Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0040411301\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 16x^{7} + 45x^{6} + 67x^{5} - 166x^{4} - 83x^{3} + 152x^{2} + 51x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.58856\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.588564 | 0.263214 | 0.131607 | − | 0.991302i | \(-0.457986\pi\) | ||||
0.131607 | + | 0.991302i | \(0.457986\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.23518 | −0.466855 | −0.233428 | − | 0.972374i | \(-0.574994\pi\) | ||||
−0.233428 | + | 0.972374i | \(0.574994\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.01763 | −1.51287 | −0.756437 | − | 0.654067i | \(-0.773061\pi\) | ||||
−0.756437 | + | 0.654067i | \(0.773061\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.86230 | 1.34856 | 0.674280 | − | 0.738476i | \(-0.264454\pi\) | ||||
0.674280 | + | 0.738476i | \(0.264454\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.588564 | 0.151966 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.70724 | −1.62675 | −0.813373 | − | 0.581743i | \(-0.802371\pi\) | ||||
−0.813373 | + | 0.581743i | \(0.802371\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.72560 | −0.395880 | −0.197940 | − | 0.980214i | \(-0.563425\pi\) | ||||
−0.197940 | + | 0.980214i | \(0.563425\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.23518 | −0.269539 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.90691 | 0.814648 | 0.407324 | − | 0.913284i | \(-0.366462\pi\) | ||||
0.407324 | + | 0.913284i | \(0.366462\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65359 | −0.930719 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.98846 | 1.66912 | 0.834558 | − | 0.550920i | \(-0.185723\pi\) | ||||
0.834558 | + | 0.550920i | \(0.185723\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.36898 | −0.964297 | −0.482149 | − | 0.876089i | \(-0.660144\pi\) | ||||
−0.482149 | + | 0.876089i | \(0.660144\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.01763 | −0.873458 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.726984 | −0.122883 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.07031 | 0.175957 | 0.0879786 | − | 0.996122i | \(-0.471959\pi\) | ||||
0.0879786 | + | 0.996122i | \(0.471959\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.86230 | 0.778591 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.22415 | 0.972050 | 0.486025 | − | 0.873945i | \(-0.338446\pi\) | ||||
0.486025 | + | 0.873945i | \(0.338446\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.74169 | −1.48559 | −0.742797 | − | 0.669517i | \(-0.766501\pi\) | ||||
−0.742797 | + | 0.669517i | \(0.766501\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.588564 | 0.0877379 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.85840 | 0.562806 | 0.281403 | − | 0.959590i | \(-0.409200\pi\) | ||||
0.281403 | + | 0.959590i | \(0.409200\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.47432 | −0.782046 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.70724 | −0.939202 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.57769 | −1.04088 | −0.520438 | − | 0.853900i | \(-0.674231\pi\) | ||||
−0.520438 | + | 0.853900i | \(0.674231\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.95320 | −0.398209 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.72560 | −0.228562 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.99297 | −1.17079 | −0.585393 | − | 0.810750i | \(-0.699060\pi\) | ||||
−0.585393 | + | 0.810750i | \(0.699060\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.59852 | −0.588780 | −0.294390 | − | 0.955685i | \(-0.595116\pi\) | ||||
−0.294390 | + | 0.955685i | \(0.595116\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.23518 | −0.155618 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.86177 | 0.354959 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.2918 | −1.86819 | −0.934093 | − | 0.357029i | \(-0.883790\pi\) | ||||
−0.934093 | + | 0.357029i | \(0.883790\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.90691 | 0.470337 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.37962 | −0.757122 | −0.378561 | − | 0.925576i | \(-0.623581\pi\) | ||||
−0.378561 | + | 0.925576i | \(0.623581\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.12499 | 0.950959 | 0.475479 | − | 0.879727i | \(-0.342275\pi\) | ||||
0.475479 | + | 0.879727i | \(0.342275\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.65359 | −0.537351 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.19770 | 0.706293 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.10983 | −0.687410 | −0.343705 | − | 0.939078i | \(-0.611682\pi\) | ||||
−0.343705 | + | 0.939078i | \(0.611682\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.46966 | 0.380844 | 0.190422 | − | 0.981702i | \(-0.439014\pi\) | ||||
0.190422 | + | 0.981702i | \(0.439014\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.94764 | −0.428182 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.98846 | 0.963664 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.15759 | 0.546703 | 0.273351 | − | 0.961914i | \(-0.411868\pi\) | ||||
0.273351 | + | 0.961914i | \(0.411868\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00583 | −0.629582 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.36898 | −0.556737 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.01563 | −0.104201 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.6764 | −1.38863 | −0.694315 | − | 0.719671i | \(-0.744293\pi\) | ||||
−0.694315 | + | 0.719671i | \(0.744293\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.01763 | −0.504291 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.33213 | −0.331559 | −0.165780 | − | 0.986163i | \(-0.553014\pi\) | ||||
−0.165780 | + | 0.986163i | \(0.553014\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.59690 | −0.157347 | −0.0786737 | − | 0.996900i | \(-0.525069\pi\) | ||||
−0.0786737 | + | 0.996900i | \(0.525069\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.726984 | −0.0709464 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.8858 | 1.24571 | 0.622857 | − | 0.782335i | \(-0.285972\pi\) | ||||
0.622857 | + | 0.782335i | \(0.285972\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.41783 | −0.135804 | −0.0679018 | − | 0.997692i | \(-0.521630\pi\) | ||||
−0.0679018 | + | 0.997692i | \(0.521630\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.07031 | 0.101589 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0186 | −1.69505 | −0.847524 | − | 0.530757i | \(-0.821908\pi\) | ||||
−0.847524 | + | 0.530757i | \(0.821908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.29947 | 0.214426 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.86230 | 0.449520 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.28468 | 0.759455 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.1766 | 1.28879 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.22415 | 0.561213 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.68175 | −0.508191 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.7958 | 1.75659 | 0.878295 | − | 0.478120i | \(-0.158682\pi\) | ||||
0.878295 | + | 0.478120i | \(0.158682\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.74169 | −0.857708 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.29378 | −0.113038 | −0.0565191 | − | 0.998402i | \(-0.518000\pi\) | ||||
−0.0565191 | + | 0.998402i | \(0.518000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.13144 | 0.184819 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.588564 | 0.0506555 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.2142 | 1.29983 | 0.649917 | − | 0.760005i | \(-0.274804\pi\) | ||||
0.649917 | + | 0.760005i | \(0.274804\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.1674 | −1.28649 | −0.643243 | − | 0.765662i | \(-0.722411\pi\) | ||||
−0.643243 | + | 0.765662i | \(0.722411\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.85840 | 0.324936 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −24.3972 | −2.04020 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.29028 | 0.439334 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.47432 | −0.451514 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.4870 | −1.18682 | −0.593412 | − | 0.804899i | \(-0.702220\pi\) | ||||
−0.593412 | + | 0.804899i | \(0.702220\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.68695 | −0.381419 | −0.190709 | − | 0.981647i | \(-0.561079\pi\) | ||||
−0.190709 | + | 0.981647i | \(0.561079\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.70724 | −0.542249 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.15999 | −0.253816 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.2647 | −1.77692 | −0.888458 | − | 0.458958i | \(-0.848223\pi\) | ||||
−0.888458 | + | 0.458958i | \(0.848223\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.57769 | −0.600950 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.82576 | −0.380323 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.8338 | −1.47517 | −0.737587 | − | 0.675252i | \(-0.764035\pi\) | ||||
−0.737587 | + | 0.675252i | \(0.764035\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.95320 | −0.229906 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.6420 | 0.818612 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.72560 | −0.131960 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.471351 | −0.0358362 | −0.0179181 | − | 0.999839i | \(-0.505704\pi\) | ||||
−0.0179181 | + | 0.999839i | \(0.505704\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.74804 | 0.434511 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.99297 | −0.675953 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.7303 | 1.17574 | 0.587868 | − | 0.808957i | \(-0.299967\pi\) | ||||
0.587868 | + | 0.808957i | \(0.299967\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.6079 | 1.01147 | 0.505735 | − | 0.862689i | \(-0.331221\pi\) | ||||
0.505735 | + | 0.862689i | \(0.331221\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.59852 | −0.339932 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.629943 | 0.0463143 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 33.6545 | 2.46106 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.23518 | −0.0898464 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.61701 | −0.695862 | −0.347931 | − | 0.937520i | \(-0.613116\pi\) | ||||
−0.347931 | + | 0.937520i | \(0.613116\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.01313 | 0.216890 | 0.108445 | − | 0.994102i | \(-0.465413\pi\) | ||||
0.108445 | + | 0.994102i | \(0.465413\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.86177 | 0.204936 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.78043 | 0.198097 | 0.0990486 | − | 0.995083i | \(-0.468420\pi\) | ||||
0.0990486 | + | 0.995083i | \(0.468420\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.7220 | 0.901835 | 0.450918 | − | 0.892566i | \(-0.351097\pi\) | ||||
0.450918 | + | 0.892566i | \(0.351097\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.2918 | −1.07860 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.1024 | −0.779236 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.66331 | 0.255857 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.90691 | 0.271549 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.65844 | 0.598917 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.37467 | 0.507693 | 0.253847 | − | 0.967244i | \(-0.418304\pi\) | ||||
0.253847 | + | 0.967244i | \(0.418304\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.37962 | −0.437124 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.73360 | −0.391028 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.63168 | 0.450187 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.12499 | 0.549036 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −32.6126 | −2.19376 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.83212 | 0.457513 | 0.228756 | − | 0.973484i | \(-0.426534\pi\) | ||||
0.228756 | + | 0.973484i | \(0.426534\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.65359 | −0.310240 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.63738 | 0.440538 | 0.220269 | − | 0.975439i | \(-0.429306\pi\) | ||||
0.220269 | + | 0.975439i | \(0.429306\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.4406 | 1.48292 | 0.741458 | − | 0.670999i | \(-0.234135\pi\) | ||||
0.741458 | + | 0.670999i | \(0.234135\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.19770 | 0.407779 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.1458 | −1.71287 | −0.856435 | − | 0.516255i | \(-0.827326\pi\) | ||||
−0.856435 | + | 0.516255i | \(0.827326\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.27091 | 0.148138 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.10983 | −0.396876 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.5154 | −1.32703 | −0.663517 | − | 0.748161i | \(-0.730937\pi\) | ||||
−0.663517 | + | 0.748161i | \(0.730937\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.5369 | −1.32290 | −0.661449 | − | 0.749990i | \(-0.730058\pi\) | ||||
−0.661449 | + | 0.749990i | \(0.730058\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.22199 | −0.205845 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.39040 | −0.533868 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.46966 | 0.219881 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.12657 | 0.323586 | 0.161793 | − | 0.986825i | \(-0.448272\pi\) | ||||
0.161793 | + | 0.986825i | \(0.448272\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.6035 | −1.23246 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.94764 | −0.247211 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.5939 | 1.65888 | 0.829442 | − | 0.558593i | \(-0.188659\pi\) | ||||
0.829442 | + | 0.558593i | \(0.188659\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.32202 | −0.0821466 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.98846 | 0.556372 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.5800 | 0.652393 | 0.326196 | − | 0.945302i | \(-0.394233\pi\) | ||||
0.326196 | + | 0.945302i | \(0.394233\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.45995 | −0.273973 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.15759 | 0.315639 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0877 | 0.615056 | 0.307528 | − | 0.951539i | \(-0.400498\pi\) | ||||
0.307528 | + | 0.951539i | \(0.400498\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.1257 | −1.22255 | −0.611275 | − | 0.791418i | \(-0.709343\pi\) | ||||
−0.611275 | + | 0.791418i | \(0.709343\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.00583 | −0.363489 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.3500 | 1.40806 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.99188 | −0.299933 | −0.149966 | − | 0.988691i | \(-0.547917\pi\) | ||||
−0.149966 | + | 0.988691i | \(0.547917\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.36898 | −0.321432 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.7616 | 1.35784 | 0.678922 | − | 0.734210i | \(-0.262447\pi\) | ||||
0.678922 | + | 0.734210i | \(0.262447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.4891 | −1.39628 | −0.698141 | − | 0.715961i | \(-0.745989\pi\) | ||||
−0.698141 | + | 0.715961i | \(0.745989\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.01563 | −0.0601605 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.68797 | −0.453807 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.9871 | 1.64630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.6764 | −0.801726 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.5327 | 1.66690 | 0.833450 | − | 0.552595i | \(-0.186363\pi\) | ||||
0.833450 | + | 0.552595i | \(0.186363\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.29294 | −0.308167 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.01763 | −0.291153 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.9966 | 1.09860 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0328 | 0.693557 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.33213 | −0.191426 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.70652 | −0.154975 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.14107 | 0.0651242 | 0.0325621 | − | 0.999470i | \(-0.489633\pi\) | ||||
0.0325621 | + | 0.999470i | \(0.489633\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.59690 | −0.0908445 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.8320 | −1.57821 | −0.789103 | − | 0.614261i | \(-0.789454\pi\) | ||||
−0.789103 | + | 0.614261i | \(0.789454\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.27809 | 0.524428 | 0.262214 | − | 0.965010i | \(-0.415547\pi\) | ||||
0.262214 | + | 0.965010i | \(0.415547\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.726984 | −0.0409609 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.0846 | 0.622572 | 0.311286 | − | 0.950316i | \(-0.399240\pi\) | ||||
0.311286 | + | 0.950316i | \(0.399240\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −45.1008 | −2.52516 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.8858 | 0.719214 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.5740 | 0.643997 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.6272 | −1.25513 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.41783 | −0.0784063 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.76583 | −0.262749 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.7641 | 1.58102 | 0.790510 | − | 0.612449i | \(-0.209816\pi\) | ||||
0.790510 | + | 0.612449i | \(0.209816\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.07031 | 0.0586524 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.00018 | −0.491732 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.07043 | 0.221730 | 0.110865 | − | 0.993835i | \(-0.464638\pi\) | ||||
0.110865 | + | 0.993835i | \(0.464638\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.0186 | −0.978636 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.9396 | 1.45886 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4081 | 0.831958 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.29947 | 0.123799 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.34196 | −0.125723 | −0.0628615 | − | 0.998022i | \(-0.520023\pi\) | ||||
−0.0628615 | + | 0.998022i | \(0.520023\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.0906 | 1.07542 | 0.537711 | − | 0.843129i | \(-0.319289\pi\) | ||||
0.537711 | + | 0.843129i | \(0.319289\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.86230 | 0.259530 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.08213 | 0.0575960 | 0.0287980 | − | 0.999585i | \(-0.490832\pi\) | ||||
0.0287980 | + | 0.999585i | \(0.490832\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.75481 | −0.199285 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.28468 | 0.438472 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.25451 | −0.224545 | −0.112272 | − | 0.993677i | \(-0.535813\pi\) | ||||
−0.112272 | + | 0.993677i | \(0.535813\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.0223 | −0.843279 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.1766 | 0.744081 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.78208 | 0.250305 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.5891 | −1.12694 | −0.563472 | − | 0.826135i | \(-0.690535\pi\) | ||||
−0.563472 | + | 0.826135i | \(0.690535\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.22415 | 0.324017 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.35983 | 0.485938 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.46856 | −0.127817 | −0.0639087 | − | 0.997956i | \(-0.520357\pi\) | ||||
−0.0639087 | + | 0.997956i | \(0.520357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.68175 | −0.293404 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 43.7046 | 2.25090 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.7402 | −1.06535 | −0.532675 | − | 0.846320i | \(-0.678813\pi\) | ||||
−0.532675 | + | 0.846320i | \(0.678813\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.7958 | 1.01417 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.1308 | −0.619855 | −0.309928 | − | 0.950760i | \(-0.600305\pi\) | ||||
−0.309928 | + | 0.950760i | \(0.600305\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.64774 | 0.185906 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.74169 | −0.495198 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.2089 | −1.32884 | −0.664422 | − | 0.747358i | \(-0.731322\pi\) | ||||
−0.664422 | + | 0.747358i | \(0.731322\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.2046 | −1.32523 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.29378 | −0.0652626 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.59602 | −0.180936 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.9952 | 1.00353 | 0.501766 | − | 0.865003i | \(-0.332684\pi\) | ||||
0.501766 | + | 0.865003i | \(0.332684\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.13144 | 0.106705 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.4819 | 0.972878 | 0.486439 | − | 0.873715i | \(-0.338296\pi\) | ||||
0.486439 | + | 0.873715i | \(0.338296\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.1056 | −1.30041 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.588564 | 0.0292460 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.37040 | −0.266201 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.9296 | −0.540433 | −0.270217 | − | 0.962800i | \(-0.587095\pi\) | ||||
−0.270217 | + | 0.962800i | \(0.587095\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.2142 | 0.750460 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.1080 | 0.546588 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.04211 | 0.100243 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.1674 | −0.742753 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.80239 | −0.234612 | −0.117306 | − | 0.993096i | \(-0.537426\pi\) | ||||
−0.117306 | + | 0.993096i | \(0.537426\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.5947 | −0.613829 | −0.306915 | − | 0.951737i | \(-0.599297\pi\) | ||||
−0.306915 | + | 0.951737i | \(0.599297\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.85840 | 0.187602 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 31.2128 | 1.51404 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.68002 | 0.274875 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −24.3972 | −1.17791 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.3341 | 1.84649 | 0.923243 | − | 0.384216i | \(-0.125528\pi\) | ||||
0.923243 | + | 0.384216i | \(0.125528\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.6211 | −1.03904 | −0.519521 | − | 0.854458i | \(-0.673890\pi\) | ||||
−0.519521 | + | 0.854458i | \(0.673890\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.29028 | 0.253650 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.74178 | −0.322503 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.0736 | −0.528512 | −0.264256 | − | 0.964453i | \(-0.585126\pi\) | ||||
−0.264256 | + | 0.964453i | \(0.585126\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.47432 | −0.260682 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.7154 | −1.07924 | −0.539620 | − | 0.841909i | \(-0.681432\pi\) | ||||
−0.539620 | + | 0.841909i | \(0.681432\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.03557 | 0.143900 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.4870 | −0.685213 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.64041 | −0.218994 | −0.109497 | − | 0.993987i | \(-0.534924\pi\) | ||||
−0.109497 | + | 0.993987i | \(0.534924\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.2305 | −1.47059 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.68695 | −0.220212 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.53481 | −0.165715 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.63494 | 0.357147 | 0.178574 | − | 0.983927i | \(-0.442852\pi\) | ||||
0.178574 | + | 0.983927i | \(0.442852\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.70724 | −0.313067 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.87870 | −0.0874999 | −0.0437500 | − | 0.999043i | \(-0.513930\pi\) | ||||
−0.0437500 | + | 0.999043i | \(0.513930\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.1989 | −0.473985 | −0.236993 | − | 0.971511i | \(-0.576162\pi\) | ||||
−0.236993 | + | 0.971511i | \(0.576162\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.15999 | −0.146541 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.4879 | 1.27199 | 0.635995 | − | 0.771694i | \(-0.280590\pi\) | ||||
0.635995 | + | 0.771694i | \(0.280590\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.8881 | 0.872173 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.2647 | −1.02590 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 48.8802 | 2.24752 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.03025 | 0.368453 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.57769 | −0.346958 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.84027 | 0.221158 | 0.110579 | − | 0.993867i | \(-0.464730\pi\) | ||||
0.110579 | + | 0.993867i | \(0.464730\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.20415 | 0.237289 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.82576 | −0.219580 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.04944 | −0.365506 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.00720 | 0.226898 | 0.113449 | − | 0.993544i | \(-0.463810\pi\) | ||||
0.113449 | + | 0.993544i | \(0.463810\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.8338 | −0.851692 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.70630 | −0.0770041 | −0.0385021 | − | 0.999259i | \(-0.512259\pi\) | ||||
−0.0385021 | + | 0.999259i | \(0.512259\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −60.2878 | −2.71523 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.95320 | −0.132736 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.88000 | 0.353466 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.2962 | −0.998114 | −0.499057 | − | 0.866569i | \(-0.666320\pi\) | ||||
−0.499057 | + | 0.866569i | \(0.666320\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.40579 | −0.0626811 | −0.0313406 | − | 0.999509i | \(-0.509978\pi\) | ||||
−0.0313406 | + | 0.999509i | \(0.509978\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.96117 | −0.0872709 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.6420 | 0.472626 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −43.1248 | −1.91147 | −0.955737 | − | 0.294223i | \(-0.904939\pi\) | ||||
−0.955737 | + | 0.294223i | \(0.904939\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0359 | −0.443960 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.72560 | −0.0761872 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.939878 | −0.0414160 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.3600 | −0.851454 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.471351 | −0.0206900 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.5381 | 0.812169 | 0.406085 | − | 0.913836i | \(-0.366894\pi\) | ||||
0.406085 | + | 0.913836i | \(0.366894\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.6425 | −1.07754 | −0.538771 | − | 0.842452i | \(-0.681111\pi\) | ||||
−0.538771 | + | 0.842452i | \(0.681111\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.74804 | 0.250865 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 36.0111 | 1.56867 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.73602 | −0.336349 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.99297 | −0.390262 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.2637 | 1.31087 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.58410 | 0.327889 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.7303 | 0.678812 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.4681 | 1.18314 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.0312 | 1.76407 | 0.882034 | − | 0.471186i | \(-0.156174\pi\) | ||||
0.882034 | + | 0.471186i | \(0.156174\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.6079 | 0.583973 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.834484 | −0.0357454 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.5441 | 1.43424 | 0.717121 | − | 0.696948i | \(-0.245459\pi\) | ||||
0.717121 | + | 0.696948i | \(0.245459\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.59852 | −0.196260 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.5105 | −0.660770 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.54676 | 0.320921 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.629943 | 0.0267396 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.42968 | −0.187692 | −0.0938458 | − | 0.995587i | \(-0.529916\pi\) | ||||
−0.0938458 | + | 0.995587i | \(0.529916\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −47.3670 | −2.00341 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 33.6545 | 1.42089 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.13466 | 0.174255 | 0.0871276 | − | 0.996197i | \(-0.472231\pi\) | ||||
0.0871276 | + | 0.996197i | \(0.472231\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.6051 | −0.446160 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.23518 | −0.0518728 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.5937 | 1.49217 | 0.746083 | − | 0.665852i | \(-0.231932\pi\) | ||||
0.746083 | + | 0.665852i | \(0.231932\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.2825 | −1.64392 | −0.821962 | − | 0.569543i | \(-0.807120\pi\) | ||||
−0.821962 | + | 0.569543i | \(0.807120\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.61701 | −0.401756 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.1812 | −0.758208 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.1884 | 1.04860 | 0.524302 | − | 0.851532i | \(-0.324326\pi\) | ||||
0.524302 | + | 0.851532i | \(0.324326\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.01313 | 0.125222 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.28566 | −0.177799 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.0221 | 1.57471 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.86177 | 0.118320 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.6309 | 1.26427 | 0.632136 | − | 0.774857i | \(-0.282178\pi\) | ||||
0.632136 | + | 0.774857i | \(0.282178\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.26473 | 0.381746 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.78043 | 0.114371 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.8460 | −0.691781 | −0.345890 | − | 0.938275i | \(-0.612423\pi\) | ||||
−0.345890 | + | 0.938275i | \(0.612423\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.87606 | 0.199899 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.7220 | 0.520675 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.4465 | 0.508549 | 0.254275 | − | 0.967132i | \(-0.418163\pi\) | ||||
0.254275 | + | 0.967132i | \(0.418163\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.96091 | 0.161569 | 0.0807844 | − | 0.996732i | \(-0.474257\pi\) | ||||
0.0807844 | + | 0.996732i | \(0.474257\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.2918 | −0.622729 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.34386 | 0.339226 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.93264 | −0.240799 | −0.120399 | − | 0.992726i | \(-0.538417\pi\) | ||||
−0.120399 | + | 0.992726i | \(0.538417\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.1024 | −0.449892 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.7607 | 0.758977 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.9450 | 0.563232 | 0.281616 | − | 0.959527i | \(-0.409130\pi\) | ||||
0.281616 | + | 0.959527i | \(0.409130\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.66331 | 0.147719 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.0063 | −0.966457 | −0.483229 | − | 0.875494i | \(-0.660536\pi\) | ||||
−0.483229 | + | 0.875494i | \(0.660536\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 45.8501 | 1.84287 | 0.921435 | − | 0.388533i | \(-0.127018\pi\) | ||||
0.921435 | + | 0.388533i | \(0.127018\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.90691 | 0.156779 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.37056 | −0.255231 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9239 | 0.796956 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.65844 | 0.345785 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.17880 | −0.286238 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.7197 | −0.785030 | −0.392515 | − | 0.919746i | \(-0.628395\pi\) | ||||
−0.392515 | + | 0.919746i | \(0.628395\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.37467 | 0.293117 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.6511 | 0.462358 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.6178 | −1.05464 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.37962 | −0.252374 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.2968 | −1.35464 | −0.677322 | − | 0.735687i | \(-0.736859\pi\) | ||||
−0.677322 | + | 0.735687i | \(0.736859\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.4494 | −0.490957 | −0.245478 | − | 0.969402i | \(-0.578945\pi\) | ||||
−0.245478 | + | 0.969402i | \(0.578945\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.73360 | −0.225760 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.4089 | 1.51001 | 0.755005 | − | 0.655719i | \(-0.227635\pi\) | ||||
0.755005 | + | 0.655719i | \(0.227635\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 45.1234 | 1.77125 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.63168 | 0.259916 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.6064 | 0.728125 | 0.364062 | − | 0.931375i | \(-0.381390\pi\) | ||||
0.364062 | + | 0.931375i | \(0.381390\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.761472 | −0.0297532 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.12499 | 0.316986 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.7868 | 0.537059 | 0.268530 | − | 0.963271i | \(-0.413462\pi\) | ||||
0.268530 | + | 0.963271i | \(0.413462\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.0955 | −0.587149 | −0.293574 | − | 0.955936i | \(-0.594845\pi\) | ||||
−0.293574 | + | 0.955936i | \(0.594845\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −32.6126 | −1.26657 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.25449 | 0.0486468 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.1172 | 1.35974 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.83212 | 0.264145 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.0737 | 0.890750 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.1028 | 0.967642 | 0.483821 | − | 0.875167i | \(-0.339249\pi\) | ||||
0.483821 | + | 0.875167i | \(0.339249\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.65359 | −0.179117 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.75143 | −0.374778 | −0.187389 | − | 0.982286i | \(-0.560002\pi\) | ||||
−0.187389 | + | 0.982286i | \(0.560002\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.8929 | 0.648289 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.63738 | 0.254345 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.0994 | 0.501233 | 0.250616 | − | 0.968086i | \(-0.419367\pi\) | ||||
0.250616 | + | 0.968086i | \(0.419367\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.95450 | 0.342134 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.4406 | 0.856162 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.8450 | −1.40368 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.4983 | −0.475459 | −0.237729 | − | 0.971331i | \(-0.576403\pi\) | ||||
−0.237729 | + | 0.971331i | \(0.576403\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.19770 | 0.235431 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.92700 | −0.338621 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41.7469 | −1.58128 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.1458 | −0.988926 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.26205 | 0.312053 | 0.156027 | − | 0.987753i | \(-0.450131\pi\) | ||||
0.156027 | + | 0.987753i | \(0.450131\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.84692 | −0.0696580 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.27091 | 0.0855276 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.11579 | 0.154790 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.6255 | −0.624382 | −0.312191 | − | 0.950019i | \(-0.601063\pi\) | ||||
−0.312191 | + | 0.950019i | \(0.601063\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.10983 | −0.229137 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.9761 | −0.785563 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.3593 | −0.537008 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.5154 | −0.766163 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.7611 | 0.587788 | 0.293894 | − | 0.955838i | \(-0.405049\pi\) | ||||
0.293894 | + | 0.955838i | \(0.405049\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.97247 | 0.0734585 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.5369 | −0.763775 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −41.8287 | −1.55348 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.66621 | 0.210148 | 0.105074 | − | 0.994464i | \(-0.466492\pi\) | ||||
0.105074 | + | 0.994464i | \(0.466492\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 65.3399 | 2.41668 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.3946 | 0.605549 | 0.302775 | − | 0.953062i | \(-0.402087\pi\) | ||||
0.302775 | + | 0.953062i | \(0.402087\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.22199 | −0.118845 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 76.7285 | 2.82633 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.6648 | 0.539453 | 0.269726 | − | 0.962937i | \(-0.413067\pi\) | ||||
0.269726 | + | 0.962937i | \(0.413067\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.39040 | −0.308229 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.63935 | −0.170201 | −0.0851006 | − | 0.996372i | \(-0.527121\pi\) | ||||
−0.0851006 | + | 0.996372i | \(0.527121\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.52654 | −0.312388 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.46966 | 0.126948 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.9163 | −0.581569 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.52507 | 0.274594 | 0.137297 | − | 0.990530i | \(-0.456159\pi\) | ||||
0.137297 | + | 0.990530i | \(0.456159\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.12657 | 0.186823 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.75857 | −0.100395 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.4148 | 1.79601 | 0.898006 | − | 0.439984i | \(-0.145016\pi\) | ||||
0.898006 | + | 0.439984i | \(0.145016\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.6035 | −0.711561 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.2793 | −1.27887 | −0.639437 | − | 0.768843i | \(-0.720833\pi\) | ||||
−0.639437 | + | 0.768843i | \(0.720833\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.75128 | 0.0634007 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.94764 | −0.142727 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −43.7265 | −1.57887 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.7698 | 1.00140 | 0.500702 | − | 0.865620i | \(-0.333075\pi\) | ||||
0.500702 | + | 0.865620i | \(0.333075\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.5939 | 0.957757 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.62922 | −0.130534 | −0.0652669 | − | 0.997868i | \(-0.520790\pi\) | ||||
−0.0652669 | + | 0.997868i | \(0.520790\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.9851 | 0.897490 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.32202 | −0.0474274 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.7404 | −0.384815 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.0106 | 1.14543 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.98846 | 0.321221 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.1042 | −0.467709 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.3837 | −1.36823 | −0.684116 | − | 0.729374i | \(-0.739812\pi\) | ||||
−0.684116 | + | 0.729374i | \(0.739812\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.5800 | 0.376659 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.2563 | 0.791342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.3594 | −0.794005 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.45995 | −0.158178 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.6530 | 1.15663 | 0.578315 | − | 0.815814i | \(-0.303711\pi\) | ||||
0.578315 | + | 0.815814i | \(0.303711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.8792 | −0.915542 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.15759 | 0.182234 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −40.7682 | −1.43868 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.84026 | −0.100106 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.0877 | 0.355103 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.3338 | −0.961007 | −0.480503 | − | 0.876993i | \(-0.659546\pi\) | ||||
−0.480503 | + | 0.876993i | \(0.659546\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.5168 | −1.28228 | −0.641140 | − | 0.767424i | \(-0.721538\pi\) | ||||
−0.641140 | + | 0.767424i | \(0.721538\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.1257 | −0.705839 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.0849 | −0.388286 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.8103 | 0.588117 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.00583 | −0.209861 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.8331 | −1.21568 | −0.607842 | − | 0.794058i | \(-0.707964\pi\) | ||||
−0.607842 | + | 0.794058i | \(0.707964\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.8026 | 0.969139 | 0.484570 | − | 0.874753i | \(-0.338976\pi\) | ||||
0.484570 | + | 0.874753i | \(0.338976\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 23.3500 | 0.812944 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.08198 | −0.281038 | −0.140519 | − | 0.990078i | \(-0.544877\pi\) | ||||
−0.140519 | + | 0.990078i | \(0.544877\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.93224 | 0.310229 | 0.155115 | − | 0.987896i | \(-0.450425\pi\) | ||||
0.155115 | + | 0.987896i | \(0.450425\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.99188 | −0.173166 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 36.7176 | 1.27219 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.588564 | −0.0203681 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.36898 | −0.185579 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.89723 | −0.238119 | −0.119059 | − | 0.992887i | \(-0.537988\pi\) | ||||
−0.119059 | + | 0.992887i | \(0.537988\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 51.7925 | 1.78595 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.7616 | 0.783952 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.26347 | 0.215470 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.5108 | −0.601677 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.4891 | −0.806143 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.18159 | 0.143343 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.7250 | 1.18896 | 0.594481 | − | 0.804109i | \(-0.297357\pi\) | ||||
0.594481 | + | 0.804109i | \(0.297357\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.01563 | −0.0347337 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.9067 | −1.22655 | −0.613276 | − | 0.789869i | \(-0.710148\pi\) | ||||
−0.613276 | + | 0.789869i | \(0.710148\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.0190 | 1.91134 | 0.955671 | − | 0.294436i | \(-0.0951319\pi\) | ||||
0.955671 | + | 0.294436i | \(0.0951319\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.68797 | −0.262005 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.47561 | −0.118311 | −0.0591556 | − | 0.998249i | \(-0.518841\pi\) | ||||
−0.0591556 | + | 0.998249i | \(0.518841\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.277420 | −0.00943257 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.9871 | 0.950492 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.6569 | 1.03996 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −74.3532 | −2.51936 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.6764 | −0.462877 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.01801 | 0.237252 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.27529 | −0.178134 | −0.0890670 | − | 0.996026i | \(-0.528389\pi\) | ||||
−0.0890670 | + | 0.996026i | \(0.528389\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.5327 | 0.962385 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.5890 | 0.356751 | 0.178376 | − | 0.983962i | \(-0.442916\pi\) | ||||
0.178376 | + | 0.983962i | \(0.442916\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.3144 | −0.952855 | −0.476427 | − | 0.879214i | \(-0.658068\pi\) | ||||
−0.476427 | + | 0.879214i | \(0.658068\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.29294 | −0.177920 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.9274 | −1.10560 | −0.552798 | − | 0.833316i | \(-0.686440\pi\) | ||||
−0.552798 | + | 0.833316i | \(0.686440\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.4514 | −0.820073 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.01763 | −0.168097 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.65807 | −0.222804 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.25827 | 0.309470 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.9966 | 0.634278 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −48.2589 | −1.60952 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 50.8254 | 1.69324 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.0328 | 0.400426 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.00914 | 0.266233 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.3164 | 1.00664 | 0.503320 | − | 0.864100i | \(-0.332112\pi\) | ||||
0.503320 | + | 0.864100i | \(0.332112\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.33213 | −0.110520 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.0150 | 1.88899 | 0.944496 | − | 0.328524i | \(-0.106551\pi\) | ||||
0.944496 | + | 0.328524i | \(0.106551\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.4095 | −0.576169 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.70652 | −0.0894748 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.59806 | 0.0527725 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.9071 | −1.31641 | −0.658206 | − | 0.752838i | \(-0.728685\pi\) | ||||
−0.658206 | + | 0.752838i | \(0.728685\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.14107 | 0.0375995 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31.0196 | −1.02102 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.98077 | −0.163767 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.59690 | −0.0524491 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.0857 | 0.429327 | 0.214663 | − | 0.976688i | \(-0.431135\pi\) | ||||
0.214663 | + | 0.976688i | \(0.431135\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.44650 | 0.309597 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.8320 | −0.911178 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.8078 | 0.647785 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.4531 | −0.831516 | −0.415758 | − | 0.909475i | \(-0.636484\pi\) | ||||
−0.415758 | + | 0.909475i | \(0.636484\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.27809 | 0.302779 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.6123 | 1.51952 | 0.759759 | − | 0.650205i | \(-0.225317\pi\) | ||||
0.759759 | + | 0.650205i | \(0.225317\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.3172 | 0.791878 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.726984 | −0.0236488 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.4433 | 0.924284 | 0.462142 | − | 0.886806i | \(-0.347081\pi\) | ||||
0.462142 | + | 0.886806i | \(0.347081\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.5062 | 1.28242 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.0846 | 0.359442 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.2469 | 0.817829 | 0.408914 | − | 0.912573i | \(-0.365908\pi\) | ||||
0.408914 | + | 0.912573i | \(0.365908\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.66022 | −0.183160 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −45.1008 | −1.45790 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.7923 | −0.606835 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.17405 | −0.0701305 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.8858 | 0.415238 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.77342 | 0.0570884 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.76071 | 0.313883 | 0.156942 | − | 0.987608i | \(-0.449837\pi\) | ||||
0.156942 | + | 0.987608i | \(0.449837\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.5740 | 0.371812 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.6643 | 1.52962 | 0.764810 | − | 0.644256i | \(-0.222833\pi\) | ||||
0.764810 | + | 0.644256i | \(0.222833\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.7346 | 0.600603 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22.6272 | −0.724649 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.6661 | −1.36501 | −0.682505 | − | 0.730881i | \(-0.739110\pi\) | ||||
−0.682505 | + | 0.730881i | \(0.739110\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.8789 | −0.827092 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.41783 | −0.0452679 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.1240 | 0.450486 | 0.225243 | − | 0.974303i | \(-0.427682\pi\) | ||||
0.225243 | + | 0.974303i | \(0.427682\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.63646 | 0.0521419 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.76583 | −0.151698 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −38.0599 | −1.21024 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.5986 | 0.336677 | 0.168339 | − | 0.985729i | \(-0.446160\pi\) | ||||
0.168339 | + | 0.985729i | \(0.446160\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.7641 | 0.912802 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.48768 | 0.237375 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.7128 | −0.846002 | −0.423001 | − | 0.906129i | \(-0.639023\pi\) | ||||
−0.423001 | + | 0.906129i | \(0.639023\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.07031 | 0.0338630 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4008.2.a.i.1.7 | ✓ | 9 | |
4.3 | odd | 2 | 8016.2.a.ba.1.7 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.i.1.7 | ✓ | 9 | 1.1 | even | 1 | trivial | |
8016.2.a.ba.1.7 | 9 | 4.3 | odd | 2 |