Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(1,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.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: | \(30.9760027530\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.27492 | −0.804305 | −0.402152 | − | 0.915573i | \(-0.631738\pi\) | ||||
−0.402152 | + | 0.915573i | \(0.631738\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −2.82475 | −0.353094 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.82475 | 0.464366 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 24.6254 | 1.08830 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −40.7492 | −1.11694 | −0.558470 | − | 0.829525i | \(-0.688611\pi\) | ||||
−0.558470 | + | 0.829525i | \(0.688611\pi\) | |||||||
\(12\) | 8.47425 | 0.203859 | ||||||||
\(13\) | −53.2990 | −1.13711 | −0.568557 | − | 0.822644i | \(-0.692498\pi\) | ||||
−0.568557 | + | 0.822644i | \(0.692498\pi\) | |||||||
\(14\) | 15.9244 | 0.303999 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −33.4228 | −0.522231 | ||||||||
\(17\) | −4.54983 | −0.0649116 | −0.0324558 | − | 0.999473i | \(-0.510333\pi\) | ||||
−0.0324558 | + | 0.999473i | \(0.510333\pi\) | |||||||
\(18\) | −20.4743 | −0.268102 | ||||||||
\(19\) | 122.598 | 1.48031 | 0.740156 | − | 0.672436i | \(-0.234752\pi\) | ||||
0.740156 | + | 0.672436i | \(0.234752\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 92.7010 | 0.898360 | ||||||||
\(23\) | −131.347 | −1.19077 | −0.595387 | − | 0.803439i | \(-0.703001\pi\) | ||||
−0.595387 | + | 0.803439i | \(0.703001\pi\) | |||||||
\(24\) | −73.8762 | −0.628330 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 121.251 | 0.914586 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 19.7733 | 0.133457 | ||||||||
\(29\) | −216.598 | −1.38694 | −0.693470 | − | 0.720486i | \(-0.743919\pi\) | ||||
−0.693470 | + | 0.720486i | \(0.743919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −251.794 | −1.45882 | −0.729412 | − | 0.684075i | \(-0.760206\pi\) | ||||
−0.729412 | + | 0.684075i | \(0.760206\pi\) | |||||||
\(32\) | −120.969 | −0.668267 | ||||||||
\(33\) | 122.248 | 0.644865 | ||||||||
\(34\) | 10.3505 | 0.0522087 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −25.4228 | −0.117698 | ||||||||
\(37\) | −11.8970 | −0.0528610 | −0.0264305 | − | 0.999651i | \(-0.508414\pi\) | ||||
−0.0264305 | + | 0.999651i | \(0.508414\pi\) | |||||||
\(38\) | −278.900 | −1.19062 | ||||||||
\(39\) | 159.897 | 0.656513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −111.752 | −0.425678 | −0.212839 | − | 0.977087i | \(-0.568271\pi\) | ||||
−0.212839 | + | 0.977087i | \(0.568271\pi\) | |||||||
\(42\) | −47.7733 | −0.175514 | ||||||||
\(43\) | −369.196 | −1.30935 | −0.654673 | − | 0.755912i | \(-0.727194\pi\) | ||||
−0.654673 | + | 0.755912i | \(0.727194\pi\) | |||||||
\(44\) | 115.106 | 0.394385 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 298.804 | 0.957744 | ||||||||
\(47\) | 262.694 | 0.815275 | 0.407637 | − | 0.913144i | \(-0.366353\pi\) | ||||
0.407637 | + | 0.913144i | \(0.366353\pi\) | |||||||
\(48\) | 100.268 | 0.301510 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.6495 | 0.0374767 | ||||||||
\(52\) | 150.556 | 0.401508 | ||||||||
\(53\) | 567.100 | 1.46976 | 0.734879 | − | 0.678199i | \(-0.237239\pi\) | ||||
0.734879 | + | 0.678199i | \(0.237239\pi\) | |||||||
\(54\) | 61.4228 | 0.154789 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −172.378 | −0.411339 | ||||||||
\(57\) | −367.794 | −0.854658 | ||||||||
\(58\) | 492.743 | 1.11552 | ||||||||
\(59\) | 839.890 | 1.85330 | 0.926648 | − | 0.375931i | \(-0.122677\pi\) | ||||
0.926648 | + | 0.375931i | \(0.122677\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −485.794 | −1.01966 | −0.509832 | − | 0.860274i | \(-0.670293\pi\) | ||||
−0.509832 | + | 0.860274i | \(0.670293\pi\) | |||||||
\(62\) | 572.811 | 1.17334 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 542.577 | 1.05972 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −278.103 | −0.518668 | ||||||||
\(67\) | 333.691 | 0.608460 | 0.304230 | − | 0.952599i | \(-0.401601\pi\) | ||||
0.304230 | + | 0.952599i | \(0.401601\pi\) | |||||||
\(68\) | 12.8522 | 0.0229199 | ||||||||
\(69\) | 394.042 | 0.687493 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 590.248 | 0.986613 | 0.493306 | − | 0.869856i | \(-0.335788\pi\) | ||||
0.493306 | + | 0.869856i | \(0.335788\pi\) | |||||||
\(72\) | 221.629 | 0.362767 | ||||||||
\(73\) | −490.701 | −0.786743 | −0.393371 | − | 0.919380i | \(-0.628691\pi\) | ||||
−0.393371 | + | 0.919380i | \(0.628691\pi\) | |||||||
\(74\) | 27.0647 | 0.0425164 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −346.309 | −0.522689 | ||||||||
\(77\) | 285.244 | 0.422164 | ||||||||
\(78\) | −363.752 | −0.528037 | ||||||||
\(79\) | 121.691 | 0.173308 | 0.0866539 | − | 0.996238i | \(-0.472383\pi\) | ||||
0.0866539 | + | 0.996238i | \(0.472383\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 254.228 | 0.342375 | ||||||||
\(83\) | −609.608 | −0.806183 | −0.403091 | − | 0.915160i | \(-0.632064\pi\) | ||||
−0.403091 | + | 0.915160i | \(0.632064\pi\) | |||||||
\(84\) | −59.3198 | −0.0770514 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 839.890 | 1.05311 | ||||||||
\(87\) | 649.794 | 0.800750 | ||||||||
\(88\) | −1003.47 | −1.21557 | ||||||||
\(89\) | 719.038 | 0.856381 | 0.428190 | − | 0.903689i | \(-0.359151\pi\) | ||||
0.428190 | + | 0.903689i | \(0.359151\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 373.093 | 0.429789 | ||||||||
\(92\) | 371.023 | 0.420455 | ||||||||
\(93\) | 755.382 | 0.842252 | ||||||||
\(94\) | −597.608 | −0.655729 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 362.908 | 0.385824 | ||||||||
\(97\) | 637.877 | 0.667697 | 0.333849 | − | 0.942627i | \(-0.391653\pi\) | ||||
0.333849 | + | 0.942627i | \(0.391653\pi\) | |||||||
\(98\) | −111.471 | −0.114901 | ||||||||
\(99\) | −366.743 | −0.372313 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 671.148 | 0.661205 | 0.330603 | − | 0.943770i | \(-0.392748\pi\) | ||||
0.330603 | + | 0.943770i | \(0.392748\pi\) | |||||||
\(102\) | −31.0515 | −0.0301427 | ||||||||
\(103\) | 912.412 | 0.872841 | 0.436420 | − | 0.899743i | \(-0.356246\pi\) | ||||
0.436420 | + | 0.899743i | \(0.356246\pi\) | |||||||
\(104\) | −1312.51 | −1.23752 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1290.10 | −1.18213 | ||||||||
\(107\) | 116.736 | 0.105470 | 0.0527350 | − | 0.998609i | \(-0.483206\pi\) | ||||
0.0527350 | + | 0.998609i | \(0.483206\pi\) | |||||||
\(108\) | 76.2683 | 0.0679530 | ||||||||
\(109\) | 837.176 | 0.735660 | 0.367830 | − | 0.929893i | \(-0.380101\pi\) | ||||
0.367830 | + | 0.929893i | \(0.380101\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 35.6911 | 0.0305193 | ||||||||
\(112\) | 233.959 | 0.197385 | ||||||||
\(113\) | 1086.58 | 0.904572 | 0.452286 | − | 0.891873i | \(-0.350609\pi\) | ||||
0.452286 | + | 0.891873i | \(0.350609\pi\) | |||||||
\(114\) | 836.701 | 0.687406 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 611.836 | 0.489720 | ||||||||
\(117\) | −479.691 | −0.379038 | ||||||||
\(118\) | −1910.68 | −1.49061 | ||||||||
\(119\) | 31.8488 | 0.0245343 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 329.495 | 0.247554 | ||||||||
\(122\) | 1105.14 | 0.820121 | ||||||||
\(123\) | 335.257 | 0.245765 | ||||||||
\(124\) | 711.256 | 0.515102 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 143.320 | 0.101333 | ||||||||
\(127\) | 537.113 | 0.375284 | 0.187642 | − | 0.982237i | \(-0.439916\pi\) | ||||
0.187642 | + | 0.982237i | \(0.439916\pi\) | |||||||
\(128\) | −266.564 | −0.184071 | ||||||||
\(129\) | 1107.59 | 0.755951 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1497.39 | 0.998683 | 0.499341 | − | 0.866405i | \(-0.333575\pi\) | ||||
0.499341 | + | 0.866405i | \(0.333575\pi\) | |||||||
\(132\) | −345.319 | −0.227698 | ||||||||
\(133\) | −858.186 | −0.559505 | ||||||||
\(134\) | −759.120 | −0.489388 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −112.042 | −0.0706433 | ||||||||
\(137\) | 1380.09 | 0.860650 | 0.430325 | − | 0.902674i | \(-0.358399\pi\) | ||||
0.430325 | + | 0.902674i | \(0.358399\pi\) | |||||||
\(138\) | −896.412 | −0.552954 | ||||||||
\(139\) | −141.980 | −0.0866374 | −0.0433187 | − | 0.999061i | \(-0.513793\pi\) | ||||
−0.0433187 | + | 0.999061i | \(0.513793\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −788.083 | −0.470699 | ||||||||
\(142\) | −1342.76 | −0.793537 | ||||||||
\(143\) | 2171.89 | 1.27009 | ||||||||
\(144\) | −300.805 | −0.174077 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1116.30 | 0.632781 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 33.6061 | 0.0186649 | ||||||||
\(149\) | −1943.87 | −1.06878 | −0.534390 | − | 0.845238i | \(-0.679458\pi\) | ||||
−0.534390 | + | 0.845238i | \(0.679458\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2654.76 | −1.43074 | −0.715370 | − | 0.698746i | \(-0.753742\pi\) | ||||
−0.715370 | + | 0.698746i | \(0.753742\pi\) | |||||||
\(152\) | 3019.03 | 1.61102 | ||||||||
\(153\) | −40.9485 | −0.0216372 | ||||||||
\(154\) | −648.907 | −0.339548 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −451.669 | −0.231811 | ||||||||
\(157\) | −1665.22 | −0.846489 | −0.423244 | − | 0.906016i | \(-0.639109\pi\) | ||||
−0.423244 | + | 0.906016i | \(0.639109\pi\) | |||||||
\(158\) | −276.837 | −0.139392 | ||||||||
\(159\) | −1701.30 | −0.848565 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 919.430 | 0.450070 | ||||||||
\(162\) | −184.268 | −0.0893672 | ||||||||
\(163\) | 33.0732 | 0.0158926 | 0.00794629 | − | 0.999968i | \(-0.497471\pi\) | ||||
0.00794629 | + | 0.999968i | \(0.497471\pi\) | |||||||
\(164\) | 315.673 | 0.150304 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1386.81 | 0.648417 | ||||||||
\(167\) | −1654.48 | −0.766630 | −0.383315 | − | 0.923618i | \(-0.625218\pi\) | ||||
−0.383315 | + | 0.923618i | \(0.625218\pi\) | |||||||
\(168\) | 517.134 | 0.237486 | ||||||||
\(169\) | 643.784 | 0.293029 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1103.38 | 0.493437 | ||||||||
\(172\) | 1042.89 | 0.462322 | ||||||||
\(173\) | −64.1909 | −0.0282101 | −0.0141050 | − | 0.999901i | \(-0.504490\pi\) | ||||
−0.0141050 | + | 0.999901i | \(0.504490\pi\) | |||||||
\(174\) | −1478.23 | −0.644047 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1361.95 | 0.583300 | ||||||||
\(177\) | −2519.67 | −1.07000 | ||||||||
\(178\) | −1635.75 | −0.688791 | ||||||||
\(179\) | 3914.68 | 1.63462 | 0.817309 | − | 0.576200i | \(-0.195465\pi\) | ||||
0.817309 | + | 0.576200i | \(0.195465\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2058.04 | −0.845156 | −0.422578 | − | 0.906327i | \(-0.638875\pi\) | ||||
−0.422578 | + | 0.906327i | \(0.638875\pi\) | |||||||
\(182\) | −848.756 | −0.345681 | ||||||||
\(183\) | 1457.38 | 0.588704 | ||||||||
\(184\) | −3234.48 | −1.29592 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1718.43 | −0.677428 | ||||||||
\(187\) | 185.402 | 0.0725023 | ||||||||
\(188\) | −742.046 | −0.287869 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 428.048 | 0.162160 | 0.0810798 | − | 0.996708i | \(-0.474163\pi\) | ||||
0.0810798 | + | 0.996708i | \(0.474163\pi\) | |||||||
\(192\) | −1627.73 | −0.611830 | ||||||||
\(193\) | −1604.93 | −0.598576 | −0.299288 | − | 0.954163i | \(-0.596749\pi\) | ||||
−0.299288 | + | 0.954163i | \(0.596749\pi\) | |||||||
\(194\) | −1451.12 | −0.537032 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −138.413 | −0.0504420 | ||||||||
\(197\) | −3738.83 | −1.35218 | −0.676092 | − | 0.736817i | \(-0.736328\pi\) | ||||
−0.676092 | + | 0.736817i | \(0.736328\pi\) | |||||||
\(198\) | 834.309 | 0.299453 | ||||||||
\(199\) | −349.030 | −0.124332 | −0.0621660 | − | 0.998066i | \(-0.519801\pi\) | ||||
−0.0621660 | + | 0.998066i | \(0.519801\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1001.07 | −0.351295 | ||||||||
\(202\) | −1526.81 | −0.531810 | ||||||||
\(203\) | 1516.19 | 0.524214 | ||||||||
\(204\) | −38.5565 | −0.0132328 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2075.66 | −0.702030 | ||||||||
\(207\) | −1182.12 | −0.396924 | ||||||||
\(208\) | 1781.40 | 0.593836 | ||||||||
\(209\) | −4995.77 | −1.65342 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2588.58 | 0.844574 | 0.422287 | − | 0.906462i | \(-0.361227\pi\) | ||||
0.422287 | + | 0.906462i | \(0.361227\pi\) | |||||||
\(212\) | −1601.92 | −0.518962 | ||||||||
\(213\) | −1770.74 | −0.569621 | ||||||||
\(214\) | −265.565 | −0.0848300 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −664.886 | −0.209443 | ||||||||
\(217\) | 1762.56 | 0.551384 | ||||||||
\(218\) | −1904.51 | −0.591695 | ||||||||
\(219\) | 1472.10 | 0.454226 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 242.502 | 0.0738119 | ||||||||
\(222\) | −81.1942 | −0.0245468 | ||||||||
\(223\) | 3236.21 | 0.971804 | 0.485902 | − | 0.874013i | \(-0.338491\pi\) | ||||
0.485902 | + | 0.874013i | \(0.338491\pi\) | |||||||
\(224\) | 846.785 | 0.252581 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2471.88 | −0.727552 | ||||||||
\(227\) | 5631.62 | 1.64662 | 0.823312 | − | 0.567589i | \(-0.192124\pi\) | ||||
0.823312 | + | 0.567589i | \(0.192124\pi\) | |||||||
\(228\) | 1038.93 | 0.301775 | ||||||||
\(229\) | 3770.25 | 1.08797 | 0.543985 | − | 0.839095i | \(-0.316915\pi\) | ||||
0.543985 | + | 0.839095i | \(0.316915\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −855.733 | −0.243736 | ||||||||
\(232\) | −5333.82 | −1.50941 | ||||||||
\(233\) | 6560.90 | 1.84472 | 0.922358 | − | 0.386336i | \(-0.126259\pi\) | ||||
0.922358 | + | 0.386336i | \(0.126259\pi\) | |||||||
\(234\) | 1091.26 | 0.304862 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2372.48 | −0.654387 | ||||||||
\(237\) | −365.073 | −0.100059 | ||||||||
\(238\) | −72.4535 | −0.0197330 | ||||||||
\(239\) | −771.444 | −0.208789 | −0.104394 | − | 0.994536i | \(-0.533290\pi\) | ||||
−0.104394 | + | 0.994536i | \(0.533290\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1252.10 | 0.334668 | 0.167334 | − | 0.985900i | \(-0.446484\pi\) | ||||
0.167334 | + | 0.985900i | \(0.446484\pi\) | |||||||
\(242\) | −749.574 | −0.199109 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 1372.25 | 0.360037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −762.683 | −0.197670 | ||||||||
\(247\) | −6534.35 | −1.68328 | ||||||||
\(248\) | −6200.53 | −1.58764 | ||||||||
\(249\) | 1828.82 | 0.465450 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5166.27 | 1.29917 | 0.649586 | − | 0.760288i | \(-0.274942\pi\) | ||||
0.649586 | + | 0.760288i | \(0.274942\pi\) | |||||||
\(252\) | 177.959 | 0.0444857 | ||||||||
\(253\) | 5352.29 | 1.33002 | ||||||||
\(254\) | −1221.89 | −0.301843 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3734.21 | −0.911672 | ||||||||
\(257\) | −2767.45 | −0.671707 | −0.335854 | − | 0.941914i | \(-0.609025\pi\) | ||||
−0.335854 | + | 0.941914i | \(0.609025\pi\) | |||||||
\(258\) | −2519.67 | −0.608015 | ||||||||
\(259\) | 83.2791 | 0.0199796 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1949.38 | −0.462313 | ||||||||
\(262\) | −3406.44 | −0.803245 | ||||||||
\(263\) | 4101.78 | 0.961699 | 0.480849 | − | 0.876803i | \(-0.340328\pi\) | ||||
0.480849 | + | 0.876803i | \(0.340328\pi\) | |||||||
\(264\) | 3010.40 | 0.701807 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1952.30 | 0.450013 | ||||||||
\(267\) | −2157.11 | −0.494432 | ||||||||
\(268\) | −942.594 | −0.214844 | ||||||||
\(269\) | −6950.84 | −1.57546 | −0.787732 | − | 0.616018i | \(-0.788745\pi\) | ||||
−0.787732 | + | 0.616018i | \(0.788745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7140.29 | −1.60052 | −0.800262 | − | 0.599651i | \(-0.795306\pi\) | ||||
−0.800262 | + | 0.599651i | \(0.795306\pi\) | |||||||
\(272\) | 152.068 | 0.0338988 | ||||||||
\(273\) | −1119.28 | −0.248139 | ||||||||
\(274\) | −3139.59 | −0.692225 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1113.07 | −0.242750 | ||||||||
\(277\) | −1320.51 | −0.286433 | −0.143217 | − | 0.989691i | \(-0.545745\pi\) | ||||
−0.143217 | + | 0.989691i | \(0.545745\pi\) | |||||||
\(278\) | 322.993 | 0.0696829 | ||||||||
\(279\) | −2266.15 | −0.486275 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −204.309 | −0.0433738 | −0.0216869 | − | 0.999765i | \(-0.506904\pi\) | ||||
−0.0216869 | + | 0.999765i | \(0.506904\pi\) | |||||||
\(282\) | 1792.82 | 0.378585 | ||||||||
\(283\) | −975.794 | −0.204964 | −0.102482 | − | 0.994735i | \(-0.532678\pi\) | ||||
−0.102482 | + | 0.994735i | \(0.532678\pi\) | |||||||
\(284\) | −1667.30 | −0.348367 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4940.87 | −1.02154 | ||||||||
\(287\) | 782.267 | 0.160891 | ||||||||
\(288\) | −1088.72 | −0.222756 | ||||||||
\(289\) | −4892.30 | −0.995786 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1913.63 | −0.385495 | ||||||||
\(292\) | 1386.11 | 0.277794 | ||||||||
\(293\) | −607.919 | −0.121212 | −0.0606058 | − | 0.998162i | \(-0.519303\pi\) | ||||
−0.0606058 | + | 0.998162i | \(0.519303\pi\) | |||||||
\(294\) | 334.413 | 0.0663379 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −292.969 | −0.0575286 | ||||||||
\(297\) | 1100.23 | 0.214955 | ||||||||
\(298\) | 4422.14 | 0.859624 | ||||||||
\(299\) | 7000.67 | 1.35405 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2584.37 | 0.494886 | ||||||||
\(302\) | 6039.37 | 1.15075 | ||||||||
\(303\) | −2013.44 | −0.381747 | ||||||||
\(304\) | −4097.56 | −0.773064 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 93.1545 | 0.0174029 | ||||||||
\(307\) | −8037.08 | −1.49414 | −0.747069 | − | 0.664747i | \(-0.768539\pi\) | ||||
−0.747069 | + | 0.664747i | \(0.768539\pi\) | |||||||
\(308\) | −805.744 | −0.149063 | ||||||||
\(309\) | −2737.24 | −0.503935 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5311.60 | 0.968468 | 0.484234 | − | 0.874939i | \(-0.339098\pi\) | ||||
0.484234 | + | 0.874939i | \(0.339098\pi\) | |||||||
\(312\) | 3937.53 | 0.714483 | ||||||||
\(313\) | 1531.61 | 0.276587 | 0.138293 | − | 0.990391i | \(-0.455838\pi\) | ||||
0.138293 | + | 0.990391i | \(0.455838\pi\) | |||||||
\(314\) | 3788.23 | 0.680835 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −343.747 | −0.0611939 | ||||||||
\(317\) | −4219.19 | −0.747549 | −0.373775 | − | 0.927520i | \(-0.621937\pi\) | ||||
−0.373775 | + | 0.927520i | \(0.621937\pi\) | |||||||
\(318\) | 3870.31 | 0.682505 | ||||||||
\(319\) | 8826.19 | 1.54913 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −350.208 | −0.0608931 | ||||||||
\(322\) | −2091.63 | −0.361993 | ||||||||
\(323\) | −557.801 | −0.0960893 | ||||||||
\(324\) | −228.805 | −0.0392327 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −75.2387 | −0.0127825 | ||||||||
\(327\) | −2511.53 | −0.424733 | ||||||||
\(328\) | −2751.95 | −0.463265 | ||||||||
\(329\) | −1838.86 | −0.308145 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8298.19 | 1.37797 | 0.688987 | − | 0.724773i | \(-0.258056\pi\) | ||||
0.688987 | + | 0.724773i | \(0.258056\pi\) | |||||||
\(332\) | 1721.99 | 0.284658 | ||||||||
\(333\) | −107.073 | −0.0176203 | ||||||||
\(334\) | 3763.79 | 0.616604 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −701.878 | −0.113960 | ||||||||
\(337\) | 4348.44 | 0.702892 | 0.351446 | − | 0.936208i | \(-0.385690\pi\) | ||||
0.351446 | + | 0.936208i | \(0.385690\pi\) | |||||||
\(338\) | −1464.56 | −0.235684 | ||||||||
\(339\) | −3259.73 | −0.522255 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10260.4 | 1.62942 | ||||||||
\(342\) | −2510.10 | −0.396874 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −9091.60 | −1.42496 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 146.029 | 0.0226895 | ||||||||
\(347\) | 8345.54 | 1.29110 | 0.645550 | − | 0.763718i | \(-0.276628\pi\) | ||||
0.645550 | + | 0.763718i | \(0.276628\pi\) | |||||||
\(348\) | −1835.51 | −0.282740 | ||||||||
\(349\) | −9982.54 | −1.53110 | −0.765549 | − | 0.643378i | \(-0.777532\pi\) | ||||
−0.765549 | + | 0.643378i | \(0.777532\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1439.07 | 0.218838 | ||||||||
\(352\) | 4929.40 | 0.746414 | ||||||||
\(353\) | −8801.59 | −1.32709 | −0.663543 | − | 0.748138i | \(-0.730948\pi\) | ||||
−0.663543 | + | 0.748138i | \(0.730948\pi\) | |||||||
\(354\) | 5732.04 | 0.860606 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2031.10 | −0.302383 | ||||||||
\(357\) | −95.5465 | −0.0141649 | ||||||||
\(358\) | −8905.56 | −1.31473 | ||||||||
\(359\) | −524.039 | −0.0770409 | −0.0385205 | − | 0.999258i | \(-0.512264\pi\) | ||||
−0.0385205 | + | 0.999258i | \(0.512264\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8171.27 | 1.19132 | ||||||||
\(362\) | 4681.88 | 0.679763 | ||||||||
\(363\) | −988.485 | −0.142926 | ||||||||
\(364\) | −1053.90 | −0.151756 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3315.42 | −0.473497 | ||||||||
\(367\) | 6362.72 | 0.904991 | 0.452495 | − | 0.891767i | \(-0.350534\pi\) | ||||
0.452495 | + | 0.891767i | \(0.350534\pi\) | |||||||
\(368\) | 4389.99 | 0.621858 | ||||||||
\(369\) | −1005.77 | −0.141893 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3969.70 | −0.555516 | ||||||||
\(372\) | −2133.77 | −0.297394 | ||||||||
\(373\) | 11265.8 | 1.56387 | 0.781935 | − | 0.623361i | \(-0.214233\pi\) | ||||
0.781935 | + | 0.623361i | \(0.214233\pi\) | |||||||
\(374\) | −421.774 | −0.0583140 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6468.96 | 0.887263 | ||||||||
\(377\) | 11544.5 | 1.57711 | ||||||||
\(378\) | −429.959 | −0.0585046 | ||||||||
\(379\) | −1151.71 | −0.156094 | −0.0780470 | − | 0.996950i | \(-0.524868\pi\) | ||||
−0.0780470 | + | 0.996950i | \(0.524868\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1611.34 | −0.216670 | ||||||||
\(382\) | −973.774 | −0.130426 | ||||||||
\(383\) | 151.554 | 0.0202195 | 0.0101097 | − | 0.999949i | \(-0.496782\pi\) | ||||
0.0101097 | + | 0.999949i | \(0.496782\pi\) | |||||||
\(384\) | 799.692 | 0.106274 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3651.08 | 0.481437 | ||||||||
\(387\) | −3322.76 | −0.436449 | ||||||||
\(388\) | −1801.84 | −0.235760 | ||||||||
\(389\) | 4794.18 | 0.624870 | 0.312435 | − | 0.949939i | \(-0.398855\pi\) | ||||
0.312435 | + | 0.949939i | \(0.398855\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 597.608 | 0.0772950 | ||||||||
\(392\) | 1206.65 | 0.155471 | ||||||||
\(393\) | −4492.17 | −0.576590 | ||||||||
\(394\) | 8505.52 | 1.08757 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1035.96 | 0.131462 | ||||||||
\(397\) | 4623.94 | 0.584556 | 0.292278 | − | 0.956333i | \(-0.405587\pi\) | ||||
0.292278 | + | 0.956333i | \(0.405587\pi\) | |||||||
\(398\) | 794.014 | 0.100001 | ||||||||
\(399\) | 2574.56 | 0.323030 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3610.63 | −0.449642 | −0.224821 | − | 0.974400i | \(-0.572180\pi\) | ||||
−0.224821 | + | 0.974400i | \(0.572180\pi\) | |||||||
\(402\) | 2277.36 | 0.282548 | ||||||||
\(403\) | 13420.4 | 1.65885 | ||||||||
\(404\) | −1895.83 | −0.233467 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3449.20 | −0.421628 | ||||||||
\(407\) | 484.794 | 0.0590426 | ||||||||
\(408\) | 336.125 | 0.0407859 | ||||||||
\(409\) | 8959.57 | 1.08318 | 0.541592 | − | 0.840641i | \(-0.317822\pi\) | ||||
0.541592 | + | 0.840641i | \(0.317822\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4140.27 | −0.496896 | ||||||||
\(412\) | −2577.34 | −0.308195 | ||||||||
\(413\) | −5879.23 | −0.700480 | ||||||||
\(414\) | 2689.24 | 0.319248 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6447.54 | 0.759896 | ||||||||
\(417\) | 425.940 | 0.0500201 | ||||||||
\(418\) | 11365.0 | 1.32985 | ||||||||
\(419\) | −7078.28 | −0.825290 | −0.412645 | − | 0.910892i | \(-0.635395\pi\) | ||||
−0.412645 | + | 0.910892i | \(0.635395\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11551.5 | 1.33725 | 0.668626 | − | 0.743599i | \(-0.266883\pi\) | ||||
0.668626 | + | 0.743599i | \(0.266883\pi\) | |||||||
\(422\) | −5888.80 | −0.679295 | ||||||||
\(423\) | 2364.25 | 0.271758 | ||||||||
\(424\) | 13965.1 | 1.59954 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4028.29 | 0.458149 | ||||||||
\(427\) | 3400.56 | 0.385397 | ||||||||
\(428\) | −329.750 | −0.0372408 | ||||||||
\(429\) | −6515.67 | −0.733286 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4064.38 | −0.454232 | −0.227116 | − | 0.973868i | \(-0.572930\pi\) | ||||
−0.227116 | + | 0.973868i | \(0.572930\pi\) | |||||||
\(432\) | 902.415 | 0.100503 | ||||||||
\(433\) | −17456.3 | −1.93740 | −0.968701 | − | 0.248229i | \(-0.920151\pi\) | ||||
−0.968701 | + | 0.248229i | \(0.920151\pi\) | |||||||
\(434\) | −4009.67 | −0.443480 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2364.81 | −0.259757 | ||||||||
\(437\) | −16102.9 | −1.76271 | ||||||||
\(438\) | −3348.91 | −0.365336 | ||||||||
\(439\) | 4595.39 | 0.499604 | 0.249802 | − | 0.968297i | \(-0.419635\pi\) | ||||
0.249802 | + | 0.968297i | \(0.419635\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | −551.671 | −0.0593672 | ||||||||
\(443\) | 306.214 | 0.0328412 | 0.0164206 | − | 0.999865i | \(-0.494773\pi\) | ||||
0.0164206 | + | 0.999865i | \(0.494773\pi\) | |||||||
\(444\) | −100.818 | −0.0107762 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7362.10 | −0.781627 | ||||||||
\(447\) | 5831.61 | 0.617060 | ||||||||
\(448\) | −3798.04 | −0.400537 | ||||||||
\(449\) | 9229.22 | 0.970053 | 0.485026 | − | 0.874500i | \(-0.338810\pi\) | ||||
0.485026 | + | 0.874500i | \(0.338810\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4553.82 | 0.475457 | ||||||||
\(452\) | −3069.31 | −0.319399 | ||||||||
\(453\) | 7964.29 | 0.826038 | ||||||||
\(454\) | −12811.5 | −1.32439 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9057.08 | −0.930124 | ||||||||
\(457\) | 10992.2 | 1.12515 | 0.562577 | − | 0.826745i | \(-0.309810\pi\) | ||||
0.562577 | + | 0.826745i | \(0.309810\pi\) | |||||||
\(458\) | −8577.01 | −0.875059 | ||||||||
\(459\) | 122.846 | 0.0124922 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7387.88 | 0.746394 | 0.373197 | − | 0.927752i | \(-0.378261\pi\) | ||||
0.373197 | + | 0.927752i | \(0.378261\pi\) | |||||||
\(462\) | 1946.72 | 0.196038 | ||||||||
\(463\) | −10163.8 | −1.02020 | −0.510101 | − | 0.860114i | \(-0.670392\pi\) | ||||
−0.510101 | + | 0.860114i | \(0.670392\pi\) | |||||||
\(464\) | 7239.30 | 0.724302 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14925.5 | −1.48371 | ||||||||
\(467\) | 15814.6 | 1.56705 | 0.783524 | − | 0.621362i | \(-0.213420\pi\) | ||||
0.783524 | + | 0.621362i | \(0.213420\pi\) | |||||||
\(468\) | 1355.01 | 0.133836 | ||||||||
\(469\) | −2335.84 | −0.229976 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4995.65 | 0.488720 | ||||||||
\(472\) | 20682.6 | 2.01694 | ||||||||
\(473\) | 15044.4 | 1.46246 | ||||||||
\(474\) | 830.511 | 0.0804782 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −89.9651 | −0.00866290 | ||||||||
\(477\) | 5103.90 | 0.489919 | ||||||||
\(478\) | 1754.97 | 0.167930 | ||||||||
\(479\) | −1444.85 | −0.137823 | −0.0689113 | − | 0.997623i | \(-0.521953\pi\) | ||||
−0.0689113 | + | 0.997623i | \(0.521953\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 634.099 | 0.0601090 | ||||||||
\(482\) | −2848.43 | −0.269175 | ||||||||
\(483\) | −2758.29 | −0.259848 | ||||||||
\(484\) | −930.742 | −0.0874100 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 552.805 | 0.0515962 | ||||||||
\(487\) | 489.402 | 0.0455378 | 0.0227689 | − | 0.999741i | \(-0.492752\pi\) | ||||
0.0227689 | + | 0.999741i | \(0.492752\pi\) | |||||||
\(488\) | −11962.9 | −1.10970 | ||||||||
\(489\) | −99.2195 | −0.00917559 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3941.30 | −0.362257 | −0.181129 | − | 0.983459i | \(-0.557975\pi\) | ||||
−0.181129 | + | 0.983459i | \(0.557975\pi\) | |||||||
\(492\) | −947.019 | −0.0867783 | ||||||||
\(493\) | 985.485 | 0.0900284 | ||||||||
\(494\) | 14865.1 | 1.35387 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8415.65 | 0.761843 | ||||||||
\(497\) | −4131.73 | −0.372905 | ||||||||
\(498\) | −4160.42 | −0.374363 | ||||||||
\(499\) | 11.0894 | 0.000994850 0 | 0.000497425 | − | 1.00000i | \(-0.499842\pi\) | ||||
0.000497425 | 1.00000i | \(0.499842\pi\) | ||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4963.43 | 0.442614 | ||||||||
\(502\) | −11752.8 | −1.04493 | ||||||||
\(503\) | −7088.41 | −0.628343 | −0.314172 | − | 0.949366i | \(-0.601727\pi\) | ||||
−0.314172 | + | 0.949366i | \(0.601727\pi\) | |||||||
\(504\) | −1551.40 | −0.137113 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12176.0 | −1.06974 | ||||||||
\(507\) | −1931.35 | −0.169180 | ||||||||
\(508\) | −1517.21 | −0.132511 | ||||||||
\(509\) | 17588.4 | 1.53162 | 0.765810 | − | 0.643067i | \(-0.222338\pi\) | ||||
0.765810 | + | 0.643067i | \(0.222338\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3434.91 | 0.297361 | ||||||||
\(512\) | 10627.5 | 0.917333 | ||||||||
\(513\) | −3310.15 | −0.284886 | ||||||||
\(514\) | 6295.72 | 0.540257 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3128.66 | −0.266922 | ||||||||
\(517\) | −10704.6 | −0.910613 | ||||||||
\(518\) | −189.453 | −0.0160697 | ||||||||
\(519\) | 192.573 | 0.0162871 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11646.6 | −0.979360 | −0.489680 | − | 0.871902i | \(-0.662886\pi\) | ||||
−0.489680 | + | 0.871902i | \(0.662886\pi\) | |||||||
\(522\) | 4434.68 | 0.371841 | ||||||||
\(523\) | −8965.82 | −0.749614 | −0.374807 | − | 0.927103i | \(-0.622291\pi\) | ||||
−0.374807 | + | 0.927103i | \(0.622291\pi\) | |||||||
\(524\) | −4229.75 | −0.352629 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9331.22 | −0.773499 | ||||||||
\(527\) | 1145.62 | 0.0946946 | ||||||||
\(528\) | −4085.85 | −0.336769 | ||||||||
\(529\) | 5085.08 | 0.417941 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7559.01 | 0.617765 | ||||||||
\(532\) | 2424.16 | 0.197558 | ||||||||
\(533\) | 5956.30 | 0.484045 | ||||||||
\(534\) | 4907.26 | 0.397674 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8217.28 | 0.662187 | ||||||||
\(537\) | −11744.0 | −0.943747 | ||||||||
\(538\) | 15812.6 | 1.26715 | ||||||||
\(539\) | −1996.71 | −0.159563 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −195.272 | −0.0155183 | −0.00775914 | − | 0.999970i | \(-0.502470\pi\) | ||||
−0.00775914 | + | 0.999970i | \(0.502470\pi\) | |||||||
\(542\) | 16243.6 | 1.28731 | ||||||||
\(543\) | 6174.13 | 0.487951 | ||||||||
\(544\) | 550.390 | 0.0433783 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2546.27 | 0.199579 | ||||||||
\(547\) | 1399.26 | 0.109375 | 0.0546874 | − | 0.998504i | \(-0.482584\pi\) | ||||
0.0546874 | + | 0.998504i | \(0.482584\pi\) | |||||||
\(548\) | −3898.41 | −0.303890 | ||||||||
\(549\) | −4372.15 | −0.339888 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26554.5 | −2.05310 | ||||||||
\(552\) | 9703.44 | 0.748199 | ||||||||
\(553\) | −851.837 | −0.0655042 | ||||||||
\(554\) | 3004.06 | 0.230380 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 401.059 | 0.0305911 | ||||||||
\(557\) | −43.0467 | −0.00327459 | −0.00163730 | − | 0.999999i | \(-0.500521\pi\) | ||||
−0.00163730 | + | 0.999999i | \(0.500521\pi\) | |||||||
\(558\) | 5155.30 | 0.391113 | ||||||||
\(559\) | 19677.8 | 1.48888 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −556.206 | −0.0418592 | ||||||||
\(562\) | 464.786 | 0.0348858 | ||||||||
\(563\) | 19232.9 | 1.43973 | 0.719865 | − | 0.694114i | \(-0.244203\pi\) | ||||
0.719865 | + | 0.694114i | \(0.244203\pi\) | |||||||
\(564\) | 2226.14 | 0.166201 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2219.85 | 0.164854 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 14535.1 | 1.07373 | ||||||||
\(569\) | 5163.98 | 0.380466 | 0.190233 | − | 0.981739i | \(-0.439076\pi\) | ||||
0.190233 | + | 0.981739i | \(0.439076\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10231.9 | −0.749899 | −0.374950 | − | 0.927045i | \(-0.622340\pi\) | ||||
−0.374950 | + | 0.927045i | \(0.622340\pi\) | |||||||
\(572\) | −6135.05 | −0.448460 | ||||||||
\(573\) | −1284.14 | −0.0936229 | ||||||||
\(574\) | −1779.59 | −0.129406 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4883.20 | 0.353240 | ||||||||
\(577\) | −16563.7 | −1.19507 | −0.597537 | − | 0.801842i | \(-0.703854\pi\) | ||||
−0.597537 | + | 0.801842i | \(0.703854\pi\) | |||||||
\(578\) | 11129.6 | 0.800916 | ||||||||
\(579\) | 4814.78 | 0.345588 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4267.26 | 0.304708 | ||||||||
\(582\) | 4353.35 | 0.310055 | ||||||||
\(583\) | −23108.8 | −1.64163 | ||||||||
\(584\) | −12083.7 | −0.856212 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1382.96 | 0.0974910 | ||||||||
\(587\) | −16020.6 | −1.12648 | −0.563239 | − | 0.826294i | \(-0.690445\pi\) | ||||
−0.563239 | + | 0.826294i | \(0.690445\pi\) | |||||||
\(588\) | 415.238 | 0.0291227 | ||||||||
\(589\) | −30869.4 | −2.15951 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11216.5 | 0.780684 | ||||||||
\(592\) | 397.631 | 0.0276057 | ||||||||
\(593\) | 6771.14 | 0.468900 | 0.234450 | − | 0.972128i | \(-0.424671\pi\) | ||||
0.234450 | + | 0.972128i | \(0.424671\pi\) | |||||||
\(594\) | −2502.93 | −0.172889 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5490.95 | 0.377379 | ||||||||
\(597\) | 1047.09 | 0.0717831 | ||||||||
\(598\) | −15926.0 | −1.08906 | ||||||||
\(599\) | 11070.2 | 0.755120 | 0.377560 | − | 0.925985i | \(-0.376763\pi\) | ||||
0.377560 | + | 0.925985i | \(0.376763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24187.7 | −1.64166 | −0.820830 | − | 0.571173i | \(-0.806489\pi\) | ||||
−0.820830 | + | 0.571173i | \(0.806489\pi\) | |||||||
\(602\) | −5879.23 | −0.398039 | ||||||||
\(603\) | 3003.22 | 0.202820 | ||||||||
\(604\) | 7499.05 | 0.505185 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4580.42 | 0.307041 | ||||||||
\(607\) | 10074.1 | 0.673631 | 0.336816 | − | 0.941571i | \(-0.390650\pi\) | ||||
0.336816 | + | 0.941571i | \(0.390650\pi\) | |||||||
\(608\) | −14830.6 | −0.989243 | ||||||||
\(609\) | −4548.56 | −0.302655 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14001.3 | −0.927060 | ||||||||
\(612\) | 115.669 | 0.00763996 | ||||||||
\(613\) | 11114.6 | 0.732323 | 0.366161 | − | 0.930551i | \(-0.380672\pi\) | ||||
0.366161 | + | 0.930551i | \(0.380672\pi\) | |||||||
\(614\) | 18283.7 | 1.20174 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7024.26 | 0.459441 | ||||||||
\(617\) | −20496.4 | −1.33737 | −0.668683 | − | 0.743548i | \(-0.733142\pi\) | ||||
−0.668683 | + | 0.743548i | \(0.733142\pi\) | |||||||
\(618\) | 6226.98 | 0.405317 | ||||||||
\(619\) | −16714.4 | −1.08532 | −0.542658 | − | 0.839954i | \(-0.682582\pi\) | ||||
−0.542658 | + | 0.839954i | \(0.682582\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3546.37 | 0.229164 | ||||||||
\(622\) | −12083.5 | −0.778943 | ||||||||
\(623\) | −5033.27 | −0.323682 | ||||||||
\(624\) | −5344.20 | −0.342851 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3484.28 | −0.222460 | ||||||||
\(627\) | 14987.3 | 0.954602 | ||||||||
\(628\) | 4703.82 | 0.298890 | ||||||||
\(629\) | 54.1295 | 0.00343129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9168.53 | 0.578437 | 0.289218 | − | 0.957263i | \(-0.406605\pi\) | ||||
0.289218 | + | 0.957263i | \(0.406605\pi\) | |||||||
\(632\) | 2996.69 | 0.188611 | ||||||||
\(633\) | −7765.73 | −0.487615 | ||||||||
\(634\) | 9598.30 | 0.601257 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4805.75 | 0.299623 | ||||||||
\(637\) | −2611.65 | −0.162445 | ||||||||
\(638\) | −20078.9 | −1.24597 | ||||||||
\(639\) | 5312.23 | 0.328871 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4273.37 | −0.263319 | −0.131660 | − | 0.991295i | \(-0.542031\pi\) | ||||
−0.131660 | + | 0.991295i | \(0.542031\pi\) | |||||||
\(642\) | 796.694 | 0.0489766 | ||||||||
\(643\) | −2955.75 | −0.181281 | −0.0906404 | − | 0.995884i | \(-0.528891\pi\) | ||||
−0.0906404 | + | 0.995884i | \(0.528891\pi\) | |||||||
\(644\) | −2597.16 | −0.158917 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1268.95 | 0.0772851 | ||||||||
\(647\) | −22701.2 | −1.37941 | −0.689704 | − | 0.724091i | \(-0.742259\pi\) | ||||
−0.689704 | + | 0.724091i | \(0.742259\pi\) | |||||||
\(648\) | 1994.66 | 0.120922 | ||||||||
\(649\) | −34224.8 | −2.07002 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5287.67 | −0.318341 | ||||||||
\(652\) | −93.4235 | −0.00561158 | ||||||||
\(653\) | −1537.81 | −0.0921582 | −0.0460791 | − | 0.998938i | \(-0.514673\pi\) | ||||
−0.0460791 | + | 0.998938i | \(0.514673\pi\) | |||||||
\(654\) | 5713.52 | 0.341615 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3735.08 | 0.222302 | ||||||||
\(657\) | −4416.31 | −0.262248 | ||||||||
\(658\) | 4183.26 | 0.247842 | ||||||||
\(659\) | 12338.1 | 0.729323 | 0.364661 | − | 0.931140i | \(-0.381185\pi\) | ||||
0.364661 | + | 0.931140i | \(0.381185\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1845.10 | 0.108572 | 0.0542859 | − | 0.998525i | \(-0.482712\pi\) | ||||
0.0542859 | + | 0.998525i | \(0.482712\pi\) | |||||||
\(662\) | −18877.7 | −1.10831 | ||||||||
\(663\) | −727.505 | −0.0426153 | ||||||||
\(664\) | −15011.8 | −0.877369 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 243.583 | 0.0141721 | ||||||||
\(667\) | 28449.5 | 1.65153 | ||||||||
\(668\) | 4673.48 | 0.270692 | ||||||||
\(669\) | −9708.62 | −0.561072 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19795.7 | 1.13890 | ||||||||
\(672\) | −2540.36 | −0.145828 | ||||||||
\(673\) | −23955.4 | −1.37208 | −0.686041 | − | 0.727563i | \(-0.740653\pi\) | ||||
−0.686041 | + | 0.727563i | \(0.740653\pi\) | |||||||
\(674\) | −9892.34 | −0.565339 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1818.53 | −0.103467 | ||||||||
\(677\) | 3678.26 | 0.208814 | 0.104407 | − | 0.994535i | \(-0.466706\pi\) | ||||
0.104407 | + | 0.994535i | \(0.466706\pi\) | |||||||
\(678\) | 7415.63 | 0.420052 | ||||||||
\(679\) | −4465.14 | −0.252366 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16894.9 | −0.950679 | ||||||||
\(682\) | −23341.6 | −1.31055 | ||||||||
\(683\) | −4390.87 | −0.245991 | −0.122996 | − | 0.992407i | \(-0.539250\pi\) | ||||
−0.122996 | + | 0.992407i | \(0.539250\pi\) | |||||||
\(684\) | −3116.78 | −0.174230 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 780.297 | 0.0434284 | ||||||||
\(687\) | −11310.7 | −0.628140 | ||||||||
\(688\) | 12339.6 | 0.683781 | ||||||||
\(689\) | −30225.8 | −1.67128 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10371.7 | 0.570994 | 0.285497 | − | 0.958380i | \(-0.407841\pi\) | ||||
0.285497 | + | 0.958380i | \(0.407841\pi\) | |||||||
\(692\) | 181.323 | 0.00996081 | ||||||||
\(693\) | 2567.20 | 0.140721 | ||||||||
\(694\) | −18985.4 | −1.03844 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 16001.4 | 0.871456 | ||||||||
\(697\) | 508.455 | 0.0276314 | ||||||||
\(698\) | 22709.4 | 1.23147 | ||||||||
\(699\) | −19682.7 | −1.06505 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 109.675 | 0.00590922 | 0.00295461 | − | 0.999996i | \(-0.499060\pi\) | ||||
0.00295461 | + | 0.999996i | \(0.499060\pi\) | |||||||
\(702\) | −3273.77 | −0.176012 | ||||||||
\(703\) | −1458.55 | −0.0782508 | ||||||||
\(704\) | −22109.6 | −1.18364 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20022.9 | 1.06738 | ||||||||
\(707\) | −4698.03 | −0.249912 | ||||||||
\(708\) | 7117.45 | 0.377811 | ||||||||
\(709\) | 26918.8 | 1.42589 | 0.712944 | − | 0.701221i | \(-0.247361\pi\) | ||||
0.712944 | + | 0.701221i | \(0.247361\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1095.22 | 0.0577693 | ||||||||
\(712\) | 17706.6 | 0.931999 | ||||||||
\(713\) | 33072.4 | 1.73713 | ||||||||
\(714\) | 217.360 | 0.0113929 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11058.0 | −0.577174 | ||||||||
\(717\) | 2314.33 | 0.120544 | ||||||||
\(718\) | 1192.14 | 0.0619644 | ||||||||
\(719\) | 15170.8 | 0.786889 | 0.393445 | − | 0.919348i | \(-0.371283\pi\) | ||||
0.393445 | + | 0.919348i | \(0.371283\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6386.88 | −0.329903 | ||||||||
\(722\) | −18589.0 | −0.958185 | ||||||||
\(723\) | −3756.31 | −0.193221 | ||||||||
\(724\) | 5813.46 | 0.298419 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2248.72 | 0.114956 | ||||||||
\(727\) | 33286.9 | 1.69813 | 0.849066 | − | 0.528288i | \(-0.177166\pi\) | ||||
0.849066 | + | 0.528288i | \(0.177166\pi\) | |||||||
\(728\) | 9187.57 | 0.467739 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1679.78 | 0.0849917 | ||||||||
\(732\) | −4116.74 | −0.207868 | ||||||||
\(733\) | −20544.0 | −1.03521 | −0.517607 | − | 0.855619i | \(-0.673177\pi\) | ||||
−0.517607 | + | 0.855619i | \(0.673177\pi\) | |||||||
\(734\) | −14474.7 | −0.727888 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15889.0 | 0.795755 | ||||||||
\(737\) | −13597.6 | −0.679614 | ||||||||
\(738\) | 2288.05 | 0.114125 | ||||||||
\(739\) | 34357.2 | 1.71022 | 0.855109 | − | 0.518449i | \(-0.173490\pi\) | ||||
0.855109 | + | 0.518449i | \(0.173490\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19603.1 | 0.971844 | ||||||||
\(742\) | 9030.73 | 0.446804 | ||||||||
\(743\) | −8166.99 | −0.403254 | −0.201627 | − | 0.979462i | \(-0.564623\pi\) | ||||
−0.201627 | + | 0.979462i | \(0.564623\pi\) | |||||||
\(744\) | 18601.6 | 0.916623 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −25628.9 | −1.25783 | ||||||||
\(747\) | −5486.47 | −0.268728 | ||||||||
\(748\) | −523.715 | −0.0256001 | ||||||||
\(749\) | −817.151 | −0.0398639 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17080.1 | 0.829909 | 0.414954 | − | 0.909842i | \(-0.363798\pi\) | ||||
0.414954 | + | 0.909842i | \(0.363798\pi\) | |||||||
\(752\) | −8779.97 | −0.425761 | ||||||||
\(753\) | −15498.8 | −0.750077 | ||||||||
\(754\) | −26262.7 | −1.26848 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −533.878 | −0.0256838 | ||||||||
\(757\) | 16324.0 | 0.783758 | 0.391879 | − | 0.920017i | \(-0.371825\pi\) | ||||
0.391879 | + | 0.920017i | \(0.371825\pi\) | |||||||
\(758\) | 2620.06 | 0.125547 | ||||||||
\(759\) | −16056.9 | −0.767888 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32366.2 | −1.54175 | −0.770875 | − | 0.636986i | \(-0.780181\pi\) | ||||
−0.770875 | + | 0.636986i | \(0.780181\pi\) | |||||||
\(762\) | 3665.66 | 0.174269 | ||||||||
\(763\) | −5860.23 | −0.278053 | ||||||||
\(764\) | −1209.13 | −0.0572576 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −344.774 | −0.0162626 | ||||||||
\(767\) | −44765.3 | −2.10741 | ||||||||
\(768\) | 11202.6 | 0.526354 | ||||||||
\(769\) | −7948.44 | −0.372728 | −0.186364 | − | 0.982481i | \(-0.559670\pi\) | ||||
−0.186364 | + | 0.982481i | \(0.559670\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8302.35 | 0.387810 | ||||||||
\(772\) | 4533.52 | 0.211354 | ||||||||
\(773\) | −17819.3 | −0.829127 | −0.414564 | − | 0.910020i | \(-0.636066\pi\) | ||||
−0.414564 | + | 0.910020i | \(0.636066\pi\) | |||||||
\(774\) | 7559.01 | 0.351038 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15708.0 | 0.726655 | ||||||||
\(777\) | −249.837 | −0.0115352 | ||||||||
\(778\) | −10906.4 | −0.502586 | ||||||||
\(779\) | −13700.6 | −0.630136 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24052.1 | −1.10199 | ||||||||
\(782\) | −1359.51 | −0.0621687 | ||||||||
\(783\) | 5848.15 | 0.266917 | ||||||||
\(784\) | −1637.72 | −0.0746044 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 10219.3 | 0.463754 | ||||||||
\(787\) | −2912.38 | −0.131912 | −0.0659562 | − | 0.997823i | \(-0.521010\pi\) | ||||
−0.0659562 | + | 0.997823i | \(0.521010\pi\) | |||||||
\(788\) | 10561.3 | 0.477448 | ||||||||
\(789\) | −12305.3 | −0.555237 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7606.05 | −0.341896 | ||||||||
\(792\) | −9031.19 | −0.405188 | ||||||||
\(793\) | 25892.3 | 1.15948 | ||||||||
\(794\) | −10519.1 | −0.470162 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 985.923 | 0.0439009 | ||||||||
\(797\) | 33789.1 | 1.50172 | 0.750861 | − | 0.660460i | \(-0.229639\pi\) | ||||
0.750861 | + | 0.660460i | \(0.229639\pi\) | |||||||
\(798\) | −5856.91 | −0.259815 | ||||||||
\(799\) | −1195.22 | −0.0529208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6471.34 | 0.285460 | ||||||||
\(802\) | 8213.90 | 0.361649 | ||||||||
\(803\) | 19995.7 | 0.878744 | ||||||||
\(804\) | 2827.78 | 0.124040 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −30530.2 | −1.33422 | ||||||||
\(807\) | 20852.5 | 0.909595 | ||||||||
\(808\) | 16527.3 | 0.719589 | ||||||||
\(809\) | 1252.13 | 0.0544159 | 0.0272079 | − | 0.999630i | \(-0.491338\pi\) | ||||
0.0272079 | + | 0.999630i | \(0.491338\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31913.1 | −1.38178 | −0.690889 | − | 0.722961i | \(-0.742781\pi\) | ||||
−0.690889 | + | 0.722961i | \(0.742781\pi\) | |||||||
\(812\) | −4282.85 | −0.185097 | ||||||||
\(813\) | 21420.9 | 0.924063 | ||||||||
\(814\) | −1102.87 | −0.0474882 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −456.204 | −0.0195715 | ||||||||
\(817\) | −45262.7 | −1.93824 | ||||||||
\(818\) | −20382.3 | −0.871210 | ||||||||
\(819\) | 3357.84 | 0.143263 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30742.4 | 1.30684 | 0.653421 | − | 0.756995i | \(-0.273333\pi\) | ||||
0.653421 | + | 0.756995i | \(0.273333\pi\) | |||||||
\(822\) | 9418.77 | 0.399656 | ||||||||
\(823\) | 13822.6 | 0.585449 | 0.292724 | − | 0.956197i | \(-0.405438\pi\) | ||||
0.292724 | + | 0.956197i | \(0.405438\pi\) | |||||||
\(824\) | 22468.5 | 0.949913 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13374.8 | 0.563399 | ||||||||
\(827\) | 42107.1 | 1.77051 | 0.885253 | − | 0.465110i | \(-0.153985\pi\) | ||||
0.885253 | + | 0.465110i | \(0.153985\pi\) | |||||||
\(828\) | 3339.21 | 0.140152 | ||||||||
\(829\) | −38763.8 | −1.62403 | −0.812015 | − | 0.583636i | \(-0.801629\pi\) | ||||
−0.812015 | + | 0.583636i | \(0.801629\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3961.54 | 0.165372 | ||||||||
\(832\) | −28918.8 | −1.20502 | ||||||||
\(833\) | −222.942 | −0.00927308 | ||||||||
\(834\) | −968.979 | −0.0402314 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 14111.8 | 0.583812 | ||||||||
\(837\) | 6798.44 | 0.280751 | ||||||||
\(838\) | 16102.5 | 0.663784 | ||||||||
\(839\) | 16896.3 | 0.695262 | 0.347631 | − | 0.937631i | \(-0.386986\pi\) | ||||
0.347631 | + | 0.937631i | \(0.386986\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22525.7 | 0.923601 | ||||||||
\(842\) | −26278.6 | −1.07556 | ||||||||
\(843\) | 612.927 | 0.0250419 | ||||||||
\(844\) | −7312.09 | −0.298214 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5378.47 | −0.218576 | ||||||||
\(847\) | −2306.47 | −0.0935668 | ||||||||
\(848\) | −18954.0 | −0.767552 | ||||||||
\(849\) | 2927.38 | 0.118336 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1562.64 | 0.0629455 | ||||||||
\(852\) | 5001.91 | 0.201130 | ||||||||
\(853\) | −46429.3 | −1.86367 | −0.931833 | − | 0.362887i | \(-0.881791\pi\) | ||||
−0.931833 | + | 0.362887i | \(0.881791\pi\) | |||||||
\(854\) | −7735.99 | −0.309977 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2874.67 | 0.114783 | ||||||||
\(857\) | −21206.4 | −0.845272 | −0.422636 | − | 0.906300i | \(-0.638895\pi\) | ||||
−0.422636 | + | 0.906300i | \(0.638895\pi\) | |||||||
\(858\) | 14822.6 | 0.589785 | ||||||||
\(859\) | 13876.2 | 0.551163 | 0.275581 | − | 0.961278i | \(-0.411130\pi\) | ||||
0.275581 | + | 0.961278i | \(0.411130\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2346.80 | −0.0928906 | ||||||||
\(862\) | 9246.12 | 0.365341 | ||||||||
\(863\) | −14337.1 | −0.565515 | −0.282757 | − | 0.959191i | \(-0.591249\pi\) | ||||
−0.282757 | + | 0.959191i | \(0.591249\pi\) | |||||||
\(864\) | 3266.17 | 0.128608 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 39711.6 | 1.55826 | ||||||||
\(867\) | 14676.9 | 0.574918 | ||||||||
\(868\) | −4978.79 | −0.194690 | ||||||||
\(869\) | −4958.81 | −0.193574 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17785.4 | −0.691889 | ||||||||
\(872\) | 20615.8 | 0.800619 | ||||||||
\(873\) | 5740.89 | 0.222566 | ||||||||
\(874\) | 36632.8 | 1.41776 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4158.33 | −0.160384 | ||||||||
\(877\) | 24369.3 | 0.938304 | 0.469152 | − | 0.883118i | \(-0.344560\pi\) | ||||
0.469152 | + | 0.883118i | \(0.344560\pi\) | |||||||
\(878\) | −10454.1 | −0.401834 | ||||||||
\(879\) | 1823.76 | 0.0699815 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26127.0 | −0.999140 | −0.499570 | − | 0.866273i | \(-0.666509\pi\) | ||||
−0.499570 | + | 0.866273i | \(0.666509\pi\) | |||||||
\(882\) | −1003.24 | −0.0383002 | ||||||||
\(883\) | 15713.1 | 0.598855 | 0.299428 | − | 0.954119i | \(-0.403204\pi\) | ||||
0.299428 | + | 0.954119i | \(0.403204\pi\) | |||||||
\(884\) | −685.007 | −0.0260625 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −696.611 | −0.0264143 | ||||||||
\(887\) | −13139.5 | −0.497385 | −0.248692 | − | 0.968583i | \(-0.580001\pi\) | ||||
−0.248692 | + | 0.968583i | \(0.580001\pi\) | |||||||
\(888\) | 878.907 | 0.0332142 | ||||||||
\(889\) | −3759.79 | −0.141844 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3300.68 | −0.124104 | ||||||||
\(892\) | −9141.48 | −0.343138 | ||||||||
\(893\) | 32205.8 | 1.20686 | ||||||||
\(894\) | −13266.4 | −0.496304 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1865.95 | 0.0695725 | ||||||||
\(897\) | −21002.0 | −0.781758 | ||||||||
\(898\) | −20995.7 | −0.780218 | ||||||||
\(899\) | 54538.1 | 2.02330 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2580.21 | −0.0954043 | ||||||||
\(902\) | −10359.6 | −0.382412 | ||||||||
\(903\) | −7753.12 | −0.285723 | ||||||||
\(904\) | 26757.4 | 0.984446 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −18118.1 | −0.664386 | ||||||||
\(907\) | 3799.71 | 0.139104 | 0.0695519 | − | 0.997578i | \(-0.477843\pi\) | ||||
0.0695519 | + | 0.997578i | \(0.477843\pi\) | |||||||
\(908\) | −15907.9 | −0.581413 | ||||||||
\(909\) | 6040.33 | 0.220402 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51528.4 | −1.87400 | −0.936998 | − | 0.349334i | \(-0.886408\pi\) | ||||
−0.936998 | + | 0.349334i | \(0.886408\pi\) | |||||||
\(912\) | 12292.7 | 0.446329 | ||||||||
\(913\) | 24841.0 | 0.900458 | ||||||||
\(914\) | −25006.4 | −0.904966 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10650.0 | −0.384156 | ||||||||
\(917\) | −10481.7 | −0.377467 | ||||||||
\(918\) | −279.463 | −0.0100476 | ||||||||
\(919\) | −16984.7 | −0.609657 | −0.304828 | − | 0.952407i | \(-0.598599\pi\) | ||||
−0.304828 | + | 0.952407i | \(0.598599\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24111.2 | 0.862641 | ||||||||
\(922\) | −16806.8 | −0.600329 | ||||||||
\(923\) | −31459.6 | −1.12189 | ||||||||
\(924\) | 2417.23 | 0.0860618 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 23121.9 | 0.820553 | ||||||||
\(927\) | 8211.71 | 0.290947 | ||||||||
\(928\) | 26201.7 | 0.926846 | ||||||||
\(929\) | −5451.85 | −0.192540 | −0.0962699 | − | 0.995355i | \(-0.530691\pi\) | ||||
−0.0962699 | + | 0.995355i | \(0.530691\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6007.30 | 0.211473 | ||||||||
\(932\) | −18532.9 | −0.651358 | ||||||||
\(933\) | −15934.8 | −0.559145 | ||||||||
\(934\) | −35976.8 | −1.26038 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −11812.6 | −0.412507 | ||||||||
\(937\) | −42429.4 | −1.47930 | −0.739652 | − | 0.672989i | \(-0.765010\pi\) | ||||
−0.739652 | + | 0.672989i | \(0.765010\pi\) | |||||||
\(938\) | 5313.84 | 0.184971 | ||||||||
\(939\) | −4594.82 | −0.159687 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32977.9 | −1.14245 | −0.571226 | − | 0.820793i | \(-0.693532\pi\) | ||||
−0.571226 | + | 0.820793i | \(0.693532\pi\) | |||||||
\(942\) | −11364.7 | −0.393080 | ||||||||
\(943\) | 14678.4 | 0.506886 | ||||||||
\(944\) | −28071.5 | −0.967848 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34224.8 | −1.17626 | ||||||||
\(947\) | 23753.4 | 0.815082 | 0.407541 | − | 0.913187i | \(-0.366386\pi\) | ||||
0.407541 | + | 0.913187i | \(0.366386\pi\) | |||||||
\(948\) | 1031.24 | 0.0353303 | ||||||||
\(949\) | 26153.9 | 0.894616 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12657.6 | 0.431598 | ||||||||
\(952\) | 784.291 | 0.0267006 | ||||||||
\(953\) | 28074.3 | 0.954267 | 0.477134 | − | 0.878831i | \(-0.341676\pi\) | ||||
0.477134 | + | 0.878831i | \(0.341676\pi\) | |||||||
\(954\) | −11610.9 | −0.394044 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2179.14 | 0.0737221 | ||||||||
\(957\) | −26478.6 | −0.894389 | ||||||||
\(958\) | 3286.92 | 0.110851 | ||||||||
\(959\) | −9660.63 | −0.325295 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33609.2 | 1.12817 | ||||||||
\(962\) | −1442.52 | −0.0483460 | ||||||||
\(963\) | 1050.62 | 0.0351567 | ||||||||
\(964\) | −3536.88 | −0.118169 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6274.88 | 0.208997 | ||||||||
\(967\) | 11150.3 | 0.370806 | 0.185403 | − | 0.982663i | \(-0.440641\pi\) | ||||
0.185403 | + | 0.982663i | \(0.440641\pi\) | |||||||
\(968\) | 8113.95 | 0.269414 | ||||||||
\(969\) | 1673.40 | 0.0554772 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6059.04 | 0.200251 | 0.100126 | − | 0.994975i | \(-0.468076\pi\) | ||||
0.100126 | + | 0.994975i | \(0.468076\pi\) | |||||||
\(972\) | 686.415 | 0.0226510 | ||||||||
\(973\) | 993.861 | 0.0327459 | ||||||||
\(974\) | −1113.35 | −0.0366263 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16236.6 | 0.532500 | ||||||||
\(977\) | −5700.49 | −0.186668 | −0.0933341 | − | 0.995635i | \(-0.529752\pi\) | ||||
−0.0933341 | + | 0.995635i | \(0.529752\pi\) | |||||||
\(978\) | 225.716 | 0.00737997 | ||||||||
\(979\) | −29300.2 | −0.956526 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7534.59 | 0.245220 | ||||||||
\(982\) | 8966.12 | 0.291365 | ||||||||
\(983\) | −197.480 | −0.00640757 | −0.00320378 | − | 0.999995i | \(-0.501020\pi\) | ||||
−0.00320378 | + | 0.999995i | \(0.501020\pi\) | |||||||
\(984\) | 8255.85 | 0.267466 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2241.90 | −0.0724103 | ||||||||
\(987\) | 5516.58 | 0.177908 | ||||||||
\(988\) | 18457.9 | 0.594357 | ||||||||
\(989\) | 48492.9 | 1.55913 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20620.8 | 0.660990 | 0.330495 | − | 0.943808i | \(-0.392784\pi\) | ||||
0.330495 | + | 0.943808i | \(0.392784\pi\) | |||||||
\(992\) | 30459.3 | 0.974884 | ||||||||
\(993\) | −24894.6 | −0.795574 | ||||||||
\(994\) | 9399.35 | 0.299929 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5165.97 | −0.164348 | ||||||||
\(997\) | −19326.8 | −0.613928 | −0.306964 | − | 0.951721i | \(-0.599313\pi\) | ||||
−0.306964 | + | 0.951721i | \(0.599313\pi\) | |||||||
\(998\) | −25.2275 | −0.000800162 0 | ||||||||
\(999\) | 321.220 | 0.0101731 |
(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 | 525.4.a.n.1.1 | 2 | ||
3.2 | odd | 2 | 1575.4.a.p.1.2 | 2 | |||
5.2 | odd | 4 | 525.4.d.g.274.2 | 4 | |||
5.3 | odd | 4 | 525.4.d.g.274.3 | 4 | |||
5.4 | even | 2 | 21.4.a.c.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 63.4.a.e.1.1 | 2 | |||
20.19 | odd | 2 | 336.4.a.m.1.1 | 2 | |||
35.4 | even | 6 | 147.4.e.l.79.1 | 4 | |||
35.9 | even | 6 | 147.4.e.l.67.1 | 4 | |||
35.19 | odd | 6 | 147.4.e.m.67.1 | 4 | |||
35.24 | odd | 6 | 147.4.e.m.79.1 | 4 | |||
35.34 | odd | 2 | 147.4.a.i.1.2 | 2 | |||
40.19 | odd | 2 | 1344.4.a.bo.1.2 | 2 | |||
40.29 | even | 2 | 1344.4.a.bg.1.2 | 2 | |||
60.59 | even | 2 | 1008.4.a.ba.1.2 | 2 | |||
105.44 | odd | 6 | 441.4.e.q.361.2 | 4 | |||
105.59 | even | 6 | 441.4.e.p.226.2 | 4 | |||
105.74 | odd | 6 | 441.4.e.q.226.2 | 4 | |||
105.89 | even | 6 | 441.4.e.p.361.2 | 4 | |||
105.104 | even | 2 | 441.4.a.r.1.1 | 2 | |||
140.139 | even | 2 | 2352.4.a.bz.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.a.c.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
63.4.a.e.1.1 | 2 | 15.14 | odd | 2 | |||
147.4.a.i.1.2 | 2 | 35.34 | odd | 2 | |||
147.4.e.l.67.1 | 4 | 35.9 | even | 6 | |||
147.4.e.l.79.1 | 4 | 35.4 | even | 6 | |||
147.4.e.m.67.1 | 4 | 35.19 | odd | 6 | |||
147.4.e.m.79.1 | 4 | 35.24 | odd | 6 | |||
336.4.a.m.1.1 | 2 | 20.19 | odd | 2 | |||
441.4.a.r.1.1 | 2 | 105.104 | even | 2 | |||
441.4.e.p.226.2 | 4 | 105.59 | even | 6 | |||
441.4.e.p.361.2 | 4 | 105.89 | even | 6 | |||
441.4.e.q.226.2 | 4 | 105.74 | odd | 6 | |||
441.4.e.q.361.2 | 4 | 105.44 | odd | 6 | |||
525.4.a.n.1.1 | 2 | 1.1 | even | 1 | trivial | ||
525.4.d.g.274.2 | 4 | 5.2 | odd | 4 | |||
525.4.d.g.274.3 | 4 | 5.3 | odd | 4 | |||
1008.4.a.ba.1.2 | 2 | 60.59 | even | 2 | |||
1344.4.a.bg.1.2 | 2 | 40.29 | even | 2 | |||
1344.4.a.bo.1.2 | 2 | 40.19 | odd | 2 | |||
1575.4.a.p.1.2 | 2 | 3.2 | odd | 2 | |||
2352.4.a.bz.1.2 | 2 | 140.139 | even | 2 |