Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,3,Mod(2161,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4140.2161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.d (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: | \(112.806829445\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 1380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2161.18 | ||
Character | \(\chi\) | \(=\) | 4140.2161 |
Dual form | 4140.3.d.c.2161.15 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 11.5587i | − | 1.65125i | −0.564222 | − | 0.825623i | \(-0.690824\pi\) | ||
0.564222 | − | 0.825623i | \(-0.309176\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 6.61510i | − | 0.601373i | −0.953723 | − | 0.300686i | \(-0.902784\pi\) | ||
0.953723 | − | 0.300686i | \(-0.0972157\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.35365 | −0.334896 | −0.167448 | − | 0.985881i | \(-0.553553\pi\) | ||||
−0.167448 | + | 0.985881i | \(0.553553\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 15.5392i | − | 0.914068i | −0.889449 | − | 0.457034i | \(-0.848912\pi\) | ||
0.889449 | − | 0.457034i | \(-0.151088\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32.8419i | 1.72852i | 0.503043 | + | 0.864262i | \(0.332214\pi\) | ||||
−0.503043 | + | 0.864262i | \(0.667786\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.09068 | − | 22.7914i | 0.134377 | − | 0.990930i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −36.6564 | −1.26401 | −0.632007 | − | 0.774963i | \(-0.717769\pi\) | ||||
−0.632007 | + | 0.774963i | \(0.717769\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 41.7912 | 1.34810 | 0.674052 | − | 0.738684i | \(-0.264552\pi\) | ||||
0.674052 | + | 0.738684i | \(0.264552\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 25.8461 | 0.738460 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12.5508i | 0.339210i | 0.985512 | + | 0.169605i | \(0.0542491\pi\) | ||||
−0.985512 | + | 0.169605i | \(0.945751\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −40.5335 | −0.988621 | −0.494311 | − | 0.869285i | \(-0.664579\pi\) | ||||
−0.494311 | + | 0.869285i | \(0.664579\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 83.7540i | − | 1.94777i | −0.227046 | − | 0.973884i | \(-0.572907\pi\) | ||
0.227046 | − | 0.973884i | \(-0.427093\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 69.6716 | 1.48237 | 0.741187 | − | 0.671299i | \(-0.234263\pi\) | ||||
0.741187 | + | 0.671299i | \(0.234263\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −84.6040 | −1.72661 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 23.7139i | − | 0.447431i | −0.974654 | − | 0.223716i | \(-0.928181\pi\) | ||
0.974654 | − | 0.223716i | \(-0.0718187\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.7918 | 0.268942 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −45.4954 | −0.771108 | −0.385554 | − | 0.922685i | \(-0.625990\pi\) | ||||
−0.385554 | + | 0.922685i | \(0.625990\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 99.3377i | − | 1.62849i | −0.580524 | − | 0.814243i | \(-0.697152\pi\) | ||
0.580524 | − | 0.814243i | \(-0.302848\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 9.73505i | − | 0.149770i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 77.0336i | 1.14975i | 0.818240 | + | 0.574877i | \(0.194950\pi\) | ||||
−0.818240 | + | 0.574877i | \(0.805050\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −52.2590 | −0.736042 | −0.368021 | − | 0.929818i | \(-0.619965\pi\) | ||||
−0.368021 | + | 0.929818i | \(0.619965\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 91.3817 | 1.25180 | 0.625902 | − | 0.779902i | \(-0.284731\pi\) | ||||
0.625902 | + | 0.779902i | \(0.284731\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −76.4621 | −0.993014 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.5142i | 0.145749i | 0.997341 | + | 0.0728747i | \(0.0232173\pi\) | ||||
−0.997341 | + | 0.0728747i | \(0.976783\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 29.1026i | − | 0.350633i | −0.984512 | − | 0.175317i | \(-0.943905\pi\) | ||
0.984512 | − | 0.175317i | \(-0.0560949\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 34.7466 | 0.408784 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 31.3082i | 0.351777i | 0.984410 | + | 0.175889i | \(0.0562798\pi\) | ||||
−0.984410 | + | 0.175889i | \(0.943720\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 50.3226i | 0.552996i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −73.4368 | −0.773019 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 110.693i | − | 1.14116i | −0.821241 | − | 0.570582i | \(-0.806718\pi\) | ||
0.821241 | − | 0.570582i | \(-0.193282\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −165.111 | −1.63476 | −0.817379 | − | 0.576100i | \(-0.804574\pi\) | ||||
−0.817379 | + | 0.576100i | \(0.804574\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 74.1229i | 0.719640i | 0.933022 | + | 0.359820i | \(0.117162\pi\) | ||||
−0.933022 | + | 0.359820i | \(0.882838\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 43.9973i | 0.411190i | 0.978637 | + | 0.205595i | \(0.0659129\pi\) | ||||
−0.978637 | + | 0.205595i | \(0.934087\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 82.2989i | 0.755036i | 0.926002 | + | 0.377518i | \(0.123222\pi\) | ||||
−0.926002 | + | 0.377518i | \(0.876778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 112.935i | 0.999429i | 0.866190 | + | 0.499715i | \(0.166562\pi\) | ||||
−0.866190 | + | 0.499715i | \(0.833438\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 50.9631 | + | 6.91096i | 0.443157 | + | 0.0600953i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −179.613 | −1.50935 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 77.2404 | 0.638351 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −172.032 | −1.35458 | −0.677291 | − | 0.735715i | \(-0.736846\pi\) | ||||
−0.677291 | + | 0.735715i | \(0.736846\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 49.6869 | 0.379289 | 0.189645 | − | 0.981853i | \(-0.439266\pi\) | ||||
0.189645 | + | 0.981853i | \(0.439266\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 379.611 | 2.85422 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 184.096i | 1.34377i | 0.740657 | + | 0.671884i | \(0.234515\pi\) | ||||
−0.740657 | + | 0.671884i | \(0.765485\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 61.9715 | 0.445838 | 0.222919 | − | 0.974837i | \(-0.428441\pi\) | ||||
0.222919 | + | 0.974837i | \(0.428441\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 28.7998i | 0.201397i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 81.9662i | − | 0.565284i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 252.750i | − | 1.69631i | −0.529750 | − | 0.848154i | \(-0.677714\pi\) | ||
0.529750 | − | 0.848154i | \(-0.322286\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −167.183 | −1.10718 | −0.553588 | − | 0.832791i | \(-0.686742\pi\) | ||||
−0.553588 | + | 0.832791i | \(0.686742\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 93.4480i | 0.602890i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 238.657i | 1.52011i | 0.649859 | + | 0.760055i | \(0.274828\pi\) | ||||
−0.649859 | + | 0.760055i | \(0.725172\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −263.439 | − | 35.7243i | −1.63627 | − | 0.221890i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 109.935 | 0.674448 | 0.337224 | − | 0.941424i | \(-0.390512\pi\) | ||||
0.337224 | + | 0.941424i | \(0.390512\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −193.817 | −1.16058 | −0.580289 | − | 0.814410i | \(-0.697061\pi\) | ||||
−0.580289 | + | 0.814410i | \(0.697061\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −150.046 | −0.887845 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 182.435 | 1.05454 | 0.527268 | − | 0.849699i | \(-0.323216\pi\) | ||||
0.527268 | + | 0.849699i | \(0.323216\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 57.7936i | 0.330249i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −143.275 | −0.800419 | −0.400209 | − | 0.916424i | \(-0.631063\pi\) | ||||
−0.400209 | + | 0.916424i | \(0.631063\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 184.195i | 1.01765i | 0.860869 | + | 0.508826i | \(0.169920\pi\) | ||||
−0.860869 | + | 0.508826i | \(0.830080\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −28.0643 | −0.151699 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −102.793 | −0.549696 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 69.5741i | 0.364262i | 0.983274 | + | 0.182131i | \(0.0582995\pi\) | ||||
−0.983274 | + | 0.182131i | \(0.941700\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 246.167 | 1.27548 | 0.637739 | − | 0.770252i | \(-0.279870\pi\) | ||||
0.637739 | + | 0.770252i | \(0.279870\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −329.331 | −1.67173 | −0.835865 | − | 0.548935i | \(-0.815034\pi\) | ||||
−0.835865 | + | 0.548935i | \(0.815034\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 63.0077i | 0.316622i | 0.987389 | + | 0.158311i | \(0.0506048\pi\) | ||||
−0.987389 | + | 0.158311i | \(0.949395\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 423.701i | 2.08720i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 90.6356i | − | 0.442125i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 217.253 | 1.03949 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 38.9809 | 0.184744 | 0.0923719 | − | 0.995725i | \(-0.470555\pi\) | ||||
0.0923719 | + | 0.995725i | \(0.470555\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 187.280 | 0.871068 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 483.053i | − | 2.22605i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 67.6520i | 0.306118i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −414.767 | −1.85994 | −0.929971 | − | 0.367632i | \(-0.880169\pi\) | ||||
−0.929971 | + | 0.367632i | \(0.880169\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 190.504i | 0.839224i | 0.907703 | + | 0.419612i | \(0.137834\pi\) | ||||
−0.907703 | + | 0.419612i | \(0.862166\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 126.193i | 0.551063i | 0.961292 | + | 0.275532i | \(0.0888538\pi\) | ||||
−0.961292 | + | 0.275532i | \(0.911146\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −374.063 | −1.60542 | −0.802711 | − | 0.596368i | \(-0.796610\pi\) | ||||
−0.802711 | + | 0.596368i | \(0.796610\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 155.790i | 0.662938i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −112.894 | −0.472360 | −0.236180 | − | 0.971709i | \(-0.575896\pi\) | ||||
−0.236180 | + | 0.971709i | \(0.575896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 280.944i | − | 1.16574i | −0.812565 | − | 0.582870i | \(-0.801929\pi\) | ||
0.812565 | − | 0.582870i | \(-0.198071\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 189.180i | − | 0.772165i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 142.982i | − | 0.578875i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 389.074i | 1.55009i | 0.631904 | + | 0.775047i | \(0.282274\pi\) | ||||
−0.631904 | + | 0.775047i | \(0.717726\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −150.767 | − | 20.4451i | −0.595918 | − | 0.0808108i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −129.931 | −0.505568 | −0.252784 | − | 0.967523i | \(-0.581346\pi\) | ||||
−0.252784 | + | 0.967523i | \(0.581346\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 145.071 | 0.560118 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 439.611i | − | 1.67152i | −0.549091 | − | 0.835762i | \(-0.685026\pi\) | ||
0.549091 | − | 0.835762i | \(-0.314974\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 53.0258 | 0.200097 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −291.536 | −1.08378 | −0.541888 | − | 0.840450i | \(-0.682290\pi\) | ||||
−0.541888 | + | 0.840450i | \(0.682290\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 95.0531 | 0.350749 | 0.175375 | − | 0.984502i | \(-0.443886\pi\) | ||||
0.175375 | + | 0.984502i | \(0.443886\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 33.0755i | 0.120275i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 173.565 | 0.626587 | 0.313294 | − | 0.949656i | \(-0.398568\pi\) | ||||
0.313294 | + | 0.949656i | \(0.398568\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 254.496i | − | 0.905681i | −0.891591 | − | 0.452841i | \(-0.850411\pi\) | ||
0.891591 | − | 0.452841i | \(-0.149589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 49.3160i | − | 0.174261i | −0.996197 | − | 0.0871307i | \(-0.972230\pi\) | ||
0.996197 | − | 0.0871307i | \(-0.0277698\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 468.515i | 1.63246i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 47.5347 | 0.164480 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 425.822i | − | 1.45332i | −0.686999 | − | 0.726659i | \(-0.741072\pi\) | ||
0.686999 | − | 0.726659i | \(-0.258928\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 101.731i | − | 0.344850i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.4557 | + | 99.2257i | −0.0450024 | + | 0.331858i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −968.089 | −3.21624 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 222.126 | 0.728281 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −308.764 | −1.00575 | −0.502873 | − | 0.864360i | \(-0.667724\pi\) | ||||
−0.502873 | + | 0.864360i | \(0.667724\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 551.432 | 1.77309 | 0.886546 | − | 0.462640i | \(-0.153098\pi\) | ||||
0.886546 | + | 0.462640i | \(0.153098\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 193.853i | − | 0.619340i | −0.950844 | − | 0.309670i | \(-0.899781\pi\) | ||
0.950844 | − | 0.309670i | \(-0.100219\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −260.610 | −0.822113 | −0.411057 | − | 0.911610i | \(-0.634840\pi\) | ||||
−0.411057 | + | 0.911610i | \(0.634840\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 242.486i | 0.760143i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 510.336 | 1.57999 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.7682 | 0.0669792 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 805.314i | − | 2.44776i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −263.090 | −0.794834 | −0.397417 | − | 0.917638i | \(-0.630093\pi\) | ||||
−0.397417 | + | 0.917638i | \(0.630093\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −172.252 | −0.514186 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 348.620i | 1.03448i | 0.855840 | + | 0.517241i | \(0.173041\pi\) | ||||
−0.855840 | + | 0.517241i | \(0.826959\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 276.453i | − | 0.810713i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 411.537i | 1.19982i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −415.018 | −1.19602 | −0.598009 | − | 0.801489i | \(-0.704041\pi\) | ||||
−0.598009 | + | 0.801489i | \(0.704041\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 336.999 | 0.965612 | 0.482806 | − | 0.875727i | \(-0.339618\pi\) | ||||
0.482806 | + | 0.875727i | \(0.339618\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −435.958 | −1.23501 | −0.617505 | − | 0.786567i | \(-0.711856\pi\) | ||||
−0.617505 | + | 0.786567i | \(0.711856\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 116.855i | − | 0.329168i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 241.813i | − | 0.673575i | −0.941581 | − | 0.336788i | \(-0.890660\pi\) | ||
0.941581 | − | 0.336788i | \(-0.109340\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −717.593 | −1.98779 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 204.336i | 0.559824i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 429.459i | − | 1.17019i | −0.810966 | − | 0.585094i | \(-0.801058\pi\) | ||
0.810966 | − | 0.585094i | \(-0.198942\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −274.102 | −0.738819 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 422.643i | − | 1.13309i | −0.824030 | − | 0.566546i | \(-0.808280\pi\) | ||
0.824030 | − | 0.566546i | \(-0.191720\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 159.589 | 0.423313 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 678.289i | 1.78968i | 0.446386 | + | 0.894840i | \(0.352711\pi\) | ||||
−0.446386 | + | 0.894840i | \(0.647289\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 189.732i | − | 0.495385i | −0.968839 | − | 0.247692i | \(-0.920328\pi\) | ||
0.968839 | − | 0.247692i | \(-0.0796722\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 170.974i | − | 0.444090i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 150.076i | 0.385800i | 0.981218 | + | 0.192900i | \(0.0617894\pi\) | ||||
−0.981218 | + | 0.192900i | \(0.938211\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −354.159 | − | 48.0265i | −0.905777 | − | 0.122830i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −25.7465 | −0.0651811 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 654.883 | 1.64958 | 0.824789 | − | 0.565440i | \(-0.191294\pi\) | ||||
0.824789 | + | 0.565440i | \(0.191294\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 248.712i | 0.620230i | 0.950699 | + | 0.310115i | \(0.100367\pi\) | ||||
−0.950699 | + | 0.310115i | \(0.899633\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −181.944 | −0.451475 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 83.0245 | 0.203991 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −492.502 | −1.20416 | −0.602081 | − | 0.798435i | \(-0.705662\pi\) | ||||
−0.602081 | + | 0.798435i | \(0.705662\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 525.869i | 1.27329i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 65.0753 | 0.156808 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 131.015i | 0.312685i | 0.987703 | + | 0.156343i | \(0.0499704\pi\) | ||||
−0.987703 | + | 0.156343i | \(0.950030\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 119.454i | 0.283738i | 0.989885 | + | 0.141869i | \(0.0453112\pi\) | ||||
−0.989885 | + | 0.141869i | \(0.954689\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 77.6958i | 0.182814i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1148.22 | −2.68903 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 462.137i | − | 1.07224i | −0.844141 | − | 0.536121i | \(-0.819889\pi\) | ||
0.844141 | − | 0.536121i | \(-0.180111\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 88.9988i | 0.205540i | 0.994705 | + | 0.102770i | \(0.0327706\pi\) | ||||
−0.994705 | + | 0.102770i | \(0.967229\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 748.514 | + | 101.504i | 1.71285 | + | 0.232274i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −690.443 | −1.57276 | −0.786382 | − | 0.617741i | \(-0.788048\pi\) | ||||
−0.786382 | + | 0.617741i | \(0.788048\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −499.195 | −1.12685 | −0.563426 | − | 0.826167i | \(-0.690517\pi\) | ||||
−0.563426 | + | 0.826167i | \(0.690517\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −70.0072 | −0.157319 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 219.842 | 0.489627 | 0.244813 | − | 0.969570i | \(-0.421273\pi\) | ||||
0.244813 | + | 0.969570i | \(0.421273\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 268.133i | 0.594530i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −112.525 | −0.247307 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 28.0141i | − | 0.0613001i | −0.999530 | − | 0.0306501i | \(-0.990242\pi\) | ||
0.999530 | − | 0.0306501i | \(-0.00975774\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −527.172 | −1.14354 | −0.571771 | − | 0.820414i | \(-0.693743\pi\) | ||||
−0.571771 | + | 0.820414i | \(0.693743\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −66.6980 | −0.144056 | −0.0720281 | − | 0.997403i | \(-0.522947\pi\) | ||||
−0.0720281 | + | 0.997403i | \(0.522947\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 249.178i | 0.533571i | 0.963756 | + | 0.266785i | \(0.0859615\pi\) | ||||
−0.963756 | + | 0.266785i | \(0.914039\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 890.410 | 1.89853 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −554.041 | −1.17133 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 164.210i | − | 0.345705i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 669.591i | − | 1.39789i | −0.715174 | − | 0.698946i | \(-0.753653\pi\) | ||
0.715174 | − | 0.698946i | \(-0.246347\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 54.6416i | − | 0.113600i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 247.517 | 0.510344 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 42.3713 | 0.0870047 | 0.0435024 | − | 0.999053i | \(-0.486148\pi\) | ||||
0.0435024 | + | 0.999053i | \(0.486148\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 65.4718 | 0.133344 | 0.0666719 | − | 0.997775i | \(-0.478762\pi\) | ||||
0.0666719 | + | 0.997775i | \(0.478762\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 569.609i | 1.15539i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 604.047i | 1.21539i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 490.380 | 0.982725 | 0.491363 | − | 0.870955i | \(-0.336499\pi\) | ||||
0.491363 | + | 0.870955i | \(0.336499\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.7682i | 0.0611693i | 0.999532 | + | 0.0305847i | \(0.00973692\pi\) | ||||
−0.999532 | + | 0.0305847i | \(0.990263\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 369.198i | − | 0.731086i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 64.9076 | 0.127520 | 0.0637599 | − | 0.997965i | \(-0.479691\pi\) | ||||
0.0637599 | + | 0.997965i | \(0.479691\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1056.26i | − | 2.06704i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −165.744 | −0.321833 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 460.885i | − | 0.891459i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 468.510i | − | 0.899252i | −0.893217 | − | 0.449626i | \(-0.851557\pi\) | ||
0.893217 | − | 0.449626i | \(-0.148443\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 957.668i | 1.83111i | 0.402198 | + | 0.915553i | \(0.368246\pi\) | ||||
−0.402198 | + | 0.915553i | \(0.631754\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 649.400i | − | 1.23226i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −509.895 | − | 140.882i | −0.963886 | − | 0.266317i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 176.468 | 0.331085 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −98.3810 | −0.183890 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 559.664i | 1.03834i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 822.318 | 1.52000 | 0.759998 | − | 0.649925i | \(-0.225200\pi\) | ||||
0.759998 | + | 0.649925i | \(0.225200\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −184.026 | −0.337662 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −440.483 | −0.805270 | −0.402635 | − | 0.915361i | \(-0.631906\pi\) | ||||
−0.402635 | + | 0.915361i | \(0.631906\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1203.87i | − | 2.18488i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 133.089 | 0.240668 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 665.131i | 1.19413i | 0.802193 | + | 0.597065i | \(0.203667\pi\) | ||||
−0.802193 | + | 0.597065i | \(0.796333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 364.635i | 0.652300i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 517.477i | − | 0.919142i | −0.888141 | − | 0.459571i | \(-0.848003\pi\) | ||
0.888141 | − | 0.459571i | \(-0.151997\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −252.531 | −0.446958 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 440.146i | 0.773542i | 0.922176 | + | 0.386771i | \(0.126410\pi\) | ||||
−0.922176 | + | 0.386771i | \(0.873590\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 507.292i | − | 0.888427i | −0.895921 | − | 0.444214i | \(-0.853483\pi\) | ||
0.895921 | − | 0.444214i | \(-0.146517\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.4534 | + | 113.957i | −0.0268754 | + | 0.198186i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1094.87 | −1.89751 | −0.948757 | − | 0.316005i | \(-0.897658\pi\) | ||||
−0.948757 | + | 0.316005i | \(0.897658\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −336.388 | −0.578982 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −156.870 | −0.269073 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 811.775 | 1.38292 | 0.691461 | − | 0.722414i | \(-0.256967\pi\) | ||||
0.691461 | + | 0.722414i | \(0.256967\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1372.50i | 2.33023i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 384.656 | 0.648661 | 0.324331 | − | 0.945944i | \(-0.394861\pi\) | ||||
0.324331 | + | 0.945944i | \(0.394861\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 401.626i | − | 0.675002i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −503.582 | −0.840704 | −0.420352 | − | 0.907361i | \(-0.638093\pi\) | ||||
−0.420352 | + | 0.907361i | \(0.638093\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 629.639 | 1.04765 | 0.523826 | − | 0.851825i | \(-0.324504\pi\) | ||||
0.523826 | + | 0.851825i | \(0.324504\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 172.715i | 0.285479i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 528.591 | 0.870826 | 0.435413 | − | 0.900231i | \(-0.356602\pi\) | ||||
0.435413 | + | 0.900231i | \(0.356602\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −303.325 | −0.496441 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 9.16043i | − | 0.0149436i | −0.999972 | − | 0.00747180i | \(-0.997622\pi\) | ||
0.999972 | − | 0.00747180i | \(-0.00237837\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 332.958i | 0.539641i | 0.962911 | + | 0.269820i | \(0.0869643\pi\) | ||||
−0.962911 | + | 0.269820i | \(0.913036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 367.054i | − | 0.592979i | −0.955036 | − | 0.296489i | \(-0.904184\pi\) | ||
0.955036 | − | 0.296489i | \(-0.0958159\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 361.882 | 0.580870 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 195.028 | 0.310061 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 818.463i | 1.29709i | 0.761177 | + | 0.648544i | \(0.224622\pi\) | ||||
−0.761177 | + | 0.648544i | \(0.775378\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 384.675i | − | 0.605787i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 368.336 | 0.578236 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 506.746i | 0.790555i | 0.918562 | + | 0.395277i | \(0.129352\pi\) | ||||
−0.918562 | + | 0.395277i | \(0.870648\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 67.4223i | − | 0.104856i | −0.998625 | − | 0.0524279i | \(-0.983304\pi\) | ||
0.998625 | − | 0.0524279i | \(-0.0166960\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −300.396 | −0.464290 | −0.232145 | − | 0.972681i | \(-0.574574\pi\) | ||||
−0.232145 | + | 0.972681i | \(0.574574\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 300.957i | 0.463724i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 129.994 | 0.199072 | 0.0995360 | − | 0.995034i | \(-0.468264\pi\) | ||||
0.0995360 | + | 0.995034i | \(0.468264\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 111.103i | 0.169623i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 375.123i | 0.569231i | 0.958642 | + | 0.284615i | \(0.0918659\pi\) | ||||
−0.958642 | + | 0.284615i | \(0.908134\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 601.794i | − | 0.910429i | −0.890382 | − | 0.455215i | \(-0.849563\pi\) | ||
0.890382 | − | 0.455215i | \(-0.150437\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 848.836i | 1.27644i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −113.293 | + | 835.450i | −0.169855 | + | 1.25255i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −657.129 | −0.979328 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −442.603 | −0.657657 | −0.328829 | − | 0.944390i | \(-0.606654\pi\) | ||||
−0.328829 | + | 0.944390i | \(0.606654\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 303.051i | − | 0.447638i | −0.974631 | − | 0.223819i | \(-0.928148\pi\) | ||
0.974631 | − | 0.223819i | \(-0.0718524\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1279.47 | −1.88434 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −242.465 | −0.355000 | −0.177500 | − | 0.984121i | \(-0.556801\pi\) | ||||
−0.177500 | + | 0.984121i | \(0.556801\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −411.652 | −0.600951 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 103.242i | 0.149843i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 409.395 | 0.592468 | 0.296234 | − | 0.955115i | \(-0.404269\pi\) | ||||
0.296234 | + | 0.955115i | \(0.404269\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 138.573i | 0.199385i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 629.856i | 0.903667i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1359.99i | 1.94007i | 0.242963 | + | 0.970036i | \(0.421881\pi\) | ||||
−0.242963 | + | 0.970036i | \(0.578119\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −412.191 | −0.586332 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1908.47i | 2.69939i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 442.186i | 0.623676i | 0.950135 | + | 0.311838i | \(0.100945\pi\) | ||||
−0.950135 | + | 0.311838i | \(0.899055\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 129.163 | − | 952.480i | 0.181154 | − | 1.33588i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −64.3983 | −0.0900676 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −415.632 | −0.578070 | −0.289035 | − | 0.957319i | \(-0.593334\pi\) | ||||
−0.289035 | + | 0.957319i | \(0.593334\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 856.766 | 1.18830 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 183.282 | 0.252803 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 161.744i | − | 0.222482i | −0.993793 | − | 0.111241i | \(-0.964517\pi\) | ||
0.993793 | − | 0.111241i | \(-0.0354826\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1301.47 | −1.78039 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 272.499i | 0.371758i | 0.982573 | + | 0.185879i | \(0.0595133\pi\) | ||||
−0.982573 | + | 0.185879i | \(0.940487\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 509.585 | 0.691431 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −303.297 | −0.410416 | −0.205208 | − | 0.978718i | \(-0.565787\pi\) | ||||
−0.205208 | + | 0.978718i | \(0.565787\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 706.910i | 0.951426i | 0.879601 | + | 0.475713i | \(0.157810\pi\) | ||||
−0.879601 | + | 0.475713i | \(0.842190\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 565.166 | 0.758612 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 508.553 | 0.678976 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 518.357i | 0.690222i | 0.938562 | + | 0.345111i | \(0.112159\pi\) | ||||
−0.938562 | + | 0.345111i | \(0.887841\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 373.834i | − | 0.495144i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 773.832i | − | 1.02224i | −0.859511 | − | 0.511118i | \(-0.829232\pi\) | ||
0.859511 | − | 0.511118i | \(-0.170768\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 141.335 | 0.185723 | 0.0928615 | − | 0.995679i | \(-0.470399\pi\) | ||||
0.0928615 | + | 0.995679i | \(0.470399\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 951.270 | 1.24675 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 198.071 | 0.258241 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 192.492i | 0.250314i | 0.992137 | + | 0.125157i | \(0.0399435\pi\) | ||||
−0.992137 | + | 0.125157i | \(0.960057\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1394.17i | − | 1.80359i | −0.432169 | − | 0.901793i | \(-0.642252\pi\) | ||
0.432169 | − | 0.901793i | \(-0.357748\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −208.956 | −0.269621 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1331.20i | − | 1.70885i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 345.698i | 0.442635i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −533.654 | −0.679814 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 966.770i | − | 1.22842i | −0.789141 | − | 0.614212i | \(-0.789474\pi\) | ||
0.789141 | − | 0.614212i | \(-0.210526\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1305.39 | 1.65030 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 432.481i | 0.545374i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 422.069i | 0.529572i | 0.964307 | + | 0.264786i | \(0.0853014\pi\) | ||||
−0.964307 | + | 0.264786i | \(0.914699\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1082.64i | − | 1.35499i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 604.499i | − | 0.752801i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 79.8819 | − | 589.068i | 0.0992322 | − | 0.731762i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1002.82 | −1.23958 | −0.619791 | − | 0.784767i | \(-0.712783\pi\) | ||||
−0.619791 | + | 0.784767i | \(0.712783\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −879.037 | −1.08389 | −0.541946 | − | 0.840413i | \(-0.682312\pi\) | ||||
−0.541946 | + | 0.840413i | \(0.682312\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 245.822i | 0.301622i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2750.64 | 3.36676 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −147.227 | −0.179327 | −0.0896633 | − | 0.995972i | \(-0.528579\pi\) | ||||
−0.0896633 | + | 0.995972i | \(0.528579\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 893.347 | 1.08548 | 0.542738 | − | 0.839902i | \(-0.317388\pi\) | ||||
0.542738 | + | 0.839902i | \(0.317388\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1040.81i | 1.25854i | 0.777186 | + | 0.629270i | \(0.216646\pi\) | ||||
−0.777186 | + | 0.629270i | \(0.783354\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −284.524 | −0.343214 | −0.171607 | − | 0.985166i | \(-0.554896\pi\) | ||||
−0.171607 | + | 0.985166i | \(0.554896\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1314.68i | 1.57824i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 433.387i | − | 0.519027i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 369.349i | 0.440225i | 0.975474 | + | 0.220113i | \(0.0706425\pi\) | ||||
−0.975474 | + | 0.220113i | \(0.929358\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 502.691 | 0.597730 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 335.513i | − | 0.397056i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 892.801i | − | 1.05407i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 286.049 | + | 38.7903i | 0.336133 | + | 0.0455820i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1288.20 | −1.51020 | −0.755100 | − | 0.655610i | \(-0.772412\pi\) | ||||
−0.755100 | + | 0.655610i | \(0.772412\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1442.40 | 1.68308 | 0.841538 | − | 0.540198i | \(-0.181651\pi\) | ||||
0.841538 | + | 0.540198i | \(0.181651\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 997.689 | 1.16145 | 0.580727 | − | 0.814098i | \(-0.302768\pi\) | ||||
0.580727 | + | 0.814098i | \(0.302768\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −92.2907 | −0.106942 | −0.0534709 | − | 0.998569i | \(-0.517028\pi\) | ||||
−0.0534709 | + | 0.998569i | \(0.517028\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 407.937i | 0.471603i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 76.1676 | 0.0876497 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 335.377i | − | 0.385048i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −129.230 | −0.147692 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 270.272 | 0.308178 | 0.154089 | − | 0.988057i | \(-0.450756\pi\) | ||||
0.154089 | + | 0.988057i | \(0.450756\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 950.026i | − | 1.07835i | −0.842194 | − | 0.539175i | \(-0.818736\pi\) | ||
0.842194 | − | 0.539175i | \(-0.181264\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 101.560 | 0.115017 | 0.0575085 | − | 0.998345i | \(-0.481684\pi\) | ||||
0.0575085 | + | 0.998345i | \(0.481684\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1486.55 | −1.67593 | −0.837964 | − | 0.545725i | \(-0.816254\pi\) | ||||
−0.837964 | + | 0.545725i | \(0.816254\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1988.47i | 2.23675i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2288.15i | 2.56232i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 320.373i | − | 0.357958i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1531.92 | −1.70402 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −368.493 | −0.408983 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −411.873 | −0.455108 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 104.880i | − | 0.115634i | −0.998327 | − | 0.0578169i | \(-0.981586\pi\) | ||
0.998327 | − | 0.0578169i | \(-0.0184140\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 435.963i | − | 0.478555i | −0.970951 | − | 0.239277i | \(-0.923089\pi\) | ||
0.970951 | − | 0.239277i | \(-0.0769105\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −192.516 | −0.210861 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 574.317i | − | 0.626300i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 224.737i | − | 0.244546i | −0.992497 | − | 0.122273i | \(-0.960982\pi\) | ||
0.992497 | − | 0.122273i | \(-0.0390183\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 227.517 | 0.246497 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 62.7538i | − | 0.0678419i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1701.11 | 1.83112 | 0.915559 | − | 0.402183i | \(-0.131748\pi\) | ||||
0.915559 | + | 0.402183i | \(0.131748\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2778.56i | − | 2.98449i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 229.852i | − | 0.245831i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 775.110i | 0.827225i | 0.910453 | + | 0.413612i | \(0.135733\pi\) | ||||
−0.910453 | + | 0.413612i | \(0.864267\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1193.83i | − | 1.26868i | −0.773052 | − | 0.634342i | \(-0.781271\pi\) | ||
0.773052 | − | 0.634342i | \(-0.218729\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −125.276 | + | 923.815i | −0.132848 | + | 0.979655i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 430.109 | 0.454180 | 0.227090 | − | 0.973874i | \(-0.427079\pi\) | ||||
0.227090 | + | 0.973874i | \(0.427079\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −397.844 | −0.419224 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1390.03i | − | 1.45859i | −0.684200 | − | 0.729294i | \(-0.739849\pi\) | ||
0.684200 | − | 0.729294i | \(-0.260151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −155.572 | −0.162903 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2127.92 | 2.21889 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 785.507 | 0.817385 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 550.447i | 0.570411i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −824.460 | −0.852595 | −0.426298 | − | 0.904583i | \(-0.640182\pi\) | ||||
−0.426298 | + | 0.904583i | \(0.640182\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 614.100i | 0.632441i | 0.948686 | + | 0.316220i | \(0.102414\pi\) | ||||
−0.948686 | + | 0.316220i | \(0.897586\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 716.311i | − | 0.736188i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1170.50i | − | 1.19806i | −0.800728 | − | 0.599028i | \(-0.795554\pi\) | ||
0.800728 | − | 0.599028i | \(-0.204446\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 207.107 | 0.211549 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1798.20i | − | 1.82930i | −0.404244 | − | 0.914651i | \(-0.632465\pi\) | ||
0.404244 | − | 0.914651i | \(-0.367535\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 736.406i | − | 0.747621i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1908.87 | − | 258.857i | −1.93010 | − | 0.261736i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 656.246 | 0.662206 | 0.331103 | − | 0.943595i | \(-0.392579\pi\) | ||||
0.331103 | + | 0.943595i | \(0.392579\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −140.890 | −0.141598 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1483.74 | 1.48821 | 0.744103 | − | 0.668065i | \(-0.232877\pi\) | ||||
0.744103 | + | 0.668065i | \(0.232877\pi\) | |||||||
\(998\) | 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 | 4140.3.d.c.2161.18 | 32 | ||
3.2 | odd | 2 | 1380.3.d.a.781.1 | ✓ | 32 | ||
23.22 | odd | 2 | inner | 4140.3.d.c.2161.15 | 32 | ||
69.68 | even | 2 | 1380.3.d.a.781.16 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.3.d.a.781.1 | ✓ | 32 | 3.2 | odd | 2 | ||
1380.3.d.a.781.16 | yes | 32 | 69.68 | even | 2 | ||
4140.3.d.c.2161.15 | 32 | 23.22 | odd | 2 | inner | ||
4140.3.d.c.2161.18 | 32 | 1.1 | even | 1 | trivial |