Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,4,Mod(1,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, 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("76.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.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: | \(4.48414516044\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.35529.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 52x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.76918\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.26314 | 0.243092 | 0.121546 | − | 0.992586i | \(-0.461215\pi\) | ||||
0.121546 | + | 0.992586i | \(0.461215\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 11.0323 | 0.986760 | 0.493380 | − | 0.869814i | \(-0.335761\pi\) | ||||
0.493380 | + | 0.869814i | \(0.335761\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.70454 | 0.308016 | 0.154008 | − | 0.988070i | \(-0.450782\pi\) | ||||
0.154008 | + | 0.988070i | \(0.450782\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −25.4045 | −0.940907 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 59.0565 | 1.61874 | 0.809372 | − | 0.587296i | \(-0.199807\pi\) | ||||
0.809372 | + | 0.587296i | \(0.199807\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 88.0721 | 1.87898 | 0.939492 | − | 0.342570i | \(-0.111297\pi\) | ||||
0.939492 | + | 0.342570i | \(0.111297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13.9354 | 0.239873 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −113.193 | −1.61490 | −0.807452 | − | 0.589933i | \(-0.799154\pi\) | ||||
−0.807452 | + | 0.589933i | \(0.799154\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.20564 | 0.0748762 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 40.1701 | 0.364176 | 0.182088 | − | 0.983282i | \(-0.441714\pi\) | ||||
0.182088 | + | 0.983282i | \(0.441714\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.28800 | −0.0263040 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −66.1942 | −0.471818 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −66.5906 | −0.426399 | −0.213199 | − | 0.977009i | \(-0.568388\pi\) | ||||
−0.213199 | + | 0.977009i | \(0.568388\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −248.695 | −1.44087 | −0.720433 | − | 0.693524i | \(-0.756057\pi\) | ||||
−0.720433 | + | 0.693524i | \(0.756057\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 74.5966 | 0.393503 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 62.9343 | 0.303938 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −330.857 | −1.47007 | −0.735034 | − | 0.678031i | \(-0.762834\pi\) | ||||
−0.735034 | + | 0.678031i | \(0.762834\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 111.247 | 0.456765 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −172.072 | −0.655441 | −0.327721 | − | 0.944775i | \(-0.606280\pi\) | ||||
−0.327721 | + | 0.944775i | \(0.606280\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 56.9507 | 0.201974 | 0.100987 | − | 0.994888i | \(-0.467800\pi\) | ||||
0.100987 | + | 0.994888i | \(0.467800\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −280.270 | −0.928449 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 483.093 | 1.49929 | 0.749643 | − | 0.661843i | \(-0.230225\pi\) | ||||
0.749643 | + | 0.661843i | \(0.230225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −310.458 | −0.905126 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −142.979 | −0.392570 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −104.380 | −0.270521 | −0.135261 | − | 0.990810i | \(-0.543187\pi\) | ||||
−0.135261 | + | 0.990810i | \(0.543187\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 651.530 | 1.59731 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 23.9997 | 0.0557690 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 579.966 | 1.27975 | 0.639874 | − | 0.768479i | \(-0.278986\pi\) | ||||
0.639874 | + | 0.768479i | \(0.278986\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 314.576 | 0.660283 | 0.330142 | − | 0.943931i | \(-0.392903\pi\) | ||||
0.330142 | + | 0.943931i | \(0.392903\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −144.921 | −0.289815 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 971.639 | 1.85411 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.2803 | −0.0223921 | −0.0111961 | − | 0.999937i | \(-0.503564\pi\) | ||||
−0.0111961 | + | 0.999937i | \(0.503564\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 50.7405 | 0.0885280 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −711.303 | −1.18896 | −0.594480 | − | 0.804111i | \(-0.702642\pi\) | ||||
−0.594480 | + | 0.804111i | \(0.702642\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −704.738 | −1.12991 | −0.564954 | − | 0.825122i | \(-0.691106\pi\) | ||||
−0.564954 | + | 0.825122i | \(0.691106\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.15320 | −0.00639428 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 336.890 | 0.498600 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −50.4809 | −0.0718929 | −0.0359465 | − | 0.999354i | \(-0.511445\pi\) | ||||
−0.0359465 | + | 0.999354i | \(0.511445\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 602.308 | 0.826212 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 849.747 | 1.12376 | 0.561878 | − | 0.827220i | \(-0.310079\pi\) | ||||
0.561878 | + | 0.827220i | \(0.310079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1248.78 | −1.59352 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −84.1133 | −0.103654 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 704.355 | 0.838893 | 0.419447 | − | 0.907780i | \(-0.362224\pi\) | ||||
0.419447 | + | 0.907780i | \(0.362224\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 502.411 | 0.578758 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −314.136 | −0.350263 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 209.614 | 0.226378 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −232.096 | −0.242946 | −0.121473 | − | 0.992595i | \(-0.538762\pi\) | ||||
−0.121473 | + | 0.992595i | \(0.538762\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1500.30 | −1.52309 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 943.254 | 0.929280 | 0.464640 | − | 0.885500i | \(-0.346184\pi\) | ||||
0.464640 | + | 0.885500i | \(0.346184\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1796.48 | −1.71857 | −0.859286 | − | 0.511496i | \(-0.829092\pi\) | ||||
−0.859286 | + | 0.511496i | \(0.829092\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 79.4949 | 0.0738848 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1207.11 | −1.09061 | −0.545306 | − | 0.838237i | \(-0.683587\pi\) | ||||
−0.545306 | + | 0.838237i | \(0.683587\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −640.900 | −0.563185 | −0.281592 | − | 0.959534i | \(-0.590863\pi\) | ||||
−0.281592 | + | 0.959534i | \(0.590863\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −417.918 | −0.357361 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1217.17 | 1.01329 | 0.506644 | − | 0.862155i | \(-0.330886\pi\) | ||||
0.506644 | + | 0.862155i | \(0.330886\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 443.169 | 0.359354 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2237.43 | −1.76795 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −645.715 | −0.497417 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2156.66 | 1.62033 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −217.351 | −0.159332 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1415.31 | −1.01272 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 413.264 | 0.288750 | 0.144375 | − | 0.989523i | \(-0.453883\pi\) | ||||
0.144375 | + | 0.989523i | \(0.453883\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 71.9367 | 0.0490983 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −834.232 | −0.556391 | −0.278195 | − | 0.960525i | \(-0.589736\pi\) | ||||
−0.278195 | + | 0.960525i | \(0.589736\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 108.386 | 0.0706638 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −730.276 | −0.465571 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 157.186 | 0.0980243 | 0.0490122 | − | 0.998798i | \(-0.484393\pi\) | ||||
0.0490122 | + | 0.998798i | \(0.484393\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2450.06 | 1.49505 | 0.747524 | − | 0.664235i | \(-0.231242\pi\) | ||||
0.747524 | + | 0.664235i | \(0.231242\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 610.215 | 0.364464 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5201.23 | 3.04160 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −734.648 | −0.420753 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −392.152 | −0.220028 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 668.114 | 0.367343 | 0.183671 | − | 0.982988i | \(-0.441202\pi\) | ||||
0.183671 | + | 0.982988i | \(0.441202\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2437.23 | −1.31350 | −0.656750 | − | 0.754108i | \(-0.728069\pi\) | ||||
−0.656750 | + | 0.754108i | \(0.728069\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2875.61 | 1.51947 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2743.68 | −1.42179 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −464.281 | −0.236011 | −0.118005 | − | 0.993013i | \(-0.537650\pi\) | ||||
−0.118005 | + | 0.993013i | \(0.537650\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −131.846 | −0.0657615 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 229.152 | 0.112172 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1471.23 | −0.706968 | −0.353484 | − | 0.935441i | \(-0.615003\pi\) | ||||
−0.353484 | + | 0.935441i | \(0.615003\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 822.973 | 0.388293 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 380.337 | 0.176236 | 0.0881178 | − | 0.996110i | \(-0.471915\pi\) | ||||
0.0881178 | + | 0.996110i | \(0.471915\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5559.69 | 2.53058 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −482.685 | −0.215859 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1315.05 | 0.577927 | 0.288963 | − | 0.957340i | \(-0.406689\pi\) | ||||
0.288963 | + | 0.957340i | \(0.406689\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.7565 | −0.00810206 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 732.579 | 0.311096 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3965.24 | 1.65573 | 0.827866 | − | 0.560926i | \(-0.189555\pi\) | ||||
0.827866 | + | 0.560926i | \(0.189555\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 102.709 | 0.0421783 | 0.0210892 | − | 0.999778i | \(-0.493287\pi\) | ||||
0.0210892 | + | 0.999778i | \(0.493287\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 397.353 | 0.160509 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3650.11 | −1.45060 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6684.79 | −2.61412 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −377.608 | −0.145328 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3291.55 | 1.24695 | 0.623477 | − | 0.781842i | \(-0.285719\pi\) | ||||
0.623477 | + | 0.781842i | \(0.285719\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1106.18 | −0.412564 | −0.206282 | − | 0.978493i | \(-0.566136\pi\) | ||||
−0.206282 | + | 0.978493i | \(0.566136\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1227.32 | 0.450718 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1454.31 | −0.525967 | −0.262984 | − | 0.964800i | \(-0.584707\pi\) | ||||
−0.262984 | + | 0.964800i | \(0.584707\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1796.58 | −0.639979 | −0.319990 | − | 0.947421i | \(-0.603679\pi\) | ||||
−0.319990 | + | 0.947421i | \(0.603679\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.5117 | −0.00544333 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −379.869 | −0.131338 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1898.35 | −0.646764 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1020.50 | −0.342655 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1122.07 | 0.371365 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2697.12 | 0.879987 | 0.439994 | − | 0.898001i | \(-0.354981\pi\) | ||||
0.439994 | + | 0.898001i | \(0.354981\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −898.475 | −0.289026 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 628.298 | 0.199300 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1418.69 | −0.443811 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −890.183 | −0.274671 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9969.16 | −3.03438 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5405.35 | −1.62318 | −0.811590 | − | 0.584228i | \(-0.801397\pi\) | ||||
−0.811590 | + | 0.584228i | \(0.801397\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 83.5299 | 0.0247496 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 696.832 | 0.203746 | 0.101873 | − | 0.994797i | \(-0.467516\pi\) | ||||
0.101873 | + | 0.994797i | \(0.467516\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5249.49 | 1.51483 | 0.757414 | − | 0.652934i | \(-0.226462\pi\) | ||||
0.757414 | + | 0.652934i | \(0.226462\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 425.540 | 0.121205 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1209.87 | 0.340177 | 0.170089 | − | 0.985429i | \(-0.445595\pi\) | ||||
0.170089 | + | 0.985429i | \(0.445595\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5329.64 | 1.47944 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −63.7644 | −0.0174766 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1186.77 | −0.321197 | −0.160598 | − | 0.987020i | \(-0.551342\pi\) | ||||
−0.160598 | + | 0.987020i | \(0.551342\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2595.99 | −0.693869 | −0.346934 | − | 0.937889i | \(-0.612777\pi\) | ||||
−0.346934 | + | 0.937889i | \(0.612777\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2548.04 | 0.672663 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3425.07 | −0.893142 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1673.37 | 0.431069 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1073.35 | 0.273176 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1493.59 | 0.375596 | 0.187798 | − | 0.982208i | \(-0.439865\pi\) | ||||
0.187798 | + | 0.982208i | \(0.439865\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2372.30 | 0.589508 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1577.39 | −0.387372 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3323.84 | −0.806752 | −0.403376 | − | 0.915034i | \(-0.632163\pi\) | ||||
−0.403376 | + | 0.915034i | \(0.632163\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1887.39 | −0.452805 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1691.70 | 0.401201 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4258.10 | −0.998349 | −0.499175 | − | 0.866501i | \(-0.666363\pi\) | ||||
−0.499175 | + | 0.866501i | \(0.666363\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1151.55 | −0.266940 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 889.700 | 0.203928 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5924.75 | −1.34289 | −0.671447 | − | 0.741053i | \(-0.734327\pi\) | ||||
−0.671447 | + | 0.741053i | \(0.734327\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8022.37 | 1.79824 | 0.899122 | − | 0.437698i | \(-0.144206\pi\) | ||||
0.899122 | + | 0.437698i | \(0.144206\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 634.616 | 0.140691 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −194.177 | −0.0425794 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 932.970 | 0.202371 | 0.101185 | − | 0.994868i | \(-0.467736\pi\) | ||||
0.101185 | + | 0.994868i | \(0.467736\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6317.96 | 1.35572 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 956.475 | 0.203055 | 0.101528 | − | 0.994833i | \(-0.467627\pi\) | ||||
0.101528 | + | 0.994833i | \(0.467627\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4386.74 | 0.921431 | 0.460715 | − | 0.887548i | \(-0.347593\pi\) | ||||
0.460715 | + | 0.887548i | \(0.347593\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 264.772 | 0.0550307 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −981.591 | −0.201887 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7899.70 | 1.60792 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −293.170 | −0.0590581 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1357.48 | −0.270665 | −0.135332 | − | 0.990800i | \(-0.543210\pi\) | ||||
−0.135332 | + | 0.990800i | \(0.543210\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6398.37 | 1.26281 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3909.20 | −0.763753 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3537.86 | 0.684281 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 324.878 | 0.0622114 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1191.46 | 0.225900 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3470.50 | 0.651541 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9332.32 | −1.73493 | −0.867465 | − | 0.497498i | \(-0.834252\pi\) | ||||
−0.867465 | + | 0.497498i | \(0.834252\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2269.21 | −0.417770 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2944.72 | 0.536913 | 0.268456 | − | 0.963292i | \(-0.413486\pi\) | ||||
0.268456 | + | 0.963292i | \(0.413486\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2890.66 | 0.522011 | 0.261006 | − | 0.965337i | \(-0.415946\pi\) | ||||
0.261006 | + | 0.965337i | \(0.415946\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1598.81 | −0.285978 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6749.05 | 1.19579 | 0.597894 | − | 0.801575i | \(-0.296005\pi\) | ||||
0.597894 | + | 0.801575i | \(0.296005\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3932.60 | −0.690231 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1524.75 | −0.265119 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2150.67 | −0.370485 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −289.581 | −0.0494248 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −809.547 | −0.136905 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2755.83 | 0.461804 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9193.52 | 1.52665 | 0.763325 | − | 0.646014i | \(-0.223565\pi\) | ||||
0.763325 | + | 0.646014i | \(0.223565\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8405.24 | 1.38320 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −135.480 | −0.0220957 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5068.33 | −0.819257 | −0.409628 | − | 0.912252i | \(-0.634342\pi\) | ||||
−0.409628 | + | 0.912252i | \(0.634342\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1537.45 | 0.246322 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14687.0 | −2.33240 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3727.68 | −0.586810 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 559.785 | 0.0873560 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8586.97 | −1.32845 | −0.664226 | − | 0.747532i | \(-0.731239\pi\) | ||||
−0.664226 | + | 0.747532i | \(0.731239\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4670.75 | −0.716388 | −0.358194 | − | 0.933647i | \(-0.616607\pi\) | ||||
−0.358194 | + | 0.933647i | \(0.616607\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5829.86 | −0.886539 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6183.32 | −0.932308 | −0.466154 | − | 0.884703i | \(-0.654361\pi\) | ||||
−0.466154 | + | 0.884703i | \(0.654361\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7847.32 | −1.17322 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −815.629 | −0.120918 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5485.69 | 0.806473 | 0.403237 | − | 0.915096i | \(-0.367885\pi\) | ||||
0.403237 | + | 0.915096i | \(0.367885\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2724.17 | 0.393890 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7774.89 | −1.11495 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −783.301 | −0.111411 | −0.0557057 | − | 0.998447i | \(-0.517741\pi\) | ||||
−0.0557057 | + | 0.998447i | \(0.517741\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4371.39 | 0.616709 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −595.438 | −0.0833250 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7453.82 | 1.03470 | 0.517351 | − | 0.855773i | \(-0.326918\pi\) | ||||
0.517351 | + | 0.855773i | \(0.326918\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1787.74 | −0.246183 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5864.77 | −0.801197 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12884.3 | 1.74623 | 0.873116 | − | 0.487513i | \(-0.162096\pi\) | ||||
0.873116 | + | 0.487513i | \(0.162096\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 522.011 | 0.0701927 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4151.36 | 0.553850 | 0.276925 | − | 0.960892i | \(-0.410685\pi\) | ||||
0.276925 | + | 0.960892i | \(0.410685\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3716.68 | 0.491999 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1446.80 | −0.190039 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −395.512 | −0.0515508 | −0.0257754 | − | 0.999668i | \(-0.508205\pi\) | ||||
−0.0257754 | + | 0.999668i | \(0.508205\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4546.98 | −0.588109 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1053.75 | −0.135254 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −556.921 | −0.0709411 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2749.61 | −0.347604 | −0.173802 | − | 0.984781i | \(-0.555605\pi\) | ||||
−0.173802 | + | 0.984781i | \(0.555605\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 136.907 | 0.0171778 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5196.07 | 0.647080 | 0.323540 | − | 0.946214i | \(-0.395127\pi\) | ||||
0.323540 | + | 0.946214i | \(0.395127\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21903.1 | −2.70737 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6644.85 | 0.815273 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19539.2 | −2.37966 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8811.47 | −1.06528 | −0.532639 | − | 0.846342i | \(-0.678800\pi\) | ||||
−0.532639 | + | 0.846342i | \(0.678800\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 198.548 | 0.0238289 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3308.44 | 0.394184 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9374.67 | 1.10888 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3094.78 | 0.363434 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9178.16 | 1.07012 | 0.535062 | − | 0.844813i | \(-0.320288\pi\) | ||||
0.535062 | + | 0.844813i | \(0.320288\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11290.8 | 1.30708 | 0.653541 | − | 0.756891i | \(-0.273283\pi\) | ||||
0.653541 | + | 0.756891i | \(0.273283\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12272.7 | −1.41069 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 372.179 | 0.0424784 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1794.51 | 0.203378 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6569.88 | 0.739386 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1907.51 | −0.213183 | −0.106591 | − | 0.994303i | \(-0.533994\pi\) | ||||
−0.106591 | + | 0.994303i | \(0.533994\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13643.2 | 1.51421 | 0.757104 | − | 0.653294i | \(-0.226613\pi\) | ||||
0.757104 | + | 0.653294i | \(0.226613\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −927.964 | −0.102282 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 763.232 | 0.0835476 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9906.74 | −1.07705 | −0.538523 | − | 0.842611i | \(-0.681017\pi\) | ||||
−0.538523 | + | 0.842611i | \(0.681017\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7887.03 | 0.851639 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7580.47 | 0.813000 | 0.406500 | − | 0.913651i | \(-0.366749\pi\) | ||||
0.406500 | + | 0.913651i | \(0.366749\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7770.67 | 0.827787 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 843.922 | 0.0892979 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8593.98 | 0.903285 | 0.451642 | − | 0.892199i | \(-0.350838\pi\) | ||||
0.451642 | + | 0.892199i | \(0.350838\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10161.9 | −1.06099 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3078.56 | −0.319301 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5542.76 | 0.571096 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14294.6 | −1.46318 | −0.731589 | − | 0.681746i | \(-0.761221\pi\) | ||||
−0.731589 | + | 0.681746i | \(0.761221\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7492.73 | 0.761941 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16465.7 | 1.66352 | 0.831761 | − | 0.555134i | \(-0.187333\pi\) | ||||
0.831761 | + | 0.555134i | \(0.187333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15503.4 | 1.55617 | 0.778083 | − | 0.628162i | \(-0.216192\pi\) | ||||
0.778083 | + | 0.628162i | \(0.216192\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3465.65 | −0.345625 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3263.71 | 0.323397 | 0.161699 | − | 0.986840i | \(-0.448303\pi\) | ||||
0.161699 | + | 0.986840i | \(0.448303\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −70.0532 | −0.00689714 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −586.452 | −0.0573722 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3363.31 | 0.326945 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −62.4720 | −0.00603455 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2651.71 | 0.254535 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1763.00 | 0.168170 | 0.0840852 | − | 0.996459i | \(-0.473203\pi\) | ||||
0.0840852 | + | 0.996459i | \(0.473203\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29139.2 | −2.76223 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 289.451 | 0.0272681 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2560.55 | −0.239729 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9574.66 | 0.890902 | 0.445451 | − | 0.895306i | \(-0.353043\pi\) | ||||
0.445451 | + | 0.895306i | \(0.353043\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1858.37 | −0.171858 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18569.3 | 1.70676 | 0.853380 | − | 0.521290i | \(-0.174549\pi\) | ||||
0.853380 | + | 0.521290i | \(0.174549\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7537.60 | 0.688593 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16551.8 | −1.50292 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4057.66 | −0.366219 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10116.0 | −0.907523 | −0.453761 | − | 0.891123i | \(-0.649918\pi\) | ||||
−0.453761 | + | 0.891123i | \(0.649918\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 480.419 | 0.0428414 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 853.516 | 0.0756589 | 0.0378294 | − | 0.999284i | \(-0.487956\pi\) | ||||
0.0378294 | + | 0.999284i | \(0.487956\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10406.3 | 0.916977 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7022.67 | 0.615164 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5049.04 | −0.439676 | −0.219838 | − | 0.975536i | \(-0.570553\pi\) | ||||
−0.219838 | + | 0.975536i | \(0.570553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4020.21 | −0.348030 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1257.69 | −0.108242 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19819.4 | −1.69582 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28529.8 | 2.42696 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1661.09 | 0.140489 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8294.77 | −0.697506 | −0.348753 | − | 0.937215i | \(-0.613395\pi\) | ||||
−0.348753 | + | 0.937215i | \(0.613395\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3466.62 | −0.289837 | −0.144918 | − | 0.989444i | \(-0.546292\pi\) | ||||
−0.144918 | + | 0.989444i | \(0.546292\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −23.6921 | −0.00196954 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28150.5 | 2.32686 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10553.4 | −0.867376 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14733.7 | −1.20412 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15154.7 | −1.23156 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13317.2 | −1.07617 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5008.66 | 0.402495 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18334.6 | −1.46517 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14784.5 | 1.17493 | 0.587464 | − | 0.809250i | \(-0.300126\pi\) | ||||
0.587464 | + | 0.809250i | \(0.300126\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 129.736 | 0.0102532 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7070.62 | −0.555728 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2531.48 | 0.197876 | 0.0989382 | − | 0.995094i | \(-0.468455\pi\) | ||||
0.0989382 | + | 0.995094i | \(0.468455\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7991.63 | −0.621265 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1265.22 | −0.0978226 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −287.970 | −0.0221442 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4610.61 | −0.352630 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12526.9 | −0.952933 | −0.476466 | − | 0.879193i | \(-0.658083\pi\) | ||||
−0.476466 | + | 0.879193i | \(0.658083\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5015.77 | 0.379507 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8443.83 | −0.635470 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16977.2 | 1.27087 | 0.635437 | − | 0.772153i | \(-0.280820\pi\) | ||||
0.635437 | + | 0.772153i | \(0.280820\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13428.2 | 0.999872 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3435.89 | 0.254487 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12491.3 | −0.920317 | −0.460159 | − | 0.887837i | \(-0.652207\pi\) | ||||
−0.460159 | + | 0.887837i | \(0.652207\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3471.26 | 0.254410 | 0.127205 | − | 0.991876i | \(-0.459399\pi\) | ||||
0.127205 | + | 0.991876i | \(0.459399\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4157.69 | 0.303124 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −132.079 | −0.00957927 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22314.6 | −1.61000 | −0.804998 | − | 0.593277i | \(-0.797834\pi\) | ||||
−0.804998 | + | 0.593277i | \(0.797834\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1397.27 | −0.100291 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4847.42 | 0.346135 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6164.29 | −0.437905 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −24684.0 | −1.74454 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 797.363 | 0.0560659 | 0.0280329 | − | 0.999607i | \(-0.491076\pi\) | ||||
0.0280329 | + | 0.999607i | \(0.491076\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4725.20 | −0.330558 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1837.00 | −0.127858 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5229.07 | −0.362112 | −0.181056 | − | 0.983473i | \(-0.557952\pi\) | ||||
−0.181056 | + | 0.983473i | \(0.557952\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7123.74 | −0.490831 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2269.33 | −0.155574 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4520.22 | −0.308332 | −0.154166 | − | 0.988045i | \(-0.549269\pi\) | ||||
−0.154166 | + | 0.988045i | \(0.549269\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28191.4 | −1.91340 | −0.956699 | − | 0.291080i | \(-0.905986\pi\) | ||||
−0.956699 | + | 0.291080i | \(0.905986\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 311.973 | 0.0210689 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23793.0 | 1.59888 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9824.01 | 0.656910 | 0.328455 | − | 0.944520i | \(-0.393472\pi\) | ||||
0.328455 | + | 0.944520i | \(0.393472\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −479.828 | −0.0319271 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 42547.0 | 2.81713 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7236.11 | −0.476776 | −0.238388 | − | 0.971170i | \(-0.576619\pi\) | ||||
−0.238388 | + | 0.971170i | \(0.576619\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2397.88 | −0.157223 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20177.0 | 1.31653 | 0.658263 | − | 0.752788i | \(-0.271292\pi\) | ||||
0.658263 | + | 0.752788i | \(0.271292\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9836.84 | −0.638734 | −0.319367 | − | 0.947631i | \(-0.603470\pi\) | ||||
−0.319367 | + | 0.947631i | \(0.603470\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2659.03 | −0.171825 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4018.02 | 0.258393 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15203.2 | −0.973004 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1417.34 | 0.0902758 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 37450.7 | 2.37402 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5325.24 | 0.335966 | 0.167983 | − | 0.985790i | \(-0.446275\pi\) | ||||
0.167983 | + | 0.985790i | \(0.446275\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3406.84 | 0.213917 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4559.26 | 0.284927 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27342.7 | −1.70072 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18070.3 | 1.11870 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30186.7 | 1.86007 | 0.930035 | − | 0.367472i | \(-0.119777\pi\) | ||||
0.930035 | + | 0.367472i | \(0.119777\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6815.72 | 0.418018 | 0.209009 | − | 0.977914i | \(-0.432976\pi\) | ||||
0.209009 | + | 0.977914i | \(0.432976\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 793.629 | 0.0484482 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8525.98 | −0.518069 | −0.259035 | − | 0.965868i | \(-0.583404\pi\) | ||||
−0.259035 | + | 0.965868i | \(0.583404\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34250.8 | 2.07159 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1792.00 | −0.107887 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13797.4 | −0.826849 | −0.413425 | − | 0.910538i | \(-0.635668\pi\) | ||||
−0.413425 | + | 0.910538i | \(0.635668\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9203.51 | −0.549024 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17903.5 | 1.06314 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16673.7 | −0.985610 | −0.492805 | − | 0.870140i | \(-0.664028\pi\) | ||||
−0.492805 | + | 0.870140i | \(0.664028\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2752.76 | 0.161982 | 0.0809909 | − | 0.996715i | \(-0.474192\pi\) | ||||
0.0809909 | + | 0.996715i | \(0.474192\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12592.5 | −0.737632 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1195.75 | 0.0697282 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2674.95 | −0.155284 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6827.72 | −0.394581 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18577.7 | 1.06883 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3652.27 | −0.209190 | −0.104595 | − | 0.994515i | \(-0.533355\pi\) | ||||
−0.104595 | + | 0.994515i | \(0.533355\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 217.646 | 0.0124107 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13175.4 | −0.747964 | −0.373982 | − | 0.927436i | \(-0.622008\pi\) | ||||
−0.373982 | + | 0.927436i | \(0.622008\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1324.00 | −0.0748313 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 880.197 | 0.0495290 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25912.2 | 1.45169 | 0.725845 | − | 0.687859i | \(-0.241449\pi\) | ||||
0.725845 | + | 0.687859i | \(0.241449\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1734.13 | 0.0967265 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6630.84 | 0.368242 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9192.93 | −0.508306 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19933.9 | −1.09742 | −0.548712 | − | 0.836012i | \(-0.684882\pi\) | ||||
−0.548712 | + | 0.836012i | \(0.684882\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8558.52 | −0.469136 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27029.9 | 1.47525 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19477.4 | 1.05848 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1528.24 | 0.0826942 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10583.0 | −0.570208 | −0.285104 | − | 0.958497i | \(-0.592028\pi\) | ||||
−0.285104 | + | 0.958497i | \(0.592028\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6286.27 | −0.337257 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6732.08 | 0.359638 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5380.84 | 0.286234 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28731.2 | −1.52189 | −0.760947 | − | 0.648814i | \(-0.775265\pi\) | ||||
−0.760947 | + | 0.648814i | \(0.775265\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1282.44 | 0.0676445 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9990.08 | −0.524729 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 57381.6 | 3.00133 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1499.06 | −0.0780802 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7427.02 | −0.385231 | −0.192615 | − | 0.981274i | \(-0.561697\pi\) | ||||
−0.192615 | + | 0.981274i | \(0.561697\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10248.1 | −0.529348 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3279.10 | −0.168674 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 218.950 | 0.0112160 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5465.02 | 0.278798 | 0.139399 | − | 0.990236i | \(-0.455483\pi\) | ||||
0.139399 | + | 0.990236i | \(0.455483\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13043.8 | −0.662693 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6446.43 | −0.326169 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11959.6 | 0.602644 | 0.301322 | − | 0.953522i | \(-0.402572\pi\) | ||||
0.301322 | + | 0.953522i | \(0.402572\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4326.35 | −0.217115 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −725.228 | −0.0362471 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21411.4 | 1.06581 | 0.532903 | − | 0.846176i | \(-0.321101\pi\) | ||||
0.532903 | + | 0.846176i | \(0.321101\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2113.70 | 0.104789 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −39368.8 | −1.94388 | −0.971938 | − | 0.235238i | \(-0.924413\pi\) | ||||
−0.971938 | + | 0.235238i | \(0.924413\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7370.85 | 0.362479 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −21587.4 | −1.05735 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6886.00 | −0.335927 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −928.320 | −0.0451063 | −0.0225532 | − | 0.999746i | \(-0.507180\pi\) | ||||
−0.0225532 | + | 0.999746i | \(0.507180\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1886.62 | 0.0913043 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26888.2 | −1.29611 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8174.49 | 0.392480 | 0.196240 | − | 0.980556i | \(-0.437127\pi\) | ||||
0.196240 | + | 0.980556i | \(0.437127\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2996.55 | 0.143304 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21673.8 | −1.03242 | −0.516211 | − | 0.856462i | \(-0.672658\pi\) | ||||
−0.516211 | + | 0.856462i | \(0.672658\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3656.04 | −0.173470 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 31724.7 | 1.49936 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 51078.8 | 2.40463 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5279.64 | 0.247580 | 0.123790 | − | 0.992308i | \(-0.460495\pi\) | ||||
0.123790 | + | 0.992308i | \(0.460495\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4198.48 | −0.196115 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30853.7 | −1.43562 | −0.717809 | − | 0.696241i | \(-0.754855\pi\) | ||||
−0.717809 | + | 0.696241i | \(0.754855\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 817.707 | 0.0379005 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2384.03 | −0.110073 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3269.36 | −0.150369 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42007.0 | −1.92462 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4407.91 | 0.201183 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5122.10 | −0.232886 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14408.0 | −0.652590 | −0.326295 | − | 0.945268i | \(-0.605800\pi\) | ||||
−0.326295 | + | 0.945268i | \(0.605800\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5378.58 | −0.242690 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6943.38 | 0.312109 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27705.3 | 1.24066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1454.57 | −0.0648908 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6512.56 | 0.289444 | 0.144722 | − | 0.989472i | \(-0.453771\pi\) | ||||
0.144722 | + | 0.989472i | \(0.453771\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −54682.9 | −2.42120 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17893.8 | −0.789320 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −41619.3 | −1.82903 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2528.08 | 0.110687 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7483.80 | −0.326446 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22213.1 | −0.965354 | −0.482677 | − | 0.875799i | \(-0.660335\pi\) | ||||
−0.482677 | + | 0.875799i | \(0.660335\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2480.93 | 0.107420 | 0.0537098 | − | 0.998557i | \(-0.482895\pi\) | ||||
0.0537098 | + | 0.998557i | \(0.482895\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10133.4 | 0.437138 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16231.1 | −0.697608 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1082.06 | 0.0463361 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12763.5 | −0.544557 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17912.8 | 0.761461 | 0.380730 | − | 0.924686i | \(-0.375673\pi\) | ||||
0.380730 | + | 0.924686i | \(0.375673\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3445.46 | −0.145931 | −0.0729656 | − | 0.997334i | \(-0.523246\pi\) | ||||
−0.0729656 | + | 0.997334i | \(0.523246\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −245.273 | −0.0103507 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33614.6 | 1.41341 | 0.706707 | − | 0.707506i | \(-0.250180\pi\) | ||||
0.706707 | + | 0.707506i | \(0.250180\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3539.89 | 0.148306 | 0.0741529 | − | 0.997247i | \(-0.476375\pi\) | ||||
0.0741529 | + | 0.997247i | \(0.476375\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1178.47 | 0.0491947 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35141.7 | 1.46169 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4196.00 | 0.173902 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16462.1 | 0.679827 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17069.1 | −0.702374 | −0.351187 | − | 0.936305i | \(-0.614222\pi\) | ||||
−0.351187 | + | 0.936305i | \(0.614222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19954.7 | −0.818184 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1208.16 | 0.0493610 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 61336.3 | 2.49708 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12302.8 | 0.499090 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5541.08 | 0.223992 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13290.5 | −0.535363 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22496.0 | 0.902989 | 0.451495 | − | 0.892274i | \(-0.350891\pi\) | ||||
0.451495 | + | 0.892274i | \(0.350891\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5325.13 | −0.213001 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14011.8 | −0.558498 | −0.279249 | − | 0.960219i | \(-0.590085\pi\) | ||||
−0.279249 | + | 0.960219i | \(0.590085\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26340.3 | −1.04624 | −0.523120 | − | 0.852259i | \(-0.675232\pi\) | ||||
−0.523120 | + | 0.852259i | \(0.675232\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1239.89 | −0.0490769 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26311.7 | −1.03785 | −0.518924 | − | 0.854821i | \(-0.673667\pi\) | ||||
−0.518924 | + | 0.854821i | \(0.673667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14508.0 | 0.570275 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9978.43 | 0.390871 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2981.22 | −0.116376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1081.55 | −0.0420744 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5896.27 | 0.228589 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8073.72 | −0.311933 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29383.8 | 1.13138 | 0.565690 | − | 0.824618i | \(-0.308610\pi\) | ||||
0.565690 | + | 0.824618i | \(0.308610\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1714.69 | −0.0657963 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6960.95 | −0.266198 | −0.133099 | − | 0.991103i | \(-0.542493\pi\) | ||||
−0.133099 | + | 0.991103i | \(0.542493\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31161.5 | −1.18762 | −0.593810 | − | 0.804605i | \(-0.702377\pi\) | ||||
−0.593810 | + | 0.804605i | \(0.702377\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8082.04 | 0.306977 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17886.8 | −0.677091 | −0.338545 | − | 0.940950i | \(-0.609935\pi\) | ||||
−0.338545 | + | 0.940950i | \(0.609935\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2357.48 | 0.0889398 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35570.2 | 1.33743 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9178.78 | 0.343960 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 43745.8 | 1.63381 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4468.82 | 0.166343 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16560.7 | 0.614384 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11815.1 | 0.436866 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 410.366 | 0.0151231 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1133.11 | 0.0416199 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23803.3 | 0.871417 | 0.435709 | − | 0.900088i | \(-0.356498\pi\) | ||||
0.435709 | + | 0.900088i | \(0.356498\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −23962.9 | −0.874366 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41133.8 | 1.49596 | 0.747982 | − | 0.663719i | \(-0.231023\pi\) | ||||
0.747982 | + | 0.663719i | \(0.231023\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50183.0 | 1.81908 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4383.73 | 0.158384 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4758.91 | −0.171377 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9314.09 | 0.334324 | 0.167162 | − | 0.985929i | \(-0.446540\pi\) | ||||
0.167162 | + | 0.985929i | \(0.446540\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11788.0 | −0.421747 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −62645.9 | −2.23404 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1087.86 | 0.0386686 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 45638.7 | 1.61701 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29566.7 | −1.04419 | −0.522095 | − | 0.852887i | \(-0.674849\pi\) | ||||
−0.522095 | + | 0.852887i | \(0.674849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5898.71 | −0.207650 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3719.60 | 0.130519 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −73748.7 | −2.57951 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53866.5 | 1.87806 | 0.939029 | − | 0.343837i | \(-0.111727\pi\) | ||||
0.939029 | + | 0.343837i | \(0.111727\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3651.31 | 0.126897 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47012.9 | −1.62867 | −0.814334 | − | 0.580396i | \(-0.802898\pi\) | ||||
−0.814334 | + | 0.580396i | \(0.802898\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6912.14 | −0.238696 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4165.89 | −0.143404 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24305.9 | 0.834038 | 0.417019 | − | 0.908898i | \(-0.363075\pi\) | ||||
0.417019 | + | 0.908898i | \(0.363075\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −62067.7 | −2.12308 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8525.00 | 0.290686 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29214.7 | 0.993028 | 0.496514 | − | 0.868029i | \(-0.334613\pi\) | ||||
0.496514 | + | 0.868029i | \(0.334613\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36313.4 | 1.23045 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4967.43 | −0.167789 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 896.676 | 0.0301931 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32058.0 | 1.07610 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30666.0 | 1.02616 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12203.8 | −0.407102 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32370.0 | −1.07647 | −0.538236 | − | 0.842794i | \(-0.680909\pi\) | ||||
−0.538236 | + | 0.842794i | \(0.680909\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2716.60 | −0.0900617 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44819.7 | 1.48129 | 0.740644 | − | 0.671897i | \(-0.234520\pi\) | ||||
0.740644 | + | 0.671897i | \(0.234520\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13976.5 | 0.460499 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −365.781 | −0.0120147 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44799.8 | 1.46701 | 0.733507 | − | 0.679682i | \(-0.237882\pi\) | ||||
0.733507 | + | 0.679682i | \(0.237882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 41596.7 | 1.35795 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16281.7 | 0.529904 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29289.2 | −0.950335 | −0.475167 | − | 0.879895i | \(-0.657612\pi\) | ||||
−0.475167 | + | 0.879895i | \(0.657612\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16044.4 | −0.519004 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3481.00 | 0.112261 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2287.71 | 0.0735542 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23400.6 | −0.750096 | −0.375048 | − | 0.927005i | \(-0.622374\pi\) | ||||
−0.375048 | + | 0.927005i | \(0.622374\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11612.7 | 0.371116 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19820.4 | −0.631506 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −59994.4 | −1.90576 | −0.952880 | − | 0.303349i | \(-0.901895\pi\) | ||||
−0.952880 | + | 0.303349i | \(0.901895\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21900.8 | 0.693604 |
(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 | 76.4.a.b.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 684.4.a.i.1.1 | 3 | |||
4.3 | odd | 2 | 304.4.a.h.1.2 | 3 | |||
5.2 | odd | 4 | 1900.4.c.c.1749.3 | 6 | |||
5.3 | odd | 4 | 1900.4.c.c.1749.4 | 6 | |||
5.4 | even | 2 | 1900.4.a.c.1.2 | 3 | |||
8.3 | odd | 2 | 1216.4.a.v.1.2 | 3 | |||
8.5 | even | 2 | 1216.4.a.t.1.2 | 3 | |||
19.18 | odd | 2 | 1444.4.a.e.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.4.a.b.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
304.4.a.h.1.2 | 3 | 4.3 | odd | 2 | |||
684.4.a.i.1.1 | 3 | 3.2 | odd | 2 | |||
1216.4.a.t.1.2 | 3 | 8.5 | even | 2 | |||
1216.4.a.v.1.2 | 3 | 8.3 | odd | 2 | |||
1444.4.a.e.1.2 | 3 | 19.18 | odd | 2 | |||
1900.4.a.c.1.2 | 3 | 5.4 | even | 2 | |||
1900.4.c.c.1749.3 | 6 | 5.2 | odd | 4 | |||
1900.4.c.c.1749.4 | 6 | 5.3 | odd | 4 |