Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,3,Mod(10,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("33.10");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.c (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: | \(0.899184872389\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.39744.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} + 12x^{2} + 4x + 22 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 10.4 | ||
Root | \(-0.366025 + 1.29224i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.10 |
Dual form | 33.3.c.a.10.1 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.53045i | 1.76523i | 0.470100 | + | 0.882613i | \(0.344218\pi\) | ||||
−0.470100 | + | 0.882613i | \(0.655782\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −8.46410 | −2.11603 | ||||||||
\(5\) | 6.19615 | 1.23923 | 0.619615 | − | 0.784906i | \(-0.287289\pi\) | ||||
0.619615 | + | 0.784906i | \(0.287289\pi\) | |||||||
\(6\) | − | 6.11492i | − | 1.01915i | ||||||
\(7\) | 2.58447i | 0.369210i | 0.982813 | + | 0.184605i | \(0.0591006\pi\) | ||||
−0.982813 | + | 0.184605i | \(0.940899\pi\) | |||||||
\(8\) | − | 15.7603i | − | 1.97004i | ||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 21.8752i | 2.18752i | ||||||||
\(11\) | 6.73205 | + | 8.69940i | 0.612005 | + | 0.790854i | ||||
\(12\) | 14.6603 | 1.22169 | ||||||||
\(13\) | − | 23.7672i | − | 1.82825i | −0.405437 | − | 0.914123i | \(-0.632881\pi\) | ||
0.405437 | − | 0.914123i | \(-0.367119\pi\) | |||||||
\(14\) | −9.12436 | −0.651740 | ||||||||
\(15\) | −10.7321 | −0.715470 | ||||||||
\(16\) | 21.7846 | 1.36154 | ||||||||
\(17\) | − | 12.2298i | − | 0.719403i | −0.933067 | − | 0.359701i | \(-0.882879\pi\) | ||
0.933067 | − | 0.359701i | \(-0.117121\pi\) | |||||||
\(18\) | 10.5914i | 0.588409i | ||||||||
\(19\) | − | 3.27698i | − | 0.172473i | −0.996275 | − | 0.0862363i | \(-0.972516\pi\) | ||
0.996275 | − | 0.0862363i | \(-0.0274840\pi\) | |||||||
\(20\) | −52.4449 | −2.62224 | ||||||||
\(21\) | − | 4.47644i | − | 0.213164i | ||||||
\(22\) | −30.7128 | + | 23.7672i | −1.39604 | + | 1.08033i | ||||
\(23\) | −14.3397 | −0.623467 | −0.311734 | − | 0.950170i | \(-0.600910\pi\) | ||||
−0.311734 | + | 0.950170i | \(0.600910\pi\) | |||||||
\(24\) | 27.2976i | 1.13740i | ||||||||
\(25\) | 13.3923 | 0.535692 | ||||||||
\(26\) | 83.9090 | 3.22727 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | − | 21.8752i | − | 0.781258i | ||||||
\(29\) | 38.5815i | 1.33040i | 0.746667 | + | 0.665198i | \(0.231653\pi\) | ||||
−0.746667 | + | 0.665198i | \(0.768347\pi\) | |||||||
\(30\) | − | 37.8890i | − | 1.26297i | ||||||
\(31\) | −11.1769 | −0.360546 | −0.180273 | − | 0.983617i | \(-0.557698\pi\) | ||||
−0.180273 | + | 0.983617i | \(0.557698\pi\) | |||||||
\(32\) | 13.8683i | 0.433386i | ||||||||
\(33\) | −11.6603 | − | 15.0678i | −0.353341 | − | 0.456600i | ||||
\(34\) | 43.1769 | 1.26991 | ||||||||
\(35\) | 16.0138i | 0.457537i | ||||||||
\(36\) | −25.3923 | −0.705342 | ||||||||
\(37\) | −12.5359 | −0.338808 | −0.169404 | − | 0.985547i | \(-0.554184\pi\) | ||||
−0.169404 | + | 0.985547i | \(0.554184\pi\) | |||||||
\(38\) | 11.5692 | 0.304453 | ||||||||
\(39\) | 41.1660i | 1.05554i | ||||||||
\(40\) | − | 97.6532i | − | 2.44133i | ||||||
\(41\) | 1.38501i | 0.0337808i | 0.999857 | + | 0.0168904i | \(0.00537664\pi\) | ||||
−0.999857 | + | 0.0168904i | \(0.994623\pi\) | |||||||
\(42\) | 15.8038 | 0.376282 | ||||||||
\(43\) | − | 23.9527i | − | 0.557041i | −0.960430 | − | 0.278520i | \(-0.910156\pi\) | ||
0.960430 | − | 0.278520i | \(-0.0898440\pi\) | |||||||
\(44\) | −56.9808 | − | 73.6326i | −1.29502 | − | 1.67347i | ||||
\(45\) | 18.5885 | 0.413077 | ||||||||
\(46\) | − | 50.6258i | − | 1.10056i | ||||||
\(47\) | 19.8038 | 0.421358 | 0.210679 | − | 0.977555i | \(-0.432432\pi\) | ||||
0.210679 | + | 0.977555i | \(0.432432\pi\) | |||||||
\(48\) | −37.7321 | −0.786084 | ||||||||
\(49\) | 42.3205 | 0.863684 | ||||||||
\(50\) | 47.2809i | 0.945618i | ||||||||
\(51\) | 21.1827i | 0.415347i | ||||||||
\(52\) | 201.168i | 3.86861i | ||||||||
\(53\) | −12.0526 | −0.227407 | −0.113703 | − | 0.993515i | \(-0.536271\pi\) | ||||
−0.113703 | + | 0.993515i | \(0.536271\pi\) | |||||||
\(54\) | − | 18.3448i | − | 0.339718i | ||||||
\(55\) | 41.7128 | + | 53.9028i | 0.758415 | + | 0.980051i | ||||
\(56\) | 40.7321 | 0.727358 | ||||||||
\(57\) | 5.67589i | 0.0995771i | ||||||||
\(58\) | −136.210 | −2.34845 | ||||||||
\(59\) | −62.7461 | −1.06349 | −0.531747 | − | 0.846903i | \(-0.678464\pi\) | ||||
−0.531747 | + | 0.846903i | \(0.678464\pi\) | |||||||
\(60\) | 90.8372 | 1.51395 | ||||||||
\(61\) | 21.3683i | 0.350300i | 0.984542 | + | 0.175150i | \(0.0560410\pi\) | ||||
−0.984542 | + | 0.175150i | \(0.943959\pi\) | |||||||
\(62\) | − | 39.4596i | − | 0.636445i | ||||||
\(63\) | 7.75341i | 0.123070i | ||||||||
\(64\) | 38.1769 | 0.596514 | ||||||||
\(65\) | − | 147.265i | − | 2.26562i | ||||||
\(66\) | 53.1962 | − | 41.1660i | 0.806002 | − | 0.623727i | ||||
\(67\) | −34.0000 | −0.507463 | −0.253731 | − | 0.967275i | \(-0.581658\pi\) | ||||
−0.253731 | + | 0.967275i | \(0.581658\pi\) | |||||||
\(68\) | 103.515i | 1.52227i | ||||||||
\(69\) | 24.8372 | 0.359959 | ||||||||
\(70\) | −56.5359 | −0.807656 | ||||||||
\(71\) | −69.2679 | −0.975605 | −0.487802 | − | 0.872954i | \(-0.662201\pi\) | ||||
−0.487802 | + | 0.872954i | \(0.662201\pi\) | |||||||
\(72\) | − | 47.2809i | − | 0.656679i | ||||||
\(73\) | 39.9665i | 0.547487i | 0.961803 | + | 0.273743i | \(0.0882619\pi\) | ||||
−0.961803 | + | 0.273743i | \(0.911738\pi\) | |||||||
\(74\) | − | 44.2574i | − | 0.598073i | ||||||
\(75\) | −23.1962 | −0.309282 | ||||||||
\(76\) | 27.7367i | 0.364956i | ||||||||
\(77\) | −22.4833 | + | 17.3988i | −0.291991 | + | 0.225958i | ||||
\(78\) | −145.335 | −1.86326 | ||||||||
\(79\) | − | 97.6532i | − | 1.23612i | −0.786132 | − | 0.618058i | \(-0.787919\pi\) | ||
0.786132 | − | 0.618058i | \(-0.212081\pi\) | |||||||
\(80\) | 134.981 | 1.68726 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −4.88973 | −0.0596308 | ||||||||
\(83\) | 71.9941i | 0.867399i | 0.901058 | + | 0.433699i | \(0.142792\pi\) | ||||
−0.901058 | + | 0.433699i | \(0.857208\pi\) | |||||||
\(84\) | 37.8890i | 0.451060i | ||||||||
\(85\) | − | 75.7780i | − | 0.891506i | ||||||
\(86\) | 84.5641 | 0.983303 | ||||||||
\(87\) | − | 66.8251i | − | 0.768105i | ||||||
\(88\) | 137.105 | − | 106.099i | 1.55801 | − | 1.20567i | ||||
\(89\) | 107.177 | 1.20423 | 0.602117 | − | 0.798407i | \(-0.294324\pi\) | ||||
0.602117 | + | 0.798407i | \(0.294324\pi\) | |||||||
\(90\) | 65.6257i | 0.729174i | ||||||||
\(91\) | 61.4256 | 0.675007 | ||||||||
\(92\) | 121.373 | 1.31927 | ||||||||
\(93\) | 19.3590 | 0.208161 | ||||||||
\(94\) | 69.9166i | 0.743793i | ||||||||
\(95\) | − | 20.3047i | − | 0.213733i | ||||||
\(96\) | − | 24.0207i | − | 0.250215i | ||||||
\(97\) | −166.746 | −1.71903 | −0.859516 | − | 0.511109i | \(-0.829235\pi\) | ||||
−0.859516 | + | 0.511109i | \(0.829235\pi\) | |||||||
\(98\) | 149.411i | 1.52460i | ||||||||
\(99\) | 20.1962 | + | 26.0982i | 0.204002 | + | 0.263618i | ||||
\(100\) | −113.354 | −1.13354 | ||||||||
\(101\) | − | 92.6699i | − | 0.917523i | −0.888559 | − | 0.458762i | \(-0.848293\pi\) | ||
0.888559 | − | 0.458762i | \(-0.151707\pi\) | |||||||
\(102\) | −74.7846 | −0.733182 | ||||||||
\(103\) | 140.746 | 1.36647 | 0.683234 | − | 0.730200i | \(-0.260573\pi\) | ||||
0.683234 | + | 0.730200i | \(0.260573\pi\) | |||||||
\(104\) | −374.578 | −3.60171 | ||||||||
\(105\) | − | 27.7367i | − | 0.264159i | ||||||
\(106\) | − | 42.5510i | − | 0.401425i | ||||||
\(107\) | 74.8999i | 0.700000i | 0.936750 | + | 0.350000i | \(0.113818\pi\) | ||||
−0.936750 | + | 0.350000i | \(0.886182\pi\) | |||||||
\(108\) | 43.9808 | 0.407229 | ||||||||
\(109\) | 153.634i | 1.40948i | 0.709465 | + | 0.704741i | \(0.248937\pi\) | ||||
−0.709465 | + | 0.704741i | \(0.751063\pi\) | |||||||
\(110\) | −190.301 | + | 147.265i | −1.73001 | + | 1.33877i | ||||
\(111\) | 21.7128 | 0.195611 | ||||||||
\(112\) | 56.3017i | 0.502694i | ||||||||
\(113\) | 166.315 | 1.47182 | 0.735909 | − | 0.677081i | \(-0.236755\pi\) | ||||
0.735909 | + | 0.677081i | \(0.236755\pi\) | |||||||
\(114\) | −20.0385 | −0.175776 | ||||||||
\(115\) | −88.8513 | −0.772620 | ||||||||
\(116\) | − | 326.558i | − | 2.81515i | ||||||
\(117\) | − | 71.3016i | − | 0.609415i | ||||||
\(118\) | − | 221.522i | − | 1.87731i | ||||||
\(119\) | 31.6077 | 0.265611 | ||||||||
\(120\) | 169.140i | 1.40950i | ||||||||
\(121\) | −30.3590 | + | 117.130i | −0.250901 | + | 0.968013i | ||||
\(122\) | −75.4397 | −0.618358 | ||||||||
\(123\) | − | 2.39891i | − | 0.0195034i | ||||||
\(124\) | 94.6025 | 0.762924 | ||||||||
\(125\) | −71.9230 | −0.575384 | ||||||||
\(126\) | −27.3731 | −0.217247 | ||||||||
\(127\) | − | 190.323i | − | 1.49861i | −0.662227 | − | 0.749304i | \(-0.730388\pi\) | ||
0.662227 | − | 0.749304i | \(-0.269612\pi\) | |||||||
\(128\) | 190.255i | 1.48637i | ||||||||
\(129\) | 41.4874i | 0.321608i | ||||||||
\(130\) | 519.913 | 3.99933 | ||||||||
\(131\) | 99.2238i | 0.757434i | 0.925513 | + | 0.378717i | \(0.123635\pi\) | ||||
−0.925513 | + | 0.378717i | \(0.876365\pi\) | |||||||
\(132\) | 98.6936 | + | 127.535i | 0.747679 | + | 0.966177i | ||||
\(133\) | 8.46926 | 0.0636786 | ||||||||
\(134\) | − | 120.035i | − | 0.895787i | ||||||
\(135\) | −32.1962 | −0.238490 | ||||||||
\(136\) | −192.746 | −1.41725 | ||||||||
\(137\) | −29.2154 | −0.213251 | −0.106626 | − | 0.994299i | \(-0.534005\pi\) | ||||
−0.106626 | + | 0.994299i | \(0.534005\pi\) | |||||||
\(138\) | 87.6865i | 0.635409i | ||||||||
\(139\) | 171.354i | 1.23276i | 0.787449 | + | 0.616380i | \(0.211402\pi\) | ||||
−0.787449 | + | 0.616380i | \(0.788598\pi\) | |||||||
\(140\) | − | 135.542i | − | 0.968159i | ||||||
\(141\) | −34.3013 | −0.243271 | ||||||||
\(142\) | − | 244.547i | − | 1.72216i | ||||||
\(143\) | 206.760 | − | 160.002i | 1.44588 | − | 1.11889i | ||||
\(144\) | 65.3538 | 0.453846 | ||||||||
\(145\) | 239.057i | 1.64867i | ||||||||
\(146\) | −141.100 | −0.966438 | ||||||||
\(147\) | −73.3013 | −0.498648 | ||||||||
\(148\) | 106.105 | 0.716926 | ||||||||
\(149\) | 164.293i | 1.10264i | 0.834295 | + | 0.551318i | \(0.185875\pi\) | ||||
−0.834295 | + | 0.551318i | \(0.814125\pi\) | |||||||
\(150\) | − | 81.8929i | − | 0.545953i | ||||||
\(151\) | − | 229.547i | − | 1.52018i | −0.649817 | − | 0.760091i | \(-0.725154\pi\) | ||
0.649817 | − | 0.760091i | \(-0.274846\pi\) | |||||||
\(152\) | −51.6462 | −0.339777 | ||||||||
\(153\) | − | 36.6895i | − | 0.239801i | ||||||
\(154\) | −61.4256 | − | 79.3764i | −0.398868 | − | 0.515431i | ||||
\(155\) | −69.2539 | −0.446799 | ||||||||
\(156\) | − | 348.433i | − | 2.23355i | ||||||
\(157\) | −106.862 | −0.680647 | −0.340323 | − | 0.940308i | \(-0.610537\pi\) | ||||
−0.340323 | + | 0.940308i | \(0.610537\pi\) | |||||||
\(158\) | 344.760 | 2.18203 | ||||||||
\(159\) | 20.8756 | 0.131293 | ||||||||
\(160\) | 85.9303i | 0.537065i | ||||||||
\(161\) | − | 37.0607i | − | 0.230190i | ||||||
\(162\) | 31.7741i | 0.196136i | ||||||||
\(163\) | −118.067 | −0.724335 | −0.362168 | − | 0.932113i | \(-0.617963\pi\) | ||||
−0.362168 | + | 0.932113i | \(0.617963\pi\) | |||||||
\(164\) | − | 11.7229i | − | 0.0714811i | ||||||
\(165\) | −72.2487 | − | 93.3624i | −0.437871 | − | 0.565832i | ||||
\(166\) | −254.172 | −1.53116 | ||||||||
\(167\) | 1.38501i | 0.00829350i | 0.999991 | + | 0.00414675i | \(0.00131995\pi\) | ||||
−0.999991 | + | 0.00414675i | \(0.998680\pi\) | |||||||
\(168\) | −70.5500 | −0.419940 | ||||||||
\(169\) | −395.879 | −2.34248 | ||||||||
\(170\) | 267.531 | 1.57371 | ||||||||
\(171\) | − | 9.83093i | − | 0.0574908i | ||||||
\(172\) | 202.738i | 1.17871i | ||||||||
\(173\) | 67.8390i | 0.392133i | 0.980591 | + | 0.196067i | \(0.0628169\pi\) | ||||
−0.980591 | + | 0.196067i | \(0.937183\pi\) | |||||||
\(174\) | 235.923 | 1.35588 | ||||||||
\(175\) | 34.6120i | 0.197783i | ||||||||
\(176\) | 146.655 | + | 189.513i | 0.833268 | + | 1.07678i | ||||
\(177\) | 108.679 | 0.614008 | ||||||||
\(178\) | 378.383i | 2.12575i | ||||||||
\(179\) | −136.603 | −0.763143 | −0.381571 | − | 0.924339i | \(-0.624617\pi\) | ||||
−0.381571 | + | 0.924339i | \(0.624617\pi\) | |||||||
\(180\) | −157.335 | −0.874081 | ||||||||
\(181\) | 172.172 | 0.951225 | 0.475613 | − | 0.879655i | \(-0.342226\pi\) | ||||
0.475613 | + | 0.879655i | \(0.342226\pi\) | |||||||
\(182\) | 216.860i | 1.19154i | ||||||||
\(183\) | − | 37.0109i | − | 0.202246i | ||||||
\(184\) | 225.999i | 1.22825i | ||||||||
\(185\) | −77.6743 | −0.419861 | ||||||||
\(186\) | 68.3460i | 0.367452i | ||||||||
\(187\) | 106.392 | − | 82.3320i | 0.568943 | − | 0.440278i | ||||
\(188\) | −167.622 | −0.891605 | ||||||||
\(189\) | − | 13.4293i | − | 0.0710545i | ||||||
\(190\) | 71.6846 | 0.377288 | ||||||||
\(191\) | 137.765 | 0.721285 | 0.360642 | − | 0.932704i | \(-0.382558\pi\) | ||||
0.360642 | + | 0.932704i | \(0.382558\pi\) | |||||||
\(192\) | −66.1244 | −0.344398 | ||||||||
\(193\) | − | 106.421i | − | 0.551402i | −0.961243 | − | 0.275701i | \(-0.911090\pi\) | ||
0.961243 | − | 0.275701i | \(-0.0889099\pi\) | |||||||
\(194\) | − | 588.689i | − | 3.03448i | ||||||
\(195\) | 255.071i | 1.30805i | ||||||||
\(196\) | −358.205 | −1.82758 | ||||||||
\(197\) | 33.4126i | 0.169607i | 0.996398 | + | 0.0848035i | \(0.0270262\pi\) | ||||
−0.996398 | + | 0.0848035i | \(0.972974\pi\) | |||||||
\(198\) | −92.1384 | + | 71.3016i | −0.465346 | + | 0.360109i | ||||
\(199\) | 334.056 | 1.67868 | 0.839338 | − | 0.543611i | \(-0.182943\pi\) | ||||
0.839338 | + | 0.543611i | \(0.182943\pi\) | |||||||
\(200\) | − | 211.067i | − | 1.05533i | ||||||
\(201\) | 58.8897 | 0.292984 | ||||||||
\(202\) | 327.167 | 1.61964 | ||||||||
\(203\) | −99.7128 | −0.491196 | ||||||||
\(204\) | − | 179.293i | − | 0.878886i | ||||||
\(205\) | 8.58176i | 0.0418622i | ||||||||
\(206\) | 496.898i | 2.41212i | ||||||||
\(207\) | −43.0192 | −0.207822 | ||||||||
\(208\) | − | 517.759i | − | 2.48923i | ||||||
\(209\) | 28.5077 | − | 22.0608i | 0.136401 | − | 0.105554i | ||||
\(210\) | 97.9230 | 0.466300 | ||||||||
\(211\) | 31.1495i | 0.147628i | 0.997272 | + | 0.0738140i | \(0.0235171\pi\) | ||||
−0.997272 | + | 0.0738140i | \(0.976483\pi\) | |||||||
\(212\) | 102.014 | 0.481199 | ||||||||
\(213\) | 119.976 | 0.563266 | ||||||||
\(214\) | −264.431 | −1.23566 | ||||||||
\(215\) | − | 148.415i | − | 0.690302i | ||||||
\(216\) | 81.8929i | 0.379134i | ||||||||
\(217\) | − | 28.8864i | − | 0.133117i | ||||||
\(218\) | −542.396 | −2.48806 | ||||||||
\(219\) | − | 69.2241i | − | 0.316092i | ||||||
\(220\) | −353.061 | − | 456.239i | −1.60482 | − | 2.07381i | ||||
\(221\) | −290.669 | −1.31525 | ||||||||
\(222\) | 76.6561i | 0.345298i | ||||||||
\(223\) | 137.713 | 0.617546 | 0.308773 | − | 0.951136i | \(-0.400082\pi\) | ||||
0.308773 | + | 0.951136i | \(0.400082\pi\) | |||||||
\(224\) | −35.8423 | −0.160010 | ||||||||
\(225\) | 40.1769 | 0.178564 | ||||||||
\(226\) | 587.169i | 2.59809i | ||||||||
\(227\) | − | 329.835i | − | 1.45302i | −0.687158 | − | 0.726508i | \(-0.741142\pi\) | ||
0.687158 | − | 0.726508i | \(-0.258858\pi\) | |||||||
\(228\) | − | 48.0413i | − | 0.210708i | ||||||
\(229\) | 299.282 | 1.30691 | 0.653454 | − | 0.756966i | \(-0.273319\pi\) | ||||
0.653454 | + | 0.756966i | \(0.273319\pi\) | |||||||
\(230\) | − | 313.685i | − | 1.36385i | ||||||
\(231\) | 38.9423 | − | 30.1356i | 0.168581 | − | 0.130457i | ||||
\(232\) | 608.056 | 2.62093 | ||||||||
\(233\) | 146.115i | 0.627105i | 0.949571 | + | 0.313552i | \(0.101519\pi\) | ||||
−0.949571 | + | 0.313552i | \(0.898481\pi\) | |||||||
\(234\) | 251.727 | 1.07576 | ||||||||
\(235\) | 122.708 | 0.522160 | ||||||||
\(236\) | 531.090 | 2.25038 | ||||||||
\(237\) | 169.140i | 0.713672i | ||||||||
\(238\) | 111.589i | 0.468863i | ||||||||
\(239\) | 63.4123i | 0.265324i | 0.991161 | + | 0.132662i | \(0.0423524\pi\) | ||||
−0.991161 | + | 0.132662i | \(0.957648\pi\) | |||||||
\(240\) | −233.794 | −0.974140 | ||||||||
\(241\) | 351.018i | 1.45650i | 0.685309 | + | 0.728252i | \(0.259667\pi\) | ||||
−0.685309 | + | 0.728252i | \(0.740333\pi\) | |||||||
\(242\) | −413.520 | − | 107.181i | −1.70876 | − | 0.442897i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | − | 180.863i | − | 0.741243i | ||||||
\(245\) | 262.224 | 1.07030 | ||||||||
\(246\) | 8.46926 | 0.0344279 | ||||||||
\(247\) | −77.8846 | −0.315322 | ||||||||
\(248\) | 176.152i | 0.710289i | ||||||||
\(249\) | − | 124.697i | − | 0.500793i | ||||||
\(250\) | − | 253.921i | − | 1.01568i | ||||||
\(251\) | 65.7231 | 0.261845 | 0.130923 | − | 0.991393i | \(-0.458206\pi\) | ||||
0.130923 | + | 0.991393i | \(0.458206\pi\) | |||||||
\(252\) | − | 65.6257i | − | 0.260419i | ||||||
\(253\) | −96.5359 | − | 124.747i | −0.381565 | − | 0.493072i | ||||
\(254\) | 671.927 | 2.64538 | ||||||||
\(255\) | 131.251i | 0.514711i | ||||||||
\(256\) | −518.979 | −2.02726 | ||||||||
\(257\) | −206.182 | −0.802265 | −0.401132 | − | 0.916020i | \(-0.631383\pi\) | ||||
−0.401132 | + | 0.916020i | \(0.631383\pi\) | |||||||
\(258\) | −146.469 | −0.567710 | ||||||||
\(259\) | − | 32.3987i | − | 0.125091i | ||||||
\(260\) | 1246.47i | 4.79410i | ||||||||
\(261\) | 115.745i | 0.443466i | ||||||||
\(262\) | −350.305 | −1.33704 | ||||||||
\(263\) | 18.2769i | 0.0694937i | 0.999396 | + | 0.0347469i | \(0.0110625\pi\) | ||||
−0.999396 | + | 0.0347469i | \(0.988937\pi\) | |||||||
\(264\) | −237.473 | + | 183.769i | −0.899519 | + | 0.696095i | ||||
\(265\) | −74.6795 | −0.281809 | ||||||||
\(266\) | 29.9003i | 0.112407i | ||||||||
\(267\) | −185.636 | −0.695265 | ||||||||
\(268\) | 287.779 | 1.07380 | ||||||||
\(269\) | −172.130 | −0.639887 | −0.319943 | − | 0.947437i | \(-0.603664\pi\) | ||||
−0.319943 | + | 0.947437i | \(0.603664\pi\) | |||||||
\(270\) | − | 113.667i | − | 0.420989i | ||||||
\(271\) | − | 425.967i | − | 1.57183i | −0.618332 | − | 0.785917i | \(-0.712191\pi\) | ||
0.618332 | − | 0.785917i | \(-0.287809\pi\) | |||||||
\(272\) | − | 266.422i | − | 0.979494i | ||||||
\(273\) | −106.392 | −0.389715 | ||||||||
\(274\) | − | 103.144i | − | 0.376436i | ||||||
\(275\) | 90.1577 | + | 116.505i | 0.327846 | + | 0.423654i | ||||
\(276\) | −210.224 | −0.761682 | ||||||||
\(277\) | − | 261.439i | − | 0.943824i | −0.881646 | − | 0.471912i | \(-0.843564\pi\) | ||
0.881646 | − | 0.471912i | \(-0.156436\pi\) | |||||||
\(278\) | −604.956 | −2.17610 | ||||||||
\(279\) | −33.5307 | −0.120182 | ||||||||
\(280\) | 252.382 | 0.901364 | ||||||||
\(281\) | − | 329.192i | − | 1.17150i | −0.810491 | − | 0.585751i | \(-0.800800\pi\) | ||
0.810491 | − | 0.585751i | \(-0.199200\pi\) | |||||||
\(282\) | − | 121.099i | − | 0.429429i | ||||||
\(283\) | − | 231.353i | − | 0.817503i | −0.912646 | − | 0.408751i | \(-0.865964\pi\) | ||
0.912646 | − | 0.408751i | \(-0.134036\pi\) | |||||||
\(284\) | 586.291 | 2.06440 | ||||||||
\(285\) | 35.1687i | 0.123399i | ||||||||
\(286\) | 564.879 | + | 729.957i | 1.97510 | + | 2.55230i | ||||
\(287\) | −3.57953 | −0.0124722 | ||||||||
\(288\) | 41.6050i | 0.144462i | ||||||||
\(289\) | 139.431 | 0.482459 | ||||||||
\(290\) | −843.979 | −2.91027 | ||||||||
\(291\) | 288.813 | 0.992484 | ||||||||
\(292\) | − | 338.281i | − | 1.15850i | ||||||
\(293\) | − | 199.733i | − | 0.681683i | −0.940121 | − | 0.340842i | \(-0.889288\pi\) | ||
0.940121 | − | 0.340842i | \(-0.110712\pi\) | |||||||
\(294\) | − | 258.787i | − | 0.880227i | ||||||
\(295\) | −388.785 | −1.31791 | ||||||||
\(296\) | 197.570i | 0.667465i | ||||||||
\(297\) | −34.9808 | − | 45.2034i | −0.117780 | − | 0.152200i | ||||
\(298\) | −580.028 | −1.94640 | ||||||||
\(299\) | 340.815i | 1.13985i | ||||||||
\(300\) | 196.335 | 0.654449 | ||||||||
\(301\) | 61.9052 | 0.205665 | ||||||||
\(302\) | 810.406 | 2.68346 | ||||||||
\(303\) | 160.509i | 0.529732i | ||||||||
\(304\) | − | 71.3877i | − | 0.234828i | ||||||
\(305\) | 132.401i | 0.434102i | ||||||||
\(306\) | 129.531 | 0.423303 | ||||||||
\(307\) | 426.289i | 1.38856i | 0.719704 | + | 0.694281i | \(0.244278\pi\) | ||||
−0.719704 | + | 0.694281i | \(0.755722\pi\) | |||||||
\(308\) | 190.301 | − | 147.265i | 0.617861 | − | 0.478134i | ||||
\(309\) | −243.779 | −0.788930 | ||||||||
\(310\) | − | 244.498i | − | 0.788702i | ||||||
\(311\) | −301.611 | −0.969812 | −0.484906 | − | 0.874566i | \(-0.661146\pi\) | ||||
−0.484906 | + | 0.874566i | \(0.661146\pi\) | |||||||
\(312\) | 648.788 | 2.07945 | ||||||||
\(313\) | 260.697 | 0.832899 | 0.416449 | − | 0.909159i | \(-0.363274\pi\) | ||||
0.416449 | + | 0.909159i | \(0.363274\pi\) | |||||||
\(314\) | − | 377.270i | − | 1.20150i | ||||||
\(315\) | 48.0413i | 0.152512i | ||||||||
\(316\) | 826.547i | 2.61565i | ||||||||
\(317\) | 451.191 | 1.42332 | 0.711658 | − | 0.702526i | \(-0.247945\pi\) | ||||
0.711658 | + | 0.702526i | \(0.247945\pi\) | |||||||
\(318\) | 73.7005i | 0.231763i | ||||||||
\(319\) | −335.636 | + | 259.733i | −1.05215 | + | 0.814209i | ||||
\(320\) | 236.550 | 0.739219 | ||||||||
\(321\) | − | 129.731i | − | 0.404145i | ||||||
\(322\) | 130.841 | 0.406338 | ||||||||
\(323\) | −40.0770 | −0.124077 | ||||||||
\(324\) | −76.1769 | −0.235114 | ||||||||
\(325\) | − | 318.297i | − | 0.979377i | ||||||
\(326\) | − | 416.829i | − | 1.27862i | ||||||
\(327\) | − | 266.101i | − | 0.813765i | ||||||
\(328\) | 21.8282 | 0.0665495 | ||||||||
\(329\) | 51.1825i | 0.155570i | ||||||||
\(330\) | 329.611 | − | 255.071i | 0.998823 | − | 0.772942i | ||||
\(331\) | 229.569 | 0.693563 | 0.346781 | − | 0.937946i | \(-0.387275\pi\) | ||||
0.346781 | + | 0.937946i | \(0.387275\pi\) | |||||||
\(332\) | − | 609.365i | − | 1.83544i | ||||||
\(333\) | −37.6077 | −0.112936 | ||||||||
\(334\) | −4.88973 | −0.0146399 | ||||||||
\(335\) | −210.669 | −0.628863 | ||||||||
\(336\) | − | 97.5174i | − | 0.290230i | ||||||
\(337\) | 178.143i | 0.528614i | 0.964439 | + | 0.264307i | \(0.0851432\pi\) | ||||
−0.964439 | + | 0.264307i | \(0.914857\pi\) | |||||||
\(338\) | − | 1397.63i | − | 4.13501i | ||||||
\(339\) | −288.067 | −0.849754 | ||||||||
\(340\) | 641.393i | 1.88645i | ||||||||
\(341\) | −75.2436 | − | 97.2324i | −0.220656 | − | 0.285139i | ||||
\(342\) | 34.7077 | 0.101484 | ||||||||
\(343\) | 236.015i | 0.688091i | ||||||||
\(344\) | −377.503 | −1.09739 | ||||||||
\(345\) | 153.895 | 0.446072 | ||||||||
\(346\) | −239.503 | −0.692204 | ||||||||
\(347\) | 574.839i | 1.65660i | 0.560287 | + | 0.828299i | \(0.310691\pi\) | ||||
−0.560287 | + | 0.828299i | \(0.689309\pi\) | |||||||
\(348\) | 565.615i | 1.62533i | ||||||||
\(349\) | − | 182.619i | − | 0.523265i | −0.965168 | − | 0.261632i | \(-0.915739\pi\) | ||
0.965168 | − | 0.261632i | \(-0.0842608\pi\) | |||||||
\(350\) | −122.196 | −0.349132 | ||||||||
\(351\) | 123.498i | 0.351846i | ||||||||
\(352\) | −120.646 | + | 93.3624i | −0.342745 | + | 0.265234i | ||||
\(353\) | −195.990 | −0.555212 | −0.277606 | − | 0.960695i | \(-0.589541\pi\) | ||||
−0.277606 | + | 0.960695i | \(0.589541\pi\) | |||||||
\(354\) | 383.688i | 1.08386i | ||||||||
\(355\) | −429.195 | −1.20900 | ||||||||
\(356\) | −907.156 | −2.54819 | ||||||||
\(357\) | −54.7461 | −0.153351 | ||||||||
\(358\) | − | 482.269i | − | 1.34712i | ||||||
\(359\) | 707.105i | 1.96965i | 0.173548 | + | 0.984825i | \(0.444477\pi\) | ||||
−0.173548 | + | 0.984825i | \(0.555523\pi\) | |||||||
\(360\) | − | 292.960i | − | 0.813777i | ||||||
\(361\) | 350.261 | 0.970253 | ||||||||
\(362\) | 607.844i | 1.67913i | ||||||||
\(363\) | 52.5833 | − | 202.874i | 0.144858 | − | 0.558882i | ||||
\(364\) | −519.913 | −1.42833 | ||||||||
\(365\) | 247.639i | 0.678462i | ||||||||
\(366\) | 130.665 | 0.357009 | ||||||||
\(367\) | 359.415 | 0.979333 | 0.489667 | − | 0.871910i | \(-0.337118\pi\) | ||||
0.489667 | + | 0.871910i | \(0.337118\pi\) | |||||||
\(368\) | −312.386 | −0.848874 | ||||||||
\(369\) | 4.15504i | 0.0112603i | ||||||||
\(370\) | − | 274.226i | − | 0.741150i | ||||||
\(371\) | − | 31.1495i | − | 0.0839609i | ||||||
\(372\) | −163.856 | −0.440474 | ||||||||
\(373\) | − | 363.804i | − | 0.975346i | −0.873026 | − | 0.487673i | \(-0.837846\pi\) | ||
0.873026 | − | 0.487673i | \(-0.162154\pi\) | |||||||
\(374\) | 290.669 | + | 375.613i | 0.777190 | + | 1.00431i | ||||
\(375\) | 124.574 | 0.332198 | ||||||||
\(376\) | − | 312.115i | − | 0.830092i | ||||||
\(377\) | 916.974 | 2.43229 | ||||||||
\(378\) | 47.4115 | 0.125427 | ||||||||
\(379\) | −266.046 | −0.701968 | −0.350984 | − | 0.936381i | \(-0.614153\pi\) | ||||
−0.350984 | + | 0.936381i | \(0.614153\pi\) | |||||||
\(380\) | 171.861i | 0.452265i | ||||||||
\(381\) | 329.649i | 0.865221i | ||||||||
\(382\) | 486.374i | 1.27323i | ||||||||
\(383\) | 331.258 | 0.864902 | 0.432451 | − | 0.901657i | \(-0.357649\pi\) | ||||
0.432451 | + | 0.901657i | \(0.357649\pi\) | |||||||
\(384\) | − | 329.532i | − | 0.858155i | ||||||
\(385\) | −139.310 | + | 107.806i | −0.361845 | + | 0.280014i | ||||
\(386\) | 375.713 | 0.973349 | ||||||||
\(387\) | − | 71.8582i | − | 0.185680i | ||||||
\(388\) | 1411.36 | 3.63752 | ||||||||
\(389\) | 421.027 | 1.08233 | 0.541166 | − | 0.840916i | \(-0.317983\pi\) | ||||
0.541166 | + | 0.840916i | \(0.317983\pi\) | |||||||
\(390\) | −900.515 | −2.30901 | ||||||||
\(391\) | 175.373i | 0.448524i | ||||||||
\(392\) | − | 666.984i | − | 1.70149i | ||||||
\(393\) | − | 171.861i | − | 0.437305i | ||||||
\(394\) | −117.962 | −0.299395 | ||||||||
\(395\) | − | 605.074i | − | 1.53183i | ||||||
\(396\) | −170.942 | − | 220.898i | −0.431672 | − | 0.557823i | ||||
\(397\) | −421.797 | −1.06246 | −0.531231 | − | 0.847227i | \(-0.678270\pi\) | ||||
−0.531231 | + | 0.847227i | \(0.678270\pi\) | |||||||
\(398\) | 1179.37i | 2.96324i | ||||||||
\(399\) | −14.6692 | −0.0367649 | ||||||||
\(400\) | 291.746 | 0.729365 | ||||||||
\(401\) | −353.531 | −0.881623 | −0.440811 | − | 0.897600i | \(-0.645309\pi\) | ||||
−0.440811 | + | 0.897600i | \(0.645309\pi\) | |||||||
\(402\) | 207.907i | 0.517183i | ||||||||
\(403\) | 265.644i | 0.659166i | ||||||||
\(404\) | 784.367i | 1.94150i | ||||||||
\(405\) | 55.7654 | 0.137692 | ||||||||
\(406\) | − | 352.031i | − | 0.867073i | ||||||
\(407\) | −84.3923 | − | 109.055i | −0.207352 | − | 0.267948i | ||||
\(408\) | 333.846 | 0.818250 | ||||||||
\(409\) | − | 625.515i | − | 1.52938i | −0.644401 | − | 0.764688i | \(-0.722893\pi\) | ||
0.644401 | − | 0.764688i | \(-0.277107\pi\) | |||||||
\(410\) | −30.2975 | −0.0738963 | ||||||||
\(411\) | 50.6025 | 0.123121 | ||||||||
\(412\) | −1191.29 | −2.89148 | ||||||||
\(413\) | − | 162.166i | − | 0.392653i | ||||||
\(414\) | − | 151.877i | − | 0.366854i | ||||||
\(415\) | 446.086i | 1.07491i | ||||||||
\(416\) | 329.611 | 0.792335 | ||||||||
\(417\) | − | 296.793i | − | 0.711735i | ||||||
\(418\) | 77.8846 | + | 100.645i | 0.186327 | + | 0.240778i | ||||
\(419\) | 100.631 | 0.240169 | 0.120084 | − | 0.992764i | \(-0.461683\pi\) | ||||
0.120084 | + | 0.992764i | \(0.461683\pi\) | |||||||
\(420\) | 234.766i | 0.558967i | ||||||||
\(421\) | −25.7616 | −0.0611914 | −0.0305957 | − | 0.999532i | \(-0.509740\pi\) | ||||
−0.0305957 | + | 0.999532i | \(0.509740\pi\) | |||||||
\(422\) | −109.972 | −0.260597 | ||||||||
\(423\) | 59.4115 | 0.140453 | ||||||||
\(424\) | 189.952i | 0.448000i | ||||||||
\(425\) | − | 163.786i | − | 0.385379i | ||||||
\(426\) | 423.568i | 0.994292i | ||||||||
\(427\) | −55.2257 | −0.129334 | ||||||||
\(428\) | − | 633.961i | − | 1.48122i | ||||||
\(429\) | −358.119 | + | 277.131i | −0.834777 | + | 0.645994i | ||||
\(430\) | 523.972 | 1.21854 | ||||||||
\(431\) | − | 850.178i | − | 1.97257i | −0.165047 | − | 0.986286i | \(-0.552778\pi\) | ||
0.165047 | − | 0.986286i | \(-0.447222\pi\) | |||||||
\(432\) | −113.196 | −0.262028 | ||||||||
\(433\) | −502.631 | −1.16081 | −0.580405 | − | 0.814328i | \(-0.697106\pi\) | ||||
−0.580405 | + | 0.814328i | \(0.697106\pi\) | |||||||
\(434\) | 101.982 | 0.234982 | ||||||||
\(435\) | − | 414.059i | − | 0.951859i | ||||||
\(436\) | − | 1300.37i | − | 2.98250i | ||||||
\(437\) | 46.9910i | 0.107531i | ||||||||
\(438\) | 244.392 | 0.557973 | ||||||||
\(439\) | − | 141.132i | − | 0.321485i | −0.986996 | − | 0.160743i | \(-0.948611\pi\) | ||
0.986996 | − | 0.160743i | \(-0.0513889\pi\) | |||||||
\(440\) | 849.524 | − | 657.407i | 1.93074 | − | 1.49411i | ||||
\(441\) | 126.962 | 0.287895 | ||||||||
\(442\) | − | 1026.19i | − | 2.32171i | ||||||
\(443\) | −871.538 | −1.96736 | −0.983678 | − | 0.179940i | \(-0.942410\pi\) | ||||
−0.983678 | + | 0.179940i | \(0.942410\pi\) | |||||||
\(444\) | −183.779 | −0.413918 | ||||||||
\(445\) | 664.084 | 1.49232 | ||||||||
\(446\) | 486.189i | 1.09011i | ||||||||
\(447\) | − | 284.564i | − | 0.636607i | ||||||
\(448\) | 98.6671i | 0.220239i | ||||||||
\(449\) | −122.364 | −0.272526 | −0.136263 | − | 0.990673i | \(-0.543509\pi\) | ||||
−0.136263 | + | 0.990673i | \(0.543509\pi\) | |||||||
\(450\) | 141.843i | 0.315206i | ||||||||
\(451\) | −12.0488 | + | 9.32398i | −0.0267157 | + | 0.0206740i | ||||
\(452\) | −1407.71 | −3.11440 | ||||||||
\(453\) | 397.588i | 0.877677i | ||||||||
\(454\) | 1164.47 | 2.56490 | ||||||||
\(455\) | 380.603 | 0.836489 | ||||||||
\(456\) | 89.4538 | 0.196171 | ||||||||
\(457\) | 581.864i | 1.27323i | 0.771184 | + | 0.636613i | \(0.219665\pi\) | ||||
−0.771184 | + | 0.636613i | \(0.780335\pi\) | |||||||
\(458\) | 1056.60i | 2.30699i | ||||||||
\(459\) | 63.5482i | 0.138449i | ||||||||
\(460\) | 752.046 | 1.63488 | ||||||||
\(461\) | − | 54.4595i | − | 0.118133i | −0.998254 | − | 0.0590667i | \(-0.981188\pi\) | ||
0.998254 | − | 0.0590667i | \(-0.0188124\pi\) | |||||||
\(462\) | 106.392 | + | 137.484i | 0.230286 | + | 0.297584i | ||||
\(463\) | 356.382 | 0.769724 | 0.384862 | − | 0.922974i | \(-0.374249\pi\) | ||||
0.384862 | + | 0.922974i | \(0.374249\pi\) | |||||||
\(464\) | 840.483i | 1.81139i | ||||||||
\(465\) | 119.951 | 0.257960 | ||||||||
\(466\) | −515.854 | −1.10698 | ||||||||
\(467\) | 298.613 | 0.639428 | 0.319714 | − | 0.947514i | \(-0.396413\pi\) | ||||
0.319714 | + | 0.947514i | \(0.396413\pi\) | |||||||
\(468\) | 603.504i | 1.28954i | ||||||||
\(469\) | − | 87.8720i | − | 0.187360i | ||||||
\(470\) | 433.214i | 0.921731i | ||||||||
\(471\) | 185.090 | 0.392972 | ||||||||
\(472\) | 988.898i | 2.09512i | ||||||||
\(473\) | 208.374 | − | 161.251i | 0.440538 | − | 0.340911i | ||||
\(474\) | −597.142 | −1.25979 | ||||||||
\(475\) | − | 43.8863i | − | 0.0923922i | ||||||
\(476\) | −267.531 | −0.562039 | ||||||||
\(477\) | −36.1577 | −0.0758023 | ||||||||
\(478\) | −223.874 | −0.468356 | ||||||||
\(479\) | − | 333.755i | − | 0.696774i | −0.937351 | − | 0.348387i | \(-0.886730\pi\) | ||
0.937351 | − | 0.348387i | \(-0.113270\pi\) | |||||||
\(480\) | − | 148.836i | − | 0.310074i | ||||||
\(481\) | 297.943i | 0.619424i | ||||||||
\(482\) | −1239.25 | −2.57106 | ||||||||
\(483\) | 64.1909i | 0.132901i | ||||||||
\(484\) | 256.962 | − | 991.396i | 0.530912 | − | 2.04834i | ||||
\(485\) | −1033.18 | −2.13028 | ||||||||
\(486\) | − | 55.0343i | − | 0.113239i | ||||||
\(487\) | −709.251 | −1.45637 | −0.728184 | − | 0.685382i | \(-0.759635\pi\) | ||||
−0.728184 | + | 0.685382i | \(0.759635\pi\) | |||||||
\(488\) | 336.771 | 0.690104 | ||||||||
\(489\) | 204.497 | 0.418195 | ||||||||
\(490\) | 925.771i | 1.88933i | ||||||||
\(491\) | 31.9912i | 0.0651551i | 0.999469 | + | 0.0325776i | \(0.0103716\pi\) | ||||
−0.999469 | + | 0.0325776i | \(0.989628\pi\) | |||||||
\(492\) | 20.3047i | 0.0412696i | ||||||||
\(493\) | 471.846 | 0.957091 | ||||||||
\(494\) | − | 274.968i | − | 0.556615i | ||||||
\(495\) | 125.138 | + | 161.708i | 0.252805 | + | 0.326684i | ||||
\(496\) | −243.485 | −0.490897 | ||||||||
\(497\) | − | 179.021i | − | 0.360203i | ||||||
\(498\) | 440.238 | 0.884013 | ||||||||
\(499\) | 27.6922 | 0.0554954 | 0.0277477 | − | 0.999615i | \(-0.491167\pi\) | ||||
0.0277477 | + | 0.999615i | \(0.491167\pi\) | |||||||
\(500\) | 608.764 | 1.21753 | ||||||||
\(501\) | − | 2.39891i | − | 0.00478825i | ||||||
\(502\) | 232.032i | 0.462216i | ||||||||
\(503\) | − | 69.6946i | − | 0.138558i | −0.997597 | − | 0.0692789i | \(-0.977930\pi\) | ||
0.997597 | − | 0.0692789i | \(-0.0220698\pi\) | |||||||
\(504\) | 122.196 | 0.242453 | ||||||||
\(505\) | − | 574.197i | − | 1.13702i | ||||||
\(506\) | 440.414 | − | 340.815i | 0.870383 | − | 0.673548i | ||||
\(507\) | 685.683 | 1.35243 | ||||||||
\(508\) | 1610.91i | 3.17109i | ||||||||
\(509\) | −252.732 | −0.496527 | −0.248263 | − | 0.968693i | \(-0.579860\pi\) | ||||
−0.248263 | + | 0.968693i | \(0.579860\pi\) | |||||||
\(510\) | −463.377 | −0.908582 | ||||||||
\(511\) | −103.292 | −0.202138 | ||||||||
\(512\) | − | 1071.21i | − | 2.09221i | ||||||
\(513\) | 17.0277i | 0.0331924i | ||||||||
\(514\) | − | 727.916i | − | 1.41618i | ||||||
\(515\) | 872.084 | 1.69337 | ||||||||
\(516\) | − | 351.153i | − | 0.680530i | ||||||
\(517\) | 133.321 | + | 172.282i | 0.257873 | + | 0.333233i | ||||
\(518\) | 114.382 | 0.220815 | ||||||||
\(519\) | − | 117.501i | − | 0.226398i | ||||||
\(520\) | −2320.94 | −4.46335 | ||||||||
\(521\) | −611.864 | −1.17440 | −0.587201 | − | 0.809441i | \(-0.699770\pi\) | ||||
−0.587201 | + | 0.809441i | \(0.699770\pi\) | |||||||
\(522\) | −408.631 | −0.782817 | ||||||||
\(523\) | − | 6.31868i | − | 0.0120816i | −0.999982 | − | 0.00604080i | \(-0.998077\pi\) | ||
0.999982 | − | 0.00604080i | \(-0.00192286\pi\) | |||||||
\(524\) | − | 839.840i | − | 1.60275i | ||||||
\(525\) | − | 59.9498i | − | 0.114190i | ||||||
\(526\) | −64.5256 | −0.122672 | ||||||||
\(527\) | 136.692i | 0.259378i | ||||||||
\(528\) | −254.014 | − | 328.246i | −0.481087 | − | 0.621678i | ||||
\(529\) | −323.372 | −0.611289 | ||||||||
\(530\) | − | 263.652i | − | 0.497457i | ||||||
\(531\) | −188.238 | −0.354498 | ||||||||
\(532\) | −71.6846 | −0.134746 | ||||||||
\(533\) | 32.9179 | 0.0617597 | ||||||||
\(534\) | − | 655.379i | − | 1.22730i | ||||||
\(535\) | 464.091i | 0.867461i | ||||||||
\(536\) | 535.850i | 0.999721i | ||||||||
\(537\) | 236.603 | 0.440601 | ||||||||
\(538\) | − | 607.695i | − | 1.12955i | ||||||
\(539\) | 284.904 | + | 368.163i | 0.528578 | + | 0.683048i | ||||
\(540\) | 272.512 | 0.504651 | ||||||||
\(541\) | 427.018i | 0.789311i | 0.918829 | + | 0.394656i | \(0.129136\pi\) | ||||
−0.918829 | + | 0.394656i | \(0.870864\pi\) | |||||||
\(542\) | 1503.86 | 2.77464 | ||||||||
\(543\) | −298.210 | −0.549190 | ||||||||
\(544\) | 169.608 | 0.311779 | ||||||||
\(545\) | 951.937i | 1.74667i | ||||||||
\(546\) | − | 375.613i | − | 0.687936i | ||||||
\(547\) | 783.217i | 1.43184i | 0.698182 | + | 0.715921i | \(0.253993\pi\) | ||||
−0.698182 | + | 0.715921i | \(0.746007\pi\) | |||||||
\(548\) | 247.282 | 0.451245 | ||||||||
\(549\) | 64.1048i | 0.116767i | ||||||||
\(550\) | −411.315 | + | 318.297i | −0.747846 | + | 0.578723i | ||||
\(551\) | 126.431 | 0.229457 | ||||||||
\(552\) | − | 391.441i | − | 0.709133i | ||||||
\(553\) | 252.382 | 0.456387 | ||||||||
\(554\) | 922.999 | 1.66606 | ||||||||
\(555\) | 134.536 | 0.242407 | ||||||||
\(556\) | − | 1450.36i | − | 2.60855i | ||||||
\(557\) | 508.385i | 0.912720i | 0.889795 | + | 0.456360i | \(0.150847\pi\) | ||||
−0.889795 | + | 0.456360i | \(0.849153\pi\) | |||||||
\(558\) | − | 118.379i | − | 0.212148i | ||||||
\(559\) | −569.290 | −1.01841 | ||||||||
\(560\) | 348.854i | 0.622953i | ||||||||
\(561\) | −184.277 | + | 142.603i | −0.328479 | + | 0.254195i | ||||
\(562\) | 1162.20 | 2.06797 | ||||||||
\(563\) | − | 670.786i | − | 1.19145i | −0.803189 | − | 0.595725i | \(-0.796865\pi\) | ||
0.803189 | − | 0.595725i | \(-0.203135\pi\) | |||||||
\(564\) | 290.329 | 0.514769 | ||||||||
\(565\) | 1030.52 | 1.82392 | ||||||||
\(566\) | 816.782 | 1.44308 | ||||||||
\(567\) | 23.2602i | 0.0410234i | ||||||||
\(568\) | 1091.68i | 1.92198i | ||||||||
\(569\) | − | 756.359i | − | 1.32928i | −0.747165 | − | 0.664639i | \(-0.768586\pi\) | ||
0.747165 | − | 0.664639i | \(-0.231414\pi\) | |||||||
\(570\) | −124.161 | −0.217827 | ||||||||
\(571\) | − | 647.983i | − | 1.13482i | −0.823435 | − | 0.567411i | \(-0.807945\pi\) | ||
0.823435 | − | 0.567411i | \(-0.192055\pi\) | |||||||
\(572\) | −1750.04 | + | 1354.27i | −3.05951 | + | 2.36761i | ||||
\(573\) | −238.617 | −0.416434 | ||||||||
\(574\) | − | 12.6374i | − | 0.0220163i | ||||||
\(575\) | −192.042 | −0.333987 | ||||||||
\(576\) | 114.531 | 0.198838 | ||||||||
\(577\) | 78.3257 | 0.135746 | 0.0678732 | − | 0.997694i | \(-0.478379\pi\) | ||||
0.0678732 | + | 0.997694i | \(0.478379\pi\) | |||||||
\(578\) | 492.254i | 0.851650i | ||||||||
\(579\) | 184.326i | 0.318352i | ||||||||
\(580\) | − | 2023.40i | − | 3.48862i | ||||||
\(581\) | −186.067 | −0.320252 | ||||||||
\(582\) | 1019.64i | 1.75196i | ||||||||
\(583\) | −81.1384 | − | 104.850i | −0.139174 | − | 0.179846i | ||||
\(584\) | 629.885 | 1.07857 | ||||||||
\(585\) | − | 441.795i | − | 0.755206i | ||||||
\(586\) | 705.149 | 1.20333 | ||||||||
\(587\) | 190.515 | 0.324558 | 0.162279 | − | 0.986745i | \(-0.448116\pi\) | ||||
0.162279 | + | 0.986745i | \(0.448116\pi\) | |||||||
\(588\) | 620.429 | 1.05515 | ||||||||
\(589\) | 36.6265i | 0.0621842i | ||||||||
\(590\) | − | 1372.59i | − | 2.32642i | ||||||
\(591\) | − | 57.8723i | − | 0.0979226i | ||||||
\(592\) | −273.090 | −0.461300 | ||||||||
\(593\) | 770.010i | 1.29850i | 0.760575 | + | 0.649250i | \(0.224917\pi\) | ||||
−0.760575 | + | 0.649250i | \(0.775083\pi\) | |||||||
\(594\) | 159.588 | − | 123.498i | 0.268667 | − | 0.207909i | ||||
\(595\) | 195.846 | 0.329153 | ||||||||
\(596\) | − | 1390.59i | − | 2.33321i | ||||||
\(597\) | −578.603 | −0.969183 | ||||||||
\(598\) | −1203.23 | −2.01210 | ||||||||
\(599\) | −891.517 | −1.48834 | −0.744171 | − | 0.667989i | \(-0.767155\pi\) | ||||
−0.744171 | + | 0.667989i | \(0.767155\pi\) | |||||||
\(600\) | 365.578i | 0.609297i | ||||||||
\(601\) | − | 75.5063i | − | 0.125635i | −0.998025 | − | 0.0628173i | \(-0.979991\pi\) | ||
0.998025 | − | 0.0628173i | \(-0.0200085\pi\) | |||||||
\(602\) | 218.553i | 0.363046i | ||||||||
\(603\) | −102.000 | −0.169154 | ||||||||
\(604\) | 1942.91i | 3.21674i | ||||||||
\(605\) | −188.109 | + | 725.753i | −0.310924 | + | 1.19959i | ||||
\(606\) | −566.669 | −0.935098 | ||||||||
\(607\) | 442.017i | 0.728200i | 0.931360 | + | 0.364100i | \(0.118623\pi\) | ||||
−0.931360 | + | 0.364100i | \(0.881377\pi\) | |||||||
\(608\) | 45.4462 | 0.0747471 | ||||||||
\(609\) | 172.708 | 0.283592 | ||||||||
\(610\) | −467.436 | −0.766288 | ||||||||
\(611\) | − | 470.682i | − | 0.770347i | ||||||
\(612\) | 310.544i | 0.507425i | ||||||||
\(613\) | − | 544.346i | − | 0.888003i | −0.896026 | − | 0.444002i | \(-0.853558\pi\) | ||
0.896026 | − | 0.444002i | \(-0.146442\pi\) | |||||||
\(614\) | −1504.99 | −2.45113 | ||||||||
\(615\) | − | 14.8640i | − | 0.0241692i | ||||||
\(616\) | 274.210 | + | 354.344i | 0.445146 | + | 0.575234i | ||||
\(617\) | 406.946 | 0.659556 | 0.329778 | − | 0.944059i | \(-0.393026\pi\) | ||||
0.329778 | + | 0.944059i | \(0.393026\pi\) | |||||||
\(618\) | − | 860.652i | − | 1.39264i | ||||||
\(619\) | −218.939 | −0.353697 | −0.176849 | − | 0.984238i | \(-0.556590\pi\) | ||||
−0.176849 | + | 0.984238i | \(0.556590\pi\) | |||||||
\(620\) | 586.172 | 0.945438 | ||||||||
\(621\) | 74.5115 | 0.119986 | ||||||||
\(622\) | − | 1064.83i | − | 1.71194i | ||||||
\(623\) | 276.996i | 0.444616i | ||||||||
\(624\) | 896.785i | 1.43716i | ||||||||
\(625\) | −780.454 | −1.24873 | ||||||||
\(626\) | 920.380i | 1.47026i | ||||||||
\(627\) | −49.3768 | + | 38.2104i | −0.0787509 | + | 0.0609416i | ||||
\(628\) | 904.487 | 1.44027 | ||||||||
\(629\) | 153.312i | 0.243740i | ||||||||
\(630\) | −169.608 | −0.269219 | ||||||||
\(631\) | 185.664 | 0.294238 | 0.147119 | − | 0.989119i | \(-0.453000\pi\) | ||||
0.147119 | + | 0.989119i | \(0.453000\pi\) | |||||||
\(632\) | −1539.04 | −2.43520 | ||||||||
\(633\) | − | 53.9525i | − | 0.0852330i | ||||||
\(634\) | 1592.91i | 2.51247i | ||||||||
\(635\) | − | 1179.27i | − | 1.85712i | ||||||
\(636\) | −176.694 | −0.277820 | ||||||||
\(637\) | − | 1005.84i | − | 1.57903i | ||||||
\(638\) | −916.974 | − | 1184.95i | −1.43726 | − | 1.85728i | ||||
\(639\) | −207.804 | −0.325202 | ||||||||
\(640\) | 1178.85i | 1.84195i | ||||||||
\(641\) | 375.618 | 0.585988 | 0.292994 | − | 0.956114i | \(-0.405348\pi\) | ||||
0.292994 | + | 0.956114i | \(0.405348\pi\) | |||||||
\(642\) | 458.008 | 0.713407 | ||||||||
\(643\) | −454.764 | −0.707253 | −0.353627 | − | 0.935387i | \(-0.615052\pi\) | ||||
−0.353627 | + | 0.935387i | \(0.615052\pi\) | |||||||
\(644\) | 313.685i | 0.487089i | ||||||||
\(645\) | 257.062i | 0.398546i | ||||||||
\(646\) | − | 141.490i | − | 0.219024i | ||||||
\(647\) | 724.273 | 1.11943 | 0.559716 | − | 0.828684i | \(-0.310910\pi\) | ||||
0.559716 | + | 0.828684i | \(0.310910\pi\) | |||||||
\(648\) | − | 141.843i | − | 0.218893i | ||||||
\(649\) | −422.410 | − | 545.853i | −0.650863 | − | 0.841069i | ||||
\(650\) | 1123.73 | 1.72882 | ||||||||
\(651\) | 50.0327i | 0.0768552i | ||||||||
\(652\) | 999.328 | 1.53271 | ||||||||
\(653\) | −336.865 | −0.515873 | −0.257937 | − | 0.966162i | \(-0.583043\pi\) | ||||
−0.257937 | + | 0.966162i | \(0.583043\pi\) | |||||||
\(654\) | 939.458 | 1.43648 | ||||||||
\(655\) | 614.806i | 0.938635i | ||||||||
\(656\) | 30.1720i | 0.0459939i | ||||||||
\(657\) | 119.900i | 0.182496i | ||||||||
\(658\) | −180.697 | −0.274616 | ||||||||
\(659\) | − | 41.1163i | − | 0.0623919i | −0.999513 | − | 0.0311960i | \(-0.990068\pi\) | ||
0.999513 | − | 0.0311960i | \(-0.00993159\pi\) | |||||||
\(660\) | 611.520 | + | 790.229i | 0.926546 | + | 1.19732i | ||||
\(661\) | −831.969 | −1.25865 | −0.629326 | − | 0.777141i | \(-0.716669\pi\) | ||||
−0.629326 | + | 0.777141i | \(0.716669\pi\) | |||||||
\(662\) | 810.483i | 1.22430i | ||||||||
\(663\) | 503.454 | 0.759357 | ||||||||
\(664\) | 1134.65 | 1.70881 | ||||||||
\(665\) | 52.4768 | 0.0789125 | ||||||||
\(666\) | − | 132.772i | − | 0.199358i | ||||||
\(667\) | − | 553.249i | − | 0.829459i | ||||||
\(668\) | − | 11.7229i | − | 0.0175493i | ||||||
\(669\) | −238.526 | −0.356540 | ||||||||
\(670\) | − | 743.758i | − | 1.11009i | ||||||
\(671\) | −185.891 | + | 143.852i | −0.277036 | + | 0.214385i | ||||
\(672\) | 62.0807 | 0.0923820 | ||||||||
\(673\) | 682.274i | 1.01378i | 0.862011 | + | 0.506890i | \(0.169205\pi\) | ||||
−0.862011 | + | 0.506890i | \(0.830795\pi\) | |||||||
\(674\) | −628.925 | −0.933124 | ||||||||
\(675\) | −69.5885 | −0.103094 | ||||||||
\(676\) | 3350.76 | 4.95675 | ||||||||
\(677\) | − | 483.554i | − | 0.714261i | −0.934055 | − | 0.357130i | \(-0.883755\pi\) | ||
0.934055 | − | 0.357130i | \(-0.116245\pi\) | |||||||
\(678\) | − | 1017.01i | − | 1.50001i | ||||||
\(679\) | − | 430.951i | − | 0.634684i | ||||||
\(680\) | −1194.28 | −1.75630 | ||||||||
\(681\) | 571.291i | 0.838900i | ||||||||
\(682\) | 343.274 | − | 265.644i | 0.503335 | − | 0.389507i | ||||
\(683\) | 875.097 | 1.28126 | 0.640628 | − | 0.767852i | \(-0.278674\pi\) | ||||
0.640628 | + | 0.767852i | \(0.278674\pi\) | |||||||
\(684\) | 83.2100i | 0.121652i | ||||||||
\(685\) | −181.023 | −0.264267 | ||||||||
\(686\) | −833.241 | −1.21464 | ||||||||
\(687\) | −518.372 | −0.754544 | ||||||||
\(688\) | − | 521.801i | − | 0.758432i | ||||||
\(689\) | 286.455i | 0.415755i | ||||||||
\(690\) | 543.319i | 0.787418i | ||||||||
\(691\) | 845.615 | 1.22376 | 0.611878 | − | 0.790952i | \(-0.290414\pi\) | ||||
0.611878 | + | 0.790952i | \(0.290414\pi\) | |||||||
\(692\) | − | 574.197i | − | 0.829764i | ||||||
\(693\) | −67.4500 | + | 52.1964i | −0.0973305 | + | 0.0753194i | ||||
\(694\) | −2029.44 | −2.92427 | ||||||||
\(695\) | 1061.73i | 1.52767i | ||||||||
\(696\) | −1053.18 | −1.51320 | ||||||||
\(697\) | 16.9385 | 0.0243020 | ||||||||
\(698\) | 644.729 | 0.923681 | ||||||||
\(699\) | − | 253.079i | − | 0.362059i | ||||||
\(700\) | − | 292.960i | − | 0.418514i | ||||||
\(701\) | 842.982i | 1.20254i | 0.799045 | + | 0.601271i | \(0.205339\pi\) | ||||
−0.799045 | + | 0.601271i | \(0.794661\pi\) | |||||||
\(702\) | −436.004 | −0.621088 | ||||||||
\(703\) | 41.0799i | 0.0584351i | ||||||||
\(704\) | 257.009 | + | 332.116i | 0.365070 | + | 0.471756i | ||||
\(705\) | −212.536 | −0.301469 | ||||||||
\(706\) | − | 691.932i | − | 0.980074i | ||||||
\(707\) | 239.503 | 0.338759 | ||||||||
\(708\) | −919.874 | −1.29926 | ||||||||
\(709\) | 1227.03 | 1.73065 | 0.865325 | − | 0.501212i | \(-0.167112\pi\) | ||||
0.865325 | + | 0.501212i | \(0.167112\pi\) | |||||||
\(710\) | − | 1515.25i | − | 2.13416i | ||||||
\(711\) | − | 292.960i | − | 0.412039i | ||||||
\(712\) | − | 1689.14i | − | 2.37239i | ||||||
\(713\) | 160.274 | 0.224788 | ||||||||
\(714\) | − | 193.279i | − | 0.270698i | ||||||
\(715\) | 1281.12 | − | 991.396i | 1.79177 | − | 1.38657i | ||||
\(716\) | 1156.22 | 1.61483 | ||||||||
\(717\) | − | 109.833i | − | 0.153185i | ||||||
\(718\) | −2496.40 | −3.47688 | ||||||||
\(719\) | 343.986 | 0.478423 | 0.239211 | − | 0.970968i | \(-0.423111\pi\) | ||||
0.239211 | + | 0.970968i | \(0.423111\pi\) | |||||||
\(720\) | 404.942 | 0.562420 | ||||||||
\(721\) | 363.754i | 0.504514i | ||||||||
\(722\) | 1236.58i | 1.71272i | ||||||||
\(723\) | − | 607.980i | − | 0.840913i | ||||||
\(724\) | −1457.28 | −2.01282 | ||||||||
\(725\) | 516.695i | 0.712683i | ||||||||
\(726\) | 716.238 | + | 185.643i | 0.986554 | + | 0.255706i | ||||
\(727\) | 205.138 | 0.282171 | 0.141086 | − | 0.989997i | \(-0.454941\pi\) | ||||
0.141086 | + | 0.989997i | \(0.454941\pi\) | |||||||
\(728\) | − | 968.086i | − | 1.32979i | ||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −874.277 | −1.19764 | ||||||||
\(731\) | −292.939 | −0.400737 | ||||||||
\(732\) | 313.264i | 0.427957i | ||||||||
\(733\) | − | 849.486i | − | 1.15892i | −0.815002 | − | 0.579458i | \(-0.803264\pi\) | ||
0.815002 | − | 0.579458i | \(-0.196736\pi\) | |||||||
\(734\) | 1268.90i | 1.72875i | ||||||||
\(735\) | −454.186 | −0.617940 | ||||||||
\(736\) | − | 198.868i | − | 0.270202i | ||||||
\(737\) | −228.890 | − | 295.779i | −0.310570 | − | 0.401329i | ||||
\(738\) | −14.6692 | −0.0198769 | ||||||||
\(739\) | − | 1206.77i | − | 1.63298i | −0.577360 | − | 0.816490i | \(-0.695917\pi\) | ||
0.577360 | − | 0.816490i | \(-0.304083\pi\) | |||||||
\(740\) | 657.443 | 0.888437 | ||||||||
\(741\) | 134.900 | 0.182051 | ||||||||
\(742\) | 109.972 | 0.148210 | ||||||||
\(743\) | − | 229.932i | − | 0.309464i | −0.987956 | − | 0.154732i | \(-0.950549\pi\) | ||
0.987956 | − | 0.154732i | \(-0.0494514\pi\) | |||||||
\(744\) | − | 305.103i | − | 0.410085i | ||||||
\(745\) | 1017.98i | 1.36642i | ||||||||
\(746\) | 1284.39 | 1.72171 | ||||||||
\(747\) | 215.982i | 0.289133i | ||||||||
\(748\) | −900.515 | + | 696.866i | −1.20390 | + | 0.931639i | ||||
\(749\) | −193.577 | −0.258447 | ||||||||
\(750\) | 439.804i | 0.586405i | ||||||||
\(751\) | 616.269 | 0.820598 | 0.410299 | − | 0.911951i | \(-0.365424\pi\) | ||||
0.410299 | + | 0.911951i | \(0.365424\pi\) | |||||||
\(752\) | 431.419 | 0.573696 | ||||||||
\(753\) | −113.836 | −0.151176 | ||||||||
\(754\) | 3237.33i | 4.29355i | ||||||||
\(755\) | − | 1422.31i | − | 1.88386i | ||||||
\(756\) | 113.667i | 0.150353i | ||||||||
\(757\) | 85.4181 | 0.112838 | 0.0564188 | − | 0.998407i | \(-0.482032\pi\) | ||||
0.0564188 | + | 0.998407i | \(0.482032\pi\) | |||||||
\(758\) | − | 939.263i | − | 1.23913i | ||||||
\(759\) | 167.205 | + | 216.068i | 0.220297 | + | 0.284675i | ||||
\(760\) | −320.008 | −0.421063 | ||||||||
\(761\) | − | 439.940i | − | 0.578108i | −0.957313 | − | 0.289054i | \(-0.906659\pi\) | ||
0.957313 | − | 0.289054i | \(-0.0933406\pi\) | |||||||
\(762\) | −1163.81 | −1.52731 | ||||||||
\(763\) | −397.061 | −0.520395 | ||||||||
\(764\) | −1166.06 | −1.52626 | ||||||||
\(765\) | − | 227.334i | − | 0.297169i | ||||||
\(766\) | 1169.49i | 1.52675i | ||||||||
\(767\) | 1491.30i | 1.94433i | ||||||||
\(768\) | 898.899 | 1.17044 | ||||||||
\(769\) | 928.726i | 1.20771i | 0.797095 | + | 0.603853i | \(0.206369\pi\) | ||||
−0.797095 | + | 0.603853i | \(0.793631\pi\) | |||||||
\(770\) | −380.603 | − | 491.828i | −0.494289 | − | 0.638738i | ||||
\(771\) | 357.118 | 0.463188 | ||||||||
\(772\) | 900.754i | 1.16678i | ||||||||
\(773\) | 929.734 | 1.20276 | 0.601381 | − | 0.798963i | \(-0.294618\pi\) | ||||
0.601381 | + | 0.798963i | \(0.294618\pi\) | |||||||
\(774\) | 253.692 | 0.327768 | ||||||||
\(775\) | −149.685 | −0.193141 | ||||||||
\(776\) | 2627.97i | 3.38656i | ||||||||
\(777\) | 56.1161i | 0.0722215i | ||||||||
\(778\) | 1486.42i | 1.91056i | ||||||||
\(779\) | 4.53866 | 0.00582627 | ||||||||
\(780\) | − | 2158.94i | − | 2.76788i | ||||||
\(781\) | −466.315 | − | 602.589i | −0.597075 | − | 0.771561i | ||||
\(782\) | −619.146 | −0.791747 | ||||||||
\(783\) | − | 200.475i | − | 0.256035i | ||||||
\(784\) | 921.936 | 1.17594 | ||||||||
\(785\) | −662.131 | −0.843478 | ||||||||
\(786\) | 606.746 | 0.771942 | ||||||||
\(787\) | 250.644i | 0.318480i | 0.987240 | + | 0.159240i | \(0.0509044\pi\) | ||||
−0.987240 | + | 0.159240i | \(0.949096\pi\) | |||||||
\(788\) | − | 282.807i | − | 0.358893i | ||||||
\(789\) | − | 31.6564i | − | 0.0401222i | ||||||
\(790\) | 2136.19 | 2.70403 | ||||||||
\(791\) | 429.837i | 0.543410i | ||||||||
\(792\) | 411.315 | − | 318.297i | 0.519338 | − | 0.401891i | ||||
\(793\) | 507.864 | 0.640434 | ||||||||
\(794\) | − | 1489.14i | − | 1.87549i | ||||||
\(795\) | 129.349 | 0.162703 | ||||||||
\(796\) | −2827.49 | −3.55212 | ||||||||
\(797\) | 872.319 | 1.09450 | 0.547252 | − | 0.836968i | \(-0.315674\pi\) | ||||
0.547252 | + | 0.836968i | \(0.315674\pi\) | |||||||
\(798\) | − | 51.7889i | − | 0.0648983i | ||||||
\(799\) | − | 242.198i | − | 0.303127i | ||||||
\(800\) | 185.729i | 0.232161i | ||||||||
\(801\) | 321.531 | 0.401412 | ||||||||
\(802\) | − | 1248.12i | − | 1.55626i | ||||||
\(803\) | −347.685 | + | 269.057i | −0.432982 | + | 0.335064i | ||||
\(804\) | −498.449 | −0.619961 | ||||||||
\(805\) | − | 229.634i | − | 0.285259i | ||||||
\(806\) | −937.843 | −1.16358 | ||||||||
\(807\) | 298.137 | 0.369439 | ||||||||
\(808\) | −1460.50 | −1.80756 | ||||||||
\(809\) | − | 963.696i | − | 1.19122i | −0.803274 | − | 0.595609i | \(-0.796911\pi\) | ||
0.803274 | − | 0.595609i | \(-0.203089\pi\) | |||||||
\(810\) | 196.877i | 0.243058i | ||||||||
\(811\) | 583.285i | 0.719217i | 0.933103 | + | 0.359609i | \(0.117090\pi\) | ||||
−0.933103 | + | 0.359609i | \(0.882910\pi\) | |||||||
\(812\) | 843.979 | 1.03938 | ||||||||
\(813\) | 737.797i | 0.907499i | ||||||||
\(814\) | 385.013 | − | 297.943i | 0.472989 | − | 0.366023i | ||||
\(815\) | −731.559 | −0.897618 | ||||||||
\(816\) | 461.457i | 0.565511i | ||||||||
\(817\) | −78.4926 | −0.0960742 | ||||||||
\(818\) | 2208.35 | 2.69970 | ||||||||
\(819\) | 184.277 | 0.225002 | ||||||||
\(820\) | − | 72.6369i | − | 0.0885815i | ||||||
\(821\) | − | 211.927i | − | 0.258132i | −0.991636 | − | 0.129066i | \(-0.958802\pi\) | ||
0.991636 | − | 0.129066i | \(-0.0411980\pi\) | |||||||
\(822\) | 178.650i | 0.217336i | ||||||||
\(823\) | −1049.19 | −1.27484 | −0.637421 | − | 0.770516i | \(-0.719999\pi\) | ||||
−0.637421 | + | 0.770516i | \(0.719999\pi\) | |||||||
\(824\) | − | 2218.20i | − | 2.69199i | ||||||
\(825\) | −156.158 | − | 201.793i | −0.189282 | − | 0.244597i | ||||
\(826\) | 572.518 | 0.693121 | ||||||||
\(827\) | 1226.67i | 1.48328i | 0.670800 | + | 0.741638i | \(0.265951\pi\) | ||||
−0.670800 | + | 0.741638i | \(0.734049\pi\) | |||||||
\(828\) | 364.119 | 0.439757 | ||||||||
\(829\) | 579.395 | 0.698908 | 0.349454 | − | 0.936954i | \(-0.386367\pi\) | ||||
0.349454 | + | 0.936954i | \(0.386367\pi\) | |||||||
\(830\) | −1574.89 | −1.89745 | ||||||||
\(831\) | 452.826i | 0.544917i | ||||||||
\(832\) | − | 907.358i | − | 1.09057i | ||||||
\(833\) | − | 517.573i | − | 0.621337i | ||||||
\(834\) | 1047.82 | 1.25637 | ||||||||
\(835\) | 8.58176i | 0.0102776i | ||||||||
\(836\) | −241.292 | + | 186.725i | −0.288627 | + | 0.223355i | ||||
\(837\) | 58.0770 | 0.0693870 | ||||||||
\(838\) | 355.272i | 0.423952i | ||||||||
\(839\) | −1198.03 | −1.42793 | −0.713964 | − | 0.700182i | \(-0.753102\pi\) | ||||
−0.713964 | + | 0.700182i | \(0.753102\pi\) | |||||||
\(840\) | −437.138 | −0.520403 | ||||||||
\(841\) | −647.533 | −0.769956 | ||||||||
\(842\) | − | 90.9501i | − | 0.108017i | ||||||
\(843\) | 570.177i | 0.676367i | ||||||||
\(844\) | − | 263.652i | − | 0.312384i | ||||||
\(845\) | −2452.93 | −2.90287 | ||||||||
\(846\) | 209.750i | 0.247931i | ||||||||
\(847\) | −302.718 | − | 78.4619i | −0.357400 | − | 0.0926351i | ||||
\(848\) | −262.560 | −0.309623 | ||||||||
\(849\) | 400.716i | 0.471985i | ||||||||
\(850\) | 578.238 | 0.680280 | ||||||||
\(851\) | 179.762 | 0.211236 | ||||||||
\(852\) | −1015.49 | −1.19188 | ||||||||
\(853\) | − | 1015.06i | − | 1.18999i | −0.803728 | − | 0.594997i | \(-0.797153\pi\) | ||
0.803728 | − | 0.594997i | \(-0.202847\pi\) | |||||||
\(854\) | − | 194.972i | − | 0.228304i | ||||||
\(855\) | − | 60.9140i | − | 0.0712444i | ||||||
\(856\) | 1180.45 | 1.37903 | ||||||||
\(857\) | − | 1574.17i | − | 1.83684i | −0.395603 | − | 0.918422i | \(-0.629464\pi\) | ||
0.395603 | − | 0.918422i | \(-0.370536\pi\) | |||||||
\(858\) | −978.400 | − | 1264.32i | −1.14033 | − | 1.47357i | ||||
\(859\) | 99.9230 | 0.116325 | 0.0581624 | − | 0.998307i | \(-0.481476\pi\) | ||||
0.0581624 | + | 0.998307i | \(0.481476\pi\) | |||||||
\(860\) | 1256.20i | 1.46070i | ||||||||
\(861\) | 6.19993 | 0.00720084 | ||||||||
\(862\) | 3001.51 | 3.48204 | ||||||||
\(863\) | −1405.55 | −1.62868 | −0.814339 | − | 0.580389i | \(-0.802900\pi\) | ||||
−0.814339 | + | 0.580389i | \(0.802900\pi\) | |||||||
\(864\) | − | 72.0620i | − | 0.0834051i | ||||||
\(865\) | 420.341i | 0.485943i | ||||||||
\(866\) | − | 1774.51i | − | 2.04909i | ||||||
\(867\) | −241.501 | −0.278548 | ||||||||
\(868\) | 244.498i | 0.281679i | ||||||||
\(869\) | 849.524 | − | 657.407i | 0.977588 | − | 0.756509i | ||||
\(870\) | 1461.82 | 1.68025 | ||||||||
\(871\) | 808.085i | 0.927766i | ||||||||
\(872\) | 2421.31 | 2.77673 | ||||||||
\(873\) | −500.238 | −0.573011 | ||||||||
\(874\) | −165.900 | −0.189817 | ||||||||
\(875\) | − | 185.883i | − | 0.212438i | ||||||
\(876\) | 585.919i | 0.668858i | ||||||||
\(877\) | 1231.05i | 1.40370i | 0.712324 | + | 0.701851i | \(0.247643\pi\) | ||||
−0.712324 | + | 0.701851i | \(0.752357\pi\) | |||||||
\(878\) | 498.260 | 0.567494 | ||||||||
\(879\) | 345.948i | 0.393570i | ||||||||
\(880\) | 908.697 | + | 1174.25i | 1.03261 | + | 1.33438i | ||||
\(881\) | 419.359 | 0.476003 | 0.238002 | − | 0.971265i | \(-0.423508\pi\) | ||||
0.238002 | + | 0.971265i | \(0.423508\pi\) | |||||||
\(882\) | 448.232i | 0.508199i | ||||||||
\(883\) | 867.856 | 0.982850 | 0.491425 | − | 0.870920i | \(-0.336476\pi\) | ||||
0.491425 | + | 0.870920i | \(0.336476\pi\) | |||||||
\(884\) | 2460.25 | 2.78309 | ||||||||
\(885\) | 673.395 | 0.760898 | ||||||||
\(886\) | − | 3076.93i | − | 3.47283i | ||||||
\(887\) | − | 484.124i | − | 0.545800i | −0.962042 | − | 0.272900i | \(-0.912017\pi\) | ||
0.962042 | − | 0.272900i | \(-0.0879828\pi\) | |||||||
\(888\) | − | 342.201i | − | 0.385361i | ||||||
\(889\) | 491.885 | 0.553301 | ||||||||
\(890\) | 2344.52i | 2.63429i | ||||||||
\(891\) | 60.5885 | + | 78.2946i | 0.0680005 | + | 0.0878727i | ||||
\(892\) | −1165.62 | −1.30674 | ||||||||
\(893\) | − | 64.8968i | − | 0.0726728i | ||||||
\(894\) | 1004.64 | 1.12376 | ||||||||
\(895\) | −846.410 | −0.945710 | ||||||||
\(896\) | −491.709 | −0.548782 | ||||||||
\(897\) | − | 590.310i | − | 0.658093i | ||||||
\(898\) | − | 432.001i | − | 0.481070i | ||||||
\(899\) | − | 431.222i | − | 0.479669i | ||||||
\(900\) | −340.061 | −0.377846 | ||||||||
\(901\) | 147.401i | 0.163597i | ||||||||
\(902\) | −32.9179 | − | 42.5377i | −0.0364943 | − | 0.0471593i | ||||
\(903\) | −107.223 | −0.118741 | ||||||||
\(904\) | − | 2621.18i | − | 2.89954i | ||||||
\(905\) | 1066.80 | 1.17879 | ||||||||
\(906\) | −1403.67 | −1.54930 | ||||||||
\(907\) | −794.610 | −0.876086 | −0.438043 | − | 0.898954i | \(-0.644328\pi\) | ||||
−0.438043 | + | 0.898954i | \(0.644328\pi\) | |||||||
\(908\) | 2791.76i | 3.07462i | ||||||||
\(909\) | − | 278.010i | − | 0.305841i | ||||||
\(910\) | 1343.70i | 1.47659i | ||||||||
\(911\) | 256.042 | 0.281056 | 0.140528 | − | 0.990077i | \(-0.455120\pi\) | ||||
0.140528 | + | 0.990077i | \(0.455120\pi\) | |||||||
\(912\) | 123.647i | 0.135578i | ||||||||
\(913\) | −626.305 | + | 484.668i | −0.685986 | + | 0.530852i | ||||
\(914\) | −2054.24 | −2.24753 | ||||||||
\(915\) | − | 229.325i | − | 0.250629i | ||||||
\(916\) | −2533.15 | −2.76545 | ||||||||
\(917\) | −256.441 | −0.279652 | ||||||||
\(918\) | −224.354 | −0.244394 | ||||||||
\(919\) | 546.682i | 0.594866i | 0.954743 | + | 0.297433i | \(0.0961305\pi\) | ||||
−0.954743 | + | 0.297433i | \(0.903870\pi\) | |||||||
\(920\) | 1400.32i | 1.52209i | ||||||||
\(921\) | − | 738.354i | − | 0.801687i | ||||||
\(922\) | 192.267 | 0.208532 | ||||||||
\(923\) | 1646.30i | 1.78365i | ||||||||
\(924\) | −329.611 | + | 255.071i | −0.356722 | + | 0.276051i | ||||
\(925\) | −167.885 | −0.181497 | ||||||||
\(926\) | 1258.19i | 1.35874i | ||||||||
\(927\) | 422.238 | 0.455489 | ||||||||
\(928\) | −535.061 | −0.576575 | ||||||||
\(929\) | 1434.55 | 1.54419 | 0.772096 | − | 0.635506i | \(-0.219209\pi\) | ||||
0.772096 | + | 0.635506i | \(0.219209\pi\) | |||||||
\(930\) | 423.482i | 0.455357i | ||||||||
\(931\) | − | 138.683i | − | 0.148962i | ||||||
\(932\) | − | 1236.74i | − | 1.32697i | ||||||
\(933\) | 522.406 | 0.559921 | ||||||||
\(934\) | 1054.24i | 1.12874i | ||||||||
\(935\) | 659.223 | − | 510.141i | 0.705051 | − | 0.545606i | ||||
\(936\) | −1123.73 | −1.20057 | ||||||||
\(937\) | 377.432i | 0.402809i | 0.979508 | + | 0.201405i | \(0.0645506\pi\) | ||||
−0.979508 | + | 0.201405i | \(0.935449\pi\) | |||||||
\(938\) | 310.228 | 0.330734 | ||||||||
\(939\) | −451.541 | −0.480874 | ||||||||
\(940\) | −1038.61 | −1.10490 | ||||||||
\(941\) | 721.127i | 0.766341i | 0.923678 | + | 0.383171i | \(0.125168\pi\) | ||||
−0.923678 | + | 0.383171i | \(0.874832\pi\) | |||||||
\(942\) | 653.450i | 0.693684i | ||||||||
\(943\) | − | 19.8607i | − | 0.0210612i | ||||||
\(944\) | −1366.90 | −1.44799 | ||||||||
\(945\) | − | 83.2100i | − | 0.0880529i | ||||||
\(946\) | 569.290 | + | 735.656i | 0.601786 | + | 0.777649i | ||||
\(947\) | −1526.20 | −1.61162 | −0.805808 | − | 0.592177i | \(-0.798269\pi\) | ||||
−0.805808 | + | 0.592177i | \(0.798269\pi\) | |||||||
\(948\) | − | 1431.62i | − | 1.51015i | ||||||
\(949\) | 949.892 | 1.00094 | ||||||||
\(950\) | 154.939 | 0.163093 | ||||||||
\(951\) | −781.486 | −0.821752 | ||||||||
\(952\) | − | 498.147i | − | 0.523264i | ||||||
\(953\) | 252.264i | 0.264705i | 0.991203 | + | 0.132353i | \(0.0422532\pi\) | ||||
−0.991203 | + | 0.132353i | \(0.957747\pi\) | |||||||
\(954\) | − | 127.653i | − | 0.133808i | ||||||
\(955\) | 853.615 | 0.893838 | ||||||||
\(956\) | − | 536.728i | − | 0.561431i | ||||||
\(957\) | 581.338 | − | 449.870i | 0.607459 | − | 0.470084i | ||||
\(958\) | 1178.31 | 1.22996 | ||||||||
\(959\) | − | 75.5063i | − | 0.0787345i | ||||||
\(960\) | −409.717 | −0.426788 | ||||||||
\(961\) | −836.077 | −0.870007 | ||||||||
\(962\) | −1051.87 | −1.09342 | ||||||||
\(963\) | 224.700i | 0.233333i | ||||||||
\(964\) | − | 2971.05i | − | 3.08200i | ||||||
\(965\) | − | 659.398i | − | 0.683314i | ||||||
\(966\) | −226.623 | −0.234600 | ||||||||
\(967\) | − | 39.6815i | − | 0.0410357i | −0.999789 | − | 0.0205179i | \(-0.993469\pi\) | ||
0.999789 | − | 0.0205179i | \(-0.00653149\pi\) | |||||||
\(968\) | 1846.00 | + | 478.467i | 1.90702 | + | 0.494284i | ||||
\(969\) | 69.4153 | 0.0716360 | ||||||||
\(970\) | − | 3647.61i | − | 3.76042i | ||||||
\(971\) | −790.585 | −0.814196 | −0.407098 | − | 0.913384i | \(-0.633459\pi\) | ||||
−0.407098 | + | 0.913384i | \(0.633459\pi\) | |||||||
\(972\) | 131.942 | 0.135743 | ||||||||
\(973\) | −442.859 | −0.455148 | ||||||||
\(974\) | − | 2503.98i | − | 2.57082i | ||||||
\(975\) | 551.307i | 0.565443i | ||||||||
\(976\) | 465.500i | 0.476946i | ||||||||
\(977\) | −309.474 | −0.316760 | −0.158380 | − | 0.987378i | \(-0.550627\pi\) | ||||
−0.158380 | + | 0.987378i | \(0.550627\pi\) | |||||||
\(978\) | 721.969i | 0.738209i | ||||||||
\(979\) | 721.520 | + | 932.374i | 0.736997 | + | 0.952374i | ||||
\(980\) | −2219.49 | −2.26479 | ||||||||
\(981\) | 460.901i | 0.469827i | ||||||||
\(982\) | −112.943 | −0.115014 | ||||||||
\(983\) | 529.604 | 0.538763 | 0.269381 | − | 0.963034i | \(-0.413181\pi\) | ||||
0.269381 | + | 0.963034i | \(0.413181\pi\) | |||||||
\(984\) | −37.8076 | −0.0384224 | ||||||||
\(985\) | 207.029i | 0.210182i | ||||||||
\(986\) | 1665.83i | 1.68948i | ||||||||
\(987\) | − | 88.6506i | − | 0.0898183i | ||||||
\(988\) | 659.223 | 0.667230 | ||||||||
\(989\) | 343.476i | 0.347297i | ||||||||
\(990\) | −570.904 | + | 441.795i | −0.576671 | + | 0.446258i | ||||
\(991\) | 1038.56 | 1.04799 | 0.523997 | − | 0.851720i | \(-0.324440\pi\) | ||||
0.523997 | + | 0.851720i | \(0.324440\pi\) | |||||||
\(992\) | − | 155.005i | − | 0.156255i | ||||||
\(993\) | −397.626 | −0.400429 | ||||||||
\(994\) | 632.025 | 0.635840 | ||||||||
\(995\) | 2069.86 | 2.08027 | ||||||||
\(996\) | 1055.45i | 1.05969i | ||||||||
\(997\) | − | 1105.88i | − | 1.10921i | −0.832115 | − | 0.554603i | \(-0.812870\pi\) | ||
0.832115 | − | 0.554603i | \(-0.187130\pi\) | |||||||
\(998\) | 97.7660i | 0.0979619i | ||||||||
\(999\) | 65.1384 | 0.0652036 |
(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 | 33.3.c.a.10.4 | yes | 4 | |
3.2 | odd | 2 | 99.3.c.b.10.1 | 4 | |||
4.3 | odd | 2 | 528.3.j.c.241.3 | 4 | |||
5.2 | odd | 4 | 825.3.h.a.274.2 | 8 | |||
5.3 | odd | 4 | 825.3.h.a.274.7 | 8 | |||
5.4 | even | 2 | 825.3.b.a.76.1 | 4 | |||
8.3 | odd | 2 | 2112.3.j.d.769.1 | 4 | |||
8.5 | even | 2 | 2112.3.j.a.769.4 | 4 | |||
11.2 | odd | 10 | 363.3.g.e.40.1 | 16 | |||
11.3 | even | 5 | 363.3.g.e.112.4 | 16 | |||
11.4 | even | 5 | 363.3.g.e.94.1 | 16 | |||
11.5 | even | 5 | 363.3.g.e.118.1 | 16 | |||
11.6 | odd | 10 | 363.3.g.e.118.4 | 16 | |||
11.7 | odd | 10 | 363.3.g.e.94.4 | 16 | |||
11.8 | odd | 10 | 363.3.g.e.112.1 | 16 | |||
11.9 | even | 5 | 363.3.g.e.40.4 | 16 | |||
11.10 | odd | 2 | inner | 33.3.c.a.10.1 | ✓ | 4 | |
12.11 | even | 2 | 1584.3.j.f.1297.1 | 4 | |||
33.32 | even | 2 | 99.3.c.b.10.4 | 4 | |||
44.43 | even | 2 | 528.3.j.c.241.4 | 4 | |||
55.32 | even | 4 | 825.3.h.a.274.8 | 8 | |||
55.43 | even | 4 | 825.3.h.a.274.1 | 8 | |||
55.54 | odd | 2 | 825.3.b.a.76.4 | 4 | |||
88.21 | odd | 2 | 2112.3.j.a.769.3 | 4 | |||
88.43 | even | 2 | 2112.3.j.d.769.2 | 4 | |||
132.131 | odd | 2 | 1584.3.j.f.1297.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.c.a.10.1 | ✓ | 4 | 11.10 | odd | 2 | inner | |
33.3.c.a.10.4 | yes | 4 | 1.1 | even | 1 | trivial | |
99.3.c.b.10.1 | 4 | 3.2 | odd | 2 | |||
99.3.c.b.10.4 | 4 | 33.32 | even | 2 | |||
363.3.g.e.40.1 | 16 | 11.2 | odd | 10 | |||
363.3.g.e.40.4 | 16 | 11.9 | even | 5 | |||
363.3.g.e.94.1 | 16 | 11.4 | even | 5 | |||
363.3.g.e.94.4 | 16 | 11.7 | odd | 10 | |||
363.3.g.e.112.1 | 16 | 11.8 | odd | 10 | |||
363.3.g.e.112.4 | 16 | 11.3 | even | 5 | |||
363.3.g.e.118.1 | 16 | 11.5 | even | 5 | |||
363.3.g.e.118.4 | 16 | 11.6 | odd | 10 | |||
528.3.j.c.241.3 | 4 | 4.3 | odd | 2 | |||
528.3.j.c.241.4 | 4 | 44.43 | even | 2 | |||
825.3.b.a.76.1 | 4 | 5.4 | even | 2 | |||
825.3.b.a.76.4 | 4 | 55.54 | odd | 2 | |||
825.3.h.a.274.1 | 8 | 55.43 | even | 4 | |||
825.3.h.a.274.2 | 8 | 5.2 | odd | 4 | |||
825.3.h.a.274.7 | 8 | 5.3 | odd | 4 | |||
825.3.h.a.274.8 | 8 | 55.32 | even | 4 | |||
1584.3.j.f.1297.1 | 4 | 12.11 | even | 2 | |||
1584.3.j.f.1297.2 | 4 | 132.131 | odd | 2 | |||
2112.3.j.a.769.3 | 4 | 88.21 | odd | 2 | |||
2112.3.j.a.769.4 | 4 | 8.5 | even | 2 | |||
2112.3.j.d.769.1 | 4 | 8.3 | odd | 2 | |||
2112.3.j.d.769.2 | 4 | 88.43 | even | 2 |