Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,4,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(92.9280082590\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.78066700.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 18x^{3} + 7x^{2} + 30x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.35311\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.20666 | 0.780172 | 0.390086 | − | 0.920778i | \(-0.372445\pi\) | ||||
0.390086 | + | 0.920778i | \(0.372445\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.13065 | −0.391332 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −24.5616 | −1.08548 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −56.2010 | −1.54048 | −0.770238 | − | 0.637757i | \(-0.779862\pi\) | ||||
−0.770238 | + | 0.637757i | \(0.779862\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38.9026 | 0.829972 | 0.414986 | − | 0.909828i | \(-0.363786\pi\) | ||||
0.414986 | + | 0.909828i | \(0.363786\pi\) | |||||||
\(14\) | 15.4466 | 0.294877 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −29.1538 | −0.455528 | ||||||||
\(17\) | 119.322 | 1.70235 | 0.851173 | − | 0.524886i | \(-0.175892\pi\) | ||||
0.851173 | + | 0.524886i | \(0.175892\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −13.0045 | −0.157023 | −0.0785113 | − | 0.996913i | \(-0.525017\pi\) | ||||
−0.0785113 | + | 0.996913i | \(0.525017\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −124.016 | −1.20184 | ||||||||
\(23\) | 130.565 | 1.18368 | 0.591840 | − | 0.806055i | \(-0.298402\pi\) | ||||
0.591840 | + | 0.806055i | \(0.298402\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 85.8448 | 0.647521 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −21.9146 | −0.147910 | ||||||||
\(29\) | −77.9925 | −0.499408 | −0.249704 | − | 0.968322i | \(-0.580333\pi\) | ||||
−0.249704 | + | 0.968322i | \(0.580333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 61.0660 | 0.353799 | 0.176900 | − | 0.984229i | \(-0.443393\pi\) | ||||
0.176900 | + | 0.984229i | \(0.443393\pi\) | |||||||
\(32\) | 132.160 | 0.730088 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 263.303 | 1.32812 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 167.391 | 0.743757 | 0.371878 | − | 0.928282i | \(-0.378714\pi\) | ||||
0.371878 | + | 0.928282i | \(0.378714\pi\) | |||||||
\(38\) | −28.6964 | −0.122505 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −436.142 | −1.66132 | −0.830658 | − | 0.556783i | \(-0.812036\pi\) | ||||
−0.830658 | + | 0.556783i | \(0.812036\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −393.030 | −1.39387 | −0.696936 | − | 0.717134i | \(-0.745454\pi\) | ||||
−0.696936 | + | 0.717134i | \(0.745454\pi\) | |||||||
\(44\) | 175.946 | 0.602837 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 288.112 | 0.923474 | ||||||||
\(47\) | −365.271 | −1.13362 | −0.566811 | − | 0.823848i | \(-0.691823\pi\) | ||||
−0.566811 | + | 0.823848i | \(0.691823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −121.791 | −0.324794 | ||||||||
\(53\) | 282.048 | 0.730987 | 0.365494 | − | 0.930814i | \(-0.380900\pi\) | ||||
0.365494 | + | 0.930814i | \(0.380900\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −171.931 | −0.410272 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −172.103 | −0.389624 | ||||||||
\(59\) | −414.842 | −0.915388 | −0.457694 | − | 0.889110i | \(-0.651324\pi\) | ||||
−0.457694 | + | 0.889110i | \(0.651324\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −563.802 | −1.18340 | −0.591701 | − | 0.806158i | \(-0.701543\pi\) | ||||
−0.591701 | + | 0.806158i | \(0.701543\pi\) | |||||||
\(62\) | 134.752 | 0.276024 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 524.862 | 1.02512 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 395.230 | 0.720673 | 0.360336 | − | 0.932822i | \(-0.382662\pi\) | ||||
0.360336 | + | 0.932822i | \(0.382662\pi\) | |||||||
\(68\) | −373.556 | −0.666182 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −103.990 | −0.173821 | −0.0869107 | − | 0.996216i | \(-0.527699\pi\) | ||||
−0.0869107 | + | 0.996216i | \(0.527699\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −128.026 | −0.205264 | −0.102632 | − | 0.994719i | \(-0.532726\pi\) | ||||
−0.102632 | + | 0.994719i | \(0.532726\pi\) | |||||||
\(74\) | 369.376 | 0.580258 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 40.7125 | 0.0614479 | ||||||||
\(77\) | −393.407 | −0.582245 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −641.999 | −0.914310 | −0.457155 | − | 0.889387i | \(-0.651132\pi\) | ||||
−0.457155 | + | 0.889387i | \(0.651132\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −962.417 | −1.29611 | ||||||||
\(83\) | −512.010 | −0.677113 | −0.338557 | − | 0.940946i | \(-0.609939\pi\) | ||||
−0.338557 | + | 0.940946i | \(0.609939\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −867.283 | −1.08746 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1380.38 | 1.67215 | ||||||||
\(89\) | −1225.10 | −1.45911 | −0.729554 | − | 0.683923i | \(-0.760272\pi\) | ||||
−0.729554 | + | 0.683923i | \(0.760272\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 272.318 | 0.313700 | ||||||||
\(92\) | −408.753 | −0.463212 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −806.028 | −0.884420 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 186.760 | 0.195491 | 0.0977454 | − | 0.995211i | \(-0.468837\pi\) | ||||
0.0977454 | + | 0.995211i | \(0.468837\pi\) | |||||||
\(98\) | 108.126 | 0.111453 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1650.68 | −1.62623 | −0.813114 | − | 0.582104i | \(-0.802230\pi\) | ||||
−0.813114 | + | 0.582104i | \(0.802230\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −72.1876 | −0.0690568 | −0.0345284 | − | 0.999404i | \(-0.510993\pi\) | ||||
−0.0345284 | + | 0.999404i | \(0.510993\pi\) | |||||||
\(104\) | −955.508 | −0.900916 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 622.385 | 0.570296 | ||||||||
\(107\) | 1202.55 | 1.08649 | 0.543246 | − | 0.839574i | \(-0.317195\pi\) | ||||
0.543246 | + | 0.839574i | \(0.317195\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1551.36 | −1.36324 | −0.681622 | − | 0.731704i | \(-0.738725\pi\) | ||||
−0.681622 | + | 0.731704i | \(0.738725\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −204.076 | −0.172173 | ||||||||
\(113\) | −2080.90 | −1.73234 | −0.866170 | − | 0.499749i | \(-0.833426\pi\) | ||||
−0.866170 | + | 0.499749i | \(0.833426\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 244.167 | 0.195434 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −915.416 | −0.714160 | ||||||||
\(119\) | 835.255 | 0.643426 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1827.55 | 1.37306 | ||||||||
\(122\) | −1244.12 | −0.923257 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −191.177 | −0.138453 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1414.70 | 0.988461 | 0.494231 | − | 0.869331i | \(-0.335450\pi\) | ||||
0.494231 | + | 0.869331i | \(0.335450\pi\) | |||||||
\(128\) | 100.912 | 0.0696832 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2472.51 | 1.64904 | 0.824520 | − | 0.565833i | \(-0.191445\pi\) | ||||
0.824520 | + | 0.565833i | \(0.191445\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −91.0313 | −0.0593490 | ||||||||
\(134\) | 872.139 | 0.562249 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2930.74 | −1.84786 | ||||||||
\(137\) | 214.391 | 0.133698 | 0.0668491 | − | 0.997763i | \(-0.478705\pi\) | ||||
0.0668491 | + | 0.997763i | \(0.478705\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 942.774 | 0.575288 | 0.287644 | − | 0.957737i | \(-0.407128\pi\) | ||||
0.287644 | + | 0.957737i | \(0.407128\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −229.470 | −0.135611 | ||||||||
\(143\) | −2186.36 | −1.27855 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −282.509 | −0.160141 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −524.045 | −0.291056 | ||||||||
\(149\) | −1693.07 | −0.930882 | −0.465441 | − | 0.885079i | \(-0.654104\pi\) | ||||
−0.465441 | + | 0.885079i | \(0.654104\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2519.69 | 1.35795 | 0.678973 | − | 0.734163i | \(-0.262425\pi\) | ||||
0.678973 | + | 0.734163i | \(0.262425\pi\) | |||||||
\(152\) | 319.410 | 0.170445 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −868.115 | −0.454251 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1621.48 | 0.824258 | 0.412129 | − | 0.911125i | \(-0.364785\pi\) | ||||
0.412129 | + | 0.911125i | \(0.364785\pi\) | |||||||
\(158\) | −1416.67 | −0.713319 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 913.954 | 0.447389 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 925.194 | 0.444582 | 0.222291 | − | 0.974980i | \(-0.428647\pi\) | ||||
0.222291 | + | 0.974980i | \(0.428647\pi\) | |||||||
\(164\) | 1365.41 | 0.650126 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1129.83 | −0.528265 | ||||||||
\(167\) | −2681.55 | −1.24254 | −0.621271 | − | 0.783596i | \(-0.713383\pi\) | ||||
−0.621271 | + | 0.783596i | \(0.713383\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −683.589 | −0.311147 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1230.44 | 0.545466 | ||||||||
\(173\) | −287.591 | −0.126388 | −0.0631940 | − | 0.998001i | \(-0.520129\pi\) | ||||
−0.0631940 | + | 0.998001i | \(0.520129\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1638.47 | 0.701729 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2703.38 | −1.13835 | ||||||||
\(179\) | −3683.47 | −1.53808 | −0.769038 | − | 0.639203i | \(-0.779265\pi\) | ||||
−0.769038 | + | 0.639203i | \(0.779265\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3132.65 | 1.28645 | 0.643227 | − | 0.765676i | \(-0.277595\pi\) | ||||
0.643227 | + | 0.765676i | \(0.277595\pi\) | |||||||
\(182\) | 600.913 | 0.244740 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3206.88 | −1.28486 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6706.02 | −2.62242 | ||||||||
\(188\) | 1143.54 | 0.443622 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1586.93 | −0.601184 | −0.300592 | − | 0.953753i | \(-0.597184\pi\) | ||||
−0.300592 | + | 0.953753i | \(0.597184\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5179.00 | −1.93157 | −0.965783 | − | 0.259352i | \(-0.916491\pi\) | ||||
−0.965783 | + | 0.259352i | \(0.916491\pi\) | |||||||
\(194\) | 412.116 | 0.152516 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −153.402 | −0.0559045 | ||||||||
\(197\) | −903.798 | −0.326868 | −0.163434 | − | 0.986554i | \(-0.552257\pi\) | ||||
−0.163434 | + | 0.986554i | \(0.552257\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1171.51 | −0.417317 | −0.208659 | − | 0.977989i | \(-0.566910\pi\) | ||||
−0.208659 | + | 0.977989i | \(0.566910\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3642.50 | −1.26874 | ||||||||
\(203\) | −545.947 | −0.188759 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −159.293 | −0.0538762 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1134.16 | −0.378075 | ||||||||
\(209\) | 730.864 | 0.241889 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1103.16 | −0.359928 | −0.179964 | − | 0.983673i | \(-0.557598\pi\) | ||||
−0.179964 | + | 0.983673i | \(0.557598\pi\) | |||||||
\(212\) | −882.996 | −0.286059 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2653.61 | 0.847651 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 427.462 | 0.133724 | ||||||||
\(218\) | −3423.33 | −1.06357 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4641.94 | 1.41290 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4079.95 | 1.22517 | 0.612586 | − | 0.790404i | \(-0.290129\pi\) | ||||
0.612586 | + | 0.790404i | \(0.290129\pi\) | |||||||
\(224\) | 925.120 | 0.275947 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4591.83 | −1.35152 | ||||||||
\(227\) | −931.964 | −0.272496 | −0.136248 | − | 0.990675i | \(-0.543504\pi\) | ||||
−0.136248 | + | 0.990675i | \(0.543504\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1471.55 | −0.424641 | −0.212321 | − | 0.977200i | \(-0.568102\pi\) | ||||
−0.212321 | + | 0.977200i | \(0.568102\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1915.62 | 0.542097 | ||||||||
\(233\) | −2479.06 | −0.697034 | −0.348517 | − | 0.937303i | \(-0.613315\pi\) | ||||
−0.348517 | + | 0.937303i | \(0.613315\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1298.73 | 0.358220 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1843.12 | 0.501983 | ||||||||
\(239\) | 954.068 | 0.258216 | 0.129108 | − | 0.991631i | \(-0.458789\pi\) | ||||
0.129108 | + | 0.991631i | \(0.458789\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5297.02 | −1.41581 | −0.707906 | − | 0.706306i | \(-0.750360\pi\) | ||||
−0.707906 | + | 0.706306i | \(0.750360\pi\) | |||||||
\(242\) | 4032.77 | 1.07123 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1765.07 | 0.463103 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −505.907 | −0.130324 | ||||||||
\(248\) | −1499.88 | −0.384041 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1855.17 | −0.466524 | −0.233262 | − | 0.972414i | \(-0.574940\pi\) | ||||
−0.233262 | + | 0.972414i | \(0.574940\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7337.87 | −1.82343 | ||||||||
\(254\) | 3121.77 | 0.771170 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3976.22 | −0.970757 | ||||||||
\(257\) | −6233.09 | −1.51288 | −0.756438 | − | 0.654065i | \(-0.773062\pi\) | ||||
−0.756438 | + | 0.654065i | \(0.773062\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1171.74 | 0.281114 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5455.99 | 1.28653 | ||||||||
\(263\) | −1184.50 | −0.277716 | −0.138858 | − | 0.990312i | \(-0.544343\pi\) | ||||
−0.138858 | + | 0.990312i | \(0.544343\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −200.875 | −0.0463024 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1237.33 | −0.282022 | ||||||||
\(269\) | 1916.03 | 0.434283 | 0.217141 | − | 0.976140i | \(-0.430327\pi\) | ||||
0.217141 | + | 0.976140i | \(0.430327\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1168.95 | −0.262025 | −0.131013 | − | 0.991381i | \(-0.541823\pi\) | ||||
−0.131013 | + | 0.991381i | \(0.541823\pi\) | |||||||
\(272\) | −3478.69 | −0.775465 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 473.088 | 0.104308 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7269.54 | −1.57684 | −0.788419 | − | 0.615138i | \(-0.789100\pi\) | ||||
−0.788419 | + | 0.615138i | \(0.789100\pi\) | |||||||
\(278\) | 2080.38 | 0.448824 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −298.126 | −0.0632908 | −0.0316454 | − | 0.999499i | \(-0.510075\pi\) | ||||
−0.0316454 | + | 0.999499i | \(0.510075\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4496.30 | 0.944444 | 0.472222 | − | 0.881480i | \(-0.343452\pi\) | ||||
0.472222 | + | 0.881480i | \(0.343452\pi\) | |||||||
\(284\) | 325.556 | 0.0680218 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4824.56 | −0.997490 | ||||||||
\(287\) | −3053.00 | −0.627919 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9324.77 | 1.89798 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 400.804 | 0.0803264 | ||||||||
\(293\) | −1644.33 | −0.327859 | −0.163929 | − | 0.986472i | \(-0.552417\pi\) | ||||
−0.163929 | + | 0.986472i | \(0.552417\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4111.40 | −0.807331 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3736.02 | −0.726248 | ||||||||
\(299\) | 5079.31 | 0.982421 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2751.21 | −0.526834 | ||||||||
\(302\) | 5560.11 | 1.05943 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 379.129 | 0.0715281 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4726.18 | 0.878623 | 0.439312 | − | 0.898335i | \(-0.355222\pi\) | ||||
0.439312 | + | 0.898335i | \(0.355222\pi\) | |||||||
\(308\) | 1231.62 | 0.227851 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4853.99 | 0.885031 | 0.442515 | − | 0.896761i | \(-0.354086\pi\) | ||||
0.442515 | + | 0.896761i | \(0.354086\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1690.87 | −0.305348 | −0.152674 | − | 0.988277i | \(-0.548788\pi\) | ||||
−0.152674 | + | 0.988277i | \(0.548788\pi\) | |||||||
\(314\) | 3578.06 | 0.643063 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2009.88 | 0.357799 | ||||||||
\(317\) | −3878.38 | −0.687166 | −0.343583 | − | 0.939122i | \(-0.611641\pi\) | ||||
−0.343583 | + | 0.939122i | \(0.611641\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4383.25 | 0.769326 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2016.78 | 0.349040 | ||||||||
\(323\) | −1551.72 | −0.267307 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2041.59 | 0.346850 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10712.3 | 1.80332 | ||||||||
\(329\) | −2556.90 | −0.428469 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9927.71 | 1.64857 | 0.824284 | − | 0.566176i | \(-0.191578\pi\) | ||||
0.824284 | + | 0.566176i | \(0.191578\pi\) | |||||||
\(332\) | 1602.93 | 0.264976 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5917.26 | −0.969396 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5283.88 | 0.854099 | 0.427050 | − | 0.904228i | \(-0.359553\pi\) | ||||
0.427050 | + | 0.904228i | \(0.359553\pi\) | |||||||
\(338\) | −1508.45 | −0.242748 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3431.97 | −0.545019 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 9653.42 | 1.51302 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −634.615 | −0.0986044 | ||||||||
\(347\) | 10548.3 | 1.63188 | 0.815940 | − | 0.578137i | \(-0.196220\pi\) | ||||
0.815940 | + | 0.578137i | \(0.196220\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 628.411 | 0.0963841 | 0.0481921 | − | 0.998838i | \(-0.484654\pi\) | ||||
0.0481921 | + | 0.998838i | \(0.484654\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7427.52 | −1.12468 | ||||||||
\(353\) | −2548.17 | −0.384209 | −0.192104 | − | 0.981375i | \(-0.561531\pi\) | ||||
−0.192104 | + | 0.981375i | \(0.561531\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3835.37 | 0.570995 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8128.17 | −1.19996 | ||||||||
\(359\) | −13046.3 | −1.91799 | −0.958996 | − | 0.283420i | \(-0.908531\pi\) | ||||
−0.958996 | + | 0.283420i | \(0.908531\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6689.88 | −0.975344 | ||||||||
\(362\) | 6912.69 | 1.00366 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −852.534 | −0.122761 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8068.23 | 1.14757 | 0.573785 | − | 0.819006i | \(-0.305475\pi\) | ||||
0.573785 | + | 0.819006i | \(0.305475\pi\) | |||||||
\(368\) | −3806.46 | −0.539199 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1974.34 | 0.276287 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3623.32 | −0.502972 | −0.251486 | − | 0.967861i | \(-0.580919\pi\) | ||||
−0.251486 | + | 0.967861i | \(0.580919\pi\) | |||||||
\(374\) | −14797.9 | −2.04594 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8971.62 | 1.23052 | ||||||||
\(377\) | −3034.11 | −0.414495 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7486.58 | 1.01467 | 0.507335 | − | 0.861749i | \(-0.330631\pi\) | ||||
0.507335 | + | 0.861749i | \(0.330631\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3501.81 | −0.469027 | ||||||||
\(383\) | −8926.58 | −1.19093 | −0.595466 | − | 0.803381i | \(-0.703033\pi\) | ||||
−0.595466 | + | 0.803381i | \(0.703033\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11428.3 | −1.50695 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −584.681 | −0.0765018 | ||||||||
\(389\) | 12600.1 | 1.64228 | 0.821141 | − | 0.570725i | \(-0.193338\pi\) | ||||
0.821141 | + | 0.570725i | \(0.193338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15579.3 | 2.01503 | ||||||||
\(392\) | −1203.52 | −0.155068 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1994.37 | −0.255013 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12713.4 | −1.60722 | −0.803612 | − | 0.595154i | \(-0.797091\pi\) | ||||
−0.803612 | + | 0.595154i | \(0.797091\pi\) | |||||||
\(398\) | −2585.12 | −0.325579 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6133.51 | 0.763822 | 0.381911 | − | 0.924199i | \(-0.375266\pi\) | ||||
0.381911 | + | 0.924199i | \(0.375266\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2375.62 | 0.293643 | ||||||||
\(404\) | 5167.72 | 0.636395 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1204.72 | −0.147264 | ||||||||
\(407\) | −9407.56 | −1.14574 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10600.3 | 1.28154 | 0.640769 | − | 0.767733i | \(-0.278615\pi\) | ||||
0.640769 | + | 0.767733i | \(0.278615\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 225.994 | 0.0270241 | ||||||||
\(413\) | −2903.90 | −0.345984 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5141.37 | 0.605953 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1612.77 | 0.188715 | ||||||||
\(419\) | −4296.43 | −0.500941 | −0.250470 | − | 0.968124i | \(-0.580585\pi\) | ||||
−0.250470 | + | 0.968124i | \(0.580585\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3916.78 | 0.453425 | 0.226713 | − | 0.973962i | \(-0.427202\pi\) | ||||
0.226713 | + | 0.973962i | \(0.427202\pi\) | |||||||
\(422\) | −2434.30 | −0.280806 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6927.55 | −0.793471 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3946.62 | −0.447284 | ||||||||
\(428\) | −3764.76 | −0.425179 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13408.9 | −1.49857 | −0.749287 | − | 0.662246i | \(-0.769604\pi\) | ||||
−0.749287 | + | 0.662246i | \(0.769604\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7792.31 | 0.864837 | 0.432419 | − | 0.901673i | \(-0.357660\pi\) | ||||
0.432419 | + | 0.901673i | \(0.357660\pi\) | |||||||
\(434\) | 943.263 | 0.104327 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4856.78 | 0.533481 | ||||||||
\(437\) | −1697.93 | −0.185865 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1039.29 | 0.112990 | 0.0564948 | − | 0.998403i | \(-0.482008\pi\) | ||||
0.0564948 | + | 0.998403i | \(0.482008\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10243.2 | 1.10230 | ||||||||
\(443\) | 2846.33 | 0.305267 | 0.152633 | − | 0.988283i | \(-0.451225\pi\) | ||||
0.152633 | + | 0.988283i | \(0.451225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9003.05 | 0.955845 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3674.04 | 0.387460 | ||||||||
\(449\) | −7472.64 | −0.785425 | −0.392713 | − | 0.919661i | \(-0.628463\pi\) | ||||
−0.392713 | + | 0.919661i | \(0.628463\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24511.6 | 2.55922 | ||||||||
\(452\) | 6514.57 | 0.677920 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2056.53 | −0.212594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11014.3 | −1.12742 | −0.563708 | − | 0.825974i | \(-0.690626\pi\) | ||||
−0.563708 | + | 0.825974i | \(0.690626\pi\) | |||||||
\(458\) | −3247.21 | −0.331293 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7944.67 | −0.802647 | −0.401323 | − | 0.915936i | \(-0.631450\pi\) | ||||
−0.401323 | + | 0.915936i | \(0.631450\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7627.25 | −0.765591 | −0.382795 | − | 0.923833i | \(-0.625039\pi\) | ||||
−0.382795 | + | 0.923833i | \(0.625039\pi\) | |||||||
\(464\) | 2273.77 | 0.227494 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5470.45 | −0.543806 | ||||||||
\(467\) | 3284.28 | 0.325436 | 0.162718 | − | 0.986673i | \(-0.447974\pi\) | ||||
0.162718 | + | 0.986673i | \(0.447974\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2766.61 | 0.272389 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10189.2 | 0.993633 | ||||||||
\(473\) | 22088.6 | 2.14722 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2614.89 | −0.251793 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2105.30 | 0.201453 | ||||||||
\(479\) | 2909.45 | 0.277528 | 0.138764 | − | 0.990325i | \(-0.455687\pi\) | ||||
0.138764 | + | 0.990325i | \(0.455687\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6511.96 | 0.617297 | ||||||||
\(482\) | −11688.7 | −1.10458 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5721.42 | −0.537323 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2201.84 | −0.204876 | −0.102438 | − | 0.994739i | \(-0.532664\pi\) | ||||
−0.102438 | + | 0.994739i | \(0.532664\pi\) | |||||||
\(488\) | 13847.9 | 1.28456 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11827.6 | 1.08711 | 0.543556 | − | 0.839373i | \(-0.317078\pi\) | ||||
0.543556 | + | 0.839373i | \(0.317078\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9306.23 | −0.850165 | ||||||||
\(494\) | −1116.37 | −0.101675 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1780.30 | −0.161165 | ||||||||
\(497\) | −727.928 | −0.0656983 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1408.66 | 0.126374 | 0.0631868 | − | 0.998002i | \(-0.479874\pi\) | ||||
0.0631868 | + | 0.998002i | \(0.479874\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4093.74 | −0.363969 | ||||||||
\(503\) | 11018.9 | 0.976758 | 0.488379 | − | 0.872632i | \(-0.337588\pi\) | ||||
0.488379 | + | 0.872632i | \(0.337588\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −16192.2 | −1.42259 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4428.95 | −0.386816 | ||||||||
\(509\) | −7032.93 | −0.612434 | −0.306217 | − | 0.951962i | \(-0.599063\pi\) | ||||
−0.306217 | + | 0.951962i | \(0.599063\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −896.180 | −0.0775825 | ||||||||
\(512\) | −9581.46 | −0.827041 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13754.3 | −1.18030 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20528.6 | 1.74632 | ||||||||
\(518\) | 2585.63 | 0.219317 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3049.04 | −0.256394 | −0.128197 | − | 0.991749i | \(-0.540919\pi\) | ||||
−0.128197 | + | 0.991749i | \(0.540919\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8714.06 | 0.728564 | 0.364282 | − | 0.931289i | \(-0.381314\pi\) | ||||
0.364282 | + | 0.931289i | \(0.381314\pi\) | |||||||
\(524\) | −7740.58 | −0.645322 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2613.79 | −0.216666 | ||||||||
\(527\) | 7286.52 | 0.602288 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4880.17 | 0.401099 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 284.987 | 0.0232251 | ||||||||
\(533\) | −16967.1 | −1.37885 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9707.48 | −0.782275 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4228.02 | 0.338815 | ||||||||
\(539\) | −2753.85 | −0.220068 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5999.45 | −0.476778 | −0.238389 | − | 0.971170i | \(-0.576619\pi\) | ||||
−0.238389 | + | 0.971170i | \(0.576619\pi\) | |||||||
\(542\) | −2579.48 | −0.204425 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15769.6 | 1.24286 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7759.95 | 0.606566 | 0.303283 | − | 0.952901i | \(-0.401917\pi\) | ||||
0.303283 | + | 0.952901i | \(0.401917\pi\) | |||||||
\(548\) | −671.184 | −0.0523203 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1014.25 | 0.0784184 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4493.99 | −0.345577 | ||||||||
\(554\) | −16041.4 | −1.23021 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2951.50 | −0.225128 | ||||||||
\(557\) | 6392.82 | 0.486306 | 0.243153 | − | 0.969988i | \(-0.421818\pi\) | ||||
0.243153 | + | 0.969988i | \(0.421818\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15289.9 | −1.15687 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −657.863 | −0.0493777 | ||||||||
\(563\) | 7682.70 | 0.575111 | 0.287555 | − | 0.957764i | \(-0.407157\pi\) | ||||
0.287555 | + | 0.957764i | \(0.407157\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9921.81 | 0.736828 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2554.15 | 0.188679 | ||||||||
\(569\) | −143.175 | −0.0105487 | −0.00527434 | − | 0.999986i | \(-0.501679\pi\) | ||||
−0.00527434 | + | 0.999986i | \(0.501679\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1077.72 | 0.0789863 | 0.0394932 | − | 0.999220i | \(-0.487426\pi\) | ||||
0.0394932 | + | 0.999220i | \(0.487426\pi\) | |||||||
\(572\) | 6844.74 | 0.500338 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6736.92 | −0.489884 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12651.7 | −0.912818 | −0.456409 | − | 0.889770i | \(-0.650865\pi\) | ||||
−0.456409 | + | 0.889770i | \(0.650865\pi\) | |||||||
\(578\) | 20576.6 | 1.48075 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3584.07 | −0.255925 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15851.4 | −1.12607 | ||||||||
\(584\) | 3144.51 | 0.222810 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3628.47 | −0.255786 | ||||||||
\(587\) | 2920.89 | 0.205380 | 0.102690 | − | 0.994713i | \(-0.467255\pi\) | ||||
0.102690 | + | 0.994713i | \(0.467255\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −794.131 | −0.0555545 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4880.09 | −0.338802 | ||||||||
\(593\) | 9801.70 | 0.678765 | 0.339382 | − | 0.940648i | \(-0.389782\pi\) | ||||
0.339382 | + | 0.940648i | \(0.389782\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5300.41 | 0.364284 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11208.3 | 0.766458 | ||||||||
\(599\) | 6992.54 | 0.476974 | 0.238487 | − | 0.971146i | \(-0.423349\pi\) | ||||
0.238487 | + | 0.971146i | \(0.423349\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26159.1 | −1.77546 | −0.887730 | − | 0.460364i | \(-0.847719\pi\) | ||||
−0.887730 | + | 0.460364i | \(0.847719\pi\) | |||||||
\(602\) | −6070.98 | −0.411021 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7888.29 | −0.531407 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 264.526 | 0.0176883 | 0.00884415 | − | 0.999961i | \(-0.497185\pi\) | ||||
0.00884415 | + | 0.999961i | \(0.497185\pi\) | |||||||
\(608\) | −1718.67 | −0.114640 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14210.0 | −0.940875 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29371.1 | 1.93521 | 0.967607 | − | 0.252461i | \(-0.0812400\pi\) | ||||
0.967607 | + | 0.252461i | \(0.0812400\pi\) | |||||||
\(614\) | 10429.1 | 0.685477 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9662.68 | 0.632014 | ||||||||
\(617\) | 26226.1 | 1.71122 | 0.855609 | − | 0.517622i | \(-0.173183\pi\) | ||||
0.855609 | + | 0.517622i | \(0.173183\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8903.12 | −0.578105 | −0.289052 | − | 0.957313i | \(-0.593340\pi\) | ||||
−0.289052 | + | 0.957313i | \(0.593340\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10711.1 | 0.690476 | ||||||||
\(623\) | −8575.72 | −0.551491 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3731.18 | −0.238224 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5076.31 | −0.322558 | ||||||||
\(629\) | 19973.5 | 1.26613 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14136.0 | −0.891832 | −0.445916 | − | 0.895075i | \(-0.647122\pi\) | ||||
−0.445916 | + | 0.895075i | \(0.647122\pi\) | |||||||
\(632\) | 15768.5 | 0.992464 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8558.27 | −0.536108 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1906.23 | 0.118567 | ||||||||
\(638\) | 9672.34 | 0.600206 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17665.7 | −1.08854 | −0.544270 | − | 0.838910i | \(-0.683193\pi\) | ||||
−0.544270 | + | 0.838910i | \(0.683193\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10890.0 | 0.667901 | 0.333951 | − | 0.942591i | \(-0.391618\pi\) | ||||
0.333951 | + | 0.942591i | \(0.391618\pi\) | |||||||
\(644\) | −2861.27 | −0.175078 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3424.12 | −0.208545 | ||||||||
\(647\) | −24281.0 | −1.47540 | −0.737701 | − | 0.675128i | \(-0.764089\pi\) | ||||
−0.737701 | + | 0.675128i | \(0.764089\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23314.5 | 1.41013 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2896.46 | −0.173979 | ||||||||
\(653\) | −1865.16 | −0.111776 | −0.0558878 | − | 0.998437i | \(-0.517799\pi\) | ||||
−0.0558878 | + | 0.998437i | \(0.517799\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 12715.2 | 0.756775 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5642.20 | −0.334279 | ||||||||
\(659\) | 8327.14 | 0.492230 | 0.246115 | − | 0.969241i | \(-0.420846\pi\) | ||||
0.246115 | + | 0.969241i | \(0.420846\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20665.7 | −1.21604 | −0.608021 | − | 0.793921i | \(-0.708036\pi\) | ||||
−0.608021 | + | 0.793921i | \(0.708036\pi\) | |||||||
\(662\) | 21907.1 | 1.28617 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12575.8 | 0.734991 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10183.1 | −0.591140 | ||||||||
\(668\) | 8395.00 | 0.486246 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31686.2 | 1.82300 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1283.48 | −0.0735136 | −0.0367568 | − | 0.999324i | \(-0.511703\pi\) | ||||
−0.0367568 | + | 0.999324i | \(0.511703\pi\) | |||||||
\(674\) | 11659.7 | 0.666344 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2140.08 | 0.121762 | ||||||||
\(677\) | 13783.2 | 0.782467 | 0.391234 | − | 0.920291i | \(-0.372048\pi\) | ||||
0.391234 | + | 0.920291i | \(0.372048\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1307.32 | 0.0738886 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7573.18 | −0.425208 | ||||||||
\(683\) | −10796.5 | −0.604856 | −0.302428 | − | 0.953172i | \(-0.597797\pi\) | ||||
−0.302428 | + | 0.953172i | \(0.597797\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 756.884 | 0.0421253 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11458.3 | 0.634947 | ||||||||
\(689\) | 10972.4 | 0.606699 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12082.4 | −0.665173 | −0.332587 | − | 0.943073i | \(-0.607921\pi\) | ||||
−0.332587 | + | 0.943073i | \(0.607921\pi\) | |||||||
\(692\) | 900.348 | 0.0494597 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23276.5 | 1.27315 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −52041.4 | −2.82813 | ||||||||
\(698\) | 1386.69 | 0.0751962 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28753.5 | 1.54922 | 0.774610 | − | 0.632439i | \(-0.217946\pi\) | ||||
0.774610 | + | 0.632439i | \(0.217946\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2176.84 | −0.116787 | ||||||||
\(704\) | −29497.8 | −1.57917 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5622.95 | −0.299749 | ||||||||
\(707\) | −11554.8 | −0.614657 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4577.21 | 0.242455 | 0.121228 | − | 0.992625i | \(-0.461317\pi\) | ||||
0.121228 | + | 0.992625i | \(0.461317\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 30090.4 | 1.58383 | ||||||||
\(713\) | 7973.07 | 0.418785 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11531.7 | 0.601898 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28788.8 | −1.49636 | ||||||||
\(719\) | −30875.9 | −1.60150 | −0.800749 | − | 0.599000i | \(-0.795565\pi\) | ||||
−0.800749 | + | 0.599000i | \(0.795565\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −505.313 | −0.0261010 | ||||||||
\(722\) | −14762.3 | −0.760936 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9807.25 | −0.503430 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −520.090 | −0.0265324 | −0.0132662 | − | 0.999912i | \(-0.504223\pi\) | ||||
−0.0132662 | + | 0.999912i | \(0.504223\pi\) | |||||||
\(728\) | −6688.56 | −0.340514 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −46897.1 | −2.37285 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 393.396 | 0.0198232 | 0.00991160 | − | 0.999951i | \(-0.496845\pi\) | ||||
0.00991160 | + | 0.999951i | \(0.496845\pi\) | |||||||
\(734\) | 17803.8 | 0.895301 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17255.5 | 0.864191 | ||||||||
\(737\) | −22212.3 | −1.11018 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9348.92 | −0.465366 | −0.232683 | − | 0.972553i | \(-0.574750\pi\) | ||||
−0.232683 | + | 0.972553i | \(0.574750\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4356.69 | 0.215552 | ||||||||
\(743\) | 33710.8 | 1.66451 | 0.832254 | − | 0.554394i | \(-0.187050\pi\) | ||||
0.832254 | + | 0.554394i | \(0.187050\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7995.44 | −0.392405 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 20994.2 | 1.02624 | ||||||||
\(749\) | 8417.83 | 0.410655 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21116.6 | −1.02604 | −0.513019 | − | 0.858377i | \(-0.671473\pi\) | ||||
−0.513019 | + | 0.858377i | \(0.671473\pi\) | |||||||
\(752\) | 10649.0 | 0.516396 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6695.24 | −0.323377 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7385.25 | 0.354586 | 0.177293 | − | 0.984158i | \(-0.443266\pi\) | ||||
0.177293 | + | 0.984158i | \(0.443266\pi\) | |||||||
\(758\) | 16520.3 | 0.791616 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27682.0 | 1.31862 | 0.659311 | − | 0.751871i | \(-0.270848\pi\) | ||||
0.659311 | + | 0.751871i | \(0.270848\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10859.5 | −0.515258 | ||||||||
\(764\) | 4968.12 | 0.235262 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19697.9 | −0.929132 | ||||||||
\(767\) | −16138.4 | −0.759746 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22248.6 | −1.04331 | −0.521654 | − | 0.853157i | \(-0.674685\pi\) | ||||
−0.521654 | + | 0.853157i | \(0.674685\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16213.6 | 0.755883 | ||||||||
\(773\) | −11372.3 | −0.529152 | −0.264576 | − | 0.964365i | \(-0.585232\pi\) | ||||
−0.264576 | + | 0.964365i | \(0.585232\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4587.12 | −0.212201 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27804.0 | 1.28126 | ||||||||
\(779\) | 5671.80 | 0.260864 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5844.32 | 0.267767 | ||||||||
\(782\) | 34378.1 | 1.57207 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1428.53 | −0.0650754 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36561.9 | 1.65602 | 0.828012 | − | 0.560710i | \(-0.189472\pi\) | ||||
0.828012 | + | 0.560710i | \(0.189472\pi\) | |||||||
\(788\) | 2829.48 | 0.127914 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14566.3 | −0.654763 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21933.4 | −0.982190 | ||||||||
\(794\) | −28054.2 | −1.25391 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3667.59 | 0.163309 | ||||||||
\(797\) | −7436.80 | −0.330521 | −0.165260 | − | 0.986250i | \(-0.552846\pi\) | ||||
−0.165260 | + | 0.986250i | \(0.552846\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43584.9 | −1.92982 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13534.6 | 0.595913 | ||||||||
\(803\) | 7195.17 | 0.316204 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5242.20 | 0.229092 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 40543.4 | 1.76524 | ||||||||
\(809\) | 30585.4 | 1.32920 | 0.664601 | − | 0.747198i | \(-0.268601\pi\) | ||||
0.664601 | + | 0.747198i | \(0.268601\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23756.0 | 1.02859 | 0.514294 | − | 0.857614i | \(-0.328054\pi\) | ||||
0.514294 | + | 0.857614i | \(0.328054\pi\) | |||||||
\(812\) | 1709.17 | 0.0738672 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20759.3 | −0.893873 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5111.14 | 0.218869 | ||||||||
\(818\) | 23391.2 | 0.999821 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33842.2 | 1.43861 | 0.719306 | − | 0.694694i | \(-0.244460\pi\) | ||||
0.719306 | + | 0.694694i | \(0.244460\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18730.9 | 0.793340 | 0.396670 | − | 0.917961i | \(-0.370166\pi\) | ||||
0.396670 | + | 0.917961i | \(0.370166\pi\) | |||||||
\(824\) | 1773.04 | 0.0749597 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6407.91 | −0.269927 | ||||||||
\(827\) | −19107.1 | −0.803409 | −0.401705 | − | 0.915769i | \(-0.631582\pi\) | ||||
−0.401705 | + | 0.915769i | \(0.631582\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9942.59 | 0.416551 | 0.208275 | − | 0.978070i | \(-0.433215\pi\) | ||||
0.208275 | + | 0.978070i | \(0.433215\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 20418.5 | 0.850822 | ||||||||
\(833\) | 5846.78 | 0.243192 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2288.08 | −0.0946590 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9480.75 | −0.390820 | ||||||||
\(839\) | −37144.9 | −1.52847 | −0.764233 | − | 0.644940i | \(-0.776882\pi\) | ||||
−0.764233 | + | 0.644940i | \(0.776882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18306.2 | −0.750591 | ||||||||
\(842\) | 8642.99 | 0.353750 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3453.62 | 0.140851 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12792.8 | 0.518969 | ||||||||
\(848\) | −8222.78 | −0.332985 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21855.4 | 0.880370 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31377.2 | 1.25948 | 0.629739 | − | 0.776807i | \(-0.283162\pi\) | ||||
0.629739 | + | 0.776807i | \(0.283162\pi\) | |||||||
\(854\) | −8708.84 | −0.348958 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −29536.4 | −1.17936 | ||||||||
\(857\) | −24561.3 | −0.978993 | −0.489496 | − | 0.872005i | \(-0.662819\pi\) | ||||
−0.489496 | + | 0.872005i | \(0.662819\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39819.1 | −1.58162 | −0.790809 | − | 0.612063i | \(-0.790340\pi\) | ||||
−0.790809 | + | 0.612063i | \(0.790340\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −29588.9 | −1.16914 | ||||||||
\(863\) | 14702.2 | 0.579919 | 0.289959 | − | 0.957039i | \(-0.406358\pi\) | ||||
0.289959 | + | 0.957039i | \(0.406358\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17195.0 | 0.674722 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1338.24 | −0.0523303 | ||||||||
\(869\) | 36081.0 | 1.40847 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15375.5 | 0.598138 | ||||||||
\(872\) | 38103.9 | 1.47977 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3746.74 | −0.145006 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7208.31 | −0.277546 | −0.138773 | − | 0.990324i | \(-0.544316\pi\) | ||||
−0.138773 | + | 0.990324i | \(0.544316\pi\) | |||||||
\(878\) | 2293.35 | 0.0881512 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3789.00 | −0.144898 | −0.0724488 | − | 0.997372i | \(-0.523081\pi\) | ||||
−0.0724488 | + | 0.997372i | \(0.523081\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26953.7 | 1.02725 | 0.513626 | − | 0.858014i | \(-0.328302\pi\) | ||||
0.513626 | + | 0.858014i | \(0.328302\pi\) | |||||||
\(884\) | −14532.3 | −0.552912 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6280.88 | 0.238160 | ||||||||
\(887\) | −37869.8 | −1.43353 | −0.716766 | − | 0.697314i | \(-0.754379\pi\) | ||||
−0.716766 | + | 0.697314i | \(0.754379\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9902.92 | 0.373603 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12772.9 | −0.479449 | ||||||||
\(893\) | 4750.15 | 0.178004 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 706.385 | 0.0263378 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16489.6 | −0.612767 | ||||||||
\(899\) | −4762.69 | −0.176690 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33654.6 | 1.24439 | ||||||||
\(902\) | 54088.8 | 1.99663 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 51110.1 | 1.88042 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11717.5 | −0.428968 | −0.214484 | − | 0.976728i | \(-0.568807\pi\) | ||||
−0.214484 | + | 0.976728i | \(0.568807\pi\) | |||||||
\(908\) | 2917.66 | 0.106636 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15909.2 | 0.578589 | 0.289294 | − | 0.957240i | \(-0.406579\pi\) | ||||
0.289294 | + | 0.957240i | \(0.406579\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28775.4 | 1.04308 | ||||||||
\(914\) | −24304.9 | −0.879578 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4606.92 | 0.166176 | ||||||||
\(917\) | 17307.6 | 0.623279 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32933.3 | −1.18212 | −0.591060 | − | 0.806628i | \(-0.701290\pi\) | ||||
−0.591060 | + | 0.806628i | \(0.701290\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17531.2 | −0.626203 | ||||||||
\(923\) | −4045.47 | −0.144267 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16830.7 | −0.597292 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −10307.5 | −0.364612 | ||||||||
\(929\) | 30912.6 | 1.09172 | 0.545861 | − | 0.837876i | \(-0.316203\pi\) | ||||
0.545861 | + | 0.837876i | \(0.316203\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −637.219 | −0.0224318 | ||||||||
\(932\) | 7761.09 | 0.272771 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7247.29 | 0.253896 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45737.6 | 1.59465 | 0.797323 | − | 0.603553i | \(-0.206249\pi\) | ||||
0.797323 | + | 0.603553i | \(0.206249\pi\) | |||||||
\(938\) | 6104.97 | 0.212510 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2137.79 | 0.0740595 | 0.0370297 | − | 0.999314i | \(-0.488210\pi\) | ||||
0.0370297 | + | 0.999314i | \(0.488210\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −56944.8 | −1.96647 | ||||||||
\(944\) | 12094.2 | 0.416984 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 48742.1 | 1.67520 | ||||||||
\(947\) | 42513.2 | 1.45881 | 0.729405 | − | 0.684082i | \(-0.239797\pi\) | ||||
0.729405 | + | 0.684082i | \(0.239797\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4980.53 | −0.170363 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −20515.2 | −0.698425 | ||||||||
\(953\) | −9012.85 | −0.306353 | −0.153177 | − | 0.988199i | \(-0.548950\pi\) | ||||
−0.153177 | + | 0.988199i | \(0.548950\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2986.86 | −0.101048 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6420.15 | 0.216520 | ||||||||
\(959\) | 1500.74 | 0.0505332 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26061.9 | −0.874826 | ||||||||
\(962\) | 14369.7 | 0.481598 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16583.1 | 0.554053 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29024.2 | −0.965207 | −0.482604 | − | 0.875839i | \(-0.660309\pi\) | ||||
−0.482604 | + | 0.875839i | \(0.660309\pi\) | |||||||
\(968\) | −44887.4 | −1.49043 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12874.4 | −0.425498 | −0.212749 | − | 0.977107i | \(-0.568242\pi\) | ||||
−0.212749 | + | 0.977107i | \(0.568242\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6599.42 | 0.217438 | ||||||||
\(974\) | −4858.70 | −0.159839 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16437.0 | 0.539072 | ||||||||
\(977\) | −15195.8 | −0.497600 | −0.248800 | − | 0.968555i | \(-0.580036\pi\) | ||||
−0.248800 | + | 0.968555i | \(0.580036\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 68851.9 | 2.24772 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 26099.5 | 0.848134 | ||||||||
\(983\) | 12042.2 | 0.390728 | 0.195364 | − | 0.980731i | \(-0.437411\pi\) | ||||
0.195364 | + | 0.980731i | \(0.437411\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −20535.7 | −0.663275 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1583.82 | 0.0510001 | ||||||||
\(989\) | −51315.8 | −1.64990 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11490.7 | 0.368330 | 0.184165 | − | 0.982895i | \(-0.441042\pi\) | ||||
0.184165 | + | 0.982895i | \(0.441042\pi\) | |||||||
\(992\) | 8070.49 | 0.258305 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1606.29 | −0.0512560 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4076.85 | −0.129504 | −0.0647518 | − | 0.997901i | \(-0.520626\pi\) | ||||
−0.0647518 | + | 0.997901i | \(0.520626\pi\) | |||||||
\(998\) | 3108.44 | 0.0985931 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1575.4.a.bo.1.4 | 5 | ||
3.2 | odd | 2 | 525.4.a.x.1.2 | 5 | |||
5.2 | odd | 4 | 315.4.d.b.64.7 | 10 | |||
5.3 | odd | 4 | 315.4.d.b.64.4 | 10 | |||
5.4 | even | 2 | 1575.4.a.bp.1.2 | 5 | |||
15.2 | even | 4 | 105.4.d.b.64.4 | ✓ | 10 | ||
15.8 | even | 4 | 105.4.d.b.64.7 | yes | 10 | ||
15.14 | odd | 2 | 525.4.a.w.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.d.b.64.4 | ✓ | 10 | 15.2 | even | 4 | ||
105.4.d.b.64.7 | yes | 10 | 15.8 | even | 4 | ||
315.4.d.b.64.4 | 10 | 5.3 | odd | 4 | |||
315.4.d.b.64.7 | 10 | 5.2 | odd | 4 | |||
525.4.a.w.1.4 | 5 | 15.14 | odd | 2 | |||
525.4.a.x.1.2 | 5 | 3.2 | odd | 2 | |||
1575.4.a.bo.1.4 | 5 | 1.1 | even | 1 | trivial | ||
1575.4.a.bp.1.2 | 5 | 5.4 | even | 2 |