Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2475,4,Mod(1,2475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2475, 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("2475.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2475.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: | \(146.029727264\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 825) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2475.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.00000 | 1.76777 | 0.883883 | − | 0.467707i | \(-0.154920\pi\) | ||||
0.883883 | + | 0.467707i | \(0.154920\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 17.0000 | 2.12500 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00000 | −0.161985 | −0.0809924 | − | 0.996715i | \(-0.525809\pi\) | ||||
−0.0809924 | + | 0.996715i | \(0.525809\pi\) | |||||||
\(8\) | 45.0000 | 1.98874 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −32.0000 | −0.682708 | −0.341354 | − | 0.939935i | \(-0.610885\pi\) | ||||
−0.341354 | + | 0.939935i | \(0.610885\pi\) | |||||||
\(14\) | −15.0000 | −0.286351 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 89.0000 | 1.39062 | ||||||||
\(17\) | 33.0000 | 0.470804 | 0.235402 | − | 0.971898i | \(-0.424359\pi\) | ||||
0.235402 | + | 0.971898i | \(0.424359\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 47.0000 | 0.567502 | 0.283751 | − | 0.958898i | \(-0.408421\pi\) | ||||
0.283751 | + | 0.958898i | \(0.408421\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 55.0000 | 0.533002 | ||||||||
\(23\) | 113.000 | 1.02444 | 0.512220 | − | 0.858854i | \(-0.328823\pi\) | ||||
0.512220 | + | 0.858854i | \(0.328823\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −160.000 | −1.20687 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −51.0000 | −0.344218 | ||||||||
\(29\) | 54.0000 | 0.345778 | 0.172889 | − | 0.984941i | \(-0.444690\pi\) | ||||
0.172889 | + | 0.984941i | \(0.444690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 178.000 | 1.03128 | 0.515641 | − | 0.856805i | \(-0.327554\pi\) | ||||
0.515641 | + | 0.856805i | \(0.327554\pi\) | |||||||
\(32\) | 85.0000 | 0.469563 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 165.000 | 0.832273 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −19.0000 | −0.0844211 | −0.0422106 | − | 0.999109i | \(-0.513440\pi\) | ||||
−0.0422106 | + | 0.999109i | \(0.513440\pi\) | |||||||
\(38\) | 235.000 | 1.00321 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −139.000 | −0.529467 | −0.264734 | − | 0.964322i | \(-0.585284\pi\) | ||||
−0.264734 | + | 0.964322i | \(0.585284\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 308.000 | 1.09232 | 0.546158 | − | 0.837682i | \(-0.316090\pi\) | ||||
0.546158 | + | 0.837682i | \(0.316090\pi\) | |||||||
\(44\) | 187.000 | 0.640712 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 565.000 | 1.81097 | ||||||||
\(47\) | 195.000 | 0.605185 | 0.302592 | − | 0.953120i | \(-0.402148\pi\) | ||||
0.302592 | + | 0.953120i | \(0.402148\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −334.000 | −0.973761 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −544.000 | −1.45075 | ||||||||
\(53\) | 152.000 | 0.393940 | 0.196970 | − | 0.980410i | \(-0.436890\pi\) | ||||
0.196970 | + | 0.980410i | \(0.436890\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −135.000 | −0.322145 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 270.000 | 0.611254 | ||||||||
\(59\) | 625.000 | 1.37912 | 0.689560 | − | 0.724229i | \(-0.257804\pi\) | ||||
0.689560 | + | 0.724229i | \(0.257804\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 320.000 | 0.671669 | 0.335834 | − | 0.941921i | \(-0.390982\pi\) | ||||
0.335834 | + | 0.941921i | \(0.390982\pi\) | |||||||
\(62\) | 890.000 | 1.82307 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −287.000 | −0.560547 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −200.000 | −0.364685 | −0.182342 | − | 0.983235i | \(-0.558368\pi\) | ||||
−0.182342 | + | 0.983235i | \(0.558368\pi\) | |||||||
\(68\) | 561.000 | 1.00046 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 947.000 | 1.58293 | 0.791466 | − | 0.611213i | \(-0.209318\pi\) | ||||
0.791466 | + | 0.611213i | \(0.209318\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 448.000 | 0.718280 | 0.359140 | − | 0.933284i | \(-0.383070\pi\) | ||||
0.359140 | + | 0.933284i | \(0.383070\pi\) | |||||||
\(74\) | −95.0000 | −0.149237 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 799.000 | 1.20594 | ||||||||
\(77\) | −33.0000 | −0.0488402 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −721.000 | −1.02682 | −0.513410 | − | 0.858143i | \(-0.671618\pi\) | ||||
−0.513410 | + | 0.858143i | \(0.671618\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −695.000 | −0.935975 | ||||||||
\(83\) | 142.000 | 0.187789 | 0.0938947 | − | 0.995582i | \(-0.470068\pi\) | ||||
0.0938947 | + | 0.995582i | \(0.470068\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1540.00 | 1.93096 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 495.000 | 0.599627 | ||||||||
\(89\) | −404.000 | −0.481168 | −0.240584 | − | 0.970628i | \(-0.577339\pi\) | ||||
−0.240584 | + | 0.970628i | \(0.577339\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 96.0000 | 0.110588 | ||||||||
\(92\) | 1921.00 | 2.17694 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 975.000 | 1.06983 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −79.0000 | −0.0826931 | −0.0413466 | − | 0.999145i | \(-0.513165\pi\) | ||||
−0.0413466 | + | 0.999145i | \(0.513165\pi\) | |||||||
\(98\) | −1670.00 | −1.72138 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 545.000 | 0.536926 | 0.268463 | − | 0.963290i | \(-0.413484\pi\) | ||||
0.268463 | + | 0.963290i | \(0.413484\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1306.00 | 1.24936 | 0.624680 | − | 0.780881i | \(-0.285230\pi\) | ||||
0.624680 | + | 0.780881i | \(0.285230\pi\) | |||||||
\(104\) | −1440.00 | −1.35773 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 760.000 | 0.696394 | ||||||||
\(107\) | 1938.00 | 1.75097 | 0.875484 | − | 0.483247i | \(-0.160543\pi\) | ||||
0.875484 | + | 0.483247i | \(0.160543\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −576.000 | −0.506154 | −0.253077 | − | 0.967446i | \(-0.581443\pi\) | ||||
−0.253077 | + | 0.967446i | \(0.581443\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −267.000 | −0.225260 | ||||||||
\(113\) | −1104.00 | −0.919076 | −0.459538 | − | 0.888158i | \(-0.651985\pi\) | ||||
−0.459538 | + | 0.888158i | \(0.651985\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 918.000 | 0.734777 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3125.00 | 2.43796 | ||||||||
\(119\) | −99.0000 | −0.0762632 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 1600.00 | 1.18735 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3026.00 | 2.19147 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1739.00 | 1.21505 | 0.607525 | − | 0.794301i | \(-0.292163\pi\) | ||||
0.607525 | + | 0.794301i | \(0.292163\pi\) | |||||||
\(128\) | −2115.00 | −1.46048 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1818.00 | −1.21251 | −0.606257 | − | 0.795269i | \(-0.707330\pi\) | ||||
−0.606257 | + | 0.795269i | \(0.707330\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −141.000 | −0.0919267 | ||||||||
\(134\) | −1000.00 | −0.644678 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1485.00 | 0.936307 | ||||||||
\(137\) | 870.000 | 0.542548 | 0.271274 | − | 0.962502i | \(-0.412555\pi\) | ||||
0.271274 | + | 0.962502i | \(0.412555\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −636.000 | −0.388092 | −0.194046 | − | 0.980992i | \(-0.562161\pi\) | ||||
−0.194046 | + | 0.980992i | \(0.562161\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4735.00 | 2.79826 | ||||||||
\(143\) | −352.000 | −0.205844 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2240.00 | 1.26975 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −323.000 | −0.179395 | ||||||||
\(149\) | 239.000 | 0.131407 | 0.0657035 | − | 0.997839i | \(-0.479071\pi\) | ||||
0.0657035 | + | 0.997839i | \(0.479071\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1208.00 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 2115.00 | 1.12861 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −165.000 | −0.0863382 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1874.00 | 0.952621 | 0.476310 | − | 0.879277i | \(-0.341974\pi\) | ||||
0.476310 | + | 0.879277i | \(0.341974\pi\) | |||||||
\(158\) | −3605.00 | −1.81518 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −339.000 | −0.165944 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1904.00 | 0.914925 | 0.457463 | − | 0.889229i | \(-0.348758\pi\) | ||||
0.457463 | + | 0.889229i | \(0.348758\pi\) | |||||||
\(164\) | −2363.00 | −1.12512 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 710.000 | 0.331968 | ||||||||
\(167\) | −1180.00 | −0.546773 | −0.273387 | − | 0.961904i | \(-0.588144\pi\) | ||||
−0.273387 | + | 0.961904i | \(0.588144\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1173.00 | −0.533910 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5236.00 | 2.32117 | ||||||||
\(173\) | −3177.00 | −1.39620 | −0.698101 | − | 0.716000i | \(-0.745971\pi\) | ||||
−0.698101 | + | 0.716000i | \(0.745971\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 979.000 | 0.419289 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2020.00 | −0.850592 | ||||||||
\(179\) | −1787.00 | −0.746182 | −0.373091 | − | 0.927795i | \(-0.621702\pi\) | ||||
−0.373091 | + | 0.927795i | \(0.621702\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −835.000 | −0.342901 | −0.171450 | − | 0.985193i | \(-0.554845\pi\) | ||||
−0.171450 | + | 0.985193i | \(0.554845\pi\) | |||||||
\(182\) | 480.000 | 0.195494 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5085.00 | 2.03734 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 363.000 | 0.141953 | ||||||||
\(188\) | 3315.00 | 1.28602 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3613.00 | −1.36873 | −0.684365 | − | 0.729139i | \(-0.739921\pi\) | ||||
−0.684365 | + | 0.729139i | \(0.739921\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4204.00 | −1.56793 | −0.783965 | − | 0.620805i | \(-0.786806\pi\) | ||||
−0.783965 | + | 0.620805i | \(0.786806\pi\) | |||||||
\(194\) | −395.000 | −0.146182 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5678.00 | −2.06924 | ||||||||
\(197\) | −4517.00 | −1.63362 | −0.816809 | − | 0.576908i | \(-0.804259\pi\) | ||||
−0.816809 | + | 0.576908i | \(0.804259\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4164.00 | 1.48331 | 0.741654 | − | 0.670783i | \(-0.234042\pi\) | ||||
0.741654 | + | 0.670783i | \(0.234042\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2725.00 | 0.949160 | ||||||||
\(203\) | −162.000 | −0.0560107 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6530.00 | 2.20858 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2848.00 | −0.949391 | ||||||||
\(209\) | 517.000 | 0.171108 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4660.00 | 1.52042 | 0.760208 | − | 0.649680i | \(-0.225097\pi\) | ||||
0.760208 | + | 0.649680i | \(0.225097\pi\) | |||||||
\(212\) | 2584.00 | 0.837122 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9690.00 | 3.09530 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −534.000 | −0.167052 | ||||||||
\(218\) | −2880.00 | −0.894762 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1056.00 | −0.321422 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3560.00 | −1.06904 | −0.534518 | − | 0.845157i | \(-0.679507\pi\) | ||||
−0.534518 | + | 0.845157i | \(0.679507\pi\) | |||||||
\(224\) | −255.000 | −0.0760621 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5520.00 | −1.62471 | ||||||||
\(227\) | −4678.00 | −1.36780 | −0.683898 | − | 0.729577i | \(-0.739717\pi\) | ||||
−0.683898 | + | 0.729577i | \(0.739717\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4447.00 | −1.28326 | −0.641629 | − | 0.767015i | \(-0.721741\pi\) | ||||
−0.641629 | + | 0.767015i | \(0.721741\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2430.00 | 0.687661 | ||||||||
\(233\) | 411.000 | 0.115560 | 0.0577801 | − | 0.998329i | \(-0.481598\pi\) | ||||
0.0577801 | + | 0.998329i | \(0.481598\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10625.0 | 2.93063 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −495.000 | −0.134815 | ||||||||
\(239\) | 6380.00 | 1.72673 | 0.863364 | − | 0.504582i | \(-0.168353\pi\) | ||||
0.863364 | + | 0.504582i | \(0.168353\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7282.00 | 1.94637 | 0.973184 | − | 0.230027i | \(-0.0738813\pi\) | ||||
0.973184 | + | 0.230027i | \(0.0738813\pi\) | |||||||
\(242\) | 605.000 | 0.160706 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5440.00 | 1.42730 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1504.00 | −0.387438 | ||||||||
\(248\) | 8010.00 | 2.05095 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4728.00 | 1.18896 | 0.594480 | − | 0.804111i | \(-0.297358\pi\) | ||||
0.594480 | + | 0.804111i | \(0.297358\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1243.00 | 0.308880 | ||||||||
\(254\) | 8695.00 | 2.14792 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8279.00 | −2.02124 | ||||||||
\(257\) | 5418.00 | 1.31504 | 0.657521 | − | 0.753437i | \(-0.271605\pi\) | ||||
0.657521 | + | 0.753437i | \(0.271605\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 57.0000 | 0.0136749 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9090.00 | −2.14344 | ||||||||
\(263\) | −3354.00 | −0.786375 | −0.393187 | − | 0.919458i | \(-0.628628\pi\) | ||||
−0.393187 | + | 0.919458i | \(0.628628\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −705.000 | −0.162505 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3400.00 | −0.774955 | ||||||||
\(269\) | −1062.00 | −0.240711 | −0.120356 | − | 0.992731i | \(-0.538403\pi\) | ||||
−0.120356 | + | 0.992731i | \(0.538403\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4821.00 | −1.08065 | −0.540323 | − | 0.841458i | \(-0.681698\pi\) | ||||
−0.540323 | + | 0.841458i | \(0.681698\pi\) | |||||||
\(272\) | 2937.00 | 0.654712 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4350.00 | 0.959099 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.00000 | −0.000867642 0 | −0.000433821 | − | 1.00000i | \(-0.500138\pi\) | ||||
−0.000433821 | 1.00000i | \(0.500138\pi\) | ||||||||
\(278\) | −3180.00 | −0.686057 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4647.00 | −0.986537 | −0.493268 | − | 0.869877i | \(-0.664198\pi\) | ||||
−0.493268 | + | 0.869877i | \(0.664198\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4283.00 | 0.899639 | 0.449820 | − | 0.893119i | \(-0.351488\pi\) | ||||
0.449820 | + | 0.893119i | \(0.351488\pi\) | |||||||
\(284\) | 16099.0 | 3.36373 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1760.00 | −0.363885 | ||||||||
\(287\) | 417.000 | 0.0857656 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3824.00 | −0.778343 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7616.00 | 1.52634 | ||||||||
\(293\) | −6811.00 | −1.35803 | −0.679015 | − | 0.734124i | \(-0.737593\pi\) | ||||
−0.679015 | + | 0.734124i | \(0.737593\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −855.000 | −0.167891 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1195.00 | 0.232297 | ||||||||
\(299\) | −3616.00 | −0.699394 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −924.000 | −0.176938 | ||||||||
\(302\) | 6040.00 | 1.15087 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4183.00 | 0.789183 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 460.000 | 0.0855166 | 0.0427583 | − | 0.999085i | \(-0.486385\pi\) | ||||
0.0427583 | + | 0.999085i | \(0.486385\pi\) | |||||||
\(308\) | −561.000 | −0.103786 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8328.00 | −1.51845 | −0.759224 | − | 0.650829i | \(-0.774421\pi\) | ||||
−0.759224 | + | 0.650829i | \(0.774421\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5929.00 | 1.07069 | 0.535346 | − | 0.844633i | \(-0.320181\pi\) | ||||
0.535346 | + | 0.844633i | \(0.320181\pi\) | |||||||
\(314\) | 9370.00 | 1.68401 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12257.0 | −2.18199 | ||||||||
\(317\) | 5040.00 | 0.892980 | 0.446490 | − | 0.894789i | \(-0.352674\pi\) | ||||
0.446490 | + | 0.894789i | \(0.352674\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 594.000 | 0.104256 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1695.00 | −0.293350 | ||||||||
\(323\) | 1551.00 | 0.267183 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9520.00 | 1.61737 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6255.00 | −1.05297 | ||||||||
\(329\) | −585.000 | −0.0980307 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10396.0 | 1.72633 | 0.863166 | − | 0.504920i | \(-0.168478\pi\) | ||||
0.863166 | + | 0.504920i | \(0.168478\pi\) | |||||||
\(332\) | 2414.00 | 0.399053 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5900.00 | −0.966568 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7236.00 | 1.16964 | 0.584822 | − | 0.811162i | \(-0.301164\pi\) | ||||
0.584822 | + | 0.811162i | \(0.301164\pi\) | |||||||
\(338\) | −5865.00 | −0.943828 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1958.00 | 0.310943 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2031.00 | 0.319719 | ||||||||
\(344\) | 13860.0 | 2.17233 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15885.0 | −2.46816 | ||||||||
\(347\) | 1468.00 | 0.227108 | 0.113554 | − | 0.993532i | \(-0.463777\pi\) | ||||
0.113554 | + | 0.993532i | \(0.463777\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5690.00 | 0.872718 | 0.436359 | − | 0.899773i | \(-0.356268\pi\) | ||||
0.436359 | + | 0.899773i | \(0.356268\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 935.000 | 0.141579 | ||||||||
\(353\) | 5376.00 | 0.810582 | 0.405291 | − | 0.914188i | \(-0.367170\pi\) | ||||
0.405291 | + | 0.914188i | \(0.367170\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6868.00 | −1.02248 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8935.00 | −1.31908 | ||||||||
\(359\) | −3734.00 | −0.548950 | −0.274475 | − | 0.961594i | \(-0.588504\pi\) | ||||
−0.274475 | + | 0.961594i | \(0.588504\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4650.00 | −0.677941 | ||||||||
\(362\) | −4175.00 | −0.606169 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1632.00 | 0.235000 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10274.0 | 1.46130 | 0.730652 | − | 0.682750i | \(-0.239216\pi\) | ||||
0.730652 | + | 0.682750i | \(0.239216\pi\) | |||||||
\(368\) | 10057.0 | 1.42461 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −456.000 | −0.0638122 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13662.0 | −1.89649 | −0.948246 | − | 0.317537i | \(-0.897144\pi\) | ||||
−0.948246 | + | 0.317537i | \(0.897144\pi\) | |||||||
\(374\) | 1815.00 | 0.250940 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8775.00 | 1.20355 | ||||||||
\(377\) | −1728.00 | −0.236065 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7906.00 | −1.07151 | −0.535757 | − | 0.844372i | \(-0.679974\pi\) | ||||
−0.535757 | + | 0.844372i | \(0.679974\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18065.0 | −2.41960 | ||||||||
\(383\) | −3168.00 | −0.422656 | −0.211328 | − | 0.977415i | \(-0.567779\pi\) | ||||
−0.211328 | + | 0.977415i | \(0.567779\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −21020.0 | −2.77174 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1343.00 | −0.175723 | ||||||||
\(389\) | −10770.0 | −1.40375 | −0.701877 | − | 0.712298i | \(-0.747655\pi\) | ||||
−0.701877 | + | 0.712298i | \(0.747655\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3729.00 | 0.482311 | ||||||||
\(392\) | −15030.0 | −1.93656 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22585.0 | −2.88786 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5670.00 | −0.716799 | −0.358399 | − | 0.933568i | \(-0.616677\pi\) | ||||
−0.358399 | + | 0.933568i | \(0.616677\pi\) | |||||||
\(398\) | 20820.0 | 2.62214 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −832.000 | −0.103611 | −0.0518056 | − | 0.998657i | \(-0.516498\pi\) | ||||
−0.0518056 | + | 0.998657i | \(0.516498\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5696.00 | −0.704064 | ||||||||
\(404\) | 9265.00 | 1.14097 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −810.000 | −0.0990139 | ||||||||
\(407\) | −209.000 | −0.0254539 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5712.00 | −0.690563 | −0.345281 | − | 0.938499i | \(-0.612217\pi\) | ||||
−0.345281 | + | 0.938499i | \(0.612217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 22202.0 | 2.65489 | ||||||||
\(413\) | −1875.00 | −0.223396 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2720.00 | −0.320574 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2585.00 | 0.302480 | ||||||||
\(419\) | 4559.00 | 0.531555 | 0.265778 | − | 0.964034i | \(-0.414371\pi\) | ||||
0.265778 | + | 0.964034i | \(0.414371\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6855.00 | 0.793568 | 0.396784 | − | 0.917912i | \(-0.370126\pi\) | ||||
0.396784 | + | 0.917912i | \(0.370126\pi\) | |||||||
\(422\) | 23300.0 | 2.68774 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6840.00 | 0.783443 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −960.000 | −0.108800 | ||||||||
\(428\) | 32946.0 | 3.72081 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10770.0 | −1.20365 | −0.601824 | − | 0.798628i | \(-0.705559\pi\) | ||||
−0.601824 | + | 0.798628i | \(0.705559\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8498.00 | −0.943159 | −0.471579 | − | 0.881824i | \(-0.656316\pi\) | ||||
−0.471579 | + | 0.881824i | \(0.656316\pi\) | |||||||
\(434\) | −2670.00 | −0.295309 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9792.00 | −1.07558 | ||||||||
\(437\) | 5311.00 | 0.581372 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9835.00 | 1.06925 | 0.534623 | − | 0.845091i | \(-0.320454\pi\) | ||||
0.534623 | + | 0.845091i | \(0.320454\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5280.00 | −0.568199 | ||||||||
\(443\) | −10745.0 | −1.15239 | −0.576197 | − | 0.817311i | \(-0.695464\pi\) | ||||
−0.576197 | + | 0.817311i | \(0.695464\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −17800.0 | −1.88981 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 861.000 | 0.0908001 | ||||||||
\(449\) | −8356.00 | −0.878272 | −0.439136 | − | 0.898421i | \(-0.644715\pi\) | ||||
−0.439136 | + | 0.898421i | \(0.644715\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1529.00 | −0.159640 | ||||||||
\(452\) | −18768.0 | −1.95304 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −23390.0 | −2.41795 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7058.00 | 0.722449 | 0.361225 | − | 0.932479i | \(-0.382359\pi\) | ||||
0.361225 | + | 0.932479i | \(0.382359\pi\) | |||||||
\(458\) | −22235.0 | −2.26850 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −646.000 | −0.0652651 | −0.0326326 | − | 0.999467i | \(-0.510389\pi\) | ||||
−0.0326326 | + | 0.999467i | \(0.510389\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8982.00 | 0.901574 | 0.450787 | − | 0.892631i | \(-0.351143\pi\) | ||||
0.450787 | + | 0.892631i | \(0.351143\pi\) | |||||||
\(464\) | 4806.00 | 0.480847 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2055.00 | 0.204283 | ||||||||
\(467\) | −13476.0 | −1.33532 | −0.667661 | − | 0.744466i | \(-0.732704\pi\) | ||||
−0.667661 | + | 0.744466i | \(0.732704\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 600.000 | 0.0590734 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 28125.0 | 2.74271 | ||||||||
\(473\) | 3388.00 | 0.329345 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1683.00 | −0.162059 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 31900.0 | 3.05245 | ||||||||
\(479\) | −12996.0 | −1.23967 | −0.619835 | − | 0.784732i | \(-0.712801\pi\) | ||||
−0.619835 | + | 0.784732i | \(0.712801\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 608.000 | 0.0576350 | ||||||||
\(482\) | 36410.0 | 3.44073 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2057.00 | 0.193182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6026.00 | 0.560707 | 0.280353 | − | 0.959897i | \(-0.409548\pi\) | ||||
0.280353 | + | 0.959897i | \(0.409548\pi\) | |||||||
\(488\) | 14400.0 | 1.33577 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11698.0 | −1.07520 | −0.537600 | − | 0.843200i | \(-0.680669\pi\) | ||||
−0.537600 | + | 0.843200i | \(0.680669\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1782.00 | 0.162794 | ||||||||
\(494\) | −7520.00 | −0.684900 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15842.0 | 1.43413 | ||||||||
\(497\) | −2841.00 | −0.256411 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17052.0 | −1.52976 | −0.764882 | − | 0.644170i | \(-0.777203\pi\) | ||||
−0.764882 | + | 0.644170i | \(0.777203\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 23640.0 | 2.10180 | ||||||||
\(503\) | −932.000 | −0.0826160 | −0.0413080 | − | 0.999146i | \(-0.513152\pi\) | ||||
−0.0413080 | + | 0.999146i | \(0.513152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6215.00 | 0.546029 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 29563.0 | 2.58198 | ||||||||
\(509\) | −4384.00 | −0.381763 | −0.190882 | − | 0.981613i | \(-0.561135\pi\) | ||||
−0.190882 | + | 0.981613i | \(0.561135\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1344.00 | −0.116350 | ||||||||
\(512\) | −24475.0 | −2.11260 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 27090.0 | 2.32469 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2145.00 | 0.182470 | ||||||||
\(518\) | 285.000 | 0.0241741 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2322.00 | 0.195257 | 0.0976283 | − | 0.995223i | \(-0.468874\pi\) | ||||
0.0976283 | + | 0.995223i | \(0.468874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9749.00 | 0.815094 | 0.407547 | − | 0.913184i | \(-0.366384\pi\) | ||||
0.407547 | + | 0.913184i | \(0.366384\pi\) | |||||||
\(524\) | −30906.0 | −2.57659 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16770.0 | −1.39013 | ||||||||
\(527\) | 5874.00 | 0.485532 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 602.000 | 0.0494781 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2397.00 | −0.195344 | ||||||||
\(533\) | 4448.00 | 0.361471 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9000.00 | −0.725263 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5310.00 | −0.425521 | ||||||||
\(539\) | −3674.00 | −0.293600 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4208.00 | 0.334410 | 0.167205 | − | 0.985922i | \(-0.446526\pi\) | ||||
0.167205 | + | 0.985922i | \(0.446526\pi\) | |||||||
\(542\) | −24105.0 | −1.91033 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2805.00 | 0.221072 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10179.0 | −0.795654 | −0.397827 | − | 0.917461i | \(-0.630236\pi\) | ||||
−0.397827 | + | 0.917461i | \(0.630236\pi\) | |||||||
\(548\) | 14790.0 | 1.15292 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2538.00 | 0.196229 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2163.00 | 0.166329 | ||||||||
\(554\) | −20.0000 | −0.00153379 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10812.0 | −0.824696 | ||||||||
\(557\) | −2314.00 | −0.176028 | −0.0880138 | − | 0.996119i | \(-0.528052\pi\) | ||||
−0.0880138 | + | 0.996119i | \(0.528052\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9856.00 | −0.745732 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23235.0 | −1.74397 | ||||||||
\(563\) | 24330.0 | 1.82129 | 0.910646 | − | 0.413188i | \(-0.135585\pi\) | ||||
0.910646 | + | 0.413188i | \(0.135585\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 21415.0 | 1.59035 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42615.0 | 3.14804 | ||||||||
\(569\) | −3445.00 | −0.253817 | −0.126909 | − | 0.991914i | \(-0.540505\pi\) | ||||
−0.126909 | + | 0.991914i | \(0.540505\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13056.0 | −0.956877 | −0.478438 | − | 0.878121i | \(-0.658797\pi\) | ||||
−0.478438 | + | 0.878121i | \(0.658797\pi\) | |||||||
\(572\) | −5984.00 | −0.437419 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2085.00 | 0.151614 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17347.0 | 1.25159 | 0.625793 | − | 0.779989i | \(-0.284775\pi\) | ||||
0.625793 | + | 0.779989i | \(0.284775\pi\) | |||||||
\(578\) | −19120.0 | −1.37593 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −426.000 | −0.0304190 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1672.00 | 0.118777 | ||||||||
\(584\) | 20160.0 | 1.42847 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −34055.0 | −2.40068 | ||||||||
\(587\) | 8379.00 | 0.589162 | 0.294581 | − | 0.955626i | \(-0.404820\pi\) | ||||
0.294581 | + | 0.955626i | \(0.404820\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8366.00 | 0.585255 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1691.00 | −0.117398 | ||||||||
\(593\) | 1958.00 | 0.135591 | 0.0677955 | − | 0.997699i | \(-0.478403\pi\) | ||||
0.0677955 | + | 0.997699i | \(0.478403\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4063.00 | 0.279240 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18080.0 | −1.23636 | ||||||||
\(599\) | −23583.0 | −1.60864 | −0.804320 | − | 0.594196i | \(-0.797470\pi\) | ||||
−0.804320 | + | 0.594196i | \(0.797470\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15328.0 | −1.04034 | −0.520168 | − | 0.854064i | \(-0.674131\pi\) | ||||
−0.520168 | + | 0.854064i | \(0.674131\pi\) | |||||||
\(602\) | −4620.00 | −0.312786 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20536.0 | 1.38344 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −160.000 | −0.0106988 | −0.00534942 | − | 0.999986i | \(-0.501703\pi\) | ||||
−0.00534942 | + | 0.999986i | \(0.501703\pi\) | |||||||
\(608\) | 3995.00 | 0.266478 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6240.00 | −0.413164 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5948.00 | 0.391904 | 0.195952 | − | 0.980613i | \(-0.437220\pi\) | ||||
0.195952 | + | 0.980613i | \(0.437220\pi\) | |||||||
\(614\) | 2300.00 | 0.151173 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1485.00 | −0.0971304 | ||||||||
\(617\) | 334.000 | 0.0217931 | 0.0108965 | − | 0.999941i | \(-0.496531\pi\) | ||||
0.0108965 | + | 0.999941i | \(0.496531\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7202.00 | −0.467646 | −0.233823 | − | 0.972279i | \(-0.575124\pi\) | ||||
−0.233823 | + | 0.972279i | \(0.575124\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −41640.0 | −2.68426 | ||||||||
\(623\) | 1212.00 | 0.0779418 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 29645.0 | 1.89274 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 31858.0 | 2.02432 | ||||||||
\(629\) | −627.000 | −0.0397458 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10306.0 | 0.650199 | 0.325099 | − | 0.945680i | \(-0.394602\pi\) | ||||
0.325099 | + | 0.945680i | \(0.394602\pi\) | |||||||
\(632\) | −32445.0 | −2.04208 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25200.0 | 1.57858 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10688.0 | 0.664794 | ||||||||
\(638\) | 2970.00 | 0.184300 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1228.00 | 0.0756678 | 0.0378339 | − | 0.999284i | \(-0.487954\pi\) | ||||
0.0378339 | + | 0.999284i | \(0.487954\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18454.0 | 1.13181 | 0.565906 | − | 0.824470i | \(-0.308527\pi\) | ||||
0.565906 | + | 0.824470i | \(0.308527\pi\) | |||||||
\(644\) | −5763.00 | −0.352630 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7755.00 | 0.472316 | ||||||||
\(647\) | 17647.0 | 1.07230 | 0.536148 | − | 0.844124i | \(-0.319879\pi\) | ||||
0.536148 | + | 0.844124i | \(0.319879\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6875.00 | 0.415820 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32368.0 | 1.94422 | ||||||||
\(653\) | 25918.0 | 1.55322 | 0.776608 | − | 0.629984i | \(-0.216939\pi\) | ||||
0.776608 | + | 0.629984i | \(0.216939\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −12371.0 | −0.736290 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2925.00 | −0.173295 | ||||||||
\(659\) | −12864.0 | −0.760410 | −0.380205 | − | 0.924902i | \(-0.624147\pi\) | ||||
−0.380205 | + | 0.924902i | \(0.624147\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11419.0 | −0.671933 | −0.335966 | − | 0.941874i | \(-0.609063\pi\) | ||||
−0.335966 | + | 0.941874i | \(0.609063\pi\) | |||||||
\(662\) | 51980.0 | 3.05175 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6390.00 | 0.373464 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6102.00 | 0.354228 | ||||||||
\(668\) | −20060.0 | −1.16189 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3520.00 | 0.202516 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15784.0 | −0.904054 | −0.452027 | − | 0.892004i | \(-0.649299\pi\) | ||||
−0.452027 | + | 0.892004i | \(0.649299\pi\) | |||||||
\(674\) | 36180.0 | 2.06766 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19941.0 | −1.13456 | ||||||||
\(677\) | −26050.0 | −1.47885 | −0.739426 | − | 0.673238i | \(-0.764903\pi\) | ||||
−0.739426 | + | 0.673238i | \(0.764903\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 237.000 | 0.0133950 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9790.00 | 0.549675 | ||||||||
\(683\) | −15095.0 | −0.845672 | −0.422836 | − | 0.906206i | \(-0.638965\pi\) | ||||
−0.422836 | + | 0.906206i | \(0.638965\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10155.0 | 0.565189 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 27412.0 | 1.51900 | ||||||||
\(689\) | −4864.00 | −0.268946 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15896.0 | 0.875126 | 0.437563 | − | 0.899188i | \(-0.355842\pi\) | ||||
0.437563 | + | 0.899188i | \(0.355842\pi\) | |||||||
\(692\) | −54009.0 | −2.96693 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7340.00 | 0.401473 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4587.00 | −0.249275 | ||||||||
\(698\) | 28450.0 | 1.54276 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10529.0 | −0.567296 | −0.283648 | − | 0.958928i | \(-0.591545\pi\) | ||||
−0.283648 | + | 0.958928i | \(0.591545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −893.000 | −0.0479092 | ||||||||
\(704\) | −3157.00 | −0.169011 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26880.0 | 1.43292 | ||||||||
\(707\) | −1635.00 | −0.0869738 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16087.0 | −0.852130 | −0.426065 | − | 0.904693i | \(-0.640100\pi\) | ||||
−0.426065 | + | 0.904693i | \(0.640100\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −18180.0 | −0.956916 | ||||||||
\(713\) | 20114.0 | 1.05649 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −30379.0 | −1.58564 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18670.0 | −0.970415 | ||||||||
\(719\) | −24336.0 | −1.26228 | −0.631140 | − | 0.775669i | \(-0.717413\pi\) | ||||
−0.631140 | + | 0.775669i | \(0.717413\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3918.00 | −0.202377 | ||||||||
\(722\) | −23250.0 | −1.19844 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14195.0 | −0.728664 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13960.0 | −0.712170 | −0.356085 | − | 0.934454i | \(-0.615889\pi\) | ||||
−0.356085 | + | 0.934454i | \(0.615889\pi\) | |||||||
\(728\) | 4320.00 | 0.219931 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10164.0 | 0.514267 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9252.00 | −0.466208 | −0.233104 | − | 0.972452i | \(-0.574888\pi\) | ||||
−0.233104 | + | 0.972452i | \(0.574888\pi\) | |||||||
\(734\) | 51370.0 | 2.58324 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9605.00 | 0.481039 | ||||||||
\(737\) | −2200.00 | −0.109957 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28453.0 | 1.41632 | 0.708160 | − | 0.706052i | \(-0.249526\pi\) | ||||
0.708160 | + | 0.706052i | \(0.249526\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2280.00 | −0.112805 | ||||||||
\(743\) | 512.000 | 0.0252806 | 0.0126403 | − | 0.999920i | \(-0.495976\pi\) | ||||
0.0126403 | + | 0.999920i | \(0.495976\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −68310.0 | −3.35256 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6171.00 | 0.301650 | ||||||||
\(749\) | −5814.00 | −0.283630 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 772.000 | 0.0375109 | 0.0187554 | − | 0.999824i | \(-0.494030\pi\) | ||||
0.0187554 | + | 0.999824i | \(0.494030\pi\) | |||||||
\(752\) | 17355.0 | 0.841585 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8640.00 | −0.417308 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8058.00 | −0.386886 | −0.193443 | − | 0.981111i | \(-0.561966\pi\) | ||||
−0.193443 | + | 0.981111i | \(0.561966\pi\) | |||||||
\(758\) | −39530.0 | −1.89419 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18650.0 | −0.888386 | −0.444193 | − | 0.895931i | \(-0.646510\pi\) | ||||
−0.444193 | + | 0.895931i | \(0.646510\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1728.00 | 0.0819893 | ||||||||
\(764\) | −61421.0 | −2.90855 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15840.0 | −0.747157 | ||||||||
\(767\) | −20000.0 | −0.941536 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7144.00 | −0.335005 | −0.167503 | − | 0.985872i | \(-0.553570\pi\) | ||||
−0.167503 | + | 0.985872i | \(0.553570\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −71468.0 | −3.33185 | ||||||||
\(773\) | −1904.00 | −0.0885927 | −0.0442963 | − | 0.999018i | \(-0.514105\pi\) | ||||
−0.0442963 | + | 0.999018i | \(0.514105\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3555.00 | −0.164455 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −53850.0 | −2.48151 | ||||||||
\(779\) | −6533.00 | −0.300474 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10417.0 | 0.477272 | ||||||||
\(782\) | 18645.0 | 0.852614 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −29726.0 | −1.35414 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7555.00 | −0.342194 | −0.171097 | − | 0.985254i | \(-0.554731\pi\) | ||||
−0.171097 | + | 0.985254i | \(0.554731\pi\) | |||||||
\(788\) | −76789.0 | −3.47144 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3312.00 | 0.148876 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10240.0 | −0.458554 | ||||||||
\(794\) | −28350.0 | −1.26713 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 70788.0 | 3.15203 | ||||||||
\(797\) | 24950.0 | 1.10888 | 0.554438 | − | 0.832225i | \(-0.312933\pi\) | ||||
0.554438 | + | 0.832225i | \(0.312933\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6435.00 | 0.284924 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4160.00 | −0.183160 | ||||||||
\(803\) | 4928.00 | 0.216570 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −28480.0 | −1.24462 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 24525.0 | 1.06781 | ||||||||
\(809\) | −19893.0 | −0.864525 | −0.432262 | − | 0.901748i | \(-0.642285\pi\) | ||||
−0.432262 | + | 0.901748i | \(0.642285\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34503.0 | 1.49391 | 0.746957 | − | 0.664872i | \(-0.231514\pi\) | ||||
0.746957 | + | 0.664872i | \(0.231514\pi\) | |||||||
\(812\) | −2754.00 | −0.119023 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1045.00 | −0.0449966 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14476.0 | 0.619891 | ||||||||
\(818\) | −28560.0 | −1.22075 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16890.0 | −0.717984 | −0.358992 | − | 0.933341i | \(-0.616880\pi\) | ||||
−0.358992 | + | 0.933341i | \(0.616880\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34692.0 | −1.46936 | −0.734682 | − | 0.678411i | \(-0.762669\pi\) | ||||
−0.734682 | + | 0.678411i | \(0.762669\pi\) | |||||||
\(824\) | 58770.0 | 2.48465 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9375.00 | −0.394913 | ||||||||
\(827\) | 41424.0 | 1.74178 | 0.870891 | − | 0.491476i | \(-0.163543\pi\) | ||||
0.870891 | + | 0.491476i | \(0.163543\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18494.0 | −0.774817 | −0.387408 | − | 0.921908i | \(-0.626630\pi\) | ||||
−0.387408 | + | 0.921908i | \(0.626630\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9184.00 | 0.382690 | ||||||||
\(833\) | −11022.0 | −0.458451 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8789.00 | 0.363605 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22795.0 | 0.939666 | ||||||||
\(839\) | −6680.00 | −0.274874 | −0.137437 | − | 0.990511i | \(-0.543886\pi\) | ||||
−0.137437 | + | 0.990511i | \(0.543886\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21473.0 | −0.880438 | ||||||||
\(842\) | 34275.0 | 1.40284 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 79220.0 | 3.23088 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −363.000 | −0.0147259 | ||||||||
\(848\) | 13528.0 | 0.547822 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2147.00 | −0.0864844 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43358.0 | −1.74039 | −0.870193 | − | 0.492711i | \(-0.836006\pi\) | ||||
−0.870193 | + | 0.492711i | \(0.836006\pi\) | |||||||
\(854\) | −4800.00 | −0.192333 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 87210.0 | 3.48222 | ||||||||
\(857\) | 15585.0 | 0.621206 | 0.310603 | − | 0.950540i | \(-0.399469\pi\) | ||||
0.310603 | + | 0.950540i | \(0.399469\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17036.0 | −0.676672 | −0.338336 | − | 0.941025i | \(-0.609864\pi\) | ||||
−0.338336 | + | 0.941025i | \(0.609864\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −53850.0 | −2.12777 | ||||||||
\(863\) | 28064.0 | 1.10696 | 0.553482 | − | 0.832861i | \(-0.313299\pi\) | ||||
0.553482 | + | 0.832861i | \(0.313299\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −42490.0 | −1.66729 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9078.00 | −0.354985 | ||||||||
\(869\) | −7931.00 | −0.309598 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6400.00 | 0.248973 | ||||||||
\(872\) | −25920.0 | −1.00661 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 26555.0 | 1.02773 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22654.0 | 0.872259 | 0.436130 | − | 0.899884i | \(-0.356349\pi\) | ||||
0.436130 | + | 0.899884i | \(0.356349\pi\) | |||||||
\(878\) | 49175.0 | 1.89018 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22380.0 | 0.855847 | 0.427924 | − | 0.903815i | \(-0.359245\pi\) | ||||
0.427924 | + | 0.903815i | \(0.359245\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35174.0 | −1.34054 | −0.670271 | − | 0.742116i | \(-0.733822\pi\) | ||||
−0.670271 | + | 0.742116i | \(0.733822\pi\) | |||||||
\(884\) | −17952.0 | −0.683022 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −53725.0 | −2.03716 | ||||||||
\(887\) | 30868.0 | 1.16848 | 0.584242 | − | 0.811579i | \(-0.301392\pi\) | ||||
0.584242 | + | 0.811579i | \(0.301392\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5217.00 | −0.196820 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −60520.0 | −2.27170 | ||||||||
\(893\) | 9165.00 | 0.343443 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6345.00 | 0.236575 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −41780.0 | −1.55258 | ||||||||
\(899\) | 9612.00 | 0.356594 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5016.00 | 0.185469 | ||||||||
\(902\) | −7645.00 | −0.282207 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −49680.0 | −1.82780 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10070.0 | −0.368654 | −0.184327 | − | 0.982865i | \(-0.559010\pi\) | ||||
−0.184327 | + | 0.982865i | \(0.559010\pi\) | |||||||
\(908\) | −79526.0 | −2.90657 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1885.00 | −0.0685542 | −0.0342771 | − | 0.999412i | \(-0.510913\pi\) | ||||
−0.0342771 | + | 0.999412i | \(0.510913\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1562.00 | 0.0566207 | ||||||||
\(914\) | 35290.0 | 1.27712 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −75599.0 | −2.72692 | ||||||||
\(917\) | 5454.00 | 0.196409 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23703.0 | 0.850805 | 0.425403 | − | 0.905004i | \(-0.360133\pi\) | ||||
0.425403 | + | 0.905004i | \(0.360133\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3230.00 | −0.115374 | ||||||||
\(923\) | −30304.0 | −1.08068 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 44910.0 | 1.59377 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4590.00 | 0.162364 | ||||||||
\(929\) | −53804.0 | −1.90016 | −0.950082 | − | 0.312001i | \(-0.899001\pi\) | ||||
−0.950082 | + | 0.312001i | \(0.899001\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15698.0 | −0.552611 | ||||||||
\(932\) | 6987.00 | 0.245565 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −67380.0 | −2.36054 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1326.00 | −0.0462311 | −0.0231155 | − | 0.999733i | \(-0.507359\pi\) | ||||
−0.0231155 | + | 0.999733i | \(0.507359\pi\) | |||||||
\(938\) | 3000.00 | 0.104428 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27109.0 | 0.939137 | 0.469569 | − | 0.882896i | \(-0.344409\pi\) | ||||
0.469569 | + | 0.882896i | \(0.344409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15707.0 | −0.542408 | ||||||||
\(944\) | 55625.0 | 1.91784 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16940.0 | 0.582206 | ||||||||
\(947\) | 31143.0 | 1.06865 | 0.534325 | − | 0.845279i | \(-0.320566\pi\) | ||||
0.534325 | + | 0.845279i | \(0.320566\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14336.0 | −0.490375 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4455.00 | −0.151667 | ||||||||
\(953\) | −879.000 | −0.0298779 | −0.0149389 | − | 0.999888i | \(-0.504755\pi\) | ||||
−0.0149389 | + | 0.999888i | \(0.504755\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 108460. | 3.66930 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −64980.0 | −2.19145 | ||||||||
\(959\) | −2610.00 | −0.0878846 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1893.00 | 0.0635427 | ||||||||
\(962\) | 3040.00 | 0.101885 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 123794. | 4.13603 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14824.0 | 0.492976 | 0.246488 | − | 0.969146i | \(-0.420723\pi\) | ||||
0.246488 | + | 0.969146i | \(0.420723\pi\) | |||||||
\(968\) | 5445.00 | 0.180794 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34089.0 | −1.12664 | −0.563320 | − | 0.826239i | \(-0.690476\pi\) | ||||
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1908.00 | 0.0628650 | ||||||||
\(974\) | 30130.0 | 0.991199 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 28480.0 | 0.934040 | ||||||||
\(977\) | 33446.0 | 1.09522 | 0.547611 | − | 0.836733i | \(-0.315537\pi\) | ||||
0.547611 | + | 0.836733i | \(0.315537\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4444.00 | −0.145077 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −58490.0 | −1.90070 | ||||||||
\(983\) | −52025.0 | −1.68804 | −0.844018 | − | 0.536315i | \(-0.819816\pi\) | ||||
−0.844018 | + | 0.536315i | \(0.819816\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8910.00 | 0.287781 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25568.0 | −0.823306 | ||||||||
\(989\) | 34804.0 | 1.11901 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41260.0 | −1.32257 | −0.661285 | − | 0.750135i | \(-0.729989\pi\) | ||||
−0.661285 | + | 0.750135i | \(0.729989\pi\) | |||||||
\(992\) | 15130.0 | 0.484252 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −14205.0 | −0.453275 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 190.000 | 0.00603547 | 0.00301773 | − | 0.999995i | \(-0.499039\pi\) | ||||
0.00301773 | + | 0.999995i | \(0.499039\pi\) | |||||||
\(998\) | −85260.0 | −2.70427 | ||||||||
\(999\) | 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 | 2475.4.a.k.1.1 | 1 | ||
3.2 | odd | 2 | 825.4.a.a.1.1 | ✓ | 1 | ||
5.4 | even | 2 | 2475.4.a.a.1.1 | 1 | |||
15.2 | even | 4 | 825.4.c.b.199.1 | 2 | |||
15.8 | even | 4 | 825.4.c.b.199.2 | 2 | |||
15.14 | odd | 2 | 825.4.a.j.1.1 | yes | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.4.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
825.4.a.j.1.1 | yes | 1 | 15.14 | odd | 2 | ||
825.4.c.b.199.1 | 2 | 15.2 | even | 4 | |||
825.4.c.b.199.2 | 2 | 15.8 | even | 4 | |||
2475.4.a.a.1.1 | 1 | 5.4 | even | 2 | |||
2475.4.a.k.1.1 | 1 | 1.1 | even | 1 | trivial |