Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,23,Mod(5,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 23, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.5");
S:= CuspForms(chi, 23);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 23 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.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: | \(18.4024460905\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4 x^{7} - 12878974 x^{6} - 2567056924 x^{5} + 47744458496177 x^{4} + \cdots + 98\!\cdots\!84 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{53}\cdot 3^{29} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.5 | ||
Root | \(-865.062 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.5 |
Dual form | 6.23.b.a.5.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1448.15i | 0.707107i | ||||||||
\(3\) | −128493. | − | 121945.i | −0.725349 | − | 0.688382i | ||||
\(4\) | −2.09715e6 | −0.500000 | ||||||||
\(5\) | 8.15211e7i | 1.66955i | 0.550589 | + | 0.834777i | \(0.314403\pi\) | ||||
−0.550589 | + | 0.834777i | \(0.685597\pi\) | |||||||
\(6\) | 1.76595e8 | − | 1.86078e8i | 0.486759 | − | 0.512899i | ||||
\(7\) | 2.43000e9 | 1.22893 | 0.614465 | − | 0.788944i | \(-0.289372\pi\) | ||||
0.614465 | + | 0.788944i | \(0.289372\pi\) | |||||||
\(8\) | − | 3.03700e9i | − | 0.353553i | ||||||
\(9\) | 1.64002e9 | + | 3.13382e10i | 0.0522615 | + | 0.998633i | ||||
\(10\) | −1.18055e11 | −1.18055 | ||||||||
\(11\) | − | 6.25607e9i | − | 0.0219271i | −0.999940 | − | 0.0109636i | \(-0.996510\pi\) | ||
0.999940 | − | 0.0109636i | \(-0.00348988\pi\) | |||||||
\(12\) | 2.69470e11 | + | 2.55737e11i | 0.362674 | + | 0.344191i | ||||
\(13\) | −3.34030e12 | −1.86384 | −0.931919 | − | 0.362667i | \(-0.881866\pi\) | ||||
−0.931919 | + | 0.362667i | \(0.881866\pi\) | |||||||
\(14\) | 3.51901e12i | 0.868985i | ||||||||
\(15\) | 9.94107e12 | − | 1.04749e13i | 1.14929 | − | 1.21101i | ||||
\(16\) | 4.39805e12 | 0.250000 | ||||||||
\(17\) | − | 2.70899e13i | − | 0.790442i | −0.918586 | − | 0.395221i | \(-0.870668\pi\) | ||
0.918586 | − | 0.395221i | \(-0.129332\pi\) | |||||||
\(18\) | −4.53825e13 | + | 2.37500e12i | −0.706140 | + | 0.0369544i | ||||
\(19\) | −9.29168e13 | −0.797636 | −0.398818 | − | 0.917030i | \(-0.630579\pi\) | ||||
−0.398818 | + | 0.917030i | \(0.630579\pi\) | |||||||
\(20\) | − | 1.70962e14i | − | 0.834777i | ||||||
\(21\) | −3.12239e14 | − | 2.96325e14i | −0.891403 | − | 0.845973i | ||||
\(22\) | 9.05975e12 | 0.0155048 | ||||||||
\(23\) | − | 1.49571e14i | − | 0.156979i | −0.996915 | − | 0.0784896i | \(-0.974990\pi\) | ||
0.996915 | − | 0.0784896i | \(-0.0250098\pi\) | |||||||
\(24\) | −3.70346e14 | + | 3.90234e14i | −0.243380 | + | 0.256449i | ||||
\(25\) | −4.26151e15 | −1.78741 | ||||||||
\(26\) | − | 4.83727e15i | − | 1.31793i | ||||||
\(27\) | 3.61079e15 | − | 4.22674e15i | 0.649533 | − | 0.760333i | ||||
\(28\) | −5.09607e15 | −0.614465 | ||||||||
\(29\) | 2.50044e14i | 0.0204946i | 0.999947 | + | 0.0102473i | \(0.00326187\pi\) | ||||
−0.999947 | + | 0.0102473i | \(0.996738\pi\) | |||||||
\(30\) | 1.51693e16 | + | 1.43962e16i | 0.856312 | + | 0.812671i | ||||
\(31\) | 8.84301e15 | 0.348034 | 0.174017 | − | 0.984743i | \(-0.444325\pi\) | ||||
0.174017 | + | 0.984743i | \(0.444325\pi\) | |||||||
\(32\) | 6.36905e15i | 0.176777i | ||||||||
\(33\) | −7.62894e14 | + | 8.03863e14i | −0.0150942 | + | 0.0159048i | ||||
\(34\) | 3.92304e16 | 0.558927 | ||||||||
\(35\) | 1.98096e17i | 2.05177i | ||||||||
\(36\) | −3.43937e15 | − | 6.57209e16i | −0.0261307 | − | 0.499317i | ||||
\(37\) | −1.23534e17 | −0.694334 | −0.347167 | − | 0.937803i | \(-0.612856\pi\) | ||||
−0.347167 | + | 0.937803i | \(0.612856\pi\) | |||||||
\(38\) | − | 1.34558e17i | − | 0.564014i | ||||||
\(39\) | 4.29206e17 | + | 4.07332e17i | 1.35193 | + | 1.28303i | ||||
\(40\) | 2.47580e17 | 0.590276 | ||||||||
\(41\) | − | 7.10953e17i | − | 1.29187i | −0.763393 | − | 0.645935i | \(-0.776468\pi\) | ||
0.763393 | − | 0.645935i | \(-0.223532\pi\) | |||||||
\(42\) | 4.29125e17 | − | 4.52170e17i | 0.598194 | − | 0.630317i | ||||
\(43\) | −1.56221e18 | −1.68108 | −0.840539 | − | 0.541751i | \(-0.817761\pi\) | ||||
−0.840539 | + | 0.541751i | \(0.817761\pi\) | |||||||
\(44\) | 1.31199e16i | 0.0109636i | ||||||||
\(45\) | −2.55472e18 | + | 1.33696e17i | −1.66727 | + | 0.0872533i | ||||
\(46\) | 2.16603e17 | 0.111001 | ||||||||
\(47\) | − | 9.63200e15i | − | 0.00389619i | −0.999998 | − | 0.00194809i | \(-0.999380\pi\) | ||
0.999998 | − | 0.00194809i | \(-0.000620098\pi\) | |||||||
\(48\) | −5.65120e17 | − | 5.36319e17i | −0.181337 | − | 0.172095i | ||||
\(49\) | 1.99507e18 | 0.510271 | ||||||||
\(50\) | − | 6.17133e18i | − | 1.26389i | ||||||
\(51\) | −3.30347e18 | + | 3.48088e18i | −0.544125 | + | 0.573346i | ||||
\(52\) | 7.00511e18 | 0.931919 | ||||||||
\(53\) | 6.22288e18i | 0.671363i | 0.941976 | + | 0.335681i | \(0.108967\pi\) | ||||
−0.941976 | + | 0.335681i | \(0.891033\pi\) | |||||||
\(54\) | 6.12097e18 | + | 5.22899e18i | 0.537637 | + | 0.459289i | ||||
\(55\) | 5.10002e17 | 0.0366085 | ||||||||
\(56\) | − | 7.37990e18i | − | 0.434493i | ||||||
\(57\) | 1.19392e19 | + | 1.13307e19i | 0.578564 | + | 0.549078i | ||||
\(58\) | −3.62103e17 | −0.0144919 | ||||||||
\(59\) | 1.73109e18i | 0.0574048i | 0.999588 | + | 0.0287024i | \(0.00913751\pi\) | ||||
−0.999588 | + | 0.0287024i | \(0.990862\pi\) | |||||||
\(60\) | −2.08479e19 | + | 2.19675e19i | −0.574645 | + | 0.605504i | ||||
\(61\) | 1.43862e19 | 0.330611 | 0.165305 | − | 0.986242i | \(-0.447139\pi\) | ||||
0.165305 | + | 0.986242i | \(0.447139\pi\) | |||||||
\(62\) | 1.28061e19i | 0.246097i | ||||||||
\(63\) | 3.98524e18 | + | 7.61517e19i | 0.0642257 | + | 1.22725i | ||||
\(64\) | −9.22337e18 | −0.125000 | ||||||||
\(65\) | − | 2.72305e20i | − | 3.11178i | ||||||
\(66\) | −1.16412e18 | − | 1.10479e18i | −0.0112464 | − | 0.0106732i | ||||
\(67\) | −4.19715e19 | −0.343662 | −0.171831 | − | 0.985126i | \(-0.554968\pi\) | ||||
−0.171831 | + | 0.985126i | \(0.554968\pi\) | |||||||
\(68\) | 5.68117e19i | 0.395221i | ||||||||
\(69\) | −1.82394e19 | + | 1.92189e19i | −0.108062 | + | 0.113865i | ||||
\(70\) | −2.86874e20 | −1.45082 | ||||||||
\(71\) | − | 2.15220e20i | − | 0.931194i | −0.884997 | − | 0.465597i | \(-0.845840\pi\) | ||
0.884997 | − | 0.465597i | \(-0.154160\pi\) | |||||||
\(72\) | 9.51741e19 | − | 4.98074e18i | 0.353070 | − | 0.0184772i | ||||
\(73\) | −9.65337e18 | −0.0307700 | −0.0153850 | − | 0.999882i | \(-0.504897\pi\) | ||||
−0.0153850 | + | 0.999882i | \(0.504897\pi\) | |||||||
\(74\) | − | 1.78897e20i | − | 0.490968i | ||||||
\(75\) | 5.47576e20 | + | 5.19669e20i | 1.29649 | + | 1.23042i | ||||
\(76\) | 1.94861e20 | 0.398818 | ||||||||
\(77\) | − | 1.52022e19i | − | 0.0269469i | ||||||
\(78\) | −5.89879e20 | + | 6.21556e20i | −0.907240 | + | 0.955961i | ||||
\(79\) | 1.87187e20 | 0.250253 | 0.125126 | − | 0.992141i | \(-0.460066\pi\) | ||||
0.125126 | + | 0.992141i | \(0.460066\pi\) | |||||||
\(80\) | 3.58534e20i | 0.417388i | ||||||||
\(81\) | −9.79392e20 | + | 1.02790e20i | −0.994537 | + | 0.104380i | ||||
\(82\) | 1.02957e21 | 0.913490 | ||||||||
\(83\) | − | 6.23141e20i | − | 0.483868i | −0.970293 | − | 0.241934i | \(-0.922218\pi\) | ||
0.970293 | − | 0.241934i | \(-0.0777818\pi\) | |||||||
\(84\) | 6.54812e20 | + | 6.21440e20i | 0.445702 | + | 0.422987i | ||||
\(85\) | 2.20840e21 | 1.31968 | ||||||||
\(86\) | − | 2.26233e21i | − | 1.18870i | ||||||
\(87\) | 3.04916e19 | − | 3.21290e19i | 0.0141081 | − | 0.0148657i | ||||
\(88\) | −1.89997e19 | −0.00775241 | ||||||||
\(89\) | 5.00057e21i | 1.80189i | 0.433929 | + | 0.900947i | \(0.357127\pi\) | ||||
−0.433929 | + | 0.900947i | \(0.642873\pi\) | |||||||
\(90\) | −1.93613e20 | − | 3.69964e21i | −0.0616974 | − | 1.17894i | ||||
\(91\) | −8.11691e21 | −2.29053 | ||||||||
\(92\) | 3.13674e20i | 0.0784896i | ||||||||
\(93\) | −1.13627e21 | − | 1.07836e21i | −0.252446 | − | 0.239580i | ||||
\(94\) | 1.39486e19 | 0.00275502 | ||||||||
\(95\) | − | 7.57469e21i | − | 1.33170i | ||||||
\(96\) | 7.76672e20 | − | 8.18381e20i | 0.121690 | − | 0.128225i | ||||
\(97\) | −4.47780e21 | −0.626002 | −0.313001 | − | 0.949753i | \(-0.601334\pi\) | ||||
−0.313001 | + | 0.949753i | \(0.601334\pi\) | |||||||
\(98\) | 2.88917e21i | 0.360816i | ||||||||
\(99\) | 1.96054e20 | − | 1.02601e19i | 0.0218972 | − | 0.00114594i | ||||
\(100\) | 8.93704e21 | 0.893704 | ||||||||
\(101\) | 1.21971e22i | 1.09325i | 0.837377 | + | 0.546625i | \(0.184088\pi\) | ||||
−0.837377 | + | 0.546625i | \(0.815912\pi\) | |||||||
\(102\) | −5.04085e21 | − | 4.78394e21i | −0.405417 | − | 0.384755i | ||||
\(103\) | 1.78306e22 | 1.28812 | 0.644061 | − | 0.764975i | \(-0.277248\pi\) | ||||
0.644061 | + | 0.764975i | \(0.277248\pi\) | |||||||
\(104\) | 1.01445e22i | 0.658966i | ||||||||
\(105\) | 2.41568e22 | − | 2.54540e22i | 1.41240 | − | 1.48825i | ||||
\(106\) | −9.01170e21 | −0.474725 | ||||||||
\(107\) | 2.25812e22i | 1.07282i | 0.843958 | + | 0.536409i | \(0.180220\pi\) | ||||
−0.843958 | + | 0.536409i | \(0.819780\pi\) | |||||||
\(108\) | −7.57238e21 | + | 8.86411e21i | −0.324767 | + | 0.380167i | ||||
\(109\) | −3.14292e22 | −1.21798 | −0.608992 | − | 0.793177i | \(-0.708426\pi\) | ||||
−0.608992 | + | 0.793177i | \(0.708426\pi\) | |||||||
\(110\) | 7.38561e20i | 0.0258861i | ||||||||
\(111\) | 1.58733e22 | + | 1.50643e22i | 0.503634 | + | 0.477967i | ||||
\(112\) | 1.06872e22 | 0.307233 | ||||||||
\(113\) | 2.55953e22i | 0.667264i | 0.942703 | + | 0.333632i | \(0.108274\pi\) | ||||
−0.942703 | + | 0.333632i | \(0.891726\pi\) | |||||||
\(114\) | −1.64086e22 | + | 1.72898e22i | −0.388257 | + | 0.409107i | ||||
\(115\) | 1.21932e22 | 0.262085 | ||||||||
\(116\) | − | 5.24381e20i | − | 0.0102473i | ||||||
\(117\) | −5.47815e21 | − | 1.04679e23i | −0.0974069 | − | 1.86129i | ||||
\(118\) | −2.50689e21 | −0.0405913 | ||||||||
\(119\) | − | 6.58285e22i | − | 0.971398i | ||||||
\(120\) | −3.18124e22 | − | 3.01910e22i | −0.428156 | − | 0.406335i | ||||
\(121\) | 8.13636e22 | 0.999519 | ||||||||
\(122\) | 2.08334e22i | 0.233777i | ||||||||
\(123\) | −8.66970e22 | + | 9.13528e22i | −0.889299 | + | 0.937056i | ||||
\(124\) | −1.85451e22 | −0.174017 | ||||||||
\(125\) | − | 1.53042e23i | − | 1.31462i | ||||||
\(126\) | −1.10279e23 | + | 5.77125e21i | −0.867798 | + | 0.0454144i | ||||
\(127\) | −2.54447e23 | −1.83551 | −0.917753 | − | 0.397151i | \(-0.869999\pi\) | ||||
−0.917753 | + | 0.397151i | \(0.869999\pi\) | |||||||
\(128\) | − | 1.33569e22i | − | 0.0883883i | ||||||
\(129\) | 2.00734e23 | + | 1.90504e23i | 1.21937 | + | 1.15722i | ||||
\(130\) | 3.94339e23 | 2.20036 | ||||||||
\(131\) | − | 7.58864e21i | − | 0.0389206i | −0.999811 | − | 0.0194603i | \(-0.993805\pi\) | ||
0.999811 | − | 0.0194603i | \(-0.00619480\pi\) | |||||||
\(132\) | 1.59991e21 | − | 1.68582e21i | 0.00754712 | − | 0.00795241i | ||||
\(133\) | −2.25788e23 | −0.980239 | ||||||||
\(134\) | − | 6.07813e22i | − | 0.243006i | ||||||
\(135\) | 3.44569e23 | + | 2.94356e23i | 1.26942 | + | 1.08443i | ||||
\(136\) | −8.22721e22 | −0.279463 | ||||||||
\(137\) | 3.35740e23i | 1.05215i | 0.850438 | + | 0.526075i | \(0.176337\pi\) | ||||
−0.850438 | + | 0.526075i | \(0.823663\pi\) | |||||||
\(138\) | −2.78320e22 | − | 2.64135e22i | −0.0805145 | − | 0.0764111i | ||||
\(139\) | −8.70159e21 | −0.0232507 | −0.0116253 | − | 0.999932i | \(-0.503701\pi\) | ||||
−0.0116253 | + | 0.999932i | \(0.503701\pi\) | |||||||
\(140\) | − | 4.15438e23i | − | 1.02588i | ||||||
\(141\) | −1.17457e21 | + | 1.23765e21i | −0.00268207 | + | 0.00282610i | ||||
\(142\) | 3.11671e23 | 0.658454 | ||||||||
\(143\) | 2.08971e22i | 0.0408686i | ||||||||
\(144\) | 7.21288e21 | + | 1.37827e23i | 0.0130654 | + | 0.249658i | ||||
\(145\) | −2.03839e22 | −0.0342168 | ||||||||
\(146\) | − | 1.39796e22i | − | 0.0217577i | ||||||
\(147\) | −2.56353e23 | − | 2.43288e23i | −0.370124 | − | 0.351261i | ||||
\(148\) | 2.59070e23 | 0.347167 | ||||||||
\(149\) | − | 1.47004e24i | − | 1.82928i | −0.404271 | − | 0.914639i | \(-0.632475\pi\) | ||
0.404271 | − | 0.914639i | \(-0.367525\pi\) | |||||||
\(150\) | −7.52561e23 | + | 7.92975e23i | −0.870037 | + | 0.916759i | ||||
\(151\) | −1.33826e24 | −1.43811 | −0.719057 | − | 0.694951i | \(-0.755426\pi\) | ||||
−0.719057 | + | 0.694951i | \(0.755426\pi\) | |||||||
\(152\) | 2.82188e23i | 0.282007i | ||||||||
\(153\) | 8.48949e23 | − | 4.44280e22i | 0.789361 | − | 0.0413096i | ||||
\(154\) | 2.20152e22 | 0.0190544 | ||||||||
\(155\) | 7.20893e23i | 0.581061i | ||||||||
\(156\) | −9.00110e23 | − | 8.54236e23i | −0.675966 | − | 0.641516i | ||||
\(157\) | 1.57598e23 | 0.110320 | 0.0551599 | − | 0.998478i | \(-0.482433\pi\) | ||||
0.0551599 | + | 0.998478i | \(0.482433\pi\) | |||||||
\(158\) | 2.71076e23i | 0.176955i | ||||||||
\(159\) | 7.58848e23 | − | 7.99599e23i | 0.462154 | − | 0.486972i | ||||
\(160\) | −5.19212e23 | −0.295138 | ||||||||
\(161\) | − | 3.63458e23i | − | 0.192917i | ||||||
\(162\) | −1.48856e23 | − | 1.41831e24i | −0.0738079 | − | 0.703244i | ||||
\(163\) | 5.35890e23 | 0.248320 | 0.124160 | − | 0.992262i | \(-0.460376\pi\) | ||||
0.124160 | + | 0.992262i | \(0.460376\pi\) | |||||||
\(164\) | 1.49098e24i | 0.645935i | ||||||||
\(165\) | −6.55318e22 | − | 6.21920e22i | −0.0265539 | − | 0.0252006i | ||||
\(166\) | 9.02404e23 | 0.342147 | ||||||||
\(167\) | 3.92922e24i | 1.39452i | 0.716817 | + | 0.697261i | \(0.245598\pi\) | ||||
−0.716817 | + | 0.697261i | \(0.754402\pi\) | |||||||
\(168\) | −8.99941e23 | + | 9.48269e23i | −0.299097 | + | 0.315159i | ||||
\(169\) | 7.94574e24 | 2.47389 | ||||||||
\(170\) | 3.19811e24i | 0.933158i | ||||||||
\(171\) | −1.52385e23 | − | 2.91184e24i | −0.0416856 | − | 0.796546i | ||||
\(172\) | 3.27620e24 | 0.840539 | ||||||||
\(173\) | − | 2.12608e24i | − | 0.511768i | −0.966707 | − | 0.255884i | \(-0.917633\pi\) | ||
0.966707 | − | 0.255884i | \(-0.0823665\pi\) | |||||||
\(174\) | 4.65278e22 | + | 4.41566e22i | 0.0105117 | + | 0.00997593i | ||||
\(175\) | −1.03555e25 | −2.19660 | ||||||||
\(176\) | − | 2.75145e22i | − | 0.00548178i | ||||||
\(177\) | 2.11097e23 | − | 2.22434e23i | 0.0395164 | − | 0.0416385i | ||||
\(178\) | −7.24160e24 | −1.27413 | ||||||||
\(179\) | 1.09737e25i | 1.81539i | 0.419629 | + | 0.907696i | \(0.362160\pi\) | ||||
−0.419629 | + | 0.907696i | \(0.637840\pi\) | |||||||
\(180\) | 5.35764e24 | − | 2.80381e23i | 0.833636 | − | 0.0436266i | ||||
\(181\) | −3.30046e24 | −0.483181 | −0.241590 | − | 0.970378i | \(-0.577669\pi\) | ||||
−0.241590 | + | 0.970378i | \(0.577669\pi\) | |||||||
\(182\) | − | 1.17545e25i | − | 1.61965i | ||||||
\(183\) | −1.84853e24 | − | 1.75432e24i | −0.239808 | − | 0.227586i | ||||
\(184\) | −4.54248e23 | −0.0555006 | ||||||||
\(185\) | − | 1.00707e25i | − | 1.15923i | ||||||
\(186\) | 1.56163e24 | − | 1.64549e24i | 0.169409 | − | 0.178506i | ||||
\(187\) | −1.69476e23 | −0.0173321 | ||||||||
\(188\) | 2.01998e22i | 0.00194809i | ||||||||
\(189\) | 8.77422e24 | − | 1.02710e25i | 0.798231 | − | 0.934397i | ||||
\(190\) | 1.09693e25 | 0.941651 | ||||||||
\(191\) | 6.88290e24i | 0.557705i | 0.960334 | + | 0.278852i | \(0.0899540\pi\) | ||||
−0.960334 | + | 0.278852i | \(0.910046\pi\) | |||||||
\(192\) | 1.18514e24 | + | 1.12474e24i | 0.0906686 | + | 0.0860477i | ||||
\(193\) | −1.02055e25 | −0.737401 | −0.368700 | − | 0.929548i | \(-0.620197\pi\) | ||||
−0.368700 | + | 0.929548i | \(0.620197\pi\) | |||||||
\(194\) | − | 6.48455e24i | − | 0.442650i | ||||||
\(195\) | −3.32061e25 | + | 3.49894e25i | −2.14209 | + | 2.25712i | ||||
\(196\) | −4.18396e24 | −0.255135 | ||||||||
\(197\) | − | 1.83021e25i | − | 1.05529i | −0.849464 | − | 0.527647i | \(-0.823074\pi\) | ||
0.849464 | − | 0.527647i | \(-0.176926\pi\) | |||||||
\(198\) | 1.48582e22 | + | 2.83916e23i | 0.000810305 | + | 0.0154836i | ||||
\(199\) | 2.64799e25 | 1.36626 | 0.683130 | − | 0.730297i | \(-0.260618\pi\) | ||||
0.683130 | + | 0.730297i | \(0.260618\pi\) | |||||||
\(200\) | 1.29422e25i | 0.631944i | ||||||||
\(201\) | 5.39306e24 | + | 5.11821e24i | 0.249275 | + | 0.236571i | ||||
\(202\) | −1.76632e25 | −0.773045 | ||||||||
\(203\) | 6.07607e23i | 0.0251864i | ||||||||
\(204\) | 6.92789e24 | − | 7.29993e24i | 0.272063 | − | 0.286673i | ||||
\(205\) | 5.79577e25 | 2.15685 | ||||||||
\(206\) | 2.58215e25i | 0.910839i | ||||||||
\(207\) | 4.68729e24 | − | 2.45300e23i | 0.156765 | − | 0.00820397i | ||||
\(208\) | −1.46908e25 | −0.465959 | ||||||||
\(209\) | 5.81294e23i | 0.0174899i | ||||||||
\(210\) | 3.68614e25 | + | 3.49828e25i | 1.05235 | + | 0.998716i | ||||
\(211\) | −9.96760e24 | −0.270074 | −0.135037 | − | 0.990841i | \(-0.543115\pi\) | ||||
−0.135037 | + | 0.990841i | \(0.543115\pi\) | |||||||
\(212\) | − | 1.30503e25i | − | 0.335681i | ||||||
\(213\) | −2.62449e25 | + | 2.76543e25i | −0.641017 | + | 0.675440i | ||||
\(214\) | −3.27011e25 | −0.758597 | ||||||||
\(215\) | − | 1.27354e26i | − | 2.80665i | ||||||
\(216\) | −1.28366e25 | − | 1.09660e25i | −0.268818 | − | 0.229645i | ||||
\(217\) | 2.14885e25 | 0.427710 | ||||||||
\(218\) | − | 4.55143e25i | − | 0.861244i | ||||||
\(219\) | 1.24039e24 | + | 1.17718e24i | 0.0223190 | + | 0.0211815i | ||||
\(220\) | −1.06955e24 | −0.0183043 | ||||||||
\(221\) | 9.04884e25i | 1.47325i | ||||||||
\(222\) | −2.18155e25 | + | 2.29870e25i | −0.337973 | + | 0.356123i | ||||
\(223\) | −9.49048e25 | −1.39938 | −0.699689 | − | 0.714448i | \(-0.746678\pi\) | ||||
−0.699689 | + | 0.714448i | \(0.746678\pi\) | |||||||
\(224\) | 1.54768e25i | 0.217246i | ||||||||
\(225\) | −6.98896e24 | − | 1.33548e26i | −0.0934125 | − | 1.78496i | ||||
\(226\) | −3.70660e25 | −0.471827 | ||||||||
\(227\) | 1.04526e26i | 1.26748i | 0.773548 | + | 0.633738i | \(0.218480\pi\) | ||||
−0.773548 | + | 0.633738i | \(0.781520\pi\) | |||||||
\(228\) | −2.50383e25 | − | 2.37622e25i | −0.289282 | − | 0.274539i | ||||
\(229\) | 8.27122e25 | 0.910709 | 0.455354 | − | 0.890310i | \(-0.349513\pi\) | ||||
0.455354 | + | 0.890310i | \(0.349513\pi\) | |||||||
\(230\) | 1.76577e25i | 0.185322i | ||||||||
\(231\) | −1.85383e24 | + | 1.95339e24i | −0.0185498 | + | 0.0195459i | ||||
\(232\) | 7.59385e23 | 0.00724593 | ||||||||
\(233\) | − | 7.15811e25i | − | 0.651453i | −0.945464 | − | 0.325727i | \(-0.894391\pi\) | ||
0.945464 | − | 0.325727i | \(-0.105609\pi\) | |||||||
\(234\) | 1.51591e26 | − | 7.93321e24i | 1.31613 | − | 0.0688771i | ||||
\(235\) | 7.85212e23 | 0.00650489 | ||||||||
\(236\) | − | 3.63036e24i | − | 0.0287024i | ||||||
\(237\) | −2.40523e25 | − | 2.28265e25i | −0.181520 | − | 0.172269i | ||||
\(238\) | 9.53298e25 | 0.686882 | ||||||||
\(239\) | 1.10361e26i | 0.759346i | 0.925121 | + | 0.379673i | \(0.123963\pi\) | ||||
−0.925121 | + | 0.379673i | \(0.876037\pi\) | |||||||
\(240\) | 4.37213e25 | − | 4.60692e25i | 0.287322 | − | 0.302752i | ||||
\(241\) | −2.16586e26 | −1.35970 | −0.679849 | − | 0.733352i | \(-0.737955\pi\) | ||||
−0.679849 | + | 0.733352i | \(0.737955\pi\) | |||||||
\(242\) | 1.17827e26i | 0.706767i | ||||||||
\(243\) | 1.38380e26 | + | 1.06224e26i | 0.793240 | + | 0.608909i | ||||
\(244\) | −3.01700e25 | −0.165305 | ||||||||
\(245\) | 1.62640e26i | 0.851924i | ||||||||
\(246\) | −1.32293e26 | − | 1.25551e26i | −0.662599 | − | 0.628830i | ||||
\(247\) | 3.10370e26 | 1.48666 | ||||||||
\(248\) | − | 2.68562e25i | − | 0.123049i | ||||||
\(249\) | −7.59888e25 | + | 8.00695e25i | −0.333086 | + | 0.350973i | ||||
\(250\) | 2.21628e26 | 0.929576 | ||||||||
\(251\) | 2.26728e26i | 0.910109i | 0.890464 | + | 0.455054i | \(0.150380\pi\) | ||||
−0.890464 | + | 0.455054i | \(0.849620\pi\) | |||||||
\(252\) | −8.35766e24 | − | 1.59702e26i | −0.0321129 | − | 0.613626i | ||||
\(253\) | −9.35729e23 | −0.00344211 | ||||||||
\(254\) | − | 3.68478e26i | − | 1.29790i | ||||||
\(255\) | −2.83765e26 | − | 2.69303e26i | −0.957231 | − | 0.908446i | ||||
\(256\) | 1.93428e25 | 0.0625000 | ||||||||
\(257\) | − | 5.65076e25i | − | 0.174921i | −0.996168 | − | 0.0874607i | \(-0.972125\pi\) | ||
0.996168 | − | 0.0874607i | \(-0.0278752\pi\) | |||||||
\(258\) | −2.75879e26 | + | 2.90694e26i | −0.818280 | + | 0.862223i | ||||
\(259\) | −3.00188e26 | −0.853288 | ||||||||
\(260\) | 5.71065e26i | 1.55589i | ||||||||
\(261\) | −7.83594e24 | + | 4.10078e23i | −0.0204666 | + | 0.00107108i | ||||
\(262\) | 1.09895e25 | 0.0275210 | ||||||||
\(263\) | − | 6.09160e26i | − | 1.46291i | −0.681888 | − | 0.731456i | \(-0.738841\pi\) | ||
0.681888 | − | 0.731456i | \(-0.261159\pi\) | |||||||
\(264\) | 2.44133e24 | + | 2.31691e24i | 0.00562320 | + | 0.00533662i | ||||
\(265\) | −5.07297e26 | −1.12088 | ||||||||
\(266\) | − | 3.26975e26i | − | 0.693134i | ||||||
\(267\) | 6.09793e26 | − | 6.42540e26i | 1.24039 | − | 1.30700i | ||||
\(268\) | 8.80207e25 | 0.171831 | ||||||||
\(269\) | − | 5.69197e26i | − | 1.06657i | −0.845937 | − | 0.533283i | \(-0.820958\pi\) | ||
0.845937 | − | 0.533283i | \(-0.179042\pi\) | |||||||
\(270\) | −4.26273e26 | + | 4.98989e26i | −0.766808 | + | 0.897613i | ||||
\(271\) | 3.92320e26 | 0.677608 | 0.338804 | − | 0.940857i | \(-0.389978\pi\) | ||||
0.338804 | + | 0.940857i | \(0.389978\pi\) | |||||||
\(272\) | − | 1.19143e26i | − | 0.197610i | ||||||
\(273\) | 1.04297e27 | + | 9.89815e26i | 1.66143 | + | 1.57676i | ||||
\(274\) | −4.86204e26 | −0.743982 | ||||||||
\(275\) | 2.66603e25i | 0.0391927i | ||||||||
\(276\) | 3.82509e25 | − | 4.03050e25i | 0.0540308 | − | 0.0569324i | ||||
\(277\) | −4.68221e26 | −0.635585 | −0.317793 | − | 0.948160i | \(-0.602942\pi\) | ||||
−0.317793 | + | 0.948160i | \(0.602942\pi\) | |||||||
\(278\) | − | 1.26012e25i | − | 0.0164407i | ||||||
\(279\) | 1.45027e25 | + | 2.77124e26i | 0.0181888 | + | 0.347558i | ||||
\(280\) | 6.01618e26 | 0.725409 | ||||||||
\(281\) | 1.18275e27i | 1.37127i | 0.727945 | + | 0.685636i | \(0.240476\pi\) | ||||
−0.727945 | + | 0.685636i | \(0.759524\pi\) | |||||||
\(282\) | −1.79231e24 | − | 1.70096e24i | −0.00199835 | − | 0.00189651i | ||||
\(283\) | 4.88882e26 | 0.524268 | 0.262134 | − | 0.965031i | \(-0.415574\pi\) | ||||
0.262134 | + | 0.965031i | \(0.415574\pi\) | |||||||
\(284\) | 4.51348e26i | 0.465597i | ||||||||
\(285\) | −9.23693e26 | + | 9.73297e26i | −0.916715 | + | 0.965944i | ||||
\(286\) | −3.02623e25 | −0.0288985 | ||||||||
\(287\) | − | 1.72762e27i | − | 1.58762i | ||||||
\(288\) | −1.99594e26 | + | 1.04454e25i | −0.176535 | + | 0.00923861i | ||||
\(289\) | 4.40698e26 | 0.375202 | ||||||||
\(290\) | − | 2.95191e25i | − | 0.0241949i | ||||||
\(291\) | 5.75368e26 | + | 5.46044e26i | 0.454070 | + | 0.430928i | ||||
\(292\) | 2.02446e25 | 0.0153850 | ||||||||
\(293\) | − | 7.47089e26i | − | 0.546800i | −0.961900 | − | 0.273400i | \(-0.911852\pi\) | ||
0.961900 | − | 0.273400i | \(-0.0881482\pi\) | |||||||
\(294\) | 3.52319e26 | − | 3.71239e26i | 0.248379 | − | 0.261717i | ||||
\(295\) | −1.41121e26 | −0.0958403 | ||||||||
\(296\) | 3.75173e26i | 0.245484i | ||||||||
\(297\) | −2.64428e25 | − | 2.25894e25i | −0.0166719 | − | 0.0142424i | ||||
\(298\) | 2.12884e27 | 1.29350 | ||||||||
\(299\) | 4.99613e26i | 0.292584i | ||||||||
\(300\) | −1.14835e27 | − | 1.08982e27i | −0.648247 | − | 0.615209i | ||||
\(301\) | −3.79618e27 | −2.06593 | ||||||||
\(302\) | − | 1.93800e27i | − | 1.01690i | ||||||
\(303\) | 1.48737e27 | − | 1.56724e27i | 0.752574 | − | 0.792988i | ||||
\(304\) | −4.08652e26 | −0.199409 | ||||||||
\(305\) | 1.17278e27i | 0.551972i | ||||||||
\(306\) | 6.43387e25 | + | 1.22941e27i | 0.0292103 | + | 0.558163i | ||||
\(307\) | 1.44713e27 | 0.633849 | 0.316924 | − | 0.948451i | \(-0.397350\pi\) | ||||
0.316924 | + | 0.948451i | \(0.397350\pi\) | |||||||
\(308\) | 3.18814e25i | 0.0134735i | ||||||||
\(309\) | −2.29111e27 | − | 2.17435e27i | −0.934337 | − | 0.886719i | ||||
\(310\) | −1.04396e27 | −0.410872 | ||||||||
\(311\) | 1.31713e27i | 0.500338i | 0.968202 | + | 0.250169i | \(0.0804862\pi\) | ||||
−0.968202 | + | 0.250169i | \(0.919514\pi\) | |||||||
\(312\) | 1.23707e27 | − | 1.30350e27i | 0.453620 | − | 0.477980i | ||||
\(313\) | −7.65076e26 | −0.270842 | −0.135421 | − | 0.990788i | \(-0.543239\pi\) | ||||
−0.135421 | + | 0.990788i | \(0.543239\pi\) | |||||||
\(314\) | 2.28226e26i | 0.0780079i | ||||||||
\(315\) | −6.20797e27 | + | 3.24882e26i | −2.04896 | + | 0.107228i | ||||
\(316\) | −3.92560e26 | −0.125126 | ||||||||
\(317\) | 3.31997e27i | 1.02207i | 0.859559 | + | 0.511037i | \(0.170738\pi\) | ||||
−0.859559 | + | 0.511037i | \(0.829262\pi\) | |||||||
\(318\) | 1.15794e27 | + | 1.09893e27i | 0.344341 | + | 0.326792i | ||||
\(319\) | 1.56429e24 | 0.000449388 | ||||||||
\(320\) | − | 7.51900e26i | − | 0.208694i | ||||||
\(321\) | 2.75366e27 | − | 2.90154e27i | 0.738508 | − | 0.778167i | ||||
\(322\) | 5.26344e26 | 0.136413 | ||||||||
\(323\) | 2.51711e27i | 0.630485i | ||||||||
\(324\) | 2.05393e27 | − | 2.15567e26i | 0.497269 | − | 0.0521900i | ||||
\(325\) | 1.42347e28 | 3.33144 | ||||||||
\(326\) | 7.76052e26i | 0.175589i | ||||||||
\(327\) | 4.03844e27 | + | 3.83262e27i | 0.883463 | + | 0.838437i | ||||
\(328\) | −2.15917e27 | −0.456745 | ||||||||
\(329\) | − | 2.34057e25i | − | 0.00478815i | ||||||
\(330\) | 9.00637e25 | − | 9.49002e25i | 0.0178195 | − | 0.0187765i | ||||
\(331\) | −2.97386e27 | −0.569131 | −0.284566 | − | 0.958657i | \(-0.591849\pi\) | ||||
−0.284566 | + | 0.958657i | \(0.591849\pi\) | |||||||
\(332\) | 1.30682e27i | 0.241934i | ||||||||
\(333\) | −2.02599e26 | − | 3.87134e27i | −0.0362869 | − | 0.693385i | ||||
\(334\) | −5.69012e27 | −0.986076 | ||||||||
\(335\) | − | 3.42157e27i | − | 0.573763i | ||||||
\(336\) | −1.37324e27 | − | 1.30325e27i | −0.222851 | − | 0.211493i | ||||
\(337\) | −6.71977e27 | −1.05542 | −0.527710 | − | 0.849425i | \(-0.676949\pi\) | ||||
−0.527710 | + | 0.849425i | \(0.676949\pi\) | |||||||
\(338\) | 1.15067e28i | 1.74931i | ||||||||
\(339\) | 3.12122e27 | − | 3.28883e27i | 0.459332 | − | 0.483999i | ||||
\(340\) | −4.63136e27 | −0.659842 | ||||||||
\(341\) | − | 5.53225e25i | − | 0.00763139i | ||||||
\(342\) | 4.21680e27 | − | 2.20678e26i | 0.563243 | − | 0.0294762i | ||||
\(343\) | −4.65285e27 | −0.601843 | ||||||||
\(344\) | 4.74445e27i | 0.594351i | ||||||||
\(345\) | −1.56675e27 | − | 1.48690e27i | −0.190103 | − | 0.180415i | ||||
\(346\) | 3.07890e27 | 0.361875 | ||||||||
\(347\) | − | 8.45322e27i | − | 0.962494i | −0.876585 | − | 0.481247i | \(-0.840184\pi\) | ||
0.876585 | − | 0.481247i | \(-0.159816\pi\) | |||||||
\(348\) | −6.39455e25 | + | 6.73795e25i | −0.00705405 | + | 0.00743286i | ||||
\(349\) | 6.08370e27 | 0.650262 | 0.325131 | − | 0.945669i | \(-0.394592\pi\) | ||||
0.325131 | + | 0.945669i | \(0.394592\pi\) | |||||||
\(350\) | − | 1.49963e28i | − | 1.55323i | ||||||
\(351\) | −1.20611e28 | + | 1.41186e28i | −1.21062 | + | 1.41714i | ||||
\(352\) | 3.98452e25 | 0.00387621 | ||||||||
\(353\) | − | 1.71337e28i | − | 1.61558i | −0.589471 | − | 0.807790i | \(-0.700664\pi\) | ||
0.589471 | − | 0.807790i | \(-0.299336\pi\) | |||||||
\(354\) | 3.22118e26 | + | 3.05702e26i | 0.0294428 | + | 0.0279423i | ||||
\(355\) | 1.75450e28 | 1.55468 | ||||||||
\(356\) | − | 1.04870e28i | − | 0.900947i | ||||||
\(357\) | −8.02744e27 | + | 8.45852e27i | −0.668693 | + | 0.704602i | ||||
\(358\) | −1.58916e28 | −1.28368 | ||||||||
\(359\) | 1.32701e28i | 1.03953i | 0.854311 | + | 0.519763i | \(0.173980\pi\) | ||||
−0.854311 | + | 0.519763i | \(0.826020\pi\) | |||||||
\(360\) | 4.06036e26 | + | 7.75870e27i | 0.0308487 | + | 0.589469i | ||||
\(361\) | −4.93645e27 | −0.363777 | ||||||||
\(362\) | − | 4.77957e27i | − | 0.341660i | ||||||
\(363\) | −1.04547e28 | − | 9.92186e27i | −0.725000 | − | 0.688051i | ||||
\(364\) | 1.70224e28 | 1.14526 | ||||||||
\(365\) | − | 7.86954e26i | − | 0.0513722i | ||||||
\(366\) | 2.54052e27 | − | 2.67695e27i | 0.160928 | − | 0.169570i | ||||
\(367\) | −4.06121e27 | −0.249649 | −0.124824 | − | 0.992179i | \(-0.539837\pi\) | ||||
−0.124824 | + | 0.992179i | \(0.539837\pi\) | |||||||
\(368\) | − | 6.57822e26i | − | 0.0392448i | ||||||
\(369\) | 2.22800e28 | − | 1.16598e27i | 1.29010 | − | 0.0675150i | ||||
\(370\) | 1.45839e28 | 0.819697 | ||||||||
\(371\) | 1.51216e28i | 0.825058i | ||||||||
\(372\) | 2.38293e27 | + | 2.26148e27i | 0.126223 | + | 0.119790i | ||||
\(373\) | 2.81315e27 | 0.144676 | 0.0723378 | − | 0.997380i | \(-0.476954\pi\) | ||||
0.0723378 | + | 0.997380i | \(0.476954\pi\) | |||||||
\(374\) | − | 2.45428e26i | − | 0.0122557i | ||||||
\(375\) | −1.86626e28 | + | 1.96648e28i | −0.904959 | + | 0.953557i | ||||
\(376\) | −2.92524e25 | −0.00137751 | ||||||||
\(377\) | − | 8.35222e26i | − | 0.0381986i | ||||||
\(378\) | 1.48739e28 | + | 1.27064e28i | 0.660718 | + | 0.564435i | ||||
\(379\) | −1.84723e28 | −0.797057 | −0.398529 | − | 0.917156i | \(-0.630479\pi\) | ||||
−0.398529 | + | 0.917156i | \(0.630479\pi\) | |||||||
\(380\) | 1.58853e28i | 0.665848i | ||||||||
\(381\) | 3.26947e28 | + | 3.10284e28i | 1.33138 | + | 1.26353i | ||||
\(382\) | −9.96750e27 | −0.394357 | ||||||||
\(383\) | 9.71325e26i | 0.0373403i | 0.999826 | + | 0.0186702i | \(0.00594324\pi\) | ||||
−0.999826 | + | 0.0186702i | \(0.994057\pi\) | |||||||
\(384\) | −1.62880e27 | + | 1.71627e27i | −0.0608449 | + | 0.0641124i | ||||
\(385\) | 1.23930e27 | 0.0449893 | ||||||||
\(386\) | − | 1.47791e28i | − | 0.521421i | ||||||
\(387\) | −2.56206e27 | − | 4.89570e28i | −0.0878556 | − | 1.67878i | ||||
\(388\) | 9.39063e27 | 0.313001 | ||||||||
\(389\) | − | 1.69345e28i | − | 0.548689i | −0.961631 | − | 0.274345i | \(-0.911539\pi\) | ||
0.961631 | − | 0.274345i | \(-0.0884609\pi\) | |||||||
\(390\) | −5.06700e28 | − | 4.80876e28i | −1.59603 | − | 1.51469i | ||||
\(391\) | −4.05188e27 | −0.124083 | ||||||||
\(392\) | − | 6.05902e27i | − | 0.180408i | ||||||
\(393\) | −9.25394e26 | + | 9.75089e26i | −0.0267922 | + | 0.0282310i | ||||
\(394\) | 2.65043e28 | 0.746206 | ||||||||
\(395\) | 1.52597e28i | 0.417810i | ||||||||
\(396\) | −4.11154e26 | + | 2.15169e25i | −0.0109486 | + | 0.000572972i | ||||
\(397\) | −2.59381e28 | −0.671804 | −0.335902 | − | 0.941897i | \(-0.609041\pi\) | ||||
−0.335902 | + | 0.941897i | \(0.609041\pi\) | |||||||
\(398\) | 3.83471e28i | 0.966092i | ||||||||
\(399\) | 2.90122e28 | + | 2.75336e28i | 0.711015 | + | 0.674779i | ||||
\(400\) | −1.87423e28 | −0.446852 | ||||||||
\(401\) | − | 3.52251e28i | − | 0.817080i | −0.912740 | − | 0.408540i | \(-0.866038\pi\) | ||
0.912740 | − | 0.408540i | \(-0.133962\pi\) | |||||||
\(402\) | −7.41196e27 | + | 7.80999e27i | −0.167281 | + | 0.176264i | ||||
\(403\) | −2.95383e28 | −0.648679 | ||||||||
\(404\) | − | 2.55791e28i | − | 0.546625i | ||||||
\(405\) | −8.37960e27 | − | 7.98411e28i | −0.174268 | − | 1.66043i | ||||
\(406\) | −8.79909e26 | −0.0178095 | ||||||||
\(407\) | 7.72838e26i | 0.0152247i | ||||||||
\(408\) | 1.05714e28 | + | 1.00327e28i | 0.202708 | + | 0.192377i | ||||
\(409\) | −1.88501e27 | −0.0351849 | −0.0175925 | − | 0.999845i | \(-0.505600\pi\) | ||||
−0.0175925 | + | 0.999845i | \(0.505600\pi\) | |||||||
\(410\) | 8.39318e28i | 1.52512i | ||||||||
\(411\) | 4.09418e28 | − | 4.31404e28i | 0.724280 | − | 0.763175i | ||||
\(412\) | −3.73935e28 | −0.644061 | ||||||||
\(413\) | 4.20655e27i | 0.0705465i | ||||||||
\(414\) | 3.55232e26 | + | 6.78793e27i | 0.00580108 | + | 0.110849i | ||||
\(415\) | 5.07992e28 | 0.807844 | ||||||||
\(416\) | − | 2.12745e28i | − | 0.329483i | ||||||
\(417\) | 1.11810e27 | + | 1.06111e27i | 0.0168648 | + | 0.0160053i | ||||
\(418\) | −8.41803e26 | −0.0123672 | ||||||||
\(419\) | 1.12689e29i | 1.61260i | 0.591508 | + | 0.806299i | \(0.298533\pi\) | ||||
−0.591508 | + | 0.806299i | \(0.701467\pi\) | |||||||
\(420\) | −5.06605e28 | + | 5.33810e28i | −0.706199 | + | 0.744123i | ||||
\(421\) | −1.63590e27 | −0.0222154 | −0.0111077 | − | 0.999938i | \(-0.503536\pi\) | ||||
−0.0111077 | + | 0.999938i | \(0.503536\pi\) | |||||||
\(422\) | − | 1.44346e28i | − | 0.190971i | ||||||
\(423\) | 3.01849e26 | − | 1.57967e25i | 0.00389086 | − | 0.000203621i | ||||
\(424\) | 1.88989e28 | 0.237363 | ||||||||
\(425\) | 1.15444e29i | 1.41284i | ||||||||
\(426\) | −4.00477e28 | − | 3.80067e28i | −0.477608 | − | 0.453267i | ||||
\(427\) | 3.49584e28 | 0.406298 | ||||||||
\(428\) | − | 4.73563e28i | − | 0.536409i | ||||||
\(429\) | 2.54829e27 | − | 2.68514e27i | 0.0281332 | − | 0.0296440i | ||||
\(430\) | 1.84428e29 | 1.98460 | ||||||||
\(431\) | − | 1.25299e29i | − | 1.31431i | −0.753757 | − | 0.657154i | \(-0.771760\pi\) | ||
0.753757 | − | 0.657154i | \(-0.228240\pi\) | |||||||
\(432\) | 1.58804e28 | − | 1.85894e28i | 0.162383 | − | 0.190083i | ||||
\(433\) | 2.99363e28 | 0.298422 | 0.149211 | − | 0.988805i | \(-0.452327\pi\) | ||||
0.149211 | + | 0.988805i | \(0.452327\pi\) | |||||||
\(434\) | 3.11187e28i | 0.302436i | ||||||||
\(435\) | 2.61920e27 | + | 2.48571e27i | 0.0248191 | + | 0.0235542i | ||||
\(436\) | 6.59117e28 | 0.608992 | ||||||||
\(437\) | 1.38977e28i | 0.125212i | ||||||||
\(438\) | −1.70474e27 | + | 1.79628e27i | −0.0149776 | + | 0.0157819i | ||||
\(439\) | 6.93279e28 | 0.594016 | 0.297008 | − | 0.954875i | \(-0.404011\pi\) | ||||
0.297008 | + | 0.954875i | \(0.404011\pi\) | |||||||
\(440\) | − | 1.54888e27i | − | 0.0129431i | ||||||
\(441\) | 3.27195e27 | + | 6.25218e28i | 0.0266675 | + | 0.509574i | ||||
\(442\) | −1.31041e29 | −1.04175 | ||||||||
\(443\) | − | 6.10344e28i | − | 0.473297i | −0.971595 | − | 0.236649i | \(-0.923951\pi\) | ||
0.971595 | − | 0.236649i | \(-0.0760490\pi\) | |||||||
\(444\) | −3.32888e28 | − | 3.15922e28i | −0.251817 | − | 0.238983i | ||||
\(445\) | −4.07652e29 | −3.00836 | ||||||||
\(446\) | − | 1.37437e29i | − | 0.989509i | ||||||
\(447\) | −1.79263e29 | + | 1.88890e29i | −1.25924 | + | 1.32686i | ||||
\(448\) | −2.24128e28 | −0.153616 | ||||||||
\(449\) | 1.05434e29i | 0.705135i | 0.935786 | + | 0.352567i | \(0.114691\pi\) | ||||
−0.935786 | + | 0.352567i | \(0.885309\pi\) | |||||||
\(450\) | 1.93398e29 | − | 1.01211e28i | 1.26216 | − | 0.0660526i | ||||
\(451\) | −4.44777e27 | −0.0283270 | ||||||||
\(452\) | − | 5.36773e28i | − | 0.333632i | ||||||
\(453\) | 1.71957e29 | + | 1.63193e29i | 1.04313 | + | 0.989971i | ||||
\(454\) | −1.51370e29 | −0.896240 | ||||||||
\(455\) | − | 6.61700e29i | − | 3.82416i | ||||||
\(456\) | 3.44114e28 | − | 3.62593e28i | 0.194128 | − | 0.204553i | ||||
\(457\) | −9.15845e28 | −0.504363 | −0.252182 | − | 0.967680i | \(-0.581148\pi\) | ||||
−0.252182 | + | 0.967680i | \(0.581148\pi\) | |||||||
\(458\) | 1.19780e29i | 0.643968i | ||||||||
\(459\) | −1.14502e29 | − | 9.78162e28i | −0.600999 | − | 0.513418i | ||||
\(460\) | −2.55711e28 | −0.131043 | ||||||||
\(461\) | 2.43448e29i | 1.21813i | 0.793119 | + | 0.609067i | \(0.208456\pi\) | ||||
−0.793119 | + | 0.609067i | \(0.791544\pi\) | |||||||
\(462\) | −2.82880e27 | − | 2.68464e27i | −0.0138211 | − | 0.0131167i | ||||
\(463\) | 3.88463e29 | 1.85335 | 0.926677 | − | 0.375859i | \(-0.122652\pi\) | ||||
0.926677 | + | 0.375859i | \(0.122652\pi\) | |||||||
\(464\) | 1.09971e27i | 0.00512365i | ||||||||
\(465\) | 8.79091e28 | − | 9.26299e28i | 0.399992 | − | 0.421472i | ||||
\(466\) | 1.03660e29 | 0.460647 | ||||||||
\(467\) | 2.67460e28i | 0.116084i | 0.998314 | + | 0.0580420i | \(0.0184857\pi\) | ||||
−0.998314 | + | 0.0580420i | \(0.981514\pi\) | |||||||
\(468\) | 1.14885e28 | + | 2.19527e29i | 0.0487034 | + | 0.930645i | ||||
\(469\) | −1.01991e29 | −0.422337 | ||||||||
\(470\) | 1.13711e27i | 0.00459966i | ||||||||
\(471\) | −2.02502e28 | − | 1.92182e28i | −0.0800203 | − | 0.0759421i | ||||
\(472\) | 5.25733e27 | 0.0202956 | ||||||||
\(473\) | 9.77332e27i | 0.0368612i | ||||||||
\(474\) | 3.30563e28 | − | 3.48315e28i | 0.121813 | − | 0.128354i | ||||
\(475\) | 3.95966e29 | 1.42570 | ||||||||
\(476\) | 1.38052e29i | 0.485699i | ||||||||
\(477\) | −1.95014e29 | + | 1.02057e28i | −0.670445 | + | 0.0350864i | ||||
\(478\) | −1.59820e29 | −0.536939 | ||||||||
\(479\) | 5.17851e29i | 1.70026i | 0.526576 | + | 0.850128i | \(0.323475\pi\) | ||||
−0.526576 | + | 0.850128i | \(0.676525\pi\) | |||||||
\(480\) | 6.67153e28 | + | 6.33152e28i | 0.214078 | + | 0.203168i | ||||
\(481\) | 4.12641e29 | 1.29413 | ||||||||
\(482\) | − | 3.13650e29i | − | 0.961452i | ||||||
\(483\) | −4.43218e28 | + | 4.67020e28i | −0.132800 | + | 0.139932i | ||||
\(484\) | −1.70632e29 | −0.499760 | ||||||||
\(485\) | − | 3.65036e29i | − | 1.04514i | ||||||
\(486\) | −1.53828e29 | + | 2.00396e29i | −0.430564 | + | 0.560905i | ||||
\(487\) | −2.51685e29 | −0.688714 | −0.344357 | − | 0.938839i | \(-0.611903\pi\) | ||||
−0.344357 | + | 0.938839i | \(0.611903\pi\) | |||||||
\(488\) | − | 4.36908e28i | − | 0.116889i | ||||||
\(489\) | −6.88583e28 | − | 6.53490e28i | −0.180119 | − | 0.170939i | ||||
\(490\) | −2.35528e29 | −0.602402 | ||||||||
\(491\) | 5.88907e29i | 1.47282i | 0.676535 | + | 0.736411i | \(0.263481\pi\) | ||||
−0.676535 | + | 0.736411i | \(0.736519\pi\) | |||||||
\(492\) | 1.81817e29 | − | 1.91581e29i | 0.444650 | − | 0.468528i | ||||
\(493\) | 6.77369e27 | 0.0161998 | ||||||||
\(494\) | 4.49463e29i | 1.05123i | ||||||||
\(495\) | 8.36413e26 | + | 1.59825e28i | 0.00191321 | + | 0.0365585i | ||||
\(496\) | 3.88920e28 | 0.0870085 | ||||||||
\(497\) | − | 5.22983e29i | − | 1.14437i | ||||||
\(498\) | −1.15953e29 | − | 1.10043e29i | −0.248176 | − | 0.235527i | ||||
\(499\) | 7.36099e29 | 1.54110 | 0.770549 | − | 0.637381i | \(-0.219982\pi\) | ||||
0.770549 | + | 0.637381i | \(0.219982\pi\) | |||||||
\(500\) | 3.20952e29i | 0.657309i | ||||||||
\(501\) | 4.79148e29 | − | 5.04879e29i | 0.959964 | − | 1.01152i | ||||
\(502\) | −3.28337e29 | −0.643544 | ||||||||
\(503\) | − | 6.61522e29i | − | 1.26852i | −0.773121 | − | 0.634258i | \(-0.781306\pi\) | ||
0.773121 | − | 0.634258i | \(-0.218694\pi\) | |||||||
\(504\) | 2.31273e29 | − | 1.21032e28i | 0.433899 | − | 0.0227072i | ||||
\(505\) | −9.94318e29 | −1.82524 | ||||||||
\(506\) | − | 1.35508e27i | − | 0.00243394i | ||||||
\(507\) | −1.02097e30 | − | 9.68941e29i | −1.79443 | − | 1.70298i | ||||
\(508\) | 5.33613e29 | 0.917753 | ||||||||
\(509\) | 1.68144e29i | 0.283000i | 0.989938 | + | 0.141500i | \(0.0451925\pi\) | ||||
−0.989938 | + | 0.141500i | \(0.954807\pi\) | |||||||
\(510\) | 3.89992e29 | − | 4.10936e29i | 0.642369 | − | 0.676865i | ||||
\(511\) | −2.34577e28 | −0.0378142 | ||||||||
\(512\) | 2.80114e28i | 0.0441942i | ||||||||
\(513\) | −3.35503e29 | + | 3.92735e29i | −0.518091 | + | 0.606469i | ||||
\(514\) | 8.18318e28 | 0.123688 | ||||||||
\(515\) | 1.45357e30i | 2.15059i | ||||||||
\(516\) | −4.20970e29 | − | 3.99516e29i | −0.609684 | − | 0.578611i | ||||
\(517\) | −6.02584e25 | −8.54323e−5 | ||||||||
\(518\) | − | 4.34718e29i | − | 0.603366i | ||||||
\(519\) | −2.59265e29 | + | 2.73188e29i | −0.352292 | + | 0.371210i | ||||
\(520\) | −8.26990e29 | −1.10018 | ||||||||
\(521\) | − | 3.58985e29i | − | 0.467586i | −0.972286 | − | 0.233793i | \(-0.924886\pi\) | ||
0.972286 | − | 0.233793i | \(-0.0751138\pi\) | |||||||
\(522\) | −5.93856e26 | − | 1.13476e28i | −0.000757366 | − | 0.0144721i | ||||
\(523\) | −1.39459e29 | −0.174152 | −0.0870759 | − | 0.996202i | \(-0.527752\pi\) | ||||
−0.0870759 | + | 0.996202i | \(0.527752\pi\) | |||||||
\(524\) | 1.59145e28i | 0.0194603i | ||||||||
\(525\) | 1.33061e30 | + | 1.26279e30i | 1.59330 | + | 1.51210i | ||||
\(526\) | 8.82159e29 | 1.03444 | ||||||||
\(527\) | − | 2.39557e29i | − | 0.275101i | ||||||
\(528\) | −3.35525e27 | + | 3.53543e27i | −0.00377356 | + | 0.00397620i | ||||
\(529\) | 8.85475e29 | 0.975358 | ||||||||
\(530\) | − | 7.34644e29i | − | 0.792579i | ||||||
\(531\) | −5.42492e28 | + | 2.83902e27i | −0.0573263 | + | 0.00300006i | ||||
\(532\) | 4.73511e29 | 0.490120 | ||||||||
\(533\) | 2.37480e30i | 2.40784i | ||||||||
\(534\) | 9.30497e29 | + | 8.83075e29i | 0.924190 | + | 0.877089i | ||||
\(535\) | −1.84085e30 | −1.79113 | ||||||||
\(536\) | 1.27468e29i | 0.121503i | ||||||||
\(537\) | 1.33819e30 | − | 1.41005e30i | 1.24968 | − | 1.31679i | ||||
\(538\) | 8.24286e29 | 0.754176 | ||||||||
\(539\) | − | 1.24813e28i | − | 0.0111888i | ||||||
\(540\) | −7.22613e29 | − | 6.17309e29i | −0.634708 | − | 0.542215i | ||||
\(541\) | −1.08758e30 | −0.936030 | −0.468015 | − | 0.883720i | \(-0.655031\pi\) | ||||
−0.468015 | + | 0.883720i | \(0.655031\pi\) | |||||||
\(542\) | 5.68141e29i | 0.479141i | ||||||||
\(543\) | 4.24087e29 | + | 4.02473e29i | 0.350474 | + | 0.332613i | ||||
\(544\) | 1.72537e29 | 0.139732 | ||||||||
\(545\) | − | 2.56214e30i | − | 2.03349i | ||||||
\(546\) | −1.43340e30 | + | 1.51038e30i | −1.11494 | + | 1.17481i | ||||
\(547\) | −1.88013e29 | −0.143327 | −0.0716635 | − | 0.997429i | \(-0.522831\pi\) | ||||
−0.0716635 | + | 0.997429i | \(0.522831\pi\) | |||||||
\(548\) | − | 7.04099e29i | − | 0.526075i | ||||||
\(549\) | 2.35936e28 | + | 4.50836e29i | 0.0172782 | + | 0.330159i | ||||
\(550\) | −3.86082e28 | −0.0277134 | ||||||||
\(551\) | − | 2.32333e28i | − | 0.0163472i | ||||||
\(552\) | 5.83679e28 | + | 5.53932e28i | 0.0402573 | + | 0.0382056i | ||||
\(553\) | 4.54865e29 | 0.307543 | ||||||||
\(554\) | − | 6.78057e29i | − | 0.449427i | ||||||
\(555\) | −1.22806e30 | + | 1.29401e30i | −0.797991 | + | 0.840844i | ||||
\(556\) | 1.82485e28 | 0.0116253 | ||||||||
\(557\) | − | 2.83210e30i | − | 1.76889i | −0.466640 | − | 0.884447i | \(-0.654536\pi\) | ||
0.466640 | − | 0.884447i | \(-0.345464\pi\) | |||||||
\(558\) | −4.01318e29 | + | 2.10022e28i | −0.245761 | + | 0.0128614i | ||||
\(559\) | 5.21826e30 | 3.13326 | ||||||||
\(560\) | 8.71236e29i | 0.512941i | ||||||||
\(561\) | 2.17766e28 | + | 2.06668e28i | 0.0125718 | + | 0.0119311i | ||||
\(562\) | −1.71281e30 | −0.969636 | ||||||||
\(563\) | − | 1.38770e30i | − | 0.770379i | −0.922837 | − | 0.385190i | \(-0.874136\pi\) | ||
0.922837 | − | 0.385190i | \(-0.125864\pi\) | |||||||
\(564\) | 2.46326e27 | − | 2.59554e27i | 0.00134103 | − | 0.00141305i | ||||
\(565\) | −2.08656e30 | −1.11403 | ||||||||
\(566\) | 7.07977e29i | 0.370714i | ||||||||
\(567\) | −2.37992e30 | + | 2.49781e29i | −1.22222 | + | 0.128276i | ||||
\(568\) | −6.53622e29 | −0.329227 | ||||||||
\(569\) | 1.15851e30i | 0.572354i | 0.958177 | + | 0.286177i | \(0.0923845\pi\) | ||||
−0.958177 | + | 0.286177i | \(0.907616\pi\) | |||||||
\(570\) | −1.40948e30 | − | 1.33765e30i | −0.683025 | − | 0.648215i | ||||
\(571\) | −2.95736e30 | −1.40575 | −0.702873 | − | 0.711315i | \(-0.748100\pi\) | ||||
−0.702873 | + | 0.711315i | \(0.748100\pi\) | |||||||
\(572\) | − | 4.38244e28i | − | 0.0204343i | ||||||
\(573\) | 8.39333e29 | − | 8.84406e29i | 0.383914 | − | 0.404530i | ||||
\(574\) | 2.50185e30 | 1.12262 | ||||||||
\(575\) | 6.37400e29i | 0.280586i | ||||||||
\(576\) | −1.51265e28 | − | 2.89044e29i | −0.00653268 | − | 0.124829i | ||||
\(577\) | −1.38283e30 | −0.585914 | −0.292957 | − | 0.956126i | \(-0.594639\pi\) | ||||
−0.292957 | + | 0.956126i | \(0.594639\pi\) | |||||||
\(578\) | 6.38200e29i | 0.265308i | ||||||||
\(579\) | 1.31134e30 | + | 1.24451e30i | 0.534873 | + | 0.507613i | ||||
\(580\) | 4.27482e28 | 0.0171084 | ||||||||
\(581\) | − | 1.51423e30i | − | 0.594641i | ||||||
\(582\) | −7.90757e29 | + | 8.33221e29i | −0.304712 | + | 0.321076i | ||||
\(583\) | 3.89308e28 | 0.0147211 | ||||||||
\(584\) | 2.93173e28i | 0.0108788i | ||||||||
\(585\) | 8.53353e30 | − | 4.46585e29i | 3.10752 | − | 0.162626i | ||||
\(586\) | 1.08190e30 | 0.386646 | ||||||||
\(587\) | − | 3.03148e30i | − | 1.06325i | −0.846980 | − | 0.531625i | \(-0.821581\pi\) | ||
0.846980 | − | 0.531625i | \(-0.178419\pi\) | |||||||
\(588\) | 5.37611e29 | + | 5.10212e29i | 0.185062 | + | 0.175631i | ||||
\(589\) | −8.21665e29 | −0.277604 | ||||||||
\(590\) | − | 2.04364e29i | − | 0.0677693i | ||||||
\(591\) | −2.23185e30 | + | 2.35170e30i | −0.726445 | + | 0.765456i | ||||
\(592\) | −5.43309e29 | −0.173583 | ||||||||
\(593\) | 5.60572e30i | 1.75804i | 0.476782 | + | 0.879021i | \(0.341803\pi\) | ||||
−0.476782 | + | 0.879021i | \(0.658197\pi\) | |||||||
\(594\) | 3.27129e28 | − | 3.82932e28i | 0.0100709 | − | 0.0117888i | ||||
\(595\) | 5.36641e30 | 1.62180 | ||||||||
\(596\) | 3.08289e30i | 0.914639i | ||||||||
\(597\) | −3.40250e30 | − | 3.22909e30i | −0.991015 | − | 0.940508i | ||||
\(598\) | −7.23517e29 | −0.206888 | ||||||||
\(599\) | 3.48458e30i | 0.978263i | 0.872210 | + | 0.489131i | \(0.162686\pi\) | ||||
−0.872210 | + | 0.489131i | \(0.837314\pi\) | |||||||
\(600\) | 1.57823e30 | − | 1.66299e30i | 0.435019 | − | 0.458380i | ||||
\(601\) | −7.67603e29 | −0.207739 | −0.103869 | − | 0.994591i | \(-0.533122\pi\) | ||||
−0.103869 | + | 0.994591i | \(0.533122\pi\) | |||||||
\(602\) | − | 5.49745e30i | − | 1.46083i | ||||||
\(603\) | −6.88342e28 | − | 1.31531e30i | −0.0179603 | − | 0.343193i | ||||
\(604\) | 2.80653e30 | 0.719057 | ||||||||
\(605\) | 6.63285e30i | 1.66875i | ||||||||
\(606\) | 2.26961e30 | + | 2.15394e30i | 0.560727 | + | 0.532150i | ||||
\(607\) | −1.21587e30 | −0.294993 | −0.147497 | − | 0.989063i | \(-0.547122\pi\) | ||||
−0.147497 | + | 0.989063i | \(0.547122\pi\) | |||||||
\(608\) | − | 5.91792e29i | − | 0.141003i | ||||||
\(609\) | 7.40945e28 | − | 7.80735e28i | 0.0173379 | − | 0.0182689i | ||||
\(610\) | −1.69836e30 | −0.390303 | ||||||||
\(611\) | 3.21737e28i | 0.00726186i | ||||||||
\(612\) | −1.78038e30 | + | 9.31723e28i | −0.394681 | + | 0.0206548i | ||||
\(613\) | −5.96084e30 | −1.29790 | −0.648951 | − | 0.760830i | \(-0.724792\pi\) | ||||
−0.648951 | + | 0.760830i | \(0.724792\pi\) | |||||||
\(614\) | 2.09567e30i | 0.448199i | ||||||||
\(615\) | −7.44718e30 | − | 7.06764e30i | −1.56446 | − | 1.48473i | ||||
\(616\) | −4.61692e28 | −0.00952718 | ||||||||
\(617\) | − | 7.40435e30i | − | 1.50090i | −0.660930 | − | 0.750448i | \(-0.729838\pi\) | ||
0.660930 | − | 0.750448i | \(-0.270162\pi\) | |||||||
\(618\) | 3.14879e30 | − | 3.31789e30i | 0.627005 | − | 0.660676i | ||||
\(619\) | −1.30025e30 | −0.254349 | −0.127174 | − | 0.991880i | \(-0.540591\pi\) | ||||
−0.127174 | + | 0.991880i | \(0.540591\pi\) | |||||||
\(620\) | − | 1.51182e30i | − | 0.290531i | ||||||
\(621\) | −6.32199e29 | − | 5.40072e29i | −0.119357 | − | 0.101963i | ||||
\(622\) | −1.90740e30 | −0.353792 | ||||||||
\(623\) | 1.21514e31i | 2.21440i | ||||||||
\(624\) | 1.88767e30 | + | 1.79146e30i | 0.337983 | + | 0.320758i | ||||
\(625\) | 2.31590e30 | 0.407418 | ||||||||
\(626\) | − | 1.10795e30i | − | 0.191515i | ||||||
\(627\) | 7.08857e28 | − | 7.46924e28i | 0.0120397 | − | 0.0126863i | ||||
\(628\) | −3.30506e29 | −0.0551599 | ||||||||
\(629\) | 3.34653e30i | 0.548830i | ||||||||
\(630\) | −4.70479e29 | − | 8.99011e30i | −0.0758218 | − | 1.44883i | ||||
\(631\) | 8.75982e30 | 1.38731 | 0.693653 | − | 0.720309i | \(-0.256000\pi\) | ||||
0.693653 | + | 0.720309i | \(0.256000\pi\) | |||||||
\(632\) | − | 5.68488e29i | − | 0.0884776i | ||||||
\(633\) | 1.28077e30 | + | 1.21550e30i | 0.195898 | + | 0.185914i | ||||
\(634\) | −4.80783e30 | −0.722715 | ||||||||
\(635\) | − | 2.07428e31i | − | 3.06448i | ||||||
\(636\) | −1.59142e30 | + | 1.67688e30i | −0.231077 | + | 0.243486i | ||||
\(637\) | −6.66412e30 | −0.951062 | ||||||||
\(638\) | 2.26534e27i | 0.000317765i | ||||||||
\(639\) | 6.74459e30 | − | 3.52965e29i | 0.929921 | − | 0.0486655i | ||||
\(640\) | 1.08887e30 | 0.147569 | ||||||||
\(641\) | 1.38460e30i | 0.184453i | 0.995738 | + | 0.0922263i | \(0.0293983\pi\) | ||||
−0.995738 | + | 0.0922263i | \(0.970602\pi\) | |||||||
\(642\) | 4.20188e30 | + | 3.98773e30i | 0.550247 | + | 0.522204i | ||||
\(643\) | 1.46506e31 | 1.88596 | 0.942982 | − | 0.332844i | \(-0.108008\pi\) | ||||
0.942982 | + | 0.332844i | \(0.108008\pi\) | |||||||
\(644\) | 7.62227e29i | 0.0964583i | ||||||||
\(645\) | −1.55301e31 | + | 1.63641e31i | −1.93204 | + | 2.03580i | ||||
\(646\) | −3.64516e30 | −0.445820 | ||||||||
\(647\) | − | 6.52633e30i | − | 0.784733i | −0.919809 | − | 0.392367i | \(-0.871656\pi\) | ||
0.919809 | − | 0.392367i | \(-0.128344\pi\) | |||||||
\(648\) | 3.12175e29 | + | 2.97441e30i | 0.0369039 | + | 0.351622i | ||||
\(649\) | 1.08298e28 | 0.00125872 | ||||||||
\(650\) | 2.06141e31i | 2.35568i | ||||||||
\(651\) | −2.76113e30 | − | 2.62041e30i | −0.310239 | − | 0.294428i | ||||
\(652\) | −1.12384e30 | −0.124160 | ||||||||
\(653\) | 2.21687e30i | 0.240821i | 0.992724 | + | 0.120411i | \(0.0384211\pi\) | ||||
−0.992724 | + | 0.120411i | \(0.961579\pi\) | |||||||
\(654\) | −5.55023e30 | + | 5.84828e30i | −0.592865 | + | 0.624702i | ||||
\(655\) | 6.18634e29 | 0.0649800 | ||||||||
\(656\) | − | 3.12681e30i | − | 0.322967i | ||||||
\(657\) | −1.58317e28 | − | 3.02519e29i | −0.00160809 | − | 0.0307280i | ||||
\(658\) | 3.38951e28 | 0.00338573 | ||||||||
\(659\) | 1.13807e31i | 1.11797i | 0.829179 | + | 0.558983i | \(0.188808\pi\) | ||||
−0.829179 | + | 0.558983i | \(0.811192\pi\) | |||||||
\(660\) | 1.37430e29 | + | 1.30426e29i | 0.0132770 | + | 0.0126003i | ||||
\(661\) | 1.34060e31 | 1.27375 | 0.636873 | − | 0.770969i | \(-0.280227\pi\) | ||||
0.636873 | + | 0.770969i | \(0.280227\pi\) | |||||||
\(662\) | − | 4.30661e30i | − | 0.402437i | ||||||
\(663\) | 1.10346e31 | − | 1.16272e31i | 1.01416 | − | 1.06862i | ||||
\(664\) | −1.89248e30 | −0.171073 | ||||||||
\(665\) | − | 1.84065e31i | − | 1.63656i | ||||||
\(666\) | 5.60629e30 | − | 2.93394e29i | 0.490297 | − | 0.0256587i | ||||
\(667\) | 3.73995e28 | 0.00321723 | ||||||||
\(668\) | − | 8.24018e30i | − | 0.697261i | ||||||
\(669\) | 1.21946e31 | + | 1.15731e31i | 1.01504 | + | 0.963305i | ||||
\(670\) | 4.95496e30 | 0.405712 | ||||||||
\(671\) | − | 9.00008e28i | − | 0.00724934i | ||||||
\(672\) | 1.88731e30 | − | 1.98866e30i | 0.149548 | − | 0.157579i | ||||
\(673\) | −3.17018e29 | −0.0247126 | −0.0123563 | − | 0.999924i | \(-0.503933\pi\) | ||||
−0.0123563 | + | 0.999924i | \(0.503933\pi\) | |||||||
\(674\) | − | 9.73126e30i | − | 0.746295i | ||||||
\(675\) | −1.53874e31 | + | 1.80123e31i | −1.16098 | + | 1.35903i | ||||
\(676\) | −1.66634e31 | −1.23695 | ||||||||
\(677\) | 1.91763e31i | 1.40052i | 0.713887 | + | 0.700261i | \(0.246933\pi\) | ||||
−0.713887 | + | 0.700261i | \(0.753067\pi\) | |||||||
\(678\) | 4.76273e30 | + | 4.52000e30i | 0.342239 | + | 0.324797i | ||||
\(679\) | −1.08810e31 | −0.769313 | ||||||||
\(680\) | − | 6.70692e30i | − | 0.466579i | ||||||
\(681\) | 1.27464e31 | − | 1.34309e31i | 0.872507 | − | 0.919361i | ||||
\(682\) | 8.01155e28 | 0.00539621 | ||||||||
\(683\) | − | 1.56555e31i | − | 1.03762i | −0.854889 | − | 0.518812i | \(-0.826375\pi\) | ||
0.854889 | − | 0.518812i | \(-0.173625\pi\) | |||||||
\(684\) | 3.19575e29 | + | 6.10658e30i | 0.0208428 | + | 0.398273i | ||||
\(685\) | −2.73699e31 | −1.75662 | ||||||||
\(686\) | − | 6.73804e30i | − | 0.425567i | ||||||
\(687\) | −1.06280e31 | − | 1.00863e31i | −0.660581 | − | 0.626915i | ||||
\(688\) | −6.87069e30 | −0.420269 | ||||||||
\(689\) | − | 2.07863e31i | − | 1.25131i | ||||||
\(690\) | 2.15326e30 | − | 2.26890e30i | 0.127572 | − | 0.134423i | ||||
\(691\) | 1.45653e30 | 0.0849301 | 0.0424651 | − | 0.999098i | \(-0.486479\pi\) | ||||
0.0424651 | + | 0.999098i | \(0.486479\pi\) | |||||||
\(692\) | 4.45872e30i | 0.255884i | ||||||||
\(693\) | 4.76410e29 | − | 2.49320e28i | 0.0269101 | − | 0.00140829i | ||||
\(694\) | 1.22416e31 | 0.680586 | ||||||||
\(695\) | − | 7.09363e29i | − | 0.0388182i | ||||||
\(696\) | −9.75759e28 | − | 9.26030e28i | −0.00525583 | − | 0.00498797i | ||||
\(697\) | −1.92597e31 | −1.02115 | ||||||||
\(698\) | 8.81014e30i | 0.459805i | ||||||||
\(699\) | −8.72894e30 | + | 9.19769e30i | −0.448448 | + | 0.472531i | ||||
\(700\) | 2.17170e31 | 1.09830 | ||||||||
\(701\) | 1.44651e31i | 0.720150i | 0.932923 | + | 0.360075i | \(0.117249\pi\) | ||||
−0.932923 | + | 0.360075i | \(0.882751\pi\) | |||||||
\(702\) | −2.04459e31 | − | 1.74664e31i | −1.00207 | − | 0.856041i | ||||
\(703\) | 1.14784e31 | 0.553826 | ||||||||
\(704\) | 5.77020e28i | 0.00274089i | ||||||||
\(705\) | −1.00894e29 | − | 9.57524e28i | −0.00471832 | − | 0.00447785i | ||||
\(706\) | 2.48122e31 | 1.14239 | ||||||||
\(707\) | 2.96388e31i | 1.34353i | ||||||||
\(708\) | −4.42704e29 | + | 4.66477e29i | −0.0197582 | + | 0.0208192i | ||||
\(709\) | 6.60398e30 | 0.290200 | 0.145100 | − | 0.989417i | \(-0.453650\pi\) | ||||
0.145100 | + | 0.989417i | \(0.453650\pi\) | |||||||
\(710\) | 2.54078e31i | 1.09932i | ||||||||
\(711\) | 3.06991e29 | + | 5.86611e30i | 0.0130786 | + | 0.249911i | ||||
\(712\) | 1.51867e31 | 0.637066 | ||||||||
\(713\) | − | 1.32266e30i | − | 0.0546341i | ||||||
\(714\) | −1.22492e31 | − | 1.16250e31i | −0.498229 | − | 0.472837i | ||||
\(715\) | −1.70356e30 | −0.0682323 | ||||||||
\(716\) | − | 2.30135e31i | − | 0.907696i | ||||||
\(717\) | 1.34580e31 | − | 1.41807e31i | 0.522720 | − | 0.550790i | ||||
\(718\) | −1.92172e31 | −0.735056 | ||||||||
\(719\) | 8.90367e30i | 0.335391i | 0.985839 | + | 0.167695i | \(0.0536325\pi\) | ||||
−0.985839 | + | 0.167695i | \(0.946368\pi\) | |||||||
\(720\) | −1.12358e31 | + | 5.88002e29i | −0.416818 | + | 0.0218133i | ||||
\(721\) | 4.33283e31 | 1.58301 | ||||||||
\(722\) | − | 7.14874e30i | − | 0.257229i | ||||||
\(723\) | 2.78298e31 | + | 2.64115e31i | 0.986256 | + | 0.935992i | ||||
\(724\) | 6.92156e30 | 0.241590 | ||||||||
\(725\) | − | 1.06557e30i | − | 0.0366322i | ||||||
\(726\) | 1.43684e31 | − | 1.51400e31i | 0.486525 | − | 0.512652i | ||||
\(727\) | −1.29208e31 | −0.430933 | −0.215467 | − | 0.976511i | \(-0.569127\pi\) | ||||
−0.215467 | + | 0.976511i | \(0.569127\pi\) | |||||||
\(728\) | 2.46511e31i | 0.809824i | ||||||||
\(729\) | −4.82749e30 | − | 3.05238e31i | −0.156213 | − | 0.987723i | ||||
\(730\) | 1.13963e30 | 0.0363256 | ||||||||
\(731\) | 4.23203e31i | 1.32879i | ||||||||
\(732\) | 3.87664e30 | + | 3.67907e30i | 0.119904 | + | 0.113793i | ||||
\(733\) | −4.83812e31 | −1.47412 | −0.737060 | − | 0.675827i | \(-0.763787\pi\) | ||||
−0.737060 | + | 0.675827i | \(0.763787\pi\) | |||||||
\(734\) | − | 5.88126e30i | − | 0.176528i | ||||||
\(735\) | 1.98331e31 | − | 2.08982e31i | 0.586449 | − | 0.617942i | ||||
\(736\) | 9.52628e29 | 0.0277503 | ||||||||
\(737\) | 2.62577e29i | 0.00753553i | ||||||||
\(738\) | 1.68852e30 | + | 3.22649e31i | 0.0477403 | + | 0.912242i | ||||
\(739\) | −4.94638e31 | −1.37784 | −0.688919 | − | 0.724838i | \(-0.741915\pi\) | ||||
−0.688919 | + | 0.724838i | \(0.741915\pi\) | |||||||
\(740\) | 2.11197e31i | 0.579614i | ||||||||
\(741\) | −3.98804e31 | − | 3.78480e31i | −1.07835 | − | 1.02339i | ||||
\(742\) | −2.18984e31 | −0.583404 | ||||||||
\(743\) | − | 1.54838e31i | − | 0.406445i | −0.979133 | − | 0.203222i | \(-0.934859\pi\) | ||
0.979133 | − | 0.203222i | \(-0.0651414\pi\) | |||||||
\(744\) | −3.27498e30 | + | 3.45085e30i | −0.0847044 | + | 0.0892531i | ||||
\(745\) | 1.19839e32 | 3.05408 | ||||||||
\(746\) | 4.07387e30i | 0.102301i | ||||||||
\(747\) | 1.95281e31 | − | 1.02196e30i | 0.483207 | − | 0.0252877i | ||||
\(748\) | 3.55418e29 | 0.00866606 | ||||||||
\(749\) | 5.48723e31i | 1.31842i | ||||||||
\(750\) | −2.84777e31 | − | 2.70264e31i | −0.674266 | − | 0.639903i | ||||
\(751\) | −3.61372e31 | −0.843171 | −0.421586 | − | 0.906789i | \(-0.638526\pi\) | ||||
−0.421586 | + | 0.906789i | \(0.638526\pi\) | |||||||
\(752\) | − | 4.23620e28i | − | 0.000974047i | ||||||
\(753\) | 2.76482e31 | − | 2.91330e31i | 0.626502 | − | 0.660146i | ||||
\(754\) | 1.20953e30 | 0.0270105 | ||||||||
\(755\) | − | 1.09096e32i | − | 2.40101i | ||||||
\(756\) | −1.84009e31 | + | 2.15398e31i | −0.399116 | + | 0.467199i | ||||
\(757\) | −4.28262e31 | −0.915493 | −0.457746 | − | 0.889083i | \(-0.651343\pi\) | ||||
−0.457746 | + | 0.889083i | \(0.651343\pi\) | |||||||
\(758\) | − | 2.67507e31i | − | 0.563605i | ||||||
\(759\) | 1.20235e29 | + | 1.14107e29i | 0.00249673 | + | 0.00236948i | ||||
\(760\) | −2.30043e31 | −0.470825 | ||||||||
\(761\) | − | 5.59183e31i | − | 1.12804i | −0.825763 | − | 0.564018i | \(-0.809255\pi\) | ||
0.825763 | − | 0.564018i | \(-0.190745\pi\) | |||||||
\(762\) | −4.49340e31 | + | 4.73470e31i | −0.893450 | + | 0.941429i | ||||
\(763\) | −7.63728e31 | −1.49682 | ||||||||
\(764\) | − | 1.44345e31i | − | 0.278852i | ||||||
\(765\) | 3.62182e30 | + | 6.92073e31i | 0.0689686 | + | 1.31788i | ||||
\(766\) | −1.40663e30 | −0.0264036 | ||||||||
\(767\) | − | 5.78236e30i | − | 0.106993i | ||||||
\(768\) | −2.48542e30 | − | 2.35875e30i | −0.0453343 | − | 0.0430239i | ||||
\(769\) | 9.27501e31 | 1.66773 | 0.833863 | − | 0.551972i | \(-0.186125\pi\) | ||||
0.833863 | + | 0.551972i | \(0.186125\pi\) | |||||||
\(770\) | 1.79470e30i | 0.0318123i | ||||||||
\(771\) | −6.89081e30 | + | 7.26086e30i | −0.120413 | + | 0.126879i | ||||
\(772\) | 2.14025e31 | 0.368700 | ||||||||
\(773\) | − | 3.19744e31i | − | 0.543035i | −0.962434 | − | 0.271517i | \(-0.912475\pi\) | ||
0.962434 | − | 0.271517i | \(-0.0875255\pi\) | |||||||
\(774\) | 7.08973e31 | − | 3.71026e30i | 1.18708 | − | 0.0621233i | ||||
\(775\) | −3.76846e31 | −0.622079 | ||||||||
\(776\) | 1.35991e31i | 0.221325i | ||||||||
\(777\) | 3.85721e31 | + | 3.66063e31i | 0.618931 | + | 0.587388i | ||||
\(778\) | 2.45238e31 | 0.387982 | ||||||||
\(779\) | 6.60595e31i | 1.03044i | ||||||||
\(780\) | 6.96383e31 | − | 7.33780e31i | 1.07104 | − | 1.12856i | ||||
\(781\) | −1.34643e30 | −0.0204184 | ||||||||
\(782\) | − | 5.86775e30i | − | 0.0877399i | ||||||
\(783\) | 1.05687e30 | + | 9.02859e29i | 0.0155827 | + | 0.0133119i | ||||
\(784\) | 8.77440e30 | 0.127568 | ||||||||
\(785\) | 1.28475e31i | 0.184185i | ||||||||
\(786\) | −1.41208e30 | − | 1.34011e30i | −0.0199623 | − | 0.0189450i | ||||
\(787\) | 1.12073e32 | 1.56235 | 0.781173 | − | 0.624315i | \(-0.214622\pi\) | ||||
0.781173 | + | 0.624315i | \(0.214622\pi\) | |||||||
\(788\) | 3.83824e31i | 0.527647i | ||||||||
\(789\) | −7.42839e31 | + | 7.82731e31i | −1.00704 | + | 1.06112i | ||||
\(790\) | −2.20984e31 | −0.295436 | ||||||||
\(791\) | 6.21966e31i | 0.820021i | ||||||||
\(792\) | −3.11598e28 | − | 5.95415e29i | −0.000405152 | − | 0.00774182i | ||||
\(793\) | −4.80541e31 | −0.616205 | ||||||||
\(794\) | − | 3.75624e31i | − | 0.475037i | ||||||
\(795\) | 6.51842e31 | + | 6.18622e31i | 0.813026 | + | 0.771590i | ||||
\(796\) | −5.55325e31 | −0.683130 | ||||||||
\(797\) | − | 3.03484e31i | − | 0.368209i | −0.982907 | − | 0.184105i | \(-0.941061\pi\) | ||
0.982907 | − | 0.184105i | \(-0.0589385\pi\) | |||||||
\(798\) | −3.98729e31 | + | 4.20142e31i | −0.477141 | + | 0.502764i | ||||
\(799\) | −2.60930e29 | −0.00307971 | ||||||||
\(800\) | − | 2.71418e31i | − | 0.315972i | ||||||
\(801\) | −1.56709e32 | + | 8.20103e30i | −1.79943 | + | 0.0941696i | ||||
\(802\) | 5.10115e31 | 0.577763 | ||||||||
\(803\) | 6.03921e28i | 0.000674698i | ||||||||
\(804\) | −1.13101e31 | − | 1.07337e31i | −0.124638 | − | 0.118285i | ||||
\(805\) | 2.96295e31 | 0.322085 | ||||||||
\(806\) | − | 4.27760e31i | − | 0.458685i | ||||||
\(807\) | −6.94106e31 | + | 7.31381e31i | −0.734204 | + | 0.773632i | ||||
\(808\) | 3.70425e31 | 0.386522 | ||||||||
\(809\) | − | 1.14120e32i | − | 1.17470i | −0.809333 | − | 0.587349i | \(-0.800171\pi\) | ||
0.809333 | − | 0.587349i | \(-0.199829\pi\) | |||||||
\(810\) | 1.15622e32 | − | 1.21350e31i | 1.17410 | − | 0.123226i | ||||
\(811\) | 3.53046e31 | 0.353673 | 0.176836 | − | 0.984240i | \(-0.443414\pi\) | ||||
0.176836 | + | 0.984240i | \(0.443414\pi\) | |||||||
\(812\) | − | 1.27425e30i | − | 0.0125932i | ||||||
\(813\) | −5.04106e31 | − | 4.78414e31i | −0.491502 | − | 0.466453i | ||||
\(814\) | −1.11919e30 | −0.0107655 | ||||||||
\(815\) | 4.36864e31i | 0.414584i | ||||||||
\(816\) | −1.45288e31 | + | 1.53091e31i | −0.136031 | + | 0.143336i | ||||
\(817\) | 1.45156e32 | 1.34089 | ||||||||
\(818\) | − | 2.72978e30i | − | 0.0248795i | ||||||
\(819\) | −1.33119e31 | − | 2.54369e32i | −0.119706 | − | 2.28740i | ||||
\(820\) | −1.21546e32 | −1.07842 | ||||||||
\(821\) | − | 1.09798e32i | − | 0.961211i | −0.876937 | − | 0.480606i | \(-0.840417\pi\) | ||
0.876937 | − | 0.480606i | \(-0.159583\pi\) | |||||||
\(822\) | 6.24740e31 | + | 5.92900e31i | 0.539646 | + | 0.512144i | ||||
\(823\) | 2.58120e31 | 0.220001 | 0.110000 | − | 0.993932i | \(-0.464915\pi\) | ||||
0.110000 | + | 0.993932i | \(0.464915\pi\) | |||||||
\(824\) | − | 5.41516e31i | − | 0.455420i | ||||||
\(825\) | 3.25108e30 | − | 3.42567e30i | 0.0269795 | − | 0.0284284i | ||||
\(826\) | −6.09173e30 | −0.0498839 | ||||||||
\(827\) | 1.47626e32i | 1.19289i | 0.802653 | + | 0.596447i | \(0.203421\pi\) | ||||
−0.802653 | + | 0.596447i | \(0.796579\pi\) | |||||||
\(828\) | −9.82997e30 | + | 5.14431e29i | −0.0783824 | + | 0.00410198i | ||||
\(829\) | −1.70341e32 | −1.34035 | −0.670177 | − | 0.742201i | \(-0.733782\pi\) | ||||
−0.670177 | + | 0.742201i | \(0.733782\pi\) | |||||||
\(830\) | 7.35650e31i | 0.571232i | ||||||||
\(831\) | 6.01633e31 | + | 5.70971e31i | 0.461021 | + | 0.437525i | ||||
\(832\) | 3.08088e31 | 0.232980 | ||||||||
\(833\) | − | 5.40463e31i | − | 0.403339i | ||||||
\(834\) | −1.53666e30 | + | 1.61918e30i | −0.0113175 | + | 0.0119252i | ||||
\(835\) | −3.20315e32 | −2.32823 | ||||||||
\(836\) | − | 1.21906e30i | − | 0.00874493i | ||||||
\(837\) | 3.19303e31 | − | 3.73771e31i | 0.226060 | − | 0.264622i | ||||
\(838\) | −1.63191e32 | −1.14028 | ||||||||
\(839\) | − | 1.84528e32i | − | 1.27256i | −0.771456 | − | 0.636282i | \(-0.780471\pi\) | ||
0.771456 | − | 0.636282i | \(-0.219529\pi\) | |||||||
\(840\) | −7.73039e31 | − | 7.33642e31i | −0.526174 | − | 0.499358i | ||||
\(841\) | 1.48790e32 | 0.999580 | ||||||||
\(842\) | − | 2.36904e30i | − | 0.0157087i | ||||||
\(843\) | 1.44230e32 | − | 1.51976e32i | 0.943958 | − | 0.994650i | ||||
\(844\) | 2.09036e31 | 0.135037 | ||||||||
\(845\) | 6.47746e32i | 4.13029i | ||||||||
\(846\) | 2.28760e28 | + | 4.37124e29i | 0.000143981 | + | 0.00275126i | ||||
\(847\) | 1.97713e32 | 1.22834 | ||||||||
\(848\) | 2.73685e31i | 0.167841i | ||||||||
\(849\) | −6.28181e31 | − | 5.96166e31i | −0.380277 | − | 0.360897i | ||||
\(850\) | −1.67181e32 | −0.999030 | ||||||||
\(851\) | 1.84772e31i | 0.108996i | ||||||||
\(852\) | 5.50396e31 | − | 5.79953e31i | 0.320508 | − | 0.337720i | ||||
\(853\) | −2.18762e31 | −0.125757 | −0.0628784 | − | 0.998021i | \(-0.520028\pi\) | ||||
−0.0628784 | + | 0.998021i | \(0.520028\pi\) | |||||||
\(854\) | 5.06251e31i | 0.287296i | ||||||||
\(855\) | 2.37377e32 | − | 1.24226e31i | 1.32988 | − | 0.0695963i | ||||
\(856\) | 6.85792e31 | 0.379298 | ||||||||
\(857\) | − | 2.06327e31i | − | 0.112660i | −0.998412 | − | 0.0563298i | \(-0.982060\pi\) | ||
0.998412 | − | 0.0563298i | \(-0.0179398\pi\) | |||||||
\(858\) | 3.88850e30 | + | 3.69032e30i | 0.0209615 | + | 0.0198932i | ||||
\(859\) | 1.35417e32 | 0.720688 | 0.360344 | − | 0.932820i | \(-0.382659\pi\) | ||||
0.360344 | + | 0.932820i | \(0.382659\pi\) | |||||||
\(860\) | 2.67080e32i | 1.40332i | ||||||||
\(861\) | −2.10674e32 | + | 2.21987e32i | −1.09289 | + | 1.15158i | ||||
\(862\) | 1.81452e32 | 0.929355 | ||||||||
\(863\) | − | 3.40137e32i | − | 1.72003i | −0.510270 | − | 0.860014i | \(-0.670454\pi\) | ||
0.510270 | − | 0.860014i | \(-0.329546\pi\) | |||||||
\(864\) | 2.69203e31 | + | 2.29973e31i | 0.134409 | + | 0.114822i | ||||
\(865\) | 1.73321e32 | 0.854424 | ||||||||
\(866\) | 4.33524e31i | 0.211016i | ||||||||
\(867\) | −5.66268e31 | − | 5.37409e31i | −0.272152 | − | 0.258282i | ||||
\(868\) | −4.50647e31 | −0.213855 | ||||||||
\(869\) | − | 1.17106e30i | − | 0.00548732i | ||||||
\(870\) | −3.59969e30 | + | 3.79300e30i | −0.0166553 | + | 0.0175498i | ||||
\(871\) | 1.40197e32 | 0.640531 | ||||||||
\(872\) | 9.54504e31i | 0.430622i | ||||||||
\(873\) | −7.34368e30 | − | 1.40326e32i | −0.0327158 | − | 0.625147i | ||||
\(874\) | −2.01260e31 | −0.0885385 | ||||||||
\(875\) | − | 3.71891e32i | − | 1.61557i | ||||||
\(876\) | −2.60130e30 | − | 2.46872e30i | −0.0111595 | − | 0.0105908i | ||||
\(877\) | 7.22813e31 | 0.306218 | 0.153109 | − | 0.988209i | \(-0.451071\pi\) | ||||
0.153109 | + | 0.988209i | \(0.451071\pi\) | |||||||
\(878\) | 1.00397e32i | 0.420033i | ||||||||
\(879\) | −9.11035e31 | + | 9.59959e31i | −0.376407 | + | 0.396621i | ||||
\(880\) | 2.24301e30 | 0.00915213 | ||||||||
\(881\) | 1.95541e32i | 0.787957i | 0.919120 | + | 0.393979i | \(0.128902\pi\) | ||||
−0.919120 | + | 0.393979i | \(0.871098\pi\) | |||||||
\(882\) | −9.05412e31 | + | 4.73829e30i | −0.360323 | + | 0.0188568i | ||||
\(883\) | −8.63196e30 | −0.0339267 | −0.0169634 | − | 0.999856i | \(-0.505400\pi\) | ||||
−0.0169634 | + | 0.999856i | \(0.505400\pi\) | |||||||
\(884\) | − | 1.89768e32i | − | 0.736627i | ||||||
\(885\) | 1.81331e31 | + | 1.72089e31i | 0.0695176 | + | 0.0659747i | ||||
\(886\) | 8.83873e31 | 0.334672 | ||||||||
\(887\) | 4.69289e32i | 1.75502i | 0.479562 | + | 0.877508i | \(0.340795\pi\) | ||||
−0.479562 | + | 0.877508i | \(0.659205\pi\) | |||||||
\(888\) | 4.57504e31 | − | 4.82073e31i | 0.168987 | − | 0.178062i | ||||
\(889\) | −6.18305e32 | −2.25571 | ||||||||
\(890\) | − | 5.90343e32i | − | 2.12723i | ||||||
\(891\) | 6.43064e29 | + | 6.12714e30i | 0.00228876 | + | 0.0218074i | ||||
\(892\) | 1.99030e32 | 0.699689 | ||||||||
\(893\) | 8.94975e29i | 0.00310774i | ||||||||
\(894\) | −2.73542e32 | − | 2.59601e32i | −0.938235 | − | 0.890418i | ||||
\(895\) | −8.94590e32 | −3.03089 | ||||||||
\(896\) | − | 3.24572e31i | − | 0.108623i | ||||||
\(897\) | 6.09252e31 | − | 6.41969e31i | 0.201409 | − | 0.212225i | ||||
\(898\) | −1.52685e32 | −0.498606 | ||||||||
\(899\) | 2.21115e30i | 0.00713281i | ||||||||
\(900\) | 1.46569e31 | + | 2.80070e32i | 0.0467063 | + | 0.892482i | ||||
\(901\) | 1.68578e32 | 0.530673 | ||||||||
\(902\) | − | 6.44106e30i | − | 0.0200302i | ||||||
\(903\) | 4.87784e32 | + | 4.62924e32i | 1.49852 | + | 1.42215i | ||||
\(904\) | 7.77330e31 | 0.235913 | ||||||||
\(905\) | − | 2.69057e32i | − | 0.806696i | ||||||
\(906\) | −2.36329e32 | + | 2.49021e32i | −0.700015 | + | 0.737607i | ||||
\(907\) | 3.98603e32 | 1.16643 | 0.583217 | − | 0.812316i | \(-0.301794\pi\) | ||||
0.583217 | + | 0.812316i | \(0.301794\pi\) | |||||||
\(908\) | − | 2.19207e32i | − | 0.633738i | ||||||
\(909\) | −3.82233e32 | + | 2.00034e31i | −1.09176 | + | 0.0571349i | ||||
\(910\) | 9.58244e32 | 2.70409 | ||||||||
\(911\) | − | 6.46638e32i | − | 1.80285i | −0.432937 | − | 0.901424i | \(-0.642523\pi\) | ||
0.432937 | − | 0.901424i | \(-0.357477\pi\) | |||||||
\(912\) | 5.25091e31 | + | 4.98330e31i | 0.144641 | + | 0.137269i | ||||
\(913\) | −3.89841e30 | −0.0106098 | ||||||||
\(914\) | − | 1.32628e32i | − | 0.356639i | ||||||
\(915\) | 1.43014e32 | − | 1.50694e32i | 0.379967 | − | 0.400372i | ||||
\(916\) | −1.73460e32 | −0.455354 | ||||||||
\(917\) | − | 1.84404e31i | − | 0.0478307i | ||||||
\(918\) | 1.41653e32 | − | 1.65817e32i | 0.363041 | − | 0.424971i | ||||
\(919\) | −3.77545e32 | −0.956088 | −0.478044 | − | 0.878336i | \(-0.658654\pi\) | ||||
−0.478044 | + | 0.878336i | \(0.658654\pi\) | |||||||
\(920\) | − | 3.70309e31i | − | 0.0926611i | ||||||
\(921\) | −1.85947e32 | − | 1.76470e32i | −0.459761 | − | 0.436330i | ||||
\(922\) | −3.52550e32 | −0.861351 | ||||||||
\(923\) | 7.18897e32i | 1.73559i | ||||||||
\(924\) | 3.88777e30 | − | 4.09655e30i | 0.00927488 | − | 0.00977296i | ||||
\(925\) | 5.26442e32 | 1.24106 | ||||||||
\(926\) | 5.62554e32i | 1.31052i | ||||||||
\(927\) | 2.92426e31 | + | 5.58779e32i | 0.0673191 | + | 1.28636i | ||||
\(928\) | −1.59255e30 | −0.00362297 | ||||||||
\(929\) | − | 5.76621e31i | − | 0.129634i | −0.997897 | − | 0.0648168i | \(-0.979354\pi\) | ||
0.997897 | − | 0.0648168i | \(-0.0206463\pi\) | |||||||
\(930\) | 1.34142e32 | + | 1.27306e32i | 0.298026 | + | 0.282837i | ||||
\(931\) | −1.85375e32 | −0.407010 | ||||||||
\(932\) | 1.50116e32i | 0.325727i | ||||||||
\(933\) | 1.60617e32 | − | 1.69242e32i | 0.344424 | − | 0.362920i | ||||
\(934\) | −3.87323e31 | −0.0820838 | ||||||||
\(935\) | − | 1.38159e31i | − | 0.0289369i | ||||||
\(936\) | −3.17910e32 | + | 1.66372e31i | −0.658066 | + | 0.0344385i | ||||
\(937\) | 4.02717e32 | 0.823880 | 0.411940 | − | 0.911211i | \(-0.364851\pi\) | ||||
0.411940 | + | 0.911211i | \(0.364851\pi\) | |||||||
\(938\) | − | 1.47698e32i | − | 0.298638i | ||||||
\(939\) | 9.83072e31 | + | 9.32970e31i | 0.196455 | + | 0.186443i | ||||
\(940\) | −1.64671e30 | −0.00325245 | ||||||||
\(941\) | − | 3.33355e32i | − | 0.650760i | −0.945583 | − | 0.325380i | \(-0.894508\pi\) | ||
0.945583 | − | 0.325380i | \(-0.105492\pi\) | |||||||
\(942\) | 2.78309e31 | − | 2.93255e31i | 0.0536992 | − | 0.0565829i | ||||
\(943\) | −1.06338e32 | −0.202797 | ||||||||
\(944\) | 7.61342e30i | 0.0143512i | ||||||||
\(945\) | 8.37301e32 | + | 7.15285e32i | 1.56003 | + | 1.33269i | ||||
\(946\) | −1.41533e31 | −0.0260648 | ||||||||
\(947\) | − | 3.75870e32i | − | 0.684207i | −0.939662 | − | 0.342103i | \(-0.888861\pi\) | ||
0.939662 | − | 0.342103i | \(-0.111139\pi\) | |||||||
\(948\) | 5.04414e31 | + | 4.78707e31i | 0.0907602 | + | 0.0861346i | ||||
\(949\) | 3.22451e31 | 0.0573503 | ||||||||
\(950\) | 5.73420e32i | 1.00812i | ||||||||
\(951\) | 4.04853e32 | − | 4.26594e32i | 0.703576 | − | 0.741360i | ||||
\(952\) | −1.99921e32 | −0.343441 | ||||||||
\(953\) | − | 2.96604e32i | − | 0.503680i | −0.967769 | − | 0.251840i | \(-0.918964\pi\) | ||
0.967769 | − | 0.251840i | \(-0.0810357\pi\) | |||||||
\(954\) | −1.47794e31 | − | 2.82410e32i | −0.0248098 | − | 0.474076i | ||||
\(955\) | −5.61102e32 | −0.931117 | ||||||||
\(956\) | − | 2.31444e32i | − | 0.379673i | ||||||
\(957\) | −2.01001e29 | − | 1.90757e29i | −0.000325963 | − | 0.000309350i | ||||
\(958\) | −7.49928e32 | −1.20226 | ||||||||
\(959\) | 8.15848e32i | 1.29302i | ||||||||
\(960\) | −9.16902e31 | + | 9.66141e31i | −0.143661 | + | 0.151376i | ||||
\(961\) | −5.67392e32 | −0.878872 | ||||||||
\(962\) | 5.97568e32i | 0.915085i | ||||||||
\(963\) | −7.07655e32 | + | 3.70337e31i | −1.07135 | + | 0.0560670i | ||||
\(964\) | 4.54213e32 | 0.679849 | ||||||||
\(965\) | − | 8.31963e32i | − | 1.23113i | ||||||
\(966\) | −6.76317e31 | − | 6.41848e31i | −0.0989468 | − | 0.0939040i | ||||
\(967\) | 7.15946e32 | 1.03559 | 0.517796 | − | 0.855504i | \(-0.326753\pi\) | ||||
0.517796 | + | 0.855504i | \(0.326753\pi\) | |||||||
\(968\) | − | 2.47101e32i | − | 0.353383i | ||||||
\(969\) | 3.06948e32 | − | 3.23432e32i | 0.434014 | − | 0.457321i | ||||
\(970\) | 5.28628e32 | 0.739028 | ||||||||
\(971\) | 2.32402e32i | 0.321239i | 0.987016 | + | 0.160619i | \(0.0513491\pi\) | ||||
−0.987016 | + | 0.160619i | \(0.948651\pi\) | |||||||
\(972\) | −2.90204e32 | − | 2.22767e32i | −0.396620 | − | 0.304455i | ||||
\(973\) | −2.11448e31 | −0.0285735 | ||||||||
\(974\) | − | 3.64479e32i | − | 0.486995i | ||||||
\(975\) | −1.82907e33 | − | 1.73585e33i | −2.41645 | − | 2.29330i | ||||
\(976\) | 6.32710e31 | 0.0826527 | ||||||||
\(977\) | 4.69586e32i | 0.606562i | 0.952901 | + | 0.303281i | \(0.0980821\pi\) | ||||
−0.952901 | + | 0.303281i | \(0.901918\pi\) | |||||||
\(978\) | 9.46354e31 | − | 9.97175e31i | 0.120872 | − | 0.127363i | ||||
\(979\) | 3.12839e31 | 0.0395104 | ||||||||
\(980\) | − | 3.41081e32i | − | 0.425962i | ||||||
\(981\) | −5.15445e31 | − | 9.84933e32i | −0.0636536 | − | 1.21632i | ||||
\(982\) | −8.52828e32 | −1.04144 | ||||||||
\(983\) | 2.33933e32i | 0.282490i | 0.989975 | + | 0.141245i | \(0.0451105\pi\) | ||||
−0.989975 | + | 0.141245i | \(0.954889\pi\) | |||||||
\(984\) | 2.77438e32 | + | 2.63299e32i | 0.331299 | + | 0.314415i | ||||
\(985\) | 1.49201e33 | 1.76187 | ||||||||
\(986\) | 9.80935e30i | 0.0114550i | ||||||||
\(987\) | −2.85421e30 | + | 3.00748e30i | −0.00329607 | + | 0.00347308i | ||||
\(988\) | −6.50892e32 | −0.743332 | ||||||||
\(989\) | 2.33663e32i | 0.263894i | ||||||||
\(990\) | −2.31452e31 | + | 1.21126e30i | −0.0258507 | + | 0.00135285i | ||||
\(991\) | 1.06857e33 | 1.18030 | 0.590149 | − | 0.807294i | \(-0.299069\pi\) | ||||
0.590149 | + | 0.807294i | \(0.299069\pi\) | |||||||
\(992\) | 5.63216e31i | 0.0615243i | ||||||||
\(993\) | 3.82121e32 | + | 3.62646e32i | 0.412819 | + | 0.391779i | ||||
\(994\) | 7.57361e32 | 0.809194 | ||||||||
\(995\) | 2.15868e33i | 2.28104i | ||||||||
\(996\) | 1.59360e32 | − | 1.67918e32i | 0.166543 | − | 0.175487i | ||||
\(997\) | −1.04461e33 | −1.07971 | −0.539856 | − | 0.841757i | \(-0.681521\pi\) | ||||
−0.539856 | + | 0.841757i | \(0.681521\pi\) | |||||||
\(998\) | 1.06598e33i | 1.08972i | ||||||||
\(999\) | −4.46057e32 | + | 5.22147e32i | −0.450993 | + | 0.527925i |
(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 | 6.23.b.a.5.5 | yes | 8 | |
3.2 | odd | 2 | inner | 6.23.b.a.5.1 | ✓ | 8 | |
4.3 | odd | 2 | 48.23.e.d.17.8 | 8 | |||
12.11 | even | 2 | 48.23.e.d.17.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.23.b.a.5.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
6.23.b.a.5.5 | yes | 8 | 1.1 | even | 1 | trivial | |
48.23.e.d.17.7 | 8 | 12.11 | even | 2 | |||
48.23.e.d.17.8 | 8 | 4.3 | odd | 2 |