Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [180,7,Mod(19,180)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(180, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("180.19");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 180.f (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: | \(41.4097350516\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 16x^{10} - 10x^{8} - 1775x^{6} - 1000x^{4} + 160000x^{2} + 1000000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{2}\cdot 5^{2}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.8 | ||
Root | \(3.06674 + 0.771446i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 180.19 |
Dual form | 180.7.f.e.19.7 |
$q$-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 \(\left(\mathbb{Z}/180\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(91\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.68788 | + | 7.09927i | 0.460984 | + | 0.887408i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −36.7991 | + | 52.3624i | −0.574987 | + | 0.818163i | ||||
\(5\) | −121.131 | − | 30.8579i | −0.969050 | − | 0.246863i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 88.8045 | 0.258905 | 0.129453 | − | 0.991586i | \(-0.458678\pi\) | ||||
0.129453 | + | 0.991586i | \(0.458678\pi\) | |||||||
\(8\) | −507.445 | − | 68.1408i | −0.991104 | − | 0.133088i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −227.649 | − | 973.743i | −0.227649 | − | 0.973743i | ||||
\(11\) | − | 1790.06i | − | 1.34490i | −0.740142 | − | 0.672450i | \(-0.765242\pi\) | ||
0.740142 | − | 0.672450i | \(-0.234758\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3328.41i | 1.51498i | 0.652847 | + | 0.757490i | \(0.273574\pi\) | ||||
−0.652847 | + | 0.757490i | \(0.726426\pi\) | |||||||
\(14\) | 327.500 | + | 630.447i | 0.119351 | + | 0.229755i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1387.65 | − | 3853.78i | −0.338781 | − | 0.940865i | ||||
\(17\) | − | 3001.09i | − | 0.610846i | −0.952217 | − | 0.305423i | \(-0.901202\pi\) | ||
0.952217 | − | 0.305423i | \(-0.0987979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6872.67i | − | 1.00199i | −0.865449 | − | 0.500997i | \(-0.832967\pi\) | ||
0.865449 | − | 0.500997i | \(-0.167033\pi\) | |||||||
\(20\) | 6073.32 | − | 5207.19i | 0.759165 | − | 0.650898i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12708.1 | − | 6601.53i | 1.19348 | − | 0.619978i | ||||
\(23\) | 5908.85 | 0.485646 | 0.242823 | − | 0.970071i | \(-0.421927\pi\) | ||||
0.242823 | + | 0.970071i | \(0.421927\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13720.6 | + | 7475.70i | 0.878118 | + | 0.478445i | ||||
\(26\) | −23629.3 | + | 12274.8i | −1.34441 | + | 0.698382i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3267.93 | + | 4650.02i | −0.148867 | + | 0.211827i | ||||
\(29\) | 14040.2 | 0.575677 | 0.287839 | − | 0.957679i | \(-0.407063\pi\) | ||||
0.287839 | + | 0.957679i | \(0.407063\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 51272.4i | 1.72107i | 0.509392 | + | 0.860534i | \(0.329870\pi\) | ||||
−0.509392 | + | 0.860534i | \(0.670130\pi\) | |||||||
\(32\) | 22241.6 | − | 24063.5i | 0.678759 | − | 0.734361i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 21305.5 | − | 11067.6i | 0.542070 | − | 0.281591i | ||||
\(35\) | −10757.0 | − | 2740.32i | −0.250892 | − | 0.0639141i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 18940.9i | − | 0.373935i | −0.982366 | − | 0.186967i | \(-0.940134\pi\) | ||
0.982366 | − | 0.186967i | \(-0.0598659\pi\) | |||||||
\(38\) | 48790.9 | − | 25345.6i | 0.889177 | − | 0.461903i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 59364.8 | + | 23912.7i | 0.927576 | + | 0.373635i | ||||
\(41\) | 11762.3 | 0.170664 | 0.0853320 | − | 0.996353i | \(-0.472805\pi\) | ||||
0.0853320 | + | 0.996353i | \(0.472805\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 100904. | 1.26912 | 0.634561 | − | 0.772873i | \(-0.281181\pi\) | ||||
0.634561 | + | 0.772873i | \(0.281181\pi\) | |||||||
\(44\) | 93732.0 | + | 65872.8i | 1.10035 | + | 0.773300i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 21791.1 | + | 41948.5i | 0.223875 | + | 0.430966i | ||||
\(47\) | 129204. | 1.24446 | 0.622232 | − | 0.782833i | \(-0.286226\pi\) | ||||
0.622232 | + | 0.782833i | \(0.286226\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −109763. | −0.932968 | ||||||||
\(50\) | −2472.19 | + | 124976.i | −0.0197775 | + | 0.999804i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −174284. | − | 122483.i | −1.23950 | − | 0.871093i | ||||
\(53\) | 47508.5i | 0.319112i | 0.987189 | + | 0.159556i | \(0.0510063\pi\) | ||||
−0.987189 | + | 0.159556i | \(0.948994\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −55237.5 | + | 216833.i | −0.332006 | + | 1.30328i | ||||
\(56\) | −45063.4 | − | 6051.21i | −0.256602 | − | 0.0344571i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 51778.5 | + | 99675.1i | 0.265378 | + | 0.510861i | ||||
\(59\) | − | 139889.i | − | 0.681127i | −0.940221 | − | 0.340564i | \(-0.889382\pi\) | ||
0.940221 | − | 0.340564i | \(-0.110618\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 299920. | 1.32134 | 0.660672 | − | 0.750675i | \(-0.270271\pi\) | ||||
0.660672 | + | 0.750675i | \(0.270271\pi\) | |||||||
\(62\) | −363996. | + | 189086.i | −1.52729 | + | 0.793386i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 252858. | + | 69155.5i | 0.964575 | + | 0.263807i | ||||
\(65\) | 102708. | − | 403175.i | 0.373992 | − | 1.46809i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 40858.7 | 0.135850 | 0.0679251 | − | 0.997690i | \(-0.478362\pi\) | ||||
0.0679251 | + | 0.997690i | \(0.478362\pi\) | |||||||
\(68\) | 157144. | + | 110437.i | 0.499772 | + | 0.351229i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −20216.3 | − | 86472.8i | −0.0589395 | − | 0.252107i | ||||
\(71\) | 222756.i | 0.622378i | 0.950348 | + | 0.311189i | \(0.100727\pi\) | ||||
−0.950348 | + | 0.311189i | \(0.899273\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 633436.i | − | 1.62830i | −0.580656 | − | 0.814149i | \(-0.697204\pi\) | ||
0.580656 | − | 0.814149i | \(-0.302796\pi\) | |||||||
\(74\) | 134467. | − | 69851.8i | 0.331833 | − | 0.172378i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 359870. | + | 252909.i | 0.819794 | + | 0.576133i | ||||
\(77\) | − | 158966.i | − | 0.348202i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 166771.i | 0.338251i | 0.985594 | + | 0.169126i | \(0.0540944\pi\) | ||||
−0.985594 | + | 0.169126i | \(0.945906\pi\) | |||||||
\(80\) | 49167.8 | + | 509634.i | 0.0960309 | + | 0.995378i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 43378.0 | + | 83503.9i | 0.0786734 | + | 0.151449i | ||||
\(83\) | −328119. | −0.573848 | −0.286924 | − | 0.957953i | \(-0.592633\pi\) | ||||
−0.286924 | + | 0.957953i | \(0.592633\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −92607.1 | + | 363526.i | −0.150795 | + | 0.591941i | ||||
\(86\) | 372122. | + | 716345.i | 0.585046 | + | 1.12623i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −121976. | + | 908359.i | −0.178990 | + | 1.33294i | ||||
\(89\) | −27762.8 | −0.0393816 | −0.0196908 | − | 0.999806i | \(-0.506268\pi\) | ||||
−0.0196908 | + | 0.999806i | \(0.506268\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 295578.i | 0.392236i | ||||||||
\(92\) | −217441. | + | 309402.i | −0.279240 | + | 0.397337i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 476488. | + | 917254.i | 0.573679 | + | 1.10435i | ||||
\(95\) | −212076. | + | 832496.i | −0.247355 | + | 0.970982i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 220750.i | − | 0.241872i | −0.992660 | − | 0.120936i | \(-0.961410\pi\) | ||
0.992660 | − | 0.120936i | \(-0.0385895\pi\) | |||||||
\(98\) | −404791. | − | 779235.i | −0.430084 | − | 0.827924i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −896352. | + | 443344.i | −0.896352 | + | 0.443344i | ||||
\(101\) | −186720. | −0.181229 | −0.0906144 | − | 0.995886i | \(-0.528883\pi\) | ||||
−0.0906144 | + | 0.995886i | \(0.528883\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.15683e6 | 1.05866 | 0.529332 | − | 0.848415i | \(-0.322443\pi\) | ||||
0.529332 | + | 0.848415i | \(0.322443\pi\) | |||||||
\(104\) | 226801. | − | 1.68899e6i | 0.201625 | − | 1.50150i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −337275. | + | 175205.i | −0.283183 | + | 0.147106i | ||||
\(107\) | 1.55229e6 | 1.26713 | 0.633566 | − | 0.773689i | \(-0.281591\pi\) | ||||
0.633566 | + | 0.773689i | \(0.281591\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.76722e6 | 1.36462 | 0.682310 | − | 0.731063i | \(-0.260975\pi\) | ||||
0.682310 | + | 0.731063i | \(0.260975\pi\) | |||||||
\(110\) | −1.74306e6 | + | 407506.i | −1.30959 | + | 0.306165i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −123229. | − | 342233.i | −0.0877121 | − | 0.243595i | ||||
\(113\) | − | 1.35571e6i | − | 0.939572i | −0.882780 | − | 0.469786i | \(-0.844331\pi\) | ||
0.882780 | − | 0.469786i | \(-0.155669\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −715747. | − | 182335.i | −0.470615 | − | 0.119888i | ||||
\(116\) | −516667. | + | 735178.i | −0.331007 | + | 0.470998i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 993111. | − | 515894.i | 0.604438 | − | 0.313989i | ||||
\(119\) | − | 266510.i | − | 0.158151i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.43276e6 | −0.808757 | ||||||||
\(122\) | 1.10607e6 | + | 2.12921e6i | 0.609119 | + | 1.17257i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.68474e6 | − | 1.88678e6i | −1.40811 | − | 0.989592i | ||||
\(125\) | −1.43131e6 | − | 1.32893e6i | −0.732830 | − | 0.680412i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −933285. | −0.455620 | −0.227810 | − | 0.973706i | \(-0.573157\pi\) | ||||
−0.227810 | + | 0.973706i | \(0.573157\pi\) | |||||||
\(128\) | 441554. | + | 2.05014e6i | 0.210549 | + | 0.977583i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.24102e6 | − | 757710.i | 1.47520 | − | 0.344884i | ||||
\(131\) | − | 10503.7i | − | 0.00467227i | −0.999997 | − | 0.00233614i | \(-0.999256\pi\) | ||
0.999997 | − | 0.00233614i | \(-0.000743616\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 610324.i | − | 0.259421i | ||||||
\(134\) | 150682. | + | 290067.i | 0.0626248 | + | 0.120555i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −204497. | + | 1.52289e6i | −0.0812961 | + | 0.605412i | ||||
\(137\) | − | 2.10446e6i | − | 0.818425i | −0.912439 | − | 0.409213i | \(-0.865803\pi\) | ||
0.912439 | − | 0.409213i | \(-0.134197\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.09139e6i | − | 1.15109i | −0.817770 | − | 0.575545i | \(-0.804790\pi\) | ||
0.817770 | − | 0.575545i | \(-0.195210\pi\) | |||||||
\(140\) | 539338. | − | 462421.i | 0.196552 | − | 0.168521i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.58140e6 | + | 821496.i | −0.552303 | + | 0.286906i | ||||
\(143\) | 5.95806e6 | 2.03750 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.70071e6 | − | 433250.i | −0.557860 | − | 0.142113i | ||||
\(146\) | 4.49693e6 | − | 2.33603e6i | 1.44497 | − | 0.750620i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 991792. | + | 697010.i | 0.305940 | + | 0.215008i | ||||
\(149\) | −1.54748e6 | −0.467806 | −0.233903 | − | 0.972260i | \(-0.575150\pi\) | ||||
−0.233903 | + | 0.972260i | \(0.575150\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.13696e6i | − | 0.620677i | −0.950626 | − | 0.310339i | \(-0.899558\pi\) | ||
0.950626 | − | 0.310339i | \(-0.100442\pi\) | |||||||
\(152\) | −468310. | + | 3.48751e6i | −0.133353 | + | 0.993080i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.12854e6 | − | 586245.i | 0.308997 | − | 0.160516i | ||||
\(155\) | 1.58215e6 | − | 6.21069e6i | 0.424868 | − | 1.66780i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 6.53669e6i | − | 1.68911i | −0.535467 | − | 0.844556i | \(-0.679864\pi\) | ||
0.535467 | − | 0.844556i | \(-0.320136\pi\) | |||||||
\(158\) | −1.18395e6 | + | 615031.i | −0.300167 | + | 0.155929i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.43670e6 | + | 2.22852e6i | −0.839038 | + | 0.544073i | ||||
\(161\) | 524733. | 0.125736 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.13681e6 | 1.64794 | 0.823970 | − | 0.566633i | \(-0.191754\pi\) | ||||
0.823970 | + | 0.566633i | \(0.191754\pi\) | |||||||
\(164\) | −432844. | + | 615904.i | −0.0981295 | + | 0.139631i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.21006e6 | − | 2.32940e6i | −0.264535 | − | 0.509237i | ||||
\(167\) | −4.55070e6 | −0.977078 | −0.488539 | − | 0.872542i | \(-0.662470\pi\) | ||||
−0.488539 | + | 0.872542i | \(0.662470\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.25151e6 | −1.29516 | ||||||||
\(170\) | −2.92229e6 | + | 683195.i | −0.594807 | + | 0.139059i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.71319e6 | + | 5.28358e6i | −0.729729 | + | 1.03835i | ||||
\(173\) | − | 8.29944e6i | − | 1.60292i | −0.598051 | − | 0.801458i | \(-0.704058\pi\) | ||
0.598051 | − | 0.801458i | \(-0.295942\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.21845e6 | + | 663876.i | 0.227349 | + | 0.123872i | ||||
\(176\) | −6.89852e6 | + | 2.48397e6i | −1.26537 | + | 0.455626i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −102386. | − | 197096.i | −0.0181543 | − | 0.0349476i | ||||
\(179\) | 3.03619e6i | 0.529384i | 0.964333 | + | 0.264692i | \(0.0852702\pi\) | ||||
−0.964333 | + | 0.264692i | \(0.914730\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −644931. | −0.108762 | −0.0543811 | − | 0.998520i | \(-0.517319\pi\) | ||||
−0.0543811 | + | 0.998520i | \(0.517319\pi\) | |||||||
\(182\) | −2.09839e6 | + | 1.09005e6i | −0.348074 | + | 0.180815i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.99842e6 | − | 402634.i | −0.481326 | − | 0.0646335i | ||||
\(185\) | −584476. | + | 2.29434e6i | −0.0923106 | + | 0.362362i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.37214e6 | −0.821528 | ||||||||
\(188\) | −4.75460e6 | + | 6.76543e6i | −0.715550 | + | 1.01817i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.69222e6 | + | 1.56456e6i | −0.975684 | + | 0.228103i | ||||
\(191\) | − | 4.62842e6i | − | 0.664252i | −0.943235 | − | 0.332126i | \(-0.892234\pi\) | ||
0.943235 | − | 0.332126i | \(-0.107766\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.13781e6i | 0.714671i | 0.933976 | + | 0.357335i | \(0.116315\pi\) | ||||
−0.933976 | + | 0.357335i | \(0.883685\pi\) | |||||||
\(194\) | 1.56716e6 | − | 814098.i | 0.214639 | − | 0.111499i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.03918e6 | − | 5.74744e6i | 0.536444 | − | 0.763320i | ||||
\(197\) | − | 5.52253e6i | − | 0.722337i | −0.932501 | − | 0.361168i | \(-0.882378\pi\) | ||
0.932501 | − | 0.361168i | \(-0.117622\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.29058e6i | − | 0.544449i | −0.962234 | − | 0.272224i | \(-0.912241\pi\) | ||
0.962234 | − | 0.272224i | \(-0.0877593\pi\) | |||||||
\(200\) | −6.45305e6 | − | 4.72844e6i | −0.806631 | − | 0.591055i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −688601. | − | 1.32558e6i | −0.0835437 | − | 0.160824i | ||||
\(203\) | 1.24683e6 | 0.149046 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.42479e6 | − | 362960.i | −0.165382 | − | 0.0421306i | ||||
\(206\) | 4.26625e6 | + | 8.21265e6i | 0.488028 | + | 0.939467i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.28270e7 | − | 4.61865e6i | 1.42539 | − | 0.513246i | ||||
\(209\) | −1.23025e7 | −1.34758 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.06723e7i | 1.13608i | 0.823000 | + | 0.568041i | \(0.192298\pi\) | ||||
−0.823000 | + | 0.568041i | \(0.807702\pi\) | |||||||
\(212\) | −2.48766e6 | − | 1.74827e6i | −0.261086 | − | 0.183485i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.72465e6 | + | 1.10201e7i | 0.584128 | + | 1.12446i | ||||
\(215\) | −1.22226e7 | − | 3.11368e6i | −1.22984 | − | 0.313299i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.55322e6i | 0.445594i | ||||||||
\(218\) | 6.51730e6 | + | 1.25460e7i | 0.629069 | + | 1.21097i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.32119e6 | − | 1.08716e7i | −0.875393 | − | 1.02100i | ||||
\(221\) | 9.98885e6 | 0.925420 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.50950e6 | −0.586993 | −0.293497 | − | 0.955960i | \(-0.594819\pi\) | ||||
−0.293497 | + | 0.955960i | \(0.594819\pi\) | |||||||
\(224\) | 1.97515e6 | − | 2.13695e6i | 0.175734 | − | 0.190130i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.62451e6 | − | 4.99967e6i | 0.833784 | − | 0.433128i | ||||
\(227\) | 8.28329e6 | 0.708150 | 0.354075 | − | 0.935217i | \(-0.384796\pi\) | ||||
0.354075 | + | 0.935217i | \(0.384796\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.99134e6 | 0.498904 | 0.249452 | − | 0.968387i | \(-0.419749\pi\) | ||||
0.249452 | + | 0.968387i | \(0.419749\pi\) | |||||||
\(230\) | −1.34515e6 | − | 5.75371e6i | −0.110557 | − | 0.472895i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.12463e6 | − | 956711.i | −0.570556 | − | 0.0766155i | ||||
\(233\) | 1.67538e6i | 0.132448i | 0.997805 | + | 0.0662239i | \(0.0210952\pi\) | ||||
−0.997805 | + | 0.0662239i | \(0.978905\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.56506e7 | − | 3.98696e6i | −1.20595 | − | 0.307212i | ||||
\(236\) | 7.32494e6 | + | 5.14780e6i | 0.557273 | + | 0.391639i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.89203e6 | − | 982856.i | 0.140345 | − | 0.0729053i | ||||
\(239\) | 4.03994e6i | 0.295925i | 0.988993 | + | 0.147962i | \(0.0472715\pi\) | ||||
−0.988993 | + | 0.147962i | \(0.952729\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.32032e6 | 0.665855 | 0.332928 | − | 0.942952i | \(-0.391964\pi\) | ||||
0.332928 | + | 0.942952i | \(0.391964\pi\) | |||||||
\(242\) | −5.28385e6 | − | 1.01716e7i | −0.372824 | − | 0.717698i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.10368e7 | + | 1.57045e7i | −0.759755 | + | 1.08107i | ||||
\(245\) | 1.32957e7 | + | 3.38704e6i | 0.904093 | + | 0.230315i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.28751e7 | 1.51800 | ||||||||
\(248\) | 3.49374e6 | − | 2.60179e7i | 0.229053 | − | 1.70576i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.15594e6 | − | 1.50622e7i | 0.265980 | − | 0.963979i | ||||
\(251\) | 2.59353e7i | 1.64010i | 0.572291 | + | 0.820051i | \(0.306055\pi\) | ||||
−0.572291 | + | 0.820051i | \(0.693945\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.05772e7i | − | 0.653146i | ||||||
\(254\) | −3.44184e6 | − | 6.62564e6i | −0.210034 | − | 0.404321i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.29261e7 | + | 1.06954e7i | −0.770455 | + | 0.637494i | ||||
\(257\) | 1.61283e7i | 0.950146i | 0.879946 | + | 0.475073i | \(0.157578\pi\) | ||||
−0.879946 | + | 0.475073i | \(0.842422\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.68204e6i | − | 0.0968137i | ||||||
\(260\) | 1.73316e7 | + | 2.02145e7i | 0.986097 | + | 1.15012i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 74568.5 | − | 38736.3i | 0.00414621 | − | 0.00215385i | ||||
\(263\) | 91845.2 | 0.00504881 | 0.00252441 | − | 0.999997i | \(-0.499196\pi\) | ||||
0.00252441 | + | 0.999997i | \(0.499196\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.46601e6 | − | 5.75476e6i | 0.0787769 | − | 0.309236i | ||||
\(266\) | 4.33285e6 | − | 2.25080e6i | 0.230213 | − | 0.119589i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.50357e6 | + | 2.13946e6i | −0.0781121 | + | 0.111148i | ||||
\(269\) | 5.38438e6 | 0.276617 | 0.138308 | − | 0.990389i | \(-0.455833\pi\) | ||||
0.138308 | + | 0.990389i | \(0.455833\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.91843e6i | 0.448106i | 0.974577 | + | 0.224053i | \(0.0719289\pi\) | ||||
−0.974577 | + | 0.224053i | \(0.928071\pi\) | |||||||
\(272\) | −1.15655e7 | + | 4.16445e6i | −0.574724 | + | 0.206943i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.49401e7 | − | 7.76099e6i | 0.726277 | − | 0.377281i | ||||
\(275\) | 1.33820e7 | − | 2.45607e7i | 0.643461 | − | 1.18098i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.85192e6i | 0.416484i | 0.978077 | + | 0.208242i | \(0.0667742\pi\) | ||||
−0.978077 | + | 0.208242i | \(0.933226\pi\) | |||||||
\(278\) | 2.19466e7 | − | 1.14007e7i | 1.02149 | − | 0.530635i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.27186e6 | + | 2.12355e6i | 0.240154 | + | 0.0967361i | ||||
\(281\) | −4.54352e6 | −0.204774 | −0.102387 | − | 0.994745i | \(-0.532648\pi\) | ||||
−0.102387 | + | 0.994745i | \(0.532648\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.97987e7 | 0.873528 | 0.436764 | − | 0.899576i | \(-0.356125\pi\) | ||||
0.436764 | + | 0.899576i | \(0.356125\pi\) | |||||||
\(284\) | −1.16640e7 | − | 8.19722e6i | −0.509206 | − | 0.357859i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.19726e7 | + | 4.22979e7i | 0.939254 | + | 1.80809i | ||||
\(287\) | 1.04455e6 | 0.0441858 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.51310e7 | 0.626867 | ||||||||
\(290\) | −3.19624e6 | − | 1.36715e7i | −0.131052 | − | 0.560562i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.31682e7 | + | 2.33099e7i | 1.33221 | + | 0.936250i | ||||
\(293\) | 3.44412e7i | 1.36923i | 0.728906 | + | 0.684614i | \(0.240029\pi\) | ||||
−0.728906 | + | 0.684614i | \(0.759971\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.31668e6 | + | 1.69450e7i | −0.168145 | + | 0.660047i | ||||
\(296\) | −1.29065e6 | + | 9.61148e6i | −0.0497661 | + | 0.370608i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.70691e6 | − | 1.09860e7i | −0.215651 | − | 0.415135i | ||||
\(299\) | 1.96671e7i | 0.735744i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.96074e6 | 0.328582 | ||||||||
\(302\) | 1.51709e7 | − | 7.88085e6i | 0.550794 | − | 0.286123i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.64858e7 | + | 9.53683e6i | −0.942741 | + | 0.339456i | ||||
\(305\) | −3.63297e7 | − | 9.25489e6i | −1.28045 | − | 0.326191i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.94134e7 | −0.670944 | −0.335472 | − | 0.942050i | \(-0.608896\pi\) | ||||
−0.335472 | + | 0.942050i | \(0.608896\pi\) | |||||||
\(308\) | 8.32382e6 | + | 5.84980e6i | 0.284886 | + | 0.200211i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.99261e7 | − | 1.16721e7i | 1.67588 | − | 0.391800i | ||||
\(311\) | 2.64127e7i | 0.878075i | 0.898469 | + | 0.439038i | \(0.144681\pi\) | ||||
−0.898469 | + | 0.439038i | \(0.855319\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.96526e6i | − | 0.161923i | −0.996717 | − | 0.0809616i | \(-0.974201\pi\) | ||
0.996717 | − | 0.0809616i | \(-0.0257991\pi\) | |||||||
\(314\) | 4.64057e7 | − | 2.41065e7i | 1.49893 | − | 0.778655i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.73254e6 | − | 6.13704e6i | −0.276745 | − | 0.194490i | ||||
\(317\) | − | 3.24542e7i | − | 1.01881i | −0.860527 | − | 0.509405i | \(-0.829865\pi\) | ||
0.860527 | − | 0.509405i | \(-0.170135\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.51328e7i | − | 0.774229i | ||||||
\(320\) | −2.84950e7 | − | 1.61795e7i | −0.869598 | − | 0.493760i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.93515e6 | + | 3.72522e6i | 0.0579625 | + | 0.111579i | ||||
\(323\) | −2.06255e7 | −0.612064 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.48822e7 | + | 4.56677e7i | −0.724834 | + | 1.33033i | ||||
\(326\) | 2.63197e7 | + | 5.06661e7i | 0.759675 | + | 1.46240i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.96874e6 | − | 801495.i | −0.169146 | − | 0.0227133i | ||||
\(329\) | 1.14739e7 | 0.322198 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.50251e7i | 1.24157i | 0.783981 | + | 0.620784i | \(0.213186\pi\) | ||||
−0.783981 | + | 0.620784i | \(0.786814\pi\) | |||||||
\(332\) | 1.20745e7 | − | 1.71811e7i | 0.329955 | − | 0.469501i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.67824e7 | − | 3.23067e7i | −0.450418 | − | 0.867067i | ||||
\(335\) | −4.94927e6 | − | 1.26081e6i | −0.131646 | − | 0.0335364i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.36631e6i | − | 0.0618275i | −0.999522 | − | 0.0309137i | \(-0.990158\pi\) | ||
0.999522 | − | 0.0309137i | \(-0.00984172\pi\) | |||||||
\(338\) | −2.30548e7 | − | 4.43811e7i | −0.597050 | − | 1.14934i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.56272e7 | − | 1.82266e7i | −0.397599 | − | 0.463733i | ||||
\(341\) | 9.17807e7 | 2.31467 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.01952e7 | −0.500456 | ||||||||
\(344\) | −5.12033e7 | − | 6.87569e6i | −1.25783 | − | 0.168904i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.89200e7 | − | 3.06073e7i | 1.42244 | − | 0.738919i | ||||
\(347\) | −3.57456e7 | −0.855528 | −0.427764 | − | 0.903890i | \(-0.640699\pi\) | ||||
−0.427764 | + | 0.903890i | \(0.640699\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.95982e7 | 0.696288 | 0.348144 | − | 0.937441i | \(-0.386812\pi\) | ||||
0.348144 | + | 0.937441i | \(0.386812\pi\) | |||||||
\(350\) | −219542. | + | 1.10984e7i | −0.00512050 | + | 0.258855i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.30752e7 | − | 3.98138e7i | −0.987642 | − | 0.912863i | ||||
\(353\) | 6.19569e7i | 1.40853i | 0.709938 | + | 0.704264i | \(0.248723\pi\) | ||||
−0.709938 | + | 0.704264i | \(0.751277\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.87376e6 | − | 2.69827e7i | 0.153642 | − | 0.603115i | ||||
\(356\) | 1.02165e6 | − | 1.45373e6i | 0.0226439 | − | 0.0322206i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.15547e7 | + | 1.11971e7i | −0.469779 | + | 0.244038i | ||||
\(359\) | − | 4.08262e7i | − | 0.882380i | −0.897414 | − | 0.441190i | \(-0.854556\pi\) | ||
0.897414 | − | 0.441190i | \(-0.145444\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −187766. | −0.00399111 | ||||||||
\(362\) | −2.37843e6 | − | 4.57854e6i | −0.0501377 | − | 0.0965164i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.54772e7 | − | 1.08770e7i | −0.320913 | − | 0.225531i | ||||
\(365\) | −1.95465e7 | + | 7.67289e7i | −0.401966 | + | 1.57790i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.51049e7 | 0.305577 | 0.152788 | − | 0.988259i | \(-0.451175\pi\) | ||||
0.152788 | + | 0.988259i | \(0.451175\pi\) | |||||||
\(368\) | −8.19940e6 | − | 2.27715e7i | −0.164527 | − | 0.456928i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.84436e7 | + | 4.31188e6i | −0.364117 | + | 0.0851259i | ||||
\(371\) | 4.21896e6i | 0.0826198i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.32493e7i | 1.02610i | 0.858360 | + | 0.513048i | \(0.171484\pi\) | ||||
−0.858360 | + | 0.513048i | \(0.828516\pi\) | |||||||
\(374\) | −1.98118e7 | − | 3.81382e7i | −0.378711 | − | 0.729030i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.55640e7 | − | 8.80407e6i | −1.23339 | − | 0.165623i | ||||
\(377\) | 4.67315e7i | 0.872139i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 329020.i | − | 0.00604373i | −0.999995 | − | 0.00302187i | \(-0.999038\pi\) | ||
0.999995 | − | 0.00302187i | \(-0.000961891\pi\) | |||||||
\(380\) | −3.57873e7 | − | 4.17400e7i | −0.652196 | − | 0.760679i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.28584e7 | − | 1.70691e7i | 0.589463 | − | 0.306210i | ||||
\(383\) | −8.05002e7 | −1.43285 | −0.716424 | − | 0.697665i | \(-0.754223\pi\) | ||||
−0.716424 | + | 0.697665i | \(0.754223\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.90534e6 | + | 1.92557e7i | −0.0859581 | + | 0.337425i | ||||
\(386\) | −3.64747e7 | + | 1.89476e7i | −0.634205 | + | 0.329452i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.15590e7 | + | 8.12340e6i | 0.197890 | + | 0.139073i | ||||
\(389\) | −4.89579e7 | −0.831713 | −0.415857 | − | 0.909430i | \(-0.636518\pi\) | ||||
−0.415857 | + | 0.909430i | \(0.636518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.77330e7i | − | 0.296655i | ||||||
\(392\) | 5.56986e7 | + | 7.47933e6i | 0.924669 | + | 0.124166i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.92059e7 | − | 2.03664e7i | 0.641008 | − | 0.332986i | ||||
\(395\) | 5.14620e6 | − | 2.02012e7i | 0.0835017 | − | 0.327783i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 6.21417e7i | − | 0.993142i | −0.867996 | − | 0.496571i | \(-0.834592\pi\) | ||
0.867996 | − | 0.496571i | \(-0.165408\pi\) | |||||||
\(398\) | 3.04600e7 | − | 1.58231e7i | 0.483148 | − | 0.250982i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.77044e6 | − | 6.32498e7i | 0.152663 | − | 0.988278i | ||||
\(401\) | −382303. | −0.00592891 | −0.00296445 | − | 0.999996i | \(-0.500944\pi\) | ||||
−0.00296445 | + | 0.999996i | \(0.500944\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.70655e8 | −2.60738 | ||||||||
\(404\) | 6.87115e6 | − | 9.77713e6i | 0.104204 | − | 0.148275i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.59816e6 | + | 8.85159e6i | 0.0687078 | + | 0.132265i | ||||
\(407\) | −3.39054e7 | −0.502905 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.10847e8 | −1.62015 | −0.810074 | − | 0.586327i | \(-0.800573\pi\) | ||||
−0.810074 | + | 0.586327i | \(0.800573\pi\) | |||||||
\(410\) | −2.67768e6 | − | 1.14535e7i | −0.0388515 | − | 0.166183i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.25704e7 | + | 6.05745e7i | −0.608718 | + | 0.866159i | ||||
\(413\) | − | 1.24228e7i | − | 0.176347i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.97454e7 | + | 1.01250e7i | 0.556087 | + | 0.141662i | ||||
\(416\) | 8.00933e7 | + | 7.40291e7i | 1.11254 | + | 1.02831i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.53701e7 | − | 8.73388e7i | −0.621214 | − | 1.19585i | ||||
\(419\) | − | 1.21226e8i | − | 1.64799i | −0.566596 | − | 0.823995i | \(-0.691740\pi\) | ||
0.566596 | − | 0.823995i | \(-0.308260\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −826557. | −0.0110771 | −0.00553856 | − | 0.999985i | \(-0.501763\pi\) | ||||
−0.00553856 | + | 0.999985i | \(0.501763\pi\) | |||||||
\(422\) | −7.57653e7 | + | 3.93580e7i | −1.00817 | + | 0.523716i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.23727e6 | − | 2.41080e7i | 0.0424699 | − | 0.316273i | ||||
\(425\) | 2.24352e7 | − | 4.11767e7i | 0.292256 | − | 0.536395i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.66342e7 | 0.342103 | ||||||||
\(428\) | −5.71230e7 | + | 8.12817e7i | −0.728584 | + | 1.03672i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.29707e7 | − | 9.82547e7i | −0.288915 | − | 1.23580i | ||||
\(431\) | 1.26492e8i | 1.57990i | 0.613169 | + | 0.789952i | \(0.289894\pi\) | ||||
−0.613169 | + | 0.789952i | \(0.710106\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.05162e8i | 1.29537i | 0.761907 | + | 0.647687i | \(0.224263\pi\) | ||||
−0.761907 | + | 0.647687i | \(0.775737\pi\) | |||||||
\(434\) | −3.23245e7 | + | 1.67917e7i | −0.395424 | + | 0.205412i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.50323e7 | + | 9.25360e7i | −0.784638 | + | 1.11648i | ||||
\(437\) | − | 4.06096e7i | − | 0.486614i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.67453e7i | − | 0.316122i | −0.987429 | − | 0.158061i | \(-0.949476\pi\) | ||
0.987429 | − | 0.158061i | \(-0.0505242\pi\) | |||||||
\(440\) | 4.28052e7 | − | 1.06267e8i | 0.502502 | − | 1.24750i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.68376e7 | + | 7.09135e7i | 0.426604 | + | 0.821225i | ||||
\(443\) | 8.39480e7 | 0.965604 | 0.482802 | − | 0.875730i | \(-0.339619\pi\) | ||||
0.482802 | + | 0.875730i | \(0.339619\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.36294e6 | + | 856700.i | 0.0381628 | + | 0.00972185i | ||||
\(446\) | −2.40062e7 | − | 4.62127e7i | −0.270595 | − | 0.520903i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.24549e7 | + | 6.14132e6i | 0.249734 | + | 0.0683011i | ||||
\(449\) | 3.85437e7 | 0.425808 | 0.212904 | − | 0.977073i | \(-0.431708\pi\) | ||||
0.212904 | + | 0.977073i | \(0.431708\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.10553e7i | − | 0.229526i | ||||||
\(452\) | 7.09880e7 | + | 4.98888e7i | 0.768723 | + | 0.540241i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.05477e7 | + | 5.88053e7i | 0.326446 | + | 0.628418i | ||||
\(455\) | 9.12089e6 | − | 3.58037e7i | 0.0968285 | − | 0.380097i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.01357e8i | − | 1.06196i | −0.847386 | − | 0.530978i | \(-0.821825\pi\) | ||
0.847386 | − | 0.530978i | \(-0.178175\pi\) | |||||||
\(458\) | 2.20953e7 | + | 4.25341e7i | 0.229987 | + | 0.442732i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.58864e7 | − | 3.07685e7i | 0.368685 | − | 0.316106i | ||||
\(461\) | −9.49132e7 | −0.968777 | −0.484388 | − | 0.874853i | \(-0.660958\pi\) | ||||
−0.484388 | + | 0.874853i | \(0.660958\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.18102e8 | 1.18991 | 0.594955 | − | 0.803759i | \(-0.297170\pi\) | ||||
0.594955 | + | 0.803759i | \(0.297170\pi\) | |||||||
\(464\) | −1.94828e7 | − | 5.41079e7i | −0.195028 | − | 0.541635i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.18939e7 | + | 6.17858e6i | −0.117535 | + | 0.0610564i | ||||
\(467\) | 1.86109e8 | 1.82733 | 0.913663 | − | 0.406473i | \(-0.133241\pi\) | ||||
0.913663 | + | 0.406473i | \(0.133241\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.62844e6 | 0.0351723 | ||||||||
\(470\) | −2.94132e7 | − | 1.25812e8i | −0.283301 | − | 1.21179i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.53217e6 | + | 7.09861e7i | −0.0906496 | + | 0.675068i | ||||
\(473\) | − | 1.80625e8i | − | 1.70684i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.13781e7 | − | 9.42971e7i | 0.479399 | − | 0.879868i | ||||
\(476\) | 1.39551e7 | + | 9.80734e6i | 0.129394 | + | 0.0909349i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.86806e7 | + | 1.48988e7i | −0.262606 | + | 0.136417i | ||||
\(479\) | 5.01949e7i | 0.456723i | 0.973576 | + | 0.228362i | \(0.0733368\pi\) | ||||
−0.973576 | + | 0.228362i | \(0.926663\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.30432e7 | 0.566504 | ||||||||
\(482\) | 3.43722e7 | + | 6.61674e7i | 0.306949 | + | 0.590885i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.27244e7 | − | 7.50229e7i | 0.465025 | − | 0.661695i | ||||
\(485\) | −6.81186e6 | + | 2.67397e7i | −0.0597091 | + | 0.234386i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.08896e8 | 0.942816 | 0.471408 | − | 0.881915i | \(-0.343746\pi\) | ||||
0.471408 | + | 0.881915i | \(0.343746\pi\) | |||||||
\(488\) | −1.52193e8 | − | 2.04368e7i | −1.30959 | − | 0.175854i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.49874e7 | + | 1.06881e8i | 0.212389 | + | 0.908471i | ||||
\(491\) | − | 1.71108e7i | − | 0.144553i | −0.997385 | − | 0.0722764i | \(-0.976974\pi\) | ||
0.997385 | − | 0.0722764i | \(-0.0230264\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.21359e7i | − | 0.351650i | ||||||
\(494\) | 8.43604e7 | + | 1.62396e8i | 0.699774 | + | 1.34709i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.97593e8 | − | 7.11479e7i | 1.61929 | − | 0.583065i | ||||
\(497\) | 1.97817e7i | 0.161137i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 2.08493e7i | − | 0.167799i | −0.996474 | − | 0.0838994i | \(-0.973263\pi\) | ||
0.996474 | − | 0.0838994i | \(-0.0267374\pi\) | |||||||
\(500\) | 1.22257e8 | − | 2.60433e7i | 0.978055 | − | 0.208346i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.84122e8 | + | 9.56463e7i | −1.45544 | + | 0.756061i | ||||
\(503\) | −1.34897e7 | −0.105998 | −0.0529991 | − | 0.998595i | \(-0.516878\pi\) | ||||
−0.0529991 | + | 0.998595i | \(0.516878\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.26177e7 | + | 5.76179e6i | 0.175620 | + | 0.0447387i | ||||
\(506\) | 7.50905e7 | − | 3.90075e7i | 0.579607 | − | 0.301090i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.43441e7 | − | 4.88691e7i | 0.261976 | − | 0.372772i | ||||
\(509\) | −1.73454e8 | −1.31531 | −0.657657 | − | 0.753317i | \(-0.728453\pi\) | ||||
−0.657657 | + | 0.753317i | \(0.728453\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 5.62519e7i | − | 0.421575i | ||||||
\(512\) | −1.23599e8 | − | 5.23226e7i | −0.920885 | − | 0.389834i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.14499e8 | + | 5.94793e7i | −0.843167 | + | 0.438002i | ||||
\(515\) | −1.40128e8 | − | 3.56973e7i | −1.02590 | − | 0.261345i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.31283e8i | − | 1.67368i | ||||||
\(518\) | 1.19412e7 | − | 6.20315e6i | 0.0859133 | − | 0.0446296i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.95912e7 | + | 1.97591e8i | −0.566050 | + | 1.40526i | ||||
\(521\) | 1.78879e8 | 1.26487 | 0.632437 | − | 0.774612i | \(-0.282055\pi\) | ||||
0.632437 | + | 0.774612i | \(0.282055\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.77417e8 | −1.24020 | −0.620098 | − | 0.784525i | \(-0.712907\pi\) | ||||
−0.620098 | + | 0.784525i | \(0.712907\pi\) | |||||||
\(524\) | 549999. | + | 386527.i | 0.00382268 | + | 0.00268649i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 338714. | + | 652034.i | 0.00232742 | + | 0.00448036i | ||||
\(527\) | 1.53873e8 | 1.05131 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.13121e8 | −0.764148 | ||||||||
\(530\) | 4.62610e7 | − | 1.08153e7i | 0.310733 | − | 0.0726456i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.19581e7 | + | 2.24594e7i | 0.212249 | + | 0.149164i | ||||
\(533\) | 3.91499e7i | 0.258552i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.88031e8 | − | 4.79003e7i | −1.22791 | − | 0.312808i | ||||
\(536\) | −2.07336e7 | − | 2.78415e6i | −0.134642 | − | 0.0180800i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.98569e7 | + | 3.82251e7i | 0.127516 | + | 0.245472i | ||||
\(539\) | 1.96482e8i | 1.25475i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.34835e8 | 0.851553 | 0.425777 | − | 0.904828i | \(-0.360001\pi\) | ||||
0.425777 | + | 0.904828i | \(0.360001\pi\) | |||||||
\(542\) | −6.33143e7 | + | 3.28901e7i | −0.397653 | + | 0.206570i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.22168e7 | − | 6.67489e7i | −0.448582 | − | 0.414617i | ||||
\(545\) | −2.14066e8 | − | 5.45327e7i | −1.32239 | − | 0.336874i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.22069e8 | 1.35683 | 0.678416 | − | 0.734678i | \(-0.262667\pi\) | ||||
0.678416 | + | 0.734678i | \(0.262667\pi\) | |||||||
\(548\) | 1.10195e8 | + | 7.74423e7i | 0.669605 | + | 0.470583i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.23714e8 | + | 4.42538e6i | 1.34464 | + | 0.0265988i | ||||
\(551\) | − | 9.64937e7i | − | 0.576825i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.48100e7i | 0.0875751i | ||||||||
\(554\) | −6.28422e7 | + | 3.26448e7i | −0.369591 | + | 0.191993i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.61873e8 | + | 1.13760e8i | 0.941779 | + | 0.661861i | ||||
\(557\) | − | 2.84443e8i | − | 1.64600i | −0.568042 | − | 0.823000i | \(-0.692299\pi\) | ||
0.568042 | − | 0.823000i | \(-0.307701\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.35850e8i | 1.92269i | ||||||||
\(560\) | 4.36632e6 | + | 4.52578e7i | 0.0248629 | + | 0.257709i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.67560e7 | − | 3.22557e7i | −0.0943974 | − | 0.181718i | ||||
\(563\) | −4.28842e7 | −0.240310 | −0.120155 | − | 0.992755i | \(-0.538339\pi\) | ||||
−0.120155 | + | 0.992755i | \(0.538339\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.18341e7 | + | 1.64218e8i | −0.231945 | + | 0.910492i | ||||
\(566\) | 7.30150e7 | + | 1.40556e8i | 0.402683 | + | 0.775176i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.51788e7 | − | 1.13036e8i | 0.0828307 | − | 0.616841i | ||||
\(569\) | 3.24019e8 | 1.75887 | 0.879435 | − | 0.476019i | \(-0.157921\pi\) | ||||
0.879435 | + | 0.476019i | \(0.157921\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.28824e8i | 1.76626i | 0.469126 | + | 0.883131i | \(0.344569\pi\) | ||||
−0.469126 | + | 0.883131i | \(0.655431\pi\) | |||||||
\(572\) | −2.19252e8 | + | 3.11979e8i | −1.17153 | + | 1.66700i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.85216e6 | + | 7.41552e6i | 0.0203690 | + | 0.0392108i | ||||
\(575\) | 8.10730e7 | + | 4.41728e7i | 0.426454 | + | 0.232355i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 9.48080e7i | − | 0.493534i | −0.969075 | − | 0.246767i | \(-0.920632\pi\) | ||
0.969075 | − | 0.246767i | \(-0.0793683\pi\) | |||||||
\(578\) | 5.58014e7 | + | 1.07419e8i | 0.288976 | + | 0.556287i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.52706e7 | − | 7.31099e7i | 0.437034 | − | 0.374707i | ||||
\(581\) | −2.91384e7 | −0.148572 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.50431e7 | 0.429174 | ||||||||
\(584\) | −4.31628e7 | + | 3.21434e8i | −0.216706 | + | 1.61381i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.44507e8 | + | 1.27015e8i | −1.21506 | + | 0.631193i | ||||
\(587\) | 5.12804e7 | 0.253534 | 0.126767 | − | 0.991932i | \(-0.459540\pi\) | ||||
0.126767 | + | 0.991932i | \(0.459540\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.52378e8 | 1.72450 | ||||||||
\(590\) | −1.36216e8 | + | 3.18457e7i | −0.663243 | + | 0.155058i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.29942e7 | + | 2.62833e7i | −0.351822 | + | 0.126682i | ||||
\(593\) | − | 2.12368e7i | − | 0.101842i | −0.998703 | − | 0.0509208i | \(-0.983784\pi\) | ||
0.998703 | − | 0.0509208i | \(-0.0162156\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.22393e6 | + | 3.22827e7i | −0.0390417 | + | 0.153257i | ||||
\(596\) | 5.69459e7 | − | 8.10297e7i | 0.268982 | − | 0.382741i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.39622e8 | + | 7.25298e7i | −0.652905 | + | 0.339166i | ||||
\(599\) | − | 2.38008e8i | − | 1.10742i | −0.832710 | − | 0.553709i | \(-0.813212\pi\) | ||
0.832710 | − | 0.553709i | \(-0.186788\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.59516e8 | −0.734822 | −0.367411 | − | 0.930059i | \(-0.619756\pi\) | ||||
−0.367411 | + | 0.930059i | \(0.619756\pi\) | |||||||
\(602\) | 3.30461e7 | + | 6.36147e7i | 0.151471 | + | 0.291587i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.11896e8 | + | 7.86384e7i | 0.507815 | + | 0.356881i | ||||
\(605\) | 1.73552e8 | + | 4.42120e7i | 0.783727 | + | 0.199652i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.87552e8 | −0.838602 | −0.419301 | − | 0.907847i | \(-0.637725\pi\) | ||||
−0.419301 | + | 0.907847i | \(0.637725\pi\) | |||||||
\(608\) | −1.65381e8 | − | 1.52859e8i | −0.735825 | − | 0.680112i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.82765e7 | − | 2.92045e8i | −0.300803 | − | 1.28665i | ||||
\(611\) | 4.30044e8i | 1.88534i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.96888e7i | 0.0854749i | 0.999086 | + | 0.0427374i | \(0.0136079\pi\) | ||||
−0.999086 | + | 0.0427374i | \(0.986392\pi\) | |||||||
\(614\) | −7.15942e7 | − | 1.37821e8i | −0.309295 | − | 0.595401i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.08320e7 | + | 8.06664e7i | −0.0463413 | + | 0.345104i | ||||
\(617\) | − | 2.99111e8i | − | 1.27344i | −0.771096 | − | 0.636719i | \(-0.780291\pi\) | ||
0.771096 | − | 0.636719i | \(-0.219709\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.73241e7i | 0.283856i | 0.989877 | + | 0.141928i | \(0.0453302\pi\) | ||||
−0.989877 | + | 0.141928i | \(0.954670\pi\) | |||||||
\(620\) | 2.66985e8 | + | 3.11393e8i | 1.12024 | + | 1.30658i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.87511e8 | + | 9.74068e7i | −0.779211 | + | 0.404779i | ||||
\(623\) | −2.46546e6 | −0.0101961 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.32368e8 | + | 2.05142e8i | 0.542181 | + | 0.840262i | ||||
\(626\) | 3.52497e7 | − | 1.83113e7i | 0.143692 | − | 0.0746441i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.42277e8 | + | 2.40544e8i | 1.38197 | + | 0.971217i | ||||
\(629\) | −5.68434e7 | −0.228417 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 3.74586e8i | − | 1.49095i | −0.666533 | − | 0.745476i | \(-0.732222\pi\) | ||
0.666533 | − | 0.745476i | \(-0.267778\pi\) | |||||||
\(632\) | 1.13639e7 | − | 8.46272e7i | 0.0450171 | − | 0.335242i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.30401e8 | − | 1.19687e8i | 0.904101 | − | 0.469656i | ||||
\(635\) | 1.13050e8 | + | 2.87992e7i | 0.441519 | + | 0.112476i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 3.65335e8i | − | 1.41343i | ||||||
\(638\) | 1.78425e8 | − | 9.26867e7i | 0.687057 | − | 0.356907i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.77690e6 | − | 2.61962e8i | 0.0372959 | − | 0.999304i | ||||
\(641\) | −3.70848e8 | −1.40806 | −0.704031 | − | 0.710169i | \(-0.748618\pi\) | ||||
−0.704031 | + | 0.710169i | \(0.748618\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.50751e8 | 1.69552 | 0.847761 | − | 0.530378i | \(-0.177950\pi\) | ||||
0.847761 | + | 0.530378i | \(0.177950\pi\) | |||||||
\(644\) | −1.93097e7 | + | 2.74763e7i | −0.0722967 | + | 0.102873i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.60643e7 | − | 1.46426e8i | −0.282152 | − | 0.543151i | ||||
\(647\) | −3.12382e8 | −1.15338 | −0.576691 | − | 0.816962i | \(-0.695656\pi\) | ||||
−0.576691 | + | 0.816962i | \(0.695656\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.50410e8 | −0.916048 | ||||||||
\(650\) | −4.15970e8 | − | 8.22846e6i | −1.51468 | − | 0.0299625i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.62629e8 | + | 3.73701e8i | −0.947544 | + | 1.34828i | ||||
\(653\) | 1.75008e8i | 0.628519i | 0.949337 | + | 0.314260i | \(0.101756\pi\) | ||||
−0.949337 | + | 0.314260i | \(0.898244\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −324121. | + | 1.27233e6i | −0.00115341 | + | 0.00452767i | ||||
\(656\) | −1.63219e7 | − | 4.53295e7i | −0.0578176 | − | 0.160572i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.23143e7 | + | 8.14562e7i | 0.148528 | + | 0.285921i | ||||
\(659\) | − | 5.04270e8i | − | 1.76200i | −0.473113 | − | 0.881002i | \(-0.656870\pi\) | ||
0.473113 | − | 0.881002i | \(-0.343130\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.10890e8 | −1.07647 | −0.538236 | − | 0.842794i | \(-0.680909\pi\) | ||||
−0.538236 | + | 0.842794i | \(0.680909\pi\) | |||||||
\(662\) | −3.19645e8 | + | 1.66047e8i | −1.10178 | + | 0.572344i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.66502e8 | + | 2.23583e7i | 0.568743 | + | 0.0763720i | ||||
\(665\) | −1.88333e7 | + | 7.39294e7i | −0.0640415 | + | 0.251392i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.29615e7 | 0.279575 | ||||||||
\(668\) | 1.67462e8 | − | 2.38286e8i | 0.561807 | − | 0.799409i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.30145e6 | − | 3.97859e7i | −0.0309262 | − | 0.132283i | ||||
\(671\) | − | 5.36875e8i | − | 1.77708i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4.42525e8i | − | 1.45175i | −0.687826 | − | 0.725876i | \(-0.741435\pi\) | ||
0.687826 | − | 0.725876i | \(-0.258565\pi\) | |||||||
\(674\) | 1.67990e7 | − | 8.72665e6i | 0.0548662 | − | 0.0285015i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.30050e8 | − | 3.27344e8i | 0.744702 | − | 1.05965i | ||||
\(677\) | − | 3.01059e8i | − | 0.970255i | −0.874443 | − | 0.485128i | \(-0.838773\pi\) | ||
0.874443 | − | 0.485128i | \(-0.161227\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.96036e7i | − | 0.0626218i | ||||||
\(680\) | 7.17640e7 | − | 1.78159e8i | 0.228234 | − | 0.566606i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.38476e8 | + | 6.51576e8i | 1.06703 | + | 2.05405i | ||||
\(683\) | 2.52236e8 | 0.791673 | 0.395836 | − | 0.918321i | \(-0.370455\pi\) | ||||
0.395836 | + | 0.918321i | \(0.370455\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.49391e7 | + | 2.54916e8i | −0.202039 | + | 0.793095i | ||||
\(686\) | −7.44773e7 | − | 1.43371e8i | −0.230702 | − | 0.444108i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.40019e8 | − | 3.88863e8i | −0.429954 | − | 1.19407i | ||||
\(689\) | −1.58128e8 | −0.483448 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.69200e7i | 0.202825i | 0.994844 | + | 0.101413i | \(0.0323362\pi\) | ||||
−0.994844 | + | 0.101413i | \(0.967664\pi\) | |||||||
\(692\) | 4.34579e8 | + | 3.05413e8i | 1.31145 | + | 0.921655i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.31825e8 | − | 2.53768e8i | −0.394385 | − | 0.759203i | ||||
\(695\) | −9.53936e7 | + | 3.74464e8i | −0.284161 | + | 1.11546i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.52998e7i | − | 0.104249i | ||||||
\(698\) | 1.09154e8 | + | 2.10125e8i | 0.320978 | + | 0.617892i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.96001e7 | + | 3.93709e7i | −0.232070 | + | 0.114784i | ||||
\(701\) | 4.07068e8 | 1.18171 | 0.590857 | − | 0.806776i | \(-0.298790\pi\) | ||||
0.590857 | + | 0.806776i | \(0.298790\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.30175e8 | −0.374680 | ||||||||
\(704\) | 1.23793e8 | − | 4.52631e8i | 0.354795 | − | 1.29726i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.39849e8 | + | 2.28489e8i | −1.24994 | + | 0.649310i | ||||
\(707\) | −1.65816e7 | −0.0469211 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.14836e7 | 0.0602793 | 0.0301396 | − | 0.999546i | \(-0.490405\pi\) | ||||
0.0301396 | + | 0.999546i | \(0.490405\pi\) | |||||||
\(710\) | 2.16907e8 | − | 5.07102e7i | 0.606036 | − | 0.141684i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.40881e7 | + | 1.89178e6i | 0.0390313 | + | 0.00524120i | ||||
\(713\) | 3.02961e8i | 0.835830i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.21708e8 | − | 1.83853e8i | −1.97444 | − | 0.502982i | ||||
\(716\) | −1.58982e8 | − | 1.11729e8i | −0.433122 | − | 0.304388i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.89836e8 | − | 1.50562e8i | 0.783031 | − | 0.406764i | ||||
\(719\) | 4.75458e8i | 1.27916i | 0.768724 | + | 0.639581i | \(0.220892\pi\) | ||||
−0.768724 | + | 0.639581i | \(0.779108\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.02732e8 | 0.274094 | ||||||||
\(722\) | −692456. | − | 1.33300e6i | −0.00183984 | − | 0.00354175i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.37329e7 | − | 3.37702e7i | 0.0625368 | − | 0.0889851i | ||||
\(725\) | 1.92640e8 | + | 1.04960e8i | 0.505512 | + | 0.275430i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.11316e8 | 1.59097 | 0.795486 | − | 0.605972i | \(-0.207216\pi\) | ||||
0.795486 | + | 0.605972i | \(0.207216\pi\) | |||||||
\(728\) | 2.01409e7 | − | 1.49990e8i | 0.0522018 | − | 0.388747i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.16804e8 | + | 1.44201e8i | −1.58554 | + | 0.370681i | ||||
\(731\) | − | 3.02822e8i | − | 0.775239i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.86490e8i | 1.48919i | 0.667519 | + | 0.744593i | \(0.267356\pi\) | ||||
−0.667519 | + | 0.744593i | \(0.732644\pi\) | |||||||
\(734\) | 5.57050e7 | + | 1.07234e8i | 0.140866 | + | 0.271171i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.31422e8 | − | 1.42188e8i | 0.329637 | − | 0.356639i | ||||
\(737\) | − | 7.31397e7i | − | 0.182705i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 5.79830e8i | − | 1.43671i | −0.695679 | − | 0.718353i | \(-0.744896\pi\) | ||
0.695679 | − | 0.718353i | \(-0.255104\pi\) | |||||||
\(740\) | −9.86289e7 | − | 1.15034e8i | −0.243394 | − | 0.283878i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.99516e7 | + | 1.55590e7i | −0.0733175 | + | 0.0380864i | ||||
\(743\) | 3.73947e8 | 0.911681 | 0.455841 | − | 0.890061i | \(-0.349339\pi\) | ||||
0.455841 | + | 0.890061i | \(0.349339\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.87448e8 | + | 4.77518e7i | 0.453327 | + | 0.115484i | ||||
\(746\) | −3.78031e8 | + | 1.96377e8i | −0.910565 | + | 0.473014i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.97690e8 | − | 2.81298e8i | 0.472367 | − | 0.672143i | ||||
\(749\) | 1.37850e8 | 0.328067 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.27510e8i | − | 0.301041i | −0.988607 | − | 0.150521i | \(-0.951905\pi\) | ||
0.988607 | − | 0.150521i | \(-0.0480950\pi\) | |||||||
\(752\) | −1.79289e8 | − | 4.97924e8i | −0.421600 | − | 1.17087i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.31760e8 | + | 1.72340e8i | −0.773944 | + | 0.402043i | ||||
\(755\) | −6.59421e7 | + | 2.58853e8i | −0.153222 | + | 0.601468i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.33748e7i | − | 0.0538841i | −0.999637 | − | 0.0269420i | \(-0.991423\pi\) | ||
0.999637 | − | 0.0269420i | \(-0.00857696\pi\) | |||||||
\(758\) | 2.33580e6 | − | 1.21339e6i | 0.00536326 | − | 0.00278607i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.64344e8 | − | 4.07995e8i | 0.374380 | − | 0.929425i | ||||
\(761\) | −7.53332e8 | −1.70936 | −0.854678 | − | 0.519159i | \(-0.826245\pi\) | ||||
−0.854678 | + | 0.519159i | \(0.826245\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.56937e8 | 0.353307 | ||||||||
\(764\) | 2.42355e8 | + | 1.70322e8i | 0.543467 | + | 0.381936i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.96875e8 | − | 5.71492e8i | −0.660521 | − | 1.27152i | ||||
\(767\) | 4.65609e8 | 1.03189 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.33859e8 | −1.39384 | −0.696921 | − | 0.717148i | \(-0.745447\pi\) | ||||
−0.696921 | + | 0.717148i | \(0.745447\pi\) | |||||||
\(770\) | −1.54792e8 | + | 3.61884e7i | −0.339059 | + | 0.0792678i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.69028e8 | − | 1.89067e8i | −0.584717 | − | 0.410926i | ||||
\(773\) | 1.08448e8i | 0.234793i | 0.993085 | + | 0.117396i | \(0.0374548\pi\) | ||||
−0.993085 | + | 0.117396i | \(0.962545\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.83297e8 | + | 7.03487e8i | −0.823437 | + | 1.51130i | ||||
\(776\) | −1.50421e7 | + | 1.12018e8i | −0.0321901 | + | 0.239720i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.80551e8 | − | 3.47565e8i | −0.383407 | − | 0.738069i | ||||
\(779\) | − | 8.08387e7i | − | 0.171004i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.98747e8 | 0.837036 | ||||||||
\(782\) | 1.25891e8 | − | 6.53971e7i | 0.263254 | − | 0.136753i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.52312e8 | + | 4.23002e8i | 0.316072 | + | 0.877797i | ||||
\(785\) | −2.01708e8 | + | 7.91797e8i | −0.416979 | + | 1.63684i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.53415e8 | −0.725039 | −0.362519 | − | 0.931976i | \(-0.618083\pi\) | ||||
−0.362519 | + | 0.931976i | \(0.618083\pi\) | |||||||
\(788\) | 2.89173e8 | + | 2.03225e8i | 0.590989 | + | 0.415334i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.62392e8 | − | 3.79653e7i | 0.329370 | − | 0.0770026i | ||||
\(791\) | − | 1.20393e8i | − | 0.243260i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.98257e8i | 2.00181i | ||||||||
\(794\) | 4.41160e8 | − | 2.29171e8i | 0.881322 | − | 0.457823i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.24665e8 | + | 1.57890e8i | 0.445448 | + | 0.313051i | ||||
\(797\) | 5.64122e8i | 1.11429i | 0.830415 | + | 0.557145i | \(0.188103\pi\) | ||||
−0.830415 | + | 0.557145i | \(0.811897\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.87753e8i | − | 0.760176i | ||||||
\(800\) | 4.85059e8 | − | 1.63894e8i | 0.947382 | − | 0.320106i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.40989e6 | − | 2.71407e6i | −0.00273313 | − | 0.00526136i | ||||
\(803\) | −1.13389e9 | −2.18990 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.35616e7 | − | 1.61921e7i | −0.121845 | − | 0.0310396i | ||||
\(806\) | −6.29356e8 | − | 1.21153e9i | −1.20196 | − | 2.31381i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.47504e7 | + | 1.27233e7i | 0.179617 | + | 0.0241193i | ||||
\(809\) | 2.93587e8 | 0.554487 | 0.277243 | − | 0.960800i | \(-0.410579\pi\) | ||||
0.277243 | + | 0.960800i | \(0.410579\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.58312e8i | − | 1.42163i | −0.703381 | − | 0.710813i | \(-0.748327\pi\) | ||
0.703381 | − | 0.710813i | \(-0.251673\pi\) | |||||||
\(812\) | −4.58824e7 | + | 6.52871e7i | −0.0856994 | + | 0.121944i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.25039e8 | − | 2.40704e8i | −0.231831 | − | 0.446282i | ||||
\(815\) | −8.64492e8 | − | 2.20227e8i | −1.59694 | − | 0.406815i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.93481e8i | − | 1.27165i | ||||||
\(818\) | −4.08791e8 | − | 7.86934e8i | −0.746863 | − | 1.43773i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.14364e7 | − | 6.12486e7i | 0.129562 | − | 0.111085i | ||||
\(821\) | 2.11510e7 | 0.0382209 | 0.0191104 | − | 0.999817i | \(-0.493917\pi\) | ||||
0.0191104 | + | 0.999817i | \(0.493917\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.99192e8 | −1.79246 | −0.896230 | − | 0.443590i | \(-0.853705\pi\) | ||||
−0.896230 | + | 0.443590i | \(0.853705\pi\) | |||||||
\(824\) | −5.87028e8 | − | 7.88274e7i | −1.04925 | − | 0.140895i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.81927e7 | − | 4.58137e7i | 0.156492 | − | 0.0812934i | ||||
\(827\) | −5.08817e8 | −0.899591 | −0.449796 | − | 0.893131i | \(-0.648503\pi\) | ||||
−0.449796 | + | 0.893131i | \(0.648503\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.05552e8 | 1.58946 | 0.794730 | − | 0.606963i | \(-0.207612\pi\) | ||||
0.794730 | + | 0.606963i | \(0.207612\pi\) | |||||||
\(830\) | 7.46959e7 | + | 3.19503e8i | 0.130636 | + | 0.558780i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.30178e8 | + | 8.41614e8i | −0.399663 | + | 1.46131i | ||||
\(833\) | 3.29408e8i | 0.569900i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.51233e8 | + | 1.40425e8i | 0.946838 | + | 0.241204i | ||||
\(836\) | 4.52722e8 | − | 6.44189e8i | 0.774841 | − | 1.10254i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.60618e8 | − | 4.47068e8i | 1.46244 | − | 0.759698i | ||||
\(839\) | 8.22611e8i | 1.39286i | 0.717623 | + | 0.696432i | \(0.245230\pi\) | ||||
−0.717623 | + | 0.696432i | \(0.754770\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.97696e8 | −0.668596 | ||||||||
\(842\) | −3.04824e6 | − | 5.86795e6i | −0.00510638 | − | 0.00982992i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.58826e8 | − | 3.92730e8i | −0.929500 | − | 0.653232i | ||||
\(845\) | 7.57253e8 | + | 1.92908e8i | 1.25508 | + | 0.319728i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.27236e8 | −0.209391 | ||||||||
\(848\) | 1.83087e8 | − | 6.59249e7i | 0.300242 | − | 0.108109i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.75063e8 | + | 7.41926e6i | 0.610727 | + | 0.0120810i | ||||
\(851\) | − | 1.11919e8i | − | 0.181600i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.56058e8i | − | 0.251443i | −0.992066 | − | 0.125722i | \(-0.959875\pi\) | ||
0.992066 | − | 0.125722i | \(-0.0401246\pi\) | |||||||
\(854\) | 9.82238e7 | + | 1.89084e8i | 0.157704 | + | 0.303585i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.87703e8 | − | 1.05774e8i | −1.25586 | − | 0.168639i | ||||
\(857\) | 3.39476e8i | 0.539345i | 0.962952 | + | 0.269672i | \(0.0869154\pi\) | ||||
−0.962952 | + | 0.269672i | \(0.913085\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.27544e8i | 0.990068i | 0.868874 | + | 0.495034i | \(0.164844\pi\) | ||||
−0.868874 | + | 0.495034i | \(0.835156\pi\) | |||||||
\(860\) | 6.12823e8 | − | 5.25427e8i | 0.963474 | − | 0.826070i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.97999e8 | + | 4.66486e8i | −1.40202 | + | 0.728311i | ||||
\(863\) | 5.09291e8 | 0.792381 | 0.396190 | − | 0.918168i | \(-0.370332\pi\) | ||||
0.396190 | + | 0.918168i | \(0.370332\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.56103e8 | + | 1.00532e9i | −0.395700 | + | 1.55331i | ||||
\(866\) | −7.46573e8 | + | 3.87824e8i | −1.14953 | + | 0.597147i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.38417e8 | − | 1.67554e8i | −0.364568 | − | 0.256210i | ||||
\(869\) | 2.98531e8 | 0.454914 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.35995e8i | 0.205810i | ||||||||
\(872\) | −8.96769e8 | − | 1.20420e8i | −1.35248 | − | 0.181614i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.88299e8 | − | 1.49763e8i | 0.431825 | − | 0.224322i | ||||
\(875\) | −1.27107e8 | − | 1.18015e8i | −0.189733 | − | 0.176162i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 6.30685e8i | − | 0.935004i | −0.883992 | − | 0.467502i | \(-0.845154\pi\) | ||
0.883992 | − | 0.467502i | \(-0.154846\pi\) | |||||||
\(878\) | 1.89872e8 | − | 9.86334e7i | 0.280529 | − | 0.145727i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.12276e8 | − | 8.80134e7i | 1.33868 | − | 0.129152i | ||||
\(881\) | −2.54533e8 | −0.372235 | −0.186117 | − | 0.982528i | \(-0.559590\pi\) | ||||
−0.186117 | + | 0.982528i | \(0.559590\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.28879e7 | −0.0477698 | −0.0238849 | − | 0.999715i | \(-0.507604\pi\) | ||||
−0.0238849 | + | 0.999715i | \(0.507604\pi\) | |||||||
\(884\) | −3.67581e8 | + | 5.23040e8i | −0.532104 | + | 0.757144i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.09590e8 | + | 5.95969e8i | 0.445128 | + | 0.856885i | ||||
\(887\) | −2.38053e8 | −0.341116 | −0.170558 | − | 0.985348i | \(-0.554557\pi\) | ||||
−0.170558 | + | 0.985348i | \(0.554557\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.28799e7 | −0.117962 | ||||||||
\(890\) | 6.32018e6 | + | 2.70338e7i | 0.00896519 | + | 0.0383476i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.39544e8 | − | 3.40853e8i | 0.337513 | − | 0.480256i | ||||
\(893\) | − | 8.87977e8i | − | 1.24695i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.36904e7 | − | 3.67778e8i | 0.130685 | − | 0.512999i | ||||
\(896\) | 3.92120e7 | + | 1.82062e8i | 0.0545123 | + | 0.253101i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.42144e8 | + | 2.73632e8i | 0.196291 | + | 0.377866i | ||||
\(899\) | 7.19874e8i | 0.990780i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.42577e8 | 0.194928 | ||||||||
\(902\) | 1.49477e8 | − | 7.76493e7i | 0.203683 | − | 0.105808i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.23789e7 | + | 6.87946e8i | −0.125045 | + | 0.931213i | ||||
\(905\) | 7.81214e7 | + | 1.99012e7i | 0.105396 | + | 0.0268493i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.69796e8 | 1.16572 | 0.582861 | − | 0.812572i | \(-0.301933\pi\) | ||||
0.582861 | + | 0.812572i | \(0.301933\pi\) | |||||||
\(908\) | −3.04818e8 | + | 4.33733e8i | −0.407177 | + | 0.579382i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.87817e8 | − | 6.72880e7i | 0.381937 | − | 0.0892922i | ||||
\(911\) | − | 3.98390e8i | − | 0.526931i | −0.964669 | − | 0.263466i | \(-0.915134\pi\) | ||
0.964669 | − | 0.263466i | \(-0.0848655\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.87353e8i | 0.771768i | ||||||||
\(914\) | 7.19563e8 | − | 3.73793e8i | 0.942388 | − | 0.489545i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.20476e8 | + | 3.13721e8i | −0.286863 | + | 0.408185i | ||||
\(917\) | − | 932775.i | − | 0.00120968i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.03935e9i | 1.33911i | 0.742762 | + | 0.669555i | \(0.233515\pi\) | ||||
−0.742762 | + | 0.669555i | \(0.766485\pi\) | |||||||
\(920\) | 3.50778e8 | + | 1.41296e8i | 0.450473 | + | 0.181455i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.50028e8 | − | 6.73814e8i | −0.446591 | − | 0.859700i | ||||
\(923\) | −7.41423e8 | −0.942889 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.41597e8 | − | 2.59881e8i | 0.178907 | − | 0.328359i | ||||
\(926\) | 4.35545e8 | + | 8.38437e8i | 0.548530 | + | 1.05594i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.12276e8 | − | 3.37857e8i | 0.390746 | − | 0.422755i | ||||
\(929\) | −9.01112e8 | −1.12391 | −0.561955 | − | 0.827168i | \(-0.689951\pi\) | ||||
−0.561955 | + | 0.827168i | \(0.689951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.54364e8i | 0.934828i | ||||||||
\(932\) | −8.77268e7 | − | 6.16525e7i | −0.108364 | − | 0.0761557i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.86346e8 | + | 1.32123e9i | 0.842369 | + | 1.62158i | ||||
\(935\) | 6.50734e8 | + | 1.65773e8i | 0.796102 | + | 0.202805i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.08145e7i | − | 0.0982360i | −0.998793 | − | 0.0491180i | \(-0.984359\pi\) | ||
0.998793 | − | 0.0491180i | \(-0.0156410\pi\) | |||||||
\(938\) | 1.33812e7 | + | 2.57592e7i | 0.0162139 | + | 0.0312122i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.84697e8 | − | 6.72789e8i | 0.944754 | − | 0.810019i | ||||
\(941\) | 5.21062e8 | 0.625346 | 0.312673 | − | 0.949861i | \(-0.398776\pi\) | ||||
0.312673 | + | 0.949861i | \(0.398776\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.95019e7 | 0.0828823 | ||||||||
\(944\) | −5.39103e8 | + | 1.94117e8i | −0.640849 | + | 0.230753i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.28230e9 | − | 6.66121e8i | 1.51467 | − | 0.786828i | ||||
\(947\) | 1.67327e9 | 1.97023 | 0.985114 | − | 0.171902i | \(-0.0549911\pi\) | ||||
0.985114 | + | 0.171902i | \(0.0549911\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.10833e9 | 2.46684 | ||||||||
\(950\) | 8.58916e8 | + | 1.69906e7i | 1.00180 | + | 0.0198170i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.81602e7 | + | 1.35239e8i | −0.0210480 | + | 0.156744i | ||||
\(953\) | 5.89780e8i | 0.681414i | 0.940170 | + | 0.340707i | \(0.110666\pi\) | ||||
−0.940170 | + | 0.340707i | \(0.889334\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.42823e8 | + | 5.60647e8i | −0.163979 | + | 0.643694i | ||||
\(956\) | −2.11541e8 | − | 1.48666e8i | −0.242115 | − | 0.170153i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.56347e8 | + | 1.85112e8i | −0.405300 | + | 0.210542i | ||||
\(959\) | − | 1.86885e8i | − | 0.211895i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.74135e9 | −1.96208 | ||||||||
\(962\) | 2.32495e8 | + | 4.47560e8i | 0.261149 | + | 0.502720i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.42980e8 | + | 4.88035e8i | −0.382858 | + | 0.544778i | ||||
\(965\) | 1.58542e8 | − | 6.22350e8i | 0.176426 | − | 0.692552i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.41406e8 | 1.04111 | 0.520556 | − | 0.853828i | \(-0.325725\pi\) | ||||
0.520556 | + | 0.853828i | \(0.325725\pi\) | |||||||
\(968\) | 7.27049e8 | + | 9.76297e7i | 0.801563 | + | 0.107636i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.14954e8 | + | 5.02535e7i | −0.235521 | + | 0.0550619i | ||||
\(971\) | − | 1.61734e9i | − | 1.76662i | −0.468787 | − | 0.883311i | \(-0.655309\pi\) | ||
0.468787 | − | 0.883311i | \(-0.344691\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2.74529e8i | − | 0.298023i | ||||||
\(974\) | 4.01597e8 | + | 7.73085e8i | 0.434623 | + | 0.836662i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.16183e8 | − | 1.15583e9i | −0.447646 | − | 1.24321i | ||||
\(977\) | − | 6.67855e8i | − | 0.716141i | −0.933695 | − | 0.358070i | \(-0.883435\pi\) | ||
0.933695 | − | 0.358070i | \(-0.116565\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.96972e7i | 0.0529643i | ||||||||
\(980\) | −6.66624e8 | + | 5.71555e8i | −0.708277 | + | 0.607267i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.21474e8 | − | 6.31026e7i | 0.128277 | − | 0.0666366i | ||||
\(983\) | 8.58744e7 | 0.0904073 | 0.0452036 | − | 0.998978i | \(-0.485606\pi\) | ||||
0.0452036 | + | 0.998978i | \(0.485606\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.70414e8 | + | 6.68952e8i | −0.178318 | + | 0.699981i | ||||
\(986\) | 2.99134e8 | − | 1.55392e8i | 0.312057 | − | 0.162105i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.41783e8 | + | 1.19779e9i | −0.872830 | + | 1.24197i | ||||
\(989\) | 5.96228e8 | 0.616344 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.76605e8i | 0.695208i | 0.937642 | + | 0.347604i | \(0.113005\pi\) | ||||
−0.937642 | + | 0.347604i | \(0.886995\pi\) | |||||||
\(992\) | 1.23379e9 | + | 1.14038e9i | 1.26389 | + | 1.16819i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.40436e8 | + | 7.29525e7i | −0.142994 | + | 0.0742816i | ||||
\(995\) | −1.32398e8 | + | 5.19724e8i | −0.134404 | + | 0.527598i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.53009e9i | − | 1.54394i | −0.635659 | − | 0.771970i | \(-0.719272\pi\) | ||
0.635659 | − | 0.771970i | \(-0.280728\pi\) | |||||||
\(998\) | 1.48014e8 | − | 7.68895e7i | 0.148906 | − | 0.0773526i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 180.7.f.e.19.8 | 12 | ||
3.2 | odd | 2 | 20.7.d.d.19.5 | ✓ | 12 | ||
4.3 | odd | 2 | inner | 180.7.f.e.19.6 | 12 | ||
5.4 | even | 2 | inner | 180.7.f.e.19.5 | 12 | ||
12.11 | even | 2 | 20.7.d.d.19.7 | yes | 12 | ||
15.2 | even | 4 | 100.7.b.f.51.11 | 12 | |||
15.8 | even | 4 | 100.7.b.f.51.2 | 12 | |||
15.14 | odd | 2 | 20.7.d.d.19.8 | yes | 12 | ||
20.19 | odd | 2 | inner | 180.7.f.e.19.7 | 12 | ||
24.5 | odd | 2 | 320.7.h.f.319.9 | 12 | |||
24.11 | even | 2 | 320.7.h.f.319.3 | 12 | |||
60.23 | odd | 4 | 100.7.b.f.51.1 | 12 | |||
60.47 | odd | 4 | 100.7.b.f.51.12 | 12 | |||
60.59 | even | 2 | 20.7.d.d.19.6 | yes | 12 | ||
120.29 | odd | 2 | 320.7.h.f.319.4 | 12 | |||
120.59 | even | 2 | 320.7.h.f.319.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.7.d.d.19.5 | ✓ | 12 | 3.2 | odd | 2 | ||
20.7.d.d.19.6 | yes | 12 | 60.59 | even | 2 | ||
20.7.d.d.19.7 | yes | 12 | 12.11 | even | 2 | ||
20.7.d.d.19.8 | yes | 12 | 15.14 | odd | 2 | ||
100.7.b.f.51.1 | 12 | 60.23 | odd | 4 | |||
100.7.b.f.51.2 | 12 | 15.8 | even | 4 | |||
100.7.b.f.51.11 | 12 | 15.2 | even | 4 | |||
100.7.b.f.51.12 | 12 | 60.47 | odd | 4 | |||
180.7.f.e.19.5 | 12 | 5.4 | even | 2 | inner | ||
180.7.f.e.19.6 | 12 | 4.3 | odd | 2 | inner | ||
180.7.f.e.19.7 | 12 | 20.19 | odd | 2 | inner | ||
180.7.f.e.19.8 | 12 | 1.1 | even | 1 | trivial | ||
320.7.h.f.319.3 | 12 | 24.11 | even | 2 | |||
320.7.h.f.319.4 | 12 | 120.29 | odd | 2 | |||
320.7.h.f.319.9 | 12 | 24.5 | odd | 2 | |||
320.7.h.f.319.10 | 12 | 120.59 | even | 2 |