Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,4,Mod(217,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.217");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.i (of order \(3\), degree \(2\), 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: | \(38.2332376837\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-67})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 16x^{2} - 17x + 289 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 433.2 | ||
Root | \(-3.29436 + 2.47935i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.433 |
Dual form | 648.4.i.t.217.2 |
$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.08872 | − | 15.7421i | 0.812920 | − | 1.40802i | −0.0978916 | − | 0.995197i | \(-0.531210\pi\) |
0.910812 | − | 0.412822i | \(-0.135457\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.411277 | + | 0.712352i | 0.0222068 | + | 0.0384634i | 0.876915 | − | 0.480645i | \(-0.159597\pi\) |
−0.854708 | + | 0.519108i | \(0.826264\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −32.7662 | − | 56.7527i | −0.898125 | − | 1.55560i | −0.829889 | − | 0.557928i | \(-0.811596\pi\) |
−0.0682357 | − | 0.997669i | \(-0.521737\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −15.9113 | + | 27.5591i | −0.339461 | + | 0.587964i | −0.984331 | − | 0.176328i | \(-0.943578\pi\) |
0.644870 | + | 0.764292i | \(0.276911\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −124.420 | −1.77507 | −0.887535 | − | 0.460741i | \(-0.847584\pi\) | ||||
−0.887535 | + | 0.460741i | \(0.847584\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 27.8872 | 0.336725 | 0.168362 | − | 0.985725i | \(-0.446152\pi\) | ||||
0.168362 | + | 0.985725i | \(0.446152\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −21.5887 | + | 37.3928i | −0.195720 | + | 0.338997i | −0.947136 | − | 0.320831i | \(-0.896038\pi\) |
0.751416 | + | 0.659828i | \(0.229371\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −102.710 | − | 177.899i | −0.821678 | − | 1.42319i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 19.9113 | + | 34.4873i | 0.127498 | + | 0.220832i | 0.922706 | − | 0.385503i | \(-0.125972\pi\) |
−0.795209 | + | 0.606336i | \(0.792639\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −147.420 | + | 255.338i | −0.854108 | + | 1.47936i | 0.0233627 | + | 0.999727i | \(0.492563\pi\) |
−0.877470 | + | 0.479631i | \(0.840771\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.9519 | 0.0722096 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −104.177 | −0.462883 | −0.231441 | − | 0.972849i | \(-0.574344\pi\) | ||||
−0.231441 | + | 0.972849i | \(0.574344\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 153.823 | − | 266.428i | 0.585928 | − | 1.01486i | −0.408831 | − | 0.912610i | \(-0.634063\pi\) |
0.994759 | − | 0.102247i | \(-0.0326032\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 180.541 | + | 312.706i | 0.640283 | + | 1.10900i | 0.985369 | + | 0.170432i | \(0.0545164\pi\) |
−0.345086 | + | 0.938571i | \(0.612150\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 198.823 | + | 344.371i | 0.617048 | + | 1.06876i | 0.990022 | + | 0.140916i | \(0.0450049\pi\) |
−0.372974 | + | 0.927842i | \(0.621662\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 171.162 | − | 296.461i | 0.499014 | − | 0.864317i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −107.161 | −0.277730 | −0.138865 | − | 0.990311i | \(-0.544345\pi\) | ||||
−0.138865 | + | 0.990311i | \(0.544345\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1191.21 | −2.92041 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 94.4677 | − | 163.623i | 0.208452 | − | 0.361049i | −0.742775 | − | 0.669541i | \(-0.766491\pi\) |
0.951227 | + | 0.308492i | \(0.0998243\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 49.5083 | + | 85.7509i | 0.103916 | + | 0.179988i | 0.913295 | − | 0.407299i | \(-0.133529\pi\) |
−0.809379 | + | 0.587287i | \(0.800196\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 289.226 | + | 500.955i | 0.551910 | + | 0.955935i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −212.524 | + | 368.102i | −0.387522 | + | 0.671207i | −0.992116 | − | 0.125327i | \(-0.960002\pi\) |
0.604594 | + | 0.796534i | \(0.293335\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 445.532 | 0.744718 | 0.372359 | − | 0.928089i | \(-0.378549\pi\) | ||||
0.372359 | + | 0.928089i | \(0.378549\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −499.806 | −0.801341 | −0.400670 | − | 0.916222i | \(-0.631223\pi\) | ||||
−0.400670 | + | 0.916222i | \(0.631223\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 26.9519 | − | 46.6821i | 0.0398890 | − | 0.0690898i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −285.138 | − | 493.873i | −0.406082 | − | 0.703355i | 0.588365 | − | 0.808596i | \(-0.299772\pi\) |
−0.994447 | + | 0.105241i | \(0.966439\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 654.371 | + | 1133.40i | 0.865381 | + | 1.49888i | 0.866669 | + | 0.498884i | \(0.166257\pi\) |
−0.00128787 | + | 0.999999i | \(0.500410\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1130.82 | + | 1958.63i | −1.44299 | + | 2.49933i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1323.00 | −1.57570 | −0.787852 | − | 0.615864i | \(-0.788807\pi\) | ||||
−0.787852 | + | 0.615864i | \(0.788807\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −26.1757 | −0.0301534 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 253.459 | − | 439.004i | 0.273730 | − | 0.474115i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −472.436 | − | 818.283i | −0.494522 | − | 0.856537i | 0.505458 | − | 0.862851i | \(-0.331323\pi\) |
−0.999980 | + | 0.00631404i | \(0.997990\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −699.050 | − | 1210.79i | −0.688694 | − | 1.19285i | −0.972261 | − | 0.233900i | \(-0.924851\pi\) |
0.283567 | − | 0.958952i | \(-0.408482\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 480.275 | − | 831.861i | 0.459446 | − | 0.795784i | −0.539486 | − | 0.841995i | \(-0.681381\pi\) |
0.998932 | + | 0.0462110i | \(0.0147147\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1935.87 | −1.74905 | −0.874523 | − | 0.484983i | \(-0.838826\pi\) | ||||
−0.874523 | + | 0.484983i | \(0.838826\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1305.40 | −1.14711 | −0.573555 | − | 0.819167i | \(-0.694436\pi\) | ||||
−0.573555 | + | 0.819167i | \(0.694436\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 547.016 | − | 947.459i | 0.455389 | − | 0.788756i | −0.543322 | − | 0.839524i | \(-0.682834\pi\) |
0.998710 | + | 0.0507683i | \(0.0161670\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 392.428 | + | 679.705i | 0.318209 | + | 0.551155i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −51.1709 | − | 88.6305i | −0.0394187 | − | 0.0682752i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1481.74 | + | 2566.46i | −1.11326 | + | 1.92822i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1461.82 | −1.04600 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1301.05 | −0.909050 | −0.454525 | − | 0.890734i | \(-0.650191\pi\) | ||||
−0.454525 | + | 0.890734i | \(0.650191\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 978.833 | − | 1695.39i | 0.652832 | − | 1.13074i | −0.329601 | − | 0.944120i | \(-0.606914\pi\) |
0.982433 | − | 0.186618i | \(-0.0597526\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.4694 | + | 19.8655i | 0.00747760 | + | 0.0129516i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1276.98 | − | 2211.80i | −0.796351 | − | 1.37932i | −0.921978 | − | 0.387243i | \(-0.873427\pi\) |
0.125626 | − | 0.992078i | \(-0.459906\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −102.630 | + | 177.761i | −0.0626258 | + | 0.108471i | −0.895638 | − | 0.444783i | \(-0.853281\pi\) |
0.833013 | + | 0.553254i | \(0.186614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2085.41 | 1.21951 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 723.872 | 0.414582 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 82.1202 | − | 142.236i | 0.0451513 | − | 0.0782044i | −0.842567 | − | 0.538592i | \(-0.818956\pi\) |
0.887718 | + | 0.460388i | \(0.152290\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1713.86 | − | 2968.49i | −0.923654 | − | 1.59982i | −0.793712 | − | 0.608294i | \(-0.791854\pi\) |
−0.129942 | − | 0.991522i | \(-0.541479\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2679.71 | + | 4641.40i | 1.38864 | + | 2.40520i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 494.042 | − | 855.706i | 0.251139 | − | 0.434986i | −0.712700 | − | 0.701468i | \(-0.752528\pi\) |
0.963840 | + | 0.266482i | \(0.0858614\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −35.5157 | −0.0173853 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2845.45 | −1.36732 | −0.683660 | − | 0.729801i | \(-0.739613\pi\) | ||||
−0.683660 | + | 0.729801i | \(0.739613\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1602.95 | + | 2776.38i | −0.742752 | + | 1.28648i | 0.208485 | + | 0.978026i | \(0.433147\pi\) |
−0.951238 | + | 0.308459i | \(0.900187\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 592.163 | + | 1025.66i | 0.269532 | + | 0.466844i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 892.817 | + | 1546.40i | 0.392368 | + | 0.679601i | 0.992761 | − | 0.120104i | \(-0.0383228\pi\) |
−0.600394 | + | 0.799705i | \(0.704989\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 84.4843 | − | 146.331i | 0.0364938 | − | 0.0632091i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1318.84 | 0.550696 | 0.275348 | − | 0.961345i | \(-0.411207\pi\) | ||||
0.275348 | + | 0.961345i | \(0.411207\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3462.97 | 1.42210 | 0.711051 | − | 0.703141i | \(-0.248220\pi\) | ||||
0.711051 | + | 0.703141i | \(0.248220\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −946.840 | + | 1639.97i | −0.376287 | + | 0.651748i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4076.75 | + | 7061.14i | 1.59423 | + | 2.76129i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 795.655 | + | 1378.12i | 0.301422 | + | 0.522078i | 0.976458 | − | 0.215706i | \(-0.0692054\pi\) |
−0.675036 | + | 0.737784i | \(0.735872\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 382.228 | − | 662.038i | 0.142556 | − | 0.246915i | −0.785902 | − | 0.618351i | \(-0.787801\pi\) |
0.928459 | + | 0.371436i | \(0.121134\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1191.63 | −0.430965 | −0.215483 | − | 0.976508i | \(-0.569132\pi\) | ||||
−0.215483 | + | 0.976508i | \(0.569132\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2708.20 | −0.964719 | −0.482360 | − | 0.875973i | \(-0.660220\pi\) | ||||
−0.482360 | + | 0.875973i | \(0.660220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.3781 | + | 28.3677i | −0.00566264 | + | 0.00980798i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2796.10 | − | 4842.99i | −0.952625 | − | 1.65000i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −913.758 | − | 1582.68i | −0.302421 | − | 0.523808i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1649.48 | − | 2856.98i | 0.538173 | − | 0.932144i | −0.460829 | − | 0.887489i | \(-0.652448\pi\) |
0.999002 | − | 0.0446549i | \(-0.0142188\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6563.54 | 2.08200 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −242.521 | −0.0758682 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1979.67 | − | 3428.90i | 0.602567 | − | 1.04368i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1260.83 | + | 2183.83i | 0.378617 | + | 0.655784i | 0.990861 | − | 0.134885i | \(-0.0430664\pi\) |
−0.612244 | + | 0.790669i | \(0.709733\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1657.33 | − | 2870.59i | −0.484586 | − | 0.839328i | 0.515257 | − | 0.857036i | \(-0.327696\pi\) |
−0.999843 | + | 0.0177077i | \(0.994363\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2064.83 | − | 3576.39i | 0.595842 | − | 1.03203i | −0.397585 | − | 0.917565i | \(-0.630152\pi\) |
0.993427 | − | 0.114464i | \(-0.0365151\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −986.257 | −0.277304 | −0.138652 | − | 0.990341i | \(-0.544277\pi\) | ||||
−0.138652 | + | 0.990341i | \(0.544277\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7228.17 | 2.00644 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 179.499 | − | 310.902i | 0.0485809 | − | 0.0841446i | −0.840712 | − | 0.541482i | \(-0.817863\pi\) |
0.889293 | + | 0.457337i | \(0.151197\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1021.02 | − | 1768.45i | −0.272902 | − | 0.472680i | 0.696702 | − | 0.717361i | \(-0.254650\pi\) |
−0.969604 | + | 0.244681i | \(0.921317\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3111.28 | − | 5388.90i | −0.811317 | − | 1.40524i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −443.721 | + | 768.548i | −0.114305 | + | 0.197982i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2609.69 | 0.656264 | 0.328132 | − | 0.944632i | \(-0.393581\pi\) | ||||
0.328132 | + | 0.944632i | \(0.393581\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2829.52 | 0.703124 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −439.419 | + | 761.096i | −0.106654 | + | 0.184731i | −0.914413 | − | 0.404783i | \(-0.867347\pi\) |
0.807759 | + | 0.589514i | \(0.200681\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −42.8457 | − | 74.2110i | −0.0102792 | − | 0.0178040i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1608.67 | − | 2786.29i | −0.377166 | − | 0.653271i | 0.613483 | − | 0.789708i | \(-0.289768\pi\) |
−0.990649 | + | 0.136438i | \(0.956435\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −973.955 | + | 1686.94i | −0.225772 | + | 0.391049i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7978.38 | −1.80837 | −0.904183 | − | 0.427146i | \(-0.859519\pi\) | ||||
−0.904183 | + | 0.427146i | \(0.859519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4248.21 | 0.952251 | 0.476126 | − | 0.879377i | \(-0.342041\pi\) | ||||
0.476126 | + | 0.879377i | \(0.342041\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6730.81 | + | 11658.1i | −1.47594 | + | 2.55640i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −415.517 | − | 719.697i | −0.0901301 | − | 0.156110i | 0.817436 | − | 0.576020i | \(-0.195395\pi\) |
−0.907566 | + | 0.419910i | \(0.862062\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1481.00 | − | 2565.17i | −0.314410 | − | 0.544573i | 0.664902 | − | 0.746930i | \(-0.268473\pi\) |
−0.979312 | + | 0.202357i | \(0.935140\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2215.42 | − | 3837.22i | 0.465346 | − | 0.806004i | −0.533871 | − | 0.845566i | \(-0.679263\pi\) |
0.999217 | + | 0.0395625i | \(0.0125964\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 253.054 | 0.0520465 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10567.2 | 2.15087 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1711.43 | + | 2964.29i | −0.341239 | + | 0.591043i | −0.984663 | − | 0.174467i | \(-0.944180\pi\) |
0.643424 | + | 0.765510i | \(0.277513\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1717.18 | − | 2974.24i | −0.338909 | − | 0.587007i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −687.008 | − | 1189.93i | −0.132879 | − | 0.230153i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −148.504 | + | 257.217i | −0.0284374 | + | 0.0492549i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1799.87 | 0.337902 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 139.734 | 0.0259774 | 0.0129887 | − | 0.999916i | \(-0.495865\pi\) | ||||
0.0129887 | + | 0.999916i | \(0.495865\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3799.94 | − | 6581.69i | 0.692845 | − | 1.20004i | −0.278057 | − | 0.960565i | \(-0.589690\pi\) |
0.970902 | − | 0.239478i | \(-0.0769764\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1508.76 | + | 2613.25i | 0.272460 | + | 0.471915i | 0.969491 | − | 0.245126i | \(-0.0788293\pi\) |
−0.697031 | + | 0.717041i | \(0.745496\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −960.603 | − | 1663.81i | −0.170198 | − | 0.294792i | 0.768291 | − | 0.640101i | \(-0.221107\pi\) |
−0.938489 | + | 0.345309i | \(0.887774\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1304.83 | − | 2260.04i | 0.229018 | − | 0.396670i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3469.72 | −0.597710 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6536.98 | 1.11571 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −163.542 | + | 283.263i | −0.0274054 | + | 0.0474675i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −456.206 | − | 790.172i | −0.0757563 | − | 0.131214i | 0.825659 | − | 0.564170i | \(-0.190804\pi\) |
−0.901415 | + | 0.432956i | \(0.857470\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3863.14 | + | 6691.16i | 0.630048 | + | 1.09128i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3007.31 | − | 5208.82i | 0.486109 | − | 0.841965i | −0.513764 | − | 0.857932i | \(-0.671749\pi\) |
0.999873 | + | 0.0159664i | \(0.00508248\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19321.5 | 3.06838 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 563.715 | 0.0887398 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1369.92 | − | 2372.77i | 0.211934 | − | 0.367080i | −0.740386 | − | 0.672182i | \(-0.765357\pi\) |
0.952320 | + | 0.305102i | \(0.0986906\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3804.34 | + | 6589.32i | 0.583501 | + | 1.01065i | 0.995060 | + | 0.0992704i | \(0.0316509\pi\) |
−0.411560 | + | 0.911383i | \(0.635016\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4362.56 | − | 7556.17i | −0.657777 | − | 1.13930i | −0.981190 | − | 0.193046i | \(-0.938163\pi\) |
0.323412 | − | 0.946258i | \(-0.395170\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4049.32 | − | 7013.63i | 0.605396 | − | 1.04858i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10470.0 | 1.53923 | 0.769614 | − | 0.638509i | \(-0.220449\pi\) | ||||
0.769614 | + | 0.638509i | \(0.220449\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6081.30 | −0.886616 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4542.60 | + | 7868.01i | −0.651426 | + | 1.12830i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3947.07 | + | 6836.53i | 0.561405 | + | 0.972381i | 0.997374 | + | 0.0724198i | \(0.0230721\pi\) |
−0.435970 | + | 0.899961i | \(0.643595\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −44.0727 | − | 76.3362i | −0.00616750 | − | 0.0106824i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 134.970 | − | 233.775i | 0.0187359 | − | 0.0324515i | −0.856505 | − | 0.516138i | \(-0.827369\pi\) |
0.875241 | + | 0.483686i | \(0.160702\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1267.26 | −0.173122 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8580.72 | −1.16296 | −0.581480 | − | 0.813561i | \(-0.697526\pi\) | ||||
−0.581480 | + | 0.813561i | \(0.697526\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1707.46 | − | 2957.41i | 0.227800 | − | 0.394561i | −0.729356 | − | 0.684134i | \(-0.760180\pi\) |
0.957156 | + | 0.289574i | \(0.0935135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −489.917 | − | 848.561i | −0.0648532 | − | 0.112329i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1652.00 | + | 2861.35i | 0.215321 | + | 0.372947i | 0.953372 | − | 0.301798i | \(-0.0975869\pi\) |
−0.738051 | + | 0.674745i | \(0.764254\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2686.06 | − | 4652.39i | 0.347417 | − | 0.601743i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10366.1 | −1.32045 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12756.1 | −1.61262 | −0.806311 | − | 0.591492i | \(-0.798539\pi\) | ||||
−0.806311 | + | 0.591492i | \(0.798539\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2314.26 | + | 4008.42i | −0.288201 | + | 0.499179i | −0.973380 | − | 0.229195i | \(-0.926391\pi\) |
0.685179 | + | 0.728375i | \(0.259724\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4691.27 | − | 8125.51i | −0.579873 | − | 1.00437i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3413.50 | + | 5912.35i | 0.415727 | + | 0.720060i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1482.78 | − | 2568.24i | 0.179263 | − | 0.310492i | −0.762365 | − | 0.647147i | \(-0.775962\pi\) |
0.941628 | + | 0.336654i | \(0.109295\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 155.409 | 0.0185162 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23789.6 | 2.81394 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −935.131 | + | 1619.69i | −0.109031 | + | 0.188848i | −0.915378 | − | 0.402595i | \(-0.868108\pi\) |
0.806347 | + | 0.591443i | \(0.201442\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6325.31 | + | 10955.8i | 0.732248 | + | 1.26829i | 0.955920 | + | 0.293627i | \(0.0948623\pi\) |
−0.223672 | + | 0.974665i | \(0.571804\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12779.1 | + | 22134.1i | 1.45854 | + | 2.52626i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −40.7232 | + | 70.5347i | −0.00461530 | + | 0.00799394i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3266.47 | −0.365059 | −0.182530 | − | 0.983200i | \(-0.558429\pi\) | ||||
−0.182530 | + | 0.983200i | \(0.558429\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6788.95 | 0.753478 | 0.376739 | − | 0.926319i | \(-0.377045\pi\) | ||||
0.376739 | + | 0.926319i | \(0.377045\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −602.050 | + | 1042.78i | −0.0659038 | + | 0.114149i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2459.27 | − | 4259.59i | −0.267368 | − | 0.463096i | 0.700813 | − | 0.713345i | \(-0.252821\pi\) |
−0.968181 | + | 0.250249i | \(0.919487\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7016.74 | − | 12153.4i | −0.752540 | − | 1.30344i | −0.946588 | − | 0.322446i | \(-0.895495\pi\) |
0.194047 | − | 0.980992i | \(-0.437838\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12024.4 | + | 20826.8i | −1.28092 | + | 2.21862i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5374.04 | 0.564848 | 0.282424 | − | 0.959290i | \(-0.408862\pi\) | ||||
0.282424 | + | 0.959290i | \(0.408862\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20160.7 | −2.10495 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −237.904 | + | 412.062i | −0.0245123 | + | 0.0424566i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6084.62 | − | 10538.9i | −0.622815 | − | 1.07875i | −0.988959 | − | 0.148189i | \(-0.952655\pi\) |
0.366144 | − | 0.930558i | \(-0.380678\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3093.04 | − | 5357.30i | −0.312489 | − | 0.541246i | 0.666412 | − | 0.745584i | \(-0.267829\pi\) |
−0.978900 | + | 0.204338i | \(0.934496\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7598.89 | + | 13161.7i | −0.762743 | + | 1.32111i | 0.178688 | + | 0.983906i | \(0.442815\pi\) |
−0.941431 | + | 0.337204i | \(0.890519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1981.82 | −0.196377 | −0.0981883 | − | 0.995168i | \(-0.531305\pi\) | ||||
−0.0981883 | + | 0.995168i | \(0.531305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −349.625 | −0.0344225 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11831.3 | − | 20492.3i | 1.15011 | − | 1.99205i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2864.29 | − | 4961.10i | −0.276679 | − | 0.479223i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4889.76 | − | 8469.31i | −0.466427 | − | 0.807876i | 0.532837 | − | 0.846218i | \(-0.321126\pi\) |
−0.999265 | + | 0.0383417i | \(0.987792\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1657.60 | − | 2871.04i | 0.157131 | − | 0.272158i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17175.4 | −1.60803 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18668.9 | 1.73710 | 0.868549 | − | 0.495603i | \(-0.165053\pi\) | ||||
0.868549 | + | 0.495603i | \(0.165053\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8003.11 | + | 13861.8i | −0.735591 | + | 1.27408i | 0.218872 | + | 0.975753i | \(0.429762\pi\) |
−0.954464 | + | 0.298328i | \(0.903571\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2477.35 | − | 4290.90i | −0.226317 | − | 0.391993i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 183.237 | + | 317.376i | 0.0165378 | + | 0.0286444i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4930.29 | + | 8539.50i | −0.442304 | + | 0.766094i | −0.997860 | − | 0.0653857i | \(-0.979172\pi\) |
0.555556 | + | 0.831479i | \(0.312506\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10512.0 | −0.931825 | −0.465913 | − | 0.884831i | \(-0.654274\pi\) | ||||
−0.465913 | + | 0.884831i | \(0.654274\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25413.9 | −2.23941 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8333.63 | − | 14434.3i | 0.725700 | − | 1.25695i | −0.232985 | − | 0.972480i | \(-0.574849\pi\) |
0.958685 | − | 0.284470i | \(-0.0918175\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −205.558 | − | 356.038i | −0.0177952 | − | 0.0308223i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8730.18 | − | 15121.1i | −0.746986 | − | 1.29382i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13029.3 | − | 22567.4i | 1.10837 | − | 1.91976i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10923.9 | −0.918586 | −0.459293 | − | 0.888285i | \(-0.651897\pi\) | ||||
−0.459293 | + | 0.888285i | \(0.651897\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17488.0 | −1.46213 | −0.731067 | − | 0.682305i | \(-0.760978\pi\) | ||||
−0.731067 | + | 0.682305i | \(0.760978\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18341.9 | − | 31769.1i | 1.51610 | − | 2.62596i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5151.35 | + | 8922.41i | 0.423387 | + | 0.733328i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4895.03 | + | 8478.43i | 0.397799 | + | 0.689009i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17594.6 | + | 30474.8i | −1.42184 | + | 2.46269i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22433.3 | −1.79271 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8724.14 | −0.693309 | −0.346655 | − | 0.937993i | \(-0.612682\pi\) | ||||
−0.346655 | + | 0.937993i | \(0.612682\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11864.5 | + | 20549.9i | −0.932510 | + | 1.61515i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 479.917 | + | 831.241i | 0.0375133 | + | 0.0649749i | 0.884172 | − | 0.467161i | \(-0.154723\pi\) |
−0.846659 | + | 0.532136i | \(0.821390\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 555.270 | + | 961.757i | 0.0429316 | + | 0.0743597i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 234.541 | − | 406.237i | 0.0180356 | − | 0.0312386i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14212.0 | 1.08112 | 0.540558 | − | 0.841307i | \(-0.318213\pi\) | ||||
0.540558 | + | 0.841307i | \(0.318213\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11490.5 | −0.869405 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3555.28 | + | 6157.93i | −0.266141 | + | 0.460969i | −0.967862 | − | 0.251483i | \(-0.919082\pi\) |
0.701721 | + | 0.712452i | \(0.252415\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9943.35 | − | 17222.4i | −0.740389 | − | 1.28239i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2429.59 | + | 4208.17i | 0.179005 | + | 0.310045i | 0.941540 | − | 0.336901i | \(-0.109379\pi\) |
−0.762535 | + | 0.646947i | \(0.776046\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4290.14 | + | 7430.74i | −0.314425 | + | 0.544601i | −0.979315 | − | 0.202341i | \(-0.935145\pi\) |
0.664890 | + | 0.746941i | \(0.268478\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8869.49 | 0.643276 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1029.99 | −0.0743136 | −0.0371568 | − | 0.999309i | \(-0.511830\pi\) | ||||
−0.0371568 | + | 0.999309i | \(0.511830\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −538.255 | + | 932.286i | −0.0384348 | + | 0.0665709i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3511.25 | + | 6081.66i | 0.249436 | + | 0.432036i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7770.72 | + | 13459.3i | 0.546391 | + | 0.946378i | 0.998518 | + | 0.0544239i | \(0.0173322\pi\) |
−0.452126 | + | 0.891954i | \(0.649334\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4111.12 | + | 7120.68i | −0.287599 | + | 0.498136i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12643.5 | 0.875562 | 0.437781 | − | 0.899082i | \(-0.355765\pi\) | ||||
0.437781 | + | 0.899082i | \(0.355765\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1860.31 | −0.128177 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8581.46 | − | 14863.5i | 0.585357 | − | 1.01387i | −0.409474 | − | 0.912322i | \(-0.634288\pi\) |
0.994831 | − | 0.101546i | \(-0.0323789\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2005.09 | + | 3472.92i | 0.136089 | + | 0.235713i | 0.926013 | − | 0.377492i | \(-0.123213\pi\) |
−0.789924 | + | 0.613205i | \(0.789880\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 26934.3 | + | 46651.6i | 1.80998 | + | 3.13497i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8660.58 | + | 15000.6i | −0.579114 | + | 1.00305i | 0.416468 | + | 0.909151i | \(0.363268\pi\) |
−0.995581 | + | 0.0939037i | \(0.970065\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12654.1 | −0.837855 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2474.79 | 0.163060 | 0.0815300 | − | 0.996671i | \(-0.474019\pi\) | ||||
0.0815300 | + | 0.996671i | \(0.474019\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5922.19 | − | 10257.5i | 0.386416 | − | 0.669291i | −0.605549 | − | 0.795808i | \(-0.707046\pi\) |
0.991964 | + | 0.126517i | \(0.0403797\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3924.32 | + | 6797.12i | 0.254817 | + | 0.441356i | 0.964846 | − | 0.262817i | \(-0.0846515\pi\) |
−0.710029 | + | 0.704173i | \(0.751318\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −544.119 | − | 942.442i | −0.0349914 | − | 0.0606069i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −447.377 | + | 774.880i | −0.0286322 | + | 0.0495924i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12961.7 | 0.821649 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11346.0 | −0.715811 | −0.357906 | − | 0.933758i | \(-0.616509\pi\) | ||||
−0.357906 | + | 0.933758i | \(0.616509\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11824.9 | + | 20481.3i | −0.738985 | + | 1.27996i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5446.80 | + | 9434.14i | 0.338791 | + | 0.586804i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8792.62 | + | 15229.3i | 0.541791 | + | 0.938409i | 0.998801 | + | 0.0489477i | \(0.0155868\pi\) |
−0.457011 | + | 0.889461i | \(0.651080\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5322.44 | − | 9218.73i | 0.326433 | − | 0.565399i | −0.655368 | − | 0.755309i | \(-0.727487\pi\) |
0.981801 | + | 0.189911i | \(0.0608199\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7872.89 | −0.478385 | −0.239193 | − | 0.970972i | \(-0.576883\pi\) | ||||
−0.239193 | + | 0.970972i | \(0.576883\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12381.4 | −0.748862 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1360.54 | + | 2356.53i | −0.0815347 | + | 0.141222i | −0.903909 | − | 0.427724i | \(-0.859315\pi\) |
0.822375 | + | 0.568946i | \(0.192649\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17792.7 | − | 30817.8i | −1.06140 | − | 1.83840i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1000.38 | − | 1732.71i | −0.0591338 | − | 0.102423i | 0.834943 | − | 0.550336i | \(-0.185501\pi\) |
−0.894077 | + | 0.447914i | \(0.852167\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13869.0 | − | 24021.8i | 0.816100 | − | 1.41353i | −0.0924356 | − | 0.995719i | \(-0.529465\pi\) |
0.908535 | − | 0.417808i | \(-0.137201\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 416.968 | 0.0243148 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1719.44 | −0.0998153 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3244.39 | − | 5619.46i | 0.186659 | − | 0.323304i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12346.5 | + | 21384.8i | 0.707166 | + | 1.22485i | 0.965904 | + | 0.258900i | \(0.0833601\pi\) |
−0.258738 | + | 0.965948i | \(0.583307\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7382.36 | − | 12786.6i | −0.419095 | − | 0.725893i | 0.576754 | − | 0.816918i | \(-0.304319\pi\) |
−0.995849 | + | 0.0910246i | \(0.970986\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 388.604 | − | 673.082i | 0.0219635 | − | 0.0380420i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −571.548 | −0.0320200 | −0.0160100 | − | 0.999872i | \(-0.505096\pi\) | ||||
−0.0160100 | + | 0.999872i | \(0.505096\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46424.6 | −2.58948 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1705.07 | − | 2953.26i | 0.0942784 | − | 0.163295i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1753.79 | + | 3037.66i | 0.0965519 | + | 0.167233i | 0.910255 | − | 0.414048i | \(-0.135885\pi\) |
−0.813703 | + | 0.581280i | \(0.802552\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1865.56 | + | 3231.24i | 0.101819 | + | 0.176357i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19138.5 | + | 33148.9i | −1.04006 | + | 1.80144i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21145.2 | −1.13929 | −0.569644 | − | 0.821891i | \(-0.692919\pi\) | ||||
−0.569644 | + | 0.821891i | \(0.692919\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2905.22 | −0.155864 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 575.006 | − | 995.939i | 0.0305874 | − | 0.0529790i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7907.61 | + | 13696.4i | 0.418867 | + | 0.725499i | 0.995826 | − | 0.0912745i | \(-0.0290941\pi\) |
−0.576959 | + | 0.816773i | \(0.695761\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6365.20 | − | 11024.9i | −0.334332 | − | 0.579080i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18953.7 | − | 32828.7i | 0.991367 | − | 1.71710i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33309.8 | 1.72774 | 0.863871 | − | 0.503713i | \(-0.168033\pi\) | ||||
0.863871 | + | 0.503713i | \(0.168033\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 790.104 | 0.0408114 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4090.17 | − | 7084.38i | 0.209524 | − | 0.362906i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3518.65 | − | 6094.48i | −0.179504 | − | 0.310910i | 0.762207 | − | 0.647334i | \(-0.224116\pi\) |
−0.941711 | + | 0.336424i | \(0.890783\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22462.8 | − | 38906.7i | −1.13655 | − | 1.96856i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6330.63 | + | 10965.0i | −0.319000 | + | 0.552524i | −0.980280 | − | 0.197615i | \(-0.936680\pi\) |
0.661280 | + | 0.750140i | \(0.270014\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27854.4 | 1.39217 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32709.4 | 1.62819 | 0.814096 | − | 0.580730i | \(-0.197233\pi\) | ||||
0.814096 | + | 0.580730i | \(0.197233\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14690.6 | − | 25444.8i | 0.725364 | − | 1.25637i | −0.233460 | − | 0.972366i | \(-0.575005\pi\) |
0.958824 | − | 0.284001i | \(-0.0916619\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1492.74 | − | 2585.49i | −0.0734089 | − | 0.127148i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −796.180 | − | 1379.02i | −0.0388408 | − | 0.0672743i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1112.82 | + | 1927.46i | −0.0540712 | + | 0.0936540i | −0.891794 | − | 0.452442i | \(-0.850553\pi\) |
0.837723 | + | 0.546096i | \(0.183886\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −62307.1 | −3.00343 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32628.1 | 1.56656 | 0.783281 | − | 0.621668i | \(-0.213545\pi\) | ||||
0.783281 | + | 0.621668i | \(0.213545\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9345.32 | + | 16186.6i | −0.445161 | + | 0.771041i | −0.998063 | − | 0.0622046i | \(-0.980187\pi\) |
0.552903 | + | 0.833246i | \(0.313520\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −536.882 | − | 929.908i | −0.0254737 | − | 0.0441218i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3006.20 | + | 5206.89i | 0.141522 | + | 0.245124i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3422.83 | + | 5928.52i | −0.160508 | + | 0.278008i | −0.935051 | − | 0.354513i | \(-0.884647\pi\) |
0.774543 | + | 0.632521i | \(0.217980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −161.873 | −0.00753190 | −0.00376595 | − | 0.999993i | \(-0.501199\pi\) | ||||
−0.00376595 | + | 0.999993i | \(0.501199\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 60565.7 | 2.80721 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4289.69 | − | 7429.95i | 0.197296 | − | 0.341727i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14598.4 | − | 25285.2i | −0.668849 | − | 1.15848i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8980.43 | − | 15554.6i | −0.408312 | − | 0.707218i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4979.56 | + | 8624.85i | −0.225543 | + | 0.390651i | −0.956482 | − | 0.291791i | \(-0.905749\pi\) |
0.730939 | + | 0.682442i | \(0.239082\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 899.899 | 0.0404510 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3150.96 | −0.141102 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2328.18 | − | 4032.53i | 0.103473 | − | 0.179221i | −0.809640 | − | 0.586927i | \(-0.800338\pi\) |
0.913114 | + | 0.407705i | \(0.133671\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24737.4 | − | 42846.5i | −1.09530 | − | 1.89712i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16376.7 | + | 28365.3i | 0.719704 | + | 1.24656i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −322.793 | + | 559.093i | −0.0141329 | + | 0.0244788i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 173.564 | 0.00754289 | 0.00377144 | − | 0.999993i | \(-0.498800\pi\) | ||||
0.00377144 | + | 0.999993i | \(0.498800\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22674.1 | −0.981744 | −0.490872 | − | 0.871232i | \(-0.663322\pi\) | ||||
−0.490872 | + | 0.871232i | \(0.663322\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25861.5 | + | 44793.5i | −1.11152 | + | 1.92521i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5034.78 | + | 8720.49i | 0.215599 | + | 0.373429i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20416.1 | − | 35361.7i | −0.867877 | − | 1.50321i | −0.864162 | − | 0.503214i | \(-0.832151\pi\) |
−0.00371541 | − | 0.999993i | \(-0.501183\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2440.51 | − | 4227.08i | 0.103367 | − | 0.179036i | −0.809703 | − | 0.586840i | \(-0.800372\pi\) |
0.913070 | + | 0.407804i | \(0.133705\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22213.4 | −0.934022 | −0.467011 | − | 0.884251i | \(-0.654669\pi\) | ||||
−0.467011 | + | 0.884251i | \(0.654669\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35477.2 | 1.48634 | 0.743168 | − | 0.669104i | \(-0.233322\pi\) | ||||
0.743168 | + | 0.669104i | \(0.233322\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21295.9 | + | 36885.5i | −0.885784 | + | 1.53422i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29137.5 | + | 50467.5i | 1.20760 | + | 2.09162i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11752.6 | − | 20356.2i | −0.483607 | − | 0.837631i | 0.516216 | − | 0.856458i | \(-0.327340\pi\) |
−0.999823 | + | 0.0188271i | \(0.994007\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11401.6 | − | 19748.1i | 0.467489 | − | 0.809714i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21528.0 | 0.876433 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2437.63 | −0.0988876 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2249.06 | − | 3895.48i | 0.0905954 | − | 0.156916i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6217.04 | + | 10768.2i | 0.249551 | + | 0.432236i | 0.963401 | − | 0.268063i | \(-0.0863835\pi\) |
−0.713850 | + | 0.700299i | \(0.753050\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −397.933 | − | 689.240i | −0.0158613 | − | 0.0274726i | 0.857986 | − | 0.513673i | \(-0.171716\pi\) |
−0.873847 | + | 0.486201i | \(0.838382\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4291.98 | − | 7433.92i | 0.170478 | − | 0.295276i | −0.768109 | − | 0.640319i | \(-0.778802\pi\) |
0.938587 | + | 0.345043i | \(0.112136\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37865.4 | 1.49357 | 0.746787 | − | 0.665063i | \(-0.231595\pi\) | ||||
0.746787 | + | 0.665063i | \(0.231595\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32458.3 | 1.27585 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18685.7 | + | 32364.6i | −0.729425 | + | 1.26340i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6763.06 | − | 11714.0i | −0.263097 | − | 0.455697i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −601.213 | − | 1041.33i | −0.0232283 | − | 0.0402325i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2302.28 | + | 3987.66i | −0.0886459 | + | 0.153539i | −0.906939 | − | 0.421262i | \(-0.861587\pi\) |
0.818293 | + | 0.574801i | \(0.194921\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13021.9 | −0.497979 | −0.248990 | − | 0.968506i | \(-0.580099\pi\) | ||||
−0.248990 | + | 0.968506i | \(0.580099\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4301.10 | −0.163923 | −0.0819613 | − | 0.996636i | \(-0.526118\pi\) | ||||
−0.0819613 | + | 0.996636i | \(0.526118\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7597.89 | − | 13159.9i | 0.287613 | − | 0.498160i | −0.685627 | − | 0.727953i | \(-0.740472\pi\) |
0.973239 | + | 0.229794i | \(0.0738051\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −535.091 | − | 926.804i | −0.0201871 | − | 0.0349651i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5544.61 | + | 9603.55i | 0.207775 | + | 0.359877i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11986.6 | − | 20761.3i | 0.447672 | − | 0.775391i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11741.2 | −0.435587 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13332.9 | 0.492990 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 31474.0 | − | 54514.5i | 1.15606 | − | 2.00235i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2328.99 | + | 4033.94i | 0.0852624 | + | 0.147679i | 0.905503 | − | 0.424340i | \(-0.139494\pi\) |
−0.820241 | + | 0.572019i | \(0.806160\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6446.40 | − | 11165.5i | −0.234444 | − | 0.406069i | 0.724667 | − | 0.689099i | \(-0.241994\pi\) |
−0.959111 | + | 0.283030i | \(0.908660\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42882.5 | − | 74274.7i | 1.55444 | − | 2.69237i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1610.28 | 0.0579894 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36405.3 | −1.30675 | −0.653373 | − | 0.757036i | \(-0.726647\pi\) | ||||
−0.653373 | + | 0.757036i | \(0.726647\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7088.99 | + | 12278.5i | −0.252803 | + | 0.437867i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10700.0 | + | 18533.0i | 0.380341 | + | 0.658770i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2139.85 | + | 3706.33i | 0.0755717 | + | 0.130894i | 0.901335 | − | 0.433123i | \(-0.142588\pi\) |
−0.825763 | + | 0.564017i | \(0.809255\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4773.23 | − | 8267.47i | 0.168030 | − | 0.291037i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 148210. | 5.18394 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21006.6 | 0.732396 | 0.366198 | − | 0.930537i | \(-0.380659\pi\) | ||||
0.366198 | + | 0.930537i | \(0.380659\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6764.54 | + | 11716.5i | −0.234344 | + | 0.405896i | −0.959082 | − | 0.283129i | \(-0.908628\pi\) |
0.724738 | + | 0.689025i | \(0.241961\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6641.67 | + | 11503.7i | 0.229356 | + | 0.397256i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2076.57 | − | 3596.73i | −0.0712561 | − | 0.123419i | 0.828196 | − | 0.560439i | \(-0.189367\pi\) |
−0.899452 | + | 0.437019i | \(0.856034\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7952.55 | − | 13774.2i | 0.272024 | − | 0.471159i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18387.5 | 0.625005 | 0.312503 | − | 0.949917i | \(-0.398833\pi\) | ||||
0.312503 | + | 0.949917i | \(0.398833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28926.0 | 0.980128 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1050.39 | − | 1819.32i | 0.0353689 | − | 0.0612607i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28569.6 | − | 49483.9i | −0.959000 | − | 1.66104i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6947.93 | − | 12034.2i | −0.231774 | − | 0.401444i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17227.0 | − | 29838.1i | 0.572889 | − | 0.992273i | −0.423378 | − | 0.905953i | \(-0.639156\pi\) |
0.996267 | − | 0.0863204i | \(-0.0275109\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2689.17 | 0.0888770 | 0.0444385 | − | 0.999012i | \(-0.485850\pi\) | ||||
0.0444385 | + | 0.999012i | \(0.485850\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −168.838 | −0.00556288 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 74.4796 | − | 129.002i | 0.00243891 | − | 0.00422431i | −0.864803 | − | 0.502111i | \(-0.832557\pi\) |
0.867242 | + | 0.497886i | \(0.165890\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43349.6 | + | 75083.8i | 1.41518 | + | 2.45116i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16110.9 | + | 27904.9i | 0.522744 | + | 0.905419i | 0.999650 | + | 0.0264649i | \(0.00842501\pi\) |
−0.476906 | + | 0.878955i | \(0.658242\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10830.4 | + | 18758.8i | −0.350340 | + | 0.606807i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15590.6 | −0.501265 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2979.37 | 0.0955023 | 0.0477512 | − | 0.998859i | \(-0.484795\pi\) | ||||
0.0477512 | + | 0.998859i | \(0.484795\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24614.1 | + | 42632.8i | −0.784240 | + | 1.35834i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16046.9 | + | 27794.1i | 0.509740 | + | 0.882896i | 0.999936 | + | 0.0112838i | \(0.00359182\pi\) |
−0.490196 | + | 0.871612i | \(0.663075\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 648.4.i.t.433.2 | 4 | ||
3.2 | odd | 2 | 648.4.i.n.433.1 | 4 | |||
9.2 | odd | 6 | 648.4.i.n.217.1 | 4 | |||
9.4 | even | 3 | 648.4.a.c.1.1 | ✓ | 2 | ||
9.5 | odd | 6 | 648.4.a.f.1.2 | yes | 2 | ||
9.7 | even | 3 | inner | 648.4.i.t.217.2 | 4 | ||
36.23 | even | 6 | 1296.4.a.q.1.2 | 2 | |||
36.31 | odd | 6 | 1296.4.a.m.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.4.a.c.1.1 | ✓ | 2 | 9.4 | even | 3 | ||
648.4.a.f.1.2 | yes | 2 | 9.5 | odd | 6 | ||
648.4.i.n.217.1 | 4 | 9.2 | odd | 6 | |||
648.4.i.n.433.1 | 4 | 3.2 | odd | 2 | |||
648.4.i.t.217.2 | 4 | 9.7 | even | 3 | inner | ||
648.4.i.t.433.2 | 4 | 1.1 | even | 1 | trivial | ||
1296.4.a.m.1.1 | 2 | 36.31 | odd | 6 | |||
1296.4.a.q.1.2 | 2 | 36.23 | even | 6 |