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: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 7x^{5} + 11x^{4} + 12x^{3} - 14x^{2} - 6x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
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 | 1.5 | ||
Root | \(1.31154\) 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 | ||||||||
\(5\) | 0.0621653 | 0.0278011 | 0.0139006 | − | 0.999903i | \(-0.495575\pi\) | ||||
0.0139006 | + | 0.999903i | \(0.495575\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.782308 | −0.295685 | −0.147842 | − | 0.989011i | \(-0.547233\pi\) | ||||
−0.147842 | + | 0.989011i | \(0.547233\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.68525 | −0.809633 | −0.404817 | − | 0.914398i | \(-0.632665\pi\) | ||||
−0.404817 | + | 0.914398i | \(0.632665\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.79339 | 1.88415 | 0.942073 | − | 0.335407i | \(-0.108874\pi\) | ||||
0.942073 | + | 0.335407i | \(0.108874\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0621653 | 0.0160510 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.20707 | 1.02036 | 0.510182 | − | 0.860067i | \(-0.329578\pi\) | ||||
0.510182 | + | 0.860067i | \(0.329578\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.94188 | −1.82199 | −0.910996 | − | 0.412416i | \(-0.864685\pi\) | ||||
−0.910996 | + | 0.412416i | \(0.864685\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.782308 | −0.170714 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.42476 | −1.13114 | −0.565570 | − | 0.824700i | \(-0.691344\pi\) | ||||
−0.565570 | + | 0.824700i | \(0.691344\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99614 | −0.999227 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.95740 | 0.363480 | 0.181740 | − | 0.983347i | \(-0.441827\pi\) | ||||
0.181740 | + | 0.983347i | \(0.441827\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.86384 | −0.514361 | −0.257180 | − | 0.966363i | \(-0.582793\pi\) | ||||
−0.257180 | + | 0.966363i | \(0.582793\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.68525 | −0.467442 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0486324 | −0.00822037 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.68582 | −1.26354 | −0.631771 | − | 0.775155i | \(-0.717672\pi\) | ||||
−0.631771 | + | 0.775155i | \(0.717672\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.79339 | 1.08781 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.03431 | −0.317706 | −0.158853 | − | 0.987302i | \(-0.550780\pi\) | ||||
−0.158853 | + | 0.987302i | \(0.550780\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.17082 | 0.788543 | 0.394271 | − | 0.918994i | \(-0.370997\pi\) | ||||
0.394271 | + | 0.918994i | \(0.370997\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0621653 | 0.00926705 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.62796 | 1.11265 | 0.556326 | − | 0.830964i | \(-0.312210\pi\) | ||||
0.556326 | + | 0.830964i | \(0.312210\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.38799 | −0.912571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.20707 | 0.589107 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.26794 | 0.448886 | 0.224443 | − | 0.974487i | \(-0.427944\pi\) | ||||
0.224443 | + | 0.974487i | \(0.427944\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.166929 | −0.0225087 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.94188 | −1.05193 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.33656 | −0.304195 | −0.152097 | − | 0.988366i | \(-0.548603\pi\) | ||||
−0.152097 | + | 0.988366i | \(0.548603\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.7201 | −1.62864 | −0.814322 | − | 0.580413i | \(-0.802891\pi\) | ||||
−0.814322 | + | 0.580413i | \(0.802891\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.782308 | −0.0985615 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.422313 | 0.0523814 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.25024 | 0.152741 | 0.0763706 | − | 0.997080i | \(-0.475667\pi\) | ||||
0.0763706 | + | 0.997080i | \(0.475667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.42476 | −0.653064 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.3346 | −1.46384 | −0.731922 | − | 0.681388i | \(-0.761377\pi\) | ||||
−0.731922 | + | 0.681388i | \(0.761377\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0502 | 1.17628 | 0.588141 | − | 0.808758i | \(-0.299860\pi\) | ||||
0.588141 | + | 0.808758i | \(0.299860\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.99614 | −0.576904 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.10069 | 0.239396 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.71570 | −0.418049 | −0.209025 | − | 0.977910i | \(-0.567029\pi\) | ||||
−0.209025 | + | 0.977910i | \(0.567029\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.1647 | −1.11572 | −0.557861 | − | 0.829934i | \(-0.688378\pi\) | ||||
−0.557861 | + | 0.829934i | \(0.688378\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.261533 | 0.0283673 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.95740 | 0.209855 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.74777 | −0.291263 | −0.145631 | − | 0.989339i | \(-0.546521\pi\) | ||||
−0.145631 | + | 0.989339i | \(0.546521\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.31452 | −0.557113 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.86384 | −0.296966 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.493709 | −0.0506534 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.54807 | 0.157183 | 0.0785914 | − | 0.996907i | \(-0.474958\pi\) | ||||
0.0785914 | + | 0.996907i | \(0.474958\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.68525 | −0.269878 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.5022 | −1.14451 | −0.572254 | − | 0.820076i | \(-0.693931\pi\) | ||||
−0.572254 | + | 0.820076i | \(0.693931\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.8029 | 1.16298 | 0.581489 | − | 0.813554i | \(-0.302470\pi\) | ||||
0.581489 | + | 0.813554i | \(0.302470\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0486324 | −0.00474603 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.5983 | −1.50795 | −0.753974 | − | 0.656904i | \(-0.771866\pi\) | ||||
−0.753974 | + | 0.656904i | \(0.771866\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.4215 | 1.66867 | 0.834337 | − | 0.551255i | \(-0.185851\pi\) | ||||
0.834337 | + | 0.551255i | \(0.185851\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.68582 | −0.729506 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.23856 | −0.398731 | −0.199365 | − | 0.979925i | \(-0.563888\pi\) | ||||
−0.199365 | + | 0.979925i | \(0.563888\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.337232 | −0.0314470 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.79339 | 0.628049 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.29122 | −0.301706 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.78944 | −0.344494 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.03431 | −0.183428 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.621412 | −0.0555808 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.23657 | −0.553406 | −0.276703 | − | 0.960955i | \(-0.589242\pi\) | ||||
−0.276703 | + | 0.960955i | \(0.589242\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.17082 | 0.455265 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.03122 | 0.526950 | 0.263475 | − | 0.964666i | \(-0.415131\pi\) | ||||
0.263475 | + | 0.964666i | \(0.415131\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.21299 | 0.538735 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.0621653 | 0.00535033 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.9123 | −0.932301 | −0.466151 | − | 0.884705i | \(-0.654359\pi\) | ||||
−0.466151 | + | 0.884705i | \(0.654359\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.5444 | 1.48810 | 0.744049 | − | 0.668125i | \(-0.232903\pi\) | ||||
0.744049 | + | 0.668125i | \(0.232903\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.62796 | 0.642390 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.2419 | −1.52547 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.121682 | 0.0101052 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.38799 | −0.526873 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.5444 | 1.10960 | 0.554802 | − | 0.831982i | \(-0.312794\pi\) | ||||
0.554802 | + | 0.831982i | \(0.312794\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.98785 | 0.405905 | 0.202953 | − | 0.979189i | \(-0.434946\pi\) | ||||
0.202953 | + | 0.979189i | \(0.434946\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.20707 | 0.340121 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.178031 | −0.0142998 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.1442 | −0.809593 | −0.404797 | − | 0.914407i | \(-0.632658\pi\) | ||||
−0.404797 | + | 0.914407i | \(0.632658\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.26794 | 0.259164 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.24383 | 0.334461 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.5338 | −1.06005 | −0.530025 | − | 0.847982i | \(-0.677817\pi\) | ||||
−0.530025 | + | 0.847982i | \(0.677817\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.166929 | −0.0129954 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.1501 | 2.55001 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.94188 | −0.607330 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.5805 | 0.956476 | 0.478238 | − | 0.878230i | \(-0.341276\pi\) | ||||
0.478238 | + | 0.878230i | \(0.341276\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.90852 | 0.295456 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.33656 | −0.175627 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.52638 | 0.188830 | 0.0944151 | − | 0.995533i | \(-0.469902\pi\) | ||||
0.0944151 | + | 0.995533i | \(0.469902\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.84207 | 0.731555 | 0.365778 | − | 0.930702i | \(-0.380803\pi\) | ||||
0.365778 | + | 0.930702i | \(0.380803\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.7201 | −0.940298 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.477791 | −0.0351279 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.2970 | −0.826120 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.782308 | −0.0569045 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.47483 | −0.106715 | −0.0533574 | − | 0.998575i | \(-0.516992\pi\) | ||||
−0.0533574 | + | 0.998575i | \(0.516992\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.2332 | −1.09651 | −0.548256 | − | 0.836311i | \(-0.684708\pi\) | ||||
−0.548256 | + | 0.836311i | \(0.684708\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.422313 | 0.0302424 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.2117 | −1.86750 | −0.933752 | − | 0.357920i | \(-0.883486\pi\) | ||||
−0.933752 | + | 0.357920i | \(0.883486\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.1733 | 1.21739 | 0.608693 | − | 0.793406i | \(-0.291694\pi\) | ||||
0.608693 | + | 0.793406i | \(0.291694\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.25024 | 0.0881852 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.53129 | −0.107476 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.126463 | −0.00883259 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.42476 | −0.377047 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.3259 | 1.47514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.7930 | 1.22492 | 0.612461 | − | 0.790501i | \(-0.290180\pi\) | ||||
0.612461 | + | 0.790501i | \(0.290180\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.3346 | −0.845151 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.321445 | 0.0219224 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.24040 | 0.152089 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.0502 | 0.679127 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.5802 | 1.92251 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.3886 | −1.16443 | −0.582214 | − | 0.813035i | \(-0.697813\pi\) | ||||
−0.582214 | + | 0.813035i | \(0.697813\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.99614 | −0.333076 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.9318 | −0.858313 | −0.429157 | − | 0.903230i | \(-0.641189\pi\) | ||||
−0.429157 | + | 0.903230i | \(0.641189\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.6209 | −1.56092 | −0.780458 | − | 0.625209i | \(-0.785014\pi\) | ||||
−0.780458 | + | 0.625209i | \(0.785014\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.10069 | 0.138215 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.4494 | −1.40520 | −0.702598 | − | 0.711587i | \(-0.747977\pi\) | ||||
−0.702598 | + | 0.711587i | \(0.747977\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.474194 | 0.0309330 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.71570 | −0.241361 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.3499 | −1.57506 | −0.787531 | − | 0.616275i | \(-0.788641\pi\) | ||||
−0.787531 | + | 0.616275i | \(0.788641\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.1838 | 0.913656 | 0.456828 | − | 0.889555i | \(-0.348985\pi\) | ||||
0.456828 | + | 0.889555i | \(0.348985\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.397111 | −0.0253705 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −53.9522 | −3.43290 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.1647 | −0.644162 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.79375 | 0.555057 | 0.277528 | − | 0.960717i | \(-0.410485\pi\) | ||||
0.277528 | + | 0.960717i | \(0.410485\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.5668 | 0.915809 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.261533 | 0.0163779 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.693124 | 0.0432359 | 0.0216179 | − | 0.999766i | \(-0.493118\pi\) | ||||
0.0216179 | + | 0.999766i | \(0.493118\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.01268 | 0.373610 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.95740 | 0.121160 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.8980 | −0.918653 | −0.459326 | − | 0.888268i | \(-0.651909\pi\) | ||||
−0.459326 | + | 0.888268i | \(0.651909\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.203152 | 0.0124795 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.74777 | −0.168161 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.68185 | −0.285458 | −0.142729 | − | 0.989762i | \(-0.545588\pi\) | ||||
−0.142729 | + | 0.989762i | \(0.545588\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.76324 | −0.471583 | −0.235792 | − | 0.971804i | \(-0.575768\pi\) | ||||
−0.235792 | + | 0.971804i | \(0.575768\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.31452 | −0.321649 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.4159 | 0.809007 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.5566 | −0.934703 | −0.467352 | − | 0.884072i | \(-0.654792\pi\) | ||||
−0.467352 | + | 0.884072i | \(0.654792\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.86384 | −0.171454 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.94616 | −0.593338 | −0.296669 | − | 0.954980i | \(-0.595876\pi\) | ||||
−0.296669 | + | 0.954980i | \(0.595876\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.1239 | −0.601802 | −0.300901 | − | 0.953655i | \(-0.597287\pi\) | ||||
−0.300901 | + | 0.953655i | \(0.597287\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.493709 | −0.0292448 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.59146 | 0.0939407 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.699411 | 0.0411418 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.54807 | 0.0907495 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.1886 | −1.06259 | −0.531294 | − | 0.847187i | \(-0.678294\pi\) | ||||
−0.531294 | + | 0.847187i | \(0.678294\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.145253 | −0.00845696 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.68525 | −0.155814 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −36.8525 | −2.13123 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.04517 | −0.233160 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.5022 | −0.660782 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.790749 | −0.0452782 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.83095 | 0.504009 | 0.252004 | − | 0.967726i | \(-0.418910\pi\) | ||||
0.252004 | + | 0.967726i | \(0.418910\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.8029 | 0.671446 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.6371 | 0.886699 | 0.443349 | − | 0.896349i | \(-0.353790\pi\) | ||||
0.443349 | + | 0.896349i | \(0.353790\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.0920 | −0.796526 | −0.398263 | − | 0.917271i | \(-0.630387\pi\) | ||||
−0.398263 | + | 0.917271i | \(0.630387\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0486324 | −0.00274012 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.3138 | 0.916273 | 0.458136 | − | 0.888882i | \(-0.348517\pi\) | ||||
0.458136 | + | 0.888882i | \(0.348517\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.25611 | −0.294286 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.5983 | −0.870615 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.4120 | −1.85909 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −33.9407 | −1.88269 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.4215 | 0.963409 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.96741 | −0.328994 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.18087 | 0.449661 | 0.224831 | − | 0.974398i | \(-0.427817\pi\) | ||||
0.224831 | + | 0.974398i | \(0.427817\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.68582 | −0.421181 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.0777215 | 0.00424638 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.5232 | 0.736654 | 0.368327 | − | 0.929696i | \(-0.379931\pi\) | ||||
0.368327 | + | 0.929696i | \(0.379931\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.23856 | −0.230207 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.69012 | 0.416444 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.4735 | 0.565518 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.337232 | −0.0181559 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.4880 | −0.616706 | −0.308353 | − | 0.951272i | \(-0.599778\pi\) | ||||
−0.308353 | + | 0.951272i | \(0.599778\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.7858 | −0.577351 | −0.288676 | − | 0.957427i | \(-0.593215\pi\) | ||||
−0.288676 | + | 0.957427i | \(0.593215\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.79339 | 0.362604 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.6103 | 1.46955 | 0.734773 | − | 0.678313i | \(-0.237289\pi\) | ||||
0.734773 | + | 0.678313i | \(0.237289\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.766782 | −0.0406965 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.29122 | −0.174190 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.3864 | −1.18151 | −0.590755 | − | 0.806851i | \(-0.701170\pi\) | ||||
−0.590755 | + | 0.806851i | \(0.701170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 44.0734 | 2.31965 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.78944 | −0.198894 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.624771 | 0.0327020 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.00665 | −0.104746 | −0.0523731 | − | 0.998628i | \(-0.516678\pi\) | ||||
−0.0523731 | + | 0.998628i | \(0.516678\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.03431 | −0.105902 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.55653 | −0.132729 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.7031 | −0.709519 | −0.354759 | − | 0.934958i | \(-0.615437\pi\) | ||||
−0.354759 | + | 0.934958i | \(0.615437\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.621412 | −0.0320896 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.2974 | 0.684850 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.3044 | 0.837499 | 0.418749 | − | 0.908102i | \(-0.362469\pi\) | ||||
0.418749 | + | 0.908102i | \(0.362469\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.23657 | −0.319509 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.4410 | −0.942293 | −0.471146 | − | 0.882055i | \(-0.656160\pi\) | ||||
−0.471146 | + | 0.882055i | \(0.656160\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.130590 | 0.00665548 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.17082 | 0.262848 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.0693 | −1.01756 | −0.508778 | − | 0.860898i | \(-0.669902\pi\) | ||||
−0.508778 | + | 0.860898i | \(0.669902\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.8223 | −1.15417 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.03122 | 0.304235 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.230988 | −0.0116222 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.72441 | −0.287300 | −0.143650 | − | 0.989629i | \(-0.545884\pi\) | ||||
−0.143650 | + | 0.989629i | \(0.545884\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.21299 | 0.311039 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.6836 | 0.533512 | 0.266756 | − | 0.963764i | \(-0.414048\pi\) | ||||
0.266756 | + | 0.963764i | \(0.414048\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.4552 | −0.969131 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.0621653 | 0.00308902 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.6384 | 1.02301 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.95014 | 0.393109 | 0.196554 | − | 0.980493i | \(-0.437025\pi\) | ||||
0.196554 | + | 0.980493i | \(0.437025\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.9123 | −0.538264 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.82791 | 0.0899457 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.631892 | −0.0310183 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.5444 | 0.859154 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.68925 | −0.229085 | −0.114542 | − | 0.993418i | \(-0.536540\pi\) | ||||
−0.114542 | + | 0.993418i | \(0.536540\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.84889 | −0.480006 | −0.240003 | − | 0.970772i | \(-0.577148\pi\) | ||||
−0.240003 | + | 0.970772i | \(0.577148\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.62796 | 0.370884 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.0191 | −1.01957 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.95105 | 0.481565 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.2419 | −0.880729 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.8797 | −1.53559 | −0.767796 | − | 0.640694i | \(-0.778647\pi\) | ||||
−0.767796 | + | 0.640694i | \(0.778647\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.80718 | −0.279075 | −0.139538 | − | 0.990217i | \(-0.544562\pi\) | ||||
−0.139538 | + | 0.990217i | \(0.544562\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.121682 | 0.00583422 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 43.0828 | 2.06093 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.0785 | 1.19693 | 0.598465 | − | 0.801149i | \(-0.295778\pi\) | ||||
0.598465 | + | 0.801149i | \(0.295778\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.38799 | −0.304190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.2338 | 1.48396 | 0.741981 | − | 0.670421i | \(-0.233886\pi\) | ||||
0.741981 | + | 0.670421i | \(0.233886\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.170816 | −0.00809743 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.5444 | 0.640630 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.12427 | 0.194636 | 0.0973182 | − | 0.995253i | \(-0.468974\pi\) | ||||
0.0973182 | + | 0.995253i | \(0.468974\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.46263 | 0.257225 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.98785 | 0.234350 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.330378 | −0.0154884 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.0521369 | 0.00243886 | 0.00121943 | − | 0.999999i | \(-0.499612\pi\) | ||||
0.00121943 | + | 0.999999i | \(0.499612\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.20707 | 0.196369 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.15218 | −0.239961 | −0.119981 | − | 0.992776i | \(-0.538283\pi\) | ||||
−0.119981 | + | 0.992776i | \(0.538283\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.4668 | 1.41591 | 0.707957 | − | 0.706256i | \(-0.249617\pi\) | ||||
0.707957 | + | 0.706256i | \(0.249617\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.178031 | −0.00825601 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.8990 | 0.689444 | 0.344722 | − | 0.938705i | \(-0.387973\pi\) | ||||
0.344722 | + | 0.938705i | \(0.387973\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.978073 | −0.0451632 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.1442 | −0.467419 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.8849 | −0.638430 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 39.6787 | 1.82058 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.26794 | 0.149629 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.7395 | −0.490702 | −0.245351 | − | 0.969434i | \(-0.578903\pi\) | ||||
−0.245351 | + | 0.969434i | \(0.578903\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −52.2128 | −2.38070 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.24383 | 0.193101 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.0962362 | 0.00436986 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.7875 | −1.25917 | −0.629587 | − | 0.776930i | \(-0.716776\pi\) | ||||
−0.629587 | + | 0.776930i | \(0.716776\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.5338 | −0.612020 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.3242 | −0.917216 | −0.458608 | − | 0.888639i | \(-0.651652\pi\) | ||||
−0.458608 | + | 0.888639i | \(0.651652\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.23492 | 0.370882 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.166929 | −0.00750291 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.64943 | 0.432836 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.4727 | −1.14032 | −0.570158 | − | 0.821535i | \(-0.693118\pi\) | ||||
−0.570158 | + | 0.821535i | \(0.693118\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.3937 | −0.730959 | −0.365480 | − | 0.930819i | \(-0.619095\pi\) | ||||
−0.365480 | + | 0.930819i | \(0.619095\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.715035 | −0.0318186 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 33.1501 | 1.47225 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.3496 | 1.21225 | 0.606124 | − | 0.795370i | \(-0.292723\pi\) | ||||
0.606124 | + | 0.795370i | \(0.292723\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.86232 | −0.347809 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.94188 | −0.350642 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.733733 | 0.0323321 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.4830 | −0.900840 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.5805 | 0.552222 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.2555 | 0.799788 | 0.399894 | − | 0.916562i | \(-0.369047\pi\) | ||||
0.399894 | + | 0.916562i | \(0.369047\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.8011 | −0.647205 | −0.323603 | − | 0.946193i | \(-0.604894\pi\) | ||||
−0.323603 | + | 0.946193i | \(0.604894\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.90852 | 0.170582 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.0484 | −0.524835 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.42801 | 0.279479 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.33656 | −0.101398 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.8199 | −0.598604 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.969675 | −0.0419227 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.52638 | 0.109021 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.1534 | 0.738847 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.165065 | 0.00709671 | 0.00354835 | − | 0.999994i | \(-0.498871\pi\) | ||||
0.00354835 | + | 0.999994i | \(0.498871\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.84207 | 0.422363 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.08301 | 0.0463910 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.3907 | 0.615300 | 0.307650 | − | 0.951500i | \(-0.400457\pi\) | ||||
0.307650 | + | 0.951500i | \(0.400457\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.7201 | −0.542881 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.5454 | −0.662258 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.90682 | 0.123611 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.477791 | −0.0202811 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.70371 | 0.156931 | 0.0784656 | − | 0.996917i | \(-0.474998\pi\) | ||||
0.0784656 | + | 0.996917i | \(0.474998\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.1274 | 1.48573 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.2970 | −0.476961 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39.3783 | 1.65960 | 0.829798 | − | 0.558064i | \(-0.188456\pi\) | ||||
0.829798 | + | 0.558064i | \(0.188456\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.263491 | −0.0110852 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.782308 | −0.0328538 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.8473 | −0.832041 | −0.416020 | − | 0.909355i | \(-0.636575\pi\) | ||||
−0.416020 | + | 0.909355i | \(0.636575\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.1013 | 0.590120 | 0.295060 | − | 0.955479i | \(-0.404660\pi\) | ||||
0.295060 | + | 0.955479i | \(0.404660\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.47483 | −0.0616118 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.1028 | 1.13027 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.5547 | 1.06385 | 0.531927 | − | 0.846790i | \(-0.321468\pi\) | ||||
0.531927 | + | 0.846790i | \(0.321468\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.2332 | −0.633071 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.95193 | 0.329902 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.77522 | −0.363433 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.422313 | 0.0174605 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.2117 | −0.999323 | −0.499661 | − | 0.866221i | \(-0.666542\pi\) | ||||
−0.499661 | + | 0.866221i | \(0.666542\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.7443 | 0.937161 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.2117 | −1.07820 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.2622 | −0.791005 | −0.395503 | − | 0.918465i | \(-0.629430\pi\) | ||||
−0.395503 | + | 0.918465i | \(0.629430\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.204600 | −0.00838777 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.1733 | 0.702858 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.33279 | −0.136174 | −0.0680870 | − | 0.997679i | \(-0.521690\pi\) | ||||
−0.0680870 | + | 0.997679i | \(0.521690\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.2581 | 0.948719 | 0.474359 | − | 0.880331i | \(-0.342680\pi\) | ||||
0.474359 | + | 0.880331i | \(0.342680\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.25024 | 0.0509137 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.235571 | −0.00957733 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.74996 | −0.395739 | −0.197869 | − | 0.980228i | \(-0.563402\pi\) | ||||
−0.197869 | + | 0.980228i | \(0.563402\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.53129 | −0.0620510 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 51.8197 | 2.09640 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.41453 | 0.218691 | 0.109345 | − | 0.994004i | \(-0.465125\pi\) | ||||
0.109345 | + | 0.994004i | \(0.465125\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.126463 | −0.00509950 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.5966 | 1.51358 | 0.756792 | − | 0.653656i | \(-0.226766\pi\) | ||||
0.756792 | + | 0.653656i | \(0.226766\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.5427 | 0.906066 | 0.453033 | − | 0.891494i | \(-0.350342\pi\) | ||||
0.453033 | + | 0.891494i | \(0.350342\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.42476 | −0.217688 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.14960 | 0.0861219 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9420 | 0.997682 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.3259 | 0.851675 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −32.3348 | −1.28927 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.8468 | −1.38723 | −0.693615 | − | 0.720346i | \(-0.743983\pi\) | ||||
−0.693615 | + | 0.720346i | \(0.743983\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.7930 | 0.707209 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.387698 | −0.0153853 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −43.3961 | −1.71942 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.3346 | −0.487948 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.8042 | 0.940211 | 0.470106 | − | 0.882610i | \(-0.344216\pi\) | ||||
0.470106 | + | 0.882610i | \(0.344216\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.8213 | 1.72814 | 0.864072 | − | 0.503369i | \(-0.167906\pi\) | ||||
0.864072 | + | 0.503369i | \(0.167906\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.321445 | 0.0126569 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.9087 | −1.01858 | −0.509288 | − | 0.860596i | \(-0.670091\pi\) | ||||
−0.509288 | + | 0.860596i | \(0.670091\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.27426 | 0.246286 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.24040 | 0.0878084 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.32912 | −0.0520125 | −0.0260063 | − | 0.999662i | \(-0.508279\pi\) | ||||
−0.0260063 | + | 0.999662i | \(0.508279\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.374932 | 0.0146498 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.0502 | 0.392094 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.44424 | −0.134168 | −0.0670842 | − | 0.997747i | \(-0.521370\pi\) | ||||
−0.0670842 | + | 0.997747i | \(0.521370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.5969 | −1.69572 | −0.847862 | − | 0.530217i | \(-0.822111\pi\) | ||||
−0.847862 | + | 0.530217i | \(0.822111\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 28.5802 | 1.10996 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.386232 | 0.0149774 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.6184 | −0.411147 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.3886 | −0.672283 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.1567 | 1.31860 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.8422 | −0.610674 | −0.305337 | − | 0.952244i | \(-0.598769\pi\) | ||||
−0.305337 | + | 0.952244i | \(0.598769\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.99614 | −0.192301 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.0836 | −1.27151 | −0.635753 | − | 0.771893i | \(-0.719310\pi\) | ||||
−0.635753 | + | 0.771893i | \(0.719310\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.21107 | −0.0464765 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.9318 | −0.495547 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.85853 | −0.300698 | −0.150349 | − | 0.988633i | \(-0.548040\pi\) | ||||
−0.150349 | + | 0.988633i | \(0.548040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.678366 | −0.0259190 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.6209 | −0.901195 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.2004 | 0.845766 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.6961 | 1.16773 | 0.583867 | − | 0.811849i | \(-0.301539\pi\) | ||||
0.583867 | + | 0.811849i | \(0.301539\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.10069 | 0.0797987 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.09065 | 0.0413708 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.55848 | −0.324176 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.4494 | −0.811290 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.9235 | −0.752498 | −0.376249 | − | 0.926519i | \(-0.622786\pi\) | ||||
−0.376249 | + | 0.926519i | \(0.622786\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 61.0399 | 2.30216 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.474194 | 0.0178592 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.99823 | 0.338413 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.7984 | 0.630879 | 0.315439 | − | 0.948946i | \(-0.397848\pi\) | ||||
0.315439 | + | 0.948946i | \(0.397848\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.71570 | −0.139350 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.5356 | 0.581814 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.13401 | −0.0424097 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.3499 | −0.909362 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.9584 | −1.22914 | −0.614571 | − | 0.788862i | \(-0.710671\pi\) | ||||
−0.614571 | + | 0.788862i | \(0.710671\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.23354 | −0.343875 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.1838 | 0.527500 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.77944 | −0.363199 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.70734 | 0.137498 | 0.0687488 | − | 0.997634i | \(-0.478099\pi\) | ||||
0.0687488 | + | 0.997634i | \(0.478099\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.7540 | 0.804600 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.2151 | 1.33763 | 0.668817 | − | 0.743427i | \(-0.266801\pi\) | ||||
0.668817 | + | 0.743427i | \(0.266801\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.397111 | −0.0146477 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.35721 | −0.123664 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.7819 | 0.396620 | 0.198310 | − | 0.980139i | \(-0.436455\pi\) | ||||
0.198310 | + | 0.980139i | \(0.436455\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −53.9522 | −1.98198 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.6242 | 0.719941 | 0.359970 | − | 0.932964i | \(-0.382787\pi\) | ||||
0.359970 | + | 0.932964i | \(0.382787\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.841994 | 0.0308483 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.1647 | −0.371907 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.2027 | 0.445877 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.30083 | 0.156939 | 0.0784697 | − | 0.996916i | \(-0.474997\pi\) | ||||
0.0784697 | + | 0.996916i | \(0.474997\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.79375 | 0.320462 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.310071 | 0.0112846 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.62298 | −0.277062 | −0.138531 | − | 0.990358i | \(-0.544238\pi\) | ||||
−0.138531 | + | 0.990358i | \(0.544238\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.5668 | 0.528742 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.0907 | −0.619538 | −0.309769 | − | 0.950812i | \(-0.600252\pi\) | ||||
−0.309769 | + | 0.950812i | \(0.600252\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.6289 | −0.493401 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.261533 | 0.00945576 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.8732 | −0.573147 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.19109 | 0.0790126 | 0.0395063 | − | 0.999219i | \(-0.487421\pi\) | ||||
0.0395063 | + | 0.999219i | \(0.487421\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.693124 | 0.0249623 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.07474 | 0.326396 | 0.163198 | − | 0.986593i | \(-0.447819\pi\) | ||||
0.163198 | + | 0.986593i | \(0.447819\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.3081 | 0.513963 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.01268 | 0.215704 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.1562 | 0.578857 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.1214 | 1.18518 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.95740 | 0.0699518 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.630615 | −0.0225076 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.6175 | −0.592349 | −0.296174 | − | 0.955134i | \(-0.595711\pi\) | ||||
−0.296174 | + | 0.955134i | \(0.595711\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.8980 | −0.530384 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.31586 | 0.117898 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −86.4127 | −3.06860 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.203152 | 0.00720506 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.1950 | −1.06956 | −0.534781 | − | 0.844991i | \(-0.679606\pi\) | ||||
−0.534781 | + | 0.844991i | \(0.679606\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.0913 | 1.13531 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.74777 | −0.0970875 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.9872 | −0.952358 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.263819 | 0.00929839 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.68185 | −0.164809 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.1345 | −1.44621 | −0.723106 | − | 0.690737i | \(-0.757286\pi\) | ||||
−0.723106 | + | 0.690737i | \(0.757286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.9200 | −0.734599 | −0.367299 | − | 0.930103i | \(-0.619718\pi\) | ||||
−0.367299 | + | 0.930103i | \(0.619718\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.76324 | −0.272269 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.841332 | −0.0294706 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −41.0660 | −1.43672 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.31452 | −0.185704 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −53.3825 | −1.86306 | −0.931531 | − | 0.363661i | \(-0.881527\pi\) | ||||
−0.931531 | + | 0.363661i | \(0.881527\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.6317 | −1.34661 | −0.673307 | − | 0.739363i | \(-0.735127\pi\) | ||||
−0.673307 | + | 0.739363i | \(0.735127\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.4159 | 0.467081 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.9769 | 1.04240 | 0.521199 | − | 0.853435i | \(-0.325485\pi\) | ||||
0.521199 | + | 0.853435i | \(0.325485\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.8928 | 1.24661 | 0.623304 | − | 0.781980i | \(-0.285790\pi\) | ||||
0.623304 | + | 0.781980i | \(0.285790\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.5566 | −0.539651 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.8747 | −0.931154 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.0621653 | 0.00215132 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.86384 | −0.0989888 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.0957 | −1.03902 | −0.519510 | − | 0.854464i | \(-0.673885\pi\) | ||||
−0.519510 | + | 0.854464i | \(0.673885\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.1686 | −0.867882 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.94616 | −0.342564 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.06078 | 0.0708931 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.96451 | 0.101862 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.1239 | −0.347450 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 41.6937 | 1.42924 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.80634 | −0.267284 | −0.133642 | − | 0.991030i | \(-0.542667\pi\) | ||||
−0.133642 | + | 0.991030i | \(0.542667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.493709 | −0.0168845 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.4720 | 1.62161 | 0.810806 | − | 0.585315i | \(-0.199029\pi\) | ||||
0.810806 | + | 0.585315i | \(0.199029\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.5484 | 0.496385 | 0.248192 | − | 0.968711i | \(-0.420164\pi\) | ||||
0.248192 | + | 0.968711i | \(0.420164\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.59146 | 0.0542367 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.9903 | −1.49745 | −0.748724 | − | 0.662882i | \(-0.769333\pi\) | ||||
−0.748724 | + | 0.662882i | \(0.769333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.782069 | 0.0265911 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.699411 | 0.0237532 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.97759 | 0.338467 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.49337 | 0.287787 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.54807 | 0.0523943 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.486136 | 0.0164344 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.2054 | −0.614754 | −0.307377 | − | 0.951588i | \(-0.599451\pi\) | ||||
−0.307377 | + | 0.951588i | \(0.599451\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.1886 | −0.613486 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.0285 | −1.82027 | −0.910134 | − | 0.414315i | \(-0.864021\pi\) | ||||
−0.910134 | + | 0.414315i | \(0.864021\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.34816 | 0.247285 | 0.123643 | − | 0.992327i | \(-0.460542\pi\) | ||||
0.123643 | + | 0.992327i | \(0.460542\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.145253 | −0.00488263 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.37946 | −0.314931 | −0.157466 | − | 0.987524i | \(-0.550332\pi\) | ||||
−0.157466 | + | 0.987524i | \(0.550332\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.87892 | 0.163634 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.68525 | −0.0899592 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −60.5803 | −2.02724 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.157053 | 0.00524970 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −36.8525 | −1.23047 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.60568 | −0.186960 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.7484 | 0.458026 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.04517 | −0.134615 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.611835 | 0.0203381 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.2416 | 1.43582 | 0.717908 | − | 0.696138i | \(-0.245100\pi\) | ||||
0.717908 | + | 0.696138i | \(0.245100\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.5022 | −0.381503 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.3176 | 1.07073 | 0.535366 | − | 0.844620i | \(-0.320174\pi\) | ||||
0.535366 | + | 0.844620i | \(0.320174\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.2948 | 0.903325 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.790749 | −0.0261414 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.71827 | −0.155811 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.5180 | 0.907735 | 0.453868 | − | 0.891069i | \(-0.350044\pi\) | ||||
0.453868 | + | 0.891069i | \(0.350044\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.83095 | 0.290990 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −83.7935 | −2.75810 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.3994 | 1.26257 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.8029 | 0.387660 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.3400 | 1.84846 | 0.924228 | − | 0.381841i | \(-0.124710\pi\) | ||||
0.924228 | + | 0.381841i | \(0.124710\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50.7327 | 1.66270 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.6371 | 0.511936 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.702282 | −0.0229671 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.2162 | 0.693104 | 0.346552 | − | 0.938031i | \(-0.387352\pi\) | ||||
0.346552 | + | 0.938031i | \(0.387352\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.0920 | −0.459874 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51.1429 | 1.66721 | 0.833606 | − | 0.552360i | \(-0.186273\pi\) | ||||
0.833606 | + | 0.552360i | \(0.186273\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.0356 | 0.359370 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.0486324 | −0.00158201 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.3320 | 0.985658 | 0.492829 | − | 0.870126i | \(-0.335963\pi\) | ||||
0.492829 | + | 0.870126i | \(0.335963\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 68.2746 | 2.21629 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.3138 | 0.529010 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.9277 | −1.00184 | −0.500922 | − | 0.865492i | \(-0.667006\pi\) | ||||
−0.500922 | + | 0.865492i | \(0.667006\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.0916830 | −0.00296679 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.25611 | −0.169906 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.53678 | 0.275667 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.7984 | −0.735433 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.5983 | −0.502650 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.946977 | −0.0304843 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.89168 | −0.189464 | −0.0947318 | − | 0.995503i | \(-0.530199\pi\) | ||||
−0.0947318 | + | 0.995503i | \(0.530199\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −33.4120 | −1.07335 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.9307 | −0.896340 | −0.448170 | − | 0.893948i | \(-0.647924\pi\) | ||||
−0.448170 | + | 0.893948i | \(0.647924\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.7251 | −0.440008 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −33.9407 | −1.08697 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.6646 | 0.565141 | 0.282570 | − | 0.959247i | \(-0.408813\pi\) | ||||
0.282570 | + | 0.959247i | \(0.408813\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.37844 | 0.235816 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.4215 | 0.556224 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.1753 | −0.834863 | −0.417432 | − | 0.908708i | \(-0.637070\pi\) | ||||
−0.417432 | + | 0.908708i | \(0.637070\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.62946 | −0.0519188 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.96741 | −0.189945 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.0505 | −0.891953 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.799067 | 0.0253832 | 0.0126916 | − | 0.999919i | \(-0.495960\pi\) | ||||
0.0126916 | + | 0.999919i | \(0.495960\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.18087 | 0.259612 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.06758 | 0.0338447 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.0295 | 1.52111 | 0.760555 | − | 0.649274i | \(-0.224927\pi\) | ||||
0.760555 | + | 0.649274i | \(0.224927\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.68582 | −0.243169 |
(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.w.1.5 | 7 | ||
4.3 | odd | 2 | 4008.2.a.g.1.5 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.g.1.5 | ✓ | 7 | 4.3 | odd | 2 | ||
8016.2.a.w.1.5 | 7 | 1.1 | even | 1 | trivial |