Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,5,Mod(65,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.65");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.h (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(39.6940658242\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.26 | ||
Character | \(\chi\) | \(=\) | 384.65 |
Dual form | 384.5.h.h.65.28 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 8.10449 | − | 3.91372i | 0.900499 | − | 0.434858i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 29.9378 | 1.19751 | 0.598757 | − | 0.800931i | \(-0.295662\pi\) | ||||
0.598757 | + | 0.800931i | \(0.295662\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.14305 | −0.104960 | −0.0524801 | − | 0.998622i | \(-0.516713\pi\) | ||||
−0.0524801 | + | 0.998622i | \(0.516713\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 50.3656 | − | 63.4374i | 0.621797 | − | 0.783178i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 170.063 | 1.40548 | 0.702741 | − | 0.711446i | \(-0.251959\pi\) | ||||
0.702741 | + | 0.711446i | \(0.251959\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 161.374i | 0.954875i | 0.878666 | + | 0.477438i | \(0.158434\pi\) | ||||
−0.878666 | + | 0.477438i | \(0.841566\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 242.631 | − | 117.168i | 1.07836 | − | 0.520748i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 32.6278i | − | 0.112899i | −0.998405 | − | 0.0564495i | \(-0.982022\pi\) | ||
0.998405 | − | 0.0564495i | \(-0.0179780\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 299.419i | 0.829417i | 0.909954 | + | 0.414708i | \(0.136116\pi\) | ||||
−0.909954 | + | 0.414708i | \(0.863884\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −41.6818 | + | 20.1284i | −0.0945165 | + | 0.0456427i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 333.638i | − | 0.630696i | −0.948976 | − | 0.315348i | \(-0.897879\pi\) | ||
0.948976 | − | 0.315348i | \(-0.102121\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 271.273 | 0.434038 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 159.911 | − | 711.245i | 0.219357 | − | 0.975645i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 930.939 | 1.10694 | 0.553471 | − | 0.832868i | \(-0.313303\pi\) | ||||
0.553471 | + | 0.832868i | \(0.313303\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 128.177 | 0.133379 | 0.0666895 | − | 0.997774i | \(-0.478756\pi\) | ||||
0.0666895 | + | 0.997774i | \(0.478756\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1378.28 | − | 665.580i | 1.26564 | − | 0.611185i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −153.972 | −0.125691 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2410.31i | 1.76064i | 0.474383 | + | 0.880318i | \(0.342671\pi\) | ||||
−0.474383 | + | 0.880318i | \(0.657329\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 631.572 | + | 1307.85i | 0.415235 | + | 0.859864i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1190.24i | − | 0.708057i | −0.935235 | − | 0.354028i | \(-0.884812\pi\) | ||
0.935235 | − | 0.354028i | \(-0.115188\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2969.61i | − | 1.60606i | −0.595937 | − | 0.803031i | \(-0.703219\pi\) | ||
0.595937 | − | 0.803031i | \(-0.296781\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1507.84 | − | 1899.18i | 0.744611 | − | 0.937866i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3959.61i | 1.79249i | 0.443558 | + | 0.896246i | \(0.353716\pi\) | ||||
−0.443558 | + | 0.896246i | \(0.646284\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2374.55 | −0.988983 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −127.696 | − | 264.432i | −0.0490950 | − | 0.101666i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3587.36 | −1.27709 | −0.638547 | − | 0.769583i | \(-0.720464\pi\) | ||||
−0.638547 | + | 0.769583i | \(0.720464\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5091.33 | 1.68308 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1171.84 | + | 2426.64i | 0.360678 | + | 0.746889i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1882.24 | 0.540719 | 0.270359 | − | 0.962759i | \(-0.412857\pi\) | ||||
0.270359 | + | 0.962759i | \(0.412857\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1616.86i | − | 0.434523i | −0.976113 | − | 0.217262i | \(-0.930287\pi\) | ||
0.976113 | − | 0.217262i | \(-0.0697125\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −259.033 | + | 326.262i | −0.0652639 | + | 0.0822025i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4831.18i | 1.14348i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8281.38i | − | 1.84482i | −0.386216 | − | 0.922408i | \(-0.626218\pi\) | ||
0.386216 | − | 0.922408i | \(-0.373782\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1305.77 | − | 2703.97i | −0.274263 | − | 0.567941i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3154.62i | − | 0.625793i | −0.949787 | − | 0.312897i | \(-0.898701\pi\) | ||
0.949787 | − | 0.312897i | \(-0.101299\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5570.00 | −1.04522 | −0.522612 | − | 0.852571i | \(-0.675042\pi\) | ||||
−0.522612 | + | 0.852571i | \(0.675042\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2198.53 | − | 1061.69i | 0.390850 | − | 0.188745i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −874.643 | −0.147520 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9861.40 | 1.58010 | 0.790049 | − | 0.613043i | \(-0.210055\pi\) | ||||
0.790049 | + | 0.613043i | \(0.210055\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1487.61 | − | 6390.13i | −0.226736 | − | 0.973956i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8992.50 | 1.30534 | 0.652671 | − | 0.757641i | \(-0.273648\pi\) | ||||
0.652671 | + | 0.757641i | \(0.273648\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 976.806i | − | 0.135198i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7544.79 | − | 3643.43i | 0.996801 | − | 0.481363i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1596.14i | 0.201507i | 0.994911 | + | 0.100754i | \(0.0321254\pi\) | ||||
−0.994911 | + | 0.100754i | \(0.967875\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 829.953i | − | 0.100224i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1038.81 | − | 501.649i | 0.120108 | − | 0.0580009i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8963.97i | 0.993237i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2547.74 | 0.270777 | 0.135389 | − | 0.990793i | \(-0.456772\pi\) | ||||
0.135389 | + | 0.990793i | \(0.456772\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8565.34 | − | 10788.4i | 0.873925 | − | 1.10074i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3280.32 | −0.321568 | −0.160784 | − | 0.986990i | \(-0.551402\pi\) | ||||
−0.160784 | + | 0.986990i | \(0.551402\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10235.3 | 0.964773 | 0.482386 | − | 0.875959i | \(-0.339770\pi\) | ||||
0.482386 | + | 0.875959i | \(0.339770\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1247.86 | + | 602.602i | −0.113185 | + | 0.0546577i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1304.53 | 0.113943 | 0.0569714 | − | 0.998376i | \(-0.481856\pi\) | ||||
0.0569714 | + | 0.998376i | \(0.481856\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4833.00i | − | 0.406784i | −0.979097 | − | 0.203392i | \(-0.934803\pi\) | ||
0.979097 | − | 0.203392i | \(-0.0651966\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9433.28 | + | 19534.4i | 0.765627 | + | 1.58545i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17488.4i | 1.36960i | 0.728732 | + | 0.684799i | \(0.240110\pi\) | ||||
−0.728732 | + | 0.684799i | \(0.759890\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 9988.40i | − | 0.755266i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10237.1 | + | 8127.69i | 0.747837 | + | 0.593739i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 167.806i | 0.0118499i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14280.5 | 0.975380 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4658.28 | − | 9646.32i | −0.307904 | − | 0.637605i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10589.8 | −0.677747 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −24860.7 | −1.54137 | −0.770683 | − | 0.637219i | \(-0.780085\pi\) | ||||
−0.770683 | + | 0.637219i | \(0.780085\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11622.2 | − | 24067.2i | −0.698409 | − | 1.44626i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13359.8 | −0.778497 | −0.389248 | − | 0.921133i | \(-0.627265\pi\) | ||||
−0.389248 | + | 0.921133i | \(0.627265\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1539.93i | − | 0.0870557i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4787.40 | − | 21293.1i | 0.262683 | − | 1.16835i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 19181.4i | − | 1.02197i | −0.859589 | − | 0.510987i | \(-0.829280\pi\) | ||
0.859589 | − | 0.510987i | \(-0.170720\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10860.0i | − | 0.562083i | −0.959696 | − | 0.281042i | \(-0.909320\pi\) | ||
0.959696 | − | 0.281042i | \(-0.0906799\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15496.8 | + | 32090.7i | 0.779479 | + | 1.61414i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 27443.8i | 1.34206i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 27870.3 | 1.32558 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −19244.5 | + | 9293.32i | −0.890579 | + | 0.430067i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11052.1 | 0.497818 | 0.248909 | − | 0.968527i | \(-0.419928\pi\) | ||||
0.248909 | + | 0.968527i | \(0.419928\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 26646.9 | 1.16867 | 0.584336 | − | 0.811512i | \(-0.301355\pi\) | ||||
0.584336 | + | 0.811512i | \(0.301355\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2069.83 | − | 1643.32i | −0.0884201 | − | 0.0702004i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3837.35 | 0.159723 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11601.5i | 0.470666i | 0.971915 | + | 0.235333i | \(0.0756181\pi\) | ||||
−0.971915 | + | 0.235333i | \(0.924382\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −29073.7 | + | 14039.9i | −1.15002 | + | 0.555354i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1715.92i | 0.0661979i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 32130.6i | 1.20932i | 0.796482 | + | 0.604662i | \(0.206692\pi\) | ||||
−0.796482 | + | 0.604662i | \(0.793308\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 41262.6 | − | 19926.0i | 1.51561 | − | 0.731902i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 52364.2i | − | 1.87759i | −0.344474 | − | 0.938796i | \(-0.611943\pi\) | ||
0.344474 | − | 0.938796i | \(-0.388057\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2519.47 | 0.0882135 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18994.4 | + | 15080.4i | 0.649581 | + | 0.515729i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −50794.7 | −1.69717 | −0.848587 | − | 0.529056i | \(-0.822546\pi\) | ||||
−0.848587 | + | 0.529056i | \(0.822546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1395.17 | −0.0455566 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15254.6 | − | 7366.57i | 0.486917 | − | 0.235136i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16928.7 | 0.528344 | 0.264172 | − | 0.964476i | \(-0.414901\pi\) | ||||
0.264172 | + | 0.964476i | \(0.414901\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 20632.5i | − | 0.629788i | −0.949127 | − | 0.314894i | \(-0.898031\pi\) | ||
0.949127 | − | 0.314894i | \(-0.101969\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6327.94 | − | 13103.8i | −0.188956 | − | 0.391288i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 72159.5i | 2.10839i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5548.80i | − | 0.158678i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −822.431 | + | 3657.96i | −0.0230237 | + | 0.102404i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11052.1i | 0.302955i | 0.988461 | + | 0.151478i | \(0.0484032\pi\) | ||||
−0.988461 | + | 0.151478i | \(0.951597\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −54333.7 | −1.45866 | −0.729330 | − | 0.684162i | \(-0.760168\pi\) | ||||
−0.729330 | + | 0.684162i | \(0.760168\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 18907.9 | + | 39154.3i | 0.497249 | + | 1.02970i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −44287.8 | −1.14117 | −0.570586 | − | 0.821238i | \(-0.693284\pi\) | ||||
−0.570586 | + | 0.821238i | \(0.693284\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −38718.7 | −0.977720 | −0.488860 | − | 0.872362i | \(-0.662587\pi\) | ||||
−0.488860 | + | 0.872362i | \(0.662587\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −32411.0 | − | 67116.4i | −0.802233 | − | 1.66126i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4787.86 | −0.116185 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 35633.3i | − | 0.847907i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −21165.1 | − | 16803.9i | −0.493947 | − | 0.392165i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 50920.3i | 1.16573i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 33390.2i | 0.749987i | 0.927027 | + | 0.374993i | \(0.122355\pi\) | ||||
−0.927027 | + | 0.374993i | \(0.877645\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12346.3 | − | 25566.6i | −0.272131 | − | 0.563526i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 88903.7i | − | 1.92328i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −659.221 | −0.0139995 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −45142.0 | + | 21799.4i | −0.941223 | + | 0.454524i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5265.28 | 0.107805 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −63239.5 | −1.27168 | −0.635841 | − | 0.771820i | \(-0.719347\pi\) | ||||
−0.635841 | + | 0.771820i | \(0.719347\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13662.9 | − | 17208.9i | 0.269883 | − | 0.339929i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −67121.7 | −1.30260 | −0.651300 | − | 0.758820i | \(-0.725776\pi\) | ||||
−0.651300 | + | 0.758820i | \(0.725776\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 83285.2i | 1.58817i | 0.607807 | + | 0.794084i | \(0.292049\pi\) | ||||
−0.607807 | + | 0.794084i | \(0.707951\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7088.54 | + | 3423.11i | −0.132841 | + | 0.0641500i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 43135.7i | 0.794558i | 0.917698 | + | 0.397279i | \(0.130045\pi\) | ||||
−0.917698 | + | 0.397279i | \(0.869955\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 118542.i | 2.14653i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 79921.6 | − | 38594.7i | 1.42288 | − | 0.687118i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 67814.2i | 1.18720i | 0.804759 | + | 0.593601i | \(0.202294\pi\) | ||||
−0.804759 | + | 0.593601i | \(0.797706\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25824.5 | −0.444630 | −0.222315 | − | 0.974975i | \(-0.571361\pi\) | ||||
−0.222315 | + | 0.974975i | \(0.571361\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −37065.5 | − | 45966.6i | −0.627708 | − | 0.778449i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −71088.8 | −1.18432 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −48318.5 | −0.791989 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 72879.7 | − | 35194.1i | 1.17546 | − | 0.567638i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −75750.6 | −1.20237 | −0.601186 | − | 0.799109i | \(-0.705305\pi\) | ||||
−0.601186 | + | 0.799109i | \(0.705305\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 56739.6i | − | 0.886431i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3822.95 | − | 7916.52i | −0.0587919 | − | 0.121746i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3320.52i | − | 0.0502735i | −0.999684 | − | 0.0251368i | \(-0.991998\pi\) | ||
0.999684 | − | 0.0251368i | \(-0.00800212\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 12396.3i | − | 0.184797i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 46887.3 | − | 59056.4i | 0.688294 | − | 0.866933i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9496.36i | 0.137292i | 0.997641 | + | 0.0686461i | \(0.0218679\pi\) | ||||
−0.997641 | + | 0.0686461i | \(0.978132\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −107398. | −1.52934 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6246.84 | + | 12935.9i | 0.0876270 | + | 0.181457i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −55521.4 | −0.767283 | −0.383642 | − | 0.923482i | \(-0.625330\pi\) | ||||
−0.383642 | + | 0.923482i | \(0.625330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −123146. | −1.67680 | −0.838400 | − | 0.545055i | \(-0.816509\pi\) | ||||
−0.838400 | + | 0.545055i | \(0.816509\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3248.20 | − | 6726.35i | −0.0435831 | − | 0.0902514i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 46133.7 | 0.610032 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 107683.i | 1.40342i | 0.712462 | + | 0.701711i | \(0.247580\pi\) | ||||
−0.712462 | + | 0.701711i | \(0.752420\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6455.72 | − | 8131.23i | 0.0829347 | − | 0.104459i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 99208.5i | 1.25642i | 0.778042 | + | 0.628212i | \(0.216213\pi\) | ||||
−0.778042 | + | 0.628212i | \(0.783787\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18221.6i | 0.227517i | 0.993508 | + | 0.113759i | \(0.0362890\pi\) | ||||
−0.993508 | + | 0.113759i | \(0.963711\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 35082.5 | + | 72648.4i | 0.431917 | + | 0.894409i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6121.48i | 0.0743177i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 82456.4 | 0.987254 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20648.2 | − | 9971.15i | 0.243835 | − | 0.117750i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −89818.1 | −1.04623 | −0.523117 | − | 0.852261i | \(-0.675231\pi\) | ||||
−0.523117 | + | 0.852261i | \(0.675231\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 56350.2 | 0.647518 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 27195.0 | − | 120957.i | 0.308302 | − | 1.37125i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 53840.5 | 0.602236 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15272.8i | 0.168572i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −26585.3 | + | 12838.3i | −0.289572 | + | 0.139837i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 48405.3i | − | 0.520348i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23652.4i | 0.250957i | 0.992096 | + | 0.125478i | \(0.0400465\pi\) | ||||
−0.992096 | + | 0.125478i | \(0.959953\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 82951.7 | − | 40058.0i | 0.868777 | − | 0.419539i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4995.98i | 0.0516535i | 0.999666 | + | 0.0258268i | \(0.00822183\pi\) | ||||
−0.999666 | + | 0.0258268i | \(0.991778\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 123447. | 1.26007 | 0.630033 | − | 0.776569i | \(-0.283041\pi\) | ||||
0.630033 | + | 0.776569i | \(0.283041\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7754.87 | + | 9767.56i | −0.0781544 | + | 0.0984385i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 84116.1 | 0.837067 | 0.418534 | − | 0.908201i | \(-0.362544\pi\) | ||||
0.418534 | + | 0.908201i | \(0.362544\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 158319. | 1.55579 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10572.6 | − | 5105.57i | 0.102605 | − | 0.0495489i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9769.41 | 0.0936404 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 43776.5i | 0.414452i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18915.0 | − | 39169.0i | −0.176893 | − | 0.366309i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 20364.5i | − | 0.188140i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 67717.3i | − | 0.618079i | −0.951049 | − | 0.309039i | \(-0.899992\pi\) | ||
0.951049 | − | 0.309039i | \(-0.100008\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 152904. | + | 121397.i | 1.37889 | + | 1.09476i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 247927.i | − | 2.20919i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11076.2 | 0.0975282 | 0.0487641 | − | 0.998810i | \(-0.484472\pi\) | ||||
0.0487641 | + | 0.998810i | \(0.484472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 68444.7 | + | 141735.i | 0.595580 | + | 1.23332i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21798.2 | 0.187462 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 24560.9 | 0.208764 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −39091.8 | − | 80950.9i | −0.328433 | − | 0.680117i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −33822.4 | −0.280896 | −0.140448 | − | 0.990088i | \(-0.544854\pi\) | ||||
−0.140448 | + | 0.990088i | \(0.544854\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 157980.i | − | 1.29703i | −0.761202 | − | 0.648515i | \(-0.775390\pi\) | ||
0.761202 | − | 0.648515i | \(-0.224610\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 114776. | + | 25805.5i | 0.931619 | + | 0.209459i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 40542.5i | 0.325358i | 0.986679 | + | 0.162679i | \(0.0520134\pi\) | ||||
−0.986679 | + | 0.162679i | \(0.947987\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 94442.6i | − | 0.749395i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 656.747 | + | 1359.99i | 0.00515302 | + | 0.0106708i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 174457.i | 1.35363i | 0.736155 | + | 0.676813i | \(0.236639\pi\) | ||||
−0.736155 | + | 0.676813i | \(0.763361\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40669.0 | 0.312068 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 115736. | − | 55890.0i | 0.878328 | − | 0.424151i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −166754. | −1.25167 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 140984. | 1.04674 | 0.523370 | − | 0.852106i | \(-0.324675\pi\) | ||||
0.523370 | + | 0.852106i | \(0.324675\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −75506.0 | − | 59947.3i | −0.554535 | − | 0.440268i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18449.9 | 0.134044 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 129523.i | 0.930953i | 0.885060 | + | 0.465476i | \(0.154117\pi\) | ||||
−0.885060 | + | 0.465476i | \(0.845883\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −85825.0 | + | 41445.5i | −0.610311 | + | 0.294724i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 150229.i | 1.05699i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 282353.i | − | 1.96569i | −0.184442 | − | 0.982843i | \(-0.559048\pi\) | ||
0.184442 | − | 0.982843i | \(-0.440952\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −201483. | + | 97297.7i | −1.38800 | + | 0.670275i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 43563.6i | 0.296979i | 0.988914 | + | 0.148490i | \(0.0474412\pi\) | ||||
−0.988914 | + | 0.148490i | \(0.952559\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26184.9 | −0.176657 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −188384. | − | 149566.i | −1.25783 | − | 0.998646i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21525.5 | −0.142250 | −0.0711252 | − | 0.997467i | \(-0.522659\pi\) | ||||
−0.0711252 | + | 0.997467i | \(0.522659\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10885.9 | −0.0712049 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −108274. | + | 52286.5i | −0.701036 | + | 0.338535i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 295229. | 1.89219 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 248536.i | − | 1.57692i | −0.615088 | − | 0.788458i | \(-0.710880\pi\) | ||
0.615088 | − | 0.788458i | \(-0.289120\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6026.84 | − | 12480.3i | −0.0378568 | − | 0.0783935i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 169418.i | 1.05359i | 0.849993 | + | 0.526794i | \(0.176606\pi\) | ||||
−0.849993 | + | 0.526794i | \(0.823394\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20684.4i | 0.127360i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −44535.9 | − | 191307.i | −0.271519 | − | 1.16633i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 409906.i | 2.47454i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −124151. | −0.742169 | −0.371085 | − | 0.928599i | \(-0.621014\pi\) | ||||
−0.371085 | + | 0.928599i | \(0.621014\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −75070.7 | − | 155456.i | −0.444413 | − | 0.920286i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9680.46 | −0.0567539 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 269216. | 1.56316 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −42503.0 | − | 88014.8i | −0.244426 | − | 0.506155i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37995.6 | −0.216424 | −0.108212 | − | 0.994128i | \(-0.534512\pi\) | ||||
−0.108212 | + | 0.994128i | \(0.534512\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 240982.i | − | 1.35963i | −0.733383 | − | 0.679815i | \(-0.762060\pi\) | ||
0.733383 | − | 0.679815i | \(-0.237940\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 251188. | + | 199428.i | 1.40384 | + | 1.11457i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 8851.07i | − | 0.0490024i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8315.59i | 0.0456076i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 107407. | + | 222418.i | 0.583605 | + | 1.20852i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 27547.2i | − | 0.148294i | −0.997247 | − | 0.0741470i | \(-0.976377\pi\) | ||
0.997247 | − | 0.0741470i | \(-0.0236234\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 113306. | 0.604333 | 0.302167 | − | 0.953255i | \(-0.402290\pi\) | ||||
0.302167 | + | 0.953255i | \(0.402290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 225875. | − | 109077.i | 1.19368 | − | 0.576438i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 99897.7 | 0.523109 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −90326.6 | −0.468691 | −0.234345 | − | 0.972153i | \(-0.575295\pi\) | ||||
−0.234345 | + | 0.972153i | \(0.575295\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −119596. | + | 150635.i | −0.614947 | + | 0.774550i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −293915. | −1.49766 | −0.748832 | − | 0.662760i | \(-0.769385\pi\) | ||||
−0.748832 | + | 0.662760i | \(0.769385\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 47784.9i | 0.241308i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 89571.3 | − | 43254.7i | 0.448285 | − | 0.216480i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 56159.4i | 0.278567i | 0.990253 | + | 0.139284i | \(0.0444800\pi\) | ||||
−0.990253 | + | 0.139284i | \(0.955520\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 202417.i | − | 0.995161i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 215960. | − | 104289.i | 1.05239 | − | 0.508206i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 24847.0i | − | 0.120019i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 218485. | 1.04614 | 0.523069 | − | 0.852290i | \(-0.324787\pi\) | ||||
0.523069 | + | 0.852290i | \(0.324787\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −23206.4 | − | 5217.56i | −0.110149 | − | 0.0247652i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −300747. | −1.41514 | −0.707571 | − | 0.706643i | \(-0.750209\pi\) | ||||
−0.707571 | + | 0.706643i | \(0.750209\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −121032. | −0.564597 | −0.282298 | − | 0.959327i | \(-0.591097\pi\) | ||||
−0.282298 | + | 0.959327i | \(0.591097\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 31099.7 | − | 15018.3i | 0.143830 | − | 0.0694568i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 63141.2 | 0.289520 | 0.144760 | − | 0.989467i | \(-0.453759\pi\) | ||||
0.144760 | + | 0.989467i | \(0.453759\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 42591.5i | 0.193632i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 45404.8 | + | 94023.9i | 0.204673 | + | 0.423835i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 505022.i | − | 2.25729i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 81224.5i | 0.359998i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −180679. | + | 227573.i | −0.794094 | + | 1.00019i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 243193.i | − | 1.05994i | −0.848017 | − | 0.529969i | \(-0.822204\pi\) | ||
0.848017 | − | 0.529969i | \(-0.177796\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −388961. | −1.68119 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6715.61 | + | 13906.6i | 0.0287867 | + | 0.0596111i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 76273.9 | 0.324259 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 165816. | 0.699149 | 0.349574 | − | 0.936909i | \(-0.386326\pi\) | ||||
0.349574 | + | 0.936909i | \(0.386326\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 125750. | + | 260402.i | 0.525884 | + | 1.08900i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 291207. | 1.20792 | 0.603961 | − | 0.797014i | \(-0.293588\pi\) | ||||
0.603961 | + | 0.797014i | \(0.293588\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 30374.5i | − | 0.124973i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 256428. | − | 322981.i | 1.04654 | − | 1.31815i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16224.4i | 0.0656833i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 92369.0i | − | 0.370959i | −0.982648 | − | 0.185479i | \(-0.940616\pi\) | ||
0.982648 | − | 0.185479i | \(-0.0593838\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −204939. | − | 424385.i | −0.816485 | − | 1.69077i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 125137.i | − | 0.494595i | −0.968940 | − | 0.247297i | \(-0.920458\pi\) | ||
0.968940 | − | 0.247297i | \(-0.0795425\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −98205.6 | −0.385082 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20419.0 | − | 9860.48i | 0.0794362 | − | 0.0383603i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 245886. | 0.949071 | 0.474536 | − | 0.880236i | \(-0.342616\pi\) | ||||
0.474536 | + | 0.880236i | \(0.342616\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28646.8 | 0.109707 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 212961. | + | 47880.5i | 0.809216 | + | 0.181938i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 306422. | 1.15533 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 673385.i | 2.51931i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −411665. | + | 198796.i | −1.52830 | + | 0.738029i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 145433.i | 0.535781i | 0.963449 | + | 0.267890i | \(0.0863265\pi\) | ||||
−0.963449 | + | 0.267890i | \(0.913673\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 203742.i | 0.744865i | 0.928059 | + | 0.372433i | \(0.121476\pi\) | ||||
−0.928059 | + | 0.372433i | \(0.878524\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11307.2 | + | 5460.31i | −0.0410237 | + | 0.0198107i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4182.14i | − | 0.0150584i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 168527. | 0.602223 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 94800.2 | − | 119405.i | 0.336218 | − | 0.423479i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 192074. | 0.676106 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39054.8 | 0.136448 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 137198. | − | 66254.1i | 0.475773 | − | 0.229755i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −403824. | −1.39000 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 316003.i | − | 1.07968i | −0.841767 | − | 0.539842i | \(-0.818484\pi\) | ||
0.841767 | − | 0.539842i | \(-0.181516\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −80749.8 | − | 167216.i | −0.273868 | − | 0.567124i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 144689.i | − | 0.487129i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 76410.8i | 0.255376i | 0.991814 | + | 0.127688i | \(0.0407556\pi\) | ||||
−0.991814 | + | 0.127688i | \(0.959244\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −102570. | − | 81434.2i | −0.340309 | − | 0.270186i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 278741.i | 0.918117i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −50717.6 | −0.165847 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 282412. | + | 584816.i | 0.916848 | + | 1.89860i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 484406. | 1.56135 | 0.780673 | − | 0.624939i | \(-0.214876\pi\) | ||||
0.780673 | + | 0.624939i | \(0.214876\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 479217. | 1.53359 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21716.4 | − | 44970.2i | −0.0690022 | − | 0.142889i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −91818.6 | −0.289677 | −0.144838 | − | 0.989455i | \(-0.546266\pi\) | ||||
−0.144838 | + | 0.989455i | \(0.546266\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 523565.i | 1.64011i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7650.86 | + | 32864.7i | 0.0237982 | + | 0.102227i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 430154.i | − | 1.32862i | −0.747459 | − | 0.664308i | \(-0.768726\pi\) | ||
0.747459 | − | 0.664308i | \(-0.231274\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 120296.i | − | 0.368960i | −0.982836 | − | 0.184480i | \(-0.940940\pi\) | ||
0.982836 | − | 0.184480i | \(-0.0590601\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 43254.9 | + | 89571.8i | 0.131743 | + | 0.272811i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 90507.1i | − | 0.273746i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 493660. | 1.48278 | 0.741389 | − | 0.671076i | \(-0.234167\pi\) | ||||
0.741389 | + | 0.671076i | \(0.234167\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −440347. | + | 212647.i | −1.31352 | + | 0.634310i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −46248.8 | −0.137009 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −610078. | −1.79493 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 306478. | + | 243325.i | 0.895545 | + | 0.711010i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 365807. | 1.06164 | 0.530819 | − | 0.847485i | \(-0.321884\pi\) | ||||
0.530819 | + | 0.847485i | \(0.321884\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 38378.7i | 0.110627i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −358930. | + | 173330.i | −1.02763 | + | 0.496248i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 490452.i | − | 1.39472i | −0.716721 | − | 0.697360i | \(-0.754358\pi\) | ||
0.716721 | − | 0.697360i | \(-0.245642\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5023.76i | 0.0141904i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −313795. | + | 151534.i | −0.880436 | + | 0.425169i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 37189.5i | − | 0.103649i | −0.998656 | − | 0.0518247i | \(-0.983496\pi\) | ||
0.998656 | − | 0.0518247i | \(-0.0165037\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −461210. | −1.27688 | −0.638440 | − | 0.769672i | \(-0.720420\pi\) | ||||
−0.638440 | + | 0.769672i | \(0.720420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −525350. | − | 417097.i | −1.44482 | − | 1.14710i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 427528. | 1.16803 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −594036. | −1.61226 | −0.806130 | − | 0.591738i | \(-0.798442\pi\) | ||||
−0.806130 | + | 0.591738i | \(0.798442\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −38803.2 | + | 18738.3i | −0.104624 | + | 0.0505239i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −638978. | −1.71161 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 134516.i | 0.357975i | 0.983851 | + | 0.178987i | \(0.0572821\pi\) | ||||
−0.983851 | + | 0.178987i | \(0.942718\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −139459. | − | 288790.i | −0.368719 | − | 0.763540i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 97225.4i | − | 0.255393i | −0.991813 | − | 0.127697i | \(-0.959242\pi\) | ||
0.991813 | − | 0.127697i | \(-0.0407584\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 241624.i | 0.630608i | 0.948991 | + | 0.315304i | \(0.102106\pi\) | ||||
−0.948991 | + | 0.315304i | \(0.897894\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −237298. | − | 53352.5i | −0.615335 | − | 0.138348i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 8209.02i | − | 0.0211502i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −486582. | −1.24565 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 199288. | + | 412683.i | 0.506927 | + | 1.04974i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 78643.2 | 0.198774 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −199271. | −0.500478 | −0.250239 | − | 0.968184i | \(-0.580509\pi\) | ||||
−0.250239 | + | 0.968184i | \(0.580509\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 130680. | + | 270610.i | 0.326138 | + | 0.675363i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −744275. | −1.84580 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 383190.i | − | 0.944356i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −200121. | − | 158884.i | −0.490107 | − | 0.389117i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 648365.i | 1.57799i | 0.614401 | + | 0.788994i | \(0.289398\pi\) | ||||
−0.614401 | + | 0.788994i | \(0.710602\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 701137.i | 1.69582i | 0.530137 | + | 0.847912i | \(0.322140\pi\) | ||||
−0.530137 | + | 0.847912i | \(0.677860\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −347944. | − | 720519.i | −0.836354 | − | 1.73191i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 176172.i | − | 0.420852i | −0.977610 | − | 0.210426i | \(-0.932515\pi\) | ||
0.977610 | − | 0.210426i | \(-0.0674851\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 320100. | 0.759970 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5342.65 | + | 2580.01i | −0.0126065 | + | 0.00608778i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 82082.5 | 0.192497 | 0.0962486 | − | 0.995357i | \(-0.469316\pi\) | ||||
0.0962486 | + | 0.995357i | \(0.469316\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −399963. | −0.932260 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −280536. | + | 353346.i | −0.649918 | + | 0.818596i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −90850.5 | −0.209198 | −0.104599 | − | 0.994515i | \(-0.533356\pi\) | ||||
−0.104599 | + | 0.994515i | \(0.533356\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 93338.4i | − | 0.213628i | −0.994279 | − | 0.106814i | \(-0.965935\pi\) | ||
0.994279 | − | 0.106814i | \(-0.0340649\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 42672.4 | − | 20606.8i | 0.0970779 | − | 0.0468796i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 46102.1i | − | 0.104250i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 310597.i | − | 0.698144i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −512524. | + | 247502.i | −1.14515 | + | 0.553001i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 274969.i | − | 0.610715i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −193401. | −0.427002 | −0.213501 | − | 0.976943i | \(-0.568487\pi\) | ||||
−0.213501 | + | 0.976943i | \(0.568487\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 43379.7 | − | 192942.i | 0.0952092 | − | 0.423466i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −118624. | −0.258818 | −0.129409 | − | 0.991591i | \(-0.541308\pi\) | ||||
−0.129409 | + | 0.991591i | \(0.541308\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13103.2 | −0.0284208 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −543987. | + | 262695.i | −1.17299 | + | 0.566446i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 578837. | 1.24084 | 0.620419 | − | 0.784270i | \(-0.286962\pi\) | ||||
0.620419 | + | 0.784270i | \(0.286962\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 574250.i | − | 1.22383i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 325955. | + | 674984.i | 0.690628 | + | 1.43014i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 578906.i | − | 1.21947i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 825321.i | 1.72849i | 0.503071 | + | 0.864245i | \(0.332203\pi\) | ||||
−0.503071 | + | 0.864245i | \(0.667797\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −44051.9 | + | 55485.1i | −0.0917273 | + | 0.115534i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 325125.i | − | 0.673102i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −38835.1 | −0.0799390 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 168821. | + | 349593.i | 0.345520 | + | 0.715498i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −105553. | −0.214801 | −0.107401 | − | 0.994216i | \(-0.534253\pi\) | ||||
−0.107401 | + | 0.994216i | \(0.534253\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −721694. | −1.46030 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 463941. | + | 960725.i | 0.933436 | + | 1.93295i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16870.8 | 0.0337519 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40012.7i | 0.0795985i | 0.999208 | + | 0.0397993i | \(0.0126718\pi\) | ||||
−0.999208 | + | 0.0397993i | \(0.987328\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 496675. | − | 625582.i | 0.982501 | − | 1.23750i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 42764.8i | − | 0.0841215i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 821607.i | 1.60713i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 265406. | + | 549600.i | 0.516264 | + | 1.06907i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 69687.8i | 0.134803i | 0.997726 | + | 0.0674015i | \(0.0214708\pi\) | ||||
−0.997726 | + | 0.0674015i | \(0.978529\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −52640.5 | −0.101263 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −209295. | + | 101070.i | −0.400389 | + | 0.193351i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 252539. | 0.480455 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 278432. | 0.526805 | 0.263402 | − | 0.964686i | \(-0.415155\pi\) | ||||
0.263402 | + | 0.964686i | \(0.415155\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −480298. | − | 227472.i | −0.903765 | − | 0.428029i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −96891.9 | −0.181323 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 211684.i | − | 0.393986i | −0.980405 | − | 0.196993i | \(-0.936882\pi\) | ||
0.980405 | − | 0.196993i | \(-0.0631176\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −576139. | + | 278222.i | −1.06648 | + | 0.515011i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.40836e6i | − | 2.59286i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 319029.i | − | 0.584172i | −0.956392 | − | 0.292086i | \(-0.905651\pi\) | ||
0.956392 | − | 0.292086i | \(-0.0943494\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −391597. | + | 189105.i | −0.713186 | + | 0.344403i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 514092.i | − | 0.931244i | −0.884984 | − | 0.465622i | \(-0.845831\pi\) | ||
0.884984 | − | 0.465622i | \(-0.154169\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 330875. | 0.596144 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 452913. | − | 570461.i | 0.811659 | − | 1.02232i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6709.27 | −0.0119595 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 283278. | 0.502265 | 0.251133 | − | 0.967953i | \(-0.419197\pi\) | ||||
0.251133 | + | 0.967953i | \(0.419197\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −613920. | + | 296467.i | −1.08273 | + | 0.522861i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 797750. | 1.39950 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 116594.i | − | 0.203463i | −0.994812 | − | 0.101732i | \(-0.967562\pi\) | ||
0.994812 | − | 0.101732i | \(-0.0324383\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −222063. | − | 459845.i | −0.385471 | − | 0.798231i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 191031.i | 0.329863i | 0.986305 | + | 0.164932i | \(0.0527403\pi\) | ||||
−0.986305 | + | 0.164932i | \(0.947260\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24856.3i | 0.0426961i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −61966.1 | − | 49197.4i | −0.105884 | − | 0.0840658i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 303745.i | 0.516319i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 389168. | 0.658088 | 0.329044 | − | 0.944315i | \(-0.393273\pi\) | ||||
0.329044 | + | 0.944315i | \(0.393273\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12995.6 | − | 26911.1i | −0.0218618 | − | 0.0452713i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 568776. | 0.951880 | 0.475940 | − | 0.879478i | \(-0.342108\pi\) | ||||
0.475940 | + | 0.879478i | \(0.342108\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34771.1 | 0.0578915 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −48515.8 | − | 100466.i | −0.0803602 | − | 0.166409i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 356382. | 0.587274 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 536486.i | − | 0.879541i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 148868. | − | 662126.i | 0.242816 | − | 1.07998i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 347322.i | 0.563629i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 467885.i | − | 0.755422i | −0.925923 | − | 0.377711i | \(-0.876711\pi\) | ||
0.925923 | − | 0.377711i | \(-0.123289\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 37166.1 | + | 76963.2i | 0.0597025 | + | 0.123631i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 89943.6i | − | 0.143753i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 260919. | 0.414916 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −870404. | + | 420325.i | −1.37717 | + | 0.665044i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 592697. | 0.933074 | 0.466537 | − | 0.884502i | \(-0.345502\pi\) | ||||
0.466537 | + | 0.884502i | \(0.345502\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 129194. | 0.202371 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 101255. | + | 80390.5i | 0.157816 | + | 0.125297i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −947252. | −1.46904 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 51370.8i | 0.0792728i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −449973. | + | 217295.i | −0.690938 | + | 0.333659i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 491874.i | 0.751548i | 0.926711 | + | 0.375774i | \(0.122623\pi\) | ||||
−0.926711 | + | 0.375774i | \(0.877377\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 140444.i | 0.213531i | 0.994284 | + | 0.106766i | \(0.0340494\pi\) | ||||
−0.994284 | + | 0.106766i | \(0.965951\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −998035. | + | 481958.i | −1.50996 | + | 0.729170i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 961919.i | 1.44818i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 889159. | 1.33209 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −52650.1 | − | 41801.1i | −0.0784931 | − | 0.0623189i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36236.4 | −0.0537600 | −0.0268800 | − | 0.999639i | \(-0.508557\pi\) | ||||
−0.0268800 | + | 0.999639i | \(0.508557\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 306097. | 0.451918 | 0.225959 | − | 0.974137i | \(-0.427448\pi\) | ||||
0.225959 | + | 0.974137i | \(0.427448\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 373890. | − | 180554.i | 0.549333 | − | 0.265277i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.01391e6 | −1.48247 | −0.741236 | − | 0.671244i | \(-0.765760\pi\) | ||||
−0.741236 | + | 0.671244i | \(0.765760\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 921062.i | 1.34023i | 0.742257 | + | 0.670116i | \(0.233756\pi\) | ||||
−0.742257 | + | 0.670116i | \(0.766244\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 421442. | + | 872717.i | 0.610289 | + | 1.26378i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 77476.4i | 0.111655i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.56767e6i | − | 2.24844i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20497.0 | − | 91165.4i | 0.0292576 | − | 0.130130i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 801936.i | − | 1.13924i | −0.821908 | − | 0.569620i | \(-0.807090\pi\) | ||
0.821908 | − | 0.569620i | \(-0.192910\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 159366. | 0.225323 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 388274. | + | 804034.i | 0.546366 | + | 1.13141i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 75427.3 | 0.105637 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −73445.4 | −0.102376 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 71314.3 | + | 147677.i | 0.0989376 | + | 0.204879i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 804171. | 1.11043 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 270671.i | − | 0.372000i | −0.982550 | − | 0.186000i | \(-0.940448\pi\) | ||
0.982550 | − | 0.186000i | \(-0.0595525\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 568651. | + | 451476.i | 0.777882 | + | 0.617592i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 872199.i | − | 1.18755i | −0.804629 | − | 0.593777i | \(-0.797636\pi\) | ||
0.804629 | − | 0.593777i | \(-0.202364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 989515.i | − | 1.34102i | −0.741900 | − | 0.670511i | \(-0.766075\pi\) | ||
0.741900 | − | 0.670511i | \(-0.233925\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23957.7 | + | 49611.5i | 0.0323176 | + | 0.0669230i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.28954e6i | 1.73147i | 0.500507 | + | 0.865733i | \(0.333147\pi\) | ||||
−0.500507 | + | 0.865733i | \(0.666853\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.52068e6 | −2.03239 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 668267. | − | 322711.i | 0.889021 | − | 0.429315i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.67706e6 | 2.22080 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.33640e6 | 1.76157 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 128319. | − | 161622.i | 0.168369 | − | 0.212067i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 54463.8 | 0.0711364 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 762506.i | 0.991389i | 0.868497 | + | 0.495695i | \(0.165086\pi\) | ||||
−0.868497 | + | 0.495695i | \(0.834914\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −727930. | + | 351523.i | −0.942132 | + | 0.454963i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.07039e6i | − | 1.37908i | −0.724247 | − | 0.689540i | \(-0.757813\pi\) | ||
0.724247 | − | 0.689540i | \(-0.242187\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 379958.i | 0.487320i | 0.969861 | + | 0.243660i | \(0.0783480\pi\) | ||||
−0.969861 | + | 0.243660i | \(0.921652\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 456690. | − | 220539.i | 0.583089 | − | 0.281578i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33846.7i | 0.0430198i | 0.999769 | + | 0.0215099i | \(0.00684734\pi\) | ||||
−0.999769 | + | 0.0215099i | \(0.993153\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 127860. | 0.161782 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −252988. | − | 1.08673e6i | −0.318673 | − | 1.36888i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.18559e6 | −1.48672 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 506808. | 0.632699 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 436350. | − | 210716.i | 0.542313 | − | 0.261887i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 119325. | 0.147643 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 117048.i | 0.144183i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 59773.6 | + | 123779.i | 0.0733051 | + | 0.151799i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 617692.i | − | 0.754180i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 650249.i | − | 0.790433i | −0.918588 | − | 0.395217i | \(-0.870670\pi\) | ||
0.918588 | − | 0.395217i | \(-0.129330\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −165215. | + | 208095.i | −0.199950 | + | 0.251845i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.03580e6i | 1.24807i | 0.781395 | + | 0.624037i | \(0.214508\pi\) | ||||
−0.781395 | + | 0.624037i | \(0.785492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.52929e6 | 1.83463 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −189445. | − | 392301.i | −0.226277 | − | 0.468573i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 68710.0 | 0.0817111 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 386764. | 0.457947 | 0.228974 | − | 0.973433i | \(-0.426463\pi\) | ||||
0.228974 | + | 0.973433i | \(0.426463\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 92568.9 | + | 191691.i | 0.109130 | + | 0.225986i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 509074. | 0.597554 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 653854.i | 0.764182i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 515506. | − | 649299.i | 0.599893 | − | 0.755589i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 258141.i | 0.299106i | 0.988754 | + | 0.149553i | \(0.0477835\pi\) | ||||
−0.988754 | + | 0.149553i | \(0.952216\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 710986.i | − | 0.820279i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19552.9 | + | 40489.9i | 0.0224619 | + | 0.0465140i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 166119.i | − | 0.190019i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −294387. | −0.335305 | −0.167652 | − | 0.985846i | \(-0.553619\pi\) | ||||
−0.167652 | + | 0.985846i | \(0.553619\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.00048e6 | − | 483138.i | 1.13469 | − | 0.547949i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 935546. | 1.05654 | 0.528270 | − | 0.849076i | \(-0.322841\pi\) | ||||
0.528270 | + | 0.849076i | \(0.322841\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −397110. | −0.446568 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −24621.8 | + | 109512.i | −0.0275712 | + | 0.122630i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 762646. | 0.850400 | 0.425200 | − | 0.905099i | \(-0.360204\pi\) | ||||
0.425200 | + | 0.905099i | \(0.360204\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 898852.i | − | 0.998058i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 681718. | − | 329207.i | 0.753778 | − | 0.364005i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.66347e6i | 1.83159i | 0.401646 | + | 0.915795i | \(0.368438\pi\) | ||||
−0.401646 | + | 0.915795i | \(0.631562\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 330876.i | 0.362793i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.28309e6 | − | 619615.i | 1.40099 | − | 0.676547i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 98650.9i | 0.107266i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −907092. | −0.982210 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 65703.5 | − | 82756.1i | 0.0708494 | − | 0.0892376i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.62663e6 | −1.74677 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 709312. | 0.758550 | 0.379275 | − | 0.925284i | \(-0.376173\pi\) | ||||
0.379275 | + | 0.925284i | \(0.376173\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 79176.1 | − | 38234.7i | 0.0843231 | − | 0.0407202i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.18218e6 | 1.25385 | 0.626924 | − | 0.779081i | \(-0.284314\pi\) | ||||
0.626924 | + | 0.779081i | \(0.284314\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 55853.5i | 0.0589963i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 171329. | + | 354786.i | 0.180228 | + | 0.373213i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.20925e6i | 1.26685i | 0.773804 | + | 0.633425i | \(0.218352\pi\) | ||||
−0.773804 | + | 0.633425i | \(0.781648\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 271445.i | 0.283215i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −306593. | − | 243417.i | −0.318584 | − | 0.252937i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1.61497e6i | − | 1.67132i | −0.549250 | − | 0.835658i | \(-0.685087\pi\) | ||
0.549250 | − | 0.835658i | \(-0.314913\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.32588e6 | −1.36657 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −79700.8 | − | 165044.i | −0.0818142 | − | 0.169420i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −990774. | −1.01294 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 730687. | 0.744019 | 0.372010 | − | 0.928229i | \(-0.378669\pi\) | ||||
0.372010 | + | 0.928229i | \(0.378669\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −265027. | − | 548815.i | −0.268776 | − | 0.556580i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.15915e6 | −1.17083 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 626076.i | 0.629850i | 0.949117 | + | 0.314925i | \(0.101979\pi\) | ||||
−0.949117 | + | 0.314925i | \(0.898021\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.71432e6 | + | 385436.i | 1.71776 | + | 0.386208i |
(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 | 384.5.h.h.65.26 | yes | 32 | |
3.2 | odd | 2 | inner | 384.5.h.h.65.5 | ✓ | 32 | |
4.3 | odd | 2 | inner | 384.5.h.h.65.8 | yes | 32 | |
8.3 | odd | 2 | inner | 384.5.h.h.65.25 | yes | 32 | |
8.5 | even | 2 | inner | 384.5.h.h.65.7 | yes | 32 | |
12.11 | even | 2 | inner | 384.5.h.h.65.27 | yes | 32 | |
24.5 | odd | 2 | inner | 384.5.h.h.65.28 | yes | 32 | |
24.11 | even | 2 | inner | 384.5.h.h.65.6 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.h.h.65.5 | ✓ | 32 | 3.2 | odd | 2 | inner | |
384.5.h.h.65.6 | yes | 32 | 24.11 | even | 2 | inner | |
384.5.h.h.65.7 | yes | 32 | 8.5 | even | 2 | inner | |
384.5.h.h.65.8 | yes | 32 | 4.3 | odd | 2 | inner | |
384.5.h.h.65.25 | yes | 32 | 8.3 | odd | 2 | inner | |
384.5.h.h.65.26 | yes | 32 | 1.1 | even | 1 | trivial | |
384.5.h.h.65.27 | yes | 32 | 12.11 | even | 2 | inner | |
384.5.h.h.65.28 | yes | 32 | 24.5 | odd | 2 | inner |