Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
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: | \( x^{13} - 2 x^{12} - 49 x^{11} + 99 x^{10} + 901 x^{9} - 1879 x^{8} - 7582 x^{7} + 16968 x^{6} + \cdots + 12144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(2.79706\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(5\) | 2.79706 | 1.25088 | 0.625442 | − | 0.780271i | \(-0.284919\pi\) | ||||
0.625442 | + | 0.780271i | \(0.284919\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.56518 | −1.72547 | −0.862737 | − | 0.505652i | \(-0.831252\pi\) | ||||
−0.862737 | + | 0.505652i | \(0.831252\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.91073 | −0.877618 | −0.438809 | − | 0.898580i | \(-0.644599\pi\) | ||||
−0.438809 | + | 0.898580i | \(0.644599\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.850435 | −0.235868 | −0.117934 | − | 0.993021i | \(-0.537627\pi\) | ||||
−0.117934 | + | 0.993021i | \(0.537627\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.79706 | −0.722198 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.79699 | −1.89105 | −0.945523 | − | 0.325554i | \(-0.894449\pi\) | ||||
−0.945523 | + | 0.325554i | \(0.894449\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.29761 | −0.527108 | −0.263554 | − | 0.964645i | \(-0.584895\pi\) | ||||
−0.263554 | + | 0.964645i | \(0.584895\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.56518 | 0.996203 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.74788 | −0.572972 | −0.286486 | − | 0.958084i | \(-0.592487\pi\) | ||||
−0.286486 | + | 0.958084i | \(0.592487\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.82355 | 0.564710 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.57467 | −1.22088 | −0.610442 | − | 0.792061i | \(-0.709008\pi\) | ||||
−0.610442 | + | 0.792061i | \(0.709008\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.06047 | 1.26810 | 0.634049 | − | 0.773293i | \(-0.281392\pi\) | ||||
0.634049 | + | 0.773293i | \(0.281392\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.91073 | 0.506693 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.7691 | −2.15837 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.35845 | 1.37412 | 0.687060 | − | 0.726600i | \(-0.258901\pi\) | ||||
0.687060 | + | 0.726600i | \(0.258901\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.850435 | 0.136179 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.96938 | 0.776087 | 0.388043 | − | 0.921641i | \(-0.373151\pi\) | ||||
0.388043 | + | 0.921641i | \(0.373151\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.4328 | −1.74349 | −0.871745 | − | 0.489960i | \(-0.837011\pi\) | ||||
−0.871745 | + | 0.489960i | \(0.837011\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.79706 | 0.416961 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.1758 | −1.77602 | −0.888010 | − | 0.459824i | \(-0.847912\pi\) | ||||
−0.888010 | + | 0.459824i | \(0.847912\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.8408 | 1.97726 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.79699 | 1.09180 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.03568 | −0.829065 | −0.414532 | − | 0.910035i | \(-0.636055\pi\) | ||||
−0.414532 | + | 0.910035i | \(0.636055\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.14149 | −1.09780 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.29761 | 0.304326 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.64159 | 0.474094 | 0.237047 | − | 0.971498i | \(-0.423820\pi\) | ||||
0.237047 | + | 0.971498i | \(0.423820\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.09676 | 0.396500 | 0.198250 | − | 0.980151i | \(-0.436474\pi\) | ||||
0.198250 | + | 0.980151i | \(0.436474\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.56518 | −0.575158 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.37872 | −0.295044 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.0723 | 1.71921 | 0.859603 | − | 0.510963i | \(-0.170711\pi\) | ||||
0.859603 | + | 0.510963i | \(0.170711\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.74788 | 0.330806 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.961653 | 0.114127 | 0.0570636 | − | 0.998371i | \(-0.481826\pi\) | ||||
0.0570636 | + | 0.998371i | \(0.481826\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.57980 | −0.770108 | −0.385054 | − | 0.922894i | \(-0.625817\pi\) | ||||
−0.385054 | + | 0.922894i | \(0.625817\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.82355 | −0.326036 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.2880 | 1.51431 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.76849 | −0.311479 | −0.155740 | − | 0.987798i | \(-0.549776\pi\) | ||||
−0.155740 | + | 0.987798i | \(0.549776\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.8645 | 1.85112 | 0.925562 | − | 0.378596i | \(-0.123593\pi\) | ||||
0.925562 | + | 0.378596i | \(0.123593\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.8086 | −2.36548 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.57467 | 0.704878 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.20258 | 0.869472 | 0.434736 | − | 0.900558i | \(-0.356842\pi\) | ||||
0.434736 | + | 0.900558i | \(0.356842\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.88239 | 0.406985 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.06047 | −0.732136 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.42656 | −0.659351 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.44292 | −0.857249 | −0.428624 | − | 0.903483i | \(-0.641002\pi\) | ||||
−0.428624 | + | 0.903483i | \(0.641002\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.91073 | −0.292539 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.35436 | 0.134764 | 0.0673821 | − | 0.997727i | \(-0.478535\pi\) | ||||
0.0673821 | + | 0.997727i | \(0.478535\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.24034 | 0.319280 | 0.159640 | − | 0.987175i | \(-0.448967\pi\) | ||||
0.159640 | + | 0.987175i | \(0.448967\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.7691 | 1.24613 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.4272 | 1.20138 | 0.600690 | − | 0.799482i | \(-0.294893\pi\) | ||||
0.600690 | + | 0.799482i | \(0.294893\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.9444 | 1.91033 | 0.955163 | − | 0.296082i | \(-0.0956800\pi\) | ||||
0.955163 | + | 0.296082i | \(0.0956800\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.35845 | −0.793349 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.83295 | 0.548718 | 0.274359 | − | 0.961627i | \(-0.411534\pi\) | ||||
0.274359 | + | 0.961627i | \(0.411534\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.68598 | −0.716722 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.850435 | −0.0786228 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 35.5946 | 3.26295 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.52766 | −0.229787 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.96938 | −0.448074 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.08766 | −0.544497 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.57092 | −0.139397 | −0.0696984 | − | 0.997568i | \(-0.522204\pi\) | ||||
−0.0696984 | + | 0.997568i | \(0.522204\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.4328 | 1.00660 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.67110 | −0.146005 | −0.0730025 | − | 0.997332i | \(-0.523258\pi\) | ||||
−0.0730025 | + | 0.997332i | \(0.523258\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.4890 | 0.909511 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.79706 | −0.240733 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0249 | 0.856481 | 0.428240 | − | 0.903665i | \(-0.359134\pi\) | ||||
0.428240 | + | 0.903665i | \(0.359134\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.6598 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.1758 | 1.02539 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.47539 | 0.207002 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.3897 | −1.52719 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.8408 | −1.14157 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.1913 | −1.57221 | −0.786107 | − | 0.618090i | \(-0.787907\pi\) | ||||
−0.786107 | + | 0.618090i | \(0.787907\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.2906 | −1.08157 | −0.540786 | − | 0.841160i | \(-0.681873\pi\) | ||||
−0.540786 | + | 0.841160i | \(0.681873\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.79699 | −0.630349 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.7486 | 1.58624 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.624256 | −0.0498211 | −0.0249105 | − | 0.999690i | \(-0.507930\pi\) | ||||
−0.0249105 | + | 0.999690i | \(0.507930\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.03568 | 0.478661 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.5445 | 0.988649 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.71759 | −0.526163 | −0.263081 | − | 0.964774i | \(-0.584739\pi\) | ||||
−0.263081 | + | 0.964774i | \(0.584739\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.14149 | 0.633814 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2768 | −0.944366 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.29761 | −0.175703 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.4371 | 1.62983 | 0.814917 | − | 0.579578i | \(-0.196783\pi\) | ||||
0.814917 | + | 0.579578i | \(0.196783\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.8900 | −0.974394 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.64159 | −0.273718 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.637299 | 0.0476340 | 0.0238170 | − | 0.999716i | \(-0.492418\pi\) | ||||
0.0238170 | + | 0.999716i | \(0.492418\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.5472 | −1.08128 | −0.540642 | − | 0.841253i | \(-0.681819\pi\) | ||||
−0.540642 | + | 0.841253i | \(0.681819\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.09676 | −0.228919 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 23.3791 | 1.71887 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.6949 | 1.65962 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.56518 | 0.332068 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.3497 | 1.47245 | 0.736225 | − | 0.676737i | \(-0.236606\pi\) | ||||
0.736225 | + | 0.676737i | \(0.236606\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0666 | 0.724612 | 0.362306 | − | 0.932059i | \(-0.381990\pi\) | ||||
0.362306 | + | 0.932059i | \(0.381990\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.37872 | 0.170344 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.11488 | −0.0794322 | −0.0397161 | − | 0.999211i | \(-0.512645\pi\) | ||||
−0.0397161 | + | 0.999211i | \(0.512645\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.21029 | −0.227572 | −0.113786 | − | 0.993505i | \(-0.536298\pi\) | ||||
−0.113786 | + | 0.993505i | \(0.536298\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.0723 | −0.992584 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 30.0145 | 2.10661 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.8997 | 0.970794 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.74788 | −0.190991 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.68772 | 0.462599 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.1441 | 1.66215 | 0.831073 | − | 0.556164i | \(-0.187727\pi\) | ||||
0.831073 | + | 0.556164i | \(0.187727\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.961653 | −0.0658913 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −31.9783 | −2.18090 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −32.2323 | −2.18807 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.57980 | 0.444622 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.63083 | 0.446038 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.4018 | 1.09835 | 0.549174 | − | 0.835708i | \(-0.314942\pi\) | ||||
0.549174 | + | 0.835708i | \(0.314942\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.82355 | 0.188237 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.8181 | −1.24900 | −0.624500 | − | 0.781025i | \(-0.714697\pi\) | ||||
−0.624500 | + | 0.781025i | \(0.714697\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.7703 | 0.843885 | 0.421943 | − | 0.906623i | \(-0.361348\pi\) | ||||
0.421943 | + | 0.906623i | \(0.361348\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.2880 | −0.874286 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.2136 | −1.19321 | −0.596606 | − | 0.802534i | \(-0.703485\pi\) | ||||
−0.596606 | + | 0.802534i | \(0.703485\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −34.0564 | −2.22159 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.76849 | 0.179833 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.53425 | 0.163927 | 0.0819637 | − | 0.996635i | \(-0.473881\pi\) | ||||
0.0819637 | + | 0.996635i | \(0.473881\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.9201 | 0.703426 | 0.351713 | − | 0.936108i | \(-0.385599\pi\) | ||||
0.351713 | + | 0.936108i | \(0.385599\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 38.7137 | 2.47333 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.95397 | 0.124328 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.8645 | −1.06875 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.08878 | −0.447440 | −0.223720 | − | 0.974653i | \(-0.571820\pi\) | ||||
−0.223720 | + | 0.974653i | \(0.571820\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.99833 | 0.502851 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21.8086 | 1.36571 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.0298 | −1.43656 | −0.718280 | − | 0.695754i | \(-0.755070\pi\) | ||||
−0.718280 | + | 0.695754i | \(0.755070\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −38.1578 | −2.37101 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.57467 | −0.406962 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.6362 | −0.779181 | −0.389591 | − | 0.920988i | \(-0.627383\pi\) | ||||
−0.389591 | + | 0.920988i | \(0.627383\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.8822 | −1.03706 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.20258 | −0.501990 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.8615 | 1.82069 | 0.910343 | − | 0.413854i | \(-0.135818\pi\) | ||||
0.910343 | + | 0.413854i | \(0.135818\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.38067 | −0.387598 | −0.193799 | − | 0.981041i | \(-0.562081\pi\) | ||||
−0.193799 | + | 0.981041i | \(0.562081\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.88239 | −0.234973 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.21859 | −0.495600 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.5063 | 1.41235 | 0.706177 | − | 0.708035i | \(-0.250418\pi\) | ||||
0.706177 | + | 0.708035i | \(0.250418\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.06047 | 0.422699 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.4338 | −1.39794 | −0.698972 | − | 0.715149i | \(-0.746359\pi\) | ||||
−0.698972 | + | 0.715149i | \(0.746359\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.6525 | −1.04933 | −0.524666 | − | 0.851308i | \(-0.675810\pi\) | ||||
−0.524666 | + | 0.851308i | \(0.675810\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.42656 | 0.380676 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.6861 | −1.33912 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 43.7930 | 2.57606 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.44292 | 0.494933 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.9734 | −1.69265 | −0.846323 | − | 0.532671i | \(-0.821188\pi\) | ||||
−0.846323 | + | 0.532671i | \(0.821188\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.1857 | 0.593037 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.91073 | 0.168898 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.33689 | 0.135146 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 52.1929 | 3.00835 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.35436 | −0.0778062 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.66184 | 0.495975 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.5494 | −1.51525 | −0.757627 | − | 0.652688i | \(-0.773641\pi\) | ||||
−0.757627 | + | 0.652688i | \(0.773641\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.24034 | −0.184336 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.57114 | 0.372615 | 0.186308 | − | 0.982491i | \(-0.440348\pi\) | ||||
0.186308 | + | 0.982491i | \(0.440348\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.39897 | 0.0790747 | 0.0395374 | − | 0.999218i | \(-0.487412\pi\) | ||||
0.0395374 | + | 0.999218i | \(0.487412\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.7691 | −0.719456 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −32.0982 | −1.80282 | −0.901408 | − | 0.432971i | \(-0.857465\pi\) | ||||
−0.901408 | + | 0.432971i | \(0.857465\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.1371 | 1.07147 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.4272 | −0.693617 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.9144 | 0.996786 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.40125 | −0.133197 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.9444 | −1.10293 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 55.5846 | 3.06448 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.4241 | 1.67226 | 0.836130 | − | 0.548532i | \(-0.184813\pi\) | ||||
0.836130 | + | 0.548532i | \(0.184813\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.35845 | 0.458040 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 39.3611 | 2.15053 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.18567 | 0.500375 | 0.250188 | − | 0.968197i | \(-0.419508\pi\) | ||||
0.250188 | + | 0.968197i | \(0.419508\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.83295 | −0.316802 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.5511 | −1.11290 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −31.2296 | −1.68624 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.68598 | 0.413799 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.2584 | 1.14121 | 0.570604 | − | 0.821225i | \(-0.306709\pi\) | ||||
0.570604 | + | 0.821225i | \(0.306709\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.23246 | −0.280087 | −0.140044 | − | 0.990145i | \(-0.544724\pi\) | ||||
−0.140044 | + | 0.990145i | \(0.544724\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.850435 | 0.0453929 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.0428 | −1.27967 | −0.639834 | − | 0.768513i | \(-0.720997\pi\) | ||||
−0.639834 | + | 0.768513i | \(0.720997\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.68980 | 0.142760 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −35.5946 | −1.88387 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.99756 | 0.316539 | 0.158270 | − | 0.987396i | \(-0.449409\pi\) | ||||
0.158270 | + | 0.987396i | \(0.449409\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7210 | −0.722157 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.52766 | 0.132668 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.4041 | −0.963315 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.5632 | 0.655793 | 0.327896 | − | 0.944714i | \(-0.393660\pi\) | ||||
0.327896 | + | 0.944714i | \(0.393660\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.96938 | 0.258696 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.5540 | 1.43053 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.156554 | −0.00810604 | −0.00405302 | − | 0.999992i | \(-0.501290\pi\) | ||||
−0.00405302 | + | 0.999992i | \(0.501290\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.08766 | 0.314365 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.59133 | 0.287968 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.2254 | −0.833444 | −0.416722 | − | 0.909034i | \(-0.636821\pi\) | ||||
−0.416722 | + | 0.909034i | \(0.636821\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.57092 | 0.0804808 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.9406 | −0.661232 | −0.330616 | − | 0.943765i | \(-0.607257\pi\) | ||||
−0.330616 | + | 0.943765i | \(0.607257\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 37.1673 | 1.89422 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.4328 | −0.581163 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.2828 | 0.876271 | 0.438136 | − | 0.898909i | \(-0.355639\pi\) | ||||
0.438136 | + | 0.898909i | \(0.355639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.4252 | 1.08352 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.67110 | 0.0842960 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.74363 | −0.389624 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.2136 | −0.612982 | −0.306491 | − | 0.951873i | \(-0.599155\pi\) | ||||
−0.306491 | + | 0.951873i | \(0.599155\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.4890 | −0.525107 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.2780 | 1.31226 | 0.656129 | − | 0.754648i | \(-0.272193\pi\) | ||||
0.656129 | + | 0.754648i | \(0.272193\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.00447 | −0.299104 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.79706 | 0.138987 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.3292 | −1.20595 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.32947 | −0.164632 | −0.0823159 | − | 0.996606i | \(-0.526232\pi\) | ||||
−0.0823159 | + | 0.996606i | \(0.526232\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.0249 | −0.494489 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.6245 | −0.818038 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 47.1712 | 2.31554 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.6598 | −0.619953 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.6768 | −0.521594 | −0.260797 | − | 0.965394i | \(-0.583985\pi\) | ||||
−0.260797 | + | 0.965394i | \(0.583985\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.4760 | −1.77773 | −0.888866 | − | 0.458167i | \(-0.848506\pi\) | ||||
−0.888866 | + | 0.458167i | \(0.848506\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.1758 | −0.592007 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22.0152 | −1.06789 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.1373 | −0.684151 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.47539 | −0.119513 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.0164 | 1.10866 | 0.554330 | − | 0.832297i | \(-0.312975\pi\) | ||||
0.554330 | + | 0.832297i | \(0.312975\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.8633 | 1.19486 | 0.597428 | − | 0.801923i | \(-0.296190\pi\) | ||||
0.597428 | + | 0.801923i | \(0.296190\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.3897 | 0.881721 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.31355 | 0.302018 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.84142 | −0.326523 | −0.163262 | − | 0.986583i | \(-0.552201\pi\) | ||||
−0.163262 | + | 0.986583i | \(0.552201\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.8408 | 0.659087 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.9161 | 1.08878 | 0.544389 | − | 0.838833i | \(-0.316762\pi\) | ||||
0.544389 | + | 0.838833i | \(0.316762\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.9431 | 1.08761 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.1913 | 0.907719 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.55643 | −0.120645 | −0.0603226 | − | 0.998179i | \(-0.519213\pi\) | ||||
−0.0603226 | + | 0.998179i | \(0.519213\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.4645 | −0.681107 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.2906 | 0.624446 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.8593 | 0.509091 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.3051 | 0.856277 | 0.428139 | − | 0.903713i | \(-0.359170\pi\) | ||||
0.428139 | + | 0.903713i | \(0.359170\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.79699 | 0.363932 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.9794 | 0.744236 | 0.372118 | − | 0.928185i | \(-0.378632\pi\) | ||||
0.372118 | + | 0.928185i | \(0.378632\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.0301 | 1.86036 | 0.930178 | − | 0.367108i | \(-0.119652\pi\) | ||||
0.930178 | + | 0.367108i | \(0.119652\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.7486 | −0.915817 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.8776 | −0.919825 | −0.459913 | − | 0.887964i | \(-0.652119\pi\) | ||||
−0.459913 | + | 0.887964i | \(0.652119\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −64.2426 | −2.96645 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.624256 | 0.0287642 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.2779 | 1.53012 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.48742 | −0.297663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.03568 | −0.276355 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.8981 | 1.00055 | 0.500274 | − | 0.865867i | \(-0.333233\pi\) | ||||
0.500274 | + | 0.865867i | \(0.333233\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.10832 | −0.324112 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.5445 | −0.570797 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.6154 | −1.07232 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.4280 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.71759 | 0.303780 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.9355 | −1.21558 | −0.607792 | − | 0.794097i | \(-0.707944\pi\) | ||||
−0.607792 | + | 0.794097i | \(0.707944\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 51.2626 | 2.30875 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.14149 | −0.365933 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.39011 | −0.196924 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.9321 | 1.11611 | 0.558057 | − | 0.829802i | \(-0.311547\pi\) | ||||
0.558057 | + | 0.829802i | \(0.311547\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.9427 | 1.06755 | 0.533776 | − | 0.845626i | \(-0.320773\pi\) | ||||
0.533776 | + | 0.845626i | \(0.320773\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.78824 | 0.168574 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.2768 | 0.545230 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.2763 | −0.499813 | −0.249906 | − | 0.968270i | \(-0.580400\pi\) | ||||
−0.249906 | + | 0.968270i | \(0.580400\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.0380 | 1.32880 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.29761 | 0.101442 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.06343 | 0.399382 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.4404 | 1.55867 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.4371 | −0.940985 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.3218 | 0.802693 | 0.401347 | − | 0.915926i | \(-0.368542\pi\) | ||||
0.401347 | + | 0.915926i | \(0.368542\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.2678 | −1.41097 | −0.705487 | − | 0.708723i | \(-0.749272\pi\) | ||||
−0.705487 | + | 0.708723i | \(0.749272\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.8900 | 0.562566 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −55.0504 | −2.39803 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.4492 | −0.671703 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.64159 | 0.158031 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.22614 | −0.183054 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 34.7596 | 1.50279 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.637299 | −0.0275015 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −40.2869 | −1.73528 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.6203 | 1.57443 | 0.787215 | − | 0.616678i | \(-0.211522\pi\) | ||||
0.787215 | + | 0.616678i | \(0.211522\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.5472 | 0.624280 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 55.7857 | 2.38960 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.7390 | −1.27155 | −0.635774 | − | 0.771875i | \(-0.719319\pi\) | ||||
−0.635774 | + | 0.771875i | \(0.719319\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.09676 | 0.132167 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.1060 | 0.643538 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.6386 | 0.537450 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −23.3791 | −0.992387 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.1579 | −0.896490 | −0.448245 | − | 0.893911i | \(-0.647951\pi\) | ||||
−0.448245 | + | 0.893911i | \(0.647951\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.72288 | 0.411234 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.6949 | −0.958180 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.7313 | 1.50589 | 0.752946 | − | 0.658082i | \(-0.228632\pi\) | ||||
0.752946 | + | 0.658082i | \(0.228632\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.3151 | 0.686382 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.56518 | −0.191719 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.2786 | −0.514745 | −0.257373 | − | 0.966312i | \(-0.582857\pi\) | ||||
−0.257373 | + | 0.966312i | \(0.582857\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.8771 | 0.580740 | 0.290370 | − | 0.956914i | \(-0.406222\pi\) | ||||
0.290370 | + | 0.956914i | \(0.406222\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.3497 | −0.850120 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.75878 | −0.323563 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.7746 | 1.11464 | 0.557321 | − | 0.830297i | \(-0.311829\pi\) | ||||
0.557321 | + | 0.830297i | \(0.311829\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.0666 | −0.418355 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −76.9896 | −3.19407 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.5682 | 0.727602 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.37872 | −0.0983480 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.941202 | −0.0388476 | −0.0194238 | − | 0.999811i | \(-0.506183\pi\) | ||||
−0.0194238 | + | 0.999811i | \(0.506183\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.2222 | −0.668424 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.11488 | 0.0458602 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.9662 | 1.47695 | 0.738477 | − | 0.674279i | \(-0.235545\pi\) | ||||
0.738477 | + | 0.674279i | \(0.235545\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 99.5603 | 4.08158 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.21029 | 0.131388 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.9543 | 1.10132 | 0.550662 | − | 0.834728i | \(-0.314375\pi\) | ||||
0.550662 | + | 0.834728i | \(0.314375\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.3201 | 1.52232 | 0.761159 | − | 0.648566i | \(-0.224631\pi\) | ||||
0.761159 | + | 0.648566i | \(0.224631\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.0723 | 0.573069 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.07002 | −0.287437 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.98231 | −0.202226 | −0.101113 | − | 0.994875i | \(-0.532240\pi\) | ||||
−0.101113 | + | 0.994875i | \(0.532240\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −30.0145 | −1.21625 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.3547 | 0.418907 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.9611 | 0.725441 | 0.362720 | − | 0.931898i | \(-0.381848\pi\) | ||||
0.362720 | + | 0.931898i | \(0.381848\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.8997 | −0.560488 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.8834 | 0.599184 | 0.299592 | − | 0.954067i | \(-0.403149\pi\) | ||||
0.299592 | + | 0.954067i | \(0.403149\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.4829 | −0.783086 | −0.391543 | − | 0.920160i | \(-0.628059\pi\) | ||||
−0.391543 | + | 0.920160i | \(0.628059\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.74788 | 0.110269 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −37.4462 | −1.50025 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1453 | −1.24581 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.68772 | −0.267082 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −65.1707 | −2.59853 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.1689 | −0.643674 | −0.321837 | − | 0.946795i | \(-0.604300\pi\) | ||||
−0.321837 | + | 0.946795i | \(0.604300\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.1441 | −0.959640 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.39397 | −0.174369 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.7707 | −0.466374 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.961653 | 0.0380424 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.4316 | −1.35997 | −0.679984 | − | 0.733227i | \(-0.738013\pi\) | ||||
−0.679984 | + | 0.733227i | \(0.738013\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.4242 | 0.884325 | 0.442163 | − | 0.896935i | \(-0.354211\pi\) | ||||
0.442163 | + | 0.896935i | \(0.354211\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.9783 | 1.25915 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.63740 | 0.260943 | 0.130472 | − | 0.991452i | \(-0.458351\pi\) | ||||
0.130472 | + | 0.991452i | \(0.458351\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.5997 | −0.416074 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.2323 | 1.26328 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.1259 | −1.13978 | −0.569892 | − | 0.821720i | \(-0.693015\pi\) | ||||
−0.569892 | + | 0.821720i | \(0.693015\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.67418 | −0.182635 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.57980 | −0.256703 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.0489 | −0.975766 | −0.487883 | − | 0.872909i | \(-0.662231\pi\) | ||||
−0.487883 | + | 0.872909i | \(0.662231\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.1690 | 0.745589 | 0.372795 | − | 0.927914i | \(-0.378400\pi\) | ||||
0.372795 | + | 0.927914i | \(0.378400\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.63083 | −0.257520 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 29.3384 | 1.13769 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.0664 | 0.699533 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.4018 | −0.634132 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.01384 | −0.347975 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.4432 | −1.09640 | −0.548202 | − | 0.836346i | \(-0.684687\pi\) | ||||
−0.548202 | + | 0.836346i | \(0.684687\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.82355 | −0.108679 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.9968 | −0.845405 | −0.422703 | − | 0.906268i | \(-0.638919\pi\) | ||||
−0.422703 | + | 0.906268i | \(0.638919\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.5434 | 1.47916 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.8181 | 0.721111 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.0973 | 1.11338 | 0.556689 | − | 0.830721i | \(-0.312071\pi\) | ||||
0.556689 | + | 0.830721i | \(0.312071\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.0401 | 1.07136 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.7703 | −0.487217 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.13296 | 0.195550 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.5824 | −0.897118 | −0.448559 | − | 0.893753i | \(-0.648063\pi\) | ||||
−0.448559 | + | 0.893753i | \(0.648063\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.2880 | 0.504769 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35.4102 | 1.34319 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −38.7462 | −1.46762 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.2136 | 0.688902 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.2444 | 0.877928 | 0.438964 | − | 0.898505i | \(-0.355346\pi\) | ||||
0.438964 | + | 0.898505i | \(0.355346\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.2045 | −0.724310 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 34.0564 | 1.28264 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.18291 | −0.232532 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.7991 | −0.706016 | −0.353008 | − | 0.935620i | \(-0.614841\pi\) | ||||
−0.353008 | + | 0.935620i | \(0.614841\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.76849 | −0.103826 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.4013 | −0.726584 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.92381 | 0.258936 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.53425 | −0.0946435 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.0101 | 0.932721 | 0.466360 | − | 0.884595i | \(-0.345565\pi\) | ||||
0.466360 | + | 0.884595i | \(0.345565\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.7927 | −0.550910 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.9201 | −0.406123 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.5639 | −0.689446 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.1165 | 1.30240 | 0.651199 | − | 0.758907i | \(-0.274266\pi\) | ||||
0.651199 | + | 0.758907i | \(0.274266\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 89.1416 | 3.29702 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.3756 | 1.15889 | 0.579443 | − | 0.815013i | \(-0.303270\pi\) | ||||
0.579443 | + | 0.815013i | \(0.303270\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −38.7137 | −1.42798 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −40.9607 | −1.50881 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.6202 | −0.648169 | −0.324085 | − | 0.946028i | \(-0.605056\pi\) | ||||
−0.324085 | + | 0.946028i | \(0.605056\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.95397 | −0.0717808 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.3274 | 1.55284 | 0.776421 | − | 0.630214i | \(-0.217033\pi\) | ||||
0.776421 | + | 0.630214i | \(0.217033\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −53.6793 | −1.96666 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.8645 | 0.617041 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −56.7323 | −2.07295 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.22171 | 0.336505 | 0.168253 | − | 0.985744i | \(-0.446188\pi\) | ||||
0.168253 | + | 0.985744i | \(0.446188\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.08878 | 0.258329 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37.1746 | −1.35292 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.8185 | 1.41088 | 0.705441 | − | 0.708769i | \(-0.250749\pi\) | ||||
0.705441 | + | 0.708769i | \(0.250749\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.99833 | −0.290321 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.9586 | −0.433498 | −0.216749 | − | 0.976227i | \(-0.569545\pi\) | ||||
−0.216749 | + | 0.976227i | \(0.569545\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −91.0496 | −3.29622 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −21.8086 | −0.788493 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.09693 | −0.111824 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.8376 | 1.22021 | 0.610107 | − | 0.792319i | \(-0.291127\pi\) | ||||
0.610107 | + | 0.792319i | \(0.291127\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.0298 | 0.829399 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.8998 | 0.679778 | 0.339889 | − | 0.940466i | \(-0.389610\pi\) | ||||
0.339889 | + | 0.940466i | \(0.389610\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.9356 | 0.716108 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 38.1578 | 1.36890 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.4177 | −0.409081 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.79911 | −0.100160 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.57467 | 0.234959 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.74608 | −0.0623204 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.91461 | −0.210833 | −0.105416 | − | 0.994428i | \(-0.533618\pi\) | ||||
−0.105416 | + | 0.994428i | \(0.533618\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.6362 | 0.449860 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.6285 | −0.946799 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.63360 | −0.0935218 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16.8822 | 0.598749 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.51329 | 0.336978 | 0.168489 | − | 0.985704i | \(-0.446111\pi\) | ||||
0.168489 | + | 0.985704i | \(0.446111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 94.9344 | 3.35854 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.20258 | 0.289824 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.1520 | 0.675860 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35.0879 | 1.23668 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.8615 | −1.05117 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.7944 | −0.379510 | −0.189755 | − | 0.981831i | \(-0.560769\pi\) | ||||
−0.189755 | + | 0.981831i | \(0.560769\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.89452 | −0.277214 | −0.138607 | − | 0.990347i | \(-0.544262\pi\) | ||||
−0.138607 | + | 0.990347i | \(0.544262\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.38067 | 0.223780 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.7895 | −0.658168 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.2682 | 0.919007 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.88239 | 0.135662 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.60687 | 0.300382 | 0.150191 | − | 0.988657i | \(-0.452011\pi\) | ||||
0.150191 | + | 0.988657i | \(0.452011\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.40078 | −0.0488280 | −0.0244140 | − | 0.999702i | \(-0.507772\pi\) | ||||
−0.0244140 | + | 0.999702i | \(0.507772\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.21859 | 0.286135 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.7472 | 0.582358 | 0.291179 | − | 0.956669i | \(-0.405952\pi\) | ||||
0.291179 | + | 0.956669i | \(0.405952\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.6416 | −0.543256 | −0.271628 | − | 0.962402i | \(-0.587562\pi\) | ||||
−0.271628 | + | 0.962402i | \(0.587562\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.5063 | −0.815423 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −107.917 | −3.73910 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.79706 | 0.0967963 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.06047 | −0.244045 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.9539 | −1.20674 | −0.603371 | − | 0.797461i | \(-0.706176\pi\) | ||||
−0.603371 | + | 0.797461i | \(0.706176\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.2262 | 0.490560 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.4338 | 0.807103 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34.3389 | −1.18129 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.5392 | 0.396492 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.6525 | 0.605832 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.9680 | −0.787333 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.43085 | 0.220188 | 0.110094 | − | 0.993921i | \(-0.464885\pi\) | ||||
0.110094 | + | 0.993921i | \(0.464885\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.42656 | −0.219784 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.2815 | −0.453686 | −0.226843 | − | 0.973931i | \(-0.572840\pi\) | ||||
−0.226843 | + | 0.973931i | \(0.572840\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.8157 | −1.01730 | −0.508650 | − | 0.860974i | \(-0.669855\pi\) | ||||
−0.508650 | + | 0.860974i | \(0.669855\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.6861 | 0.773140 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.5960 | −0.598974 | −0.299487 | − | 0.954100i | \(-0.596816\pi\) | ||||
−0.299487 | + | 0.954100i | \(0.596816\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 59.9609 | 2.03873 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −43.7930 | −1.48729 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.05832 | 0.273360 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.9676 | −0.405506 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.44292 | −0.285750 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.7912 | 0.939515 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.3636 | −0.924003 | −0.462001 | − | 0.886879i | \(-0.652868\pi\) | ||||
−0.462001 | + | 0.886879i | \(0.652868\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.9734 | 0.977249 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.2657 | 0.918604 | 0.459302 | − | 0.888280i | \(-0.348100\pi\) | ||||
0.459302 | + | 0.888280i | \(0.348100\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.1255 | 0.475360 | 0.237680 | − | 0.971344i | \(-0.423613\pi\) | ||||
0.237680 | + | 0.971344i | \(0.423613\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.1857 | −0.342390 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.1172 | 0.474010 | 0.237005 | − | 0.971508i | \(-0.423834\pi\) | ||||
0.237005 | + | 0.971508i | \(0.423834\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.17154 | 0.240526 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.91073 | −0.0975131 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.9752 | 0.936154 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.78257 | 0.0595846 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.33689 | −0.0780266 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −46.4202 | −1.54820 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.0601 | 1.56780 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −52.1929 | −1.73687 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40.6894 | −1.35256 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.3644 | 1.57271 | 0.786354 | − | 0.617776i | \(-0.211966\pi\) | ||||
0.786354 | + | 0.617776i | \(0.211966\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.35436 | 0.0449214 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.8073 | 1.08696 | 0.543478 | − | 0.839423i | \(-0.317107\pi\) | ||||
0.543478 | + | 0.839423i | \(0.317107\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −49.0881 | −1.62458 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.66184 | −0.286352 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.62888 | 0.251928 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.12933 | −0.169201 | −0.0846005 | − | 0.996415i | \(-0.526961\pi\) | ||||
−0.0846005 | + | 0.996415i | \(0.526961\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.5494 | 0.874832 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.817823 | −0.0269190 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.6005 | 0.775980 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.24034 | 0.106427 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 57.3874 | 1.88282 | 0.941410 | − | 0.337264i | \(-0.109501\pi\) | ||||
0.941410 | + | 0.337264i | \(0.109501\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.8008 | −1.04223 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.57114 | −0.215129 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 63.4791 | 2.07599 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.5812 | 0.770366 | 0.385183 | − | 0.922840i | \(-0.374138\pi\) | ||||
0.385183 | + | 0.922840i | \(0.374138\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.39897 | −0.0456538 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.3255 | 0.401800 | 0.200900 | − | 0.979612i | \(-0.435613\pi\) | ||||
0.200900 | + | 0.979612i | \(0.435613\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.6552 | −0.444676 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12.7691 | 0.415378 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.48420 | 0.0807256 | 0.0403628 | − | 0.999185i | \(-0.487149\pi\) | ||||
0.0403628 | + | 0.999185i | \(0.487149\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.59570 | 0.181644 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.0982 | 1.04086 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.7243 | −1.15722 | −0.578612 | − | 0.815603i | \(-0.696405\pi\) | ||||
−0.578612 | + | 0.815603i | \(0.696405\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 56.9193 | 1.84186 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.1371 | −0.618614 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −45.7652 | −1.47784 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.8502 | 0.608071 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.4272 | 0.400460 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28.1570 | 0.906405 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.3114 | 0.460224 | 0.230112 | − | 0.973164i | \(-0.426091\pi\) | ||||
0.230112 | + | 0.973164i | \(0.426091\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.9144 | −0.575494 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.01096 | −0.224992 | −0.112496 | − | 0.993652i | \(-0.535885\pi\) | ||||
−0.112496 | + | 0.993652i | \(0.535885\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −57.7942 | −1.85280 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.40125 | 0.0769015 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.2826 | 0.744876 | 0.372438 | − | 0.928057i | \(-0.378522\pi\) | ||||
0.372438 | + | 0.928057i | \(0.378522\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.8755 | −0.763064 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.9444 | 0.636775 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.28649 | −0.104823 | −0.0524114 | − | 0.998626i | \(-0.516691\pi\) | ||||
−0.0524114 | + | 0.998626i | \(0.516691\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.11840 | −0.0993605 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −55.5846 | −1.76928 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.4160 | 0.998971 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0707 | −0.510502 | −0.255251 | − | 0.966875i | \(-0.582158\pi\) | ||||
−0.255251 | + | 0.966875i | \(0.582158\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30.4241 | −0.965479 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.97938 | −0.284666 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.3838 | −0.898924 | −0.449462 | − | 0.893299i | \(-0.648384\pi\) | ||||
−0.449462 | + | 0.893299i | \(0.648384\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.35845 | −0.264450 |
(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 | 8016.2.a.bg.1.10 | 13 | ||
4.3 | odd | 2 | 4008.2.a.m.1.10 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.m.1.10 | ✓ | 13 | 4.3 | odd | 2 | ||
8016.2.a.bg.1.10 | 13 | 1.1 | even | 1 | trivial |