Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,4,Mod(1,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, 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("1350.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.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: | \(79.6525785077\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1350.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −23.0000 | −1.24188 | −0.620942 | − | 0.783857i | \(-0.713250\pi\) | ||||
−0.620942 | + | 0.783857i | \(0.713250\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 30.0000 | 0.822304 | 0.411152 | − | 0.911567i | \(-0.365127\pi\) | ||||
0.411152 | + | 0.911567i | \(0.365127\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 34.0000 | 0.725377 | 0.362689 | − | 0.931910i | \(-0.381859\pi\) | ||||
0.362689 | + | 0.931910i | \(0.381859\pi\) | |||||||
\(14\) | −46.0000 | −0.878144 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 42.0000 | 0.599206 | 0.299603 | − | 0.954064i | \(-0.403146\pi\) | ||||
0.299603 | + | 0.954064i | \(0.403146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −139.000 | −1.67836 | −0.839179 | − | 0.543856i | \(-0.816964\pi\) | ||||
−0.839179 | + | 0.543856i | \(0.816964\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 60.0000 | 0.581456 | ||||||||
\(23\) | −192.000 | −1.74064 | −0.870321 | − | 0.492485i | \(-0.836089\pi\) | ||||
−0.870321 | + | 0.492485i | \(0.836089\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 68.0000 | 0.512919 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −92.0000 | −0.620942 | ||||||||
\(29\) | 234.000 | 1.49837 | 0.749185 | − | 0.662361i | \(-0.230446\pi\) | ||||
0.749185 | + | 0.662361i | \(0.230446\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −55.0000 | −0.318655 | −0.159327 | − | 0.987226i | \(-0.550933\pi\) | ||||
−0.159327 | + | 0.987226i | \(0.550933\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 84.0000 | 0.423702 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −191.000 | −0.848654 | −0.424327 | − | 0.905509i | \(-0.639489\pi\) | ||||
−0.424327 | + | 0.905509i | \(0.639489\pi\) | |||||||
\(38\) | −278.000 | −1.18678 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 138.000 | 0.525658 | 0.262829 | − | 0.964842i | \(-0.415344\pi\) | ||||
0.262829 | + | 0.964842i | \(0.415344\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −53.0000 | −0.187963 | −0.0939817 | − | 0.995574i | \(-0.529960\pi\) | ||||
−0.0939817 | + | 0.995574i | \(0.529960\pi\) | |||||||
\(44\) | 120.000 | 0.411152 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −384.000 | −1.23082 | ||||||||
\(47\) | −366.000 | −1.13588 | −0.567942 | − | 0.823068i | \(-0.692260\pi\) | ||||
−0.567942 | + | 0.823068i | \(0.692260\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 186.000 | 0.542274 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 136.000 | 0.362689 | ||||||||
\(53\) | 330.000 | 0.855264 | 0.427632 | − | 0.903953i | \(-0.359348\pi\) | ||||
0.427632 | + | 0.903953i | \(0.359348\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −184.000 | −0.439072 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 468.000 | 1.05951 | ||||||||
\(59\) | −396.000 | −0.873810 | −0.436905 | − | 0.899508i | \(-0.643925\pi\) | ||||
−0.436905 | + | 0.899508i | \(0.643925\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23.0000 | 0.0482762 | 0.0241381 | − | 0.999709i | \(-0.492316\pi\) | ||||
0.0241381 | + | 0.999709i | \(0.492316\pi\) | |||||||
\(62\) | −110.000 | −0.225323 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −452.000 | −0.824188 | −0.412094 | − | 0.911141i | \(-0.635202\pi\) | ||||
−0.412094 | + | 0.911141i | \(0.635202\pi\) | |||||||
\(68\) | 168.000 | 0.299603 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 204.000 | 0.340991 | 0.170495 | − | 0.985358i | \(-0.445463\pi\) | ||||
0.170495 | + | 0.985358i | \(0.445463\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 691.000 | 1.10788 | 0.553941 | − | 0.832556i | \(-0.313123\pi\) | ||||
0.553941 | + | 0.832556i | \(0.313123\pi\) | |||||||
\(74\) | −382.000 | −0.600089 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −556.000 | −0.839179 | ||||||||
\(77\) | −690.000 | −1.02121 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −709.000 | −1.00973 | −0.504865 | − | 0.863198i | \(-0.668458\pi\) | ||||
−0.504865 | + | 0.863198i | \(0.668458\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 276.000 | 0.371696 | ||||||||
\(83\) | −1098.00 | −1.45206 | −0.726031 | − | 0.687662i | \(-0.758637\pi\) | ||||
−0.726031 | + | 0.687662i | \(0.758637\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −106.000 | −0.132910 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 240.000 | 0.290728 | ||||||||
\(89\) | −816.000 | −0.971863 | −0.485932 | − | 0.873997i | \(-0.661520\pi\) | ||||
−0.485932 | + | 0.873997i | \(0.661520\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −782.000 | −0.900834 | ||||||||
\(92\) | −768.000 | −0.870321 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −732.000 | −0.803192 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −905.000 | −0.947308 | −0.473654 | − | 0.880711i | \(-0.657065\pi\) | ||||
−0.473654 | + | 0.880711i | \(0.657065\pi\) | |||||||
\(98\) | 372.000 | 0.383446 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1278.00 | −1.25907 | −0.629533 | − | 0.776973i | \(-0.716754\pi\) | ||||
−0.629533 | + | 0.776973i | \(0.716754\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −605.000 | −0.578761 | −0.289381 | − | 0.957214i | \(-0.593449\pi\) | ||||
−0.289381 | + | 0.957214i | \(0.593449\pi\) | |||||||
\(104\) | 272.000 | 0.256460 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 660.000 | 0.604763 | ||||||||
\(107\) | −1488.00 | −1.34440 | −0.672198 | − | 0.740371i | \(-0.734650\pi\) | ||||
−0.672198 | + | 0.740371i | \(0.734650\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 593.000 | 0.521093 | 0.260546 | − | 0.965461i | \(-0.416097\pi\) | ||||
0.260546 | + | 0.965461i | \(0.416097\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −368.000 | −0.310471 | ||||||||
\(113\) | −324.000 | −0.269729 | −0.134864 | − | 0.990864i | \(-0.543060\pi\) | ||||
−0.134864 | + | 0.990864i | \(0.543060\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 936.000 | 0.749185 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −792.000 | −0.617877 | ||||||||
\(119\) | −966.000 | −0.744143 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −431.000 | −0.323817 | ||||||||
\(122\) | 46.0000 | 0.0341364 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −220.000 | −0.159327 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1928.00 | −1.34711 | −0.673553 | − | 0.739139i | \(-0.735232\pi\) | ||||
−0.673553 | + | 0.739139i | \(0.735232\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2742.00 | 1.82878 | 0.914388 | − | 0.404839i | \(-0.132672\pi\) | ||||
0.914388 | + | 0.404839i | \(0.132672\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3197.00 | 2.08432 | ||||||||
\(134\) | −904.000 | −0.582789 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 336.000 | 0.211851 | ||||||||
\(137\) | −1326.00 | −0.826918 | −0.413459 | − | 0.910523i | \(-0.635680\pi\) | ||||
−0.413459 | + | 0.910523i | \(0.635680\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 893.000 | 0.544916 | 0.272458 | − | 0.962168i | \(-0.412163\pi\) | ||||
0.272458 | + | 0.962168i | \(0.412163\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 408.000 | 0.241117 | ||||||||
\(143\) | 1020.00 | 0.596480 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1382.00 | 0.783391 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −764.000 | −0.424327 | ||||||||
\(149\) | −2502.00 | −1.37565 | −0.687825 | − | 0.725877i | \(-0.741434\pi\) | ||||
−0.687825 | + | 0.725877i | \(0.741434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2767.00 | −1.49123 | −0.745613 | − | 0.666379i | \(-0.767843\pi\) | ||||
−0.745613 | + | 0.666379i | \(0.767843\pi\) | |||||||
\(152\) | −1112.00 | −0.593389 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1380.00 | −0.722101 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2701.00 | 1.37301 | 0.686507 | − | 0.727123i | \(-0.259143\pi\) | ||||
0.686507 | + | 0.727123i | \(0.259143\pi\) | |||||||
\(158\) | −1418.00 | −0.713987 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4416.00 | 2.16167 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1748.00 | −0.839963 | −0.419981 | − | 0.907533i | \(-0.637963\pi\) | ||||
−0.419981 | + | 0.907533i | \(0.637963\pi\) | |||||||
\(164\) | 552.000 | 0.262829 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2196.00 | −1.02676 | ||||||||
\(167\) | 534.000 | 0.247438 | 0.123719 | − | 0.992317i | \(-0.460518\pi\) | ||||
0.123719 | + | 0.992317i | \(0.460518\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1041.00 | −0.473828 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −212.000 | −0.0939817 | ||||||||
\(173\) | 192.000 | 0.0843786 | 0.0421893 | − | 0.999110i | \(-0.486567\pi\) | ||||
0.0421893 | + | 0.999110i | \(0.486567\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 480.000 | 0.205576 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1632.00 | −0.687211 | ||||||||
\(179\) | 1140.00 | 0.476020 | 0.238010 | − | 0.971263i | \(-0.423505\pi\) | ||||
0.238010 | + | 0.971263i | \(0.423505\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 398.000 | 0.163443 | 0.0817213 | − | 0.996655i | \(-0.473958\pi\) | ||||
0.0817213 | + | 0.996655i | \(0.473958\pi\) | |||||||
\(182\) | −1564.00 | −0.636986 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1536.00 | −0.615410 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1260.00 | 0.492729 | ||||||||
\(188\) | −1464.00 | −0.567942 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3474.00 | 1.31607 | 0.658036 | − | 0.752986i | \(-0.271387\pi\) | ||||
0.658036 | + | 0.752986i | \(0.271387\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2713.00 | 1.01184 | 0.505922 | − | 0.862579i | \(-0.331152\pi\) | ||||
0.505922 | + | 0.862579i | \(0.331152\pi\) | |||||||
\(194\) | −1810.00 | −0.669848 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 744.000 | 0.271137 | ||||||||
\(197\) | −4734.00 | −1.71210 | −0.856050 | − | 0.516894i | \(-0.827088\pi\) | ||||
−0.856050 | + | 0.516894i | \(0.827088\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5132.00 | 1.82813 | 0.914065 | − | 0.405568i | \(-0.132926\pi\) | ||||
0.914065 | + | 0.405568i | \(0.132926\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2556.00 | −0.890295 | ||||||||
\(203\) | −5382.00 | −1.86080 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1210.00 | −0.409246 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 544.000 | 0.181344 | ||||||||
\(209\) | −4170.00 | −1.38012 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5240.00 | 1.70965 | 0.854826 | − | 0.518915i | \(-0.173664\pi\) | ||||
0.854826 | + | 0.518915i | \(0.173664\pi\) | |||||||
\(212\) | 1320.00 | 0.427632 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2976.00 | −0.950632 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1265.00 | 0.395732 | ||||||||
\(218\) | 1186.00 | 0.368468 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1428.00 | 0.434650 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4519.00 | 1.35702 | 0.678508 | − | 0.734593i | \(-0.262627\pi\) | ||||
0.678508 | + | 0.734593i | \(0.262627\pi\) | |||||||
\(224\) | −736.000 | −0.219536 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −648.000 | −0.190727 | ||||||||
\(227\) | −5064.00 | −1.48066 | −0.740329 | − | 0.672244i | \(-0.765330\pi\) | ||||
−0.740329 | + | 0.672244i | \(0.765330\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2573.00 | 0.742483 | 0.371242 | − | 0.928536i | \(-0.378932\pi\) | ||||
0.371242 | + | 0.928536i | \(0.378932\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1872.00 | 0.529754 | ||||||||
\(233\) | −4098.00 | −1.15223 | −0.576114 | − | 0.817370i | \(-0.695431\pi\) | ||||
−0.576114 | + | 0.817370i | \(0.695431\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1584.00 | −0.436905 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1932.00 | −0.526189 | ||||||||
\(239\) | −306.000 | −0.0828180 | −0.0414090 | − | 0.999142i | \(-0.513185\pi\) | ||||
−0.0414090 | + | 0.999142i | \(0.513185\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6482.00 | 1.73254 | 0.866270 | − | 0.499575i | \(-0.166511\pi\) | ||||
0.866270 | + | 0.499575i | \(0.166511\pi\) | |||||||
\(242\) | −862.000 | −0.228973 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 92.0000 | 0.0241381 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4726.00 | −1.21744 | ||||||||
\(248\) | −440.000 | −0.112661 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5850.00 | −1.47111 | −0.735555 | − | 0.677465i | \(-0.763079\pi\) | ||||
−0.735555 | + | 0.677465i | \(0.763079\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5760.00 | −1.43134 | ||||||||
\(254\) | −3856.00 | −0.952547 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −5598.00 | −1.35873 | −0.679365 | − | 0.733800i | \(-0.737745\pi\) | ||||
−0.679365 | + | 0.733800i | \(0.737745\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4393.00 | 1.05393 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5484.00 | 1.29314 | ||||||||
\(263\) | 8286.00 | 1.94272 | 0.971362 | − | 0.237603i | \(-0.0763616\pi\) | ||||
0.971362 | + | 0.237603i | \(0.0763616\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6394.00 | 1.47384 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1808.00 | −0.412094 | ||||||||
\(269\) | −504.000 | −0.114236 | −0.0571179 | − | 0.998367i | \(-0.518191\pi\) | ||||
−0.0571179 | + | 0.998367i | \(0.518191\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4489.00 | −1.00623 | −0.503113 | − | 0.864221i | \(-0.667812\pi\) | ||||
−0.503113 | + | 0.864221i | \(0.667812\pi\) | |||||||
\(272\) | 672.000 | 0.149801 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2652.00 | −0.584720 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2213.00 | −0.480023 | −0.240011 | − | 0.970770i | \(-0.577151\pi\) | ||||
−0.240011 | + | 0.970770i | \(0.577151\pi\) | |||||||
\(278\) | 1786.00 | 0.385314 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2718.00 | −0.577019 | −0.288509 | − | 0.957477i | \(-0.593160\pi\) | ||||
−0.288509 | + | 0.957477i | \(0.593160\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5615.00 | −1.17942 | −0.589712 | − | 0.807613i | \(-0.700759\pi\) | ||||
−0.589712 | + | 0.807613i | \(0.700759\pi\) | |||||||
\(284\) | 816.000 | 0.170495 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2040.00 | 0.421775 | ||||||||
\(287\) | −3174.00 | −0.652806 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3149.00 | −0.640953 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2764.00 | 0.553941 | ||||||||
\(293\) | −1488.00 | −0.296689 | −0.148345 | − | 0.988936i | \(-0.547394\pi\) | ||||
−0.148345 | + | 0.988936i | \(0.547394\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1528.00 | −0.300045 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5004.00 | −0.972731 | ||||||||
\(299\) | −6528.00 | −1.26262 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1219.00 | 0.233429 | ||||||||
\(302\) | −5534.00 | −1.05446 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2224.00 | −0.419589 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7487.00 | −1.39188 | −0.695938 | − | 0.718102i | \(-0.745011\pi\) | ||||
−0.695938 | + | 0.718102i | \(0.745011\pi\) | |||||||
\(308\) | −2760.00 | −0.510603 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8118.00 | 1.48016 | 0.740080 | − | 0.672519i | \(-0.234788\pi\) | ||||
0.740080 | + | 0.672519i | \(0.234788\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5002.00 | 0.903290 | 0.451645 | − | 0.892198i | \(-0.350837\pi\) | ||||
0.451645 | + | 0.892198i | \(0.350837\pi\) | |||||||
\(314\) | 5402.00 | 0.970868 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2836.00 | −0.504865 | ||||||||
\(317\) | −5082.00 | −0.900421 | −0.450211 | − | 0.892922i | \(-0.648651\pi\) | ||||
−0.450211 | + | 0.892922i | \(0.648651\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7020.00 | 1.23211 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8832.00 | 1.52853 | ||||||||
\(323\) | −5838.00 | −1.00568 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3496.00 | −0.593943 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1104.00 | 0.185848 | ||||||||
\(329\) | 8418.00 | 1.41064 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7625.00 | 1.26619 | 0.633094 | − | 0.774075i | \(-0.281785\pi\) | ||||
0.633094 | + | 0.774075i | \(0.281785\pi\) | |||||||
\(332\) | −4392.00 | −0.726031 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1068.00 | 0.174965 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3778.00 | 0.610685 | 0.305342 | − | 0.952243i | \(-0.401229\pi\) | ||||
0.305342 | + | 0.952243i | \(0.401229\pi\) | |||||||
\(338\) | −2082.00 | −0.335047 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1650.00 | −0.262031 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3611.00 | 0.568442 | ||||||||
\(344\) | −424.000 | −0.0664551 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 384.000 | 0.0596646 | ||||||||
\(347\) | 8268.00 | 1.27911 | 0.639553 | − | 0.768747i | \(-0.279120\pi\) | ||||
0.639553 | + | 0.768747i | \(0.279120\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1379.00 | 0.211508 | 0.105754 | − | 0.994392i | \(-0.466274\pi\) | ||||
0.105754 | + | 0.994392i | \(0.466274\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 960.000 | 0.145364 | ||||||||
\(353\) | −3072.00 | −0.463190 | −0.231595 | − | 0.972812i | \(-0.574394\pi\) | ||||
−0.231595 | + | 0.972812i | \(0.574394\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3264.00 | −0.485932 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2280.00 | 0.336597 | ||||||||
\(359\) | −7446.00 | −1.09467 | −0.547333 | − | 0.836915i | \(-0.684357\pi\) | ||||
−0.547333 | + | 0.836915i | \(0.684357\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12462.0 | 1.81688 | ||||||||
\(362\) | 796.000 | 0.115571 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3128.00 | −0.450417 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6496.00 | 0.923947 | 0.461973 | − | 0.886894i | \(-0.347142\pi\) | ||||
0.461973 | + | 0.886894i | \(0.347142\pi\) | |||||||
\(368\) | −3072.00 | −0.435161 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7590.00 | −1.06214 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1633.00 | 0.226685 | 0.113343 | − | 0.993556i | \(-0.463844\pi\) | ||||
0.113343 | + | 0.993556i | \(0.463844\pi\) | |||||||
\(374\) | 2520.00 | 0.348412 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2928.00 | −0.401596 | ||||||||
\(377\) | 7956.00 | 1.08688 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6788.00 | 0.919990 | 0.459995 | − | 0.887922i | \(-0.347851\pi\) | ||||
0.459995 | + | 0.887922i | \(0.347851\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6948.00 | 0.930604 | ||||||||
\(383\) | −6582.00 | −0.878132 | −0.439066 | − | 0.898455i | \(-0.644691\pi\) | ||||
−0.439066 | + | 0.898455i | \(0.644691\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5426.00 | 0.715482 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3620.00 | −0.473654 | ||||||||
\(389\) | 2850.00 | 0.371467 | 0.185734 | − | 0.982600i | \(-0.440534\pi\) | ||||
0.185734 | + | 0.982600i | \(0.440534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8064.00 | −1.04300 | ||||||||
\(392\) | 1488.00 | 0.191723 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9468.00 | −1.21064 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7451.00 | −0.941952 | −0.470976 | − | 0.882146i | \(-0.656098\pi\) | ||||
−0.470976 | + | 0.882146i | \(0.656098\pi\) | |||||||
\(398\) | 10264.0 | 1.29268 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14124.0 | 1.75890 | 0.879450 | − | 0.475991i | \(-0.157911\pi\) | ||||
0.879450 | + | 0.475991i | \(0.157911\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1870.00 | −0.231145 | ||||||||
\(404\) | −5112.00 | −0.629533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10764.0 | −1.31578 | ||||||||
\(407\) | −5730.00 | −0.697851 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6374.00 | 0.770597 | 0.385298 | − | 0.922792i | \(-0.374099\pi\) | ||||
0.385298 | + | 0.922792i | \(0.374099\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2420.00 | −0.289381 | ||||||||
\(413\) | 9108.00 | 1.08517 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1088.00 | 0.128230 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8340.00 | −0.975892 | ||||||||
\(419\) | 3948.00 | 0.460316 | 0.230158 | − | 0.973153i | \(-0.426076\pi\) | ||||
0.230158 | + | 0.973153i | \(0.426076\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12629.0 | 1.46199 | 0.730997 | − | 0.682380i | \(-0.239055\pi\) | ||||
0.730997 | + | 0.682380i | \(0.239055\pi\) | |||||||
\(422\) | 10480.0 | 1.20891 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2640.00 | 0.302381 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −529.000 | −0.0599534 | ||||||||
\(428\) | −5952.00 | −0.672198 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4842.00 | 0.541139 | 0.270570 | − | 0.962700i | \(-0.412788\pi\) | ||||
0.270570 | + | 0.962700i | \(0.412788\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3851.00 | −0.427407 | −0.213704 | − | 0.976899i | \(-0.568553\pi\) | ||||
−0.213704 | + | 0.976899i | \(0.568553\pi\) | |||||||
\(434\) | 2530.00 | 0.279825 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2372.00 | 0.260546 | ||||||||
\(437\) | 26688.0 | 2.92142 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7435.00 | −0.808322 | −0.404161 | − | 0.914688i | \(-0.632436\pi\) | ||||
−0.404161 | + | 0.914688i | \(0.632436\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2856.00 | 0.307344 | ||||||||
\(443\) | 5760.00 | 0.617756 | 0.308878 | − | 0.951102i | \(-0.400047\pi\) | ||||
0.308878 | + | 0.951102i | \(0.400047\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9038.00 | 0.959555 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1472.00 | −0.155235 | ||||||||
\(449\) | −2190.00 | −0.230184 | −0.115092 | − | 0.993355i | \(-0.536716\pi\) | ||||
−0.115092 | + | 0.993355i | \(0.536716\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4140.00 | 0.432251 | ||||||||
\(452\) | −1296.00 | −0.134864 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10128.0 | −1.04698 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7202.00 | −0.737189 | −0.368594 | − | 0.929590i | \(-0.620161\pi\) | ||||
−0.368594 | + | 0.929590i | \(0.620161\pi\) | |||||||
\(458\) | 5146.00 | 0.525015 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13476.0 | −1.36147 | −0.680737 | − | 0.732528i | \(-0.738341\pi\) | ||||
−0.680737 | + | 0.732528i | \(0.738341\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10843.0 | 1.08837 | 0.544187 | − | 0.838964i | \(-0.316838\pi\) | ||||
0.544187 | + | 0.838964i | \(0.316838\pi\) | |||||||
\(464\) | 3744.00 | 0.374592 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8196.00 | −0.814748 | ||||||||
\(467\) | −6108.00 | −0.605235 | −0.302617 | − | 0.953112i | \(-0.597860\pi\) | ||||
−0.302617 | + | 0.953112i | \(0.597860\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10396.0 | 1.02355 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3168.00 | −0.308939 | ||||||||
\(473\) | −1590.00 | −0.154563 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3864.00 | −0.372072 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −612.000 | −0.0585611 | ||||||||
\(479\) | 9852.00 | 0.939769 | 0.469885 | − | 0.882728i | \(-0.344296\pi\) | ||||
0.469885 | + | 0.882728i | \(0.344296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6494.00 | −0.615594 | ||||||||
\(482\) | 12964.0 | 1.22509 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1724.00 | −0.161908 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7796.00 | −0.725401 | −0.362701 | − | 0.931906i | \(-0.618145\pi\) | ||||
−0.362701 | + | 0.931906i | \(0.618145\pi\) | |||||||
\(488\) | 184.000 | 0.0170682 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2454.00 | 0.225555 | 0.112777 | − | 0.993620i | \(-0.464025\pi\) | ||||
0.112777 | + | 0.993620i | \(0.464025\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9828.00 | 0.897831 | ||||||||
\(494\) | −9452.00 | −0.860862 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −880.000 | −0.0796636 | ||||||||
\(497\) | −4692.00 | −0.423471 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2953.00 | −0.264919 | −0.132459 | − | 0.991188i | \(-0.542287\pi\) | ||||
−0.132459 | + | 0.991188i | \(0.542287\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11700.0 | −1.04023 | ||||||||
\(503\) | 11322.0 | 1.00362 | 0.501812 | − | 0.864977i | \(-0.332667\pi\) | ||||
0.501812 | + | 0.864977i | \(0.332667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11520.0 | −1.01211 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7712.00 | −0.673553 | ||||||||
\(509\) | 9696.00 | 0.844337 | 0.422169 | − | 0.906517i | \(-0.361269\pi\) | ||||
0.422169 | + | 0.906517i | \(0.361269\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15893.0 | −1.37586 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11196.0 | −0.960767 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10980.0 | −0.934042 | ||||||||
\(518\) | 8786.00 | 0.745241 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12192.0 | −1.02522 | −0.512612 | − | 0.858621i | \(-0.671322\pi\) | ||||
−0.512612 | + | 0.858621i | \(0.671322\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8491.00 | 0.709915 | 0.354957 | − | 0.934882i | \(-0.384495\pi\) | ||||
0.354957 | + | 0.934882i | \(0.384495\pi\) | |||||||
\(524\) | 10968.0 | 0.914388 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16572.0 | 1.37371 | ||||||||
\(527\) | −2310.00 | −0.190940 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24697.0 | 2.02983 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12788.0 | 1.04216 | ||||||||
\(533\) | 4692.00 | 0.381300 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3616.00 | −0.291394 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1008.00 | −0.0807769 | ||||||||
\(539\) | 5580.00 | 0.445914 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9355.00 | −0.743443 | −0.371722 | − | 0.928344i | \(-0.621232\pi\) | ||||
−0.371722 | + | 0.928344i | \(0.621232\pi\) | |||||||
\(542\) | −8978.00 | −0.711509 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1344.00 | 0.105926 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 295.000 | 0.0230590 | 0.0115295 | − | 0.999934i | \(-0.496330\pi\) | ||||
0.0115295 | + | 0.999934i | \(0.496330\pi\) | |||||||
\(548\) | −5304.00 | −0.413459 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32526.0 | −2.51480 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16307.0 | 1.25397 | ||||||||
\(554\) | −4426.00 | −0.339427 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3572.00 | 0.272458 | ||||||||
\(557\) | 16914.0 | 1.28666 | 0.643330 | − | 0.765589i | \(-0.277552\pi\) | ||||
0.643330 | + | 0.765589i | \(0.277552\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1802.00 | −0.136344 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5436.00 | −0.408014 | ||||||||
\(563\) | 12108.0 | 0.906379 | 0.453189 | − | 0.891414i | \(-0.350286\pi\) | ||||
0.453189 | + | 0.891414i | \(0.350286\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11230.0 | −0.833979 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1632.00 | 0.120558 | ||||||||
\(569\) | −6960.00 | −0.512792 | −0.256396 | − | 0.966572i | \(-0.582535\pi\) | ||||
−0.256396 | + | 0.966572i | \(0.582535\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10687.0 | −0.783252 | −0.391626 | − | 0.920124i | \(-0.628087\pi\) | ||||
−0.391626 | + | 0.920124i | \(0.628087\pi\) | |||||||
\(572\) | 4080.00 | 0.298240 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6348.00 | −0.461603 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8329.00 | 0.600937 | 0.300469 | − | 0.953792i | \(-0.402857\pi\) | ||||
0.300469 | + | 0.953792i | \(0.402857\pi\) | |||||||
\(578\) | −6298.00 | −0.453222 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25254.0 | 1.80329 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9900.00 | 0.703287 | ||||||||
\(584\) | 5528.00 | 0.391696 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2976.00 | −0.209791 | ||||||||
\(587\) | 25302.0 | 1.77909 | 0.889545 | − | 0.456848i | \(-0.151022\pi\) | ||||
0.889545 | + | 0.456848i | \(0.151022\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7645.00 | 0.534816 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3056.00 | −0.212164 | ||||||||
\(593\) | 22248.0 | 1.54067 | 0.770334 | − | 0.637641i | \(-0.220090\pi\) | ||||
0.770334 | + | 0.637641i | \(0.220090\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10008.0 | −0.687825 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13056.0 | −0.892809 | ||||||||
\(599\) | 24252.0 | 1.65427 | 0.827137 | − | 0.562001i | \(-0.189968\pi\) | ||||
0.827137 | + | 0.562001i | \(0.189968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9829.00 | −0.667110 | −0.333555 | − | 0.942731i | \(-0.608248\pi\) | ||||
−0.333555 | + | 0.942731i | \(0.608248\pi\) | |||||||
\(602\) | 2438.00 | 0.165059 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11068.0 | −0.745613 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14155.0 | 0.946514 | 0.473257 | − | 0.880925i | \(-0.343078\pi\) | ||||
0.473257 | + | 0.880925i | \(0.343078\pi\) | |||||||
\(608\) | −4448.00 | −0.296694 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12444.0 | −0.823945 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23051.0 | −1.51879 | −0.759397 | − | 0.650627i | \(-0.774506\pi\) | ||||
−0.759397 | + | 0.650627i | \(0.774506\pi\) | |||||||
\(614\) | −14974.0 | −0.984204 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5520.00 | −0.361051 | ||||||||
\(617\) | 8352.00 | 0.544958 | 0.272479 | − | 0.962162i | \(-0.412157\pi\) | ||||
0.272479 | + | 0.962162i | \(0.412157\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24331.0 | −1.57988 | −0.789940 | − | 0.613184i | \(-0.789888\pi\) | ||||
−0.789940 | + | 0.613184i | \(0.789888\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16236.0 | 1.04663 | ||||||||
\(623\) | 18768.0 | 1.20694 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10004.0 | 0.638722 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10804.0 | 0.686507 | ||||||||
\(629\) | −8022.00 | −0.508518 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2216.00 | 0.139806 | 0.0699030 | − | 0.997554i | \(-0.477731\pi\) | ||||
0.0699030 | + | 0.997554i | \(0.477731\pi\) | |||||||
\(632\) | −5672.00 | −0.356994 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10164.0 | −0.636694 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6324.00 | 0.393353 | ||||||||
\(638\) | 14040.0 | 0.871237 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28500.0 | −1.75613 | −0.878067 | − | 0.478537i | \(-0.841167\pi\) | ||||
−0.878067 | + | 0.478537i | \(0.841167\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25252.0 | 1.54874 | 0.774371 | − | 0.632731i | \(-0.218066\pi\) | ||||
0.774371 | + | 0.632731i | \(0.218066\pi\) | |||||||
\(644\) | 17664.0 | 1.08084 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11676.0 | −0.711124 | ||||||||
\(647\) | 28920.0 | 1.75728 | 0.878642 | − | 0.477481i | \(-0.158450\pi\) | ||||
0.878642 | + | 0.477481i | \(0.158450\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11880.0 | −0.718537 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6992.00 | −0.419981 | ||||||||
\(653\) | −32268.0 | −1.93376 | −0.966879 | − | 0.255234i | \(-0.917848\pi\) | ||||
−0.966879 | + | 0.255234i | \(0.917848\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2208.00 | 0.131415 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 16836.0 | 0.997471 | ||||||||
\(659\) | −10050.0 | −0.594070 | −0.297035 | − | 0.954867i | \(-0.595998\pi\) | ||||
−0.297035 | + | 0.954867i | \(0.595998\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4561.00 | −0.268385 | −0.134192 | − | 0.990955i | \(-0.542844\pi\) | ||||
−0.134192 | + | 0.990955i | \(0.542844\pi\) | |||||||
\(662\) | 15250.0 | 0.895329 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8784.00 | −0.513381 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −44928.0 | −2.60812 | ||||||||
\(668\) | 2136.00 | 0.123719 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 690.000 | 0.0396977 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21359.0 | −1.22337 | −0.611686 | − | 0.791101i | \(-0.709508\pi\) | ||||
−0.611686 | + | 0.791101i | \(0.709508\pi\) | |||||||
\(674\) | 7556.00 | 0.431819 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4164.00 | −0.236914 | ||||||||
\(677\) | −15042.0 | −0.853931 | −0.426965 | − | 0.904268i | \(-0.640417\pi\) | ||||
−0.426965 | + | 0.904268i | \(0.640417\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20815.0 | 1.17645 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3300.00 | −0.185284 | ||||||||
\(683\) | −27462.0 | −1.53851 | −0.769256 | − | 0.638940i | \(-0.779373\pi\) | ||||
−0.769256 | + | 0.638940i | \(0.779373\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7222.00 | 0.401949 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −848.000 | −0.0469908 | ||||||||
\(689\) | 11220.0 | 0.620389 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6212.00 | 0.341991 | 0.170995 | − | 0.985272i | \(-0.445302\pi\) | ||||
0.170995 | + | 0.985272i | \(0.445302\pi\) | |||||||
\(692\) | 768.000 | 0.0421893 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16536.0 | 0.904464 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5796.00 | 0.314977 | ||||||||
\(698\) | 2758.00 | 0.149559 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13224.0 | −0.712502 | −0.356251 | − | 0.934390i | \(-0.615945\pi\) | ||||
−0.356251 | + | 0.934390i | \(0.615945\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26549.0 | 1.42434 | ||||||||
\(704\) | 1920.00 | 0.102788 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6144.00 | −0.327525 | ||||||||
\(707\) | 29394.0 | 1.56361 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34709.0 | 1.83854 | 0.919269 | − | 0.393629i | \(-0.128781\pi\) | ||||
0.919269 | + | 0.393629i | \(0.128781\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6528.00 | −0.343606 | ||||||||
\(713\) | 10560.0 | 0.554664 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4560.00 | 0.238010 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14892.0 | −0.774045 | ||||||||
\(719\) | 32070.0 | 1.66343 | 0.831717 | − | 0.555200i | \(-0.187358\pi\) | ||||
0.831717 | + | 0.555200i | \(0.187358\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13915.0 | 0.718754 | ||||||||
\(722\) | 24924.0 | 1.28473 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1592.00 | 0.0817213 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −125.000 | −0.00637688 | −0.00318844 | − | 0.999995i | \(-0.501015\pi\) | ||||
−0.00318844 | + | 0.999995i | \(0.501015\pi\) | |||||||
\(728\) | −6256.00 | −0.318493 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2226.00 | −0.112629 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32222.0 | −1.62367 | −0.811833 | − | 0.583890i | \(-0.801530\pi\) | ||||
−0.811833 | + | 0.583890i | \(0.801530\pi\) | |||||||
\(734\) | 12992.0 | 0.653329 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6144.00 | −0.307705 | ||||||||
\(737\) | −13560.0 | −0.677733 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19240.0 | −0.957720 | −0.478860 | − | 0.877891i | \(-0.658950\pi\) | ||||
−0.478860 | + | 0.877891i | \(0.658950\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15180.0 | −0.751045 | ||||||||
\(743\) | −30252.0 | −1.49373 | −0.746863 | − | 0.664978i | \(-0.768441\pi\) | ||||
−0.746863 | + | 0.664978i | \(0.768441\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3266.00 | 0.160291 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5040.00 | 0.246365 | ||||||||
\(749\) | 34224.0 | 1.66958 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12517.0 | −0.608192 | −0.304096 | − | 0.952641i | \(-0.598354\pi\) | ||||
−0.304096 | + | 0.952641i | \(0.598354\pi\) | |||||||
\(752\) | −5856.00 | −0.283971 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15912.0 | 0.768542 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2201.00 | −0.105676 | −0.0528380 | − | 0.998603i | \(-0.516827\pi\) | ||||
−0.0528380 | + | 0.998603i | \(0.516827\pi\) | |||||||
\(758\) | 13576.0 | 0.650531 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8742.00 | 0.416422 | 0.208211 | − | 0.978084i | \(-0.433236\pi\) | ||||
0.208211 | + | 0.978084i | \(0.433236\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13639.0 | −0.647136 | ||||||||
\(764\) | 13896.0 | 0.658036 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13164.0 | −0.620933 | ||||||||
\(767\) | −13464.0 | −0.633842 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28618.0 | −1.34199 | −0.670996 | − | 0.741461i | \(-0.734133\pi\) | ||||
−0.670996 | + | 0.741461i | \(0.734133\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10852.0 | 0.505922 | ||||||||
\(773\) | −6594.00 | −0.306817 | −0.153409 | − | 0.988163i | \(-0.549025\pi\) | ||||
−0.153409 | + | 0.988163i | \(0.549025\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7240.00 | −0.334924 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5700.00 | 0.262667 | ||||||||
\(779\) | −19182.0 | −0.882242 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6120.00 | 0.280398 | ||||||||
\(782\) | −16128.0 | −0.737514 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2976.00 | 0.135569 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15881.0 | −0.719309 | −0.359655 | − | 0.933085i | \(-0.617106\pi\) | ||||
−0.359655 | + | 0.933085i | \(0.617106\pi\) | |||||||
\(788\) | −18936.0 | −0.856050 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7452.00 | 0.334972 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 782.000 | 0.0350185 | ||||||||
\(794\) | −14902.0 | −0.666061 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20528.0 | 0.914065 | ||||||||
\(797\) | 26052.0 | 1.15785 | 0.578927 | − | 0.815380i | \(-0.303472\pi\) | ||||
0.578927 | + | 0.815380i | \(0.303472\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15372.0 | −0.680629 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28248.0 | 1.24373 | ||||||||
\(803\) | 20730.0 | 0.911016 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3740.00 | −0.163444 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10224.0 | −0.445147 | ||||||||
\(809\) | 12648.0 | 0.549666 | 0.274833 | − | 0.961492i | \(-0.411377\pi\) | ||||
0.274833 | + | 0.961492i | \(0.411377\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27179.0 | 1.17680 | 0.588399 | − | 0.808570i | \(-0.299758\pi\) | ||||
0.588399 | + | 0.808570i | \(0.299758\pi\) | |||||||
\(812\) | −21528.0 | −0.930400 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11460.0 | −0.493456 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7367.00 | 0.315470 | ||||||||
\(818\) | 12748.0 | 0.544894 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11874.0 | 0.504757 | 0.252378 | − | 0.967629i | \(-0.418787\pi\) | ||||
0.252378 | + | 0.967629i | \(0.418787\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18448.0 | 0.781357 | 0.390679 | − | 0.920527i | \(-0.372240\pi\) | ||||
0.390679 | + | 0.920527i | \(0.372240\pi\) | |||||||
\(824\) | −4840.00 | −0.204623 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18216.0 | 0.767331 | ||||||||
\(827\) | 3234.00 | 0.135982 | 0.0679911 | − | 0.997686i | \(-0.478341\pi\) | ||||
0.0679911 | + | 0.997686i | \(0.478341\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32155.0 | −1.34715 | −0.673576 | − | 0.739118i | \(-0.735243\pi\) | ||||
−0.673576 | + | 0.739118i | \(0.735243\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2176.00 | 0.0906721 | ||||||||
\(833\) | 7812.00 | 0.324934 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −16680.0 | −0.690060 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7896.00 | 0.325493 | ||||||||
\(839\) | −21996.0 | −0.905109 | −0.452554 | − | 0.891737i | \(-0.649487\pi\) | ||||
−0.452554 | + | 0.891737i | \(0.649487\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30367.0 | 1.24511 | ||||||||
\(842\) | 25258.0 | 1.03379 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20960.0 | 0.854826 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9913.00 | 0.402143 | ||||||||
\(848\) | 5280.00 | 0.213816 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36672.0 | 1.47720 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3278.00 | −0.131579 | −0.0657893 | − | 0.997834i | \(-0.520957\pi\) | ||||
−0.0657893 | + | 0.997834i | \(0.520957\pi\) | |||||||
\(854\) | −1058.00 | −0.0423935 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11904.0 | −0.475316 | ||||||||
\(857\) | 21228.0 | 0.846131 | 0.423066 | − | 0.906099i | \(-0.360954\pi\) | ||||
0.423066 | + | 0.906099i | \(0.360954\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5767.00 | −0.229066 | −0.114533 | − | 0.993419i | \(-0.536537\pi\) | ||||
−0.114533 | + | 0.993419i | \(0.536537\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9684.00 | 0.382643 | ||||||||
\(863\) | 5322.00 | 0.209922 | 0.104961 | − | 0.994476i | \(-0.466528\pi\) | ||||
0.104961 | + | 0.994476i | \(0.466528\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7702.00 | −0.302222 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5060.00 | 0.197866 | ||||||||
\(869\) | −21270.0 | −0.830305 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15368.0 | −0.597847 | ||||||||
\(872\) | 4744.00 | 0.184234 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 53376.0 | 2.06576 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42097.0 | 1.62088 | 0.810442 | − | 0.585819i | \(-0.199227\pi\) | ||||
0.810442 | + | 0.585819i | \(0.199227\pi\) | |||||||
\(878\) | −14870.0 | −0.571570 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17658.0 | −0.675270 | −0.337635 | − | 0.941277i | \(-0.609627\pi\) | ||||
−0.337635 | + | 0.941277i | \(0.609627\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22297.0 | 0.849778 | 0.424889 | − | 0.905246i | \(-0.360313\pi\) | ||||
0.424889 | + | 0.905246i | \(0.360313\pi\) | |||||||
\(884\) | 5712.00 | 0.217325 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11520.0 | 0.436819 | ||||||||
\(887\) | 10542.0 | 0.399059 | 0.199530 | − | 0.979892i | \(-0.436059\pi\) | ||||
0.199530 | + | 0.979892i | \(0.436059\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 44344.0 | 1.67295 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18076.0 | 0.678508 | ||||||||
\(893\) | 50874.0 | 1.90642 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2944.00 | −0.109768 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4380.00 | −0.162764 | ||||||||
\(899\) | −12870.0 | −0.477462 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13860.0 | 0.512479 | ||||||||
\(902\) | 8280.00 | 0.305647 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2592.00 | −0.0953635 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47639.0 | −1.74402 | −0.872010 | − | 0.489487i | \(-0.837184\pi\) | ||||
−0.872010 | + | 0.489487i | \(0.837184\pi\) | |||||||
\(908\) | −20256.0 | −0.740329 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10326.0 | −0.375539 | −0.187769 | − | 0.982213i | \(-0.560126\pi\) | ||||
−0.187769 | + | 0.982213i | \(0.560126\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32940.0 | −1.19404 | ||||||||
\(914\) | −14404.0 | −0.521271 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10292.0 | 0.371242 | ||||||||
\(917\) | −63066.0 | −2.27113 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5147.00 | 0.184748 | 0.0923742 | − | 0.995724i | \(-0.470554\pi\) | ||||
0.0923742 | + | 0.995724i | \(0.470554\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26952.0 | −0.962708 | ||||||||
\(923\) | 6936.00 | 0.247347 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 21686.0 | 0.769596 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7488.00 | 0.264877 | ||||||||
\(929\) | −47064.0 | −1.66213 | −0.831066 | − | 0.556175i | \(-0.812269\pi\) | ||||
−0.831066 | + | 0.556175i | \(0.812269\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25854.0 | −0.910130 | ||||||||
\(932\) | −16392.0 | −0.576114 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12216.0 | −0.427965 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15385.0 | 0.536399 | 0.268200 | − | 0.963363i | \(-0.413571\pi\) | ||||
0.268200 | + | 0.963363i | \(0.413571\pi\) | |||||||
\(938\) | 20792.0 | 0.723756 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34914.0 | −1.20953 | −0.604763 | − | 0.796406i | \(-0.706732\pi\) | ||||
−0.604763 | + | 0.796406i | \(0.706732\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26496.0 | −0.914982 | ||||||||
\(944\) | −6336.00 | −0.218453 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3180.00 | −0.109293 | ||||||||
\(947\) | −37434.0 | −1.28452 | −0.642261 | − | 0.766486i | \(-0.722003\pi\) | ||||
−0.642261 | + | 0.766486i | \(0.722003\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23494.0 | 0.803633 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7728.00 | −0.263094 | ||||||||
\(953\) | −8778.00 | −0.298371 | −0.149185 | − | 0.988809i | \(-0.547665\pi\) | ||||
−0.149185 | + | 0.988809i | \(0.547665\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1224.00 | −0.0414090 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19704.0 | 0.664517 | ||||||||
\(959\) | 30498.0 | 1.02694 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26766.0 | −0.898459 | ||||||||
\(962\) | −12988.0 | −0.435291 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25928.0 | 0.866270 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54061.0 | 1.79781 | 0.898906 | − | 0.438141i | \(-0.144363\pi\) | ||||
0.898906 | + | 0.438141i | \(0.144363\pi\) | |||||||
\(968\) | −3448.00 | −0.114486 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3084.00 | −0.101926 | −0.0509631 | − | 0.998701i | \(-0.516229\pi\) | ||||
−0.0509631 | + | 0.998701i | \(0.516229\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20539.0 | −0.676722 | ||||||||
\(974\) | −15592.0 | −0.512936 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 368.000 | 0.0120691 | ||||||||
\(977\) | −12048.0 | −0.394524 | −0.197262 | − | 0.980351i | \(-0.563205\pi\) | ||||
−0.197262 | + | 0.980351i | \(0.563205\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24480.0 | −0.799167 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4908.00 | 0.159491 | ||||||||
\(983\) | −33618.0 | −1.09079 | −0.545396 | − | 0.838179i | \(-0.683621\pi\) | ||||
−0.545396 | + | 0.838179i | \(0.683621\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 19656.0 | 0.634863 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18904.0 | −0.608721 | ||||||||
\(989\) | 10176.0 | 0.327177 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25043.0 | 0.802742 | 0.401371 | − | 0.915916i | \(-0.368534\pi\) | ||||
0.401371 | + | 0.915916i | \(0.368534\pi\) | |||||||
\(992\) | −1760.00 | −0.0563307 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9384.00 | −0.299439 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17710.0 | 0.562569 | 0.281285 | − | 0.959624i | \(-0.409240\pi\) | ||||
0.281285 | + | 0.959624i | \(0.409240\pi\) | |||||||
\(998\) | −5906.00 | −0.187326 | ||||||||
\(999\) | 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 | 1350.4.a.p.1.1 | yes | 1 | |
3.2 | odd | 2 | 1350.4.a.b.1.1 | ✓ | 1 | ||
5.2 | odd | 4 | 1350.4.c.p.649.2 | 2 | |||
5.3 | odd | 4 | 1350.4.c.p.649.1 | 2 | |||
5.4 | even | 2 | 1350.4.a.m.1.1 | yes | 1 | ||
15.2 | even | 4 | 1350.4.c.e.649.1 | 2 | |||
15.8 | even | 4 | 1350.4.c.e.649.2 | 2 | |||
15.14 | odd | 2 | 1350.4.a.ba.1.1 | yes | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1350.4.a.b.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
1350.4.a.m.1.1 | yes | 1 | 5.4 | even | 2 | ||
1350.4.a.p.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
1350.4.a.ba.1.1 | yes | 1 | 15.14 | odd | 2 | ||
1350.4.c.e.649.1 | 2 | 15.2 | even | 4 | |||
1350.4.c.e.649.2 | 2 | 15.8 | even | 4 | |||
1350.4.c.p.649.1 | 2 | 5.3 | odd | 4 | |||
1350.4.c.p.649.2 | 2 | 5.2 | odd | 4 |