Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1225,4,Mod(1,1225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1225, 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("1225.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1225.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: | \(72.2773397570\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.1163891200.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 23x^{4} + 12x^{3} + 154x^{2} + 152x + 28 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 7 \) |
Twist minimal: | no (minimal twist has level 245) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.05323\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.46745 | −1.57948 | −0.789740 | − | 0.613441i | \(-0.789785\pi\) | ||||
−0.789740 | + | 0.613441i | \(0.789785\pi\) | |||||||
\(3\) | 9.80920 | 1.88778 | 0.943890 | − | 0.330259i | \(-0.107136\pi\) | ||||
0.943890 | + | 0.330259i | \(0.107136\pi\) | |||||||
\(4\) | 11.9581 | 1.49476 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −43.8221 | −2.98171 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −17.6824 | −0.781461 | ||||||||
\(9\) | 69.2204 | 2.56372 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −56.5404 | −1.54978 | −0.774890 | − | 0.632096i | \(-0.782195\pi\) | ||||
−0.774890 | + | 0.632096i | \(0.782195\pi\) | |||||||
\(12\) | 117.299 | 2.82178 | ||||||||
\(13\) | 40.9643 | 0.873958 | 0.436979 | − | 0.899472i | \(-0.356048\pi\) | ||||
0.436979 | + | 0.899472i | \(0.356048\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16.6692 | −0.260456 | ||||||||
\(17\) | 2.18896 | 0.0312295 | 0.0156148 | − | 0.999878i | \(-0.495029\pi\) | ||||
0.0156148 | + | 0.999878i | \(0.495029\pi\) | |||||||
\(18\) | −309.238 | −4.04934 | ||||||||
\(19\) | −16.4735 | −0.198910 | −0.0994549 | − | 0.995042i | \(-0.531710\pi\) | ||||
−0.0994549 | + | 0.995042i | \(0.531710\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 252.591 | 2.44785 | ||||||||
\(23\) | 155.272 | 1.40767 | 0.703837 | − | 0.710361i | \(-0.251468\pi\) | ||||
0.703837 | + | 0.710361i | \(0.251468\pi\) | |||||||
\(24\) | −173.451 | −1.47523 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −183.006 | −1.38040 | ||||||||
\(27\) | 414.148 | 2.95195 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.26048 | −0.0400876 | −0.0200438 | − | 0.999799i | \(-0.506381\pi\) | ||||
−0.0200438 | + | 0.999799i | \(0.506381\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −168.680 | −0.977286 | −0.488643 | − | 0.872484i | \(-0.662508\pi\) | ||||
−0.488643 | + | 0.872484i | \(0.662508\pi\) | |||||||
\(32\) | 215.928 | 1.19285 | ||||||||
\(33\) | −554.616 | −2.92564 | ||||||||
\(34\) | −9.77908 | −0.0493264 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 827.742 | 3.83214 | ||||||||
\(37\) | 37.1738 | 0.165171 | 0.0825856 | − | 0.996584i | \(-0.473682\pi\) | ||||
0.0825856 | + | 0.996584i | \(0.473682\pi\) | |||||||
\(38\) | 73.5946 | 0.314174 | ||||||||
\(39\) | 401.827 | 1.64984 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 266.804 | 1.01629 | 0.508143 | − | 0.861273i | \(-0.330332\pi\) | ||||
0.508143 | + | 0.861273i | \(0.330332\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 14.6549 | 0.0519735 | 0.0259867 | − | 0.999662i | \(-0.491727\pi\) | ||||
0.0259867 | + | 0.999662i | \(0.491727\pi\) | |||||||
\(44\) | −676.114 | −2.31655 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −693.670 | −2.22339 | ||||||||
\(47\) | −169.840 | −0.527102 | −0.263551 | − | 0.964646i | \(-0.584894\pi\) | ||||
−0.263551 | + | 0.964646i | \(0.584894\pi\) | |||||||
\(48\) | −163.511 | −0.491684 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 21.4720 | 0.0589545 | ||||||||
\(52\) | 489.854 | 1.30636 | ||||||||
\(53\) | 151.391 | 0.392361 | 0.196180 | − | 0.980568i | \(-0.437146\pi\) | ||||
0.196180 | + | 0.980568i | \(0.437146\pi\) | |||||||
\(54\) | −1850.18 | −4.66255 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −161.592 | −0.375498 | ||||||||
\(58\) | 27.9683 | 0.0633176 | ||||||||
\(59\) | 234.076 | 0.516510 | 0.258255 | − | 0.966077i | \(-0.416853\pi\) | ||||
0.258255 | + | 0.966077i | \(0.416853\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 242.411 | 0.508813 | 0.254407 | − | 0.967097i | \(-0.418120\pi\) | ||||
0.254407 | + | 0.967097i | \(0.418120\pi\) | |||||||
\(62\) | 753.569 | 1.54360 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −831.294 | −1.62362 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2477.72 | 4.62100 | ||||||||
\(67\) | −820.771 | −1.49661 | −0.748307 | − | 0.663353i | \(-0.769133\pi\) | ||||
−0.748307 | + | 0.663353i | \(0.769133\pi\) | |||||||
\(68\) | 26.1758 | 0.0466806 | ||||||||
\(69\) | 1523.10 | 2.65738 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 961.611 | 1.60736 | 0.803678 | − | 0.595065i | \(-0.202874\pi\) | ||||
0.803678 | + | 0.595065i | \(0.202874\pi\) | |||||||
\(72\) | −1223.98 | −2.00344 | ||||||||
\(73\) | 934.026 | 1.49753 | 0.748763 | − | 0.662837i | \(-0.230648\pi\) | ||||
0.748763 | + | 0.662837i | \(0.230648\pi\) | |||||||
\(74\) | −166.072 | −0.260885 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −196.992 | −0.297322 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1795.14 | −2.60589 | ||||||||
\(79\) | 300.236 | 0.427584 | 0.213792 | − | 0.976879i | \(-0.431419\pi\) | ||||
0.213792 | + | 0.976879i | \(0.431419\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2193.51 | 3.00893 | ||||||||
\(82\) | −1191.93 | −1.60520 | ||||||||
\(83\) | 1087.60 | 1.43830 | 0.719151 | − | 0.694854i | \(-0.244531\pi\) | ||||
0.719151 | + | 0.694854i | \(0.244531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −65.4702 | −0.0820910 | ||||||||
\(87\) | −61.4103 | −0.0756767 | ||||||||
\(88\) | 999.773 | 1.21109 | ||||||||
\(89\) | 1124.05 | 1.33875 | 0.669375 | − | 0.742925i | \(-0.266562\pi\) | ||||
0.669375 | + | 0.742925i | \(0.266562\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1856.76 | 2.10413 | ||||||||
\(93\) | −1654.62 | −1.84490 | ||||||||
\(94\) | 758.753 | 0.832547 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2118.08 | 2.25183 | ||||||||
\(97\) | 752.168 | 0.787330 | 0.393665 | − | 0.919254i | \(-0.371207\pi\) | ||||
0.393665 | + | 0.919254i | \(0.371207\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3913.75 | −3.97320 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −559.226 | −0.550941 | −0.275471 | − | 0.961310i | \(-0.588834\pi\) | ||||
−0.275471 | + | 0.961310i | \(0.588834\pi\) | |||||||
\(102\) | −95.9249 | −0.0931175 | ||||||||
\(103\) | −205.331 | −0.196426 | −0.0982128 | − | 0.995165i | \(-0.531313\pi\) | ||||
−0.0982128 | + | 0.995165i | \(0.531313\pi\) | |||||||
\(104\) | −724.349 | −0.682964 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −676.330 | −0.619726 | ||||||||
\(107\) | 1470.17 | 1.32829 | 0.664145 | − | 0.747604i | \(-0.268796\pi\) | ||||
0.664145 | + | 0.747604i | \(0.268796\pi\) | |||||||
\(108\) | 4952.41 | 4.41246 | ||||||||
\(109\) | −774.193 | −0.680314 | −0.340157 | − | 0.940369i | \(-0.610480\pi\) | ||||
−0.340157 | + | 0.940369i | \(0.610480\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 364.645 | 0.311807 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 406.121 | 0.338094 | 0.169047 | − | 0.985608i | \(-0.445931\pi\) | ||||
0.169047 | + | 0.985608i | \(0.445931\pi\) | |||||||
\(114\) | 721.904 | 0.593092 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −74.8632 | −0.0599213 | ||||||||
\(117\) | 2835.56 | 2.24058 | ||||||||
\(118\) | −1045.72 | −0.815817 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1865.82 | 1.40182 | ||||||||
\(122\) | −1082.96 | −0.803660 | ||||||||
\(123\) | 2617.13 | 1.91853 | ||||||||
\(124\) | −2017.09 | −1.46081 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 451.639 | 0.315563 | 0.157781 | − | 0.987474i | \(-0.449566\pi\) | ||||
0.157781 | + | 0.987474i | \(0.449566\pi\) | |||||||
\(128\) | 1986.33 | 1.37163 | ||||||||
\(129\) | 143.753 | 0.0981145 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −361.932 | −0.241390 | −0.120695 | − | 0.992690i | \(-0.538512\pi\) | ||||
−0.120695 | + | 0.992690i | \(0.538512\pi\) | |||||||
\(132\) | −6632.14 | −4.37313 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3666.75 | 2.36387 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −38.7062 | −0.0244047 | ||||||||
\(137\) | −2512.72 | −1.56698 | −0.783490 | − | 0.621404i | \(-0.786563\pi\) | ||||
−0.783490 | + | 0.621404i | \(0.786563\pi\) | |||||||
\(138\) | −6804.35 | −4.19728 | ||||||||
\(139\) | −1165.71 | −0.711324 | −0.355662 | − | 0.934615i | \(-0.615745\pi\) | ||||
−0.355662 | + | 0.934615i | \(0.615745\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1666.00 | −0.995052 | ||||||||
\(142\) | −4295.94 | −2.53879 | ||||||||
\(143\) | −2316.14 | −1.35444 | ||||||||
\(144\) | −1153.85 | −0.667736 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4172.71 | −2.36531 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 444.526 | 0.246891 | ||||||||
\(149\) | −2637.49 | −1.45014 | −0.725072 | − | 0.688673i | \(-0.758194\pi\) | ||||
−0.725072 | + | 0.688673i | \(0.758194\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2582.32 | −1.39170 | −0.695849 | − | 0.718188i | \(-0.744972\pi\) | ||||
−0.695849 | + | 0.718188i | \(0.744972\pi\) | |||||||
\(152\) | 291.292 | 0.155440 | ||||||||
\(153\) | 151.521 | 0.0800637 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4805.07 | 2.46611 | ||||||||
\(157\) | 225.788 | 0.114776 | 0.0573880 | − | 0.998352i | \(-0.481723\pi\) | ||||
0.0573880 | + | 0.998352i | \(0.481723\pi\) | |||||||
\(158\) | −1341.29 | −0.675361 | ||||||||
\(159\) | 1485.02 | 0.740691 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −9799.38 | −4.75254 | ||||||||
\(163\) | −1489.01 | −0.715509 | −0.357755 | − | 0.933816i | \(-0.616458\pi\) | ||||
−0.357755 | + | 0.933816i | \(0.616458\pi\) | |||||||
\(164\) | 3190.46 | 1.51910 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4858.77 | −2.27177 | ||||||||
\(167\) | 2858.73 | 1.32464 | 0.662322 | − | 0.749220i | \(-0.269571\pi\) | ||||
0.662322 | + | 0.749220i | \(0.269571\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −518.925 | −0.236197 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1140.30 | −0.509948 | ||||||||
\(172\) | 175.245 | 0.0776877 | ||||||||
\(173\) | −32.0040 | −0.0140648 | −0.00703242 | − | 0.999975i | \(-0.502239\pi\) | ||||
−0.00703242 | + | 0.999975i | \(0.502239\pi\) | |||||||
\(174\) | 274.347 | 0.119530 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 942.483 | 0.403650 | ||||||||
\(177\) | 2296.10 | 0.975057 | ||||||||
\(178\) | −5021.62 | −2.11453 | ||||||||
\(179\) | 738.444 | 0.308346 | 0.154173 | − | 0.988044i | \(-0.450729\pi\) | ||||
0.154173 | + | 0.988044i | \(0.450729\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1991.91 | 0.817997 | 0.408998 | − | 0.912535i | \(-0.365878\pi\) | ||||
0.408998 | + | 0.912535i | \(0.365878\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2377.86 | 0.960528 | ||||||||
\(184\) | −2745.59 | −1.10004 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7391.91 | 2.91399 | ||||||||
\(187\) | −123.765 | −0.0483989 | ||||||||
\(188\) | −2030.96 | −0.787890 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2153.68 | 0.815890 | 0.407945 | − | 0.913006i | \(-0.366245\pi\) | ||||
0.407945 | + | 0.913006i | \(0.366245\pi\) | |||||||
\(192\) | −8154.33 | −3.06504 | ||||||||
\(193\) | −1003.94 | −0.374431 | −0.187215 | − | 0.982319i | \(-0.559946\pi\) | ||||
−0.187215 | + | 0.982319i | \(0.559946\pi\) | |||||||
\(194\) | −3360.27 | −1.24357 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1716.80 | −0.620899 | −0.310449 | − | 0.950590i | \(-0.600479\pi\) | ||||
−0.310449 | + | 0.950590i | \(0.600479\pi\) | |||||||
\(198\) | 17484.5 | 6.27559 | ||||||||
\(199\) | 5337.86 | 1.90146 | 0.950730 | − | 0.310019i | \(-0.100335\pi\) | ||||
0.950730 | + | 0.310019i | \(0.100335\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8051.10 | −2.82528 | ||||||||
\(202\) | 2498.31 | 0.870201 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 256.763 | 0.0881227 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 917.304 | 0.310250 | ||||||||
\(207\) | 10748.0 | 3.60888 | ||||||||
\(208\) | −682.842 | −0.227628 | ||||||||
\(209\) | 931.420 | 0.308266 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 860.589 | 0.280784 | 0.140392 | − | 0.990096i | \(-0.455164\pi\) | ||||
0.140392 | + | 0.990096i | \(0.455164\pi\) | |||||||
\(212\) | 1810.34 | 0.586485 | ||||||||
\(213\) | 9432.63 | 3.03433 | ||||||||
\(214\) | −6567.92 | −2.09801 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7323.14 | −2.30684 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3458.66 | 1.07454 | ||||||||
\(219\) | 9162.04 | 2.82700 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 89.6695 | 0.0272933 | ||||||||
\(222\) | −1629.03 | −0.492493 | ||||||||
\(223\) | −3661.12 | −1.09940 | −0.549701 | − | 0.835361i | \(-0.685259\pi\) | ||||
−0.549701 | + | 0.835361i | \(0.685259\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1814.32 | −0.534013 | ||||||||
\(227\) | 6032.38 | 1.76380 | 0.881902 | − | 0.471434i | \(-0.156263\pi\) | ||||
0.881902 | + | 0.471434i | \(0.156263\pi\) | |||||||
\(228\) | −1932.33 | −0.561279 | ||||||||
\(229\) | 3849.64 | 1.11088 | 0.555439 | − | 0.831557i | \(-0.312550\pi\) | ||||
0.555439 | + | 0.831557i | \(0.312550\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 110.701 | 0.0313269 | ||||||||
\(233\) | 1705.20 | 0.479448 | 0.239724 | − | 0.970841i | \(-0.422943\pi\) | ||||
0.239724 | + | 0.970841i | \(0.422943\pi\) | |||||||
\(234\) | −12667.7 | −3.53895 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2799.09 | 0.772057 | ||||||||
\(237\) | 2945.07 | 0.807185 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6804.54 | 1.84163 | 0.920814 | − | 0.390001i | \(-0.127525\pi\) | ||||
0.920814 | + | 0.390001i | \(0.127525\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4642.98 | −1.24100 | −0.620499 | − | 0.784207i | \(-0.713070\pi\) | ||||
−0.620499 | + | 0.784207i | \(0.713070\pi\) | |||||||
\(242\) | −8335.44 | −2.21414 | ||||||||
\(243\) | 10334.6 | 2.72824 | ||||||||
\(244\) | 2898.77 | 0.760553 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11691.9 | −3.03027 | ||||||||
\(247\) | −674.827 | −0.173839 | ||||||||
\(248\) | 2982.68 | 0.763711 | ||||||||
\(249\) | 10668.4 | 2.71520 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5912.64 | −1.48686 | −0.743431 | − | 0.668813i | \(-0.766803\pi\) | ||||
−0.743431 | + | 0.668813i | \(0.766803\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8779.16 | −2.18159 | ||||||||
\(254\) | −2017.67 | −0.498425 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2223.49 | −0.542844 | ||||||||
\(257\) | −1697.83 | −0.412093 | −0.206047 | − | 0.978542i | \(-0.566060\pi\) | ||||
−0.206047 | + | 0.978542i | \(0.566060\pi\) | |||||||
\(258\) | −642.210 | −0.154970 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −433.352 | −0.102773 | ||||||||
\(262\) | 1616.91 | 0.381271 | ||||||||
\(263\) | 5661.78 | 1.32745 | 0.663727 | − | 0.747975i | \(-0.268974\pi\) | ||||
0.663727 | + | 0.747975i | \(0.268974\pi\) | |||||||
\(264\) | 9806.97 | 2.28628 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11026.0 | 2.52727 | ||||||||
\(268\) | −9814.83 | −2.23708 | ||||||||
\(269\) | −5330.01 | −1.20809 | −0.604046 | − | 0.796950i | \(-0.706446\pi\) | ||||
−0.604046 | + | 0.796950i | \(0.706446\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2034.94 | 0.456139 | 0.228069 | − | 0.973645i | \(-0.426759\pi\) | ||||
0.228069 | + | 0.973645i | \(0.426759\pi\) | |||||||
\(272\) | −36.4883 | −0.00813392 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11225.5 | 2.47502 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 18213.3 | 3.97214 | ||||||||
\(277\) | 867.657 | 0.188204 | 0.0941019 | − | 0.995563i | \(-0.470002\pi\) | ||||
0.0941019 | + | 0.995563i | \(0.470002\pi\) | |||||||
\(278\) | 5207.73 | 1.12352 | ||||||||
\(279\) | −11676.1 | −2.50548 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2049.70 | 0.435142 | 0.217571 | − | 0.976045i | \(-0.430187\pi\) | ||||
0.217571 | + | 0.976045i | \(0.430187\pi\) | |||||||
\(282\) | 7442.76 | 1.57167 | ||||||||
\(283\) | 6625.11 | 1.39160 | 0.695799 | − | 0.718237i | \(-0.255051\pi\) | ||||
0.695799 | + | 0.718237i | \(0.255051\pi\) | |||||||
\(284\) | 11499.0 | 2.40261 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10347.2 | 2.13932 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 14946.6 | 3.05812 | ||||||||
\(289\) | −4908.21 | −0.999025 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7378.16 | 1.48631 | ||||||||
\(292\) | 11169.1 | 2.23844 | ||||||||
\(293\) | −5670.84 | −1.13070 | −0.565348 | − | 0.824852i | \(-0.691258\pi\) | ||||
−0.565348 | + | 0.824852i | \(0.691258\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −657.323 | −0.129075 | ||||||||
\(297\) | −23416.1 | −4.57488 | ||||||||
\(298\) | 11782.8 | 2.29048 | ||||||||
\(299\) | 6360.62 | 1.23025 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11536.4 | 2.19816 | ||||||||
\(303\) | −5485.56 | −1.04006 | ||||||||
\(304\) | 274.600 | 0.0518073 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −676.911 | −0.126459 | ||||||||
\(307\) | −272.638 | −0.0506849 | −0.0253424 | − | 0.999679i | \(-0.508068\pi\) | ||||
−0.0253424 | + | 0.999679i | \(0.508068\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2014.13 | −0.370808 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1220.83 | 0.222595 | 0.111298 | − | 0.993787i | \(-0.464499\pi\) | ||||
0.111298 | + | 0.993787i | \(0.464499\pi\) | |||||||
\(312\) | −7105.28 | −1.28929 | ||||||||
\(313\) | 775.195 | 0.139989 | 0.0699946 | − | 0.997547i | \(-0.477702\pi\) | ||||
0.0699946 | + | 0.997547i | \(0.477702\pi\) | |||||||
\(314\) | −1008.69 | −0.181286 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3590.24 | 0.639135 | ||||||||
\(317\) | −7393.24 | −1.30992 | −0.654962 | − | 0.755662i | \(-0.727315\pi\) | ||||
−0.654962 | + | 0.755662i | \(0.727315\pi\) | |||||||
\(318\) | −6634.25 | −1.16991 | ||||||||
\(319\) | 353.970 | 0.0621270 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14421.2 | 2.50752 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −36.0600 | −0.00621186 | ||||||||
\(324\) | 26230.1 | 4.49762 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6652.06 | 1.13013 | ||||||||
\(327\) | −7594.21 | −1.28428 | ||||||||
\(328\) | −4717.74 | −0.794188 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3736.95 | −0.620548 | −0.310274 | − | 0.950647i | \(-0.600421\pi\) | ||||
−0.310274 | + | 0.950647i | \(0.600421\pi\) | |||||||
\(332\) | 13005.5 | 2.14991 | ||||||||
\(333\) | 2573.18 | 0.423452 | ||||||||
\(334\) | −12771.2 | −2.09225 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8230.24 | 1.33036 | 0.665178 | − | 0.746685i | \(-0.268356\pi\) | ||||
0.665178 | + | 0.746685i | \(0.268356\pi\) | |||||||
\(338\) | 2318.27 | 0.373068 | ||||||||
\(339\) | 3983.72 | 0.638247 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9537.25 | 1.51458 | ||||||||
\(342\) | 5094.24 | 0.805453 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −259.135 | −0.0406152 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 142.976 | 0.0222151 | ||||||||
\(347\) | 12730.5 | 1.96948 | 0.984739 | − | 0.174036i | \(-0.0556809\pi\) | ||||
0.984739 | + | 0.174036i | \(0.0556809\pi\) | |||||||
\(348\) | −734.348 | −0.113118 | ||||||||
\(349\) | −4487.30 | −0.688252 | −0.344126 | − | 0.938924i | \(-0.611825\pi\) | ||||
−0.344126 | + | 0.938924i | \(0.611825\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16965.3 | 2.57989 | ||||||||
\(352\) | −12208.7 | −1.84865 | ||||||||
\(353\) | −12263.5 | −1.84906 | −0.924532 | − | 0.381106i | \(-0.875543\pi\) | ||||
−0.924532 | + | 0.381106i | \(0.875543\pi\) | |||||||
\(354\) | −10257.7 | −1.54008 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13441.4 | 2.00111 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3298.96 | −0.487026 | ||||||||
\(359\) | −11073.2 | −1.62791 | −0.813957 | − | 0.580925i | \(-0.802691\pi\) | ||||
−0.813957 | + | 0.580925i | \(0.802691\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6587.62 | −0.960435 | ||||||||
\(362\) | −8898.74 | −1.29201 | ||||||||
\(363\) | 18302.2 | 2.64632 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10623.0 | −1.51713 | ||||||||
\(367\) | 5864.72 | 0.834157 | 0.417079 | − | 0.908870i | \(-0.363054\pi\) | ||||
0.417079 | + | 0.908870i | \(0.363054\pi\) | |||||||
\(368\) | −2588.26 | −0.366637 | ||||||||
\(369\) | 18468.3 | 2.60547 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −19786.0 | −2.75768 | ||||||||
\(373\) | 9368.17 | 1.30044 | 0.650222 | − | 0.759744i | \(-0.274676\pi\) | ||||
0.650222 | + | 0.759744i | \(0.274676\pi\) | |||||||
\(374\) | 552.913 | 0.0764451 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3003.19 | 0.411909 | ||||||||
\(377\) | −256.456 | −0.0350349 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5537.81 | 0.750549 | 0.375275 | − | 0.926914i | \(-0.377548\pi\) | ||||
0.375275 | + | 0.926914i | \(0.377548\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4430.21 | 0.595713 | ||||||||
\(382\) | −9621.46 | −1.28868 | ||||||||
\(383\) | 5243.17 | 0.699513 | 0.349756 | − | 0.936841i | \(-0.386264\pi\) | ||||
0.349756 | + | 0.936841i | \(0.386264\pi\) | |||||||
\(384\) | 19484.3 | 2.58934 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4485.05 | 0.591406 | ||||||||
\(387\) | 1014.42 | 0.133245 | ||||||||
\(388\) | 8994.47 | 1.17687 | ||||||||
\(389\) | −10890.5 | −1.41947 | −0.709733 | − | 0.704471i | \(-0.751184\pi\) | ||||
−0.709733 | + | 0.704471i | \(0.751184\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 339.886 | 0.0439610 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3550.26 | −0.455692 | ||||||||
\(394\) | 7669.71 | 0.980697 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −46800.8 | −5.93897 | ||||||||
\(397\) | 13307.0 | 1.68227 | 0.841135 | − | 0.540826i | \(-0.181888\pi\) | ||||
0.841135 | + | 0.540826i | \(0.181888\pi\) | |||||||
\(398\) | −23846.6 | −3.00332 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7227.02 | 0.900001 | 0.450000 | − | 0.893028i | \(-0.351424\pi\) | ||||
0.450000 | + | 0.893028i | \(0.351424\pi\) | |||||||
\(402\) | 35967.9 | 4.46247 | ||||||||
\(403\) | −6909.87 | −0.854107 | ||||||||
\(404\) | −6687.26 | −0.823524 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2101.82 | −0.255979 | ||||||||
\(408\) | −379.677 | −0.0460706 | ||||||||
\(409\) | −5852.64 | −0.707565 | −0.353783 | − | 0.935328i | \(-0.615105\pi\) | ||||
−0.353783 | + | 0.935328i | \(0.615105\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24647.8 | −2.95812 | ||||||||
\(412\) | −2455.36 | −0.293609 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −48016.1 | −5.70015 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 8845.35 | 1.04250 | ||||||||
\(417\) | −11434.7 | −1.34282 | ||||||||
\(418\) | −4161.07 | −0.486901 | ||||||||
\(419\) | 8344.19 | 0.972889 | 0.486444 | − | 0.873712i | \(-0.338294\pi\) | ||||
0.486444 | + | 0.873712i | \(0.338294\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10955.3 | −1.26824 | −0.634122 | − | 0.773233i | \(-0.718638\pi\) | ||||
−0.634122 | + | 0.773233i | \(0.718638\pi\) | |||||||
\(422\) | −3844.63 | −0.443493 | ||||||||
\(423\) | −11756.4 | −1.35134 | ||||||||
\(424\) | −2676.96 | −0.306615 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −42139.8 | −4.79267 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 17580.4 | 1.98547 | ||||||||
\(429\) | −22719.5 | −2.55689 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9417.43 | 1.05249 | 0.526243 | − | 0.850334i | \(-0.323600\pi\) | ||||
0.526243 | + | 0.850334i | \(0.323600\pi\) | |||||||
\(432\) | −6903.51 | −0.768855 | ||||||||
\(433\) | 8783.79 | 0.974878 | 0.487439 | − | 0.873157i | \(-0.337931\pi\) | ||||
0.487439 | + | 0.873157i | \(0.337931\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9257.85 | −1.01690 | ||||||||
\(437\) | −2557.88 | −0.280000 | ||||||||
\(438\) | −40930.9 | −4.46519 | ||||||||
\(439\) | −10559.6 | −1.14802 | −0.574011 | − | 0.818847i | \(-0.694614\pi\) | ||||
−0.574011 | + | 0.818847i | \(0.694614\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −400.593 | −0.0431092 | ||||||||
\(443\) | 4878.14 | 0.523177 | 0.261589 | − | 0.965179i | \(-0.415754\pi\) | ||||
0.261589 | + | 0.965179i | \(0.415754\pi\) | |||||||
\(444\) | 4360.45 | 0.466076 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16355.9 | 1.73649 | ||||||||
\(447\) | −25871.7 | −2.73756 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 43.7917 | 0.00460280 | 0.00230140 | − | 0.999997i | \(-0.499267\pi\) | ||||
0.00230140 | + | 0.999997i | \(0.499267\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15085.2 | −1.57502 | ||||||||
\(452\) | 4856.42 | 0.505369 | ||||||||
\(453\) | −25330.5 | −2.62722 | ||||||||
\(454\) | −26949.3 | −2.78589 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2857.34 | 0.293437 | ||||||||
\(457\) | −2869.76 | −0.293745 | −0.146873 | − | 0.989155i | \(-0.546921\pi\) | ||||
−0.146873 | + | 0.989155i | \(0.546921\pi\) | |||||||
\(458\) | −17198.0 | −1.75461 | ||||||||
\(459\) | 906.555 | 0.0921882 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17910.1 | 1.80945 | 0.904723 | − | 0.426001i | \(-0.140078\pi\) | ||||
0.904723 | + | 0.426001i | \(0.140078\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7630.72 | 0.765938 | 0.382969 | − | 0.923761i | \(-0.374902\pi\) | ||||
0.382969 | + | 0.923761i | \(0.374902\pi\) | |||||||
\(464\) | 104.357 | 0.0104411 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7617.89 | −0.757279 | ||||||||
\(467\) | −6246.30 | −0.618939 | −0.309469 | − | 0.950909i | \(-0.600151\pi\) | ||||
−0.309469 | + | 0.950909i | \(0.600151\pi\) | |||||||
\(468\) | 33907.9 | 3.34913 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2214.80 | 0.216672 | ||||||||
\(472\) | −4139.03 | −0.403632 | ||||||||
\(473\) | −828.597 | −0.0805474 | ||||||||
\(474\) | −13156.9 | −1.27493 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10479.3 | 1.00590 | ||||||||
\(478\) | −30398.9 | −2.90882 | ||||||||
\(479\) | 4119.58 | 0.392961 | 0.196480 | − | 0.980508i | \(-0.437049\pi\) | ||||
0.196480 | + | 0.980508i | \(0.437049\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1522.80 | 0.144353 | ||||||||
\(482\) | 20742.2 | 1.96013 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22311.6 | 2.09538 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −46169.1 | −4.30920 | ||||||||
\(487\) | 1421.46 | 0.132264 | 0.0661320 | − | 0.997811i | \(-0.478934\pi\) | ||||
0.0661320 | + | 0.997811i | \(0.478934\pi\) | |||||||
\(488\) | −4286.43 | −0.397618 | ||||||||
\(489\) | −14606.0 | −1.35073 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19241.1 | 1.76851 | 0.884253 | − | 0.467007i | \(-0.154668\pi\) | ||||
0.884253 | + | 0.467007i | \(0.154668\pi\) | |||||||
\(492\) | 31295.8 | 2.86773 | ||||||||
\(493\) | −13.7040 | −0.00125192 | ||||||||
\(494\) | 3014.75 | 0.274575 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2811.76 | 0.254540 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −47660.6 | −4.28860 | ||||||||
\(499\) | 9576.48 | 0.859123 | 0.429561 | − | 0.903038i | \(-0.358668\pi\) | ||||
0.429561 | + | 0.903038i | \(0.358668\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28041.9 | 2.50064 | ||||||||
\(502\) | 26414.4 | 2.34847 | ||||||||
\(503\) | −10581.9 | −0.938019 | −0.469009 | − | 0.883193i | \(-0.655389\pi\) | ||||
−0.469009 | + | 0.883193i | \(0.655389\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 39220.4 | 3.44577 | ||||||||
\(507\) | −5090.24 | −0.445888 | ||||||||
\(508\) | 5400.72 | 0.471690 | ||||||||
\(509\) | −7082.86 | −0.616782 | −0.308391 | − | 0.951260i | \(-0.599791\pi\) | ||||
−0.308391 | + | 0.951260i | \(0.599791\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −5957.37 | −0.514220 | ||||||||
\(513\) | −6822.47 | −0.587173 | ||||||||
\(514\) | 7584.98 | 0.650893 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1719.01 | 0.146657 | ||||||||
\(517\) | 9602.85 | 0.816891 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −313.933 | −0.0265513 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7153.92 | 0.601572 | 0.300786 | − | 0.953692i | \(-0.402751\pi\) | ||||
0.300786 | + | 0.953692i | \(0.402751\pi\) | |||||||
\(522\) | 1935.98 | 0.162328 | ||||||||
\(523\) | −15781.3 | −1.31944 | −0.659721 | − | 0.751511i | \(-0.729326\pi\) | ||||
−0.659721 | + | 0.751511i | \(0.729326\pi\) | |||||||
\(524\) | −4328.00 | −0.360820 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −25293.7 | −2.09669 | ||||||||
\(527\) | −369.235 | −0.0305202 | ||||||||
\(528\) | 9245.00 | 0.762002 | ||||||||
\(529\) | 11942.5 | 0.981547 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16202.8 | 1.32418 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10929.4 | 0.888192 | ||||||||
\(534\) | −49258.0 | −3.99177 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 14513.2 | 1.16955 | ||||||||
\(537\) | 7243.54 | 0.582089 | ||||||||
\(538\) | 23811.5 | 1.90816 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24277.2 | −1.92931 | −0.964656 | − | 0.263511i | \(-0.915119\pi\) | ||||
−0.964656 | + | 0.263511i | \(0.915119\pi\) | |||||||
\(542\) | −9090.97 | −0.720463 | ||||||||
\(543\) | 19539.0 | 1.54420 | ||||||||
\(544\) | 472.659 | 0.0372520 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 191.079 | 0.0149359 | 0.00746796 | − | 0.999972i | \(-0.497623\pi\) | ||||
0.00746796 | + | 0.999972i | \(0.497623\pi\) | |||||||
\(548\) | −30047.3 | −2.34226 | ||||||||
\(549\) | 16779.8 | 1.30445 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 103.132 | 0.00797382 | ||||||||
\(552\) | −26932.1 | −2.07664 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3876.21 | −0.297264 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13939.6 | −1.06326 | ||||||||
\(557\) | 15721.6 | 1.19595 | 0.597974 | − | 0.801515i | \(-0.295972\pi\) | ||||
0.597974 | + | 0.801515i | \(0.295972\pi\) | |||||||
\(558\) | 52162.3 | 3.95736 | ||||||||
\(559\) | 600.330 | 0.0454226 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1214.04 | −0.0913665 | ||||||||
\(562\) | −9156.92 | −0.687298 | ||||||||
\(563\) | 3044.50 | 0.227905 | 0.113952 | − | 0.993486i | \(-0.463649\pi\) | ||||
0.113952 | + | 0.993486i | \(0.463649\pi\) | |||||||
\(564\) | −19922.1 | −1.48736 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −29597.3 | −2.19800 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17003.6 | −1.25609 | ||||||||
\(569\) | 13052.2 | 0.961647 | 0.480823 | − | 0.876817i | \(-0.340338\pi\) | ||||
0.480823 | + | 0.876817i | \(0.340338\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5811.05 | −0.425893 | −0.212946 | − | 0.977064i | \(-0.568306\pi\) | ||||
−0.212946 | + | 0.977064i | \(0.568306\pi\) | |||||||
\(572\) | −27696.5 | −2.02456 | ||||||||
\(573\) | 21125.9 | 1.54022 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −57542.5 | −4.16250 | ||||||||
\(577\) | −22790.3 | −1.64432 | −0.822162 | − | 0.569254i | \(-0.807232\pi\) | ||||
−0.822162 | + | 0.569254i | \(0.807232\pi\) | |||||||
\(578\) | 21927.2 | 1.57794 | ||||||||
\(579\) | −9847.84 | −0.706844 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −32961.5 | −2.34759 | ||||||||
\(583\) | −8559.70 | −0.608073 | ||||||||
\(584\) | −16515.9 | −1.17026 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25334.2 | 1.78591 | ||||||||
\(587\) | −20600.3 | −1.44850 | −0.724248 | − | 0.689540i | \(-0.757813\pi\) | ||||
−0.724248 | + | 0.689540i | \(0.757813\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2778.76 | 0.194392 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16840.4 | −1.17212 | ||||||||
\(592\) | −619.657 | −0.0430198 | ||||||||
\(593\) | 773.830 | 0.0535875 | 0.0267938 | − | 0.999641i | \(-0.491470\pi\) | ||||
0.0267938 | + | 0.999641i | \(0.491470\pi\) | |||||||
\(594\) | 104610. | 7.22593 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −31539.3 | −2.16762 | ||||||||
\(597\) | 52360.1 | 3.58954 | ||||||||
\(598\) | −28415.7 | −1.94315 | ||||||||
\(599\) | −13641.0 | −0.930479 | −0.465239 | − | 0.885185i | \(-0.654032\pi\) | ||||
−0.465239 | + | 0.885185i | \(0.654032\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14271.8 | −0.968650 | −0.484325 | − | 0.874888i | \(-0.660935\pi\) | ||||
−0.484325 | + | 0.874888i | \(0.660935\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −56814.1 | −3.83689 | ||||||||
\(604\) | −30879.6 | −2.08025 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 24506.4 | 1.64275 | ||||||||
\(607\) | 3234.90 | 0.216311 | 0.108155 | − | 0.994134i | \(-0.465506\pi\) | ||||
0.108155 | + | 0.994134i | \(0.465506\pi\) | |||||||
\(608\) | −3557.10 | −0.237269 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6957.40 | −0.460665 | ||||||||
\(612\) | 1811.90 | 0.119676 | ||||||||
\(613\) | −8413.52 | −0.554354 | −0.277177 | − | 0.960819i | \(-0.589399\pi\) | ||||
−0.277177 | + | 0.960819i | \(0.589399\pi\) | |||||||
\(614\) | 1217.99 | 0.0800558 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7077.93 | −0.461826 | −0.230913 | − | 0.972974i | \(-0.574171\pi\) | ||||
−0.230913 | + | 0.972974i | \(0.574171\pi\) | |||||||
\(618\) | 8998.01 | 0.585685 | ||||||||
\(619\) | −5464.74 | −0.354841 | −0.177420 | − | 0.984135i | \(-0.556775\pi\) | ||||
−0.177420 | + | 0.984135i | \(0.556775\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 64305.7 | 4.15539 | ||||||||
\(622\) | −5454.01 | −0.351585 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6698.13 | −0.429711 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3463.14 | −0.221110 | ||||||||
\(627\) | 9136.48 | 0.581939 | ||||||||
\(628\) | 2699.98 | 0.171562 | ||||||||
\(629\) | 81.3721 | 0.00515822 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1569.98 | −0.0990492 | −0.0495246 | − | 0.998773i | \(-0.515771\pi\) | ||||
−0.0495246 | + | 0.998773i | \(0.515771\pi\) | |||||||
\(632\) | −5308.90 | −0.334140 | ||||||||
\(633\) | 8441.69 | 0.530058 | ||||||||
\(634\) | 33028.9 | 2.06900 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 17758.0 | 1.10715 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1581.34 | −0.0981284 | ||||||||
\(639\) | 66563.0 | 4.12080 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14578.3 | −0.898298 | −0.449149 | − | 0.893457i | \(-0.648273\pi\) | ||||
−0.449149 | + | 0.893457i | \(0.648273\pi\) | |||||||
\(642\) | −64426.0 | −3.96058 | ||||||||
\(643\) | −11980.0 | −0.734750 | −0.367375 | − | 0.930073i | \(-0.619744\pi\) | ||||
−0.367375 | + | 0.930073i | \(0.619744\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 161.096 | 0.00981151 | ||||||||
\(647\) | −5651.81 | −0.343424 | −0.171712 | − | 0.985147i | \(-0.554930\pi\) | ||||
−0.171712 | + | 0.985147i | \(0.554930\pi\) | |||||||
\(648\) | −38786.6 | −2.35136 | ||||||||
\(649\) | −13234.7 | −0.800476 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17805.6 | −1.06951 | ||||||||
\(653\) | 2370.86 | 0.142081 | 0.0710405 | − | 0.997473i | \(-0.477368\pi\) | ||||
0.0710405 | + | 0.997473i | \(0.477368\pi\) | |||||||
\(654\) | 33926.7 | 2.02850 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4447.40 | −0.264698 | ||||||||
\(657\) | 64653.6 | 3.83923 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5233.92 | 0.309385 | 0.154692 | − | 0.987963i | \(-0.450561\pi\) | ||||
0.154692 | + | 0.987963i | \(0.450561\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10456.0 | −0.615265 | −0.307633 | − | 0.951505i | \(-0.599537\pi\) | ||||
−0.307633 | + | 0.951505i | \(0.599537\pi\) | |||||||
\(662\) | 16694.6 | 0.980144 | ||||||||
\(663\) | 879.585 | 0.0515238 | ||||||||
\(664\) | −19231.3 | −1.12398 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11495.5 | −0.668834 | ||||||||
\(667\) | −972.079 | −0.0564303 | ||||||||
\(668\) | 34184.9 | 1.98002 | ||||||||
\(669\) | −35912.7 | −2.07543 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13706.0 | −0.788548 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17658.6 | 1.01143 | 0.505714 | − | 0.862701i | \(-0.331229\pi\) | ||||
0.505714 | + | 0.862701i | \(0.331229\pi\) | |||||||
\(674\) | −36768.1 | −2.10127 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6205.34 | −0.353057 | ||||||||
\(677\) | −9124.03 | −0.517969 | −0.258984 | − | 0.965881i | \(-0.583388\pi\) | ||||
−0.258984 | + | 0.965881i | \(0.583388\pi\) | |||||||
\(678\) | −17797.0 | −1.00810 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 59172.8 | 3.32967 | ||||||||
\(682\) | −42607.1 | −2.39225 | ||||||||
\(683\) | −10523.7 | −0.589570 | −0.294785 | − | 0.955564i | \(-0.595248\pi\) | ||||
−0.294785 | + | 0.955564i | \(0.595248\pi\) | |||||||
\(684\) | −13635.8 | −0.762250 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 37761.9 | 2.09710 | ||||||||
\(688\) | −244.286 | −0.0135368 | ||||||||
\(689\) | 6201.62 | 0.342907 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32928.1 | −1.81280 | −0.906400 | − | 0.422420i | \(-0.861181\pi\) | ||||
−0.906400 | + | 0.422420i | \(0.861181\pi\) | |||||||
\(692\) | −382.706 | −0.0210235 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −56872.8 | −3.11075 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1085.88 | 0.0591384 | ||||||||
\(697\) | 584.024 | 0.0317381 | ||||||||
\(698\) | 20046.8 | 1.08708 | ||||||||
\(699\) | 16726.7 | 0.905093 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2582.50 | −0.139144 | −0.0695719 | − | 0.997577i | \(-0.522163\pi\) | ||||
−0.0695719 | + | 0.997577i | \(0.522163\pi\) | |||||||
\(702\) | −75791.5 | −4.07488 | ||||||||
\(703\) | −612.383 | −0.0328542 | ||||||||
\(704\) | 47001.7 | 2.51625 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 54786.4 | 2.92056 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 27456.9 | 1.45748 | ||||||||
\(709\) | −6866.00 | −0.363693 | −0.181846 | − | 0.983327i | \(-0.558207\pi\) | ||||
−0.181846 | + | 0.983327i | \(0.558207\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20782.4 | 1.09620 | ||||||||
\(712\) | −19875.9 | −1.04618 | ||||||||
\(713\) | −26191.4 | −1.37570 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8830.36 | 0.460902 | ||||||||
\(717\) | 66747.1 | 3.47659 | ||||||||
\(718\) | 49468.9 | 2.57126 | ||||||||
\(719\) | 6581.85 | 0.341393 | 0.170696 | − | 0.985324i | \(-0.445398\pi\) | ||||
0.170696 | + | 0.985324i | \(0.445398\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 29429.8 | 1.51699 | ||||||||
\(723\) | −45543.9 | −2.34273 | ||||||||
\(724\) | 23819.4 | 1.22271 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −81764.0 | −4.17982 | ||||||||
\(727\) | 15527.2 | 0.792119 | 0.396060 | − | 0.918225i | \(-0.370377\pi\) | ||||
0.396060 | + | 0.918225i | \(0.370377\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 42149.0 | 2.14139 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.0792 | 0.00162311 | ||||||||
\(732\) | 28434.6 | 1.43576 | ||||||||
\(733\) | −3391.32 | −0.170889 | −0.0854443 | − | 0.996343i | \(-0.527231\pi\) | ||||
−0.0854443 | + | 0.996343i | \(0.527231\pi\) | |||||||
\(734\) | −26200.3 | −1.31754 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 33527.7 | 1.67914 | ||||||||
\(737\) | 46406.7 | 2.31942 | ||||||||
\(738\) | −82505.9 | −4.11529 | ||||||||
\(739\) | −14335.0 | −0.713562 | −0.356781 | − | 0.934188i | \(-0.616126\pi\) | ||||
−0.356781 | + | 0.934188i | \(0.616126\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6619.51 | −0.328170 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27668.2 | 1.36615 | 0.683073 | − | 0.730350i | \(-0.260643\pi\) | ||||
0.683073 | + | 0.730350i | \(0.260643\pi\) | |||||||
\(744\) | 29257.7 | 1.44172 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −41851.8 | −2.05403 | ||||||||
\(747\) | 75283.7 | 3.68740 | ||||||||
\(748\) | −1479.99 | −0.0723446 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16929.9 | −0.822609 | −0.411305 | − | 0.911498i | \(-0.634927\pi\) | ||||
−0.411305 | + | 0.911498i | \(0.634927\pi\) | |||||||
\(752\) | 2831.10 | 0.137287 | ||||||||
\(753\) | −57998.2 | −2.80687 | ||||||||
\(754\) | 1145.70 | 0.0553370 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19445.3 | −0.933622 | −0.466811 | − | 0.884357i | \(-0.654597\pi\) | ||||
−0.466811 | + | 0.884357i | \(0.654597\pi\) | |||||||
\(758\) | −24739.9 | −1.18548 | ||||||||
\(759\) | −86116.5 | −4.11836 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9996.97 | −0.476202 | −0.238101 | − | 0.971240i | \(-0.576525\pi\) | ||||
−0.238101 | + | 0.971240i | \(0.576525\pi\) | |||||||
\(762\) | −19791.7 | −0.940917 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 25753.9 | 1.21956 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23423.6 | −1.10487 | ||||||||
\(767\) | 9588.76 | 0.451408 | ||||||||
\(768\) | −21810.6 | −1.02477 | ||||||||
\(769\) | −8382.34 | −0.393075 | −0.196538 | − | 0.980496i | \(-0.562970\pi\) | ||||
−0.196538 | + | 0.980496i | \(0.562970\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16654.4 | −0.777942 | ||||||||
\(772\) | −12005.2 | −0.559684 | ||||||||
\(773\) | −11297.5 | −0.525668 | −0.262834 | − | 0.964841i | \(-0.584657\pi\) | ||||
−0.262834 | + | 0.964841i | \(0.584657\pi\) | |||||||
\(774\) | −4531.87 | −0.210458 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13300.2 | −0.615268 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 48652.9 | 2.24202 | ||||||||
\(779\) | −4395.20 | −0.202149 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54369.9 | −2.49105 | ||||||||
\(782\) | −1518.42 | −0.0694356 | ||||||||
\(783\) | −2592.76 | −0.118337 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 15860.6 | 0.719756 | ||||||||
\(787\) | −25174.4 | −1.14024 | −0.570120 | − | 0.821561i | \(-0.693103\pi\) | ||||
−0.570120 | + | 0.821561i | \(0.693103\pi\) | |||||||
\(788\) | −20529.6 | −0.928093 | ||||||||
\(789\) | 55537.5 | 2.50594 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 69204.6 | 3.10490 | ||||||||
\(793\) | 9930.22 | 0.444681 | ||||||||
\(794\) | −59448.4 | −2.65711 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 63830.5 | 2.84222 | ||||||||
\(797\) | −26277.4 | −1.16787 | −0.583936 | − | 0.811800i | \(-0.698488\pi\) | ||||
−0.583936 | + | 0.811800i | \(0.698488\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −371.775 | −0.0164611 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 77806.9 | 3.43217 | ||||||||
\(802\) | −32286.3 | −1.42153 | ||||||||
\(803\) | −52810.2 | −2.32084 | ||||||||
\(804\) | −96275.6 | −4.22311 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 30869.5 | 1.34905 | ||||||||
\(807\) | −52283.1 | −2.28061 | ||||||||
\(808\) | 9888.48 | 0.430539 | ||||||||
\(809\) | 15676.9 | 0.681298 | 0.340649 | − | 0.940191i | \(-0.389353\pi\) | ||||
0.340649 | + | 0.940191i | \(0.389353\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26600.5 | −1.15175 | −0.575876 | − | 0.817537i | \(-0.695339\pi\) | ||||
−0.575876 | + | 0.817537i | \(0.695339\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19961.1 | 0.861090 | ||||||||
\(814\) | 9389.77 | 0.404314 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −357.921 | −0.0153551 | ||||||||
\(817\) | −241.419 | −0.0103380 | ||||||||
\(818\) | 26146.3 | 1.11759 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35601.3 | 1.51339 | 0.756696 | − | 0.653767i | \(-0.226812\pi\) | ||||
0.756696 | + | 0.653767i | \(0.226812\pi\) | |||||||
\(822\) | 110113. | 4.67229 | ||||||||
\(823\) | −41975.0 | −1.77783 | −0.888916 | − | 0.458071i | \(-0.848541\pi\) | ||||
−0.888916 | + | 0.458071i | \(0.848541\pi\) | |||||||
\(824\) | 3630.75 | 0.153499 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27719.4 | −1.16554 | −0.582768 | − | 0.812639i | \(-0.698030\pi\) | ||||
−0.582768 | + | 0.812639i | \(0.698030\pi\) | |||||||
\(828\) | 128525. | 5.39440 | ||||||||
\(829\) | −27222.3 | −1.14049 | −0.570246 | − | 0.821474i | \(-0.693152\pi\) | ||||
−0.570246 | + | 0.821474i | \(0.693152\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8511.01 | 0.355287 | ||||||||
\(832\) | −34053.4 | −1.41898 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 51083.7 | 2.12096 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11138.0 | 0.460784 | ||||||||
\(837\) | −69858.5 | −2.88490 | ||||||||
\(838\) | −37277.2 | −1.53666 | ||||||||
\(839\) | 24081.1 | 0.990909 | 0.495454 | − | 0.868634i | \(-0.335002\pi\) | ||||
0.495454 | + | 0.868634i | \(0.335002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24349.8 | −0.998393 | ||||||||
\(842\) | 48942.4 | 2.00317 | ||||||||
\(843\) | 20105.9 | 0.821452 | ||||||||
\(844\) | 10291.0 | 0.419704 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 52521.1 | 2.13441 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2523.56 | −0.102193 | ||||||||
\(849\) | 64987.0 | 2.62703 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5772.06 | 0.232507 | ||||||||
\(852\) | 112796. | 4.53560 | ||||||||
\(853\) | −18493.0 | −0.742309 | −0.371155 | − | 0.928571i | \(-0.621038\pi\) | ||||
−0.371155 | + | 0.928571i | \(0.621038\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25996.2 | −1.03801 | ||||||||
\(857\) | −3499.25 | −0.139477 | −0.0697387 | − | 0.997565i | \(-0.522217\pi\) | ||||
−0.0697387 | + | 0.997565i | \(0.522217\pi\) | |||||||
\(858\) | 101498. | 4.03856 | ||||||||
\(859\) | 32158.0 | 1.27732 | 0.638660 | − | 0.769489i | \(-0.279489\pi\) | ||||
0.638660 | + | 0.769489i | \(0.279489\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −42071.9 | −1.66238 | ||||||||
\(863\) | 47704.7 | 1.88168 | 0.940838 | − | 0.338857i | \(-0.110040\pi\) | ||||
0.940838 | + | 0.338857i | \(0.110040\pi\) | |||||||
\(864\) | 89426.2 | 3.52123 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −39241.1 | −1.53980 | ||||||||
\(867\) | −48145.6 | −1.88594 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16975.4 | −0.662661 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33622.3 | −1.30798 | ||||||||
\(872\) | 13689.6 | 0.531639 | ||||||||
\(873\) | 52065.3 | 2.01849 | ||||||||
\(874\) | 11427.2 | 0.442255 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 109560. | 4.22569 | ||||||||
\(877\) | 24437.3 | 0.940923 | 0.470461 | − | 0.882421i | \(-0.344087\pi\) | ||||
0.470461 | + | 0.882421i | \(0.344087\pi\) | |||||||
\(878\) | 47174.4 | 1.81328 | ||||||||
\(879\) | −55626.4 | −2.13451 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13975.8 | 0.534458 | 0.267229 | − | 0.963633i | \(-0.413892\pi\) | ||||
0.267229 | + | 0.963633i | \(0.413892\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3193.55 | −0.121712 | −0.0608558 | − | 0.998147i | \(-0.519383\pi\) | ||||
−0.0608558 | + | 0.998147i | \(0.519383\pi\) | |||||||
\(884\) | 1072.27 | 0.0407969 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21792.8 | −0.826348 | ||||||||
\(887\) | 20099.3 | 0.760843 | 0.380422 | − | 0.924813i | \(-0.375779\pi\) | ||||
0.380422 | + | 0.924813i | \(0.375779\pi\) | |||||||
\(888\) | −6447.81 | −0.243665 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −124022. | −4.66317 | ||||||||
\(892\) | −43779.9 | −1.64334 | ||||||||
\(893\) | 2797.87 | 0.104846 | ||||||||
\(894\) | 115580. | 4.32392 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 62392.6 | 2.32244 | ||||||||
\(898\) | −195.637 | −0.00727004 | ||||||||
\(899\) | 1056.02 | 0.0391771 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 331.389 | 0.0122532 | ||||||||
\(902\) | 67392.3 | 2.48771 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7181.20 | −0.264207 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 113163. | 4.14965 | ||||||||
\(907\) | −23212.6 | −0.849792 | −0.424896 | − | 0.905242i | \(-0.639689\pi\) | ||||
−0.424896 | + | 0.905242i | \(0.639689\pi\) | |||||||
\(908\) | 72135.6 | 2.63646 | ||||||||
\(909\) | −38709.8 | −1.41246 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2754.63 | 0.100181 | 0.0500905 | − | 0.998745i | \(-0.484049\pi\) | ||||
0.0500905 | + | 0.998745i | \(0.484049\pi\) | |||||||
\(912\) | 2693.61 | 0.0978008 | ||||||||
\(913\) | −61493.1 | −2.22905 | ||||||||
\(914\) | 12820.5 | 0.463965 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 46034.2 | 1.66049 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4049.98 | −0.145609 | ||||||||
\(919\) | 16218.0 | 0.582137 | 0.291068 | − | 0.956702i | \(-0.405989\pi\) | ||||
0.291068 | + | 0.956702i | \(0.405989\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2674.36 | −0.0956819 | ||||||||
\(922\) | −80012.2 | −2.85798 | ||||||||
\(923\) | 39391.7 | 1.40476 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −34089.8 | −1.20978 | ||||||||
\(927\) | −14213.1 | −0.503580 | ||||||||
\(928\) | −1351.81 | −0.0478184 | ||||||||
\(929\) | −42592.6 | −1.50422 | −0.752109 | − | 0.659038i | \(-0.770964\pi\) | ||||
−0.752109 | + | 0.659038i | \(0.770964\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20390.9 | 0.716659 | ||||||||
\(933\) | 11975.4 | 0.420211 | ||||||||
\(934\) | 27905.0 | 0.977602 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −50139.7 | −1.75093 | ||||||||
\(937\) | −4670.79 | −0.162848 | −0.0814238 | − | 0.996680i | \(-0.525947\pi\) | ||||
−0.0814238 | + | 0.996680i | \(0.525947\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7604.04 | 0.264269 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11036.5 | −0.382338 | −0.191169 | − | 0.981557i | \(-0.561228\pi\) | ||||
−0.191169 | + | 0.981557i | \(0.561228\pi\) | |||||||
\(942\) | −9894.48 | −0.342229 | ||||||||
\(943\) | 41427.2 | 1.43060 | ||||||||
\(944\) | −3901.86 | −0.134528 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3701.71 | 0.127223 | ||||||||
\(947\) | −28219.0 | −0.968314 | −0.484157 | − | 0.874981i | \(-0.660874\pi\) | ||||
−0.484157 | + | 0.874981i | \(0.660874\pi\) | |||||||
\(948\) | 35217.3 | 1.20655 | ||||||||
\(949\) | 38261.7 | 1.30878 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −72521.7 | −2.47285 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42209.7 | −1.43474 | −0.717370 | − | 0.696693i | \(-0.754654\pi\) | ||||
−0.717370 | + | 0.696693i | \(0.754654\pi\) | |||||||
\(954\) | −46815.8 | −1.58880 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 81369.2 | 2.75279 | ||||||||
\(957\) | 3472.16 | 0.117282 | ||||||||
\(958\) | −18404.0 | −0.620674 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1337.99 | −0.0449126 | ||||||||
\(962\) | −6803.02 | −0.228002 | ||||||||
\(963\) | 101766. | 3.40536 | ||||||||
\(964\) | −55521.0 | −1.85499 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11522.8 | −0.383193 | −0.191596 | − | 0.981474i | \(-0.561366\pi\) | ||||
−0.191596 | + | 0.981474i | \(0.561366\pi\) | |||||||
\(968\) | −32992.2 | −1.09547 | ||||||||
\(969\) | −353.719 | −0.0117266 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42660.3 | −1.40992 | −0.704961 | − | 0.709246i | \(-0.749035\pi\) | ||||
−0.704961 | + | 0.709246i | \(0.749035\pi\) | |||||||
\(972\) | 123581. | 4.07806 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6350.30 | −0.208908 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4040.80 | −0.132524 | ||||||||
\(977\) | 13991.7 | 0.458171 | 0.229085 | − | 0.973406i | \(-0.426427\pi\) | ||||
0.229085 | + | 0.973406i | \(0.426427\pi\) | |||||||
\(978\) | 65251.3 | 2.13344 | ||||||||
\(979\) | −63554.1 | −2.07477 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −53589.9 | −1.74413 | ||||||||
\(982\) | −85958.4 | −2.79332 | ||||||||
\(983\) | 25963.2 | 0.842420 | 0.421210 | − | 0.906963i | \(-0.361606\pi\) | ||||
0.421210 | + | 0.906963i | \(0.361606\pi\) | |||||||
\(984\) | −46277.3 | −1.49925 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 61.2217 | 0.00197738 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8069.62 | −0.259847 | ||||||||
\(989\) | 2275.51 | 0.0731617 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14482.3 | 0.464224 | 0.232112 | − | 0.972689i | \(-0.425436\pi\) | ||||
0.232112 | + | 0.972689i | \(0.425436\pi\) | |||||||
\(992\) | −36422.8 | −1.16575 | ||||||||
\(993\) | −36656.5 | −1.17146 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 127574. | 4.05857 | ||||||||
\(997\) | −4184.45 | −0.132922 | −0.0664609 | − | 0.997789i | \(-0.521171\pi\) | ||||
−0.0664609 | + | 0.997789i | \(0.521171\pi\) | |||||||
\(998\) | −42782.4 | −1.35697 | ||||||||
\(999\) | 15395.4 | 0.487578 |
(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 | 1225.4.a.bj.1.1 | 6 | ||
5.4 | even | 2 | 245.4.a.o.1.6 | ✓ | 6 | ||
7.6 | odd | 2 | 1225.4.a.bi.1.1 | 6 | |||
15.14 | odd | 2 | 2205.4.a.bz.1.1 | 6 | |||
35.4 | even | 6 | 245.4.e.q.226.1 | 12 | |||
35.9 | even | 6 | 245.4.e.q.116.1 | 12 | |||
35.19 | odd | 6 | 245.4.e.p.116.1 | 12 | |||
35.24 | odd | 6 | 245.4.e.p.226.1 | 12 | |||
35.34 | odd | 2 | 245.4.a.p.1.6 | yes | 6 | ||
105.104 | even | 2 | 2205.4.a.ca.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.a.o.1.6 | ✓ | 6 | 5.4 | even | 2 | ||
245.4.a.p.1.6 | yes | 6 | 35.34 | odd | 2 | ||
245.4.e.p.116.1 | 12 | 35.19 | odd | 6 | |||
245.4.e.p.226.1 | 12 | 35.24 | odd | 6 | |||
245.4.e.q.116.1 | 12 | 35.9 | even | 6 | |||
245.4.e.q.226.1 | 12 | 35.4 | even | 6 | |||
1225.4.a.bi.1.1 | 6 | 7.6 | odd | 2 | |||
1225.4.a.bj.1.1 | 6 | 1.1 | even | 1 | trivial | ||
2205.4.a.bz.1.1 | 6 | 15.14 | odd | 2 | |||
2205.4.a.ca.1.1 | 6 | 105.104 | even | 2 |