Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,4,Mod(1,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, 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("60.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.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: | \(3.54011460034\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 60.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 32.0000 | 1.72784 | 0.863919 | − | 0.503631i | \(-0.168003\pi\) | ||||
0.863919 | + | 0.503631i | \(0.168003\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36.0000 | 0.986764 | 0.493382 | − | 0.869813i | \(-0.335760\pi\) | ||||
0.493382 | + | 0.869813i | \(0.335760\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.0000 | −0.213346 | −0.106673 | − | 0.994294i | \(-0.534020\pi\) | ||||
−0.106673 | + | 0.994294i | \(0.534020\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −78.0000 | −1.11281 | −0.556405 | − | 0.830911i | \(-0.687820\pi\) | ||||
−0.556405 | + | 0.830911i | \(0.687820\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 140.000 | 1.69043 | 0.845216 | − | 0.534425i | \(-0.179472\pi\) | ||||
0.845216 | + | 0.534425i | \(0.179472\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −96.0000 | −0.997567 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −192.000 | −1.74064 | −0.870321 | − | 0.492485i | \(-0.836089\pi\) | ||||
−0.870321 | + | 0.492485i | \(0.836089\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 0.0384197 | 0.0192099 | − | 0.999815i | \(-0.493885\pi\) | ||||
0.0192099 | + | 0.999815i | \(0.493885\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −16.0000 | −0.0926995 | −0.0463498 | − | 0.998925i | \(-0.514759\pi\) | ||||
−0.0463498 | + | 0.998925i | \(0.514759\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −108.000 | −0.569709 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 160.000 | 0.772712 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −34.0000 | −0.151069 | −0.0755347 | − | 0.997143i | \(-0.524066\pi\) | ||||
−0.0755347 | + | 0.997143i | \(0.524066\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 30.0000 | 0.123176 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −390.000 | −1.48556 | −0.742778 | − | 0.669538i | \(-0.766492\pi\) | ||||
−0.742778 | + | 0.669538i | \(0.766492\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −52.0000 | −0.184417 | −0.0922084 | − | 0.995740i | \(-0.529393\pi\) | ||||
−0.0922084 | + | 0.995740i | \(0.529393\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 408.000 | 1.26623 | 0.633116 | − | 0.774057i | \(-0.281776\pi\) | ||||
0.633116 | + | 0.774057i | \(0.281776\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 681.000 | 1.98542 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 234.000 | 0.642481 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −114.000 | −0.295455 | −0.147727 | − | 0.989028i | \(-0.547196\pi\) | ||||
−0.147727 | + | 0.989028i | \(0.547196\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 180.000 | 0.441294 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −420.000 | −0.975971 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 516.000 | 1.13860 | 0.569301 | − | 0.822129i | \(-0.307214\pi\) | ||||
0.569301 | + | 0.822129i | \(0.307214\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −58.0000 | −0.121740 | −0.0608700 | − | 0.998146i | \(-0.519388\pi\) | ||||
−0.0608700 | + | 0.998146i | \(0.519388\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 288.000 | 0.575946 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −50.0000 | −0.0954113 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −892.000 | −1.62649 | −0.813247 | − | 0.581918i | \(-0.802302\pi\) | ||||
−0.813247 | + | 0.581918i | \(0.802302\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 576.000 | 1.00496 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −120.000 | −0.200583 | −0.100291 | − | 0.994958i | \(-0.531978\pi\) | ||||
−0.100291 | + | 0.994958i | \(0.531978\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −646.000 | −1.03573 | −0.517867 | − | 0.855461i | \(-0.673274\pi\) | ||||
−0.517867 | + | 0.855461i | \(0.673274\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1152.00 | 1.70497 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1168.00 | −1.66342 | −0.831711 | − | 0.555209i | \(-0.812638\pi\) | ||||
−0.831711 | + | 0.555209i | \(0.812638\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −732.000 | −0.968041 | −0.484021 | − | 0.875057i | \(-0.660824\pi\) | ||||
−0.484021 | + | 0.875057i | \(0.660824\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −390.000 | −0.497664 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.0000 | −0.0221816 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1590.00 | −1.89370 | −0.946852 | − | 0.321669i | \(-0.895756\pi\) | ||||
−0.946852 | + | 0.321669i | \(0.895756\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −320.000 | −0.368628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 48.0000 | 0.0535201 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 700.000 | 0.755984 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 194.000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 324.000 | 0.328921 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 798.000 | 0.786178 | 0.393089 | − | 0.919500i | \(-0.371406\pi\) | ||||
0.393089 | + | 0.919500i | \(0.371406\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 272.000 | 0.260203 | 0.130102 | − | 0.991501i | \(-0.458470\pi\) | ||||
0.130102 | + | 0.991501i | \(0.458470\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −480.000 | −0.446126 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 156.000 | 0.140945 | 0.0704724 | − | 0.997514i | \(-0.477549\pi\) | ||||
0.0704724 | + | 0.997514i | \(0.477549\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1622.00 | 1.42532 | 0.712658 | − | 0.701512i | \(-0.247491\pi\) | ||||
0.712658 | + | 0.701512i | \(0.247491\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 102.000 | 0.0872199 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1074.00 | 0.894101 | 0.447051 | − | 0.894509i | \(-0.352474\pi\) | ||||
0.447051 | + | 0.894509i | \(0.352474\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −960.000 | −0.778439 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −90.0000 | −0.0711154 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2496.00 | −1.92276 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −35.0000 | −0.0262960 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1170.00 | 0.857686 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1528.00 | −1.06762 | −0.533811 | − | 0.845604i | \(-0.679241\pi\) | ||||
−0.533811 | + | 0.845604i | \(0.679241\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 156.000 | 0.106473 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2412.00 | 1.60868 | 0.804341 | − | 0.594168i | \(-0.202518\pi\) | ||||
0.804341 | + | 0.594168i | \(0.202518\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4480.00 | 2.92079 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2106.00 | 1.31334 | 0.656671 | − | 0.754178i | \(-0.271964\pi\) | ||||
0.656671 | + | 0.754178i | \(0.271964\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −556.000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1224.00 | −0.731060 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −360.000 | −0.210522 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 30.0000 | 0.0171818 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2043.00 | −1.14628 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2418.00 | −1.32946 | −0.664732 | − | 0.747081i | \(-0.731454\pi\) | ||||
−0.664732 | + | 0.747081i | \(0.731454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2840.00 | 1.53057 | 0.765285 | − | 0.643692i | \(-0.222598\pi\) | ||||
0.765285 | + | 0.643692i | \(0.222598\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −702.000 | −0.370937 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −80.0000 | −0.0414565 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2054.00 | 1.04412 | 0.522061 | − | 0.852908i | \(-0.325163\pi\) | ||||
0.522061 | + | 0.852908i | \(0.325163\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 342.000 | 0.170581 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6144.00 | −3.00755 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −460.000 | −0.221043 | −0.110521 | − | 0.993874i | \(-0.535252\pi\) | ||||
−0.110521 | + | 0.993874i | \(0.535252\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −540.000 | −0.254781 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2016.00 | 0.934148 | 0.467074 | − | 0.884218i | \(-0.345308\pi\) | ||||
0.467074 | + | 0.884218i | \(0.345308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2097.00 | −0.954483 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1260.00 | 0.563477 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −618.000 | −0.271593 | −0.135797 | − | 0.990737i | \(-0.543359\pi\) | ||||
−0.135797 | + | 0.990737i | \(0.543359\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 800.000 | 0.345568 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1548.00 | −0.657372 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2964.00 | −1.23765 | −0.618826 | − | 0.785528i | \(-0.712391\pi\) | ||||
−0.618826 | + | 0.785528i | \(0.712391\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −370.000 | −0.151944 | −0.0759721 | − | 0.997110i | \(-0.524206\pi\) | ||||
−0.0759721 | + | 0.997110i | \(0.524206\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 174.000 | 0.0702866 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −170.000 | −0.0675603 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2808.00 | −1.09808 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −864.000 | −0.332522 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1104.00 | 0.418234 | 0.209117 | − | 0.977891i | \(-0.432941\pi\) | ||||
0.209117 | + | 0.977891i | \(0.432941\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2398.00 | −0.894362 | −0.447181 | − | 0.894444i | \(-0.647572\pi\) | ||||
−0.447181 | + | 0.894444i | \(0.647572\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 150.000 | 0.0550858 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1278.00 | 0.462202 | 0.231101 | − | 0.972930i | \(-0.425767\pi\) | ||||
0.231101 | + | 0.972930i | \(0.425767\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4472.00 | 1.59302 | 0.796512 | − | 0.604623i | \(-0.206676\pi\) | ||||
0.796512 | + | 0.604623i | \(0.206676\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2676.00 | 0.939057 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 192.000 | 0.0663830 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1950.00 | −0.664361 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1728.00 | −0.580214 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5040.00 | 1.66806 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1340.00 | 0.437201 | 0.218600 | − | 0.975814i | \(-0.429851\pi\) | ||||
0.218600 | + | 0.975814i | \(0.429851\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 360.000 | 0.115807 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −260.000 | −0.0824737 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −512.000 | −0.160170 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1938.00 | 0.597981 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 780.000 | 0.237414 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2360.00 | 0.708687 | 0.354344 | − | 0.935115i | \(-0.384704\pi\) | ||||
0.354344 | + | 0.935115i | \(0.384704\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1380.00 | 0.403497 | 0.201748 | − | 0.979437i | \(-0.435338\pi\) | ||||
0.201748 | + | 0.979437i | \(0.435338\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1694.00 | 0.488833 | 0.244416 | − | 0.969670i | \(-0.421404\pi\) | ||||
0.244416 | + | 0.969670i | \(0.421404\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3456.00 | −0.984364 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5190.00 | −1.45926 | −0.729631 | − | 0.683841i | \(-0.760308\pi\) | ||||
−0.729631 | + | 0.683841i | \(0.760308\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2040.00 | 0.566276 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3504.00 | 0.960377 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2352.00 | 0.636562 | 0.318281 | − | 0.947996i | \(-0.396895\pi\) | ||||
0.318281 | + | 0.947996i | \(0.396895\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3502.00 | −0.936032 | −0.468016 | − | 0.883720i | \(-0.655031\pi\) | ||||
−0.468016 | + | 0.883720i | \(0.655031\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3405.00 | 0.887908 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1400.00 | −0.360647 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2196.00 | 0.558899 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4788.00 | 1.20405 | 0.602024 | − | 0.798478i | \(-0.294361\pi\) | ||||
0.602024 | + | 0.798478i | \(0.294361\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6912.00 | −1.71760 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1170.00 | 0.287326 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1506.00 | 0.365532 | 0.182766 | − | 0.983156i | \(-0.441495\pi\) | ||||
0.182766 | + | 0.983156i | \(0.441495\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1088.00 | −0.261023 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 54.0000 | 0.0128066 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −432.000 | −0.101286 | −0.0506431 | − | 0.998717i | \(-0.516127\pi\) | ||||
−0.0506431 | + | 0.998717i | \(0.516127\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −570.000 | −0.132131 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4770.00 | 1.09333 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 54.0000 | 0.0122395 | 0.00611977 | − | 0.999981i | \(-0.498052\pi\) | ||||
0.00611977 | + | 0.999981i | \(0.498052\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6496.00 | −1.45610 | −0.728051 | − | 0.685522i | \(-0.759574\pi\) | ||||
−0.728051 | + | 0.685522i | \(0.759574\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 960.000 | 0.212827 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 900.000 | 0.197353 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −466.000 | −0.101080 | −0.0505401 | − | 0.998722i | \(-0.516094\pi\) | ||||
−0.0505401 | + | 0.998722i | \(0.516094\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −144.000 | −0.0308998 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4854.00 | −1.03048 | −0.515241 | − | 0.857045i | \(-0.672298\pi\) | ||||
−0.515241 | + | 0.857045i | \(0.672298\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4516.00 | −0.948581 | −0.474290 | − | 0.880368i | \(-0.657295\pi\) | ||||
−0.474290 | + | 0.880368i | \(0.657295\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2100.00 | −0.436468 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12480.0 | −2.56680 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1171.00 | 0.238347 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −582.000 | −0.117242 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8574.00 | 1.70955 | 0.854775 | − | 0.518998i | \(-0.173695\pi\) | ||||
0.854775 | + | 0.518998i | \(0.173695\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2580.00 | 0.509198 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −972.000 | −0.189903 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1920.00 | 0.371359 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1664.00 | −0.318642 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2394.00 | −0.453900 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −290.000 | −0.0544438 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3476.00 | 0.646208 | 0.323104 | − | 0.946363i | \(-0.395274\pi\) | ||||
0.323104 | + | 0.946363i | \(0.395274\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −816.000 | −0.150229 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2424.00 | 0.441969 | 0.220985 | − | 0.975277i | \(-0.429073\pi\) | ||||
0.220985 | + | 0.975277i | \(0.429073\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1558.00 | −0.281353 | −0.140676 | − | 0.990056i | \(-0.544928\pi\) | ||||
−0.140676 | + | 0.990056i | \(0.544928\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1440.00 | 0.257571 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8538.00 | −1.51275 | −0.756375 | − | 0.654138i | \(-0.773032\pi\) | ||||
−0.756375 | + | 0.654138i | \(0.773032\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 216.000 | 0.0379112 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −468.000 | −0.0813745 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10920.0 | −1.88113 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −250.000 | −0.0426692 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4866.00 | −0.822906 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13056.0 | 2.18784 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −988.000 | −0.164065 | −0.0820323 | − | 0.996630i | \(-0.526141\pi\) | ||||
−0.0820323 | + | 0.996630i | \(0.526141\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −306.000 | −0.0503564 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4460.00 | −0.727391 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2546.00 | 0.411541 | 0.205771 | − | 0.978600i | \(-0.434030\pi\) | ||||
0.205771 | + | 0.978600i | \(0.434030\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3222.00 | −0.516209 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −576.000 | −0.0914726 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10816.0 | 1.70265 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2880.00 | 0.449432 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8556.00 | 1.32366 | 0.661830 | − | 0.749654i | \(-0.269780\pi\) | ||||
0.661830 | + | 0.749654i | \(0.269780\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3706.00 | −0.568417 | −0.284209 | − | 0.958762i | \(-0.591731\pi\) | ||||
−0.284209 | + | 0.958762i | \(0.591731\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 270.000 | 0.0410585 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11394.0 | 1.71796 | 0.858982 | − | 0.512005i | \(-0.171097\pi\) | ||||
0.858982 | + | 0.512005i | \(0.171097\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −600.000 | −0.0897034 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7488.00 | 1.11010 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −264.000 | −0.0388117 | −0.0194058 | − | 0.999812i | \(-0.506177\pi\) | ||||
−0.0194058 | + | 0.999812i | \(0.506177\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12741.0 | 1.85756 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 105.000 | 0.0151820 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3230.00 | −0.463194 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10232.0 | 1.45533 | 0.727665 | − | 0.685933i | \(-0.240606\pi\) | ||||
0.727665 | + | 0.685933i | \(0.240606\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3510.00 | −0.495185 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3648.00 | −0.510498 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −562.000 | −0.0780141 | −0.0390070 | − | 0.999239i | \(-0.512419\pi\) | ||||
−0.0390070 | + | 0.999239i | \(0.512419\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −60.0000 | −0.00819670 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7228.00 | −0.979624 | −0.489812 | − | 0.871828i | \(-0.662935\pi\) | ||||
−0.489812 | + | 0.871828i | \(0.662935\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4584.00 | 0.616392 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5736.00 | −0.765263 | −0.382632 | − | 0.923901i | \(-0.624982\pi\) | ||||
−0.382632 | + | 0.923901i | \(0.624982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5760.00 | 0.762485 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −468.000 | −0.0614723 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9186.00 | −1.19730 | −0.598649 | − | 0.801012i | \(-0.704295\pi\) | ||||
−0.598649 | + | 0.801012i | \(0.704295\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14976.0 | 1.93700 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7236.00 | −0.928773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5840.00 | −0.743905 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −394.000 | −0.0498093 | −0.0249047 | − | 0.999690i | \(-0.507928\pi\) | ||||
−0.0249047 | + | 0.999690i | \(0.507928\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13440.0 | −1.68632 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1614.00 | −0.200996 | −0.100498 | − | 0.994937i | \(-0.532044\pi\) | ||||
−0.100498 | + | 0.994937i | \(0.532044\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 160.000 | 0.0197771 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1224.00 | −0.149070 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1034.00 | 0.125007 | 0.0625037 | − | 0.998045i | \(-0.480091\pi\) | ||||
0.0625037 | + | 0.998045i | \(0.480091\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6318.00 | −0.758258 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16512.0 | 1.96732 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3660.00 | −0.432921 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1668.00 | 0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3708.00 | 0.432333 | 0.216167 | − | 0.976356i | \(-0.430645\pi\) | ||||
0.216167 | + | 0.976356i | \(0.430645\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4930.00 | −0.570721 | −0.285360 | − | 0.958420i | \(-0.592113\pi\) | ||||
−0.285360 | + | 0.958420i | \(0.592113\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3672.00 | 0.422077 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1950.00 | −0.222562 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1856.00 | −0.210347 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1080.00 | 0.121545 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2592.00 | −0.289680 | −0.144840 | − | 0.989455i | \(-0.546267\pi\) | ||||
−0.144840 | + | 0.989455i | \(0.546267\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2162.00 | 0.239952 | 0.119976 | − | 0.992777i | \(-0.461718\pi\) | ||||
0.119976 | + | 0.992777i | \(0.461718\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −90.0000 | −0.00991993 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26880.0 | −2.94244 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1352.00 | 0.146987 | 0.0734937 | − | 0.997296i | \(-0.476585\pi\) | ||||
0.0734937 | + | 0.997296i | \(0.476585\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6129.00 | 0.661808 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5532.00 | 0.593303 | 0.296652 | − | 0.954986i | \(-0.404130\pi\) | ||||
0.296652 | + | 0.954986i | \(0.404130\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7950.00 | −0.846890 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7254.00 | 0.767567 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3198.00 | −0.336131 | −0.168066 | − | 0.985776i | \(-0.553752\pi\) | ||||
−0.168066 | + | 0.985776i | \(0.553752\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14040.0 | −1.46589 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8520.00 | −0.883674 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1600.00 | −0.164855 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1510.00 | −0.154562 | −0.0772810 | − | 0.997009i | \(-0.524624\pi\) | ||||
−0.0772810 | + | 0.997009i | \(0.524624\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2106.00 | 0.214160 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16086.0 | 1.62516 | 0.812581 | − | 0.582848i | \(-0.198062\pi\) | ||||
0.812581 | + | 0.582848i | \(0.198062\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5384.00 | 0.540423 | 0.270211 | − | 0.962801i | \(-0.412906\pi\) | ||||
0.270211 | + | 0.962801i | \(0.412906\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 240.000 | 0.0239349 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2604.00 | −0.258027 | −0.129014 | − | 0.991643i | \(-0.541181\pi\) | ||||
−0.129014 | + | 0.991643i | \(0.541181\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28544.0 | −2.81032 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6162.00 | −0.602824 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1872.00 | −0.181976 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3500.00 | 0.338086 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1026.00 | −0.0984849 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11136.0 | 1.06225 | 0.531124 | − | 0.847294i | \(-0.321770\pi\) | ||||
0.531124 | + | 0.847294i | \(0.321770\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 340.000 | 0.0322301 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18432.0 | 1.73641 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 970.000 | 0.0908153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14624.0 | 1.36073 | 0.680366 | − | 0.732872i | \(-0.261821\pi\) | ||||
0.680366 | + | 0.732872i | \(0.261821\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1380.00 | 0.127619 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11844.0 | 1.08862 | 0.544310 | − | 0.838884i | \(-0.316792\pi\) | ||||
0.544310 | + | 0.838884i | \(0.316792\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −468.000 | −0.0427539 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1620.00 | 0.147098 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3840.00 | −0.346575 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11284.0 | −1.01231 | −0.506154 | − | 0.862443i | \(-0.668933\pi\) | ||||
−0.506154 | + | 0.862443i | \(0.668933\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6048.00 | −0.539331 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4032.00 | 0.357412 | 0.178706 | − | 0.983903i | \(-0.442809\pi\) | ||||
0.178706 | + | 0.983903i | \(0.442809\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3990.00 | 0.351589 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6291.00 | 0.551071 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17562.0 | −1.52932 | −0.764658 | − | 0.644436i | \(-0.777092\pi\) | ||||
−0.764658 | + | 0.644436i | \(0.777092\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20672.0 | −1.78958 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3780.00 | −0.325324 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1360.00 | 0.116367 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14688.0 | 1.24947 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1854.00 | 0.156805 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3162.00 | 0.265892 | 0.132946 | − | 0.991123i | \(-0.457556\pi\) | ||||
0.132946 | + | 0.991123i | \(0.457556\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6764.00 | 0.565524 | 0.282762 | − | 0.959190i | \(-0.408749\pi\) | ||||
0.282762 | + | 0.959190i | \(0.408749\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2400.00 | −0.199513 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1248.00 | 0.103157 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24697.0 | 2.02983 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4644.00 | 0.379534 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3900.00 | 0.316938 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 780.000 | 0.0630324 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8892.00 | 0.714559 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24516.0 | 1.95914 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17798.0 | 1.41441 | 0.707205 | − | 0.707009i | \(-0.249956\pi\) | ||||
0.707205 | + | 0.707009i | \(0.249956\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1110.00 | 0.0877250 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8110.00 | 0.637421 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19996.0 | −1.56301 | −0.781506 | − | 0.623898i | \(-0.785548\pi\) | ||||
−0.781506 | + | 0.623898i | \(0.785548\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −522.000 | −0.0405800 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 840.000 | 0.0649459 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −37376.0 | −2.87412 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 510.000 | 0.0390059 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11094.0 | 0.843928 | 0.421964 | − | 0.906613i | \(-0.361341\pi\) | ||||
0.421964 | + | 0.906613i | \(0.361341\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 520.000 | 0.0393446 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8424.00 | 0.633978 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 900.000 | 0.0673721 | 0.0336860 | − | 0.999432i | \(-0.489275\pi\) | ||||
0.0336860 | + | 0.999432i | \(0.489275\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5370.00 | 0.399854 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2592.00 | 0.191982 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7914.00 | 0.583079 | 0.291540 | − | 0.956559i | \(-0.405832\pi\) | ||||
0.291540 | + | 0.956559i | \(0.405832\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2380.00 | −0.174431 | −0.0872153 | − | 0.996189i | \(-0.527797\pi\) | ||||
−0.0872153 | + | 0.996189i | \(0.527797\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3312.00 | −0.241467 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4800.00 | −0.348128 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25726.0 | −1.85613 | −0.928065 | − | 0.372417i | \(-0.878529\pi\) | ||||
−0.928065 | + | 0.372417i | \(0.878529\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7194.00 | 0.516360 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23424.0 | −1.67262 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4104.00 | −0.291544 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −450.000 | −0.0318038 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3612.00 | 0.253975 | 0.126987 | − | 0.991904i | \(-0.459469\pi\) | ||||
0.126987 | + | 0.991904i | \(0.459469\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2240.00 | −0.156702 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3834.00 | −0.266852 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2898.00 | 0.200686 | 0.100343 | − | 0.994953i | \(-0.468006\pi\) | ||||
0.100343 | + | 0.994953i | \(0.468006\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12480.0 | −0.859883 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13416.0 | −0.919733 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2664.00 | 0.181716 | 0.0908582 | − | 0.995864i | \(-0.471039\pi\) | ||||
0.0908582 | + | 0.995864i | \(0.471039\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −502.000 | −0.0340716 | −0.0170358 | − | 0.999855i | \(-0.505423\pi\) | ||||
−0.0170358 | + | 0.999855i | \(0.505423\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8028.00 | −0.542165 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −175.000 | −0.0117599 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7976.00 | 0.533337 | 0.266669 | − | 0.963788i | \(-0.414077\pi\) | ||||
0.266669 | + | 0.963788i | \(0.414077\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −576.000 | −0.0383263 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4080.00 | −0.270146 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20414.0 | 1.34505 | 0.672523 | − | 0.740076i | \(-0.265210\pi\) | ||||
0.672523 | + | 0.740076i | \(0.265210\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5850.00 | 0.383569 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6342.00 | −0.413808 | −0.206904 | − | 0.978361i | \(-0.566339\pi\) | ||||
−0.206904 | + | 0.978361i | \(0.566339\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22676.0 | 1.47242 | 0.736208 | − | 0.676755i | \(-0.236615\pi\) | ||||
0.736208 | + | 0.676755i | \(0.236615\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5184.00 | 0.334987 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −50880.0 | −3.27201 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15120.0 | −0.963054 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2652.00 | 0.168112 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7048.00 | −0.444654 | −0.222327 | − | 0.974972i | \(-0.571365\pi\) | ||||
−0.222327 | + | 0.974972i | \(0.571365\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4020.00 | −0.252418 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7640.00 | −0.477455 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6810.00 | −0.423582 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1080.00 | −0.0668609 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20286.0 | −1.25000 | −0.624999 | − | 0.780625i | \(-0.714901\pi\) | ||||
−0.624999 | + | 0.780625i | \(0.714901\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16108.0 | −0.987928 | −0.493964 | − | 0.869482i | \(-0.664452\pi\) | ||||
−0.493964 | + | 0.869482i | \(0.664452\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 780.000 | 0.0476162 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27456.0 | 1.66833 | 0.834163 | − | 0.551518i | \(-0.185951\pi\) | ||||
0.834163 | + | 0.551518i | \(0.185951\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18576.0 | 1.12353 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1536.00 | 0.0924740 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12522.0 | −0.750419 | −0.375210 | − | 0.926940i | \(-0.622429\pi\) | ||||
−0.375210 | + | 0.926940i | \(0.622429\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12060.0 | 0.719425 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5814.00 | −0.345245 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16308.0 | −0.963990 | −0.481995 | − | 0.876174i | \(-0.660088\pi\) | ||||
−0.481995 | + | 0.876174i | \(0.660088\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32078.0 | 1.88758 | 0.943789 | − | 0.330547i | \(-0.107233\pi\) | ||||
0.943789 | + | 0.330547i | \(0.107233\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2340.00 | −0.137071 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22400.0 | 1.30622 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1152.00 | −0.0668750 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7080.00 | −0.409161 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2088.00 | −0.120129 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4610.00 | 0.264045 | 0.132023 | − | 0.991247i | \(-0.457853\pi\) | ||||
0.132023 | + | 0.991247i | \(0.457853\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10782.0 | 0.612091 | 0.306046 | − | 0.952017i | \(-0.400994\pi\) | ||||
0.306046 | + | 0.952017i | \(0.400994\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6208.00 | 0.350871 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4140.00 | −0.232959 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2892.00 | 0.162019 | 0.0810097 | − | 0.996713i | \(-0.474186\pi\) | ||||
0.0810097 | + | 0.996713i | \(0.474186\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10530.0 | 0.587344 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5082.00 | −0.282228 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1140.00 | 0.0630342 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29572.0 | −1.62803 | −0.814017 | − | 0.580841i | \(-0.802724\pi\) | ||||
−0.814017 | + | 0.580841i | \(0.802724\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10368.0 | 0.568323 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2780.00 | −0.151729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30420.0 | 1.65314 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15570.0 | 0.842506 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5766.00 | 0.310669 | 0.155334 | − | 0.987862i | \(-0.450354\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450354\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4760.00 | −0.255372 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6120.00 | −0.326940 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25536.0 | 1.35839 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3326.00 | 0.176178 | 0.0880892 | − | 0.996113i | \(-0.471924\pi\) | ||||
0.0880892 | + | 0.996113i | \(0.471924\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10512.0 | −0.554474 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3072.00 | 0.161357 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1800.00 | −0.0941485 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7056.00 | −0.367519 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7728.00 | −0.400843 | −0.200421 | − | 0.979710i | \(-0.564231\pi\) | ||||
−0.200421 | + | 0.979710i | \(0.564231\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8704.00 | 0.449589 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10506.0 | 0.540418 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 150.000 | 0.00768395 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21616.0 | −1.10274 | −0.551371 | − | 0.834260i | \(-0.685895\pi\) | ||||
−0.551371 | + | 0.834260i | \(0.685895\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4056.00 | 0.205221 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10118.0 | 0.509846 | 0.254923 | − | 0.966961i | \(-0.417950\pi\) | ||||
0.254923 | + | 0.966961i | \(0.417950\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10215.0 | −0.512634 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32112.0 | −1.60497 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10460.0 | 0.520673 | 0.260336 | − | 0.965518i | \(-0.416167\pi\) | ||||
0.260336 | + | 0.965518i | \(0.416167\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4200.00 | 0.208220 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17232.0 | 0.850849 | 0.425424 | − | 0.904994i | \(-0.360125\pi\) | ||||
0.425424 | + | 0.904994i | \(0.360125\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12090.0 | −0.594555 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6588.00 | −0.322680 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4992.00 | 0.243530 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26912.0 | 1.30763 | 0.653817 | − | 0.756653i | \(-0.273167\pi\) | ||||
0.653817 | + | 0.756653i | \(0.273167\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14364.0 | −0.695157 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14200.0 | 0.684491 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13838.0 | 0.664400 | 0.332200 | − | 0.943209i | \(-0.392209\pi\) | ||||
0.332200 | + | 0.943209i | \(0.392209\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20736.0 | 0.991659 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17238.0 | −0.821126 | −0.410563 | − | 0.911832i | \(-0.634668\pi\) | ||||
−0.410563 | + | 0.911832i | \(0.634668\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 51904.0 | 2.46271 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3510.00 | −0.165888 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5160.00 | −0.242916 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21698.0 | 1.01749 | 0.508745 | − | 0.860917i | \(-0.330110\pi\) | ||||
0.508745 | + | 0.860917i | \(0.330110\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4518.00 | −0.211040 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18366.0 | 0.854565 | 0.427283 | − | 0.904118i | \(-0.359471\pi\) | ||||
0.427283 | + | 0.904118i | \(0.359471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −400.000 | −0.0185399 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3264.00 | 0.150702 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −54600.0 | −2.51123 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4320.00 | −0.197928 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −162.000 | −0.00739388 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10270.0 | 0.466945 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30316.0 | −1.37312 | −0.686562 | − | 0.727071i | \(-0.740881\pi\) | ||||
−0.686562 | + | 0.727071i | \(0.740881\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1296.00 | 0.0584776 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34368.0 | 1.54486 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 580.000 | 0.0259728 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1710.00 | 0.0762861 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7494.00 | 0.333063 | 0.166531 | − | 0.986036i | \(-0.446743\pi\) | ||||
0.166531 | + | 0.986036i | \(0.446743\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31824.0 | −1.40908 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14310.0 | −0.631235 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23256.0 | −1.02203 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −30720.0 | −1.34502 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −162.000 | −0.00706651 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11526.0 | −0.500906 | −0.250453 | − | 0.968129i | \(-0.580579\pi\) | ||||
−0.250453 | + | 0.968129i | \(0.580579\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33820.0 | −1.46434 | −0.732171 | − | 0.681121i | \(-0.761493\pi\) | ||||
−0.732171 | + | 0.681121i | \(0.761493\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19488.0 | 0.840681 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2300.00 | −0.0988534 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7280.00 | −0.311744 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2880.00 | −0.122876 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19566.0 | 0.831739 | 0.415870 | − | 0.909424i | \(-0.363477\pi\) | ||||
0.415870 | + | 0.909424i | \(0.363477\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40096.0 | −1.69825 | −0.849124 | − | 0.528193i | \(-0.822870\pi\) | ||||
−0.849124 | + | 0.528193i | \(0.822870\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2700.00 | −0.113942 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31884.0 | 1.34065 | 0.670324 | − | 0.742069i | \(-0.266155\pi\) | ||||
0.670324 | + | 0.742069i | \(0.266155\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24442.0 | −1.02401 | −0.512006 | − | 0.858982i | \(-0.671097\pi\) | ||||
−0.512006 | + | 0.858982i | \(0.671097\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1398.00 | 0.0583587 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −53118.0 | −2.20940 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10080.0 | 0.417764 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 432.000 | 0.0178400 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31944.0 | −1.31446 | −0.657228 | − | 0.753691i | \(-0.728271\pi\) | ||||
−0.657228 | + | 0.753691i | \(0.728271\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24353.0 | −0.998524 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14562.0 | 0.594949 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10485.0 | −0.426858 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1120.00 | −0.0454352 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13548.0 | 0.547663 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6528.00 | 0.262958 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17486.0 | 0.701887 | 0.350943 | − | 0.936397i | \(-0.385861\pi\) | ||||
0.350943 | + | 0.936397i | \(0.385861\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6300.00 | 0.251995 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43434.0 | 1.73125 | 0.865623 | − | 0.500697i | \(-0.166923\pi\) | ||||
0.865623 | + | 0.500697i | \(0.166923\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10820.0 | 0.429771 | 0.214886 | − | 0.976639i | \(-0.431062\pi\) | ||||
0.214886 | + | 0.976639i | \(0.431062\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 37440.0 | 1.48194 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29976.0 | 1.18238 | 0.591191 | − | 0.806532i | \(-0.298658\pi\) | ||||
0.591191 | + | 0.806532i | \(0.298658\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3090.00 | −0.121460 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3513.00 | −0.137610 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42048.0 | −1.64140 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8920.00 | 0.347007 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1746.00 | 0.0676897 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4000.00 | 0.154542 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40522.0 | −1.56024 | −0.780120 | − | 0.625630i | \(-0.784842\pi\) | ||||
−0.780120 | + | 0.625630i | \(0.784842\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25722.0 | −0.987010 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15570.0 | 0.595422 | 0.297711 | − | 0.954656i | \(-0.403777\pi\) | ||||
0.297711 | + | 0.954656i | \(0.403777\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1084.00 | −0.0413131 | −0.0206566 | − | 0.999787i | \(-0.506576\pi\) | ||||
−0.0206566 | + | 0.999787i | \(0.506576\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7740.00 | −0.293986 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8208.00 | −0.310708 | −0.155354 | − | 0.987859i | \(-0.549652\pi\) | ||||
−0.155354 | + | 0.987859i | \(0.549652\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −48896.0 | −1.84468 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2916.00 | 0.109640 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 57120.0 | 2.14048 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14820.0 | −0.553495 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5760.00 | −0.214404 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −96.0000 | −0.00356149 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8892.00 | 0.328785 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4992.00 | 0.183968 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1850.00 | −0.0679515 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34076.0 | 1.24749 | 0.623746 | − | 0.781627i | \(-0.285610\pi\) | ||||
0.623746 | + | 0.781627i | \(0.285610\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7182.00 | 0.262059 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15072.0 | −0.548142 | −0.274071 | − | 0.961709i | \(-0.588370\pi\) | ||||
−0.274071 | + | 0.961709i | \(0.588370\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26352.0 | −0.955229 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 870.000 | 0.0314331 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 77184.0 | 2.77954 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24392.0 | 0.875536 | 0.437768 | − | 0.899088i | \(-0.355769\pi\) | ||||
0.437768 | + | 0.899088i | \(0.355769\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10428.0 | −0.373088 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1200.00 | 0.0427936 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −850.000 | −0.0302139 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2448.00 | 0.0867345 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13602.0 | 0.480374 | 0.240187 | − | 0.970727i | \(-0.422791\pi\) | ||||
0.240187 | + | 0.970727i | \(0.422791\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 95340.0 | 3.35622 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7272.00 | −0.255171 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14040.0 | −0.491077 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47974.0 | −1.67262 | −0.836309 | − | 0.548259i | \(-0.815291\pi\) | ||||
−0.836309 | + | 0.548259i | \(0.815291\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4674.00 | 0.162439 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48330.0 | −1.67430 | −0.837148 | − | 0.546976i | \(-0.815779\pi\) | ||||
−0.837148 | + | 0.546976i | \(0.815779\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 74880.0 | 2.58582 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4320.00 | −0.148709 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9324.00 | −0.319946 | −0.159973 | − | 0.987121i | \(-0.551141\pi\) | ||||
−0.159973 | + | 0.987121i | \(0.551141\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6460.00 | 0.220970 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25614.0 | 0.873387 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14838.0 | −0.504355 | −0.252177 | − | 0.967681i | \(-0.581147\pi\) | ||||
−0.252177 | + | 0.967681i | \(0.581147\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5520.00 | 0.187040 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −648.000 | −0.0218881 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 67392.0 | 2.26924 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29535.0 | −0.991407 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1404.00 | 0.0469816 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11990.0 | −0.399971 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11360.0 | 0.377780 | 0.188890 | − | 0.981998i | \(-0.439511\pi\) | ||||
0.188890 | + | 0.981998i | \(0.439511\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 32760.0 | 1.08607 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6972.00 | −0.230424 | −0.115212 | − | 0.993341i | \(-0.536755\pi\) | ||||
−0.115212 | + | 0.993341i | \(0.536755\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17792.0 | −0.586213 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 750.000 | 0.0246351 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41166.0 | −1.34802 | −0.674011 | − | 0.738722i | \(-0.735430\pi\) | ||||
−0.674011 | + | 0.738722i | \(0.735430\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −57240.0 | −1.86864 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14598.0 | 0.475105 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22464.0 | 0.728881 | 0.364441 | − | 0.931227i | \(-0.381260\pi\) | ||||
0.364441 | + | 0.931227i | \(0.381260\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6390.00 | 0.206703 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −39168.0 | −1.26315 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9984.00 | 0.321004 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10192.0 | −0.326700 | −0.163350 | − | 0.986568i | \(-0.552230\pi\) | ||||
−0.163350 | + | 0.986568i | \(0.552230\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2964.00 | 0.0947228 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22360.0 | 0.712422 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −322.000 | −0.0102285 | −0.00511426 | − | 0.999987i | \(-0.501628\pi\) | ||||
−0.00511426 | + | 0.999987i | \(0.501628\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 918.000 | 0.0290733 |
(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 | 60.4.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 180.4.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 240.4.a.j.1.1 | 1 | |||
5.2 | odd | 4 | 300.4.d.d.49.2 | 2 | |||
5.3 | odd | 4 | 300.4.d.d.49.1 | 2 | |||
5.4 | even | 2 | 300.4.a.e.1.1 | 1 | |||
8.3 | odd | 2 | 960.4.a.a.1.1 | 1 | |||
8.5 | even | 2 | 960.4.a.bb.1.1 | 1 | |||
9.2 | odd | 6 | 1620.4.i.g.1081.1 | 2 | |||
9.4 | even | 3 | 1620.4.i.a.541.1 | 2 | |||
9.5 | odd | 6 | 1620.4.i.g.541.1 | 2 | |||
9.7 | even | 3 | 1620.4.i.a.1081.1 | 2 | |||
12.11 | even | 2 | 720.4.a.c.1.1 | 1 | |||
15.2 | even | 4 | 900.4.d.b.649.2 | 2 | |||
15.8 | even | 4 | 900.4.d.b.649.1 | 2 | |||
15.14 | odd | 2 | 900.4.a.b.1.1 | 1 | |||
20.3 | even | 4 | 1200.4.f.e.49.2 | 2 | |||
20.7 | even | 4 | 1200.4.f.e.49.1 | 2 | |||
20.19 | odd | 2 | 1200.4.a.s.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.4.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
180.4.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
240.4.a.j.1.1 | 1 | 4.3 | odd | 2 | |||
300.4.a.e.1.1 | 1 | 5.4 | even | 2 | |||
300.4.d.d.49.1 | 2 | 5.3 | odd | 4 | |||
300.4.d.d.49.2 | 2 | 5.2 | odd | 4 | |||
720.4.a.c.1.1 | 1 | 12.11 | even | 2 | |||
900.4.a.b.1.1 | 1 | 15.14 | odd | 2 | |||
900.4.d.b.649.1 | 2 | 15.8 | even | 4 | |||
900.4.d.b.649.2 | 2 | 15.2 | even | 4 | |||
960.4.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
960.4.a.bb.1.1 | 1 | 8.5 | even | 2 | |||
1200.4.a.s.1.1 | 1 | 20.19 | odd | 2 | |||
1200.4.f.e.49.1 | 2 | 20.7 | even | 4 | |||
1200.4.f.e.49.2 | 2 | 20.3 | even | 4 | |||
1620.4.i.a.541.1 | 2 | 9.4 | even | 3 | |||
1620.4.i.a.1081.1 | 2 | 9.7 | even | 3 | |||
1620.4.i.g.541.1 | 2 | 9.5 | odd | 6 | |||
1620.4.i.g.1081.1 | 2 | 9.2 | odd | 6 |