Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [102,4,Mod(1,102)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(102, 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("102.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 102 = 2 \cdot 3 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 102.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: | \(6.01819482059\) |
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 | \(\chi\) | \(=\) | 102.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −5.00000 | −0.447214 | −0.223607 | − | 0.974679i | \(-0.571783\pi\) | ||||
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | −32.0000 | −1.72784 | −0.863919 | − | 0.503631i | \(-0.831997\pi\) | ||||
−0.863919 | + | 0.503631i | \(0.831997\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 10.0000 | 0.316228 | ||||||||
\(11\) | 27.0000 | 0.740073 | 0.370037 | − | 0.929017i | \(-0.379345\pi\) | ||||
0.370037 | + | 0.929017i | \(0.379345\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | −69.0000 | −1.47209 | −0.736044 | − | 0.676933i | \(-0.763309\pi\) | ||||
−0.736044 | + | 0.676933i | \(0.763309\pi\) | |||||||
\(14\) | 64.0000 | 1.22177 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −17.0000 | −0.242536 | ||||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | −83.0000 | −1.00218 | −0.501092 | − | 0.865394i | \(-0.667068\pi\) | ||||
−0.501092 | + | 0.865394i | \(0.667068\pi\) | |||||||
\(20\) | −20.0000 | −0.223607 | ||||||||
\(21\) | −96.0000 | −0.997567 | ||||||||
\(22\) | −54.0000 | −0.523311 | ||||||||
\(23\) | −117.000 | −1.06070 | −0.530352 | − | 0.847778i | \(-0.677940\pi\) | ||||
−0.530352 | + | 0.847778i | \(0.677940\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | −100.000 | −0.800000 | ||||||||
\(26\) | 138.000 | 1.04092 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −128.000 | −0.863919 | ||||||||
\(29\) | 94.0000 | 0.601909 | 0.300955 | − | 0.953638i | \(-0.402695\pi\) | ||||
0.300955 | + | 0.953638i | \(0.402695\pi\) | |||||||
\(30\) | 30.0000 | 0.182574 | ||||||||
\(31\) | 198.000 | 1.14716 | 0.573578 | − | 0.819151i | \(-0.305555\pi\) | ||||
0.573578 | + | 0.819151i | \(0.305555\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 81.0000 | 0.427282 | ||||||||
\(34\) | 34.0000 | 0.171499 | ||||||||
\(35\) | 160.000 | 0.772712 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −244.000 | −1.08414 | −0.542072 | − | 0.840332i | \(-0.682360\pi\) | ||||
−0.542072 | + | 0.840332i | \(0.682360\pi\) | |||||||
\(38\) | 166.000 | 0.708651 | ||||||||
\(39\) | −207.000 | −0.849911 | ||||||||
\(40\) | 40.0000 | 0.158114 | ||||||||
\(41\) | 169.000 | 0.643741 | 0.321870 | − | 0.946784i | \(-0.395688\pi\) | ||||
0.321870 | + | 0.946784i | \(0.395688\pi\) | |||||||
\(42\) | 192.000 | 0.705387 | ||||||||
\(43\) | 227.000 | 0.805051 | 0.402525 | − | 0.915409i | \(-0.368133\pi\) | ||||
0.402525 | + | 0.915409i | \(0.368133\pi\) | |||||||
\(44\) | 108.000 | 0.370037 | ||||||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | 234.000 | 0.750031 | ||||||||
\(47\) | −382.000 | −1.18554 | −0.592770 | − | 0.805371i | \(-0.701966\pi\) | ||||
−0.592770 | + | 0.805371i | \(0.701966\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 681.000 | 1.98542 | ||||||||
\(50\) | 200.000 | 0.565685 | ||||||||
\(51\) | −51.0000 | −0.140028 | ||||||||
\(52\) | −276.000 | −0.736044 | ||||||||
\(53\) | 686.000 | 1.77791 | 0.888956 | − | 0.457992i | \(-0.151431\pi\) | ||||
0.888956 | + | 0.457992i | \(0.151431\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | −135.000 | −0.330971 | ||||||||
\(56\) | 256.000 | 0.610883 | ||||||||
\(57\) | −249.000 | −0.578612 | ||||||||
\(58\) | −188.000 | −0.425614 | ||||||||
\(59\) | 450.000 | 0.992966 | 0.496483 | − | 0.868046i | \(-0.334624\pi\) | ||||
0.496483 | + | 0.868046i | \(0.334624\pi\) | |||||||
\(60\) | −60.0000 | −0.129099 | ||||||||
\(61\) | −700.000 | −1.46928 | −0.734638 | − | 0.678459i | \(-0.762648\pi\) | ||||
−0.734638 | + | 0.678459i | \(0.762648\pi\) | |||||||
\(62\) | −396.000 | −0.811162 | ||||||||
\(63\) | −288.000 | −0.575946 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 345.000 | 0.658338 | ||||||||
\(66\) | −162.000 | −0.302134 | ||||||||
\(67\) | 540.000 | 0.984649 | 0.492325 | − | 0.870412i | \(-0.336147\pi\) | ||||
0.492325 | + | 0.870412i | \(0.336147\pi\) | |||||||
\(68\) | −68.0000 | −0.121268 | ||||||||
\(69\) | −351.000 | −0.612398 | ||||||||
\(70\) | −320.000 | −0.546390 | ||||||||
\(71\) | −276.000 | −0.461340 | −0.230670 | − | 0.973032i | \(-0.574092\pi\) | ||||
−0.230670 | + | 0.973032i | \(0.574092\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | −298.000 | −0.477784 | −0.238892 | − | 0.971046i | \(-0.576784\pi\) | ||||
−0.238892 | + | 0.971046i | \(0.576784\pi\) | |||||||
\(74\) | 488.000 | 0.766606 | ||||||||
\(75\) | −300.000 | −0.461880 | ||||||||
\(76\) | −332.000 | −0.501092 | ||||||||
\(77\) | −864.000 | −1.27873 | ||||||||
\(78\) | 414.000 | 0.600978 | ||||||||
\(79\) | −182.000 | −0.259197 | −0.129599 | − | 0.991567i | \(-0.541369\pi\) | ||||
−0.129599 | + | 0.991567i | \(0.541369\pi\) | |||||||
\(80\) | −80.0000 | −0.111803 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −338.000 | −0.455193 | ||||||||
\(83\) | 282.000 | 0.372934 | 0.186467 | − | 0.982461i | \(-0.440296\pi\) | ||||
0.186467 | + | 0.982461i | \(0.440296\pi\) | |||||||
\(84\) | −384.000 | −0.498784 | ||||||||
\(85\) | 85.0000 | 0.108465 | ||||||||
\(86\) | −454.000 | −0.569257 | ||||||||
\(87\) | 282.000 | 0.347512 | ||||||||
\(88\) | −216.000 | −0.261655 | ||||||||
\(89\) | −1468.00 | −1.74840 | −0.874200 | − | 0.485565i | \(-0.838614\pi\) | ||||
−0.874200 | + | 0.485565i | \(0.838614\pi\) | |||||||
\(90\) | 90.0000 | 0.105409 | ||||||||
\(91\) | 2208.00 | 2.54353 | ||||||||
\(92\) | −468.000 | −0.530352 | ||||||||
\(93\) | 594.000 | 0.662311 | ||||||||
\(94\) | 764.000 | 0.838304 | ||||||||
\(95\) | 415.000 | 0.448191 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | −1140.00 | −1.19329 | −0.596647 | − | 0.802504i | \(-0.703501\pi\) | ||||
−0.596647 | + | 0.802504i | \(0.703501\pi\) | |||||||
\(98\) | −1362.00 | −1.40391 | ||||||||
\(99\) | 243.000 | 0.246691 | ||||||||
\(100\) | −400.000 | −0.400000 | ||||||||
\(101\) | −1400.00 | −1.37926 | −0.689630 | − | 0.724162i | \(-0.742227\pi\) | ||||
−0.689630 | + | 0.724162i | \(0.742227\pi\) | |||||||
\(102\) | 102.000 | 0.0990148 | ||||||||
\(103\) | 1939.00 | 1.85491 | 0.927453 | − | 0.373939i | \(-0.121993\pi\) | ||||
0.927453 | + | 0.373939i | \(0.121993\pi\) | |||||||
\(104\) | 552.000 | 0.520462 | ||||||||
\(105\) | 480.000 | 0.446126 | ||||||||
\(106\) | −1372.00 | −1.25717 | ||||||||
\(107\) | 39.0000 | 0.0352362 | 0.0176181 | − | 0.999845i | \(-0.494392\pi\) | ||||
0.0176181 | + | 0.999845i | \(0.494392\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | −428.000 | −0.376101 | −0.188050 | − | 0.982159i | \(-0.560217\pi\) | ||||
−0.188050 | + | 0.982159i | \(0.560217\pi\) | |||||||
\(110\) | 270.000 | 0.234032 | ||||||||
\(111\) | −732.000 | −0.625931 | ||||||||
\(112\) | −512.000 | −0.431959 | ||||||||
\(113\) | 715.000 | 0.595235 | 0.297617 | − | 0.954685i | \(-0.403808\pi\) | ||||
0.297617 | + | 0.954685i | \(0.403808\pi\) | |||||||
\(114\) | 498.000 | 0.409140 | ||||||||
\(115\) | 585.000 | 0.474361 | ||||||||
\(116\) | 376.000 | 0.300955 | ||||||||
\(117\) | −621.000 | −0.490696 | ||||||||
\(118\) | −900.000 | −0.702133 | ||||||||
\(119\) | 544.000 | 0.419062 | ||||||||
\(120\) | 120.000 | 0.0912871 | ||||||||
\(121\) | −602.000 | −0.452292 | ||||||||
\(122\) | 1400.00 | 1.03893 | ||||||||
\(123\) | 507.000 | 0.371664 | ||||||||
\(124\) | 792.000 | 0.573578 | ||||||||
\(125\) | 1125.00 | 0.804984 | ||||||||
\(126\) | 576.000 | 0.407255 | ||||||||
\(127\) | 797.000 | 0.556869 | 0.278434 | − | 0.960455i | \(-0.410185\pi\) | ||||
0.278434 | + | 0.960455i | \(0.410185\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 681.000 | 0.464796 | ||||||||
\(130\) | −690.000 | −0.465515 | ||||||||
\(131\) | 373.000 | 0.248772 | 0.124386 | − | 0.992234i | \(-0.460304\pi\) | ||||
0.124386 | + | 0.992234i | \(0.460304\pi\) | |||||||
\(132\) | 324.000 | 0.213641 | ||||||||
\(133\) | 2656.00 | 1.73161 | ||||||||
\(134\) | −1080.00 | −0.696252 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 136.000 | 0.0857493 | ||||||||
\(137\) | −2706.00 | −1.68751 | −0.843756 | − | 0.536727i | \(-0.819661\pi\) | ||||
−0.843756 | + | 0.536727i | \(0.819661\pi\) | |||||||
\(138\) | 702.000 | 0.433030 | ||||||||
\(139\) | −2086.00 | −1.27289 | −0.636447 | − | 0.771321i | \(-0.719597\pi\) | ||||
−0.636447 | + | 0.771321i | \(0.719597\pi\) | |||||||
\(140\) | 640.000 | 0.386356 | ||||||||
\(141\) | −1146.00 | −0.684472 | ||||||||
\(142\) | 552.000 | 0.326217 | ||||||||
\(143\) | −1863.00 | −1.08945 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −470.000 | −0.269182 | ||||||||
\(146\) | 596.000 | 0.337845 | ||||||||
\(147\) | 2043.00 | 1.14628 | ||||||||
\(148\) | −976.000 | −0.542072 | ||||||||
\(149\) | −1446.00 | −0.795040 | −0.397520 | − | 0.917594i | \(-0.630129\pi\) | ||||
−0.397520 | + | 0.917594i | \(0.630129\pi\) | |||||||
\(150\) | 600.000 | 0.326599 | ||||||||
\(151\) | −744.000 | −0.400966 | −0.200483 | − | 0.979697i | \(-0.564251\pi\) | ||||
−0.200483 | + | 0.979697i | \(0.564251\pi\) | |||||||
\(152\) | 664.000 | 0.354326 | ||||||||
\(153\) | −153.000 | −0.0808452 | ||||||||
\(154\) | 1728.00 | 0.904196 | ||||||||
\(155\) | −990.000 | −0.513024 | ||||||||
\(156\) | −828.000 | −0.424955 | ||||||||
\(157\) | 207.000 | 0.105225 | 0.0526127 | − | 0.998615i | \(-0.483245\pi\) | ||||
0.0526127 | + | 0.998615i | \(0.483245\pi\) | |||||||
\(158\) | 364.000 | 0.183280 | ||||||||
\(159\) | 2058.00 | 1.02648 | ||||||||
\(160\) | 160.000 | 0.0790569 | ||||||||
\(161\) | 3744.00 | 1.83272 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | −1746.00 | −0.839002 | −0.419501 | − | 0.907755i | \(-0.637795\pi\) | ||||
−0.419501 | + | 0.907755i | \(0.637795\pi\) | |||||||
\(164\) | 676.000 | 0.321870 | ||||||||
\(165\) | −405.000 | −0.191086 | ||||||||
\(166\) | −564.000 | −0.263704 | ||||||||
\(167\) | −1153.00 | −0.534262 | −0.267131 | − | 0.963660i | \(-0.586076\pi\) | ||||
−0.267131 | + | 0.963660i | \(0.586076\pi\) | |||||||
\(168\) | 768.000 | 0.352693 | ||||||||
\(169\) | 2564.00 | 1.16705 | ||||||||
\(170\) | −170.000 | −0.0766965 | ||||||||
\(171\) | −747.000 | −0.334062 | ||||||||
\(172\) | 908.000 | 0.402525 | ||||||||
\(173\) | −3521.00 | −1.54738 | −0.773690 | − | 0.633565i | \(-0.781591\pi\) | ||||
−0.773690 | + | 0.633565i | \(0.781591\pi\) | |||||||
\(174\) | −564.000 | −0.245728 | ||||||||
\(175\) | 3200.00 | 1.38227 | ||||||||
\(176\) | 432.000 | 0.185018 | ||||||||
\(177\) | 1350.00 | 0.573289 | ||||||||
\(178\) | 2936.00 | 1.23631 | ||||||||
\(179\) | 2646.00 | 1.10487 | 0.552434 | − | 0.833557i | \(-0.313699\pi\) | ||||
0.552434 | + | 0.833557i | \(0.313699\pi\) | |||||||
\(180\) | −180.000 | −0.0745356 | ||||||||
\(181\) | −1454.00 | −0.597099 | −0.298550 | − | 0.954394i | \(-0.596503\pi\) | ||||
−0.298550 | + | 0.954394i | \(0.596503\pi\) | |||||||
\(182\) | −4416.00 | −1.79855 | ||||||||
\(183\) | −2100.00 | −0.848287 | ||||||||
\(184\) | 936.000 | 0.375015 | ||||||||
\(185\) | 1220.00 | 0.484844 | ||||||||
\(186\) | −1188.00 | −0.468325 | ||||||||
\(187\) | −459.000 | −0.179494 | ||||||||
\(188\) | −1528.00 | −0.592770 | ||||||||
\(189\) | −864.000 | −0.332522 | ||||||||
\(190\) | −830.000 | −0.316919 | ||||||||
\(191\) | 3730.00 | 1.41305 | 0.706527 | − | 0.707686i | \(-0.250261\pi\) | ||||
0.706527 | + | 0.707686i | \(0.250261\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | −2478.00 | −0.924199 | −0.462099 | − | 0.886828i | \(-0.652904\pi\) | ||||
−0.462099 | + | 0.886828i | \(0.652904\pi\) | |||||||
\(194\) | 2280.00 | 0.843786 | ||||||||
\(195\) | 1035.00 | 0.380092 | ||||||||
\(196\) | 2724.00 | 0.992711 | ||||||||
\(197\) | −2141.00 | −0.774314 | −0.387157 | − | 0.922014i | \(-0.626543\pi\) | ||||
−0.387157 | + | 0.922014i | \(0.626543\pi\) | |||||||
\(198\) | −486.000 | −0.174437 | ||||||||
\(199\) | −580.000 | −0.206609 | −0.103304 | − | 0.994650i | \(-0.532942\pi\) | ||||
−0.103304 | + | 0.994650i | \(0.532942\pi\) | |||||||
\(200\) | 800.000 | 0.282843 | ||||||||
\(201\) | 1620.00 | 0.568488 | ||||||||
\(202\) | 2800.00 | 0.975284 | ||||||||
\(203\) | −3008.00 | −1.04000 | ||||||||
\(204\) | −204.000 | −0.0700140 | ||||||||
\(205\) | −845.000 | −0.287890 | ||||||||
\(206\) | −3878.00 | −1.31162 | ||||||||
\(207\) | −1053.00 | −0.353568 | ||||||||
\(208\) | −1104.00 | −0.368022 | ||||||||
\(209\) | −2241.00 | −0.741690 | ||||||||
\(210\) | −960.000 | −0.315459 | ||||||||
\(211\) | −3826.00 | −1.24831 | −0.624153 | − | 0.781302i | \(-0.714556\pi\) | ||||
−0.624153 | + | 0.781302i | \(0.714556\pi\) | |||||||
\(212\) | 2744.00 | 0.888956 | ||||||||
\(213\) | −828.000 | −0.266355 | ||||||||
\(214\) | −78.0000 | −0.0249157 | ||||||||
\(215\) | −1135.00 | −0.360030 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | −6336.00 | −1.98210 | ||||||||
\(218\) | 856.000 | 0.265943 | ||||||||
\(219\) | −894.000 | −0.275849 | ||||||||
\(220\) | −540.000 | −0.165485 | ||||||||
\(221\) | 1173.00 | 0.357034 | ||||||||
\(222\) | 1464.00 | 0.442600 | ||||||||
\(223\) | −1759.00 | −0.528212 | −0.264106 | − | 0.964494i | \(-0.585077\pi\) | ||||
−0.264106 | + | 0.964494i | \(0.585077\pi\) | |||||||
\(224\) | 1024.00 | 0.305441 | ||||||||
\(225\) | −900.000 | −0.266667 | ||||||||
\(226\) | −1430.00 | −0.420895 | ||||||||
\(227\) | 341.000 | 0.0997047 | 0.0498523 | − | 0.998757i | \(-0.484125\pi\) | ||||
0.0498523 | + | 0.998757i | \(0.484125\pi\) | |||||||
\(228\) | −996.000 | −0.289306 | ||||||||
\(229\) | 3958.00 | 1.14215 | 0.571074 | − | 0.820898i | \(-0.306527\pi\) | ||||
0.571074 | + | 0.820898i | \(0.306527\pi\) | |||||||
\(230\) | −1170.00 | −0.335424 | ||||||||
\(231\) | −2592.00 | −0.738273 | ||||||||
\(232\) | −752.000 | −0.212807 | ||||||||
\(233\) | 3009.00 | 0.846035 | 0.423017 | − | 0.906122i | \(-0.360971\pi\) | ||||
0.423017 | + | 0.906122i | \(0.360971\pi\) | |||||||
\(234\) | 1242.00 | 0.346975 | ||||||||
\(235\) | 1910.00 | 0.530190 | ||||||||
\(236\) | 1800.00 | 0.496483 | ||||||||
\(237\) | −546.000 | −0.149648 | ||||||||
\(238\) | −1088.00 | −0.296322 | ||||||||
\(239\) | 3464.00 | 0.937521 | 0.468761 | − | 0.883325i | \(-0.344701\pi\) | ||||
0.468761 | + | 0.883325i | \(0.344701\pi\) | |||||||
\(240\) | −240.000 | −0.0645497 | ||||||||
\(241\) | 156.000 | 0.0416964 | 0.0208482 | − | 0.999783i | \(-0.493363\pi\) | ||||
0.0208482 | + | 0.999783i | \(0.493363\pi\) | |||||||
\(242\) | 1204.00 | 0.319818 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −2800.00 | −0.734638 | ||||||||
\(245\) | −3405.00 | −0.887908 | ||||||||
\(246\) | −1014.00 | −0.262806 | ||||||||
\(247\) | 5727.00 | 1.47530 | ||||||||
\(248\) | −1584.00 | −0.405581 | ||||||||
\(249\) | 846.000 | 0.215314 | ||||||||
\(250\) | −2250.00 | −0.569210 | ||||||||
\(251\) | −4464.00 | −1.12257 | −0.561285 | − | 0.827622i | \(-0.689693\pi\) | ||||
−0.561285 | + | 0.827622i | \(0.689693\pi\) | |||||||
\(252\) | −1152.00 | −0.287973 | ||||||||
\(253\) | −3159.00 | −0.784999 | ||||||||
\(254\) | −1594.00 | −0.393766 | ||||||||
\(255\) | 255.000 | 0.0626224 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5544.00 | 1.34562 | 0.672812 | − | 0.739814i | \(-0.265086\pi\) | ||||
0.672812 | + | 0.739814i | \(0.265086\pi\) | |||||||
\(258\) | −1362.00 | −0.328661 | ||||||||
\(259\) | 7808.00 | 1.87323 | ||||||||
\(260\) | 1380.00 | 0.329169 | ||||||||
\(261\) | 846.000 | 0.200636 | ||||||||
\(262\) | −746.000 | −0.175909 | ||||||||
\(263\) | 612.000 | 0.143489 | 0.0717444 | − | 0.997423i | \(-0.477143\pi\) | ||||
0.0717444 | + | 0.997423i | \(0.477143\pi\) | |||||||
\(264\) | −648.000 | −0.151067 | ||||||||
\(265\) | −3430.00 | −0.795107 | ||||||||
\(266\) | −5312.00 | −1.22443 | ||||||||
\(267\) | −4404.00 | −1.00944 | ||||||||
\(268\) | 2160.00 | 0.492325 | ||||||||
\(269\) | 5601.00 | 1.26951 | 0.634757 | − | 0.772712i | \(-0.281100\pi\) | ||||
0.634757 | + | 0.772712i | \(0.281100\pi\) | |||||||
\(270\) | 270.000 | 0.0608581 | ||||||||
\(271\) | −5851.00 | −1.31152 | −0.655762 | − | 0.754968i | \(-0.727652\pi\) | ||||
−0.655762 | + | 0.754968i | \(0.727652\pi\) | |||||||
\(272\) | −272.000 | −0.0606339 | ||||||||
\(273\) | 6624.00 | 1.46851 | ||||||||
\(274\) | 5412.00 | 1.19325 | ||||||||
\(275\) | −2700.00 | −0.592059 | ||||||||
\(276\) | −1404.00 | −0.306199 | ||||||||
\(277\) | −5138.00 | −1.11449 | −0.557243 | − | 0.830350i | \(-0.688141\pi\) | ||||
−0.557243 | + | 0.830350i | \(0.688141\pi\) | |||||||
\(278\) | 4172.00 | 0.900072 | ||||||||
\(279\) | 1782.00 | 0.382385 | ||||||||
\(280\) | −1280.00 | −0.273195 | ||||||||
\(281\) | 7608.00 | 1.61514 | 0.807572 | − | 0.589770i | \(-0.200781\pi\) | ||||
0.807572 | + | 0.589770i | \(0.200781\pi\) | |||||||
\(282\) | 2292.00 | 0.483995 | ||||||||
\(283\) | 8474.00 | 1.77995 | 0.889977 | − | 0.456005i | \(-0.150720\pi\) | ||||
0.889977 | + | 0.456005i | \(0.150720\pi\) | |||||||
\(284\) | −1104.00 | −0.230670 | ||||||||
\(285\) | 1245.00 | 0.258763 | ||||||||
\(286\) | 3726.00 | 0.770360 | ||||||||
\(287\) | −5408.00 | −1.11228 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | 289.000 | 0.0588235 | ||||||||
\(290\) | 940.000 | 0.190340 | ||||||||
\(291\) | −3420.00 | −0.688948 | ||||||||
\(292\) | −1192.00 | −0.238892 | ||||||||
\(293\) | 7672.00 | 1.52970 | 0.764852 | − | 0.644207i | \(-0.222812\pi\) | ||||
0.764852 | + | 0.644207i | \(0.222812\pi\) | |||||||
\(294\) | −4086.00 | −0.810545 | ||||||||
\(295\) | −2250.00 | −0.444068 | ||||||||
\(296\) | 1952.00 | 0.383303 | ||||||||
\(297\) | 729.000 | 0.142427 | ||||||||
\(298\) | 2892.00 | 0.562178 | ||||||||
\(299\) | 8073.00 | 1.56145 | ||||||||
\(300\) | −1200.00 | −0.230940 | ||||||||
\(301\) | −7264.00 | −1.39100 | ||||||||
\(302\) | 1488.00 | 0.283526 | ||||||||
\(303\) | −4200.00 | −0.796316 | ||||||||
\(304\) | −1328.00 | −0.250546 | ||||||||
\(305\) | 3500.00 | 0.657080 | ||||||||
\(306\) | 306.000 | 0.0571662 | ||||||||
\(307\) | −3396.00 | −0.631335 | −0.315668 | − | 0.948870i | \(-0.602228\pi\) | ||||
−0.315668 | + | 0.948870i | \(0.602228\pi\) | |||||||
\(308\) | −3456.00 | −0.639363 | ||||||||
\(309\) | 5817.00 | 1.07093 | ||||||||
\(310\) | 1980.00 | 0.362763 | ||||||||
\(311\) | 6480.00 | 1.18150 | 0.590751 | − | 0.806854i | \(-0.298832\pi\) | ||||
0.590751 | + | 0.806854i | \(0.298832\pi\) | |||||||
\(312\) | 1656.00 | 0.300489 | ||||||||
\(313\) | −4940.00 | −0.892094 | −0.446047 | − | 0.895010i | \(-0.647169\pi\) | ||||
−0.446047 | + | 0.895010i | \(0.647169\pi\) | |||||||
\(314\) | −414.000 | −0.0744056 | ||||||||
\(315\) | 1440.00 | 0.257571 | ||||||||
\(316\) | −728.000 | −0.129599 | ||||||||
\(317\) | −3998.00 | −0.708360 | −0.354180 | − | 0.935177i | \(-0.615240\pi\) | ||||
−0.354180 | + | 0.935177i | \(0.615240\pi\) | |||||||
\(318\) | −4116.00 | −0.725830 | ||||||||
\(319\) | 2538.00 | 0.445457 | ||||||||
\(320\) | −320.000 | −0.0559017 | ||||||||
\(321\) | 117.000 | 0.0203436 | ||||||||
\(322\) | −7488.00 | −1.29593 | ||||||||
\(323\) | 1411.00 | 0.243065 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 6900.00 | 1.17767 | ||||||||
\(326\) | 3492.00 | 0.593264 | ||||||||
\(327\) | −1284.00 | −0.217142 | ||||||||
\(328\) | −1352.00 | −0.227597 | ||||||||
\(329\) | 12224.0 | 2.04842 | ||||||||
\(330\) | 810.000 | 0.135118 | ||||||||
\(331\) | 2105.00 | 0.349551 | 0.174775 | − | 0.984608i | \(-0.444080\pi\) | ||||
0.174775 | + | 0.984608i | \(0.444080\pi\) | |||||||
\(332\) | 1128.00 | 0.186467 | ||||||||
\(333\) | −2196.00 | −0.361382 | ||||||||
\(334\) | 2306.00 | 0.377781 | ||||||||
\(335\) | −2700.00 | −0.440349 | ||||||||
\(336\) | −1536.00 | −0.249392 | ||||||||
\(337\) | 7818.00 | 1.26372 | 0.631860 | − | 0.775083i | \(-0.282292\pi\) | ||||
0.631860 | + | 0.775083i | \(0.282292\pi\) | |||||||
\(338\) | −5128.00 | −0.825226 | ||||||||
\(339\) | 2145.00 | 0.343659 | ||||||||
\(340\) | 340.000 | 0.0542326 | ||||||||
\(341\) | 5346.00 | 0.848980 | ||||||||
\(342\) | 1494.00 | 0.236217 | ||||||||
\(343\) | −10816.0 | −1.70265 | ||||||||
\(344\) | −1816.00 | −0.284628 | ||||||||
\(345\) | 1755.00 | 0.273873 | ||||||||
\(346\) | 7042.00 | 1.09416 | ||||||||
\(347\) | −1388.00 | −0.214731 | −0.107366 | − | 0.994220i | \(-0.534242\pi\) | ||||
−0.107366 | + | 0.994220i | \(0.534242\pi\) | |||||||
\(348\) | 1128.00 | 0.173756 | ||||||||
\(349\) | −9591.00 | −1.47104 | −0.735522 | − | 0.677501i | \(-0.763063\pi\) | ||||
−0.735522 | + | 0.677501i | \(0.763063\pi\) | |||||||
\(350\) | −6400.00 | −0.977413 | ||||||||
\(351\) | −1863.00 | −0.283304 | ||||||||
\(352\) | −864.000 | −0.130828 | ||||||||
\(353\) | −1442.00 | −0.217422 | −0.108711 | − | 0.994073i | \(-0.534672\pi\) | ||||
−0.108711 | + | 0.994073i | \(0.534672\pi\) | |||||||
\(354\) | −2700.00 | −0.405377 | ||||||||
\(355\) | 1380.00 | 0.206318 | ||||||||
\(356\) | −5872.00 | −0.874200 | ||||||||
\(357\) | 1632.00 | 0.241946 | ||||||||
\(358\) | −5292.00 | −0.781259 | ||||||||
\(359\) | 4104.00 | 0.603345 | 0.301672 | − | 0.953412i | \(-0.402455\pi\) | ||||
0.301672 | + | 0.953412i | \(0.402455\pi\) | |||||||
\(360\) | 360.000 | 0.0527046 | ||||||||
\(361\) | 30.0000 | 0.00437382 | ||||||||
\(362\) | 2908.00 | 0.422213 | ||||||||
\(363\) | −1806.00 | −0.261131 | ||||||||
\(364\) | 8832.00 | 1.27177 | ||||||||
\(365\) | 1490.00 | 0.213672 | ||||||||
\(366\) | 4200.00 | 0.599829 | ||||||||
\(367\) | 3904.00 | 0.555278 | 0.277639 | − | 0.960685i | \(-0.410448\pi\) | ||||
0.277639 | + | 0.960685i | \(0.410448\pi\) | |||||||
\(368\) | −1872.00 | −0.265176 | ||||||||
\(369\) | 1521.00 | 0.214580 | ||||||||
\(370\) | −2440.00 | −0.342837 | ||||||||
\(371\) | −21952.0 | −3.07194 | ||||||||
\(372\) | 2376.00 | 0.331156 | ||||||||
\(373\) | 4882.00 | 0.677695 | 0.338848 | − | 0.940841i | \(-0.389963\pi\) | ||||
0.338848 | + | 0.940841i | \(0.389963\pi\) | |||||||
\(374\) | 918.000 | 0.126922 | ||||||||
\(375\) | 3375.00 | 0.464758 | ||||||||
\(376\) | 3056.00 | 0.419152 | ||||||||
\(377\) | −6486.00 | −0.886064 | ||||||||
\(378\) | 1728.00 | 0.235129 | ||||||||
\(379\) | −10324.0 | −1.39923 | −0.699615 | − | 0.714520i | \(-0.746645\pi\) | ||||
−0.699615 | + | 0.714520i | \(0.746645\pi\) | |||||||
\(380\) | 1660.00 | 0.224095 | ||||||||
\(381\) | 2391.00 | 0.321508 | ||||||||
\(382\) | −7460.00 | −0.999180 | ||||||||
\(383\) | −10480.0 | −1.39818 | −0.699090 | − | 0.715034i | \(-0.746411\pi\) | ||||
−0.699090 | + | 0.715034i | \(0.746411\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 4320.00 | 0.571864 | ||||||||
\(386\) | 4956.00 | 0.653507 | ||||||||
\(387\) | 2043.00 | 0.268350 | ||||||||
\(388\) | −4560.00 | −0.596647 | ||||||||
\(389\) | −9724.00 | −1.26742 | −0.633710 | − | 0.773571i | \(-0.718469\pi\) | ||||
−0.633710 | + | 0.773571i | \(0.718469\pi\) | |||||||
\(390\) | −2070.00 | −0.268765 | ||||||||
\(391\) | 1989.00 | 0.257258 | ||||||||
\(392\) | −5448.00 | −0.701953 | ||||||||
\(393\) | 1119.00 | 0.143629 | ||||||||
\(394\) | 4282.00 | 0.547523 | ||||||||
\(395\) | 910.000 | 0.115917 | ||||||||
\(396\) | 972.000 | 0.123346 | ||||||||
\(397\) | −14632.0 | −1.84977 | −0.924885 | − | 0.380246i | \(-0.875839\pi\) | ||||
−0.924885 | + | 0.380246i | \(0.875839\pi\) | |||||||
\(398\) | 1160.00 | 0.146094 | ||||||||
\(399\) | 7968.00 | 0.999747 | ||||||||
\(400\) | −1600.00 | −0.200000 | ||||||||
\(401\) | −8907.00 | −1.10921 | −0.554606 | − | 0.832113i | \(-0.687131\pi\) | ||||
−0.554606 | + | 0.832113i | \(0.687131\pi\) | |||||||
\(402\) | −3240.00 | −0.401981 | ||||||||
\(403\) | −13662.0 | −1.68872 | ||||||||
\(404\) | −5600.00 | −0.689630 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | 6016.00 | 0.735392 | ||||||||
\(407\) | −6588.00 | −0.802347 | ||||||||
\(408\) | 408.000 | 0.0495074 | ||||||||
\(409\) | −4859.00 | −0.587438 | −0.293719 | − | 0.955892i | \(-0.594893\pi\) | ||||
−0.293719 | + | 0.955892i | \(0.594893\pi\) | |||||||
\(410\) | 1690.00 | 0.203569 | ||||||||
\(411\) | −8118.00 | −0.974286 | ||||||||
\(412\) | 7756.00 | 0.927453 | ||||||||
\(413\) | −14400.0 | −1.71568 | ||||||||
\(414\) | 2106.00 | 0.250010 | ||||||||
\(415\) | −1410.00 | −0.166781 | ||||||||
\(416\) | 2208.00 | 0.260231 | ||||||||
\(417\) | −6258.00 | −0.734905 | ||||||||
\(418\) | 4482.00 | 0.524454 | ||||||||
\(419\) | −444.000 | −0.0517681 | −0.0258840 | − | 0.999665i | \(-0.508240\pi\) | ||||
−0.0258840 | + | 0.999665i | \(0.508240\pi\) | |||||||
\(420\) | 1920.00 | 0.223063 | ||||||||
\(421\) | 14731.0 | 1.70533 | 0.852666 | − | 0.522456i | \(-0.174984\pi\) | ||||
0.852666 | + | 0.522456i | \(0.174984\pi\) | |||||||
\(422\) | 7652.00 | 0.882686 | ||||||||
\(423\) | −3438.00 | −0.395180 | ||||||||
\(424\) | −5488.00 | −0.628587 | ||||||||
\(425\) | 1700.00 | 0.194029 | ||||||||
\(426\) | 1656.00 | 0.188341 | ||||||||
\(427\) | 22400.0 | 2.53867 | ||||||||
\(428\) | 156.000 | 0.0176181 | ||||||||
\(429\) | −5589.00 | −0.628996 | ||||||||
\(430\) | 2270.00 | 0.254579 | ||||||||
\(431\) | −9968.00 | −1.11402 | −0.557009 | − | 0.830507i | \(-0.688051\pi\) | ||||
−0.557009 | + | 0.830507i | \(0.688051\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | 1167.00 | 0.129521 | 0.0647603 | − | 0.997901i | \(-0.479372\pi\) | ||||
0.0647603 | + | 0.997901i | \(0.479372\pi\) | |||||||
\(434\) | 12672.0 | 1.40156 | ||||||||
\(435\) | −1410.00 | −0.155412 | ||||||||
\(436\) | −1712.00 | −0.188050 | ||||||||
\(437\) | 9711.00 | 1.06302 | ||||||||
\(438\) | 1788.00 | 0.195055 | ||||||||
\(439\) | 16532.0 | 1.79733 | 0.898667 | − | 0.438632i | \(-0.144537\pi\) | ||||
0.898667 | + | 0.438632i | \(0.144537\pi\) | |||||||
\(440\) | 1080.00 | 0.117016 | ||||||||
\(441\) | 6129.00 | 0.661808 | ||||||||
\(442\) | −2346.00 | −0.252461 | ||||||||
\(443\) | 10398.0 | 1.11518 | 0.557589 | − | 0.830117i | \(-0.311727\pi\) | ||||
0.557589 | + | 0.830117i | \(0.311727\pi\) | |||||||
\(444\) | −2928.00 | −0.312966 | ||||||||
\(445\) | 7340.00 | 0.781909 | ||||||||
\(446\) | 3518.00 | 0.373503 | ||||||||
\(447\) | −4338.00 | −0.459016 | ||||||||
\(448\) | −2048.00 | −0.215980 | ||||||||
\(449\) | 4922.00 | 0.517335 | 0.258668 | − | 0.965966i | \(-0.416717\pi\) | ||||
0.258668 | + | 0.965966i | \(0.416717\pi\) | |||||||
\(450\) | 1800.00 | 0.188562 | ||||||||
\(451\) | 4563.00 | 0.476415 | ||||||||
\(452\) | 2860.00 | 0.297617 | ||||||||
\(453\) | −2232.00 | −0.231498 | ||||||||
\(454\) | −682.000 | −0.0705019 | ||||||||
\(455\) | −11040.0 | −1.13750 | ||||||||
\(456\) | 1992.00 | 0.204570 | ||||||||
\(457\) | 4573.00 | 0.468087 | 0.234044 | − | 0.972226i | \(-0.424804\pi\) | ||||
0.234044 | + | 0.972226i | \(0.424804\pi\) | |||||||
\(458\) | −7916.00 | −0.807621 | ||||||||
\(459\) | −459.000 | −0.0466760 | ||||||||
\(460\) | 2340.00 | 0.237181 | ||||||||
\(461\) | −13586.0 | −1.37259 | −0.686294 | − | 0.727324i | \(-0.740764\pi\) | ||||
−0.686294 | + | 0.727324i | \(0.740764\pi\) | |||||||
\(462\) | 5184.00 | 0.522038 | ||||||||
\(463\) | −4120.00 | −0.413548 | −0.206774 | − | 0.978389i | \(-0.566296\pi\) | ||||
−0.206774 | + | 0.978389i | \(0.566296\pi\) | |||||||
\(464\) | 1504.00 | 0.150477 | ||||||||
\(465\) | −2970.00 | −0.296195 | ||||||||
\(466\) | −6018.00 | −0.598237 | ||||||||
\(467\) | −174.000 | −0.0172415 | −0.00862073 | − | 0.999963i | \(-0.502744\pi\) | ||||
−0.00862073 | + | 0.999963i | \(0.502744\pi\) | |||||||
\(468\) | −2484.00 | −0.245348 | ||||||||
\(469\) | −17280.0 | −1.70131 | ||||||||
\(470\) | −3820.00 | −0.374901 | ||||||||
\(471\) | 621.000 | 0.0607520 | ||||||||
\(472\) | −3600.00 | −0.351067 | ||||||||
\(473\) | 6129.00 | 0.595796 | ||||||||
\(474\) | 1092.00 | 0.105817 | ||||||||
\(475\) | 8300.00 | 0.801748 | ||||||||
\(476\) | 2176.00 | 0.209531 | ||||||||
\(477\) | 6174.00 | 0.592637 | ||||||||
\(478\) | −6928.00 | −0.662927 | ||||||||
\(479\) | 18311.0 | 1.74666 | 0.873331 | − | 0.487128i | \(-0.161955\pi\) | ||||
0.873331 | + | 0.487128i | \(0.161955\pi\) | |||||||
\(480\) | 480.000 | 0.0456435 | ||||||||
\(481\) | 16836.0 | 1.59596 | ||||||||
\(482\) | −312.000 | −0.0294838 | ||||||||
\(483\) | 11232.0 | 1.05812 | ||||||||
\(484\) | −2408.00 | −0.226146 | ||||||||
\(485\) | 5700.00 | 0.533657 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | 6766.00 | 0.629562 | 0.314781 | − | 0.949164i | \(-0.398069\pi\) | ||||
0.314781 | + | 0.949164i | \(0.398069\pi\) | |||||||
\(488\) | 5600.00 | 0.519467 | ||||||||
\(489\) | −5238.00 | −0.484398 | ||||||||
\(490\) | 6810.00 | 0.627846 | ||||||||
\(491\) | −13846.0 | −1.27263 | −0.636315 | − | 0.771429i | \(-0.719542\pi\) | ||||
−0.636315 | + | 0.771429i | \(0.719542\pi\) | |||||||
\(492\) | 2028.00 | 0.185832 | ||||||||
\(493\) | −1598.00 | −0.145984 | ||||||||
\(494\) | −11454.0 | −1.04320 | ||||||||
\(495\) | −1215.00 | −0.110324 | ||||||||
\(496\) | 3168.00 | 0.286789 | ||||||||
\(497\) | 8832.00 | 0.797121 | ||||||||
\(498\) | −1692.00 | −0.152250 | ||||||||
\(499\) | −5854.00 | −0.525172 | −0.262586 | − | 0.964909i | \(-0.584575\pi\) | ||||
−0.262586 | + | 0.964909i | \(0.584575\pi\) | |||||||
\(500\) | 4500.00 | 0.402492 | ||||||||
\(501\) | −3459.00 | −0.308457 | ||||||||
\(502\) | 8928.00 | 0.793777 | ||||||||
\(503\) | −883.000 | −0.0782724 | −0.0391362 | − | 0.999234i | \(-0.512461\pi\) | ||||
−0.0391362 | + | 0.999234i | \(0.512461\pi\) | |||||||
\(504\) | 2304.00 | 0.203628 | ||||||||
\(505\) | 7000.00 | 0.616824 | ||||||||
\(506\) | 6318.00 | 0.555078 | ||||||||
\(507\) | 7692.00 | 0.673794 | ||||||||
\(508\) | 3188.00 | 0.278434 | ||||||||
\(509\) | 6748.00 | 0.587622 | 0.293811 | − | 0.955863i | \(-0.405076\pi\) | ||||
0.293811 | + | 0.955863i | \(0.405076\pi\) | |||||||
\(510\) | −510.000 | −0.0442807 | ||||||||
\(511\) | 9536.00 | 0.825534 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −2241.00 | −0.192871 | ||||||||
\(514\) | −11088.0 | −0.951499 | ||||||||
\(515\) | −9695.00 | −0.829539 | ||||||||
\(516\) | 2724.00 | 0.232398 | ||||||||
\(517\) | −10314.0 | −0.877387 | ||||||||
\(518\) | −15616.0 | −1.32457 | ||||||||
\(519\) | −10563.0 | −0.893380 | ||||||||
\(520\) | −2760.00 | −0.232758 | ||||||||
\(521\) | −9263.00 | −0.778924 | −0.389462 | − | 0.921043i | \(-0.627339\pi\) | ||||
−0.389462 | + | 0.921043i | \(0.627339\pi\) | |||||||
\(522\) | −1692.00 | −0.141871 | ||||||||
\(523\) | 3868.00 | 0.323395 | 0.161698 | − | 0.986840i | \(-0.448303\pi\) | ||||
0.161698 | + | 0.986840i | \(0.448303\pi\) | |||||||
\(524\) | 1492.00 | 0.124386 | ||||||||
\(525\) | 9600.00 | 0.798054 | ||||||||
\(526\) | −1224.00 | −0.101462 | ||||||||
\(527\) | −3366.00 | −0.278226 | ||||||||
\(528\) | 1296.00 | 0.106820 | ||||||||
\(529\) | 1522.00 | 0.125092 | ||||||||
\(530\) | 6860.00 | 0.562225 | ||||||||
\(531\) | 4050.00 | 0.330989 | ||||||||
\(532\) | 10624.0 | 0.865806 | ||||||||
\(533\) | −11661.0 | −0.947643 | ||||||||
\(534\) | 8808.00 | 0.713782 | ||||||||
\(535\) | −195.000 | −0.0157581 | ||||||||
\(536\) | −4320.00 | −0.348126 | ||||||||
\(537\) | 7938.00 | 0.637896 | ||||||||
\(538\) | −11202.0 | −0.897681 | ||||||||
\(539\) | 18387.0 | 1.46936 | ||||||||
\(540\) | −540.000 | −0.0430331 | ||||||||
\(541\) | −6840.00 | −0.543576 | −0.271788 | − | 0.962357i | \(-0.587615\pi\) | ||||
−0.271788 | + | 0.962357i | \(0.587615\pi\) | |||||||
\(542\) | 11702.0 | 0.927387 | ||||||||
\(543\) | −4362.00 | −0.344735 | ||||||||
\(544\) | 544.000 | 0.0428746 | ||||||||
\(545\) | 2140.00 | 0.168197 | ||||||||
\(546\) | −13248.0 | −1.03839 | ||||||||
\(547\) | −5564.00 | −0.434917 | −0.217458 | − | 0.976070i | \(-0.569777\pi\) | ||||
−0.217458 | + | 0.976070i | \(0.569777\pi\) | |||||||
\(548\) | −10824.0 | −0.843756 | ||||||||
\(549\) | −6300.00 | −0.489759 | ||||||||
\(550\) | 5400.00 | 0.418649 | ||||||||
\(551\) | −7802.00 | −0.603224 | ||||||||
\(552\) | 2808.00 | 0.216515 | ||||||||
\(553\) | 5824.00 | 0.447851 | ||||||||
\(554\) | 10276.0 | 0.788060 | ||||||||
\(555\) | 3660.00 | 0.279925 | ||||||||
\(556\) | −8344.00 | −0.636447 | ||||||||
\(557\) | 1618.00 | 0.123082 | 0.0615412 | − | 0.998105i | \(-0.480398\pi\) | ||||
0.0615412 | + | 0.998105i | \(0.480398\pi\) | |||||||
\(558\) | −3564.00 | −0.270387 | ||||||||
\(559\) | −15663.0 | −1.18511 | ||||||||
\(560\) | 2560.00 | 0.193178 | ||||||||
\(561\) | −1377.00 | −0.103631 | ||||||||
\(562\) | −15216.0 | −1.14208 | ||||||||
\(563\) | −21050.0 | −1.57576 | −0.787879 | − | 0.615830i | \(-0.788821\pi\) | ||||
−0.787879 | + | 0.615830i | \(0.788821\pi\) | |||||||
\(564\) | −4584.00 | −0.342236 | ||||||||
\(565\) | −3575.00 | −0.266197 | ||||||||
\(566\) | −16948.0 | −1.25862 | ||||||||
\(567\) | −2592.00 | −0.191982 | ||||||||
\(568\) | 2208.00 | 0.163108 | ||||||||
\(569\) | 26484.0 | 1.95126 | 0.975630 | − | 0.219422i | \(-0.0704171\pi\) | ||||
0.975630 | + | 0.219422i | \(0.0704171\pi\) | |||||||
\(570\) | −2490.00 | −0.182973 | ||||||||
\(571\) | −10996.0 | −0.805899 | −0.402949 | − | 0.915222i | \(-0.632015\pi\) | ||||
−0.402949 | + | 0.915222i | \(0.632015\pi\) | |||||||
\(572\) | −7452.00 | −0.544727 | ||||||||
\(573\) | 11190.0 | 0.815827 | ||||||||
\(574\) | 10816.0 | 0.786500 | ||||||||
\(575\) | 11700.0 | 0.848563 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 16089.0 | 1.16082 | 0.580411 | − | 0.814324i | \(-0.302892\pi\) | ||||
0.580411 | + | 0.814324i | \(0.302892\pi\) | |||||||
\(578\) | −578.000 | −0.0415945 | ||||||||
\(579\) | −7434.00 | −0.533586 | ||||||||
\(580\) | −1880.00 | −0.134591 | ||||||||
\(581\) | −9024.00 | −0.644369 | ||||||||
\(582\) | 6840.00 | 0.487160 | ||||||||
\(583\) | 18522.0 | 1.31579 | ||||||||
\(584\) | 2384.00 | 0.168922 | ||||||||
\(585\) | 3105.00 | 0.219446 | ||||||||
\(586\) | −15344.0 | −1.08166 | ||||||||
\(587\) | 5700.00 | 0.400791 | 0.200395 | − | 0.979715i | \(-0.435777\pi\) | ||||
0.200395 | + | 0.979715i | \(0.435777\pi\) | |||||||
\(588\) | 8172.00 | 0.573142 | ||||||||
\(589\) | −16434.0 | −1.14966 | ||||||||
\(590\) | 4500.00 | 0.314004 | ||||||||
\(591\) | −6423.00 | −0.447051 | ||||||||
\(592\) | −3904.00 | −0.271036 | ||||||||
\(593\) | 3474.00 | 0.240573 | 0.120287 | − | 0.992739i | \(-0.461619\pi\) | ||||
0.120287 | + | 0.992739i | \(0.461619\pi\) | |||||||
\(594\) | −1458.00 | −0.100711 | ||||||||
\(595\) | −2720.00 | −0.187410 | ||||||||
\(596\) | −5784.00 | −0.397520 | ||||||||
\(597\) | −1740.00 | −0.119286 | ||||||||
\(598\) | −16146.0 | −1.10411 | ||||||||
\(599\) | −12710.0 | −0.866972 | −0.433486 | − | 0.901160i | \(-0.642717\pi\) | ||||
−0.433486 | + | 0.901160i | \(0.642717\pi\) | |||||||
\(600\) | 2400.00 | 0.163299 | ||||||||
\(601\) | 8806.00 | 0.597678 | 0.298839 | − | 0.954304i | \(-0.403401\pi\) | ||||
0.298839 | + | 0.954304i | \(0.403401\pi\) | |||||||
\(602\) | 14528.0 | 0.983583 | ||||||||
\(603\) | 4860.00 | 0.328216 | ||||||||
\(604\) | −2976.00 | −0.200483 | ||||||||
\(605\) | 3010.00 | 0.202271 | ||||||||
\(606\) | 8400.00 | 0.563080 | ||||||||
\(607\) | 6022.00 | 0.402678 | 0.201339 | − | 0.979522i | \(-0.435471\pi\) | ||||
0.201339 | + | 0.979522i | \(0.435471\pi\) | |||||||
\(608\) | 2656.00 | 0.177163 | ||||||||
\(609\) | −9024.00 | −0.600445 | ||||||||
\(610\) | −7000.00 | −0.464626 | ||||||||
\(611\) | 26358.0 | 1.74522 | ||||||||
\(612\) | −612.000 | −0.0404226 | ||||||||
\(613\) | −2337.00 | −0.153981 | −0.0769907 | − | 0.997032i | \(-0.524531\pi\) | ||||
−0.0769907 | + | 0.997032i | \(0.524531\pi\) | |||||||
\(614\) | 6792.00 | 0.446422 | ||||||||
\(615\) | −2535.00 | −0.166213 | ||||||||
\(616\) | 6912.00 | 0.452098 | ||||||||
\(617\) | 23082.0 | 1.50607 | 0.753036 | − | 0.657979i | \(-0.228589\pi\) | ||||
0.753036 | + | 0.657979i | \(0.228589\pi\) | |||||||
\(618\) | −11634.0 | −0.757262 | ||||||||
\(619\) | −20510.0 | −1.33177 | −0.665886 | − | 0.746054i | \(-0.731946\pi\) | ||||
−0.665886 | + | 0.746054i | \(0.731946\pi\) | |||||||
\(620\) | −3960.00 | −0.256512 | ||||||||
\(621\) | −3159.00 | −0.204133 | ||||||||
\(622\) | −12960.0 | −0.835448 | ||||||||
\(623\) | 46976.0 | 3.02095 | ||||||||
\(624\) | −3312.00 | −0.212478 | ||||||||
\(625\) | 6875.00 | 0.440000 | ||||||||
\(626\) | 9880.00 | 0.630805 | ||||||||
\(627\) | −6723.00 | −0.428215 | ||||||||
\(628\) | 828.000 | 0.0526127 | ||||||||
\(629\) | 4148.00 | 0.262944 | ||||||||
\(630\) | −2880.00 | −0.182130 | ||||||||
\(631\) | 29453.0 | 1.85817 | 0.929085 | − | 0.369866i | \(-0.120596\pi\) | ||||
0.929085 | + | 0.369866i | \(0.120596\pi\) | |||||||
\(632\) | 1456.00 | 0.0916401 | ||||||||
\(633\) | −11478.0 | −0.720710 | ||||||||
\(634\) | 7996.00 | 0.500886 | ||||||||
\(635\) | −3985.00 | −0.249039 | ||||||||
\(636\) | 8232.00 | 0.513239 | ||||||||
\(637\) | −46989.0 | −2.92272 | ||||||||
\(638\) | −5076.00 | −0.314986 | ||||||||
\(639\) | −2484.00 | −0.153780 | ||||||||
\(640\) | 640.000 | 0.0395285 | ||||||||
\(641\) | −4045.00 | −0.249248 | −0.124624 | − | 0.992204i | \(-0.539772\pi\) | ||||
−0.124624 | + | 0.992204i | \(0.539772\pi\) | |||||||
\(642\) | −234.000 | −0.0143851 | ||||||||
\(643\) | −30188.0 | −1.85148 | −0.925738 | − | 0.378167i | \(-0.876555\pi\) | ||||
−0.925738 | + | 0.378167i | \(0.876555\pi\) | |||||||
\(644\) | 14976.0 | 0.916362 | ||||||||
\(645\) | −3405.00 | −0.207863 | ||||||||
\(646\) | −2822.00 | −0.171873 | ||||||||
\(647\) | −28246.0 | −1.71633 | −0.858164 | − | 0.513375i | \(-0.828395\pi\) | ||||
−0.858164 | + | 0.513375i | \(0.828395\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | 12150.0 | 0.734868 | ||||||||
\(650\) | −13800.0 | −0.832739 | ||||||||
\(651\) | −19008.0 | −1.14437 | ||||||||
\(652\) | −6984.00 | −0.419501 | ||||||||
\(653\) | −1301.00 | −0.0779664 | −0.0389832 | − | 0.999240i | \(-0.512412\pi\) | ||||
−0.0389832 | + | 0.999240i | \(0.512412\pi\) | |||||||
\(654\) | 2568.00 | 0.153542 | ||||||||
\(655\) | −1865.00 | −0.111254 | ||||||||
\(656\) | 2704.00 | 0.160935 | ||||||||
\(657\) | −2682.00 | −0.159261 | ||||||||
\(658\) | −24448.0 | −1.44845 | ||||||||
\(659\) | −6450.00 | −0.381269 | −0.190635 | − | 0.981661i | \(-0.561055\pi\) | ||||
−0.190635 | + | 0.981661i | \(0.561055\pi\) | |||||||
\(660\) | −1620.00 | −0.0955431 | ||||||||
\(661\) | 12445.0 | 0.732306 | 0.366153 | − | 0.930555i | \(-0.380675\pi\) | ||||
0.366153 | + | 0.930555i | \(0.380675\pi\) | |||||||
\(662\) | −4210.00 | −0.247170 | ||||||||
\(663\) | 3519.00 | 0.206134 | ||||||||
\(664\) | −2256.00 | −0.131852 | ||||||||
\(665\) | −13280.0 | −0.774400 | ||||||||
\(666\) | 4392.00 | 0.255535 | ||||||||
\(667\) | −10998.0 | −0.638447 | ||||||||
\(668\) | −4612.00 | −0.267131 | ||||||||
\(669\) | −5277.00 | −0.304964 | ||||||||
\(670\) | 5400.00 | 0.311373 | ||||||||
\(671\) | −18900.0 | −1.08737 | ||||||||
\(672\) | 3072.00 | 0.176347 | ||||||||
\(673\) | 5566.00 | 0.318802 | 0.159401 | − | 0.987214i | \(-0.449044\pi\) | ||||
0.159401 | + | 0.987214i | \(0.449044\pi\) | |||||||
\(674\) | −15636.0 | −0.893585 | ||||||||
\(675\) | −2700.00 | −0.153960 | ||||||||
\(676\) | 10256.0 | 0.583523 | ||||||||
\(677\) | −33539.0 | −1.90400 | −0.952000 | − | 0.306097i | \(-0.900977\pi\) | ||||
−0.952000 | + | 0.306097i | \(0.900977\pi\) | |||||||
\(678\) | −4290.00 | −0.243004 | ||||||||
\(679\) | 36480.0 | 2.06182 | ||||||||
\(680\) | −680.000 | −0.0383482 | ||||||||
\(681\) | 1023.00 | 0.0575645 | ||||||||
\(682\) | −10692.0 | −0.600319 | ||||||||
\(683\) | 29517.0 | 1.65364 | 0.826820 | − | 0.562466i | \(-0.190147\pi\) | ||||
0.826820 | + | 0.562466i | \(0.190147\pi\) | |||||||
\(684\) | −2988.00 | −0.167031 | ||||||||
\(685\) | 13530.0 | 0.754678 | ||||||||
\(686\) | 21632.0 | 1.20396 | ||||||||
\(687\) | 11874.0 | 0.659420 | ||||||||
\(688\) | 3632.00 | 0.201263 | ||||||||
\(689\) | −47334.0 | −2.61724 | ||||||||
\(690\) | −3510.00 | −0.193657 | ||||||||
\(691\) | 1684.00 | 0.0927097 | 0.0463548 | − | 0.998925i | \(-0.485240\pi\) | ||||
0.0463548 | + | 0.998925i | \(0.485240\pi\) | |||||||
\(692\) | −14084.0 | −0.773690 | ||||||||
\(693\) | −7776.00 | −0.426242 | ||||||||
\(694\) | 2776.00 | 0.151838 | ||||||||
\(695\) | 10430.0 | 0.569255 | ||||||||
\(696\) | −2256.00 | −0.122864 | ||||||||
\(697\) | −2873.00 | −0.156130 | ||||||||
\(698\) | 19182.0 | 1.04019 | ||||||||
\(699\) | 9027.00 | 0.488459 | ||||||||
\(700\) | 12800.0 | 0.691135 | ||||||||
\(701\) | 34152.0 | 1.84009 | 0.920045 | − | 0.391812i | \(-0.128152\pi\) | ||||
0.920045 | + | 0.391812i | \(0.128152\pi\) | |||||||
\(702\) | 3726.00 | 0.200326 | ||||||||
\(703\) | 20252.0 | 1.08651 | ||||||||
\(704\) | 1728.00 | 0.0925092 | ||||||||
\(705\) | 5730.00 | 0.306105 | ||||||||
\(706\) | 2884.00 | 0.153740 | ||||||||
\(707\) | 44800.0 | 2.38314 | ||||||||
\(708\) | 5400.00 | 0.286645 | ||||||||
\(709\) | 7994.00 | 0.423443 | 0.211721 | − | 0.977330i | \(-0.432093\pi\) | ||||
0.211721 | + | 0.977330i | \(0.432093\pi\) | |||||||
\(710\) | −2760.00 | −0.145889 | ||||||||
\(711\) | −1638.00 | −0.0863992 | ||||||||
\(712\) | 11744.0 | 0.618153 | ||||||||
\(713\) | −23166.0 | −1.21679 | ||||||||
\(714\) | −3264.00 | −0.171081 | ||||||||
\(715\) | 9315.00 | 0.487219 | ||||||||
\(716\) | 10584.0 | 0.552434 | ||||||||
\(717\) | 10392.0 | 0.541278 | ||||||||
\(718\) | −8208.00 | −0.426629 | ||||||||
\(719\) | 22713.0 | 1.17810 | 0.589049 | − | 0.808098i | \(-0.299503\pi\) | ||||
0.589049 | + | 0.808098i | \(0.299503\pi\) | |||||||
\(720\) | −720.000 | −0.0372678 | ||||||||
\(721\) | −62048.0 | −3.20498 | ||||||||
\(722\) | −60.0000 | −0.00309275 | ||||||||
\(723\) | 468.000 | 0.0240735 | ||||||||
\(724\) | −5816.00 | −0.298550 | ||||||||
\(725\) | −9400.00 | −0.481527 | ||||||||
\(726\) | 3612.00 | 0.184647 | ||||||||
\(727\) | 21712.0 | 1.10764 | 0.553819 | − | 0.832637i | \(-0.313170\pi\) | ||||
0.553819 | + | 0.832637i | \(0.313170\pi\) | |||||||
\(728\) | −17664.0 | −0.899274 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −2980.00 | −0.151089 | ||||||||
\(731\) | −3859.00 | −0.195253 | ||||||||
\(732\) | −8400.00 | −0.424143 | ||||||||
\(733\) | −5430.00 | −0.273617 | −0.136809 | − | 0.990597i | \(-0.543685\pi\) | ||||
−0.136809 | + | 0.990597i | \(0.543685\pi\) | |||||||
\(734\) | −7808.00 | −0.392641 | ||||||||
\(735\) | −10215.0 | −0.512634 | ||||||||
\(736\) | 3744.00 | 0.187508 | ||||||||
\(737\) | 14580.0 | 0.728713 | ||||||||
\(738\) | −3042.00 | −0.151731 | ||||||||
\(739\) | −30723.0 | −1.52932 | −0.764658 | − | 0.644437i | \(-0.777092\pi\) | ||||
−0.764658 | + | 0.644437i | \(0.777092\pi\) | |||||||
\(740\) | 4880.00 | 0.242422 | ||||||||
\(741\) | 17181.0 | 0.851768 | ||||||||
\(742\) | 43904.0 | 2.17219 | ||||||||
\(743\) | 28096.0 | 1.38727 | 0.693635 | − | 0.720326i | \(-0.256008\pi\) | ||||
0.693635 | + | 0.720326i | \(0.256008\pi\) | |||||||
\(744\) | −4752.00 | −0.234162 | ||||||||
\(745\) | 7230.00 | 0.355553 | ||||||||
\(746\) | −9764.00 | −0.479203 | ||||||||
\(747\) | 2538.00 | 0.124311 | ||||||||
\(748\) | −1836.00 | −0.0897471 | ||||||||
\(749\) | −1248.00 | −0.0608824 | ||||||||
\(750\) | −6750.00 | −0.328634 | ||||||||
\(751\) | −5458.00 | −0.265200 | −0.132600 | − | 0.991170i | \(-0.542333\pi\) | ||||
−0.132600 | + | 0.991170i | \(0.542333\pi\) | |||||||
\(752\) | −6112.00 | −0.296385 | ||||||||
\(753\) | −13392.0 | −0.648116 | ||||||||
\(754\) | 12972.0 | 0.626542 | ||||||||
\(755\) | 3720.00 | 0.179317 | ||||||||
\(756\) | −3456.00 | −0.166261 | ||||||||
\(757\) | −24319.0 | −1.16762 | −0.583810 | − | 0.811890i | \(-0.698439\pi\) | ||||
−0.583810 | + | 0.811890i | \(0.698439\pi\) | |||||||
\(758\) | 20648.0 | 0.989405 | ||||||||
\(759\) | −9477.00 | −0.453219 | ||||||||
\(760\) | −3320.00 | −0.158459 | ||||||||
\(761\) | 2126.00 | 0.101271 | 0.0506356 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506356 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(762\) | −4782.00 | −0.227341 | ||||||||
\(763\) | 13696.0 | 0.649841 | ||||||||
\(764\) | 14920.0 | 0.706527 | ||||||||
\(765\) | 765.000 | 0.0361551 | ||||||||
\(766\) | 20960.0 | 0.988663 | ||||||||
\(767\) | −31050.0 | −1.46173 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | −2503.00 | −0.117374 | −0.0586869 | − | 0.998276i | \(-0.518691\pi\) | ||||
−0.0586869 | + | 0.998276i | \(0.518691\pi\) | |||||||
\(770\) | −8640.00 | −0.404369 | ||||||||
\(771\) | 16632.0 | 0.776896 | ||||||||
\(772\) | −9912.00 | −0.462099 | ||||||||
\(773\) | 36780.0 | 1.71136 | 0.855682 | − | 0.517502i | \(-0.173138\pi\) | ||||
0.855682 | + | 0.517502i | \(0.173138\pi\) | |||||||
\(774\) | −4086.00 | −0.189752 | ||||||||
\(775\) | −19800.0 | −0.917725 | ||||||||
\(776\) | 9120.00 | 0.421893 | ||||||||
\(777\) | 23424.0 | 1.08151 | ||||||||
\(778\) | 19448.0 | 0.896201 | ||||||||
\(779\) | −14027.0 | −0.645147 | ||||||||
\(780\) | 4140.00 | 0.190046 | ||||||||
\(781\) | −7452.00 | −0.341426 | ||||||||
\(782\) | −3978.00 | −0.181909 | ||||||||
\(783\) | 2538.00 | 0.115837 | ||||||||
\(784\) | 10896.0 | 0.496356 | ||||||||
\(785\) | −1035.00 | −0.0470583 | ||||||||
\(786\) | −2238.00 | −0.101561 | ||||||||
\(787\) | 7356.00 | 0.333181 | 0.166590 | − | 0.986026i | \(-0.446724\pi\) | ||||
0.166590 | + | 0.986026i | \(0.446724\pi\) | |||||||
\(788\) | −8564.00 | −0.387157 | ||||||||
\(789\) | 1836.00 | 0.0828433 | ||||||||
\(790\) | −1820.00 | −0.0819654 | ||||||||
\(791\) | −22880.0 | −1.02847 | ||||||||
\(792\) | −1944.00 | −0.0872185 | ||||||||
\(793\) | 48300.0 | 2.16290 | ||||||||
\(794\) | 29264.0 | 1.30799 | ||||||||
\(795\) | −10290.0 | −0.459055 | ||||||||
\(796\) | −2320.00 | −0.103304 | ||||||||
\(797\) | −19672.0 | −0.874301 | −0.437151 | − | 0.899388i | \(-0.644012\pi\) | ||||
−0.437151 | + | 0.899388i | \(0.644012\pi\) | |||||||
\(798\) | −15936.0 | −0.706928 | ||||||||
\(799\) | 6494.00 | 0.287536 | ||||||||
\(800\) | 3200.00 | 0.141421 | ||||||||
\(801\) | −13212.0 | −0.582800 | ||||||||
\(802\) | 17814.0 | 0.784332 | ||||||||
\(803\) | −8046.00 | −0.353595 | ||||||||
\(804\) | 6480.00 | 0.284244 | ||||||||
\(805\) | −18720.0 | −0.819619 | ||||||||
\(806\) | 27324.0 | 1.19410 | ||||||||
\(807\) | 16803.0 | 0.732954 | ||||||||
\(808\) | 11200.0 | 0.487642 | ||||||||
\(809\) | 18713.0 | 0.813244 | 0.406622 | − | 0.913597i | \(-0.366707\pi\) | ||||
0.406622 | + | 0.913597i | \(0.366707\pi\) | |||||||
\(810\) | 810.000 | 0.0351364 | ||||||||
\(811\) | 16062.0 | 0.695454 | 0.347727 | − | 0.937596i | \(-0.386954\pi\) | ||||
0.347727 | + | 0.937596i | \(0.386954\pi\) | |||||||
\(812\) | −12032.0 | −0.520001 | ||||||||
\(813\) | −17553.0 | −0.757209 | ||||||||
\(814\) | 13176.0 | 0.567345 | ||||||||
\(815\) | 8730.00 | 0.375213 | ||||||||
\(816\) | −816.000 | −0.0350070 | ||||||||
\(817\) | −18841.0 | −0.806809 | ||||||||
\(818\) | 9718.00 | 0.415381 | ||||||||
\(819\) | 19872.0 | 0.847844 | ||||||||
\(820\) | −3380.00 | −0.143945 | ||||||||
\(821\) | −19653.0 | −0.835438 | −0.417719 | − | 0.908576i | \(-0.637170\pi\) | ||||
−0.417719 | + | 0.908576i | \(0.637170\pi\) | |||||||
\(822\) | 16236.0 | 0.688924 | ||||||||
\(823\) | −3276.00 | −0.138754 | −0.0693768 | − | 0.997591i | \(-0.522101\pi\) | ||||
−0.0693768 | + | 0.997591i | \(0.522101\pi\) | |||||||
\(824\) | −15512.0 | −0.655808 | ||||||||
\(825\) | −8100.00 | −0.341825 | ||||||||
\(826\) | 28800.0 | 1.21317 | ||||||||
\(827\) | −11491.0 | −0.483170 | −0.241585 | − | 0.970380i | \(-0.577667\pi\) | ||||
−0.241585 | + | 0.970380i | \(0.577667\pi\) | |||||||
\(828\) | −4212.00 | −0.176784 | ||||||||
\(829\) | 3606.00 | 0.151075 | 0.0755377 | − | 0.997143i | \(-0.475933\pi\) | ||||
0.0755377 | + | 0.997143i | \(0.475933\pi\) | |||||||
\(830\) | 2820.00 | 0.117932 | ||||||||
\(831\) | −15414.0 | −0.643449 | ||||||||
\(832\) | −4416.00 | −0.184011 | ||||||||
\(833\) | −11577.0 | −0.481536 | ||||||||
\(834\) | 12516.0 | 0.519657 | ||||||||
\(835\) | 5765.00 | 0.238929 | ||||||||
\(836\) | −8964.00 | −0.370845 | ||||||||
\(837\) | 5346.00 | 0.220770 | ||||||||
\(838\) | 888.000 | 0.0366056 | ||||||||
\(839\) | −36027.0 | −1.48247 | −0.741234 | − | 0.671247i | \(-0.765759\pi\) | ||||
−0.741234 | + | 0.671247i | \(0.765759\pi\) | |||||||
\(840\) | −3840.00 | −0.157729 | ||||||||
\(841\) | −15553.0 | −0.637706 | ||||||||
\(842\) | −29462.0 | −1.20585 | ||||||||
\(843\) | 22824.0 | 0.932503 | ||||||||
\(844\) | −15304.0 | −0.624153 | ||||||||
\(845\) | −12820.0 | −0.521919 | ||||||||
\(846\) | 6876.00 | 0.279435 | ||||||||
\(847\) | 19264.0 | 0.781486 | ||||||||
\(848\) | 10976.0 | 0.444478 | ||||||||
\(849\) | 25422.0 | 1.02766 | ||||||||
\(850\) | −3400.00 | −0.137199 | ||||||||
\(851\) | 28548.0 | 1.14996 | ||||||||
\(852\) | −3312.00 | −0.133178 | ||||||||
\(853\) | −31078.0 | −1.24747 | −0.623734 | − | 0.781637i | \(-0.714385\pi\) | ||||
−0.623734 | + | 0.781637i | \(0.714385\pi\) | |||||||
\(854\) | −44800.0 | −1.79511 | ||||||||
\(855\) | 3735.00 | 0.149397 | ||||||||
\(856\) | −312.000 | −0.0124579 | ||||||||
\(857\) | −22106.0 | −0.881128 | −0.440564 | − | 0.897721i | \(-0.645221\pi\) | ||||
−0.440564 | + | 0.897721i | \(0.645221\pi\) | |||||||
\(858\) | 11178.0 | 0.444768 | ||||||||
\(859\) | 23924.0 | 0.950263 | 0.475132 | − | 0.879915i | \(-0.342400\pi\) | ||||
0.475132 | + | 0.879915i | \(0.342400\pi\) | |||||||
\(860\) | −4540.00 | −0.180015 | ||||||||
\(861\) | −16224.0 | −0.642175 | ||||||||
\(862\) | 19936.0 | 0.787730 | ||||||||
\(863\) | 31860.0 | 1.25669 | 0.628347 | − | 0.777933i | \(-0.283732\pi\) | ||||
0.628347 | + | 0.777933i | \(0.283732\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 17605.0 | 0.692009 | ||||||||
\(866\) | −2334.00 | −0.0915849 | ||||||||
\(867\) | 867.000 | 0.0339618 | ||||||||
\(868\) | −25344.0 | −0.991050 | ||||||||
\(869\) | −4914.00 | −0.191825 | ||||||||
\(870\) | 2820.00 | 0.109893 | ||||||||
\(871\) | −37260.0 | −1.44949 | ||||||||
\(872\) | 3424.00 | 0.132972 | ||||||||
\(873\) | −10260.0 | −0.397764 | ||||||||
\(874\) | −19422.0 | −0.751669 | ||||||||
\(875\) | −36000.0 | −1.39088 | ||||||||
\(876\) | −3576.00 | −0.137924 | ||||||||
\(877\) | 34122.0 | 1.31382 | 0.656909 | − | 0.753970i | \(-0.271864\pi\) | ||||
0.656909 | + | 0.753970i | \(0.271864\pi\) | |||||||
\(878\) | −33064.0 | −1.27091 | ||||||||
\(879\) | 23016.0 | 0.883175 | ||||||||
\(880\) | −2160.00 | −0.0827427 | ||||||||
\(881\) | −48062.0 | −1.83797 | −0.918984 | − | 0.394295i | \(-0.870989\pi\) | ||||
−0.918984 | + | 0.394295i | \(0.870989\pi\) | |||||||
\(882\) | −12258.0 | −0.467969 | ||||||||
\(883\) | 6185.00 | 0.235721 | 0.117861 | − | 0.993030i | \(-0.462396\pi\) | ||||
0.117861 | + | 0.993030i | \(0.462396\pi\) | |||||||
\(884\) | 4692.00 | 0.178517 | ||||||||
\(885\) | −6750.00 | −0.256383 | ||||||||
\(886\) | −20796.0 | −0.788550 | ||||||||
\(887\) | −41835.0 | −1.58363 | −0.791816 | − | 0.610760i | \(-0.790864\pi\) | ||||
−0.791816 | + | 0.610760i | \(0.790864\pi\) | |||||||
\(888\) | 5856.00 | 0.221300 | ||||||||
\(889\) | −25504.0 | −0.962179 | ||||||||
\(890\) | −14680.0 | −0.552893 | ||||||||
\(891\) | 2187.00 | 0.0822304 | ||||||||
\(892\) | −7036.00 | −0.264106 | ||||||||
\(893\) | 31706.0 | 1.18813 | ||||||||
\(894\) | 8676.00 | 0.324574 | ||||||||
\(895\) | −13230.0 | −0.494112 | ||||||||
\(896\) | 4096.00 | 0.152721 | ||||||||
\(897\) | 24219.0 | 0.901504 | ||||||||
\(898\) | −9844.00 | −0.365811 | ||||||||
\(899\) | 18612.0 | 0.690484 | ||||||||
\(900\) | −3600.00 | −0.133333 | ||||||||
\(901\) | −11662.0 | −0.431207 | ||||||||
\(902\) | −9126.00 | −0.336876 | ||||||||
\(903\) | −21792.0 | −0.803092 | ||||||||
\(904\) | −5720.00 | −0.210447 | ||||||||
\(905\) | 7270.00 | 0.267031 | ||||||||
\(906\) | 4464.00 | 0.163694 | ||||||||
\(907\) | −12174.0 | −0.445679 | −0.222840 | − | 0.974855i | \(-0.571533\pi\) | ||||
−0.222840 | + | 0.974855i | \(0.571533\pi\) | |||||||
\(908\) | 1364.00 | 0.0498523 | ||||||||
\(909\) | −12600.0 | −0.459753 | ||||||||
\(910\) | 22080.0 | 0.804335 | ||||||||
\(911\) | −24089.0 | −0.876075 | −0.438037 | − | 0.898957i | \(-0.644326\pi\) | ||||
−0.438037 | + | 0.898957i | \(0.644326\pi\) | |||||||
\(912\) | −3984.00 | −0.144653 | ||||||||
\(913\) | 7614.00 | 0.275998 | ||||||||
\(914\) | −9146.00 | −0.330988 | ||||||||
\(915\) | 10500.0 | 0.379365 | ||||||||
\(916\) | 15832.0 | 0.571074 | ||||||||
\(917\) | −11936.0 | −0.429838 | ||||||||
\(918\) | 918.000 | 0.0330049 | ||||||||
\(919\) | −55163.0 | −1.98004 | −0.990021 | − | 0.140917i | \(-0.954995\pi\) | ||||
−0.990021 | + | 0.140917i | \(0.954995\pi\) | |||||||
\(920\) | −4680.00 | −0.167712 | ||||||||
\(921\) | −10188.0 | −0.364502 | ||||||||
\(922\) | 27172.0 | 0.970566 | ||||||||
\(923\) | 19044.0 | 0.679134 | ||||||||
\(924\) | −10368.0 | −0.369137 | ||||||||
\(925\) | 24400.0 | 0.867316 | ||||||||
\(926\) | 8240.00 | 0.292422 | ||||||||
\(927\) | 17451.0 | 0.618302 | ||||||||
\(928\) | −3008.00 | −0.106403 | ||||||||
\(929\) | 19555.0 | 0.690612 | 0.345306 | − | 0.938490i | \(-0.387775\pi\) | ||||
0.345306 | + | 0.938490i | \(0.387775\pi\) | |||||||
\(930\) | 5940.00 | 0.209441 | ||||||||
\(931\) | −56523.0 | −1.98976 | ||||||||
\(932\) | 12036.0 | 0.423017 | ||||||||
\(933\) | 19440.0 | 0.682140 | ||||||||
\(934\) | 348.000 | 0.0121916 | ||||||||
\(935\) | 2295.00 | 0.0802722 | ||||||||
\(936\) | 4968.00 | 0.173487 | ||||||||
\(937\) | 10066.0 | 0.350952 | 0.175476 | − | 0.984484i | \(-0.443854\pi\) | ||||
0.175476 | + | 0.984484i | \(0.443854\pi\) | |||||||
\(938\) | 34560.0 | 1.20301 | ||||||||
\(939\) | −14820.0 | −0.515051 | ||||||||
\(940\) | 7640.00 | 0.265095 | ||||||||
\(941\) | −10998.0 | −0.381004 | −0.190502 | − | 0.981687i | \(-0.561012\pi\) | ||||
−0.190502 | + | 0.981687i | \(0.561012\pi\) | |||||||
\(942\) | −1242.00 | −0.0429581 | ||||||||
\(943\) | −19773.0 | −0.682818 | ||||||||
\(944\) | 7200.00 | 0.248242 | ||||||||
\(945\) | 4320.00 | 0.148709 | ||||||||
\(946\) | −12258.0 | −0.421292 | ||||||||
\(947\) | −2268.00 | −0.0778248 | −0.0389124 | − | 0.999243i | \(-0.512389\pi\) | ||||
−0.0389124 | + | 0.999243i | \(0.512389\pi\) | |||||||
\(948\) | −2184.00 | −0.0748239 | ||||||||
\(949\) | 20562.0 | 0.703341 | ||||||||
\(950\) | −16600.0 | −0.566921 | ||||||||
\(951\) | −11994.0 | −0.408972 | ||||||||
\(952\) | −4352.00 | −0.148161 | ||||||||
\(953\) | 23876.0 | 0.811563 | 0.405781 | − | 0.913970i | \(-0.366999\pi\) | ||||
0.405781 | + | 0.913970i | \(0.366999\pi\) | |||||||
\(954\) | −12348.0 | −0.419058 | ||||||||
\(955\) | −18650.0 | −0.631937 | ||||||||
\(956\) | 13856.0 | 0.468761 | ||||||||
\(957\) | 7614.00 | 0.257185 | ||||||||
\(958\) | −36622.0 | −1.23508 | ||||||||
\(959\) | 86592.0 | 2.91575 | ||||||||
\(960\) | −960.000 | −0.0322749 | ||||||||
\(961\) | 9413.00 | 0.315968 | ||||||||
\(962\) | −33672.0 | −1.12851 | ||||||||
\(963\) | 351.000 | 0.0117454 | ||||||||
\(964\) | 624.000 | 0.0208482 | ||||||||
\(965\) | 12390.0 | 0.413314 | ||||||||
\(966\) | −22464.0 | −0.748206 | ||||||||
\(967\) | −12113.0 | −0.402821 | −0.201410 | − | 0.979507i | \(-0.564553\pi\) | ||||
−0.201410 | + | 0.979507i | \(0.564553\pi\) | |||||||
\(968\) | 4816.00 | 0.159909 | ||||||||
\(969\) | 4233.00 | 0.140334 | ||||||||
\(970\) | −11400.0 | −0.377353 | ||||||||
\(971\) | −1190.00 | −0.0393295 | −0.0196647 | − | 0.999807i | \(-0.506260\pi\) | ||||
−0.0196647 | + | 0.999807i | \(0.506260\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 66752.0 | 2.19935 | ||||||||
\(974\) | −13532.0 | −0.445168 | ||||||||
\(975\) | 20700.0 | 0.679929 | ||||||||
\(976\) | −11200.0 | −0.367319 | ||||||||
\(977\) | 10474.0 | 0.342982 | 0.171491 | − | 0.985186i | \(-0.445142\pi\) | ||||
0.171491 | + | 0.985186i | \(0.445142\pi\) | |||||||
\(978\) | 10476.0 | 0.342521 | ||||||||
\(979\) | −39636.0 | −1.29394 | ||||||||
\(980\) | −13620.0 | −0.443954 | ||||||||
\(981\) | −3852.00 | −0.125367 | ||||||||
\(982\) | 27692.0 | 0.899885 | ||||||||
\(983\) | −48259.0 | −1.56584 | −0.782921 | − | 0.622121i | \(-0.786271\pi\) | ||||
−0.782921 | + | 0.622121i | \(0.786271\pi\) | |||||||
\(984\) | −4056.00 | −0.131403 | ||||||||
\(985\) | 10705.0 | 0.346284 | ||||||||
\(986\) | 3196.00 | 0.103227 | ||||||||
\(987\) | 36672.0 | 1.18266 | ||||||||
\(988\) | 22908.0 | 0.737652 | ||||||||
\(989\) | −26559.0 | −0.853920 | ||||||||
\(990\) | 2430.00 | 0.0780106 | ||||||||
\(991\) | 37256.0 | 1.19422 | 0.597112 | − | 0.802158i | \(-0.296315\pi\) | ||||
0.597112 | + | 0.802158i | \(0.296315\pi\) | |||||||
\(992\) | −6336.00 | −0.202791 | ||||||||
\(993\) | 6315.00 | 0.201813 | ||||||||
\(994\) | −17664.0 | −0.563650 | ||||||||
\(995\) | 2900.00 | 0.0923982 | ||||||||
\(996\) | 3384.00 | 0.107657 | ||||||||
\(997\) | 17830.0 | 0.566381 | 0.283190 | − | 0.959064i | \(-0.408607\pi\) | ||||
0.283190 | + | 0.959064i | \(0.408607\pi\) | |||||||
\(998\) | 11708.0 | 0.371353 | ||||||||
\(999\) | −6588.00 | −0.208644 |
(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 | 102.4.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 306.4.a.g.1.1 | 1 | |||
4.3 | odd | 2 | 816.4.a.c.1.1 | 1 | |||
12.11 | even | 2 | 2448.4.a.j.1.1 | 1 | |||
17.16 | even | 2 | 1734.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
102.4.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
306.4.a.g.1.1 | 1 | 3.2 | odd | 2 | |||
816.4.a.c.1.1 | 1 | 4.3 | odd | 2 | |||
1734.4.a.a.1.1 | 1 | 17.16 | even | 2 | |||
2448.4.a.j.1.1 | 1 | 12.11 | even | 2 |