Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,4,Mod(1,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, 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("900.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.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: | \(53.1017190052\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{19}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 19 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 20) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.35890\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.1 |
$q$-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 | ||||||||
\(7\) | 8.71780 | 0.470717 | 0.235358 | − | 0.971909i | \(-0.424374\pi\) | ||||
0.235358 | + | 0.971909i | \(0.424374\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −20.0000 | −0.548202 | −0.274101 | − | 0.961701i | \(-0.588380\pi\) | ||||
−0.274101 | + | 0.961701i | \(0.588380\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −52.3068 | −1.11595 | −0.557973 | − | 0.829859i | \(-0.688421\pi\) | ||||
−0.557973 | + | 0.829859i | \(0.688421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 69.7424 | 0.995001 | 0.497500 | − | 0.867464i | \(-0.334251\pi\) | ||||
0.497500 | + | 0.867464i | \(0.334251\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 84.0000 | 1.01426 | 0.507130 | − | 0.861870i | \(-0.330707\pi\) | ||||
0.507130 | + | 0.861870i | \(0.330707\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −61.0246 | −0.553239 | −0.276620 | − | 0.960979i | \(-0.589214\pi\) | ||||
−0.276620 | + | 0.960979i | \(0.589214\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 0.0384197 | 0.0192099 | − | 0.999815i | \(-0.493885\pi\) | ||||
0.0192099 | + | 0.999815i | \(0.493885\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −224.000 | −1.29779 | −0.648897 | − | 0.760877i | \(-0.724769\pi\) | ||||
−0.648897 | + | 0.760877i | \(0.724769\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −122.049 | −0.542291 | −0.271145 | − | 0.962538i | \(-0.587402\pi\) | ||||
−0.271145 | + | 0.962538i | \(0.587402\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −266.000 | −1.01322 | −0.506612 | − | 0.862174i | \(-0.669102\pi\) | ||||
−0.506612 | + | 0.862174i | \(0.669102\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −305.123 | −1.08211 | −0.541056 | − | 0.840987i | \(-0.681975\pi\) | ||||
−0.541056 | + | 0.840987i | \(0.681975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 374.865 | 1.16340 | 0.581699 | − | 0.813404i | \(-0.302388\pi\) | ||||
0.581699 | + | 0.813404i | \(0.302388\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −267.000 | −0.778426 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 366.148 | 0.948948 | 0.474474 | − | 0.880270i | \(-0.342638\pi\) | ||||
0.474474 | + | 0.880270i | \(0.342638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −28.0000 | −0.0617846 | −0.0308923 | − | 0.999523i | \(-0.509835\pi\) | ||||
−0.0308923 | + | 0.999523i | \(0.509835\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 182.000 | 0.382012 | 0.191006 | − | 0.981589i | \(-0.438825\pi\) | ||||
0.191006 | + | 0.981589i | \(0.438825\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −427.172 | −0.778916 | −0.389458 | − | 0.921044i | \(-0.627338\pi\) | ||||
−0.389458 | + | 0.921044i | \(0.627338\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −408.000 | −0.681982 | −0.340991 | − | 0.940067i | \(-0.610762\pi\) | ||||
−0.340991 | + | 0.940067i | \(0.610762\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1081.01 | 1.73318 | 0.866591 | − | 0.499019i | \(-0.166306\pi\) | ||||
0.866591 | + | 0.499019i | \(0.166306\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −174.356 | −0.258048 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −48.0000 | −0.0683598 | −0.0341799 | − | 0.999416i | \(-0.510882\pi\) | ||||
−0.0341799 | + | 0.999416i | \(0.510882\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 200.509 | 0.265166 | 0.132583 | − | 0.991172i | \(-0.457673\pi\) | ||||
0.132583 | + | 0.991172i | \(0.457673\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1526.00 | −1.81748 | −0.908740 | − | 0.417363i | \(-0.862954\pi\) | ||||
−0.908740 | + | 0.417363i | \(0.862954\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −456.000 | −0.525294 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −557.939 | −0.584022 | −0.292011 | − | 0.956415i | \(-0.594324\pi\) | ||||
−0.292011 | + | 0.956415i | \(0.594324\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1246.00 | −1.22754 | −0.613770 | − | 0.789485i | \(-0.710348\pi\) | ||||
−0.613770 | + | 0.789485i | \(0.710348\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −845.626 | −0.808952 | −0.404476 | − | 0.914549i | \(-0.632546\pi\) | ||||
−0.404476 | + | 0.914549i | \(0.632546\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1281.52 | −1.15784 | −0.578920 | − | 0.815384i | \(-0.696526\pi\) | ||||
−0.578920 | + | 0.815384i | \(0.696526\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −902.000 | −0.792623 | −0.396312 | − | 0.918116i | \(-0.629710\pi\) | ||||
−0.396312 | + | 0.918116i | \(0.629710\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1464.59 | −1.21927 | −0.609633 | − | 0.792684i | \(-0.708683\pi\) | ||||
−0.609633 | + | 0.792684i | \(0.708683\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 608.000 | 0.468364 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −931.000 | −0.699474 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2624.06 | 1.83344 | 0.916722 | − | 0.399525i | \(-0.130825\pi\) | ||||
0.916722 | + | 0.399525i | \(0.130825\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2940.00 | −1.96083 | −0.980416 | − | 0.196938i | \(-0.936900\pi\) | ||||
−0.980416 | + | 0.196938i | \(0.936900\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 732.295 | 0.477429 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −732.295 | −0.456673 | −0.228336 | − | 0.973582i | \(-0.573329\pi\) | ||||
−0.228336 | + | 0.973582i | \(0.573329\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 364.000 | 0.222116 | 0.111058 | − | 0.993814i | \(-0.464576\pi\) | ||||
0.111058 | + | 0.993814i | \(0.464576\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1046.14 | 0.611764 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 254.000 | 0.139654 | 0.0698272 | − | 0.997559i | \(-0.477755\pi\) | ||||
0.0698272 | + | 0.997559i | \(0.477755\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2360.00 | −1.27188 | −0.635941 | − | 0.771738i | \(-0.719388\pi\) | ||||
−0.635941 | + | 0.771738i | \(0.719388\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2214.32 | 1.12562 | 0.562809 | − | 0.826587i | \(-0.309721\pi\) | ||||
0.562809 | + | 0.826587i | \(0.309721\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −532.000 | −0.260419 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1525.61 | −0.733100 | −0.366550 | − | 0.930398i | \(-0.619461\pi\) | ||||
−0.366550 | + | 0.930398i | \(0.619461\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3059.95 | 1.41788 | 0.708940 | − | 0.705269i | \(-0.249174\pi\) | ||||
0.708940 | + | 0.705269i | \(0.249174\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 539.000 | 0.245335 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1900.48 | −0.835207 | −0.417604 | − | 0.908629i | \(-0.637130\pi\) | ||||
−0.417604 | + | 0.908629i | \(0.637130\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1972.00 | −0.823431 | −0.411716 | − | 0.911312i | \(-0.635070\pi\) | ||||
−0.411716 | + | 0.911312i | \(0.635070\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1330.00 | −0.546177 | −0.273089 | − | 0.961989i | \(-0.588045\pi\) | ||||
−0.273089 | + | 0.961989i | \(0.588045\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1394.85 | −0.545462 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1728.00 | −0.654627 | −0.327313 | − | 0.944916i | \(-0.606143\pi\) | ||||
−0.327313 | + | 0.944916i | \(0.606143\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 976.393 | 0.364157 | 0.182079 | − | 0.983284i | \(-0.441717\pi\) | ||||
0.182079 | + | 0.983284i | \(0.441717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3783.52 | −1.36835 | −0.684175 | − | 0.729318i | \(-0.739838\pi\) | ||||
−0.684175 | + | 0.729318i | \(0.739838\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1512.00 | 0.538607 | 0.269304 | − | 0.963055i | \(-0.413206\pi\) | ||||
0.269304 | + | 0.963055i | \(0.413206\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 52.3068 | 0.0180848 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1680.00 | −0.556019 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1644.00 | 0.536387 | 0.268193 | − | 0.963365i | \(-0.413573\pi\) | ||||
0.268193 | + | 0.963365i | \(0.413573\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1952.79 | −0.610893 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3648.00 | −1.11037 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1089.72 | −0.327235 | −0.163617 | − | 0.986524i | \(-0.552316\pi\) | ||||
−0.163617 | + | 0.986524i | \(0.552316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 985.111 | 0.288036 | 0.144018 | − | 0.989575i | \(-0.453998\pi\) | ||||
0.144018 | + | 0.989575i | \(0.453998\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3934.00 | −1.13522 | −0.567611 | − | 0.823297i | \(-0.692132\pi\) | ||||
−0.567611 | + | 0.823297i | \(0.692132\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4637.87 | 1.30402 | 0.652010 | − | 0.758210i | \(-0.273926\pi\) | ||||
0.652010 | + | 0.758210i | \(0.273926\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3856.00 | 1.04361 | 0.521807 | − | 0.853063i | \(-0.325258\pi\) | ||||
0.521807 | + | 0.853063i | \(0.325258\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 994.000 | 0.265681 | 0.132841 | − | 0.991137i | \(-0.457590\pi\) | ||||
0.132841 | + | 0.991137i | \(0.457590\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4393.77 | −1.13186 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6300.00 | 1.58427 | 0.792136 | − | 0.610344i | \(-0.208969\pi\) | ||||
0.792136 | + | 0.610344i | \(0.208969\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1220.49 | 0.303287 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6695.27 | 1.62506 | 0.812528 | − | 0.582922i | \(-0.198091\pi\) | ||||
0.812528 | + | 0.582922i | \(0.198091\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1064.00 | −0.255265 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1403.57 | 0.329078 | 0.164539 | − | 0.986371i | \(-0.447386\pi\) | ||||
0.164539 | + | 0.986371i | \(0.447386\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5082.00 | −1.15188 | −0.575939 | − | 0.817493i | \(-0.695363\pi\) | ||||
−0.575939 | + | 0.817493i | \(0.695363\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2800.00 | 0.627631 | 0.313815 | − | 0.949484i | \(-0.398393\pi\) | ||||
0.313815 | + | 0.949484i | \(0.398393\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1586.64 | −0.344159 | −0.172079 | − | 0.985083i | \(-0.555049\pi\) | ||||
−0.172079 | + | 0.985083i | \(0.555049\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1254.00 | 0.266218 | 0.133109 | − | 0.991101i | \(-0.457504\pi\) | ||||
0.133109 | + | 0.991101i | \(0.457504\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4646.59 | 0.976010 | 0.488005 | − | 0.872841i | \(-0.337725\pi\) | ||||
0.488005 | + | 0.872841i | \(0.337725\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2318.93 | −0.476942 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −49.0000 | −0.00997354 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6538.35 | −1.30367 | −0.651833 | − | 0.758362i | \(-0.726000\pi\) | ||||
−0.651833 | + | 0.758362i | \(0.726000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3192.00 | 0.617385 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2660.00 | −0.509368 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6355.27 | −1.18148 | −0.590741 | − | 0.806862i | \(-0.701164\pi\) | ||||
−0.590741 | + | 0.806862i | \(0.701164\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5208.00 | 0.949577 | 0.474789 | − | 0.880100i | \(-0.342524\pi\) | ||||
0.474789 | + | 0.880100i | \(0.342524\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4568.13 | −0.824939 | −0.412469 | − | 0.910972i | \(-0.635334\pi\) | ||||
−0.412469 | + | 0.910972i | \(0.635334\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 854.344 | 0.151371 | 0.0756857 | − | 0.997132i | \(-0.475885\pi\) | ||||
0.0756857 | + | 0.997132i | \(0.475885\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −120.000 | −0.0210618 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5858.36 | 1.00919 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3268.00 | 0.547631 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7828.00 | 1.29990 | 0.649948 | − | 0.759978i | \(-0.274791\pi\) | ||||
0.649948 | + | 0.759978i | \(0.274791\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5370.16 | 0.868046 | 0.434023 | − | 0.900902i | \(-0.357094\pi\) | ||||
0.434023 | + | 0.900902i | \(0.357094\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4480.00 | 0.711453 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5317.86 | −0.837135 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2746.11 | −0.424838 | −0.212419 | − | 0.977179i | \(-0.568134\pi\) | ||||
−0.212419 | + | 0.977179i | \(0.568134\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8890.00 | 1.36353 | 0.681763 | − | 0.731573i | \(-0.261213\pi\) | ||||
0.681763 | + | 0.731573i | \(0.261213\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1534.33 | −0.231344 | −0.115672 | − | 0.993287i | \(-0.536902\pi\) | ||||
−0.115672 | + | 0.993287i | \(0.536902\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9144.00 | 1.34429 | 0.672147 | − | 0.740417i | \(-0.265372\pi\) | ||||
0.672147 | + | 0.740417i | \(0.265372\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 197.000 | 0.0287214 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10365.5 | 1.47431 | 0.737156 | − | 0.675722i | \(-0.236168\pi\) | ||||
0.737156 | + | 0.675722i | \(0.236168\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3192.00 | 0.446686 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3295.33 | −0.457441 | −0.228721 | − | 0.973492i | \(-0.573454\pi\) | ||||
−0.228721 | + | 0.973492i | \(0.573454\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −313.841 | −0.0428743 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2588.00 | 0.350756 | 0.175378 | − | 0.984501i | \(-0.443885\pi\) | ||||
0.175378 | + | 0.984501i | \(0.443885\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4071.21 | −0.543157 | −0.271579 | − | 0.962416i | \(-0.587546\pi\) | ||||
−0.271579 | + | 0.962416i | \(0.587546\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5426.00 | −0.707221 | −0.353611 | − | 0.935393i | \(-0.615046\pi\) | ||||
−0.353611 | + | 0.935393i | \(0.615046\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4256.00 | −0.550474 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9816.24 | 1.24096 | 0.620482 | − | 0.784220i | \(-0.286937\pi\) | ||||
0.620482 | + | 0.784220i | \(0.286937\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −370.000 | −0.0460771 | −0.0230386 | − | 0.999735i | \(-0.507334\pi\) | ||||
−0.0230386 | + | 0.999735i | \(0.507334\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11716.7 | 1.44827 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2440.98 | 0.297285 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4186.00 | −0.506074 | −0.253037 | − | 0.967457i | \(-0.581429\pi\) | ||||
−0.253037 | + | 0.967457i | \(0.581429\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −244.098 | −0.0290830 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2716.00 | 0.316671 | 0.158336 | − | 0.987385i | \(-0.449387\pi\) | ||||
0.158336 | + | 0.987385i | \(0.449387\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1966.00 | 0.227594 | 0.113797 | − | 0.993504i | \(-0.463699\pi\) | ||||
0.113797 | + | 0.993504i | \(0.463699\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1586.64 | 0.179819 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11824.0 | 1.32144 | 0.660722 | − | 0.750631i | \(-0.270250\pi\) | ||||
0.660722 | + | 0.750631i | \(0.270250\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2580.47 | −0.286396 | −0.143198 | − | 0.989694i | \(-0.545739\pi\) | ||||
−0.143198 | + | 0.989694i | \(0.545739\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5126.07 | −0.561128 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13272.0 | 1.44291 | 0.721456 | − | 0.692461i | \(-0.243473\pi\) | ||||
0.721456 | + | 0.692461i | \(0.243473\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3112.25 | −0.333787 | −0.166894 | − | 0.985975i | \(-0.553374\pi\) | ||||
−0.166894 | + | 0.985975i | \(0.553374\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2094.00 | −0.220093 | −0.110047 | − | 0.993926i | \(-0.535100\pi\) | ||||
−0.110047 | + | 0.993926i | \(0.535100\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5320.00 | 0.555452 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7078.85 | −0.724584 | −0.362292 | − | 0.932065i | \(-0.618006\pi\) | ||||
−0.362292 | + | 0.932065i | \(0.618006\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9450.00 | 0.954730 | 0.477365 | − | 0.878705i | \(-0.341592\pi\) | ||||
0.477365 | + | 0.878705i | \(0.341592\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3112.25 | −0.312395 | −0.156197 | − | 0.987726i | \(-0.549924\pi\) | ||||
−0.156197 | + | 0.987726i | \(0.549924\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5361.45 | −0.531259 | −0.265630 | − | 0.964075i | \(-0.585580\pi\) | ||||
−0.265630 | + | 0.964075i | \(0.585580\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3724.00 | −0.366649 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6102.46 | 0.593216 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13216.0 | 1.26066 | 0.630328 | − | 0.776329i | \(-0.282920\pi\) | ||||
0.630328 | + | 0.776329i | \(0.282920\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6384.00 | 0.605167 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2379.96 | 0.221450 | 0.110725 | − | 0.993851i | \(-0.464683\pi\) | ||||
0.110725 | + | 0.993851i | \(0.464683\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12300.0 | 1.13053 | 0.565266 | − | 0.824909i | \(-0.308774\pi\) | ||||
0.565266 | + | 0.824909i | \(0.308774\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 418.454 | 0.0382277 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3556.86 | −0.321020 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15756.0 | −1.41350 | −0.706749 | − | 0.707464i | \(-0.749839\pi\) | ||||
−0.706749 | + | 0.707464i | \(0.749839\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19170.4 | −1.69934 | −0.849670 | − | 0.527316i | \(-0.823199\pi\) | ||||
−0.849670 | + | 0.527316i | \(0.823199\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2394.00 | −0.208472 | −0.104236 | − | 0.994553i | \(-0.533240\pi\) | ||||
−0.104236 | + | 0.994553i | \(0.533240\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9424.00 | 0.815838 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7497.31 | −0.637778 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6874.00 | −0.578033 | −0.289017 | − | 0.957324i | \(-0.593328\pi\) | ||||
−0.289017 | + | 0.957324i | \(0.593328\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16154.1 | 1.35061 | 0.675305 | − | 0.737539i | \(-0.264012\pi\) | ||||
0.675305 | + | 0.737539i | \(0.264012\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15622.3 | −1.29131 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8443.00 | −0.693926 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13913.6 | 1.13070 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5340.00 | 0.426735 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7174.00 | 0.570119 | 0.285059 | − | 0.958510i | \(-0.407987\pi\) | ||||
0.285059 | + | 0.958510i | \(0.407987\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4332.75 | −0.338674 | −0.169337 | − | 0.985558i | \(-0.554163\pi\) | ||||
−0.169337 | + | 0.985558i | \(0.554163\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 504.000 | 0.0389676 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −418.454 | −0.0321781 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9153.69 | 0.696327 | 0.348164 | − | 0.937434i | \(-0.386805\pi\) | ||||
0.348164 | + | 0.937434i | \(0.386805\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15960.0 | 1.20758 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13870.0 | 1.03828 | 0.519140 | − | 0.854689i | \(-0.326252\pi\) | ||||
0.519140 | + | 0.854689i | \(0.326252\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16070.0 | −1.18399 | −0.591994 | − | 0.805942i | \(-0.701659\pi\) | ||||
−0.591994 | + | 0.805942i | \(0.701659\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3932.00 | −0.288177 | −0.144089 | − | 0.989565i | \(-0.546025\pi\) | ||||
−0.144089 | + | 0.989565i | \(0.546025\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16180.2 | −1.16740 | −0.583702 | − | 0.811968i | \(-0.698396\pi\) | ||||
−0.583702 | + | 0.811968i | \(0.698396\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1748.00 | 0.124818 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7322.95 | −0.520215 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11272.1 | 0.792589 | 0.396295 | − | 0.918123i | \(-0.370296\pi\) | ||||
0.396295 | + | 0.918123i | \(0.370296\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18816.0 | −1.31630 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10670.6 | 0.738935 | 0.369467 | − | 0.929244i | \(-0.379540\pi\) | ||||
0.369467 | + | 0.929244i | \(0.379540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6840.00 | −0.466569 | −0.233284 | − | 0.972409i | \(-0.574947\pi\) | ||||
−0.233284 | + | 0.972409i | \(0.574947\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10150.0 | −0.688897 | −0.344449 | − | 0.938805i | \(-0.611934\pi\) | ||||
−0.344449 | + | 0.938805i | \(0.611934\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1839.46 | −0.123000 | −0.0615002 | − | 0.998107i | \(-0.519588\pi\) | ||||
−0.0615002 | + | 0.998107i | \(0.519588\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19608.0 | −1.29829 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5004.02 | 0.329707 | 0.164853 | − | 0.986318i | \(-0.447285\pi\) | ||||
0.164853 | + | 0.986318i | \(0.447285\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24653.9 | 1.60864 | 0.804319 | − | 0.594197i | \(-0.202530\pi\) | ||||
0.804319 | + | 0.594197i | \(0.202530\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27020.0 | 1.75448 | 0.877242 | − | 0.480049i | \(-0.159381\pi\) | ||||
0.877242 | + | 0.480049i | \(0.159381\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13303.4 | −0.855518 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8512.00 | −0.539580 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10648.0 | −0.671775 | −0.335888 | − | 0.941902i | \(-0.609036\pi\) | ||||
−0.335888 | + | 0.941902i | \(0.609036\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13965.9 | 0.868681 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1682.00 | −0.103643 | −0.0518214 | − | 0.998656i | \(-0.516503\pi\) | ||||
−0.0518214 | + | 0.998656i | \(0.516503\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18542.8 | −1.13725 | −0.568627 | − | 0.822595i | \(-0.692525\pi\) | ||||
−0.568627 | + | 0.822595i | \(0.692525\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30677.9 | 1.86410 | 0.932051 | − | 0.362327i | \(-0.118018\pi\) | ||||
0.932051 | + | 0.362327i | \(0.118018\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 560.000 | 0.0338705 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1342.54 | −0.0804559 | −0.0402279 | − | 0.999191i | \(-0.512808\pi\) | ||||
−0.0402279 | + | 0.999191i | \(0.512808\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21356.0 | 1.26238 | 0.631192 | − | 0.775626i | \(-0.282566\pi\) | ||||
0.631192 | + | 0.775626i | \(0.282566\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13762.0 | −0.809803 | −0.404901 | − | 0.914360i | \(-0.632694\pi\) | ||||
−0.404901 | + | 0.914360i | \(0.632694\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −366.148 | −0.0212553 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3640.00 | −0.209420 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5858.36 | −0.335547 | −0.167774 | − | 0.985826i | \(-0.553658\pi\) | ||||
−0.167774 | + | 0.985826i | \(0.553658\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29588.2 | −1.67972 | −0.839858 | − | 0.542807i | \(-0.817362\pi\) | ||||
−0.839858 | + | 0.542807i | \(0.817362\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4864.00 | −0.274909 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17270.0 | −0.967521 | −0.483760 | − | 0.875201i | \(-0.660729\pi\) | ||||
−0.483760 | + | 0.875201i | \(0.660729\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19152.0 | −1.05897 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1652.00 | −0.0909480 | −0.0454740 | − | 0.998966i | \(-0.514480\pi\) | ||||
−0.0454740 | + | 0.998966i | \(0.514480\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18551.5 | −1.00816 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28790.0 | −1.55119 | −0.775594 | − | 0.631232i | \(-0.782550\pi\) | ||||
−0.775594 | + | 0.631232i | \(0.782550\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10252.1 | −0.550023 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10862.4 | −0.577824 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7554.00 | 0.400136 | 0.200068 | − | 0.979782i | \(-0.435884\pi\) | ||||
0.200068 | + | 0.979782i | \(0.435884\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13669.5 | 0.717990 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28336.0 | 1.46976 | 0.734878 | − | 0.678199i | \(-0.237239\pi\) | ||||
0.734878 | + | 0.678199i | \(0.237239\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7372.00 | −0.380787 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23511.9 | 1.19946 | 0.599730 | − | 0.800202i | \(-0.295274\pi\) | ||||
0.599730 | + | 0.800202i | \(0.295274\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21280.0 | −1.07670 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3365.07 | 0.169566 | 0.0847829 | − | 0.996399i | \(-0.472980\pi\) | ||||
0.0847829 | + | 0.996399i | \(0.472980\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8543.44 | 0.427004 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14300.0 | −0.711819 | −0.355909 | − | 0.934520i | \(-0.615829\pi\) | ||||
−0.355909 | + | 0.934520i | \(0.615829\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31671.8 | 1.56383 | 0.781914 | − | 0.623386i | \(-0.214244\pi\) | ||||
0.781914 | + | 0.623386i | \(0.214244\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11172.0 | −0.545015 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11824.0 | −0.574519 | −0.287260 | − | 0.957853i | \(-0.592744\pi\) | ||||
−0.287260 | + | 0.957853i | \(0.592744\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1342.54 | 0.0644590 | 0.0322295 | − | 0.999480i | \(-0.489739\pi\) | ||||
0.0322295 | + | 0.999480i | \(0.489739\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6762.00 | −0.322106 | −0.161053 | − | 0.986946i | \(-0.551489\pi\) | ||||
−0.161053 | + | 0.986946i | \(0.551489\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7863.45 | −0.373101 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1464.59 | 0.0689482 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29442.0 | −1.38063 | −0.690316 | − | 0.723508i | \(-0.742528\pi\) | ||||
−0.690316 | + | 0.723508i | \(0.742528\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35830.1 | −1.66717 | −0.833584 | − | 0.552393i | \(-0.813715\pi\) | ||||
−0.833584 | + | 0.552393i | \(0.813715\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22344.0 | −1.02767 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8160.00 | 0.373864 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23912.9 | 1.08310 | 0.541552 | − | 0.840667i | \(-0.317837\pi\) | ||||
0.541552 | + | 0.840667i | \(0.317837\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12768.0 | −0.573929 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9519.84 | −0.426304 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17139.2 | −0.761733 | −0.380867 | − | 0.924630i | \(-0.624374\pi\) | ||||
−0.380867 | + | 0.924630i | \(0.624374\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26144.0 | 1.15758 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21620.1 | −0.950135 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8646.00 | −0.375744 | −0.187872 | − | 0.982193i | \(-0.560159\pi\) | ||||
−0.187872 | + | 0.982193i | \(0.560159\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18956.0 | −0.820759 | −0.410379 | − | 0.911915i | \(-0.634604\pi\) | ||||
−0.410379 | + | 0.911915i | \(0.634604\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25630.3 | −1.09754 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13726.0 | −0.583484 | −0.291742 | − | 0.956497i | \(-0.594235\pi\) | ||||
−0.291742 | + | 0.956497i | \(0.594235\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45951.5 | 1.94626 | 0.973128 | − | 0.230264i | \(-0.0739590\pi\) | ||||
0.973128 | + | 0.230264i | \(0.0739590\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2135.86 | 0.0898079 | 0.0449040 | − | 0.998991i | \(-0.485702\pi\) | ||||
0.0449040 | + | 0.998991i | \(0.485702\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8778.00 | 0.367759 | 0.183880 | − | 0.982949i | \(-0.441134\pi\) | ||||
0.183880 | + | 0.982949i | \(0.441134\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18621.2 | −0.774534 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18088.0 | −0.744299 | −0.372150 | − | 0.928173i | \(-0.621379\pi\) | ||||
−0.372150 | + | 0.928173i | \(0.621379\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24353.0 | −0.998524 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8116.27 | −0.329254 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7448.00 | 0.300017 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22927.8 | 0.920320 | 0.460160 | − | 0.887836i | \(-0.347792\pi\) | ||||
0.460160 | + | 0.887836i | \(0.347792\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4498.38 | 0.179302 | 0.0896510 | − | 0.995973i | \(-0.471425\pi\) | ||||
0.0896510 | + | 0.995973i | \(0.471425\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40516.0 | −1.60930 | −0.804650 | − | 0.593750i | \(-0.797647\pi\) | ||||
−0.804650 | + | 0.593750i | \(0.797647\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28010.3 | 1.10484 | 0.552422 | − | 0.833564i | \(-0.313704\pi\) | ||||
0.552422 | + | 0.833564i | \(0.313704\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 960.000 | 0.0374750 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22344.0 | 0.869228 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33807.6 | 1.30171 | 0.650856 | − | 0.759201i | \(-0.274410\pi\) | ||||
0.650856 | + | 0.759201i | \(0.274410\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19362.0 | −0.740434 | −0.370217 | − | 0.928945i | \(-0.620717\pi\) | ||||
−0.370217 | + | 0.928945i | \(0.620717\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4942.99 | −0.188386 | −0.0941930 | − | 0.995554i | \(-0.530027\pi\) | ||||
−0.0941930 | + | 0.995554i | \(0.530027\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44016.2 | −1.66620 | −0.833099 | − | 0.553124i | \(-0.813436\pi\) | ||||
−0.833099 | + | 0.553124i | \(0.813436\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22876.0 | 0.863033 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 31488.7 | 1.17999 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1344.00 | −0.0498609 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25536.0 | 0.944204 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42656.2 | −1.56160 | −0.780802 | − | 0.624778i | \(-0.785189\pi\) | ||||
−0.780802 | + | 0.624778i | \(0.785189\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15888.0 | 0.577819 | 0.288909 | − | 0.957356i | \(-0.406707\pi\) | ||||
0.288909 | + | 0.957356i | \(0.406707\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4010.19 | −0.145365 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25630.3 | −0.922997 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7944.00 | −0.285145 | −0.142573 | − | 0.989784i | \(-0.545537\pi\) | ||||
−0.142573 | + | 0.989784i | \(0.545537\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21341.2 | 0.761054 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20622.0 | −0.728295 | −0.364147 | − | 0.931341i | \(-0.618640\pi\) | ||||
−0.364147 | + | 0.931341i | \(0.618640\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22428.0 | −0.789525 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41182.9 | 1.43584 | 0.717922 | − | 0.696123i | \(-0.245093\pi\) | ||||
0.717922 | + | 0.696123i | \(0.245093\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40502.0 | −1.40311 | −0.701556 | − | 0.712615i | \(-0.747511\pi\) | ||||
−0.701556 | + | 0.712615i | \(0.747511\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16232.5 | 0.560556 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3844.55 | 0.131923 | 0.0659615 | − | 0.997822i | \(-0.478989\pi\) | ||||
0.0659615 | + | 0.997822i | \(0.478989\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −56544.0 | −1.93414 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31976.9 | −1.08692 | −0.543459 | − | 0.839436i | \(-0.682886\pi\) | ||||
−0.543459 | + | 0.839436i | \(0.682886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6384.00 | −0.214964 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20385.0 | 0.684267 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19100.7 | −0.635198 | −0.317599 | − | 0.948225i | \(-0.602877\pi\) | ||||
−0.317599 | + | 0.948225i | \(0.602877\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17556.0 | −0.580225 | −0.290113 | − | 0.956992i | \(-0.593693\pi\) | ||||
−0.290113 | + | 0.956992i | \(0.593693\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3173.28 | 0.104554 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4393.77 | −0.143878 | −0.0719392 | − | 0.997409i | \(-0.522919\pi\) | ||||
−0.0719392 | + | 0.997409i | \(0.522919\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30520.0 | 0.996347 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9406.50 | −0.305209 | −0.152605 | − | 0.988287i | \(-0.548766\pi\) | ||||
−0.152605 | + | 0.988287i | \(0.548766\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18620.0 | 0.598667 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28576.0 | 0.915990 | 0.457995 | − | 0.888955i | \(-0.348568\pi\) | ||||
0.457995 | + | 0.888955i | \(0.348568\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31541.0 | 1.00192 | 0.500960 | − | 0.865471i | \(-0.332981\pi\) | ||||
0.500960 | + | 0.865471i | \(0.332981\pi\) | |||||||
\(998\) | 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 | 900.4.a.s.1.2 | 2 | ||
3.2 | odd | 2 | 100.4.a.d.1.2 | 2 | |||
5.2 | odd | 4 | 180.4.d.a.109.1 | 2 | |||
5.3 | odd | 4 | 180.4.d.a.109.2 | 2 | |||
5.4 | even | 2 | inner | 900.4.a.s.1.1 | 2 | ||
12.11 | even | 2 | 400.4.a.w.1.1 | 2 | |||
15.2 | even | 4 | 20.4.c.a.9.1 | ✓ | 2 | ||
15.8 | even | 4 | 20.4.c.a.9.2 | yes | 2 | ||
15.14 | odd | 2 | 100.4.a.d.1.1 | 2 | |||
20.3 | even | 4 | 720.4.f.a.289.2 | 2 | |||
20.7 | even | 4 | 720.4.f.a.289.1 | 2 | |||
24.5 | odd | 2 | 1600.4.a.cj.1.1 | 2 | |||
24.11 | even | 2 | 1600.4.a.ck.1.2 | 2 | |||
60.23 | odd | 4 | 80.4.c.b.49.1 | 2 | |||
60.47 | odd | 4 | 80.4.c.b.49.2 | 2 | |||
60.59 | even | 2 | 400.4.a.w.1.2 | 2 | |||
105.62 | odd | 4 | 980.4.e.a.589.2 | 2 | |||
105.83 | odd | 4 | 980.4.e.a.589.1 | 2 | |||
120.29 | odd | 2 | 1600.4.a.cj.1.2 | 2 | |||
120.53 | even | 4 | 320.4.c.a.129.1 | 2 | |||
120.59 | even | 2 | 1600.4.a.ck.1.1 | 2 | |||
120.77 | even | 4 | 320.4.c.a.129.2 | 2 | |||
120.83 | odd | 4 | 320.4.c.b.129.2 | 2 | |||
120.107 | odd | 4 | 320.4.c.b.129.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.4.c.a.9.1 | ✓ | 2 | 15.2 | even | 4 | ||
20.4.c.a.9.2 | yes | 2 | 15.8 | even | 4 | ||
80.4.c.b.49.1 | 2 | 60.23 | odd | 4 | |||
80.4.c.b.49.2 | 2 | 60.47 | odd | 4 | |||
100.4.a.d.1.1 | 2 | 15.14 | odd | 2 | |||
100.4.a.d.1.2 | 2 | 3.2 | odd | 2 | |||
180.4.d.a.109.1 | 2 | 5.2 | odd | 4 | |||
180.4.d.a.109.2 | 2 | 5.3 | odd | 4 | |||
320.4.c.a.129.1 | 2 | 120.53 | even | 4 | |||
320.4.c.a.129.2 | 2 | 120.77 | even | 4 | |||
320.4.c.b.129.1 | 2 | 120.107 | odd | 4 | |||
320.4.c.b.129.2 | 2 | 120.83 | odd | 4 | |||
400.4.a.w.1.1 | 2 | 12.11 | even | 2 | |||
400.4.a.w.1.2 | 2 | 60.59 | even | 2 | |||
720.4.f.a.289.1 | 2 | 20.7 | even | 4 | |||
720.4.f.a.289.2 | 2 | 20.3 | even | 4 | |||
900.4.a.s.1.1 | 2 | 5.4 | even | 2 | inner | ||
900.4.a.s.1.2 | 2 | 1.1 | even | 1 | trivial | ||
980.4.e.a.589.1 | 2 | 105.83 | odd | 4 | |||
980.4.e.a.589.2 | 2 | 105.62 | odd | 4 | |||
1600.4.a.cj.1.1 | 2 | 24.5 | odd | 2 | |||
1600.4.a.cj.1.2 | 2 | 120.29 | odd | 2 | |||
1600.4.a.ck.1.1 | 2 | 120.59 | even | 2 | |||
1600.4.a.ck.1.2 | 2 | 24.11 | even | 2 |