Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,4,Mod(1,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, 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("1950.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.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: | \(115.053724511\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1950.1 |
$q$-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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | −8.00000 | −0.431959 | −0.215980 | − | 0.976398i | \(-0.569295\pi\) | ||||
−0.215980 | + | 0.976398i | \(0.569295\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.0000 | 0.328921 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 16.0000 | 0.305441 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 42.0000 | 0.599206 | 0.299603 | − | 0.954064i | \(-0.403146\pi\) | ||||
0.299603 | + | 0.954064i | \(0.403146\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | −52.0000 | −0.627875 | −0.313937 | − | 0.949444i | \(-0.601648\pi\) | ||||
−0.313937 | + | 0.949444i | \(0.601648\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −24.0000 | −0.249392 | ||||||||
\(22\) | −24.0000 | −0.232583 | ||||||||
\(23\) | −132.000 | −1.19669 | −0.598346 | − | 0.801238i | \(-0.704175\pi\) | ||||
−0.598346 | + | 0.801238i | \(0.704175\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 26.0000 | 0.196116 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −32.0000 | −0.215980 | ||||||||
\(29\) | 282.000 | 1.80573 | 0.902864 | − | 0.429927i | \(-0.141461\pi\) | ||||
0.902864 | + | 0.429927i | \(0.141461\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 116.000 | 0.672071 | 0.336036 | − | 0.941849i | \(-0.390914\pi\) | ||||
0.336036 | + | 0.941849i | \(0.390914\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 36.0000 | 0.189903 | ||||||||
\(34\) | −84.0000 | −0.423702 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −398.000 | −1.76840 | −0.884200 | − | 0.467109i | \(-0.845296\pi\) | ||||
−0.884200 | + | 0.467109i | \(0.845296\pi\) | |||||||
\(38\) | 104.000 | 0.443974 | ||||||||
\(39\) | −39.0000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 174.000 | 0.662786 | 0.331393 | − | 0.943493i | \(-0.392481\pi\) | ||||
0.331393 | + | 0.943493i | \(0.392481\pi\) | |||||||
\(42\) | 48.0000 | 0.176347 | ||||||||
\(43\) | 76.0000 | 0.269532 | 0.134766 | − | 0.990877i | \(-0.456972\pi\) | ||||
0.134766 | + | 0.990877i | \(0.456972\pi\) | |||||||
\(44\) | 48.0000 | 0.164461 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 264.000 | 0.846189 | ||||||||
\(47\) | −456.000 | −1.41520 | −0.707600 | − | 0.706613i | \(-0.750222\pi\) | ||||
−0.707600 | + | 0.706613i | \(0.750222\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | −279.000 | −0.813411 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 126.000 | 0.345952 | ||||||||
\(52\) | −52.0000 | −0.138675 | ||||||||
\(53\) | −150.000 | −0.388756 | −0.194378 | − | 0.980927i | \(-0.562269\pi\) | ||||
−0.194378 | + | 0.980927i | \(0.562269\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 64.0000 | 0.152721 | ||||||||
\(57\) | −156.000 | −0.362504 | ||||||||
\(58\) | −564.000 | −1.27684 | ||||||||
\(59\) | −156.000 | −0.344228 | −0.172114 | − | 0.985077i | \(-0.555060\pi\) | ||||
−0.172114 | + | 0.985077i | \(0.555060\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 230.000 | 0.482762 | 0.241381 | − | 0.970430i | \(-0.422400\pi\) | ||||
0.241381 | + | 0.970430i | \(0.422400\pi\) | |||||||
\(62\) | −232.000 | −0.475226 | ||||||||
\(63\) | −72.0000 | −0.143986 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −72.0000 | −0.134282 | ||||||||
\(67\) | 592.000 | 1.07947 | 0.539734 | − | 0.841836i | \(-0.318525\pi\) | ||||
0.539734 | + | 0.841836i | \(0.318525\pi\) | |||||||
\(68\) | 168.000 | 0.299603 | ||||||||
\(69\) | −396.000 | −0.690910 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 408.000 | 0.681982 | 0.340991 | − | 0.940067i | \(-0.389238\pi\) | ||||
0.340991 | + | 0.940067i | \(0.389238\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | 730.000 | 1.17041 | 0.585206 | − | 0.810885i | \(-0.301014\pi\) | ||||
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 796.000 | 1.25045 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −208.000 | −0.313937 | ||||||||
\(77\) | −96.0000 | −0.142081 | ||||||||
\(78\) | 78.0000 | 0.113228 | ||||||||
\(79\) | 728.000 | 1.03679 | 0.518395 | − | 0.855141i | \(-0.326530\pi\) | ||||
0.518395 | + | 0.855141i | \(0.326530\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −348.000 | −0.468661 | ||||||||
\(83\) | −36.0000 | −0.0476086 | −0.0238043 | − | 0.999717i | \(-0.507578\pi\) | ||||
−0.0238043 | + | 0.999717i | \(0.507578\pi\) | |||||||
\(84\) | −96.0000 | −0.124696 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −152.000 | −0.190588 | ||||||||
\(87\) | 846.000 | 1.04254 | ||||||||
\(88\) | −96.0000 | −0.116291 | ||||||||
\(89\) | −1482.00 | −1.76508 | −0.882538 | − | 0.470242i | \(-0.844167\pi\) | ||||
−0.882538 | + | 0.470242i | \(0.844167\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 104.000 | 0.119804 | ||||||||
\(92\) | −528.000 | −0.598346 | ||||||||
\(93\) | 348.000 | 0.388021 | ||||||||
\(94\) | 912.000 | 1.00070 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | −1742.00 | −1.82344 | −0.911718 | − | 0.410816i | \(-0.865244\pi\) | ||||
−0.911718 | + | 0.410816i | \(0.865244\pi\) | |||||||
\(98\) | 558.000 | 0.575168 | ||||||||
\(99\) | 108.000 | 0.109640 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −534.000 | −0.526089 | −0.263044 | − | 0.964784i | \(-0.584727\pi\) | ||||
−0.263044 | + | 0.964784i | \(0.584727\pi\) | |||||||
\(102\) | −252.000 | −0.244625 | ||||||||
\(103\) | −248.000 | −0.237244 | −0.118622 | − | 0.992939i | \(-0.537848\pi\) | ||||
−0.118622 | + | 0.992939i | \(0.537848\pi\) | |||||||
\(104\) | 104.000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 300.000 | 0.274892 | ||||||||
\(107\) | −1044.00 | −0.943246 | −0.471623 | − | 0.881800i | \(-0.656332\pi\) | ||||
−0.471623 | + | 0.881800i | \(0.656332\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | −1342.00 | −1.17927 | −0.589634 | − | 0.807670i | \(-0.700728\pi\) | ||||
−0.589634 | + | 0.807670i | \(0.700728\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1194.00 | −1.02099 | ||||||||
\(112\) | −128.000 | −0.107990 | ||||||||
\(113\) | 186.000 | 0.154844 | 0.0774222 | − | 0.996998i | \(-0.475331\pi\) | ||||
0.0774222 | + | 0.996998i | \(0.475331\pi\) | |||||||
\(114\) | 312.000 | 0.256329 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1128.00 | 0.902864 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 312.000 | 0.243406 | ||||||||
\(119\) | −336.000 | −0.258833 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | −460.000 | −0.341364 | ||||||||
\(123\) | 522.000 | 0.382660 | ||||||||
\(124\) | 464.000 | 0.336036 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 144.000 | 0.101814 | ||||||||
\(127\) | 1096.00 | 0.765782 | 0.382891 | − | 0.923794i | \(-0.374929\pi\) | ||||
0.382891 | + | 0.923794i | \(0.374929\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 228.000 | 0.155615 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1200.00 | −0.800340 | −0.400170 | − | 0.916441i | \(-0.631049\pi\) | ||||
−0.400170 | + | 0.916441i | \(0.631049\pi\) | |||||||
\(132\) | 144.000 | 0.0949514 | ||||||||
\(133\) | 416.000 | 0.271216 | ||||||||
\(134\) | −1184.00 | −0.763299 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −336.000 | −0.211851 | ||||||||
\(137\) | −534.000 | −0.333012 | −0.166506 | − | 0.986040i | \(-0.553249\pi\) | ||||
−0.166506 | + | 0.986040i | \(0.553249\pi\) | |||||||
\(138\) | 792.000 | 0.488547 | ||||||||
\(139\) | −1756.00 | −1.07153 | −0.535763 | − | 0.844369i | \(-0.679976\pi\) | ||||
−0.535763 | + | 0.844369i | \(0.679976\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1368.00 | −0.817067 | ||||||||
\(142\) | −816.000 | −0.482234 | ||||||||
\(143\) | −156.000 | −0.0912264 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1460.00 | −0.827606 | ||||||||
\(147\) | −837.000 | −0.469623 | ||||||||
\(148\) | −1592.00 | −0.884200 | ||||||||
\(149\) | 690.000 | 0.379376 | 0.189688 | − | 0.981844i | \(-0.439252\pi\) | ||||
0.189688 | + | 0.981844i | \(0.439252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 308.000 | 0.165991 | 0.0829956 | − | 0.996550i | \(-0.473551\pi\) | ||||
0.0829956 | + | 0.996550i | \(0.473551\pi\) | |||||||
\(152\) | 416.000 | 0.221987 | ||||||||
\(153\) | 378.000 | 0.199735 | ||||||||
\(154\) | 192.000 | 0.100466 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −156.000 | −0.0800641 | ||||||||
\(157\) | 490.000 | 0.249084 | 0.124542 | − | 0.992214i | \(-0.460254\pi\) | ||||
0.124542 | + | 0.992214i | \(0.460254\pi\) | |||||||
\(158\) | −1456.00 | −0.733121 | ||||||||
\(159\) | −450.000 | −0.224449 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1056.00 | 0.516922 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | 952.000 | 0.457463 | 0.228731 | − | 0.973490i | \(-0.426542\pi\) | ||||
0.228731 | + | 0.973490i | \(0.426542\pi\) | |||||||
\(164\) | 696.000 | 0.331393 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 72.0000 | 0.0336644 | ||||||||
\(167\) | −3480.00 | −1.61252 | −0.806259 | − | 0.591563i | \(-0.798511\pi\) | ||||
−0.806259 | + | 0.591563i | \(0.798511\pi\) | |||||||
\(168\) | 192.000 | 0.0881733 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −468.000 | −0.209292 | ||||||||
\(172\) | 304.000 | 0.134766 | ||||||||
\(173\) | 1530.00 | 0.672392 | 0.336196 | − | 0.941792i | \(-0.390860\pi\) | ||||
0.336196 | + | 0.941792i | \(0.390860\pi\) | |||||||
\(174\) | −1692.00 | −0.737185 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 192.000 | 0.0822304 | ||||||||
\(177\) | −468.000 | −0.198740 | ||||||||
\(178\) | 2964.00 | 1.24810 | ||||||||
\(179\) | 2280.00 | 0.952040 | 0.476020 | − | 0.879434i | \(-0.342079\pi\) | ||||
0.476020 | + | 0.879434i | \(0.342079\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2554.00 | −1.04882 | −0.524412 | − | 0.851464i | \(-0.675715\pi\) | ||||
−0.524412 | + | 0.851464i | \(0.675715\pi\) | |||||||
\(182\) | −208.000 | −0.0847142 | ||||||||
\(183\) | 690.000 | 0.278723 | ||||||||
\(184\) | 1056.00 | 0.423094 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −696.000 | −0.274372 | ||||||||
\(187\) | 504.000 | 0.197092 | ||||||||
\(188\) | −1824.00 | −0.707600 | ||||||||
\(189\) | −216.000 | −0.0831306 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 360.000 | 0.136381 | 0.0681903 | − | 0.997672i | \(-0.478278\pi\) | ||||
0.0681903 | + | 0.997672i | \(0.478278\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | 2242.00 | 0.836180 | 0.418090 | − | 0.908406i | \(-0.362700\pi\) | ||||
0.418090 | + | 0.908406i | \(0.362700\pi\) | |||||||
\(194\) | 3484.00 | 1.28936 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1116.00 | −0.406706 | ||||||||
\(197\) | 318.000 | 0.115008 | 0.0575040 | − | 0.998345i | \(-0.481686\pi\) | ||||
0.0575040 | + | 0.998345i | \(0.481686\pi\) | |||||||
\(198\) | −216.000 | −0.0775275 | ||||||||
\(199\) | 4376.00 | 1.55883 | 0.779413 | − | 0.626510i | \(-0.215517\pi\) | ||||
0.779413 | + | 0.626510i | \(0.215517\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1776.00 | 0.623231 | ||||||||
\(202\) | 1068.00 | 0.372001 | ||||||||
\(203\) | −2256.00 | −0.780001 | ||||||||
\(204\) | 504.000 | 0.172976 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 496.000 | 0.167757 | ||||||||
\(207\) | −1188.00 | −0.398897 | ||||||||
\(208\) | −208.000 | −0.0693375 | ||||||||
\(209\) | −624.000 | −0.206521 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1532.00 | 0.499845 | 0.249922 | − | 0.968266i | \(-0.419595\pi\) | ||||
0.249922 | + | 0.968266i | \(0.419595\pi\) | |||||||
\(212\) | −600.000 | −0.194378 | ||||||||
\(213\) | 1224.00 | 0.393742 | ||||||||
\(214\) | 2088.00 | 0.666975 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | −928.000 | −0.290308 | ||||||||
\(218\) | 2684.00 | 0.833869 | ||||||||
\(219\) | 2190.00 | 0.675737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −546.000 | −0.166190 | ||||||||
\(222\) | 2388.00 | 0.721946 | ||||||||
\(223\) | 5848.00 | 1.75610 | 0.878052 | − | 0.478566i | \(-0.158843\pi\) | ||||
0.878052 | + | 0.478566i | \(0.158843\pi\) | |||||||
\(224\) | 256.000 | 0.0763604 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −372.000 | −0.109491 | ||||||||
\(227\) | −4884.00 | −1.42803 | −0.714014 | − | 0.700131i | \(-0.753125\pi\) | ||||
−0.714014 | + | 0.700131i | \(0.753125\pi\) | |||||||
\(228\) | −624.000 | −0.181252 | ||||||||
\(229\) | −5254.00 | −1.51613 | −0.758066 | − | 0.652178i | \(-0.773855\pi\) | ||||
−0.758066 | + | 0.652178i | \(0.773855\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −288.000 | −0.0820303 | ||||||||
\(232\) | −2256.00 | −0.638421 | ||||||||
\(233\) | −2358.00 | −0.662994 | −0.331497 | − | 0.943456i | \(-0.607554\pi\) | ||||
−0.331497 | + | 0.943456i | \(0.607554\pi\) | |||||||
\(234\) | 234.000 | 0.0653720 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −624.000 | −0.172114 | ||||||||
\(237\) | 2184.00 | 0.598591 | ||||||||
\(238\) | 672.000 | 0.183022 | ||||||||
\(239\) | −2328.00 | −0.630066 | −0.315033 | − | 0.949081i | \(-0.602016\pi\) | ||||
−0.315033 | + | 0.949081i | \(0.602016\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3670.00 | −0.980936 | −0.490468 | − | 0.871459i | \(-0.663174\pi\) | ||||
−0.490468 | + | 0.871459i | \(0.663174\pi\) | |||||||
\(242\) | 2374.00 | 0.630605 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 920.000 | 0.241381 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1044.00 | −0.270581 | ||||||||
\(247\) | 676.000 | 0.174141 | ||||||||
\(248\) | −928.000 | −0.237613 | ||||||||
\(249\) | −108.000 | −0.0274868 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6312.00 | −1.58729 | −0.793645 | − | 0.608381i | \(-0.791819\pi\) | ||||
−0.793645 | + | 0.608381i | \(0.791819\pi\) | |||||||
\(252\) | −288.000 | −0.0719932 | ||||||||
\(253\) | −1584.00 | −0.393617 | ||||||||
\(254\) | −2192.00 | −0.541489 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −6006.00 | −1.45776 | −0.728879 | − | 0.684642i | \(-0.759958\pi\) | ||||
−0.728879 | + | 0.684642i | \(0.759958\pi\) | |||||||
\(258\) | −456.000 | −0.110036 | ||||||||
\(259\) | 3184.00 | 0.763877 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2538.00 | 0.601909 | ||||||||
\(262\) | 2400.00 | 0.565926 | ||||||||
\(263\) | −5220.00 | −1.22387 | −0.611937 | − | 0.790906i | \(-0.709610\pi\) | ||||
−0.611937 | + | 0.790906i | \(0.709610\pi\) | |||||||
\(264\) | −288.000 | −0.0671408 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −832.000 | −0.191779 | ||||||||
\(267\) | −4446.00 | −1.01907 | ||||||||
\(268\) | 2368.00 | 0.539734 | ||||||||
\(269\) | −126.000 | −0.0285589 | −0.0142795 | − | 0.999898i | \(-0.504545\pi\) | ||||
−0.0142795 | + | 0.999898i | \(0.504545\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3244.00 | −0.727155 | −0.363577 | − | 0.931564i | \(-0.618445\pi\) | ||||
−0.363577 | + | 0.931564i | \(0.618445\pi\) | |||||||
\(272\) | 672.000 | 0.149801 | ||||||||
\(273\) | 312.000 | 0.0691689 | ||||||||
\(274\) | 1068.00 | 0.235475 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1584.00 | −0.345455 | ||||||||
\(277\) | 7666.00 | 1.66284 | 0.831418 | − | 0.555648i | \(-0.187530\pi\) | ||||
0.831418 | + | 0.555648i | \(0.187530\pi\) | |||||||
\(278\) | 3512.00 | 0.757683 | ||||||||
\(279\) | 1044.00 | 0.224024 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1458.00 | −0.309527 | −0.154763 | − | 0.987952i | \(-0.549462\pi\) | ||||
−0.154763 | + | 0.987952i | \(0.549462\pi\) | |||||||
\(282\) | 2736.00 | 0.577753 | ||||||||
\(283\) | −188.000 | −0.0394892 | −0.0197446 | − | 0.999805i | \(-0.506285\pi\) | ||||
−0.0197446 | + | 0.999805i | \(0.506285\pi\) | |||||||
\(284\) | 1632.00 | 0.340991 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 312.000 | 0.0645068 | ||||||||
\(287\) | −1392.00 | −0.286297 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | −3149.00 | −0.640953 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5226.00 | −1.05276 | ||||||||
\(292\) | 2920.00 | 0.585206 | ||||||||
\(293\) | −3738.00 | −0.745312 | −0.372656 | − | 0.927970i | \(-0.621553\pi\) | ||||
−0.372656 | + | 0.927970i | \(0.621553\pi\) | |||||||
\(294\) | 1674.00 | 0.332074 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3184.00 | 0.625224 | ||||||||
\(297\) | 324.000 | 0.0633010 | ||||||||
\(298\) | −1380.00 | −0.268259 | ||||||||
\(299\) | 1716.00 | 0.331902 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −608.000 | −0.116427 | ||||||||
\(302\) | −616.000 | −0.117374 | ||||||||
\(303\) | −1602.00 | −0.303738 | ||||||||
\(304\) | −832.000 | −0.156969 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −756.000 | −0.141234 | ||||||||
\(307\) | −8216.00 | −1.52740 | −0.763700 | − | 0.645571i | \(-0.776619\pi\) | ||||
−0.763700 | + | 0.645571i | \(0.776619\pi\) | |||||||
\(308\) | −384.000 | −0.0710404 | ||||||||
\(309\) | −744.000 | −0.136973 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6288.00 | 1.14649 | 0.573247 | − | 0.819382i | \(-0.305683\pi\) | ||||
0.573247 | + | 0.819382i | \(0.305683\pi\) | |||||||
\(312\) | 312.000 | 0.0566139 | ||||||||
\(313\) | 2446.00 | 0.441713 | 0.220856 | − | 0.975306i | \(-0.429115\pi\) | ||||
0.220856 | + | 0.975306i | \(0.429115\pi\) | |||||||
\(314\) | −980.000 | −0.176129 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2912.00 | 0.518395 | ||||||||
\(317\) | 5430.00 | 0.962079 | 0.481040 | − | 0.876699i | \(-0.340259\pi\) | ||||
0.481040 | + | 0.876699i | \(0.340259\pi\) | |||||||
\(318\) | 900.000 | 0.158709 | ||||||||
\(319\) | 3384.00 | 0.593942 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3132.00 | −0.544583 | ||||||||
\(322\) | −2112.00 | −0.365519 | ||||||||
\(323\) | −2184.00 | −0.376226 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1904.00 | −0.323475 | ||||||||
\(327\) | −4026.00 | −0.680851 | ||||||||
\(328\) | −1392.00 | −0.234330 | ||||||||
\(329\) | 3648.00 | 0.611309 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1628.00 | 0.270341 | 0.135171 | − | 0.990822i | \(-0.456842\pi\) | ||||
0.135171 | + | 0.990822i | \(0.456842\pi\) | |||||||
\(332\) | −144.000 | −0.0238043 | ||||||||
\(333\) | −3582.00 | −0.589467 | ||||||||
\(334\) | 6960.00 | 1.14022 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −384.000 | −0.0623480 | ||||||||
\(337\) | −5546.00 | −0.896468 | −0.448234 | − | 0.893916i | \(-0.647947\pi\) | ||||
−0.448234 | + | 0.893916i | \(0.647947\pi\) | |||||||
\(338\) | −338.000 | −0.0543928 | ||||||||
\(339\) | 558.000 | 0.0893994 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1392.00 | 0.221059 | ||||||||
\(342\) | 936.000 | 0.147991 | ||||||||
\(343\) | 4976.00 | 0.783320 | ||||||||
\(344\) | −608.000 | −0.0952941 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3060.00 | −0.475453 | ||||||||
\(347\) | −2772.00 | −0.428844 | −0.214422 | − | 0.976741i | \(-0.568787\pi\) | ||||
−0.214422 | + | 0.976741i | \(0.568787\pi\) | |||||||
\(348\) | 3384.00 | 0.521269 | ||||||||
\(349\) | 10538.0 | 1.61629 | 0.808146 | − | 0.588982i | \(-0.200471\pi\) | ||||
0.808146 | + | 0.588982i | \(0.200471\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −351.000 | −0.0533761 | ||||||||
\(352\) | −384.000 | −0.0581456 | ||||||||
\(353\) | −942.000 | −0.142033 | −0.0710164 | − | 0.997475i | \(-0.522624\pi\) | ||||
−0.0710164 | + | 0.997475i | \(0.522624\pi\) | |||||||
\(354\) | 936.000 | 0.140531 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5928.00 | −0.882538 | ||||||||
\(357\) | −1008.00 | −0.149437 | ||||||||
\(358\) | −4560.00 | −0.673194 | ||||||||
\(359\) | 6000.00 | 0.882083 | 0.441042 | − | 0.897487i | \(-0.354609\pi\) | ||||
0.441042 | + | 0.897487i | \(0.354609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4155.00 | −0.605773 | ||||||||
\(362\) | 5108.00 | 0.741631 | ||||||||
\(363\) | −3561.00 | −0.514887 | ||||||||
\(364\) | 416.000 | 0.0599020 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1380.00 | −0.197087 | ||||||||
\(367\) | −8264.00 | −1.17541 | −0.587707 | − | 0.809073i | \(-0.699969\pi\) | ||||
−0.587707 | + | 0.809073i | \(0.699969\pi\) | |||||||
\(368\) | −2112.00 | −0.299173 | ||||||||
\(369\) | 1566.00 | 0.220929 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1200.00 | 0.167927 | ||||||||
\(372\) | 1392.00 | 0.194010 | ||||||||
\(373\) | −2654.00 | −0.368415 | −0.184208 | − | 0.982887i | \(-0.558972\pi\) | ||||
−0.184208 | + | 0.982887i | \(0.558972\pi\) | |||||||
\(374\) | −1008.00 | −0.139365 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3648.00 | 0.500349 | ||||||||
\(377\) | −3666.00 | −0.500819 | ||||||||
\(378\) | 432.000 | 0.0587822 | ||||||||
\(379\) | −3076.00 | −0.416896 | −0.208448 | − | 0.978033i | \(-0.566841\pi\) | ||||
−0.208448 | + | 0.978033i | \(0.566841\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3288.00 | 0.442124 | ||||||||
\(382\) | −720.000 | −0.0964356 | ||||||||
\(383\) | −12864.0 | −1.71624 | −0.858120 | − | 0.513450i | \(-0.828367\pi\) | ||||
−0.858120 | + | 0.513450i | \(0.828367\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4484.00 | −0.591268 | ||||||||
\(387\) | 684.000 | 0.0898441 | ||||||||
\(388\) | −6968.00 | −0.911718 | ||||||||
\(389\) | −10974.0 | −1.43034 | −0.715172 | − | 0.698948i | \(-0.753652\pi\) | ||||
−0.715172 | + | 0.698948i | \(0.753652\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5544.00 | −0.717064 | ||||||||
\(392\) | 2232.00 | 0.287584 | ||||||||
\(393\) | −3600.00 | −0.462076 | ||||||||
\(394\) | −636.000 | −0.0813229 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 432.000 | 0.0548202 | ||||||||
\(397\) | −8582.00 | −1.08493 | −0.542466 | − | 0.840078i | \(-0.682509\pi\) | ||||
−0.542466 | + | 0.840078i | \(0.682509\pi\) | |||||||
\(398\) | −8752.00 | −1.10226 | ||||||||
\(399\) | 1248.00 | 0.156587 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2142.00 | 0.266749 | 0.133375 | − | 0.991066i | \(-0.457419\pi\) | ||||
0.133375 | + | 0.991066i | \(0.457419\pi\) | |||||||
\(402\) | −3552.00 | −0.440691 | ||||||||
\(403\) | −1508.00 | −0.186399 | ||||||||
\(404\) | −2136.00 | −0.263044 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4512.00 | 0.551544 | ||||||||
\(407\) | −4776.00 | −0.581665 | ||||||||
\(408\) | −1008.00 | −0.122312 | ||||||||
\(409\) | 6122.00 | 0.740131 | 0.370065 | − | 0.929006i | \(-0.379335\pi\) | ||||
0.370065 | + | 0.929006i | \(0.379335\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1602.00 | −0.192265 | ||||||||
\(412\) | −992.000 | −0.118622 | ||||||||
\(413\) | 1248.00 | 0.148693 | ||||||||
\(414\) | 2376.00 | 0.282063 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 416.000 | 0.0490290 | ||||||||
\(417\) | −5268.00 | −0.618645 | ||||||||
\(418\) | 1248.00 | 0.146033 | ||||||||
\(419\) | −13056.0 | −1.52226 | −0.761130 | − | 0.648599i | \(-0.775355\pi\) | ||||
−0.761130 | + | 0.648599i | \(0.775355\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7582.00 | −0.877729 | −0.438865 | − | 0.898553i | \(-0.644619\pi\) | ||||
−0.438865 | + | 0.898553i | \(0.644619\pi\) | |||||||
\(422\) | −3064.00 | −0.353444 | ||||||||
\(423\) | −4104.00 | −0.471734 | ||||||||
\(424\) | 1200.00 | 0.137446 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2448.00 | −0.278418 | ||||||||
\(427\) | −1840.00 | −0.208534 | ||||||||
\(428\) | −4176.00 | −0.471623 | ||||||||
\(429\) | −468.000 | −0.0526696 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3888.00 | −0.434521 | −0.217260 | − | 0.976114i | \(-0.569712\pi\) | ||||
−0.217260 | + | 0.976114i | \(0.569712\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | 2710.00 | 0.300772 | 0.150386 | − | 0.988627i | \(-0.451948\pi\) | ||||
0.150386 | + | 0.988627i | \(0.451948\pi\) | |||||||
\(434\) | 1856.00 | 0.205278 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5368.00 | −0.589634 | ||||||||
\(437\) | 6864.00 | 0.751372 | ||||||||
\(438\) | −4380.00 | −0.477818 | ||||||||
\(439\) | 6008.00 | 0.653180 | 0.326590 | − | 0.945166i | \(-0.394100\pi\) | ||||
0.326590 | + | 0.945166i | \(0.394100\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2511.00 | −0.271137 | ||||||||
\(442\) | 1092.00 | 0.117514 | ||||||||
\(443\) | −13884.0 | −1.48905 | −0.744525 | − | 0.667595i | \(-0.767324\pi\) | ||||
−0.744525 | + | 0.667595i | \(0.767324\pi\) | |||||||
\(444\) | −4776.00 | −0.510493 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11696.0 | −1.24175 | ||||||||
\(447\) | 2070.00 | 0.219033 | ||||||||
\(448\) | −512.000 | −0.0539949 | ||||||||
\(449\) | −8706.00 | −0.915059 | −0.457530 | − | 0.889194i | \(-0.651266\pi\) | ||||
−0.457530 | + | 0.889194i | \(0.651266\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2088.00 | 0.218005 | ||||||||
\(452\) | 744.000 | 0.0774222 | ||||||||
\(453\) | 924.000 | 0.0958351 | ||||||||
\(454\) | 9768.00 | 1.00977 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1248.00 | 0.128164 | ||||||||
\(457\) | −5078.00 | −0.519779 | −0.259889 | − | 0.965638i | \(-0.583686\pi\) | ||||
−0.259889 | + | 0.965638i | \(0.583686\pi\) | |||||||
\(458\) | 10508.0 | 1.07207 | ||||||||
\(459\) | 1134.00 | 0.115317 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14934.0 | −1.50878 | −0.754388 | − | 0.656429i | \(-0.772066\pi\) | ||||
−0.754388 | + | 0.656429i | \(0.772066\pi\) | |||||||
\(462\) | 576.000 | 0.0580042 | ||||||||
\(463\) | 3448.00 | 0.346095 | 0.173048 | − | 0.984913i | \(-0.444639\pi\) | ||||
0.173048 | + | 0.984913i | \(0.444639\pi\) | |||||||
\(464\) | 4512.00 | 0.451432 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4716.00 | 0.468808 | ||||||||
\(467\) | 10332.0 | 1.02379 | 0.511893 | − | 0.859049i | \(-0.328944\pi\) | ||||
0.511893 | + | 0.859049i | \(0.328944\pi\) | |||||||
\(468\) | −468.000 | −0.0462250 | ||||||||
\(469\) | −4736.00 | −0.466286 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1470.00 | 0.143809 | ||||||||
\(472\) | 1248.00 | 0.121703 | ||||||||
\(473\) | 912.000 | 0.0886550 | ||||||||
\(474\) | −4368.00 | −0.423268 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1344.00 | −0.129416 | ||||||||
\(477\) | −1350.00 | −0.129585 | ||||||||
\(478\) | 4656.00 | 0.445524 | ||||||||
\(479\) | −2328.00 | −0.222065 | −0.111032 | − | 0.993817i | \(-0.535416\pi\) | ||||
−0.111032 | + | 0.993817i | \(0.535416\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5174.00 | 0.490466 | ||||||||
\(482\) | 7340.00 | 0.693626 | ||||||||
\(483\) | 3168.00 | 0.298445 | ||||||||
\(484\) | −4748.00 | −0.445905 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | −13160.0 | −1.22451 | −0.612255 | − | 0.790660i | \(-0.709737\pi\) | ||||
−0.612255 | + | 0.790660i | \(0.709737\pi\) | |||||||
\(488\) | −1840.00 | −0.170682 | ||||||||
\(489\) | 2856.00 | 0.264116 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8688.00 | 0.798542 | 0.399271 | − | 0.916833i | \(-0.369263\pi\) | ||||
0.399271 | + | 0.916833i | \(0.369263\pi\) | |||||||
\(492\) | 2088.00 | 0.191330 | ||||||||
\(493\) | 11844.0 | 1.08200 | ||||||||
\(494\) | −1352.00 | −0.123136 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1856.00 | 0.168018 | ||||||||
\(497\) | −3264.00 | −0.294588 | ||||||||
\(498\) | 216.000 | 0.0194361 | ||||||||
\(499\) | −15460.0 | −1.38694 | −0.693472 | − | 0.720484i | \(-0.743920\pi\) | ||||
−0.693472 | + | 0.720484i | \(0.743920\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10440.0 | −0.930988 | ||||||||
\(502\) | 12624.0 | 1.12238 | ||||||||
\(503\) | 7116.00 | 0.630789 | 0.315394 | − | 0.948961i | \(-0.397863\pi\) | ||||
0.315394 | + | 0.948961i | \(0.397863\pi\) | |||||||
\(504\) | 576.000 | 0.0509069 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3168.00 | 0.278330 | ||||||||
\(507\) | 507.000 | 0.0444116 | ||||||||
\(508\) | 4384.00 | 0.382891 | ||||||||
\(509\) | −14694.0 | −1.27957 | −0.639784 | − | 0.768555i | \(-0.720976\pi\) | ||||
−0.639784 | + | 0.768555i | \(0.720976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5840.00 | −0.505570 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −1404.00 | −0.120835 | ||||||||
\(514\) | 12012.0 | 1.03079 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 912.000 | 0.0778073 | ||||||||
\(517\) | −5472.00 | −0.465490 | ||||||||
\(518\) | −6368.00 | −0.540143 | ||||||||
\(519\) | 4590.00 | 0.388205 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13782.0 | −1.15893 | −0.579463 | − | 0.814999i | \(-0.696738\pi\) | ||||
−0.579463 | + | 0.814999i | \(0.696738\pi\) | |||||||
\(522\) | −5076.00 | −0.425614 | ||||||||
\(523\) | 5596.00 | 0.467870 | 0.233935 | − | 0.972252i | \(-0.424840\pi\) | ||||
0.233935 | + | 0.972252i | \(0.424840\pi\) | |||||||
\(524\) | −4800.00 | −0.400170 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10440.0 | 0.865410 | ||||||||
\(527\) | 4872.00 | 0.402709 | ||||||||
\(528\) | 576.000 | 0.0474757 | ||||||||
\(529\) | 5257.00 | 0.432070 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1404.00 | −0.114743 | ||||||||
\(532\) | 1664.00 | 0.135608 | ||||||||
\(533\) | −2262.00 | −0.183824 | ||||||||
\(534\) | 8892.00 | 0.720589 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4736.00 | −0.381649 | ||||||||
\(537\) | 6840.00 | 0.549661 | ||||||||
\(538\) | 252.000 | 0.0201942 | ||||||||
\(539\) | −3348.00 | −0.267548 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7322.00 | 0.581881 | 0.290940 | − | 0.956741i | \(-0.406032\pi\) | ||||
0.290940 | + | 0.956741i | \(0.406032\pi\) | |||||||
\(542\) | 6488.00 | 0.514176 | ||||||||
\(543\) | −7662.00 | −0.605539 | ||||||||
\(544\) | −1344.00 | −0.105926 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −624.000 | −0.0489098 | ||||||||
\(547\) | 15652.0 | 1.22346 | 0.611729 | − | 0.791068i | \(-0.290474\pi\) | ||||
0.611729 | + | 0.791068i | \(0.290474\pi\) | |||||||
\(548\) | −2136.00 | −0.166506 | ||||||||
\(549\) | 2070.00 | 0.160921 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14664.0 | −1.13377 | ||||||||
\(552\) | 3168.00 | 0.244274 | ||||||||
\(553\) | −5824.00 | −0.447851 | ||||||||
\(554\) | −15332.0 | −1.17580 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7024.00 | −0.535763 | ||||||||
\(557\) | −13458.0 | −1.02376 | −0.511879 | − | 0.859057i | \(-0.671051\pi\) | ||||
−0.511879 | + | 0.859057i | \(0.671051\pi\) | |||||||
\(558\) | −2088.00 | −0.158409 | ||||||||
\(559\) | −988.000 | −0.0747548 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1512.00 | 0.113791 | ||||||||
\(562\) | 2916.00 | 0.218868 | ||||||||
\(563\) | 18108.0 | 1.35553 | 0.677763 | − | 0.735280i | \(-0.262950\pi\) | ||||
0.677763 | + | 0.735280i | \(0.262950\pi\) | |||||||
\(564\) | −5472.00 | −0.408533 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 376.000 | 0.0279231 | ||||||||
\(567\) | −648.000 | −0.0479955 | ||||||||
\(568\) | −3264.00 | −0.241117 | ||||||||
\(569\) | −20118.0 | −1.48223 | −0.741116 | − | 0.671377i | \(-0.765703\pi\) | ||||
−0.741116 | + | 0.671377i | \(0.765703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4156.00 | −0.304594 | −0.152297 | − | 0.988335i | \(-0.548667\pi\) | ||||
−0.152297 | + | 0.988335i | \(0.548667\pi\) | |||||||
\(572\) | −624.000 | −0.0456132 | ||||||||
\(573\) | 1080.00 | 0.0787393 | ||||||||
\(574\) | 2784.00 | 0.202442 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 7378.00 | 0.532323 | 0.266161 | − | 0.963929i | \(-0.414245\pi\) | ||||
0.266161 | + | 0.963929i | \(0.414245\pi\) | |||||||
\(578\) | 6298.00 | 0.453222 | ||||||||
\(579\) | 6726.00 | 0.482769 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 288.000 | 0.0205650 | ||||||||
\(582\) | 10452.0 | 0.744415 | ||||||||
\(583\) | −1800.00 | −0.127870 | ||||||||
\(584\) | −5840.00 | −0.413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7476.00 | 0.527015 | ||||||||
\(587\) | −6372.00 | −0.448042 | −0.224021 | − | 0.974584i | \(-0.571918\pi\) | ||||
−0.224021 | + | 0.974584i | \(0.571918\pi\) | |||||||
\(588\) | −3348.00 | −0.234812 | ||||||||
\(589\) | −6032.00 | −0.421977 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 954.000 | 0.0663999 | ||||||||
\(592\) | −6368.00 | −0.442100 | ||||||||
\(593\) | −2382.00 | −0.164953 | −0.0824764 | − | 0.996593i | \(-0.526283\pi\) | ||||
−0.0824764 | + | 0.996593i | \(0.526283\pi\) | |||||||
\(594\) | −648.000 | −0.0447605 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2760.00 | 0.189688 | ||||||||
\(597\) | 13128.0 | 0.899989 | ||||||||
\(598\) | −3432.00 | −0.234690 | ||||||||
\(599\) | 10536.0 | 0.718680 | 0.359340 | − | 0.933207i | \(-0.383002\pi\) | ||||
0.359340 | + | 0.933207i | \(0.383002\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13610.0 | 0.923733 | 0.461866 | − | 0.886949i | \(-0.347180\pi\) | ||||
0.461866 | + | 0.886949i | \(0.347180\pi\) | |||||||
\(602\) | 1216.00 | 0.0823263 | ||||||||
\(603\) | 5328.00 | 0.359822 | ||||||||
\(604\) | 1232.00 | 0.0829956 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3204.00 | 0.214775 | ||||||||
\(607\) | −13736.0 | −0.918496 | −0.459248 | − | 0.888308i | \(-0.651881\pi\) | ||||
−0.459248 | + | 0.888308i | \(0.651881\pi\) | |||||||
\(608\) | 1664.00 | 0.110994 | ||||||||
\(609\) | −6768.00 | −0.450334 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5928.00 | 0.392506 | ||||||||
\(612\) | 1512.00 | 0.0998676 | ||||||||
\(613\) | 10882.0 | 0.716998 | 0.358499 | − | 0.933530i | \(-0.383289\pi\) | ||||
0.358499 | + | 0.933530i | \(0.383289\pi\) | |||||||
\(614\) | 16432.0 | 1.08004 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 768.000 | 0.0502331 | ||||||||
\(617\) | −4902.00 | −0.319849 | −0.159925 | − | 0.987129i | \(-0.551125\pi\) | ||||
−0.159925 | + | 0.987129i | \(0.551125\pi\) | |||||||
\(618\) | 1488.00 | 0.0968546 | ||||||||
\(619\) | −20692.0 | −1.34359 | −0.671795 | − | 0.740737i | \(-0.734476\pi\) | ||||
−0.671795 | + | 0.740737i | \(0.734476\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3564.00 | −0.230303 | ||||||||
\(622\) | −12576.0 | −0.810694 | ||||||||
\(623\) | 11856.0 | 0.762441 | ||||||||
\(624\) | −624.000 | −0.0400320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4892.00 | −0.312338 | ||||||||
\(627\) | −1872.00 | −0.119235 | ||||||||
\(628\) | 1960.00 | 0.124542 | ||||||||
\(629\) | −16716.0 | −1.05964 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14348.0 | 0.905206 | 0.452603 | − | 0.891712i | \(-0.350496\pi\) | ||||
0.452603 | + | 0.891712i | \(0.350496\pi\) | |||||||
\(632\) | −5824.00 | −0.366561 | ||||||||
\(633\) | 4596.00 | 0.288585 | ||||||||
\(634\) | −10860.0 | −0.680293 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1800.00 | −0.112224 | ||||||||
\(637\) | 3627.00 | 0.225600 | ||||||||
\(638\) | −6768.00 | −0.419981 | ||||||||
\(639\) | 3672.00 | 0.227327 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1182.00 | −0.0728334 | −0.0364167 | − | 0.999337i | \(-0.511594\pi\) | ||||
−0.0364167 | + | 0.999337i | \(0.511594\pi\) | |||||||
\(642\) | 6264.00 | 0.385078 | ||||||||
\(643\) | 26080.0 | 1.59953 | 0.799763 | − | 0.600316i | \(-0.204959\pi\) | ||||
0.799763 | + | 0.600316i | \(0.204959\pi\) | |||||||
\(644\) | 4224.00 | 0.258461 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4368.00 | 0.266032 | ||||||||
\(647\) | 21852.0 | 1.32781 | 0.663903 | − | 0.747819i | \(-0.268899\pi\) | ||||
0.663903 | + | 0.747819i | \(0.268899\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | −1872.00 | −0.113224 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2784.00 | −0.167609 | ||||||||
\(652\) | 3808.00 | 0.228731 | ||||||||
\(653\) | 12018.0 | 0.720215 | 0.360108 | − | 0.932911i | \(-0.382740\pi\) | ||||
0.360108 | + | 0.932911i | \(0.382740\pi\) | |||||||
\(654\) | 8052.00 | 0.481434 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2784.00 | 0.165697 | ||||||||
\(657\) | 6570.00 | 0.390137 | ||||||||
\(658\) | −7296.00 | −0.432261 | ||||||||
\(659\) | 23400.0 | 1.38321 | 0.691604 | − | 0.722277i | \(-0.256904\pi\) | ||||
0.691604 | + | 0.722277i | \(0.256904\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11354.0 | 0.668108 | 0.334054 | − | 0.942554i | \(-0.391583\pi\) | ||||
0.334054 | + | 0.942554i | \(0.391583\pi\) | |||||||
\(662\) | −3256.00 | −0.191160 | ||||||||
\(663\) | −1638.00 | −0.0959497 | ||||||||
\(664\) | 288.000 | 0.0168322 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7164.00 | 0.416816 | ||||||||
\(667\) | −37224.0 | −2.16090 | ||||||||
\(668\) | −13920.0 | −0.806259 | ||||||||
\(669\) | 17544.0 | 1.01389 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2760.00 | 0.158791 | ||||||||
\(672\) | 768.000 | 0.0440867 | ||||||||
\(673\) | 23374.0 | 1.33878 | 0.669392 | − | 0.742909i | \(-0.266555\pi\) | ||||
0.669392 | + | 0.742909i | \(0.266555\pi\) | |||||||
\(674\) | 11092.0 | 0.633899 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 676.000 | 0.0384615 | ||||||||
\(677\) | 22866.0 | 1.29810 | 0.649049 | − | 0.760747i | \(-0.275167\pi\) | ||||
0.649049 | + | 0.760747i | \(0.275167\pi\) | |||||||
\(678\) | −1116.00 | −0.0632149 | ||||||||
\(679\) | 13936.0 | 0.787650 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14652.0 | −0.824473 | ||||||||
\(682\) | −2784.00 | −0.156312 | ||||||||
\(683\) | 13164.0 | 0.737491 | 0.368746 | − | 0.929530i | \(-0.379787\pi\) | ||||
0.368746 | + | 0.929530i | \(0.379787\pi\) | |||||||
\(684\) | −1872.00 | −0.104646 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9952.00 | −0.553891 | ||||||||
\(687\) | −15762.0 | −0.875339 | ||||||||
\(688\) | 1216.00 | 0.0673831 | ||||||||
\(689\) | 1950.00 | 0.107822 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17012.0 | 0.936566 | 0.468283 | − | 0.883579i | \(-0.344873\pi\) | ||||
0.468283 | + | 0.883579i | \(0.344873\pi\) | |||||||
\(692\) | 6120.00 | 0.336196 | ||||||||
\(693\) | −864.000 | −0.0473602 | ||||||||
\(694\) | 5544.00 | 0.303238 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6768.00 | −0.368592 | ||||||||
\(697\) | 7308.00 | 0.397145 | ||||||||
\(698\) | −21076.0 | −1.14289 | ||||||||
\(699\) | −7074.00 | −0.382780 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17910.0 | −0.964981 | −0.482490 | − | 0.875901i | \(-0.660268\pi\) | ||||
−0.482490 | + | 0.875901i | \(0.660268\pi\) | |||||||
\(702\) | 702.000 | 0.0377426 | ||||||||
\(703\) | 20696.0 | 1.11033 | ||||||||
\(704\) | 768.000 | 0.0411152 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1884.00 | 0.100432 | ||||||||
\(707\) | 4272.00 | 0.227249 | ||||||||
\(708\) | −1872.00 | −0.0993702 | ||||||||
\(709\) | −10918.0 | −0.578327 | −0.289164 | − | 0.957280i | \(-0.593377\pi\) | ||||
−0.289164 | + | 0.957280i | \(0.593377\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6552.00 | 0.345597 | ||||||||
\(712\) | 11856.0 | 0.624048 | ||||||||
\(713\) | −15312.0 | −0.804262 | ||||||||
\(714\) | 2016.00 | 0.105668 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9120.00 | 0.476020 | ||||||||
\(717\) | −6984.00 | −0.363769 | ||||||||
\(718\) | −12000.0 | −0.623727 | ||||||||
\(719\) | −26064.0 | −1.35191 | −0.675955 | − | 0.736943i | \(-0.736269\pi\) | ||||
−0.675955 | + | 0.736943i | \(0.736269\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1984.00 | 0.102480 | ||||||||
\(722\) | 8310.00 | 0.428347 | ||||||||
\(723\) | −11010.0 | −0.566343 | ||||||||
\(724\) | −10216.0 | −0.524412 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7122.00 | 0.364080 | ||||||||
\(727\) | −1688.00 | −0.0861134 | −0.0430567 | − | 0.999073i | \(-0.513710\pi\) | ||||
−0.0430567 | + | 0.999073i | \(0.513710\pi\) | |||||||
\(728\) | −832.000 | −0.0423571 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3192.00 | 0.161505 | ||||||||
\(732\) | 2760.00 | 0.139361 | ||||||||
\(733\) | 20626.0 | 1.03934 | 0.519672 | − | 0.854366i | \(-0.326054\pi\) | ||||
0.519672 | + | 0.854366i | \(0.326054\pi\) | |||||||
\(734\) | 16528.0 | 0.831144 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4224.00 | 0.211547 | ||||||||
\(737\) | 7104.00 | 0.355060 | ||||||||
\(738\) | −3132.00 | −0.156220 | ||||||||
\(739\) | 16292.0 | 0.810976 | 0.405488 | − | 0.914100i | \(-0.367102\pi\) | ||||
0.405488 | + | 0.914100i | \(0.367102\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2028.00 | 0.100540 | ||||||||
\(742\) | −2400.00 | −0.118742 | ||||||||
\(743\) | −24048.0 | −1.18740 | −0.593698 | − | 0.804688i | \(-0.702333\pi\) | ||||
−0.593698 | + | 0.804688i | \(0.702333\pi\) | |||||||
\(744\) | −2784.00 | −0.137186 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5308.00 | 0.260509 | ||||||||
\(747\) | −324.000 | −0.0158695 | ||||||||
\(748\) | 2016.00 | 0.0985458 | ||||||||
\(749\) | 8352.00 | 0.407444 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15248.0 | 0.740889 | 0.370444 | − | 0.928855i | \(-0.379205\pi\) | ||||
0.370444 | + | 0.928855i | \(0.379205\pi\) | |||||||
\(752\) | −7296.00 | −0.353800 | ||||||||
\(753\) | −18936.0 | −0.916423 | ||||||||
\(754\) | 7332.00 | 0.354132 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −864.000 | −0.0415653 | ||||||||
\(757\) | −4286.00 | −0.205782 | −0.102891 | − | 0.994693i | \(-0.532809\pi\) | ||||
−0.102891 | + | 0.994693i | \(0.532809\pi\) | |||||||
\(758\) | 6152.00 | 0.294790 | ||||||||
\(759\) | −4752.00 | −0.227255 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21294.0 | 1.01433 | 0.507166 | − | 0.861848i | \(-0.330693\pi\) | ||||
0.507166 | + | 0.861848i | \(0.330693\pi\) | |||||||
\(762\) | −6576.00 | −0.312629 | ||||||||
\(763\) | 10736.0 | 0.509396 | ||||||||
\(764\) | 1440.00 | 0.0681903 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25728.0 | 1.21356 | ||||||||
\(767\) | 2028.00 | 0.0954718 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | −7198.00 | −0.337538 | −0.168769 | − | 0.985656i | \(-0.553979\pi\) | ||||
−0.168769 | + | 0.985656i | \(0.553979\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18018.0 | −0.841637 | ||||||||
\(772\) | 8968.00 | 0.418090 | ||||||||
\(773\) | −11322.0 | −0.526810 | −0.263405 | − | 0.964685i | \(-0.584846\pi\) | ||||
−0.263405 | + | 0.964685i | \(0.584846\pi\) | |||||||
\(774\) | −1368.00 | −0.0635294 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 13936.0 | 0.644682 | ||||||||
\(777\) | 9552.00 | 0.441025 | ||||||||
\(778\) | 21948.0 | 1.01141 | ||||||||
\(779\) | −9048.00 | −0.416147 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4896.00 | 0.224318 | ||||||||
\(782\) | 11088.0 | 0.507041 | ||||||||
\(783\) | 7614.00 | 0.347512 | ||||||||
\(784\) | −4464.00 | −0.203353 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7200.00 | 0.326737 | ||||||||
\(787\) | −13424.0 | −0.608023 | −0.304011 | − | 0.952668i | \(-0.598326\pi\) | ||||
−0.304011 | + | 0.952668i | \(0.598326\pi\) | |||||||
\(788\) | 1272.00 | 0.0575040 | ||||||||
\(789\) | −15660.0 | −0.706604 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1488.00 | −0.0668865 | ||||||||
\(792\) | −864.000 | −0.0387638 | ||||||||
\(793\) | −2990.00 | −0.133894 | ||||||||
\(794\) | 17164.0 | 0.767163 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17504.0 | 0.779413 | ||||||||
\(797\) | 23202.0 | 1.03119 | 0.515594 | − | 0.856833i | \(-0.327571\pi\) | ||||
0.515594 | + | 0.856833i | \(0.327571\pi\) | |||||||
\(798\) | −2496.00 | −0.110724 | ||||||||
\(799\) | −19152.0 | −0.847996 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13338.0 | −0.588358 | ||||||||
\(802\) | −4284.00 | −0.188620 | ||||||||
\(803\) | 8760.00 | 0.384973 | ||||||||
\(804\) | 7104.00 | 0.311615 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3016.00 | 0.131804 | ||||||||
\(807\) | −378.000 | −0.0164885 | ||||||||
\(808\) | 4272.00 | 0.186001 | ||||||||
\(809\) | −38814.0 | −1.68681 | −0.843404 | − | 0.537280i | \(-0.819452\pi\) | ||||
−0.843404 | + | 0.537280i | \(0.819452\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9292.00 | −0.402326 | −0.201163 | − | 0.979558i | \(-0.564472\pi\) | ||||
−0.201163 | + | 0.979558i | \(0.564472\pi\) | |||||||
\(812\) | −9024.00 | −0.390000 | ||||||||
\(813\) | −9732.00 | −0.419823 | ||||||||
\(814\) | 9552.00 | 0.411299 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2016.00 | 0.0864879 | ||||||||
\(817\) | −3952.00 | −0.169233 | ||||||||
\(818\) | −12244.0 | −0.523351 | ||||||||
\(819\) | 936.000 | 0.0399347 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40338.0 | 1.71475 | 0.857373 | − | 0.514696i | \(-0.172095\pi\) | ||||
0.857373 | + | 0.514696i | \(0.172095\pi\) | |||||||
\(822\) | 3204.00 | 0.135952 | ||||||||
\(823\) | 33352.0 | 1.41261 | 0.706305 | − | 0.707908i | \(-0.250361\pi\) | ||||
0.706305 | + | 0.707908i | \(0.250361\pi\) | |||||||
\(824\) | 1984.00 | 0.0838785 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2496.00 | −0.105142 | ||||||||
\(827\) | −35076.0 | −1.47486 | −0.737432 | − | 0.675422i | \(-0.763962\pi\) | ||||
−0.737432 | + | 0.675422i | \(0.763962\pi\) | |||||||
\(828\) | −4752.00 | −0.199449 | ||||||||
\(829\) | 32678.0 | 1.36906 | 0.684532 | − | 0.728983i | \(-0.260007\pi\) | ||||
0.684532 | + | 0.728983i | \(0.260007\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22998.0 | 0.960038 | ||||||||
\(832\) | −832.000 | −0.0346688 | ||||||||
\(833\) | −11718.0 | −0.487401 | ||||||||
\(834\) | 10536.0 | 0.437448 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2496.00 | −0.103261 | ||||||||
\(837\) | 3132.00 | 0.129340 | ||||||||
\(838\) | 26112.0 | 1.07640 | ||||||||
\(839\) | 11424.0 | 0.470084 | 0.235042 | − | 0.971985i | \(-0.424477\pi\) | ||||
0.235042 | + | 0.971985i | \(0.424477\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55135.0 | 2.26065 | ||||||||
\(842\) | 15164.0 | 0.620648 | ||||||||
\(843\) | −4374.00 | −0.178705 | ||||||||
\(844\) | 6128.00 | 0.249922 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8208.00 | 0.333566 | ||||||||
\(847\) | 9496.00 | 0.385226 | ||||||||
\(848\) | −2400.00 | −0.0971891 | ||||||||
\(849\) | −564.000 | −0.0227991 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 52536.0 | 2.11623 | ||||||||
\(852\) | 4896.00 | 0.196871 | ||||||||
\(853\) | −15374.0 | −0.617111 | −0.308556 | − | 0.951206i | \(-0.599846\pi\) | ||||
−0.308556 | + | 0.951206i | \(0.599846\pi\) | |||||||
\(854\) | 3680.00 | 0.147456 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8352.00 | 0.333488 | ||||||||
\(857\) | 17010.0 | 0.678005 | 0.339003 | − | 0.940785i | \(-0.389910\pi\) | ||||
0.339003 | + | 0.940785i | \(0.389910\pi\) | |||||||
\(858\) | 936.000 | 0.0372430 | ||||||||
\(859\) | −19516.0 | −0.775177 | −0.387589 | − | 0.921832i | \(-0.626692\pi\) | ||||
−0.387589 | + | 0.921832i | \(0.626692\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4176.00 | −0.165293 | ||||||||
\(862\) | 7776.00 | 0.307252 | ||||||||
\(863\) | 672.000 | 0.0265065 | 0.0132533 | − | 0.999912i | \(-0.495781\pi\) | ||||
0.0132533 | + | 0.999912i | \(0.495781\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5420.00 | −0.212678 | ||||||||
\(867\) | −9447.00 | −0.370054 | ||||||||
\(868\) | −3712.00 | −0.145154 | ||||||||
\(869\) | 8736.00 | 0.341022 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7696.00 | −0.299390 | ||||||||
\(872\) | 10736.0 | 0.416934 | ||||||||
\(873\) | −15678.0 | −0.607812 | ||||||||
\(874\) | −13728.0 | −0.531300 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8760.00 | 0.337869 | ||||||||
\(877\) | −35390.0 | −1.36264 | −0.681320 | − | 0.731986i | \(-0.738594\pi\) | ||||
−0.681320 | + | 0.731986i | \(0.738594\pi\) | |||||||
\(878\) | −12016.0 | −0.461868 | ||||||||
\(879\) | −11214.0 | −0.430306 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10206.0 | −0.390294 | −0.195147 | − | 0.980774i | \(-0.562518\pi\) | ||||
−0.195147 | + | 0.980774i | \(0.562518\pi\) | |||||||
\(882\) | 5022.00 | 0.191723 | ||||||||
\(883\) | −21884.0 | −0.834038 | −0.417019 | − | 0.908898i | \(-0.636925\pi\) | ||||
−0.417019 | + | 0.908898i | \(0.636925\pi\) | |||||||
\(884\) | −2184.00 | −0.0830949 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27768.0 | 1.05292 | ||||||||
\(887\) | −9588.00 | −0.362946 | −0.181473 | − | 0.983396i | \(-0.558087\pi\) | ||||
−0.181473 | + | 0.983396i | \(0.558087\pi\) | |||||||
\(888\) | 9552.00 | 0.360973 | ||||||||
\(889\) | −8768.00 | −0.330787 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 972.000 | 0.0365468 | ||||||||
\(892\) | 23392.0 | 0.878052 | ||||||||
\(893\) | 23712.0 | 0.888569 | ||||||||
\(894\) | −4140.00 | −0.154880 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1024.00 | 0.0381802 | ||||||||
\(897\) | 5148.00 | 0.191624 | ||||||||
\(898\) | 17412.0 | 0.647045 | ||||||||
\(899\) | 32712.0 | 1.21358 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6300.00 | −0.232945 | ||||||||
\(902\) | −4176.00 | −0.154153 | ||||||||
\(903\) | −1824.00 | −0.0672192 | ||||||||
\(904\) | −1488.00 | −0.0547457 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1848.00 | −0.0677657 | ||||||||
\(907\) | 27124.0 | 0.992985 | 0.496493 | − | 0.868041i | \(-0.334621\pi\) | ||||
0.496493 | + | 0.868041i | \(0.334621\pi\) | |||||||
\(908\) | −19536.0 | −0.714014 | ||||||||
\(909\) | −4806.00 | −0.175363 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3168.00 | 0.115215 | 0.0576073 | − | 0.998339i | \(-0.481653\pi\) | ||||
0.0576073 | + | 0.998339i | \(0.481653\pi\) | |||||||
\(912\) | −2496.00 | −0.0906259 | ||||||||
\(913\) | −432.000 | −0.0156595 | ||||||||
\(914\) | 10156.0 | 0.367539 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21016.0 | −0.758066 | ||||||||
\(917\) | 9600.00 | 0.345714 | ||||||||
\(918\) | −2268.00 | −0.0815416 | ||||||||
\(919\) | 19784.0 | 0.710135 | 0.355067 | − | 0.934841i | \(-0.384458\pi\) | ||||
0.355067 | + | 0.934841i | \(0.384458\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24648.0 | −0.881845 | ||||||||
\(922\) | 29868.0 | 1.06687 | ||||||||
\(923\) | −5304.00 | −0.189148 | ||||||||
\(924\) | −1152.00 | −0.0410152 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6896.00 | −0.244726 | ||||||||
\(927\) | −2232.00 | −0.0790814 | ||||||||
\(928\) | −9024.00 | −0.319210 | ||||||||
\(929\) | 32454.0 | 1.14616 | 0.573079 | − | 0.819500i | \(-0.305749\pi\) | ||||
0.573079 | + | 0.819500i | \(0.305749\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14508.0 | 0.510720 | ||||||||
\(932\) | −9432.00 | −0.331497 | ||||||||
\(933\) | 18864.0 | 0.661929 | ||||||||
\(934\) | −20664.0 | −0.723926 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 936.000 | 0.0326860 | ||||||||
\(937\) | 34198.0 | 1.19232 | 0.596158 | − | 0.802867i | \(-0.296693\pi\) | ||||
0.596158 | + | 0.802867i | \(0.296693\pi\) | |||||||
\(938\) | 9472.00 | 0.329714 | ||||||||
\(939\) | 7338.00 | 0.255023 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6090.00 | 0.210976 | 0.105488 | − | 0.994421i | \(-0.466360\pi\) | ||||
0.105488 | + | 0.994421i | \(0.466360\pi\) | |||||||
\(942\) | −2940.00 | −0.101688 | ||||||||
\(943\) | −22968.0 | −0.793151 | ||||||||
\(944\) | −2496.00 | −0.0860571 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1824.00 | −0.0626885 | ||||||||
\(947\) | −12324.0 | −0.422889 | −0.211445 | − | 0.977390i | \(-0.567817\pi\) | ||||
−0.211445 | + | 0.977390i | \(0.567817\pi\) | |||||||
\(948\) | 8736.00 | 0.299295 | ||||||||
\(949\) | −9490.00 | −0.324614 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16290.0 | 0.555457 | ||||||||
\(952\) | 2688.00 | 0.0915111 | ||||||||
\(953\) | 5034.00 | 0.171109 | 0.0855547 | − | 0.996333i | \(-0.472734\pi\) | ||||
0.0855547 | + | 0.996333i | \(0.472734\pi\) | |||||||
\(954\) | 2700.00 | 0.0916307 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9312.00 | −0.315033 | ||||||||
\(957\) | 10152.0 | 0.342913 | ||||||||
\(958\) | 4656.00 | 0.157024 | ||||||||
\(959\) | 4272.00 | 0.143848 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16335.0 | −0.548320 | ||||||||
\(962\) | −10348.0 | −0.346812 | ||||||||
\(963\) | −9396.00 | −0.314415 | ||||||||
\(964\) | −14680.0 | −0.490468 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6336.00 | −0.211033 | ||||||||
\(967\) | 21256.0 | 0.706874 | 0.353437 | − | 0.935458i | \(-0.385013\pi\) | ||||
0.353437 | + | 0.935458i | \(0.385013\pi\) | |||||||
\(968\) | 9496.00 | 0.315303 | ||||||||
\(969\) | −6552.00 | −0.217214 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11832.0 | 0.391047 | 0.195524 | − | 0.980699i | \(-0.437359\pi\) | ||||
0.195524 | + | 0.980699i | \(0.437359\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 14048.0 | 0.462855 | ||||||||
\(974\) | 26320.0 | 0.865860 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3680.00 | 0.120691 | ||||||||
\(977\) | 34386.0 | 1.12600 | 0.563002 | − | 0.826456i | \(-0.309646\pi\) | ||||
0.563002 | + | 0.826456i | \(0.309646\pi\) | |||||||
\(978\) | −5712.00 | −0.186758 | ||||||||
\(979\) | −17784.0 | −0.580571 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12078.0 | −0.393090 | ||||||||
\(982\) | −17376.0 | −0.564654 | ||||||||
\(983\) | −10752.0 | −0.348866 | −0.174433 | − | 0.984669i | \(-0.555809\pi\) | ||||
−0.174433 | + | 0.984669i | \(0.555809\pi\) | |||||||
\(984\) | −4176.00 | −0.135291 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −23688.0 | −0.765091 | ||||||||
\(987\) | 10944.0 | 0.352940 | ||||||||
\(988\) | 2704.00 | 0.0870705 | ||||||||
\(989\) | −10032.0 | −0.322547 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32672.0 | 1.04729 | 0.523643 | − | 0.851938i | \(-0.324573\pi\) | ||||
0.523643 | + | 0.851938i | \(0.324573\pi\) | |||||||
\(992\) | −3712.00 | −0.118807 | ||||||||
\(993\) | 4884.00 | 0.156082 | ||||||||
\(994\) | 6528.00 | 0.208305 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −432.000 | −0.0137434 | ||||||||
\(997\) | 34.0000 | 0.00108003 | 0.000540015 | − | 1.00000i | \(-0.499828\pi\) | ||||
0.000540015 | 1.00000i | \(0.499828\pi\) | ||||||||
\(998\) | 30920.0 | 0.980717 | ||||||||
\(999\) | −10746.0 | −0.340329 |
(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 | 1950.4.a.e.1.1 | 1 | ||
5.4 | even | 2 | 390.4.a.i.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 1170.4.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.4.a.i.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
1170.4.a.g.1.1 | 1 | 15.14 | odd | 2 | |||
1950.4.a.e.1.1 | 1 | 1.1 | even | 1 | trivial |