Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1318017734\) |
Analytic rank: | \(0\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-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 | ||||||||
\(3\) | −0.502871 | −0.290333 | −0.145166 | − | 0.989407i | \(-0.546372\pi\) | ||||
−0.145166 | + | 0.989407i | \(0.546372\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.85170 | −0.828107 | −0.414053 | − | 0.910253i | \(-0.635887\pi\) | ||||
−0.414053 | + | 0.910253i | \(0.635887\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.22131 | 0.461612 | 0.230806 | − | 0.973000i | \(-0.425864\pi\) | ||||
0.230806 | + | 0.973000i | \(0.425864\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.74712 | −0.915707 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.21482 | 1.27082 | 0.635408 | − | 0.772177i | \(-0.280832\pi\) | ||||
0.635408 | + | 0.772177i | \(0.280832\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.01706 | −1.66883 | −0.834416 | − | 0.551134i | \(-0.814195\pi\) | ||||
−0.834416 | + | 0.551134i | \(0.814195\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.931168 | 0.240427 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.53168 | −1.58417 | −0.792083 | − | 0.610414i | \(-0.791003\pi\) | ||||
−0.792083 | + | 0.610414i | \(0.791003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.84005 | −0.880968 | −0.440484 | − | 0.897761i | \(-0.645193\pi\) | ||||
−0.440484 | + | 0.897761i | \(0.645193\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.614162 | −0.134021 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.97402 | 0.828641 | 0.414321 | − | 0.910131i | \(-0.364019\pi\) | ||||
0.414321 | + | 0.910131i | \(0.364019\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.57120 | −0.314239 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.89006 | 0.556193 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.39246 | 0.258573 | 0.129286 | − | 0.991607i | \(-0.458731\pi\) | ||||
0.129286 | + | 0.991607i | \(0.458731\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.43535 | 0.796612 | 0.398306 | − | 0.917253i | \(-0.369598\pi\) | ||||
0.398306 | + | 0.917253i | \(0.369598\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.11951 | −0.368959 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.26150 | −0.382264 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.19690 | 0.361169 | 0.180584 | − | 0.983560i | \(-0.442201\pi\) | ||||
0.180584 | + | 0.983560i | \(0.442201\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.02581 | 0.484517 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.88073 | 0.606068 | 0.303034 | − | 0.952980i | \(-0.402000\pi\) | ||||
0.303034 | + | 0.952980i | \(0.402000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.46434 | 1.44330 | 0.721649 | − | 0.692259i | \(-0.243384\pi\) | ||||
0.721649 | + | 0.692259i | \(0.243384\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.08685 | 0.758303 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.20672 | −0.905343 | −0.452671 | − | 0.891677i | \(-0.649529\pi\) | ||||
−0.452671 | + | 0.891677i | \(0.649529\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.50840 | −0.786914 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.28460 | 0.459936 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.9641 | −1.91812 | −0.959058 | − | 0.283210i | \(-0.908601\pi\) | ||||
−0.959058 | + | 0.283210i | \(0.908601\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.80459 | −1.05237 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.93105 | 0.255774 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.95939 | 0.515468 | 0.257734 | − | 0.966216i | \(-0.417024\pi\) | ||||
0.257734 | + | 0.966216i | \(0.417024\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.2661 | 1.44248 | 0.721239 | − | 0.692686i | \(-0.243573\pi\) | ||||
0.721239 | + | 0.692686i | \(0.243573\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.35509 | −0.422701 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.1418 | 1.38197 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.46928 | 0.301671 | 0.150836 | − | 0.988559i | \(-0.451804\pi\) | ||||
0.150836 | + | 0.988559i | \(0.451804\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.99842 | −0.240582 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.6474 | 1.61964 | 0.809822 | − | 0.586676i | \(-0.199564\pi\) | ||||
0.809822 | + | 0.586676i | \(0.199564\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.80859 | 0.679844 | 0.339922 | − | 0.940454i | \(-0.389599\pi\) | ||||
0.339922 | + | 0.940454i | \(0.389599\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.790110 | 0.0912340 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.14760 | 0.586624 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.22002 | 0.137262 | 0.0686312 | − | 0.997642i | \(-0.478137\pi\) | ||||
0.0686312 | + | 0.997642i | \(0.478137\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.78803 | 0.754226 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.451577 | −0.0495670 | −0.0247835 | − | 0.999693i | \(-0.507890\pi\) | ||||
−0.0247835 | + | 0.999693i | \(0.507890\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0947 | 1.31186 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.700227 | −0.0750722 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.12204 | 0.436935 | 0.218468 | − | 0.975844i | \(-0.429894\pi\) | ||||
0.218468 | + | 0.975844i | \(0.429894\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.34870 | −0.770353 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.23041 | −0.231283 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.11063 | 0.729535 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.44281 | 0.146495 | 0.0732477 | − | 0.997314i | \(-0.476664\pi\) | ||||
0.0732477 | + | 0.997314i | \(0.476664\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.5786 | −1.16369 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.7500 | −1.26868 | −0.634338 | − | 0.773056i | \(-0.718727\pi\) | ||||
−0.634338 | + | 0.773056i | \(0.718727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.7269 | −1.25402 | −0.627011 | − | 0.779011i | \(-0.715722\pi\) | ||||
−0.627011 | + | 0.779011i | \(0.715722\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.13725 | 0.110984 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.70081 | 0.164424 | 0.0822118 | − | 0.996615i | \(-0.473802\pi\) | ||||
0.0822118 | + | 0.996615i | \(0.473802\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.16832 | −0.878165 | −0.439083 | − | 0.898447i | \(-0.644696\pi\) | ||||
−0.439083 | + | 0.898447i | \(0.644696\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.10476 | −0.104859 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.4252 | −1.54515 | −0.772577 | − | 0.634921i | \(-0.781033\pi\) | ||||
−0.772577 | + | 0.634921i | \(0.781033\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.35871 | −0.686203 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.5296 | 1.52816 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.97721 | −0.731270 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.76468 | 0.614971 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.95151 | −0.175962 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1679 | 1.08833 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.67901 | 0.770137 | 0.385069 | − | 0.922888i | \(-0.374178\pi\) | ||||
0.385069 | + | 0.922888i | \(0.374178\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.75935 | −0.419037 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.27041 | −0.373108 | −0.186554 | − | 0.982445i | \(-0.559732\pi\) | ||||
−0.186554 | + | 0.982445i | \(0.559732\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.68989 | −0.406665 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.35154 | −0.460587 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.10572 | 0.692519 | 0.346259 | − | 0.938139i | \(-0.387452\pi\) | ||||
0.346259 | + | 0.938139i | \(0.387452\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.7478 | 1.33571 | 0.667855 | − | 0.744292i | \(-0.267213\pi\) | ||||
0.667855 | + | 0.744292i | \(0.267213\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.12118 | 0.262851 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −25.3608 | −2.12078 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.57842 | −0.214126 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.77002 | 0.228467 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.5303 | 0.944597 | 0.472299 | − | 0.881439i | \(-0.343424\pi\) | ||||
0.472299 | + | 0.881439i | \(0.343424\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1568 | −0.907927 | −0.453964 | − | 0.891020i | \(-0.649990\pi\) | ||||
−0.453964 | + | 0.891020i | \(0.649990\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.9433 | 1.45063 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.21295 | −0.659680 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.8327 | 1.58282 | 0.791410 | − | 0.611286i | \(-0.209347\pi\) | ||||
0.791410 | + | 0.611286i | \(0.209347\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.02214 | 0.556892 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.85352 | 0.382511 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.9357 | 0.934877 | 0.467439 | − | 0.884025i | \(-0.345177\pi\) | ||||
0.467439 | + | 0.884025i | \(0.345177\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.92470 | 0.305538 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.16238 | 0.0899480 | 0.0449740 | − | 0.998988i | \(-0.485680\pi\) | ||||
0.0449740 | + | 0.998988i | \(0.485680\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.2050 | 1.78500 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.5491 | 0.806708 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.8853 | 0.903621 | 0.451810 | − | 0.892114i | \(-0.350778\pi\) | ||||
0.451810 | + | 0.892114i | \(0.350778\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.91892 | −0.145057 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.99106 | −0.149657 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.0215 | 1.27225 | 0.636125 | − | 0.771586i | \(-0.280536\pi\) | ||||
0.636125 | + | 0.771586i | \(0.280536\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.41457 | 0.402462 | 0.201231 | − | 0.979544i | \(-0.435506\pi\) | ||||
0.201231 | + | 0.979544i | \(0.435506\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.66541 | −0.418799 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.06801 | −0.299086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −27.5298 | −2.01318 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.52966 | 0.256745 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0658 | 0.873049 | 0.436524 | − | 0.899692i | \(-0.356209\pi\) | ||||
0.436524 | + | 0.899692i | \(0.356209\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.9406 | −0.931486 | −0.465743 | − | 0.884920i | \(-0.654213\pi\) | ||||
−0.465743 | + | 0.884920i | \(0.654213\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.60290 | −0.401232 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.9387 | 1.27808 | 0.639039 | − | 0.769174i | \(-0.279332\pi\) | ||||
0.639039 | + | 0.769174i | \(0.279332\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.9805 | 1.27460 | 0.637301 | − | 0.770615i | \(-0.280051\pi\) | ||||
0.637301 | + | 0.770615i | \(0.280051\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.24173 | −0.0875850 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.70062 | 0.119360 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.18596 | −0.501889 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.9171 | −0.758792 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.1851 | −1.11955 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.37520 | 0.576573 | 0.288286 | − | 0.957544i | \(-0.406914\pi\) | ||||
0.288286 | + | 0.957544i | \(0.406914\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.86287 | −0.470236 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.5252 | −1.19521 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.41694 | 0.367726 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.92097 | −0.197381 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 39.3015 | 2.64371 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.67169 | −0.379805 | −0.189902 | − | 0.981803i | \(-0.560817\pi\) | ||||
−0.189902 | + | 0.981803i | \(0.560817\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.31627 | 0.287751 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.6346 | 0.971331 | 0.485665 | − | 0.874145i | \(-0.338577\pi\) | ||||
0.485665 | + | 0.874145i | \(0.338577\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.780709 | 0.0515907 | 0.0257953 | − | 0.999667i | \(-0.491788\pi\) | ||||
0.0257953 | + | 0.999667i | \(0.491788\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.58858 | −0.170316 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.62716 | 0.237623 | 0.118811 | − | 0.992917i | \(-0.462092\pi\) | ||||
0.118811 | + | 0.992917i | \(0.462092\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.4930 | 0.749720 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.613511 | −0.0398518 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.16918 | 0.593105 | 0.296552 | − | 0.955017i | \(-0.404163\pi\) | ||||
0.296552 | + | 0.955017i | \(0.404163\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.08353 | −0.327459 | −0.163730 | − | 0.986505i | \(-0.552352\pi\) | ||||
−0.163730 | + | 0.986505i | \(0.552352\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.0837 | −0.775169 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.1999 | 0.651649 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.1058 | 1.47019 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.227085 | 0.0143909 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.53339 | −0.349264 | −0.174632 | − | 0.984634i | \(-0.555874\pi\) | ||||
−0.174632 | + | 0.984634i | \(0.555874\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.7498 | 1.05305 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.08210 | −0.380876 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.48145 | 0.341924 | 0.170962 | − | 0.985278i | \(-0.445313\pi\) | ||||
0.170962 | + | 0.985278i | \(0.445313\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.68310 | 0.166720 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.82525 | −0.236777 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.23059 | 0.445857 | 0.222929 | − | 0.974835i | \(-0.428438\pi\) | ||||
0.222929 | + | 0.974835i | \(0.428438\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.8574 | 1.58840 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.07286 | −0.126857 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.76103 | 0.107372 | 0.0536861 | − | 0.998558i | \(-0.482903\pi\) | ||||
0.0536861 | + | 0.998558i | \(0.482903\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.2906 | 1.65779 | 0.828894 | − | 0.559406i | \(-0.188971\pi\) | ||||
0.828894 | + | 0.559406i | \(0.188971\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.69545 | 0.223659 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.62231 | −0.399340 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.494771 | 0.0297279 | 0.0148639 | − | 0.999890i | \(-0.495268\pi\) | ||||
0.0148639 | + | 0.999890i | \(0.495268\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.1844 | −0.729463 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.5571 | −1.88254 | −0.941268 | − | 0.337660i | \(-0.890365\pi\) | ||||
−0.941268 | + | 0.337660i | \(0.890365\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.7781 | −0.640691 | −0.320345 | − | 0.947301i | \(-0.603799\pi\) | ||||
−0.320345 | + | 0.947301i | \(0.603799\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.57573 | −0.211808 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.73958 | 0.279769 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.6629 | 1.50958 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.725549 | −0.0425325 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.57891 | 0.384344 | 0.192172 | − | 0.981361i | \(-0.438447\pi\) | ||||
0.192172 | + | 0.981361i | \(0.438447\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.33160 | −0.426863 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.1811 | 0.706818 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.9119 | −1.38286 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.5589 | 0.666244 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.41162 | 0.368338 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.8615 | −1.19453 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −31.7686 | −1.81313 | −0.906565 | − | 0.422066i | \(-0.861305\pi\) | ||||
−0.906565 | + | 0.422066i | \(0.861305\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.40001 | 0.364084 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.4947 | 1.89931 | 0.949656 | − | 0.313296i | \(-0.101433\pi\) | ||||
0.949656 | + | 0.313296i | \(0.101433\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.5558 | −1.10536 | −0.552678 | − | 0.833395i | \(-0.686394\pi\) | ||||
−0.552678 | + | 0.833395i | \(0.686394\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.21262 | 0.350042 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.0205 | 0.562807 | 0.281403 | − | 0.959590i | \(-0.409200\pi\) | ||||
0.281403 | + | 0.959590i | \(0.409200\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.86895 | 0.328598 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.855289 | −0.0477376 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.0820 | 1.39560 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.45399 | 0.524413 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.61048 | 0.254960 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.58033 | −0.417917 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.67434 | −0.256925 | −0.128462 | − | 0.991714i | \(-0.541004\pi\) | ||||
−0.128462 | + | 0.991714i | \(0.541004\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.03516 | −0.330725 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.57238 | −0.249816 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.1097 | −1.14992 | −0.574959 | − | 0.818182i | \(-0.694982\pi\) | ||||
−0.574959 | + | 0.818182i | \(0.694982\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.25977 | 0.448609 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.6942 | 1.01235 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.2766 | −0.824861 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.70048 | 0.199227 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.4328 | 0.935841 | 0.467920 | − | 0.883771i | \(-0.345003\pi\) | ||||
0.467920 | + | 0.883771i | \(0.345003\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.8948 | −1.60023 | −0.800116 | − | 0.599845i | \(-0.795229\pi\) | ||||
−0.800116 | + | 0.599845i | \(0.795229\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.3897 | −0.928193 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.40961 | 0.447599 | 0.223799 | − | 0.974635i | \(-0.428154\pi\) | ||||
0.223799 | + | 0.974635i | \(0.428154\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.2709 | −1.34124 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.01151 | 0.212312 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.0122 | 1.74232 | 0.871158 | − | 0.491002i | \(-0.163369\pi\) | ||||
0.871158 | + | 0.491002i | \(0.163369\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.25403 | −0.223896 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.40177 | −0.178546 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.7558 | −0.562983 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.9314 | −1.66681 | −0.833404 | − | 0.552665i | \(-0.813611\pi\) | ||||
−0.833404 | + | 0.552665i | \(0.813611\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.6608 | −0.554981 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.0545 | −0.885425 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.5612 | 0.546839 | 0.273419 | − | 0.961895i | \(-0.411845\pi\) | ||||
0.273419 | + | 0.961895i | \(0.411845\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.11889 | −0.315978 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.37850 | −0.431515 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.4432 | −0.639165 | −0.319583 | − | 0.947558i | \(-0.603543\pi\) | ||||
−0.319583 | + | 0.947558i | \(0.603543\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.36442 | −0.223596 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.91094 | 0.302035 | 0.151018 | − | 0.988531i | \(-0.451745\pi\) | ||||
0.151018 | + | 0.988531i | \(0.451745\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.53183 | −0.485787 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.9997 | −1.32164 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.5597 | −0.738206 | −0.369103 | − | 0.929388i | \(-0.620335\pi\) | ||||
−0.369103 | + | 0.929388i | \(0.620335\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.9571 | −1.31270 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.14747 | 0.108325 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.25911 | −0.113668 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.36575 | 0.369677 | 0.184838 | − | 0.982769i | \(-0.440824\pi\) | ||||
0.184838 | + | 0.982769i | \(0.440824\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.35841 | 0.118068 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.5359 | 0.925638 | 0.462819 | − | 0.886453i | \(-0.346838\pi\) | ||||
0.462819 | + | 0.886453i | \(0.346838\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.6878 | −1.32941 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.5694 | −0.624579 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.25954 | 0.458979 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.3341 | −1.20324 | −0.601622 | − | 0.798781i | \(-0.705479\pi\) | ||||
−0.601622 | + | 0.798781i | \(0.705479\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.07614 | −0.201061 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.83564 | 0.237946 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.836186 | 0.0410468 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.91911 | −0.387801 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.9419 | 1.12079 | 0.560393 | − | 0.828227i | \(-0.310650\pi\) | ||||
0.560393 | + | 0.828227i | \(0.310650\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.32299 | −0.161953 | −0.0809763 | − | 0.996716i | \(-0.525804\pi\) | ||||
−0.0809763 | + | 0.996716i | \(0.525804\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.0506 | 0.829028 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.2626 | 0.497807 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.7594 | 0.665865 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.7532 | 0.615732 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.9210 | 1.00773 | 0.503864 | − | 0.863783i | \(-0.331911\pi\) | ||||
0.503864 | + | 0.863783i | \(0.331911\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.542592 | −0.0260753 | −0.0130377 | − | 0.999915i | \(-0.504150\pi\) | ||||
−0.0130377 | + | 0.999915i | \(0.504150\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.29661 | 0.0621678 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.2604 | −0.730006 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.16784 | 0.0557380 | 0.0278690 | − | 0.999612i | \(-0.491128\pi\) | ||||
0.0278690 | + | 0.999612i | \(0.491128\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.1322 | 0.720583 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.8412 | 1.37029 | 0.685144 | − | 0.728408i | \(-0.259739\pi\) | ||||
0.685144 | + | 0.728408i | \(0.259739\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.63279 | −0.361829 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.79825 | −0.274248 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.7006 | −0.929727 | −0.464864 | − | 0.885382i | \(-0.653897\pi\) | ||||
−0.464864 | + | 0.885382i | \(0.653897\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.3566 | 0.770201 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.61044 | 0.263601 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.6076 | 0.637935 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.6170 | 0.496641 | 0.248321 | − | 0.968678i | \(-0.420121\pi\) | ||||
0.248321 | + | 0.968678i | \(0.420121\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.8770 | −0.881102 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.1370 | 0.937875 | 0.468937 | − | 0.883231i | \(-0.344637\pi\) | ||||
0.468937 | + | 0.883231i | \(0.344637\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.3526 | −1.41061 | −0.705303 | − | 0.708906i | \(-0.749189\pi\) | ||||
−0.705303 | + | 0.708906i | \(0.749189\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.13006 | 0.191527 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.8800 | 1.29013 | 0.645067 | − | 0.764126i | \(-0.276829\pi\) | ||||
0.645067 | + | 0.764126i | \(0.276829\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.01576 | 0.139255 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.97328 | −0.459545 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 39.8905 | 1.83417 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.03347 | 0.276835 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 38.3610 | 1.75643 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −41.1827 | −1.88169 | −0.940843 | − | 0.338843i | \(-0.889965\pi\) | ||||
−0.940843 | + | 0.338843i | \(0.889965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.2189 | −0.602730 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.44069 | −0.111055 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.67166 | −0.121314 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.39414 | −0.108489 | −0.0542443 | − | 0.998528i | \(-0.517275\pi\) | ||||
−0.0542443 | + | 0.998528i | \(0.517275\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.00213 | −0.271426 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.50302 | 0.338606 | 0.169303 | − | 0.985564i | \(-0.445848\pi\) | ||||
0.169303 | + | 0.985564i | \(0.445848\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.09509 | −0.409622 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 21.4401 | 0.963663 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.6677 | 0.747647 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.3451 | 1.31367 | 0.656833 | − | 0.754036i | \(-0.271896\pi\) | ||||
0.656833 | + | 0.754036i | \(0.271896\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.584530 | −0.0261149 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.6093 | 1.05060 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.6692 | −0.518245 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.26012 | −0.321799 | −0.160900 | − | 0.986971i | \(-0.551440\pi\) | ||||
−0.160900 | + | 0.986971i | \(0.551440\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.09409 | 0.313824 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.0980 | −0.489988 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23.5665 | 1.03846 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.1602 | −1.15052 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.97676 | −0.262351 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −44.5673 | −1.95253 | −0.976263 | − | 0.216587i | \(-0.930508\pi\) | ||||
−0.976263 | + | 0.216587i | \(0.930508\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.1505 | −0.924849 | −0.462424 | − | 0.886659i | \(-0.653020\pi\) | ||||
−0.462424 | + | 0.886659i | \(0.653020\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.964970 | 0.0421147 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −28.9703 | −1.26197 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.20714 | −0.313354 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.8769 | −0.472018 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.3506 | −1.01143 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.14940 | −0.136160 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.55965 | −0.369376 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.2169 | −1.00002 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.9194 | 1.97423 | 0.987114 | − | 0.160019i | \(-0.0511557\pi\) | ||||
0.987114 | + | 0.160019i | \(0.0511557\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.72283 | −0.116848 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.9770 | 0.727215 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.5102 | 1.47555 | 0.737774 | − | 0.675048i | \(-0.235877\pi\) | ||||
0.737774 | + | 0.675048i | \(0.235877\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −30.9494 | −1.32089 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.34710 | −0.227794 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.49002 | 0.0633620 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.04569 | 0.0868346 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.6084 | 0.873207 | 0.436603 | − | 0.899654i | \(-0.356181\pi\) | ||||
0.436603 | + | 0.899654i | \(0.356181\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −56.9476 | −2.40862 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.8440 | 0.584493 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.94528 | 0.124129 | 0.0620644 | − | 0.998072i | \(-0.480232\pi\) | ||||
0.0620644 | + | 0.998072i | \(0.480232\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.4146 | 1.27955 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.29030 | 0.348160 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.10275 | 0.213918 | 0.106959 | − | 0.994263i | \(-0.465889\pi\) | ||||
0.106959 | + | 0.994263i | \(0.465889\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.51107 | 0.188782 | 0.0943912 | − | 0.995535i | \(-0.469910\pi\) | ||||
0.0943912 | + | 0.995535i | \(0.469910\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.06753 | −0.253475 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.24397 | −0.260392 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.3780 | −1.72259 | −0.861294 | − | 0.508107i | \(-0.830346\pi\) | ||||
−0.861294 | + | 0.508107i | \(0.830346\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.50747 | 0.270441 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.551516 | −0.0228807 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −58.8561 | −2.43757 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −30.6079 | −1.26548 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.89400 | 0.0781739 | 0.0390869 | − | 0.999236i | \(-0.487555\pi\) | ||||
0.0390869 | + | 0.999236i | \(0.487555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.0320 | −0.701789 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.02085 | −0.371068 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.8856 | −0.488082 | −0.244041 | − | 0.969765i | \(-0.578473\pi\) | ||||
−0.244041 | + | 0.969765i | \(0.578473\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.7714 | 0.605570 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.04187 | −0.370059 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.4594 | 0.795090 | 0.397545 | − | 0.917583i | \(-0.369862\pi\) | ||||
0.397545 | + | 0.917583i | \(0.369862\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.3289 | 0.543697 | 0.271849 | − | 0.962340i | \(-0.412365\pi\) | ||||
0.271849 | + | 0.962340i | \(0.412365\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.78342 | −0.276242 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.5262 | −0.509262 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.8607 | −1.21201 | −0.606005 | − | 0.795461i | \(-0.707229\pi\) | ||||
−0.606005 | + | 0.795461i | \(0.707229\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.855194 | −0.0346542 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.3462 | 1.51087 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.6023 | 1.23601 | 0.618007 | − | 0.786173i | \(-0.287940\pi\) | ||||
0.618007 | + | 0.786173i | \(0.287940\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.61361 | 0.145715 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.47971 | −0.0998292 | −0.0499146 | − | 0.998753i | \(-0.515895\pi\) | ||||
−0.0499146 | + | 0.998753i | \(0.515895\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.9839 | −1.72767 | −0.863835 | − | 0.503775i | \(-0.831944\pi\) | ||||
−0.863835 | + | 0.503775i | \(0.831944\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.4852 | 0.460884 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.03429 | 0.201695 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.6754 | −0.587014 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.13902 | 0.325041 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.3495 | −0.572151 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.6885 | −0.505121 | −0.252561 | − | 0.967581i | \(-0.581273\pi\) | ||||
−0.252561 | + | 0.967581i | \(0.581273\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.21165 | −0.167398 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.0709 | −0.637756 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.1444 | 1.31323 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −37.4909 | −1.48312 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.0042 | −0.790117 | −0.395059 | − | 0.918656i | \(-0.629276\pi\) | ||||
−0.395059 | + | 0.918656i | \(0.629276\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.6939 | −0.421727 | −0.210864 | − | 0.977516i | \(-0.567628\pi\) | ||||
−0.210864 | + | 0.977516i | \(0.567628\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.81290 | 0.347007 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.4438 | 0.489215 | 0.244608 | − | 0.969622i | \(-0.421341\pi\) | ||||
0.244608 | + | 0.969622i | \(0.421341\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.6881 | 0.655065 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.72402 | −0.106763 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.7924 | 0.500607 | 0.250304 | − | 0.968167i | \(-0.419470\pi\) | ||||
0.250304 | + | 0.968167i | \(0.419470\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.90754 | 0.308973 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.9569 | −0.622537 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.4856 | −0.642188 | −0.321094 | − | 0.947047i | \(-0.604050\pi\) | ||||
−0.321094 | + | 0.947047i | \(0.604050\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.14716 | 0.239097 | 0.119548 | − | 0.992828i | \(-0.461855\pi\) | ||||
0.119548 | + | 0.992828i | \(0.461855\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.7636 | −0.767556 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.68429 | 0.336762 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.53366 | 0.214264 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.85213 | 0.110270 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 47.4846 | 1.83312 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.44712 | −0.0943295 | −0.0471648 | − | 0.998887i | \(-0.515019\pi\) | ||||
−0.0471648 | + | 0.998887i | \(0.515019\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.54086 | −0.174778 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.1453 | 1.61978 | 0.809888 | − | 0.586584i | \(-0.199528\pi\) | ||||
0.809888 | + | 0.586584i | \(0.199528\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.76212 | 0.0676241 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.35931 | −0.282009 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.19027 | −0.236864 | −0.118432 | − | 0.992962i | \(-0.537787\pi\) | ||||
−0.118432 | + | 0.992962i | \(0.537787\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.0094 | −0.573479 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.392596 | −0.0149785 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 84.0228 | 3.20102 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.03146 | −0.0772804 | −0.0386402 | − | 0.999253i | \(-0.512303\pi\) | ||||
−0.0386402 | + | 0.999253i | \(0.512303\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.1411 | −0.537175 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.1602 | −1.10611 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.3477 | −0.960113 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.82399 | −0.0689897 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.49497 | −0.245311 | −0.122656 | − | 0.992449i | \(-0.539141\pi\) | ||||
−0.122656 | + | 0.992449i | \(0.539141\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.43621 | −0.318178 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.77950 | −0.217668 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.5717 | −0.585636 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.90116 | −0.371846 | −0.185923 | − | 0.982564i | \(-0.559527\pi\) | ||||
−0.185923 | + | 0.982564i | \(0.559527\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.35153 | −0.125692 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.6262 | 0.660106 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 46.9607 | 1.75623 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.61092 | −0.172198 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 48.7629 | 1.81855 | 0.909275 | − | 0.416196i | \(-0.136637\pi\) | ||||
0.909275 | + | 0.416196i | \(0.136637\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.5435 | −0.578871 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.55636 | 0.0950721 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.18782 | −0.0812537 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.0112 | −0.630909 | −0.315455 | − | 0.948941i | \(-0.602157\pi\) | ||||
−0.315455 | + | 0.948941i | \(0.602157\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.2876 | −0.529169 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −61.8181 | −2.28642 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.5302 | −1.79250 | −0.896251 | − | 0.443547i | \(-0.853720\pi\) | ||||
−0.896251 | + | 0.443547i | \(0.853720\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.12925 | −0.189195 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.4076 | 0.383368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.57201 | −0.315327 | −0.157663 | − | 0.987493i | \(-0.550396\pi\) | ||||
−0.157663 | + | 0.987493i | \(0.550396\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.6193 | −0.426844 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.9505 | −0.585166 | −0.292583 | − | 0.956240i | \(-0.594515\pi\) | ||||
−0.292583 | + | 0.956240i | \(0.594515\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.3506 | −0.782227 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.24054 | 0.0453888 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.07722 | 0.0758999 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.1045 | 1.75536 | 0.877678 | − | 0.479250i | \(-0.159091\pi\) | ||||
0.877678 | + | 0.479250i | \(0.159091\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.78258 | 0.101403 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.6591 | 0.751861 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.9865 | 1.01719 | 0.508593 | − | 0.861007i | \(-0.330166\pi\) | ||||
0.508593 | + | 0.861007i | \(0.330166\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.42299 | −0.305735 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 53.1084 | 1.92518 | 0.962590 | − | 0.270963i | \(-0.0873420\pi\) | ||||
0.962590 | + | 0.270963i | \(0.0873420\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.1974 | −0.405372 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −33.2257 | −1.20128 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.8239 | −0.860230 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.67056 | −0.0602418 | −0.0301209 | − | 0.999546i | \(-0.509589\pi\) | ||||
−0.0301209 | + | 0.999546i | \(0.509589\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.75646 | −0.0992717 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.7799 | −0.855305 | −0.427652 | − | 0.903943i | \(-0.640659\pi\) | ||||
−0.427652 | + | 0.903943i | \(0.640659\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.96881 | −0.250327 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.34925 | −0.0484042 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.9022 | −0.533927 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 57.5211 | 2.05827 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.02429 | 0.143816 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.7242 | −1.31074 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.0846 | 0.430768 | 0.215384 | − | 0.976529i | \(-0.430900\pi\) | ||||
0.215384 | + | 0.976529i | \(0.430900\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.63606 | −0.129447 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.0603 | −0.713262 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −67.7889 | −2.40725 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.0029 | −0.461166 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.78088 | −0.275613 | −0.137806 | − | 0.990459i | \(-0.544005\pi\) | ||||
−0.137806 | + | 0.990459i | \(0.544005\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.5403 | 1.43421 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.3237 | −0.400105 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.4821 | 0.863955 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.98727 | −0.316760 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.885574 | −0.0311737 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.15102 | −0.0756260 | −0.0378130 | − | 0.999285i | \(-0.512039\pi\) | ||||
−0.0378130 | + | 0.999285i | \(0.512039\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.8624 | 1.68068 | 0.840339 | − | 0.542062i | \(-0.182356\pi\) | ||||
0.840339 | + | 0.542062i | \(0.182356\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.7237 | −0.481310 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.1014 | −0.774178 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.3435 | −1.27150 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.1878 | 0.705418 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.2698 | −1.89403 | −0.947014 | − | 0.321193i | \(-0.895916\pi\) | ||||
−0.947014 | + | 0.321193i | \(0.895916\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.8639 | −0.413550 | −0.206775 | − | 0.978389i | \(-0.566297\pi\) | ||||
−0.206775 | + | 0.978389i | \(0.566297\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.33017 | 0.115942 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.86474 | 0.343031 | 0.171515 | − | 0.985181i | \(-0.445134\pi\) | ||||
0.171515 | + | 0.985181i | \(0.445134\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.84772 | 0.0641739 | 0.0320870 | − | 0.999485i | \(-0.489785\pi\) | ||||
0.0320870 | + | 0.999485i | \(0.489785\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.248806 | −0.00863099 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.9791 | 1.24660 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.15239 | −0.0744865 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.8184 | 0.443070 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.86442 | 0.236986 | 0.118493 | − | 0.992955i | \(-0.462194\pi\) | ||||
0.118493 | + | 0.992955i | \(0.462194\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0611 | −0.933140 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.8691 | 0.546562 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −42.9688 | −1.47817 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.26178 | 0.283878 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.41999 | 0.186014 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.73054 | 0.299279 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.98820 | −0.0680746 | −0.0340373 | − | 0.999421i | \(-0.510836\pi\) | ||||
−0.0340373 | + | 0.999421i | \(0.510836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.5338 | −0.668040 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.6812 | −0.808936 | −0.404468 | − | 0.914552i | \(-0.632543\pi\) | ||||
−0.404468 | + | 0.914552i | \(0.632543\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.65466 | 0.0564563 | 0.0282282 | − | 0.999602i | \(-0.491014\pi\) | ||||
0.0282282 | + | 0.999602i | \(0.491014\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.38340 | −0.0812260 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.33561 | 0.113545 | 0.0567727 | − | 0.998387i | \(-0.481919\pi\) | ||||
0.0567727 | + | 0.998387i | \(0.481919\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.0080 | −0.748294 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.9051 | −0.438281 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.14214 | 0.174435 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.8578 | −0.503439 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.96358 | −0.134147 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.8608 | 0.502386 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.3800 | −0.451809 | −0.225905 | − | 0.974149i | \(-0.572534\pi\) | ||||
−0.225905 | + | 0.974149i | \(0.572534\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.30835 | −0.111588 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.7165 | −1.27070 | −0.635351 | − | 0.772224i | \(-0.719144\pi\) | ||||
−0.635351 | + | 0.772224i | \(0.719144\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.3426 | −1.55955 | −0.779776 | − | 0.626059i | \(-0.784667\pi\) | ||||
−0.779776 | + | 0.626059i | \(0.784667\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.68685 | 0.123932 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.6527 | −0.592721 | −0.296360 | − | 0.955076i | \(-0.595773\pi\) | ||||
−0.296360 | + | 0.955076i | \(0.595773\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.5998 | 0.355505 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.6103 | 0.958481 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.8341 | 0.797577 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.5188 | −1.05356 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.0246 | 0.401491 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.17603 | 0.205982 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 91.2090 | 3.03861 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.81264 | −0.193433 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.0262 | −0.333281 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.1702 | 1.20101 | 0.600506 | − | 0.799620i | \(-0.294966\pi\) | ||||
0.600506 | + | 0.799620i | \(0.294966\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 35.0259 | 1.16173 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.4723 | 1.24151 | 0.620756 | − | 0.784004i | \(-0.286826\pi\) | ||||
0.620756 | + | 0.784004i | \(0.286826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.90331 | −0.0629905 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.4906 | 0.346810 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.21550 | −0.172231 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.1712 | 0.599413 | 0.299707 | − | 0.954031i | \(-0.403111\pi\) | ||||
0.299707 | + | 0.954031i | \(0.403111\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.9755 | 0.526411 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −82.1170 | −2.70292 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.45177 | −0.113493 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 34.9624 | 1.14832 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.291725 | 0.00957120 | 0.00478560 | − | 0.999989i | \(-0.498477\pi\) | ||||
0.00478560 | + | 0.999989i | \(0.498477\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.1525 | 0.693246 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.8435 | −0.551433 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 50.9771 | 1.66713 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.8841 | −0.780259 | −0.390129 | − | 0.920760i | \(-0.627570\pi\) | ||||
−0.390129 | + | 0.920760i | \(0.627570\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.83403 | 0.320921 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.95666 | 0.291979 | 0.145989 | − | 0.989286i | \(-0.453363\pi\) | ||||
0.145989 | + | 0.989286i | \(0.453363\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.4221 | 0.502213 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.53589 | −0.212612 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.5212 | −0.601860 | −0.300930 | − | 0.953646i | \(-0.597297\pi\) | ||||
−0.300930 | + | 0.953646i | \(0.597297\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.9506 | −1.13455 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.03902 | −0.163401 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.3162 | 1.04682 | 0.523412 | − | 0.852080i | \(-0.324659\pi\) | ||||
0.523412 | + | 0.852080i | \(0.324659\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.3422 | −0.722978 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.95133 | −0.0954029 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.89961 | 0.319675 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.3277 | −0.365409 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.67233 | −0.150564 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.9622 | 0.771370 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.5321 | −1.27127 | −0.635633 | − | 0.771991i | \(-0.719261\pi\) | ||||
−0.635633 | + | 0.771991i | \(0.719261\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.6130 | −0.405188 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.5506 | −1.07669 | −0.538344 | − | 0.842725i | \(-0.680950\pi\) | ||||
−0.538344 | + | 0.842725i | \(0.680950\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.2329 | 0.616580 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.75414 | −0.152254 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.9643 | 1.18259 | 0.591297 | − | 0.806454i | \(-0.298616\pi\) | ||||
0.591297 | + | 0.806454i | \(0.298616\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.3736 | 0.555264 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.1865 | 0.804142 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.678201 | −0.0216313 | −0.0108156 | − | 0.999942i | \(-0.503443\pi\) | ||||
−0.0108156 | + | 0.999942i | \(0.503443\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.2171 | −1.05839 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.81193 | 0.121335 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.6115 | 1.19598 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.821791 | 0.0261051 | 0.0130525 | − | 0.999915i | \(-0.495845\pi\) | ||||
0.0130525 | + | 0.999915i | \(0.495845\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.35059 | 0.0745937 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −33.2945 | −1.05551 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.4500 | −1.31273 | −0.656367 | − | 0.754442i | \(-0.727908\pi\) | ||||
−0.656367 | + | 0.754442i | \(0.727908\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.34919 | 0.200879 |
(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 | 4024.2.a.f.1.14 | ✓ | 33 | |
4.3 | odd | 2 | 8048.2.a.y.1.20 | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.f.1.14 | ✓ | 33 | 1.1 | even | 1 | trivial | |
8048.2.a.y.1.20 | 33 | 4.3 | odd | 2 |