Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2175,4,Mod(1,2175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2175, 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("2175.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2175 = 3 \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2175.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: | \(128.329154262\) |
Analytic rank: | \(2\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 435) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2175.1 |
$q$-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 | \(-0.845080\pi\) | ||||
−0.883883 | + | 0.467707i | \(0.845080\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 17.0000 | 2.12500 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −15.0000 | −1.02062 | ||||||||
\(7\) | −16.0000 | −0.863919 | −0.431959 | − | 0.901893i | \(-0.642178\pi\) | ||||
−0.431959 | + | 0.901893i | \(0.642178\pi\) | |||||||
\(8\) | −45.0000 | −1.98874 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −44.0000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 51.0000 | 1.22687 | ||||||||
\(13\) | −78.0000 | −1.66410 | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 80.0000 | 1.52721 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 89.0000 | 1.39062 | ||||||||
\(17\) | −18.0000 | −0.256802 | −0.128401 | − | 0.991722i | \(-0.540985\pi\) | ||||
−0.128401 | + | 0.991722i | \(0.540985\pi\) | |||||||
\(18\) | −45.0000 | −0.589256 | ||||||||
\(19\) | −28.0000 | −0.338086 | −0.169043 | − | 0.985609i | \(-0.554068\pi\) | ||||
−0.169043 | + | 0.985609i | \(0.554068\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −48.0000 | −0.498784 | ||||||||
\(22\) | 220.000 | 2.13201 | ||||||||
\(23\) | −184.000 | −1.66812 | −0.834058 | − | 0.551677i | \(-0.813988\pi\) | ||||
−0.834058 | + | 0.551677i | \(0.813988\pi\) | |||||||
\(24\) | −135.000 | −1.14820 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 390.000 | 2.94174 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −272.000 | −1.83583 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −224.000 | −1.29779 | −0.648897 | − | 0.760877i | \(-0.724769\pi\) | ||||
−0.648897 | + | 0.760877i | \(0.724769\pi\) | |||||||
\(32\) | −85.0000 | −0.469563 | ||||||||
\(33\) | −132.000 | −0.696311 | ||||||||
\(34\) | 90.0000 | 0.453967 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 153.000 | 0.708333 | ||||||||
\(37\) | −254.000 | −1.12858 | −0.564288 | − | 0.825578i | \(-0.690849\pi\) | ||||
−0.564288 | + | 0.825578i | \(0.690849\pi\) | |||||||
\(38\) | 140.000 | 0.597658 | ||||||||
\(39\) | −234.000 | −0.960769 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −78.0000 | −0.297111 | −0.148556 | − | 0.988904i | \(-0.547462\pi\) | ||||
−0.148556 | + | 0.988904i | \(0.547462\pi\) | |||||||
\(42\) | 240.000 | 0.881733 | ||||||||
\(43\) | 260.000 | 0.922084 | 0.461042 | − | 0.887378i | \(-0.347476\pi\) | ||||
0.461042 | + | 0.887378i | \(0.347476\pi\) | |||||||
\(44\) | −748.000 | −2.56285 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 920.000 | 2.94884 | ||||||||
\(47\) | −312.000 | −0.968295 | −0.484148 | − | 0.874986i | \(-0.660870\pi\) | ||||
−0.484148 | + | 0.874986i | \(0.660870\pi\) | |||||||
\(48\) | 267.000 | 0.802878 | ||||||||
\(49\) | −87.0000 | −0.253644 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −54.0000 | −0.148265 | ||||||||
\(52\) | −1326.00 | −3.53621 | ||||||||
\(53\) | −574.000 | −1.48764 | −0.743820 | − | 0.668380i | \(-0.766988\pi\) | ||||
−0.743820 | + | 0.668380i | \(0.766988\pi\) | |||||||
\(54\) | −135.000 | −0.340207 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 720.000 | 1.71811 | ||||||||
\(57\) | −84.0000 | −0.195194 | ||||||||
\(58\) | −145.000 | −0.328266 | ||||||||
\(59\) | 180.000 | 0.397187 | 0.198593 | − | 0.980082i | \(-0.436363\pi\) | ||||
0.198593 | + | 0.980082i | \(0.436363\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −610.000 | −1.28037 | −0.640184 | − | 0.768221i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | 1120.00 | 2.29420 | ||||||||
\(63\) | −144.000 | −0.287973 | ||||||||
\(64\) | −287.000 | −0.560547 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 660.000 | 1.23091 | ||||||||
\(67\) | 340.000 | 0.619964 | 0.309982 | − | 0.950742i | \(-0.399677\pi\) | ||||
0.309982 | + | 0.950742i | \(0.399677\pi\) | |||||||
\(68\) | −306.000 | −0.545705 | ||||||||
\(69\) | −552.000 | −0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 296.000 | 0.494771 | 0.247385 | − | 0.968917i | \(-0.420429\pi\) | ||||
0.247385 | + | 0.968917i | \(0.420429\pi\) | |||||||
\(72\) | −405.000 | −0.662913 | ||||||||
\(73\) | −394.000 | −0.631702 | −0.315851 | − | 0.948809i | \(-0.602290\pi\) | ||||
−0.315851 | + | 0.948809i | \(0.602290\pi\) | |||||||
\(74\) | 1270.00 | 1.99506 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −476.000 | −0.718433 | ||||||||
\(77\) | 704.000 | 1.04193 | ||||||||
\(78\) | 1170.00 | 1.69842 | ||||||||
\(79\) | −960.000 | −1.36720 | −0.683598 | − | 0.729859i | \(-0.739586\pi\) | ||||
−0.683598 | + | 0.729859i | \(0.739586\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 390.000 | 0.525223 | ||||||||
\(83\) | 908.000 | 1.20079 | 0.600397 | − | 0.799702i | \(-0.295009\pi\) | ||||
0.600397 | + | 0.799702i | \(0.295009\pi\) | |||||||
\(84\) | −816.000 | −1.05992 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1300.00 | −1.63003 | ||||||||
\(87\) | 87.0000 | 0.107211 | ||||||||
\(88\) | 1980.00 | 2.39851 | ||||||||
\(89\) | −990.000 | −1.17910 | −0.589549 | − | 0.807732i | \(-0.700695\pi\) | ||||
−0.589549 | + | 0.807732i | \(0.700695\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1248.00 | 1.43765 | ||||||||
\(92\) | −3128.00 | −3.54475 | ||||||||
\(93\) | −672.000 | −0.749281 | ||||||||
\(94\) | 1560.00 | 1.71172 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −255.000 | −0.271102 | ||||||||
\(97\) | −1234.00 | −1.29169 | −0.645844 | − | 0.763469i | \(-0.723494\pi\) | ||||
−0.645844 | + | 0.763469i | \(0.723494\pi\) | |||||||
\(98\) | 435.000 | 0.448384 | ||||||||
\(99\) | −396.000 | −0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1022.00 | 1.00686 | 0.503430 | − | 0.864036i | \(-0.332071\pi\) | ||||
0.503430 | + | 0.864036i | \(0.332071\pi\) | |||||||
\(102\) | 270.000 | 0.262098 | ||||||||
\(103\) | 1248.00 | 1.19387 | 0.596937 | − | 0.802288i | \(-0.296384\pi\) | ||||
0.596937 | + | 0.802288i | \(0.296384\pi\) | |||||||
\(104\) | 3510.00 | 3.30946 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2870.00 | 2.62980 | ||||||||
\(107\) | 116.000 | 0.104805 | 0.0524025 | − | 0.998626i | \(-0.483312\pi\) | ||||
0.0524025 | + | 0.998626i | \(0.483312\pi\) | |||||||
\(108\) | 459.000 | 0.408956 | ||||||||
\(109\) | −826.000 | −0.725839 | −0.362920 | − | 0.931820i | \(-0.618220\pi\) | ||||
−0.362920 | + | 0.931820i | \(0.618220\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −762.000 | −0.651584 | ||||||||
\(112\) | −1424.00 | −1.20139 | ||||||||
\(113\) | 2206.00 | 1.83649 | 0.918243 | − | 0.396016i | \(-0.129608\pi\) | ||||
0.918243 | + | 0.396016i | \(0.129608\pi\) | |||||||
\(114\) | 420.000 | 0.345058 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 493.000 | 0.394603 | ||||||||
\(117\) | −702.000 | −0.554700 | ||||||||
\(118\) | −900.000 | −0.702133 | ||||||||
\(119\) | 288.000 | 0.221856 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 605.000 | 0.454545 | ||||||||
\(122\) | 3050.00 | 2.26339 | ||||||||
\(123\) | −234.000 | −0.171537 | ||||||||
\(124\) | −3808.00 | −2.75781 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 720.000 | 0.509069 | ||||||||
\(127\) | 2056.00 | 1.43654 | 0.718270 | − | 0.695765i | \(-0.244934\pi\) | ||||
0.718270 | + | 0.695765i | \(0.244934\pi\) | |||||||
\(128\) | 2115.00 | 1.46048 | ||||||||
\(129\) | 780.000 | 0.532366 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | 0.00800340 | 0.00400170 | − | 0.999992i | \(-0.498726\pi\) | ||||
0.00400170 | + | 0.999992i | \(0.498726\pi\) | |||||||
\(132\) | −2244.00 | −1.47966 | ||||||||
\(133\) | 448.000 | 0.292079 | ||||||||
\(134\) | −1700.00 | −1.09595 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 810.000 | 0.510713 | ||||||||
\(137\) | 2758.00 | 1.71994 | 0.859970 | − | 0.510344i | \(-0.170482\pi\) | ||||
0.859970 | + | 0.510344i | \(0.170482\pi\) | |||||||
\(138\) | 2760.00 | 1.70251 | ||||||||
\(139\) | −1436.00 | −0.876258 | −0.438129 | − | 0.898912i | \(-0.644359\pi\) | ||||
−0.438129 | + | 0.898912i | \(0.644359\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −936.000 | −0.559046 | ||||||||
\(142\) | −1480.00 | −0.874640 | ||||||||
\(143\) | 3432.00 | 2.00698 | ||||||||
\(144\) | 801.000 | 0.463542 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1970.00 | 1.11670 | ||||||||
\(147\) | −261.000 | −0.146442 | ||||||||
\(148\) | −4318.00 | −2.39823 | ||||||||
\(149\) | −498.000 | −0.273810 | −0.136905 | − | 0.990584i | \(-0.543716\pi\) | ||||
−0.136905 | + | 0.990584i | \(0.543716\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2696.00 | −1.45296 | −0.726481 | − | 0.687186i | \(-0.758846\pi\) | ||||
−0.726481 | + | 0.687186i | \(0.758846\pi\) | |||||||
\(152\) | 1260.00 | 0.672365 | ||||||||
\(153\) | −162.000 | −0.0856008 | ||||||||
\(154\) | −3520.00 | −1.84188 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3978.00 | −2.04163 | ||||||||
\(157\) | −534.000 | −0.271451 | −0.135726 | − | 0.990746i | \(-0.543337\pi\) | ||||
−0.135726 | + | 0.990746i | \(0.543337\pi\) | |||||||
\(158\) | 4800.00 | 2.41688 | ||||||||
\(159\) | −1722.00 | −0.858890 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2944.00 | 1.44112 | ||||||||
\(162\) | −405.000 | −0.196419 | ||||||||
\(163\) | −1380.00 | −0.663128 | −0.331564 | − | 0.943433i | \(-0.607576\pi\) | ||||
−0.331564 | + | 0.943433i | \(0.607576\pi\) | |||||||
\(164\) | −1326.00 | −0.631361 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4540.00 | −2.12272 | ||||||||
\(167\) | −2616.00 | −1.21217 | −0.606084 | − | 0.795400i | \(-0.707261\pi\) | ||||
−0.606084 | + | 0.795400i | \(0.707261\pi\) | |||||||
\(168\) | 2160.00 | 0.991950 | ||||||||
\(169\) | 3887.00 | 1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −252.000 | −0.112695 | ||||||||
\(172\) | 4420.00 | 1.95943 | ||||||||
\(173\) | 330.000 | 0.145026 | 0.0725128 | − | 0.997367i | \(-0.476898\pi\) | ||||
0.0725128 | + | 0.997367i | \(0.476898\pi\) | |||||||
\(174\) | −435.000 | −0.189525 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3916.00 | −1.67716 | ||||||||
\(177\) | 540.000 | 0.229316 | ||||||||
\(178\) | 4950.00 | 2.08437 | ||||||||
\(179\) | −372.000 | −0.155333 | −0.0776664 | − | 0.996979i | \(-0.524747\pi\) | ||||
−0.0776664 | + | 0.996979i | \(0.524747\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1010.00 | −0.414766 | −0.207383 | − | 0.978260i | \(-0.566495\pi\) | ||||
−0.207383 | + | 0.978260i | \(0.566495\pi\) | |||||||
\(182\) | −6240.00 | −2.54143 | ||||||||
\(183\) | −1830.00 | −0.739221 | ||||||||
\(184\) | 8280.00 | 3.31744 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3360.00 | 1.32455 | ||||||||
\(187\) | 792.000 | 0.309715 | ||||||||
\(188\) | −5304.00 | −2.05763 | ||||||||
\(189\) | −432.000 | −0.166261 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2008.00 | 0.760700 | 0.380350 | − | 0.924843i | \(-0.375803\pi\) | ||||
0.380350 | + | 0.924843i | \(0.375803\pi\) | |||||||
\(192\) | −861.000 | −0.323632 | ||||||||
\(193\) | −2578.00 | −0.961495 | −0.480747 | − | 0.876859i | \(-0.659635\pi\) | ||||
−0.480747 | + | 0.876859i | \(0.659635\pi\) | |||||||
\(194\) | 6170.00 | 2.28340 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1479.00 | −0.538994 | ||||||||
\(197\) | −526.000 | −0.190233 | −0.0951166 | − | 0.995466i | \(-0.530322\pi\) | ||||
−0.0951166 | + | 0.995466i | \(0.530322\pi\) | |||||||
\(198\) | 1980.00 | 0.710669 | ||||||||
\(199\) | 4440.00 | 1.58162 | 0.790812 | − | 0.612059i | \(-0.209658\pi\) | ||||
0.790812 | + | 0.612059i | \(0.209658\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1020.00 | 0.357937 | ||||||||
\(202\) | −5110.00 | −1.77989 | ||||||||
\(203\) | −464.000 | −0.160426 | ||||||||
\(204\) | −918.000 | −0.315063 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6240.00 | −2.11049 | ||||||||
\(207\) | −1656.00 | −0.556038 | ||||||||
\(208\) | −6942.00 | −2.31414 | ||||||||
\(209\) | 1232.00 | 0.407747 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 308.000 | 0.100491 | 0.0502455 | − | 0.998737i | \(-0.484000\pi\) | ||||
0.0502455 | + | 0.998737i | \(0.484000\pi\) | |||||||
\(212\) | −9758.00 | −3.16124 | ||||||||
\(213\) | 888.000 | 0.285656 | ||||||||
\(214\) | −580.000 | −0.185271 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1215.00 | −0.382733 | ||||||||
\(217\) | 3584.00 | 1.12119 | ||||||||
\(218\) | 4130.00 | 1.28311 | ||||||||
\(219\) | −1182.00 | −0.364713 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1404.00 | 0.427345 | ||||||||
\(222\) | 3810.00 | 1.15185 | ||||||||
\(223\) | −4120.00 | −1.23720 | −0.618600 | − | 0.785706i | \(-0.712300\pi\) | ||||
−0.618600 | + | 0.785706i | \(0.712300\pi\) | |||||||
\(224\) | 1360.00 | 0.405664 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11030.0 | −3.24648 | ||||||||
\(227\) | −4932.00 | −1.44206 | −0.721032 | − | 0.692902i | \(-0.756332\pi\) | ||||
−0.721032 | + | 0.692902i | \(0.756332\pi\) | |||||||
\(228\) | −1428.00 | −0.414788 | ||||||||
\(229\) | −3050.00 | −0.880130 | −0.440065 | − | 0.897966i | \(-0.645045\pi\) | ||||
−0.440065 | + | 0.897966i | \(0.645045\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2112.00 | 0.601556 | ||||||||
\(232\) | −1305.00 | −0.369299 | ||||||||
\(233\) | −82.0000 | −0.0230558 | −0.0115279 | − | 0.999934i | \(-0.503670\pi\) | ||||
−0.0115279 | + | 0.999934i | \(0.503670\pi\) | |||||||
\(234\) | 3510.00 | 0.980581 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3060.00 | 0.844021 | ||||||||
\(237\) | −2880.00 | −0.789351 | ||||||||
\(238\) | −1440.00 | −0.392190 | ||||||||
\(239\) | −5104.00 | −1.38138 | −0.690691 | − | 0.723150i | \(-0.742694\pi\) | ||||
−0.690691 | + | 0.723150i | \(0.742694\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2158.00 | −0.576801 | −0.288400 | − | 0.957510i | \(-0.593123\pi\) | ||||
−0.288400 | + | 0.957510i | \(0.593123\pi\) | |||||||
\(242\) | −3025.00 | −0.803530 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −10370.0 | −2.72078 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1170.00 | 0.303238 | ||||||||
\(247\) | 2184.00 | 0.562610 | ||||||||
\(248\) | 10080.0 | 2.58097 | ||||||||
\(249\) | 2724.00 | 0.693279 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6116.00 | 1.53800 | 0.769001 | − | 0.639248i | \(-0.220754\pi\) | ||||
0.769001 | + | 0.639248i | \(0.220754\pi\) | |||||||
\(252\) | −2448.00 | −0.611942 | ||||||||
\(253\) | 8096.00 | 2.01182 | ||||||||
\(254\) | −10280.0 | −2.53947 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8279.00 | −2.02124 | ||||||||
\(257\) | −3418.00 | −0.829607 | −0.414803 | − | 0.909911i | \(-0.636150\pi\) | ||||
−0.414803 | + | 0.909911i | \(0.636150\pi\) | |||||||
\(258\) | −3900.00 | −0.941098 | ||||||||
\(259\) | 4064.00 | 0.974999 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 261.000 | 0.0618984 | ||||||||
\(262\) | −60.0000 | −0.0141481 | ||||||||
\(263\) | −7440.00 | −1.74437 | −0.872186 | − | 0.489174i | \(-0.837298\pi\) | ||||
−0.872186 | + | 0.489174i | \(0.837298\pi\) | |||||||
\(264\) | 5940.00 | 1.38478 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2240.00 | −0.516328 | ||||||||
\(267\) | −2970.00 | −0.680753 | ||||||||
\(268\) | 5780.00 | 1.31742 | ||||||||
\(269\) | 6582.00 | 1.49186 | 0.745932 | − | 0.666022i | \(-0.232004\pi\) | ||||
0.745932 | + | 0.666022i | \(0.232004\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5504.00 | −1.23374 | −0.616871 | − | 0.787064i | \(-0.711600\pi\) | ||||
−0.616871 | + | 0.787064i | \(0.711600\pi\) | |||||||
\(272\) | −1602.00 | −0.357116 | ||||||||
\(273\) | 3744.00 | 0.830026 | ||||||||
\(274\) | −13790.0 | −3.04045 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9384.00 | −2.04656 | ||||||||
\(277\) | −3718.00 | −0.806473 | −0.403236 | − | 0.915096i | \(-0.632115\pi\) | ||||
−0.403236 | + | 0.915096i | \(0.632115\pi\) | |||||||
\(278\) | 7180.00 | 1.54902 | ||||||||
\(279\) | −2016.00 | −0.432598 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1754.00 | 0.372366 | 0.186183 | − | 0.982515i | \(-0.440388\pi\) | ||||
0.186183 | + | 0.982515i | \(0.440388\pi\) | |||||||
\(282\) | 4680.00 | 0.988262 | ||||||||
\(283\) | −3572.00 | −0.750295 | −0.375147 | − | 0.926965i | \(-0.622408\pi\) | ||||
−0.375147 | + | 0.926965i | \(0.622408\pi\) | |||||||
\(284\) | 5032.00 | 1.05139 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17160.0 | −3.54787 | ||||||||
\(287\) | 1248.00 | 0.256680 | ||||||||
\(288\) | −765.000 | −0.156521 | ||||||||
\(289\) | −4589.00 | −0.934053 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3702.00 | −0.745756 | ||||||||
\(292\) | −6698.00 | −1.34237 | ||||||||
\(293\) | −126.000 | −0.0251229 | −0.0125614 | − | 0.999921i | \(-0.503999\pi\) | ||||
−0.0125614 | + | 0.999921i | \(0.503999\pi\) | |||||||
\(294\) | 1305.00 | 0.258875 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 11430.0 | 2.24444 | ||||||||
\(297\) | −1188.00 | −0.232104 | ||||||||
\(298\) | 2490.00 | 0.484033 | ||||||||
\(299\) | 14352.0 | 2.77591 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4160.00 | −0.796606 | ||||||||
\(302\) | 13480.0 | 2.56850 | ||||||||
\(303\) | 3066.00 | 0.581311 | ||||||||
\(304\) | −2492.00 | −0.470151 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 810.000 | 0.151322 | ||||||||
\(307\) | 2412.00 | 0.448404 | 0.224202 | − | 0.974543i | \(-0.428022\pi\) | ||||
0.224202 | + | 0.974543i | \(0.428022\pi\) | |||||||
\(308\) | 11968.0 | 2.21409 | ||||||||
\(309\) | 3744.00 | 0.689284 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2928.00 | −0.533864 | −0.266932 | − | 0.963715i | \(-0.586010\pi\) | ||||
−0.266932 | + | 0.963715i | \(0.586010\pi\) | |||||||
\(312\) | 10530.0 | 1.91072 | ||||||||
\(313\) | −2874.00 | −0.519003 | −0.259502 | − | 0.965743i | \(-0.583558\pi\) | ||||
−0.259502 | + | 0.965743i | \(0.583558\pi\) | |||||||
\(314\) | 2670.00 | 0.479862 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16320.0 | −2.90529 | ||||||||
\(317\) | 26.0000 | 0.00460664 | 0.00230332 | − | 0.999997i | \(-0.499267\pi\) | ||||
0.00230332 | + | 0.999997i | \(0.499267\pi\) | |||||||
\(318\) | 8610.00 | 1.51832 | ||||||||
\(319\) | −1276.00 | −0.223957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 348.000 | 0.0605092 | ||||||||
\(322\) | −14720.0 | −2.54756 | ||||||||
\(323\) | 504.000 | 0.0868214 | ||||||||
\(324\) | 1377.00 | 0.236111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6900.00 | 1.17226 | ||||||||
\(327\) | −2478.00 | −0.419063 | ||||||||
\(328\) | 3510.00 | 0.590876 | ||||||||
\(329\) | 4992.00 | 0.836528 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9340.00 | 1.55098 | 0.775488 | − | 0.631363i | \(-0.217504\pi\) | ||||
0.775488 | + | 0.631363i | \(0.217504\pi\) | |||||||
\(332\) | 15436.0 | 2.55169 | ||||||||
\(333\) | −2286.00 | −0.376192 | ||||||||
\(334\) | 13080.0 | 2.14283 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4272.00 | −0.693621 | ||||||||
\(337\) | 10302.0 | 1.66524 | 0.832620 | − | 0.553845i | \(-0.186840\pi\) | ||||
0.832620 | + | 0.553845i | \(0.186840\pi\) | |||||||
\(338\) | −19435.0 | −3.12759 | ||||||||
\(339\) | 6618.00 | 1.06030 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9856.00 | 1.56520 | ||||||||
\(342\) | 1260.00 | 0.199219 | ||||||||
\(343\) | 6880.00 | 1.08305 | ||||||||
\(344\) | −11700.0 | −1.83378 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1650.00 | −0.256372 | ||||||||
\(347\) | 8020.00 | 1.24074 | 0.620369 | − | 0.784310i | \(-0.286983\pi\) | ||||
0.620369 | + | 0.784310i | \(0.286983\pi\) | |||||||
\(348\) | 1479.00 | 0.227824 | ||||||||
\(349\) | −1306.00 | −0.200311 | −0.100156 | − | 0.994972i | \(-0.531934\pi\) | ||||
−0.100156 | + | 0.994972i | \(0.531934\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2106.00 | −0.320256 | ||||||||
\(352\) | 3740.00 | 0.566314 | ||||||||
\(353\) | −5658.00 | −0.853102 | −0.426551 | − | 0.904464i | \(-0.640272\pi\) | ||||
−0.426551 | + | 0.904464i | \(0.640272\pi\) | |||||||
\(354\) | −2700.00 | −0.405377 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −16830.0 | −2.50558 | ||||||||
\(357\) | 864.000 | 0.128089 | ||||||||
\(358\) | 1860.00 | 0.274592 | ||||||||
\(359\) | −12240.0 | −1.79945 | −0.899725 | − | 0.436457i | \(-0.856233\pi\) | ||||
−0.899725 | + | 0.436457i | \(0.856233\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6075.00 | −0.885698 | ||||||||
\(362\) | 5050.00 | 0.733210 | ||||||||
\(363\) | 1815.00 | 0.262432 | ||||||||
\(364\) | 21216.0 | 3.05500 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9150.00 | 1.30677 | ||||||||
\(367\) | −8984.00 | −1.27782 | −0.638911 | − | 0.769280i | \(-0.720615\pi\) | ||||
−0.638911 | + | 0.769280i | \(0.720615\pi\) | |||||||
\(368\) | −16376.0 | −2.31972 | ||||||||
\(369\) | −702.000 | −0.0990370 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9184.00 | 1.28520 | ||||||||
\(372\) | −11424.0 | −1.59222 | ||||||||
\(373\) | 938.000 | 0.130209 | 0.0651043 | − | 0.997878i | \(-0.479262\pi\) | ||||
0.0651043 | + | 0.997878i | \(0.479262\pi\) | |||||||
\(374\) | −3960.00 | −0.547505 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14040.0 | 1.92569 | ||||||||
\(377\) | −2262.00 | −0.309016 | ||||||||
\(378\) | 2160.00 | 0.293911 | ||||||||
\(379\) | −7796.00 | −1.05661 | −0.528303 | − | 0.849056i | \(-0.677171\pi\) | ||||
−0.528303 | + | 0.849056i | \(0.677171\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6168.00 | 0.829386 | ||||||||
\(382\) | −10040.0 | −1.34474 | ||||||||
\(383\) | 6944.00 | 0.926428 | 0.463214 | − | 0.886247i | \(-0.346696\pi\) | ||||
0.463214 | + | 0.886247i | \(0.346696\pi\) | |||||||
\(384\) | 6345.00 | 0.843208 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12890.0 | 1.69970 | ||||||||
\(387\) | 2340.00 | 0.307361 | ||||||||
\(388\) | −20978.0 | −2.74484 | ||||||||
\(389\) | 2126.00 | 0.277101 | 0.138551 | − | 0.990355i | \(-0.455756\pi\) | ||||
0.138551 | + | 0.990355i | \(0.455756\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3312.00 | 0.428376 | ||||||||
\(392\) | 3915.00 | 0.504432 | ||||||||
\(393\) | 36.0000 | 0.00462076 | ||||||||
\(394\) | 2630.00 | 0.336288 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6732.00 | −0.854282 | ||||||||
\(397\) | 3346.00 | 0.423000 | 0.211500 | − | 0.977378i | \(-0.432165\pi\) | ||||
0.211500 | + | 0.977378i | \(0.432165\pi\) | |||||||
\(398\) | −22200.0 | −2.79594 | ||||||||
\(399\) | 1344.00 | 0.168632 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12850.0 | 1.60025 | 0.800123 | − | 0.599836i | \(-0.204768\pi\) | ||||
0.800123 | + | 0.599836i | \(0.204768\pi\) | |||||||
\(402\) | −5100.00 | −0.632748 | ||||||||
\(403\) | 17472.0 | 2.15966 | ||||||||
\(404\) | 17374.0 | 2.13958 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2320.00 | 0.283595 | ||||||||
\(407\) | 11176.0 | 1.36111 | ||||||||
\(408\) | 2430.00 | 0.294860 | ||||||||
\(409\) | 6122.00 | 0.740131 | 0.370065 | − | 0.929006i | \(-0.379335\pi\) | ||||
0.370065 | + | 0.929006i | \(0.379335\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8274.00 | 0.993008 | ||||||||
\(412\) | 21216.0 | 2.53698 | ||||||||
\(413\) | −2880.00 | −0.343137 | ||||||||
\(414\) | 8280.00 | 0.982946 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6630.00 | 0.781400 | ||||||||
\(417\) | −4308.00 | −0.505908 | ||||||||
\(418\) | −6160.00 | −0.720803 | ||||||||
\(419\) | 1372.00 | 0.159968 | 0.0799840 | − | 0.996796i | \(-0.474513\pi\) | ||||
0.0799840 | + | 0.996796i | \(0.474513\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12150.0 | 1.40654 | 0.703272 | − | 0.710921i | \(-0.251722\pi\) | ||||
0.703272 | + | 0.710921i | \(0.251722\pi\) | |||||||
\(422\) | −1540.00 | −0.177645 | ||||||||
\(423\) | −2808.00 | −0.322765 | ||||||||
\(424\) | 25830.0 | 2.95853 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4440.00 | −0.504973 | ||||||||
\(427\) | 9760.00 | 1.10613 | ||||||||
\(428\) | 1972.00 | 0.222711 | ||||||||
\(429\) | 10296.0 | 1.15873 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6288.00 | 0.702743 | 0.351372 | − | 0.936236i | \(-0.385715\pi\) | ||||
0.351372 | + | 0.936236i | \(0.385715\pi\) | |||||||
\(432\) | 2403.00 | 0.267626 | ||||||||
\(433\) | −15650.0 | −1.73693 | −0.868465 | − | 0.495750i | \(-0.834893\pi\) | ||||
−0.868465 | + | 0.495750i | \(0.834893\pi\) | |||||||
\(434\) | −17920.0 | −1.98200 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14042.0 | −1.54241 | ||||||||
\(437\) | 5152.00 | 0.563967 | ||||||||
\(438\) | 5910.00 | 0.644728 | ||||||||
\(439\) | −14520.0 | −1.57859 | −0.789296 | − | 0.614013i | \(-0.789554\pi\) | ||||
−0.789296 | + | 0.614013i | \(0.789554\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −783.000 | −0.0845481 | ||||||||
\(442\) | −7020.00 | −0.755446 | ||||||||
\(443\) | −7372.00 | −0.790642 | −0.395321 | − | 0.918543i | \(-0.629367\pi\) | ||||
−0.395321 | + | 0.918543i | \(0.629367\pi\) | |||||||
\(444\) | −12954.0 | −1.38462 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 20600.0 | 2.18708 | ||||||||
\(447\) | −1494.00 | −0.158085 | ||||||||
\(448\) | 4592.00 | 0.484267 | ||||||||
\(449\) | 10666.0 | 1.12107 | 0.560534 | − | 0.828131i | \(-0.310596\pi\) | ||||
0.560534 | + | 0.828131i | \(0.310596\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3432.00 | 0.358329 | ||||||||
\(452\) | 37502.0 | 3.90253 | ||||||||
\(453\) | −8088.00 | −0.838868 | ||||||||
\(454\) | 24660.0 | 2.54923 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3780.00 | 0.388190 | ||||||||
\(457\) | 8006.00 | 0.819486 | 0.409743 | − | 0.912201i | \(-0.365618\pi\) | ||||
0.409743 | + | 0.912201i | \(0.365618\pi\) | |||||||
\(458\) | 15250.0 | 1.55586 | ||||||||
\(459\) | −486.000 | −0.0494217 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1254.00 | 0.126691 | 0.0633456 | − | 0.997992i | \(-0.479823\pi\) | ||||
0.0633456 | + | 0.997992i | \(0.479823\pi\) | |||||||
\(462\) | −10560.0 | −1.06341 | ||||||||
\(463\) | 4584.00 | 0.460122 | 0.230061 | − | 0.973176i | \(-0.426107\pi\) | ||||
0.230061 | + | 0.973176i | \(0.426107\pi\) | |||||||
\(464\) | 2581.00 | 0.258233 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 410.000 | 0.0407573 | ||||||||
\(467\) | −11588.0 | −1.14824 | −0.574121 | − | 0.818771i | \(-0.694656\pi\) | ||||
−0.574121 | + | 0.818771i | \(0.694656\pi\) | |||||||
\(468\) | −11934.0 | −1.17874 | ||||||||
\(469\) | −5440.00 | −0.535599 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1602.00 | −0.156722 | ||||||||
\(472\) | −8100.00 | −0.789900 | ||||||||
\(473\) | −11440.0 | −1.11208 | ||||||||
\(474\) | 14400.0 | 1.39539 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4896.00 | 0.471445 | ||||||||
\(477\) | −5166.00 | −0.495880 | ||||||||
\(478\) | 25520.0 | 2.44196 | ||||||||
\(479\) | −18200.0 | −1.73607 | −0.868037 | − | 0.496500i | \(-0.834618\pi\) | ||||
−0.868037 | + | 0.496500i | \(0.834618\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19812.0 | 1.87807 | ||||||||
\(482\) | 10790.0 | 1.01965 | ||||||||
\(483\) | 8832.00 | 0.832029 | ||||||||
\(484\) | 10285.0 | 0.965909 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1215.00 | −0.113402 | ||||||||
\(487\) | −3824.00 | −0.355815 | −0.177908 | − | 0.984047i | \(-0.556933\pi\) | ||||
−0.177908 | + | 0.984047i | \(0.556933\pi\) | |||||||
\(488\) | 27450.0 | 2.54632 | ||||||||
\(489\) | −4140.00 | −0.382857 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3100.00 | −0.284931 | −0.142465 | − | 0.989800i | \(-0.545503\pi\) | ||||
−0.142465 | + | 0.989800i | \(0.545503\pi\) | |||||||
\(492\) | −3978.00 | −0.364516 | ||||||||
\(493\) | −522.000 | −0.0476870 | ||||||||
\(494\) | −10920.0 | −0.994563 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −19936.0 | −1.80474 | ||||||||
\(497\) | −4736.00 | −0.427442 | ||||||||
\(498\) | −13620.0 | −1.22556 | ||||||||
\(499\) | 19740.0 | 1.77091 | 0.885455 | − | 0.464726i | \(-0.153847\pi\) | ||||
0.885455 | + | 0.464726i | \(0.153847\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7848.00 | −0.699846 | ||||||||
\(502\) | −30580.0 | −2.71883 | ||||||||
\(503\) | 6720.00 | 0.595686 | 0.297843 | − | 0.954615i | \(-0.403733\pi\) | ||||
0.297843 | + | 0.954615i | \(0.403733\pi\) | |||||||
\(504\) | 6480.00 | 0.572703 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −40480.0 | −3.55643 | ||||||||
\(507\) | 11661.0 | 1.02147 | ||||||||
\(508\) | 34952.0 | 3.05265 | ||||||||
\(509\) | 10886.0 | 0.947964 | 0.473982 | − | 0.880535i | \(-0.342816\pi\) | ||||
0.473982 | + | 0.880535i | \(0.342816\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6304.00 | 0.545739 | ||||||||
\(512\) | 24475.0 | 2.11260 | ||||||||
\(513\) | −756.000 | −0.0650647 | ||||||||
\(514\) | 17090.0 | 1.46655 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 13260.0 | 1.13128 | ||||||||
\(517\) | 13728.0 | 1.16781 | ||||||||
\(518\) | −20320.0 | −1.72357 | ||||||||
\(519\) | 990.000 | 0.0837306 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22522.0 | 1.89387 | 0.946935 | − | 0.321424i | \(-0.104161\pi\) | ||||
0.946935 | + | 0.321424i | \(0.104161\pi\) | |||||||
\(522\) | −1305.00 | −0.109422 | ||||||||
\(523\) | 13212.0 | 1.10463 | 0.552314 | − | 0.833636i | \(-0.313745\pi\) | ||||
0.552314 | + | 0.833636i | \(0.313745\pi\) | |||||||
\(524\) | 204.000 | 0.0170072 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 37200.0 | 3.08364 | ||||||||
\(527\) | 4032.00 | 0.333276 | ||||||||
\(528\) | −11748.0 | −0.968307 | ||||||||
\(529\) | 21689.0 | 1.78261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1620.00 | 0.132396 | ||||||||
\(532\) | 7616.00 | 0.620668 | ||||||||
\(533\) | 6084.00 | 0.494423 | ||||||||
\(534\) | 14850.0 | 1.20341 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −15300.0 | −1.23295 | ||||||||
\(537\) | −1116.00 | −0.0896815 | ||||||||
\(538\) | −32910.0 | −2.63727 | ||||||||
\(539\) | 3828.00 | 0.305907 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4642.00 | −0.368900 | −0.184450 | − | 0.982842i | \(-0.559050\pi\) | ||||
−0.184450 | + | 0.982842i | \(0.559050\pi\) | |||||||
\(542\) | 27520.0 | 2.18097 | ||||||||
\(543\) | −3030.00 | −0.239465 | ||||||||
\(544\) | 1530.00 | 0.120585 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −18720.0 | −1.46729 | ||||||||
\(547\) | −4060.00 | −0.317355 | −0.158677 | − | 0.987330i | \(-0.550723\pi\) | ||||
−0.158677 | + | 0.987330i | \(0.550723\pi\) | |||||||
\(548\) | 46886.0 | 3.65487 | ||||||||
\(549\) | −5490.00 | −0.426790 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −812.000 | −0.0627811 | ||||||||
\(552\) | 24840.0 | 1.91533 | ||||||||
\(553\) | 15360.0 | 1.18115 | ||||||||
\(554\) | 18590.0 | 1.42566 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −24412.0 | −1.86205 | ||||||||
\(557\) | 1386.00 | 0.105434 | 0.0527170 | − | 0.998609i | \(-0.483212\pi\) | ||||
0.0527170 | + | 0.998609i | \(0.483212\pi\) | |||||||
\(558\) | 10080.0 | 0.764732 | ||||||||
\(559\) | −20280.0 | −1.53444 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2376.00 | 0.178814 | ||||||||
\(562\) | −8770.00 | −0.658256 | ||||||||
\(563\) | −2452.00 | −0.183551 | −0.0917757 | − | 0.995780i | \(-0.529254\pi\) | ||||
−0.0917757 | + | 0.995780i | \(0.529254\pi\) | |||||||
\(564\) | −15912.0 | −1.18797 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 17860.0 | 1.32635 | ||||||||
\(567\) | −1296.00 | −0.0959910 | ||||||||
\(568\) | −13320.0 | −0.983970 | ||||||||
\(569\) | −20862.0 | −1.53705 | −0.768524 | − | 0.639821i | \(-0.779009\pi\) | ||||
−0.768524 | + | 0.639821i | \(0.779009\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9420.00 | −0.690394 | −0.345197 | − | 0.938530i | \(-0.612188\pi\) | ||||
−0.345197 | + | 0.938530i | \(0.612188\pi\) | |||||||
\(572\) | 58344.0 | 4.26483 | ||||||||
\(573\) | 6024.00 | 0.439191 | ||||||||
\(574\) | −6240.00 | −0.453750 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2583.00 | −0.186849 | ||||||||
\(577\) | −13202.0 | −0.952524 | −0.476262 | − | 0.879303i | \(-0.658009\pi\) | ||||
−0.476262 | + | 0.879303i | \(0.658009\pi\) | |||||||
\(578\) | 22945.0 | 1.65119 | ||||||||
\(579\) | −7734.00 | −0.555119 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14528.0 | −1.03739 | ||||||||
\(582\) | 18510.0 | 1.31832 | ||||||||
\(583\) | 25256.0 | 1.79416 | ||||||||
\(584\) | 17730.0 | 1.25629 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 630.000 | 0.0444114 | ||||||||
\(587\) | 8708.00 | 0.612296 | 0.306148 | − | 0.951984i | \(-0.400960\pi\) | ||||
0.306148 | + | 0.951984i | \(0.400960\pi\) | |||||||
\(588\) | −4437.00 | −0.311188 | ||||||||
\(589\) | 6272.00 | 0.438766 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1578.00 | −0.109831 | ||||||||
\(592\) | −22606.0 | −1.56943 | ||||||||
\(593\) | 4390.00 | 0.304006 | 0.152003 | − | 0.988380i | \(-0.451428\pi\) | ||||
0.152003 | + | 0.988380i | \(0.451428\pi\) | |||||||
\(594\) | 5940.00 | 0.410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8466.00 | −0.581847 | ||||||||
\(597\) | 13320.0 | 0.913151 | ||||||||
\(598\) | −71760.0 | −4.90716 | ||||||||
\(599\) | −20256.0 | −1.38170 | −0.690850 | − | 0.722999i | \(-0.742763\pi\) | ||||
−0.690850 | + | 0.722999i | \(0.742763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9610.00 | 0.652246 | 0.326123 | − | 0.945327i | \(-0.394258\pi\) | ||||
0.326123 | + | 0.945327i | \(0.394258\pi\) | |||||||
\(602\) | 20800.0 | 1.40821 | ||||||||
\(603\) | 3060.00 | 0.206655 | ||||||||
\(604\) | −45832.0 | −3.08755 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15330.0 | −1.02762 | ||||||||
\(607\) | −10376.0 | −0.693820 | −0.346910 | − | 0.937898i | \(-0.612769\pi\) | ||||
−0.346910 | + | 0.937898i | \(0.612769\pi\) | |||||||
\(608\) | 2380.00 | 0.158753 | ||||||||
\(609\) | −1392.00 | −0.0926218 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24336.0 | 1.61134 | ||||||||
\(612\) | −2754.00 | −0.181902 | ||||||||
\(613\) | −6822.00 | −0.449491 | −0.224746 | − | 0.974417i | \(-0.572155\pi\) | ||||
−0.224746 | + | 0.974417i | \(0.572155\pi\) | |||||||
\(614\) | −12060.0 | −0.792674 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −31680.0 | −2.07212 | ||||||||
\(617\) | 20070.0 | 1.30954 | 0.654771 | − | 0.755827i | \(-0.272765\pi\) | ||||
0.654771 | + | 0.755827i | \(0.272765\pi\) | |||||||
\(618\) | −18720.0 | −1.21849 | ||||||||
\(619\) | 19228.0 | 1.24853 | 0.624264 | − | 0.781214i | \(-0.285399\pi\) | ||||
0.624264 | + | 0.781214i | \(0.285399\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4968.00 | −0.321029 | ||||||||
\(622\) | 14640.0 | 0.943747 | ||||||||
\(623\) | 15840.0 | 1.01865 | ||||||||
\(624\) | −20826.0 | −1.33607 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 14370.0 | 0.917477 | ||||||||
\(627\) | 3696.00 | 0.235413 | ||||||||
\(628\) | −9078.00 | −0.576834 | ||||||||
\(629\) | 4572.00 | 0.289821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6552.00 | 0.413361 | 0.206681 | − | 0.978408i | \(-0.433734\pi\) | ||||
0.206681 | + | 0.978408i | \(0.433734\pi\) | |||||||
\(632\) | 43200.0 | 2.71899 | ||||||||
\(633\) | 924.000 | 0.0580185 | ||||||||
\(634\) | −130.000 | −0.00814347 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −29274.0 | −1.82514 | ||||||||
\(637\) | 6786.00 | 0.422090 | ||||||||
\(638\) | 6380.00 | 0.395904 | ||||||||
\(639\) | 2664.00 | 0.164924 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14422.0 | −0.888666 | −0.444333 | − | 0.895862i | \(-0.646559\pi\) | ||||
−0.444333 | + | 0.895862i | \(0.646559\pi\) | |||||||
\(642\) | −1740.00 | −0.106966 | ||||||||
\(643\) | 6212.00 | 0.380991 | 0.190496 | − | 0.981688i | \(-0.438991\pi\) | ||||
0.190496 | + | 0.981688i | \(0.438991\pi\) | |||||||
\(644\) | 50048.0 | 3.06237 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2520.00 | −0.153480 | ||||||||
\(647\) | −22024.0 | −1.33826 | −0.669129 | − | 0.743146i | \(-0.733333\pi\) | ||||
−0.669129 | + | 0.743146i | \(0.733333\pi\) | |||||||
\(648\) | −3645.00 | −0.220971 | ||||||||
\(649\) | −7920.00 | −0.479025 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10752.0 | 0.647318 | ||||||||
\(652\) | −23460.0 | −1.40915 | ||||||||
\(653\) | −16630.0 | −0.996604 | −0.498302 | − | 0.867004i | \(-0.666043\pi\) | ||||
−0.498302 | + | 0.867004i | \(0.666043\pi\) | |||||||
\(654\) | 12390.0 | 0.740806 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6942.00 | −0.413170 | ||||||||
\(657\) | −3546.00 | −0.210567 | ||||||||
\(658\) | −24960.0 | −1.47879 | ||||||||
\(659\) | −24468.0 | −1.44634 | −0.723170 | − | 0.690670i | \(-0.757316\pi\) | ||||
−0.723170 | + | 0.690670i | \(0.757316\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10226.0 | −0.601733 | −0.300866 | − | 0.953666i | \(-0.597276\pi\) | ||||
−0.300866 | + | 0.953666i | \(0.597276\pi\) | |||||||
\(662\) | −46700.0 | −2.74176 | ||||||||
\(663\) | 4212.00 | 0.246728 | ||||||||
\(664\) | −40860.0 | −2.38807 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11430.0 | 0.665020 | ||||||||
\(667\) | −5336.00 | −0.309761 | ||||||||
\(668\) | −44472.0 | −2.57586 | ||||||||
\(669\) | −12360.0 | −0.714298 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26840.0 | 1.54418 | ||||||||
\(672\) | 4080.00 | 0.234210 | ||||||||
\(673\) | −13458.0 | −0.770829 | −0.385414 | − | 0.922744i | \(-0.625941\pi\) | ||||
−0.385414 | + | 0.922744i | \(0.625941\pi\) | |||||||
\(674\) | −51510.0 | −2.94376 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 66079.0 | 3.75962 | ||||||||
\(677\) | −22174.0 | −1.25881 | −0.629406 | − | 0.777076i | \(-0.716702\pi\) | ||||
−0.629406 | + | 0.777076i | \(0.716702\pi\) | |||||||
\(678\) | −33090.0 | −1.87436 | ||||||||
\(679\) | 19744.0 | 1.11591 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14796.0 | −0.832576 | ||||||||
\(682\) | −49280.0 | −2.76690 | ||||||||
\(683\) | 2404.00 | 0.134680 | 0.0673400 | − | 0.997730i | \(-0.478549\pi\) | ||||
0.0673400 | + | 0.997730i | \(0.478549\pi\) | |||||||
\(684\) | −4284.00 | −0.239478 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −34400.0 | −1.91457 | ||||||||
\(687\) | −9150.00 | −0.508143 | ||||||||
\(688\) | 23140.0 | 1.28227 | ||||||||
\(689\) | 44772.0 | 2.47558 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5956.00 | −0.327897 | −0.163949 | − | 0.986469i | \(-0.552423\pi\) | ||||
−0.163949 | + | 0.986469i | \(0.552423\pi\) | |||||||
\(692\) | 5610.00 | 0.308179 | ||||||||
\(693\) | 6336.00 | 0.347308 | ||||||||
\(694\) | −40100.0 | −2.19334 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3915.00 | −0.213215 | ||||||||
\(697\) | 1404.00 | 0.0762988 | ||||||||
\(698\) | 6530.00 | 0.354103 | ||||||||
\(699\) | −246.000 | −0.0133113 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14586.0 | −0.785885 | −0.392943 | − | 0.919563i | \(-0.628543\pi\) | ||||
−0.392943 | + | 0.919563i | \(0.628543\pi\) | |||||||
\(702\) | 10530.0 | 0.566139 | ||||||||
\(703\) | 7112.00 | 0.381556 | ||||||||
\(704\) | 12628.0 | 0.676045 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28290.0 | 1.50809 | ||||||||
\(707\) | −16352.0 | −0.869845 | ||||||||
\(708\) | 9180.00 | 0.487296 | ||||||||
\(709\) | −4370.00 | −0.231479 | −0.115740 | − | 0.993280i | \(-0.536924\pi\) | ||||
−0.115740 | + | 0.993280i | \(0.536924\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8640.00 | −0.455732 | ||||||||
\(712\) | 44550.0 | 2.34492 | ||||||||
\(713\) | 41216.0 | 2.16487 | ||||||||
\(714\) | −4320.00 | −0.226431 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6324.00 | −0.330082 | ||||||||
\(717\) | −15312.0 | −0.797541 | ||||||||
\(718\) | 61200.0 | 3.18101 | ||||||||
\(719\) | 144.000 | 0.00746912 | 0.00373456 | − | 0.999993i | \(-0.498811\pi\) | ||||
0.00373456 | + | 0.999993i | \(0.498811\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19968.0 | −1.03141 | ||||||||
\(722\) | 30375.0 | 1.56571 | ||||||||
\(723\) | −6474.00 | −0.333016 | ||||||||
\(724\) | −17170.0 | −0.881378 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −9075.00 | −0.463919 | ||||||||
\(727\) | 9632.00 | 0.491377 | 0.245689 | − | 0.969349i | \(-0.420986\pi\) | ||||
0.245689 | + | 0.969349i | \(0.420986\pi\) | |||||||
\(728\) | −56160.0 | −2.85910 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4680.00 | −0.236794 | ||||||||
\(732\) | −31110.0 | −1.57085 | ||||||||
\(733\) | 19306.0 | 0.972829 | 0.486414 | − | 0.873728i | \(-0.338305\pi\) | ||||
0.486414 | + | 0.873728i | \(0.338305\pi\) | |||||||
\(734\) | 44920.0 | 2.25889 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15640.0 | 0.783285 | ||||||||
\(737\) | −14960.0 | −0.747705 | ||||||||
\(738\) | 3510.00 | 0.175074 | ||||||||
\(739\) | −36540.0 | −1.81887 | −0.909435 | − | 0.415845i | \(-0.863486\pi\) | ||||
−0.909435 | + | 0.415845i | \(0.863486\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6552.00 | 0.324823 | ||||||||
\(742\) | −45920.0 | −2.27194 | ||||||||
\(743\) | −5408.00 | −0.267026 | −0.133513 | − | 0.991047i | \(-0.542626\pi\) | ||||
−0.133513 | + | 0.991047i | \(0.542626\pi\) | |||||||
\(744\) | 30240.0 | 1.49012 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4690.00 | −0.230178 | ||||||||
\(747\) | 8172.00 | 0.400265 | ||||||||
\(748\) | 13464.0 | 0.658145 | ||||||||
\(749\) | −1856.00 | −0.0905431 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13952.0 | −0.677917 | −0.338959 | − | 0.940801i | \(-0.610075\pi\) | ||||
−0.338959 | + | 0.940801i | \(0.610075\pi\) | |||||||
\(752\) | −27768.0 | −1.34654 | ||||||||
\(753\) | 18348.0 | 0.887966 | ||||||||
\(754\) | 11310.0 | 0.546268 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −7344.00 | −0.353305 | ||||||||
\(757\) | 4274.00 | 0.205206 | 0.102603 | − | 0.994722i | \(-0.467283\pi\) | ||||
0.102603 | + | 0.994722i | \(0.467283\pi\) | |||||||
\(758\) | 38980.0 | 1.86783 | ||||||||
\(759\) | 24288.0 | 1.16153 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −230.000 | −0.0109560 | −0.00547799 | − | 0.999985i | \(-0.501744\pi\) | ||||
−0.00547799 | + | 0.999985i | \(0.501744\pi\) | |||||||
\(762\) | −30840.0 | −1.46616 | ||||||||
\(763\) | 13216.0 | 0.627066 | ||||||||
\(764\) | 34136.0 | 1.61649 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −34720.0 | −1.63771 | ||||||||
\(767\) | −14040.0 | −0.660958 | ||||||||
\(768\) | −24837.0 | −1.16696 | ||||||||
\(769\) | −7854.00 | −0.368300 | −0.184150 | − | 0.982898i | \(-0.558953\pi\) | ||||
−0.184150 | + | 0.982898i | \(0.558953\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10254.0 | −0.478974 | ||||||||
\(772\) | −43826.0 | −2.04318 | ||||||||
\(773\) | −19550.0 | −0.909657 | −0.454828 | − | 0.890579i | \(-0.650299\pi\) | ||||
−0.454828 | + | 0.890579i | \(0.650299\pi\) | |||||||
\(774\) | −11700.0 | −0.543343 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 55530.0 | 2.56883 | ||||||||
\(777\) | 12192.0 | 0.562916 | ||||||||
\(778\) | −10630.0 | −0.489851 | ||||||||
\(779\) | 2184.00 | 0.100449 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13024.0 | −0.596716 | ||||||||
\(782\) | −16560.0 | −0.757269 | ||||||||
\(783\) | 783.000 | 0.0357371 | ||||||||
\(784\) | −7743.00 | −0.352724 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −180.000 | −0.00816843 | ||||||||
\(787\) | −27228.0 | −1.23326 | −0.616629 | − | 0.787254i | \(-0.711502\pi\) | ||||
−0.616629 | + | 0.787254i | \(0.711502\pi\) | |||||||
\(788\) | −8942.00 | −0.404246 | ||||||||
\(789\) | −22320.0 | −1.00711 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35296.0 | −1.58658 | ||||||||
\(792\) | 17820.0 | 0.799503 | ||||||||
\(793\) | 47580.0 | 2.13066 | ||||||||
\(794\) | −16730.0 | −0.747765 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 75480.0 | 3.36095 | ||||||||
\(797\) | 3386.00 | 0.150487 | 0.0752436 | − | 0.997165i | \(-0.476027\pi\) | ||||
0.0752436 | + | 0.997165i | \(0.476027\pi\) | |||||||
\(798\) | −6720.00 | −0.298102 | ||||||||
\(799\) | 5616.00 | 0.248661 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8910.00 | −0.393033 | ||||||||
\(802\) | −64250.0 | −2.82886 | ||||||||
\(803\) | 17336.0 | 0.761861 | ||||||||
\(804\) | 17340.0 | 0.760615 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −87360.0 | −3.81777 | ||||||||
\(807\) | 19746.0 | 0.861329 | ||||||||
\(808\) | −45990.0 | −2.00238 | ||||||||
\(809\) | 26994.0 | 1.17313 | 0.586563 | − | 0.809904i | \(-0.300481\pi\) | ||||
0.586563 | + | 0.809904i | \(0.300481\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8356.00 | 0.361799 | 0.180899 | − | 0.983502i | \(-0.442099\pi\) | ||||
0.180899 | + | 0.983502i | \(0.442099\pi\) | |||||||
\(812\) | −7888.00 | −0.340905 | ||||||||
\(813\) | −16512.0 | −0.712302 | ||||||||
\(814\) | −55880.0 | −2.40613 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4806.00 | −0.206181 | ||||||||
\(817\) | −7280.00 | −0.311744 | ||||||||
\(818\) | −30610.0 | −1.30838 | ||||||||
\(819\) | 11232.0 | 0.479216 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9838.00 | 0.418208 | 0.209104 | − | 0.977893i | \(-0.432945\pi\) | ||||
0.209104 | + | 0.977893i | \(0.432945\pi\) | |||||||
\(822\) | −41370.0 | −1.75541 | ||||||||
\(823\) | 29552.0 | 1.25166 | 0.625831 | − | 0.779959i | \(-0.284760\pi\) | ||||
0.625831 | + | 0.779959i | \(0.284760\pi\) | |||||||
\(824\) | −56160.0 | −2.37430 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14400.0 | 0.606586 | ||||||||
\(827\) | −18556.0 | −0.780236 | −0.390118 | − | 0.920765i | \(-0.627566\pi\) | ||||
−0.390118 | + | 0.920765i | \(0.627566\pi\) | |||||||
\(828\) | −28152.0 | −1.18158 | ||||||||
\(829\) | 7966.00 | 0.333740 | 0.166870 | − | 0.985979i | \(-0.446634\pi\) | ||||
0.166870 | + | 0.985979i | \(0.446634\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11154.0 | −0.465617 | ||||||||
\(832\) | 22386.0 | 0.932806 | ||||||||
\(833\) | 1566.00 | 0.0651365 | ||||||||
\(834\) | 21540.0 | 0.894328 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 20944.0 | 0.866463 | ||||||||
\(837\) | −6048.00 | −0.249760 | ||||||||
\(838\) | −6860.00 | −0.282786 | ||||||||
\(839\) | −42048.0 | −1.73022 | −0.865112 | − | 0.501578i | \(-0.832753\pi\) | ||||
−0.865112 | + | 0.501578i | \(0.832753\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | −60750.0 | −2.48644 | ||||||||
\(843\) | 5262.00 | 0.214986 | ||||||||
\(844\) | 5236.00 | 0.213543 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 14040.0 | 0.570573 | ||||||||
\(847\) | −9680.00 | −0.392690 | ||||||||
\(848\) | −51086.0 | −2.06875 | ||||||||
\(849\) | −10716.0 | −0.433183 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 46736.0 | 1.88260 | ||||||||
\(852\) | 15096.0 | 0.607019 | ||||||||
\(853\) | −29950.0 | −1.20219 | −0.601095 | − | 0.799177i | \(-0.705269\pi\) | ||||
−0.601095 | + | 0.799177i | \(0.705269\pi\) | |||||||
\(854\) | −48800.0 | −1.95539 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5220.00 | −0.208430 | ||||||||
\(857\) | 31454.0 | 1.25373 | 0.626866 | − | 0.779127i | \(-0.284337\pi\) | ||||
0.626866 | + | 0.779127i | \(0.284337\pi\) | |||||||
\(858\) | −51480.0 | −2.04837 | ||||||||
\(859\) | −22036.0 | −0.875272 | −0.437636 | − | 0.899152i | \(-0.644184\pi\) | ||||
−0.437636 | + | 0.899152i | \(0.644184\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3744.00 | 0.148194 | ||||||||
\(862\) | −31440.0 | −1.24229 | ||||||||
\(863\) | −14048.0 | −0.554113 | −0.277056 | − | 0.960854i | \(-0.589359\pi\) | ||||
−0.277056 | + | 0.960854i | \(0.589359\pi\) | |||||||
\(864\) | −2295.00 | −0.0903675 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 78250.0 | 3.07049 | ||||||||
\(867\) | −13767.0 | −0.539275 | ||||||||
\(868\) | 60928.0 | 2.38252 | ||||||||
\(869\) | 42240.0 | 1.64890 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26520.0 | −1.03168 | ||||||||
\(872\) | 37170.0 | 1.44350 | ||||||||
\(873\) | −11106.0 | −0.430563 | ||||||||
\(874\) | −25760.0 | −0.996962 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −20094.0 | −0.775015 | ||||||||
\(877\) | 39922.0 | 1.53714 | 0.768569 | − | 0.639767i | \(-0.220969\pi\) | ||||
0.768569 | + | 0.639767i | \(0.220969\pi\) | |||||||
\(878\) | 72600.0 | 2.79058 | ||||||||
\(879\) | −378.000 | −0.0145047 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38730.0 | 1.48110 | 0.740549 | − | 0.672003i | \(-0.234566\pi\) | ||||
0.740549 | + | 0.672003i | \(0.234566\pi\) | |||||||
\(882\) | 3915.00 | 0.149461 | ||||||||
\(883\) | 32948.0 | 1.25571 | 0.627853 | − | 0.778332i | \(-0.283934\pi\) | ||||
0.627853 | + | 0.778332i | \(0.283934\pi\) | |||||||
\(884\) | 23868.0 | 0.908108 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36860.0 | 1.39767 | ||||||||
\(887\) | 21680.0 | 0.820680 | 0.410340 | − | 0.911933i | \(-0.365410\pi\) | ||||
0.410340 | + | 0.911933i | \(0.365410\pi\) | |||||||
\(888\) | 34290.0 | 1.29583 | ||||||||
\(889\) | −32896.0 | −1.24105 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3564.00 | −0.134005 | ||||||||
\(892\) | −70040.0 | −2.62905 | ||||||||
\(893\) | 8736.00 | 0.327367 | ||||||||
\(894\) | 7470.00 | 0.279457 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −33840.0 | −1.26174 | ||||||||
\(897\) | 43056.0 | 1.60267 | ||||||||
\(898\) | −53330.0 | −1.98179 | ||||||||
\(899\) | −6496.00 | −0.240994 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10332.0 | 0.382030 | ||||||||
\(902\) | −17160.0 | −0.633443 | ||||||||
\(903\) | −12480.0 | −0.459921 | ||||||||
\(904\) | −99270.0 | −3.65229 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 40440.0 | 1.48292 | ||||||||
\(907\) | −2236.00 | −0.0818580 | −0.0409290 | − | 0.999162i | \(-0.513032\pi\) | ||||
−0.0409290 | + | 0.999162i | \(0.513032\pi\) | |||||||
\(908\) | −83844.0 | −3.06438 | ||||||||
\(909\) | 9198.00 | 0.335620 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35816.0 | 1.30257 | 0.651283 | − | 0.758835i | \(-0.274231\pi\) | ||||
0.651283 | + | 0.758835i | \(0.274231\pi\) | |||||||
\(912\) | −7476.00 | −0.271442 | ||||||||
\(913\) | −39952.0 | −1.44821 | ||||||||
\(914\) | −40030.0 | −1.44866 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −51850.0 | −1.87028 | ||||||||
\(917\) | −192.000 | −0.00691428 | ||||||||
\(918\) | 2430.00 | 0.0873660 | ||||||||
\(919\) | 39704.0 | 1.42515 | 0.712576 | − | 0.701595i | \(-0.247529\pi\) | ||||
0.712576 | + | 0.701595i | \(0.247529\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7236.00 | 0.258886 | ||||||||
\(922\) | −6270.00 | −0.223960 | ||||||||
\(923\) | −23088.0 | −0.823349 | ||||||||
\(924\) | 35904.0 | 1.27831 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −22920.0 | −0.813389 | ||||||||
\(927\) | 11232.0 | 0.397958 | ||||||||
\(928\) | −2465.00 | −0.0871957 | ||||||||
\(929\) | −19534.0 | −0.689871 | −0.344935 | − | 0.938626i | \(-0.612099\pi\) | ||||
−0.344935 | + | 0.938626i | \(0.612099\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2436.00 | 0.0857537 | ||||||||
\(932\) | −1394.00 | −0.0489935 | ||||||||
\(933\) | −8784.00 | −0.308226 | ||||||||
\(934\) | 57940.0 | 2.02982 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 31590.0 | 1.10315 | ||||||||
\(937\) | 8678.00 | 0.302559 | 0.151280 | − | 0.988491i | \(-0.451661\pi\) | ||||
0.151280 | + | 0.988491i | \(0.451661\pi\) | |||||||
\(938\) | 27200.0 | 0.946814 | ||||||||
\(939\) | −8622.00 | −0.299647 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7050.00 | −0.244233 | −0.122117 | − | 0.992516i | \(-0.538968\pi\) | ||||
−0.122117 | + | 0.992516i | \(0.538968\pi\) | |||||||
\(942\) | 8010.00 | 0.277049 | ||||||||
\(943\) | 14352.0 | 0.495616 | ||||||||
\(944\) | 16020.0 | 0.552337 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 57200.0 | 1.96589 | ||||||||
\(947\) | −23396.0 | −0.802817 | −0.401409 | − | 0.915899i | \(-0.631479\pi\) | ||||
−0.401409 | + | 0.915899i | \(0.631479\pi\) | |||||||
\(948\) | −48960.0 | −1.67737 | ||||||||
\(949\) | 30732.0 | 1.05121 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 78.0000 | 0.00265965 | ||||||||
\(952\) | −12960.0 | −0.441214 | ||||||||
\(953\) | 36126.0 | 1.22795 | 0.613975 | − | 0.789326i | \(-0.289570\pi\) | ||||
0.613975 | + | 0.789326i | \(0.289570\pi\) | |||||||
\(954\) | 25830.0 | 0.876601 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −86768.0 | −2.93544 | ||||||||
\(957\) | −3828.00 | −0.129302 | ||||||||
\(958\) | 91000.0 | 3.06897 | ||||||||
\(959\) | −44128.0 | −1.48589 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20385.0 | 0.684267 | ||||||||
\(962\) | −99060.0 | −3.31998 | ||||||||
\(963\) | 1044.00 | 0.0349350 | ||||||||
\(964\) | −36686.0 | −1.22570 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −44160.0 | −1.47083 | ||||||||
\(967\) | −38624.0 | −1.28445 | −0.642225 | − | 0.766516i | \(-0.721989\pi\) | ||||
−0.642225 | + | 0.766516i | \(0.721989\pi\) | |||||||
\(968\) | −27225.0 | −0.903972 | ||||||||
\(969\) | 1512.00 | 0.0501264 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7292.00 | −0.241000 | −0.120500 | − | 0.992713i | \(-0.538450\pi\) | ||||
−0.120500 | + | 0.992713i | \(0.538450\pi\) | |||||||
\(972\) | 4131.00 | 0.136319 | ||||||||
\(973\) | 22976.0 | 0.757016 | ||||||||
\(974\) | 19120.0 | 0.628998 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −54290.0 | −1.78051 | ||||||||
\(977\) | 26838.0 | 0.878837 | 0.439418 | − | 0.898282i | \(-0.355185\pi\) | ||||
0.439418 | + | 0.898282i | \(0.355185\pi\) | |||||||
\(978\) | 20700.0 | 0.676803 | ||||||||
\(979\) | 43560.0 | 1.42205 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7434.00 | −0.241946 | ||||||||
\(982\) | 15500.0 | 0.503691 | ||||||||
\(983\) | −20192.0 | −0.655163 | −0.327581 | − | 0.944823i | \(-0.606234\pi\) | ||||
−0.327581 | + | 0.944823i | \(0.606234\pi\) | |||||||
\(984\) | 10530.0 | 0.341142 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2610.00 | 0.0842995 | ||||||||
\(987\) | 14976.0 | 0.482970 | ||||||||
\(988\) | 37128.0 | 1.19555 | ||||||||
\(989\) | −47840.0 | −1.53814 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34400.0 | 1.10268 | 0.551338 | − | 0.834282i | \(-0.314117\pi\) | ||||
0.551338 | + | 0.834282i | \(0.314117\pi\) | |||||||
\(992\) | 19040.0 | 0.609396 | ||||||||
\(993\) | 28020.0 | 0.895456 | ||||||||
\(994\) | 23680.0 | 0.755618 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 46308.0 | 1.47322 | ||||||||
\(997\) | −58430.0 | −1.85606 | −0.928032 | − | 0.372499i | \(-0.878501\pi\) | ||||
−0.928032 | + | 0.372499i | \(0.878501\pi\) | |||||||
\(998\) | −98700.0 | −3.13056 | ||||||||
\(999\) | −6858.00 | −0.217195 |
(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 | 2175.4.a.a.1.1 | 1 | ||
5.4 | even | 2 | 435.4.a.c.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 1305.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.4.a.c.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
1305.4.a.a.1.1 | 1 | 15.14 | odd | 2 | |||
2175.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial |