Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,4,Mod(1,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, 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("1470.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.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: | \(86.7328077084\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1470.1 |
$q$-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 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 10.0000 | 0.316228 | ||||||||
\(11\) | −32.0000 | −0.877124 | −0.438562 | − | 0.898701i | \(-0.644512\pi\) | ||||
−0.438562 | + | 0.898701i | \(0.644512\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | −15.0000 | −0.320019 | −0.160010 | − | 0.987115i | \(-0.551153\pi\) | ||||
−0.160010 | + | 0.987115i | \(0.551153\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 70.0000 | 0.998676 | 0.499338 | − | 0.866407i | \(-0.333577\pi\) | ||||
0.499338 | + | 0.866407i | \(0.333577\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | −15.0000 | −0.181118 | −0.0905588 | − | 0.995891i | \(-0.528865\pi\) | ||||
−0.0905588 | + | 0.995891i | \(0.528865\pi\) | |||||||
\(20\) | −20.0000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 64.0000 | 0.620220 | ||||||||
\(23\) | −42.0000 | −0.380765 | −0.190383 | − | 0.981710i | \(-0.560973\pi\) | ||||
−0.190383 | + | 0.981710i | \(0.560973\pi\) | |||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 30.0000 | 0.226288 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 90.0000 | 0.576296 | 0.288148 | − | 0.957586i | \(-0.406961\pi\) | ||||
0.288148 | + | 0.957586i | \(0.406961\pi\) | |||||||
\(30\) | −30.0000 | −0.182574 | ||||||||
\(31\) | 85.0000 | 0.492466 | 0.246233 | − | 0.969211i | \(-0.420807\pi\) | ||||
0.246233 | + | 0.969211i | \(0.420807\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 96.0000 | 0.506408 | ||||||||
\(34\) | −140.000 | −0.706171 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 113.000 | 0.502083 | 0.251042 | − | 0.967976i | \(-0.419227\pi\) | ||||
0.251042 | + | 0.967976i | \(0.419227\pi\) | |||||||
\(38\) | 30.0000 | 0.128070 | ||||||||
\(39\) | 45.0000 | 0.184763 | ||||||||
\(40\) | 40.0000 | 0.158114 | ||||||||
\(41\) | −164.000 | −0.624695 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 169.000 | 0.599355 | 0.299677 | − | 0.954041i | \(-0.403121\pi\) | ||||
0.299677 | + | 0.954041i | \(0.403121\pi\) | |||||||
\(44\) | −128.000 | −0.438562 | ||||||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | 84.0000 | 0.269242 | ||||||||
\(47\) | −326.000 | −1.01174 | −0.505872 | − | 0.862608i | \(-0.668829\pi\) | ||||
−0.505872 | + | 0.862608i | \(0.668829\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −50.0000 | −0.141421 | ||||||||
\(51\) | −210.000 | −0.576586 | ||||||||
\(52\) | −60.0000 | −0.160010 | ||||||||
\(53\) | −44.0000 | −0.114035 | −0.0570176 | − | 0.998373i | \(-0.518159\pi\) | ||||
−0.0570176 | + | 0.998373i | \(0.518159\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | 160.000 | 0.392262 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 45.0000 | 0.104568 | ||||||||
\(58\) | −180.000 | −0.407503 | ||||||||
\(59\) | 782.000 | 1.72555 | 0.862777 | − | 0.505584i | \(-0.168723\pi\) | ||||
0.862777 | + | 0.505584i | \(0.168723\pi\) | |||||||
\(60\) | 60.0000 | 0.129099 | ||||||||
\(61\) | −658.000 | −1.38112 | −0.690560 | − | 0.723276i | \(-0.742636\pi\) | ||||
−0.690560 | + | 0.723276i | \(0.742636\pi\) | |||||||
\(62\) | −170.000 | −0.348226 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 75.0000 | 0.143117 | ||||||||
\(66\) | −192.000 | −0.358084 | ||||||||
\(67\) | 1071.00 | 1.95289 | 0.976444 | − | 0.215772i | \(-0.0692267\pi\) | ||||
0.976444 | + | 0.215772i | \(0.0692267\pi\) | |||||||
\(68\) | 280.000 | 0.499338 | ||||||||
\(69\) | 126.000 | 0.219835 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 344.000 | 0.575004 | 0.287502 | − | 0.957780i | \(-0.407175\pi\) | ||||
0.287502 | + | 0.957780i | \(0.407175\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | −431.000 | −0.691024 | −0.345512 | − | 0.938414i | \(-0.612295\pi\) | ||||
−0.345512 | + | 0.938414i | \(0.612295\pi\) | |||||||
\(74\) | −226.000 | −0.355027 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | −60.0000 | −0.0905588 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −90.0000 | −0.130647 | ||||||||
\(79\) | 397.000 | 0.565392 | 0.282696 | − | 0.959210i | \(-0.408771\pi\) | ||||
0.282696 | + | 0.959210i | \(0.408771\pi\) | |||||||
\(80\) | −80.0000 | −0.111803 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 328.000 | 0.441726 | ||||||||
\(83\) | −680.000 | −0.899273 | −0.449637 | − | 0.893212i | \(-0.648447\pi\) | ||||
−0.449637 | + | 0.893212i | \(0.648447\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −350.000 | −0.446622 | ||||||||
\(86\) | −338.000 | −0.423808 | ||||||||
\(87\) | −270.000 | −0.332725 | ||||||||
\(88\) | 256.000 | 0.310110 | ||||||||
\(89\) | −1534.00 | −1.82701 | −0.913504 | − | 0.406830i | \(-0.866634\pi\) | ||||
−0.913504 | + | 0.406830i | \(0.866634\pi\) | |||||||
\(90\) | 90.0000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −168.000 | −0.190383 | ||||||||
\(93\) | −255.000 | −0.284325 | ||||||||
\(94\) | 652.000 | 0.715411 | ||||||||
\(95\) | 75.0000 | 0.0809983 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | 1234.00 | 1.29169 | 0.645844 | − | 0.763469i | \(-0.276506\pi\) | ||||
0.645844 | + | 0.763469i | \(0.276506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −288.000 | −0.292375 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 420.000 | 0.407708 | ||||||||
\(103\) | 1691.00 | 1.61766 | 0.808831 | − | 0.588041i | \(-0.200101\pi\) | ||||
0.808831 | + | 0.588041i | \(0.200101\pi\) | |||||||
\(104\) | 120.000 | 0.113144 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 88.0000 | 0.0806351 | ||||||||
\(107\) | 162.000 | 0.146366 | 0.0731829 | − | 0.997319i | \(-0.476684\pi\) | ||||
0.0731829 | + | 0.997319i | \(0.476684\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | 1221.00 | 1.07294 | 0.536471 | − | 0.843919i | \(-0.319757\pi\) | ||||
0.536471 | + | 0.843919i | \(0.319757\pi\) | |||||||
\(110\) | −320.000 | −0.277371 | ||||||||
\(111\) | −339.000 | −0.289878 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −274.000 | −0.228104 | −0.114052 | − | 0.993475i | \(-0.536383\pi\) | ||||
−0.114052 | + | 0.993475i | \(0.536383\pi\) | |||||||
\(114\) | −90.0000 | −0.0739410 | ||||||||
\(115\) | 210.000 | 0.170283 | ||||||||
\(116\) | 360.000 | 0.288148 | ||||||||
\(117\) | −135.000 | −0.106673 | ||||||||
\(118\) | −1564.00 | −1.22015 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −120.000 | −0.0912871 | ||||||||
\(121\) | −307.000 | −0.230654 | ||||||||
\(122\) | 1316.00 | 0.976599 | ||||||||
\(123\) | 492.000 | 0.360668 | ||||||||
\(124\) | 340.000 | 0.246233 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 529.000 | 0.369615 | 0.184808 | − | 0.982775i | \(-0.440834\pi\) | ||||
0.184808 | + | 0.982775i | \(0.440834\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −507.000 | −0.346038 | ||||||||
\(130\) | −150.000 | −0.101199 | ||||||||
\(131\) | −326.000 | −0.217426 | −0.108713 | − | 0.994073i | \(-0.534673\pi\) | ||||
−0.108713 | + | 0.994073i | \(0.534673\pi\) | |||||||
\(132\) | 384.000 | 0.253204 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2142.00 | −1.38090 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | −560.000 | −0.353085 | ||||||||
\(137\) | 894.000 | 0.557515 | 0.278758 | − | 0.960362i | \(-0.410077\pi\) | ||||
0.278758 | + | 0.960362i | \(0.410077\pi\) | |||||||
\(138\) | −252.000 | −0.155447 | ||||||||
\(139\) | −895.000 | −0.546136 | −0.273068 | − | 0.961995i | \(-0.588038\pi\) | ||||
−0.273068 | + | 0.961995i | \(0.588038\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 978.000 | 0.584131 | ||||||||
\(142\) | −688.000 | −0.406589 | ||||||||
\(143\) | 480.000 | 0.280697 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −450.000 | −0.257727 | ||||||||
\(146\) | 862.000 | 0.488628 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 452.000 | 0.251042 | ||||||||
\(149\) | −840.000 | −0.461849 | −0.230924 | − | 0.972972i | \(-0.574175\pi\) | ||||
−0.230924 | + | 0.972972i | \(0.574175\pi\) | |||||||
\(150\) | 150.000 | 0.0816497 | ||||||||
\(151\) | 920.000 | 0.495818 | 0.247909 | − | 0.968783i | \(-0.420257\pi\) | ||||
0.247909 | + | 0.968783i | \(0.420257\pi\) | |||||||
\(152\) | 120.000 | 0.0640348 | ||||||||
\(153\) | 630.000 | 0.332892 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −425.000 | −0.220238 | ||||||||
\(156\) | 180.000 | 0.0923816 | ||||||||
\(157\) | −910.000 | −0.462585 | −0.231293 | − | 0.972884i | \(-0.574296\pi\) | ||||
−0.231293 | + | 0.972884i | \(0.574296\pi\) | |||||||
\(158\) | −794.000 | −0.399793 | ||||||||
\(159\) | 132.000 | 0.0658382 | ||||||||
\(160\) | 160.000 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | −2068.00 | −0.993732 | −0.496866 | − | 0.867827i | \(-0.665516\pi\) | ||||
−0.496866 | + | 0.867827i | \(0.665516\pi\) | |||||||
\(164\) | −656.000 | −0.312348 | ||||||||
\(165\) | −480.000 | −0.226472 | ||||||||
\(166\) | 1360.00 | 0.635882 | ||||||||
\(167\) | −3504.00 | −1.62364 | −0.811819 | − | 0.583909i | \(-0.801523\pi\) | ||||
−0.811819 | + | 0.583909i | \(0.801523\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1972.00 | −0.897588 | ||||||||
\(170\) | 700.000 | 0.315809 | ||||||||
\(171\) | −135.000 | −0.0603726 | ||||||||
\(172\) | 676.000 | 0.299677 | ||||||||
\(173\) | 1948.00 | 0.856091 | 0.428045 | − | 0.903757i | \(-0.359202\pi\) | ||||
0.428045 | + | 0.903757i | \(0.359202\pi\) | |||||||
\(174\) | 540.000 | 0.235272 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −512.000 | −0.219281 | ||||||||
\(177\) | −2346.00 | −0.996249 | ||||||||
\(178\) | 3068.00 | 1.29189 | ||||||||
\(179\) | −3030.00 | −1.26521 | −0.632606 | − | 0.774474i | \(-0.718015\pi\) | ||||
−0.632606 | + | 0.774474i | \(0.718015\pi\) | |||||||
\(180\) | −180.000 | −0.0745356 | ||||||||
\(181\) | −3133.00 | −1.28660 | −0.643298 | − | 0.765615i | \(-0.722435\pi\) | ||||
−0.643298 | + | 0.765615i | \(0.722435\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1974.00 | 0.797390 | ||||||||
\(184\) | 336.000 | 0.134621 | ||||||||
\(185\) | −565.000 | −0.224539 | ||||||||
\(186\) | 510.000 | 0.201048 | ||||||||
\(187\) | −2240.00 | −0.875963 | ||||||||
\(188\) | −1304.00 | −0.505872 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −150.000 | −0.0572744 | ||||||||
\(191\) | −4422.00 | −1.67521 | −0.837604 | − | 0.546278i | \(-0.816044\pi\) | ||||
−0.837604 | + | 0.546278i | \(0.816044\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | 2825.00 | 1.05362 | 0.526808 | − | 0.849984i | \(-0.323389\pi\) | ||||
0.526808 | + | 0.849984i | \(0.323389\pi\) | |||||||
\(194\) | −2468.00 | −0.913361 | ||||||||
\(195\) | −225.000 | −0.0826286 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3170.00 | 1.14646 | 0.573231 | − | 0.819394i | \(-0.305690\pi\) | ||||
0.573231 | + | 0.819394i | \(0.305690\pi\) | |||||||
\(198\) | 576.000 | 0.206740 | ||||||||
\(199\) | 3064.00 | 1.09146 | 0.545732 | − | 0.837960i | \(-0.316252\pi\) | ||||
0.545732 | + | 0.837960i | \(0.316252\pi\) | |||||||
\(200\) | −200.000 | −0.0707107 | ||||||||
\(201\) | −3213.00 | −1.12750 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −840.000 | −0.288293 | ||||||||
\(205\) | 820.000 | 0.279372 | ||||||||
\(206\) | −3382.00 | −1.14386 | ||||||||
\(207\) | −378.000 | −0.126922 | ||||||||
\(208\) | −240.000 | −0.0800048 | ||||||||
\(209\) | 480.000 | 0.158863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 460.000 | 0.150084 | 0.0750420 | − | 0.997180i | \(-0.476091\pi\) | ||||
0.0750420 | + | 0.997180i | \(0.476091\pi\) | |||||||
\(212\) | −176.000 | −0.0570176 | ||||||||
\(213\) | −1032.00 | −0.331979 | ||||||||
\(214\) | −324.000 | −0.103496 | ||||||||
\(215\) | −845.000 | −0.268040 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2442.00 | −0.758684 | ||||||||
\(219\) | 1293.00 | 0.398963 | ||||||||
\(220\) | 640.000 | 0.196131 | ||||||||
\(221\) | −1050.00 | −0.319596 | ||||||||
\(222\) | 678.000 | 0.204975 | ||||||||
\(223\) | −4156.00 | −1.24801 | −0.624005 | − | 0.781420i | \(-0.714496\pi\) | ||||
−0.624005 | + | 0.781420i | \(0.714496\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 548.000 | 0.161294 | ||||||||
\(227\) | 2740.00 | 0.801146 | 0.400573 | − | 0.916265i | \(-0.368811\pi\) | ||||
0.400573 | + | 0.916265i | \(0.368811\pi\) | |||||||
\(228\) | 180.000 | 0.0522842 | ||||||||
\(229\) | −4921.00 | −1.42004 | −0.710019 | − | 0.704182i | \(-0.751314\pi\) | ||||
−0.710019 | + | 0.704182i | \(0.751314\pi\) | |||||||
\(230\) | −420.000 | −0.120409 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −720.000 | −0.203751 | ||||||||
\(233\) | −4038.00 | −1.13536 | −0.567678 | − | 0.823250i | \(-0.692158\pi\) | ||||
−0.567678 | + | 0.823250i | \(0.692158\pi\) | |||||||
\(234\) | 270.000 | 0.0754293 | ||||||||
\(235\) | 1630.00 | 0.452466 | ||||||||
\(236\) | 3128.00 | 0.862777 | ||||||||
\(237\) | −1191.00 | −0.326429 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2930.00 | −0.792996 | −0.396498 | − | 0.918036i | \(-0.629775\pi\) | ||||
−0.396498 | + | 0.918036i | \(0.629775\pi\) | |||||||
\(240\) | 240.000 | 0.0645497 | ||||||||
\(241\) | −1834.00 | −0.490201 | −0.245100 | − | 0.969498i | \(-0.578821\pi\) | ||||
−0.245100 | + | 0.969498i | \(0.578821\pi\) | |||||||
\(242\) | 614.000 | 0.163097 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −2632.00 | −0.690560 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −984.000 | −0.255031 | ||||||||
\(247\) | 225.000 | 0.0579612 | ||||||||
\(248\) | −680.000 | −0.174113 | ||||||||
\(249\) | 2040.00 | 0.519196 | ||||||||
\(250\) | 250.000 | 0.0632456 | ||||||||
\(251\) | −1014.00 | −0.254992 | −0.127496 | − | 0.991839i | \(-0.540694\pi\) | ||||
−0.127496 | + | 0.991839i | \(0.540694\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1344.00 | 0.333978 | ||||||||
\(254\) | −1058.00 | −0.261358 | ||||||||
\(255\) | 1050.00 | 0.257857 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2816.00 | −0.683491 | −0.341746 | − | 0.939792i | \(-0.611018\pi\) | ||||
−0.341746 | + | 0.939792i | \(0.611018\pi\) | |||||||
\(258\) | 1014.00 | 0.244686 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 300.000 | 0.0715585 | ||||||||
\(261\) | 810.000 | 0.192099 | ||||||||
\(262\) | 652.000 | 0.153743 | ||||||||
\(263\) | 6788.00 | 1.59151 | 0.795753 | − | 0.605621i | \(-0.207075\pi\) | ||||
0.795753 | + | 0.605621i | \(0.207075\pi\) | |||||||
\(264\) | −768.000 | −0.179042 | ||||||||
\(265\) | 220.000 | 0.0509981 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4602.00 | 1.05482 | ||||||||
\(268\) | 4284.00 | 0.976444 | ||||||||
\(269\) | −6198.00 | −1.40483 | −0.702414 | − | 0.711769i | \(-0.747894\pi\) | ||||
−0.702414 | + | 0.711769i | \(0.747894\pi\) | |||||||
\(270\) | −270.000 | −0.0608581 | ||||||||
\(271\) | −3984.00 | −0.893029 | −0.446514 | − | 0.894776i | \(-0.647335\pi\) | ||||
−0.446514 | + | 0.894776i | \(0.647335\pi\) | |||||||
\(272\) | 1120.00 | 0.249669 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1788.00 | −0.394223 | ||||||||
\(275\) | −800.000 | −0.175425 | ||||||||
\(276\) | 504.000 | 0.109918 | ||||||||
\(277\) | 5127.00 | 1.11210 | 0.556050 | − | 0.831149i | \(-0.312316\pi\) | ||||
0.556050 | + | 0.831149i | \(0.312316\pi\) | |||||||
\(278\) | 1790.00 | 0.386176 | ||||||||
\(279\) | 765.000 | 0.164155 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6196.00 | −1.31538 | −0.657691 | − | 0.753288i | \(-0.728467\pi\) | ||||
−0.657691 | + | 0.753288i | \(0.728467\pi\) | |||||||
\(282\) | −1956.00 | −0.413043 | ||||||||
\(283\) | −5789.00 | −1.21597 | −0.607986 | − | 0.793947i | \(-0.708023\pi\) | ||||
−0.607986 | + | 0.793947i | \(0.708023\pi\) | |||||||
\(284\) | 1376.00 | 0.287502 | ||||||||
\(285\) | −225.000 | −0.0467644 | ||||||||
\(286\) | −960.000 | −0.198482 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | −13.0000 | −0.00264604 | ||||||||
\(290\) | 900.000 | 0.182241 | ||||||||
\(291\) | −3702.00 | −0.745756 | ||||||||
\(292\) | −1724.00 | −0.345512 | ||||||||
\(293\) | 2108.00 | 0.420309 | 0.210155 | − | 0.977668i | \(-0.432603\pi\) | ||||
0.210155 | + | 0.977668i | \(0.432603\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3910.00 | −0.771692 | ||||||||
\(296\) | −904.000 | −0.177513 | ||||||||
\(297\) | 864.000 | 0.168803 | ||||||||
\(298\) | 1680.00 | 0.326576 | ||||||||
\(299\) | 630.000 | 0.121852 | ||||||||
\(300\) | −300.000 | −0.0577350 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1840.00 | −0.350596 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −240.000 | −0.0452794 | ||||||||
\(305\) | 3290.00 | 0.617655 | ||||||||
\(306\) | −1260.00 | −0.235390 | ||||||||
\(307\) | 1121.00 | 0.208400 | 0.104200 | − | 0.994556i | \(-0.466772\pi\) | ||||
0.104200 | + | 0.994556i | \(0.466772\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5073.00 | −0.933958 | ||||||||
\(310\) | 850.000 | 0.155731 | ||||||||
\(311\) | −8028.00 | −1.46375 | −0.731875 | − | 0.681439i | \(-0.761354\pi\) | ||||
−0.731875 | + | 0.681439i | \(0.761354\pi\) | |||||||
\(312\) | −360.000 | −0.0653237 | ||||||||
\(313\) | −5093.00 | −0.919723 | −0.459862 | − | 0.887991i | \(-0.652101\pi\) | ||||
−0.459862 | + | 0.887991i | \(0.652101\pi\) | |||||||
\(314\) | 1820.00 | 0.327097 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1588.00 | 0.282696 | ||||||||
\(317\) | −3746.00 | −0.663711 | −0.331855 | − | 0.943330i | \(-0.607675\pi\) | ||||
−0.331855 | + | 0.943330i | \(0.607675\pi\) | |||||||
\(318\) | −264.000 | −0.0465547 | ||||||||
\(319\) | −2880.00 | −0.505483 | ||||||||
\(320\) | −320.000 | −0.0559017 | ||||||||
\(321\) | −486.000 | −0.0845043 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1050.00 | −0.180878 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −375.000 | −0.0640039 | ||||||||
\(326\) | 4136.00 | 0.702674 | ||||||||
\(327\) | −3663.00 | −0.619463 | ||||||||
\(328\) | 1312.00 | 0.220863 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 960.000 | 0.160140 | ||||||||
\(331\) | 7261.00 | 1.20574 | 0.602871 | − | 0.797839i | \(-0.294023\pi\) | ||||
0.602871 | + | 0.797839i | \(0.294023\pi\) | |||||||
\(332\) | −2720.00 | −0.449637 | ||||||||
\(333\) | 1017.00 | 0.167361 | ||||||||
\(334\) | 7008.00 | 1.14809 | ||||||||
\(335\) | −5355.00 | −0.873358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2945.00 | −0.476037 | −0.238018 | − | 0.971261i | \(-0.576498\pi\) | ||||
−0.238018 | + | 0.971261i | \(0.576498\pi\) | |||||||
\(338\) | 3944.00 | 0.634690 | ||||||||
\(339\) | 822.000 | 0.131696 | ||||||||
\(340\) | −1400.00 | −0.223311 | ||||||||
\(341\) | −2720.00 | −0.431954 | ||||||||
\(342\) | 270.000 | 0.0426898 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1352.00 | −0.211904 | ||||||||
\(345\) | −630.000 | −0.0983132 | ||||||||
\(346\) | −3896.00 | −0.605348 | ||||||||
\(347\) | −11060.0 | −1.71104 | −0.855521 | − | 0.517767i | \(-0.826763\pi\) | ||||
−0.855521 | + | 0.517767i | \(0.826763\pi\) | |||||||
\(348\) | −1080.00 | −0.166362 | ||||||||
\(349\) | −6298.00 | −0.965972 | −0.482986 | − | 0.875628i | \(-0.660448\pi\) | ||||
−0.482986 | + | 0.875628i | \(0.660448\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 405.000 | 0.0615878 | ||||||||
\(352\) | 1024.00 | 0.155055 | ||||||||
\(353\) | −10092.0 | −1.52165 | −0.760826 | − | 0.648956i | \(-0.775206\pi\) | ||||
−0.760826 | + | 0.648956i | \(0.775206\pi\) | |||||||
\(354\) | 4692.00 | 0.704455 | ||||||||
\(355\) | −1720.00 | −0.257150 | ||||||||
\(356\) | −6136.00 | −0.913504 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6060.00 | 0.894640 | ||||||||
\(359\) | −11122.0 | −1.63509 | −0.817544 | − | 0.575866i | \(-0.804665\pi\) | ||||
−0.817544 | + | 0.575866i | \(0.804665\pi\) | |||||||
\(360\) | 360.000 | 0.0527046 | ||||||||
\(361\) | −6634.00 | −0.967196 | ||||||||
\(362\) | 6266.00 | 0.909761 | ||||||||
\(363\) | 921.000 | 0.133168 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2155.00 | 0.309035 | ||||||||
\(366\) | −3948.00 | −0.563840 | ||||||||
\(367\) | −5287.00 | −0.751987 | −0.375993 | − | 0.926622i | \(-0.622698\pi\) | ||||
−0.375993 | + | 0.926622i | \(0.622698\pi\) | |||||||
\(368\) | −672.000 | −0.0951914 | ||||||||
\(369\) | −1476.00 | −0.208232 | ||||||||
\(370\) | 1130.00 | 0.158773 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1020.00 | −0.142163 | ||||||||
\(373\) | 13025.0 | 1.80807 | 0.904033 | − | 0.427462i | \(-0.140592\pi\) | ||||
0.904033 | + | 0.427462i | \(0.140592\pi\) | |||||||
\(374\) | 4480.00 | 0.619399 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | 2608.00 | 0.357706 | ||||||||
\(377\) | −1350.00 | −0.184426 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13869.0 | 1.87969 | 0.939845 | − | 0.341601i | \(-0.110969\pi\) | ||||
0.939845 | + | 0.341601i | \(0.110969\pi\) | |||||||
\(380\) | 300.000 | 0.0404991 | ||||||||
\(381\) | −1587.00 | −0.213398 | ||||||||
\(382\) | 8844.00 | 1.18455 | ||||||||
\(383\) | 1764.00 | 0.235343 | 0.117671 | − | 0.993053i | \(-0.462457\pi\) | ||||
0.117671 | + | 0.993053i | \(0.462457\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5650.00 | −0.745019 | ||||||||
\(387\) | 1521.00 | 0.199785 | ||||||||
\(388\) | 4936.00 | 0.645844 | ||||||||
\(389\) | −6064.00 | −0.790378 | −0.395189 | − | 0.918600i | \(-0.629321\pi\) | ||||
−0.395189 | + | 0.918600i | \(0.629321\pi\) | |||||||
\(390\) | 450.000 | 0.0584273 | ||||||||
\(391\) | −2940.00 | −0.380261 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 978.000 | 0.125531 | ||||||||
\(394\) | −6340.00 | −0.810672 | ||||||||
\(395\) | −1985.00 | −0.252851 | ||||||||
\(396\) | −1152.00 | −0.146187 | ||||||||
\(397\) | −9373.00 | −1.18493 | −0.592465 | − | 0.805596i | \(-0.701845\pi\) | ||||
−0.592465 | + | 0.805596i | \(0.701845\pi\) | |||||||
\(398\) | −6128.00 | −0.771781 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | 9580.00 | 1.19302 | 0.596512 | − | 0.802604i | \(-0.296553\pi\) | ||||
0.596512 | + | 0.802604i | \(0.296553\pi\) | |||||||
\(402\) | 6426.00 | 0.797263 | ||||||||
\(403\) | −1275.00 | −0.157599 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3616.00 | −0.440389 | ||||||||
\(408\) | 1680.00 | 0.203854 | ||||||||
\(409\) | 10107.0 | 1.22190 | 0.610952 | − | 0.791667i | \(-0.290787\pi\) | ||||
0.610952 | + | 0.791667i | \(0.290787\pi\) | |||||||
\(410\) | −1640.00 | −0.197546 | ||||||||
\(411\) | −2682.00 | −0.321882 | ||||||||
\(412\) | 6764.00 | 0.808831 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 756.000 | 0.0897473 | ||||||||
\(415\) | 3400.00 | 0.402167 | ||||||||
\(416\) | 480.000 | 0.0565720 | ||||||||
\(417\) | 2685.00 | 0.315312 | ||||||||
\(418\) | −960.000 | −0.112333 | ||||||||
\(419\) | −8934.00 | −1.04166 | −0.520829 | − | 0.853661i | \(-0.674377\pi\) | ||||
−0.520829 | + | 0.853661i | \(0.674377\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3389.00 | 0.392327 | 0.196164 | − | 0.980571i | \(-0.437152\pi\) | ||||
0.196164 | + | 0.980571i | \(0.437152\pi\) | |||||||
\(422\) | −920.000 | −0.106125 | ||||||||
\(423\) | −2934.00 | −0.337248 | ||||||||
\(424\) | 352.000 | 0.0403175 | ||||||||
\(425\) | 1750.00 | 0.199735 | ||||||||
\(426\) | 2064.00 | 0.234744 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 648.000 | 0.0731829 | ||||||||
\(429\) | −1440.00 | −0.162060 | ||||||||
\(430\) | 1690.00 | 0.189533 | ||||||||
\(431\) | −17514.0 | −1.95735 | −0.978677 | − | 0.205405i | \(-0.934149\pi\) | ||||
−0.978677 | + | 0.205405i | \(0.934149\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | −13457.0 | −1.49354 | −0.746769 | − | 0.665083i | \(-0.768396\pi\) | ||||
−0.746769 | + | 0.665083i | \(0.768396\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1350.00 | 0.148799 | ||||||||
\(436\) | 4884.00 | 0.536471 | ||||||||
\(437\) | 630.000 | 0.0689634 | ||||||||
\(438\) | −2586.00 | −0.282109 | ||||||||
\(439\) | 9428.00 | 1.02500 | 0.512499 | − | 0.858688i | \(-0.328720\pi\) | ||||
0.512499 | + | 0.858688i | \(0.328720\pi\) | |||||||
\(440\) | −1280.00 | −0.138685 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2100.00 | 0.225988 | ||||||||
\(443\) | 16888.0 | 1.81123 | 0.905613 | − | 0.424105i | \(-0.139411\pi\) | ||||
0.905613 | + | 0.424105i | \(0.139411\pi\) | |||||||
\(444\) | −1356.00 | −0.144939 | ||||||||
\(445\) | 7670.00 | 0.817063 | ||||||||
\(446\) | 8312.00 | 0.882477 | ||||||||
\(447\) | 2520.00 | 0.266649 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −822.000 | −0.0863977 | −0.0431989 | − | 0.999066i | \(-0.513755\pi\) | ||||
−0.0431989 | + | 0.999066i | \(0.513755\pi\) | |||||||
\(450\) | −450.000 | −0.0471405 | ||||||||
\(451\) | 5248.00 | 0.547935 | ||||||||
\(452\) | −1096.00 | −0.114052 | ||||||||
\(453\) | −2760.00 | −0.286261 | ||||||||
\(454\) | −5480.00 | −0.566496 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −360.000 | −0.0369705 | ||||||||
\(457\) | −10865.0 | −1.11213 | −0.556065 | − | 0.831139i | \(-0.687689\pi\) | ||||
−0.556065 | + | 0.831139i | \(0.687689\pi\) | |||||||
\(458\) | 9842.00 | 1.00412 | ||||||||
\(459\) | −1890.00 | −0.192195 | ||||||||
\(460\) | 840.000 | 0.0851417 | ||||||||
\(461\) | 9518.00 | 0.961600 | 0.480800 | − | 0.876830i | \(-0.340346\pi\) | ||||
0.480800 | + | 0.876830i | \(0.340346\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9227.00 | 0.926166 | 0.463083 | − | 0.886315i | \(-0.346743\pi\) | ||||
0.463083 | + | 0.886315i | \(0.346743\pi\) | |||||||
\(464\) | 1440.00 | 0.144074 | ||||||||
\(465\) | 1275.00 | 0.127154 | ||||||||
\(466\) | 8076.00 | 0.802819 | ||||||||
\(467\) | 5530.00 | 0.547961 | 0.273981 | − | 0.961735i | \(-0.411660\pi\) | ||||
0.273981 | + | 0.961735i | \(0.411660\pi\) | |||||||
\(468\) | −540.000 | −0.0533366 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3260.00 | −0.319942 | ||||||||
\(471\) | 2730.00 | 0.267074 | ||||||||
\(472\) | −6256.00 | −0.610076 | ||||||||
\(473\) | −5408.00 | −0.525708 | ||||||||
\(474\) | 2382.00 | 0.230820 | ||||||||
\(475\) | −375.000 | −0.0362235 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −396.000 | −0.0380117 | ||||||||
\(478\) | 5860.00 | 0.560733 | ||||||||
\(479\) | 4812.00 | 0.459010 | 0.229505 | − | 0.973307i | \(-0.426289\pi\) | ||||
0.229505 | + | 0.973307i | \(0.426289\pi\) | |||||||
\(480\) | −480.000 | −0.0456435 | ||||||||
\(481\) | −1695.00 | −0.160676 | ||||||||
\(482\) | 3668.00 | 0.346624 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1228.00 | −0.115327 | ||||||||
\(485\) | −6170.00 | −0.577660 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 8315.00 | 0.773693 | 0.386847 | − | 0.922144i | \(-0.373564\pi\) | ||||
0.386847 | + | 0.922144i | \(0.373564\pi\) | |||||||
\(488\) | 5264.00 | 0.488299 | ||||||||
\(489\) | 6204.00 | 0.573731 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10212.0 | 0.938617 | 0.469309 | − | 0.883034i | \(-0.344503\pi\) | ||||
0.469309 | + | 0.883034i | \(0.344503\pi\) | |||||||
\(492\) | 1968.00 | 0.180334 | ||||||||
\(493\) | 6300.00 | 0.575533 | ||||||||
\(494\) | −450.000 | −0.0409847 | ||||||||
\(495\) | 1440.00 | 0.130754 | ||||||||
\(496\) | 1360.00 | 0.123117 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4080.00 | −0.367127 | ||||||||
\(499\) | −11229.0 | −1.00737 | −0.503686 | − | 0.863887i | \(-0.668023\pi\) | ||||
−0.503686 | + | 0.863887i | \(0.668023\pi\) | |||||||
\(500\) | −500.000 | −0.0447214 | ||||||||
\(501\) | 10512.0 | 0.937408 | ||||||||
\(502\) | 2028.00 | 0.180307 | ||||||||
\(503\) | 3786.00 | 0.335605 | 0.167803 | − | 0.985821i | \(-0.446333\pi\) | ||||
0.167803 | + | 0.985821i | \(0.446333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2688.00 | −0.236158 | ||||||||
\(507\) | 5916.00 | 0.518222 | ||||||||
\(508\) | 2116.00 | 0.184808 | ||||||||
\(509\) | 12206.0 | 1.06291 | 0.531455 | − | 0.847086i | \(-0.321645\pi\) | ||||
0.531455 | + | 0.847086i | \(0.321645\pi\) | |||||||
\(510\) | −2100.00 | −0.182332 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 405.000 | 0.0348561 | ||||||||
\(514\) | 5632.00 | 0.483301 | ||||||||
\(515\) | −8455.00 | −0.723440 | ||||||||
\(516\) | −2028.00 | −0.173019 | ||||||||
\(517\) | 10432.0 | 0.887425 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5844.00 | −0.494264 | ||||||||
\(520\) | −600.000 | −0.0505995 | ||||||||
\(521\) | −13952.0 | −1.17322 | −0.586611 | − | 0.809869i | \(-0.699538\pi\) | ||||
−0.586611 | + | 0.809869i | \(0.699538\pi\) | |||||||
\(522\) | −1620.00 | −0.135834 | ||||||||
\(523\) | 10181.0 | 0.851212 | 0.425606 | − | 0.904909i | \(-0.360061\pi\) | ||||
0.425606 | + | 0.904909i | \(0.360061\pi\) | |||||||
\(524\) | −1304.00 | −0.108713 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13576.0 | −1.12536 | ||||||||
\(527\) | 5950.00 | 0.491814 | ||||||||
\(528\) | 1536.00 | 0.126602 | ||||||||
\(529\) | −10403.0 | −0.855018 | ||||||||
\(530\) | −440.000 | −0.0360611 | ||||||||
\(531\) | 7038.00 | 0.575185 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2460.00 | 0.199914 | ||||||||
\(534\) | −9204.00 | −0.745873 | ||||||||
\(535\) | −810.000 | −0.0654567 | ||||||||
\(536\) | −8568.00 | −0.690450 | ||||||||
\(537\) | 9090.00 | 0.730470 | ||||||||
\(538\) | 12396.0 | 0.993363 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 540.000 | 0.0430331 | ||||||||
\(541\) | −14055.0 | −1.11695 | −0.558477 | − | 0.829520i | \(-0.688614\pi\) | ||||
−0.558477 | + | 0.829520i | \(0.688614\pi\) | |||||||
\(542\) | 7968.00 | 0.631467 | ||||||||
\(543\) | 9399.00 | 0.742817 | ||||||||
\(544\) | −2240.00 | −0.176543 | ||||||||
\(545\) | −6105.00 | −0.479834 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6144.00 | −0.480253 | −0.240127 | − | 0.970742i | \(-0.577189\pi\) | ||||
−0.240127 | + | 0.970742i | \(0.577189\pi\) | |||||||
\(548\) | 3576.00 | 0.278758 | ||||||||
\(549\) | −5922.00 | −0.460373 | ||||||||
\(550\) | 1600.00 | 0.124044 | ||||||||
\(551\) | −1350.00 | −0.104377 | ||||||||
\(552\) | −1008.00 | −0.0777234 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10254.0 | −0.786373 | ||||||||
\(555\) | 1695.00 | 0.129637 | ||||||||
\(556\) | −3580.00 | −0.273068 | ||||||||
\(557\) | −14342.0 | −1.09101 | −0.545503 | − | 0.838109i | \(-0.683661\pi\) | ||||
−0.545503 | + | 0.838109i | \(0.683661\pi\) | |||||||
\(558\) | −1530.00 | −0.116075 | ||||||||
\(559\) | −2535.00 | −0.191805 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6720.00 | 0.505737 | ||||||||
\(562\) | 12392.0 | 0.930116 | ||||||||
\(563\) | 9658.00 | 0.722977 | 0.361489 | − | 0.932377i | \(-0.382269\pi\) | ||||
0.361489 | + | 0.932377i | \(0.382269\pi\) | |||||||
\(564\) | 3912.00 | 0.292065 | ||||||||
\(565\) | 1370.00 | 0.102011 | ||||||||
\(566\) | 11578.0 | 0.859823 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2752.00 | −0.203295 | ||||||||
\(569\) | −14592.0 | −1.07509 | −0.537547 | − | 0.843234i | \(-0.680649\pi\) | ||||
−0.537547 | + | 0.843234i | \(0.680649\pi\) | |||||||
\(570\) | 450.000 | 0.0330674 | ||||||||
\(571\) | 15699.0 | 1.15058 | 0.575291 | − | 0.817949i | \(-0.304889\pi\) | ||||
0.575291 | + | 0.817949i | \(0.304889\pi\) | |||||||
\(572\) | 1920.00 | 0.140348 | ||||||||
\(573\) | 13266.0 | 0.967182 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1050.00 | −0.0761531 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 9779.00 | 0.705555 | 0.352777 | − | 0.935707i | \(-0.385237\pi\) | ||||
0.352777 | + | 0.935707i | \(0.385237\pi\) | |||||||
\(578\) | 26.0000 | 0.00187103 | ||||||||
\(579\) | −8475.00 | −0.608306 | ||||||||
\(580\) | −1800.00 | −0.128864 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7404.00 | 0.527329 | ||||||||
\(583\) | 1408.00 | 0.100023 | ||||||||
\(584\) | 3448.00 | 0.244314 | ||||||||
\(585\) | 675.000 | 0.0477057 | ||||||||
\(586\) | −4216.00 | −0.297204 | ||||||||
\(587\) | 9454.00 | 0.664750 | 0.332375 | − | 0.943147i | \(-0.392150\pi\) | ||||
0.332375 | + | 0.943147i | \(0.392150\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1275.00 | −0.0891943 | ||||||||
\(590\) | 7820.00 | 0.545668 | ||||||||
\(591\) | −9510.00 | −0.661911 | ||||||||
\(592\) | 1808.00 | 0.125521 | ||||||||
\(593\) | 7668.00 | 0.531007 | 0.265503 | − | 0.964110i | \(-0.414462\pi\) | ||||
0.265503 | + | 0.964110i | \(0.414462\pi\) | |||||||
\(594\) | −1728.00 | −0.119361 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3360.00 | −0.230924 | ||||||||
\(597\) | −9192.00 | −0.630157 | ||||||||
\(598\) | −1260.00 | −0.0861626 | ||||||||
\(599\) | 2052.00 | 0.139971 | 0.0699853 | − | 0.997548i | \(-0.477705\pi\) | ||||
0.0699853 | + | 0.997548i | \(0.477705\pi\) | |||||||
\(600\) | 600.000 | 0.0408248 | ||||||||
\(601\) | 19857.0 | 1.34773 | 0.673863 | − | 0.738856i | \(-0.264634\pi\) | ||||
0.673863 | + | 0.738856i | \(0.264634\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9639.00 | 0.650963 | ||||||||
\(604\) | 3680.00 | 0.247909 | ||||||||
\(605\) | 1535.00 | 0.103151 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10615.0 | −0.709802 | −0.354901 | − | 0.934904i | \(-0.615485\pi\) | ||||
−0.354901 | + | 0.934904i | \(0.615485\pi\) | |||||||
\(608\) | 480.000 | 0.0320174 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6580.00 | −0.436748 | ||||||||
\(611\) | 4890.00 | 0.323778 | ||||||||
\(612\) | 2520.00 | 0.166446 | ||||||||
\(613\) | −9642.00 | −0.635296 | −0.317648 | − | 0.948209i | \(-0.602893\pi\) | ||||
−0.317648 | + | 0.948209i | \(0.602893\pi\) | |||||||
\(614\) | −2242.00 | −0.147361 | ||||||||
\(615\) | −2460.00 | −0.161296 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1694.00 | 0.110531 | 0.0552657 | − | 0.998472i | \(-0.482399\pi\) | ||||
0.0552657 | + | 0.998472i | \(0.482399\pi\) | |||||||
\(618\) | 10146.0 | 0.660408 | ||||||||
\(619\) | 4399.00 | 0.285639 | 0.142820 | − | 0.989749i | \(-0.454383\pi\) | ||||
0.142820 | + | 0.989749i | \(0.454383\pi\) | |||||||
\(620\) | −1700.00 | −0.110119 | ||||||||
\(621\) | 1134.00 | 0.0732783 | ||||||||
\(622\) | 16056.0 | 1.03503 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 720.000 | 0.0461908 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 10186.0 | 0.650343 | ||||||||
\(627\) | −1440.00 | −0.0917194 | ||||||||
\(628\) | −3640.00 | −0.231293 | ||||||||
\(629\) | 7910.00 | 0.501419 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5336.00 | 0.336645 | 0.168322 | − | 0.985732i | \(-0.446165\pi\) | ||||
0.168322 | + | 0.985732i | \(0.446165\pi\) | |||||||
\(632\) | −3176.00 | −0.199896 | ||||||||
\(633\) | −1380.00 | −0.0866510 | ||||||||
\(634\) | 7492.00 | 0.469314 | ||||||||
\(635\) | −2645.00 | −0.165297 | ||||||||
\(636\) | 528.000 | 0.0329191 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5760.00 | 0.357430 | ||||||||
\(639\) | 3096.00 | 0.191668 | ||||||||
\(640\) | 640.000 | 0.0395285 | ||||||||
\(641\) | −18562.0 | −1.14377 | −0.571884 | − | 0.820335i | \(-0.693787\pi\) | ||||
−0.571884 | + | 0.820335i | \(0.693787\pi\) | |||||||
\(642\) | 972.000 | 0.0597536 | ||||||||
\(643\) | 5687.00 | 0.348792 | 0.174396 | − | 0.984676i | \(-0.444203\pi\) | ||||
0.174396 | + | 0.984676i | \(0.444203\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2535.00 | 0.154753 | ||||||||
\(646\) | 2100.00 | 0.127900 | ||||||||
\(647\) | −24712.0 | −1.50159 | −0.750795 | − | 0.660535i | \(-0.770329\pi\) | ||||
−0.750795 | + | 0.660535i | \(0.770329\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | −25024.0 | −1.51353 | ||||||||
\(650\) | 750.000 | 0.0452576 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8272.00 | −0.496866 | ||||||||
\(653\) | 20552.0 | 1.23164 | 0.615821 | − | 0.787886i | \(-0.288825\pi\) | ||||
0.615821 | + | 0.787886i | \(0.288825\pi\) | |||||||
\(654\) | 7326.00 | 0.438026 | ||||||||
\(655\) | 1630.00 | 0.0972357 | ||||||||
\(656\) | −2624.00 | −0.156174 | ||||||||
\(657\) | −3879.00 | −0.230341 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4472.00 | −0.264347 | −0.132173 | − | 0.991227i | \(-0.542196\pi\) | ||||
−0.132173 | + | 0.991227i | \(0.542196\pi\) | |||||||
\(660\) | −1920.00 | −0.113236 | ||||||||
\(661\) | 10505.0 | 0.618150 | 0.309075 | − | 0.951038i | \(-0.399981\pi\) | ||||
0.309075 | + | 0.951038i | \(0.399981\pi\) | |||||||
\(662\) | −14522.0 | −0.852588 | ||||||||
\(663\) | 3150.00 | 0.184519 | ||||||||
\(664\) | 5440.00 | 0.317941 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2034.00 | −0.118342 | ||||||||
\(667\) | −3780.00 | −0.219434 | ||||||||
\(668\) | −14016.0 | −0.811819 | ||||||||
\(669\) | 12468.0 | 0.720539 | ||||||||
\(670\) | 10710.0 | 0.617557 | ||||||||
\(671\) | 21056.0 | 1.21141 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19285.0 | 1.10458 | 0.552290 | − | 0.833652i | \(-0.313754\pi\) | ||||
0.552290 | + | 0.833652i | \(0.313754\pi\) | |||||||
\(674\) | 5890.00 | 0.336609 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | −7888.00 | −0.448794 | ||||||||
\(677\) | 18114.0 | 1.02833 | 0.514164 | − | 0.857692i | \(-0.328102\pi\) | ||||
0.514164 | + | 0.857692i | \(0.328102\pi\) | |||||||
\(678\) | −1644.00 | −0.0931231 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2800.00 | 0.157905 | ||||||||
\(681\) | −8220.00 | −0.462542 | ||||||||
\(682\) | 5440.00 | 0.305437 | ||||||||
\(683\) | −13606.0 | −0.762253 | −0.381127 | − | 0.924523i | \(-0.624464\pi\) | ||||
−0.381127 | + | 0.924523i | \(0.624464\pi\) | |||||||
\(684\) | −540.000 | −0.0301863 | ||||||||
\(685\) | −4470.00 | −0.249328 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14763.0 | 0.819860 | ||||||||
\(688\) | 2704.00 | 0.149839 | ||||||||
\(689\) | 660.000 | 0.0364935 | ||||||||
\(690\) | 1260.00 | 0.0695179 | ||||||||
\(691\) | 6863.00 | 0.377830 | 0.188915 | − | 0.981993i | \(-0.439503\pi\) | ||||
0.188915 | + | 0.981993i | \(0.439503\pi\) | |||||||
\(692\) | 7792.00 | 0.428045 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22120.0 | 1.20989 | ||||||||
\(695\) | 4475.00 | 0.244239 | ||||||||
\(696\) | 2160.00 | 0.117636 | ||||||||
\(697\) | −11480.0 | −0.623868 | ||||||||
\(698\) | 12596.0 | 0.683045 | ||||||||
\(699\) | 12114.0 | 0.655499 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14458.0 | 0.778989 | 0.389494 | − | 0.921029i | \(-0.372650\pi\) | ||||
0.389494 | + | 0.921029i | \(0.372650\pi\) | |||||||
\(702\) | −810.000 | −0.0435491 | ||||||||
\(703\) | −1695.00 | −0.0909362 | ||||||||
\(704\) | −2048.00 | −0.109640 | ||||||||
\(705\) | −4890.00 | −0.261231 | ||||||||
\(706\) | 20184.0 | 1.07597 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9384.00 | −0.498125 | ||||||||
\(709\) | 8278.00 | 0.438486 | 0.219243 | − | 0.975670i | \(-0.429641\pi\) | ||||
0.219243 | + | 0.975670i | \(0.429641\pi\) | |||||||
\(710\) | 3440.00 | 0.181832 | ||||||||
\(711\) | 3573.00 | 0.188464 | ||||||||
\(712\) | 12272.0 | 0.645945 | ||||||||
\(713\) | −3570.00 | −0.187514 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2400.00 | −0.125531 | ||||||||
\(716\) | −12120.0 | −0.632606 | ||||||||
\(717\) | 8790.00 | 0.457836 | ||||||||
\(718\) | 22244.0 | 1.15618 | ||||||||
\(719\) | 29718.0 | 1.54144 | 0.770719 | − | 0.637175i | \(-0.219897\pi\) | ||||
0.770719 | + | 0.637175i | \(0.219897\pi\) | |||||||
\(720\) | −720.000 | −0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13268.0 | 0.683911 | ||||||||
\(723\) | 5502.00 | 0.283017 | ||||||||
\(724\) | −12532.0 | −0.643298 | ||||||||
\(725\) | 2250.00 | 0.115259 | ||||||||
\(726\) | −1842.00 | −0.0941640 | ||||||||
\(727\) | 24069.0 | 1.22788 | 0.613941 | − | 0.789352i | \(-0.289583\pi\) | ||||
0.613941 | + | 0.789352i | \(0.289583\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −4310.00 | −0.218521 | ||||||||
\(731\) | 11830.0 | 0.598561 | ||||||||
\(732\) | 7896.00 | 0.398695 | ||||||||
\(733\) | 1973.00 | 0.0994194 | 0.0497097 | − | 0.998764i | \(-0.484170\pi\) | ||||
0.0497097 | + | 0.998764i | \(0.484170\pi\) | |||||||
\(734\) | 10574.0 | 0.531735 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1344.00 | 0.0673105 | ||||||||
\(737\) | −34272.0 | −1.71292 | ||||||||
\(738\) | 2952.00 | 0.147242 | ||||||||
\(739\) | −37085.0 | −1.84600 | −0.923000 | − | 0.384800i | \(-0.874270\pi\) | ||||
−0.923000 | + | 0.384800i | \(0.874270\pi\) | |||||||
\(740\) | −2260.00 | −0.112269 | ||||||||
\(741\) | −675.000 | −0.0334639 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4368.00 | 0.215675 | 0.107837 | − | 0.994169i | \(-0.465607\pi\) | ||||
0.107837 | + | 0.994169i | \(0.465607\pi\) | |||||||
\(744\) | 2040.00 | 0.100524 | ||||||||
\(745\) | 4200.00 | 0.206545 | ||||||||
\(746\) | −26050.0 | −1.27850 | ||||||||
\(747\) | −6120.00 | −0.299758 | ||||||||
\(748\) | −8960.00 | −0.437981 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −750.000 | −0.0365148 | ||||||||
\(751\) | −25813.0 | −1.25423 | −0.627117 | − | 0.778925i | \(-0.715765\pi\) | ||||
−0.627117 | + | 0.778925i | \(0.715765\pi\) | |||||||
\(752\) | −5216.00 | −0.252936 | ||||||||
\(753\) | 3042.00 | 0.147220 | ||||||||
\(754\) | 2700.00 | 0.130409 | ||||||||
\(755\) | −4600.00 | −0.221737 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18034.0 | 0.865861 | 0.432931 | − | 0.901427i | \(-0.357480\pi\) | ||||
0.432931 | + | 0.901427i | \(0.357480\pi\) | |||||||
\(758\) | −27738.0 | −1.32914 | ||||||||
\(759\) | −4032.00 | −0.192823 | ||||||||
\(760\) | −600.000 | −0.0286372 | ||||||||
\(761\) | −9882.00 | −0.470726 | −0.235363 | − | 0.971908i | \(-0.575628\pi\) | ||||
−0.235363 | + | 0.971908i | \(0.575628\pi\) | |||||||
\(762\) | 3174.00 | 0.150895 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −17688.0 | −0.837604 | ||||||||
\(765\) | −3150.00 | −0.148874 | ||||||||
\(766\) | −3528.00 | −0.166412 | ||||||||
\(767\) | −11730.0 | −0.552211 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 21845.0 | 1.02438 | 0.512192 | − | 0.858871i | \(-0.328834\pi\) | ||||
0.512192 | + | 0.858871i | \(0.328834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8448.00 | 0.394614 | ||||||||
\(772\) | 11300.0 | 0.526808 | ||||||||
\(773\) | 2976.00 | 0.138473 | 0.0692363 | − | 0.997600i | \(-0.477944\pi\) | ||||
0.0692363 | + | 0.997600i | \(0.477944\pi\) | |||||||
\(774\) | −3042.00 | −0.141269 | ||||||||
\(775\) | 2125.00 | 0.0984932 | ||||||||
\(776\) | −9872.00 | −0.456681 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12128.0 | 0.558882 | ||||||||
\(779\) | 2460.00 | 0.113143 | ||||||||
\(780\) | −900.000 | −0.0413143 | ||||||||
\(781\) | −11008.0 | −0.504350 | ||||||||
\(782\) | 5880.00 | 0.268885 | ||||||||
\(783\) | −2430.00 | −0.110908 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4550.00 | 0.206874 | ||||||||
\(786\) | −1956.00 | −0.0887636 | ||||||||
\(787\) | −4708.00 | −0.213243 | −0.106621 | − | 0.994300i | \(-0.534003\pi\) | ||||
−0.106621 | + | 0.994300i | \(0.534003\pi\) | |||||||
\(788\) | 12680.0 | 0.573231 | ||||||||
\(789\) | −20364.0 | −0.918856 | ||||||||
\(790\) | 3970.00 | 0.178793 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2304.00 | 0.103370 | ||||||||
\(793\) | 9870.00 | 0.441985 | ||||||||
\(794\) | 18746.0 | 0.837872 | ||||||||
\(795\) | −660.000 | −0.0294438 | ||||||||
\(796\) | 12256.0 | 0.545732 | ||||||||
\(797\) | −37950.0 | −1.68665 | −0.843324 | − | 0.537406i | \(-0.819404\pi\) | ||||
−0.843324 | + | 0.537406i | \(0.819404\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22820.0 | −1.01040 | ||||||||
\(800\) | −800.000 | −0.0353553 | ||||||||
\(801\) | −13806.0 | −0.609003 | ||||||||
\(802\) | −19160.0 | −0.843595 | ||||||||
\(803\) | 13792.0 | 0.606113 | ||||||||
\(804\) | −12852.0 | −0.563750 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2550.00 | 0.111439 | ||||||||
\(807\) | 18594.0 | 0.811078 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1062.00 | 0.0461532 | 0.0230766 | − | 0.999734i | \(-0.492654\pi\) | ||||
0.0230766 | + | 0.999734i | \(0.492654\pi\) | |||||||
\(810\) | 810.000 | 0.0351364 | ||||||||
\(811\) | 28852.0 | 1.24924 | 0.624618 | − | 0.780930i | \(-0.285255\pi\) | ||||
0.624618 | + | 0.780930i | \(0.285255\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11952.0 | 0.515590 | ||||||||
\(814\) | 7232.00 | 0.311402 | ||||||||
\(815\) | 10340.0 | 0.444410 | ||||||||
\(816\) | −3360.00 | −0.144146 | ||||||||
\(817\) | −2535.00 | −0.108554 | ||||||||
\(818\) | −20214.0 | −0.864017 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3280.00 | 0.139686 | ||||||||
\(821\) | −20580.0 | −0.874844 | −0.437422 | − | 0.899256i | \(-0.644108\pi\) | ||||
−0.437422 | + | 0.899256i | \(0.644108\pi\) | |||||||
\(822\) | 5364.00 | 0.227605 | ||||||||
\(823\) | 41176.0 | 1.74399 | 0.871996 | − | 0.489513i | \(-0.162826\pi\) | ||||
0.871996 | + | 0.489513i | \(0.162826\pi\) | |||||||
\(824\) | −13528.0 | −0.571930 | ||||||||
\(825\) | 2400.00 | 0.101282 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29158.0 | −1.22603 | −0.613013 | − | 0.790073i | \(-0.710043\pi\) | ||||
−0.613013 | + | 0.790073i | \(0.710043\pi\) | |||||||
\(828\) | −1512.00 | −0.0634609 | ||||||||
\(829\) | 33415.0 | 1.39994 | 0.699970 | − | 0.714172i | \(-0.253197\pi\) | ||||
0.699970 | + | 0.714172i | \(0.253197\pi\) | |||||||
\(830\) | −6800.00 | −0.284375 | ||||||||
\(831\) | −15381.0 | −0.642071 | ||||||||
\(832\) | −960.000 | −0.0400024 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5370.00 | −0.222959 | ||||||||
\(835\) | 17520.0 | 0.726113 | ||||||||
\(836\) | 1920.00 | 0.0794313 | ||||||||
\(837\) | −2295.00 | −0.0947752 | ||||||||
\(838\) | 17868.0 | 0.736563 | ||||||||
\(839\) | 11506.0 | 0.473458 | 0.236729 | − | 0.971576i | \(-0.423925\pi\) | ||||
0.236729 | + | 0.971576i | \(0.423925\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16289.0 | −0.667883 | ||||||||
\(842\) | −6778.00 | −0.277417 | ||||||||
\(843\) | 18588.0 | 0.759436 | ||||||||
\(844\) | 1840.00 | 0.0750420 | ||||||||
\(845\) | 9860.00 | 0.401413 | ||||||||
\(846\) | 5868.00 | 0.238470 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −704.000 | −0.0285088 | ||||||||
\(849\) | 17367.0 | 0.702042 | ||||||||
\(850\) | −3500.00 | −0.141234 | ||||||||
\(851\) | −4746.00 | −0.191176 | ||||||||
\(852\) | −4128.00 | −0.165989 | ||||||||
\(853\) | −34889.0 | −1.40044 | −0.700221 | − | 0.713926i | \(-0.746915\pi\) | ||||
−0.700221 | + | 0.713926i | \(0.746915\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 675.000 | 0.0269994 | ||||||||
\(856\) | −1296.00 | −0.0517481 | ||||||||
\(857\) | −34818.0 | −1.38782 | −0.693909 | − | 0.720063i | \(-0.744113\pi\) | ||||
−0.693909 | + | 0.720063i | \(0.744113\pi\) | |||||||
\(858\) | 2880.00 | 0.114594 | ||||||||
\(859\) | −12204.0 | −0.484744 | −0.242372 | − | 0.970183i | \(-0.577925\pi\) | ||||
−0.242372 | + | 0.970183i | \(0.577925\pi\) | |||||||
\(860\) | −3380.00 | −0.134020 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 35028.0 | 1.38406 | ||||||||
\(863\) | 38422.0 | 1.51553 | 0.757764 | − | 0.652529i | \(-0.226292\pi\) | ||||
0.757764 | + | 0.652529i | \(0.226292\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | −9740.00 | −0.382855 | ||||||||
\(866\) | 26914.0 | 1.05609 | ||||||||
\(867\) | 39.0000 | 0.00152769 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12704.0 | −0.495919 | ||||||||
\(870\) | −2700.00 | −0.105217 | ||||||||
\(871\) | −16065.0 | −0.624962 | ||||||||
\(872\) | −9768.00 | −0.379342 | ||||||||
\(873\) | 11106.0 | 0.430563 | ||||||||
\(874\) | −1260.00 | −0.0487645 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5172.00 | 0.199481 | ||||||||
\(877\) | −26230.0 | −1.00995 | −0.504974 | − | 0.863135i | \(-0.668498\pi\) | ||||
−0.504974 | + | 0.863135i | \(0.668498\pi\) | |||||||
\(878\) | −18856.0 | −0.724783 | ||||||||
\(879\) | −6324.00 | −0.242666 | ||||||||
\(880\) | 2560.00 | 0.0980654 | ||||||||
\(881\) | 1768.00 | 0.0676112 | 0.0338056 | − | 0.999428i | \(-0.489237\pi\) | ||||
0.0338056 | + | 0.999428i | \(0.489237\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19887.0 | 0.757928 | 0.378964 | − | 0.925411i | \(-0.376280\pi\) | ||||
0.378964 | + | 0.925411i | \(0.376280\pi\) | |||||||
\(884\) | −4200.00 | −0.159798 | ||||||||
\(885\) | 11730.0 | 0.445536 | ||||||||
\(886\) | −33776.0 | −1.28073 | ||||||||
\(887\) | 6436.00 | 0.243630 | 0.121815 | − | 0.992553i | \(-0.461129\pi\) | ||||
0.121815 | + | 0.992553i | \(0.461129\pi\) | |||||||
\(888\) | 2712.00 | 0.102487 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −15340.0 | −0.577751 | ||||||||
\(891\) | −2592.00 | −0.0974582 | ||||||||
\(892\) | −16624.0 | −0.624005 | ||||||||
\(893\) | 4890.00 | 0.183245 | ||||||||
\(894\) | −5040.00 | −0.188549 | ||||||||
\(895\) | 15150.0 | 0.565820 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1890.00 | −0.0703515 | ||||||||
\(898\) | 1644.00 | 0.0610924 | ||||||||
\(899\) | 7650.00 | 0.283806 | ||||||||
\(900\) | 900.000 | 0.0333333 | ||||||||
\(901\) | −3080.00 | −0.113884 | ||||||||
\(902\) | −10496.0 | −0.387449 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2192.00 | 0.0806469 | ||||||||
\(905\) | 15665.0 | 0.575384 | ||||||||
\(906\) | 5520.00 | 0.202417 | ||||||||
\(907\) | −32065.0 | −1.17387 | −0.586935 | − | 0.809634i | \(-0.699666\pi\) | ||||
−0.586935 | + | 0.809634i | \(0.699666\pi\) | |||||||
\(908\) | 10960.0 | 0.400573 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14394.0 | −0.523485 | −0.261742 | − | 0.965138i | \(-0.584297\pi\) | ||||
−0.261742 | + | 0.965138i | \(0.584297\pi\) | |||||||
\(912\) | 720.000 | 0.0261421 | ||||||||
\(913\) | 21760.0 | 0.788774 | ||||||||
\(914\) | 21730.0 | 0.786394 | ||||||||
\(915\) | −9870.00 | −0.356603 | ||||||||
\(916\) | −19684.0 | −0.710019 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3780.00 | 0.135903 | ||||||||
\(919\) | −15367.0 | −0.551589 | −0.275795 | − | 0.961217i | \(-0.588941\pi\) | ||||
−0.275795 | + | 0.961217i | \(0.588941\pi\) | |||||||
\(920\) | −1680.00 | −0.0602043 | ||||||||
\(921\) | −3363.00 | −0.120320 | ||||||||
\(922\) | −19036.0 | −0.679954 | ||||||||
\(923\) | −5160.00 | −0.184012 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2825.00 | 0.100417 | ||||||||
\(926\) | −18454.0 | −0.654899 | ||||||||
\(927\) | 15219.0 | 0.539221 | ||||||||
\(928\) | −2880.00 | −0.101876 | ||||||||
\(929\) | −19936.0 | −0.704068 | −0.352034 | − | 0.935987i | \(-0.614510\pi\) | ||||
−0.352034 | + | 0.935987i | \(0.614510\pi\) | |||||||
\(930\) | −2550.00 | −0.0899116 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −16152.0 | −0.567678 | ||||||||
\(933\) | 24084.0 | 0.845096 | ||||||||
\(934\) | −11060.0 | −0.387467 | ||||||||
\(935\) | 11200.0 | 0.391742 | ||||||||
\(936\) | 1080.00 | 0.0377146 | ||||||||
\(937\) | −45953.0 | −1.60215 | −0.801077 | − | 0.598561i | \(-0.795740\pi\) | ||||
−0.801077 | + | 0.598561i | \(0.795740\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15279.0 | 0.531002 | ||||||||
\(940\) | 6520.00 | 0.226233 | ||||||||
\(941\) | −48782.0 | −1.68996 | −0.844978 | − | 0.534802i | \(-0.820386\pi\) | ||||
−0.844978 | + | 0.534802i | \(0.820386\pi\) | |||||||
\(942\) | −5460.00 | −0.188850 | ||||||||
\(943\) | 6888.00 | 0.237862 | ||||||||
\(944\) | 12512.0 | 0.431389 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10816.0 | 0.371732 | ||||||||
\(947\) | 51704.0 | 1.77419 | 0.887093 | − | 0.461591i | \(-0.152721\pi\) | ||||
0.887093 | + | 0.461591i | \(0.152721\pi\) | |||||||
\(948\) | −4764.00 | −0.163215 | ||||||||
\(949\) | 6465.00 | 0.221141 | ||||||||
\(950\) | 750.000 | 0.0256139 | ||||||||
\(951\) | 11238.0 | 0.383194 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5916.00 | 0.201089 | 0.100545 | − | 0.994933i | \(-0.467941\pi\) | ||||
0.100545 | + | 0.994933i | \(0.467941\pi\) | |||||||
\(954\) | 792.000 | 0.0268784 | ||||||||
\(955\) | 22110.0 | 0.749176 | ||||||||
\(956\) | −11720.0 | −0.396498 | ||||||||
\(957\) | 8640.00 | 0.291841 | ||||||||
\(958\) | −9624.00 | −0.324569 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 960.000 | 0.0322749 | ||||||||
\(961\) | −22566.0 | −0.757477 | ||||||||
\(962\) | 3390.00 | 0.113615 | ||||||||
\(963\) | 1458.00 | 0.0487886 | ||||||||
\(964\) | −7336.00 | −0.245100 | ||||||||
\(965\) | −14125.0 | −0.471192 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44981.0 | −1.49585 | −0.747927 | − | 0.663781i | \(-0.768951\pi\) | ||||
−0.747927 | + | 0.663781i | \(0.768951\pi\) | |||||||
\(968\) | 2456.00 | 0.0815484 | ||||||||
\(969\) | 3150.00 | 0.104430 | ||||||||
\(970\) | 12340.0 | 0.408468 | ||||||||
\(971\) | 1980.00 | 0.0654390 | 0.0327195 | − | 0.999465i | \(-0.489583\pi\) | ||||
0.0327195 | + | 0.999465i | \(0.489583\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −16630.0 | −0.547084 | ||||||||
\(975\) | 1125.00 | 0.0369527 | ||||||||
\(976\) | −10528.0 | −0.345280 | ||||||||
\(977\) | 132.000 | 0.00432247 | 0.00216124 | − | 0.999998i | \(-0.499312\pi\) | ||||
0.00216124 | + | 0.999998i | \(0.499312\pi\) | |||||||
\(978\) | −12408.0 | −0.405689 | ||||||||
\(979\) | 49088.0 | 1.60251 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10989.0 | 0.357647 | ||||||||
\(982\) | −20424.0 | −0.663703 | ||||||||
\(983\) | 28798.0 | 0.934398 | 0.467199 | − | 0.884152i | \(-0.345263\pi\) | ||||
0.467199 | + | 0.884152i | \(0.345263\pi\) | |||||||
\(984\) | −3936.00 | −0.127515 | ||||||||
\(985\) | −15850.0 | −0.512714 | ||||||||
\(986\) | −12600.0 | −0.406963 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 900.000 | 0.0289806 | ||||||||
\(989\) | −7098.00 | −0.228214 | ||||||||
\(990\) | −2880.00 | −0.0924570 | ||||||||
\(991\) | 38707.0 | 1.24073 | 0.620367 | − | 0.784311i | \(-0.286983\pi\) | ||||
0.620367 | + | 0.784311i | \(0.286983\pi\) | |||||||
\(992\) | −2720.00 | −0.0870565 | ||||||||
\(993\) | −21783.0 | −0.696136 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15320.0 | −0.488117 | ||||||||
\(996\) | 8160.00 | 0.259598 | ||||||||
\(997\) | −22673.0 | −0.720222 | −0.360111 | − | 0.932910i | \(-0.617261\pi\) | ||||
−0.360111 | + | 0.932910i | \(0.617261\pi\) | |||||||
\(998\) | 22458.0 | 0.712320 | ||||||||
\(999\) | −3051.00 | −0.0966260 |
(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 | 1470.4.a.b.1.1 | 1 | ||
7.3 | odd | 6 | 210.4.i.e.121.1 | ✓ | 2 | ||
7.5 | odd | 6 | 210.4.i.e.151.1 | yes | 2 | ||
7.6 | odd | 2 | 1470.4.a.l.1.1 | 1 | |||
21.5 | even | 6 | 630.4.k.d.361.1 | 2 | |||
21.17 | even | 6 | 630.4.k.d.541.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.4.i.e.121.1 | ✓ | 2 | 7.3 | odd | 6 | ||
210.4.i.e.151.1 | yes | 2 | 7.5 | odd | 6 | ||
630.4.k.d.361.1 | 2 | 21.5 | even | 6 | |||
630.4.k.d.541.1 | 2 | 21.17 | even | 6 | |||
1470.4.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1470.4.a.l.1.1 | 1 | 7.6 | odd | 2 |