Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,4,Mod(1,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1800.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.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: | \(106.203438010\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{6}, \sqrt{46})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 26x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 360) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.61591\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −28.2616 | −1.52598 | −0.762991 | − | 0.646409i | \(-0.776270\pi\) | ||||
−0.762991 | + | 0.646409i | \(0.776270\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −47.8575 | −1.31178 | −0.655890 | − | 0.754856i | \(-0.727707\pi\) | ||||
−0.655890 | + | 0.754856i | \(0.727707\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.9302 | −0.233192 | −0.116596 | − | 0.993179i | \(-0.537198\pi\) | ||||
−0.116596 | + | 0.993179i | \(0.537198\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 28.6132 | 0.408220 | 0.204110 | − | 0.978948i | \(-0.434570\pi\) | ||||
0.204110 | + | 0.978948i | \(0.434570\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 86.4530 | 1.04388 | 0.521939 | − | 0.852983i | \(-0.325209\pi\) | ||||
0.521939 | + | 0.852983i | \(0.325209\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 49.2265 | 0.446280 | 0.223140 | − | 0.974786i | \(-0.428369\pi\) | ||||
0.223140 | + | 0.974786i | \(0.428369\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −165.433 | −1.05932 | −0.529658 | − | 0.848212i | \(-0.677680\pi\) | ||||
−0.529658 | + | 0.848212i | \(0.677680\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −247.359 | −1.43313 | −0.716564 | − | 0.697521i | \(-0.754286\pi\) | ||||
−0.716564 | + | 0.697521i | \(0.754286\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −375.674 | −1.66920 | −0.834600 | − | 0.550856i | \(-0.814301\pi\) | ||||
−0.834600 | + | 0.550856i | \(0.814301\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −504.180 | −1.92048 | −0.960239 | − | 0.279178i | \(-0.909938\pi\) | ||||
−0.960239 | + | 0.279178i | \(0.909938\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 207.976 | 0.737584 | 0.368792 | − | 0.929512i | \(-0.379772\pi\) | ||||
0.368792 | + | 0.929512i | \(0.379772\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −70.1325 | −0.217657 | −0.108828 | − | 0.994061i | \(-0.534710\pi\) | ||||
−0.108828 | + | 0.994061i | \(0.534710\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 455.718 | 1.32862 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −286.425 | −0.742331 | −0.371165 | − | 0.928567i | \(-0.621042\pi\) | ||||
−0.371165 | + | 0.928567i | \(0.621042\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 92.3636 | 0.203809 | 0.101904 | − | 0.994794i | \(-0.467506\pi\) | ||||
0.101904 | + | 0.994794i | \(0.467506\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −697.624 | −1.46429 | −0.732144 | − | 0.681150i | \(-0.761480\pi\) | ||||
−0.732144 | + | 0.681150i | \(0.761480\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 840.360 | 1.53233 | 0.766166 | − | 0.642642i | \(-0.222162\pi\) | ||||
0.766166 | + | 0.642642i | \(0.222162\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 303.691 | 0.507627 | 0.253814 | − | 0.967253i | \(-0.418315\pi\) | ||||
0.253814 | + | 0.967253i | \(0.418315\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 251.697 | 0.403547 | 0.201774 | − | 0.979432i | \(-0.435329\pi\) | ||||
0.201774 | + | 0.979432i | \(0.435329\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1352.53 | 2.00175 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 745.171 | 1.06124 | 0.530622 | − | 0.847609i | \(-0.321958\pi\) | ||||
0.530622 | + | 0.847609i | \(0.321958\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1327.89 | 1.75608 | 0.878041 | − | 0.478586i | \(-0.158851\pi\) | ||||
0.878041 | + | 0.478586i | \(0.158851\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 415.953 | 0.495403 | 0.247702 | − | 0.968836i | \(-0.420325\pi\) | ||||
0.247702 | + | 0.968836i | \(0.420325\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 308.906 | 0.355848 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −656.418 | −0.687105 | −0.343552 | − | 0.939134i | \(-0.611630\pi\) | ||||
−0.343552 | + | 0.939134i | \(0.611630\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1228.14 | 1.20995 | 0.604974 | − | 0.796246i | \(-0.293184\pi\) | ||||
0.604974 | + | 0.796246i | \(0.293184\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 598.808 | 0.572838 | 0.286419 | − | 0.958105i | \(-0.407535\pi\) | ||||
0.286419 | + | 0.958105i | \(0.407535\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −462.607 | −0.417962 | −0.208981 | − | 0.977920i | \(-0.567015\pi\) | ||||
−0.208981 | + | 0.977920i | \(0.567015\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1427.44 | −1.25434 | −0.627172 | − | 0.778881i | \(-0.715788\pi\) | ||||
−0.627172 | + | 0.778881i | \(0.715788\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −654.955 | −0.545248 | −0.272624 | − | 0.962121i | \(-0.587891\pi\) | ||||
−0.272624 | + | 0.962121i | \(0.587891\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −808.656 | −0.622936 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 959.342 | 0.720768 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −75.1229 | −0.0524888 | −0.0262444 | − | 0.999656i | \(-0.508355\pi\) | ||||
−0.0262444 | + | 0.999656i | \(0.508355\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1888.12 | 1.25928 | 0.629641 | − | 0.776886i | \(-0.283202\pi\) | ||||
0.629641 | + | 0.776886i | \(0.283202\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2443.30 | −1.59294 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3027.28 | 1.88787 | 0.943933 | − | 0.330137i | \(-0.107095\pi\) | ||||
0.943933 | + | 0.330137i | \(0.107095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −911.513 | −0.556212 | −0.278106 | − | 0.960550i | \(-0.589707\pi\) | ||||
−0.278106 | + | 0.960550i | \(0.589707\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 523.094 | 0.305897 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3103.85 | 1.70656 | 0.853281 | − | 0.521452i | \(-0.174609\pi\) | ||||
0.853281 | + | 0.521452i | \(0.174609\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1082.98 | 0.583655 | 0.291827 | − | 0.956471i | \(-0.405737\pi\) | ||||
0.291827 | + | 0.956471i | \(0.405737\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 215.766 | 0.109682 | 0.0548408 | − | 0.998495i | \(-0.482535\pi\) | ||||
0.0548408 | + | 0.998495i | \(0.482535\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1391.22 | −0.681015 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1869.61 | −0.898401 | −0.449201 | − | 0.893431i | \(-0.648291\pi\) | ||||
−0.449201 | + | 0.893431i | \(0.648291\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3799.30 | 1.76047 | 0.880236 | − | 0.474536i | \(-0.157384\pi\) | ||||
0.880236 | + | 0.474536i | \(0.157384\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2077.53 | −0.945621 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1005.25 | 0.441781 | 0.220890 | − | 0.975299i | \(-0.429104\pi\) | ||||
0.220890 | + | 0.975299i | \(0.429104\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2393.09 | −0.999261 | −0.499630 | − | 0.866239i | \(-0.666531\pi\) | ||||
−0.499630 | + | 0.866239i | \(0.666531\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2378.31 | 0.976675 | 0.488338 | − | 0.872655i | \(-0.337603\pi\) | ||||
0.488338 | + | 0.872655i | \(0.337603\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1369.36 | −0.535494 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3152.32 | −1.19421 | −0.597103 | − | 0.802164i | \(-0.703682\pi\) | ||||
−0.597103 | + | 0.802164i | \(0.703682\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4313.28 | 1.60869 | 0.804343 | − | 0.594165i | \(-0.202518\pi\) | ||||
0.804343 | + | 0.594165i | \(0.202518\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2892.08 | 1.04595 | 0.522976 | − | 0.852348i | \(-0.324822\pi\) | ||||
0.522976 | + | 0.852348i | \(0.324822\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −952.949 | −0.339461 | −0.169731 | − | 0.985491i | \(-0.554290\pi\) | ||||
−0.169731 | + | 0.985491i | \(0.554290\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4675.40 | 1.61650 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4137.43 | −1.36934 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2536.79 | 0.827678 | 0.413839 | − | 0.910350i | \(-0.364188\pi\) | ||||
0.413839 | + | 0.910350i | \(0.364188\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6990.76 | 2.18693 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −312.750 | −0.0951937 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1956.33 | −0.587469 | −0.293735 | − | 0.955887i | \(-0.594898\pi\) | ||||
−0.293735 | + | 0.955887i | \(0.594898\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3664.11 | 1.07135 | 0.535673 | − | 0.844425i | \(-0.320058\pi\) | ||||
0.535673 | + | 0.844425i | \(0.320058\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2296.19 | −0.662604 | −0.331302 | − | 0.943525i | \(-0.607488\pi\) | ||||
−0.331302 | + | 0.943525i | \(0.607488\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2886.31 | 0.811540 | 0.405770 | − | 0.913975i | \(-0.367003\pi\) | ||||
0.405770 | + | 0.913975i | \(0.367003\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4994.15 | 1.35165 | 0.675826 | − | 0.737061i | \(-0.263787\pi\) | ||||
0.675826 | + | 0.737061i | \(0.263787\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5735.37 | −1.53298 | −0.766489 | − | 0.642258i | \(-0.777998\pi\) | ||||
−0.766489 | + | 0.642258i | \(0.777998\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −944.952 | −0.243424 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3503.44 | −0.881017 | −0.440509 | − | 0.897748i | \(-0.645202\pi\) | ||||
−0.440509 | + | 0.897748i | \(0.645202\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2355.86 | −0.585421 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3512.51 | 0.852547 | 0.426274 | − | 0.904594i | \(-0.359826\pi\) | ||||
0.426274 | + | 0.904594i | \(0.359826\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10617.1 | 2.54717 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6722.79 | −1.57622 | −0.788108 | − | 0.615536i | \(-0.788939\pi\) | ||||
−0.788108 | + | 0.615536i | \(0.788939\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3727.78 | −0.844933 | −0.422466 | − | 0.906379i | \(-0.638836\pi\) | ||||
−0.422466 | + | 0.906379i | \(0.638836\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.0769 | −0.00315539 | −0.00157770 | − | 0.999999i | \(-0.500502\pi\) | ||||
−0.00157770 | + | 0.999999i | \(0.500502\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2055.06 | −0.445765 | −0.222882 | − | 0.974845i | \(-0.571547\pi\) | ||||
−0.222882 | + | 0.974845i | \(0.571547\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4287.07 | −0.910125 | −0.455062 | − | 0.890460i | \(-0.650383\pi\) | ||||
−0.455062 | + | 0.890460i | \(0.650383\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4888.77 | 1.02688 | 0.513441 | − | 0.858125i | \(-0.328371\pi\) | ||||
0.513441 | + | 0.858125i | \(0.328371\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14248.9 | 2.93062 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4094.28 | −0.833357 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5724.92 | 1.14148 | 0.570740 | − | 0.821131i | \(-0.306657\pi\) | ||||
0.570740 | + | 0.821131i | \(0.306657\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −538.057 | −0.104069 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5877.74 | −1.12554 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6253.78 | −1.16261 | −0.581307 | − | 0.813685i | \(-0.697458\pi\) | ||||
−0.581307 | + | 0.813685i | \(0.697458\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4527.71 | 0.825541 | 0.412770 | − | 0.910835i | \(-0.364561\pi\) | ||||
0.412770 | + | 0.910835i | \(0.364561\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7737.03 | 1.39720 | 0.698599 | − | 0.715513i | \(-0.253807\pi\) | ||||
0.698599 | + | 0.715513i | \(0.253807\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1151.57 | 0.204033 | 0.102016 | − | 0.994783i | \(-0.467471\pi\) | ||||
0.102016 | + | 0.994783i | \(0.467471\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7917.21 | 1.38959 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2473.70 | 0.426131 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1982.06 | 0.332141 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6596.81 | −1.09545 | −0.547724 | − | 0.836659i | \(-0.684506\pi\) | ||||
−0.547724 | + | 0.836659i | \(0.684506\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4365.09 | −0.705583 | −0.352792 | − | 0.935702i | \(-0.614768\pi\) | ||||
−0.352792 | + | 0.935702i | \(0.614768\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11838.0 | 1.87995 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3185.59 | −0.501474 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1002.43 | −0.155081 | −0.0775405 | − | 0.996989i | \(-0.524707\pi\) | ||||
−0.0775405 | + | 0.996989i | \(0.524707\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4042.17 | 0.619978 | 0.309989 | − | 0.950740i | \(-0.399675\pi\) | ||||
0.309989 | + | 0.950740i | \(0.399675\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10488.1 | 1.58137 | 0.790687 | − | 0.612220i | \(-0.209723\pi\) | ||||
0.790687 | + | 0.612220i | \(0.209723\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6852.95 | 1.00748 | 0.503740 | − | 0.863856i | \(-0.331957\pi\) | ||||
0.503740 | + | 0.863856i | \(0.331957\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 615.120 | 0.0896807 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2137.98 | −0.304091 | −0.152046 | − | 0.988373i | \(-0.548586\pi\) | ||||
−0.152046 | + | 0.988373i | \(0.548586\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8094.83 | 1.13278 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13254.9 | −1.83998 | −0.919988 | − | 0.391946i | \(-0.871802\pi\) | ||||
−0.919988 | + | 0.391946i | \(0.871802\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1808.22 | 0.247024 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2309.84 | 0.313056 | 0.156528 | − | 0.987673i | \(-0.449970\pi\) | ||||
0.156528 | + | 0.987673i | \(0.449970\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3123.01 | −0.416654 | −0.208327 | − | 0.978059i | \(-0.566802\pi\) | ||||
−0.208327 | + | 0.978059i | \(0.566802\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4031.11 | −0.525413 | −0.262706 | − | 0.964876i | \(-0.584615\pi\) | ||||
−0.262706 | + | 0.964876i | \(0.584615\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1408.53 | 0.182180 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7703.16 | −0.973830 | −0.486915 | − | 0.873449i | \(-0.661878\pi\) | ||||
−0.486915 | + | 0.873449i | \(0.661878\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6871.01 | 0.855666 | 0.427833 | − | 0.903858i | \(-0.359277\pi\) | ||||
0.427833 | + | 0.903858i | \(0.359277\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2703.69 | 0.334195 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17978.8 | 2.18962 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12212.6 | −1.47647 | −0.738236 | − | 0.674543i | \(-0.764341\pi\) | ||||
−0.738236 | + | 0.674543i | \(0.764341\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2610.34 | −0.311009 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3634.55 | 0.423769 | 0.211884 | − | 0.977295i | \(-0.432040\pi\) | ||||
0.211884 | + | 0.977295i | \(0.432040\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5104.50 | −0.590921 | −0.295461 | − | 0.955355i | \(-0.595473\pi\) | ||||
−0.295461 | + | 0.955355i | \(0.595473\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19716.0 | 2.23448 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14460.5 | −1.61610 | −0.808049 | − | 0.589115i | \(-0.799477\pi\) | ||||
−0.808049 | + | 0.589115i | \(0.799477\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8668.46 | 0.962078 | 0.481039 | − | 0.876699i | \(-0.340260\pi\) | ||||
0.481039 | + | 0.876699i | \(0.340260\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4255.78 | 0.465861 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11041.5 | 1.20041 | 0.600206 | − | 0.799845i | \(-0.295085\pi\) | ||||
0.600206 | + | 0.799845i | \(0.295085\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5711.44 | 0.612548 | 0.306274 | − | 0.951943i | \(-0.400918\pi\) | ||||
0.306274 | + | 0.951943i | \(0.400918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9454.89 | 0.993773 | 0.496886 | − | 0.867816i | \(-0.334477\pi\) | ||||
0.496886 | + | 0.867816i | \(0.334477\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24128.8 | 2.51925 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1649.44 | −0.168835 | −0.0844174 | − | 0.996430i | \(-0.526903\pi\) | ||||
−0.0844174 | + | 0.996430i | \(0.526903\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11194.3 | −1.13096 | −0.565480 | − | 0.824762i | \(-0.691309\pi\) | ||||
−0.565480 | + | 0.824762i | \(0.691309\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9702.91 | 0.973936 | 0.486968 | − | 0.873420i | \(-0.338103\pi\) | ||||
0.486968 | + | 0.873420i | \(0.338103\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10614.4 | −1.05176 | −0.525882 | − | 0.850557i | \(-0.676265\pi\) | ||||
−0.525882 | + | 0.850557i | \(0.676265\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23749.9 | −2.33831 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9953.23 | −0.967548 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18297.3 | −1.74535 | −0.872676 | − | 0.488299i | \(-0.837617\pi\) | ||||
−0.872676 | + | 0.488299i | \(0.837617\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4106.21 | 0.389245 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18775.1 | 1.74699 | 0.873493 | − | 0.486837i | \(-0.161849\pi\) | ||||
0.873493 | + | 0.486837i | \(0.161849\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5582.90 | 0.513142 | 0.256571 | − | 0.966525i | \(-0.417407\pi\) | ||||
0.256571 | + | 0.966525i | \(0.417407\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4733.58 | −0.432433 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8582.80 | −0.774630 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2517.00 | 0.225804 | 0.112902 | − | 0.993606i | \(-0.463985\pi\) | ||||
0.112902 | + | 0.993606i | \(0.463985\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9246.22 | −0.819619 | −0.409810 | − | 0.912171i | \(-0.634405\pi\) | ||||
−0.409810 | + | 0.912171i | \(0.634405\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10051.4 | 0.875284 | 0.437642 | − | 0.899149i | \(-0.355814\pi\) | ||||
0.437642 | + | 0.899149i | \(0.355814\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7113.37 | −0.615806 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3356.37 | 0.285518 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4805.38 | 0.404083 | 0.202042 | − | 0.979377i | \(-0.435242\pi\) | ||||
0.202042 | + | 0.979377i | \(0.435242\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18434.3 | −1.54125 | −0.770626 | − | 0.637287i | \(-0.780057\pi\) | ||||
−0.770626 | + | 0.637287i | \(0.780057\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7077.74 | −0.585031 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9743.75 | −0.800834 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5510.80 | 0.447841 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21809.5 | −1.74286 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6437.04 | 0.511553 | 0.255776 | − | 0.966736i | \(-0.417669\pi\) | ||||
0.255776 | + | 0.966736i | \(0.417669\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10635.8 | −0.831359 | −0.415679 | − | 0.909511i | \(-0.636456\pi\) | ||||
−0.415679 | + | 0.909511i | \(0.636456\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14302.2 | −1.10580 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21059.7 | −1.61944 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3571.98 | 0.271723 | 0.135861 | − | 0.990728i | \(-0.456620\pi\) | ||||
0.135861 | + | 0.990728i | \(0.456620\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2273.23 | −0.171999 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26445.3 | 1.97964 | 0.989821 | − | 0.142321i | \(-0.0454566\pi\) | ||||
0.989821 | + | 0.142321i | \(0.0454566\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11021.0 | −0.811993 | −0.405997 | − | 0.913875i | \(-0.633076\pi\) | ||||
−0.405997 | + | 0.913875i | \(0.633076\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18553.4 | 1.35978 | 0.679891 | − | 0.733313i | \(-0.262027\pi\) | ||||
0.679891 | + | 0.733313i | \(0.262027\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10253.4 | 0.739783 | 0.369891 | − | 0.929075i | \(-0.379395\pi\) | ||||
0.369891 | + | 0.929075i | \(0.379395\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37528.3 | −2.67975 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13707.6 | 0.973775 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20577.3 | −1.44688 | −0.723439 | − | 0.690388i | \(-0.757440\pi\) | ||||
−0.723439 | + | 0.690388i | \(0.757440\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21384.9 | −1.49601 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12428.4 | −0.860662 | −0.430331 | − | 0.902671i | \(-0.641603\pi\) | ||||
−0.430331 | + | 0.902671i | \(0.641603\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22657.2 | 1.54549 | 0.772746 | − | 0.634716i | \(-0.218883\pi\) | ||||
0.772746 | + | 0.634716i | \(0.218883\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11771.5 | −0.798948 | −0.399474 | − | 0.916745i | \(-0.630807\pi\) | ||||
−0.399474 | + | 0.916745i | \(0.630807\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24031.3 | −1.60692 | −0.803460 | − | 0.595359i | \(-0.797010\pi\) | ||||
−0.803460 | + | 0.595359i | \(0.797010\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 766.565 | 0.0507560 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21456.8 | 1.41375 | 0.706877 | − | 0.707337i | \(-0.250104\pi\) | ||||
0.706877 | + | 0.707337i | \(0.250104\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21534.5 | 1.40510 | 0.702550 | − | 0.711634i | \(-0.252045\pi\) | ||||
0.702550 | + | 0.711634i | \(0.252045\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24043.5 | 1.56121 | 0.780607 | − | 0.625023i | \(-0.214910\pi\) | ||||
0.780607 | + | 0.625023i | \(0.214910\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11755.5 | −0.755977 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10749.3 | −0.681400 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7000.28 | 0.441643 | 0.220822 | − | 0.975314i | \(-0.429126\pi\) | ||||
0.220822 | + | 0.975314i | \(0.429126\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4981.11 | −0.309825 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19557.4 | 1.20511 | 0.602553 | − | 0.798079i | \(-0.294150\pi\) | ||||
0.602553 | + | 0.798079i | \(0.294150\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5640.24 | −0.345925 | −0.172962 | − | 0.984928i | \(-0.555334\pi\) | ||||
−0.172962 | + | 0.984928i | \(0.555334\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23410.0 | −1.42247 | −0.711237 | − | 0.702953i | \(-0.751865\pi\) | ||||
−0.711237 | + | 0.702953i | \(0.751865\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4420.29 | −0.267352 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24659.1 | −1.47777 | −0.738887 | − | 0.673830i | \(-0.764648\pi\) | ||||
−0.738887 | + | 0.673830i | \(0.764648\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21423.4 | 1.26637 | 0.633185 | − | 0.774001i | \(-0.281747\pi\) | ||||
0.633185 | + | 0.774001i | \(0.281747\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7120.12 | −0.418972 | −0.209486 | − | 0.977812i | \(-0.567179\pi\) | ||||
−0.209486 | + | 0.977812i | \(0.567179\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8143.69 | −0.472751 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33386.5 | 1.92082 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6092.55 | 0.348961 | 0.174480 | − | 0.984661i | \(-0.444175\pi\) | ||||
0.174480 | + | 0.984661i | \(0.444175\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24575.9 | −1.39517 | −0.697583 | − | 0.716504i | \(-0.745741\pi\) | ||||
−0.697583 | + | 0.716504i | \(0.745741\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18551.4 | 1.04851 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6977.95 | −0.390928 | −0.195464 | − | 0.980711i | \(-0.562621\pi\) | ||||
−0.195464 | + | 0.980711i | \(0.562621\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3130.70 | 0.173106 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11730.7 | −0.645815 | −0.322907 | − | 0.946431i | \(-0.604660\pi\) | ||||
−0.322907 | + | 0.946431i | \(0.604660\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14426.2 | −0.783977 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6659.02 | 0.358784 | 0.179392 | − | 0.983778i | \(-0.442587\pi\) | ||||
0.179392 | + | 0.983778i | \(0.442587\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32478.1 | −1.74244 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −34709.2 | −1.84636 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15052.8 | 0.797350 | 0.398675 | − | 0.917092i | \(-0.369470\pi\) | ||||
0.398675 | + | 0.917092i | \(0.369470\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12176.6 | −0.639576 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −634.195 | −0.0328949 | −0.0164475 | − | 0.999865i | \(-0.505236\pi\) | ||||
−0.0164475 | + | 0.999865i | \(0.505236\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16923.3 | −0.874141 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9672.48 | 0.493442 | 0.246721 | − | 0.969087i | \(-0.420647\pi\) | ||||
0.246721 | + | 0.969087i | \(0.420647\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5950.88 | 0.301096 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5566.87 | 0.280514 | 0.140257 | − | 0.990115i | \(-0.455207\pi\) | ||||
0.140257 | + | 0.990115i | \(0.455207\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −40217.5 | −2.01008 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22861.0 | 1.13797 | 0.568983 | − | 0.822349i | \(-0.307337\pi\) | ||||
0.568983 | + | 0.822349i | \(0.307337\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15838.3 | 0.782032 | 0.391016 | − | 0.920384i | \(-0.372124\pi\) | ||||
0.391016 | + | 0.920384i | \(0.372124\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13074.0 | 0.637802 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26296.1 | −1.27771 | −0.638855 | − | 0.769327i | \(-0.720592\pi\) | ||||
−0.638855 | + | 0.769327i | \(0.720592\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33171.7 | 1.59266 | 0.796331 | − | 0.604861i | \(-0.206771\pi\) | ||||
0.796331 | + | 0.604861i | \(0.206771\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 343.309 | 0.0163534 | 0.00817670 | − | 0.999967i | \(-0.497397\pi\) | ||||
0.00817670 | + | 0.999967i | \(0.497397\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40341.6 | 1.91411 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1009.56 | −0.0475267 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4648.82 | 0.217998 | 0.108999 | − | 0.994042i | \(-0.465235\pi\) | ||||
0.108999 | + | 0.994042i | \(0.465235\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5421.42 | −0.252257 | −0.126129 | − | 0.992014i | \(-0.540255\pi\) | ||||
−0.126129 | + | 0.992014i | \(0.540255\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −43587.8 | −2.00475 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14533.9 | −0.665895 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18357.5 | −0.831478 | −0.415739 | − | 0.909484i | \(-0.636477\pi\) | ||||
−0.415739 | + | 0.909484i | \(0.636477\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18510.1 | 0.832039 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7625.20 | 0.341461 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5677.15 | 0.252315 | 0.126157 | − | 0.992010i | \(-0.459736\pi\) | ||||
0.126157 | + | 0.992010i | \(0.459736\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2006.72 | −0.0888518 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12045.6 | −0.529365 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24875.0 | 1.08104 | 0.540518 | − | 0.841333i | \(-0.318228\pi\) | ||||
0.540518 | + | 0.841333i | \(0.318228\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6323.63 | 0.273801 | 0.136901 | − | 0.990585i | \(-0.456286\pi\) | ||||
0.136901 | + | 0.990585i | \(0.456286\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17980.2 | 0.769947 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31744.6 | 1.34944 | 0.674722 | − | 0.738072i | \(-0.264264\pi\) | ||||
0.674722 | + | 0.738072i | \(0.264264\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6599.93 | 0.279537 | 0.139769 | − | 0.990184i | \(-0.455364\pi\) | ||||
0.139769 | + | 0.990184i | \(0.455364\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1552.94 | −0.0652975 | −0.0326487 | − | 0.999467i | \(-0.510394\pi\) | ||||
−0.0326487 | + | 0.999467i | \(0.510394\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18949.1 | −0.793884 | −0.396942 | − | 0.917844i | \(-0.629929\pi\) | ||||
−0.396942 | + | 0.917844i | \(0.629929\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13039.6 | 0.542370 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33786.4 | 1.39027 | 0.695134 | − | 0.718880i | \(-0.255345\pi\) | ||||
0.695134 | + | 0.718880i | \(0.255345\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2979.09 | 0.122149 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27112.5 | −1.09988 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18493.1 | −0.744930 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27376.2 | 1.09888 | 0.549440 | − | 0.835533i | \(-0.314841\pi\) | ||||
0.549440 | + | 0.835533i | \(0.314841\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23105.5 | −0.920969 | −0.460485 | − | 0.887668i | \(-0.652324\pi\) | ||||
−0.460485 | + | 0.887668i | \(0.652324\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22947.0 | 0.911457 | 0.455728 | − | 0.890119i | \(-0.349379\pi\) | ||||
0.455728 | + | 0.890119i | \(0.349379\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30590.2 | −1.20661 | −0.603304 | − | 0.797511i | \(-0.706150\pi\) | ||||
−0.603304 | + | 0.797511i | \(0.706150\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −35662.0 | −1.39212 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9185.33 | −0.357329 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13685.2 | 0.526928 | 0.263464 | − | 0.964669i | \(-0.415135\pi\) | ||||
0.263464 | + | 0.964669i | \(0.415135\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33737.2 | −1.29017 | −0.645083 | − | 0.764113i | \(-0.723177\pi\) | ||||
−0.645083 | + | 0.764113i | \(0.723177\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3738.74 | −0.142490 | −0.0712450 | − | 0.997459i | \(-0.522697\pi\) | ||||
−0.0712450 | + | 0.997459i | \(0.522697\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37168.3 | −1.40698 | −0.703489 | − | 0.710706i | \(-0.748375\pi\) | ||||
−0.703489 | + | 0.710706i | \(0.748375\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2123.09 | 0.0800971 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6063.16 | −0.227207 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 40921.3 | 1.51813 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8195.56 | −0.303034 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21277.6 | 0.778954 | 0.389477 | − | 0.921036i | \(-0.372656\pi\) | ||||
0.389477 | + | 0.921036i | \(0.372656\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41401.1 | −1.50568 | −0.752842 | − | 0.658201i | \(-0.771318\pi\) | ||||
−0.752842 | + | 0.658201i | \(0.771318\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −63549.5 | −2.30359 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −53361.4 | −1.92164 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2049.62 | −0.0735697 | −0.0367849 | − | 0.999323i | \(-0.511712\pi\) | ||||
−0.0367849 | + | 0.999323i | \(0.511712\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3319.42 | −0.118375 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14404.0 | −0.508699 | −0.254350 | − | 0.967112i | \(-0.581861\pi\) | ||||
−0.254350 | + | 0.967112i | \(0.581861\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 39398.2 | 1.38692 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36602.2 | −1.27614 | −0.638068 | − | 0.769980i | \(-0.720266\pi\) | ||||
−0.638068 | + | 0.769980i | \(0.720266\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5472.52 | 0.189584 | 0.0947922 | − | 0.995497i | \(-0.469781\pi\) | ||||
0.0947922 | + | 0.995497i | \(0.469781\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24819.0 | −0.857071 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22467.1 | 0.770944 | 0.385472 | − | 0.922720i | \(-0.374039\pi\) | ||||
0.385472 | + | 0.922720i | \(0.374039\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2751.11 | −0.0941042 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13989.7 | −0.475520 | −0.237760 | − | 0.971324i | \(-0.576413\pi\) | ||||
−0.237760 | + | 0.971324i | \(0.576413\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −85555.6 | −2.88085 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31395.5 | 1.05386 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37809.4 | 1.25736 | 0.628681 | − | 0.777663i | \(-0.283595\pi\) | ||||
0.628681 | + | 0.777663i | \(0.283595\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8527.36 | −0.281829 | −0.140915 | − | 0.990022i | \(-0.545004\pi\) | ||||
−0.140915 | + | 0.990022i | \(0.545004\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25760.8 | 0.848770 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19536.5 | −0.639744 | −0.319872 | − | 0.947461i | \(-0.603640\pi\) | ||||
−0.319872 | + | 0.947461i | \(0.603640\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19906.5 | −0.649860 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17524.1 | −0.568599 | −0.284300 | − | 0.958735i | \(-0.591761\pi\) | ||||
−0.284300 | + | 0.958735i | \(0.591761\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10237.9 | 0.329169 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2581.67 | 0.0827541 | 0.0413771 | − | 0.999144i | \(-0.486826\pi\) | ||||
0.0413771 | + | 0.999144i | \(0.486826\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42014.1 | −1.33460 | −0.667301 | − | 0.744788i | \(-0.732551\pi\) | ||||
−0.667301 | + | 0.744788i | \(0.732551\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1800.4.a.bw.1.1 | 4 | ||
3.2 | odd | 2 | 1800.4.a.bv.1.1 | 4 | |||
5.2 | odd | 4 | 360.4.f.f.289.6 | yes | 8 | ||
5.3 | odd | 4 | 360.4.f.f.289.5 | yes | 8 | ||
5.4 | even | 2 | 1800.4.a.bv.1.4 | 4 | |||
15.2 | even | 4 | 360.4.f.f.289.3 | ✓ | 8 | ||
15.8 | even | 4 | 360.4.f.f.289.4 | yes | 8 | ||
15.14 | odd | 2 | inner | 1800.4.a.bw.1.4 | 4 | ||
20.3 | even | 4 | 720.4.f.n.289.5 | 8 | |||
20.7 | even | 4 | 720.4.f.n.289.6 | 8 | |||
60.23 | odd | 4 | 720.4.f.n.289.4 | 8 | |||
60.47 | odd | 4 | 720.4.f.n.289.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.4.f.f.289.3 | ✓ | 8 | 15.2 | even | 4 | ||
360.4.f.f.289.4 | yes | 8 | 15.8 | even | 4 | ||
360.4.f.f.289.5 | yes | 8 | 5.3 | odd | 4 | ||
360.4.f.f.289.6 | yes | 8 | 5.2 | odd | 4 | ||
720.4.f.n.289.3 | 8 | 60.47 | odd | 4 | |||
720.4.f.n.289.4 | 8 | 60.23 | odd | 4 | |||
720.4.f.n.289.5 | 8 | 20.3 | even | 4 | |||
720.4.f.n.289.6 | 8 | 20.7 | even | 4 | |||
1800.4.a.bv.1.1 | 4 | 3.2 | odd | 2 | |||
1800.4.a.bv.1.4 | 4 | 5.4 | even | 2 | |||
1800.4.a.bw.1.1 | 4 | 1.1 | even | 1 | trivial | ||
1800.4.a.bw.1.4 | 4 | 15.14 | odd | 2 | inner |