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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 29.0000 | 1.56585 | 0.782926 | − | 0.622114i | \(-0.213726\pi\) | ||||
0.782926 | + | 0.622114i | \(0.213726\pi\) | |||||||
\(8\) | 24.0000 | 1.06066 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −10.0000 | −0.316228 | ||||||||
\(11\) | −15.0000 | −0.411152 | −0.205576 | − | 0.978641i | \(-0.565907\pi\) | ||||
−0.205576 | + | 0.978641i | \(0.565907\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | 3.00000 | 0.0640039 | 0.0320019 | − | 0.999488i | \(-0.489812\pi\) | ||||
0.0320019 | + | 0.999488i | \(0.489812\pi\) | |||||||
\(14\) | −58.0000 | −1.10723 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | −16.0000 | −0.250000 | ||||||||
\(17\) | 121.000 | 1.72628 | 0.863141 | − | 0.504962i | \(-0.168494\pi\) | ||||
0.863141 | + | 0.504962i | \(0.168494\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | −40.0000 | −0.482980 | −0.241490 | − | 0.970403i | \(-0.577636\pi\) | ||||
−0.241490 | + | 0.970403i | \(0.577636\pi\) | |||||||
\(20\) | −20.0000 | −0.223607 | ||||||||
\(21\) | −87.0000 | −0.904046 | ||||||||
\(22\) | 30.0000 | 0.290728 | ||||||||
\(23\) | −116.000 | −1.05164 | −0.525819 | − | 0.850597i | \(-0.676241\pi\) | ||||
−0.525819 | + | 0.850597i | \(0.676241\pi\) | |||||||
\(24\) | −72.0000 | −0.612372 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −6.00000 | −0.0452576 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −116.000 | −0.782926 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 30.0000 | 0.182574 | ||||||||
\(31\) | −116.000 | −0.672071 | −0.336036 | − | 0.941849i | \(-0.609086\pi\) | ||||
−0.336036 | + | 0.941849i | \(0.609086\pi\) | |||||||
\(32\) | −160.000 | −0.883883 | ||||||||
\(33\) | 45.0000 | 0.237379 | ||||||||
\(34\) | −242.000 | −1.22067 | ||||||||
\(35\) | 145.000 | 0.700271 | ||||||||
\(36\) | −36.0000 | −0.166667 | ||||||||
\(37\) | 36.0000 | 0.159956 | 0.0799779 | − | 0.996797i | \(-0.474515\pi\) | ||||
0.0799779 | + | 0.996797i | \(0.474515\pi\) | |||||||
\(38\) | 80.0000 | 0.341519 | ||||||||
\(39\) | −9.00000 | −0.0369527 | ||||||||
\(40\) | 120.000 | 0.474342 | ||||||||
\(41\) | −170.000 | −0.647550 | −0.323775 | − | 0.946134i | \(-0.604952\pi\) | ||||
−0.323775 | + | 0.946134i | \(0.604952\pi\) | |||||||
\(42\) | 174.000 | 0.639257 | ||||||||
\(43\) | 230.000 | 0.815690 | 0.407845 | − | 0.913051i | \(-0.366280\pi\) | ||||
0.407845 | + | 0.913051i | \(0.366280\pi\) | |||||||
\(44\) | 60.0000 | 0.205576 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 232.000 | 0.743620 | ||||||||
\(47\) | 231.000 | 0.716911 | 0.358455 | − | 0.933547i | \(-0.383303\pi\) | ||||
0.358455 | + | 0.933547i | \(0.383303\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 498.000 | 1.45190 | ||||||||
\(50\) | −50.0000 | −0.141421 | ||||||||
\(51\) | −363.000 | −0.996670 | ||||||||
\(52\) | −12.0000 | −0.0320019 | ||||||||
\(53\) | 456.000 | 1.18182 | 0.590910 | − | 0.806738i | \(-0.298769\pi\) | ||||
0.590910 | + | 0.806738i | \(0.298769\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | −75.0000 | −0.183873 | ||||||||
\(56\) | 696.000 | 1.66084 | ||||||||
\(57\) | 120.000 | 0.278849 | ||||||||
\(58\) | −58.0000 | −0.131306 | ||||||||
\(59\) | 576.000 | 1.27100 | 0.635498 | − | 0.772102i | \(-0.280795\pi\) | ||||
0.635498 | + | 0.772102i | \(0.280795\pi\) | |||||||
\(60\) | 60.0000 | 0.129099 | ||||||||
\(61\) | 342.000 | 0.717846 | 0.358923 | − | 0.933367i | \(-0.383144\pi\) | ||||
0.358923 | + | 0.933367i | \(0.383144\pi\) | |||||||
\(62\) | 232.000 | 0.475226 | ||||||||
\(63\) | 261.000 | 0.521951 | ||||||||
\(64\) | 448.000 | 0.875000 | ||||||||
\(65\) | 15.0000 | 0.0286234 | ||||||||
\(66\) | −90.0000 | −0.167852 | ||||||||
\(67\) | −269.000 | −0.490501 | −0.245251 | − | 0.969460i | \(-0.578870\pi\) | ||||
−0.245251 | + | 0.969460i | \(0.578870\pi\) | |||||||
\(68\) | −484.000 | −0.863141 | ||||||||
\(69\) | 348.000 | 0.607163 | ||||||||
\(70\) | −290.000 | −0.495166 | ||||||||
\(71\) | 302.000 | 0.504800 | 0.252400 | − | 0.967623i | \(-0.418780\pi\) | ||||
0.252400 | + | 0.967623i | \(0.418780\pi\) | |||||||
\(72\) | 216.000 | 0.353553 | ||||||||
\(73\) | −372.000 | −0.596429 | −0.298214 | − | 0.954499i | \(-0.596391\pi\) | ||||
−0.298214 | + | 0.954499i | \(0.596391\pi\) | |||||||
\(74\) | −72.0000 | −0.113106 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 160.000 | 0.241490 | ||||||||
\(77\) | −435.000 | −0.643803 | ||||||||
\(78\) | 18.0000 | 0.0261295 | ||||||||
\(79\) | −348.000 | −0.495608 | −0.247804 | − | 0.968810i | \(-0.579709\pi\) | ||||
−0.247804 | + | 0.968810i | \(0.579709\pi\) | |||||||
\(80\) | −80.0000 | −0.111803 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 340.000 | 0.457887 | ||||||||
\(83\) | −512.000 | −0.677100 | −0.338550 | − | 0.940948i | \(-0.609936\pi\) | ||||
−0.338550 | + | 0.940948i | \(0.609936\pi\) | |||||||
\(84\) | 348.000 | 0.452023 | ||||||||
\(85\) | 605.000 | 0.772017 | ||||||||
\(86\) | −460.000 | −0.576780 | ||||||||
\(87\) | −87.0000 | −0.107211 | ||||||||
\(88\) | −360.000 | −0.436092 | ||||||||
\(89\) | 1525.00 | 1.81629 | 0.908144 | − | 0.418657i | \(-0.137499\pi\) | ||||
0.908144 | + | 0.418657i | \(0.137499\pi\) | |||||||
\(90\) | −90.0000 | −0.105409 | ||||||||
\(91\) | 87.0000 | 0.100221 | ||||||||
\(92\) | 464.000 | 0.525819 | ||||||||
\(93\) | 348.000 | 0.388021 | ||||||||
\(94\) | −462.000 | −0.506933 | ||||||||
\(95\) | −200.000 | −0.215995 | ||||||||
\(96\) | 480.000 | 0.510310 | ||||||||
\(97\) | −560.000 | −0.586179 | −0.293090 | − | 0.956085i | \(-0.594683\pi\) | ||||
−0.293090 | + | 0.956085i | \(0.594683\pi\) | |||||||
\(98\) | −996.000 | −1.02664 | ||||||||
\(99\) | −135.000 | −0.137051 | ||||||||
\(100\) | −100.000 | −0.100000 | ||||||||
\(101\) | 1447.00 | 1.42556 | 0.712782 | − | 0.701386i | \(-0.247435\pi\) | ||||
0.712782 | + | 0.701386i | \(0.247435\pi\) | |||||||
\(102\) | 726.000 | 0.704752 | ||||||||
\(103\) | 556.000 | 0.531886 | 0.265943 | − | 0.963989i | \(-0.414317\pi\) | ||||
0.265943 | + | 0.963989i | \(0.414317\pi\) | |||||||
\(104\) | 72.0000 | 0.0678864 | ||||||||
\(105\) | −435.000 | −0.404301 | ||||||||
\(106\) | −912.000 | −0.835672 | ||||||||
\(107\) | 1558.00 | 1.40764 | 0.703820 | − | 0.710378i | \(-0.251476\pi\) | ||||
0.703820 | + | 0.710378i | \(0.251476\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | −881.000 | −0.774170 | −0.387085 | − | 0.922044i | \(-0.626518\pi\) | ||||
−0.387085 | + | 0.922044i | \(0.626518\pi\) | |||||||
\(110\) | 150.000 | 0.130018 | ||||||||
\(111\) | −108.000 | −0.0923505 | ||||||||
\(112\) | −464.000 | −0.391463 | ||||||||
\(113\) | 313.000 | 0.260571 | 0.130286 | − | 0.991476i | \(-0.458411\pi\) | ||||
0.130286 | + | 0.991476i | \(0.458411\pi\) | |||||||
\(114\) | −240.000 | −0.197176 | ||||||||
\(115\) | −580.000 | −0.470307 | ||||||||
\(116\) | −116.000 | −0.0928477 | ||||||||
\(117\) | 27.0000 | 0.0213346 | ||||||||
\(118\) | −1152.00 | −0.898730 | ||||||||
\(119\) | 3509.00 | 2.70311 | ||||||||
\(120\) | −360.000 | −0.273861 | ||||||||
\(121\) | −1106.00 | −0.830954 | ||||||||
\(122\) | −684.000 | −0.507594 | ||||||||
\(123\) | 510.000 | 0.373863 | ||||||||
\(124\) | 464.000 | 0.336036 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −522.000 | −0.369075 | ||||||||
\(127\) | −494.000 | −0.345161 | −0.172580 | − | 0.984995i | \(-0.555210\pi\) | ||||
−0.172580 | + | 0.984995i | \(0.555210\pi\) | |||||||
\(128\) | 384.000 | 0.265165 | ||||||||
\(129\) | −690.000 | −0.470939 | ||||||||
\(130\) | −30.0000 | −0.0202398 | ||||||||
\(131\) | −2007.00 | −1.33857 | −0.669284 | − | 0.743007i | \(-0.733399\pi\) | ||||
−0.669284 | + | 0.743007i | \(0.733399\pi\) | |||||||
\(132\) | −180.000 | −0.118689 | ||||||||
\(133\) | −1160.00 | −0.756276 | ||||||||
\(134\) | 538.000 | 0.346837 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 2904.00 | 1.83100 | ||||||||
\(137\) | 918.000 | 0.572482 | 0.286241 | − | 0.958158i | \(-0.407594\pi\) | ||||
0.286241 | + | 0.958158i | \(0.407594\pi\) | |||||||
\(138\) | −696.000 | −0.429329 | ||||||||
\(139\) | 1619.00 | 0.987927 | 0.493963 | − | 0.869483i | \(-0.335548\pi\) | ||||
0.493963 | + | 0.869483i | \(0.335548\pi\) | |||||||
\(140\) | −580.000 | −0.350135 | ||||||||
\(141\) | −693.000 | −0.413909 | ||||||||
\(142\) | −604.000 | −0.356948 | ||||||||
\(143\) | −45.0000 | −0.0263153 | ||||||||
\(144\) | −144.000 | −0.0833333 | ||||||||
\(145\) | 145.000 | 0.0830455 | ||||||||
\(146\) | 744.000 | 0.421739 | ||||||||
\(147\) | −1494.00 | −0.838252 | ||||||||
\(148\) | −144.000 | −0.0799779 | ||||||||
\(149\) | 3046.00 | 1.67475 | 0.837376 | − | 0.546627i | \(-0.184089\pi\) | ||||
0.837376 | + | 0.546627i | \(0.184089\pi\) | |||||||
\(150\) | 150.000 | 0.0816497 | ||||||||
\(151\) | 1576.00 | 0.849358 | 0.424679 | − | 0.905344i | \(-0.360387\pi\) | ||||
0.424679 | + | 0.905344i | \(0.360387\pi\) | |||||||
\(152\) | −960.000 | −0.512278 | ||||||||
\(153\) | 1089.00 | 0.575428 | ||||||||
\(154\) | 870.000 | 0.455238 | ||||||||
\(155\) | −580.000 | −0.300559 | ||||||||
\(156\) | 36.0000 | 0.0184763 | ||||||||
\(157\) | −3544.00 | −1.80154 | −0.900771 | − | 0.434295i | \(-0.856998\pi\) | ||||
−0.900771 | + | 0.434295i | \(0.856998\pi\) | |||||||
\(158\) | 696.000 | 0.350448 | ||||||||
\(159\) | −1368.00 | −0.682324 | ||||||||
\(160\) | −800.000 | −0.395285 | ||||||||
\(161\) | −3364.00 | −1.64671 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | −768.000 | −0.369045 | −0.184523 | − | 0.982828i | \(-0.559074\pi\) | ||||
−0.184523 | + | 0.982828i | \(0.559074\pi\) | |||||||
\(164\) | 680.000 | 0.323775 | ||||||||
\(165\) | 225.000 | 0.106159 | ||||||||
\(166\) | 1024.00 | 0.478782 | ||||||||
\(167\) | −1624.00 | −0.752508 | −0.376254 | − | 0.926516i | \(-0.622788\pi\) | ||||
−0.376254 | + | 0.926516i | \(0.622788\pi\) | |||||||
\(168\) | −2088.00 | −0.958885 | ||||||||
\(169\) | −2188.00 | −0.995904 | ||||||||
\(170\) | −1210.00 | −0.545899 | ||||||||
\(171\) | −360.000 | −0.160993 | ||||||||
\(172\) | −920.000 | −0.407845 | ||||||||
\(173\) | 1700.00 | 0.747102 | 0.373551 | − | 0.927610i | \(-0.378140\pi\) | ||||
0.373551 | + | 0.927610i | \(0.378140\pi\) | |||||||
\(174\) | 174.000 | 0.0758098 | ||||||||
\(175\) | 725.000 | 0.313171 | ||||||||
\(176\) | 240.000 | 0.102788 | ||||||||
\(177\) | −1728.00 | −0.733810 | ||||||||
\(178\) | −3050.00 | −1.28431 | ||||||||
\(179\) | 3870.00 | 1.61596 | 0.807982 | − | 0.589208i | \(-0.200560\pi\) | ||||
0.807982 | + | 0.589208i | \(0.200560\pi\) | |||||||
\(180\) | −180.000 | −0.0745356 | ||||||||
\(181\) | 1757.00 | 0.721529 | 0.360765 | − | 0.932657i | \(-0.382516\pi\) | ||||
0.360765 | + | 0.932657i | \(0.382516\pi\) | |||||||
\(182\) | −174.000 | −0.0708667 | ||||||||
\(183\) | −1026.00 | −0.414449 | ||||||||
\(184\) | −2784.00 | −1.11543 | ||||||||
\(185\) | 180.000 | 0.0715344 | ||||||||
\(186\) | −696.000 | −0.274372 | ||||||||
\(187\) | −1815.00 | −0.709764 | ||||||||
\(188\) | −924.000 | −0.358455 | ||||||||
\(189\) | −783.000 | −0.301349 | ||||||||
\(190\) | 400.000 | 0.152732 | ||||||||
\(191\) | −2048.00 | −0.775854 | −0.387927 | − | 0.921690i | \(-0.626809\pi\) | ||||
−0.387927 | + | 0.921690i | \(0.626809\pi\) | |||||||
\(192\) | −1344.00 | −0.505181 | ||||||||
\(193\) | −2398.00 | −0.894362 | −0.447181 | − | 0.894444i | \(-0.647572\pi\) | ||||
−0.447181 | + | 0.894444i | \(0.647572\pi\) | |||||||
\(194\) | 1120.00 | 0.414491 | ||||||||
\(195\) | −45.0000 | −0.0165257 | ||||||||
\(196\) | −1992.00 | −0.725948 | ||||||||
\(197\) | 3966.00 | 1.43434 | 0.717172 | − | 0.696896i | \(-0.245436\pi\) | ||||
0.717172 | + | 0.696896i | \(0.245436\pi\) | |||||||
\(198\) | 270.000 | 0.0969094 | ||||||||
\(199\) | 641.000 | 0.228338 | 0.114169 | − | 0.993461i | \(-0.463579\pi\) | ||||
0.114169 | + | 0.993461i | \(0.463579\pi\) | |||||||
\(200\) | 600.000 | 0.212132 | ||||||||
\(201\) | 807.000 | 0.283191 | ||||||||
\(202\) | −2894.00 | −1.00803 | ||||||||
\(203\) | 841.000 | 0.290772 | ||||||||
\(204\) | 1452.00 | 0.498335 | ||||||||
\(205\) | −850.000 | −0.289593 | ||||||||
\(206\) | −1112.00 | −0.376101 | ||||||||
\(207\) | −1044.00 | −0.350546 | ||||||||
\(208\) | −48.0000 | −0.0160010 | ||||||||
\(209\) | 600.000 | 0.198578 | ||||||||
\(210\) | 870.000 | 0.285884 | ||||||||
\(211\) | 5438.00 | 1.77425 | 0.887126 | − | 0.461526i | \(-0.152698\pi\) | ||||
0.887126 | + | 0.461526i | \(0.152698\pi\) | |||||||
\(212\) | −1824.00 | −0.590910 | ||||||||
\(213\) | −906.000 | −0.291446 | ||||||||
\(214\) | −3116.00 | −0.995352 | ||||||||
\(215\) | 1150.00 | 0.364788 | ||||||||
\(216\) | −648.000 | −0.204124 | ||||||||
\(217\) | −3364.00 | −1.05236 | ||||||||
\(218\) | 1762.00 | 0.547421 | ||||||||
\(219\) | 1116.00 | 0.344348 | ||||||||
\(220\) | 300.000 | 0.0919363 | ||||||||
\(221\) | 363.000 | 0.110489 | ||||||||
\(222\) | 216.000 | 0.0653017 | ||||||||
\(223\) | 2799.00 | 0.840515 | 0.420258 | − | 0.907405i | \(-0.361940\pi\) | ||||
0.420258 | + | 0.907405i | \(0.361940\pi\) | |||||||
\(224\) | −4640.00 | −1.38403 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −626.000 | −0.184252 | ||||||||
\(227\) | 1492.00 | 0.436245 | 0.218122 | − | 0.975921i | \(-0.430007\pi\) | ||||
0.218122 | + | 0.975921i | \(0.430007\pi\) | |||||||
\(228\) | −480.000 | −0.139424 | ||||||||
\(229\) | 4622.00 | 1.33376 | 0.666879 | − | 0.745166i | \(-0.267630\pi\) | ||||
0.666879 | + | 0.745166i | \(0.267630\pi\) | |||||||
\(230\) | 1160.00 | 0.332557 | ||||||||
\(231\) | 1305.00 | 0.371700 | ||||||||
\(232\) | 696.000 | 0.196960 | ||||||||
\(233\) | 4170.00 | 1.17247 | 0.586236 | − | 0.810141i | \(-0.300609\pi\) | ||||
0.586236 | + | 0.810141i | \(0.300609\pi\) | |||||||
\(234\) | −54.0000 | −0.0150859 | ||||||||
\(235\) | 1155.00 | 0.320612 | ||||||||
\(236\) | −2304.00 | −0.635498 | ||||||||
\(237\) | 1044.00 | 0.286140 | ||||||||
\(238\) | −7018.00 | −1.91138 | ||||||||
\(239\) | 1686.00 | 0.456311 | 0.228155 | − | 0.973625i | \(-0.426731\pi\) | ||||
0.228155 | + | 0.973625i | \(0.426731\pi\) | |||||||
\(240\) | 240.000 | 0.0645497 | ||||||||
\(241\) | −3925.00 | −1.04909 | −0.524547 | − | 0.851382i | \(-0.675765\pi\) | ||||
−0.524547 | + | 0.851382i | \(0.675765\pi\) | |||||||
\(242\) | 2212.00 | 0.587573 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −1368.00 | −0.358923 | ||||||||
\(245\) | 2490.00 | 0.649307 | ||||||||
\(246\) | −1020.00 | −0.264361 | ||||||||
\(247\) | −120.000 | −0.0309126 | ||||||||
\(248\) | −2784.00 | −0.712839 | ||||||||
\(249\) | 1536.00 | 0.390924 | ||||||||
\(250\) | −250.000 | −0.0632456 | ||||||||
\(251\) | −5775.00 | −1.45225 | −0.726125 | − | 0.687563i | \(-0.758681\pi\) | ||||
−0.726125 | + | 0.687563i | \(0.758681\pi\) | |||||||
\(252\) | −1044.00 | −0.260975 | ||||||||
\(253\) | 1740.00 | 0.432383 | ||||||||
\(254\) | 988.000 | 0.244065 | ||||||||
\(255\) | −1815.00 | −0.445724 | ||||||||
\(256\) | −4352.00 | −1.06250 | ||||||||
\(257\) | −3146.00 | −0.763588 | −0.381794 | − | 0.924247i | \(-0.624694\pi\) | ||||
−0.381794 | + | 0.924247i | \(0.624694\pi\) | |||||||
\(258\) | 1380.00 | 0.333004 | ||||||||
\(259\) | 1044.00 | 0.250467 | ||||||||
\(260\) | −60.0000 | −0.0143117 | ||||||||
\(261\) | 261.000 | 0.0618984 | ||||||||
\(262\) | 4014.00 | 0.946510 | ||||||||
\(263\) | −5768.00 | −1.35236 | −0.676179 | − | 0.736737i | \(-0.736365\pi\) | ||||
−0.676179 | + | 0.736737i | \(0.736365\pi\) | |||||||
\(264\) | 1080.00 | 0.251778 | ||||||||
\(265\) | 2280.00 | 0.528526 | ||||||||
\(266\) | 2320.00 | 0.534768 | ||||||||
\(267\) | −4575.00 | −1.04863 | ||||||||
\(268\) | 1076.00 | 0.245251 | ||||||||
\(269\) | −7341.00 | −1.66390 | −0.831949 | − | 0.554852i | \(-0.812775\pi\) | ||||
−0.831949 | + | 0.554852i | \(0.812775\pi\) | |||||||
\(270\) | 270.000 | 0.0608581 | ||||||||
\(271\) | −14.0000 | −0.00313815 | −0.00156908 | − | 0.999999i | \(-0.500499\pi\) | ||||
−0.00156908 | + | 0.999999i | \(0.500499\pi\) | |||||||
\(272\) | −1936.00 | −0.431571 | ||||||||
\(273\) | −261.000 | −0.0578624 | ||||||||
\(274\) | −1836.00 | −0.404806 | ||||||||
\(275\) | −375.000 | −0.0822304 | ||||||||
\(276\) | −1392.00 | −0.303582 | ||||||||
\(277\) | 3721.00 | 0.807124 | 0.403562 | − | 0.914952i | \(-0.367772\pi\) | ||||
0.403562 | + | 0.914952i | \(0.367772\pi\) | |||||||
\(278\) | −3238.00 | −0.698570 | ||||||||
\(279\) | −1044.00 | −0.224024 | ||||||||
\(280\) | 3480.00 | 0.742749 | ||||||||
\(281\) | 924.000 | 0.196161 | 0.0980805 | − | 0.995178i | \(-0.468730\pi\) | ||||
0.0980805 | + | 0.995178i | \(0.468730\pi\) | |||||||
\(282\) | 1386.00 | 0.292678 | ||||||||
\(283\) | 1940.00 | 0.407495 | 0.203747 | − | 0.979023i | \(-0.434688\pi\) | ||||
0.203747 | + | 0.979023i | \(0.434688\pi\) | |||||||
\(284\) | −1208.00 | −0.252400 | ||||||||
\(285\) | 600.000 | 0.124705 | ||||||||
\(286\) | 90.0000 | 0.0186077 | ||||||||
\(287\) | −4930.00 | −1.01397 | ||||||||
\(288\) | −1440.00 | −0.294628 | ||||||||
\(289\) | 9728.00 | 1.98005 | ||||||||
\(290\) | −290.000 | −0.0587220 | ||||||||
\(291\) | 1680.00 | 0.338431 | ||||||||
\(292\) | 1488.00 | 0.298214 | ||||||||
\(293\) | 5267.00 | 1.05018 | 0.525088 | − | 0.851048i | \(-0.324032\pi\) | ||||
0.525088 | + | 0.851048i | \(0.324032\pi\) | |||||||
\(294\) | 2988.00 | 0.592734 | ||||||||
\(295\) | 2880.00 | 0.568407 | ||||||||
\(296\) | 864.000 | 0.169659 | ||||||||
\(297\) | 405.000 | 0.0791262 | ||||||||
\(298\) | −6092.00 | −1.18423 | ||||||||
\(299\) | −348.000 | −0.0673089 | ||||||||
\(300\) | 300.000 | 0.0577350 | ||||||||
\(301\) | 6670.00 | 1.27725 | ||||||||
\(302\) | −3152.00 | −0.600587 | ||||||||
\(303\) | −4341.00 | −0.823049 | ||||||||
\(304\) | 640.000 | 0.120745 | ||||||||
\(305\) | 1710.00 | 0.321031 | ||||||||
\(306\) | −2178.00 | −0.406889 | ||||||||
\(307\) | 6856.00 | 1.27457 | 0.637284 | − | 0.770629i | \(-0.280058\pi\) | ||||
0.637284 | + | 0.770629i | \(0.280058\pi\) | |||||||
\(308\) | 1740.00 | 0.321902 | ||||||||
\(309\) | −1668.00 | −0.307085 | ||||||||
\(310\) | 1160.00 | 0.212528 | ||||||||
\(311\) | −2447.00 | −0.446163 | −0.223081 | − | 0.974800i | \(-0.571612\pi\) | ||||
−0.223081 | + | 0.974800i | \(0.571612\pi\) | |||||||
\(312\) | −216.000 | −0.0391942 | ||||||||
\(313\) | 511.000 | 0.0922793 | 0.0461397 | − | 0.998935i | \(-0.485308\pi\) | ||||
0.0461397 | + | 0.998935i | \(0.485308\pi\) | |||||||
\(314\) | 7088.00 | 1.27388 | ||||||||
\(315\) | 1305.00 | 0.233424 | ||||||||
\(316\) | 1392.00 | 0.247804 | ||||||||
\(317\) | 7167.00 | 1.26984 | 0.634919 | − | 0.772578i | \(-0.281033\pi\) | ||||
0.634919 | + | 0.772578i | \(0.281033\pi\) | |||||||
\(318\) | 2736.00 | 0.482476 | ||||||||
\(319\) | −435.000 | −0.0763490 | ||||||||
\(320\) | 2240.00 | 0.391312 | ||||||||
\(321\) | −4674.00 | −0.812702 | ||||||||
\(322\) | 6728.00 | 1.16440 | ||||||||
\(323\) | −4840.00 | −0.833761 | ||||||||
\(324\) | −324.000 | −0.0555556 | ||||||||
\(325\) | 75.0000 | 0.0128008 | ||||||||
\(326\) | 1536.00 | 0.260955 | ||||||||
\(327\) | 2643.00 | 0.446967 | ||||||||
\(328\) | −4080.00 | −0.686830 | ||||||||
\(329\) | 6699.00 | 1.12258 | ||||||||
\(330\) | −450.000 | −0.0750657 | ||||||||
\(331\) | −8962.00 | −1.48821 | −0.744103 | − | 0.668065i | \(-0.767123\pi\) | ||||
−0.744103 | + | 0.668065i | \(0.767123\pi\) | |||||||
\(332\) | 2048.00 | 0.338550 | ||||||||
\(333\) | 324.000 | 0.0533186 | ||||||||
\(334\) | 3248.00 | 0.532104 | ||||||||
\(335\) | −1345.00 | −0.219359 | ||||||||
\(336\) | 1392.00 | 0.226011 | ||||||||
\(337\) | 2706.00 | 0.437404 | 0.218702 | − | 0.975792i | \(-0.429818\pi\) | ||||
0.218702 | + | 0.975792i | \(0.429818\pi\) | |||||||
\(338\) | 4376.00 | 0.704210 | ||||||||
\(339\) | −939.000 | −0.150441 | ||||||||
\(340\) | −2420.00 | −0.386009 | ||||||||
\(341\) | 1740.00 | 0.276323 | ||||||||
\(342\) | 720.000 | 0.113840 | ||||||||
\(343\) | 4495.00 | 0.707601 | ||||||||
\(344\) | 5520.00 | 0.865170 | ||||||||
\(345\) | 1740.00 | 0.271532 | ||||||||
\(346\) | −3400.00 | −0.528281 | ||||||||
\(347\) | 2232.00 | 0.345303 | 0.172651 | − | 0.984983i | \(-0.444767\pi\) | ||||
0.172651 | + | 0.984983i | \(0.444767\pi\) | |||||||
\(348\) | 348.000 | 0.0536056 | ||||||||
\(349\) | 9742.00 | 1.49420 | 0.747102 | − | 0.664709i | \(-0.231445\pi\) | ||||
0.747102 | + | 0.664709i | \(0.231445\pi\) | |||||||
\(350\) | −1450.00 | −0.221445 | ||||||||
\(351\) | −81.0000 | −0.0123176 | ||||||||
\(352\) | 2400.00 | 0.363410 | ||||||||
\(353\) | −2694.00 | −0.406196 | −0.203098 | − | 0.979158i | \(-0.565101\pi\) | ||||
−0.203098 | + | 0.979158i | \(0.565101\pi\) | |||||||
\(354\) | 3456.00 | 0.518882 | ||||||||
\(355\) | 1510.00 | 0.225753 | ||||||||
\(356\) | −6100.00 | −0.908144 | ||||||||
\(357\) | −10527.0 | −1.56064 | ||||||||
\(358\) | −7740.00 | −1.14266 | ||||||||
\(359\) | −960.000 | −0.141133 | −0.0705667 | − | 0.997507i | \(-0.522481\pi\) | ||||
−0.0705667 | + | 0.997507i | \(0.522481\pi\) | |||||||
\(360\) | 1080.00 | 0.158114 | ||||||||
\(361\) | −5259.00 | −0.766730 | ||||||||
\(362\) | −3514.00 | −0.510198 | ||||||||
\(363\) | 3318.00 | 0.479752 | ||||||||
\(364\) | −348.000 | −0.0501103 | ||||||||
\(365\) | −1860.00 | −0.266731 | ||||||||
\(366\) | 2052.00 | 0.293059 | ||||||||
\(367\) | −4632.00 | −0.658824 | −0.329412 | − | 0.944186i | \(-0.606851\pi\) | ||||
−0.329412 | + | 0.944186i | \(0.606851\pi\) | |||||||
\(368\) | 1856.00 | 0.262909 | ||||||||
\(369\) | −1530.00 | −0.215850 | ||||||||
\(370\) | −360.000 | −0.0505825 | ||||||||
\(371\) | 13224.0 | 1.85055 | ||||||||
\(372\) | −1392.00 | −0.194010 | ||||||||
\(373\) | −6682.00 | −0.927563 | −0.463781 | − | 0.885950i | \(-0.653508\pi\) | ||||
−0.463781 | + | 0.885950i | \(0.653508\pi\) | |||||||
\(374\) | 3630.00 | 0.501879 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 5544.00 | 0.760399 | ||||||||
\(377\) | 87.0000 | 0.0118852 | ||||||||
\(378\) | 1566.00 | 0.213086 | ||||||||
\(379\) | 11270.0 | 1.52744 | 0.763722 | − | 0.645546i | \(-0.223370\pi\) | ||||
0.763722 | + | 0.645546i | \(0.223370\pi\) | |||||||
\(380\) | 800.000 | 0.107998 | ||||||||
\(381\) | 1482.00 | 0.199279 | ||||||||
\(382\) | 4096.00 | 0.548611 | ||||||||
\(383\) | 1016.00 | 0.135549 | 0.0677744 | − | 0.997701i | \(-0.478410\pi\) | ||||
0.0677744 | + | 0.997701i | \(0.478410\pi\) | |||||||
\(384\) | −1152.00 | −0.153093 | ||||||||
\(385\) | −2175.00 | −0.287918 | ||||||||
\(386\) | 4796.00 | 0.632409 | ||||||||
\(387\) | 2070.00 | 0.271897 | ||||||||
\(388\) | 2240.00 | 0.293090 | ||||||||
\(389\) | −3727.00 | −0.485775 | −0.242887 | − | 0.970054i | \(-0.578095\pi\) | ||||
−0.242887 | + | 0.970054i | \(0.578095\pi\) | |||||||
\(390\) | 90.0000 | 0.0116855 | ||||||||
\(391\) | −14036.0 | −1.81542 | ||||||||
\(392\) | 11952.0 | 1.53997 | ||||||||
\(393\) | 6021.00 | 0.772823 | ||||||||
\(394\) | −7932.00 | −1.01423 | ||||||||
\(395\) | −1740.00 | −0.221643 | ||||||||
\(396\) | 540.000 | 0.0685253 | ||||||||
\(397\) | 1990.00 | 0.251575 | 0.125787 | − | 0.992057i | \(-0.459854\pi\) | ||||
0.125787 | + | 0.992057i | \(0.459854\pi\) | |||||||
\(398\) | −1282.00 | −0.161459 | ||||||||
\(399\) | 3480.00 | 0.436636 | ||||||||
\(400\) | −400.000 | −0.0500000 | ||||||||
\(401\) | 6696.00 | 0.833871 | 0.416936 | − | 0.908936i | \(-0.363104\pi\) | ||||
0.416936 | + | 0.908936i | \(0.363104\pi\) | |||||||
\(402\) | −1614.00 | −0.200246 | ||||||||
\(403\) | −348.000 | −0.0430152 | ||||||||
\(404\) | −5788.00 | −0.712782 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | −1682.00 | −0.205607 | ||||||||
\(407\) | −540.000 | −0.0657661 | ||||||||
\(408\) | −8712.00 | −1.05713 | ||||||||
\(409\) | 252.000 | 0.0304660 | 0.0152330 | − | 0.999884i | \(-0.495151\pi\) | ||||
0.0152330 | + | 0.999884i | \(0.495151\pi\) | |||||||
\(410\) | 1700.00 | 0.204773 | ||||||||
\(411\) | −2754.00 | −0.330523 | ||||||||
\(412\) | −2224.00 | −0.265943 | ||||||||
\(413\) | 16704.0 | 1.99019 | ||||||||
\(414\) | 2088.00 | 0.247873 | ||||||||
\(415\) | −2560.00 | −0.302808 | ||||||||
\(416\) | −480.000 | −0.0565720 | ||||||||
\(417\) | −4857.00 | −0.570380 | ||||||||
\(418\) | −1200.00 | −0.140416 | ||||||||
\(419\) | 7418.00 | 0.864900 | 0.432450 | − | 0.901658i | \(-0.357649\pi\) | ||||
0.432450 | + | 0.901658i | \(0.357649\pi\) | |||||||
\(420\) | 1740.00 | 0.202151 | ||||||||
\(421\) | 11268.0 | 1.30444 | 0.652219 | − | 0.758030i | \(-0.273838\pi\) | ||||
0.652219 | + | 0.758030i | \(0.273838\pi\) | |||||||
\(422\) | −10876.0 | −1.25459 | ||||||||
\(423\) | 2079.00 | 0.238970 | ||||||||
\(424\) | 10944.0 | 1.25351 | ||||||||
\(425\) | 3025.00 | 0.345257 | ||||||||
\(426\) | 1812.00 | 0.206084 | ||||||||
\(427\) | 9918.00 | 1.12404 | ||||||||
\(428\) | −6232.00 | −0.703820 | ||||||||
\(429\) | 135.000 | 0.0151932 | ||||||||
\(430\) | −2300.00 | −0.257944 | ||||||||
\(431\) | −11600.0 | −1.29641 | −0.648205 | − | 0.761466i | \(-0.724480\pi\) | ||||
−0.648205 | + | 0.761466i | \(0.724480\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | 1072.00 | 0.118977 | 0.0594885 | − | 0.998229i | \(-0.481053\pi\) | ||||
0.0594885 | + | 0.998229i | \(0.481053\pi\) | |||||||
\(434\) | 6728.00 | 0.744134 | ||||||||
\(435\) | −435.000 | −0.0479463 | ||||||||
\(436\) | 3524.00 | 0.387085 | ||||||||
\(437\) | 4640.00 | 0.507921 | ||||||||
\(438\) | −2232.00 | −0.243491 | ||||||||
\(439\) | −12339.0 | −1.34148 | −0.670738 | − | 0.741694i | \(-0.734023\pi\) | ||||
−0.670738 | + | 0.741694i | \(0.734023\pi\) | |||||||
\(440\) | −1800.00 | −0.195026 | ||||||||
\(441\) | 4482.00 | 0.483965 | ||||||||
\(442\) | −726.000 | −0.0781274 | ||||||||
\(443\) | −15263.0 | −1.63695 | −0.818473 | − | 0.574545i | \(-0.805179\pi\) | ||||
−0.818473 | + | 0.574545i | \(0.805179\pi\) | |||||||
\(444\) | 432.000 | 0.0461753 | ||||||||
\(445\) | 7625.00 | 0.812269 | ||||||||
\(446\) | −5598.00 | −0.594334 | ||||||||
\(447\) | −9138.00 | −0.966918 | ||||||||
\(448\) | 12992.0 | 1.37012 | ||||||||
\(449\) | 11019.0 | 1.15817 | 0.579085 | − | 0.815267i | \(-0.303410\pi\) | ||||
0.579085 | + | 0.815267i | \(0.303410\pi\) | |||||||
\(450\) | −450.000 | −0.0471405 | ||||||||
\(451\) | 2550.00 | 0.266241 | ||||||||
\(452\) | −1252.00 | −0.130286 | ||||||||
\(453\) | −4728.00 | −0.490377 | ||||||||
\(454\) | −2984.00 | −0.308471 | ||||||||
\(455\) | 435.000 | 0.0448200 | ||||||||
\(456\) | 2880.00 | 0.295764 | ||||||||
\(457\) | −6769.00 | −0.692868 | −0.346434 | − | 0.938074i | \(-0.612607\pi\) | ||||
−0.346434 | + | 0.938074i | \(0.612607\pi\) | |||||||
\(458\) | −9244.00 | −0.943109 | ||||||||
\(459\) | −3267.00 | −0.332223 | ||||||||
\(460\) | 2320.00 | 0.235153 | ||||||||
\(461\) | −5514.00 | −0.557077 | −0.278539 | − | 0.960425i | \(-0.589850\pi\) | ||||
−0.278539 | + | 0.960425i | \(0.589850\pi\) | |||||||
\(462\) | −2610.00 | −0.262832 | ||||||||
\(463\) | −14205.0 | −1.42584 | −0.712918 | − | 0.701247i | \(-0.752627\pi\) | ||||
−0.712918 | + | 0.701247i | \(0.752627\pi\) | |||||||
\(464\) | −464.000 | −0.0464238 | ||||||||
\(465\) | 1740.00 | 0.173528 | ||||||||
\(466\) | −8340.00 | −0.829062 | ||||||||
\(467\) | −9660.00 | −0.957198 | −0.478599 | − | 0.878034i | \(-0.658855\pi\) | ||||
−0.478599 | + | 0.878034i | \(0.658855\pi\) | |||||||
\(468\) | −108.000 | −0.0106673 | ||||||||
\(469\) | −7801.00 | −0.768053 | ||||||||
\(470\) | −2310.00 | −0.226707 | ||||||||
\(471\) | 10632.0 | 1.04012 | ||||||||
\(472\) | 13824.0 | 1.34810 | ||||||||
\(473\) | −3450.00 | −0.335372 | ||||||||
\(474\) | −2088.00 | −0.202331 | ||||||||
\(475\) | −1000.00 | −0.0965961 | ||||||||
\(476\) | −14036.0 | −1.35155 | ||||||||
\(477\) | 4104.00 | 0.393940 | ||||||||
\(478\) | −3372.00 | −0.322660 | ||||||||
\(479\) | −7656.00 | −0.730296 | −0.365148 | − | 0.930950i | \(-0.618982\pi\) | ||||
−0.365148 | + | 0.930950i | \(0.618982\pi\) | |||||||
\(480\) | 2400.00 | 0.228218 | ||||||||
\(481\) | 108.000 | 0.0102378 | ||||||||
\(482\) | 7850.00 | 0.741821 | ||||||||
\(483\) | 10092.0 | 0.950729 | ||||||||
\(484\) | 4424.00 | 0.415477 | ||||||||
\(485\) | −2800.00 | −0.262147 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | −15968.0 | −1.48579 | −0.742894 | − | 0.669409i | \(-0.766548\pi\) | ||||
−0.742894 | + | 0.669409i | \(0.766548\pi\) | |||||||
\(488\) | 8208.00 | 0.761391 | ||||||||
\(489\) | 2304.00 | 0.213068 | ||||||||
\(490\) | −4980.00 | −0.459130 | ||||||||
\(491\) | 4236.00 | 0.389344 | 0.194672 | − | 0.980868i | \(-0.437636\pi\) | ||||
0.194672 | + | 0.980868i | \(0.437636\pi\) | |||||||
\(492\) | −2040.00 | −0.186932 | ||||||||
\(493\) | 3509.00 | 0.320563 | ||||||||
\(494\) | 240.000 | 0.0218585 | ||||||||
\(495\) | −675.000 | −0.0612909 | ||||||||
\(496\) | 1856.00 | 0.168018 | ||||||||
\(497\) | 8758.00 | 0.790443 | ||||||||
\(498\) | −3072.00 | −0.276425 | ||||||||
\(499\) | −16941.0 | −1.51981 | −0.759903 | − | 0.650036i | \(-0.774754\pi\) | ||||
−0.759903 | + | 0.650036i | \(0.774754\pi\) | |||||||
\(500\) | −500.000 | −0.0447214 | ||||||||
\(501\) | 4872.00 | 0.434461 | ||||||||
\(502\) | 11550.0 | 1.02690 | ||||||||
\(503\) | −1857.00 | −0.164611 | −0.0823057 | − | 0.996607i | \(-0.526228\pi\) | ||||
−0.0823057 | + | 0.996607i | \(0.526228\pi\) | |||||||
\(504\) | 6264.00 | 0.553613 | ||||||||
\(505\) | 7235.00 | 0.637531 | ||||||||
\(506\) | −3480.00 | −0.305741 | ||||||||
\(507\) | 6564.00 | 0.574985 | ||||||||
\(508\) | 1976.00 | 0.172580 | ||||||||
\(509\) | −3096.00 | −0.269603 | −0.134801 | − | 0.990873i | \(-0.543040\pi\) | ||||
−0.134801 | + | 0.990873i | \(0.543040\pi\) | |||||||
\(510\) | 3630.00 | 0.315175 | ||||||||
\(511\) | −10788.0 | −0.933920 | ||||||||
\(512\) | 5632.00 | 0.486136 | ||||||||
\(513\) | 1080.00 | 0.0929496 | ||||||||
\(514\) | 6292.00 | 0.539938 | ||||||||
\(515\) | 2780.00 | 0.237867 | ||||||||
\(516\) | 2760.00 | 0.235469 | ||||||||
\(517\) | −3465.00 | −0.294759 | ||||||||
\(518\) | −2088.00 | −0.177107 | ||||||||
\(519\) | −5100.00 | −0.431339 | ||||||||
\(520\) | 360.000 | 0.0303597 | ||||||||
\(521\) | 7530.00 | 0.633196 | 0.316598 | − | 0.948560i | \(-0.397459\pi\) | ||||
0.316598 | + | 0.948560i | \(0.397459\pi\) | |||||||
\(522\) | −522.000 | −0.0437688 | ||||||||
\(523\) | −5767.00 | −0.482167 | −0.241083 | − | 0.970504i | \(-0.577503\pi\) | ||||
−0.241083 | + | 0.970504i | \(0.577503\pi\) | |||||||
\(524\) | 8028.00 | 0.669284 | ||||||||
\(525\) | −2175.00 | −0.180809 | ||||||||
\(526\) | 11536.0 | 0.956261 | ||||||||
\(527\) | −14036.0 | −1.16019 | ||||||||
\(528\) | −720.000 | −0.0593447 | ||||||||
\(529\) | 1289.00 | 0.105942 | ||||||||
\(530\) | −4560.00 | −0.373724 | ||||||||
\(531\) | 5184.00 | 0.423666 | ||||||||
\(532\) | 4640.00 | 0.378138 | ||||||||
\(533\) | −510.000 | −0.0414457 | ||||||||
\(534\) | 9150.00 | 0.741497 | ||||||||
\(535\) | 7790.00 | 0.629516 | ||||||||
\(536\) | −6456.00 | −0.520255 | ||||||||
\(537\) | −11610.0 | −0.932977 | ||||||||
\(538\) | 14682.0 | 1.17655 | ||||||||
\(539\) | −7470.00 | −0.596949 | ||||||||
\(540\) | 540.000 | 0.0430331 | ||||||||
\(541\) | −21122.0 | −1.67857 | −0.839284 | − | 0.543693i | \(-0.817026\pi\) | ||||
−0.839284 | + | 0.543693i | \(0.817026\pi\) | |||||||
\(542\) | 28.0000 | 0.00221901 | ||||||||
\(543\) | −5271.00 | −0.416575 | ||||||||
\(544\) | −19360.0 | −1.52583 | ||||||||
\(545\) | −4405.00 | −0.346219 | ||||||||
\(546\) | 522.000 | 0.0409149 | ||||||||
\(547\) | 17857.0 | 1.39581 | 0.697907 | − | 0.716188i | \(-0.254115\pi\) | ||||
0.697907 | + | 0.716188i | \(0.254115\pi\) | |||||||
\(548\) | −3672.00 | −0.286241 | ||||||||
\(549\) | 3078.00 | 0.239282 | ||||||||
\(550\) | 750.000 | 0.0581456 | ||||||||
\(551\) | −1160.00 | −0.0896872 | ||||||||
\(552\) | 8352.00 | 0.643994 | ||||||||
\(553\) | −10092.0 | −0.776050 | ||||||||
\(554\) | −7442.00 | −0.570723 | ||||||||
\(555\) | −540.000 | −0.0413004 | ||||||||
\(556\) | −6476.00 | −0.493963 | ||||||||
\(557\) | 6040.00 | 0.459467 | 0.229733 | − | 0.973254i | \(-0.426215\pi\) | ||||
0.229733 | + | 0.973254i | \(0.426215\pi\) | |||||||
\(558\) | 2088.00 | 0.158409 | ||||||||
\(559\) | 690.000 | 0.0522073 | ||||||||
\(560\) | −2320.00 | −0.175068 | ||||||||
\(561\) | 5445.00 | 0.409783 | ||||||||
\(562\) | −1848.00 | −0.138707 | ||||||||
\(563\) | −15371.0 | −1.15064 | −0.575320 | − | 0.817928i | \(-0.695123\pi\) | ||||
−0.575320 | + | 0.817928i | \(0.695123\pi\) | |||||||
\(564\) | 2772.00 | 0.206954 | ||||||||
\(565\) | 1565.00 | 0.116531 | ||||||||
\(566\) | −3880.00 | −0.288142 | ||||||||
\(567\) | 2349.00 | 0.173984 | ||||||||
\(568\) | 7248.00 | 0.535421 | ||||||||
\(569\) | 17901.0 | 1.31889 | 0.659445 | − | 0.751752i | \(-0.270791\pi\) | ||||
0.659445 | + | 0.751752i | \(0.270791\pi\) | |||||||
\(570\) | −1200.00 | −0.0881798 | ||||||||
\(571\) | −10056.0 | −0.737006 | −0.368503 | − | 0.929627i | \(-0.620130\pi\) | ||||
−0.368503 | + | 0.929627i | \(0.620130\pi\) | |||||||
\(572\) | 180.000 | 0.0131577 | ||||||||
\(573\) | 6144.00 | 0.447939 | ||||||||
\(574\) | 9860.00 | 0.716983 | ||||||||
\(575\) | −2900.00 | −0.210328 | ||||||||
\(576\) | 4032.00 | 0.291667 | ||||||||
\(577\) | 3068.00 | 0.221356 | 0.110678 | − | 0.993856i | \(-0.464698\pi\) | ||||
0.110678 | + | 0.993856i | \(0.464698\pi\) | |||||||
\(578\) | −19456.0 | −1.40011 | ||||||||
\(579\) | 7194.00 | 0.516360 | ||||||||
\(580\) | −580.000 | −0.0415227 | ||||||||
\(581\) | −14848.0 | −1.06024 | ||||||||
\(582\) | −3360.00 | −0.239307 | ||||||||
\(583\) | −6840.00 | −0.485907 | ||||||||
\(584\) | −8928.00 | −0.632608 | ||||||||
\(585\) | 135.000 | 0.00954113 | ||||||||
\(586\) | −10534.0 | −0.742586 | ||||||||
\(587\) | −2984.00 | −0.209817 | −0.104909 | − | 0.994482i | \(-0.533455\pi\) | ||||
−0.104909 | + | 0.994482i | \(0.533455\pi\) | |||||||
\(588\) | 5976.00 | 0.419126 | ||||||||
\(589\) | 4640.00 | 0.324597 | ||||||||
\(590\) | −5760.00 | −0.401924 | ||||||||
\(591\) | −11898.0 | −0.828119 | ||||||||
\(592\) | −576.000 | −0.0399889 | ||||||||
\(593\) | 5952.00 | 0.412174 | 0.206087 | − | 0.978534i | \(-0.433927\pi\) | ||||
0.206087 | + | 0.978534i | \(0.433927\pi\) | |||||||
\(594\) | −810.000 | −0.0559507 | ||||||||
\(595\) | 17545.0 | 1.20887 | ||||||||
\(596\) | −12184.0 | −0.837376 | ||||||||
\(597\) | −1923.00 | −0.131831 | ||||||||
\(598\) | 696.000 | 0.0475946 | ||||||||
\(599\) | −12999.0 | −0.886686 | −0.443343 | − | 0.896352i | \(-0.646208\pi\) | ||||
−0.443343 | + | 0.896352i | \(0.646208\pi\) | |||||||
\(600\) | −1800.00 | −0.122474 | ||||||||
\(601\) | 23398.0 | 1.58806 | 0.794030 | − | 0.607878i | \(-0.207979\pi\) | ||||
0.794030 | + | 0.607878i | \(0.207979\pi\) | |||||||
\(602\) | −13340.0 | −0.903153 | ||||||||
\(603\) | −2421.00 | −0.163500 | ||||||||
\(604\) | −6304.00 | −0.424679 | ||||||||
\(605\) | −5530.00 | −0.371614 | ||||||||
\(606\) | 8682.00 | 0.581984 | ||||||||
\(607\) | 26116.0 | 1.74632 | 0.873160 | − | 0.487434i | \(-0.162067\pi\) | ||||
0.873160 | + | 0.487434i | \(0.162067\pi\) | |||||||
\(608\) | 6400.00 | 0.426898 | ||||||||
\(609\) | −2523.00 | −0.167877 | ||||||||
\(610\) | −3420.00 | −0.227003 | ||||||||
\(611\) | 693.000 | 0.0458851 | ||||||||
\(612\) | −4356.00 | −0.287714 | ||||||||
\(613\) | −24185.0 | −1.59351 | −0.796756 | − | 0.604301i | \(-0.793452\pi\) | ||||
−0.796756 | + | 0.604301i | \(0.793452\pi\) | |||||||
\(614\) | −13712.0 | −0.901256 | ||||||||
\(615\) | 2550.00 | 0.167197 | ||||||||
\(616\) | −10440.0 | −0.682856 | ||||||||
\(617\) | 2214.00 | 0.144461 | 0.0722304 | − | 0.997388i | \(-0.476988\pi\) | ||||
0.0722304 | + | 0.997388i | \(0.476988\pi\) | |||||||
\(618\) | 3336.00 | 0.217142 | ||||||||
\(619\) | −19586.0 | −1.27177 | −0.635887 | − | 0.771782i | \(-0.719365\pi\) | ||||
−0.635887 | + | 0.771782i | \(0.719365\pi\) | |||||||
\(620\) | 2320.00 | 0.150280 | ||||||||
\(621\) | 3132.00 | 0.202388 | ||||||||
\(622\) | 4894.00 | 0.315485 | ||||||||
\(623\) | 44225.0 | 2.84404 | ||||||||
\(624\) | 144.000 | 0.00923816 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −1022.00 | −0.0652513 | ||||||||
\(627\) | −1800.00 | −0.114649 | ||||||||
\(628\) | 14176.0 | 0.900771 | ||||||||
\(629\) | 4356.00 | 0.276129 | ||||||||
\(630\) | −2610.00 | −0.165055 | ||||||||
\(631\) | 4377.00 | 0.276142 | 0.138071 | − | 0.990422i | \(-0.455910\pi\) | ||||
0.138071 | + | 0.990422i | \(0.455910\pi\) | |||||||
\(632\) | −8352.00 | −0.525672 | ||||||||
\(633\) | −16314.0 | −1.02437 | ||||||||
\(634\) | −14334.0 | −0.897911 | ||||||||
\(635\) | −2470.00 | −0.154361 | ||||||||
\(636\) | 5472.00 | 0.341162 | ||||||||
\(637\) | 1494.00 | 0.0929269 | ||||||||
\(638\) | 870.000 | 0.0539869 | ||||||||
\(639\) | 2718.00 | 0.168267 | ||||||||
\(640\) | 1920.00 | 0.118585 | ||||||||
\(641\) | −24015.0 | −1.47977 | −0.739887 | − | 0.672731i | \(-0.765121\pi\) | ||||
−0.739887 | + | 0.672731i | \(0.765121\pi\) | |||||||
\(642\) | 9348.00 | 0.574667 | ||||||||
\(643\) | −19465.0 | −1.19382 | −0.596909 | − | 0.802309i | \(-0.703605\pi\) | ||||
−0.596909 | + | 0.802309i | \(0.703605\pi\) | |||||||
\(644\) | 13456.0 | 0.823355 | ||||||||
\(645\) | −3450.00 | −0.210610 | ||||||||
\(646\) | 9680.00 | 0.589558 | ||||||||
\(647\) | −19954.0 | −1.21248 | −0.606239 | − | 0.795283i | \(-0.707322\pi\) | ||||
−0.606239 | + | 0.795283i | \(0.707322\pi\) | |||||||
\(648\) | 1944.00 | 0.117851 | ||||||||
\(649\) | −8640.00 | −0.522573 | ||||||||
\(650\) | −150.000 | −0.00905151 | ||||||||
\(651\) | 10092.0 | 0.607583 | ||||||||
\(652\) | 3072.00 | 0.184523 | ||||||||
\(653\) | −22597.0 | −1.35419 | −0.677097 | − | 0.735894i | \(-0.736762\pi\) | ||||
−0.677097 | + | 0.735894i | \(0.736762\pi\) | |||||||
\(654\) | −5286.00 | −0.316053 | ||||||||
\(655\) | −10035.0 | −0.598626 | ||||||||
\(656\) | 2720.00 | 0.161887 | ||||||||
\(657\) | −3348.00 | −0.198810 | ||||||||
\(658\) | −13398.0 | −0.793782 | ||||||||
\(659\) | 7467.00 | 0.441385 | 0.220693 | − | 0.975343i | \(-0.429168\pi\) | ||||
0.220693 | + | 0.975343i | \(0.429168\pi\) | |||||||
\(660\) | −900.000 | −0.0530795 | ||||||||
\(661\) | 16601.0 | 0.976859 | 0.488430 | − | 0.872603i | \(-0.337570\pi\) | ||||
0.488430 | + | 0.872603i | \(0.337570\pi\) | |||||||
\(662\) | 17924.0 | 1.05232 | ||||||||
\(663\) | −1089.00 | −0.0637907 | ||||||||
\(664\) | −12288.0 | −0.718173 | ||||||||
\(665\) | −5800.00 | −0.338217 | ||||||||
\(666\) | −648.000 | −0.0377019 | ||||||||
\(667\) | −3364.00 | −0.195284 | ||||||||
\(668\) | 6496.00 | 0.376254 | ||||||||
\(669\) | −8397.00 | −0.485272 | ||||||||
\(670\) | 2690.00 | 0.155110 | ||||||||
\(671\) | −5130.00 | −0.295144 | ||||||||
\(672\) | 13920.0 | 0.799071 | ||||||||
\(673\) | 23571.0 | 1.35007 | 0.675034 | − | 0.737787i | \(-0.264129\pi\) | ||||
0.675034 | + | 0.737787i | \(0.264129\pi\) | |||||||
\(674\) | −5412.00 | −0.309291 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | 8752.00 | 0.497952 | ||||||||
\(677\) | −16963.0 | −0.962985 | −0.481493 | − | 0.876450i | \(-0.659905\pi\) | ||||
−0.481493 | + | 0.876450i | \(0.659905\pi\) | |||||||
\(678\) | 1878.00 | 0.106378 | ||||||||
\(679\) | −16240.0 | −0.917870 | ||||||||
\(680\) | 14520.0 | 0.818848 | ||||||||
\(681\) | −4476.00 | −0.251866 | ||||||||
\(682\) | −3480.00 | −0.195390 | ||||||||
\(683\) | 6144.00 | 0.344207 | 0.172104 | − | 0.985079i | \(-0.444944\pi\) | ||||
0.172104 | + | 0.985079i | \(0.444944\pi\) | |||||||
\(684\) | 1440.00 | 0.0804967 | ||||||||
\(685\) | 4590.00 | 0.256022 | ||||||||
\(686\) | −8990.00 | −0.500350 | ||||||||
\(687\) | −13866.0 | −0.770045 | ||||||||
\(688\) | −3680.00 | −0.203923 | ||||||||
\(689\) | 1368.00 | 0.0756410 | ||||||||
\(690\) | −3480.00 | −0.192002 | ||||||||
\(691\) | 18461.0 | 1.01634 | 0.508169 | − | 0.861257i | \(-0.330323\pi\) | ||||
0.508169 | + | 0.861257i | \(0.330323\pi\) | |||||||
\(692\) | −6800.00 | −0.373551 | ||||||||
\(693\) | −3915.00 | −0.214601 | ||||||||
\(694\) | −4464.00 | −0.244166 | ||||||||
\(695\) | 8095.00 | 0.441814 | ||||||||
\(696\) | −2088.00 | −0.113715 | ||||||||
\(697\) | −20570.0 | −1.11785 | ||||||||
\(698\) | −19484.0 | −1.05656 | ||||||||
\(699\) | −12510.0 | −0.676927 | ||||||||
\(700\) | −2900.00 | −0.156585 | ||||||||
\(701\) | −7550.00 | −0.406790 | −0.203395 | − | 0.979097i | \(-0.565198\pi\) | ||||
−0.203395 | + | 0.979097i | \(0.565198\pi\) | |||||||
\(702\) | 162.000 | 0.00870982 | ||||||||
\(703\) | −1440.00 | −0.0772555 | ||||||||
\(704\) | −6720.00 | −0.359758 | ||||||||
\(705\) | −3465.00 | −0.185106 | ||||||||
\(706\) | 5388.00 | 0.287224 | ||||||||
\(707\) | 41963.0 | 2.23222 | ||||||||
\(708\) | 6912.00 | 0.366905 | ||||||||
\(709\) | 29126.0 | 1.54281 | 0.771403 | − | 0.636347i | \(-0.219555\pi\) | ||||
0.771403 | + | 0.636347i | \(0.219555\pi\) | |||||||
\(710\) | −3020.00 | −0.159632 | ||||||||
\(711\) | −3132.00 | −0.165203 | ||||||||
\(712\) | 36600.0 | 1.92646 | ||||||||
\(713\) | 13456.0 | 0.706776 | ||||||||
\(714\) | 21054.0 | 1.10354 | ||||||||
\(715\) | −225.000 | −0.0117686 | ||||||||
\(716\) | −15480.0 | −0.807982 | ||||||||
\(717\) | −5058.00 | −0.263451 | ||||||||
\(718\) | 1920.00 | 0.0997963 | ||||||||
\(719\) | −31670.0 | −1.64269 | −0.821343 | − | 0.570434i | \(-0.806775\pi\) | ||||
−0.821343 | + | 0.570434i | \(0.806775\pi\) | |||||||
\(720\) | −720.000 | −0.0372678 | ||||||||
\(721\) | 16124.0 | 0.832856 | ||||||||
\(722\) | 10518.0 | 0.542160 | ||||||||
\(723\) | 11775.0 | 0.605694 | ||||||||
\(724\) | −7028.00 | −0.360765 | ||||||||
\(725\) | 725.000 | 0.0371391 | ||||||||
\(726\) | −6636.00 | −0.339236 | ||||||||
\(727\) | 21080.0 | 1.07540 | 0.537699 | − | 0.843137i | \(-0.319294\pi\) | ||||
0.537699 | + | 0.843137i | \(0.319294\pi\) | |||||||
\(728\) | 2088.00 | 0.106300 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 3720.00 | 0.188607 | ||||||||
\(731\) | 27830.0 | 1.40811 | ||||||||
\(732\) | 4104.00 | 0.207224 | ||||||||
\(733\) | −31730.0 | −1.59887 | −0.799437 | − | 0.600750i | \(-0.794869\pi\) | ||||
−0.799437 | + | 0.600750i | \(0.794869\pi\) | |||||||
\(734\) | 9264.00 | 0.465859 | ||||||||
\(735\) | −7470.00 | −0.374878 | ||||||||
\(736\) | 18560.0 | 0.929525 | ||||||||
\(737\) | 4035.00 | 0.201670 | ||||||||
\(738\) | 3060.00 | 0.152629 | ||||||||
\(739\) | −35010.0 | −1.74271 | −0.871356 | − | 0.490652i | \(-0.836759\pi\) | ||||
−0.871356 | + | 0.490652i | \(0.836759\pi\) | |||||||
\(740\) | −720.000 | −0.0357672 | ||||||||
\(741\) | 360.000 | 0.0178474 | ||||||||
\(742\) | −26448.0 | −1.30854 | ||||||||
\(743\) | −36625.0 | −1.80840 | −0.904200 | − | 0.427110i | \(-0.859532\pi\) | ||||
−0.904200 | + | 0.427110i | \(0.859532\pi\) | |||||||
\(744\) | 8352.00 | 0.411558 | ||||||||
\(745\) | 15230.0 | 0.748972 | ||||||||
\(746\) | 13364.0 | 0.655886 | ||||||||
\(747\) | −4608.00 | −0.225700 | ||||||||
\(748\) | 7260.00 | 0.354882 | ||||||||
\(749\) | 45182.0 | 2.20416 | ||||||||
\(750\) | 750.000 | 0.0365148 | ||||||||
\(751\) | 8420.00 | 0.409121 | 0.204561 | − | 0.978854i | \(-0.434423\pi\) | ||||
0.204561 | + | 0.978854i | \(0.434423\pi\) | |||||||
\(752\) | −3696.00 | −0.179228 | ||||||||
\(753\) | 17325.0 | 0.838457 | ||||||||
\(754\) | −174.000 | −0.00840412 | ||||||||
\(755\) | 7880.00 | 0.379844 | ||||||||
\(756\) | 3132.00 | 0.150674 | ||||||||
\(757\) | −14404.0 | −0.691575 | −0.345788 | − | 0.938313i | \(-0.612388\pi\) | ||||
−0.345788 | + | 0.938313i | \(0.612388\pi\) | |||||||
\(758\) | −22540.0 | −1.08007 | ||||||||
\(759\) | −5220.00 | −0.249636 | ||||||||
\(760\) | −4800.00 | −0.229098 | ||||||||
\(761\) | 7208.00 | 0.343351 | 0.171675 | − | 0.985154i | \(-0.445082\pi\) | ||||
0.171675 | + | 0.985154i | \(0.445082\pi\) | |||||||
\(762\) | −2964.00 | −0.140911 | ||||||||
\(763\) | −25549.0 | −1.21224 | ||||||||
\(764\) | 8192.00 | 0.387927 | ||||||||
\(765\) | 5445.00 | 0.257339 | ||||||||
\(766\) | −2032.00 | −0.0958474 | ||||||||
\(767\) | 1728.00 | 0.0813487 | ||||||||
\(768\) | 13056.0 | 0.613435 | ||||||||
\(769\) | −31638.0 | −1.48361 | −0.741805 | − | 0.670616i | \(-0.766030\pi\) | ||||
−0.741805 | + | 0.670616i | \(0.766030\pi\) | |||||||
\(770\) | 4350.00 | 0.203588 | ||||||||
\(771\) | 9438.00 | 0.440858 | ||||||||
\(772\) | 9592.00 | 0.447181 | ||||||||
\(773\) | −930.000 | −0.0432727 | −0.0216363 | − | 0.999766i | \(-0.506888\pi\) | ||||
−0.0216363 | + | 0.999766i | \(0.506888\pi\) | |||||||
\(774\) | −4140.00 | −0.192260 | ||||||||
\(775\) | −2900.00 | −0.134414 | ||||||||
\(776\) | −13440.0 | −0.621737 | ||||||||
\(777\) | −3132.00 | −0.144607 | ||||||||
\(778\) | 7454.00 | 0.343495 | ||||||||
\(779\) | 6800.00 | 0.312754 | ||||||||
\(780\) | 180.000 | 0.00826286 | ||||||||
\(781\) | −4530.00 | −0.207549 | ||||||||
\(782\) | 28072.0 | 1.28370 | ||||||||
\(783\) | −783.000 | −0.0357371 | ||||||||
\(784\) | −7968.00 | −0.362974 | ||||||||
\(785\) | −17720.0 | −0.805674 | ||||||||
\(786\) | −12042.0 | −0.546468 | ||||||||
\(787\) | 7188.00 | 0.325571 | 0.162786 | − | 0.986661i | \(-0.447952\pi\) | ||||
0.162786 | + | 0.986661i | \(0.447952\pi\) | |||||||
\(788\) | −15864.0 | −0.717172 | ||||||||
\(789\) | 17304.0 | 0.780784 | ||||||||
\(790\) | 3480.00 | 0.156725 | ||||||||
\(791\) | 9077.00 | 0.408016 | ||||||||
\(792\) | −3240.00 | −0.145364 | ||||||||
\(793\) | 1026.00 | 0.0459449 | ||||||||
\(794\) | −3980.00 | −0.177890 | ||||||||
\(795\) | −6840.00 | −0.305144 | ||||||||
\(796\) | −2564.00 | −0.114169 | ||||||||
\(797\) | −31986.0 | −1.42158 | −0.710792 | − | 0.703402i | \(-0.751663\pi\) | ||||
−0.710792 | + | 0.703402i | \(0.751663\pi\) | |||||||
\(798\) | −6960.00 | −0.308749 | ||||||||
\(799\) | 27951.0 | 1.23759 | ||||||||
\(800\) | −4000.00 | −0.176777 | ||||||||
\(801\) | 13725.0 | 0.605430 | ||||||||
\(802\) | −13392.0 | −0.589636 | ||||||||
\(803\) | 5580.00 | 0.245223 | ||||||||
\(804\) | −3228.00 | −0.141596 | ||||||||
\(805\) | −16820.0 | −0.736431 | ||||||||
\(806\) | 696.000 | 0.0304163 | ||||||||
\(807\) | 22023.0 | 0.960652 | ||||||||
\(808\) | 34728.0 | 1.51204 | ||||||||
\(809\) | 8235.00 | 0.357883 | 0.178941 | − | 0.983860i | \(-0.442733\pi\) | ||||
0.178941 | + | 0.983860i | \(0.442733\pi\) | |||||||
\(810\) | −810.000 | −0.0351364 | ||||||||
\(811\) | −9031.00 | −0.391025 | −0.195513 | − | 0.980701i | \(-0.562637\pi\) | ||||
−0.195513 | + | 0.980701i | \(0.562637\pi\) | |||||||
\(812\) | −3364.00 | −0.145386 | ||||||||
\(813\) | 42.0000 | 0.00181181 | ||||||||
\(814\) | 1080.00 | 0.0465037 | ||||||||
\(815\) | −3840.00 | −0.165042 | ||||||||
\(816\) | 5808.00 | 0.249167 | ||||||||
\(817\) | −9200.00 | −0.393962 | ||||||||
\(818\) | −504.000 | −0.0215427 | ||||||||
\(819\) | 783.000 | 0.0334069 | ||||||||
\(820\) | 3400.00 | 0.144797 | ||||||||
\(821\) | 41318.0 | 1.75640 | 0.878202 | − | 0.478289i | \(-0.158743\pi\) | ||||
0.878202 | + | 0.478289i | \(0.158743\pi\) | |||||||
\(822\) | 5508.00 | 0.233715 | ||||||||
\(823\) | 31150.0 | 1.31934 | 0.659672 | − | 0.751553i | \(-0.270695\pi\) | ||||
0.659672 | + | 0.751553i | \(0.270695\pi\) | |||||||
\(824\) | 13344.0 | 0.564151 | ||||||||
\(825\) | 1125.00 | 0.0474757 | ||||||||
\(826\) | −33408.0 | −1.40728 | ||||||||
\(827\) | 7584.00 | 0.318889 | 0.159445 | − | 0.987207i | \(-0.449030\pi\) | ||||
0.159445 | + | 0.987207i | \(0.449030\pi\) | |||||||
\(828\) | 4176.00 | 0.175273 | ||||||||
\(829\) | −28316.0 | −1.18632 | −0.593158 | − | 0.805086i | \(-0.702119\pi\) | ||||
−0.593158 | + | 0.805086i | \(0.702119\pi\) | |||||||
\(830\) | 5120.00 | 0.214118 | ||||||||
\(831\) | −11163.0 | −0.465993 | ||||||||
\(832\) | 1344.00 | 0.0560034 | ||||||||
\(833\) | 60258.0 | 2.50638 | ||||||||
\(834\) | 9714.00 | 0.403319 | ||||||||
\(835\) | −8120.00 | −0.336532 | ||||||||
\(836\) | −2400.00 | −0.0992892 | ||||||||
\(837\) | 3132.00 | 0.129340 | ||||||||
\(838\) | −14836.0 | −0.611577 | ||||||||
\(839\) | −26615.0 | −1.09518 | −0.547588 | − | 0.836748i | \(-0.684454\pi\) | ||||
−0.547588 | + | 0.836748i | \(0.684454\pi\) | |||||||
\(840\) | −10440.0 | −0.428826 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | −22536.0 | −0.922377 | ||||||||
\(843\) | −2772.00 | −0.113254 | ||||||||
\(844\) | −21752.0 | −0.887126 | ||||||||
\(845\) | −10940.0 | −0.445382 | ||||||||
\(846\) | −4158.00 | −0.168978 | ||||||||
\(847\) | −32074.0 | −1.30115 | ||||||||
\(848\) | −7296.00 | −0.295455 | ||||||||
\(849\) | −5820.00 | −0.235267 | ||||||||
\(850\) | −6050.00 | −0.244133 | ||||||||
\(851\) | −4176.00 | −0.168216 | ||||||||
\(852\) | 3624.00 | 0.145723 | ||||||||
\(853\) | 33538.0 | 1.34621 | 0.673106 | − | 0.739546i | \(-0.264960\pi\) | ||||
0.673106 | + | 0.739546i | \(0.264960\pi\) | |||||||
\(854\) | −19836.0 | −0.794817 | ||||||||
\(855\) | −1800.00 | −0.0719985 | ||||||||
\(856\) | 37392.0 | 1.49303 | ||||||||
\(857\) | −26394.0 | −1.05204 | −0.526022 | − | 0.850471i | \(-0.676317\pi\) | ||||
−0.526022 | + | 0.850471i | \(0.676317\pi\) | |||||||
\(858\) | −270.000 | −0.0107432 | ||||||||
\(859\) | −12076.0 | −0.479660 | −0.239830 | − | 0.970815i | \(-0.577092\pi\) | ||||
−0.239830 | + | 0.970815i | \(0.577092\pi\) | |||||||
\(860\) | −4600.00 | −0.182394 | ||||||||
\(861\) | 14790.0 | 0.585414 | ||||||||
\(862\) | 23200.0 | 0.916700 | ||||||||
\(863\) | −2450.00 | −0.0966384 | −0.0483192 | − | 0.998832i | \(-0.515386\pi\) | ||||
−0.0483192 | + | 0.998832i | \(0.515386\pi\) | |||||||
\(864\) | 4320.00 | 0.170103 | ||||||||
\(865\) | 8500.00 | 0.334114 | ||||||||
\(866\) | −2144.00 | −0.0841294 | ||||||||
\(867\) | −29184.0 | −1.14318 | ||||||||
\(868\) | 13456.0 | 0.526182 | ||||||||
\(869\) | 5220.00 | 0.203770 | ||||||||
\(870\) | 870.000 | 0.0339032 | ||||||||
\(871\) | −807.000 | −0.0313940 | ||||||||
\(872\) | −21144.0 | −0.821131 | ||||||||
\(873\) | −5040.00 | −0.195393 | ||||||||
\(874\) | −9280.00 | −0.359154 | ||||||||
\(875\) | 3625.00 | 0.140054 | ||||||||
\(876\) | −4464.00 | −0.172174 | ||||||||
\(877\) | −15566.0 | −0.599346 | −0.299673 | − | 0.954042i | \(-0.596878\pi\) | ||||
−0.299673 | + | 0.954042i | \(0.596878\pi\) | |||||||
\(878\) | 24678.0 | 0.948567 | ||||||||
\(879\) | −15801.0 | −0.606319 | ||||||||
\(880\) | 1200.00 | 0.0459682 | ||||||||
\(881\) | 34497.0 | 1.31922 | 0.659610 | − | 0.751608i | \(-0.270721\pi\) | ||||
0.659610 | + | 0.751608i | \(0.270721\pi\) | |||||||
\(882\) | −8964.00 | −0.342215 | ||||||||
\(883\) | 17044.0 | 0.649577 | 0.324788 | − | 0.945787i | \(-0.394707\pi\) | ||||
0.324788 | + | 0.945787i | \(0.394707\pi\) | |||||||
\(884\) | −1452.00 | −0.0552444 | ||||||||
\(885\) | −8640.00 | −0.328170 | ||||||||
\(886\) | 30526.0 | 1.15750 | ||||||||
\(887\) | −16903.0 | −0.639850 | −0.319925 | − | 0.947443i | \(-0.603658\pi\) | ||||
−0.319925 | + | 0.947443i | \(0.603658\pi\) | |||||||
\(888\) | −2592.00 | −0.0979525 | ||||||||
\(889\) | −14326.0 | −0.540471 | ||||||||
\(890\) | −15250.0 | −0.574361 | ||||||||
\(891\) | −1215.00 | −0.0456835 | ||||||||
\(892\) | −11196.0 | −0.420258 | ||||||||
\(893\) | −9240.00 | −0.346254 | ||||||||
\(894\) | 18276.0 | 0.683715 | ||||||||
\(895\) | 19350.0 | 0.722681 | ||||||||
\(896\) | 11136.0 | 0.415209 | ||||||||
\(897\) | 1044.00 | 0.0388608 | ||||||||
\(898\) | −22038.0 | −0.818951 | ||||||||
\(899\) | −3364.00 | −0.124801 | ||||||||
\(900\) | −900.000 | −0.0333333 | ||||||||
\(901\) | 55176.0 | 2.04015 | ||||||||
\(902\) | −5100.00 | −0.188261 | ||||||||
\(903\) | −20010.0 | −0.737421 | ||||||||
\(904\) | 7512.00 | 0.276378 | ||||||||
\(905\) | 8785.00 | 0.322678 | ||||||||
\(906\) | 9456.00 | 0.346749 | ||||||||
\(907\) | 40504.0 | 1.48282 | 0.741408 | − | 0.671055i | \(-0.234159\pi\) | ||||
0.741408 | + | 0.671055i | \(0.234159\pi\) | |||||||
\(908\) | −5968.00 | −0.218122 | ||||||||
\(909\) | 13023.0 | 0.475188 | ||||||||
\(910\) | −870.000 | −0.0316925 | ||||||||
\(911\) | −14783.0 | −0.537632 | −0.268816 | − | 0.963192i | \(-0.586632\pi\) | ||||
−0.268816 | + | 0.963192i | \(0.586632\pi\) | |||||||
\(912\) | −1920.00 | −0.0697122 | ||||||||
\(913\) | 7680.00 | 0.278391 | ||||||||
\(914\) | 13538.0 | 0.489931 | ||||||||
\(915\) | −5130.00 | −0.185347 | ||||||||
\(916\) | −18488.0 | −0.666879 | ||||||||
\(917\) | −58203.0 | −2.09600 | ||||||||
\(918\) | 6534.00 | 0.234917 | ||||||||
\(919\) | 42241.0 | 1.51622 | 0.758108 | − | 0.652129i | \(-0.226124\pi\) | ||||
0.758108 | + | 0.652129i | \(0.226124\pi\) | |||||||
\(920\) | −13920.0 | −0.498836 | ||||||||
\(921\) | −20568.0 | −0.735873 | ||||||||
\(922\) | 11028.0 | 0.393913 | ||||||||
\(923\) | 906.000 | 0.0323092 | ||||||||
\(924\) | −5220.00 | −0.185850 | ||||||||
\(925\) | 900.000 | 0.0319912 | ||||||||
\(926\) | 28410.0 | 1.00822 | ||||||||
\(927\) | 5004.00 | 0.177295 | ||||||||
\(928\) | −4640.00 | −0.164133 | ||||||||
\(929\) | 28686.0 | 1.01309 | 0.506543 | − | 0.862215i | \(-0.330923\pi\) | ||||
0.506543 | + | 0.862215i | \(0.330923\pi\) | |||||||
\(930\) | −3480.00 | −0.122703 | ||||||||
\(931\) | −19920.0 | −0.701237 | ||||||||
\(932\) | −16680.0 | −0.586236 | ||||||||
\(933\) | 7341.00 | 0.257592 | ||||||||
\(934\) | 19320.0 | 0.676841 | ||||||||
\(935\) | −9075.00 | −0.317416 | ||||||||
\(936\) | 648.000 | 0.0226288 | ||||||||
\(937\) | −53063.0 | −1.85005 | −0.925023 | − | 0.379912i | \(-0.875954\pi\) | ||||
−0.925023 | + | 0.379912i | \(0.875954\pi\) | |||||||
\(938\) | 15602.0 | 0.543095 | ||||||||
\(939\) | −1533.00 | −0.0532775 | ||||||||
\(940\) | −4620.00 | −0.160306 | ||||||||
\(941\) | −16542.0 | −0.573065 | −0.286532 | − | 0.958071i | \(-0.592503\pi\) | ||||
−0.286532 | + | 0.958071i | \(0.592503\pi\) | |||||||
\(942\) | −21264.0 | −0.735476 | ||||||||
\(943\) | 19720.0 | 0.680988 | ||||||||
\(944\) | −9216.00 | −0.317749 | ||||||||
\(945\) | −3915.00 | −0.134767 | ||||||||
\(946\) | 6900.00 | 0.237144 | ||||||||
\(947\) | 30839.0 | 1.05822 | 0.529109 | − | 0.848554i | \(-0.322526\pi\) | ||||
0.529109 | + | 0.848554i | \(0.322526\pi\) | |||||||
\(948\) | −4176.00 | −0.143070 | ||||||||
\(949\) | −1116.00 | −0.0381738 | ||||||||
\(950\) | 2000.00 | 0.0683038 | ||||||||
\(951\) | −21501.0 | −0.733142 | ||||||||
\(952\) | 84216.0 | 2.86708 | ||||||||
\(953\) | 46314.0 | 1.57425 | 0.787124 | − | 0.616795i | \(-0.211569\pi\) | ||||
0.787124 | + | 0.616795i | \(0.211569\pi\) | |||||||
\(954\) | −8208.00 | −0.278557 | ||||||||
\(955\) | −10240.0 | −0.346972 | ||||||||
\(956\) | −6744.00 | −0.228155 | ||||||||
\(957\) | 1305.00 | 0.0440801 | ||||||||
\(958\) | 15312.0 | 0.516397 | ||||||||
\(959\) | 26622.0 | 0.896423 | ||||||||
\(960\) | −6720.00 | −0.225924 | ||||||||
\(961\) | −16335.0 | −0.548320 | ||||||||
\(962\) | −216.000 | −0.00723921 | ||||||||
\(963\) | 14022.0 | 0.469214 | ||||||||
\(964\) | 15700.0 | 0.524547 | ||||||||
\(965\) | −11990.0 | −0.399971 | ||||||||
\(966\) | −20184.0 | −0.672267 | ||||||||
\(967\) | −12904.0 | −0.429126 | −0.214563 | − | 0.976710i | \(-0.568833\pi\) | ||||
−0.214563 | + | 0.976710i | \(0.568833\pi\) | |||||||
\(968\) | −26544.0 | −0.881360 | ||||||||
\(969\) | 14520.0 | 0.481372 | ||||||||
\(970\) | 5600.00 | 0.185366 | ||||||||
\(971\) | −900.000 | −0.0297450 | −0.0148725 | − | 0.999889i | \(-0.504734\pi\) | ||||
−0.0148725 | + | 0.999889i | \(0.504734\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 46951.0 | 1.54695 | ||||||||
\(974\) | 31936.0 | 1.05061 | ||||||||
\(975\) | −225.000 | −0.00739053 | ||||||||
\(976\) | −5472.00 | −0.179462 | ||||||||
\(977\) | −20376.0 | −0.667232 | −0.333616 | − | 0.942709i | \(-0.608269\pi\) | ||||
−0.333616 | + | 0.942709i | \(0.608269\pi\) | |||||||
\(978\) | −4608.00 | −0.150662 | ||||||||
\(979\) | −22875.0 | −0.746770 | ||||||||
\(980\) | −9960.00 | −0.324654 | ||||||||
\(981\) | −7929.00 | −0.258057 | ||||||||
\(982\) | −8472.00 | −0.275308 | ||||||||
\(983\) | 13456.0 | 0.436602 | 0.218301 | − | 0.975881i | \(-0.429949\pi\) | ||||
0.218301 | + | 0.975881i | \(0.429949\pi\) | |||||||
\(984\) | 12240.0 | 0.396542 | ||||||||
\(985\) | 19830.0 | 0.641458 | ||||||||
\(986\) | −7018.00 | −0.226672 | ||||||||
\(987\) | −20097.0 | −0.648120 | ||||||||
\(988\) | 480.000 | 0.0154563 | ||||||||
\(989\) | −26680.0 | −0.857811 | ||||||||
\(990\) | 1350.00 | 0.0433392 | ||||||||
\(991\) | −27245.0 | −0.873326 | −0.436663 | − | 0.899625i | \(-0.643840\pi\) | ||||
−0.436663 | + | 0.899625i | \(0.643840\pi\) | |||||||
\(992\) | 18560.0 | 0.594033 | ||||||||
\(993\) | 26886.0 | 0.859216 | ||||||||
\(994\) | −17516.0 | −0.558927 | ||||||||
\(995\) | 3205.00 | 0.102116 | ||||||||
\(996\) | −6144.00 | −0.195462 | ||||||||
\(997\) | −1552.00 | −0.0493002 | −0.0246501 | − | 0.999696i | \(-0.507847\pi\) | ||||
−0.0246501 | + | 0.999696i | \(0.507847\pi\) | |||||||
\(998\) | 33882.0 | 1.07467 | ||||||||
\(999\) | −972.000 | −0.0307835 |
(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.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 1305.4.a.d.1.1 | 1 | |||
5.4 | even | 2 | 2175.4.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.4.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
1305.4.a.d.1.1 | 1 | 3.2 | odd | 2 | |||
2175.4.a.c.1.1 | 1 | 5.4 | even | 2 |