Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [95,4,Mod(1,95)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(95, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("95.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 95 = 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 95.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: | \(5.60518145055\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 95.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | 4.00000 | 0.769800 | 0.384900 | − | 0.922958i | \(-0.374236\pi\) | ||||
0.384900 | + | 0.922958i | \(0.374236\pi\) | |||||||
\(4\) | −8.00000 | −1.00000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −22.0000 | −1.18789 | −0.593944 | − | 0.804506i | \(-0.702430\pi\) | ||||
−0.593944 | + | 0.804506i | \(0.702430\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −11.0000 | −0.407407 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.0000 | −0.328921 | −0.164461 | − | 0.986384i | \(-0.552588\pi\) | ||||
−0.164461 | + | 0.986384i | \(0.552588\pi\) | |||||||
\(12\) | −32.0000 | −0.769800 | ||||||||
\(13\) | 8.00000 | 0.170677 | 0.0853385 | − | 0.996352i | \(-0.472803\pi\) | ||||
0.0853385 | + | 0.996352i | \(0.472803\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −20.0000 | −0.344265 | ||||||||
\(16\) | 64.0000 | 1.00000 | ||||||||
\(17\) | −66.0000 | −0.941609 | −0.470804 | − | 0.882238i | \(-0.656036\pi\) | ||||
−0.470804 | + | 0.882238i | \(0.656036\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 40.0000 | 0.447214 | ||||||||
\(21\) | −88.0000 | −0.914437 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −30.0000 | −0.271975 | −0.135988 | − | 0.990711i | \(-0.543421\pi\) | ||||
−0.135988 | + | 0.990711i | \(0.543421\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −152.000 | −1.08342 | ||||||||
\(28\) | 176.000 | 1.18789 | ||||||||
\(29\) | −6.00000 | −0.0384197 | −0.0192099 | − | 0.999815i | \(-0.506115\pi\) | ||||
−0.0192099 | + | 0.999815i | \(0.506115\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −64.0000 | −0.370798 | −0.185399 | − | 0.982663i | \(-0.559358\pi\) | ||||
−0.185399 | + | 0.982663i | \(0.559358\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −48.0000 | −0.253204 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 110.000 | 0.531240 | ||||||||
\(36\) | 88.0000 | 0.407407 | ||||||||
\(37\) | −16.0000 | −0.0710915 | −0.0355457 | − | 0.999368i | \(-0.511317\pi\) | ||||
−0.0355457 | + | 0.999368i | \(0.511317\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 32.0000 | 0.131387 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 54.0000 | 0.205692 | 0.102846 | − | 0.994697i | \(-0.467205\pi\) | ||||
0.102846 | + | 0.994697i | \(0.467205\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 182.000 | 0.645459 | 0.322730 | − | 0.946491i | \(-0.395400\pi\) | ||||
0.322730 | + | 0.946491i | \(0.395400\pi\) | |||||||
\(44\) | 96.0000 | 0.328921 | ||||||||
\(45\) | 55.0000 | 0.182198 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 594.000 | 1.84349 | 0.921743 | − | 0.387802i | \(-0.126766\pi\) | ||||
0.921743 | + | 0.387802i | \(0.126766\pi\) | |||||||
\(48\) | 256.000 | 0.769800 | ||||||||
\(49\) | 141.000 | 0.411079 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −264.000 | −0.724851 | ||||||||
\(52\) | −64.0000 | −0.170677 | ||||||||
\(53\) | 396.000 | 1.02632 | 0.513158 | − | 0.858294i | \(-0.328475\pi\) | ||||
0.513158 | + | 0.858294i | \(0.328475\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 60.0000 | 0.147098 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 76.0000 | 0.176604 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −564.000 | −1.24452 | −0.622259 | − | 0.782812i | \(-0.713785\pi\) | ||||
−0.622259 | + | 0.782812i | \(0.713785\pi\) | |||||||
\(60\) | 160.000 | 0.344265 | ||||||||
\(61\) | −706.000 | −1.48187 | −0.740935 | − | 0.671577i | \(-0.765617\pi\) | ||||
−0.740935 | + | 0.671577i | \(0.765617\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 242.000 | 0.483955 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | −40.0000 | −0.0763291 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −628.000 | −1.14511 | −0.572555 | − | 0.819866i | \(-0.694048\pi\) | ||||
−0.572555 | + | 0.819866i | \(0.694048\pi\) | |||||||
\(68\) | 528.000 | 0.941609 | ||||||||
\(69\) | −120.000 | −0.209367 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −984.000 | −1.64478 | −0.822390 | − | 0.568925i | \(-0.807360\pi\) | ||||
−0.822390 | + | 0.568925i | \(0.807360\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.0000 | 0.0224462 | 0.0112231 | − | 0.999937i | \(-0.496427\pi\) | ||||
0.0112231 | + | 0.999937i | \(0.496427\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 100.000 | 0.153960 | ||||||||
\(76\) | −152.000 | −0.229416 | ||||||||
\(77\) | 264.000 | 0.390722 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −328.000 | −0.467125 | −0.233563 | − | 0.972342i | \(-0.575038\pi\) | ||||
−0.233563 | + | 0.972342i | \(0.575038\pi\) | |||||||
\(80\) | −320.000 | −0.447214 | ||||||||
\(81\) | −311.000 | −0.426612 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −294.000 | −0.388804 | −0.194402 | − | 0.980922i | \(-0.562277\pi\) | ||||
−0.194402 | + | 0.980922i | \(0.562277\pi\) | |||||||
\(84\) | 704.000 | 0.914437 | ||||||||
\(85\) | 330.000 | 0.421100 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −24.0000 | −0.0295755 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 918.000 | 1.09335 | 0.546673 | − | 0.837346i | \(-0.315894\pi\) | ||||
0.546673 | + | 0.837346i | \(0.315894\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −176.000 | −0.202745 | ||||||||
\(92\) | 240.000 | 0.271975 | ||||||||
\(93\) | −256.000 | −0.285440 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −95.0000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1564.00 | −1.63711 | −0.818557 | − | 0.574425i | \(-0.805226\pi\) | ||||
−0.818557 | + | 0.574425i | \(0.805226\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 132.000 | 0.134005 | ||||||||
\(100\) | −200.000 | −0.200000 | ||||||||
\(101\) | −294.000 | −0.289644 | −0.144822 | − | 0.989458i | \(-0.546261\pi\) | ||||
−0.144822 | + | 0.989458i | \(0.546261\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 752.000 | 0.719386 | 0.359693 | − | 0.933071i | \(-0.382881\pi\) | ||||
0.359693 | + | 0.933071i | \(0.382881\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 440.000 | 0.408949 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −216.000 | −0.195154 | −0.0975771 | − | 0.995228i | \(-0.531109\pi\) | ||||
−0.0975771 | + | 0.995228i | \(0.531109\pi\) | |||||||
\(108\) | 1216.00 | 1.08342 | ||||||||
\(109\) | −754.000 | −0.662570 | −0.331285 | − | 0.943531i | \(-0.607482\pi\) | ||||
−0.331285 | + | 0.943531i | \(0.607482\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −64.0000 | −0.0547262 | ||||||||
\(112\) | −1408.00 | −1.18789 | ||||||||
\(113\) | −12.0000 | −0.00998996 | −0.00499498 | − | 0.999988i | \(-0.501590\pi\) | ||||
−0.00499498 | + | 0.999988i | \(0.501590\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 150.000 | 0.121631 | ||||||||
\(116\) | 48.0000 | 0.0384197 | ||||||||
\(117\) | −88.0000 | −0.0695351 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1452.00 | 1.11853 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 216.000 | 0.158342 | ||||||||
\(124\) | 512.000 | 0.370798 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 344.000 | 0.240355 | 0.120177 | − | 0.992752i | \(-0.461654\pi\) | ||||
0.120177 | + | 0.992752i | \(0.461654\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 728.000 | 0.496875 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2520.00 | 1.68071 | 0.840357 | − | 0.542034i | \(-0.182346\pi\) | ||||
0.840357 | + | 0.542034i | \(0.182346\pi\) | |||||||
\(132\) | 384.000 | 0.253204 | ||||||||
\(133\) | −418.000 | −0.272520 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 760.000 | 0.484521 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 654.000 | 0.407847 | 0.203923 | − | 0.978987i | \(-0.434631\pi\) | ||||
0.203923 | + | 0.978987i | \(0.434631\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2392.00 | −1.45962 | −0.729809 | − | 0.683652i | \(-0.760391\pi\) | ||||
−0.729809 | + | 0.683652i | \(0.760391\pi\) | |||||||
\(140\) | −880.000 | −0.531240 | ||||||||
\(141\) | 2376.00 | 1.41912 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −96.0000 | −0.0561393 | ||||||||
\(144\) | −704.000 | −0.407407 | ||||||||
\(145\) | 30.0000 | 0.0171818 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 564.000 | 0.316449 | ||||||||
\(148\) | 128.000 | 0.0710915 | ||||||||
\(149\) | −1266.00 | −0.696072 | −0.348036 | − | 0.937481i | \(-0.613151\pi\) | ||||
−0.348036 | + | 0.937481i | \(0.613151\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3080.00 | 1.65991 | 0.829956 | − | 0.557828i | \(-0.188365\pi\) | ||||
0.829956 | + | 0.557828i | \(0.188365\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 726.000 | 0.383618 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 320.000 | 0.165826 | ||||||||
\(156\) | −256.000 | −0.131387 | ||||||||
\(157\) | 1838.00 | 0.934321 | 0.467160 | − | 0.884173i | \(-0.345277\pi\) | ||||
0.467160 | + | 0.884173i | \(0.345277\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1584.00 | 0.790059 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 660.000 | 0.323076 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −850.000 | −0.408449 | −0.204224 | − | 0.978924i | \(-0.565467\pi\) | ||||
−0.204224 | + | 0.978924i | \(0.565467\pi\) | |||||||
\(164\) | −432.000 | −0.205692 | ||||||||
\(165\) | 240.000 | 0.113236 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3804.00 | 1.76265 | 0.881324 | − | 0.472512i | \(-0.156653\pi\) | ||||
0.881324 | + | 0.472512i | \(0.156653\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2133.00 | −0.970869 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −209.000 | −0.0934657 | ||||||||
\(172\) | −1456.00 | −0.645459 | ||||||||
\(173\) | −564.000 | −0.247862 | −0.123931 | − | 0.992291i | \(-0.539550\pi\) | ||||
−0.123931 | + | 0.992291i | \(0.539550\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −550.000 | −0.237578 | ||||||||
\(176\) | −768.000 | −0.328921 | ||||||||
\(177\) | −2256.00 | −0.958030 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1812.00 | −0.756621 | −0.378311 | − | 0.925679i | \(-0.623495\pi\) | ||||
−0.378311 | + | 0.925679i | \(0.623495\pi\) | |||||||
\(180\) | −440.000 | −0.182198 | ||||||||
\(181\) | −4498.00 | −1.84715 | −0.923574 | − | 0.383421i | \(-0.874746\pi\) | ||||
−0.923574 | + | 0.383421i | \(0.874746\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2824.00 | −1.14074 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 80.0000 | 0.0317931 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 792.000 | 0.309715 | ||||||||
\(188\) | −4752.00 | −1.84349 | ||||||||
\(189\) | 3344.00 | 1.28699 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3588.00 | 1.35926 | 0.679630 | − | 0.733555i | \(-0.262140\pi\) | ||||
0.679630 | + | 0.733555i | \(0.262140\pi\) | |||||||
\(192\) | −2048.00 | −0.769800 | ||||||||
\(193\) | −4492.00 | −1.67534 | −0.837672 | − | 0.546174i | \(-0.816084\pi\) | ||||
−0.837672 | + | 0.546174i | \(0.816084\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −160.000 | −0.0587581 | ||||||||
\(196\) | −1128.00 | −0.411079 | ||||||||
\(197\) | 2466.00 | 0.891854 | 0.445927 | − | 0.895069i | \(-0.352874\pi\) | ||||
0.445927 | + | 0.895069i | \(0.352874\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 824.000 | 0.293527 | 0.146763 | − | 0.989172i | \(-0.453114\pi\) | ||||
0.146763 | + | 0.989172i | \(0.453114\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2512.00 | −0.881507 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 132.000 | 0.0456383 | ||||||||
\(204\) | 2112.00 | 0.724851 | ||||||||
\(205\) | −270.000 | −0.0919884 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 330.000 | 0.110805 | ||||||||
\(208\) | 512.000 | 0.170677 | ||||||||
\(209\) | −228.000 | −0.0754598 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4244.00 | 1.38469 | 0.692344 | − | 0.721568i | \(-0.256578\pi\) | ||||
0.692344 | + | 0.721568i | \(0.256578\pi\) | |||||||
\(212\) | −3168.00 | −1.02632 | ||||||||
\(213\) | −3936.00 | −1.26615 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −910.000 | −0.288658 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1408.00 | 0.440467 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 56.0000 | 0.0172791 | ||||||||
\(220\) | −480.000 | −0.147098 | ||||||||
\(221\) | −528.000 | −0.160711 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5480.00 | 1.64560 | 0.822798 | − | 0.568334i | \(-0.192412\pi\) | ||||
0.822798 | + | 0.568334i | \(0.192412\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −275.000 | −0.0814815 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5544.00 | 1.62101 | 0.810503 | − | 0.585735i | \(-0.199194\pi\) | ||||
0.810503 | + | 0.585735i | \(0.199194\pi\) | |||||||
\(228\) | −608.000 | −0.176604 | ||||||||
\(229\) | 2930.00 | 0.845502 | 0.422751 | − | 0.906246i | \(-0.361065\pi\) | ||||
0.422751 | + | 0.906246i | \(0.361065\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1056.00 | 0.300778 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4398.00 | −1.23658 | −0.618289 | − | 0.785951i | \(-0.712174\pi\) | ||||
−0.618289 | + | 0.785951i | \(0.712174\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2970.00 | −0.824432 | ||||||||
\(236\) | 4512.00 | 1.24452 | ||||||||
\(237\) | −1312.00 | −0.359593 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6480.00 | −1.75379 | −0.876896 | − | 0.480680i | \(-0.840390\pi\) | ||||
−0.876896 | + | 0.480680i | \(0.840390\pi\) | |||||||
\(240\) | −1280.00 | −0.344265 | ||||||||
\(241\) | −5770.00 | −1.54223 | −0.771117 | − | 0.636694i | \(-0.780302\pi\) | ||||
−0.771117 | + | 0.636694i | \(0.780302\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2860.00 | 0.755017 | ||||||||
\(244\) | 5648.00 | 1.48187 | ||||||||
\(245\) | −705.000 | −0.183840 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 152.000 | 0.0391560 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1176.00 | −0.299301 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −624.000 | −0.156918 | −0.0784592 | − | 0.996917i | \(-0.525000\pi\) | ||||
−0.0784592 | + | 0.996917i | \(0.525000\pi\) | |||||||
\(252\) | −1936.00 | −0.483955 | ||||||||
\(253\) | 360.000 | 0.0894585 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1320.00 | 0.324163 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | 120.000 | 0.0291260 | 0.0145630 | − | 0.999894i | \(-0.495364\pi\) | ||||
0.0145630 | + | 0.999894i | \(0.495364\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 352.000 | 0.0844487 | ||||||||
\(260\) | 320.000 | 0.0763291 | ||||||||
\(261\) | 66.0000 | 0.0156525 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1842.00 | 0.431873 | 0.215936 | − | 0.976407i | \(-0.430720\pi\) | ||||
0.215936 | + | 0.976407i | \(0.430720\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1980.00 | −0.458983 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3672.00 | 0.841658 | ||||||||
\(268\) | 5024.00 | 1.14511 | ||||||||
\(269\) | −3234.00 | −0.733013 | −0.366506 | − | 0.930416i | \(-0.619446\pi\) | ||||
−0.366506 | + | 0.930416i | \(0.619446\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4664.00 | 1.04545 | 0.522727 | − | 0.852500i | \(-0.324915\pi\) | ||||
0.522727 | + | 0.852500i | \(0.324915\pi\) | |||||||
\(272\) | −4224.00 | −0.941609 | ||||||||
\(273\) | −704.000 | −0.156073 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −300.000 | −0.0657843 | ||||||||
\(276\) | 960.000 | 0.209367 | ||||||||
\(277\) | 5222.00 | 1.13271 | 0.566353 | − | 0.824163i | \(-0.308354\pi\) | ||||
0.566353 | + | 0.824163i | \(0.308354\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 704.000 | 0.151066 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7566.00 | 1.60623 | 0.803113 | − | 0.595826i | \(-0.203175\pi\) | ||||
0.803113 | + | 0.595826i | \(0.203175\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5614.00 | −1.17921 | −0.589607 | − | 0.807690i | \(-0.700717\pi\) | ||||
−0.589607 | + | 0.807690i | \(0.700717\pi\) | |||||||
\(284\) | 7872.00 | 1.64478 | ||||||||
\(285\) | −380.000 | −0.0789799 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1188.00 | −0.244339 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −557.000 | −0.113373 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6256.00 | −1.26025 | ||||||||
\(292\) | −112.000 | −0.0224462 | ||||||||
\(293\) | 924.000 | 0.184234 | 0.0921172 | − | 0.995748i | \(-0.470637\pi\) | ||||
0.0921172 | + | 0.995748i | \(0.470637\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2820.00 | 0.556565 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1824.00 | 0.356361 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −240.000 | −0.0464199 | ||||||||
\(300\) | −800.000 | −0.153960 | ||||||||
\(301\) | −4004.00 | −0.766733 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1176.00 | −0.222968 | ||||||||
\(304\) | 1216.00 | 0.229416 | ||||||||
\(305\) | 3530.00 | 0.662712 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4480.00 | −0.832857 | −0.416429 | − | 0.909168i | \(-0.636718\pi\) | ||||
−0.416429 | + | 0.909168i | \(0.636718\pi\) | |||||||
\(308\) | −2112.00 | −0.390722 | ||||||||
\(309\) | 3008.00 | 0.553784 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1272.00 | 0.231924 | 0.115962 | − | 0.993254i | \(-0.463005\pi\) | ||||
0.115962 | + | 0.993254i | \(0.463005\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1370.00 | 0.247402 | 0.123701 | − | 0.992320i | \(-0.460524\pi\) | ||||
0.123701 | + | 0.992320i | \(0.460524\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1210.00 | −0.216431 | ||||||||
\(316\) | 2624.00 | 0.467125 | ||||||||
\(317\) | 3552.00 | 0.629338 | 0.314669 | − | 0.949201i | \(-0.398106\pi\) | ||||
0.314669 | + | 0.949201i | \(0.398106\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 72.0000 | 0.0126371 | ||||||||
\(320\) | 2560.00 | 0.447214 | ||||||||
\(321\) | −864.000 | −0.150230 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1254.00 | −0.216020 | ||||||||
\(324\) | 2488.00 | 0.426612 | ||||||||
\(325\) | 200.000 | 0.0341354 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3016.00 | −0.510046 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13068.0 | −2.18985 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4532.00 | 0.752572 | 0.376286 | − | 0.926504i | \(-0.377201\pi\) | ||||
0.376286 | + | 0.926504i | \(0.377201\pi\) | |||||||
\(332\) | 2352.00 | 0.388804 | ||||||||
\(333\) | 176.000 | 0.0289632 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3140.00 | 0.512109 | ||||||||
\(336\) | −5632.00 | −0.914437 | ||||||||
\(337\) | −10036.0 | −1.62224 | −0.811121 | − | 0.584878i | \(-0.801142\pi\) | ||||
−0.811121 | + | 0.584878i | \(0.801142\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −48.0000 | −0.00769027 | ||||||||
\(340\) | −2640.00 | −0.421100 | ||||||||
\(341\) | 768.000 | 0.121963 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4444.00 | 0.699573 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 600.000 | 0.0936316 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2178.00 | −0.336949 | −0.168474 | − | 0.985706i | \(-0.553884\pi\) | ||||
−0.168474 | + | 0.985706i | \(0.553884\pi\) | |||||||
\(348\) | 192.000 | 0.0295755 | ||||||||
\(349\) | −10042.0 | −1.54022 | −0.770109 | − | 0.637913i | \(-0.779798\pi\) | ||||
−0.770109 | + | 0.637913i | \(0.779798\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1216.00 | −0.184915 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6102.00 | 0.920047 | 0.460024 | − | 0.887907i | \(-0.347841\pi\) | ||||
0.460024 | + | 0.887907i | \(0.347841\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4920.00 | 0.735568 | ||||||||
\(356\) | −7344.00 | −1.09335 | ||||||||
\(357\) | 5808.00 | 0.861042 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1140.00 | −0.167596 | −0.0837979 | − | 0.996483i | \(-0.526705\pi\) | ||||
−0.0837979 | + | 0.996483i | \(0.526705\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4748.00 | −0.686516 | ||||||||
\(364\) | 1408.00 | 0.202745 | ||||||||
\(365\) | −70.0000 | −0.0100383 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5614.00 | −0.798497 | −0.399249 | − | 0.916843i | \(-0.630729\pi\) | ||||
−0.399249 | + | 0.916843i | \(0.630729\pi\) | |||||||
\(368\) | −1920.00 | −0.271975 | ||||||||
\(369\) | −594.000 | −0.0838006 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8712.00 | −1.21915 | ||||||||
\(372\) | 2048.00 | 0.285440 | ||||||||
\(373\) | −3652.00 | −0.506953 | −0.253476 | − | 0.967342i | \(-0.581574\pi\) | ||||
−0.253476 | + | 0.967342i | \(0.581574\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −500.000 | −0.0688530 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −48.0000 | −0.00655736 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −316.000 | −0.0428280 | −0.0214140 | − | 0.999771i | \(-0.506817\pi\) | ||||
−0.0214140 | + | 0.999771i | \(0.506817\pi\) | |||||||
\(380\) | 760.000 | 0.102598 | ||||||||
\(381\) | 1376.00 | 0.185025 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8844.00 | −1.17991 | −0.589957 | − | 0.807434i | \(-0.700855\pi\) | ||||
−0.589957 | + | 0.807434i | \(0.700855\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1320.00 | −0.174736 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2002.00 | −0.262965 | ||||||||
\(388\) | 12512.0 | 1.63711 | ||||||||
\(389\) | −7230.00 | −0.942354 | −0.471177 | − | 0.882039i | \(-0.656171\pi\) | ||||
−0.471177 | + | 0.882039i | \(0.656171\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1980.00 | 0.256094 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10080.0 | 1.29381 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1640.00 | 0.208905 | ||||||||
\(396\) | −1056.00 | −0.134005 | ||||||||
\(397\) | 3446.00 | 0.435642 | 0.217821 | − | 0.975989i | \(-0.430105\pi\) | ||||
0.217821 | + | 0.975989i | \(0.430105\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1672.00 | −0.209786 | ||||||||
\(400\) | 1600.00 | 0.200000 | ||||||||
\(401\) | −14478.0 | −1.80298 | −0.901492 | − | 0.432795i | \(-0.857527\pi\) | ||||
−0.901492 | + | 0.432795i | \(0.857527\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −512.000 | −0.0632867 | ||||||||
\(404\) | 2352.00 | 0.289644 | ||||||||
\(405\) | 1555.00 | 0.190787 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 192.000 | 0.0233835 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9074.00 | 1.09702 | 0.548509 | − | 0.836145i | \(-0.315196\pi\) | ||||
0.548509 | + | 0.836145i | \(0.315196\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2616.00 | 0.313960 | ||||||||
\(412\) | −6016.00 | −0.719386 | ||||||||
\(413\) | 12408.0 | 1.47835 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1470.00 | 0.173878 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9568.00 | −1.12361 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7068.00 | −0.824092 | −0.412046 | − | 0.911163i | \(-0.635186\pi\) | ||||
−0.412046 | + | 0.911163i | \(0.635186\pi\) | |||||||
\(420\) | −3520.00 | −0.408949 | ||||||||
\(421\) | −7342.00 | −0.849946 | −0.424973 | − | 0.905206i | \(-0.639716\pi\) | ||||
−0.424973 | + | 0.905206i | \(0.639716\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6534.00 | −0.751050 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1650.00 | −0.188322 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15532.0 | 1.76030 | ||||||||
\(428\) | 1728.00 | 0.195154 | ||||||||
\(429\) | −384.000 | −0.0432161 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2976.00 | 0.332596 | 0.166298 | − | 0.986076i | \(-0.446819\pi\) | ||||
0.166298 | + | 0.986076i | \(0.446819\pi\) | |||||||
\(432\) | −9728.00 | −1.08342 | ||||||||
\(433\) | 3476.00 | 0.385787 | 0.192894 | − | 0.981220i | \(-0.438213\pi\) | ||||
0.192894 | + | 0.981220i | \(0.438213\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 120.000 | 0.0132266 | ||||||||
\(436\) | 6032.00 | 0.662570 | ||||||||
\(437\) | −570.000 | −0.0623954 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6200.00 | 0.674054 | 0.337027 | − | 0.941495i | \(-0.390579\pi\) | ||||
0.337027 | + | 0.941495i | \(0.390579\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1551.00 | −0.167477 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16026.0 | 1.71878 | 0.859389 | − | 0.511323i | \(-0.170844\pi\) | ||||
0.859389 | + | 0.511323i | \(0.170844\pi\) | |||||||
\(444\) | 512.000 | 0.0547262 | ||||||||
\(445\) | −4590.00 | −0.488959 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5064.00 | −0.535837 | ||||||||
\(448\) | 11264.0 | 1.18789 | ||||||||
\(449\) | −1830.00 | −0.192345 | −0.0961726 | − | 0.995365i | \(-0.530660\pi\) | ||||
−0.0961726 | + | 0.995365i | \(0.530660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −648.000 | −0.0676566 | ||||||||
\(452\) | 96.0000 | 0.00998996 | ||||||||
\(453\) | 12320.0 | 1.27780 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 880.000 | 0.0906704 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12986.0 | 1.32923 | 0.664616 | − | 0.747185i | \(-0.268595\pi\) | ||||
0.664616 | + | 0.747185i | \(0.268595\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10032.0 | 1.02016 | ||||||||
\(460\) | −1200.00 | −0.121631 | ||||||||
\(461\) | −10506.0 | −1.06142 | −0.530708 | − | 0.847554i | \(-0.678074\pi\) | ||||
−0.530708 | + | 0.847554i | \(0.678074\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1562.00 | 0.156787 | 0.0783934 | − | 0.996923i | \(-0.475021\pi\) | ||||
0.0783934 | + | 0.996923i | \(0.475021\pi\) | |||||||
\(464\) | −384.000 | −0.0384197 | ||||||||
\(465\) | 1280.00 | 0.127653 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.00000 | 0.000594533 0 | 0.000297266 | − | 1.00000i | \(-0.499905\pi\) | ||||
0.000297266 | 1.00000i | \(0.499905\pi\) | ||||||||
\(468\) | 704.000 | 0.0695351 | ||||||||
\(469\) | 13816.0 | 1.36026 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7352.00 | 0.719241 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2184.00 | −0.212305 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 475.000 | 0.0458831 | ||||||||
\(476\) | −11616.0 | −1.11853 | ||||||||
\(477\) | −4356.00 | −0.418129 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3132.00 | 0.298757 | 0.149379 | − | 0.988780i | \(-0.452273\pi\) | ||||
0.149379 | + | 0.988780i | \(0.452273\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −128.000 | −0.0121337 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2640.00 | 0.248704 | ||||||||
\(484\) | 9496.00 | 0.891811 | ||||||||
\(485\) | 7820.00 | 0.732140 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12436.0 | −1.15714 | −0.578572 | − | 0.815631i | \(-0.696390\pi\) | ||||
−0.578572 | + | 0.815631i | \(0.696390\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3400.00 | −0.314424 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7848.00 | −0.721335 | −0.360667 | − | 0.932695i | \(-0.617451\pi\) | ||||
−0.360667 | + | 0.932695i | \(0.617451\pi\) | |||||||
\(492\) | −1728.00 | −0.158342 | ||||||||
\(493\) | 396.000 | 0.0361764 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −660.000 | −0.0599289 | ||||||||
\(496\) | −4096.00 | −0.370798 | ||||||||
\(497\) | 21648.0 | 1.95381 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17720.0 | 1.58969 | 0.794846 | − | 0.606811i | \(-0.207552\pi\) | ||||
0.794846 | + | 0.606811i | \(0.207552\pi\) | |||||||
\(500\) | 1000.00 | 0.0894427 | ||||||||
\(501\) | 15216.0 | 1.35689 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5094.00 | −0.451551 | −0.225776 | − | 0.974179i | \(-0.572492\pi\) | ||||
−0.225776 | + | 0.974179i | \(0.572492\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1470.00 | 0.129533 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8532.00 | −0.747376 | ||||||||
\(508\) | −2752.00 | −0.240355 | ||||||||
\(509\) | −5670.00 | −0.493749 | −0.246875 | − | 0.969047i | \(-0.579404\pi\) | ||||
−0.246875 | + | 0.969047i | \(0.579404\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −308.000 | −0.0266636 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2888.00 | −0.248554 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3760.00 | −0.321719 | ||||||||
\(516\) | −5824.00 | −0.496875 | ||||||||
\(517\) | −7128.00 | −0.606362 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2256.00 | −0.190804 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20670.0 | −1.73814 | −0.869068 | − | 0.494692i | \(-0.835281\pi\) | ||||
−0.869068 | + | 0.494692i | \(0.835281\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16816.0 | −1.40595 | −0.702975 | − | 0.711214i | \(-0.748146\pi\) | ||||
−0.702975 | + | 0.711214i | \(0.748146\pi\) | |||||||
\(524\) | −20160.0 | −1.68071 | ||||||||
\(525\) | −2200.00 | −0.182887 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4224.00 | 0.349147 | ||||||||
\(528\) | −3072.00 | −0.253204 | ||||||||
\(529\) | −11267.0 | −0.926029 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6204.00 | 0.507026 | ||||||||
\(532\) | 3344.00 | 0.272520 | ||||||||
\(533\) | 432.000 | 0.0351069 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1080.00 | 0.0872756 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7248.00 | −0.582447 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1692.00 | −0.135213 | ||||||||
\(540\) | −6080.00 | −0.484521 | ||||||||
\(541\) | 9530.00 | 0.757351 | 0.378675 | − | 0.925530i | \(-0.376380\pi\) | ||||
0.378675 | + | 0.925530i | \(0.376380\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17992.0 | −1.42193 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3770.00 | 0.296310 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5264.00 | 0.411467 | 0.205733 | − | 0.978608i | \(-0.434042\pi\) | ||||
0.205733 | + | 0.978608i | \(0.434042\pi\) | |||||||
\(548\) | −5232.00 | −0.407847 | ||||||||
\(549\) | 7766.00 | 0.603725 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −114.000 | −0.00881409 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7216.00 | 0.554892 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 320.000 | 0.0244743 | ||||||||
\(556\) | 19136.0 | 1.45962 | ||||||||
\(557\) | 16542.0 | 1.25836 | 0.629180 | − | 0.777259i | \(-0.283391\pi\) | ||||
0.629180 | + | 0.777259i | \(0.283391\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1456.00 | 0.110165 | ||||||||
\(560\) | 7040.00 | 0.531240 | ||||||||
\(561\) | 3168.00 | 0.238419 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5232.00 | −0.391656 | −0.195828 | − | 0.980638i | \(-0.562739\pi\) | ||||
−0.195828 | + | 0.980638i | \(0.562739\pi\) | |||||||
\(564\) | −19008.0 | −1.41912 | ||||||||
\(565\) | 60.0000 | 0.00446764 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6842.00 | 0.506767 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15114.0 | 1.11355 | 0.556777 | − | 0.830662i | \(-0.312038\pi\) | ||||
0.556777 | + | 0.830662i | \(0.312038\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11764.0 | −0.862186 | −0.431093 | − | 0.902308i | \(-0.641872\pi\) | ||||
−0.431093 | + | 0.902308i | \(0.641872\pi\) | |||||||
\(572\) | 768.000 | 0.0561393 | ||||||||
\(573\) | 14352.0 | 1.04636 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −750.000 | −0.0543951 | ||||||||
\(576\) | 5632.00 | 0.407407 | ||||||||
\(577\) | −25198.0 | −1.81804 | −0.909018 | − | 0.416757i | \(-0.863166\pi\) | ||||
−0.909018 | + | 0.416757i | \(0.863166\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17968.0 | −1.28968 | ||||||||
\(580\) | −240.000 | −0.0171818 | ||||||||
\(581\) | 6468.00 | 0.461855 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4752.00 | −0.337578 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 440.000 | 0.0310970 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20190.0 | 1.41964 | 0.709822 | − | 0.704382i | \(-0.248776\pi\) | ||||
0.709822 | + | 0.704382i | \(0.248776\pi\) | |||||||
\(588\) | −4512.00 | −0.316449 | ||||||||
\(589\) | −1216.00 | −0.0850669 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9864.00 | 0.686549 | ||||||||
\(592\) | −1024.00 | −0.0710915 | ||||||||
\(593\) | −2886.00 | −0.199855 | −0.0999273 | − | 0.994995i | \(-0.531861\pi\) | ||||
−0.0999273 | + | 0.994995i | \(0.531861\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7260.00 | −0.500220 | ||||||||
\(596\) | 10128.0 | 0.696072 | ||||||||
\(597\) | 3296.00 | 0.225957 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4464.00 | −0.304498 | −0.152249 | − | 0.988342i | \(-0.548652\pi\) | ||||
−0.152249 | + | 0.988342i | \(0.548652\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15874.0 | −1.07739 | −0.538697 | − | 0.842499i | \(-0.681083\pi\) | ||||
−0.538697 | + | 0.842499i | \(0.681083\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6908.00 | 0.466527 | ||||||||
\(604\) | −24640.0 | −1.65991 | ||||||||
\(605\) | 5935.00 | 0.398830 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18916.0 | −1.26487 | −0.632436 | − | 0.774613i | \(-0.717945\pi\) | ||||
−0.632436 | + | 0.774613i | \(0.717945\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 528.000 | 0.0351324 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4752.00 | 0.314640 | ||||||||
\(612\) | −5808.00 | −0.383618 | ||||||||
\(613\) | −3058.00 | −0.201487 | −0.100743 | − | 0.994912i | \(-0.532122\pi\) | ||||
−0.100743 | + | 0.994912i | \(0.532122\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1080.00 | −0.0708127 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4158.00 | 0.271304 | 0.135652 | − | 0.990757i | \(-0.456687\pi\) | ||||
0.135652 | + | 0.990757i | \(0.456687\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22864.0 | −1.48462 | −0.742312 | − | 0.670055i | \(-0.766271\pi\) | ||||
−0.742312 | + | 0.670055i | \(0.766271\pi\) | |||||||
\(620\) | −2560.00 | −0.165826 | ||||||||
\(621\) | 4560.00 | 0.294664 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −20196.0 | −1.29877 | ||||||||
\(624\) | 2048.00 | 0.131387 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −912.000 | −0.0580890 | ||||||||
\(628\) | −14704.0 | −0.934321 | ||||||||
\(629\) | 1056.00 | 0.0669403 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18536.0 | 1.16942 | 0.584712 | − | 0.811241i | \(-0.301208\pi\) | ||||
0.584712 | + | 0.811241i | \(0.301208\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16976.0 | 1.06593 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1720.00 | −0.107490 | ||||||||
\(636\) | −12672.0 | −0.790059 | ||||||||
\(637\) | 1128.00 | 0.0701617 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10824.0 | 0.670095 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15630.0 | 0.963101 | 0.481551 | − | 0.876418i | \(-0.340074\pi\) | ||||
0.481551 | + | 0.876418i | \(0.340074\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27574.0 | −1.69115 | −0.845577 | − | 0.533853i | \(-0.820744\pi\) | ||||
−0.845577 | + | 0.533853i | \(0.820744\pi\) | |||||||
\(644\) | −5280.00 | −0.323076 | ||||||||
\(645\) | −3640.00 | −0.222209 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8826.00 | −0.536300 | −0.268150 | − | 0.963377i | \(-0.586412\pi\) | ||||
−0.268150 | + | 0.963377i | \(0.586412\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6768.00 | 0.409349 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5632.00 | 0.339071 | ||||||||
\(652\) | 6800.00 | 0.408449 | ||||||||
\(653\) | 18678.0 | 1.11934 | 0.559668 | − | 0.828717i | \(-0.310929\pi\) | ||||
0.559668 | + | 0.828717i | \(0.310929\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12600.0 | −0.751638 | ||||||||
\(656\) | 3456.00 | 0.205692 | ||||||||
\(657\) | −154.000 | −0.00914477 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16980.0 | 1.00371 | 0.501857 | − | 0.864951i | \(-0.332651\pi\) | ||||
0.501857 | + | 0.864951i | \(0.332651\pi\) | |||||||
\(660\) | −1920.00 | −0.113236 | ||||||||
\(661\) | −9358.00 | −0.550657 | −0.275328 | − | 0.961350i | \(-0.588787\pi\) | ||||
−0.275328 | + | 0.961350i | \(0.588787\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2112.00 | −0.123715 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2090.00 | 0.121875 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 180.000 | 0.0104492 | ||||||||
\(668\) | −30432.0 | −1.76265 | ||||||||
\(669\) | 21920.0 | 1.26678 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8472.00 | 0.487419 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16120.0 | −0.923299 | −0.461650 | − | 0.887062i | \(-0.652742\pi\) | ||||
−0.461650 | + | 0.887062i | \(0.652742\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3800.00 | −0.216685 | ||||||||
\(676\) | 17064.0 | 0.970869 | ||||||||
\(677\) | 27876.0 | 1.58251 | 0.791257 | − | 0.611484i | \(-0.209427\pi\) | ||||
0.791257 | + | 0.611484i | \(0.209427\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34408.0 | 1.94471 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22176.0 | 1.24785 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4872.00 | −0.272946 | −0.136473 | − | 0.990644i | \(-0.543577\pi\) | ||||
−0.136473 | + | 0.990644i | \(0.543577\pi\) | |||||||
\(684\) | 1672.00 | 0.0934657 | ||||||||
\(685\) | −3270.00 | −0.182395 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11720.0 | 0.650867 | ||||||||
\(688\) | 11648.0 | 0.645459 | ||||||||
\(689\) | 3168.00 | 0.175169 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13412.0 | 0.738374 | 0.369187 | − | 0.929355i | \(-0.379636\pi\) | ||||
0.369187 | + | 0.929355i | \(0.379636\pi\) | |||||||
\(692\) | 4512.00 | 0.247862 | ||||||||
\(693\) | −2904.00 | −0.159183 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11960.0 | 0.652761 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3564.00 | −0.193682 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17592.0 | −0.951918 | ||||||||
\(700\) | 4400.00 | 0.237578 | ||||||||
\(701\) | 1926.00 | 0.103772 | 0.0518859 | − | 0.998653i | \(-0.483477\pi\) | ||||
0.0518859 | + | 0.998653i | \(0.483477\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −304.000 | −0.0163095 | ||||||||
\(704\) | 6144.00 | 0.328921 | ||||||||
\(705\) | −11880.0 | −0.634648 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6468.00 | 0.344065 | ||||||||
\(708\) | 18048.0 | 0.958030 | ||||||||
\(709\) | 17534.0 | 0.928777 | 0.464389 | − | 0.885631i | \(-0.346274\pi\) | ||||
0.464389 | + | 0.885631i | \(0.346274\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3608.00 | 0.190310 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1920.00 | 0.100848 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 480.000 | 0.0251063 | ||||||||
\(716\) | 14496.0 | 0.756621 | ||||||||
\(717\) | −25920.0 | −1.35007 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11220.0 | −0.581969 | −0.290984 | − | 0.956728i | \(-0.593983\pi\) | ||||
−0.290984 | + | 0.956728i | \(0.593983\pi\) | |||||||
\(720\) | 3520.00 | 0.182198 | ||||||||
\(721\) | −16544.0 | −0.854550 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23080.0 | −1.18721 | ||||||||
\(724\) | 35984.0 | 1.84715 | ||||||||
\(725\) | −150.000 | −0.00768395 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25078.0 | −1.27936 | −0.639678 | − | 0.768643i | \(-0.720932\pi\) | ||||
−0.639678 | + | 0.768643i | \(0.720932\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19837.0 | 1.00782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12012.0 | −0.607770 | ||||||||
\(732\) | 22592.0 | 1.14074 | ||||||||
\(733\) | 434.000 | 0.0218692 | 0.0109346 | − | 0.999940i | \(-0.496519\pi\) | ||||
0.0109346 | + | 0.999940i | \(0.496519\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2820.00 | −0.141520 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7536.00 | 0.376651 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2564.00 | 0.127630 | 0.0638148 | − | 0.997962i | \(-0.479673\pi\) | ||||
0.0638148 | + | 0.997962i | \(0.479673\pi\) | |||||||
\(740\) | −640.000 | −0.0317931 | ||||||||
\(741\) | 608.000 | 0.0301423 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21948.0 | 1.08371 | 0.541853 | − | 0.840473i | \(-0.317723\pi\) | ||||
0.541853 | + | 0.840473i | \(0.317723\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6330.00 | 0.311293 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3234.00 | 0.158401 | ||||||||
\(748\) | −6336.00 | −0.309715 | ||||||||
\(749\) | 4752.00 | 0.231821 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7648.00 | −0.371610 | −0.185805 | − | 0.982587i | \(-0.559489\pi\) | ||||
−0.185805 | + | 0.982587i | \(0.559489\pi\) | |||||||
\(752\) | 38016.0 | 1.84349 | ||||||||
\(753\) | −2496.00 | −0.120796 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15400.0 | −0.742336 | ||||||||
\(756\) | −26752.0 | −1.28699 | ||||||||
\(757\) | −30190.0 | −1.44950 | −0.724752 | − | 0.689010i | \(-0.758046\pi\) | ||||
−0.724752 | + | 0.689010i | \(0.758046\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1440.00 | 0.0688652 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1242.00 | −0.0591622 | −0.0295811 | − | 0.999562i | \(-0.509417\pi\) | ||||
−0.0295811 | + | 0.999562i | \(0.509417\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16588.0 | 0.787059 | ||||||||
\(764\) | −28704.0 | −1.35926 | ||||||||
\(765\) | −3630.00 | −0.171559 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4512.00 | −0.212411 | ||||||||
\(768\) | 16384.0 | 0.769800 | ||||||||
\(769\) | −28738.0 | −1.34762 | −0.673809 | − | 0.738905i | \(-0.735343\pi\) | ||||
−0.673809 | + | 0.738905i | \(0.735343\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 480.000 | 0.0224212 | ||||||||
\(772\) | 35936.0 | 1.67534 | ||||||||
\(773\) | −40128.0 | −1.86715 | −0.933573 | − | 0.358387i | \(-0.883327\pi\) | ||||
−0.933573 | + | 0.358387i | \(0.883327\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1600.00 | −0.0741596 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1408.00 | 0.0650086 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1026.00 | 0.0471890 | ||||||||
\(780\) | 1280.00 | 0.0587581 | ||||||||
\(781\) | 11808.0 | 0.541003 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 912.000 | 0.0416248 | ||||||||
\(784\) | 9024.00 | 0.411079 | ||||||||
\(785\) | −9190.00 | −0.417841 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15448.0 | −0.699697 | −0.349849 | − | 0.936806i | \(-0.613767\pi\) | ||||
−0.349849 | + | 0.936806i | \(0.613767\pi\) | |||||||
\(788\) | −19728.0 | −0.891854 | ||||||||
\(789\) | 7368.00 | 0.332456 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 264.000 | 0.0118670 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5648.00 | −0.252921 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7920.00 | −0.353325 | ||||||||
\(796\) | −6592.00 | −0.293527 | ||||||||
\(797\) | −27324.0 | −1.21439 | −0.607193 | − | 0.794554i | \(-0.707705\pi\) | ||||
−0.607193 | + | 0.794554i | \(0.707705\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39204.0 | −1.73584 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10098.0 | −0.445437 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −168.000 | −0.00738305 | ||||||||
\(804\) | 20096.0 | 0.881507 | ||||||||
\(805\) | −3300.00 | −0.144484 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12936.0 | −0.564274 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17766.0 | −0.772088 | −0.386044 | − | 0.922480i | \(-0.626159\pi\) | ||||
−0.386044 | + | 0.922480i | \(0.626159\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7396.00 | −0.320233 | −0.160116 | − | 0.987098i | \(-0.551187\pi\) | ||||
−0.160116 | + | 0.987098i | \(0.551187\pi\) | |||||||
\(812\) | −1056.00 | −0.0456383 | ||||||||
\(813\) | 18656.0 | 0.804790 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4250.00 | 0.182664 | ||||||||
\(816\) | −16896.0 | −0.724851 | ||||||||
\(817\) | 3458.00 | 0.148078 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1936.00 | 0.0825999 | ||||||||
\(820\) | 2160.00 | 0.0919884 | ||||||||
\(821\) | 26898.0 | 1.14342 | 0.571709 | − | 0.820456i | \(-0.306281\pi\) | ||||
0.571709 | + | 0.820456i | \(0.306281\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24442.0 | −1.03523 | −0.517615 | − | 0.855614i | \(-0.673180\pi\) | ||||
−0.517615 | + | 0.855614i | \(0.673180\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1200.00 | −0.0506408 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13524.0 | 0.568652 | 0.284326 | − | 0.958728i | \(-0.408230\pi\) | ||||
0.284326 | + | 0.958728i | \(0.408230\pi\) | |||||||
\(828\) | −2640.00 | −0.110805 | ||||||||
\(829\) | −7714.00 | −0.323183 | −0.161591 | − | 0.986858i | \(-0.551663\pi\) | ||||
−0.161591 | + | 0.986858i | \(0.551663\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20888.0 | 0.871958 | ||||||||
\(832\) | −4096.00 | −0.170677 | ||||||||
\(833\) | −9306.00 | −0.387075 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19020.0 | −0.788281 | ||||||||
\(836\) | 1824.00 | 0.0754598 | ||||||||
\(837\) | 9728.00 | 0.401731 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16248.0 | −0.668586 | −0.334293 | − | 0.942469i | \(-0.608497\pi\) | ||||
−0.334293 | + | 0.942469i | \(0.608497\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24353.0 | −0.998524 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30264.0 | 1.23647 | ||||||||
\(844\) | −33952.0 | −1.38469 | ||||||||
\(845\) | 10665.0 | 0.434186 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26114.0 | 1.05937 | ||||||||
\(848\) | 25344.0 | 1.02632 | ||||||||
\(849\) | −22456.0 | −0.907760 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 480.000 | 0.0193351 | ||||||||
\(852\) | 31488.0 | 1.26615 | ||||||||
\(853\) | 35498.0 | 1.42489 | 0.712443 | − | 0.701730i | \(-0.247589\pi\) | ||||
0.712443 | + | 0.701730i | \(0.247589\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1045.00 | 0.0417991 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40344.0 | −1.60808 | −0.804040 | − | 0.594575i | \(-0.797320\pi\) | ||||
−0.804040 | + | 0.594575i | \(0.797320\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31484.0 | 1.25055 | 0.625274 | − | 0.780406i | \(-0.284987\pi\) | ||||
0.625274 | + | 0.780406i | \(0.284987\pi\) | |||||||
\(860\) | 7280.00 | 0.288658 | ||||||||
\(861\) | −4752.00 | −0.188093 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28836.0 | −1.13741 | −0.568707 | − | 0.822540i | \(-0.692556\pi\) | ||||
−0.568707 | + | 0.822540i | \(0.692556\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2820.00 | 0.110847 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2228.00 | −0.0872743 | ||||||||
\(868\) | −11264.0 | −0.440467 | ||||||||
\(869\) | 3936.00 | 0.153647 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5024.00 | −0.195444 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17204.0 | 0.666973 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2750.00 | 0.106248 | ||||||||
\(876\) | −448.000 | −0.0172791 | ||||||||
\(877\) | 22796.0 | 0.877727 | 0.438863 | − | 0.898554i | \(-0.355381\pi\) | ||||
0.438863 | + | 0.898554i | \(0.355381\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3696.00 | 0.141824 | ||||||||
\(880\) | 3840.00 | 0.147098 | ||||||||
\(881\) | −18822.0 | −0.719784 | −0.359892 | − | 0.932994i | \(-0.617186\pi\) | ||||
−0.359892 | + | 0.932994i | \(0.617186\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7526.00 | 0.286829 | 0.143415 | − | 0.989663i | \(-0.454192\pi\) | ||||
0.143415 | + | 0.989663i | \(0.454192\pi\) | |||||||
\(884\) | 4224.00 | 0.160711 | ||||||||
\(885\) | 11280.0 | 0.428444 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33816.0 | 1.28008 | 0.640040 | − | 0.768342i | \(-0.278918\pi\) | ||||
0.640040 | + | 0.768342i | \(0.278918\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7568.00 | −0.285515 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3732.00 | 0.140322 | ||||||||
\(892\) | −43840.0 | −1.64560 | ||||||||
\(893\) | 11286.0 | 0.422925 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9060.00 | 0.338371 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −960.000 | −0.0357341 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 384.000 | 0.0142460 | ||||||||
\(900\) | 2200.00 | 0.0814815 | ||||||||
\(901\) | −26136.0 | −0.966389 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16016.0 | −0.590232 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22490.0 | 0.826069 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33784.0 | −1.23680 | −0.618401 | − | 0.785863i | \(-0.712219\pi\) | ||||
−0.618401 | + | 0.785863i | \(0.712219\pi\) | |||||||
\(908\) | −44352.0 | −1.62101 | ||||||||
\(909\) | 3234.00 | 0.118003 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15216.0 | −0.553379 | −0.276690 | − | 0.960959i | \(-0.589237\pi\) | ||||
−0.276690 | + | 0.960959i | \(0.589237\pi\) | |||||||
\(912\) | 4864.00 | 0.176604 | ||||||||
\(913\) | 3528.00 | 0.127886 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14120.0 | 0.510156 | ||||||||
\(916\) | −23440.0 | −0.845502 | ||||||||
\(917\) | −55440.0 | −1.99650 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19760.0 | 0.709273 | 0.354637 | − | 0.935004i | \(-0.384605\pi\) | ||||
0.354637 | + | 0.935004i | \(0.384605\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17920.0 | −0.641134 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7872.00 | −0.280726 | ||||||||
\(924\) | −8448.00 | −0.300778 | ||||||||
\(925\) | −400.000 | −0.0142183 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8272.00 | −0.293083 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16278.0 | 0.574880 | 0.287440 | − | 0.957799i | \(-0.407196\pi\) | ||||
0.287440 | + | 0.957799i | \(0.407196\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2679.00 | 0.0943079 | ||||||||
\(932\) | 35184.0 | 1.23658 | ||||||||
\(933\) | 5088.00 | 0.178536 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3960.00 | −0.138509 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6994.00 | −0.243846 | −0.121923 | − | 0.992540i | \(-0.538906\pi\) | ||||
−0.121923 | + | 0.992540i | \(0.538906\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5480.00 | 0.190451 | ||||||||
\(940\) | 23760.0 | 0.824432 | ||||||||
\(941\) | 32502.0 | 1.12597 | 0.562983 | − | 0.826468i | \(-0.309653\pi\) | ||||
0.562983 | + | 0.826468i | \(0.309653\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1620.00 | −0.0559432 | ||||||||
\(944\) | −36096.0 | −1.24452 | ||||||||
\(945\) | −16720.0 | −0.575557 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50358.0 | 1.72800 | 0.864000 | − | 0.503493i | \(-0.167952\pi\) | ||||
0.864000 | + | 0.503493i | \(0.167952\pi\) | |||||||
\(948\) | 10496.0 | 0.359593 | ||||||||
\(949\) | 112.000 | 0.00383106 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14208.0 | 0.484465 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39816.0 | 1.35338 | 0.676688 | − | 0.736270i | \(-0.263415\pi\) | ||||
0.676688 | + | 0.736270i | \(0.263415\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17940.0 | −0.607879 | ||||||||
\(956\) | 51840.0 | 1.75379 | ||||||||
\(957\) | 288.000 | 0.00972802 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14388.0 | −0.484476 | ||||||||
\(960\) | 10240.0 | 0.344265 | ||||||||
\(961\) | −25695.0 | −0.862509 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2376.00 | 0.0795073 | ||||||||
\(964\) | 46160.0 | 1.54223 | ||||||||
\(965\) | 22460.0 | 0.749236 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 590.000 | 0.0196206 | 0.00981030 | − | 0.999952i | \(-0.496877\pi\) | ||||
0.00981030 | + | 0.999952i | \(0.496877\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5016.00 | −0.166292 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26820.0 | 0.886400 | 0.443200 | − | 0.896423i | \(-0.353843\pi\) | ||||
0.443200 | + | 0.896423i | \(0.353843\pi\) | |||||||
\(972\) | −22880.0 | −0.755017 | ||||||||
\(973\) | 52624.0 | 1.73386 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 800.000 | 0.0262774 | ||||||||
\(976\) | −45184.0 | −1.48187 | ||||||||
\(977\) | −33312.0 | −1.09083 | −0.545417 | − | 0.838165i | \(-0.683629\pi\) | ||||
−0.545417 | + | 0.838165i | \(0.683629\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11016.0 | −0.359625 | ||||||||
\(980\) | 5640.00 | 0.183840 | ||||||||
\(981\) | 8294.00 | 0.269936 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 612.000 | 0.0198573 | 0.00992867 | − | 0.999951i | \(-0.496840\pi\) | ||||
0.00992867 | + | 0.999951i | \(0.496840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12330.0 | −0.398849 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −52272.0 | −1.68575 | ||||||||
\(988\) | −1216.00 | −0.0391560 | ||||||||
\(989\) | −5460.00 | −0.175549 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39416.0 | 1.26346 | 0.631731 | − | 0.775188i | \(-0.282345\pi\) | ||||
0.631731 | + | 0.775188i | \(0.282345\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18128.0 | 0.579330 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4120.00 | −0.131269 | ||||||||
\(996\) | 9408.00 | 0.299301 | ||||||||
\(997\) | 36614.0 | 1.16307 | 0.581533 | − | 0.813523i | \(-0.302453\pi\) | ||||
0.581533 | + | 0.813523i | \(0.302453\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2432.00 | 0.0770221 |
(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 | 95.4.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 855.4.a.e.1.1 | 1 | |||
4.3 | odd | 2 | 1520.4.a.b.1.1 | 1 | |||
5.2 | odd | 4 | 475.4.b.e.324.1 | 2 | |||
5.3 | odd | 4 | 475.4.b.e.324.2 | 2 | |||
5.4 | even | 2 | 475.4.a.d.1.1 | 1 | |||
19.18 | odd | 2 | 1805.4.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.4.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
475.4.a.d.1.1 | 1 | 5.4 | even | 2 | |||
475.4.b.e.324.1 | 2 | 5.2 | odd | 4 | |||
475.4.b.e.324.2 | 2 | 5.3 | odd | 4 | |||
855.4.a.e.1.1 | 1 | 3.2 | odd | 2 | |||
1520.4.a.b.1.1 | 1 | 4.3 | odd | 2 | |||
1805.4.a.f.1.1 | 1 | 19.18 | odd | 2 |