Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(419,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.419");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.34436701122\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 26 x^{18} + 281 x^{16} + 1640 x^{14} + 5623 x^{12} + 11551 x^{10} + 13894 x^{8} + 9095 x^{6} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 419.19 | ||
Root | \(2.33380i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.419 |
Dual form | 1045.2.b.c.419.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(761\) | \(837\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.33380i | 1.65024i | 0.564955 | + | 0.825122i | \(0.308894\pi\) | ||||
−0.564955 | + | 0.825122i | \(0.691106\pi\) | |||||||
\(3\) | 1.97214i | 1.13861i | 0.822125 | + | 0.569307i | \(0.192789\pi\) | ||||
−0.822125 | + | 0.569307i | \(0.807211\pi\) | |||||||
\(4\) | −3.44661 | −1.72330 | ||||||||
\(5\) | −1.75107 | + | 1.39059i | −0.783103 | + | 0.621892i | ||||
\(6\) | −4.60257 | −1.87899 | ||||||||
\(7\) | − | 4.79282i | − | 1.81152i | −0.423794 | − | 0.905759i | \(-0.639302\pi\) | ||
0.423794 | − | 0.905759i | \(-0.360698\pi\) | |||||||
\(8\) | − | 3.37609i | − | 1.19363i | ||||||
\(9\) | −0.889329 | −0.296443 | ||||||||
\(10\) | −3.24536 | − | 4.08665i | −1.02627 | − | 1.29231i | ||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | − | 6.79719i | − | 1.96218i | ||||||
\(13\) | − | 6.97588i | − | 1.93476i | −0.253325 | − | 0.967381i | \(-0.581524\pi\) | ||
0.253325 | − | 0.967381i | \(-0.418476\pi\) | |||||||
\(14\) | 11.1855 | 2.98944 | ||||||||
\(15\) | −2.74244 | − | 3.45336i | −0.708095 | − | 0.891653i | ||||
\(16\) | 0.985888 | 0.246472 | ||||||||
\(17\) | 1.90231i | 0.461378i | 0.973028 | + | 0.230689i | \(0.0740980\pi\) | ||||
−0.973028 | + | 0.230689i | \(0.925902\pi\) | |||||||
\(18\) | − | 2.07551i | − | 0.489203i | ||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 6.03526 | − | 4.79282i | 1.34952 | − | 1.07171i | ||||
\(21\) | 9.45211 | 2.06262 | ||||||||
\(22\) | 2.33380i | 0.497567i | ||||||||
\(23\) | − | 4.07925i | − | 0.850582i | −0.905057 | − | 0.425291i | \(-0.860172\pi\) | ||
0.905057 | − | 0.425291i | \(-0.139828\pi\) | |||||||
\(24\) | 6.65811 | 1.35908 | ||||||||
\(25\) | 1.13251 | − | 4.87005i | 0.226502 | − | 0.974011i | ||||
\(26\) | 16.2803 | 3.19283 | ||||||||
\(27\) | 4.16254i | 0.801080i | ||||||||
\(28\) | 16.5190i | 3.12179i | ||||||||
\(29\) | −2.15857 | −0.400837 | −0.200418 | − | 0.979710i | \(-0.564230\pi\) | ||||
−0.200418 | + | 0.979710i | \(0.564230\pi\) | |||||||
\(30\) | 8.05943 | − | 6.40030i | 1.47144 | − | 1.16853i | ||||
\(31\) | −10.6067 | −1.90502 | −0.952511 | − | 0.304505i | \(-0.901509\pi\) | ||||
−0.952511 | + | 0.304505i | \(0.901509\pi\) | |||||||
\(32\) | − | 4.45131i | − | 0.786889i | ||||||
\(33\) | 1.97214i | 0.343305i | ||||||||
\(34\) | −4.43961 | −0.761386 | ||||||||
\(35\) | 6.66486 | + | 8.39258i | 1.12657 | + | 1.41861i | ||||
\(36\) | 3.06517 | 0.510861 | ||||||||
\(37\) | − | 5.25363i | − | 0.863691i | −0.901948 | − | 0.431845i | \(-0.857863\pi\) | ||
0.901948 | − | 0.431845i | \(-0.142137\pi\) | |||||||
\(38\) | 2.33380i | 0.378592i | ||||||||
\(39\) | 13.7574 | 2.20295 | ||||||||
\(40\) | 4.69476 | + | 5.91177i | 0.742307 | + | 0.934734i | ||||
\(41\) | −4.11322 | −0.642377 | −0.321188 | − | 0.947015i | \(-0.604082\pi\) | ||||
−0.321188 | + | 0.947015i | \(0.604082\pi\) | |||||||
\(42\) | 22.0593i | 3.40382i | ||||||||
\(43\) | − | 2.83644i | − | 0.432553i | −0.976332 | − | 0.216277i | \(-0.930609\pi\) | ||
0.976332 | − | 0.216277i | \(-0.0693913\pi\) | |||||||
\(44\) | −3.44661 | −0.519596 | ||||||||
\(45\) | 1.55728 | − | 1.23669i | 0.232145 | − | 0.184355i | ||||
\(46\) | 9.52013 | 1.40367 | ||||||||
\(47\) | − | 9.58734i | − | 1.39846i | −0.714898 | − | 0.699229i | \(-0.753527\pi\) | ||
0.714898 | − | 0.699229i | \(-0.246473\pi\) | |||||||
\(48\) | 1.94431i | 0.280637i | ||||||||
\(49\) | −15.9712 | −2.28159 | ||||||||
\(50\) | 11.3657 | + | 2.64304i | 1.60735 | + | 0.373783i | ||||
\(51\) | −3.75162 | −0.525332 | ||||||||
\(52\) | 24.0431i | 3.33418i | ||||||||
\(53\) | 4.41619i | 0.606610i | 0.952894 | + | 0.303305i | \(0.0980901\pi\) | ||||
−0.952894 | + | 0.303305i | \(0.901910\pi\) | |||||||
\(54\) | −9.71451 | −1.32198 | ||||||||
\(55\) | −1.75107 | + | 1.39059i | −0.236115 | + | 0.187507i | ||||
\(56\) | −16.1810 | −2.16228 | ||||||||
\(57\) | 1.97214i | 0.261216i | ||||||||
\(58\) | − | 5.03767i | − | 0.661478i | ||||||
\(59\) | 3.08053 | 0.401050 | 0.200525 | − | 0.979689i | \(-0.435735\pi\) | ||||
0.200525 | + | 0.979689i | \(0.435735\pi\) | |||||||
\(60\) | 9.45211 | + | 11.9024i | 1.22026 | + | 1.53659i | ||||
\(61\) | −5.73895 | −0.734797 | −0.367398 | − | 0.930064i | \(-0.619751\pi\) | ||||
−0.367398 | + | 0.930064i | \(0.619751\pi\) | |||||||
\(62\) | − | 24.7539i | − | 3.14375i | ||||||
\(63\) | 4.26240i | 0.537011i | ||||||||
\(64\) | 12.3602 | 1.54503 | ||||||||
\(65\) | 9.70061 | + | 12.2153i | 1.20321 | + | 1.51512i | ||||
\(66\) | −4.60257 | −0.566537 | ||||||||
\(67\) | 5.17167i | 0.631820i | 0.948789 | + | 0.315910i | \(0.102310\pi\) | ||||
−0.948789 | + | 0.315910i | \(0.897690\pi\) | |||||||
\(68\) | − | 6.55652i | − | 0.795095i | ||||||
\(69\) | 8.04484 | 0.968485 | ||||||||
\(70\) | −19.5866 | + | 15.5544i | −2.34104 | + | 1.85911i | ||||
\(71\) | −8.60081 | −1.02073 | −0.510364 | − | 0.859958i | \(-0.670489\pi\) | ||||
−0.510364 | + | 0.859958i | \(0.670489\pi\) | |||||||
\(72\) | 3.00245i | 0.353842i | ||||||||
\(73\) | − | 2.32205i | − | 0.271776i | −0.990724 | − | 0.135888i | \(-0.956611\pi\) | ||
0.990724 | − | 0.135888i | \(-0.0433887\pi\) | |||||||
\(74\) | 12.2609 | 1.42530 | ||||||||
\(75\) | 9.60442 | + | 2.23346i | 1.10902 | + | 0.257898i | ||||
\(76\) | −3.44661 | −0.395353 | ||||||||
\(77\) | − | 4.79282i | − | 0.546193i | ||||||
\(78\) | 32.1070i | 3.63540i | ||||||||
\(79\) | 15.8136 | 1.77917 | 0.889584 | − | 0.456772i | \(-0.150994\pi\) | ||||
0.889584 | + | 0.456772i | \(0.150994\pi\) | |||||||
\(80\) | −1.72636 | + | 1.37097i | −0.193013 | + | 0.153279i | ||||
\(81\) | −10.8771 | −1.20856 | ||||||||
\(82\) | − | 9.59942i | − | 1.06008i | ||||||
\(83\) | − | 2.49359i | − | 0.273707i | −0.990591 | − | 0.136854i | \(-0.956301\pi\) | ||
0.990591 | − | 0.136854i | \(-0.0436990\pi\) | |||||||
\(84\) | −32.5777 | −3.55452 | ||||||||
\(85\) | −2.64534 | − | 3.33108i | −0.286927 | − | 0.361307i | ||||
\(86\) | 6.61968 | 0.713818 | ||||||||
\(87\) | − | 4.25700i | − | 0.456398i | ||||||
\(88\) | − | 3.37609i | − | 0.359892i | ||||||
\(89\) | −8.26610 | −0.876205 | −0.438102 | − | 0.898925i | \(-0.644349\pi\) | ||||
−0.438102 | + | 0.898925i | \(0.644349\pi\) | |||||||
\(90\) | 2.88619 | + | 3.63437i | 0.304231 | + | 0.383096i | ||||
\(91\) | −33.4342 | −3.50486 | ||||||||
\(92\) | 14.0596i | 1.46581i | ||||||||
\(93\) | − | 20.9179i | − | 2.16908i | ||||||
\(94\) | 22.3749 | 2.30780 | ||||||||
\(95\) | −1.75107 | + | 1.39059i | −0.179656 | + | 0.142672i | ||||
\(96\) | 8.77861 | 0.895963 | ||||||||
\(97\) | 0.339216i | 0.0344422i | 0.999852 | + | 0.0172211i | \(0.00548192\pi\) | ||||
−0.999852 | + | 0.0172211i | \(0.994518\pi\) | |||||||
\(98\) | − | 37.2735i | − | 3.76519i | ||||||
\(99\) | −0.889329 | −0.0893809 | ||||||||
\(100\) | −3.90331 | + | 16.7852i | −0.390331 | + | 1.67852i | ||||
\(101\) | −1.65580 | −0.164758 | −0.0823789 | − | 0.996601i | \(-0.526252\pi\) | ||||
−0.0823789 | + | 0.996601i | \(0.526252\pi\) | |||||||
\(102\) | − | 8.75552i | − | 0.866925i | ||||||
\(103\) | 4.79043i | 0.472015i | 0.971751 | + | 0.236008i | \(0.0758390\pi\) | ||||
−0.971751 | + | 0.236008i | \(0.924161\pi\) | |||||||
\(104\) | −23.5512 | −2.30938 | ||||||||
\(105\) | −16.5513 | + | 13.1440i | −1.61524 | + | 1.28273i | ||||
\(106\) | −10.3065 | −1.00105 | ||||||||
\(107\) | − | 3.17144i | − | 0.306595i | −0.988180 | − | 0.153298i | \(-0.951011\pi\) | ||
0.988180 | − | 0.153298i | \(-0.0489893\pi\) | |||||||
\(108\) | − | 14.3466i | − | 1.38050i | ||||||
\(109\) | 13.3407 | 1.27781 | 0.638905 | − | 0.769285i | \(-0.279388\pi\) | ||||
0.638905 | + | 0.769285i | \(0.279388\pi\) | |||||||
\(110\) | −3.24536 | − | 4.08665i | −0.309433 | − | 0.389646i | ||||
\(111\) | 10.3609 | 0.983411 | ||||||||
\(112\) | − | 4.72519i | − | 0.446488i | ||||||
\(113\) | 5.03001i | 0.473184i | 0.971609 | + | 0.236592i | \(0.0760304\pi\) | ||||
−0.971609 | + | 0.236592i | \(0.923970\pi\) | |||||||
\(114\) | −4.60257 | −0.431070 | ||||||||
\(115\) | 5.67257 | + | 7.14306i | 0.528970 | + | 0.666093i | ||||
\(116\) | 7.43975 | 0.690763 | ||||||||
\(117\) | 6.20385i | 0.573546i | ||||||||
\(118\) | 7.18932i | 0.661831i | ||||||||
\(119\) | 9.11744 | 0.835794 | ||||||||
\(120\) | −11.6588 | + | 9.25872i | −1.06430 | + | 0.845201i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − | 13.3935i | − | 1.21259i | ||||||
\(123\) | − | 8.11184i | − | 0.731420i | ||||||
\(124\) | 36.5572 | 3.28293 | ||||||||
\(125\) | 4.78915 | + | 10.1027i | 0.428355 | + | 0.903611i | ||||
\(126\) | −9.94757 | −0.886200 | ||||||||
\(127\) | 2.31203i | 0.205159i | 0.994725 | + | 0.102580i | \(0.0327096\pi\) | ||||
−0.994725 | + | 0.102580i | \(0.967290\pi\) | |||||||
\(128\) | 19.9437i | 1.76279i | ||||||||
\(129\) | 5.59385 | 0.492511 | ||||||||
\(130\) | −28.5080 | + | 22.6392i | −2.50031 | + | 1.98559i | ||||
\(131\) | −6.53445 | −0.570917 | −0.285459 | − | 0.958391i | \(-0.592146\pi\) | ||||
−0.285459 | + | 0.958391i | \(0.592146\pi\) | |||||||
\(132\) | − | 6.79719i | − | 0.591619i | ||||||
\(133\) | − | 4.79282i | − | 0.415591i | ||||||
\(134\) | −12.0696 | −1.04266 | ||||||||
\(135\) | −5.78839 | − | 7.28890i | −0.498185 | − | 0.627329i | ||||
\(136\) | 6.42237 | 0.550713 | ||||||||
\(137\) | 1.80366i | 0.154097i | 0.997027 | + | 0.0770487i | \(0.0245497\pi\) | ||||
−0.997027 | + | 0.0770487i | \(0.975450\pi\) | |||||||
\(138\) | 18.7750i | 1.59824i | ||||||||
\(139\) | 5.61633 | 0.476371 | 0.238185 | − | 0.971220i | \(-0.423447\pi\) | ||||
0.238185 | + | 0.971220i | \(0.423447\pi\) | |||||||
\(140\) | −22.9712 | − | 28.9259i | −1.94142 | − | 2.44469i | ||||
\(141\) | 18.9076 | 1.59230 | ||||||||
\(142\) | − | 20.0725i | − | 1.68445i | ||||||
\(143\) | − | 6.97588i | − | 0.583353i | ||||||
\(144\) | −0.876778 | −0.0730649 | ||||||||
\(145\) | 3.77982 | − | 3.00169i | 0.313897 | − | 0.249277i | ||||
\(146\) | 5.41920 | 0.448496 | ||||||||
\(147\) | − | 31.4973i | − | 2.59786i | ||||||
\(148\) | 18.1072i | 1.48840i | ||||||||
\(149\) | 12.4592 | 1.02070 | 0.510349 | − | 0.859968i | \(-0.329516\pi\) | ||||
0.510349 | + | 0.859968i | \(0.329516\pi\) | |||||||
\(150\) | −5.21245 | + | 22.4148i | −0.425595 | + | 1.83016i | ||||
\(151\) | −15.1218 | −1.23060 | −0.615298 | − | 0.788294i | \(-0.710964\pi\) | ||||
−0.615298 | + | 0.788294i | \(0.710964\pi\) | |||||||
\(152\) | − | 3.37609i | − | 0.273837i | ||||||
\(153\) | − | 1.69178i | − | 0.136772i | ||||||
\(154\) | 11.1855 | 0.901351 | ||||||||
\(155\) | 18.5731 | − | 14.7496i | 1.49183 | − | 1.18472i | ||||
\(156\) | −47.4164 | −3.79635 | ||||||||
\(157\) | − | 11.8420i | − | 0.945096i | −0.881305 | − | 0.472548i | \(-0.843334\pi\) | ||
0.881305 | − | 0.472548i | \(-0.156666\pi\) | |||||||
\(158\) | 36.9057i | 2.93606i | ||||||||
\(159\) | −8.70933 | −0.690695 | ||||||||
\(160\) | 6.18996 | + | 7.79457i | 0.489359 | + | 0.616215i | ||||
\(161\) | −19.5511 | −1.54084 | ||||||||
\(162\) | − | 25.3849i | − | 1.99443i | ||||||
\(163\) | − | 1.12465i | − | 0.0880897i | −0.999030 | − | 0.0440448i | \(-0.985976\pi\) | ||
0.999030 | − | 0.0440448i | \(-0.0140244\pi\) | |||||||
\(164\) | 14.1767 | 1.10701 | ||||||||
\(165\) | −2.74244 | − | 3.45336i | −0.213499 | − | 0.268843i | ||||
\(166\) | 5.81954 | 0.451684 | ||||||||
\(167\) | 8.92311i | 0.690491i | 0.938512 | + | 0.345246i | \(0.112204\pi\) | ||||
−0.938512 | + | 0.345246i | \(0.887796\pi\) | |||||||
\(168\) | − | 31.9112i | − | 2.46200i | ||||||
\(169\) | −35.6630 | −2.74330 | ||||||||
\(170\) | 7.77407 | − | 6.17368i | 0.596244 | − | 0.473500i | ||||
\(171\) | −0.889329 | −0.0680087 | ||||||||
\(172\) | 9.77610i | 0.745421i | ||||||||
\(173\) | 20.4108i | 1.55180i | 0.630853 | + | 0.775902i | \(0.282705\pi\) | ||||
−0.630853 | + | 0.775902i | \(0.717295\pi\) | |||||||
\(174\) | 9.93498 | 0.753169 | ||||||||
\(175\) | −23.3413 | − | 5.42791i | −1.76444 | − | 0.410312i | ||||
\(176\) | 0.985888 | 0.0743141 | ||||||||
\(177\) | 6.07522i | 0.456642i | ||||||||
\(178\) | − | 19.2914i | − | 1.44595i | ||||||
\(179\) | 9.19132 | 0.686991 | 0.343496 | − | 0.939154i | \(-0.388389\pi\) | ||||
0.343496 | + | 0.939154i | \(0.388389\pi\) | |||||||
\(180\) | −5.36733 | + | 4.26240i | −0.400057 | + | 0.317700i | ||||
\(181\) | 4.87696 | 0.362501 | 0.181251 | − | 0.983437i | \(-0.441985\pi\) | ||||
0.181251 | + | 0.983437i | \(0.441985\pi\) | |||||||
\(182\) | − | 78.0286i | − | 5.78386i | ||||||
\(183\) | − | 11.3180i | − | 0.836650i | ||||||
\(184\) | −13.7719 | −1.01528 | ||||||||
\(185\) | 7.30565 | + | 9.19948i | 0.537122 | + | 0.676359i | ||||
\(186\) | 48.8181 | 3.57952 | ||||||||
\(187\) | 1.90231i | 0.139111i | ||||||||
\(188\) | 33.0438i | 2.40997i | ||||||||
\(189\) | 19.9503 | 1.45117 | ||||||||
\(190\) | −3.24536 | − | 4.08665i | −0.235443 | − | 0.296477i | ||||
\(191\) | 6.07137 | 0.439309 | 0.219655 | − | 0.975578i | \(-0.429507\pi\) | ||||
0.219655 | + | 0.975578i | \(0.429507\pi\) | |||||||
\(192\) | 24.3761i | 1.75919i | ||||||||
\(193\) | − | 22.7808i | − | 1.63980i | −0.572508 | − | 0.819899i | \(-0.694029\pi\) | ||
0.572508 | − | 0.819899i | \(-0.305971\pi\) | |||||||
\(194\) | −0.791662 | −0.0568380 | ||||||||
\(195\) | −24.0902 | + | 19.1309i | −1.72514 | + | 1.36999i | ||||
\(196\) | 55.0463 | 3.93188 | ||||||||
\(197\) | 7.06623i | 0.503448i | 0.967799 | + | 0.251724i | \(0.0809976\pi\) | ||||
−0.967799 | + | 0.251724i | \(0.919002\pi\) | |||||||
\(198\) | − | 2.07551i | − | 0.147500i | ||||||
\(199\) | 23.6586 | 1.67711 | 0.838555 | − | 0.544817i | \(-0.183401\pi\) | ||||
0.838555 | + | 0.544817i | \(0.183401\pi\) | |||||||
\(200\) | −16.4417 | − | 3.82345i | −1.16261 | − | 0.270359i | ||||
\(201\) | −10.1992 | −0.719399 | ||||||||
\(202\) | − | 3.86429i | − | 0.271891i | ||||||
\(203\) | 10.3457i | 0.726123i | ||||||||
\(204\) | 12.9304 | 0.905306 | ||||||||
\(205\) | 7.20255 | − | 5.71981i | 0.503048 | − | 0.399489i | ||||
\(206\) | −11.1799 | −0.778940 | ||||||||
\(207\) | 3.62779i | 0.252149i | ||||||||
\(208\) | − | 6.87744i | − | 0.476865i | ||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | −30.6755 | − | 38.6274i | −2.11681 | − | 2.66555i | ||||
\(211\) | −0.374072 | −0.0257522 | −0.0128761 | − | 0.999917i | \(-0.504099\pi\) | ||||
−0.0128761 | + | 0.999917i | \(0.504099\pi\) | |||||||
\(212\) | − | 15.2209i | − | 1.04537i | ||||||
\(213\) | − | 16.9620i | − | 1.16222i | ||||||
\(214\) | 7.40151 | 0.505956 | ||||||||
\(215\) | 3.94433 | + | 4.96681i | 0.269001 | + | 0.338734i | ||||
\(216\) | 14.0531 | 0.956191 | ||||||||
\(217\) | 50.8361i | 3.45098i | ||||||||
\(218\) | 31.1346i | 2.10870i | ||||||||
\(219\) | 4.57941 | 0.309448 | ||||||||
\(220\) | 6.03526 | − | 4.79282i | 0.406897 | − | 0.323132i | ||||
\(221\) | 13.2703 | 0.892657 | ||||||||
\(222\) | 24.1802i | 1.62287i | ||||||||
\(223\) | − | 17.9582i | − | 1.20257i | −0.799035 | − | 0.601285i | \(-0.794656\pi\) | ||
0.799035 | − | 0.601285i | \(-0.205344\pi\) | |||||||
\(224\) | −21.3344 | −1.42546 | ||||||||
\(225\) | −1.00717 | + | 4.33108i | −0.0671448 | + | 0.288739i | ||||
\(226\) | −11.7390 | −0.780869 | ||||||||
\(227\) | 4.54401i | 0.301596i | 0.988565 | + | 0.150798i | \(0.0481844\pi\) | ||||
−0.988565 | + | 0.150798i | \(0.951816\pi\) | |||||||
\(228\) | − | 6.79719i | − | 0.450155i | ||||||
\(229\) | −17.7415 | −1.17239 | −0.586196 | − | 0.810170i | \(-0.699375\pi\) | ||||
−0.586196 | + | 0.810170i | \(0.699375\pi\) | |||||||
\(230\) | −16.6704 | + | 13.2386i | −1.09922 | + | 0.872929i | ||||
\(231\) | 9.45211 | 0.621903 | ||||||||
\(232\) | 7.28753i | 0.478450i | ||||||||
\(233\) | 4.25651i | 0.278853i | 0.990232 | + | 0.139427i | \(0.0445259\pi\) | ||||
−0.990232 | + | 0.139427i | \(0.955474\pi\) | |||||||
\(234\) | −14.4785 | −0.946491 | ||||||||
\(235\) | 13.3321 | + | 16.7881i | 0.869689 | + | 1.09514i | ||||
\(236\) | −10.6174 | −0.691131 | ||||||||
\(237\) | 31.1866i | 2.02579i | ||||||||
\(238\) | 21.2783i | 1.37926i | ||||||||
\(239\) | −27.3004 | −1.76592 | −0.882958 | − | 0.469452i | \(-0.844452\pi\) | ||||
−0.882958 | + | 0.469452i | \(0.844452\pi\) | |||||||
\(240\) | −2.70374 | − | 3.40462i | −0.174526 | − | 0.219767i | ||||
\(241\) | 25.7828 | 1.66081 | 0.830407 | − | 0.557157i | \(-0.188108\pi\) | ||||
0.830407 | + | 0.557157i | \(0.188108\pi\) | |||||||
\(242\) | 2.33380i | 0.150022i | ||||||||
\(243\) | − | 8.96350i | − | 0.575009i | ||||||
\(244\) | 19.7799 | 1.26628 | ||||||||
\(245\) | 27.9667 | − | 22.2094i | 1.78672 | − | 1.41890i | ||||
\(246\) | 18.9314 | 1.20702 | ||||||||
\(247\) | − | 6.97588i | − | 0.443865i | ||||||
\(248\) | 35.8092i | 2.27389i | ||||||||
\(249\) | 4.91771 | 0.311647 | ||||||||
\(250\) | −23.5776 | + | 11.1769i | −1.49118 | + | 0.706890i | ||||
\(251\) | −1.69221 | −0.106811 | −0.0534055 | − | 0.998573i | \(-0.517008\pi\) | ||||
−0.0534055 | + | 0.998573i | \(0.517008\pi\) | |||||||
\(252\) | − | 14.6908i | − | 0.925434i | ||||||
\(253\) | − | 4.07925i | − | 0.256460i | ||||||
\(254\) | −5.39580 | −0.338562 | ||||||||
\(255\) | 6.56936 | − | 5.21697i | 0.411389 | − | 0.326699i | ||||
\(256\) | −21.8240 | −1.36400 | ||||||||
\(257\) | − | 22.4357i | − | 1.39950i | −0.714388 | − | 0.699750i | \(-0.753295\pi\) | ||
0.714388 | − | 0.699750i | \(-0.246705\pi\) | |||||||
\(258\) | 13.0549i | 0.812764i | ||||||||
\(259\) | −25.1797 | −1.56459 | ||||||||
\(260\) | −33.4342 | − | 42.1013i | −2.07350 | − | 2.61101i | ||||
\(261\) | 1.91968 | 0.118825 | ||||||||
\(262\) | − | 15.2501i | − | 0.942153i | ||||||
\(263\) | − | 6.15036i | − | 0.379247i | −0.981857 | − | 0.189624i | \(-0.939273\pi\) | ||
0.981857 | − | 0.189624i | \(-0.0607268\pi\) | |||||||
\(264\) | 6.65811 | 0.409778 | ||||||||
\(265\) | −6.14111 | − | 7.73306i | −0.377246 | − | 0.475038i | ||||
\(266\) | 11.1855 | 0.685826 | ||||||||
\(267\) | − | 16.3019i | − | 0.997659i | ||||||
\(268\) | − | 17.8247i | − | 1.08882i | ||||||
\(269\) | 6.79348 | 0.414206 | 0.207103 | − | 0.978319i | \(-0.433597\pi\) | ||||
0.207103 | + | 0.978319i | \(0.433597\pi\) | |||||||
\(270\) | 17.0108 | − | 13.5089i | 1.03525 | − | 0.822127i | ||||
\(271\) | −7.20564 | −0.437712 | −0.218856 | − | 0.975757i | \(-0.570232\pi\) | ||||
−0.218856 | + | 0.975757i | \(0.570232\pi\) | |||||||
\(272\) | 1.87546i | 0.113717i | ||||||||
\(273\) | − | 65.9368i | − | 3.99068i | ||||||
\(274\) | −4.20938 | −0.254298 | ||||||||
\(275\) | 1.13251 | − | 4.87005i | 0.0682928 | − | 0.293675i | ||||
\(276\) | −27.7274 | −1.66899 | ||||||||
\(277\) | − | 28.8256i | − | 1.73197i | −0.500074 | − | 0.865983i | \(-0.666694\pi\) | ||
0.500074 | − | 0.865983i | \(-0.333306\pi\) | |||||||
\(278\) | 13.1074i | 0.786128i | ||||||||
\(279\) | 9.43285 | 0.564730 | ||||||||
\(280\) | 28.3341 | − | 22.5012i | 1.69329 | − | 1.34470i | ||||
\(281\) | −17.7854 | −1.06099 | −0.530493 | − | 0.847689i | \(-0.677993\pi\) | ||||
−0.530493 | + | 0.847689i | \(0.677993\pi\) | |||||||
\(282\) | 44.1264i | 2.62769i | ||||||||
\(283\) | − | 12.3079i | − | 0.731628i | −0.930688 | − | 0.365814i | \(-0.880791\pi\) | ||
0.930688 | − | 0.365814i | \(-0.119209\pi\) | |||||||
\(284\) | 29.6436 | 1.75903 | ||||||||
\(285\) | −2.74244 | − | 3.45336i | −0.162448 | − | 0.204559i | ||||
\(286\) | 16.2803 | 0.962674 | ||||||||
\(287\) | 19.7139i | 1.16368i | ||||||||
\(288\) | 3.95868i | 0.233267i | ||||||||
\(289\) | 13.3812 | 0.787130 | ||||||||
\(290\) | 7.00534 | + | 8.82132i | 0.411368 | + | 0.518006i | ||||
\(291\) | −0.668981 | −0.0392164 | ||||||||
\(292\) | 8.00321i | 0.468352i | ||||||||
\(293\) | − | 32.4497i | − | 1.89573i | −0.318668 | − | 0.947866i | \(-0.603235\pi\) | ||
0.318668 | − | 0.947866i | \(-0.396765\pi\) | |||||||
\(294\) | 73.5084 | 4.28710 | ||||||||
\(295\) | −5.39422 | + | 4.28375i | −0.314064 | + | 0.249410i | ||||
\(296\) | −17.7367 | −1.03092 | ||||||||
\(297\) | 4.16254i | 0.241535i | ||||||||
\(298\) | 29.0772i | 1.68440i | ||||||||
\(299\) | −28.4564 | −1.64567 | ||||||||
\(300\) | −33.1027 | − | 7.69787i | −1.91118 | − | 0.444437i | ||||
\(301\) | −13.5946 | −0.783578 | ||||||||
\(302\) | − | 35.2913i | − | 2.03078i | ||||||
\(303\) | − | 3.26546i | − | 0.187596i | ||||||
\(304\) | 0.985888 | 0.0565445 | ||||||||
\(305\) | 10.0493 | − | 7.98053i | 0.575422 | − | 0.456964i | ||||
\(306\) | 3.94827 | 0.225708 | ||||||||
\(307\) | 21.8459i | 1.24681i | 0.781898 | + | 0.623406i | \(0.214252\pi\) | ||||
−0.781898 | + | 0.623406i | \(0.785748\pi\) | |||||||
\(308\) | 16.5190i | 0.941256i | ||||||||
\(309\) | −9.44739 | −0.537443 | ||||||||
\(310\) | 34.4226 | + | 43.3459i | 1.95507 | + | 2.46188i | ||||
\(311\) | −3.21297 | −0.182191 | −0.0910953 | − | 0.995842i | \(-0.529037\pi\) | ||||
−0.0910953 | + | 0.995842i | \(0.529037\pi\) | |||||||
\(312\) | − | 46.4462i | − | 2.62950i | ||||||
\(313\) | − | 19.1387i | − | 1.08178i | −0.841092 | − | 0.540892i | \(-0.818087\pi\) | ||
0.841092 | − | 0.540892i | \(-0.181913\pi\) | |||||||
\(314\) | 27.6369 | 1.55964 | ||||||||
\(315\) | −5.92725 | − | 7.46376i | −0.333963 | − | 0.420535i | ||||
\(316\) | −54.5032 | −3.06605 | ||||||||
\(317\) | − | 29.0432i | − | 1.63123i | −0.578597 | − | 0.815613i | \(-0.696400\pi\) | ||
0.578597 | − | 0.815613i | \(-0.303600\pi\) | |||||||
\(318\) | − | 20.3258i | − | 1.13981i | ||||||
\(319\) | −2.15857 | −0.120857 | ||||||||
\(320\) | −21.6437 | + | 17.1880i | −1.20992 | + | 0.960841i | ||||
\(321\) | 6.25453 | 0.349094 | ||||||||
\(322\) | − | 45.6283i | − | 2.54277i | ||||||
\(323\) | 1.90231i | 0.105847i | ||||||||
\(324\) | 37.4890 | 2.08272 | ||||||||
\(325\) | −33.9729 | − | 7.90025i | −1.88448 | − | 0.438227i | ||||
\(326\) | 2.62471 | 0.145369 | ||||||||
\(327\) | 26.3098i | 1.45493i | ||||||||
\(328\) | 13.8866i | 0.766759i | ||||||||
\(329\) | −45.9504 | −2.53333 | ||||||||
\(330\) | 8.05943 | − | 6.40030i | 0.443657 | − | 0.352325i | ||||
\(331\) | 6.66834 | 0.366525 | 0.183263 | − | 0.983064i | \(-0.441334\pi\) | ||||
0.183263 | + | 0.983064i | \(0.441334\pi\) | |||||||
\(332\) | 8.59443i | 0.471681i | ||||||||
\(333\) | 4.67220i | 0.256035i | ||||||||
\(334\) | −20.8247 | −1.13948 | ||||||||
\(335\) | −7.19168 | − | 9.05596i | −0.392923 | − | 0.494780i | ||||
\(336\) | 9.31872 | 0.508378 | ||||||||
\(337\) | 13.4640i | 0.733432i | 0.930333 | + | 0.366716i | \(0.119518\pi\) | ||||
−0.930333 | + | 0.366716i | \(0.880482\pi\) | |||||||
\(338\) | − | 83.2301i | − | 4.52712i | ||||||
\(339\) | −9.91988 | −0.538774 | ||||||||
\(340\) | 9.11744 | + | 11.4809i | 0.494463 | + | 0.622641i | ||||
\(341\) | −10.6067 | −0.574386 | ||||||||
\(342\) | − | 2.07551i | − | 0.112231i | ||||||
\(343\) | 42.9972i | 2.32163i | ||||||||
\(344\) | −9.57608 | −0.516307 | ||||||||
\(345\) | −14.0871 | + | 11.1871i | −0.758424 | + | 0.602292i | ||||
\(346\) | −47.6347 | −2.56085 | ||||||||
\(347\) | − | 31.5430i | − | 1.69332i | −0.532135 | − | 0.846659i | \(-0.678610\pi\) | ||
0.532135 | − | 0.846659i | \(-0.321390\pi\) | |||||||
\(348\) | 14.6722i | 0.786513i | ||||||||
\(349\) | −26.6513 | −1.42661 | −0.713306 | − | 0.700853i | \(-0.752803\pi\) | ||||
−0.713306 | + | 0.700853i | \(0.752803\pi\) | |||||||
\(350\) | 12.6676 | − | 54.4739i | 0.677114 | − | 2.91175i | ||||
\(351\) | 29.0374 | 1.54990 | ||||||||
\(352\) | − | 4.45131i | − | 0.237256i | ||||||
\(353\) | − | 9.84002i | − | 0.523732i | −0.965104 | − | 0.261866i | \(-0.915662\pi\) | ||
0.965104 | − | 0.261866i | \(-0.0843378\pi\) | |||||||
\(354\) | −14.1783 | −0.753570 | ||||||||
\(355\) | 15.0606 | − | 11.9602i | 0.799336 | − | 0.634782i | ||||
\(356\) | 28.4900 | 1.50997 | ||||||||
\(357\) | 17.9809i | 0.951648i | ||||||||
\(358\) | 21.4507i | 1.13370i | ||||||||
\(359\) | 33.9480 | 1.79171 | 0.895854 | − | 0.444348i | \(-0.146565\pi\) | ||||
0.895854 | + | 0.444348i | \(0.146565\pi\) | |||||||
\(360\) | −4.17518 | − | 5.25751i | −0.220052 | − | 0.277095i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 11.3818i | 0.598216i | ||||||||
\(363\) | 1.97214i | 0.103510i | ||||||||
\(364\) | 115.235 | 6.03993 | ||||||||
\(365\) | 3.22903 | + | 4.06608i | 0.169015 | + | 0.212829i | ||||
\(366\) | 26.4139 | 1.38068 | ||||||||
\(367\) | − | 18.9282i | − | 0.988046i | −0.869449 | − | 0.494023i | \(-0.835526\pi\) | ||
0.869449 | − | 0.494023i | \(-0.164474\pi\) | |||||||
\(368\) | − | 4.02168i | − | 0.209645i | ||||||
\(369\) | 3.65800 | 0.190428 | ||||||||
\(370\) | −21.4697 | + | 17.0499i | −1.11616 | + | 0.886382i | ||||
\(371\) | 21.1660 | 1.09888 | ||||||||
\(372\) | 72.0958i | 3.73799i | ||||||||
\(373\) | 1.93691i | 0.100290i | 0.998742 | + | 0.0501448i | \(0.0159683\pi\) | ||||
−0.998742 | + | 0.0501448i | \(0.984032\pi\) | |||||||
\(374\) | −4.43961 | −0.229567 | ||||||||
\(375\) | −19.9239 | + | 9.44487i | −1.02886 | + | 0.487731i | ||||
\(376\) | −32.3677 | −1.66924 | ||||||||
\(377\) | 15.0579i | 0.775524i | ||||||||
\(378\) | 46.5599i | 2.39479i | ||||||||
\(379\) | 14.8053 | 0.760498 | 0.380249 | − | 0.924884i | \(-0.375838\pi\) | ||||
0.380249 | + | 0.924884i | \(0.375838\pi\) | |||||||
\(380\) | 6.03526 | − | 4.79282i | 0.309602 | − | 0.245867i | ||||
\(381\) | −4.55963 | −0.233597 | ||||||||
\(382\) | 14.1694i | 0.724967i | ||||||||
\(383\) | 24.1747i | 1.23527i | 0.786465 | + | 0.617635i | \(0.211909\pi\) | ||||
−0.786465 | + | 0.617635i | \(0.788091\pi\) | |||||||
\(384\) | −39.3316 | −2.00713 | ||||||||
\(385\) | 6.66486 | + | 8.39258i | 0.339673 | + | 0.427726i | ||||
\(386\) | 53.1658 | 2.70607 | ||||||||
\(387\) | 2.52253i | 0.128227i | ||||||||
\(388\) | − | 1.16915i | − | 0.0593543i | ||||||
\(389\) | −8.39826 | −0.425809 | −0.212904 | − | 0.977073i | \(-0.568292\pi\) | ||||
−0.212904 | + | 0.977073i | \(0.568292\pi\) | |||||||
\(390\) | −44.6477 | − | 56.2217i | −2.26083 | − | 2.84689i | ||||
\(391\) | 7.75999 | 0.392440 | ||||||||
\(392\) | 53.9201i | 2.72337i | ||||||||
\(393\) | − | 12.8868i | − | 0.650055i | ||||||
\(394\) | −16.4912 | −0.830812 | ||||||||
\(395\) | −27.6907 | + | 21.9903i | −1.39327 | + | 1.10645i | ||||
\(396\) | 3.06517 | 0.154030 | ||||||||
\(397\) | − | 11.7512i | − | 0.589777i | −0.955532 | − | 0.294889i | \(-0.904717\pi\) | ||
0.955532 | − | 0.294889i | \(-0.0952826\pi\) | |||||||
\(398\) | 55.2143i | 2.76764i | ||||||||
\(399\) | 9.45211 | 0.473197 | ||||||||
\(400\) | 1.11653 | − | 4.80133i | 0.0558263 | − | 0.240066i | ||||
\(401\) | 13.1216 | 0.655259 | 0.327630 | − | 0.944806i | \(-0.393750\pi\) | ||||
0.327630 | + | 0.944806i | \(0.393750\pi\) | |||||||
\(402\) | − | 23.8030i | − | 1.18718i | ||||||
\(403\) | 73.9912i | 3.68576i | ||||||||
\(404\) | 5.70688 | 0.283928 | ||||||||
\(405\) | 19.0466 | − | 15.1256i | 0.946431 | − | 0.751596i | ||||
\(406\) | −24.1447 | −1.19828 | ||||||||
\(407\) | − | 5.25363i | − | 0.260413i | ||||||
\(408\) | 12.6658i | 0.627050i | ||||||||
\(409\) | −28.1968 | −1.39424 | −0.697121 | − | 0.716954i | \(-0.745536\pi\) | ||||
−0.697121 | + | 0.716954i | \(0.745536\pi\) | |||||||
\(410\) | 13.3489 | + | 16.8093i | 0.659254 | + | 0.830151i | ||||
\(411\) | −3.55707 | −0.175457 | ||||||||
\(412\) | − | 16.5107i | − | 0.813426i | ||||||
\(413\) | − | 14.7644i | − | 0.726509i | ||||||
\(414\) | −8.46653 | −0.416107 | ||||||||
\(415\) | 3.46757 | + | 4.36646i | 0.170216 | + | 0.214341i | ||||
\(416\) | −31.0518 | −1.52244 | ||||||||
\(417\) | 11.0762i | 0.542403i | ||||||||
\(418\) | 2.33380i | 0.114150i | ||||||||
\(419\) | −25.4857 | −1.24506 | −0.622529 | − | 0.782597i | \(-0.713895\pi\) | ||||
−0.622529 | + | 0.782597i | \(0.713895\pi\) | |||||||
\(420\) | 57.0459 | − | 45.3023i | 2.78356 | − | 2.21053i | ||||
\(421\) | −25.7350 | −1.25425 | −0.627123 | − | 0.778920i | \(-0.715768\pi\) | ||||
−0.627123 | + | 0.778920i | \(0.715768\pi\) | |||||||
\(422\) | − | 0.873008i | − | 0.0424974i | ||||||
\(423\) | 8.52630i | 0.414563i | ||||||||
\(424\) | 14.9094 | 0.724066 | ||||||||
\(425\) | 9.26435 | + | 2.15438i | 0.449387 | + | 0.104503i | ||||
\(426\) | 39.5858 | 1.91794 | ||||||||
\(427\) | 27.5058i | 1.33110i | ||||||||
\(428\) | 10.9307i | 0.528356i | ||||||||
\(429\) | 13.7574 | 0.664214 | ||||||||
\(430\) | −11.5915 | + | 9.20527i | −0.558994 | + | 0.443918i | ||||
\(431\) | 30.2074 | 1.45504 | 0.727519 | − | 0.686088i | \(-0.240673\pi\) | ||||
0.727519 | + | 0.686088i | \(0.240673\pi\) | |||||||
\(432\) | 4.10379i | 0.197444i | ||||||||
\(433\) | 34.1223i | 1.63981i | 0.572499 | + | 0.819905i | \(0.305974\pi\) | ||||
−0.572499 | + | 0.819905i | \(0.694026\pi\) | |||||||
\(434\) | −118.641 | −5.69496 | ||||||||
\(435\) | 5.91975 | + | 7.45432i | 0.283830 | + | 0.357407i | ||||
\(436\) | −45.9803 | −2.20206 | ||||||||
\(437\) | − | 4.07925i | − | 0.195137i | ||||||
\(438\) | 10.6874i | 0.510664i | ||||||||
\(439\) | 31.5629 | 1.50641 | 0.753207 | − | 0.657784i | \(-0.228506\pi\) | ||||
0.753207 | + | 0.657784i | \(0.228506\pi\) | |||||||
\(440\) | 4.69476 | + | 5.91177i | 0.223814 | + | 0.281833i | ||||
\(441\) | 14.2036 | 0.676363 | ||||||||
\(442\) | 30.9702i | 1.47310i | ||||||||
\(443\) | 24.4776i | 1.16297i | 0.813559 | + | 0.581483i | \(0.197527\pi\) | ||||
−0.813559 | + | 0.581483i | \(0.802473\pi\) | |||||||
\(444\) | −35.7099 | −1.69472 | ||||||||
\(445\) | 14.4745 | − | 11.4948i | 0.686159 | − | 0.544904i | ||||
\(446\) | 41.9108 | 1.98453 | ||||||||
\(447\) | 24.5713i | 1.16218i | ||||||||
\(448\) | − | 59.2404i | − | 2.79885i | ||||||
\(449\) | −26.1058 | −1.23201 | −0.616005 | − | 0.787742i | \(-0.711250\pi\) | ||||
−0.616005 | + | 0.787742i | \(0.711250\pi\) | |||||||
\(450\) | −10.1079 | − | 2.35054i | −0.476489 | − | 0.110805i | ||||
\(451\) | −4.11322 | −0.193684 | ||||||||
\(452\) | − | 17.3365i | − | 0.815439i | ||||||
\(453\) | − | 29.8223i | − | 1.40117i | ||||||
\(454\) | −10.6048 | −0.497708 | ||||||||
\(455\) | 58.5457 | − | 46.4933i | 2.74466 | − | 2.17964i | ||||
\(456\) | 6.65811 | 0.311795 | ||||||||
\(457\) | 10.1270i | 0.473722i | 0.971544 | + | 0.236861i | \(0.0761186\pi\) | ||||
−0.971544 | + | 0.236861i | \(0.923881\pi\) | |||||||
\(458\) | − | 41.4051i | − | 1.93473i | ||||||
\(459\) | −7.91844 | −0.369601 | ||||||||
\(460\) | −19.5511 | − | 24.6193i | −0.911575 | − | 1.14788i | ||||
\(461\) | −27.9693 | −1.30266 | −0.651330 | − | 0.758795i | \(-0.725789\pi\) | ||||
−0.651330 | + | 0.758795i | \(0.725789\pi\) | |||||||
\(462\) | 22.0593i | 1.02629i | ||||||||
\(463\) | 30.8194i | 1.43230i | 0.697947 | + | 0.716149i | \(0.254097\pi\) | ||||
−0.697947 | + | 0.716149i | \(0.745903\pi\) | |||||||
\(464\) | −2.12811 | −0.0987950 | ||||||||
\(465\) | 29.0883 | + | 36.6288i | 1.34894 | + | 1.69862i | ||||
\(466\) | −9.93382 | −0.460176 | ||||||||
\(467\) | 23.4293i | 1.08418i | 0.840320 | + | 0.542090i | \(0.182367\pi\) | ||||
−0.840320 | + | 0.542090i | \(0.817633\pi\) | |||||||
\(468\) | − | 21.3822i | − | 0.988395i | ||||||
\(469\) | 24.7869 | 1.14455 | ||||||||
\(470\) | −39.1801 | + | 31.1144i | −1.80724 | + | 1.43520i | ||||
\(471\) | 23.3541 | 1.07610 | ||||||||
\(472\) | − | 10.4001i | − | 0.478704i | ||||||
\(473\) | − | 2.83644i | − | 0.130420i | ||||||
\(474\) | −72.7832 | −3.34304 | ||||||||
\(475\) | 1.13251 | − | 4.87005i | 0.0519631 | − | 0.223453i | ||||
\(476\) | −31.4242 | −1.44033 | ||||||||
\(477\) | − | 3.92744i | − | 0.179825i | ||||||
\(478\) | − | 63.7136i | − | 2.91419i | ||||||
\(479\) | −25.7398 | −1.17608 | −0.588040 | − | 0.808832i | \(-0.700100\pi\) | ||||
−0.588040 | + | 0.808832i | \(0.700100\pi\) | |||||||
\(480\) | −15.3720 | + | 12.2075i | −0.701631 | + | 0.557192i | ||||
\(481\) | −36.6487 | −1.67104 | ||||||||
\(482\) | 60.1717i | 2.74075i | ||||||||
\(483\) | − | 38.5575i | − | 1.75443i | ||||||
\(484\) | −3.44661 | −0.156664 | ||||||||
\(485\) | −0.471711 | − | 0.593992i | −0.0214193 | − | 0.0269718i | ||||
\(486\) | 20.9190 | 0.948904 | ||||||||
\(487\) | 12.0033i | 0.543923i | 0.962308 | + | 0.271962i | \(0.0876724\pi\) | ||||
−0.962308 | + | 0.271962i | \(0.912328\pi\) | |||||||
\(488\) | 19.3752i | 0.877073i | ||||||||
\(489\) | 2.21797 | 0.100300 | ||||||||
\(490\) | 51.8322 | + | 65.2685i | 2.34154 | + | 2.94853i | ||||
\(491\) | −1.70788 | −0.0770754 | −0.0385377 | − | 0.999257i | \(-0.512270\pi\) | ||||
−0.0385377 | + | 0.999257i | \(0.512270\pi\) | |||||||
\(492\) | 27.9583i | 1.26046i | ||||||||
\(493\) | − | 4.10627i | − | 0.184937i | ||||||
\(494\) | 16.2803 | 0.732485 | ||||||||
\(495\) | 1.55728 | − | 1.23669i | 0.0699945 | − | 0.0555852i | ||||
\(496\) | −10.4570 | −0.469534 | ||||||||
\(497\) | 41.2222i | 1.84907i | ||||||||
\(498\) | 11.4769i | 0.514294i | ||||||||
\(499\) | 23.8364 | 1.06706 | 0.533532 | − | 0.845780i | \(-0.320864\pi\) | ||||
0.533532 | + | 0.845780i | \(0.320864\pi\) | |||||||
\(500\) | −16.5063 | − | 34.8200i | −0.738185 | − | 1.55720i | ||||
\(501\) | −17.5976 | −0.786203 | ||||||||
\(502\) | − | 3.94926i | − | 0.176264i | ||||||
\(503\) | 26.3579i | 1.17524i | 0.809137 | + | 0.587619i | \(0.199935\pi\) | ||||
−0.809137 | + | 0.587619i | \(0.800065\pi\) | |||||||
\(504\) | 14.3902 | 0.640991 | ||||||||
\(505\) | 2.89942 | − | 2.30254i | 0.129022 | − | 0.102461i | ||||
\(506\) | 9.52013 | 0.423222 | ||||||||
\(507\) | − | 70.3323i | − | 3.12357i | ||||||
\(508\) | − | 7.96864i | − | 0.353551i | ||||||
\(509\) | 37.0820 | 1.64363 | 0.821816 | − | 0.569753i | \(-0.192961\pi\) | ||||
0.821816 | + | 0.569753i | \(0.192961\pi\) | |||||||
\(510\) | 12.1754 | + | 15.3315i | 0.539134 | + | 0.678892i | ||||
\(511\) | −11.1292 | −0.492327 | ||||||||
\(512\) | − | 11.0454i | − | 0.488142i | ||||||
\(513\) | 4.16254i | 0.183780i | ||||||||
\(514\) | 52.3604 | 2.30952 | ||||||||
\(515\) | −6.66154 | − | 8.38839i | −0.293542 | − | 0.369637i | ||||
\(516\) | −19.2798 | −0.848747 | ||||||||
\(517\) | − | 9.58734i | − | 0.421651i | ||||||
\(518\) | − | 58.7643i | − | 2.58196i | ||||||
\(519\) | −40.2529 | −1.76691 | ||||||||
\(520\) | 41.2399 | − | 32.7501i | 1.80849 | − | 1.43619i | ||||
\(521\) | −17.5841 | −0.770374 | −0.385187 | − | 0.922839i | \(-0.625863\pi\) | ||||
−0.385187 | + | 0.922839i | \(0.625863\pi\) | |||||||
\(522\) | 4.48014i | 0.196090i | ||||||||
\(523\) | 3.18765i | 0.139386i | 0.997568 | + | 0.0696931i | \(0.0222020\pi\) | ||||
−0.997568 | + | 0.0696931i | \(0.977798\pi\) | |||||||
\(524\) | 22.5217 | 0.983864 | ||||||||
\(525\) | 10.7046 | − | 46.0323i | 0.467187 | − | 2.00901i | ||||
\(526\) | 14.3537 | 0.625851 | ||||||||
\(527\) | − | 20.1773i | − | 0.878935i | ||||||
\(528\) | 1.94431i | 0.0846151i | ||||||||
\(529\) | 6.35975 | 0.276511 | ||||||||
\(530\) | 18.0474 | − | 14.3321i | 0.783929 | − | 0.622547i | ||||
\(531\) | −2.73960 | −0.118888 | ||||||||
\(532\) | 16.5190i | 0.716189i | ||||||||
\(533\) | 28.6933i | 1.24285i | ||||||||
\(534\) | 38.0453 | 1.64638 | ||||||||
\(535\) | 4.41018 | + | 5.55343i | 0.190669 | + | 0.240096i | ||||
\(536\) | 17.4600 | 0.754157 | ||||||||
\(537\) | 18.1265i | 0.782218i | ||||||||
\(538\) | 15.8546i | 0.683540i | ||||||||
\(539\) | −15.9712 | −0.687927 | ||||||||
\(540\) | 19.9503 | + | 25.1220i | 0.858524 | + | 1.08108i | ||||
\(541\) | −13.4906 | −0.580005 | −0.290002 | − | 0.957026i | \(-0.593656\pi\) | ||||
−0.290002 | + | 0.957026i | \(0.593656\pi\) | |||||||
\(542\) | − | 16.8165i | − | 0.722331i | ||||||
\(543\) | 9.61803i | 0.412749i | ||||||||
\(544\) | 8.46778 | 0.363053 | ||||||||
\(545\) | −23.3606 | + | 18.5515i | −1.00066 | + | 0.794660i | ||||
\(546\) | 153.883 | 6.58559 | ||||||||
\(547\) | 34.6641i | 1.48213i | 0.671433 | + | 0.741065i | \(0.265679\pi\) | ||||
−0.671433 | + | 0.741065i | \(0.734321\pi\) | |||||||
\(548\) | − | 6.21652i | − | 0.265557i | ||||||
\(549\) | 5.10381 | 0.217825 | ||||||||
\(550\) | 11.3657 | + | 2.64304i | 0.484636 | + | 0.112700i | ||||
\(551\) | −2.15857 | −0.0919582 | ||||||||
\(552\) | − | 27.1601i | − | 1.15601i | ||||||
\(553\) | − | 75.7918i | − | 3.22299i | ||||||
\(554\) | 67.2732 | 2.85816 | ||||||||
\(555\) | −18.1426 | + | 14.4077i | −0.770112 | + | 0.611575i | ||||
\(556\) | −19.3573 | −0.820931 | ||||||||
\(557\) | 6.73433i | 0.285343i | 0.989770 | + | 0.142671i | \(0.0455692\pi\) | ||||
−0.989770 | + | 0.142671i | \(0.954431\pi\) | |||||||
\(558\) | 22.0144i | 0.931942i | ||||||||
\(559\) | −19.7867 | −0.836888 | ||||||||
\(560\) | 6.57081 | + | 8.27414i | 0.277667 | + | 0.349646i | ||||
\(561\) | −3.75162 | −0.158393 | ||||||||
\(562\) | − | 41.5074i | − | 1.75089i | ||||||
\(563\) | − | 0.220710i | − | 0.00930180i | −0.999989 | − | 0.00465090i | \(-0.998520\pi\) | ||
0.999989 | − | 0.00465090i | \(-0.00148043\pi\) | |||||||
\(564\) | −65.1669 | −2.74402 | ||||||||
\(565\) | −6.99470 | − | 8.80792i | −0.294269 | − | 0.370552i | ||||
\(566\) | 28.7241 | 1.20736 | ||||||||
\(567\) | 52.1319i | 2.18934i | ||||||||
\(568\) | 29.0371i | 1.21837i | ||||||||
\(569\) | 0.0465835 | 0.00195288 | 0.000976440 | − | 1.00000i | \(-0.499689\pi\) | ||||
0.000976440 | 1.00000i | \(0.499689\pi\) | ||||||||
\(570\) | 8.05943 | − | 6.40030i | 0.337572 | − | 0.268079i | ||||
\(571\) | 29.5536 | 1.23678 | 0.618390 | − | 0.785871i | \(-0.287785\pi\) | ||||
0.618390 | + | 0.785871i | \(0.287785\pi\) | |||||||
\(572\) | 24.0431i | 1.00529i | ||||||||
\(573\) | 11.9736i | 0.500204i | ||||||||
\(574\) | −46.0083 | −1.92035 | ||||||||
\(575\) | −19.8662 | − | 4.61978i | −0.828476 | − | 0.192658i | ||||
\(576\) | −10.9923 | −0.458013 | ||||||||
\(577\) | 6.64097i | 0.276467i | 0.990400 | + | 0.138234i | \(0.0441425\pi\) | ||||
−0.990400 | + | 0.138234i | \(0.955858\pi\) | |||||||
\(578\) | 31.2290i | 1.29896i | ||||||||
\(579\) | 44.9269 | 1.86710 | ||||||||
\(580\) | −13.0275 | + | 10.3457i | −0.540939 | + | 0.429580i | ||||
\(581\) | −11.9514 | −0.495826 | ||||||||
\(582\) | − | 1.56127i | − | 0.0647166i | ||||||
\(583\) | 4.41619i | 0.182900i | ||||||||
\(584\) | −7.83946 | −0.324399 | ||||||||
\(585\) | −8.62703 | − | 10.8634i | −0.356684 | − | 0.449146i | ||||
\(586\) | 75.7311 | 3.12842 | ||||||||
\(587\) | − | 17.0513i | − | 0.703783i | −0.936041 | − | 0.351892i | \(-0.885539\pi\) | ||
0.936041 | − | 0.351892i | \(-0.114461\pi\) | |||||||
\(588\) | 108.559i | 4.47690i | ||||||||
\(589\) | −10.6067 | −0.437042 | ||||||||
\(590\) | −9.99741 | − | 12.5890i | −0.411587 | − | 0.518282i | ||||
\(591\) | −13.9356 | −0.573234 | ||||||||
\(592\) | − | 5.17949i | − | 0.212876i | ||||||
\(593\) | − | 37.6513i | − | 1.54615i | −0.634313 | − | 0.773076i | \(-0.718717\pi\) | ||
0.634313 | − | 0.773076i | \(-0.281283\pi\) | |||||||
\(594\) | −9.71451 | −0.398591 | ||||||||
\(595\) | −15.9653 | + | 12.6786i | −0.654513 | + | 0.519773i | ||||
\(596\) | −42.9420 | −1.75897 | ||||||||
\(597\) | 46.6579i | 1.90958i | ||||||||
\(598\) | − | 66.4113i | − | 2.71576i | ||||||
\(599\) | 5.66658 | 0.231530 | 0.115765 | − | 0.993277i | \(-0.463068\pi\) | ||||
0.115765 | + | 0.993277i | \(0.463068\pi\) | |||||||
\(600\) | 7.54037 | − | 32.4254i | 0.307834 | − | 1.32376i | ||||
\(601\) | 29.1095 | 1.18740 | 0.593701 | − | 0.804686i | \(-0.297666\pi\) | ||||
0.593701 | + | 0.804686i | \(0.297666\pi\) | |||||||
\(602\) | − | 31.7270i | − | 1.29309i | ||||||
\(603\) | − | 4.59931i | − | 0.187298i | ||||||
\(604\) | 52.1190 | 2.12069 | ||||||||
\(605\) | −1.75107 | + | 1.39059i | −0.0711912 | + | 0.0565356i | ||||
\(606\) | 7.62091 | 0.309578 | ||||||||
\(607\) | 27.0839i | 1.09930i | 0.835394 | + | 0.549651i | \(0.185239\pi\) | ||||
−0.835394 | + | 0.549651i | \(0.814761\pi\) | |||||||
\(608\) | − | 4.45131i | − | 0.180525i | ||||||
\(609\) | −20.4031 | −0.826774 | ||||||||
\(610\) | 18.6249 | + | 23.4530i | 0.754102 | + | 0.949586i | ||||
\(611\) | −66.8802 | −2.70568 | ||||||||
\(612\) | 5.83090i | 0.235700i | ||||||||
\(613\) | − | 16.5050i | − | 0.666632i | −0.942815 | − | 0.333316i | \(-0.891832\pi\) | ||
0.942815 | − | 0.333316i | \(-0.108168\pi\) | |||||||
\(614\) | −50.9839 | −2.05754 | ||||||||
\(615\) | 11.2803 | + | 14.2044i | 0.454864 | + | 0.572777i | ||||
\(616\) | −16.1810 | −0.651951 | ||||||||
\(617\) | − | 9.17145i | − | 0.369229i | −0.982811 | − | 0.184614i | \(-0.940896\pi\) | ||
0.982811 | − | 0.184614i | \(-0.0591036\pi\) | |||||||
\(618\) | − | 22.0483i | − | 0.886913i | ||||||
\(619\) | −2.94996 | −0.118569 | −0.0592844 | − | 0.998241i | \(-0.518882\pi\) | ||||
−0.0592844 | + | 0.998241i | \(0.518882\pi\) | |||||||
\(620\) | −64.0142 | + | 50.8361i | −2.57087 | + | 2.04163i | ||||
\(621\) | 16.9800 | 0.681384 | ||||||||
\(622\) | − | 7.49841i | − | 0.300659i | ||||||
\(623\) | 39.6180i | 1.58726i | ||||||||
\(624\) | 13.5633 | 0.542965 | ||||||||
\(625\) | −22.4348 | − | 11.0308i | −0.897394 | − | 0.441230i | ||||
\(626\) | 44.6658 | 1.78521 | ||||||||
\(627\) | 1.97214i | 0.0787596i | ||||||||
\(628\) | 40.8148i | 1.62869i | ||||||||
\(629\) | 9.99403 | 0.398488 | ||||||||
\(630\) | 17.4189 | − | 13.8330i | 0.693986 | − | 0.551120i | ||||
\(631\) | −13.1349 | −0.522894 | −0.261447 | − | 0.965218i | \(-0.584200\pi\) | ||||
−0.261447 | + | 0.965218i | \(0.584200\pi\) | |||||||
\(632\) | − | 53.3881i | − | 2.12366i | ||||||
\(633\) | − | 0.737722i | − | 0.0293218i | ||||||
\(634\) | 67.7808 | 2.69192 | ||||||||
\(635\) | −3.21508 | − | 4.04852i | −0.127587 | − | 0.160661i | ||||
\(636\) | 30.0176 | 1.19028 | ||||||||
\(637\) | 111.413i | 4.41434i | ||||||||
\(638\) | − | 5.03767i | − | 0.199443i | ||||||
\(639\) | 7.64895 | 0.302588 | ||||||||
\(640\) | −27.7335 | − | 34.9228i | −1.09626 | − | 1.38044i | ||||
\(641\) | 17.1097 | 0.675793 | 0.337897 | − | 0.941183i | \(-0.390285\pi\) | ||||
0.337897 | + | 0.941183i | \(0.390285\pi\) | |||||||
\(642\) | 14.5968i | 0.576089i | ||||||||
\(643\) | 14.7732i | 0.582599i | 0.956632 | + | 0.291300i | \(0.0940876\pi\) | ||||
−0.956632 | + | 0.291300i | \(0.905912\pi\) | |||||||
\(644\) | 67.3850 | 2.65534 | ||||||||
\(645\) | −9.79524 | + | 7.77877i | −0.385687 | + | 0.306289i | ||||
\(646\) | −4.43961 | −0.174674 | ||||||||
\(647\) | 33.9680i | 1.33542i | 0.744422 | + | 0.667710i | \(0.232725\pi\) | ||||
−0.744422 | + | 0.667710i | \(0.767275\pi\) | |||||||
\(648\) | 36.7220i | 1.44258i | ||||||||
\(649\) | 3.08053 | 0.120921 | ||||||||
\(650\) | 18.4376 | − | 79.2859i | 0.723181 | − | 3.10985i | ||||
\(651\) | −100.256 | −3.92933 | ||||||||
\(652\) | 3.87624i | 0.151805i | ||||||||
\(653\) | − | 25.3457i | − | 0.991855i | −0.868364 | − | 0.495927i | \(-0.834828\pi\) | ||
0.868364 | − | 0.495927i | \(-0.165172\pi\) | |||||||
\(654\) | −61.4017 | −2.40099 | ||||||||
\(655\) | 11.4423 | − | 9.08675i | 0.447087 | − | 0.355049i | ||||
\(656\) | −4.05517 | −0.158328 | ||||||||
\(657\) | 2.06507i | 0.0805660i | ||||||||
\(658\) | − | 107.239i | − | 4.18061i | ||||||
\(659\) | 27.4327 | 1.06863 | 0.534313 | − | 0.845287i | \(-0.320570\pi\) | ||||
0.534313 | + | 0.845287i | \(0.320570\pi\) | |||||||
\(660\) | 9.45211 | + | 11.9024i | 0.367923 | + | 0.463299i | ||||
\(661\) | −13.2280 | −0.514509 | −0.257255 | − | 0.966344i | \(-0.582818\pi\) | ||||
−0.257255 | + | 0.966344i | \(0.582818\pi\) | |||||||
\(662\) | 15.5626i | 0.604856i | ||||||||
\(663\) | 26.1709i | 1.01639i | ||||||||
\(664\) | −8.41859 | −0.326705 | ||||||||
\(665\) | 6.66486 | + | 8.39258i | 0.258452 | + | 0.325450i | ||||
\(666\) | −10.9040 | −0.422520 | ||||||||
\(667\) | 8.80535i | 0.340944i | ||||||||
\(668\) | − | 30.7545i | − | 1.18993i | ||||||
\(669\) | 35.4160 | 1.36926 | ||||||||
\(670\) | 21.1348 | − | 16.7839i | 0.816508 | − | 0.648419i | ||||
\(671\) | −5.73895 | −0.221550 | ||||||||
\(672\) | − | 42.0743i | − | 1.62305i | ||||||
\(673\) | − | 42.4318i | − | 1.63562i | −0.575486 | − | 0.817812i | \(-0.695187\pi\) | ||
0.575486 | − | 0.817812i | \(-0.304813\pi\) | |||||||
\(674\) | −31.4223 | −1.21034 | ||||||||
\(675\) | 20.2718 | + | 4.71411i | 0.780261 | + | 0.181446i | ||||
\(676\) | 122.916 | 4.72755 | ||||||||
\(677\) | 3.83814i | 0.147512i | 0.997276 | + | 0.0737559i | \(0.0234986\pi\) | ||||
−0.997276 | + | 0.0737559i | \(0.976501\pi\) | |||||||
\(678\) | − | 23.1510i | − | 0.889108i | ||||||
\(679\) | 1.62580 | 0.0623926 | ||||||||
\(680\) | −11.2460 | + | 8.93089i | −0.431266 | + | 0.342484i | ||||
\(681\) | −8.96141 | −0.343402 | ||||||||
\(682\) | − | 24.7539i | − | 0.947876i | ||||||
\(683\) | − | 16.2575i | − | 0.622076i | −0.950398 | − | 0.311038i | \(-0.899323\pi\) | ||
0.950398 | − | 0.311038i | \(-0.100677\pi\) | |||||||
\(684\) | 3.06517 | 0.117200 | ||||||||
\(685\) | −2.50816 | − | 3.15835i | −0.0958319 | − | 0.120674i | ||||
\(686\) | −100.347 | −3.83126 | ||||||||
\(687\) | − | 34.9887i | − | 1.33490i | ||||||
\(688\) | − | 2.79641i | − | 0.106612i | ||||||
\(689\) | 30.8068 | 1.17365 | ||||||||
\(690\) | −26.1084 | − | 32.8764i | −0.993929 | − | 1.25158i | ||||
\(691\) | 36.4802 | 1.38777 | 0.693887 | − | 0.720084i | \(-0.255897\pi\) | ||||
0.693887 | + | 0.720084i | \(0.255897\pi\) | |||||||
\(692\) | − | 70.3480i | − | 2.67423i | ||||||
\(693\) | 4.26240i | 0.161915i | ||||||||
\(694\) | 73.6150 | 2.79439 | ||||||||
\(695\) | −9.83460 | + | 7.81002i | −0.373047 | + | 0.296251i | ||||
\(696\) | −14.3720 | −0.544770 | ||||||||
\(697\) | − | 7.82462i | − | 0.296379i | ||||||
\(698\) | − | 62.1987i | − | 2.35426i | ||||||
\(699\) | −8.39442 | −0.317506 | ||||||||
\(700\) | 80.4483 | + | 18.7079i | 3.04066 | + | 0.707092i | ||||
\(701\) | −4.34336 | −0.164046 | −0.0820232 | − | 0.996630i | \(-0.526138\pi\) | ||||
−0.0820232 | + | 0.996630i | \(0.526138\pi\) | |||||||
\(702\) | 67.7673i | 2.55771i | ||||||||
\(703\) | − | 5.25363i | − | 0.198144i | ||||||
\(704\) | 12.3602 | 0.465844 | ||||||||
\(705\) | −33.1085 | + | 26.2927i | −1.24694 | + | 0.990240i | ||||
\(706\) | 22.9646 | 0.864285 | ||||||||
\(707\) | 7.93594i | 0.298462i | ||||||||
\(708\) | − | 20.9389i | − | 0.786932i | ||||||
\(709\) | 37.5895 | 1.41170 | 0.705852 | − | 0.708360i | \(-0.250564\pi\) | ||||
0.705852 | + | 0.708360i | \(0.250564\pi\) | |||||||
\(710\) | 27.9127 | + | 35.1485i | 1.04755 | + | 1.31910i | ||||
\(711\) | −14.0635 | −0.527422 | ||||||||
\(712\) | 27.9071i | 1.04586i | ||||||||
\(713\) | 43.2674i | 1.62038i | ||||||||
\(714\) | −41.9637 | −1.57045 | ||||||||
\(715\) | 9.70061 | + | 12.2153i | 0.362782 | + | 0.456826i | ||||
\(716\) | −31.6789 | −1.18389 | ||||||||
\(717\) | − | 53.8402i | − | 2.01070i | ||||||
\(718\) | 79.2278i | 2.95676i | ||||||||
\(719\) | −17.5352 | −0.653952 | −0.326976 | − | 0.945033i | \(-0.606030\pi\) | ||||
−0.326976 | + | 0.945033i | \(0.606030\pi\) | |||||||
\(720\) | 1.53530 | − | 1.21924i | 0.0572173 | − | 0.0454384i | ||||
\(721\) | 22.9597 | 0.855064 | ||||||||
\(722\) | 2.33380i | 0.0868549i | ||||||||
\(723\) | 50.8472i | 1.89103i | ||||||||
\(724\) | −16.8090 | −0.624700 | ||||||||
\(725\) | −2.44460 | + | 10.5124i | −0.0907902 | + | 0.390419i | ||||
\(726\) | −4.60257 | −0.170817 | ||||||||
\(727\) | 0.0700926i | 0.00259959i | 0.999999 | + | 0.00129980i | \(0.000413738\pi\) | ||||
−0.999999 | + | 0.00129980i | \(0.999586\pi\) | |||||||
\(728\) | 112.877i | 4.18349i | ||||||||
\(729\) | −14.9540 | −0.553851 | ||||||||
\(730\) | −9.48941 | + | 7.53590i | −0.351219 | + | 0.278916i | ||||
\(731\) | 5.39579 | 0.199571 | ||||||||
\(732\) | 39.0087i | 1.44180i | ||||||||
\(733\) | − | 5.41119i | − | 0.199867i | −0.994994 | − | 0.0999335i | \(-0.968137\pi\) | ||
0.994994 | − | 0.0999335i | \(-0.0318630\pi\) | |||||||
\(734\) | 44.1747 | 1.63052 | ||||||||
\(735\) | 43.7999 | + | 55.1541i | 1.61559 | + | 2.03439i | ||||
\(736\) | −18.1580 | −0.669313 | ||||||||
\(737\) | 5.17167i | 0.190501i | ||||||||
\(738\) | 8.53704i | 0.314253i | ||||||||
\(739\) | −16.5265 | −0.607939 | −0.303969 | − | 0.952682i | \(-0.598312\pi\) | ||||
−0.303969 | + | 0.952682i | \(0.598312\pi\) | |||||||
\(740\) | −25.1797 | − | 31.7070i | −0.925624 | − | 1.16557i | ||||
\(741\) | 13.7574 | 0.505391 | ||||||||
\(742\) | 49.3972i | 1.81343i | ||||||||
\(743\) | 11.5689i | 0.424423i | 0.977224 | + | 0.212211i | \(0.0680665\pi\) | ||||
−0.977224 | + | 0.212211i | \(0.931933\pi\) | |||||||
\(744\) | −70.6207 | −2.58908 | ||||||||
\(745\) | −21.8170 | + | 17.3257i | −0.799311 | + | 0.634763i | ||||
\(746\) | −4.52036 | −0.165502 | ||||||||
\(747\) | 2.21762i | 0.0811386i | ||||||||
\(748\) | − | 6.55652i | − | 0.239730i | ||||||
\(749\) | −15.2002 | −0.555402 | ||||||||
\(750\) | −22.0424 | − | 46.4983i | −0.804875 | − | 1.69788i | ||||
\(751\) | −27.5998 | −1.00713 | −0.503566 | − | 0.863957i | \(-0.667979\pi\) | ||||
−0.503566 | + | 0.863957i | \(0.667979\pi\) | |||||||
\(752\) | − | 9.45204i | − | 0.344681i | ||||||
\(753\) | − | 3.33726i | − | 0.121617i | ||||||
\(754\) | −35.1422 | −1.27980 | ||||||||
\(755\) | 26.4794 | − | 21.0283i | 0.963684 | − | 0.765298i | ||||
\(756\) | −68.7609 | −2.50081 | ||||||||
\(757\) | − | 12.5688i | − | 0.456821i | −0.973565 | − | 0.228411i | \(-0.926647\pi\) | ||
0.973565 | − | 0.228411i | \(-0.0733529\pi\) | |||||||
\(758\) | 34.5526i | 1.25501i | ||||||||
\(759\) | 8.04484 | 0.292009 | ||||||||
\(760\) | 4.69476 | + | 5.91177i | 0.170297 | + | 0.214443i | ||||
\(761\) | 13.1005 | 0.474893 | 0.237446 | − | 0.971401i | \(-0.423690\pi\) | ||||
0.237446 | + | 0.971401i | \(0.423690\pi\) | |||||||
\(762\) | − | 10.6413i | − | 0.385492i | ||||||
\(763\) | − | 63.9398i | − | 2.31478i | ||||||
\(764\) | −20.9256 | −0.757063 | ||||||||
\(765\) | 2.35257 | + | 2.96243i | 0.0850575 | + | 0.107107i | ||||
\(766\) | −56.4189 | −2.03850 | ||||||||
\(767\) | − | 21.4894i | − | 0.775937i | ||||||
\(768\) | − | 43.0399i | − | 1.55307i | ||||||
\(769\) | 4.22081 | 0.152206 | 0.0761031 | − | 0.997100i | \(-0.475752\pi\) | ||||
0.0761031 | + | 0.997100i | \(0.475752\pi\) | |||||||
\(770\) | −19.5866 | + | 15.5544i | −0.705851 | + | 0.560543i | ||||
\(771\) | 44.2463 | 1.59349 | ||||||||
\(772\) | 78.5165i | 2.82587i | ||||||||
\(773\) | − | 52.3823i | − | 1.88406i | −0.335527 | − | 0.942031i | \(-0.608914\pi\) | ||
0.335527 | − | 0.942031i | \(-0.391086\pi\) | |||||||
\(774\) | −5.88707 | −0.211606 | ||||||||
\(775\) | −12.0122 | + | 51.6552i | −0.431491 | + | 1.85551i | ||||
\(776\) | 1.14522 | 0.0411111 | ||||||||
\(777\) | − | 49.6578i | − | 1.78147i | ||||||
\(778\) | − | 19.5998i | − | 0.702688i | ||||||
\(779\) | −4.11322 | −0.147371 | ||||||||
\(780\) | 83.0295 | − | 65.9368i | 2.97293 | − | 2.36092i | ||||
\(781\) | −8.60081 | −0.307761 | ||||||||
\(782\) | 18.1102i | 0.647621i | ||||||||
\(783\) | − | 8.98513i | − | 0.321102i | ||||||
\(784\) | −15.7458 | −0.562349 | ||||||||
\(785\) | 16.4674 | + | 20.7362i | 0.587747 | + | 0.740108i | ||||
\(786\) | 30.0753 | 1.07275 | ||||||||
\(787\) | − | 22.1383i | − | 0.789146i | −0.918865 | − | 0.394573i | \(-0.870892\pi\) | ||
0.918865 | − | 0.394573i | \(-0.129108\pi\) | |||||||
\(788\) | − | 24.3545i | − | 0.867594i | ||||||
\(789\) | 12.1294 | 0.431817 | ||||||||
\(790\) | −51.3208 | − | 64.6246i | −1.82591 | − | 2.29924i | ||||
\(791\) | 24.1080 | 0.857181 | ||||||||
\(792\) | 3.00245i | 0.106687i | ||||||||
\(793\) | 40.0342i | 1.42166i | ||||||||
\(794\) | 27.4250 | 0.973276 | ||||||||
\(795\) | 15.2507 | − | 12.1111i | 0.540885 | − | 0.429537i | ||||
\(796\) | −81.5417 | −2.89017 | ||||||||
\(797\) | − | 27.9114i | − | 0.988672i | −0.869271 | − | 0.494336i | \(-0.835411\pi\) | ||
0.869271 | − | 0.494336i | \(-0.164589\pi\) | |||||||
\(798\) | 22.0593i | 0.780891i | ||||||||
\(799\) | 18.2381 | 0.645218 | ||||||||
\(800\) | −21.6781 | − | 5.04115i | −0.766438 | − | 0.178232i | ||||
\(801\) | 7.35128 | 0.259745 | ||||||||
\(802\) | 30.6231i | 1.08134i | ||||||||
\(803\) | − | 2.32205i | − | 0.0819435i | ||||||
\(804\) | 35.1528 | 1.23974 | ||||||||
\(805\) | 34.2354 | − | 27.1876i | 1.20664 | − | 0.958238i | ||||
\(806\) | −172.680 | −6.08241 | ||||||||
\(807\) | 13.3977i | 0.471621i | ||||||||
\(808\) | 5.59011i | 0.196659i | ||||||||
\(809\) | 50.2065 | 1.76517 | 0.882583 | − | 0.470157i | \(-0.155803\pi\) | ||||
0.882583 | + | 0.470157i | \(0.155803\pi\) | |||||||
\(810\) | 35.3000 | + | 44.4508i | 1.24032 | + | 1.56184i | ||||
\(811\) | −20.8048 | −0.730556 | −0.365278 | − | 0.930899i | \(-0.619026\pi\) | ||||
−0.365278 | + | 0.930899i | \(0.619026\pi\) | |||||||
\(812\) | − | 35.6574i | − | 1.25133i | ||||||
\(813\) | − | 14.2105i | − | 0.498385i | ||||||
\(814\) | 12.2609 | 0.429744 | ||||||||
\(815\) | 1.56393 | + | 1.96935i | 0.0547822 | + | 0.0689833i | ||||
\(816\) | −3.69868 | −0.129480 | ||||||||
\(817\) | − | 2.83644i | − | 0.0992345i | ||||||
\(818\) | − | 65.8056i | − | 2.30084i | ||||||
\(819\) | 29.7340 | 1.03899 | ||||||||
\(820\) | −24.8243 | + | 19.7139i | −0.866904 | + | 0.688441i | ||||
\(821\) | −31.5126 | −1.09980 | −0.549899 | − | 0.835231i | \(-0.685334\pi\) | ||||
−0.549899 | + | 0.835231i | \(0.685334\pi\) | |||||||
\(822\) | − | 8.30149i | − | 0.289548i | ||||||
\(823\) | − | 0.755361i | − | 0.0263302i | −0.999913 | − | 0.0131651i | \(-0.995809\pi\) | ||
0.999913 | − | 0.0131651i | \(-0.00419071\pi\) | |||||||
\(824\) | 16.1729 | 0.563410 | ||||||||
\(825\) | 9.60442 | + | 2.23346i | 0.334383 | + | 0.0777592i | ||||
\(826\) | 34.4571 | 1.19892 | ||||||||
\(827\) | − | 48.2285i | − | 1.67707i | −0.544849 | − | 0.838534i | \(-0.683413\pi\) | ||
0.544849 | − | 0.838534i | \(-0.316587\pi\) | |||||||
\(828\) | − | 12.5036i | − | 0.434529i | ||||||
\(829\) | −33.2069 | −1.15332 | −0.576662 | − | 0.816983i | \(-0.695645\pi\) | ||||
−0.576662 | + | 0.816983i | \(0.695645\pi\) | |||||||
\(830\) | −10.1904 | + | 8.09260i | −0.353715 | + | 0.280898i | ||||
\(831\) | 56.8482 | 1.97204 | ||||||||
\(832\) | − | 86.2236i | − | 2.98926i | ||||||
\(833\) | − | 30.3821i | − | 1.05268i | ||||||
\(834\) | −25.8495 | −0.895096 | ||||||||
\(835\) | −12.4084 | − | 15.6250i | −0.429411 | − | 0.540726i | ||||
\(836\) | −3.44661 | −0.119203 | ||||||||
\(837\) | − | 44.1508i | − | 1.52608i | ||||||
\(838\) | − | 59.4784i | − | 2.05465i | ||||||
\(839\) | −26.6232 | −0.919134 | −0.459567 | − | 0.888143i | \(-0.651995\pi\) | ||||
−0.459567 | + | 0.888143i | \(0.651995\pi\) | |||||||
\(840\) | 44.3754 | + | 55.8787i | 1.53110 | + | 1.92800i | ||||
\(841\) | −24.3406 | −0.839330 | ||||||||
\(842\) | − | 60.0602i | − | 2.06981i | ||||||
\(843\) | − | 35.0752i | − | 1.20805i | ||||||
\(844\) | 1.28928 | 0.0443788 | ||||||||
\(845\) | 62.4484 | − | 49.5926i | 2.14829 | − | 1.70604i | ||||
\(846\) | −19.8986 | −0.684129 | ||||||||
\(847\) | − | 4.79282i | − | 0.164683i | ||||||
\(848\) | 4.35387i | 0.149512i | ||||||||
\(849\) | 24.2729 | 0.833042 | ||||||||
\(850\) | −5.02789 | + | 21.6211i | −0.172455 | + | 0.741598i | ||||
\(851\) | −21.4308 | −0.734639 | ||||||||
\(852\) | 58.4613i | 2.00285i | ||||||||
\(853\) | 20.7758i | 0.711349i | 0.934610 | + | 0.355675i | \(0.115749\pi\) | ||||
−0.934610 | + | 0.355675i | \(0.884251\pi\) | |||||||
\(854\) | −64.1928 | −2.19663 | ||||||||
\(855\) | 1.55728 | − | 1.23669i | 0.0532578 | − | 0.0422940i | ||||
\(856\) | −10.7071 | −0.365960 | ||||||||
\(857\) | 30.3639i | 1.03721i | 0.855014 | + | 0.518605i | \(0.173548\pi\) | ||||
−0.855014 | + | 0.518605i | \(0.826452\pi\) | |||||||
\(858\) | 32.1070i | 1.09611i | ||||||||
\(859\) | −12.4982 | −0.426434 | −0.213217 | − | 0.977005i | \(-0.568394\pi\) | ||||
−0.213217 | + | 0.977005i | \(0.568394\pi\) | |||||||
\(860\) | −13.5946 | − | 17.1187i | −0.463571 | − | 0.583741i | ||||
\(861\) | −38.8786 | −1.32498 | ||||||||
\(862\) | 70.4979i | 2.40117i | ||||||||
\(863\) | 25.1151i | 0.854928i | 0.904032 | + | 0.427464i | \(0.140593\pi\) | ||||
−0.904032 | + | 0.427464i | \(0.859407\pi\) | |||||||
\(864\) | 18.5288 | 0.630361 | ||||||||
\(865\) | −28.3831 | − | 35.7408i | −0.965054 | − | 1.21522i | ||||
\(866\) | −79.6344 | −2.70609 | ||||||||
\(867\) | 26.3896i | 0.896238i | ||||||||
\(868\) | − | 175.212i | − | 5.94709i | ||||||
\(869\) | 15.8136 | 0.536439 | ||||||||
\(870\) | −17.3969 | + | 13.8155i | −0.589809 | + | 0.468389i | ||||
\(871\) | 36.0769 | 1.22242 | ||||||||
\(872\) | − | 45.0395i | − | 1.52523i | ||||||
\(873\) | − | 0.301675i | − | 0.0102101i | ||||||
\(874\) | 9.52013 | 0.322023 | ||||||||
\(875\) | 48.4203 | − | 22.9536i | 1.63691 | − | 0.775972i | ||||
\(876\) | −15.7834 | −0.533273 | ||||||||
\(877\) | − | 39.6014i | − | 1.33724i | −0.743602 | − | 0.668622i | \(-0.766884\pi\) | ||
0.743602 | − | 0.668622i | \(-0.233116\pi\) | |||||||
\(878\) | 73.6613i | 2.48595i | ||||||||
\(879\) | 63.9953 | 2.15851 | ||||||||
\(880\) | −1.72636 | + | 1.37097i | −0.0581956 | + | 0.0462153i | ||||
\(881\) | −15.1847 | −0.511585 | −0.255792 | − | 0.966732i | \(-0.582336\pi\) | ||||
−0.255792 | + | 0.966732i | \(0.582336\pi\) | |||||||
\(882\) | 33.1483i | 1.11616i | ||||||||
\(883\) | 1.91096i | 0.0643088i | 0.999483 | + | 0.0321544i | \(0.0102368\pi\) | ||||
−0.999483 | + | 0.0321544i | \(0.989763\pi\) | |||||||
\(884\) | −45.7375 | −1.53832 | ||||||||
\(885\) | −8.44815 | − | 10.6382i | −0.283982 | − | 0.357598i | ||||
\(886\) | −57.1257 | −1.91918 | ||||||||
\(887\) | 48.2069i | 1.61863i | 0.587375 | + | 0.809315i | \(0.300161\pi\) | ||||
−0.587375 | + | 0.809315i | \(0.699839\pi\) | |||||||
\(888\) | − | 34.9792i | − | 1.17383i | ||||||
\(889\) | 11.0811 | 0.371649 | ||||||||
\(890\) | 26.8265 | + | 33.7806i | 0.899225 | + | 1.13233i | ||||
\(891\) | −10.8771 | −0.364396 | ||||||||
\(892\) | 61.8948i | 2.07239i | ||||||||
\(893\) | − | 9.58734i | − | 0.320828i | ||||||
\(894\) | −57.3443 | −1.91788 | ||||||||
\(895\) | −16.0947 | + | 12.7814i | −0.537985 | + | 0.427234i | ||||
\(896\) | 95.5864 | 3.19332 | ||||||||
\(897\) | − | 56.1199i | − | 1.87379i | ||||||
\(898\) | − | 60.9257i | − | 2.03312i | ||||||
\(899\) | 22.8953 | 0.763602 | ||||||||
\(900\) | 3.47133 | − | 14.9275i | 0.115711 | − | 0.497584i | ||||
\(901\) | −8.40096 | −0.279877 | ||||||||
\(902\) | − | 9.59942i | − | 0.319626i | ||||||
\(903\) | − | 26.8104i | − | 0.892193i | ||||||
\(904\) | 16.9818 | 0.564805 | ||||||||
\(905\) | −8.53990 | + | 6.78186i | −0.283876 | + | 0.225437i | ||||
\(906\) | 69.5992 | 2.31228 | ||||||||
\(907\) | 4.98348i | 0.165474i | 0.996571 | + | 0.0827369i | \(0.0263661\pi\) | ||||
−0.996571 | + | 0.0827369i | \(0.973634\pi\) | |||||||
\(908\) | − | 15.6614i | − | 0.519742i | ||||||
\(909\) | 1.47255 | 0.0488413 | ||||||||
\(910\) | 108.506 | + | 136.634i | 3.59694 | + | 4.52936i | ||||
\(911\) | −21.7087 | −0.719240 | −0.359620 | − | 0.933099i | \(-0.617094\pi\) | ||||
−0.359620 | + | 0.933099i | \(0.617094\pi\) | |||||||
\(912\) | 1.94431i | 0.0643824i | ||||||||
\(913\) | − | 2.49359i | − | 0.0825259i | ||||||
\(914\) | −23.6344 | −0.781757 | ||||||||
\(915\) | 15.7387 | + | 19.8186i | 0.520306 | + | 0.655184i | ||||
\(916\) | 61.1480 | 2.02039 | ||||||||
\(917\) | 31.3185i | 1.03423i | ||||||||
\(918\) | − | 18.4800i | − | 0.609931i | ||||||
\(919\) | 12.7377 | 0.420178 | 0.210089 | − | 0.977682i | \(-0.432625\pi\) | ||||
0.210089 | + | 0.977682i | \(0.432625\pi\) | |||||||
\(920\) | 24.1156 | − | 19.1511i | 0.795067 | − | 0.631393i | ||||
\(921\) | −43.0832 | −1.41964 | ||||||||
\(922\) | − | 65.2747i | − | 2.14971i | ||||||
\(923\) | 59.9983i | 1.97487i | ||||||||
\(924\) | −32.5777 | −1.07173 | ||||||||
\(925\) | −25.5854 | − | 5.94978i | −0.841244 | − | 0.195627i | ||||
\(926\) | −71.9262 | −2.36364 | ||||||||
\(927\) | − | 4.26027i | − | 0.139926i | ||||||
\(928\) | 9.60848i | 0.315414i | ||||||||
\(929\) | −28.0934 | −0.921713 | −0.460857 | − | 0.887475i | \(-0.652458\pi\) | ||||
−0.460857 | + | 0.887475i | \(0.652458\pi\) | |||||||
\(930\) | −85.4841 | + | 67.8861i | −2.80313 | + | 2.22607i | ||||
\(931\) | −15.9712 | −0.523434 | ||||||||
\(932\) | − | 14.6705i | − | 0.480549i | ||||||
\(933\) | − | 6.33642i | − | 0.207445i | ||||||
\(934\) | −54.6793 | −1.78916 | ||||||||
\(935\) | −2.64534 | − | 3.33108i | −0.0865118 | − | 0.108938i | ||||
\(936\) | 20.9448 | 0.684601 | ||||||||
\(937\) | 20.4039i | 0.666566i | 0.942827 | + | 0.333283i | \(0.108157\pi\) | ||||
−0.942827 | + | 0.333283i | \(0.891843\pi\) | |||||||
\(938\) | 57.8476i | 1.88879i | ||||||||
\(939\) | 37.7442 | 1.23173 | ||||||||
\(940\) | −45.9504 | − | 57.8621i | −1.49874 | − | 1.88725i | ||||
\(941\) | 30.8314 | 1.00508 | 0.502538 | − | 0.864555i | \(-0.332400\pi\) | ||||
0.502538 | + | 0.864555i | \(0.332400\pi\) | |||||||
\(942\) | 54.5037i | 1.77583i | ||||||||
\(943\) | 16.7788i | 0.546394i | ||||||||
\(944\) | 3.03705 | 0.0988476 | ||||||||
\(945\) | −34.9344 | + | 27.7427i | −1.13642 | + | 0.902471i | ||||
\(946\) | 6.61968 | 0.215224 | ||||||||
\(947\) | 24.9048i | 0.809297i | 0.914472 | + | 0.404648i | \(0.132606\pi\) | ||||
−0.914472 | + | 0.404648i | \(0.867394\pi\) | |||||||
\(948\) | − | 107.488i | − | 3.49105i | ||||||
\(949\) | −16.1984 | −0.525822 | ||||||||
\(950\) | 11.3657 | + | 2.64304i | 0.368753 | + | 0.0857517i | ||||
\(951\) | 57.2771 | 1.85734 | ||||||||
\(952\) | − | 30.7813i | − | 0.997627i | ||||||
\(953\) | 50.7623i | 1.64435i | 0.569233 | + | 0.822176i | \(0.307240\pi\) | ||||
−0.569233 | + | 0.822176i | \(0.692760\pi\) | |||||||
\(954\) | 9.16585 | 0.296755 | ||||||||
\(955\) | −10.6314 | + | 8.44280i | −0.344025 | + | 0.273203i | ||||
\(956\) | 94.0938 | 3.04321 | ||||||||
\(957\) | − | 4.25700i | − | 0.137609i | ||||||
\(958\) | − | 60.0714i | − | 1.94082i | ||||||
\(959\) | 8.64464 | 0.279150 | ||||||||
\(960\) | −33.8972 | − | 42.6843i | −1.09403 | − | 1.37763i | ||||
\(961\) | 81.5023 | 2.62911 | ||||||||
\(962\) | − | 85.5306i | − | 2.75762i | ||||||
\(963\) | 2.82046i | 0.0908879i | ||||||||
\(964\) | −88.8631 | −2.86209 | ||||||||
\(965\) | 31.6788 | + | 39.8908i | 1.01978 | + | 1.28413i | ||||
\(966\) | 89.9854 | 2.89523 | ||||||||
\(967\) | − | 41.8598i | − | 1.34612i | −0.739588 | − | 0.673060i | \(-0.764980\pi\) | ||
0.739588 | − | 0.673060i | \(-0.235020\pi\) | |||||||
\(968\) | − | 3.37609i | − | 0.108512i | ||||||
\(969\) | −3.75162 | −0.120519 | ||||||||
\(970\) | 1.38626 | − | 1.10088i | 0.0445100 | − | 0.0353471i | ||||
\(971\) | 52.9614 | 1.69961 | 0.849806 | − | 0.527095i | \(-0.176719\pi\) | ||||
0.849806 | + | 0.527095i | \(0.176719\pi\) | |||||||
\(972\) | 30.8937i | 0.990915i | ||||||||
\(973\) | − | 26.9181i | − | 0.862954i | ||||||
\(974\) | −28.0134 | −0.897606 | ||||||||
\(975\) | 15.5804 | − | 66.9993i | 0.498972 | − | 2.14570i | ||||
\(976\) | −5.65796 | −0.181107 | ||||||||
\(977\) | − | 32.4341i | − | 1.03766i | −0.854878 | − | 0.518829i | \(-0.826368\pi\) | ||
0.854878 | − | 0.518829i | \(-0.173632\pi\) | |||||||
\(978\) | 5.17630i | 0.165520i | ||||||||
\(979\) | −8.26610 | −0.264186 | ||||||||
\(980\) | −96.3901 | + | 76.5470i | −3.07907 | + | 2.44520i | ||||
\(981\) | −11.8643 | −0.378798 | ||||||||
\(982\) | − | 3.98583i | − | 0.127193i | ||||||
\(983\) | 47.5546i | 1.51675i | 0.651816 | + | 0.758377i | \(0.274008\pi\) | ||||
−0.651816 | + | 0.758377i | \(0.725992\pi\) | |||||||
\(984\) | −27.3863 | −0.873043 | ||||||||
\(985\) | −9.82625 | − | 12.3735i | −0.313090 | − | 0.394252i | ||||
\(986\) | 9.58321 | 0.305192 | ||||||||
\(987\) | − | 90.6206i | − | 2.88449i | ||||||
\(988\) | 24.0431i | 0.764914i | ||||||||
\(989\) | −11.5705 | −0.367922 | ||||||||
\(990\) | 2.88619 | + | 3.63437i | 0.0917292 | + | 0.115508i | ||||
\(991\) | 36.3103 | 1.15344 | 0.576718 | − | 0.816943i | \(-0.304333\pi\) | ||||
0.576718 | + | 0.816943i | \(0.304333\pi\) | |||||||
\(992\) | 47.2138i | 1.49904i | ||||||||
\(993\) | 13.1509i | 0.417331i | ||||||||
\(994\) | −96.2042 | −3.05141 | ||||||||
\(995\) | −41.4278 | + | 32.8994i | −1.31335 | + | 1.04298i | ||||
\(996\) | −16.9494 | −0.537063 | ||||||||
\(997\) | − | 2.22395i | − | 0.0704333i | −0.999380 | − | 0.0352167i | \(-0.988788\pi\) | ||
0.999380 | − | 0.0352167i | \(-0.0112121\pi\) | |||||||
\(998\) | 55.6294i | 1.76092i | ||||||||
\(999\) | 21.8684 | 0.691886 |
(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 | 1045.2.b.c.419.19 | yes | 20 | |
5.2 | odd | 4 | 5225.2.a.ba.1.2 | 20 | |||
5.3 | odd | 4 | 5225.2.a.ba.1.19 | 20 | |||
5.4 | even | 2 | inner | 1045.2.b.c.419.2 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.b.c.419.2 | ✓ | 20 | 5.4 | even | 2 | inner | |
1045.2.b.c.419.19 | yes | 20 | 1.1 | even | 1 | trivial | |
5225.2.a.ba.1.2 | 20 | 5.2 | odd | 4 | |||
5225.2.a.ba.1.19 | 20 | 5.3 | odd | 4 |