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 | 895.10 | ||
Character | \(\chi\) | \(=\) | 1344.895 |
Dual form | 1344.4.b.i.895.15 |
$q$-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 | ||||||||
\(5\) | − | 4.15525i | − | 0.371657i | −0.982582 | − | 0.185828i | \(-0.940503\pi\) | ||
0.982582 | − | 0.185828i | \(-0.0594969\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.5863 | − | 15.1964i | −0.571605 | − | 0.820529i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 26.7188i | − | 0.732364i | −0.930543 | − | 0.366182i | \(-0.880665\pi\) | ||
0.930543 | − | 0.366182i | \(-0.119335\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 36.8834i | − | 0.786894i | −0.919347 | − | 0.393447i | \(-0.871283\pi\) | ||
0.919347 | − | 0.393447i | \(-0.128717\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 12.4658i | 0.214576i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 41.0070i | − | 0.585039i | −0.956260 | − | 0.292519i | \(-0.905506\pi\) | ||
0.956260 | − | 0.292519i | \(-0.0944936\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 110.241 | 1.33110 | 0.665551 | − | 0.746353i | \(-0.268197\pi\) | ||||
0.665551 | + | 0.746353i | \(0.268197\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 31.7588 | + | 45.5892i | 0.330017 | + | 0.473732i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 69.5113i | − | 0.630178i | −0.949062 | − | 0.315089i | \(-0.897966\pi\) | ||
0.949062 | − | 0.315089i | \(-0.102034\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 107.734 | 0.861871 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 155.035 | 0.992736 | 0.496368 | − | 0.868112i | \(-0.334667\pi\) | ||||
0.496368 | + | 0.868112i | \(0.334667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −98.2305 | −0.569120 | −0.284560 | − | 0.958658i | \(-0.591847\pi\) | ||||
−0.284560 | + | 0.958658i | \(0.591847\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 80.1563i | 0.422831i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −63.1449 | + | 43.9886i | −0.304955 | + | 0.212441i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 210.639 | 0.935916 | 0.467958 | − | 0.883751i | \(-0.344990\pi\) | ||||
0.467958 | + | 0.883751i | \(0.344990\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 110.650i | 0.454313i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.600048i | 0.00228565i | 0.999999 | + | 0.00114283i | \(0.000363773\pi\) | ||||
−0.999999 | + | 0.00114283i | \(0.999636\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 354.960i | − | 1.25886i | −0.777058 | − | 0.629429i | \(-0.783289\pi\) | ||
0.777058 | − | 0.629429i | \(-0.216711\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 37.3973i | − | 0.123886i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −258.195 | −0.801311 | −0.400655 | − | 0.916229i | \(-0.631218\pi\) | ||||
−0.400655 | + | 0.916229i | \(0.631218\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −118.861 | + | 321.747i | −0.346534 | + | 0.938037i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 123.021i | 0.337772i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 274.991 | 0.712697 | 0.356349 | − | 0.934353i | \(-0.384022\pi\) | ||||
0.356349 | + | 0.934353i | \(0.384022\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −111.023 | −0.272188 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −330.722 | −0.768512 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 301.151 | 0.664516 | 0.332258 | − | 0.943188i | \(-0.392189\pi\) | ||||
0.332258 | + | 0.943188i | \(0.392189\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 469.215i | − | 0.984867i | −0.870350 | − | 0.492433i | \(-0.836108\pi\) | ||
0.870350 | − | 0.492433i | \(-0.163892\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −95.2765 | − | 136.768i | −0.190535 | − | 0.273510i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −153.260 | −0.292454 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 605.217i | 1.10357i | 0.833987 | + | 0.551784i | \(0.186053\pi\) | ||||
−0.833987 | + | 0.551784i | \(0.813947\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 208.534i | 0.363834i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 497.779i | − | 0.832050i | −0.909353 | − | 0.416025i | \(-0.863423\pi\) | ||
0.909353 | − | 0.416025i | \(-0.136577\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 429.333i | 0.688351i | 0.938905 | + | 0.344175i | \(0.111841\pi\) | ||||
−0.938905 | + | 0.344175i | \(0.888159\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −323.202 | −0.497602 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −406.029 | + | 282.852i | −0.600926 | + | 0.418623i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1043.89i | − | 1.48667i | −0.668922 | − | 0.743333i | \(-0.733244\pi\) | ||
0.668922 | − | 0.743333i | \(-0.266756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1020.65 | 1.34976 | 0.674882 | − | 0.737926i | \(-0.264195\pi\) | ||||
0.674882 | + | 0.737926i | \(0.264195\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −170.394 | −0.217434 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −465.106 | −0.573156 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 936.707i | 1.11563i | 0.829967 | + | 0.557813i | \(0.188359\pi\) | ||||
−0.829967 | + | 0.557813i | \(0.811641\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −560.495 | + | 390.458i | −0.645669 | + | 0.449793i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 294.691 | 0.328582 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 458.077i | − | 0.494713i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 407.850i | 0.426917i | 0.976952 | + | 0.213458i | \(0.0684727\pi\) | ||||
−0.976952 | + | 0.213458i | \(0.931527\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 240.469i | − | 0.244121i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 831.061i | − | 0.818749i | −0.912366 | − | 0.409375i | \(-0.865747\pi\) | ||
0.912366 | − | 0.409375i | \(-0.134253\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1652.29 | −1.58063 | −0.790316 | − | 0.612700i | \(-0.790083\pi\) | ||||
−0.790316 | + | 0.612700i | \(0.790083\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 189.435 | − | 131.966i | 0.176066 | − | 0.122653i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 303.007i | − | 0.273765i | −0.990587 | − | 0.136882i | \(-0.956292\pi\) | ||
0.990587 | − | 0.136882i | \(-0.0437082\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1020.52 | 0.896768 | 0.448384 | − | 0.893841i | \(-0.352000\pi\) | ||||
0.448384 | + | 0.893841i | \(0.352000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −631.918 | −0.540351 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 417.458 | 0.347532 | 0.173766 | − | 0.984787i | \(-0.444406\pi\) | ||||
0.173766 | + | 0.984787i | \(0.444406\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −288.837 | −0.234210 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 331.951i | − | 0.262298i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −623.159 | + | 434.112i | −0.480041 | + | 0.334411i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 617.108 | 0.463642 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 1.80014i | − | 0.00131962i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 967.068i | − | 0.691977i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1193.68i | − | 0.834034i | −0.908899 | − | 0.417017i | \(-0.863075\pi\) | ||
0.908899 | − | 0.417017i | \(-0.136925\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1064.88i | 0.726802i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −962.451 | −0.641906 | −0.320953 | − | 0.947095i | \(-0.604003\pi\) | ||||
−0.320953 | + | 0.947095i | \(0.604003\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1167.04 | − | 1675.26i | −0.760865 | − | 1.09221i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 112.192i | 0.0715254i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2842.24 | −1.77247 | −0.886237 | − | 0.463232i | \(-0.846690\pi\) | ||||
−0.886237 | + | 0.463232i | \(0.846690\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2012.76 | −1.22820 | −0.614101 | − | 0.789227i | \(-0.710481\pi\) | ||||
−0.614101 | + | 0.789227i | \(0.710481\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 774.585 | 0.462637 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −985.479 | −0.576293 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 644.211i | − | 0.368957i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 356.584 | − | 965.240i | 0.200072 | − | 0.541576i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1487.06 | 0.817616 | 0.408808 | − | 0.912620i | \(-0.365945\pi\) | ||||
0.408808 | + | 0.912620i | \(0.365945\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 267.813i | − | 0.144333i | −0.997393 | − | 0.0721666i | \(-0.977009\pi\) | ||
0.997393 | − | 0.0721666i | \(-0.0229913\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 369.063i | − | 0.195013i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 408.172i | 0.211517i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 569.423i | 0.289458i | 0.989471 | + | 0.144729i | \(0.0462310\pi\) | ||||
−0.989471 | + | 0.144729i | \(0.953769\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −824.974 | −0.411476 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1056.32 | + | 735.866i | −0.517079 | + | 0.360213i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1377.89i | 0.662113i | 0.943611 | + | 0.331057i | \(0.107405\pi\) | ||||
−0.943611 | + | 0.331057i | \(0.892595\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 333.069 | 0.157148 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2791.51 | −1.29349 | −0.646747 | − | 0.762705i | \(-0.723871\pi\) | ||||
−0.646747 | + | 0.762705i | \(0.723871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 836.614 | 0.380798 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 992.165 | 0.443700 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1433.66i | 0.630053i | 0.949083 | + | 0.315027i | \(0.102013\pi\) | ||||
−0.949083 | + | 0.315027i | \(0.897987\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1140.50 | − | 1637.17i | −0.492650 | − | 0.707190i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −903.452 | −0.383659 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 3472.47i | − | 1.44997i | −0.688765 | − | 0.724985i | \(-0.741847\pi\) | ||
0.688765 | − | 0.724985i | \(-0.258153\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 407.085i | − | 0.167174i | −0.996501 | − | 0.0835868i | \(-0.973362\pi\) | ||
0.996501 | − | 0.0835868i | \(-0.0266376\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1407.65i | 0.568613i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 875.259i | − | 0.347840i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1095.66 | −0.428462 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 285.830 | + | 410.303i | 0.110006 | + | 0.157911i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3898.48i | − | 1.47688i | −0.674318 | − | 0.738441i | \(-0.735562\pi\) | ||
0.674318 | − | 0.738441i | \(-0.264438\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2366.15 | 0.882483 | 0.441241 | − | 0.897389i | \(-0.354538\pi\) | ||||
0.441241 | + | 0.897389i | \(0.354538\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 459.779 | 0.168849 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2173.29 | −0.785991 | −0.392995 | − | 0.919540i | \(-0.628561\pi\) | ||||
−0.392995 | + | 0.919540i | \(0.628561\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2789.79 | 0.993784 | 0.496892 | − | 0.867812i | \(-0.334475\pi\) | ||||
0.496892 | + | 0.867812i | \(0.334475\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 1815.65i | − | 0.637145i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1641.25 | − | 2355.98i | −0.567453 | − | 0.814568i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.49335 | 0.000849479 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 625.601i | − | 0.210059i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2945.49i | − | 0.974851i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 894.802i | − | 0.291947i | −0.989289 | − | 0.145973i | \(-0.953369\pi\) | ||
0.989289 | − | 0.145973i | \(-0.0466313\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1493.34i | 0.480384i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1474.95 | −0.467864 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1039.90 | + | 1492.75i | 0.325312 | + | 0.466979i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1288.00i | − | 0.397420i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1512.48 | −0.460363 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2804.30 | −0.842108 | −0.421054 | − | 0.907036i | \(-0.638340\pi\) | ||||
−0.421054 | + | 0.907036i | \(0.638340\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 969.605 | 0.287290 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5559.46 | −1.62553 | −0.812763 | − | 0.582595i | \(-0.802037\pi\) | ||||
−0.812763 | + | 0.582595i | \(0.802037\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2366.25i | − | 0.682820i | −0.939914 | − | 0.341410i | \(-0.889095\pi\) | ||
0.939914 | − | 0.341410i | \(-0.110905\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1218.09 | − | 848.557i | 0.346945 | − | 0.241692i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3111.46 | −0.874843 | −0.437422 | − | 0.899257i | \(-0.644108\pi\) | ||||
−0.437422 | + | 0.899257i | \(0.644108\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1072.86i | 0.297813i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3131.66i | 0.858326i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4494.98i | 1.21655i | 0.793725 | + | 0.608277i | \(0.208139\pi\) | ||||
−0.793725 | + | 0.608277i | \(0.791861\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2555.56i | 0.683061i | 0.939871 | + | 0.341531i | \(0.110945\pi\) | ||||
−0.939871 | + | 0.341531i | \(0.889055\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1336.94 | + | 493.899i | 0.348628 | + | 0.128792i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4066.05i | − | 1.04743i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3061.94 | −0.779286 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 803.874 | 0.202152 | 0.101076 | − | 0.994879i | \(-0.467772\pi\) | ||||
0.101076 | + | 0.994879i | \(0.467772\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1857.25 | −0.461520 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 511.183 | 0.125535 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 7577.19i | − | 1.83911i | −0.392956 | − | 0.919557i | \(-0.628548\pi\) | ||
0.392956 | − | 0.919557i | \(-0.371452\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2229.89 | − | 3200.96i | −0.534975 | − | 0.767946i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1395.32 | 0.330912 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3561.82i | 0.835099i | 0.908654 | + | 0.417550i | \(0.137111\pi\) | ||||
−0.908654 | + | 0.417550i | \(0.862889\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1142.66i | − | 0.264879i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 2810.12i | − | 0.644107i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3944.71i | − | 0.894102i | −0.894509 | − | 0.447051i | \(-0.852474\pi\) | ||
0.894509 | − | 0.447051i | \(-0.147526\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3972.84 | 0.890526 | 0.445263 | − | 0.895400i | \(-0.353110\pi\) | ||||
0.445263 | + | 0.895400i | \(0.353110\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1681.49 | − | 1171.37i | 0.372777 | − | 0.259688i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2878.52i | − | 0.631204i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7036.30 | −1.52625 | −0.763123 | − | 0.646253i | \(-0.776335\pi\) | ||||
−0.763123 | + | 0.646253i | \(0.776335\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −884.074 | −0.189707 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −652.815 | −0.138590 | −0.0692948 | − | 0.997596i | \(-0.522075\pi\) | ||||
−0.0692948 | + | 0.997596i | \(0.522075\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6289.21 | −1.32104 | −0.660520 | − | 0.750808i | \(-0.729664\pi\) | ||||
−0.660520 | + | 0.750808i | \(0.729664\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1374.23i | 0.285623i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.11857 | − | 6.35228i | 0.00187544 | − | 0.00130649i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3231.43 | 0.657730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 1223.55i | − | 0.246480i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3451.83i | 0.688254i | 0.938923 | + | 0.344127i | \(0.111825\pi\) | ||||
−0.938923 | + | 0.344127i | \(0.888175\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1251.36i | − | 0.246972i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 721.406i | 0.140944i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2563.81 | −0.495883 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5394.12 | + | 3757.71i | −1.03293 | + | 0.719570i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2493.18i | 0.472705i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1949.71 | −0.366033 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1879.04 | −0.349324 | −0.174662 | − | 0.984628i | \(-0.555883\pi\) | ||||
−0.174662 | + | 0.984628i | \(0.555883\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4956.87 | 0.912578 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4029.94 | −0.734780 | −0.367390 | − | 0.930067i | \(-0.619749\pi\) | ||||
−0.367390 | + | 0.930067i | \(0.619749\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4724.35i | 0.853151i | 0.904452 | + | 0.426575i | \(0.140280\pi\) | ||||
−0.904452 | + | 0.426575i | \(0.859720\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −568.304 | + | 395.898i | −0.101652 | + | 0.0708137i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8399.49 | −1.48821 | −0.744104 | − | 0.668063i | \(-0.767123\pi\) | ||||
−0.744104 | + | 0.668063i | \(0.767123\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4142.35i | − | 0.727044i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 909.022i | 0.158058i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4520.63i | − | 0.778746i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3973.59i | − | 0.678201i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3061.55 | −0.517749 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2733.32 | + | 3923.64i | 0.458034 | + | 0.657498i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 175.263i | − | 0.0291037i | −0.999894 | − | 0.0145518i | \(-0.995368\pi\) | ||
0.999894 | − | 0.0145518i | \(-0.00463216\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1895.75 | 0.311972 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2514.83 | 0.410149 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9534.83 | 1.54123 | 0.770616 | − | 0.637299i | \(-0.219949\pi\) | ||||
0.770616 | + | 0.637299i | \(0.219949\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1252.37 | −0.200648 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2624.60i | 0.416803i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6147.69 | − | 1599.84i | 0.967767 | − | 0.251846i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 866.510 | 0.135221 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10295.8i | 1.59282i | 0.604758 | + | 0.796409i | \(0.293270\pi\) | ||||
−0.604758 | + | 0.796409i | \(0.706730\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12476.8i | 1.91367i | 0.290638 | + | 0.956833i | \(0.406132\pi\) | ||||
−0.290638 | + | 0.956833i | \(0.593868\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 995.852i | 0.151438i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10018.3i | − | 1.51054i | −0.655415 | − | 0.755269i | \(-0.727506\pi\) | ||
0.655415 | − | 0.755269i | \(-0.272494\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2068.40 | −0.309237 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1869.48 | − | 1302.33i | 0.277152 | − | 0.193072i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3440.45i | 0.505793i | 0.967493 | + | 0.252897i | \(0.0813833\pi\) | ||||
−0.967493 | + | 0.252897i | \(0.918617\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5293.98 | 0.771830 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1851.32 | −0.267684 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1783.99 | 0.255830 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7372.02 | 1.04855 | 0.524273 | − | 0.851550i | \(-0.324337\pi\) | ||||
0.524273 | + | 0.851550i | \(0.324337\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.40043i | 0.000761884i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2911.13 | − | 4178.88i | −0.407382 | − | 0.584788i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7872.77 | 1.09286 | 0.546430 | − | 0.837505i | \(-0.315986\pi\) | ||||
0.546430 | + | 0.837505i | \(0.315986\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2901.20i | 0.399513i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5718.23i | − | 0.781177i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3906.79i | 0.529495i | 0.964318 | + | 0.264747i | \(0.0852885\pi\) | ||||
−0.964318 | + | 0.264747i | \(0.914711\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3581.05i | 0.481530i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −823.361 | −0.109848 | −0.0549240 | − | 0.998491i | \(-0.517492\pi\) | ||||
−0.0549240 | + | 0.998491i | \(0.517492\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1175.32 | + | 1687.15i | 0.155584 | + | 0.223338i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 3194.64i | − | 0.419620i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 440.522 | 0.0574174 | 0.0287087 | − | 0.999588i | \(-0.490860\pi\) | ||||
0.0287087 | + | 0.999588i | \(0.490860\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2850.45 | −0.368679 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2887.35 | 0.370605 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4337.62 | −0.552529 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1031.17i | − | 0.130360i | −0.997874 | − | 0.0651801i | \(-0.979238\pi\) | ||
0.997874 | − | 0.0651801i | \(-0.0207622\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3501.11 | + | 5025.78i | 0.439285 | + | 0.630586i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8879.49 | −1.10579 | −0.552893 | − | 0.833252i | \(-0.686476\pi\) | ||||
−0.552893 | + | 0.833252i | \(0.686476\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3623.08i | 0.447837i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 336.575i | − | 0.0412952i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5628.02i | − | 0.685432i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9256.56i | 1.11909i | 0.828800 | + | 0.559545i | \(0.189024\pi\) | ||||
−0.828800 | + | 0.559545i | \(0.810976\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8526.72 | 1.02334 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3188.06 | − | 4576.41i | −0.379841 | − | 0.545255i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4241.04i | − | 0.501649i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6038.28 | 0.709103 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11247.8 | 1.31143 | 0.655716 | − | 0.755008i | \(-0.272367\pi\) | ||||
0.655716 | + | 0.755008i | \(0.272367\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −368.940 | −0.0427103 | −0.0213552 | − | 0.999772i | \(-0.506798\pi\) | ||||
−0.0213552 | + | 0.999772i | \(0.506798\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2323.75 | −0.267104 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 4417.84i | − | 0.504228i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7130.39 | + | 4967.25i | −0.808111 | + | 0.562955i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2956.44 | 0.332723 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5179.71i | 0.578881i | 0.957196 | + | 0.289441i | \(0.0934693\pi\) | ||||
−0.957196 | + | 0.289441i | \(0.906531\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1421.33i | − | 0.157748i | −0.996885 | − | 0.0788738i | \(-0.974868\pi\) | ||
0.996885 | − | 0.0788738i | \(-0.0251324\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1932.63i | 0.213017i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 7662.96i | − | 0.838831i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2696.52 | 0.293161 | 0.146581 | − | 0.989199i | \(-0.453173\pi\) | ||||
0.146581 | + | 0.989199i | \(0.453173\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1069.75 | + | 2895.72i | −0.115511 | + | 0.312679i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 6901.80i | − | 0.740213i | −0.928989 | − | 0.370106i | \(-0.879321\pi\) | ||
0.928989 | − | 0.370106i | \(-0.120679\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3892.25 | 0.414630 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4461.18 | −0.472051 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1515.38 | −0.159276 | −0.0796381 | − | 0.996824i | \(-0.525376\pi\) | ||||
−0.0796381 | + | 0.996824i | \(0.525376\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.0325 | 0.00167393 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 803.439i | 0.0833308i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1622.45 | + | 2329.00i | 0.167169 | + | 0.239967i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6514.32 | 0.666799 | 0.333399 | − | 0.942786i | \(-0.391804\pi\) | ||||
0.333399 | + | 0.942786i | \(0.391804\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1107.19i | 0.112591i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12310.7i | 1.24375i | 0.783118 | + | 0.621874i | \(0.213628\pi\) | ||||
−0.783118 | + | 0.621874i | \(0.786372\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7610.16i | 0.763875i | 0.924188 | + | 0.381938i | \(0.124743\pi\) | ||||
−0.924188 | + | 0.381938i | \(0.875257\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 1224.52i | − | 0.122120i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16451.3 | 1.63014 | 0.815069 | − | 0.579364i | \(-0.196699\pi\) | ||||
0.815069 | + | 0.579364i | \(0.196699\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9197.13 | − | 6407.00i | 0.905509 | − | 0.630806i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1708.27i | − | 0.167119i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9484.10 | −0.921943 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11876.6 | 1.14724 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2474.92 | 0.237566 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8221.60 | 0.784247 | 0.392124 | − | 0.919912i | \(-0.371741\pi\) | ||||
0.392124 | + | 0.919912i | \(0.371741\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 7769.10i | − | 0.736467i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3168.96 | − | 2207.60i | 0.298536 | − | 0.207969i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1694.72 | 0.158666 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14062.9i | 1.30853i | 0.756267 | + | 0.654263i | \(0.227021\pi\) | ||||
−0.756267 | + | 0.654263i | \(0.772979\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 4133.66i | − | 0.382271i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3844.14i | − | 0.353327i | −0.984271 | − | 0.176664i | \(-0.943470\pi\) | ||
0.984271 | − | 0.176664i | \(-0.0565305\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 6357.53i | − | 0.580789i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −999.208 | −0.0907294 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7564.46 | + | 5269.63i | −0.682721 | + | 0.475604i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5609.32i | 0.503221i | 0.967829 | + | 0.251611i | \(0.0809602\pi\) | ||||
−0.967829 | + | 0.251611i | \(0.919040\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8374.52 | 0.746799 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9310.28 | −0.825298 | −0.412649 | − | 0.910890i | \(-0.635396\pi\) | ||||
−0.412649 | + | 0.910890i | \(0.635396\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3453.27 | −0.304294 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2509.84 | −0.219854 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 16749.0i | − | 1.45852i | −0.684238 | − | 0.729259i | \(-0.739865\pi\) | ||
0.684238 | − | 0.729259i | \(-0.260135\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6524.31 | − | 4545.04i | 0.564812 | − | 0.393465i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2976.50 | −0.256171 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6865.68i | 0.587453i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6898.65i | 0.586852i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 4300.98i | − | 0.363761i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18811.8i | 1.58188i | 0.611891 | + | 0.790942i | \(0.290409\pi\) | ||||
−0.611891 | + | 0.790942i | \(0.709591\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3116.84 | 0.260593 | 0.130296 | − | 0.991475i | \(-0.458407\pi\) | ||||
0.130296 | + | 0.991475i | \(0.458407\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3421.50 | + | 4911.50i | 0.284432 | + | 0.408296i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4028.14i | 0.332957i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7335.18 | 0.602875 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2710.35 | 0.221505 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.1318 | 0.00179857 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1259.07 | −0.101747 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10417.4i | 0.837141i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8596.67 | + | 3175.83i | 0.686985 | + | 0.253790i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2604.72 | −0.206997 | −0.103499 | − | 0.994630i | \(-0.533004\pi\) | ||||
−0.103499 | + | 0.994630i | \(0.533004\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1221.26i | 0.0965177i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 4240.50i | − | 0.333290i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15543.1i | 1.21495i | 0.794340 | + | 0.607473i | \(0.207817\pi\) | ||||
−0.794340 | + | 0.607473i | \(0.792183\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 4222.94i | − | 0.328289i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17091.2 | 1.32143 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15863.3 | + | 11050.9i | −1.21985 | + | 0.849786i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2625.78i | 0.200825i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18480.0 | −1.40579 | −0.702894 | − | 0.711295i | \(-0.748109\pi\) | ||||
−0.702894 | + | 0.711295i | \(0.748109\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13092.1 | −0.990588 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3286.97 | 0.247372 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3343.28 | 0.250271 | 0.125135 | − | 0.992140i | \(-0.460063\pi\) | ||||
0.125135 | + | 0.992140i | \(0.460063\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1734.64i | − | 0.129163i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −857.489 | − | 1230.91i | −0.0635117 | − | 0.0911698i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7915.57 | −0.583195 | −0.291598 | − | 0.956541i | \(-0.594187\pi\) | ||||
−0.291598 | + | 0.956541i | \(0.594187\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1800.43i | 0.131954i | 0.997821 | + | 0.0659768i | \(0.0210163\pi\) | ||||
−0.997821 | + | 0.0659768i | \(0.978984\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11695.5i | 0.852678i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 7488.72i | − | 0.543132i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8357.84i | 0.603018i | 0.953463 | + | 0.301509i | \(0.0974904\pi\) | ||||
−0.953463 | + | 0.301509i | \(0.902510\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7098.45 | −0.509502 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10804.8 | − | 15510.1i | −0.771532 | − | 1.10752i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 7347.42i | − | 0.521954i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1379.34 | −0.0974848 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26414.1 | 1.85729 | 0.928643 | − | 0.370976i | \(-0.120977\pi\) | ||||
0.928643 | + | 0.370976i | \(0.120977\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10829.0 | −0.757556 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6519.86 | 0.453792 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 27293.9i | − | 1.89009i | −0.326938 | − | 0.945046i | \(-0.606017\pi\) | ||
0.326938 | − | 0.945046i | \(-0.393983\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1803.84 | + | 2589.38i | 0.124286 | + | 0.178411i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8369.37 | −0.573761 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1254.96i | 0.0856034i | 0.999084 | + | 0.0428017i | \(0.0136284\pi\) | ||||
−0.999084 | + | 0.0428017i | \(0.986372\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13532.3i | 0.918460i | 0.888317 | + | 0.459230i | \(0.151875\pi\) | ||||
−0.888317 | + | 0.459230i | \(0.848125\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5446.96i | 0.367856i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 2564.24i | − | 0.172316i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21041.4 | −1.40699 | −0.703497 | − | 0.710699i | \(-0.748379\pi\) | ||||
−0.703497 | + | 0.710699i | \(0.748379\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4923.74 | + | 7067.94i | 0.327619 | + | 0.470291i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9523.11i | 0.630546i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6166.85 | 0.406324 | 0.203162 | − | 0.979145i | \(-0.434878\pi\) | ||||
0.203162 | + | 0.979145i | \(0.434878\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.48005 | −0.000490447 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28680.9 | −1.87139 | −0.935697 | − | 0.352805i | \(-0.885228\pi\) | ||||
−0.935697 | + | 0.352805i | \(0.885228\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21715.8 | 1.41007 | 0.705035 | − | 0.709173i | \(-0.250931\pi\) | ||||
0.705035 | + | 0.709173i | \(0.250931\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1876.80i | 0.121278i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14234.6 | − | 9916.24i | 0.915403 | − | 0.637698i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9448.33 | 0.604693 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8836.47i | 0.562831i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 8637.69i | − | 0.547547i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 691.303i | 0.0436139i | 0.999762 | + | 0.0218069i | \(0.00694191\pi\) | ||||
−0.999762 | + | 0.0218069i | \(0.993058\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2684.41i | 0.168555i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4960.06 | −0.309975 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11867.1 | + | 4384.01i | 0.738136 | + | 0.272686i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 4480.01i | − | 0.277350i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5076.71 | −0.312821 | −0.156410 | − | 0.987692i | \(-0.549992\pi\) | ||||
−0.156410 | + | 0.987692i | \(0.549992\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23620.0 | 1.44865 | 0.724325 | − | 0.689458i | \(-0.242151\pi\) | ||||
0.724325 | + | 0.689458i | \(0.242151\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4424.85 | 0.270121 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22871.5 | 1.38976 | 0.694878 | − | 0.719128i | \(-0.255458\pi\) | ||||
0.694878 | + | 0.719128i | \(0.255458\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 8046.37i | − | 0.486668i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3119.69 | − | 4478.25i | −0.187819 | − | 0.269611i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11952.1 | −0.716265 | −0.358133 | − | 0.933671i | \(-0.616586\pi\) | ||||
−0.358133 | + | 0.933671i | \(0.616586\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3999.22i | 0.238569i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3864.00i | 0.229450i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15849.4i | 0.936879i | 0.883496 | + | 0.468440i | \(0.155184\pi\) | ||||
−0.883496 | + | 0.468440i | \(0.844816\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 23354.3i | − | 1.37425i | −0.726540 | − | 0.687124i | \(-0.758873\pi\) | ||
0.726540 | − | 0.687124i | \(-0.241127\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4537.43 | 0.265791 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6961.13 | + | 4849.33i | −0.405926 | + | 0.282781i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 10776.7i | − | 0.625600i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8412.91 | 0.486191 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12536.9 | −0.721281 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13707.0 | −0.785093 | −0.392546 | − | 0.919732i | \(-0.628406\pi\) | ||||
−0.392546 | + | 0.919732i | \(0.628406\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2908.82 | −0.165867 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 26246.5i | − | 1.49001i | −0.667060 | − | 0.745004i | \(-0.732448\pi\) | ||
0.667060 | − | 0.745004i | \(-0.267552\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6197.85 | − | 4317.62i | 0.350297 | − | 0.244028i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16678.4 | 0.938497 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15624.1i | 0.875317i | 0.899141 | + | 0.437658i | \(0.144192\pi\) | ||||
−0.899141 | + | 0.437658i | \(0.855808\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11810.2i | 0.658752i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7098.74i | 0.394227i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 10142.6i | − | 0.560817i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13845.8 | 0.762254 | 0.381127 | − | 0.924523i | \(-0.375536\pi\) | ||||
0.381127 | + | 0.924523i | \(0.375536\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3654.26 | + | 2545.67i | −0.200309 | + | 0.139541i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8363.52i | 0.456470i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.6062 | 0.00133720 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9334.38 | 0.505091 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5302.85 | −0.285714 | −0.142857 | − | 0.989743i | \(-0.545629\pi\) | ||||
−0.142857 | + | 0.989743i | \(0.545629\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23221.0 | 1.24580 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 3218.59i | − | 0.171942i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12629.1 | + | 8797.85i | −0.671807 | + | 0.468002i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30171.8 | 1.59820 | 0.799102 | − | 0.601196i | \(-0.205309\pi\) | ||||
0.799102 | + | 0.601196i | \(0.205309\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 9394.99i | − | 0.495555i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6828.12i | 0.358647i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4094.91i | 0.214183i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 13484.9i | − | 0.702377i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14915.6 | −0.773655 | −0.386828 | − | 0.922152i | \(-0.626429\pi\) | ||||
−0.386828 | + | 0.922152i | \(0.626429\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17491.6 | + | 25108.9i | 0.903498 | + | 1.29695i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 7666.67i | − | 0.394366i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16702.6 | 0.855610 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17914.4 | 0.913905 | 0.456952 | − | 0.889491i | \(-0.348941\pi\) | ||||
0.456952 | + | 0.889491i | \(0.348941\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14555.9 | −0.736481 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7442.95i | 0.375050i | 0.982260 | + | 0.187525i | \(0.0600465\pi\) | ||||
−0.982260 | + | 0.187525i | \(0.939953\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4010.82 | − | 1481.70i | −0.201280 | − | 0.0743581i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16170.7 | 0.808214 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 6072.67i | − | 0.302283i | −0.988512 | − | 0.151141i | \(-0.951705\pi\) | ||
0.988512 | − | 0.151141i | \(-0.0482949\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12198.1i | 0.604737i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25677.6i | 1.26786i | 0.773392 | + | 0.633929i | \(0.218559\pi\) | ||||
−0.773392 | + | 0.633929i | \(0.781441\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 6179.11i | − | 0.303873i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9185.81 | 0.449921 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4604.62 | + | 3207.72i | −0.224632 | + | 0.156485i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28754.7i | 1.39717i | 0.715528 | + | 0.698584i | \(0.246186\pi\) | ||||
−0.715528 | + | 0.698584i | \(0.753814\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2411.62 | −0.116712 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1112.83 | −0.0536424 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28046.8 | 1.34660 | 0.673301 | − | 0.739368i | \(-0.264876\pi\) | ||||
0.673301 | + | 0.739368i | \(0.264876\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5571.76 | 0.266459 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 14783.1i | − | 0.704186i | −0.935965 | − | 0.352093i | \(-0.885470\pi\) | ||
0.935965 | − | 0.352093i | \(-0.114530\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10803.5 | − | 15508.2i | −0.512598 | − | 0.735824i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1533.55 | −0.0724779 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 11107.5i | − | 0.522904i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31012.1i | − | 1.45426i | −0.686500 | − | 0.727130i | \(-0.740854\pi\) | ||
0.686500 | − | 0.727130i | \(-0.259146\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22731.6i | 1.06181i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 34993.2i | − | 1.62823i | −0.580706 | − | 0.814113i | \(-0.697223\pi\) | ||
0.580706 | − | 0.814113i | \(-0.302777\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10582.8 | −0.490508 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6689.66 | + | 9602.88i | 0.308868 | + | 0.443374i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 66.1497i | 0.00304244i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13300.0 | −0.609364 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4185.95 | −0.191052 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2366.10 | 0.107579 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12762.8 | −0.578073 | −0.289037 | − | 0.957318i | \(-0.593335\pi\) | ||||
−0.289037 | + | 0.957318i | \(0.593335\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 10685.5i | − | 0.482145i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4419.33 | − | 6343.86i | −0.198651 | − | 0.285160i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17306.3 | −0.774985 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3427.97i | 0.152928i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43638.6i | 1.93947i | 0.244155 | + | 0.969736i | \(0.421490\pi\) | ||||
−0.244155 | + | 0.969736i | \(0.578510\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10587.8i | 0.468798i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8430.36i | 0.371875i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11471.2 | 0.504124 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3057.71 | + | 4389.28i | 0.133876 | + | 0.192176i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11834.1i | 0.516210i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 344.856 | 0.0149870 | 0.00749350 | − | 0.999972i | \(-0.497615\pi\) | ||||
0.00749350 | + | 0.999972i | \(0.497615\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18390.9 | 0.796291 | 0.398145 | − | 0.917322i | \(-0.369654\pi\) | ||||
0.398145 | + | 0.917322i | \(0.369654\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11918.5 | −0.514146 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5725.47 | 0.246079 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 39131.0i | − | 1.67567i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5044.46 | + | 3514.12i | −0.215223 | + | 0.149931i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34681.7 | −1.47430 | −0.737149 | − | 0.675730i | \(-0.763828\pi\) | ||||
−0.737149 | + | 0.675730i | \(0.763828\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33952.8i | 1.43806i | 0.694981 | + | 0.719028i | \(0.255413\pi\) | ||||
−0.694981 | + | 0.719028i | \(0.744587\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8635.55i | 0.364426i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1625.51i | 0.0683487i | 0.999416 | + | 0.0341744i | \(0.0108802\pi\) | ||||
−0.999416 | + | 0.0341744i | \(0.989120\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13544.9i | 0.567470i | 0.958903 | + | 0.283735i | \(0.0915735\pi\) | ||||
−0.958903 | + | 0.283735i | \(0.908426\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21108.9 | 0.881179 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13193.9 | + | 4874.15i | 0.548788 | + | 0.202736i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11599.4i | 0.480736i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2652.22 | 0.109527 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37264.6 | −1.53339 | −0.766697 | − | 0.642009i | \(-0.778101\pi\) | ||||
−0.766697 | + | 0.642009i | \(0.778101\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −353.057 | −0.0144761 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1958.44 | 0.0800147 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 3476.34i | − | 0.141526i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6532.88 | − | 9377.82i | −0.265020 | − | 0.380432i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18867.6 | 0.762703 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 14641.8i | − | 0.589794i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48255.7i | 1.93698i | 0.249056 | + | 0.968489i | \(0.419880\pi\) | ||||
−0.249056 | + | 0.968489i | \(0.580120\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 4122.69i | − | 0.164904i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29668.8i | 1.18257i | 0.806461 | + | 0.591287i | \(0.201380\pi\) | ||||
−0.806461 | + | 0.591287i | \(0.798620\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3516.98 | 0.139695 | 0.0698474 | − | 0.997558i | \(-0.477749\pi\) | ||||
0.0698474 | + | 0.997558i | \(0.477749\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.3557 | + | 19.0568i | −0.00108279 | + | 0.000754303i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 419.237i | 0.0165365i | 0.999966 | + | 0.00826825i | \(0.00263190\pi\) | ||||
−0.999966 | + | 0.00826825i | \(0.997368\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5957.22 | 0.234164 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9694.28 | −0.379740 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27891.4 | −1.08878 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22322.5 | 0.868391 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3670.65i | 0.142306i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14695.9 | + | 10237.6i | −0.567787 | + | 0.395538i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2715.11 | 0.104541 | 0.0522707 | − | 0.998633i | \(-0.483354\pi\) | ||||
0.0522707 | + | 0.998633i | \(0.483354\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 10355.5i | − | 0.397363i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 29828.1i | − | 1.14068i | −0.821410 | − | 0.570338i | \(-0.806812\pi\) | ||
0.821410 | − | 0.570338i | \(-0.193188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 46118.5i | − | 1.75766i | −0.477137 | − | 0.878829i | \(-0.658326\pi\) | ||
0.477137 | − | 0.878829i | \(-0.341674\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3754.07i | 0.142589i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3840.97 | 0.145397 | 0.0726985 | − | 0.997354i | \(-0.476839\pi\) | ||||
0.0726985 | + | 0.997354i | \(0.476839\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18139.7 | + | 12636.7i | −0.684349 | + | 0.476739i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 2164.22i | − | 0.0813738i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28463.6 | −1.06663 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14429.0 | −0.538891 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7691.44 | 0.286298 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15229.2 | −0.564986 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 11276.6i | − | 0.416955i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16182.4 | − | 11273.1i | 0.596362 | − | 0.415444i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1691.54 | −0.0621312 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 52814.3i | − | 1.93348i | −0.255754 | − | 0.966742i | \(-0.582324\pi\) | ||
0.255754 | − | 0.966742i | \(-0.417676\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 7479.55i | − | 0.272916i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 29690.1i | − | 1.07978i | −0.841737 | − | 0.539888i | \(-0.818467\pi\) | ||
0.841737 | − | 0.539888i | \(-0.181533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 27270.4i | − | 0.988519i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5849.12 | 0.211329 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10188.8 | + | 14625.8i | 0.366917 | + | 0.526702i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 28193.7i | − | 1.01200i | −0.862534 | − | 0.505999i | \(-0.831124\pi\) | ||
0.862534 | − | 0.505999i | \(-0.168876\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5637.11 | 0.201682 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18359.8 | −0.654735 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22693.0 | 0.806639 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14870.6 | −0.526877 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 5554.27i | − | 0.196157i | −0.995179 | − | 0.0980784i | \(-0.968730\pi\) | ||
0.995179 | − | 0.0980784i | \(-0.0312696\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13103.3 | + | 35469.5i | −0.461272 | + | 1.24862i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12089.8 | 0.424226 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4552.73i | 0.159241i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 6999.65i | − | 0.244043i | −0.992527 | − | 0.122022i | \(-0.961062\pi\) | ||
0.992527 | − | 0.122022i | \(-0.0389377\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 14173.1i | − | 0.492567i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31782.0i | 1.10103i | 0.834827 | + | 0.550513i | \(0.185568\pi\) | ||||
−0.834827 | + | 0.550513i | \(0.814432\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.7101 | 0.00144037 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1704.91 | − | 1187.69i | 0.0586886 | − | 0.0408843i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 34722.9i | − | 1.19149i | −0.803173 | − | 0.595746i | \(-0.796857\pi\) | ||
0.803173 | − | 0.595746i | \(-0.203143\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15835.3 | 0.541659 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25198.5 | 0.859218 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16968.8 | −0.576783 | −0.288391 | − | 0.957513i | \(-0.593120\pi\) | ||||
−0.288391 | + | 0.957513i | \(0.593120\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16199.2 | −0.548893 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12427.1i | 0.419759i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30088.8 | + | 43191.8i | 1.01316 | + | 1.45437i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20141.8 | −0.676103 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 2727.07i | − | 0.0912549i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 9831.94i | − | 0.327981i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 6717.59i | − | 0.223395i | −0.993742 | − | 0.111698i | \(-0.964371\pi\) | ||
0.993742 | − | 0.111698i | \(-0.0356288\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13561.9i | 0.449609i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32476.5 | −1.07335 | −0.536674 | − | 0.843789i | \(-0.680320\pi\) | ||||
−0.536674 | + | 0.843789i | \(0.680320\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21307.6 | + | 30586.7i | 0.702047 | + | 1.00778i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11920.8i | 0.391559i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9656.90 | −0.316225 | −0.158112 | − | 0.987421i | \(-0.550541\pi\) | ||||
−0.158112 | + | 0.987421i | \(0.550541\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25027.6 | 0.817045 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9184.65 | 0.298923 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −731.732 | −0.0237422 | −0.0118711 | − | 0.999930i | \(-0.503779\pi\) | ||||
−0.0118711 | + | 0.999930i | \(0.503779\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9030.55i | 0.292119i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8199.97 | − | 11770.9i | −0.264446 | − | 0.379607i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24673.7 | −0.793305 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50307.5i | 1.61258i | 0.591519 | + | 0.806291i | \(0.298529\pi\) | ||||
−0.591519 | + | 0.806291i | \(0.701471\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 525.789i | 0.0168030i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 11592.3i | − | 0.369347i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1821.15i | − | 0.0578501i | −0.999582 | − | 0.0289250i | \(-0.990792\pi\) | ||
0.999582 | − | 0.0289250i | \(-0.00920841\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5687.26 | −0.180117 |
(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.895.10 | 24 | ||
4.3 | odd | 2 | 1344.4.b.j.895.10 | 24 | |||
7.6 | odd | 2 | 1344.4.b.j.895.15 | 24 | |||
8.3 | odd | 2 | 672.4.b.a.223.15 | yes | 24 | ||
8.5 | even | 2 | 672.4.b.b.223.15 | yes | 24 | ||
28.27 | even | 2 | inner | 1344.4.b.i.895.15 | 24 | ||
56.13 | odd | 2 | 672.4.b.a.223.10 | ✓ | 24 | ||
56.27 | even | 2 | 672.4.b.b.223.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.b.a.223.10 | ✓ | 24 | 56.13 | odd | 2 | ||
672.4.b.a.223.15 | yes | 24 | 8.3 | odd | 2 | ||
672.4.b.b.223.10 | yes | 24 | 56.27 | even | 2 | ||
672.4.b.b.223.15 | yes | 24 | 8.5 | even | 2 | ||
1344.4.b.i.895.10 | 24 | 1.1 | even | 1 | trivial | ||
1344.4.b.i.895.15 | 24 | 28.27 | even | 2 | inner | ||
1344.4.b.j.895.10 | 24 | 4.3 | odd | 2 | |||
1344.4.b.j.895.15 | 24 | 7.6 | odd | 2 |