + | 0.877375i | \(0.659293\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.8600 | 0.697562 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.91938 | −0.292509 | −0.146255 | − | 0.989247i | \(-0.546722\pi\) | ||||
−0.146255 | + | 0.989247i | \(0.546722\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.0904 | −0.593503 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.9210 | 1.17582 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.5229 | −0.497446 | −0.248723 | − | 0.968575i | \(-0.580011\pi\) | ||||
−0.248723 | + | 0.968575i | \(0.580011\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 33.9895 | 1.24863 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.0296 | 1.13836 | 0.569182 | − | 0.822211i | \(-0.307260\pi\) | ||||
0.569182 | + | 0.822211i | \(0.307260\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.5232 | 0.495450 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.16521 | −0.115809 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.9939 | −0.474788 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.5470 | −1.26064 | −0.630320 | − | 0.776336i | \(-0.717076\pi\) | ||||
−0.630320 | + | 0.776336i | \(0.717076\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.12412 | 0.0774071 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 40.9570 | 1.49058 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.8028 | −0.828781 | −0.414391 | − | 0.910099i | \(-0.636005\pi\) | ||||
−0.414391 | + | 0.910099i | \(0.636005\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.83249 | −0.248004 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.2303 | −0.515847 | −0.257923 | − | 0.966165i | \(-0.583038\pi\) | ||||
−0.257923 | + | 0.966165i | \(0.583038\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.17755 | 0.151237 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.23968 | −0.334061 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.03831 | 0.0374911 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.6897 | 0.637908 | 0.318954 | − | 0.947770i | \(-0.396669\pi\) | ||||
0.318954 | + | 0.947770i | \(0.396669\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.39914 | −0.0864029 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −46.6405 | −1.67754 | −0.838771 | − | 0.544485i | \(-0.816725\pi\) | ||||
−0.838771 | + | 0.544485i | \(0.816725\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 35.1496 | 1.26261 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.90647 | −0.211893 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.3959 | −0.444129 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.45828 | 0.266878 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.50556 | −0.125278 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.6768 | 0.559529 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.1135 | −1.21601 | −0.608007 | − | 0.793932i | \(-0.708031\pi\) | ||||
−0.608007 | + | 0.793932i | \(0.708031\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.69327 | −0.131484 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.3690 | −0.688683 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 61.4507 | 2.18218 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 33.5072 | 1.18838 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.1237 | −0.394022 | −0.197011 | − | 0.980401i | \(-0.563123\pi\) | ||||
−0.197011 | + | 0.980401i | \(0.563123\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.6514 | 0.801349 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.01635 | 0.283244 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37.2605 | −1.31489 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.9054 | −0.419609 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.45323 | −0.191963 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.8098 | 0.450369 | 0.225184 | − | 0.974316i | \(-0.427702\pi\) | ||||
0.225184 | + | 0.974316i | \(0.427702\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.1149 | 1.40863 | 0.704313 | − | 0.709890i | \(-0.251255\pi\) | ||||
0.704313 | + | 0.709890i | \(0.251255\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.6650 | 0.900112 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −36.5207 | −1.27927 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −42.6070 | −1.49063 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.22351 | −0.252410 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −46.9641 | −1.63906 | −0.819529 | − | 0.573037i | \(-0.805765\pi\) | ||||
−0.819529 | + | 0.573037i | \(0.805765\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.9100 | −0.868309 | −0.434154 | − | 0.900839i | \(-0.642953\pi\) | ||||
−0.434154 | + | 0.900839i | \(0.642953\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.0494 | −0.454321 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.0184 | 0.348374 | 0.174187 | − | 0.984713i | \(-0.444270\pi\) | ||||
0.174187 | + | 0.984713i | \(0.444270\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.3717 | −1.05485 | −0.527427 | − | 0.849600i | \(-0.676843\pi\) | ||||
−0.527427 | + | 0.849600i | \(0.676843\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.5266 | −0.781438 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.6824 | 0.508716 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.18209 | −0.110121 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.85751 | 0.237030 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −54.1321 | −1.86885 | −0.934424 | − | 0.356162i | \(-0.884085\pi\) | ||||
−0.934424 | + | 0.356162i | \(0.884085\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.7111 | −0.576244 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.8370 | −0.373245 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 44.0676 | 1.51597 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.29920 | 0.216443 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.38825 | 0.0819646 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.3706 | 0.389779 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.84450 | −0.234351 | −0.117176 | − | 0.993111i | \(-0.537384\pi\) | ||||
−0.117176 | + | 0.993111i | \(0.537384\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.8735 | 0.713860 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.266153 | 0.00909160 | 0.00454580 | − | 0.999990i | \(-0.498553\pi\) | ||||
0.00454580 | + | 0.999990i | \(0.498553\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.6988 | −1.45686 | −0.728431 | − | 0.685119i | \(-0.759750\pi\) | ||||
−0.728431 | + | 0.685119i | \(0.759750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.63440 | 0.0897800 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.4528 | 1.58127 | 0.790636 | − | 0.612286i | \(-0.209750\pi\) | ||||
0.790636 | + | 0.612286i | \(0.209750\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 46.6579 | 1.58642 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.56882 | −0.291012 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.98603 | −0.169139 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −64.9682 | −2.20136 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.21764 | 0.0750558 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.557635 | −0.0188515 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.1097 | 0.611522 | 0.305761 | − | 0.952108i | \(-0.401089\pi\) | ||||
0.305761 | + | 0.952108i | \(0.401089\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.2580 | −0.548367 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.6839 | −1.16853 | −0.584265 | − | 0.811563i | \(-0.698617\pi\) | ||||
−0.584265 | + | 0.811563i | \(0.698617\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.11055 | −0.138331 | −0.0691655 | − | 0.997605i | \(-0.522034\pi\) | ||||
−0.0691655 | + | 0.997605i | \(0.522034\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.637642 | 0.0214341 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.6817 | 1.13092 | 0.565460 | − | 0.824776i | \(-0.308699\pi\) | ||||
0.565460 | + | 0.824776i | \(0.308699\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.4545 | 0.350634 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.54587 | −0.0852899 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −51.1722 | −1.71241 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −62.1483 | −2.07739 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.9060 | 0.464309 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.0394 | −0.801759 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.5753 | −1.01861 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.05492 | 0.301329 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.895213 | 0.0297579 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.6896 | 1.71632 | 0.858162 | − | 0.513379i | \(-0.171606\pi\) | ||||
0.858162 | + | 0.513379i | \(0.171606\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.57057 | −0.0520924 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.5298 | 0.779578 | 0.389789 | − | 0.920904i | \(-0.372548\pi\) | ||||
0.389789 | + | 0.920904i | \(0.372548\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.05823 | 0.266688 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 37.7380 | 1.24758 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.32354 | −0.0767301 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −55.4985 | −1.83073 | −0.915363 | − | 0.402629i | \(-0.868096\pi\) | ||||
−0.915363 | + | 0.402629i | \(0.868096\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.5390 | −0.347271 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.1797 | −0.499646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.7167 | 0.714041 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.64913 | 0.284075 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.2800 | 0.698173 | 0.349086 | − | 0.937091i | \(-0.386492\pi\) | ||||
0.349086 | + | 0.937091i | \(0.386492\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.1694 | −1.08708 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.52271 | 0.279021 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23.5230 | 0.769285 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −55.8852 | −1.82569 | −0.912844 | − | 0.408307i | \(-0.866119\pi\) | ||||
−0.912844 | + | 0.408307i | \(0.866119\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.5929 | −0.508855 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.7285 | 1.88189 | 0.940947 | − | 0.338554i | \(-0.109938\pi\) | ||||
0.940947 | + | 0.338554i | \(0.109938\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.07150 | −0.165151 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.43609 | −0.144306 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.2287 | −0.787326 | −0.393663 | − | 0.919255i | \(-0.628792\pi\) | ||||
−0.393663 | + | 0.919255i | \(0.628792\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 75.8356 | 2.46173 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.8386 | −0.610885 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.6411 | 0.603845 | 0.301922 | − | 0.953333i | \(-0.402372\pi\) | ||||
0.301922 | + | 0.953333i | \(0.402372\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.38769 | 0.239060 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.92470 | 0.288494 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.5528 | 0.502227 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.0255 | 0.516951 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.32081 | 0.300359 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 72.4756 | 2.33307 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5476 | 0.499978 | 0.249989 | − | 0.968249i | \(-0.419573\pi\) | ||||
0.249989 | + | 0.968249i | \(0.419573\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19.0470 | −0.611879 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.1943 | −1.64290 | −0.821451 | − | 0.570279i | \(-0.806835\pi\) | ||||
−0.821451 | + | 0.570279i | \(0.806835\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.69885 | 0.214755 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.5592 | 0.850574 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.93866 | 0.158002 | 0.0790008 | − | 0.996875i | \(-0.474827\pi\) | ||||
0.0790008 | + | 0.996875i | \(0.474827\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.4086 | −0.652262 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.99664 | −0.0956752 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40.5536 | −1.29346 | −0.646730 | − | 0.762719i | \(-0.723864\pi\) | ||||
−0.646730 | + | 0.762719i | \(0.723864\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.1815 | −1.05725 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.8752 | 0.346162 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.4317 | −0.554296 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.0034 | −1.46135 | −0.730674 | − | 0.682727i | \(-0.760794\pi\) | ||||
−0.730674 | + | 0.682727i | \(0.760794\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.3161 | −0.771648 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −51.0461 | −1.61827 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.4720 | 1.21842 | 0.609210 | − | 0.793009i | \(-0.291486\pi\) | ||||
0.609210 | + | 0.793009i | \(0.291486\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.23682 | 0.134047 |
(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.m.1.11 | ✓ | 13 | |
4.3 | odd | 2 | 8016.2.a.bg.1.11 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.m.1.11 | ✓ | 13 | 1.1 | even | 1 | trivial | |
8016.2.a.bg.1.11 | 13 | 4.3 | odd | 2 |