Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,4,Mod(1,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("960.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.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: | \(56.6418336055\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 60) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 960.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 28.0000 | 1.51186 | 0.755929 | − | 0.654654i | \(-0.227186\pi\) | ||||
0.755929 | + | 0.654654i | \(0.227186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −24.0000 | −0.657843 | −0.328921 | − | 0.944357i | \(-0.606685\pi\) | ||||
−0.328921 | + | 0.944357i | \(0.606685\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 70.0000 | 1.49342 | 0.746712 | − | 0.665148i | \(-0.231631\pi\) | ||||
0.746712 | + | 0.665148i | \(0.231631\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 102.000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.0000 | 0.241490 | 0.120745 | − | 0.992684i | \(-0.461472\pi\) | ||||
0.120745 | + | 0.992684i | \(0.461472\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −84.0000 | −0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 72.0000 | 0.652741 | 0.326370 | − | 0.945242i | \(-0.394174\pi\) | ||||
0.326370 | + | 0.945242i | \(0.394174\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −306.000 | −1.95941 | −0.979703 | − | 0.200455i | \(-0.935758\pi\) | ||||
−0.979703 | + | 0.200455i | \(0.935758\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 136.000 | 0.787946 | 0.393973 | − | 0.919122i | \(-0.371100\pi\) | ||||
0.393973 | + | 0.919122i | \(0.371100\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 72.0000 | 0.379806 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 140.000 | 0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 214.000 | 0.950848 | 0.475424 | − | 0.879757i | \(-0.342295\pi\) | ||||
0.475424 | + | 0.879757i | \(0.342295\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −210.000 | −0.862229 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −150.000 | −0.571367 | −0.285684 | − | 0.958324i | \(-0.592221\pi\) | ||||
−0.285684 | + | 0.958324i | \(0.592221\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −292.000 | −1.03557 | −0.517786 | − | 0.855510i | \(-0.673244\pi\) | ||||
−0.517786 | + | 0.855510i | \(0.673244\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 72.0000 | 0.223453 | 0.111726 | − | 0.993739i | \(-0.464362\pi\) | ||||
0.111726 | + | 0.993739i | \(0.464362\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 441.000 | 1.28571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −306.000 | −0.840168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 414.000 | 1.07297 | 0.536484 | − | 0.843911i | \(-0.319752\pi\) | ||||
0.536484 | + | 0.843911i | \(0.319752\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −120.000 | −0.294196 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −60.0000 | −0.139424 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −744.000 | −1.64170 | −0.820852 | − | 0.571141i | \(-0.806501\pi\) | ||||
−0.820852 | + | 0.571141i | \(0.806501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 418.000 | 0.877367 | 0.438684 | − | 0.898642i | \(-0.355445\pi\) | ||||
0.438684 | + | 0.898642i | \(0.355445\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 252.000 | 0.503953 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 350.000 | 0.667879 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 188.000 | 0.342804 | 0.171402 | − | 0.985201i | \(-0.445170\pi\) | ||||
0.171402 | + | 0.985201i | \(0.445170\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −216.000 | −0.376860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −480.000 | −0.802331 | −0.401166 | − | 0.916006i | \(-0.631395\pi\) | ||||
−0.401166 | + | 0.916006i | \(0.631395\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 434.000 | 0.695834 | 0.347917 | − | 0.937525i | \(-0.386889\pi\) | ||||
0.347917 | + | 0.937525i | \(0.386889\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −672.000 | −0.994565 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1352.00 | −1.92547 | −0.962733 | − | 0.270452i | \(-0.912827\pi\) | ||||
−0.962733 | + | 0.270452i | \(0.912827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −612.000 | −0.809346 | −0.404673 | − | 0.914461i | \(-0.632615\pi\) | ||||
−0.404673 | + | 0.914461i | \(0.632615\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 510.000 | 0.650791 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 918.000 | 1.13126 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −30.0000 | −0.0357303 | −0.0178651 | − | 0.999840i | \(-0.505687\pi\) | ||||
−0.0178651 | + | 0.999840i | \(0.505687\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1960.00 | 2.25784 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −408.000 | −0.454921 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 100.000 | 0.107998 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −286.000 | −0.299370 | −0.149685 | − | 0.988734i | \(-0.547826\pi\) | ||||
−0.149685 | + | 0.988734i | \(0.547826\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −216.000 | −0.219281 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1542.00 | 1.51916 | 0.759578 | − | 0.650416i | \(-0.225406\pi\) | ||||
0.759578 | + | 0.650416i | \(0.225406\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1172.00 | −1.12117 | −0.560585 | − | 0.828097i | \(-0.689424\pi\) | ||||
−0.560585 | + | 0.828097i | \(0.689424\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −420.000 | −0.390360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1956.00 | 1.76723 | 0.883615 | − | 0.468214i | \(-0.155102\pi\) | ||||
0.883615 | + | 0.468214i | \(0.155102\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1858.00 | 1.63270 | 0.816349 | − | 0.577559i | \(-0.195995\pi\) | ||||
0.816349 | + | 0.577559i | \(0.195995\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −642.000 | −0.548972 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 174.000 | 0.144854 | 0.0724272 | − | 0.997374i | \(-0.476926\pi\) | ||||
0.0724272 | + | 0.997374i | \(0.476926\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 360.000 | 0.291915 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 630.000 | 0.497808 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2856.00 | 2.20008 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −755.000 | −0.567243 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 450.000 | 0.329879 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2068.00 | 1.44492 | 0.722462 | − | 0.691411i | \(-0.243010\pi\) | ||||
0.722462 | + | 0.691411i | \(0.243010\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 876.000 | 0.597888 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 312.000 | 0.208088 | 0.104044 | − | 0.994573i | \(-0.466822\pi\) | ||||
0.104044 | + | 0.994573i | \(0.466822\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 560.000 | 0.365099 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2646.00 | 1.65010 | 0.825048 | − | 0.565063i | \(-0.191148\pi\) | ||||
0.825048 | + | 0.565063i | \(0.191148\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1276.00 | −0.778625 | −0.389313 | − | 0.921106i | \(-0.627287\pi\) | ||||
−0.389313 | + | 0.921106i | \(0.627287\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −216.000 | −0.129011 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1680.00 | −0.982438 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1530.00 | −0.876273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1323.00 | −0.742307 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3198.00 | 1.75832 | 0.879162 | − | 0.476522i | \(-0.158103\pi\) | ||||
0.879162 | + | 0.476522i | \(0.158103\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 760.000 | 0.409589 | 0.204794 | − | 0.978805i | \(-0.434347\pi\) | ||||
0.204794 | + | 0.978805i | \(0.434347\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 918.000 | 0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 680.000 | 0.352380 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 166.000 | 0.0843837 | 0.0421919 | − | 0.999110i | \(-0.486566\pi\) | ||||
0.0421919 | + | 0.999110i | \(0.486566\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1242.00 | −0.619478 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2016.00 | 0.986851 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3020.00 | 1.45119 | 0.725597 | − | 0.688120i | \(-0.241564\pi\) | ||||
0.725597 | + | 0.688120i | \(0.241564\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 360.000 | 0.169854 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 984.000 | 0.455953 | 0.227977 | − | 0.973667i | \(-0.426789\pi\) | ||||
0.227977 | + | 0.973667i | \(0.426789\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2703.00 | 1.23031 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 180.000 | 0.0804967 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1962.00 | −0.862243 | −0.431122 | − | 0.902294i | \(-0.641882\pi\) | ||||
−0.431122 | + | 0.902294i | \(0.641882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 700.000 | 0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2232.00 | 0.947838 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 576.000 | 0.240515 | 0.120258 | − | 0.992743i | \(-0.461628\pi\) | ||||
0.120258 | + | 0.992743i | \(0.461628\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1210.00 | 0.496898 | 0.248449 | − | 0.968645i | \(-0.420079\pi\) | ||||
0.248449 | + | 0.968645i | \(0.420079\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1254.00 | −0.506548 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1070.00 | 0.425232 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2448.00 | −0.957302 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −756.000 | −0.290957 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3384.00 | −1.28198 | −0.640989 | − | 0.767550i | \(-0.721475\pi\) | ||||
−0.640989 | + | 0.767550i | \(0.721475\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2038.00 | −0.760096 | −0.380048 | − | 0.924967i | \(-0.624092\pi\) | ||||
−0.380048 | + | 0.924967i | \(0.624092\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1050.00 | −0.385600 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4098.00 | −1.48208 | −0.741042 | − | 0.671459i | \(-0.765668\pi\) | ||||
−0.741042 | + | 0.671459i | \(0.765668\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2248.00 | 0.800786 | 0.400393 | − | 0.916343i | \(-0.368874\pi\) | ||||
0.400393 | + | 0.916343i | \(0.368874\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −564.000 | −0.197918 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8568.00 | −2.96234 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −750.000 | −0.255523 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 648.000 | 0.217580 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −480.000 | −0.158863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3260.00 | 1.06364 | 0.531819 | − | 0.846858i | \(-0.321509\pi\) | ||||
0.531819 | + | 0.846858i | \(0.321509\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1440.00 | 0.463226 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1460.00 | −0.463122 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3808.00 | 1.19126 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1302.00 | −0.401740 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7140.00 | 2.17325 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2980.00 | 0.894868 | 0.447434 | − | 0.894317i | \(-0.352338\pi\) | ||||
0.447434 | + | 0.894317i | \(0.352338\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3180.00 | −0.929797 | −0.464899 | − | 0.885364i | \(-0.653909\pi\) | ||||
−0.464899 | + | 0.885364i | \(0.653909\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3374.00 | −0.973625 | −0.486813 | − | 0.873506i | \(-0.661841\pi\) | ||||
−0.486813 | + | 0.873506i | \(0.661841\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2016.00 | 0.574212 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1950.00 | 0.548278 | 0.274139 | − | 0.961690i | \(-0.411607\pi\) | ||||
0.274139 | + | 0.961690i | \(0.411607\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 360.000 | 0.0999311 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4056.00 | 1.11167 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2232.00 | −0.604084 | −0.302042 | − | 0.953295i | \(-0.597668\pi\) | ||||
−0.302042 | + | 0.953295i | \(0.597668\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1822.00 | −0.486993 | −0.243497 | − | 0.969902i | \(-0.578294\pi\) | ||||
−0.243497 | + | 0.969902i | \(0.578294\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2205.00 | 0.574989 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1400.00 | 0.360647 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1836.00 | 0.467276 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1488.00 | 0.374190 | 0.187095 | − | 0.982342i | \(-0.440093\pi\) | ||||
0.187095 | + | 0.982342i | \(0.440093\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1728.00 | −0.429401 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1530.00 | −0.375735 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2994.00 | −0.726695 | −0.363347 | − | 0.931654i | \(-0.618366\pi\) | ||||
−0.363347 | + | 0.931654i | \(0.618366\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5992.00 | 1.43755 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2754.00 | −0.653135 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2472.00 | 0.579582 | 0.289791 | − | 0.957090i | \(-0.406414\pi\) | ||||
0.289791 | + | 0.957090i | \(0.406414\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2070.00 | 0.479846 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 90.0000 | 0.0206289 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3954.00 | −0.896207 | −0.448103 | − | 0.893982i | \(-0.647900\pi\) | ||||
−0.448103 | + | 0.893982i | \(0.647900\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2176.00 | 0.487759 | 0.243879 | − | 0.969806i | \(-0.421580\pi\) | ||||
0.243879 | + | 0.969806i | \(0.421580\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5880.00 | −1.30357 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −600.000 | −0.131569 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1034.00 | −0.224285 | −0.112143 | − | 0.993692i | \(-0.535771\pi\) | ||||
−0.112143 | + | 0.993692i | \(0.535771\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1224.00 | 0.262649 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6654.00 | −1.41261 | −0.706307 | − | 0.707906i | \(-0.749640\pi\) | ||||
−0.706307 | + | 0.707906i | \(0.749640\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1756.00 | −0.368846 | −0.184423 | − | 0.982847i | \(-0.559042\pi\) | ||||
−0.184423 | + | 0.982847i | \(0.559042\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −300.000 | −0.0623525 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4200.00 | −0.863826 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5491.00 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 858.000 | 0.172841 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3234.00 | −0.644820 | −0.322410 | − | 0.946600i | \(-0.604493\pi\) | ||||
−0.322410 | + | 0.946600i | \(0.604493\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3720.00 | −0.734192 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 648.000 | 0.126602 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5040.00 | 0.974818 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8176.00 | −1.56564 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4626.00 | −0.877085 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2090.00 | 0.392371 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2036.00 | 0.378504 | 0.189252 | − | 0.981929i | \(-0.439394\pi\) | ||||
0.189252 | + | 0.981929i | \(0.439394\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3516.00 | 0.647308 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 96.0000 | 0.0175037 | 0.00875187 | − | 0.999962i | \(-0.497214\pi\) | ||||
0.00875187 | + | 0.999962i | \(0.497214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1202.00 | 0.217064 | 0.108532 | − | 0.994093i | \(-0.465385\pi\) | ||||
0.108532 | + | 0.994093i | \(0.465385\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1260.00 | 0.225374 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3798.00 | 0.672924 | 0.336462 | − | 0.941697i | \(-0.390770\pi\) | ||||
0.336462 | + | 0.941697i | \(0.390770\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7344.00 | 1.28898 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5868.00 | −1.02031 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2040.00 | 0.351420 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1750.00 | 0.298685 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5574.00 | −0.942639 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2016.00 | 0.337829 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5668.00 | −0.941213 | −0.470606 | − | 0.882343i | \(-0.655965\pi\) | ||||
−0.470606 | + | 0.882343i | \(0.655965\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1926.00 | 0.316949 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 940.000 | 0.153307 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −454.000 | −0.0733856 | −0.0366928 | − | 0.999327i | \(-0.511682\pi\) | ||||
−0.0366928 | + | 0.999327i | \(0.511682\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −522.000 | −0.0836317 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3264.00 | −0.518345 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2744.00 | 0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1080.00 | −0.168537 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5604.00 | −0.866970 | −0.433485 | − | 0.901161i | \(-0.642716\pi\) | ||||
−0.433485 | + | 0.901161i | \(0.642716\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11266.0 | 1.72795 | 0.863976 | − | 0.503533i | \(-0.167967\pi\) | ||||
0.863976 | + | 0.503533i | \(0.167967\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1890.00 | −0.287410 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6426.00 | −0.968899 | −0.484450 | − | 0.874819i | \(-0.660980\pi\) | ||||
−0.484450 | + | 0.874819i | \(0.660980\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2400.00 | −0.358813 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8568.00 | −1.27021 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6936.00 | −1.01969 | −0.509844 | − | 0.860267i | \(-0.670297\pi\) | ||||
−0.509844 | + | 0.860267i | \(0.670297\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6459.00 | −0.941682 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2265.00 | 0.327498 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2170.00 | 0.311186 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 388.000 | 0.0551865 | 0.0275932 | − | 0.999619i | \(-0.491216\pi\) | ||||
0.0275932 | + | 0.999619i | \(0.491216\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1350.00 | −0.190456 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11592.0 | 1.62217 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8062.00 | 1.11913 | 0.559564 | − | 0.828787i | \(-0.310969\pi\) | ||||
0.559564 | + | 0.828787i | \(0.310969\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21420.0 | −2.92622 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3388.00 | −0.459182 | −0.229591 | − | 0.973287i | \(-0.573739\pi\) | ||||
−0.229591 | + | 0.973287i | \(0.573739\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6204.00 | −0.834227 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6984.00 | −0.931764 | −0.465882 | − | 0.884847i | \(-0.654263\pi\) | ||||
−0.465882 | + | 0.884847i | \(0.654263\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3360.00 | −0.444783 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2628.00 | −0.345191 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2526.00 | 0.329237 | 0.164619 | − | 0.986357i | \(-0.447361\pi\) | ||||
0.164619 | + | 0.986357i | \(0.447361\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7344.00 | 0.949877 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −936.000 | −0.120140 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6760.00 | −0.861095 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6146.00 | −0.776975 | −0.388487 | − | 0.921454i | \(-0.627002\pi\) | ||||
−0.388487 | + | 0.921454i | \(0.627002\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1680.00 | −0.210790 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9786.00 | 1.21868 | 0.609339 | − | 0.792910i | \(-0.291435\pi\) | ||||
0.609339 | + | 0.792910i | \(0.291435\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9520.00 | 1.17674 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5136.00 | −0.625509 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −886.000 | −0.107115 | −0.0535573 | − | 0.998565i | \(-0.517056\pi\) | ||||
−0.0535573 | + | 0.998565i | \(0.517056\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7938.00 | −0.952683 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20832.0 | −2.48202 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3060.00 | −0.361951 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3828.00 | 0.449539 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11352.0 | −1.32358 | −0.661792 | − | 0.749688i | \(-0.730204\pi\) | ||||
−0.661792 | + | 0.749688i | \(0.730204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10190.0 | −1.17964 | −0.589822 | − | 0.807533i | \(-0.700802\pi\) | ||||
−0.589822 | + | 0.807533i | \(0.700802\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 648.000 | 0.0744843 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2550.00 | 0.291043 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11704.0 | 1.32645 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5040.00 | 0.567211 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2448.00 | −0.273587 | −0.136794 | − | 0.990600i | \(-0.543680\pi\) | ||||
−0.136794 | + | 0.990600i | \(0.543680\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7078.00 | −0.785559 | −0.392779 | − | 0.919633i | \(-0.628486\pi\) | ||||
−0.392779 | + | 0.919633i | \(0.628486\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4590.00 | 0.505916 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1440.00 | 0.157631 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18088.0 | 1.96650 | 0.983250 | − | 0.182264i | \(-0.0583426\pi\) | ||||
0.983250 | + | 0.182264i | \(0.0583426\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3969.00 | 0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3852.00 | 0.413124 | 0.206562 | − | 0.978433i | \(-0.433772\pi\) | ||||
0.206562 | + | 0.978433i | \(0.433772\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −150.000 | −0.0159791 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9594.00 | −1.01517 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6522.00 | 0.685506 | 0.342753 | − | 0.939426i | \(-0.388641\pi\) | ||||
0.342753 | + | 0.939426i | \(0.388641\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3600.00 | 0.375870 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2280.00 | −0.236476 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9800.00 | 1.00974 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2090.00 | 0.213930 | 0.106965 | − | 0.994263i | \(-0.465887\pi\) | ||||
0.106965 | + | 0.994263i | \(0.465887\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2754.00 | −0.280056 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9894.00 | 0.999587 | 0.499793 | − | 0.866145i | \(-0.333409\pi\) | ||||
0.499793 | + | 0.866145i | \(0.333409\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3044.00 | −0.305544 | −0.152772 | − | 0.988261i | \(-0.548820\pi\) | ||||
−0.152772 | + | 0.988261i | \(0.548820\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2040.00 | −0.203447 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10236.0 | 1.01427 | 0.507137 | − | 0.861866i | \(-0.330704\pi\) | ||||
0.507137 | + | 0.861866i | \(0.330704\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5264.00 | 0.518271 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −498.000 | −0.0487190 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7008.00 | 0.681244 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 500.000 | 0.0482980 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3726.00 | 0.357656 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11496.0 | −1.09659 | −0.548294 | − | 0.836286i | \(-0.684723\pi\) | ||||
−0.548294 | + | 0.836286i | \(0.684723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14980.0 | 1.42002 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6048.00 | −0.569759 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1430.00 | −0.133882 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15316.0 | 1.42512 | 0.712561 | − | 0.701610i | \(-0.247535\pi\) | ||||
0.712561 | + | 0.701610i | \(0.247535\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9060.00 | −0.837847 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11616.0 | −1.06766 | −0.533832 | − | 0.845591i | \(-0.679248\pi\) | ||||
−0.533832 | + | 0.845591i | \(0.679248\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31212.0 | −2.85135 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1080.00 | −0.0980654 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13440.0 | −1.21301 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14996.0 | 1.34532 | 0.672658 | − | 0.739953i | \(-0.265152\pi\) | ||||
0.672658 | + | 0.739953i | \(0.265152\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2952.00 | −0.263245 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21648.0 | 1.91896 | 0.959480 | − | 0.281778i | \(-0.0909240\pi\) | ||||
0.959480 | + | 0.281778i | \(0.0909240\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7710.00 | 0.679387 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8109.00 | −0.710322 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3378.00 | −0.294160 | −0.147080 | − | 0.989125i | \(-0.546987\pi\) | ||||
−0.147080 | + | 0.989125i | \(0.546987\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12152.0 | 1.05200 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −540.000 | −0.0464748 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5860.00 | −0.501403 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1728.00 | −0.146997 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5886.00 | 0.497816 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16158.0 | −1.35872 | −0.679362 | − | 0.733804i | \(-0.737743\pi\) | ||||
−0.679362 | + | 0.733804i | \(0.737743\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −76.0000 | −0.00635420 | −0.00317710 | − | 0.999995i | \(-0.501011\pi\) | ||||
−0.00317710 | + | 0.999995i | \(0.501011\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2100.00 | −0.174574 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13872.0 | 1.14663 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6696.00 | −0.547235 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10500.0 | −0.853294 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9780.00 | 0.790329 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1728.00 | −0.138862 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10584.0 | −0.845798 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9278.00 | −0.737324 | −0.368662 | − | 0.929563i | \(-0.620184\pi\) | ||||
−0.368662 | + | 0.929563i | \(0.620184\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3630.00 | −0.286884 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9290.00 | 0.730165 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14564.0 | 1.13841 | 0.569206 | − | 0.822195i | \(-0.307251\pi\) | ||||
0.569206 | + | 0.822195i | \(0.307251\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3762.00 | 0.292456 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6120.00 | −0.473177 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −37856.0 | −2.91103 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3210.00 | −0.245508 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2154.00 | −0.163856 | −0.0819281 | − | 0.996638i | \(-0.526108\pi\) | ||||
−0.0819281 | + | 0.996638i | \(0.526108\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20440.0 | −1.54655 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7344.00 | 0.552699 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8700.00 | −0.651263 | −0.325632 | − | 0.945497i | \(-0.605577\pi\) | ||||
−0.325632 | + | 0.945497i | \(0.605577\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 870.000 | 0.0647808 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2268.00 | 0.167984 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4194.00 | 0.309001 | 0.154501 | − | 0.987993i | \(-0.450623\pi\) | ||||
0.154501 | + | 0.987993i | \(0.450623\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8020.00 | −0.587787 | −0.293894 | − | 0.955838i | \(-0.594951\pi\) | ||||
−0.293894 | + | 0.955838i | \(0.594951\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10152.0 | 0.740150 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1800.00 | 0.130548 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2686.00 | −0.193795 | −0.0968974 | − | 0.995294i | \(-0.530892\pi\) | ||||
−0.0968974 | + | 0.995294i | \(0.530892\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6114.00 | 0.438841 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17136.0 | −1.22362 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9936.00 | −0.705844 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3150.00 | 0.222626 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3012.00 | 0.211786 | 0.105893 | − | 0.994378i | \(-0.466230\pi\) | ||||
0.105893 | + | 0.994378i | \(0.466230\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2720.00 | 0.190281 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12294.0 | 0.855681 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15522.0 | −1.07489 | −0.537447 | − | 0.843298i | \(-0.680611\pi\) | ||||
−0.537447 | + | 0.843298i | \(0.680611\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14280.0 | 0.983904 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6744.00 | −0.462334 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19224.0 | −1.31130 | −0.655652 | − | 0.755063i | \(-0.727606\pi\) | ||||
−0.655652 | + | 0.755063i | \(0.727606\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6502.00 | −0.441301 | −0.220651 | − | 0.975353i | \(-0.570818\pi\) | ||||
−0.220651 | + | 0.975353i | \(0.570818\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1692.00 | 0.114268 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3775.00 | −0.253679 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29396.0 | −1.96565 | −0.982823 | − | 0.184552i | \(-0.940917\pi\) | ||||
−0.982823 | + | 0.184552i | \(0.940917\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25704.0 | 1.71031 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5040.00 | 0.333710 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10006.0 | 0.659280 | 0.329640 | − | 0.944107i | \(-0.393073\pi\) | ||||
0.329640 | + | 0.944107i | \(0.393073\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2250.00 | 0.147526 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23118.0 | 1.50842 | 0.754210 | − | 0.656633i | \(-0.228020\pi\) | ||||
0.754210 | + | 0.656633i | \(0.228020\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14036.0 | 0.911397 | 0.455698 | − | 0.890134i | \(-0.349390\pi\) | ||||
0.455698 | + | 0.890134i | \(0.349390\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1944.00 | −0.125620 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −840.000 | −0.0540191 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1440.00 | 0.0917194 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21828.0 | 1.38369 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4288.00 | 0.270527 | 0.135264 | − | 0.990810i | \(-0.456812\pi\) | ||||
0.135264 | + | 0.990810i | \(0.456812\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9780.00 | −0.614092 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10340.0 | 0.646190 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30870.0 | 1.92012 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4320.00 | −0.267444 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1314.00 | 0.0809671 | 0.0404835 | − | 0.999180i | \(-0.487110\pi\) | ||||
0.0404835 | + | 0.999180i | \(0.487110\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −628.000 | −0.0385162 | −0.0192581 | − | 0.999815i | \(-0.506130\pi\) | ||||
−0.0192581 | + | 0.999815i | \(0.506130\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4380.00 | 0.267383 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10944.0 | 0.664997 | 0.332498 | − | 0.943104i | \(-0.392108\pi\) | ||||
0.332498 | + | 0.943104i | \(0.392108\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17856.0 | 1.07998 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11424.0 | −0.687776 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1098.00 | −0.0658010 | −0.0329005 | − | 0.999459i | \(-0.510474\pi\) | ||||
−0.0329005 | + | 0.999459i | \(0.510474\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1560.00 | 0.0930599 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3906.00 | 0.231945 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 312.000 | 0.0184428 | 0.00922139 | − | 0.999957i | \(-0.497065\pi\) | ||||
0.00922139 | + | 0.999957i | \(0.497065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8678.00 | −0.510643 | −0.255322 | − | 0.966856i | \(-0.582181\pi\) | ||||
−0.255322 | + | 0.966856i | \(0.582181\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21420.0 | −1.25473 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2800.00 | 0.163277 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22032.0 | −1.27898 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8940.00 | −0.516652 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10032.0 | −0.577170 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14470.0 | −0.828793 | −0.414396 | − | 0.910097i | \(-0.636007\pi\) | ||||
−0.414396 | + | 0.910097i | \(0.636007\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11838.0 | 0.672040 | 0.336020 | − | 0.941855i | \(-0.390919\pi\) | ||||
0.336020 | + | 0.941855i | \(0.390919\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8008.00 | −0.452605 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9540.00 | 0.536819 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25548.0 | −1.43128 | −0.715642 | − | 0.698467i | \(-0.753866\pi\) | ||||
−0.715642 | + | 0.698467i | \(0.753866\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13230.0 | 0.737945 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10122.0 | 0.562123 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28980.0 | 1.60239 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18412.0 | −1.01364 | −0.506820 | − | 0.862052i | \(-0.669179\pi\) | ||||
−0.506820 | + | 0.862052i | \(0.669179\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6048.00 | −0.331522 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6380.00 | −0.348212 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15300.0 | −0.831462 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5850.00 | −0.316548 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8814.00 | 0.474893 | 0.237447 | − | 0.971401i | \(-0.423690\pi\) | ||||
0.237447 | + | 0.971401i | \(0.423690\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4280.00 | 0.229621 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1080.00 | −0.0576953 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 43176.0 | 2.29675 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17314.0 | 0.917124 | 0.458562 | − | 0.888662i | \(-0.348365\pi\) | ||||
0.458562 | + | 0.888662i | \(0.348365\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12168.0 | −0.641822 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9792.00 | 0.514324 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8400.00 | −0.439360 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6696.00 | 0.348768 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 768.000 | 0.0398353 | 0.0199176 | − | 0.999802i | \(-0.493660\pi\) | ||||
0.0199176 | + | 0.999802i | \(0.493660\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32816.0 | −1.69505 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5466.00 | 0.281166 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7650.00 | −0.391881 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18196.0 | 0.928270 | 0.464135 | − | 0.885764i | \(-0.346365\pi\) | ||||
0.464135 | + | 0.885764i | \(0.346365\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29784.0 | −1.50698 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18142.0 | 0.914175 | 0.457087 | − | 0.889422i | \(-0.348893\pi\) | ||||
0.457087 | + | 0.889422i | \(0.348893\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6615.00 | −0.331970 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4512.00 | −0.225511 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13660.0 | −0.679961 | −0.339981 | − | 0.940432i | \(-0.610420\pi\) | ||||
−0.339981 | + | 0.940432i | \(0.610420\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4200.00 | −0.208220 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12768.0 | 0.630434 | 0.315217 | − | 0.949020i | \(-0.397923\pi\) | ||||
0.315217 | + | 0.949020i | \(0.397923\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15990.0 | 0.786347 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5508.00 | −0.269782 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 54768.0 | 2.67180 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22952.0 | −1.11522 | −0.557610 | − | 0.830103i | \(-0.688282\pi\) | ||||
−0.557610 | + | 0.830103i | \(0.688282\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4464.00 | −0.216039 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3800.00 | 0.183174 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15818.0 | −0.759465 | −0.379732 | − | 0.925096i | \(-0.623984\pi\) | ||||
−0.379732 | + | 0.925096i | \(0.623984\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5184.00 | 0.247915 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18558.0 | −0.884004 | −0.442002 | − | 0.897014i | \(-0.645732\pi\) | ||||
−0.442002 | + | 0.897014i | \(0.645732\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 52024.0 | 2.46841 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4590.00 | 0.216930 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −52080.0 | −2.45176 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14978.0 | 0.702367 | 0.351184 | − | 0.936307i | \(-0.385779\pi\) | ||||
0.351184 | + | 0.936307i | \(0.385779\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8982.00 | 0.419557 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8946.00 | −0.416255 | −0.208128 | − | 0.978102i | \(-0.566737\pi\) | ||||
−0.208128 | + | 0.978102i | \(0.566737\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3400.00 | 0.157589 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17976.0 | −0.829968 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3000.00 | −0.137980 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11520.0 | 0.527808 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8262.00 | 0.377088 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 830.000 | 0.0377375 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18436.0 | −0.835035 | −0.417517 | − | 0.908669i | \(-0.637100\pi\) | ||||
−0.417517 | + | 0.908669i | \(0.637100\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7416.00 | −0.334622 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4872.00 | 0.218999 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29260.0 | 1.31028 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6210.00 | −0.277039 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16314.0 | −0.725058 | −0.362529 | − | 0.931972i | \(-0.618087\pi\) | ||||
−0.362529 | + | 0.931972i | \(0.618087\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7344.00 | 0.325172 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −270.000 | −0.0119101 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10416.0 | −0.457749 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10080.0 | 0.441333 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11862.0 | 0.517425 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25446.0 | −1.10585 | −0.552926 | − | 0.833231i | \(-0.686489\pi\) | ||||
−0.552926 | + | 0.833231i | \(0.686489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42740.0 | 1.85056 | 0.925280 | − | 0.379284i | \(-0.123830\pi\) | ||||
0.925280 | + | 0.379284i | \(0.123830\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6528.00 | −0.281608 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15100.0 | 0.648994 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5840.00 | −0.250080 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17640.0 | 0.752615 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29946.0 | −1.27299 | −0.636494 | − | 0.771282i | \(-0.719616\pi\) | ||||
−0.636494 | + | 0.771282i | \(0.719616\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32596.0 | 1.38059 | 0.690295 | − | 0.723528i | \(-0.257481\pi\) | ||||
0.690295 | + | 0.723528i | \(0.257481\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1800.00 | 0.0759612 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3804.00 | 0.159949 | 0.0799746 | − | 0.996797i | \(-0.474516\pi\) | ||||
0.0799746 | + | 0.996797i | \(0.474516\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3278.00 | −0.137334 | −0.0686669 | − | 0.997640i | \(-0.521875\pi\) | ||||
−0.0686669 | + | 0.997640i | \(0.521875\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3102.00 | 0.129491 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 44982.0 | 1.87099 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4920.00 | 0.203909 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3672.00 | −0.151640 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5784.00 | 0.238005 | 0.119002 | − | 0.992894i | \(-0.462030\pi\) | ||||
0.119002 | + | 0.992894i | \(0.462030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 69247.0 | 2.83927 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19962.0 | 0.815573 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13515.0 | 0.550213 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21140.0 | −0.857590 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5268.00 | 0.212953 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15408.0 | 0.620657 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17306.0 | −0.694661 | −0.347331 | − | 0.937743i | \(-0.612912\pi\) | ||||
−0.347331 | + | 0.937743i | \(0.612912\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 900.000 | 0.0359992 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31134.0 | 1.24098 | 0.620488 | − | 0.784216i | \(-0.286934\pi\) | ||||
0.620488 | + | 0.784216i | \(0.286934\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10780.0 | −0.428183 | −0.214091 | − | 0.976814i | \(-0.568679\pi\) | ||||
−0.214091 | + | 0.976814i | \(0.568679\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12600.0 | 0.498730 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3456.00 | −0.136319 | −0.0681597 | − | 0.997674i | \(-0.521713\pi\) | ||||
−0.0681597 | + | 0.997674i | \(0.521713\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9810.00 | −0.385607 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16473.0 | −0.645274 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32448.0 | 1.26665 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13160.0 | 0.511951 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2574.00 | −0.0997900 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3500.00 | 0.135225 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2618.00 | −0.100802 | −0.0504011 | − | 0.998729i | \(-0.516050\pi\) | ||||
−0.0504011 | + | 0.998729i | \(0.516050\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9702.00 | 0.372287 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26550.0 | −1.01531 | −0.507657 | − | 0.861559i | \(-0.669488\pi\) | ||||
−0.507657 | + | 0.861559i | \(0.669488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27596.0 | 1.05173 | 0.525866 | − | 0.850567i | \(-0.323741\pi\) | ||||
0.525866 | + | 0.850567i | \(0.323741\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11160.0 | 0.423886 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37848.0 | 1.43271 | 0.716354 | − | 0.697737i | \(-0.245810\pi\) | ||||
0.716354 | + | 0.697737i | \(0.245810\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 57904.0 | 2.18452 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1944.00 | −0.0730937 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1440.00 | 0.0539617 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2880.00 | 0.107562 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15120.0 | −0.562812 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41616.0 | −1.54391 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42228.0 | 1.56140 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24528.0 | 0.903921 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6050.00 | 0.222220 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4804.00 | −0.175870 | −0.0879351 | − | 0.996126i | \(-0.528027\pi\) | ||||
−0.0879351 | + | 0.996126i | \(0.528027\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13878.0 | 0.506385 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28608.0 | −1.04042 | −0.520211 | − | 0.854037i | \(-0.674147\pi\) | ||||
−0.520211 | + | 0.854037i | \(0.674147\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14688.0 | 0.532423 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6270.00 | −0.226535 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8736.00 | 0.314600 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40768.0 | 1.46334 | 0.731672 | − | 0.681657i | \(-0.238741\pi\) | ||||
0.731672 | + | 0.681657i | \(0.238741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6108.00 | −0.218529 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33600.0 | −1.19822 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5350.00 | 0.190170 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10548.0 | −0.373724 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27642.0 | 0.976216 | 0.488108 | − | 0.872783i | \(-0.337687\pi\) | ||||
0.488108 | + | 0.872783i | \(0.337687\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8820.00 | 0.310487 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −288.000 | −0.0101058 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12240.0 | −0.428119 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28106.0 | 0.979918 | 0.489959 | − | 0.871746i | \(-0.337012\pi\) | ||||
0.489959 | + | 0.871746i | \(0.337012\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3606.00 | −0.125322 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14730.0 | −0.510291 | −0.255146 | − | 0.966903i | \(-0.582123\pi\) | ||||
−0.255146 | + | 0.966903i | \(0.582123\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10800.0 | −0.372955 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3780.00 | −0.130120 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9564.00 | −0.328182 | −0.164091 | − | 0.986445i | \(-0.552469\pi\) | ||||
−0.164091 | + | 0.986445i | \(0.552469\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30380.0 | 1.03917 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11394.0 | −0.388513 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53898.0 | −1.83203 | −0.916017 | − | 0.401141i | \(-0.868614\pi\) | ||||
−0.916017 | + | 0.401141i | \(0.868614\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16920.0 | −0.573318 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −22032.0 | −0.744194 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 74088.0 | 2.49471 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11295.0 | −0.379141 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17604.0 | 0.589077 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10190.0 | −0.339925 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15140.0 | −0.503485 | −0.251742 | − | 0.967794i | \(-0.581004\pi\) | ||||
−0.251742 | + | 0.967794i | \(0.581004\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6120.00 | −0.202892 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23808.0 | 0.786854 | 0.393427 | − | 0.919356i | \(-0.371289\pi\) | ||||
0.393427 | + | 0.919356i | \(0.371289\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35728.0 | −1.17717 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5250.00 | −0.172446 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23094.0 | 0.756236 | 0.378118 | − | 0.925757i | \(-0.376571\pi\) | ||||
0.378118 | + | 0.925757i | \(0.376571\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 720.000 | 0.0235049 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16722.0 | 0.544233 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7584.00 | −0.246075 | −0.123038 | − | 0.992402i | \(-0.539264\pi\) | ||||
−0.123038 | + | 0.992402i | \(0.539264\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20490.0 | −0.662808 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6048.00 | −0.195046 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21024.0 | −0.675960 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26752.0 | 0.857523 | 0.428761 | − | 0.903418i | \(-0.358950\pi\) | ||||
0.428761 | + | 0.903418i | \(0.358950\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17004.0 | 0.543409 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11240.0 | 0.358123 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7778.00 | −0.247073 | −0.123536 | − | 0.992340i | \(-0.539424\pi\) | ||||
−0.123536 | + | 0.992340i | \(0.539424\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5778.00 | −0.182991 |
(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 | 960.4.a.r.1.1 | 1 | ||
4.3 | odd | 2 | 960.4.a.bc.1.1 | 1 | |||
8.3 | odd | 2 | 60.4.a.a.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 240.4.a.i.1.1 | 1 | |||
24.5 | odd | 2 | 720.4.a.bb.1.1 | 1 | |||
24.11 | even | 2 | 180.4.a.d.1.1 | 1 | |||
40.3 | even | 4 | 300.4.d.b.49.1 | 2 | |||
40.13 | odd | 4 | 1200.4.f.n.49.2 | 2 | |||
40.19 | odd | 2 | 300.4.a.i.1.1 | 1 | |||
40.27 | even | 4 | 300.4.d.b.49.2 | 2 | |||
40.29 | even | 2 | 1200.4.a.a.1.1 | 1 | |||
40.37 | odd | 4 | 1200.4.f.n.49.1 | 2 | |||
72.11 | even | 6 | 1620.4.i.f.1081.1 | 2 | |||
72.43 | odd | 6 | 1620.4.i.l.1081.1 | 2 | |||
72.59 | even | 6 | 1620.4.i.f.541.1 | 2 | |||
72.67 | odd | 6 | 1620.4.i.l.541.1 | 2 | |||
120.59 | even | 2 | 900.4.a.q.1.1 | 1 | |||
120.83 | odd | 4 | 900.4.d.h.649.2 | 2 | |||
120.107 | odd | 4 | 900.4.d.h.649.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.4.a.a.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
180.4.a.d.1.1 | 1 | 24.11 | even | 2 | |||
240.4.a.i.1.1 | 1 | 8.5 | even | 2 | |||
300.4.a.i.1.1 | 1 | 40.19 | odd | 2 | |||
300.4.d.b.49.1 | 2 | 40.3 | even | 4 | |||
300.4.d.b.49.2 | 2 | 40.27 | even | 4 | |||
720.4.a.bb.1.1 | 1 | 24.5 | odd | 2 | |||
900.4.a.q.1.1 | 1 | 120.59 | even | 2 | |||
900.4.d.h.649.1 | 2 | 120.107 | odd | 4 | |||
900.4.d.h.649.2 | 2 | 120.83 | odd | 4 | |||
960.4.a.r.1.1 | 1 | 1.1 | even | 1 | trivial | ||
960.4.a.bc.1.1 | 1 | 4.3 | odd | 2 | |||
1200.4.a.a.1.1 | 1 | 40.29 | even | 2 | |||
1200.4.f.n.49.1 | 2 | 40.37 | odd | 4 | |||
1200.4.f.n.49.2 | 2 | 40.13 | odd | 4 | |||
1620.4.i.f.541.1 | 2 | 72.59 | even | 6 | |||
1620.4.i.f.1081.1 | 2 | 72.11 | even | 6 | |||
1620.4.i.l.541.1 | 2 | 72.67 | odd | 6 | |||
1620.4.i.l.1081.1 | 2 | 72.43 | odd | 6 |