Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [435,4,Mod(1,435)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(435, 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("435.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 435 = 3 \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 435.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: | \(25.6658308525\) |
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 | \(\chi\) | \(=\) | 435.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.00000 | 1.76777 | 0.883883 | − | 0.467707i | \(-0.154920\pi\) | ||||
0.883883 | + | 0.467707i | \(0.154920\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 17.0000 | 2.12500 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −15.0000 | −1.02062 | ||||||||
\(7\) | 16.0000 | 0.863919 | 0.431959 | − | 0.901893i | \(-0.357822\pi\) | ||||
0.431959 | + | 0.901893i | \(0.357822\pi\) | |||||||
\(8\) | 45.0000 | 1.98874 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 25.0000 | 0.790569 | ||||||||
\(11\) | −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 | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 80.0000 | 1.52721 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 89.0000 | 1.39062 | ||||||||
\(17\) | 18.0000 | 0.256802 | 0.128401 | − | 0.991722i | \(-0.459015\pi\) | ||||
0.128401 | + | 0.991722i | \(0.459015\pi\) | |||||||
\(18\) | 45.0000 | 0.589256 | ||||||||
\(19\) | −28.0000 | −0.338086 | −0.169043 | − | 0.985609i | \(-0.554068\pi\) | ||||
−0.169043 | + | 0.985609i | \(0.554068\pi\) | |||||||
\(20\) | 85.0000 | 0.950329 | ||||||||
\(21\) | −48.0000 | −0.498784 | ||||||||
\(22\) | −220.000 | −2.13201 | ||||||||
\(23\) | 184.000 | 1.66812 | 0.834058 | − | 0.551677i | \(-0.186012\pi\) | ||||
0.834058 | + | 0.551677i | \(0.186012\pi\) | |||||||
\(24\) | −135.000 | −1.14820 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 390.000 | 2.94174 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 272.000 | 1.83583 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | −75.0000 | −0.456435 | ||||||||
\(31\) | −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 | ||||||||
\(35\) | 80.0000 | 0.386356 | ||||||||
\(36\) | 153.000 | 0.708333 | ||||||||
\(37\) | 254.000 | 1.12858 | 0.564288 | − | 0.825578i | \(-0.309151\pi\) | ||||
0.564288 | + | 0.825578i | \(0.309151\pi\) | |||||||
\(38\) | −140.000 | −0.597658 | ||||||||
\(39\) | −234.000 | −0.960769 | ||||||||
\(40\) | 225.000 | 0.889391 | ||||||||
\(41\) | −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 | \(-0.652524\pi\) | ||||
−0.461042 | + | 0.887378i | \(0.652524\pi\) | |||||||
\(44\) | −748.000 | −2.56285 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 920.000 | 2.94884 | ||||||||
\(47\) | 312.000 | 0.968295 | 0.484148 | − | 0.874986i | \(-0.339130\pi\) | ||||
0.484148 | + | 0.874986i | \(0.339130\pi\) | |||||||
\(48\) | −267.000 | −0.802878 | ||||||||
\(49\) | −87.0000 | −0.253644 | ||||||||
\(50\) | 125.000 | 0.353553 | ||||||||
\(51\) | −54.0000 | −0.148265 | ||||||||
\(52\) | 1326.00 | 3.53621 | ||||||||
\(53\) | 574.000 | 1.48764 | 0.743820 | − | 0.668380i | \(-0.233012\pi\) | ||||
0.743820 | + | 0.668380i | \(0.233012\pi\) | |||||||
\(54\) | −135.000 | −0.340207 | ||||||||
\(55\) | −220.000 | −0.539360 | ||||||||
\(56\) | 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 | \(0.436363\pi\) | |||||||
\(60\) | −255.000 | −0.548673 | ||||||||
\(61\) | −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 | ||||||||
\(65\) | 390.000 | 0.744208 | ||||||||
\(66\) | 660.000 | 1.23091 | ||||||||
\(67\) | −340.000 | −0.619964 | −0.309982 | − | 0.950742i | \(-0.600323\pi\) | ||||
−0.309982 | + | 0.950742i | \(0.600323\pi\) | |||||||
\(68\) | 306.000 | 0.545705 | ||||||||
\(69\) | −552.000 | −0.963087 | ||||||||
\(70\) | 400.000 | 0.682988 | ||||||||
\(71\) | 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 | \(-0.397710\pi\) | ||||
0.315851 | + | 0.948809i | \(0.397710\pi\) | |||||||
\(74\) | 1270.00 | 1.99506 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | −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 | \(0.739586\pi\) | |||||||
\(80\) | 445.000 | 0.621906 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −390.000 | −0.525223 | ||||||||
\(83\) | −908.000 | −1.20079 | −0.600397 | − | 0.799702i | \(-0.704991\pi\) | ||||
−0.600397 | + | 0.799702i | \(0.704991\pi\) | |||||||
\(84\) | −816.000 | −1.05992 | ||||||||
\(85\) | 90.0000 | 0.114846 | ||||||||
\(86\) | −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 | \(0.700695\pi\) | |||||||
\(90\) | 225.000 | 0.263523 | ||||||||
\(91\) | 1248.00 | 1.43765 | ||||||||
\(92\) | 3128.00 | 3.54475 | ||||||||
\(93\) | 672.000 | 0.749281 | ||||||||
\(94\) | 1560.00 | 1.71172 | ||||||||
\(95\) | −140.000 | −0.151197 | ||||||||
\(96\) | −255.000 | −0.271102 | ||||||||
\(97\) | 1234.00 | 1.29169 | 0.645844 | − | 0.763469i | \(-0.276506\pi\) | ||||
0.645844 | + | 0.763469i | \(0.276506\pi\) | |||||||
\(98\) | −435.000 | −0.448384 | ||||||||
\(99\) | −396.000 | −0.402015 | ||||||||
\(100\) | 425.000 | 0.425000 | ||||||||
\(101\) | 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 | \(-0.703616\pi\) | ||||
−0.596937 | + | 0.802288i | \(0.703616\pi\) | |||||||
\(104\) | 3510.00 | 3.30946 | ||||||||
\(105\) | −240.000 | −0.223063 | ||||||||
\(106\) | 2870.00 | 2.62980 | ||||||||
\(107\) | −116.000 | −0.104805 | −0.0524025 | − | 0.998626i | \(-0.516688\pi\) | ||||
−0.0524025 | + | 0.998626i | \(0.516688\pi\) | |||||||
\(108\) | −459.000 | −0.408956 | ||||||||
\(109\) | −826.000 | −0.725839 | −0.362920 | − | 0.931820i | \(-0.618220\pi\) | ||||
−0.362920 | + | 0.931820i | \(0.618220\pi\) | |||||||
\(110\) | −1100.00 | −0.953463 | ||||||||
\(111\) | −762.000 | −0.651584 | ||||||||
\(112\) | 1424.00 | 1.20139 | ||||||||
\(113\) | −2206.00 | −1.83649 | −0.918243 | − | 0.396016i | \(-0.870392\pi\) | ||||
−0.918243 | + | 0.396016i | \(0.870392\pi\) | |||||||
\(114\) | 420.000 | 0.345058 | ||||||||
\(115\) | 920.000 | 0.746004 | ||||||||
\(116\) | 493.000 | 0.394603 | ||||||||
\(117\) | 702.000 | 0.554700 | ||||||||
\(118\) | 900.000 | 0.702133 | ||||||||
\(119\) | 288.000 | 0.221856 | ||||||||
\(120\) | −675.000 | −0.513490 | ||||||||
\(121\) | 605.000 | 0.454545 | ||||||||
\(122\) | −3050.00 | −2.26339 | ||||||||
\(123\) | 234.000 | 0.171537 | ||||||||
\(124\) | −3808.00 | −2.75781 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 720.000 | 0.509069 | ||||||||
\(127\) | −2056.00 | −1.43654 | −0.718270 | − | 0.695765i | \(-0.755066\pi\) | ||||
−0.718270 | + | 0.695765i | \(0.755066\pi\) | |||||||
\(128\) | −2115.00 | −1.46048 | ||||||||
\(129\) | 780.000 | 0.532366 | ||||||||
\(130\) | 1950.00 | 1.31559 | ||||||||
\(131\) | 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 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 810.000 | 0.510713 | ||||||||
\(137\) | −2758.00 | −1.71994 | −0.859970 | − | 0.510344i | \(-0.829518\pi\) | ||||
−0.859970 | + | 0.510344i | \(0.829518\pi\) | |||||||
\(138\) | −2760.00 | −1.70251 | ||||||||
\(139\) | −1436.00 | −0.876258 | −0.438129 | − | 0.898912i | \(-0.644359\pi\) | ||||
−0.438129 | + | 0.898912i | \(0.644359\pi\) | |||||||
\(140\) | 1360.00 | 0.821007 | ||||||||
\(141\) | −936.000 | −0.559046 | ||||||||
\(142\) | 1480.00 | 0.874640 | ||||||||
\(143\) | −3432.00 | −2.00698 | ||||||||
\(144\) | 801.000 | 0.463542 | ||||||||
\(145\) | 145.000 | 0.0830455 | ||||||||
\(146\) | 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 | \(0.543716\pi\) | |||||||
\(150\) | −375.000 | −0.204124 | ||||||||
\(151\) | −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 | ||||||||
\(155\) | −1120.00 | −0.580391 | ||||||||
\(156\) | −3978.00 | −2.04163 | ||||||||
\(157\) | 534.000 | 0.271451 | 0.135726 | − | 0.990746i | \(-0.456663\pi\) | ||||
0.135726 | + | 0.990746i | \(0.456663\pi\) | |||||||
\(158\) | −4800.00 | −2.41688 | ||||||||
\(159\) | −1722.00 | −0.858890 | ||||||||
\(160\) | 425.000 | 0.209995 | ||||||||
\(161\) | 2944.00 | 1.44112 | ||||||||
\(162\) | 405.000 | 0.196419 | ||||||||
\(163\) | 1380.00 | 0.663128 | 0.331564 | − | 0.943433i | \(-0.392424\pi\) | ||||
0.331564 | + | 0.943433i | \(0.392424\pi\) | |||||||
\(164\) | −1326.00 | −0.631361 | ||||||||
\(165\) | 660.000 | 0.311400 | ||||||||
\(166\) | −4540.00 | −2.12272 | ||||||||
\(167\) | 2616.00 | 1.21217 | 0.606084 | − | 0.795400i | \(-0.292739\pi\) | ||||
0.606084 | + | 0.795400i | \(0.292739\pi\) | |||||||
\(168\) | −2160.00 | −0.991950 | ||||||||
\(169\) | 3887.00 | 1.76923 | ||||||||
\(170\) | 450.000 | 0.203020 | ||||||||
\(171\) | −252.000 | −0.112695 | ||||||||
\(172\) | −4420.00 | −1.95943 | ||||||||
\(173\) | −330.000 | −0.145026 | −0.0725128 | − | 0.997367i | \(-0.523102\pi\) | ||||
−0.0725128 | + | 0.997367i | \(0.523102\pi\) | |||||||
\(174\) | −435.000 | −0.189525 | ||||||||
\(175\) | 400.000 | 0.172784 | ||||||||
\(176\) | −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 | \(0.524747\pi\) | |||||||
\(180\) | 765.000 | 0.316776 | ||||||||
\(181\) | −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 | ||||||||
\(185\) | 1270.00 | 0.504715 | ||||||||
\(186\) | 3360.00 | 1.32455 | ||||||||
\(187\) | −792.000 | −0.309715 | ||||||||
\(188\) | 5304.00 | 2.05763 | ||||||||
\(189\) | −432.000 | −0.166261 | ||||||||
\(190\) | −700.000 | −0.267281 | ||||||||
\(191\) | 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 | \(-0.340365\pi\) | ||||
0.480747 | + | 0.876859i | \(0.340365\pi\) | |||||||
\(194\) | 6170.00 | 2.28340 | ||||||||
\(195\) | −1170.00 | −0.429669 | ||||||||
\(196\) | −1479.00 | −0.538994 | ||||||||
\(197\) | 526.000 | 0.190233 | 0.0951166 | − | 0.995466i | \(-0.469678\pi\) | ||||
0.0951166 | + | 0.995466i | \(0.469678\pi\) | |||||||
\(198\) | −1980.00 | −0.710669 | ||||||||
\(199\) | 4440.00 | 1.58162 | 0.790812 | − | 0.612059i | \(-0.209658\pi\) | ||||
0.790812 | + | 0.612059i | \(0.209658\pi\) | |||||||
\(200\) | 1125.00 | 0.397748 | ||||||||
\(201\) | 1020.00 | 0.357937 | ||||||||
\(202\) | 5110.00 | 1.77989 | ||||||||
\(203\) | 464.000 | 0.160426 | ||||||||
\(204\) | −918.000 | −0.315063 | ||||||||
\(205\) | −390.000 | −0.132872 | ||||||||
\(206\) | −6240.00 | −2.11049 | ||||||||
\(207\) | 1656.00 | 0.556038 | ||||||||
\(208\) | 6942.00 | 2.31414 | ||||||||
\(209\) | 1232.00 | 0.407747 | ||||||||
\(210\) | −1200.00 | −0.394323 | ||||||||
\(211\) | 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 | ||||||||
\(215\) | −1300.00 | −0.412369 | ||||||||
\(216\) | −1215.00 | −0.382733 | ||||||||
\(217\) | −3584.00 | −1.12119 | ||||||||
\(218\) | −4130.00 | −1.28311 | ||||||||
\(219\) | −1182.00 | −0.364713 | ||||||||
\(220\) | −3740.00 | −1.14614 | ||||||||
\(221\) | 1404.00 | 0.427345 | ||||||||
\(222\) | −3810.00 | −1.15185 | ||||||||
\(223\) | 4120.00 | 1.23720 | 0.618600 | − | 0.785706i | \(-0.287700\pi\) | ||||
0.618600 | + | 0.785706i | \(0.287700\pi\) | |||||||
\(224\) | 1360.00 | 0.405664 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −11030.0 | −3.24648 | ||||||||
\(227\) | 4932.00 | 1.44206 | 0.721032 | − | 0.692902i | \(-0.243668\pi\) | ||||
0.721032 | + | 0.692902i | \(0.243668\pi\) | |||||||
\(228\) | 1428.00 | 0.414788 | ||||||||
\(229\) | −3050.00 | −0.880130 | −0.440065 | − | 0.897966i | \(-0.645045\pi\) | ||||
−0.440065 | + | 0.897966i | \(0.645045\pi\) | |||||||
\(230\) | 4600.00 | 1.31876 | ||||||||
\(231\) | 2112.00 | 0.601556 | ||||||||
\(232\) | 1305.00 | 0.369299 | ||||||||
\(233\) | 82.0000 | 0.0230558 | 0.0115279 | − | 0.999934i | \(-0.496330\pi\) | ||||
0.0115279 | + | 0.999934i | \(0.496330\pi\) | |||||||
\(234\) | 3510.00 | 0.980581 | ||||||||
\(235\) | 1560.00 | 0.433035 | ||||||||
\(236\) | 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 | \(0.742694\pi\) | |||||||
\(240\) | −1335.00 | −0.359058 | ||||||||
\(241\) | −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 | ||||||||
\(245\) | −435.000 | −0.113433 | ||||||||
\(246\) | 1170.00 | 0.303238 | ||||||||
\(247\) | −2184.00 | −0.562610 | ||||||||
\(248\) | −10080.0 | −2.58097 | ||||||||
\(249\) | 2724.00 | 0.693279 | ||||||||
\(250\) | 625.000 | 0.158114 | ||||||||
\(251\) | 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 | ||||||||
\(255\) | −270.000 | −0.0663061 | ||||||||
\(256\) | −8279.00 | −2.02124 | ||||||||
\(257\) | 3418.00 | 0.829607 | 0.414803 | − | 0.909911i | \(-0.363850\pi\) | ||||
0.414803 | + | 0.909911i | \(0.363850\pi\) | |||||||
\(258\) | 3900.00 | 0.941098 | ||||||||
\(259\) | 4064.00 | 0.974999 | ||||||||
\(260\) | 6630.00 | 1.58144 | ||||||||
\(261\) | 261.000 | 0.0618984 | ||||||||
\(262\) | 60.0000 | 0.0141481 | ||||||||
\(263\) | 7440.00 | 1.74437 | 0.872186 | − | 0.489174i | \(-0.162702\pi\) | ||||
0.872186 | + | 0.489174i | \(0.162702\pi\) | |||||||
\(264\) | 5940.00 | 1.38478 | ||||||||
\(265\) | 2870.00 | 0.665293 | ||||||||
\(266\) | −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 | \(0.232004\pi\) | |||||||
\(270\) | −675.000 | −0.152145 | ||||||||
\(271\) | −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 | ||||||||
\(275\) | −1100.00 | −0.241209 | ||||||||
\(276\) | −9384.00 | −2.04656 | ||||||||
\(277\) | 3718.00 | 0.806473 | 0.403236 | − | 0.915096i | \(-0.367885\pi\) | ||||
0.403236 | + | 0.915096i | \(0.367885\pi\) | |||||||
\(278\) | −7180.00 | −1.54902 | ||||||||
\(279\) | −2016.00 | −0.432598 | ||||||||
\(280\) | 3600.00 | 0.768361 | ||||||||
\(281\) | 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 | \(-0.377592\pi\) | ||||
0.375147 | + | 0.926965i | \(0.377592\pi\) | |||||||
\(284\) | 5032.00 | 1.05139 | ||||||||
\(285\) | 420.000 | 0.0872935 | ||||||||
\(286\) | −17160.0 | −3.54787 | ||||||||
\(287\) | −1248.00 | −0.256680 | ||||||||
\(288\) | 765.000 | 0.156521 | ||||||||
\(289\) | −4589.00 | −0.934053 | ||||||||
\(290\) | 725.000 | 0.146805 | ||||||||
\(291\) | −3702.00 | −0.745756 | ||||||||
\(292\) | 6698.00 | 1.34237 | ||||||||
\(293\) | 126.000 | 0.0251229 | 0.0125614 | − | 0.999921i | \(-0.496001\pi\) | ||||
0.0125614 | + | 0.999921i | \(0.496001\pi\) | |||||||
\(294\) | 1305.00 | 0.258875 | ||||||||
\(295\) | 900.000 | 0.177627 | ||||||||
\(296\) | 11430.0 | 2.24444 | ||||||||
\(297\) | 1188.00 | 0.232104 | ||||||||
\(298\) | −2490.00 | −0.484033 | ||||||||
\(299\) | 14352.0 | 2.77591 | ||||||||
\(300\) | −1275.00 | −0.245374 | ||||||||
\(301\) | −4160.00 | −0.796606 | ||||||||
\(302\) | −13480.0 | −2.56850 | ||||||||
\(303\) | −3066.00 | −0.581311 | ||||||||
\(304\) | −2492.00 | −0.470151 | ||||||||
\(305\) | −3050.00 | −0.572598 | ||||||||
\(306\) | 810.000 | 0.151322 | ||||||||
\(307\) | −2412.00 | −0.448404 | −0.224202 | − | 0.974543i | \(-0.571978\pi\) | ||||
−0.224202 | + | 0.974543i | \(0.571978\pi\) | |||||||
\(308\) | −11968.0 | −2.21409 | ||||||||
\(309\) | 3744.00 | 0.689284 | ||||||||
\(310\) | −5600.00 | −1.02600 | ||||||||
\(311\) | −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 | \(-0.416442\pi\) | ||||
0.259502 | + | 0.965743i | \(0.416442\pi\) | |||||||
\(314\) | 2670.00 | 0.479862 | ||||||||
\(315\) | 720.000 | 0.128785 | ||||||||
\(316\) | −16320.0 | −2.90529 | ||||||||
\(317\) | −26.0000 | −0.00460664 | −0.00230332 | − | 0.999997i | \(-0.500733\pi\) | ||||
−0.00230332 | + | 0.999997i | \(0.500733\pi\) | |||||||
\(318\) | −8610.00 | −1.51832 | ||||||||
\(319\) | −1276.00 | −0.223957 | ||||||||
\(320\) | −1435.00 | −0.250684 | ||||||||
\(321\) | 348.000 | 0.0605092 | ||||||||
\(322\) | 14720.0 | 2.54756 | ||||||||
\(323\) | −504.000 | −0.0868214 | ||||||||
\(324\) | 1377.00 | 0.236111 | ||||||||
\(325\) | 1950.00 | 0.332820 | ||||||||
\(326\) | 6900.00 | 1.17226 | ||||||||
\(327\) | 2478.00 | 0.419063 | ||||||||
\(328\) | −3510.00 | −0.590876 | ||||||||
\(329\) | 4992.00 | 0.836528 | ||||||||
\(330\) | 3300.00 | 0.550482 | ||||||||
\(331\) | 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 | ||||||||
\(335\) | −1700.00 | −0.277256 | ||||||||
\(336\) | −4272.00 | −0.693621 | ||||||||
\(337\) | −10302.0 | −1.66524 | −0.832620 | − | 0.553845i | \(-0.813160\pi\) | ||||
−0.832620 | + | 0.553845i | \(0.813160\pi\) | |||||||
\(338\) | 19435.0 | 3.12759 | ||||||||
\(339\) | 6618.00 | 1.06030 | ||||||||
\(340\) | 1530.00 | 0.244047 | ||||||||
\(341\) | 9856.00 | 1.56520 | ||||||||
\(342\) | −1260.00 | −0.199219 | ||||||||
\(343\) | −6880.00 | −1.08305 | ||||||||
\(344\) | −11700.0 | −1.83378 | ||||||||
\(345\) | −2760.00 | −0.430706 | ||||||||
\(346\) | −1650.00 | −0.256372 | ||||||||
\(347\) | −8020.00 | −1.24074 | −0.620369 | − | 0.784310i | \(-0.713017\pi\) | ||||
−0.620369 | + | 0.784310i | \(0.713017\pi\) | |||||||
\(348\) | −1479.00 | −0.227824 | ||||||||
\(349\) | −1306.00 | −0.200311 | −0.100156 | − | 0.994972i | \(-0.531934\pi\) | ||||
−0.100156 | + | 0.994972i | \(0.531934\pi\) | |||||||
\(350\) | 2000.00 | 0.305441 | ||||||||
\(351\) | −2106.00 | −0.320256 | ||||||||
\(352\) | −3740.00 | −0.566314 | ||||||||
\(353\) | 5658.00 | 0.853102 | 0.426551 | − | 0.904464i | \(-0.359728\pi\) | ||||
0.426551 | + | 0.904464i | \(0.359728\pi\) | |||||||
\(354\) | −2700.00 | −0.405377 | ||||||||
\(355\) | 1480.00 | 0.221268 | ||||||||
\(356\) | −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 | \(0.856233\pi\) | |||||||
\(360\) | 2025.00 | 0.296464 | ||||||||
\(361\) | −6075.00 | −0.885698 | ||||||||
\(362\) | −5050.00 | −0.733210 | ||||||||
\(363\) | −1815.00 | −0.262432 | ||||||||
\(364\) | 21216.0 | 3.05500 | ||||||||
\(365\) | 1970.00 | 0.282506 | ||||||||
\(366\) | 9150.00 | 1.30677 | ||||||||
\(367\) | 8984.00 | 1.27782 | 0.638911 | − | 0.769280i | \(-0.279385\pi\) | ||||
0.638911 | + | 0.769280i | \(0.279385\pi\) | |||||||
\(368\) | 16376.0 | 2.31972 | ||||||||
\(369\) | −702.000 | −0.0990370 | ||||||||
\(370\) | 6350.00 | 0.892218 | ||||||||
\(371\) | 9184.00 | 1.28520 | ||||||||
\(372\) | 11424.0 | 1.59222 | ||||||||
\(373\) | −938.000 | −0.130209 | −0.0651043 | − | 0.997878i | \(-0.520738\pi\) | ||||
−0.0651043 | + | 0.997878i | \(0.520738\pi\) | |||||||
\(374\) | −3960.00 | −0.547505 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 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 | \(0.677171\pi\) | |||||||
\(380\) | −2380.00 | −0.321293 | ||||||||
\(381\) | 6168.00 | 0.829386 | ||||||||
\(382\) | 10040.0 | 1.34474 | ||||||||
\(383\) | −6944.00 | −0.926428 | −0.463214 | − | 0.886247i | \(-0.653304\pi\) | ||||
−0.463214 | + | 0.886247i | \(0.653304\pi\) | |||||||
\(384\) | 6345.00 | 0.843208 | ||||||||
\(385\) | −3520.00 | −0.465963 | ||||||||
\(386\) | 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 | \(0.455756\pi\) | |||||||
\(390\) | −5850.00 | −0.759555 | ||||||||
\(391\) | 3312.00 | 0.428376 | ||||||||
\(392\) | −3915.00 | −0.504432 | ||||||||
\(393\) | −36.0000 | −0.00462076 | ||||||||
\(394\) | 2630.00 | 0.336288 | ||||||||
\(395\) | −4800.00 | −0.611428 | ||||||||
\(396\) | −6732.00 | −0.854282 | ||||||||
\(397\) | −3346.00 | −0.423000 | −0.211500 | − | 0.977378i | \(-0.567835\pi\) | ||||
−0.211500 | + | 0.977378i | \(0.567835\pi\) | |||||||
\(398\) | 22200.0 | 2.79594 | ||||||||
\(399\) | 1344.00 | 0.168632 | ||||||||
\(400\) | 2225.00 | 0.278125 | ||||||||
\(401\) | 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 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 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 | \(0.379335\pi\) | |||||||
\(410\) | −1950.00 | −0.234887 | ||||||||
\(411\) | 8274.00 | 0.993008 | ||||||||
\(412\) | −21216.0 | −2.53698 | ||||||||
\(413\) | 2880.00 | 0.343137 | ||||||||
\(414\) | 8280.00 | 0.982946 | ||||||||
\(415\) | −4540.00 | −0.537012 | ||||||||
\(416\) | 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 | \(0.474513\pi\) | |||||||
\(420\) | −4080.00 | −0.474009 | ||||||||
\(421\) | 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 | ||||||||
\(425\) | 450.000 | 0.0513605 | ||||||||
\(426\) | −4440.00 | −0.504973 | ||||||||
\(427\) | −9760.00 | −1.10613 | ||||||||
\(428\) | −1972.00 | −0.222711 | ||||||||
\(429\) | 10296.0 | 1.15873 | ||||||||
\(430\) | −6500.00 | −0.728972 | ||||||||
\(431\) | 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 | \(-0.165107\pi\) | ||||
0.868465 | + | 0.495750i | \(0.165107\pi\) | |||||||
\(434\) | −17920.0 | −1.98200 | ||||||||
\(435\) | −435.000 | −0.0479463 | ||||||||
\(436\) | −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 | \(0.789554\pi\) | |||||||
\(440\) | −9900.00 | −1.07265 | ||||||||
\(441\) | −783.000 | −0.0845481 | ||||||||
\(442\) | 7020.00 | 0.755446 | ||||||||
\(443\) | 7372.00 | 0.790642 | 0.395321 | − | 0.918543i | \(-0.370633\pi\) | ||||
0.395321 | + | 0.918543i | \(0.370633\pi\) | |||||||
\(444\) | −12954.0 | −1.38462 | ||||||||
\(445\) | −4950.00 | −0.527309 | ||||||||
\(446\) | 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 | \(0.310596\pi\) | |||||||
\(450\) | 1125.00 | 0.117851 | ||||||||
\(451\) | 3432.00 | 0.358329 | ||||||||
\(452\) | −37502.0 | −3.90253 | ||||||||
\(453\) | 8088.00 | 0.838868 | ||||||||
\(454\) | 24660.0 | 2.54923 | ||||||||
\(455\) | 6240.00 | 0.642936 | ||||||||
\(456\) | 3780.00 | 0.388190 | ||||||||
\(457\) | −8006.00 | −0.819486 | −0.409743 | − | 0.912201i | \(-0.634382\pi\) | ||||
−0.409743 | + | 0.912201i | \(0.634382\pi\) | |||||||
\(458\) | −15250.0 | −1.55586 | ||||||||
\(459\) | −486.000 | −0.0494217 | ||||||||
\(460\) | 15640.0 | 1.58526 | ||||||||
\(461\) | 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 | \(-0.573893\pi\) | ||||
−0.230061 | + | 0.973176i | \(0.573893\pi\) | |||||||
\(464\) | 2581.00 | 0.258233 | ||||||||
\(465\) | 3360.00 | 0.335089 | ||||||||
\(466\) | 410.000 | 0.0407573 | ||||||||
\(467\) | 11588.0 | 1.14824 | 0.574121 | − | 0.818771i | \(-0.305344\pi\) | ||||
0.574121 | + | 0.818771i | \(0.305344\pi\) | |||||||
\(468\) | 11934.0 | 1.17874 | ||||||||
\(469\) | −5440.00 | −0.535599 | ||||||||
\(470\) | 7800.00 | 0.765505 | ||||||||
\(471\) | −1602.00 | −0.156722 | ||||||||
\(472\) | 8100.00 | 0.789900 | ||||||||
\(473\) | 11440.0 | 1.11208 | ||||||||
\(474\) | 14400.0 | 1.39539 | ||||||||
\(475\) | −700.000 | −0.0676173 | ||||||||
\(476\) | 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 | \(0.834618\pi\) | |||||||
\(480\) | −1275.00 | −0.121241 | ||||||||
\(481\) | 19812.0 | 1.87807 | ||||||||
\(482\) | −10790.0 | −1.01965 | ||||||||
\(483\) | −8832.00 | −0.832029 | ||||||||
\(484\) | 10285.0 | 0.965909 | ||||||||
\(485\) | 6170.00 | 0.577660 | ||||||||
\(486\) | −1215.00 | −0.113402 | ||||||||
\(487\) | 3824.00 | 0.355815 | 0.177908 | − | 0.984047i | \(-0.443067\pi\) | ||||
0.177908 | + | 0.984047i | \(0.443067\pi\) | |||||||
\(488\) | −27450.0 | −2.54632 | ||||||||
\(489\) | −4140.00 | −0.382857 | ||||||||
\(490\) | −2175.00 | −0.200523 | ||||||||
\(491\) | −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 | ||||||||
\(495\) | −1980.00 | −0.179787 | ||||||||
\(496\) | −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 | \(0.153847\pi\) | |||||||
\(500\) | 2125.00 | 0.190066 | ||||||||
\(501\) | −7848.00 | −0.699846 | ||||||||
\(502\) | 30580.0 | 2.71883 | ||||||||
\(503\) | −6720.00 | −0.595686 | −0.297843 | − | 0.954615i | \(-0.596267\pi\) | ||||
−0.297843 | + | 0.954615i | \(0.596267\pi\) | |||||||
\(504\) | 6480.00 | 0.572703 | ||||||||
\(505\) | 5110.00 | 0.450281 | ||||||||
\(506\) | −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 | \(0.342816\pi\) | |||||||
\(510\) | −1350.00 | −0.117214 | ||||||||
\(511\) | 6304.00 | 0.545739 | ||||||||
\(512\) | −24475.0 | −2.11260 | ||||||||
\(513\) | 756.000 | 0.0650647 | ||||||||
\(514\) | 17090.0 | 1.46655 | ||||||||
\(515\) | −6240.00 | −0.533917 | ||||||||
\(516\) | 13260.0 | 1.13128 | ||||||||
\(517\) | −13728.0 | −1.16781 | ||||||||
\(518\) | 20320.0 | 1.72357 | ||||||||
\(519\) | 990.000 | 0.0837306 | ||||||||
\(520\) | 17550.0 | 1.48004 | ||||||||
\(521\) | 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 | \(-0.686255\pi\) | ||||
−0.552314 | + | 0.833636i | \(0.686255\pi\) | |||||||
\(524\) | 204.000 | 0.0170072 | ||||||||
\(525\) | −1200.00 | −0.0997567 | ||||||||
\(526\) | 37200.0 | 3.08364 | ||||||||
\(527\) | −4032.00 | −0.333276 | ||||||||
\(528\) | 11748.0 | 0.968307 | ||||||||
\(529\) | 21689.0 | 1.78261 | ||||||||
\(530\) | 14350.0 | 1.17608 | ||||||||
\(531\) | 1620.00 | 0.132396 | ||||||||
\(532\) | −7616.00 | −0.620668 | ||||||||
\(533\) | −6084.00 | −0.494423 | ||||||||
\(534\) | 14850.0 | 1.20341 | ||||||||
\(535\) | −580.000 | −0.0468703 | ||||||||
\(536\) | −15300.0 | −1.23295 | ||||||||
\(537\) | 1116.00 | 0.0896815 | ||||||||
\(538\) | 32910.0 | 2.63727 | ||||||||
\(539\) | 3828.00 | 0.305907 | ||||||||
\(540\) | −2295.00 | −0.182891 | ||||||||
\(541\) | −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 | ||||||||
\(545\) | −4130.00 | −0.324605 | ||||||||
\(546\) | −18720.0 | −1.46729 | ||||||||
\(547\) | 4060.00 | 0.317355 | 0.158677 | − | 0.987330i | \(-0.449277\pi\) | ||||
0.158677 | + | 0.987330i | \(0.449277\pi\) | |||||||
\(548\) | −46886.0 | −3.65487 | ||||||||
\(549\) | −5490.00 | −0.426790 | ||||||||
\(550\) | −5500.00 | −0.426401 | ||||||||
\(551\) | −812.000 | −0.0627811 | ||||||||
\(552\) | −24840.0 | −1.91533 | ||||||||
\(553\) | −15360.0 | −1.18115 | ||||||||
\(554\) | 18590.0 | 1.42566 | ||||||||
\(555\) | −3810.00 | −0.291397 | ||||||||
\(556\) | −24412.0 | −1.86205 | ||||||||
\(557\) | −1386.00 | −0.105434 | −0.0527170 | − | 0.998609i | \(-0.516788\pi\) | ||||
−0.0527170 | + | 0.998609i | \(0.516788\pi\) | |||||||
\(558\) | −10080.0 | −0.764732 | ||||||||
\(559\) | −20280.0 | −1.53444 | ||||||||
\(560\) | 7120.00 | 0.537277 | ||||||||
\(561\) | 2376.00 | 0.178814 | ||||||||
\(562\) | 8770.00 | 0.658256 | ||||||||
\(563\) | 2452.00 | 0.183551 | 0.0917757 | − | 0.995780i | \(-0.470746\pi\) | ||||
0.0917757 | + | 0.995780i | \(0.470746\pi\) | |||||||
\(564\) | −15912.0 | −1.18797 | ||||||||
\(565\) | −11030.0 | −0.821302 | ||||||||
\(566\) | 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 | \(0.779009\pi\) | |||||||
\(570\) | 2100.00 | 0.154315 | ||||||||
\(571\) | −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 | ||||||||
\(575\) | 4600.00 | 0.333623 | ||||||||
\(576\) | −2583.00 | −0.186849 | ||||||||
\(577\) | 13202.0 | 0.952524 | 0.476262 | − | 0.879303i | \(-0.341991\pi\) | ||||
0.476262 | + | 0.879303i | \(0.341991\pi\) | |||||||
\(578\) | −22945.0 | −1.65119 | ||||||||
\(579\) | −7734.00 | −0.555119 | ||||||||
\(580\) | 2465.00 | 0.176472 | ||||||||
\(581\) | −14528.0 | −1.03739 | ||||||||
\(582\) | −18510.0 | −1.31832 | ||||||||
\(583\) | −25256.0 | −1.79416 | ||||||||
\(584\) | 17730.0 | 1.25629 | ||||||||
\(585\) | 3510.00 | 0.248069 | ||||||||
\(586\) | 630.000 | 0.0444114 | ||||||||
\(587\) | −8708.00 | −0.612296 | −0.306148 | − | 0.951984i | \(-0.599040\pi\) | ||||
−0.306148 | + | 0.951984i | \(0.599040\pi\) | |||||||
\(588\) | 4437.00 | 0.311188 | ||||||||
\(589\) | 6272.00 | 0.438766 | ||||||||
\(590\) | 4500.00 | 0.314004 | ||||||||
\(591\) | −1578.00 | −0.109831 | ||||||||
\(592\) | 22606.0 | 1.56943 | ||||||||
\(593\) | −4390.00 | −0.304006 | −0.152003 | − | 0.988380i | \(-0.548572\pi\) | ||||
−0.152003 | + | 0.988380i | \(0.548572\pi\) | |||||||
\(594\) | 5940.00 | 0.410305 | ||||||||
\(595\) | 1440.00 | 0.0992172 | ||||||||
\(596\) | −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 | \(0.742763\pi\) | |||||||
\(600\) | −3375.00 | −0.229640 | ||||||||
\(601\) | 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 | ||||||||
\(605\) | 3025.00 | 0.203279 | ||||||||
\(606\) | −15330.0 | −1.02762 | ||||||||
\(607\) | 10376.0 | 0.693820 | 0.346910 | − | 0.937898i | \(-0.387231\pi\) | ||||
0.346910 | + | 0.937898i | \(0.387231\pi\) | |||||||
\(608\) | −2380.00 | −0.158753 | ||||||||
\(609\) | −1392.00 | −0.0926218 | ||||||||
\(610\) | −15250.0 | −1.01222 | ||||||||
\(611\) | 24336.0 | 1.61134 | ||||||||
\(612\) | 2754.00 | 0.181902 | ||||||||
\(613\) | 6822.00 | 0.449491 | 0.224746 | − | 0.974417i | \(-0.427845\pi\) | ||||
0.224746 | + | 0.974417i | \(0.427845\pi\) | |||||||
\(614\) | −12060.0 | −0.792674 | ||||||||
\(615\) | 1170.00 | 0.0767137 | ||||||||
\(616\) | −31680.0 | −2.07212 | ||||||||
\(617\) | −20070.0 | −1.30954 | −0.654771 | − | 0.755827i | \(-0.727235\pi\) | ||||
−0.654771 | + | 0.755827i | \(0.727235\pi\) | |||||||
\(618\) | 18720.0 | 1.21849 | ||||||||
\(619\) | 19228.0 | 1.24853 | 0.624264 | − | 0.781214i | \(-0.285399\pi\) | ||||
0.624264 | + | 0.781214i | \(0.285399\pi\) | |||||||
\(620\) | −19040.0 | −1.23333 | ||||||||
\(621\) | −4968.00 | −0.321029 | ||||||||
\(622\) | −14640.0 | −0.943747 | ||||||||
\(623\) | −15840.0 | −1.01865 | ||||||||
\(624\) | −20826.0 | −1.33607 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 14370.0 | 0.917477 | ||||||||
\(627\) | −3696.00 | −0.235413 | ||||||||
\(628\) | 9078.00 | 0.576834 | ||||||||
\(629\) | 4572.00 | 0.289821 | ||||||||
\(630\) | 3600.00 | 0.227663 | ||||||||
\(631\) | 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 | ||||||||
\(635\) | −10280.0 | −0.642440 | ||||||||
\(636\) | −29274.0 | −1.82514 | ||||||||
\(637\) | −6786.00 | −0.422090 | ||||||||
\(638\) | −6380.00 | −0.395904 | ||||||||
\(639\) | 2664.00 | 0.164924 | ||||||||
\(640\) | −10575.0 | −0.653146 | ||||||||
\(641\) | −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 | \(-0.561009\pi\) | ||||
−0.190496 | + | 0.981688i | \(0.561009\pi\) | |||||||
\(644\) | 50048.0 | 3.06237 | ||||||||
\(645\) | 3900.00 | 0.238081 | ||||||||
\(646\) | −2520.00 | −0.153480 | ||||||||
\(647\) | 22024.0 | 1.33826 | 0.669129 | − | 0.743146i | \(-0.266667\pi\) | ||||
0.669129 | + | 0.743146i | \(0.266667\pi\) | |||||||
\(648\) | 3645.00 | 0.220971 | ||||||||
\(649\) | −7920.00 | −0.479025 | ||||||||
\(650\) | 9750.00 | 0.588348 | ||||||||
\(651\) | 10752.0 | 0.647318 | ||||||||
\(652\) | 23460.0 | 1.40915 | ||||||||
\(653\) | 16630.0 | 0.996604 | 0.498302 | − | 0.867004i | \(-0.333957\pi\) | ||||
0.498302 | + | 0.867004i | \(0.333957\pi\) | |||||||
\(654\) | 12390.0 | 0.740806 | ||||||||
\(655\) | 60.0000 | 0.00357923 | ||||||||
\(656\) | −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 | \(0.757316\pi\) | |||||||
\(660\) | 11220.0 | 0.661724 | ||||||||
\(661\) | −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 | ||||||||
\(665\) | −2240.00 | −0.130622 | ||||||||
\(666\) | 11430.0 | 0.665020 | ||||||||
\(667\) | 5336.00 | 0.309761 | ||||||||
\(668\) | 44472.0 | 2.57586 | ||||||||
\(669\) | −12360.0 | −0.714298 | ||||||||
\(670\) | −8500.00 | −0.490125 | ||||||||
\(671\) | 26840.0 | 1.54418 | ||||||||
\(672\) | −4080.00 | −0.234210 | ||||||||
\(673\) | 13458.0 | 0.770829 | 0.385414 | − | 0.922744i | \(-0.374059\pi\) | ||||
0.385414 | + | 0.922744i | \(0.374059\pi\) | |||||||
\(674\) | −51510.0 | −2.94376 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | 66079.0 | 3.75962 | ||||||||
\(677\) | 22174.0 | 1.25881 | 0.629406 | − | 0.777076i | \(-0.283298\pi\) | ||||
0.629406 | + | 0.777076i | \(0.283298\pi\) | |||||||
\(678\) | 33090.0 | 1.87436 | ||||||||
\(679\) | 19744.0 | 1.11591 | ||||||||
\(680\) | 4050.00 | 0.228398 | ||||||||
\(681\) | −14796.0 | −0.832576 | ||||||||
\(682\) | 49280.0 | 2.76690 | ||||||||
\(683\) | −2404.00 | −0.134680 | −0.0673400 | − | 0.997730i | \(-0.521451\pi\) | ||||
−0.0673400 | + | 0.997730i | \(0.521451\pi\) | |||||||
\(684\) | −4284.00 | −0.239478 | ||||||||
\(685\) | −13790.0 | −0.769181 | ||||||||
\(686\) | −34400.0 | −1.91457 | ||||||||
\(687\) | 9150.00 | 0.508143 | ||||||||
\(688\) | −23140.0 | −1.28227 | ||||||||
\(689\) | 44772.0 | 2.47558 | ||||||||
\(690\) | −13800.0 | −0.761387 | ||||||||
\(691\) | −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 | ||||||||
\(695\) | −7180.00 | −0.391875 | ||||||||
\(696\) | −3915.00 | −0.213215 | ||||||||
\(697\) | −1404.00 | −0.0762988 | ||||||||
\(698\) | −6530.00 | −0.354103 | ||||||||
\(699\) | −246.000 | −0.0133113 | ||||||||
\(700\) | 6800.00 | 0.367165 | ||||||||
\(701\) | −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 | ||||||||
\(705\) | −4680.00 | −0.250013 | ||||||||
\(706\) | 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 | \(0.536924\pi\) | |||||||
\(710\) | 7400.00 | 0.391151 | ||||||||
\(711\) | −8640.00 | −0.455732 | ||||||||
\(712\) | −44550.0 | −2.34492 | ||||||||
\(713\) | −41216.0 | −2.16487 | ||||||||
\(714\) | −4320.00 | −0.226431 | ||||||||
\(715\) | −17160.0 | −0.897549 | ||||||||
\(716\) | −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 | \(0.498811\pi\) | |||||||
\(720\) | 4005.00 | 0.207302 | ||||||||
\(721\) | −19968.0 | −1.03141 | ||||||||
\(722\) | −30375.0 | −1.56571 | ||||||||
\(723\) | 6474.00 | 0.333016 | ||||||||
\(724\) | −17170.0 | −0.881378 | ||||||||
\(725\) | 725.000 | 0.0371391 | ||||||||
\(726\) | −9075.00 | −0.463919 | ||||||||
\(727\) | −9632.00 | −0.491377 | −0.245689 | − | 0.969349i | \(-0.579014\pi\) | ||||
−0.245689 | + | 0.969349i | \(0.579014\pi\) | |||||||
\(728\) | 56160.0 | 2.85910 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 9850.00 | 0.499404 | ||||||||
\(731\) | −4680.00 | −0.236794 | ||||||||
\(732\) | 31110.0 | 1.57085 | ||||||||
\(733\) | −19306.0 | −0.972829 | −0.486414 | − | 0.873728i | \(-0.661695\pi\) | ||||
−0.486414 | + | 0.873728i | \(0.661695\pi\) | |||||||
\(734\) | 44920.0 | 2.25889 | ||||||||
\(735\) | 1305.00 | 0.0654907 | ||||||||
\(736\) | 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 | \(0.863486\pi\) | |||||||
\(740\) | 21590.0 | 1.07252 | ||||||||
\(741\) | 6552.00 | 0.324823 | ||||||||
\(742\) | 45920.0 | 2.27194 | ||||||||
\(743\) | 5408.00 | 0.267026 | 0.133513 | − | 0.991047i | \(-0.457374\pi\) | ||||
0.133513 | + | 0.991047i | \(0.457374\pi\) | |||||||
\(744\) | 30240.0 | 1.49012 | ||||||||
\(745\) | −2490.00 | −0.122452 | ||||||||
\(746\) | −4690.00 | −0.230178 | ||||||||
\(747\) | −8172.00 | −0.400265 | ||||||||
\(748\) | −13464.0 | −0.658145 | ||||||||
\(749\) | −1856.00 | −0.0905431 | ||||||||
\(750\) | −1875.00 | −0.0912871 | ||||||||
\(751\) | −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 | ||||||||
\(755\) | −13480.0 | −0.649785 | ||||||||
\(756\) | −7344.00 | −0.353305 | ||||||||
\(757\) | −4274.00 | −0.205206 | −0.102603 | − | 0.994722i | \(-0.532717\pi\) | ||||
−0.102603 | + | 0.994722i | \(0.532717\pi\) | |||||||
\(758\) | −38980.0 | −1.86783 | ||||||||
\(759\) | 24288.0 | 1.16153 | ||||||||
\(760\) | −6300.00 | −0.300691 | ||||||||
\(761\) | −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 | ||||||||
\(765\) | 810.000 | 0.0382818 | ||||||||
\(766\) | −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 | \(0.558953\pi\) | |||||||
\(770\) | −17600.0 | −0.823714 | ||||||||
\(771\) | −10254.0 | −0.478974 | ||||||||
\(772\) | 43826.0 | 2.04318 | ||||||||
\(773\) | 19550.0 | 0.909657 | 0.454828 | − | 0.890579i | \(-0.349701\pi\) | ||||
0.454828 | + | 0.890579i | \(0.349701\pi\) | |||||||
\(774\) | −11700.0 | −0.543343 | ||||||||
\(775\) | −5600.00 | −0.259559 | ||||||||
\(776\) | 55530.0 | 2.56883 | ||||||||
\(777\) | −12192.0 | −0.562916 | ||||||||
\(778\) | 10630.0 | 0.489851 | ||||||||
\(779\) | 2184.00 | 0.100449 | ||||||||
\(780\) | −19890.0 | −0.913046 | ||||||||
\(781\) | −13024.0 | −0.596716 | ||||||||
\(782\) | 16560.0 | 0.757269 | ||||||||
\(783\) | −783.000 | −0.0357371 | ||||||||
\(784\) | −7743.00 | −0.352724 | ||||||||
\(785\) | 2670.00 | 0.121397 | ||||||||
\(786\) | −180.000 | −0.00816843 | ||||||||
\(787\) | 27228.0 | 1.23326 | 0.616629 | − | 0.787254i | \(-0.288498\pi\) | ||||
0.616629 | + | 0.787254i | \(0.288498\pi\) | |||||||
\(788\) | 8942.00 | 0.404246 | ||||||||
\(789\) | −22320.0 | −1.00711 | ||||||||
\(790\) | −24000.0 | −1.08086 | ||||||||
\(791\) | −35296.0 | −1.58658 | ||||||||
\(792\) | −17820.0 | −0.799503 | ||||||||
\(793\) | −47580.0 | −2.13066 | ||||||||
\(794\) | −16730.0 | −0.747765 | ||||||||
\(795\) | −8610.00 | −0.384107 | ||||||||
\(796\) | 75480.0 | 3.36095 | ||||||||
\(797\) | −3386.00 | −0.150487 | −0.0752436 | − | 0.997165i | \(-0.523973\pi\) | ||||
−0.0752436 | + | 0.997165i | \(0.523973\pi\) | |||||||
\(798\) | 6720.00 | 0.298102 | ||||||||
\(799\) | 5616.00 | 0.248661 | ||||||||
\(800\) | 2125.00 | 0.0939126 | ||||||||
\(801\) | −8910.00 | −0.393033 | ||||||||
\(802\) | 64250.0 | 2.82886 | ||||||||
\(803\) | −17336.0 | −0.761861 | ||||||||
\(804\) | 17340.0 | 0.760615 | ||||||||
\(805\) | 14720.0 | 0.644487 | ||||||||
\(806\) | −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 | \(0.300481\pi\) | |||||||
\(810\) | 2025.00 | 0.0878410 | ||||||||
\(811\) | 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 | ||||||||
\(815\) | 6900.00 | 0.296560 | ||||||||
\(816\) | −4806.00 | −0.206181 | ||||||||
\(817\) | 7280.00 | 0.311744 | ||||||||
\(818\) | 30610.0 | 1.30838 | ||||||||
\(819\) | 11232.0 | 0.479216 | ||||||||
\(820\) | −6630.00 | −0.282353 | ||||||||
\(821\) | 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 | \(-0.715240\pi\) | ||||
−0.625831 | + | 0.779959i | \(0.715240\pi\) | |||||||
\(824\) | −56160.0 | −2.37430 | ||||||||
\(825\) | 3300.00 | 0.139262 | ||||||||
\(826\) | 14400.0 | 0.606586 | ||||||||
\(827\) | 18556.0 | 0.780236 | 0.390118 | − | 0.920765i | \(-0.372434\pi\) | ||||
0.390118 | + | 0.920765i | \(0.372434\pi\) | |||||||
\(828\) | 28152.0 | 1.18158 | ||||||||
\(829\) | 7966.00 | 0.333740 | 0.166870 | − | 0.985979i | \(-0.446634\pi\) | ||||
0.166870 | + | 0.985979i | \(0.446634\pi\) | |||||||
\(830\) | −22700.0 | −0.949311 | ||||||||
\(831\) | −11154.0 | −0.465617 | ||||||||
\(832\) | −22386.0 | −0.932806 | ||||||||
\(833\) | −1566.00 | −0.0651365 | ||||||||
\(834\) | 21540.0 | 0.894328 | ||||||||
\(835\) | 13080.0 | 0.542098 | ||||||||
\(836\) | 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 | \(0.832753\pi\) | |||||||
\(840\) | −10800.0 | −0.443614 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 60750.0 | 2.48644 | ||||||||
\(843\) | −5262.00 | −0.214986 | ||||||||
\(844\) | 5236.00 | 0.213543 | ||||||||
\(845\) | 19435.0 | 0.791224 | ||||||||
\(846\) | 14040.0 | 0.570573 | ||||||||
\(847\) | 9680.00 | 0.392690 | ||||||||
\(848\) | 51086.0 | 2.06875 | ||||||||
\(849\) | −10716.0 | −0.433183 | ||||||||
\(850\) | 2250.00 | 0.0907934 | ||||||||
\(851\) | 46736.0 | 1.88260 | ||||||||
\(852\) | −15096.0 | −0.607019 | ||||||||
\(853\) | 29950.0 | 1.20219 | 0.601095 | − | 0.799177i | \(-0.294731\pi\) | ||||
0.601095 | + | 0.799177i | \(0.294731\pi\) | |||||||
\(854\) | −48800.0 | −1.95539 | ||||||||
\(855\) | −1260.00 | −0.0503989 | ||||||||
\(856\) | −5220.00 | −0.208430 | ||||||||
\(857\) | −31454.0 | −1.25373 | −0.626866 | − | 0.779127i | \(-0.715663\pi\) | ||||
−0.626866 | + | 0.779127i | \(0.715663\pi\) | |||||||
\(858\) | 51480.0 | 2.04837 | ||||||||
\(859\) | −22036.0 | −0.875272 | −0.437636 | − | 0.899152i | \(-0.644184\pi\) | ||||
−0.437636 | + | 0.899152i | \(0.644184\pi\) | |||||||
\(860\) | −22100.0 | −0.876283 | ||||||||
\(861\) | 3744.00 | 0.148194 | ||||||||
\(862\) | 31440.0 | 1.24229 | ||||||||
\(863\) | 14048.0 | 0.554113 | 0.277056 | − | 0.960854i | \(-0.410641\pi\) | ||||
0.277056 | + | 0.960854i | \(0.410641\pi\) | |||||||
\(864\) | −2295.00 | −0.0903675 | ||||||||
\(865\) | −1650.00 | −0.0648574 | ||||||||
\(866\) | 78250.0 | 3.07049 | ||||||||
\(867\) | 13767.0 | 0.539275 | ||||||||
\(868\) | −60928.0 | −2.38252 | ||||||||
\(869\) | 42240.0 | 1.64890 | ||||||||
\(870\) | −2175.00 | −0.0847579 | ||||||||
\(871\) | −26520.0 | −1.03168 | ||||||||
\(872\) | −37170.0 | −1.44350 | ||||||||
\(873\) | 11106.0 | 0.430563 | ||||||||
\(874\) | −25760.0 | −0.996962 | ||||||||
\(875\) | 2000.00 | 0.0772712 | ||||||||
\(876\) | −20094.0 | −0.775015 | ||||||||
\(877\) | −39922.0 | −1.53714 | −0.768569 | − | 0.639767i | \(-0.779031\pi\) | ||||
−0.768569 | + | 0.639767i | \(0.779031\pi\) | |||||||
\(878\) | −72600.0 | −2.79058 | ||||||||
\(879\) | −378.000 | −0.0145047 | ||||||||
\(880\) | −19580.0 | −0.750047 | ||||||||
\(881\) | 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 | \(-0.716066\pi\) | ||||
−0.627853 | + | 0.778332i | \(0.716066\pi\) | |||||||
\(884\) | 23868.0 | 0.908108 | ||||||||
\(885\) | −2700.00 | −0.102553 | ||||||||
\(886\) | 36860.0 | 1.39767 | ||||||||
\(887\) | −21680.0 | −0.820680 | −0.410340 | − | 0.911933i | \(-0.634590\pi\) | ||||
−0.410340 | + | 0.911933i | \(0.634590\pi\) | |||||||
\(888\) | −34290.0 | −1.29583 | ||||||||
\(889\) | −32896.0 | −1.24105 | ||||||||
\(890\) | −24750.0 | −0.932159 | ||||||||
\(891\) | −3564.00 | −0.134005 | ||||||||
\(892\) | 70040.0 | 2.62905 | ||||||||
\(893\) | −8736.00 | −0.327367 | ||||||||
\(894\) | 7470.00 | 0.279457 | ||||||||
\(895\) | −1860.00 | −0.0694670 | ||||||||
\(896\) | −33840.0 | −1.26174 | ||||||||
\(897\) | −43056.0 | −1.60267 | ||||||||
\(898\) | 53330.0 | 1.98179 | ||||||||
\(899\) | −6496.00 | −0.240994 | ||||||||
\(900\) | 3825.00 | 0.141667 | ||||||||
\(901\) | 10332.0 | 0.382030 | ||||||||
\(902\) | 17160.0 | 0.633443 | ||||||||
\(903\) | 12480.0 | 0.459921 | ||||||||
\(904\) | −99270.0 | −3.65229 | ||||||||
\(905\) | −5050.00 | −0.185489 | ||||||||
\(906\) | 40440.0 | 1.48292 | ||||||||
\(907\) | 2236.00 | 0.0818580 | 0.0409290 | − | 0.999162i | \(-0.486968\pi\) | ||||
0.0409290 | + | 0.999162i | \(0.486968\pi\) | |||||||
\(908\) | 83844.0 | 3.06438 | ||||||||
\(909\) | 9198.00 | 0.335620 | ||||||||
\(910\) | 31200.0 | 1.13656 | ||||||||
\(911\) | 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 | ||||||||
\(915\) | 9150.00 | 0.330590 | ||||||||
\(916\) | −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 | \(0.247529\pi\) | |||||||
\(920\) | 41400.0 | 1.48361 | ||||||||
\(921\) | 7236.00 | 0.258886 | ||||||||
\(922\) | 6270.00 | 0.223960 | ||||||||
\(923\) | 23088.0 | 0.823349 | ||||||||
\(924\) | 35904.0 | 1.27831 | ||||||||
\(925\) | 6350.00 | 0.225715 | ||||||||
\(926\) | −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 | \(0.612099\pi\) | |||||||
\(930\) | 16800.0 | 0.592359 | ||||||||
\(931\) | 2436.00 | 0.0857537 | ||||||||
\(932\) | 1394.00 | 0.0489935 | ||||||||
\(933\) | 8784.00 | 0.308226 | ||||||||
\(934\) | 57940.0 | 2.02982 | ||||||||
\(935\) | −3960.00 | −0.138509 | ||||||||
\(936\) | 31590.0 | 1.10315 | ||||||||
\(937\) | −8678.00 | −0.302559 | −0.151280 | − | 0.988491i | \(-0.548339\pi\) | ||||
−0.151280 | + | 0.988491i | \(0.548339\pi\) | |||||||
\(938\) | −27200.0 | −0.946814 | ||||||||
\(939\) | −8622.00 | −0.299647 | ||||||||
\(940\) | 26520.0 | 0.920199 | ||||||||
\(941\) | −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 | ||||||||
\(945\) | −2160.00 | −0.0743543 | ||||||||
\(946\) | 57200.0 | 1.96589 | ||||||||
\(947\) | 23396.0 | 0.802817 | 0.401409 | − | 0.915899i | \(-0.368521\pi\) | ||||
0.401409 | + | 0.915899i | \(0.368521\pi\) | |||||||
\(948\) | 48960.0 | 1.67737 | ||||||||
\(949\) | 30732.0 | 1.05121 | ||||||||
\(950\) | −3500.00 | −0.119532 | ||||||||
\(951\) | 78.0000 | 0.00265965 | ||||||||
\(952\) | 12960.0 | 0.441214 | ||||||||
\(953\) | −36126.0 | −1.22795 | −0.613975 | − | 0.789326i | \(-0.710430\pi\) | ||||
−0.613975 | + | 0.789326i | \(0.710430\pi\) | |||||||
\(954\) | 25830.0 | 0.876601 | ||||||||
\(955\) | 10040.0 | 0.340196 | ||||||||
\(956\) | −86768.0 | −2.93544 | ||||||||
\(957\) | 3828.00 | 0.129302 | ||||||||
\(958\) | −91000.0 | −3.06897 | ||||||||
\(959\) | −44128.0 | −1.48589 | ||||||||
\(960\) | 4305.00 | 0.144733 | ||||||||
\(961\) | 20385.0 | 0.684267 | ||||||||
\(962\) | 99060.0 | 3.31998 | ||||||||
\(963\) | −1044.00 | −0.0349350 | ||||||||
\(964\) | −36686.0 | −1.22570 | ||||||||
\(965\) | 12890.0 | 0.429994 | ||||||||
\(966\) | −44160.0 | −1.47083 | ||||||||
\(967\) | 38624.0 | 1.28445 | 0.642225 | − | 0.766516i | \(-0.278011\pi\) | ||||
0.642225 | + | 0.766516i | \(0.278011\pi\) | |||||||
\(968\) | 27225.0 | 0.903972 | ||||||||
\(969\) | 1512.00 | 0.0501264 | ||||||||
\(970\) | 30850.0 | 1.02117 | ||||||||
\(971\) | −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 | ||||||||
\(975\) | −5850.00 | −0.192154 | ||||||||
\(976\) | −54290.0 | −1.78051 | ||||||||
\(977\) | −26838.0 | −0.878837 | −0.439418 | − | 0.898282i | \(-0.644815\pi\) | ||||
−0.439418 | + | 0.898282i | \(0.644815\pi\) | |||||||
\(978\) | −20700.0 | −0.676803 | ||||||||
\(979\) | 43560.0 | 1.42205 | ||||||||
\(980\) | −7395.00 | −0.241046 | ||||||||
\(981\) | −7434.00 | −0.241946 | ||||||||
\(982\) | −15500.0 | −0.503691 | ||||||||
\(983\) | 20192.0 | 0.655163 | 0.327581 | − | 0.944823i | \(-0.393766\pi\) | ||||
0.327581 | + | 0.944823i | \(0.393766\pi\) | |||||||
\(984\) | 10530.0 | 0.341142 | ||||||||
\(985\) | 2630.00 | 0.0850749 | ||||||||
\(986\) | 2610.00 | 0.0842995 | ||||||||
\(987\) | −14976.0 | −0.482970 | ||||||||
\(988\) | −37128.0 | −1.19555 | ||||||||
\(989\) | −47840.0 | −1.53814 | ||||||||
\(990\) | −9900.00 | −0.317821 | ||||||||
\(991\) | 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 | ||||||||
\(995\) | 22200.0 | 0.707324 | ||||||||
\(996\) | 46308.0 | 1.47322 | ||||||||
\(997\) | 58430.0 | 1.85606 | 0.928032 | − | 0.372499i | \(-0.121499\pi\) | ||||
0.928032 | + | 0.372499i | \(0.121499\pi\) | |||||||
\(998\) | 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 | 435.4.a.c.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 1305.4.a.a.1.1 | 1 | |||
5.4 | even | 2 | 2175.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.4.a.c.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
1305.4.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
2175.4.a.a.1.1 | 1 | 5.4 | even | 2 |