Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,3,Mod(890,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1143.890");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.1444942164\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 890.10 | ||
Character | \(\chi\) | \(=\) | 1143.890 |
Dual form | 1143.3.b.a.890.75 |
$q$-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 \(\left(\mathbb{Z}/1143\mathbb{Z}\right)^\times\).
\(n\) | \(128\) | \(892\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.21080i | − 1.60540i | −0.596384 | − | 0.802699i | \(-0.703396\pi\) | ||||
0.596384 | − | 0.802699i | \(-0.296604\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.30922 | −1.57730 | ||||||||
\(5\) | − 0.600942i | − 0.120188i | −0.998193 | − | 0.0600942i | \(-0.980860\pi\) | ||||
0.998193 | − | 0.0600942i | \(-0.0191401\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.4847 | 1.78352 | 0.891762 | − | 0.452504i | \(-0.149469\pi\) | ||||
0.891762 | + | 0.452504i | \(0.149469\pi\) | |||||||
\(8\) | 7.41443i | 0.926804i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.92950 | −0.192950 | ||||||||
\(11\) | 13.0330i | 1.18482i | 0.805637 | + | 0.592409i | \(0.201823\pi\) | ||||
−0.805637 | + | 0.592409i | \(0.798177\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.5720 | −1.27477 | −0.637384 | − | 0.770547i | \(-0.719983\pi\) | ||||
−0.637384 | + | 0.770547i | \(0.719983\pi\) | |||||||
\(14\) | − 40.0858i | − 2.86327i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.43064 | −0.0894147 | ||||||||
\(17\) | − 8.91048i | − 0.524146i | −0.965048 | − | 0.262073i | \(-0.915594\pi\) | ||||
0.965048 | − | 0.262073i | \(-0.0844061\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 36.7009 | 1.93163 | 0.965813 | − | 0.259240i | \(-0.0834722\pi\) | ||||
0.965813 | + | 0.259240i | \(0.0834722\pi\) | |||||||
\(20\) | 3.79147i | 0.189574i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 41.8463 | 1.90211 | ||||||||
\(23\) | 24.0665i | 1.04637i | 0.852220 | + | 0.523184i | \(0.175256\pi\) | ||||
−0.852220 | + | 0.523184i | \(0.824744\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.6389 | 0.985555 | ||||||||
\(26\) | 53.2092i | 2.04651i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −78.7685 | −2.81316 | ||||||||
\(29\) | − 31.9489i | − 1.10169i | −0.834608 | − | 0.550844i | \(-0.814306\pi\) | ||||
0.834608 | − | 0.550844i | \(-0.185694\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −22.1728 | −0.715251 | −0.357625 | − | 0.933865i | \(-0.616414\pi\) | ||||
−0.357625 | + | 0.933865i | \(0.616414\pi\) | |||||||
\(32\) | 34.2512i | 1.07035i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −28.6097 | −0.841463 | ||||||||
\(35\) | − 7.50256i | − 0.214359i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 51.0182 | 1.37887 | 0.689436 | − | 0.724347i | \(-0.257859\pi\) | ||||
0.689436 | + | 0.724347i | \(0.257859\pi\) | |||||||
\(38\) | − 117.839i | − 3.10103i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.45564 | 0.111391 | ||||||||
\(41\) | − 20.9151i | − 0.510125i | −0.966925 | − | 0.255062i | \(-0.917904\pi\) | ||||
0.966925 | − | 0.255062i | \(-0.0820960\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 23.4145 | 0.544523 | 0.272262 | − | 0.962223i | \(-0.412228\pi\) | ||||
0.272262 | + | 0.962223i | \(0.412228\pi\) | |||||||
\(44\) | − 82.2281i | − 1.86882i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 77.2725 | 1.67984 | ||||||||
\(47\) | − 36.6261i | − 0.779278i | −0.920968 | − | 0.389639i | \(-0.872600\pi\) | ||||
0.920968 | − | 0.389639i | \(-0.127400\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 106.867 | 2.18096 | ||||||||
\(50\) | − 79.1104i | − 1.58221i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 104.556 | 2.01070 | ||||||||
\(53\) | 6.11869i | 0.115447i | 0.998333 | + | 0.0577235i | \(0.0183842\pi\) | ||||
−0.998333 | + | 0.0577235i | \(0.981616\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.83207 | 0.142401 | ||||||||
\(56\) | 92.5668i | 1.65298i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −102.582 | −1.76865 | ||||||||
\(59\) | − 48.2618i | − 0.817996i | −0.912535 | − | 0.408998i | \(-0.865878\pi\) | ||||
0.912535 | − | 0.408998i | \(-0.134122\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 103.264 | 1.69285 | 0.846424 | − | 0.532509i | \(-0.178751\pi\) | ||||
0.846424 | + | 0.532509i | \(0.178751\pi\) | |||||||
\(62\) | 71.1923i | 1.14826i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 104.251 | 1.62892 | ||||||||
\(65\) | 9.95879i | 0.153212i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 39.6988 | 0.592520 | 0.296260 | − | 0.955107i | \(-0.404261\pi\) | ||||
0.296260 | + | 0.955107i | \(0.404261\pi\) | |||||||
\(68\) | 56.2182i | 0.826738i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −24.0892 | −0.344131 | ||||||||
\(71\) | 19.8363i | 0.279384i | 0.990195 | + | 0.139692i | \(0.0446113\pi\) | ||||
−0.990195 | + | 0.139692i | \(0.955389\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.6967 | 0.187625 | 0.0938127 | − | 0.995590i | \(-0.470095\pi\) | ||||
0.0938127 | + | 0.995590i | \(0.470095\pi\) | |||||||
\(74\) | − 163.809i | − 2.21364i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −231.554 | −3.04676 | ||||||||
\(77\) | 162.713i | 2.11315i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −81.4768 | −1.03135 | −0.515676 | − | 0.856784i | \(-0.672459\pi\) | ||||
−0.515676 | + | 0.856784i | \(0.672459\pi\) | |||||||
\(80\) | 0.859729i | 0.0107466i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −67.1542 | −0.818954 | ||||||||
\(83\) | − 64.4091i | − 0.776013i | −0.921657 | − | 0.388007i | \(-0.873164\pi\) | ||||
0.921657 | − | 0.388007i | \(-0.126836\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.35468 | −0.0629962 | ||||||||
\(86\) | − 75.1792i | − 0.874177i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −96.6323 | −1.09809 | ||||||||
\(89\) | − 106.593i | − 1.19768i | −0.800870 | − | 0.598838i | \(-0.795629\pi\) | ||||
0.800870 | − | 0.598838i | \(-0.204371\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −206.896 | −2.27358 | ||||||||
\(92\) | − 151.841i | − 1.65044i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −117.599 | −1.25105 | ||||||||
\(95\) | − 22.0551i | − 0.232159i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 97.3467 | 1.00357 | 0.501787 | − | 0.864991i | \(-0.332676\pi\) | ||||
0.501787 | + | 0.864991i | \(0.332676\pi\) | |||||||
\(98\) | − 343.129i | − 3.50131i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −155.452 | −1.55452 | ||||||||
\(101\) | − 149.590i | − 1.48109i | −0.672009 | − | 0.740543i | \(-0.734569\pi\) | ||||
0.672009 | − | 0.740543i | \(-0.265431\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −162.609 | −1.57873 | −0.789364 | − | 0.613925i | \(-0.789590\pi\) | ||||
−0.789364 | + | 0.613925i | \(0.789590\pi\) | |||||||
\(104\) | − 122.872i | − 1.18146i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 19.6459 | 0.185338 | ||||||||
\(107\) | 87.0737i | 0.813773i | 0.913479 | + | 0.406886i | \(0.133386\pi\) | ||||
−0.913479 | + | 0.406886i | \(0.866614\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −80.7161 | −0.740515 | −0.370257 | − | 0.928929i | \(-0.620731\pi\) | ||||
−0.370257 | + | 0.928929i | \(0.620731\pi\) | |||||||
\(110\) | − 25.1472i | − 0.228611i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −17.8610 | −0.159473 | ||||||||
\(113\) | 184.031i | 1.62859i | 0.580450 | + | 0.814296i | \(0.302876\pi\) | ||||
−0.580450 | + | 0.814296i | \(0.697124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.4625 | 0.125761 | ||||||||
\(116\) | 201.573i | 1.73770i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −154.959 | −1.31321 | ||||||||
\(119\) | − 111.244i | − 0.934827i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −48.8592 | −0.403795 | ||||||||
\(122\) | − 331.559i | − 2.71770i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 139.893 | 1.12817 | ||||||||
\(125\) | − 29.8301i | − 0.238640i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.2694 | −0.0887357 | ||||||||
\(128\) | − 197.724i | − 1.54472i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 31.9756 | 0.245967 | ||||||||
\(131\) | 220.741i | 1.68505i | 0.538659 | + | 0.842524i | \(0.318931\pi\) | ||||
−0.538659 | + | 0.842524i | \(0.681069\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 458.199 | 3.44510 | ||||||||
\(134\) | − 127.465i | − 0.951231i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 66.0662 | 0.485781 | ||||||||
\(137\) | 200.417i | 1.46290i | 0.681896 | + | 0.731450i | \(0.261156\pi\) | ||||
−0.681896 | + | 0.731450i | \(0.738844\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −196.038 | −1.41035 | −0.705173 | − | 0.709035i | \(-0.749131\pi\) | ||||
−0.705173 | + | 0.709035i | \(0.749131\pi\) | |||||||
\(140\) | 47.3353i | 0.338109i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 63.6903 | 0.448523 | ||||||||
\(143\) | − 215.983i | − 1.51037i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.1994 | −0.132410 | ||||||||
\(146\) | − 43.9772i | − 0.301214i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −321.885 | −2.17490 | ||||||||
\(149\) | 67.1955i | 0.450976i | 0.974246 | + | 0.225488i | \(0.0723977\pi\) | ||||
−0.974246 | + | 0.225488i | \(0.927602\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −67.9887 | −0.450257 | −0.225128 | − | 0.974329i | \(-0.572280\pi\) | ||||
−0.225128 | + | 0.974329i | \(0.572280\pi\) | |||||||
\(152\) | 272.116i | 1.79024i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 522.438 | 3.39245 | ||||||||
\(155\) | 13.3245i | 0.0859648i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −32.1609 | −0.204846 | −0.102423 | − | 0.994741i | \(-0.532660\pi\) | ||||
−0.102423 | + | 0.994741i | \(0.532660\pi\) | |||||||
\(158\) | 261.606i | 1.65573i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 20.5830 | 0.128644 | ||||||||
\(161\) | 300.462i | 1.86622i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −125.911 | −0.772461 | −0.386231 | − | 0.922402i | \(-0.626223\pi\) | ||||
−0.386231 | + | 0.922402i | \(0.626223\pi\) | |||||||
\(164\) | 131.958i | 0.804622i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −206.805 | −1.24581 | ||||||||
\(167\) | − 287.574i | − 1.72200i | −0.508603 | − | 0.861001i | \(-0.669838\pi\) | ||||
0.508603 | − | 0.861001i | \(-0.330162\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 105.630 | 0.625031 | ||||||||
\(170\) | 17.1928i | 0.101134i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −147.727 | −0.858879 | ||||||||
\(173\) | − 249.120i | − 1.44000i | −0.693973 | − | 0.720001i | \(-0.744141\pi\) | ||||
0.693973 | − | 0.720001i | \(-0.255859\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 307.608 | 1.75776 | ||||||||
\(176\) | − 18.6455i | − 0.105940i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −342.249 | −1.92275 | ||||||||
\(179\) | − 73.5806i | − 0.411065i | −0.978650 | − | 0.205532i | \(-0.934107\pi\) | ||||
0.978650 | − | 0.205532i | \(-0.0658926\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −72.5518 | −0.400839 | −0.200419 | − | 0.979710i | \(-0.564230\pi\) | ||||
−0.200419 | + | 0.979710i | \(0.564230\pi\) | |||||||
\(182\) | 664.300i | 3.65000i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −178.439 | −0.969778 | ||||||||
\(185\) | − 30.6590i | − 0.165724i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 116.130 | 0.621018 | ||||||||
\(188\) | 231.082i | 1.22916i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −70.8144 | −0.372707 | ||||||||
\(191\) | 72.5095i | 0.379631i | 0.981820 | + | 0.189816i | \(0.0607890\pi\) | ||||
−0.981820 | + | 0.189816i | \(0.939211\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 326.580 | 1.69212 | 0.846062 | − | 0.533084i | \(-0.178967\pi\) | ||||
0.846062 | + | 0.533084i | \(0.178967\pi\) | |||||||
\(194\) | − 312.560i | − 1.61114i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −674.248 | −3.44004 | ||||||||
\(197\) | 71.2897i | 0.361877i | 0.983494 | + | 0.180938i | \(0.0579134\pi\) | ||||
−0.983494 | + | 0.180938i | \(0.942087\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −29.7643 | −0.149569 | −0.0747847 | − | 0.997200i | \(-0.523827\pi\) | ||||
−0.0747847 | + | 0.997200i | \(0.523827\pi\) | |||||||
\(200\) | 182.683i | 0.913416i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −480.302 | −2.37773 | ||||||||
\(203\) | − 398.872i | − 1.96489i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.5688 | −0.0613110 | ||||||||
\(206\) | 522.105i | 2.53449i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 23.7085 | 0.113983 | ||||||||
\(209\) | 478.323i | 2.28863i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 338.681 | 1.60513 | 0.802563 | − | 0.596568i | \(-0.203469\pi\) | ||||
0.802563 | + | 0.596568i | \(0.203469\pi\) | |||||||
\(212\) | − 38.6042i | − 0.182095i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 279.576 | 1.30643 | ||||||||
\(215\) | − 14.0707i | − 0.0654453i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −276.820 | −1.27567 | ||||||||
\(218\) | 259.163i | 1.18882i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −49.4143 | −0.224610 | ||||||||
\(221\) | 147.664i | 0.668164i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 264.383 | 1.18557 | 0.592786 | − | 0.805360i | \(-0.298028\pi\) | ||||
0.592786 | + | 0.805360i | \(0.298028\pi\) | |||||||
\(224\) | 427.615i | 1.90900i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 590.886 | 2.61454 | ||||||||
\(227\) | 378.068i | 1.66550i | 0.553649 | + | 0.832750i | \(0.313235\pi\) | ||||
−0.553649 | + | 0.832750i | \(0.686765\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 207.425 | 0.905785 | 0.452893 | − | 0.891565i | \(-0.350392\pi\) | ||||
0.452893 | + | 0.891565i | \(0.350392\pi\) | |||||||
\(230\) | − 46.4363i | − 0.201897i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 236.883 | 1.02105 | ||||||||
\(233\) | − 285.957i | − 1.22728i | −0.789584 | − | 0.613642i | \(-0.789704\pi\) | ||||
0.789584 | − | 0.613642i | \(-0.210296\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.0101 | −0.0936601 | ||||||||
\(236\) | 304.494i | 1.29023i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −357.183 | −1.50077 | ||||||||
\(239\) | − 337.604i | − 1.41257i | −0.707927 | − | 0.706285i | \(-0.750370\pi\) | ||||
0.707927 | − | 0.706285i | \(-0.249630\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 298.039 | 1.23667 | 0.618337 | − | 0.785913i | \(-0.287807\pi\) | ||||
0.618337 | + | 0.785913i | \(0.287807\pi\) | |||||||
\(242\) | 156.877i | 0.648252i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −651.514 | −2.67014 | ||||||||
\(245\) | − 64.2209i | − 0.262126i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −608.206 | −2.46237 | ||||||||
\(248\) | − 164.399i | − 0.662897i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −95.7783 | −0.383113 | ||||||||
\(251\) | 30.2125i | 0.120368i | 0.998187 | + | 0.0601842i | \(0.0191688\pi\) | ||||
−0.998187 | + | 0.0601842i | \(0.980831\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −313.658 | −1.23976 | ||||||||
\(254\) | 36.1838i | 0.142456i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −217.849 | −0.850971 | ||||||||
\(257\) | − 428.708i | − 1.66813i | −0.551670 | − | 0.834063i | \(-0.686009\pi\) | ||||
0.551670 | − | 0.834063i | \(-0.313991\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 636.946 | 2.45925 | ||||||||
\(260\) | − 62.8322i | − 0.241662i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 708.756 | 2.70517 | ||||||||
\(263\) | 129.896i | 0.493902i | 0.969028 | + | 0.246951i | \(0.0794287\pi\) | ||||
−0.969028 | + | 0.246951i | \(0.920571\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.67698 | 0.0138754 | ||||||||
\(266\) | − 1471.18i | − 5.53076i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −250.469 | −0.934584 | ||||||||
\(269\) | − 105.796i | − 0.393293i | −0.980474 | − | 0.196647i | \(-0.936995\pi\) | ||||
0.980474 | − | 0.196647i | \(-0.0630052\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −154.578 | −0.570399 | −0.285200 | − | 0.958468i | \(-0.592060\pi\) | ||||
−0.285200 | + | 0.958468i | \(0.592060\pi\) | |||||||
\(272\) | 12.7477i | 0.0468664i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 643.499 | 2.34854 | ||||||||
\(275\) | 321.118i | 1.16770i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −286.356 | −1.03377 | −0.516887 | − | 0.856054i | \(-0.672909\pi\) | ||||
−0.516887 | + | 0.856054i | \(0.672909\pi\) | |||||||
\(278\) | 629.439i | 2.26417i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 55.6272 | 0.198669 | ||||||||
\(281\) | 185.828i | 0.661311i | 0.943751 | + | 0.330656i | \(0.107270\pi\) | ||||
−0.943751 | + | 0.330656i | \(0.892730\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 72.1935 | 0.255101 | 0.127550 | − | 0.991832i | \(-0.459289\pi\) | ||||
0.127550 | + | 0.991832i | \(0.459289\pi\) | |||||||
\(284\) | − 125.151i | − 0.440674i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −693.476 | −2.42474 | ||||||||
\(287\) | − 261.118i | − 0.909820i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 209.603 | 0.725271 | ||||||||
\(290\) | 61.6455i | 0.212571i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −86.4152 | −0.295942 | ||||||||
\(293\) | 345.539i | 1.17931i | 0.807654 | + | 0.589657i | \(0.200737\pi\) | ||||
−0.807654 | + | 0.589657i | \(0.799263\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.0025 | −0.0983136 | ||||||||
\(296\) | 378.271i | 1.27794i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 215.751 | 0.723997 | ||||||||
\(299\) | − 398.829i | − 1.33388i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 292.322 | 0.971171 | ||||||||
\(302\) | 218.298i | 0.722841i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −52.5056 | −0.172716 | ||||||||
\(305\) | − 62.0555i | − 0.203461i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −252.762 | −0.823328 | −0.411664 | − | 0.911336i | \(-0.635052\pi\) | ||||
−0.411664 | + | 0.911336i | \(0.635052\pi\) | |||||||
\(308\) | − 1026.59i | − 3.33309i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 42.7824 | 0.138008 | ||||||||
\(311\) | 410.767i | 1.32079i | 0.750917 | + | 0.660397i | \(0.229612\pi\) | ||||
−0.750917 | + | 0.660397i | \(0.770388\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 309.912 | 0.990134 | 0.495067 | − | 0.868855i | \(-0.335144\pi\) | ||||
0.495067 | + | 0.868855i | \(0.335144\pi\) | |||||||
\(314\) | 103.262i | 0.328860i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 514.055 | 1.62676 | ||||||||
\(317\) | − 354.995i | − 1.11986i | −0.828541 | − | 0.559928i | \(-0.810829\pi\) | ||||
0.828541 | − | 0.559928i | \(-0.189171\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 416.391 | 1.30530 | ||||||||
\(320\) | − 62.6488i | − 0.195778i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 964.722 | 2.99603 | ||||||||
\(323\) | − 327.023i | − 1.01245i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −408.315 | −1.25635 | ||||||||
\(326\) | 404.275i | 1.24011i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 155.074 | 0.472786 | ||||||||
\(329\) | − 457.265i | − 1.38986i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −234.603 | −0.708772 | −0.354386 | − | 0.935099i | \(-0.615310\pi\) | ||||
−0.354386 | + | 0.935099i | \(0.615310\pi\) | |||||||
\(332\) | 406.371i | 1.22401i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −923.343 | −2.76450 | ||||||||
\(335\) | − 23.8567i | − 0.0712140i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −613.452 | −1.82033 | −0.910167 | − | 0.414242i | \(-0.864047\pi\) | ||||
−0.910167 | + | 0.414242i | \(0.864047\pi\) | |||||||
\(338\) | − 339.157i | − 1.00342i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 33.7838 | 0.0993642 | ||||||||
\(341\) | − 288.978i | − 0.847442i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 722.452 | 2.10627 | ||||||||
\(344\) | 173.605i | 0.504666i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −799.875 | −2.31178 | ||||||||
\(347\) | 19.2791i | 0.0555592i | 0.999614 | + | 0.0277796i | \(0.00884366\pi\) | ||||
−0.999614 | + | 0.0277796i | \(0.991156\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 85.9984 | 0.246414 | 0.123207 | − | 0.992381i | \(-0.460682\pi\) | ||||
0.123207 | + | 0.992381i | \(0.460682\pi\) | |||||||
\(350\) | − 987.668i | − 2.82191i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −446.396 | −1.26817 | ||||||||
\(353\) | 16.0427i | 0.0454467i | 0.999742 | + | 0.0227233i | \(0.00723369\pi\) | ||||
−0.999742 | + | 0.0227233i | \(0.992766\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.9204 | 0.0335787 | ||||||||
\(356\) | 672.520i | 1.88910i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −236.252 | −0.659923 | ||||||||
\(359\) | 570.789i | 1.58994i | 0.606648 | + | 0.794971i | \(0.292514\pi\) | ||||
−0.606648 | + | 0.794971i | \(0.707486\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 985.955 | 2.73118 | ||||||||
\(362\) | 232.949i | 0.643506i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1305.35 | 3.58613 | ||||||||
\(365\) | − 8.23089i | − 0.0225504i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −89.6682 | −0.244328 | −0.122164 | − | 0.992510i | \(-0.538983\pi\) | ||||
−0.122164 | + | 0.992510i | \(0.538983\pi\) | |||||||
\(368\) | − 34.4304i | − 0.0935607i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −98.4398 | −0.266053 | ||||||||
\(371\) | 76.3899i | 0.205903i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −198.369 | −0.531820 | −0.265910 | − | 0.963998i | \(-0.585672\pi\) | ||||
−0.265910 | + | 0.963998i | \(0.585672\pi\) | |||||||
\(374\) | − 372.871i | − 0.996981i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 271.562 | 0.722238 | ||||||||
\(377\) | 529.457i | 1.40439i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −186.729 | −0.492689 | −0.246345 | − | 0.969182i | \(-0.579230\pi\) | ||||
−0.246345 | + | 0.969182i | \(0.579230\pi\) | |||||||
\(380\) | 139.150i | 0.366185i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 232.813 | 0.609459 | ||||||||
\(383\) | 210.931i | 0.550734i | 0.961339 | + | 0.275367i | \(0.0887994\pi\) | ||||
−0.961339 | + | 0.275367i | \(0.911201\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 97.7809 | 0.253976 | ||||||||
\(386\) | − 1048.58i | − 2.71653i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −614.181 | −1.58294 | ||||||||
\(389\) | 396.261i | 1.01867i | 0.860570 | + | 0.509333i | \(0.170108\pi\) | ||||
−0.860570 | + | 0.509333i | \(0.829892\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 214.444 | 0.548450 | ||||||||
\(392\) | 792.359i | 2.02132i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 228.897 | 0.580956 | ||||||||
\(395\) | 48.9628i | 0.123956i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −326.905 | −0.823437 | −0.411719 | − | 0.911311i | \(-0.635071\pi\) | ||||
−0.411719 | + | 0.911311i | \(0.635071\pi\) | |||||||
\(398\) | 95.5672i | 0.240119i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −35.2493 | −0.0881231 | ||||||||
\(401\) | − 721.209i | − 1.79853i | −0.437407 | − | 0.899264i | \(-0.644103\pi\) | ||||
0.437407 | − | 0.899264i | \(-0.355897\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 367.447 | 0.911778 | ||||||||
\(404\) | 943.793i | 2.33612i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1280.70 | −3.15443 | ||||||||
\(407\) | 664.921i | 1.63371i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 152.630 | 0.373178 | 0.186589 | − | 0.982438i | \(-0.440257\pi\) | ||||
0.186589 | + | 0.982438i | \(0.440257\pi\) | |||||||
\(410\) | 40.3557i | 0.0984287i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1025.94 | 2.49014 | ||||||||
\(413\) | − 602.533i | − 1.45892i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.7061 | −0.0932678 | ||||||||
\(416\) | − 567.610i | − 1.36445i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1535.80 | 3.67416 | ||||||||
\(419\) | 145.228i | 0.346605i | 0.984869 | + | 0.173303i | \(0.0554439\pi\) | ||||
−0.984869 | + | 0.173303i | \(0.944556\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −146.196 | −0.347259 | −0.173630 | − | 0.984811i | \(-0.555550\pi\) | ||||
−0.173630 | + | 0.984811i | \(0.555550\pi\) | |||||||
\(422\) | − 1087.44i | − 2.57687i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −45.3666 | −0.106997 | ||||||||
\(425\) | − 219.544i | − 0.516575i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1289.21 | 3.01924 | ||||||||
\(428\) | − 549.367i | − 1.28357i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −45.1783 | −0.105066 | ||||||||
\(431\) | 616.911i | 1.43135i | 0.698435 | + | 0.715674i | \(0.253880\pi\) | ||||
−0.698435 | + | 0.715674i | \(0.746120\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 81.3788 | 0.187942 | 0.0939709 | − | 0.995575i | \(-0.470044\pi\) | ||||
0.0939709 | + | 0.995575i | \(0.470044\pi\) | |||||||
\(434\) | 888.813i | 2.04796i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 509.256 | 1.16802 | ||||||||
\(437\) | 883.261i | 2.02119i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 105.870 | 0.241162 | 0.120581 | − | 0.992703i | \(-0.461524\pi\) | ||||
0.120581 | + | 0.992703i | \(0.461524\pi\) | |||||||
\(440\) | 58.0704i | 0.131978i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 474.120 | 1.07267 | ||||||||
\(443\) | − 143.172i | − 0.323188i | −0.986857 | − | 0.161594i | \(-0.948336\pi\) | ||||
0.986857 | − | 0.161594i | \(-0.0516635\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −64.0563 | −0.143947 | ||||||||
\(446\) | − 848.879i | − 1.90332i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1301.54 | 2.90523 | ||||||||
\(449\) | 868.777i | 1.93492i | 0.253032 | + | 0.967458i | \(0.418572\pi\) | ||||
−0.253032 | + | 0.967458i | \(0.581428\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 272.587 | 0.604405 | ||||||||
\(452\) | − 1161.09i | − 2.56878i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1213.90 | 2.67379 | ||||||||
\(455\) | 124.332i | 0.273258i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 427.913 | 0.936353 | 0.468176 | − | 0.883635i | \(-0.344911\pi\) | ||||
0.468176 | + | 0.883635i | \(0.344911\pi\) | |||||||
\(458\) | − 665.999i | − 1.45415i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −91.2473 | −0.198364 | ||||||||
\(461\) | − 53.8113i | − 0.116727i | −0.998295 | − | 0.0583637i | \(-0.981412\pi\) | ||||
0.998295 | − | 0.0583637i | \(-0.0185883\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −222.272 | −0.480068 | −0.240034 | − | 0.970764i | \(-0.577159\pi\) | ||||
−0.240034 | + | 0.970764i | \(0.577159\pi\) | |||||||
\(464\) | 45.7073i | 0.0985071i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −918.151 | −1.97028 | ||||||||
\(467\) | − 59.2741i | − 0.126925i | −0.997984 | − | 0.0634626i | \(-0.979786\pi\) | ||||
0.997984 | − | 0.0634626i | \(-0.0202144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 495.627 | 1.05677 | ||||||||
\(470\) | 70.6701i | 0.150362i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 357.834 | 0.758122 | ||||||||
\(473\) | 305.161i | 0.645161i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 904.268 | 1.90372 | ||||||||
\(476\) | 701.866i | 1.47451i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1083.98 | −2.26774 | ||||||||
\(479\) | 726.560i | 1.51683i | 0.651774 | + | 0.758413i | \(0.274025\pi\) | ||||
−0.651774 | + | 0.758413i | \(0.725975\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −845.473 | −1.75774 | ||||||||
\(482\) | − 956.942i | − 1.98536i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 308.263 | 0.636907 | ||||||||
\(485\) | − 58.4997i | − 0.120618i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −384.609 | −0.789752 | −0.394876 | − | 0.918734i | \(-0.629213\pi\) | ||||
−0.394876 | + | 0.918734i | \(0.629213\pi\) | |||||||
\(488\) | 765.642i | 1.56894i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −206.200 | −0.420817 | ||||||||
\(491\) | 266.424i | 0.542616i | 0.962493 | + | 0.271308i | \(0.0874562\pi\) | ||||
−0.962493 | + | 0.271308i | \(0.912544\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −284.680 | −0.577445 | ||||||||
\(494\) | 1952.83i | 3.95309i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 31.7212 | 0.0639540 | ||||||||
\(497\) | 247.650i | 0.498289i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −331.733 | −0.664795 | −0.332398 | − | 0.943139i | \(-0.607858\pi\) | ||||
−0.332398 | + | 0.943139i | \(0.607858\pi\) | |||||||
\(500\) | 188.204i | 0.376409i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 97.0061 | 0.193239 | ||||||||
\(503\) | − 356.706i | − 0.709157i | −0.935026 | − | 0.354579i | \(-0.884624\pi\) | ||||
0.935026 | − | 0.354579i | \(-0.115376\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −89.8946 | −0.178009 | ||||||||
\(506\) | 1007.09i | 1.99030i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 71.1013 | 0.139963 | ||||||||
\(509\) | 0.634209i | 0.00124599i | 1.00000 | 0.000622995i | \(0.000198306\pi\) | |||||
−1.00000 | 0.000622995i | \(0.999802\pi\) | ||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 170.998 | 0.334635 | ||||||||
\(512\) | − 91.4304i | − 0.178575i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1376.49 | −2.67801 | ||||||||
\(515\) | 97.7186i | 0.189745i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 477.348 | 0.923303 | ||||||||
\(518\) | − 2045.10i | − 3.94808i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −73.8388 | −0.141998 | ||||||||
\(521\) | 674.406i | 1.29445i | 0.762301 | + | 0.647223i | \(0.224070\pi\) | ||||
−0.762301 | + | 0.647223i | \(0.775930\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −177.818 | −0.339995 | −0.169998 | − | 0.985444i | \(-0.554376\pi\) | ||||
−0.169998 | + | 0.985444i | \(0.554376\pi\) | |||||||
\(524\) | − 1392.71i | − 2.65783i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 417.071 | 0.792910 | ||||||||
\(527\) | 197.570i | 0.374896i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −50.1948 | −0.0948861 | ||||||||
\(530\) | − 11.8060i | − 0.0222755i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2890.88 | −5.43398 | ||||||||
\(533\) | 346.605i | 0.650290i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 52.3262 | 0.0978060 | ||||||||
\(536\) | 294.344i | 0.549150i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −339.689 | −0.631393 | ||||||||
\(539\) | 1392.80i | 2.58404i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 82.7287 | 0.152918 | 0.0764590 | − | 0.997073i | \(-0.475639\pi\) | ||||
0.0764590 | + | 0.997073i | \(0.475639\pi\) | |||||||
\(542\) | 496.319i | 0.915718i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 305.195 | 0.561020 | ||||||||
\(545\) | 48.5057i | 0.0890012i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −352.774 | −0.644925 | −0.322462 | − | 0.946582i | \(-0.604511\pi\) | ||||
−0.322462 | + | 0.946582i | \(0.604511\pi\) | |||||||
\(548\) | − 1264.48i | − 2.30744i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1031.05 | 1.87463 | ||||||||
\(551\) | − 1172.55i | − 2.12805i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1017.21 | −1.83944 | ||||||||
\(554\) | 919.429i | 1.65962i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1236.85 | 2.22455 | ||||||||
\(557\) | − 758.420i | − 1.36162i | −0.732462 | − | 0.680808i | \(-0.761629\pi\) | ||||
0.732462 | − | 0.680808i | \(-0.238371\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −388.024 | −0.694140 | ||||||||
\(560\) | 10.7334i | 0.0191668i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 596.657 | 1.06167 | ||||||||
\(563\) | − 32.9364i | − 0.0585017i | −0.999572 | − | 0.0292508i | \(-0.990688\pi\) | ||||
0.999572 | − | 0.0292508i | \(-0.00931216\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 110.592 | 0.195738 | ||||||||
\(566\) | − 231.799i | − 0.409538i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −147.075 | −0.258934 | ||||||||
\(569\) | − 182.967i | − 0.321559i | −0.986990 | − | 0.160780i | \(-0.948599\pi\) | ||||
0.986990 | − | 0.160780i | \(-0.0514008\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −474.017 | −0.830152 | −0.415076 | − | 0.909787i | \(-0.636245\pi\) | ||||
−0.415076 | + | 0.909787i | \(0.636245\pi\) | |||||||
\(572\) | 1362.68i | 2.38231i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −838.398 | −1.46062 | ||||||||
\(575\) | 592.970i | 1.03125i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −874.351 | −1.51534 | −0.757670 | − | 0.652638i | \(-0.773662\pi\) | ||||
−0.757670 | + | 0.652638i | \(0.773662\pi\) | |||||||
\(578\) | − 672.994i | − 1.16435i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 121.133 | 0.208851 | ||||||||
\(581\) | − 804.127i | − 1.38404i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −79.7449 | −0.136784 | ||||||||
\(584\) | 101.553i | 0.173892i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1109.46 | 1.89327 | ||||||||
\(587\) | 4.68898i | 0.00798804i | 0.999992 | + | 0.00399402i | \(0.00127134\pi\) | ||||
−0.999992 | + | 0.00399402i | \(0.998729\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −813.761 | −1.38160 | ||||||||
\(590\) | 93.1212i | 0.157833i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −72.9885 | −0.123291 | ||||||||
\(593\) | 582.642i | 0.982533i | 0.871009 | + | 0.491267i | \(0.163466\pi\) | ||||
−0.871009 | + | 0.491267i | \(0.836534\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −66.8514 | −0.112355 | ||||||||
\(596\) | − 423.951i | − 0.711327i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1280.56 | −2.14140 | ||||||||
\(599\) | 725.223i | 1.21072i | 0.795951 | + | 0.605361i | \(0.206971\pi\) | ||||
−0.795951 | + | 0.605361i | \(0.793029\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1108.14 | 1.84382 | 0.921910 | − | 0.387403i | \(-0.126628\pi\) | ||||
0.921910 | + | 0.387403i | \(0.126628\pi\) | |||||||
\(602\) | − 938.588i | − 1.55912i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 428.956 | 0.710192 | ||||||||
\(605\) | 29.3615i | 0.0485314i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −280.661 | −0.462375 | −0.231187 | − | 0.972909i | \(-0.574261\pi\) | ||||
−0.231187 | + | 0.972909i | \(0.574261\pi\) | |||||||
\(608\) | 1257.05i | 2.06752i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −199.248 | −0.326635 | ||||||||
\(611\) | 606.966i | 0.993398i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 933.143 | 1.52226 | 0.761128 | − | 0.648602i | \(-0.224646\pi\) | ||||
0.761128 | + | 0.648602i | \(0.224646\pi\) | |||||||
\(614\) | 811.567i | 1.32177i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1206.42 | −1.95848 | ||||||||
\(617\) | 456.102i | 0.739225i | 0.929186 | + | 0.369613i | \(0.120510\pi\) | ||||
−0.929186 | + | 0.369613i | \(0.879490\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −817.095 | −1.32002 | −0.660012 | − | 0.751255i | \(-0.729449\pi\) | ||||
−0.660012 | + | 0.751255i | \(0.729449\pi\) | |||||||
\(620\) | − 84.0675i | − 0.135593i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1318.89 | 2.12040 | ||||||||
\(623\) | − 1330.78i | − 2.13609i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 598.046 | 0.956873 | ||||||||
\(626\) | − 995.064i | − 1.58956i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 202.910 | 0.323105 | ||||||||
\(629\) | − 454.597i | − 0.722730i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 350.841 | 0.556007 | 0.278004 | − | 0.960580i | \(-0.410327\pi\) | ||||
0.278004 | + | 0.960580i | \(0.410327\pi\) | |||||||
\(632\) | − 604.104i | − 0.955861i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1139.82 | −1.79782 | ||||||||
\(635\) | 6.77227i | 0.0106650i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1771.00 | −2.78022 | ||||||||
\(638\) | − 1336.95i | − 2.09553i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −118.821 | −0.185658 | ||||||||
\(641\) | 379.458i | 0.591979i | 0.955191 | + | 0.295989i | \(0.0956493\pi\) | ||||
−0.955191 | + | 0.295989i | \(0.904351\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −118.904 | −0.184920 | −0.0924601 | − | 0.995716i | \(-0.529473\pi\) | ||||
−0.0924601 | + | 0.995716i | \(0.529473\pi\) | |||||||
\(644\) | − 1895.68i | − 2.94360i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1050.00 | −1.62539 | ||||||||
\(647\) | 230.598i | 0.356411i | 0.983993 | + | 0.178205i | \(0.0570291\pi\) | ||||
−0.983993 | + | 0.178205i | \(0.942971\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 628.996 | 0.969177 | ||||||||
\(650\) | 1311.02i | 2.01695i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 794.401 | 1.21841 | ||||||||
\(653\) | − 1163.78i | − 1.78221i | −0.453801 | − | 0.891103i | \(-0.649932\pi\) | ||||
0.453801 | − | 0.891103i | \(-0.350068\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 132.653 | 0.202523 | ||||||||
\(656\) | 29.9219i | 0.0456127i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1468.18 | −2.23128 | ||||||||
\(659\) | − 578.497i | − 0.877841i | −0.898526 | − | 0.438920i | \(-0.855361\pi\) | ||||
0.898526 | − | 0.438920i | \(-0.144639\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 91.1558 | 0.137906 | 0.0689530 | − | 0.997620i | \(-0.478034\pi\) | ||||
0.0689530 | + | 0.997620i | \(0.478034\pi\) | |||||||
\(662\) | 753.264i | 1.13786i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 477.557 | 0.719212 | ||||||||
\(665\) | − 275.351i | − 0.414061i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 768.898 | 1.15277 | ||||||||
\(668\) | 1814.37i | 2.71612i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −76.5990 | −0.114327 | ||||||||
\(671\) | 1345.84i | 2.00572i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −517.141 | −0.768412 | −0.384206 | − | 0.923247i | \(-0.625525\pi\) | ||||
−0.384206 | + | 0.923247i | \(0.625525\pi\) | |||||||
\(674\) | 1969.67i | 2.92236i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −666.444 | −0.985864 | ||||||||
\(677\) | − 934.397i | − 1.38020i | −0.723713 | − | 0.690101i | \(-0.757566\pi\) | ||||
0.723713 | − | 0.690101i | \(-0.242434\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1215.34 | 1.78990 | ||||||||
\(680\) | − 39.7019i | − 0.0583851i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −927.849 | −1.36048 | ||||||||
\(683\) | − 637.476i | − 0.933346i | −0.884430 | − | 0.466673i | \(-0.845452\pi\) | ||||
0.884430 | − | 0.466673i | \(-0.154548\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 120.439 | 0.175823 | ||||||||
\(686\) | − 2319.65i | − 3.38141i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −33.4976 | −0.0486884 | ||||||||
\(689\) | − 101.399i | − 0.147168i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −259.071 | −0.374922 | −0.187461 | − | 0.982272i | \(-0.560026\pi\) | ||||
−0.187461 | + | 0.982272i | \(0.560026\pi\) | |||||||
\(692\) | 1571.75i | 2.27132i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 61.9011 | 0.0891947 | ||||||||
\(695\) | 117.807i | 0.169507i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −186.364 | −0.267380 | ||||||||
\(698\) | − 276.123i | − 0.395592i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1940.77 | −2.77253 | ||||||||
\(701\) | − 472.819i | − 0.674492i | −0.941417 | − | 0.337246i | \(-0.890505\pi\) | ||||
0.941417 | − | 0.337246i | \(-0.109495\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1872.41 | 2.66346 | ||||||||
\(704\) | 1358.71i | 1.92998i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 51.5098 | 0.0729600 | ||||||||
\(707\) | − 1867.58i | − 2.64155i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1096.90 | −1.54710 | −0.773552 | − | 0.633732i | \(-0.781522\pi\) | ||||
−0.773552 | + | 0.633732i | \(0.781522\pi\) | |||||||
\(710\) | − 38.2741i | − 0.0539072i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 790.328 | 1.11001 | ||||||||
\(713\) | − 533.620i | − 0.748416i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −129.793 | −0.181529 | ||||||||
\(716\) | 464.236i | 0.648375i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1832.69 | 2.55249 | ||||||||
\(719\) | 1144.75i | 1.59214i | 0.605202 | + | 0.796072i | \(0.293092\pi\) | ||||
−0.605202 | + | 0.796072i | \(0.706908\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2030.12 | −2.81570 | ||||||||
\(722\) | − 3165.70i | − 4.38463i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 457.745 | 0.632245 | ||||||||
\(725\) | − 787.186i | − 1.08577i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 58.4006 | 0.0803309 | 0.0401654 | − | 0.999193i | \(-0.487212\pi\) | ||||
0.0401654 | + | 0.999193i | \(0.487212\pi\) | |||||||
\(728\) | − 1534.01i | − 2.10716i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −26.4277 | −0.0362023 | ||||||||
\(731\) | − 208.634i | − 0.285410i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −470.767 | −0.642247 | −0.321123 | − | 0.947037i | \(-0.604060\pi\) | ||||
−0.321123 | + | 0.947037i | \(0.604060\pi\) | |||||||
\(734\) | 287.907i | 0.392243i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −824.306 | −1.11998 | ||||||||
\(737\) | 517.395i | 0.702029i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −666.625 | −0.902063 | −0.451031 | − | 0.892508i | \(-0.648944\pi\) | ||||
−0.451031 | + | 0.892508i | \(0.648944\pi\) | |||||||
\(740\) | 193.434i | 0.261398i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 245.272 | 0.330556 | ||||||||
\(743\) | − 441.655i | − 0.594421i | −0.954812 | − | 0.297210i | \(-0.903944\pi\) | ||||
0.954812 | − | 0.297210i | \(-0.0960563\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.3806 | 0.0542021 | ||||||||
\(746\) | 636.923i | 0.853784i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −732.692 | −0.979534 | ||||||||
\(749\) | 1087.09i | 1.45138i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −521.623 | −0.694572 | −0.347286 | − | 0.937759i | \(-0.612897\pi\) | ||||
−0.347286 | + | 0.937759i | \(0.612897\pi\) | |||||||
\(752\) | 52.3986i | 0.0696790i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1699.98 | 2.25461 | ||||||||
\(755\) | 40.8573i | 0.0541156i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1155.22 | 1.52605 | 0.763023 | − | 0.646371i | \(-0.223714\pi\) | ||||
0.763023 | + | 0.646371i | \(0.223714\pi\) | |||||||
\(758\) | 599.550i | 0.790963i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 163.526 | 0.215166 | ||||||||
\(761\) | − 355.823i | − 0.467573i | −0.972288 | − | 0.233787i | \(-0.924888\pi\) | ||||
0.972288 | − | 0.233787i | \(-0.0751117\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1007.71 | −1.32073 | ||||||||
\(764\) | − 457.479i | − 0.598794i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 677.257 | 0.884148 | ||||||||
\(767\) | 799.793i | 1.04275i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −572.981 | −0.745099 | −0.372549 | − | 0.928012i | \(-0.621516\pi\) | ||||
−0.372549 | + | 0.928012i | \(0.621516\pi\) | |||||||
\(770\) | − 313.955i | − 0.407733i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2060.46 | −2.66900 | ||||||||
\(773\) | 1135.65i | 1.46915i | 0.678530 | + | 0.734573i | \(0.262617\pi\) | ||||
−0.678530 | + | 0.734573i | \(0.737383\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −546.312 | −0.704919 | ||||||||
\(776\) | 721.770i | 0.930116i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1272.31 | 1.63536 | ||||||||
\(779\) | − 767.603i | − 0.985370i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −258.526 | −0.331020 | ||||||||
\(782\) | − 688.535i | − 0.880480i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −152.888 | −0.195010 | ||||||||
\(785\) | 19.3268i | 0.0246201i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1434.07 | −1.82220 | −0.911101 | − | 0.412184i | \(-0.864766\pi\) | ||||
−0.911101 | + | 0.412184i | \(0.864766\pi\) | |||||||
\(788\) | − 449.782i | − 0.570790i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 157.210 | 0.199000 | ||||||||
\(791\) | 2297.56i | 2.90463i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1711.28 | −2.15799 | ||||||||
\(794\) | 1049.62i | 1.32195i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 187.790 | 0.235917 | ||||||||
\(797\) | 882.755i | 1.10760i | 0.832651 | + | 0.553799i | \(0.186822\pi\) | ||||
−0.832651 | + | 0.553799i | \(0.813178\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −326.356 | −0.408456 | ||||||||
\(800\) | 843.911i | 1.05489i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2315.66 | −2.88735 | ||||||||
\(803\) | 178.509i | 0.222302i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 180.560 | 0.224298 | ||||||||
\(806\) | − 1179.80i | − 1.46377i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1109.12 | 1.37268 | ||||||||
\(809\) | − 346.433i | − 0.428223i | −0.976809 | − | 0.214112i | \(-0.931314\pi\) | ||||
0.976809 | − | 0.214112i | \(-0.0686856\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.2606 | −0.0397788 | −0.0198894 | − | 0.999802i | \(-0.506331\pi\) | ||||
−0.0198894 | + | 0.999802i | \(0.506331\pi\) | |||||||
\(812\) | 2516.57i | 3.09923i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2134.93 | 2.62276 | ||||||||
\(815\) | 75.6653i | 0.0928408i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 859.333 | 1.05182 | ||||||||
\(818\) | − 490.064i | − 0.599100i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 79.2991 | 0.0967062 | ||||||||
\(821\) | 198.978i | 0.242360i | 0.992631 | + | 0.121180i | \(0.0386679\pi\) | ||||
−0.992631 | + | 0.121180i | \(0.961332\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.0628 | 0.0328831 | 0.0164415 | − | 0.999865i | \(-0.494766\pi\) | ||||
0.0164415 | + | 0.999865i | \(0.494766\pi\) | |||||||
\(824\) | − 1205.65i | − 1.46317i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1934.61 | −2.34214 | ||||||||
\(827\) | − 614.445i | − 0.742980i | −0.928437 | − | 0.371490i | \(-0.878847\pi\) | ||||
0.928437 | − | 0.371490i | \(-0.121153\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1310.05 | −1.58028 | −0.790138 | − | 0.612928i | \(-0.789991\pi\) | ||||
−0.790138 | + | 0.612928i | \(0.789991\pi\) | |||||||
\(830\) | 124.277i | 0.149732i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1727.65 | −2.07650 | ||||||||
\(833\) | − 952.237i | − 1.14314i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −172.815 | −0.206964 | ||||||||
\(836\) | − 3017.84i | − 3.60986i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 466.297 | 0.556440 | ||||||||
\(839\) | − 783.420i | − 0.933755i | −0.884322 | − | 0.466877i | \(-0.845379\pi\) | ||||
0.884322 | − | 0.466877i | \(-0.154621\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −179.735 | −0.213715 | ||||||||
\(842\) | 469.406i | 0.557490i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2136.82 | −2.53177 | ||||||||
\(845\) | − 63.4776i | − 0.0751214i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −609.991 | −0.720178 | ||||||||
\(848\) | − 8.75362i | − 0.0103227i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −704.912 | −0.829308 | ||||||||
\(851\) | 1227.83i | 1.44281i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1370.99 | −1.60726 | −0.803629 | − | 0.595131i | \(-0.797100\pi\) | ||||
−0.803629 | + | 0.595131i | \(0.797100\pi\) | |||||||
\(854\) | − 4139.41i | − 4.84708i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −645.602 | −0.754208 | ||||||||
\(857\) | 1542.77i | 1.80020i | 0.435685 | + | 0.900099i | \(0.356506\pi\) | ||||
−0.435685 | + | 0.900099i | \(0.643494\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1041.40 | −1.21234 | −0.606169 | − | 0.795336i | \(-0.707294\pi\) | ||||
−0.606169 | + | 0.795336i | \(0.707294\pi\) | |||||||
\(860\) | 88.7754i | 0.103227i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1980.78 | 2.29788 | ||||||||
\(863\) | − 341.420i | − 0.395620i | −0.980240 | − | 0.197810i | \(-0.936617\pi\) | ||||
0.980240 | − | 0.197810i | \(-0.0633829\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −149.707 | −0.173071 | ||||||||
\(866\) | − 261.291i | − 0.301722i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1746.52 | 2.01212 | ||||||||
\(869\) | − 1061.89i | − 1.22196i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −657.888 | −0.755325 | ||||||||
\(872\) | − 598.464i | − 0.686312i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2835.97 | 3.24482 | ||||||||
\(875\) | − 372.419i | − 0.425621i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1453.08 | 1.65687 | 0.828436 | − | 0.560084i | \(-0.189231\pi\) | ||||
0.828436 | + | 0.560084i | \(0.189231\pi\) | |||||||
\(878\) | − 339.927i | − 0.387161i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −11.2048 | −0.0127328 | ||||||||
\(881\) | 799.175i | 0.907123i | 0.891225 | + | 0.453561i | \(0.149847\pi\) | ||||
−0.891225 | + | 0.453561i | \(0.850153\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 103.793 | 0.117546 | 0.0587729 | − | 0.998271i | \(-0.481281\pi\) | ||||
0.0587729 | + | 0.998271i | \(0.481281\pi\) | |||||||
\(884\) | − 931.646i | − 1.05390i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −459.697 | −0.518846 | ||||||||
\(887\) | 792.458i | 0.893414i | 0.894680 | + | 0.446707i | \(0.147403\pi\) | ||||
−0.894680 | + | 0.446707i | \(0.852597\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −140.695 | −0.158262 | ||||||||
\(890\) | 205.672i | 0.231092i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1668.05 | −1.87001 | ||||||||
\(893\) | − 1344.21i | − 1.50527i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −44.2177 | −0.0494052 | ||||||||
\(896\) | − 2468.53i | − 2.75505i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2789.47 | 3.10631 | ||||||||
\(899\) | 708.397i | 0.787983i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 54.5205 | 0.0605111 | ||||||||
\(902\) | − 875.221i | − 0.970311i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1364.48 | −1.50938 | ||||||||
\(905\) | 43.5994i | 0.0481761i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 710.256 | 0.783083 | 0.391542 | − | 0.920160i | \(-0.371942\pi\) | ||||
0.391542 | + | 0.920160i | \(0.371942\pi\) | |||||||
\(908\) | − 2385.32i | − 2.62700i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 399.206 | 0.438687 | ||||||||
\(911\) | − 215.745i | − 0.236822i | −0.992965 | − | 0.118411i | \(-0.962220\pi\) | ||||
0.992965 | − | 0.118411i | \(-0.0377800\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 839.444 | 0.919435 | ||||||||
\(914\) | − 1373.94i | − 1.50322i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1308.69 | −1.42870 | ||||||||
\(917\) | 2755.88i | 3.00533i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1340.47 | 1.45862 | 0.729311 | − | 0.684182i | \(-0.239841\pi\) | ||||
0.729311 | + | 0.684182i | \(0.239841\pi\) | |||||||
\(920\) | 107.232i | 0.116556i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −172.777 | −0.187394 | ||||||||
\(923\) | − 328.726i | − 0.356150i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1257.03 | 1.35895 | ||||||||
\(926\) | 713.669i | 0.770701i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1094.29 | 1.17919 | ||||||||
\(929\) | 415.150i | 0.446878i | 0.974718 | + | 0.223439i | \(0.0717284\pi\) | ||||
−0.974718 | + | 0.223439i | \(0.928272\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3922.12 | 4.21280 | ||||||||
\(932\) | 1804.17i | 1.93580i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −190.317 | −0.203766 | ||||||||
\(935\) | − 69.7875i | − 0.0746391i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 527.696 | 0.563176 | 0.281588 | − | 0.959535i | \(-0.409139\pi\) | ||||
0.281588 | + | 0.959535i | \(0.409139\pi\) | |||||||
\(938\) | − 1591.36i | − 1.69654i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 138.867 | 0.147731 | ||||||||
\(941\) | − 599.517i | − 0.637107i | −0.947905 | − | 0.318553i | \(-0.896803\pi\) | ||||
0.947905 | − | 0.318553i | \(-0.103197\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 503.353 | 0.533778 | ||||||||
\(944\) | 69.0450i | 0.0731409i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 979.811 | 1.03574 | ||||||||
\(947\) | − 1193.07i | − 1.25985i | −0.776658 | − | 0.629923i | \(-0.783087\pi\) | ||||
0.776658 | − | 0.629923i | \(-0.216913\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −226.981 | −0.239179 | ||||||||
\(950\) | − 2903.42i | − 3.05623i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 824.814 | 0.866402 | ||||||||
\(953\) | − 774.833i | − 0.813046i | −0.913640 | − | 0.406523i | \(-0.866741\pi\) | ||||
0.913640 | − | 0.406523i | \(-0.133259\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.5740 | 0.0456272 | ||||||||
\(956\) | 2130.02i | 2.22805i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2332.84 | 2.43511 | ||||||||
\(959\) | 2502.14i | 2.60912i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −469.368 | −0.488416 | ||||||||
\(962\) | 2714.64i | 2.82187i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1880.39 | −1.95061 | ||||||||
\(965\) | − 196.255i | − 0.203374i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.7164 | 0.0431400 | 0.0215700 | − | 0.999767i | \(-0.493134\pi\) | ||||
0.0215700 | + | 0.999767i | \(0.493134\pi\) | |||||||
\(968\) | − 362.263i | − 0.374239i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −187.831 | −0.193640 | ||||||||
\(971\) | − 1043.46i | − 1.07463i | −0.843382 | − | 0.537315i | \(-0.819439\pi\) | ||||
0.843382 | − | 0.537315i | \(-0.180561\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2447.47 | −2.51539 | ||||||||
\(974\) | 1234.90i | 1.26787i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −147.733 | −0.151366 | ||||||||
\(977\) | 255.000i | 0.261003i | 0.991448 | + | 0.130501i | \(0.0416587\pi\) | ||||
−0.991448 | + | 0.130501i | \(0.958341\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1389.23 | 1.41903 | ||||||||
\(980\) | 405.184i | 0.413453i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 855.435 | 0.871115 | ||||||||
\(983\) | 1287.67i | 1.30994i | 0.755654 | + | 0.654971i | \(0.227319\pi\) | ||||
−0.755654 | + | 0.654971i | \(0.772681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42.8409 | 0.0434933 | ||||||||
\(986\) | 914.051i | 0.927029i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3837.30 | 3.88391 | ||||||||
\(989\) | 563.504i | 0.569772i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1586.51 | −1.60092 | −0.800461 | − | 0.599384i | \(-0.795412\pi\) | ||||
−0.800461 | + | 0.599384i | \(0.795412\pi\) | |||||||
\(992\) | − 759.444i | − 0.765569i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 795.152 | 0.799952 | ||||||||
\(995\) | 17.8866i | 0.0179765i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1221.04 | 1.22471 | 0.612356 | − | 0.790582i | \(-0.290222\pi\) | ||||
0.612356 | + | 0.790582i | \(0.290222\pi\) | |||||||
\(998\) | 1065.13i | 1.06726i | ||||||||
\(999\) | 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 | 1143.3.b.a.890.10 | ✓ | 84 | |
3.2 | odd | 2 | inner | 1143.3.b.a.890.75 | yes | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1143.3.b.a.890.10 | ✓ | 84 | 1.1 | even | 1 | trivial | |
1143.3.b.a.890.75 | yes | 84 | 3.2 | odd | 2 | inner |