Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(895,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.895");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.b (of order \(2\), degree \(1\), not 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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 672) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.2 | ||
Character | \(\chi\) | \(=\) | 1344.895 |
Dual form | 1344.4.b.i.895.23 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 15.7575i | − | 1.40939i | −0.709508 | − | 0.704697i | \(-0.751083\pi\) | ||
0.709508 | − | 0.704697i | \(-0.248917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.0622 | + | 10.7764i | −0.813280 | + | 0.581873i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 63.5030i | − | 1.74062i | −0.492500 | − | 0.870312i | \(-0.663917\pi\) | ||
0.492500 | − | 0.870312i | \(-0.336083\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 34.9026i | − | 0.744634i | −0.928106 | − | 0.372317i | \(-0.878563\pi\) | ||
0.928106 | − | 0.372317i | \(-0.121437\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 47.2725i | 0.813714i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 39.0949i | − | 0.557759i | −0.960326 | − | 0.278879i | \(-0.910037\pi\) | ||
0.960326 | − | 0.278879i | \(-0.0899630\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −139.703 | −1.68685 | −0.843424 | − | 0.537249i | \(-0.819464\pi\) | ||||
−0.843424 | + | 0.537249i | \(0.819464\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 45.1865 | − | 32.3293i | 0.469547 | − | 0.335945i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 123.427i | − | 1.11897i | −0.828840 | − | 0.559485i | \(-0.810999\pi\) | ||
0.828840 | − | 0.559485i | \(-0.189001\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −123.299 | −0.986394 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 131.511 | 0.842103 | 0.421051 | − | 0.907037i | \(-0.361661\pi\) | ||||
0.421051 | + | 0.907037i | \(0.361661\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −225.225 | −1.30489 | −0.652446 | − | 0.757835i | \(-0.726257\pi\) | ||||
−0.652446 | + | 0.757835i | \(0.726257\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 190.509i | 1.00495i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 169.810 | + | 237.342i | 0.820089 | + | 1.14623i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 148.493 | 0.659787 | 0.329894 | − | 0.944018i | \(-0.392987\pi\) | ||||
0.329894 | + | 0.944018i | \(0.392987\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 104.708i | 0.429915i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 174.658i | − | 0.665291i | −0.943052 | − | 0.332646i | \(-0.892059\pi\) | ||
0.943052 | − | 0.332646i | \(-0.107941\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 451.335i | − | 1.60065i | −0.599567 | − | 0.800325i | \(-0.704660\pi\) | ||
0.599567 | − | 0.800325i | \(-0.295340\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 141.818i | − | 0.469798i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 146.540 | 0.454789 | 0.227395 | − | 0.973803i | \(-0.426979\pi\) | ||||
0.227395 | + | 0.973803i | \(0.426979\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 110.737 | − | 324.633i | 0.322848 | − | 0.946451i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 117.285i | 0.322022i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 278.721 | 0.722365 | 0.361182 | − | 0.932495i | \(-0.382373\pi\) | ||||
0.361182 | + | 0.932495i | \(0.382373\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1000.65 | −2.45323 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 419.109 | 0.973902 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 26.4098 | 0.0582756 | 0.0291378 | − | 0.999575i | \(-0.490724\pi\) | ||||
0.0291378 | + | 0.999575i | \(0.490724\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 69.5922i | 0.146072i | 0.997329 | + | 0.0730358i | \(0.0232687\pi\) | ||||
−0.997329 | + | 0.0730358i | \(0.976731\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −135.559 | + | 96.9879i | −0.271093 | + | 0.193958i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −549.978 | −1.04948 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 288.829i | − | 0.526659i | −0.964706 | − | 0.263329i | \(-0.915179\pi\) | ||
0.964706 | − | 0.263329i | \(-0.0848206\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 370.281i | 0.646038i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 362.999i | − | 0.606761i | −0.952870 | − | 0.303380i | \(-0.901885\pi\) | ||
0.952870 | − | 0.303380i | \(-0.0981153\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 719.404i | − | 1.15342i | −0.816948 | − | 0.576712i | \(-0.804336\pi\) | ||
0.816948 | − | 0.576712i | \(-0.195664\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 369.898 | 0.569495 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 684.336 | + | 956.492i | 1.01282 | + | 1.41561i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 972.073i | 1.38439i | 0.721711 | + | 0.692195i | \(0.243356\pi\) | ||||
−0.721711 | + | 0.692195i | \(0.756644\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −494.011 | −0.653310 | −0.326655 | − | 0.945144i | \(-0.605921\pi\) | ||||
−0.326655 | + | 0.945144i | \(0.605921\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −616.038 | −0.786102 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −394.533 | −0.486188 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 88.7502i | 0.105702i | 0.998602 | + | 0.0528512i | \(0.0168309\pi\) | ||||
−0.998602 | + | 0.0528512i | \(0.983169\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 376.126 | + | 525.708i | 0.433282 | + | 0.605596i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 675.676 | 0.753380 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2201.37i | 2.37743i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 372.210i | − | 0.389610i | −0.980842 | − | 0.194805i | \(-0.937593\pi\) | ||
0.980842 | − | 0.194805i | \(-0.0624074\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 571.527i | − | 0.580208i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 353.995i | − | 0.348751i | −0.984679 | − | 0.174375i | \(-0.944209\pi\) | ||
0.984679 | − | 0.174375i | \(-0.0557906\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1469.01 | 1.40530 | 0.702650 | − | 0.711536i | \(-0.252000\pi\) | ||||
0.702650 | + | 0.711536i | \(0.252000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −509.430 | − | 712.026i | −0.473478 | − | 0.661777i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 353.811i | − | 0.319665i | −0.987144 | − | 0.159833i | \(-0.948905\pi\) | ||
0.987144 | − | 0.159833i | \(-0.0510954\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1714.06 | −1.50621 | −0.753107 | − | 0.657898i | \(-0.771446\pi\) | ||||
−0.753107 | + | 0.657898i | \(0.771446\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −445.480 | −0.380928 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2255.85 | −1.87799 | −0.938993 | − | 0.343936i | \(-0.888240\pi\) | ||||
−0.938993 | + | 0.343936i | \(0.888240\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1944.90 | −1.57707 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 314.123i | − | 0.248211i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 421.303 | + | 588.853i | 0.324545 | + | 0.453614i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2701.63 | −2.02978 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 523.973i | 0.384106i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 26.8002i | − | 0.0191767i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2394.07i | 1.67275i | 0.548157 | + | 0.836376i | \(0.315330\pi\) | ||||
−0.548157 | + | 0.836376i | \(0.684670\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1354.00i | 0.924135i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2873.08 | 1.91620 | 0.958100 | − | 0.286433i | \(-0.0924696\pi\) | ||||
0.958100 | + | 0.286433i | \(0.0924696\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2104.23 | − | 1505.50i | 1.37188 | − | 0.981531i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 425.453i | 0.271238i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3087.51 | 1.92543 | 0.962715 | − | 0.270519i | \(-0.0871954\pi\) | ||||
0.962715 | + | 0.270519i | \(0.0871954\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 358.649 | 0.218850 | 0.109425 | − | 0.993995i | \(-0.465099\pi\) | ||||
0.109425 | + | 0.993995i | \(0.465099\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −439.621 | −0.262573 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2216.42 | −1.29613 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2072.29i | − | 1.18686i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −332.210 | + | 973.898i | −0.186396 | + | 0.546434i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1933.03 | 1.06282 | 0.531409 | − | 0.847115i | \(-0.321663\pi\) | ||||
0.531409 | + | 0.847115i | \(0.321663\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2409.37i | 1.29849i | 0.760580 | + | 0.649245i | \(0.224915\pi\) | ||||
−0.760580 | + | 0.649245i | \(0.775085\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 351.854i | − | 0.185920i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3548.99i | 1.83911i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2404.36i | 1.22222i | 0.791544 | + | 0.611112i | \(0.209277\pi\) | ||||
−0.791544 | + | 0.611112i | \(0.790723\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −836.164 | −0.417058 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1330.10 | + | 1859.08i | 0.651099 | + | 0.910036i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2011.44i | 0.966551i | 0.875468 | + | 0.483276i | \(0.160553\pi\) | ||||
−0.875468 | + | 0.483276i | \(0.839447\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3001.95 | 1.41637 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2013.56 | −0.933016 | −0.466508 | − | 0.884517i | \(-0.654488\pi\) | ||||
−0.466508 | + | 0.884517i | \(0.654488\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 978.808 | 0.445520 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1257.33 | −0.562282 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2439.55i | 1.07211i | 0.844182 | + | 0.536057i | \(0.180087\pi\) | ||||
−0.844182 | + | 0.536057i | \(0.819913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1857.15 | − | 1328.73i | 0.802214 | − | 0.573956i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −79.2293 | −0.0336454 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 3292.25i | − | 1.37472i | −0.726319 | − | 0.687358i | \(-0.758771\pi\) | ||
0.726319 | − | 0.687358i | \(-0.241229\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 471.688i | 0.193703i | 0.995299 | + | 0.0968517i | \(0.0308773\pi\) | ||||
−0.995299 | + | 0.0968517i | \(0.969123\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 208.777i | − | 0.0843345i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2339.88i | − | 0.929901i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2482.64 | −0.970849 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 406.678 | − | 290.964i | 0.156516 | − | 0.111982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 427.664i | 0.162014i | 0.996714 | + | 0.0810070i | \(0.0258136\pi\) | ||||
−0.996714 | + | 0.0810070i | \(0.974186\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 156.240 | 0.0582714 | 0.0291357 | − | 0.999575i | \(-0.490725\pi\) | ||||
0.0291357 | + | 0.999575i | \(0.490725\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1649.93 | 0.605919 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2047.84 | −0.740623 | −0.370311 | − | 0.928908i | \(-0.620749\pi\) | ||||
−0.370311 | + | 0.928908i | \(0.620749\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2954.37 | −1.05241 | −0.526205 | − | 0.850358i | \(-0.676386\pi\) | ||||
−0.526205 | + | 0.850358i | \(0.676386\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 866.488i | 0.304066i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1980.84 | + | 1417.22i | −0.684865 | + | 0.489997i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2752.17 | −0.937658 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1110.84i | − | 0.372990i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8871.57i | 2.93617i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2145.80i | 0.700110i | 0.936729 | + | 0.350055i | \(0.113837\pi\) | ||||
−0.936729 | + | 0.350055i | \(0.886163\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1089.00i | 0.350314i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7111.91 | −2.25595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3392.38 | − | 2427.13i | 1.06124 | − | 0.759281i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2158.21i | 0.665929i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1364.51 | −0.415326 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2824.19 | 0.848080 | 0.424040 | − | 0.905643i | \(-0.360612\pi\) | ||||
0.424040 | + | 0.905643i | \(0.360612\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1109.69 | −0.328798 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1950.36 | −0.570265 | −0.285132 | − | 0.958488i | \(-0.592038\pi\) | ||||
−0.285132 | + | 0.958488i | \(0.592038\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 302.636i | 0.0873307i | 0.999046 | + | 0.0436653i | \(0.0139035\pi\) | ||||
−0.999046 | + | 0.0436653i | \(0.986096\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2053.01 | − | 2869.48i | −0.584753 | − | 0.817306i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4882.80 | −1.37289 | −0.686444 | − | 0.727182i | \(-0.740829\pi\) | ||||
−0.686444 | + | 0.727182i | \(0.740829\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2309.11i | − | 0.640978i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 2916.22i | − | 0.799278i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 247.430i | 0.0669662i | 0.999439 | + | 0.0334831i | \(0.0106600\pi\) | ||||
−0.999439 | + | 0.0334831i | \(0.989340\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1249.21i | − | 0.333894i | −0.985966 | − | 0.166947i | \(-0.946609\pi\) | ||
0.985966 | − | 0.166947i | \(-0.0533909\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5115.40 | − | 1744.94i | −1.33392 | − | 0.455020i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4876.00i | 1.25608i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1482.03 | 0.377189 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4760.98 | −1.19725 | −0.598626 | − | 0.801028i | \(-0.704287\pi\) | ||||
−0.598626 | + | 0.801028i | \(0.704287\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7837.99 | −1.94771 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1848.11 | 0.453856 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3555.00i | 0.862860i | 0.902146 | + | 0.431430i | \(0.141991\pi\) | ||||
−0.902146 | + | 0.431430i | \(0.858009\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2236.63 | + | 1600.23i | −0.536592 | + | 0.383912i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1183.60 | 0.280701 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2726.20i | − | 0.639182i | −0.947556 | − | 0.319591i | \(-0.896455\pi\) | ||
0.947556 | − | 0.319591i | \(-0.103545\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4391.96i | − | 1.01810i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 266.251i | − | 0.0610273i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2360.01i | − | 0.534916i | −0.963570 | − | 0.267458i | \(-0.913816\pi\) | ||
0.963570 | − | 0.267458i | \(-0.0861837\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −135.448 | −0.0303613 | −0.0151806 | − | 0.999885i | \(-0.504832\pi\) | ||||
−0.0151806 | + | 0.999885i | \(0.504832\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1128.38 | − | 1577.12i | −0.250156 | − | 0.349641i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7829.87i | 1.71694i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4298.01 | 0.932282 | 0.466141 | − | 0.884710i | \(-0.345644\pi\) | ||||
0.466141 | + | 0.884710i | \(0.345644\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2027.03 | −0.434964 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6617.98 | −1.40497 | −0.702483 | − | 0.711701i | \(-0.747925\pi\) | ||||
−0.702483 | + | 0.711701i | \(0.747925\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8380.43 | −1.76030 | −0.880150 | − | 0.474696i | \(-0.842558\pi\) | ||||
−0.880150 | + | 0.474696i | \(0.842558\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 6604.12i | − | 1.37261i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1882.19 | + | 2630.72i | 0.387115 | + | 0.541068i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3384.59 | 0.688905 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1116.63i | 0.224942i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8588.24i | − | 1.71239i | −0.516652 | − | 0.856195i | \(-0.672822\pi\) | ||
0.516652 | − | 0.856195i | \(-0.327178\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 416.152i | − | 0.0821333i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1714.58i | 0.334983i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4307.92 | −0.833223 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4863.78 | + | 6798.07i | 0.931375 | + | 1.30178i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1061.99i | 0.201351i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1096.60 | 0.205873 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −235.006 | −0.0436890 | −0.0218445 | − | 0.999761i | \(-0.506954\pi\) | ||||
−0.0218445 | + | 0.999761i | \(0.506954\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4407.03 | −0.811350 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9544.48 | 1.74025 | 0.870125 | − | 0.492831i | \(-0.164038\pi\) | ||||
0.870125 | + | 0.492831i | \(0.164038\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9235.69i | 1.66783i | 0.551890 | + | 0.833917i | \(0.313907\pi\) | ||||
−0.551890 | + | 0.833917i | \(0.686093\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1528.29 | + | 2136.08i | 0.273363 | + | 0.382077i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 226.546 | 0.0401390 | 0.0200695 | − | 0.999799i | \(-0.493611\pi\) | ||||
0.0200695 | + | 0.999799i | \(0.493611\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8351.34i | − | 1.46579i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1061.43i | 0.184559i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5461.68i | 0.940854i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4303.46i | 0.734502i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5142.19 | 0.869613 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2207.21 | + | 1579.18i | −0.369871 | + | 0.264630i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 8498.15i | − | 1.41118i | −0.708621 | − | 0.705590i | \(-0.750682\pi\) | ||
0.708621 | − | 0.705590i | \(-0.249318\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1336.44 | 0.219929 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4551.23 | −0.742270 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8729.62 | 1.41108 | 0.705538 | − | 0.708672i | \(-0.250705\pi\) | ||||
0.705538 | + | 0.708672i | \(0.250705\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6767.55 | 1.08426 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14302.5i | 2.27133i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1830.45 | + | 6083.01i | 0.288149 | + | 0.957586i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5834.71 | 0.910522 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9307.97i | 1.43999i | 0.693977 | + | 0.719997i | \(0.255857\pi\) | ||||
−0.693977 | + | 0.719997i | \(0.744143\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1055.71i | − | 0.161922i | −0.996717 | − | 0.0809610i | \(-0.974201\pi\) | ||
0.996717 | − | 0.0809610i | \(-0.0257989\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 942.370i | 0.143305i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 77.4512i | 0.0116779i | 0.999983 | + | 0.00583897i | \(0.00185861\pi\) | ||||
−0.999983 | + | 0.00583897i | \(0.998141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5719.96 | −0.855166 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1263.91 | − | 1766.56i | −0.187376 | − | 0.261894i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2486.10i | 0.365491i | 0.983160 | + | 0.182746i | \(0.0584985\pi\) | ||||
−0.983160 | + | 0.182746i | \(0.941502\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12658.0 | 1.84545 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8104.89 | 1.17189 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11336.0 | −1.62563 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11699.5 | 1.66406 | 0.832032 | − | 0.554728i | \(-0.187178\pi\) | ||||
0.832032 | + | 0.554728i | \(0.187178\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1571.92i | − | 0.221764i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4198.15 | + | 3003.63i | −0.587485 | + | 0.420325i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6932.47 | −0.962331 | −0.481166 | − | 0.876630i | \(-0.659786\pi\) | ||||
−0.481166 | + | 0.876630i | \(0.659786\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 80.4007i | 0.0110717i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4590.08i | − | 0.627058i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3574.75i | − | 0.484492i | −0.970215 | − | 0.242246i | \(-0.922116\pi\) | ||
0.970215 | − | 0.242246i | \(-0.0778842\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 7182.21i | − | 0.965764i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5336.96 | −0.712026 | −0.356013 | − | 0.934481i | \(-0.615864\pi\) | ||||
−0.356013 | + | 0.934481i | \(0.615864\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15071.9 | − | 10783.4i | 1.99516 | − | 1.42747i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 4062.01i | − | 0.533550i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10949.8 | 1.42719 | 0.713593 | − | 0.700560i | \(-0.247067\pi\) | ||||
0.713593 | + | 0.700560i | \(0.247067\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4825.36 | −0.624115 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8619.24 | −1.10632 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15317.5 | 1.95115 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 14793.2i | − | 1.87015i | −0.354449 | − | 0.935075i | \(-0.615332\pi\) | ||
0.354449 | − | 0.935075i | \(-0.384668\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6312.69 | + | 4516.51i | −0.792054 | + | 0.566687i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9526.62 | 1.18638 | 0.593188 | − | 0.805064i | \(-0.297869\pi\) | ||||
0.593188 | + | 0.805064i | \(0.297869\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7860.95i | 0.971667i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1276.36i | − | 0.156599i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 9429.76i | − | 1.14844i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4573.84i | − | 0.552963i | −0.961019 | − | 0.276481i | \(-0.910832\pi\) | ||
0.961019 | − | 0.276481i | \(-0.0891684\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9262.53 | −1.11165 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −397.788 | + | 284.603i | −0.0473943 | + | 0.0339090i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7784.38i | 0.920771i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1075.95 | −0.126353 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14014.3 | 1.63400 | 0.816999 | − | 0.576639i | \(-0.195636\pi\) | ||||
0.816999 | + | 0.576639i | \(0.195636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11324.2 | 1.31095 | 0.655474 | − | 0.755218i | \(-0.272469\pi\) | ||||
0.655474 | + | 0.755218i | \(0.272469\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1318.86 | 0.151596 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4820.37i | 0.550170i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −749.956 | − | 1048.21i | −0.0849951 | − | 0.118797i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6649.26 | 0.748320 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 11531.3i | − | 1.28873i | −0.764718 | − | 0.644365i | \(-0.777122\pi\) | ||
0.764718 | − | 0.644365i | \(-0.222878\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5632.81i | 0.625163i | 0.949891 | + | 0.312582i | \(0.101194\pi\) | ||||
−0.949891 | + | 0.312582i | \(0.898806\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6216.86i | 0.685231i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17243.1i | 1.88753i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8607.97 | 0.935846 | 0.467923 | − | 0.883769i | \(-0.345003\pi\) | ||||
0.467923 | + | 0.883769i | \(0.345003\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 996.631 | − | 2921.69i | 0.107616 | − | 0.315484i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 6396.61i | − | 0.686032i | −0.939330 | − | 0.343016i | \(-0.888551\pi\) | ||
0.939330 | − | 0.343016i | \(-0.111449\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1398.48 | 0.148976 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5799.09 | −0.613619 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11275.2 | −1.18510 | −0.592549 | − | 0.805534i | \(-0.701879\pi\) | ||||
−0.592549 | + | 0.805534i | \(0.701879\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11091.3 | −1.15802 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 7228.12i | − | 0.749683i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8283.85 | − | 5926.81i | 0.853523 | − | 0.610666i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11187.2 | −1.14511 | −0.572554 | − | 0.819867i | \(-0.694047\pi\) | ||||
−0.572554 | + | 0.819867i | \(0.694047\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1055.56i | 0.107341i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13198.3i | − | 1.33341i | −0.745320 | − | 0.666707i | \(-0.767703\pi\) | ||
0.745320 | − | 0.666707i | \(-0.232297\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13072.9i | − | 1.31220i | −0.754675 | − | 0.656098i | \(-0.772206\pi\) | ||
0.754675 | − | 0.656098i | \(-0.227794\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 10647.0i | − | 1.06181i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9255.58 | 0.917125 | 0.458563 | − | 0.888662i | \(-0.348365\pi\) | ||||
0.458563 | + | 0.888662i | \(0.348365\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3112.55 | + | 4350.39i | 0.306448 | + | 0.428321i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 7213.09i | − | 0.705651i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28661.1 | −2.78613 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17225.3 | 1.66390 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2508.49 | 0.240788 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12030.0 | 1.14752 | 0.573762 | − | 0.819022i | \(-0.305483\pi\) | ||||
0.573762 | + | 0.819022i | \(0.305483\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 5182.80i | − | 0.491300i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3990.31 | − | 5577.23i | −0.375912 | − | 0.525409i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5865.10 | −0.549114 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9122.55i | 0.848834i | 0.905467 | + | 0.424417i | \(0.139521\pi\) | ||||
−0.905467 | + | 0.424417i | \(0.860479\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 6034.31i | − | 0.558039i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19318.0i | − | 1.77558i | −0.460252 | − | 0.887788i | \(-0.652241\pi\) | ||
0.460252 | − | 0.887788i | \(-0.347759\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5141.41i | − | 0.469690i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9005.84 | −0.817743 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3911.83 | + | 5467.54i | 0.353058 | + | 0.493466i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5219.96i | 0.468292i | 0.972201 | + | 0.234146i | \(0.0752294\pi\) | ||||
−0.972201 | + | 0.234146i | \(0.924771\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6040.67 | 0.538677 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −544.887 | −0.0483008 | −0.0241504 | − | 0.999708i | \(-0.507688\pi\) | ||||
−0.0241504 | + | 0.999708i | \(0.507688\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5578.08 | −0.491528 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2936.42 | −0.257221 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1777.65i | 0.154800i | 0.997000 | + | 0.0773999i | \(0.0246618\pi\) | ||||
−0.997000 | + | 0.0773999i | \(0.975338\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7752.62 | + | 10835.8i | 0.671146 | + | 0.938056i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3771.98 | 0.324634 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 23147.9i | − | 1.98062i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9305.75i | − | 0.791618i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 7318.66i | − | 0.618985i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15239.0i | 1.28144i | 0.767773 | + | 0.640722i | \(0.221365\pi\) | ||||
−0.767773 | + | 0.640722i | \(0.778635\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17032.9 | 1.42408 | 0.712042 | − | 0.702137i | \(-0.247771\pi\) | ||||
0.712042 | + | 0.702137i | \(0.247771\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5571.45 | + | 3986.18i | −0.463158 | + | 0.331374i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8805.15i | 0.727815i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3067.23 | −0.252094 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 237.688 | 0.0194252 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6096.01 | −0.495398 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5575.18 | −0.450534 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9876.74i | 0.793692i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20615.1 | − | 7032.11i | −1.64742 | − | 0.561957i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6828.08 | −0.542628 | −0.271314 | − | 0.962491i | \(-0.587458\pi\) | ||||
−0.271314 | + | 0.962491i | \(0.587458\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1415.06i | − | 0.111835i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27009.4i | 2.12285i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18137.0i | − | 1.41770i | −0.705359 | − | 0.708850i | \(-0.749214\pi\) | ||
0.705359 | − | 0.708850i | \(-0.250786\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 626.330i | 0.0486905i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18372.5 | −1.42050 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10475.5 | − | 14641.5i | −0.805539 | − | 1.12590i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7019.65i | 0.536878i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3823.57 | −0.290862 | −0.145431 | − | 0.989368i | \(-0.546457\pi\) | ||||
−0.145431 | + | 0.989368i | \(0.546457\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15752.8 | −1.19190 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7447.92 | 0.560520 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2485.52 | 0.186061 | 0.0930303 | − | 0.995663i | \(-0.470345\pi\) | ||||
0.0930303 | + | 0.995663i | \(0.470345\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 35546.6i | 2.64682i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1220.03 | + | 872.892i | −0.0903644 | + | 0.0646526i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6007.73 | 0.442631 | 0.221316 | − | 0.975202i | \(-0.428965\pi\) | ||||
0.221316 | + | 0.975202i | \(0.428965\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 10646.6i | − | 0.780289i | −0.920754 | − | 0.390145i | \(-0.872425\pi\) | ||
0.920754 | − | 0.390145i | \(-0.127575\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1282.99i | − | 0.0935388i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15218.5i | 1.10375i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 6678.64i | − | 0.481864i | −0.970542 | − | 0.240932i | \(-0.922547\pi\) | ||
0.970542 | − | 0.240932i | \(-0.0774531\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −468.719 | −0.0336430 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7440.86 | − | 5323.68i | 0.531324 | − | 0.380143i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 17699.7i | − | 1.25737i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4949.80 | −0.349828 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5989.29 | −0.421132 | −0.210566 | − | 0.977580i | \(-0.567531\pi\) | ||||
−0.210566 | + | 0.977580i | \(0.567531\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31464.7 | 2.20115 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6143.53 | 0.427599 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 418.327i | 0.0289690i | 0.999895 | + | 0.0144845i | \(0.00461073\pi\) | ||||
−0.999895 | + | 0.0144845i | \(0.995389\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9278.85 | − | 6638.69i | 0.639321 | − | 0.457412i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8863.10 | 0.607609 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 6666.21i | − | 0.454715i | −0.973811 | − | 0.227357i | \(-0.926991\pi\) | ||
0.973811 | − | 0.227357i | \(-0.0730086\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10811.3i | − | 0.733778i | −0.930265 | − | 0.366889i | \(-0.880423\pi\) | ||
0.930265 | − | 0.366889i | \(-0.119577\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2599.46i | − | 0.175553i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 42571.0i | 2.86075i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15095.4 | 1.00939 | 0.504697 | − | 0.863297i | \(-0.331604\pi\) | ||||
0.504697 | + | 0.863297i | \(0.331604\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5942.52 | − | 4251.66i | 0.395407 | − | 0.282900i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 5114.64i | − | 0.338651i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8809.28 | −0.580430 | −0.290215 | − | 0.956961i | \(-0.593727\pi\) | ||||
−0.290215 | + | 0.956961i | \(0.593727\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8256.51 | 0.541357 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 638.273 | 0.0416465 | 0.0208233 | − | 0.999783i | \(-0.493371\pi\) | ||||
0.0208233 | + | 0.999783i | \(0.493371\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12363.8 | −0.802815 | −0.401408 | − | 0.915900i | \(-0.631479\pi\) | ||||
−0.401408 | + | 0.915900i | \(0.631479\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3332.53i | 0.215346i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −956.412 | − | 1336.77i | −0.0615053 | − | 0.0859656i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15834.7 | −1.01342 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 26614.7i | − | 1.69520i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 5805.32i | − | 0.368002i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7405.51i | 0.467209i | 0.972332 | + | 0.233604i | \(0.0750521\pi\) | ||||
−0.972332 | + | 0.233604i | \(0.924948\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6437.41i | − | 0.404209i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37724.6 | 2.35757 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11330.5 | − | 3865.00i | −0.704759 | − | 0.240403i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 3266.99i | − | 0.202254i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10714.3 | 0.660199 | 0.330100 | − | 0.943946i | \(-0.392918\pi\) | ||||
0.330100 | + | 0.943946i | \(0.392918\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2855.49 | −0.175132 | −0.0875659 | − | 0.996159i | \(-0.527909\pi\) | ||||
−0.0875659 | + | 0.996159i | \(0.527909\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21335.7 | 1.30247 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7315.44 | −0.444513 | −0.222256 | − | 0.974988i | \(-0.571342\pi\) | ||||
−0.222256 | + | 0.974988i | \(0.571342\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1677.10i | − | 0.101436i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10177.1 | + | 7281.38i | −0.612708 | + | 0.438371i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20654.7 | −1.23780 | −0.618898 | − | 0.785472i | \(-0.712420\pi\) | ||||
−0.618898 | + | 0.785472i | \(0.712420\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 45272.6i | − | 2.70068i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6474.64i | − | 0.384474i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 15304.8i | − | 0.904688i | −0.891843 | − | 0.452344i | \(-0.850588\pi\) | ||
0.891843 | − | 0.452344i | \(-0.149412\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13407.2i | 0.788928i | 0.918912 | + | 0.394464i | \(0.129070\pi\) | ||||
−0.918912 | + | 0.394464i | \(0.870930\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4093.54 | 0.239789 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −23723.0 | − | 33157.4i | −1.38336 | − | 1.93352i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 16232.0i | − | 0.942288i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8472.58 | −0.489639 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4419.31 | 0.254256 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14785.5 | 0.846863 | 0.423431 | − | 0.905928i | \(-0.360825\pi\) | ||||
0.423431 | + | 0.905928i | \(0.360825\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3329.08 | 0.189832 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34340.9i | 1.94953i | 0.223240 | + | 0.974763i | \(0.428337\pi\) | ||||
−0.223240 | + | 0.974763i | \(0.571663\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4011.10 | + | 5606.28i | 0.226704 | + | 0.316862i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5851.09 | 0.329243 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3806.83i | 0.213271i | 0.994298 | + | 0.106636i | \(0.0340079\pi\) | ||||
−0.994298 | + | 0.106636i | \(0.965992\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 48651.5i | − | 2.71369i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 907.907i | − | 0.0504204i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 9728.11i | − | 0.537897i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32647.0 | 1.79732 | 0.898660 | − | 0.438645i | \(-0.144541\pi\) | ||||
0.898660 | + | 0.438645i | \(0.144541\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6159.03 | + | 8608.43i | 0.337608 | + | 0.471872i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 5651.41i | − | 0.308446i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6828.22 | −0.371072 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14648.4 | 0.792638 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10926.7 | −0.588722 | −0.294361 | − | 0.955694i | \(-0.595107\pi\) | ||||
−0.294361 | + | 0.955694i | \(0.595107\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20745.0 | −1.11296 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6927.33i | 0.370069i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3814.81 | + | 5331.93i | 0.202929 | + | 0.283632i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22837.0 | 1.20968 | 0.604840 | − | 0.796347i | \(-0.293237\pi\) | ||||
0.604840 | + | 0.796347i | \(0.293237\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8748.66i | 0.461463i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27798.9i | 1.46014i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 34925.3i | 1.82676i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 742.290i | − | 0.0386630i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11476.6 | 0.595277 | 0.297638 | − | 0.954679i | \(-0.403801\pi\) | ||||
0.297638 | + | 0.954679i | \(0.403801\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22126.4 | + | 15830.7i | −1.14290 | + | 0.817706i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3747.62i | 0.192774i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16215.2 | −0.830645 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28268.3 | −1.44211 | −0.721054 | − | 0.692879i | \(-0.756342\pi\) | ||||
−0.721054 | + | 0.692879i | \(0.756342\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17644.9 | −0.892776 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 19519.1i | − | 0.983569i | −0.870717 | − | 0.491784i | \(-0.836345\pi\) | ||
0.870717 | − | 0.491784i | \(-0.163655\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15346.2 | + | 5234.81i | 0.770141 | + | 0.262706i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18341.5 | −0.916715 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 21461.4i | − | 1.06830i | −0.845391 | − | 0.534149i | \(-0.820632\pi\) | ||
0.845391 | − | 0.534149i | \(-0.179368\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 14628.0i | − | 0.725200i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21132.8i | 1.04346i | 0.853112 | + | 0.521729i | \(0.174713\pi\) | ||||
−0.853112 | + | 0.521729i | \(0.825287\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 30459.7i | − | 1.49793i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4446.10 | −0.217770 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3812.82 | + | 5329.15i | 0.186004 | + | 0.259977i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14378.9i | 0.698659i | 0.937000 | + | 0.349329i | \(0.113591\pi\) | ||||
−0.937000 | + | 0.349329i | \(0.886409\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14282.9 | 0.691234 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 37965.7 | 1.83008 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9210.36 | −0.442215 | −0.221107 | − | 0.975249i | \(-0.570967\pi\) | ||||
−0.221107 | + | 0.975249i | \(0.570967\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23514.0 | 1.12451 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25087.6i | 1.19504i | 0.801854 | + | 0.597519i | \(0.203847\pi\) | ||||
−0.801854 | + | 0.597519i | \(0.796153\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25817.5 | − | 18471.5i | 1.22497 | − | 0.876425i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5544.34 | −0.262034 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 921.770i | − | 0.0433940i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 330.201i | 0.0154842i | 0.999970 | + | 0.00774211i | \(0.00246441\pi\) | ||||
−0.999970 | + | 0.00774211i | \(0.997536\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 10665.0i | − | 0.498172i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8703.46i | 0.404970i | 0.979285 | + | 0.202485i | \(0.0649017\pi\) | ||||
−0.979285 | + | 0.202485i | \(0.935098\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27770.1 | 1.28714 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6709.88 | − | 4800.68i | 0.309801 | − | 0.221652i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24400.2i | 1.12224i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23051.5 | −1.05614 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3550.80 | −0.162063 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 37886.8 | 1.72260 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41633.7 | −1.88574 | −0.942872 | − | 0.333156i | \(-0.891886\pi\) | ||||
−0.942872 | + | 0.333156i | \(0.891886\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8178.61i | 0.369032i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33977.9 | − | 24310.0i | 1.52733 | − | 1.09275i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2428.95 | 0.108770 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13175.9i | 0.587799i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16494.2i | 0.733068i | 0.930405 | + | 0.366534i | \(0.119456\pi\) | ||||
−0.930405 | + | 0.366534i | \(0.880544\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5728.97i | − | 0.253663i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 798.752i | 0.0352341i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −45684.3 | −2.00768 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 29294.4 | − | 20959.1i | 1.28260 | − | 0.917655i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7080.03i | 0.308834i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14458.7 | −0.628359 | −0.314179 | − | 0.949364i | \(-0.601729\pi\) | ||||
−0.314179 | + | 0.949364i | \(0.601729\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26005.5 | 1.12599 | 0.562994 | − | 0.826461i | \(-0.309649\pi\) | ||||
0.562994 | + | 0.826461i | \(0.309649\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 406.345 | 0.0175291 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31695.2 | 1.36225 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 63052.9i | 2.70005i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3385.13 | + | 4731.37i | 0.144427 | + | 0.201865i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29654.2 | 1.26058 | 0.630291 | − | 0.776359i | \(-0.282935\pi\) | ||||
0.630291 | + | 0.776359i | \(0.282935\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21383.1i | 0.905672i | 0.891594 | + | 0.452836i | \(0.149588\pi\) | ||||
−0.891594 | + | 0.452836i | \(0.850412\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 23489.6i | − | 0.991277i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4239.01i | 0.178240i | 0.996021 | + | 0.0891201i | \(0.0284055\pi\) | ||||
−0.996021 | + | 0.0891201i | \(0.971594\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 18040.1i | − | 0.755799i | −0.925847 | − | 0.377900i | \(-0.876646\pi\) | ||
0.925847 | − | 0.377900i | \(-0.123354\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12894.0 | −0.538253 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12691.5 | − | 4329.24i | −0.527891 | − | 0.180071i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31728.6i | 1.31499i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6081.08 | 0.251127 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8064.28 | 0.331836 | 0.165918 | − | 0.986140i | \(-0.446941\pi\) | ||||
0.165918 | + | 0.986140i | \(0.446941\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7093.85 | −0.290863 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19853.9 | 0.811157 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 15423.6i | − | 0.627914i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 40692.4 | − | 29114.0i | 1.65077 | − | 1.18107i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25141.3 | 1.01631 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 18328.1i | − | 0.738282i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 41230.1i | − | 1.65497i | −0.561486 | − | 0.827486i | \(-0.689770\pi\) | ||
0.561486 | − | 0.827486i | \(-0.310230\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19812.4i | 0.792478i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1919.57i | 0.0765124i | 0.999268 | + | 0.0382562i | \(0.0121803\pi\) | ||||
−0.999268 | + | 0.0382562i | \(0.987820\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8841.06 | 0.351168 | 0.175584 | − | 0.984464i | \(-0.443819\pi\) | ||||
0.175584 | + | 0.984464i | \(0.443819\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5646.56 | − | 7892.16i | −0.223501 | − | 0.312386i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 30598.2i | − | 1.20692i | −0.797391 | − | 0.603462i | \(-0.793787\pi\) | ||
0.797391 | − | 0.603462i | \(-0.206213\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38441.3 | 1.51103 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10153.8 | −0.397740 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 61729.6 | 2.40970 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10080.9 | −0.392168 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3349.89i | − | 0.129870i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 288.811 | + | 403.669i | 0.0111584 | + | 0.0155960i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13839.9 | −0.532885 | −0.266442 | − | 0.963851i | \(-0.585848\pi\) | ||||
−0.266442 | + | 0.963851i | \(0.585848\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25764.7i | 0.988649i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7609.12i | − | 0.290985i | −0.989359 | − | 0.145492i | \(-0.953523\pi\) | ||
0.989359 | − | 0.145492i | \(-0.0464766\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 18613.2i | − | 0.709382i | −0.934984 | − | 0.354691i | \(-0.884586\pi\) | ||
0.934984 | − | 0.354691i | \(-0.115414\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1248.46i | 0.0474197i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16661.0 | −0.630691 | −0.315346 | − | 0.948977i | \(-0.602120\pi\) | ||||
−0.315346 | + | 0.948977i | \(0.602120\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25799.6 | − | 36059.9i | −0.973329 | − | 1.36041i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 5143.74i | − | 0.193403i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20472.1 | −0.767160 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −51877.6 | −1.93752 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12923.8 | 0.481062 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29619.6 | −1.09885 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 10896.6i | − | 0.402905i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14591.3 | − | 20394.2i | −0.537729 | − | 0.751580i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7432.63 | 0.273005 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45091.3i | 1.65075i | 0.564584 | + | 0.825376i | \(0.309037\pi\) | ||||
−0.564584 | + | 0.825376i | \(0.690963\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 3185.96i | − | 0.116250i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4614.00i | − | 0.167803i | −0.996474 | − | 0.0839015i | \(-0.973262\pi\) | ||
0.996474 | − | 0.0839015i | \(-0.0267381\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31371.2i | 1.13717i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3289.80 | −0.118861 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −43274.8 | + | 30961.6i | −1.55841 | + | 1.11499i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 38342.0i | − | 1.37626i | −0.725586 | − | 0.688131i | \(-0.758431\pi\) | ||
0.725586 | − | 0.688131i | \(-0.241569\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 705.019 | 0.0252238 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12669.6 | −0.451815 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18309.1 | −0.650810 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13221.1 | 0.468433 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30005.0i | 1.05967i | 0.848101 | + | 0.529834i | \(0.177746\pi\) | ||||
−0.848101 | + | 0.529834i | \(0.822254\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15470.3 | + | 45352.2i | −0.544595 | + | 1.59652i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28633.4 | −1.00473 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 39120.3i | 1.36831i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12167.2i | 0.424212i | 0.977247 | + | 0.212106i | \(0.0680322\pi\) | ||||
−0.977247 | + | 0.212106i | \(0.931968\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 27707.1i | − | 0.962924i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 166.924i | 0.00578275i | 0.999996 | + | 0.00289138i | \(0.000920355\pi\) | ||||
−0.999996 | + | 0.00289138i | \(0.999080\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21557.5 | −0.744441 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4584.87 | − | 6408.23i | −0.157826 | − | 0.220592i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29354.6i | 1.00728i | 0.863913 | + | 0.503642i | \(0.168007\pi\) | ||||
−0.863913 | + | 0.503642i | \(0.831993\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25109.1 | −0.858878 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −679.637 | −0.0231743 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3636.06 | 0.123592 | 0.0617961 | − | 0.998089i | \(-0.480317\pi\) | ||||
0.0617961 | + | 0.998089i | \(0.480317\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6738.92 | 0.228342 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25054.0i | 0.846272i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46504.5 | + | 33272.4i | −1.56591 | + | 1.12036i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20935.4 | 0.702743 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 3184.30i | − | 0.106555i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 2461.95i | − | 0.0821274i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 40090.0i | − | 1.33320i | −0.745414 | − | 0.666602i | \(-0.767748\pi\) | ||
0.745414 | − | 0.666602i | \(-0.232252\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 16385.0i | − | 0.543202i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −54004.4 | −1.78484 | −0.892421 | − | 0.451203i | \(-0.850995\pi\) | ||||
−0.892421 | + | 0.451203i | \(0.850995\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5402.02 | + | 3864.96i | −0.177986 | + | 0.127343i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 12910.4i | − | 0.424065i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10178.4 | −0.333303 | −0.166652 | − | 0.986016i | \(-0.553296\pi\) | ||||
−0.166652 | + | 0.986016i | \(0.553296\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5635.91 | 0.183988 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15426.6 | −0.502071 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11555.3 | 0.374932 | 0.187466 | − | 0.982271i | \(-0.439973\pi\) | ||||
0.187466 | + | 0.982271i | \(0.439973\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32268.9i | 1.04383i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6621.63 | − | 4737.55i | 0.213545 | − | 0.152784i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −55706.9 | −1.79108 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 16946.8i | − | 0.543222i | −0.962407 | − | 0.271611i | \(-0.912444\pi\) | ||
0.962407 | − | 0.271611i | \(-0.0875564\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25494.4i | 0.814745i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 46553.5i | 1.48326i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 18666.0i | − | 0.592937i | −0.955043 | − | 0.296468i | \(-0.904191\pi\) | ||
0.955043 | − | 0.296468i | \(-0.0958090\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4009.32 | −0.126976 |
(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 | 1344.4.b.i.895.2 | 24 | ||
4.3 | odd | 2 | 1344.4.b.j.895.2 | 24 | |||
7.6 | odd | 2 | 1344.4.b.j.895.23 | 24 | |||
8.3 | odd | 2 | 672.4.b.a.223.23 | yes | 24 | ||
8.5 | even | 2 | 672.4.b.b.223.23 | yes | 24 | ||
28.27 | even | 2 | inner | 1344.4.b.i.895.23 | 24 | ||
56.13 | odd | 2 | 672.4.b.a.223.2 | ✓ | 24 | ||
56.27 | even | 2 | 672.4.b.b.223.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.b.a.223.2 | ✓ | 24 | 56.13 | odd | 2 | ||
672.4.b.a.223.23 | yes | 24 | 8.3 | odd | 2 | ||
672.4.b.b.223.2 | yes | 24 | 56.27 | even | 2 | ||
672.4.b.b.223.23 | yes | 24 | 8.5 | even | 2 | ||
1344.4.b.i.895.2 | 24 | 1.1 | even | 1 | trivial | ||
1344.4.b.i.895.23 | 24 | 28.27 | even | 2 | inner | ||
1344.4.b.j.895.2 | 24 | 4.3 | odd | 2 | |||
1344.4.b.j.895.23 | 24 | 7.6 | odd | 2 |