Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(1,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("405.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.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: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73205 | −0.965926 | −0.482963 | − | 0.875641i | \(-0.660439\pi\) | ||||
−0.482963 | + | 0.875641i | \(0.660439\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.535898 | −0.0669873 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.92820 | 0.374088 | 0.187044 | − | 0.982352i | \(-0.440109\pi\) | ||||
0.187044 | + | 0.982352i | \(0.440109\pi\) | |||||||
\(8\) | 23.3205 | 1.03063 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 13.6603 | 0.431975 | ||||||||
\(11\) | 59.4974 | 1.63083 | 0.815416 | − | 0.578876i | \(-0.196508\pi\) | ||||
0.815416 | + | 0.578876i | \(0.196508\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −25.0718 | −0.534897 | −0.267449 | − | 0.963572i | \(-0.586181\pi\) | ||||
−0.267449 | + | 0.963572i | \(0.586181\pi\) | |||||||
\(14\) | −18.9282 | −0.361341 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −59.4256 | −0.928525 | ||||||||
\(17\) | −112.995 | −1.61208 | −0.806038 | − | 0.591864i | \(-0.798392\pi\) | ||||
−0.806038 | + | 0.591864i | \(0.798392\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −122.779 | −1.48250 | −0.741251 | − | 0.671228i | \(-0.765767\pi\) | ||||
−0.741251 | + | 0.671228i | \(0.765767\pi\) | |||||||
\(20\) | 2.67949 | 0.0299576 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −162.550 | −1.57526 | ||||||||
\(23\) | 97.4256 | 0.883246 | 0.441623 | − | 0.897201i | \(-0.354403\pi\) | ||||
0.441623 | + | 0.897201i | \(0.354403\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 68.4974 | 0.516671 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.71281 | −0.0250591 | ||||||||
\(29\) | 126.569 | 0.810459 | 0.405230 | − | 0.914215i | \(-0.367192\pi\) | ||||
0.405230 | + | 0.914215i | \(0.367192\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −108.215 | −0.626970 | −0.313485 | − | 0.949593i | \(-0.601496\pi\) | ||||
−0.313485 | + | 0.949593i | \(0.601496\pi\) | |||||||
\(32\) | −24.2102 | −0.133744 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 308.708 | 1.55714 | ||||||||
\(35\) | −34.6410 | −0.167297 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 294.344 | 1.30783 | 0.653916 | − | 0.756567i | \(-0.273125\pi\) | ||||
0.653916 | + | 0.756567i | \(0.273125\pi\) | |||||||
\(38\) | 335.440 | 1.43199 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −116.603 | −0.460912 | ||||||||
\(41\) | 205.862 | 0.784151 | 0.392075 | − | 0.919933i | \(-0.371757\pi\) | ||||
0.392075 | + | 0.919933i | \(0.371757\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −80.1999 | −0.284427 | −0.142214 | − | 0.989836i | \(-0.545422\pi\) | ||||
−0.142214 | + | 0.989836i | \(0.545422\pi\) | |||||||
\(44\) | −31.8846 | −0.109245 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −266.172 | −0.853150 | ||||||||
\(47\) | 269.713 | 0.837057 | 0.418528 | − | 0.908204i | \(-0.362546\pi\) | ||||
0.418528 | + | 0.908204i | \(0.362546\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −295.000 | −0.860058 | ||||||||
\(50\) | −68.3013 | −0.193185 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 13.4359 | 0.0358313 | ||||||||
\(53\) | 98.7949 | 0.256048 | 0.128024 | − | 0.991771i | \(-0.459137\pi\) | ||||
0.128024 | + | 0.991771i | \(0.459137\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −297.487 | −0.729330 | ||||||||
\(56\) | 161.569 | 0.385546 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −345.794 | −0.782843 | ||||||||
\(59\) | 304.503 | 0.671913 | 0.335956 | − | 0.941878i | \(-0.390941\pi\) | ||||
0.335956 | + | 0.941878i | \(0.390941\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 666.554 | 1.39907 | 0.699537 | − | 0.714597i | \(-0.253390\pi\) | ||||
0.699537 | + | 0.714597i | \(0.253390\pi\) | |||||||
\(62\) | 295.650 | 0.605606 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 541.549 | 1.05771 | ||||||||
\(65\) | 125.359 | 0.239213 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −635.933 | −1.15958 | −0.579788 | − | 0.814767i | \(-0.696865\pi\) | ||||
−0.579788 | + | 0.814767i | \(0.696865\pi\) | |||||||
\(68\) | 60.5538 | 0.107989 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 94.6410 | 0.161597 | ||||||||
\(71\) | 826.482 | 1.38148 | 0.690742 | − | 0.723101i | \(-0.257284\pi\) | ||||
0.690742 | + | 0.723101i | \(0.257284\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 751.349 | 1.20464 | 0.602320 | − | 0.798255i | \(-0.294243\pi\) | ||||
0.602320 | + | 0.798255i | \(0.294243\pi\) | |||||||
\(74\) | −804.161 | −1.26327 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 65.7973 | 0.0993088 | ||||||||
\(77\) | 412.210 | 0.610074 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 23.8667 | 0.0339901 | 0.0169950 | − | 0.999856i | \(-0.494590\pi\) | ||||
0.0169950 | + | 0.999856i | \(0.494590\pi\) | |||||||
\(80\) | 297.128 | 0.415249 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −562.424 | −0.757431 | ||||||||
\(83\) | −817.230 | −1.08076 | −0.540378 | − | 0.841423i | \(-0.681719\pi\) | ||||
−0.540378 | + | 0.841423i | \(0.681719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 564.974 | 0.720942 | ||||||||
\(86\) | 219.110 | 0.274736 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1387.51 | 1.68078 | ||||||||
\(89\) | 513.000 | 0.610988 | 0.305494 | − | 0.952194i | \(-0.401178\pi\) | ||||
0.305494 | + | 0.952194i | \(0.401178\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −173.703 | −0.200099 | ||||||||
\(92\) | −52.2102 | −0.0591662 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −736.869 | −0.808535 | ||||||||
\(95\) | 613.897 | 0.662995 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 428.102 | 0.448116 | 0.224058 | − | 0.974576i | \(-0.428070\pi\) | ||||
0.224058 | + | 0.974576i | \(0.428070\pi\) | |||||||
\(98\) | 805.955 | 0.830753 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.3975 | −0.0133975 | ||||||||
\(101\) | 912.087 | 0.898575 | 0.449287 | − | 0.893387i | \(-0.351678\pi\) | ||||
0.449287 | + | 0.893387i | \(0.351678\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 278.497 | 0.266419 | 0.133210 | − | 0.991088i | \(-0.457472\pi\) | ||||
0.133210 | + | 0.991088i | \(0.457472\pi\) | |||||||
\(104\) | −584.687 | −0.551282 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −269.913 | −0.247323 | ||||||||
\(107\) | −1512.33 | −1.36638 | −0.683191 | − | 0.730240i | \(-0.739408\pi\) | ||||
−0.683191 | + | 0.730240i | \(0.739408\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1991.53 | 1.75004 | 0.875020 | − | 0.484087i | \(-0.160848\pi\) | ||||
0.875020 | + | 0.484087i | \(0.160848\pi\) | |||||||
\(110\) | 812.750 | 0.704479 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −411.713 | −0.347350 | ||||||||
\(113\) | −507.902 | −0.422827 | −0.211413 | − | 0.977397i | \(-0.567807\pi\) | ||||
−0.211413 | + | 0.977397i | \(0.567807\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −487.128 | −0.394999 | ||||||||
\(116\) | −67.8282 | −0.0542905 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −831.917 | −0.649018 | ||||||||
\(119\) | −782.851 | −0.603058 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2208.94 | 1.65961 | ||||||||
\(122\) | −1821.06 | −1.35140 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 57.9925 | 0.0419990 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1845.91 | 1.28975 | 0.644873 | − | 0.764290i | \(-0.276910\pi\) | ||||
0.644873 | + | 0.764290i | \(0.276910\pi\) | |||||||
\(128\) | −1285.86 | −0.887928 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −342.487 | −0.231062 | ||||||||
\(131\) | 2564.71 | 1.71053 | 0.855265 | − | 0.518190i | \(-0.173394\pi\) | ||||
0.855265 | + | 0.518190i | \(0.173394\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −850.641 | −0.554586 | ||||||||
\(134\) | 1737.40 | 1.12006 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2635.10 | −1.66145 | ||||||||
\(137\) | 506.780 | 0.316037 | 0.158019 | − | 0.987436i | \(-0.449489\pi\) | ||||
0.158019 | + | 0.987436i | \(0.449489\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2222.65 | 1.35628 | 0.678138 | − | 0.734935i | \(-0.262787\pi\) | ||||
0.678138 | + | 0.734935i | \(0.262787\pi\) | |||||||
\(140\) | 18.5641 | 0.0112068 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2257.99 | −1.33441 | ||||||||
\(143\) | −1491.71 | −0.872327 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −632.846 | −0.362448 | ||||||||
\(146\) | −2052.72 | −1.16359 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −157.738 | −0.0876081 | ||||||||
\(149\) | 510.092 | 0.280459 | 0.140229 | − | 0.990119i | \(-0.455216\pi\) | ||||
0.140229 | + | 0.990119i | \(0.455216\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 675.261 | 0.363920 | 0.181960 | − | 0.983306i | \(-0.441756\pi\) | ||||
0.181960 | + | 0.983306i | \(0.441756\pi\) | |||||||
\(152\) | −2863.28 | −1.52791 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1126.18 | −0.589286 | ||||||||
\(155\) | 541.077 | 0.280389 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3627.98 | −1.84423 | −0.922115 | − | 0.386915i | \(-0.873541\pi\) | ||||
−0.922115 | + | 0.386915i | \(0.873541\pi\) | |||||||
\(158\) | −65.2051 | −0.0328319 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 121.051 | 0.0598121 | ||||||||
\(161\) | 674.985 | 0.330411 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −119.559 | −0.0574514 | −0.0287257 | − | 0.999587i | \(-0.509145\pi\) | ||||
−0.0287257 | + | 0.999587i | \(0.509145\pi\) | |||||||
\(164\) | −110.321 | −0.0525281 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2232.72 | 1.04393 | ||||||||
\(167\) | −3068.99 | −1.42207 | −0.711035 | − | 0.703157i | \(-0.751773\pi\) | ||||
−0.711035 | + | 0.703157i | \(0.751773\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1568.41 | −0.713885 | ||||||||
\(170\) | −1543.54 | −0.696376 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 42.9790 | 0.0190530 | ||||||||
\(173\) | 2112.61 | 0.928432 | 0.464216 | − | 0.885722i | \(-0.346336\pi\) | ||||
0.464216 | + | 0.885722i | \(0.346336\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 173.205 | 0.0748176 | ||||||||
\(176\) | −3535.67 | −1.51427 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1401.54 | −0.590169 | ||||||||
\(179\) | −1624.79 | −0.678449 | −0.339225 | − | 0.940705i | \(-0.610165\pi\) | ||||
−0.339225 | + | 0.940705i | \(0.610165\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2545.41 | −1.04530 | −0.522649 | − | 0.852548i | \(-0.675056\pi\) | ||||
−0.522649 | + | 0.852548i | \(0.675056\pi\) | |||||||
\(182\) | 474.564 | 0.193280 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2272.02 | 0.910300 | ||||||||
\(185\) | −1471.72 | −0.584880 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6722.90 | −2.62902 | ||||||||
\(188\) | −144.539 | −0.0560722 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1677.20 | −0.640404 | ||||||||
\(191\) | 4805.65 | 1.82055 | 0.910274 | − | 0.414006i | \(-0.135871\pi\) | ||||
0.910274 | + | 0.414006i | \(0.135871\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3577.84 | 1.33440 | 0.667198 | − | 0.744880i | \(-0.267493\pi\) | ||||
0.667198 | + | 0.744880i | \(0.267493\pi\) | |||||||
\(194\) | −1169.60 | −0.432846 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 158.090 | 0.0576130 | ||||||||
\(197\) | −3788.88 | −1.37029 | −0.685144 | − | 0.728408i | \(-0.740261\pi\) | ||||
−0.685144 | + | 0.728408i | \(0.740261\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2048.31 | 0.729652 | 0.364826 | − | 0.931076i | \(-0.381129\pi\) | ||||
0.364826 | + | 0.931076i | \(0.381129\pi\) | |||||||
\(200\) | 583.013 | 0.206126 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2491.87 | −0.867956 | ||||||||
\(203\) | 876.897 | 0.303183 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1029.31 | −0.350683 | ||||||||
\(206\) | −760.869 | −0.257341 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1489.91 | 0.496666 | ||||||||
\(209\) | −7305.06 | −2.41771 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2381.79 | 0.777107 | 0.388553 | − | 0.921426i | \(-0.372975\pi\) | ||||
0.388553 | + | 0.921426i | \(0.372975\pi\) | |||||||
\(212\) | −52.9440 | −0.0171519 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4131.77 | 1.31982 | ||||||||
\(215\) | 401.000 | 0.127200 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −749.738 | −0.234542 | ||||||||
\(218\) | −5440.97 | −1.69041 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 159.423 | 0.0488559 | ||||||||
\(221\) | 2832.98 | 0.862295 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −557.154 | −0.167309 | −0.0836543 | − | 0.996495i | \(-0.526659\pi\) | ||||
−0.0836543 | + | 0.996495i | \(0.526659\pi\) | |||||||
\(224\) | −167.733 | −0.0500320 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1387.62 | 0.408419 | ||||||||
\(227\) | 5178.09 | 1.51402 | 0.757008 | − | 0.653405i | \(-0.226660\pi\) | ||||
0.757008 | + | 0.653405i | \(0.226660\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −918.276 | −0.264984 | −0.132492 | − | 0.991184i | \(-0.542298\pi\) | ||||
−0.132492 | + | 0.991184i | \(0.542298\pi\) | |||||||
\(230\) | 1330.86 | 0.381540 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2951.66 | 0.835284 | ||||||||
\(233\) | 5896.92 | 1.65803 | 0.829013 | − | 0.559230i | \(-0.188903\pi\) | ||||
0.829013 | + | 0.559230i | \(0.188903\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1348.56 | −0.374343 | ||||||||
\(236\) | −163.182 | −0.0450096 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2138.79 | 0.582509 | ||||||||
\(239\) | −526.840 | −0.142588 | −0.0712938 | − | 0.997455i | \(-0.522713\pi\) | ||||
−0.0712938 | + | 0.997455i | \(0.522713\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5823.19 | −1.55645 | −0.778226 | − | 0.627984i | \(-0.783880\pi\) | ||||
−0.778226 | + | 0.627984i | \(0.783880\pi\) | |||||||
\(242\) | −6034.95 | −1.60306 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −357.205 | −0.0937201 | ||||||||
\(245\) | 1475.00 | 0.384630 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3078.30 | 0.792986 | ||||||||
\(248\) | −2523.64 | −0.646174 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 341.506 | 0.0863950 | ||||||||
\(251\) | 3244.98 | 0.816022 | 0.408011 | − | 0.912977i | \(-0.366222\pi\) | ||||
0.408011 | + | 0.912977i | \(0.366222\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5796.57 | 1.44042 | ||||||||
\(254\) | −5043.11 | −1.24580 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −819.364 | −0.200040 | ||||||||
\(257\) | 1261.40 | 0.306163 | 0.153082 | − | 0.988214i | \(-0.451080\pi\) | ||||
0.153082 | + | 0.988214i | \(0.451080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2039.27 | 0.489244 | ||||||||
\(260\) | −67.1797 | −0.0160243 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7006.91 | −1.65225 | ||||||||
\(263\) | −1924.28 | −0.451165 | −0.225582 | − | 0.974224i | \(-0.572428\pi\) | ||||
−0.225582 | + | 0.974224i | \(0.572428\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −493.975 | −0.114508 | ||||||||
\(266\) | 2323.99 | 0.535689 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 340.796 | 0.0776769 | ||||||||
\(269\) | 4762.53 | 1.07947 | 0.539733 | − | 0.841836i | \(-0.318525\pi\) | ||||
0.539733 | + | 0.841836i | \(0.318525\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1595.10 | 0.357547 | 0.178774 | − | 0.983890i | \(-0.442787\pi\) | ||||
0.178774 | + | 0.983890i | \(0.442787\pi\) | |||||||
\(272\) | 6714.79 | 1.49685 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1384.55 | −0.305269 | ||||||||
\(275\) | 1487.44 | 0.326166 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1049.58 | 0.227666 | 0.113833 | − | 0.993500i | \(-0.463687\pi\) | ||||
0.113833 | + | 0.993500i | \(0.463687\pi\) | |||||||
\(278\) | −6072.38 | −1.31006 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −807.846 | −0.172422 | ||||||||
\(281\) | −7576.04 | −1.60836 | −0.804179 | − | 0.594387i | \(-0.797395\pi\) | ||||
−0.804179 | + | 0.594387i | \(0.797395\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5852.93 | −1.22940 | −0.614701 | − | 0.788760i | \(-0.710723\pi\) | ||||
−0.614701 | + | 0.788760i | \(0.710723\pi\) | |||||||
\(284\) | −442.910 | −0.0925419 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4075.42 | 0.842604 | ||||||||
\(287\) | 1426.25 | 0.293341 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7854.84 | 1.59879 | ||||||||
\(290\) | 1728.97 | 0.350098 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −402.647 | −0.0806956 | ||||||||
\(293\) | 3539.60 | 0.705752 | 0.352876 | − | 0.935670i | \(-0.385204\pi\) | ||||
0.352876 | + | 0.935670i | \(0.385204\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1522.51 | −0.300489 | ||||||||
\(296\) | 6864.24 | 1.34789 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1393.60 | −0.270902 | ||||||||
\(299\) | −2442.64 | −0.472446 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −555.641 | −0.106401 | ||||||||
\(302\) | −1844.85 | −0.351520 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7296.25 | 1.37654 | ||||||||
\(305\) | −3332.77 | −0.625685 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −293.303 | −0.0545267 | −0.0272634 | − | 0.999628i | \(-0.508679\pi\) | ||||
−0.0272634 | + | 0.999628i | \(0.508679\pi\) | |||||||
\(308\) | −220.903 | −0.0408672 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1478.25 | −0.270835 | ||||||||
\(311\) | −4591.90 | −0.837243 | −0.418621 | − | 0.908161i | \(-0.637487\pi\) | ||||
−0.418621 | + | 0.908161i | \(0.637487\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7741.06 | 1.39792 | 0.698962 | − | 0.715159i | \(-0.253646\pi\) | ||||
0.698962 | + | 0.715159i | \(0.253646\pi\) | |||||||
\(314\) | 9911.82 | 1.78139 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.7901 | −0.00227690 | ||||||||
\(317\) | 1917.32 | 0.339709 | 0.169854 | − | 0.985469i | \(-0.445670\pi\) | ||||
0.169854 | + | 0.985469i | \(0.445670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7530.54 | 1.32172 | ||||||||
\(320\) | −2707.74 | −0.473023 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1844.09 | −0.319153 | ||||||||
\(323\) | 13873.4 | 2.38990 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −626.795 | −0.106979 | ||||||||
\(326\) | 326.641 | 0.0554938 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4800.80 | 0.808170 | ||||||||
\(329\) | 1868.63 | 0.313133 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8256.53 | 1.37106 | 0.685529 | − | 0.728046i | \(-0.259571\pi\) | ||||
0.685529 | + | 0.728046i | \(0.259571\pi\) | |||||||
\(332\) | 437.952 | 0.0723969 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8384.63 | 1.37361 | ||||||||
\(335\) | 3179.67 | 0.518578 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8518.68 | −1.37698 | −0.688490 | − | 0.725246i | \(-0.741726\pi\) | ||||
−0.688490 | + | 0.725246i | \(0.741726\pi\) | |||||||
\(338\) | 4284.96 | 0.689560 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −302.769 | −0.0482939 | ||||||||
\(341\) | −6438.54 | −1.02248 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4420.19 | −0.695825 | ||||||||
\(344\) | −1870.30 | −0.293139 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5771.76 | −0.896796 | ||||||||
\(347\) | 9627.63 | 1.48945 | 0.744724 | − | 0.667373i | \(-0.232581\pi\) | ||||
0.744724 | + | 0.667373i | \(0.232581\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7591.79 | −1.16441 | −0.582205 | − | 0.813042i | \(-0.697810\pi\) | ||||
−0.582205 | + | 0.813042i | \(0.697810\pi\) | |||||||
\(350\) | −473.205 | −0.0722682 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1440.45 | −0.218114 | ||||||||
\(353\) | 1387.23 | 0.209163 | 0.104582 | − | 0.994516i | \(-0.466650\pi\) | ||||
0.104582 | + | 0.994516i | \(0.466650\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4132.41 | −0.617818 | ||||||||
\(356\) | −274.916 | −0.0409284 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4439.01 | 0.655332 | ||||||||
\(359\) | 6335.93 | 0.931469 | 0.465735 | − | 0.884924i | \(-0.345790\pi\) | ||||
0.465735 | + | 0.884924i | \(0.345790\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8215.79 | 1.19781 | ||||||||
\(362\) | 6954.19 | 1.00968 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 93.0869 | 0.0134041 | ||||||||
\(365\) | −3756.74 | −0.538731 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9190.27 | −1.30716 | −0.653581 | − | 0.756857i | \(-0.726734\pi\) | ||||
−0.653581 | + | 0.756857i | \(0.726734\pi\) | |||||||
\(368\) | −5789.58 | −0.820116 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4020.81 | 0.564951 | ||||||||
\(371\) | 684.471 | 0.0957843 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12685.4 | −1.76092 | −0.880462 | − | 0.474116i | \(-0.842768\pi\) | ||||
−0.880462 | + | 0.474116i | \(0.842768\pi\) | |||||||
\(374\) | 18367.3 | 2.53944 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6289.84 | 0.862696 | ||||||||
\(377\) | −3173.32 | −0.433512 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13119.0 | −1.77804 | −0.889022 | − | 0.457865i | \(-0.848614\pi\) | ||||
−0.889022 | + | 0.457865i | \(0.848614\pi\) | |||||||
\(380\) | −328.987 | −0.0444122 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13129.3 | −1.75851 | ||||||||
\(383\) | −1734.25 | −0.231374 | −0.115687 | − | 0.993286i | \(-0.536907\pi\) | ||||
−0.115687 | + | 0.993286i | \(0.536907\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2061.05 | −0.272833 | ||||||||
\(386\) | −9774.84 | −1.28893 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −229.419 | −0.0300181 | ||||||||
\(389\) | 9363.99 | 1.22050 | 0.610248 | − | 0.792210i | \(-0.291070\pi\) | ||||
0.610248 | + | 0.792210i | \(0.291070\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11008.6 | −1.42386 | ||||||||
\(392\) | −6879.55 | −0.886402 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10351.4 | 1.32360 | ||||||||
\(395\) | −119.334 | −0.0152008 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7661.94 | −0.968619 | −0.484309 | − | 0.874897i | \(-0.660929\pi\) | ||||
−0.484309 | + | 0.874897i | \(0.660929\pi\) | |||||||
\(398\) | −5596.08 | −0.704789 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1485.64 | −0.185705 | ||||||||
\(401\) | −145.649 | −0.0181381 | −0.00906906 | − | 0.999959i | \(-0.502887\pi\) | ||||
−0.00906906 | + | 0.999959i | \(0.502887\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2713.15 | 0.335364 | ||||||||
\(404\) | −488.786 | −0.0601931 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2395.73 | −0.292852 | ||||||||
\(407\) | 17512.7 | 2.13285 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8890.72 | 1.07486 | 0.537430 | − | 0.843308i | \(-0.319395\pi\) | ||||
0.537430 | + | 0.843308i | \(0.319395\pi\) | |||||||
\(410\) | 2812.12 | 0.338734 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −149.246 | −0.0178467 | ||||||||
\(413\) | 2109.66 | 0.251354 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4086.15 | 0.483329 | ||||||||
\(416\) | 606.994 | 0.0715393 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 19957.8 | 2.33533 | ||||||||
\(419\) | −3168.40 | −0.369419 | −0.184709 | − | 0.982793i | \(-0.559134\pi\) | ||||
−0.184709 | + | 0.982793i | \(0.559134\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8495.03 | −0.983426 | −0.491713 | − | 0.870757i | \(-0.663629\pi\) | ||||
−0.491713 | + | 0.870757i | \(0.663629\pi\) | |||||||
\(422\) | −6507.18 | −0.750627 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2303.95 | 0.263891 | ||||||||
\(425\) | −2824.87 | −0.322415 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4618.02 | 0.523376 | ||||||||
\(428\) | 810.457 | 0.0915302 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1095.55 | −0.122866 | ||||||||
\(431\) | 2072.30 | 0.231599 | 0.115799 | − | 0.993273i | \(-0.463057\pi\) | ||||
0.115799 | + | 0.993273i | \(0.463057\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2906.44 | 0.322574 | 0.161287 | − | 0.986908i | \(-0.448435\pi\) | ||||
0.161287 | + | 0.986908i | \(0.448435\pi\) | |||||||
\(434\) | 2048.32 | 0.226550 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1067.26 | −0.117230 | ||||||||
\(437\) | −11961.9 | −1.30941 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1931.08 | 0.209944 | 0.104972 | − | 0.994475i | \(-0.466525\pi\) | ||||
0.104972 | + | 0.994475i | \(0.466525\pi\) | |||||||
\(440\) | −6937.55 | −0.751670 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7739.86 | −0.832913 | ||||||||
\(443\) | −244.624 | −0.0262358 | −0.0131179 | − | 0.999914i | \(-0.504176\pi\) | ||||
−0.0131179 | + | 0.999914i | \(0.504176\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2565.00 | −0.273242 | ||||||||
\(446\) | 1522.17 | 0.161608 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3751.96 | 0.395677 | ||||||||
\(449\) | 13276.7 | 1.39547 | 0.697734 | − | 0.716357i | \(-0.254192\pi\) | ||||
0.697734 | + | 0.716357i | \(0.254192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12248.2 | 1.27882 | ||||||||
\(452\) | 272.184 | 0.0283240 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14146.8 | −1.46243 | ||||||||
\(455\) | 868.513 | 0.0894868 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12514.2 | 1.28094 | 0.640470 | − | 0.767984i | \(-0.278740\pi\) | ||||
0.640470 | + | 0.767984i | \(0.278740\pi\) | |||||||
\(458\) | 2508.78 | 0.255955 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 261.051 | 0.0264599 | ||||||||
\(461\) | 4490.89 | 0.453712 | 0.226856 | − | 0.973928i | \(-0.427155\pi\) | ||||
0.226856 | + | 0.973928i | \(0.427155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6092.89 | −0.611578 | −0.305789 | − | 0.952099i | \(-0.598920\pi\) | ||||
−0.305789 | + | 0.952099i | \(0.598920\pi\) | |||||||
\(464\) | −7521.46 | −0.752532 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16110.7 | −1.60153 | ||||||||
\(467\) | −5193.68 | −0.514635 | −0.257318 | − | 0.966327i | \(-0.582839\pi\) | ||||
−0.257318 | + | 0.966327i | \(0.582839\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4405.88 | −0.433783 | ||||||||
\(470\) | 3684.35 | 0.361588 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7101.15 | 0.692494 | ||||||||
\(473\) | −4771.69 | −0.463853 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3069.49 | −0.296500 | ||||||||
\(476\) | 419.529 | 0.0403972 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1439.35 | 0.137729 | ||||||||
\(479\) | −18882.5 | −1.80118 | −0.900590 | − | 0.434669i | \(-0.856865\pi\) | ||||
−0.900590 | + | 0.434669i | \(0.856865\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7379.72 | −0.699556 | ||||||||
\(482\) | 15909.3 | 1.50342 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1183.77 | −0.111173 | ||||||||
\(485\) | −2140.51 | −0.200403 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17619.1 | −1.63942 | −0.819708 | − | 0.572781i | \(-0.805864\pi\) | ||||
−0.819708 | + | 0.572781i | \(0.805864\pi\) | |||||||
\(488\) | 15544.4 | 1.44193 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4029.77 | −0.371524 | ||||||||
\(491\) | −916.267 | −0.0842170 | −0.0421085 | − | 0.999113i | \(-0.513408\pi\) | ||||
−0.0421085 | + | 0.999113i | \(0.513408\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14301.7 | −1.30652 | ||||||||
\(494\) | −8410.08 | −0.765966 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6430.77 | 0.582157 | ||||||||
\(497\) | 5726.03 | 0.516796 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12463.4 | 1.11812 | 0.559058 | − | 0.829129i | \(-0.311163\pi\) | ||||
0.559058 | + | 0.829129i | \(0.311163\pi\) | |||||||
\(500\) | 66.9873 | 0.00599153 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8865.46 | −0.788217 | ||||||||
\(503\) | 49.4842 | 0.00438646 | 0.00219323 | − | 0.999998i | \(-0.499302\pi\) | ||||
0.00219323 | + | 0.999998i | \(0.499302\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4560.43 | −0.401855 | ||||||||
\(506\) | −15836.5 | −1.39134 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −989.219 | −0.0863966 | ||||||||
\(509\) | −6155.01 | −0.535985 | −0.267992 | − | 0.963421i | \(-0.586360\pi\) | ||||
−0.267992 | + | 0.963421i | \(0.586360\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5205.50 | 0.450641 | ||||||||
\(512\) | 12525.4 | 1.08115 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3446.21 | −0.295731 | ||||||||
\(515\) | −1392.49 | −0.119146 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16047.2 | 1.36510 | ||||||||
\(518\) | −5571.39 | −0.472573 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2923.44 | 0.246541 | ||||||||
\(521\) | −14718.1 | −1.23764 | −0.618821 | − | 0.785532i | \(-0.712390\pi\) | ||||
−0.618821 | + | 0.785532i | \(0.712390\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8318.46 | −0.695489 | −0.347744 | − | 0.937589i | \(-0.613052\pi\) | ||||
−0.347744 | + | 0.937589i | \(0.613052\pi\) | |||||||
\(524\) | −1374.42 | −0.114584 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5257.24 | 0.435792 | ||||||||
\(527\) | 12227.8 | 1.01072 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2675.25 | −0.219877 | ||||||||
\(530\) | 1349.56 | 0.110606 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 455.857 | 0.0371502 | ||||||||
\(533\) | −5161.32 | −0.419440 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7561.67 | 0.611064 | ||||||||
\(536\) | −14830.3 | −1.19510 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13011.5 | −1.04268 | ||||||||
\(539\) | −17551.7 | −1.40261 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19372.0 | 1.53949 | 0.769746 | − | 0.638350i | \(-0.220383\pi\) | ||||
0.769746 | + | 0.638350i | \(0.220383\pi\) | |||||||
\(542\) | −4357.89 | −0.345364 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2735.63 | 0.215605 | ||||||||
\(545\) | −9957.67 | −0.782641 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −989.727 | −0.0773632 | −0.0386816 | − | 0.999252i | \(-0.512316\pi\) | ||||
−0.0386816 | + | 0.999252i | \(0.512316\pi\) | |||||||
\(548\) | −271.582 | −0.0211705 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4063.75 | −0.315052 | ||||||||
\(551\) | −15540.1 | −1.20151 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 165.353 | 0.0127153 | ||||||||
\(554\) | −2867.52 | −0.219908 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1191.11 | −0.0908533 | ||||||||
\(557\) | 4616.60 | 0.351188 | 0.175594 | − | 0.984463i | \(-0.443815\pi\) | ||||
0.175594 | + | 0.984463i | \(0.443815\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2010.76 | 0.152139 | ||||||||
\(560\) | 2058.56 | 0.155340 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20698.1 | 1.55355 | ||||||||
\(563\) | 13509.6 | 1.01130 | 0.505649 | − | 0.862739i | \(-0.331253\pi\) | ||||
0.505649 | + | 0.862739i | \(0.331253\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2539.51 | 0.189094 | ||||||||
\(566\) | 15990.5 | 1.18751 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19274.0 | 1.42380 | ||||||||
\(569\) | −11388.1 | −0.839039 | −0.419520 | − | 0.907746i | \(-0.637801\pi\) | ||||
−0.419520 | + | 0.907746i | \(0.637801\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9417.39 | 0.690202 | 0.345101 | − | 0.938566i | \(-0.387845\pi\) | ||||
0.345101 | + | 0.938566i | \(0.387845\pi\) | |||||||
\(572\) | 799.404 | 0.0584349 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3896.59 | −0.283346 | ||||||||
\(575\) | 2435.64 | 0.176649 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3751.39 | −0.270663 | −0.135332 | − | 0.990800i | \(-0.543210\pi\) | ||||
−0.135332 | + | 0.990800i | \(0.543210\pi\) | |||||||
\(578\) | −21459.8 | −1.54431 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 339.141 | 0.0242794 | ||||||||
\(581\) | −5661.94 | −0.404297 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5878.04 | 0.417571 | ||||||||
\(584\) | 17521.8 | 1.24154 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9670.35 | −0.681704 | ||||||||
\(587\) | −9293.55 | −0.653468 | −0.326734 | − | 0.945116i | \(-0.605948\pi\) | ||||
−0.326734 | + | 0.945116i | \(0.605948\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13286.6 | 0.929484 | ||||||||
\(590\) | 4159.58 | 0.290250 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17491.5 | −1.21436 | ||||||||
\(593\) | 1527.88 | 0.105805 | 0.0529027 | − | 0.998600i | \(-0.483153\pi\) | ||||
0.0529027 | + | 0.998600i | \(0.483153\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3914.26 | 0.269696 | ||||||||
\(596\) | −273.358 | −0.0187872 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6673.40 | 0.456347 | ||||||||
\(599\) | 1670.40 | 0.113941 | 0.0569704 | − | 0.998376i | \(-0.481856\pi\) | ||||
0.0569704 | + | 0.998376i | \(0.481856\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17393.9 | 1.18055 | 0.590276 | − | 0.807201i | \(-0.299019\pi\) | ||||
0.590276 | + | 0.807201i | \(0.299019\pi\) | |||||||
\(602\) | 1518.04 | 0.102775 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −361.871 | −0.0243780 | ||||||||
\(605\) | −11044.7 | −0.742201 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4081.36 | 0.272911 | 0.136456 | − | 0.990646i | \(-0.456429\pi\) | ||||
0.136456 | + | 0.990646i | \(0.456429\pi\) | |||||||
\(608\) | 2972.52 | 0.198276 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9105.29 | 0.604365 | ||||||||
\(611\) | −6762.18 | −0.447739 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2300.45 | 0.151573 | 0.0757866 | − | 0.997124i | \(-0.475853\pi\) | ||||
0.0757866 | + | 0.997124i | \(0.475853\pi\) | |||||||
\(614\) | 801.320 | 0.0526688 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9612.95 | 0.628761 | ||||||||
\(617\) | −2905.84 | −0.189602 | −0.0948012 | − | 0.995496i | \(-0.530222\pi\) | ||||
−0.0948012 | + | 0.995496i | \(0.530222\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17855.5 | 1.15941 | 0.579703 | − | 0.814828i | \(-0.303169\pi\) | ||||
0.579703 | + | 0.814828i | \(0.303169\pi\) | |||||||
\(620\) | −289.962 | −0.0187825 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12545.3 | 0.808714 | ||||||||
\(623\) | 3554.17 | 0.228563 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −21149.0 | −1.35029 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1944.23 | 0.123540 | ||||||||
\(629\) | −33259.3 | −2.10832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24250.9 | −1.52998 | −0.764988 | − | 0.644045i | \(-0.777255\pi\) | ||||
−0.764988 | + | 0.644045i | \(0.777255\pi\) | |||||||
\(632\) | 556.584 | 0.0350312 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5238.23 | −0.328133 | ||||||||
\(635\) | −9229.54 | −0.576792 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7396.18 | 0.460043 | ||||||||
\(638\) | −20573.8 | −1.27669 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6429.28 | 0.397093 | ||||||||
\(641\) | 1499.84 | 0.0924181 | 0.0462091 | − | 0.998932i | \(-0.485286\pi\) | ||||
0.0462091 | + | 0.998932i | \(0.485286\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23120.1 | 1.41799 | 0.708996 | − | 0.705213i | \(-0.249149\pi\) | ||||
0.708996 | + | 0.705213i | \(0.249149\pi\) | |||||||
\(644\) | −361.723 | −0.0221334 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −37903.0 | −2.30847 | ||||||||
\(647\) | 10703.6 | 0.650391 | 0.325195 | − | 0.945647i | \(-0.394570\pi\) | ||||
0.325195 | + | 0.945647i | \(0.394570\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18117.1 | 1.09578 | ||||||||
\(650\) | 1712.44 | 0.103334 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 64.0714 | 0.00384851 | ||||||||
\(653\) | −18109.1 | −1.08525 | −0.542623 | − | 0.839976i | \(-0.682569\pi\) | ||||
−0.542623 | + | 0.839976i | \(0.682569\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12823.5 | −0.764973 | ||||||||
\(656\) | −12233.5 | −0.728104 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5105.18 | −0.302463 | ||||||||
\(659\) | 25113.4 | 1.48449 | 0.742244 | − | 0.670130i | \(-0.233762\pi\) | ||||
0.742244 | + | 0.670130i | \(0.233762\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18593.6 | −1.09411 | −0.547055 | − | 0.837096i | \(-0.684251\pi\) | ||||
−0.547055 | + | 0.837096i | \(0.684251\pi\) | |||||||
\(662\) | −22557.3 | −1.32434 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19058.2 | −1.11386 | ||||||||
\(665\) | 4253.21 | 0.248018 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12331.1 | 0.715834 | ||||||||
\(668\) | 1644.67 | 0.0952606 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8687.01 | −0.500908 | ||||||||
\(671\) | 39658.2 | 2.28165 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4290.38 | 0.245739 | 0.122869 | − | 0.992423i | \(-0.460790\pi\) | ||||
0.122869 | + | 0.992423i | \(0.460790\pi\) | |||||||
\(674\) | 23273.5 | 1.33006 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 840.506 | 0.0478212 | ||||||||
\(677\) | −26950.5 | −1.52998 | −0.764988 | − | 0.644045i | \(-0.777255\pi\) | ||||
−0.764988 | + | 0.644045i | \(0.777255\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2965.98 | 0.167635 | ||||||||
\(680\) | 13175.5 | 0.743025 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17590.4 | 0.987642 | ||||||||
\(683\) | 18870.9 | 1.05721 | 0.528607 | − | 0.848867i | \(-0.322715\pi\) | ||||
0.528607 | + | 0.848867i | \(0.322715\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2533.90 | −0.141336 | ||||||||
\(686\) | 12076.2 | 0.672115 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4765.93 | 0.264098 | ||||||||
\(689\) | −2476.97 | −0.136959 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3696.05 | 0.203480 | 0.101740 | − | 0.994811i | \(-0.467559\pi\) | ||||
0.101740 | + | 0.994811i | \(0.467559\pi\) | |||||||
\(692\) | −1132.14 | −0.0621931 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26303.2 | −1.43870 | ||||||||
\(695\) | −11113.2 | −0.606545 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23261.3 | −1.26411 | ||||||||
\(698\) | 20741.1 | 1.12473 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −92.8203 | −0.00501183 | ||||||||
\(701\) | −1123.53 | −0.0605349 | −0.0302674 | − | 0.999542i | \(-0.509636\pi\) | ||||
−0.0302674 | + | 0.999542i | \(0.509636\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36139.3 | −1.93886 | ||||||||
\(704\) | 32220.7 | 1.72495 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3789.97 | −0.202036 | ||||||||
\(707\) | 6319.12 | 0.336146 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26467.7 | −1.40200 | −0.700998 | − | 0.713163i | \(-0.747262\pi\) | ||||
−0.700998 | + | 0.713163i | \(0.747262\pi\) | |||||||
\(710\) | 11290.0 | 0.596767 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11963.4 | 0.629702 | ||||||||
\(713\) | −10543.0 | −0.553768 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7458.54 | 0.390117 | ||||||||
\(716\) | 870.722 | 0.0454475 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −17310.1 | −0.899730 | ||||||||
\(719\) | −7882.34 | −0.408848 | −0.204424 | − | 0.978882i | \(-0.565532\pi\) | ||||
−0.204424 | + | 0.978882i | \(0.565532\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1929.49 | 0.0996641 | ||||||||
\(722\) | −22446.0 | −1.15700 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1364.08 | 0.0700216 | ||||||||
\(725\) | 3164.23 | 0.162092 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20008.9 | 1.02076 | 0.510379 | − | 0.859950i | \(-0.329505\pi\) | ||||
0.510379 | + | 0.859950i | \(0.329505\pi\) | |||||||
\(728\) | −4050.83 | −0.206228 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10263.6 | 0.520375 | ||||||||
\(731\) | 9062.18 | 0.458518 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36293.5 | −1.82883 | −0.914414 | − | 0.404781i | \(-0.867348\pi\) | ||||
−0.914414 | + | 0.404781i | \(0.867348\pi\) | |||||||
\(734\) | 25108.3 | 1.26262 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2358.70 | −0.118129 | ||||||||
\(737\) | −37836.4 | −1.89107 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27475.5 | −1.36766 | −0.683832 | − | 0.729639i | \(-0.739688\pi\) | ||||
−0.683832 | + | 0.729639i | \(0.739688\pi\) | |||||||
\(740\) | 788.691 | 0.0391795 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1870.01 | −0.0925205 | ||||||||
\(743\) | −38148.9 | −1.88364 | −0.941822 | − | 0.336113i | \(-0.890888\pi\) | ||||
−0.941822 | + | 0.336113i | \(0.890888\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2550.46 | −0.125425 | ||||||||
\(746\) | 34657.1 | 1.70092 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3602.79 | 0.176111 | ||||||||
\(749\) | −10477.8 | −0.511146 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28223.1 | 1.37134 | 0.685669 | − | 0.727914i | \(-0.259510\pi\) | ||||
0.685669 | + | 0.727914i | \(0.259510\pi\) | |||||||
\(752\) | −16027.9 | −0.777228 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8669.67 | 0.418741 | ||||||||
\(755\) | −3376.31 | −0.162750 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34786.4 | 1.67019 | 0.835095 | − | 0.550106i | \(-0.185413\pi\) | ||||
0.835095 | + | 0.550106i | \(0.185413\pi\) | |||||||
\(758\) | 35841.8 | 1.71746 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 14316.4 | 0.683303 | ||||||||
\(761\) | −1165.96 | −0.0555403 | −0.0277702 | − | 0.999614i | \(-0.508841\pi\) | ||||
−0.0277702 | + | 0.999614i | \(0.508841\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13797.7 | 0.654668 | ||||||||
\(764\) | −2575.34 | −0.121954 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4738.07 | 0.223490 | ||||||||
\(767\) | −7634.43 | −0.359404 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26345.3 | −1.23542 | −0.617710 | − | 0.786406i | \(-0.711939\pi\) | ||||
−0.617710 | + | 0.786406i | \(0.711939\pi\) | |||||||
\(770\) | 5630.90 | 0.263537 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1917.36 | −0.0893876 | ||||||||
\(773\) | −25867.0 | −1.20358 | −0.601792 | − | 0.798653i | \(-0.705546\pi\) | ||||
−0.601792 | + | 0.798653i | \(0.705546\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2705.38 | −0.125394 | ||||||||
\(776\) | 9983.56 | 0.461842 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25582.9 | −1.17891 | ||||||||
\(779\) | −25275.6 | −1.16250 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49173.5 | 2.25297 | ||||||||
\(782\) | 30076.0 | 1.37534 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 17530.6 | 0.798586 | ||||||||
\(785\) | 18139.9 | 0.824765 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8070.97 | −0.365564 | −0.182782 | − | 0.983153i | \(-0.558510\pi\) | ||||
−0.182782 | + | 0.983153i | \(0.558510\pi\) | |||||||
\(788\) | 2030.46 | 0.0917919 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 326.025 | 0.0146829 | ||||||||
\(791\) | −3518.85 | −0.158174 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16711.7 | −0.748361 | ||||||||
\(794\) | 20932.8 | 0.935614 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1097.68 | −0.0488774 | ||||||||
\(797\) | 12901.1 | 0.573375 | 0.286688 | − | 0.958024i | \(-0.407446\pi\) | ||||
0.286688 | + | 0.958024i | \(0.407446\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30476.2 | −1.34940 | ||||||||
\(800\) | −605.256 | −0.0267488 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 397.922 | 0.0175201 | ||||||||
\(803\) | 44703.3 | 1.96456 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3374.92 | −0.147764 | ||||||||
\(806\) | −7412.48 | −0.323937 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 21270.3 | 0.926098 | ||||||||
\(809\) | −26916.2 | −1.16974 | −0.584872 | − | 0.811126i | \(-0.698855\pi\) | ||||
−0.584872 | + | 0.811126i | \(0.698855\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28082.5 | −1.21592 | −0.607959 | − | 0.793969i | \(-0.708011\pi\) | ||||
−0.607959 | + | 0.793969i | \(0.708011\pi\) | |||||||
\(812\) | −469.928 | −0.0203094 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −47845.5 | −2.06018 | ||||||||
\(815\) | 597.795 | 0.0256930 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9846.90 | 0.421664 | ||||||||
\(818\) | −24289.9 | −1.03823 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 551.604 | 0.0234913 | ||||||||
\(821\) | 46373.7 | 1.97132 | 0.985659 | − | 0.168750i | \(-0.0539731\pi\) | ||||
0.985659 | + | 0.168750i | \(0.0539731\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7804.55 | −0.330558 | −0.165279 | − | 0.986247i | \(-0.552852\pi\) | ||||
−0.165279 | + | 0.986247i | \(0.552852\pi\) | |||||||
\(824\) | 6494.70 | 0.274580 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5763.69 | −0.242790 | ||||||||
\(827\) | 23964.1 | 1.00764 | 0.503818 | − | 0.863810i | \(-0.331928\pi\) | ||||
0.503818 | + | 0.863810i | \(0.331928\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4583.86 | −0.192044 | −0.0960218 | − | 0.995379i | \(-0.530612\pi\) | ||||
−0.0960218 | + | 0.995379i | \(0.530612\pi\) | |||||||
\(830\) | −11163.6 | −0.466859 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −13577.6 | −0.565767 | ||||||||
\(833\) | 33333.5 | 1.38648 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15344.9 | 0.635969 | ||||||||
\(836\) | 3914.77 | 0.161956 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8656.23 | 0.356831 | ||||||||
\(839\) | 26928.3 | 1.10807 | 0.554034 | − | 0.832494i | \(-0.313088\pi\) | ||||
0.554034 | + | 0.832494i | \(0.313088\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8369.23 | −0.343156 | ||||||||
\(842\) | 23208.9 | 0.949917 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1276.40 | −0.0520563 | ||||||||
\(845\) | 7842.03 | 0.319259 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15304.0 | 0.620841 | ||||||||
\(848\) | −5870.95 | −0.237747 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7717.69 | 0.311429 | ||||||||
\(851\) | 28676.6 | 1.15514 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7013.39 | −0.281517 | −0.140759 | − | 0.990044i | \(-0.544954\pi\) | ||||
−0.140759 | + | 0.990044i | \(0.544954\pi\) | |||||||
\(854\) | −12616.7 | −0.505543 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −35268.4 | −1.40823 | ||||||||
\(857\) | −20665.0 | −0.823692 | −0.411846 | − | 0.911253i | \(-0.635116\pi\) | ||||
−0.411846 | + | 0.911253i | \(0.635116\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20255.9 | −0.804565 | −0.402283 | − | 0.915516i | \(-0.631783\pi\) | ||||
−0.402283 | + | 0.915516i | \(0.631783\pi\) | |||||||
\(860\) | −214.895 | −0.00852077 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5661.62 | −0.223707 | ||||||||
\(863\) | 16293.0 | 0.642666 | 0.321333 | − | 0.946966i | \(-0.395869\pi\) | ||||
0.321333 | + | 0.946966i | \(0.395869\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10563.0 | −0.415207 | ||||||||
\(866\) | −7940.54 | −0.311583 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 401.783 | 0.0157113 | ||||||||
\(869\) | 1420.01 | 0.0554321 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15944.0 | 0.620254 | ||||||||
\(872\) | 46443.6 | 1.80364 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32680.4 | 1.26480 | ||||||||
\(875\) | −866.025 | −0.0334594 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28264.1 | 1.08827 | 0.544134 | − | 0.838998i | \(-0.316858\pi\) | ||||
0.544134 | + | 0.838998i | \(0.316858\pi\) | |||||||
\(878\) | −5275.80 | −0.202790 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 17678.4 | 0.677202 | ||||||||
\(881\) | −24644.6 | −0.942447 | −0.471224 | − | 0.882014i | \(-0.656188\pi\) | ||||
−0.471224 | + | 0.882014i | \(0.656188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36026.4 | 1.37303 | 0.686515 | − | 0.727116i | \(-0.259140\pi\) | ||||
0.686515 | + | 0.727116i | \(0.259140\pi\) | |||||||
\(884\) | −1518.19 | −0.0577628 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 668.326 | 0.0253418 | ||||||||
\(887\) | 14174.7 | 0.536572 | 0.268286 | − | 0.963339i | \(-0.413543\pi\) | ||||
0.268286 | + | 0.963339i | \(0.413543\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12788.8 | 0.482478 | ||||||||
\(890\) | 7007.71 | 0.263931 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 298.578 | 0.0112075 | ||||||||
\(893\) | −33115.2 | −1.24094 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8123.95 | 0.303412 | ||||||||
\(896\) | −8908.67 | −0.332163 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −36272.5 | −1.34792 | ||||||||
\(899\) | −13696.7 | −0.508133 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11163.3 | −0.412768 | ||||||||
\(902\) | −33462.8 | −1.23524 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11844.5 | −0.435778 | ||||||||
\(905\) | 12727.0 | 0.467471 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36005.1 | 1.31812 | 0.659058 | − | 0.752092i | \(-0.270955\pi\) | ||||
0.659058 | + | 0.752092i | \(0.270955\pi\) | |||||||
\(908\) | −2774.93 | −0.101420 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2372.82 | −0.0864376 | ||||||||
\(911\) | −1202.49 | −0.0437325 | −0.0218662 | − | 0.999761i | \(-0.506961\pi\) | ||||
−0.0218662 | + | 0.999761i | \(0.506961\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48623.1 | −1.76253 | ||||||||
\(914\) | −34189.4 | −1.23729 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 492.103 | 0.0177506 | ||||||||
\(917\) | 17768.8 | 0.639889 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1151.63 | 0.0413370 | 0.0206685 | − | 0.999786i | \(-0.493421\pi\) | ||||
0.0206685 | + | 0.999786i | \(0.493421\pi\) | |||||||
\(920\) | −11360.1 | −0.407098 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12269.3 | −0.438253 | ||||||||
\(923\) | −20721.4 | −0.738952 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7358.59 | 0.261566 | ||||||||
\(926\) | 16646.1 | 0.590739 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3064.27 | −0.108394 | ||||||||
\(929\) | −5397.06 | −0.190605 | −0.0953023 | − | 0.995448i | \(-0.530382\pi\) | ||||
−0.0953023 | + | 0.995448i | \(0.530382\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36219.9 | 1.27504 | ||||||||
\(932\) | −3160.15 | −0.111067 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 14189.4 | 0.497100 | ||||||||
\(935\) | 33614.5 | 1.17573 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45594.6 | 1.58966 | 0.794830 | − | 0.606832i | \(-0.207560\pi\) | ||||
0.794830 | + | 0.606832i | \(0.207560\pi\) | |||||||
\(938\) | 12037.1 | 0.419003 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 722.693 | 0.0250762 | ||||||||
\(941\) | 37245.5 | 1.29030 | 0.645149 | − | 0.764057i | \(-0.276795\pi\) | ||||
0.645149 | + | 0.764057i | \(0.276795\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20056.2 | 0.692598 | ||||||||
\(944\) | −18095.3 | −0.623888 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13036.5 | 0.448048 | ||||||||
\(947\) | −4777.54 | −0.163938 | −0.0819689 | − | 0.996635i | \(-0.526121\pi\) | ||||
−0.0819689 | + | 0.996635i | \(0.526121\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18837.7 | −0.644359 | ||||||||
\(950\) | 8385.99 | 0.286397 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −18256.5 | −0.621530 | ||||||||
\(953\) | 56883.2 | 1.93350 | 0.966752 | − | 0.255717i | \(-0.0823114\pi\) | ||||
0.966752 | + | 0.255717i | \(0.0823114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24028.3 | −0.814174 | ||||||||
\(956\) | 282.333 | 0.00955156 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 51588.1 | 1.73981 | ||||||||
\(959\) | 3511.07 | 0.118226 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18080.4 | −0.606909 | ||||||||
\(962\) | 20161.8 | 0.675719 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3120.64 | 0.104262 | ||||||||
\(965\) | −17889.2 | −0.596760 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14050.0 | 0.467236 | 0.233618 | − | 0.972329i | \(-0.424944\pi\) | ||||
0.233618 | + | 0.972329i | \(0.424944\pi\) | |||||||
\(968\) | 51513.7 | 1.71045 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5847.99 | 0.193575 | ||||||||
\(971\) | −779.492 | −0.0257622 | −0.0128811 | − | 0.999917i | \(-0.504100\pi\) | ||||
−0.0128811 | + | 0.999917i | \(0.504100\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15398.9 | 0.507366 | ||||||||
\(974\) | 48136.2 | 1.58355 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −39610.4 | −1.29907 | ||||||||
\(977\) | −46754.9 | −1.53103 | −0.765517 | − | 0.643415i | \(-0.777517\pi\) | ||||
−0.765517 | + | 0.643415i | \(0.777517\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30522.2 | 0.996418 | ||||||||
\(980\) | −790.450 | −0.0257653 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2503.29 | 0.0813474 | ||||||||
\(983\) | 3596.10 | 0.116681 | 0.0583406 | − | 0.998297i | \(-0.481419\pi\) | ||||
0.0583406 | + | 0.998297i | \(0.481419\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18944.4 | 0.612811 | ||||||||
\(986\) | 39072.9 | 1.26200 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1649.66 | −0.0531200 | ||||||||
\(989\) | −7813.53 | −0.251219 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15143.8 | −0.485427 | −0.242713 | − | 0.970098i | \(-0.578037\pi\) | ||||
−0.242713 | + | 0.970098i | \(0.578037\pi\) | |||||||
\(992\) | 2619.92 | 0.0838534 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15643.8 | −0.499187 | ||||||||
\(995\) | −10241.5 | −0.326310 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22008.9 | 0.699126 | 0.349563 | − | 0.936913i | \(-0.386330\pi\) | ||||
0.349563 | + | 0.936913i | \(0.386330\pi\) | |||||||
\(998\) | −34050.7 | −1.08002 | ||||||||
\(999\) | 0 | 0 |
(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 | 405.4.a.c.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 405.4.a.f.1.2 | yes | 2 | ||
5.4 | even | 2 | 2025.4.a.m.1.2 | 2 | |||
9.2 | odd | 6 | 405.4.e.o.271.1 | 4 | |||
9.4 | even | 3 | 405.4.e.p.136.2 | 4 | |||
9.5 | odd | 6 | 405.4.e.o.136.1 | 4 | |||
9.7 | even | 3 | 405.4.e.p.271.2 | 4 | |||
15.14 | odd | 2 | 2025.4.a.i.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.4.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
405.4.a.f.1.2 | yes | 2 | 3.2 | odd | 2 | ||
405.4.e.o.136.1 | 4 | 9.5 | odd | 6 | |||
405.4.e.o.271.1 | 4 | 9.2 | odd | 6 | |||
405.4.e.p.136.2 | 4 | 9.4 | even | 3 | |||
405.4.e.p.271.2 | 4 | 9.7 | even | 3 | |||
2025.4.a.i.1.1 | 2 | 15.14 | odd | 2 | |||
2025.4.a.m.1.2 | 2 | 5.4 | even | 2 |