Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,14,Mod(5,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.57847431615\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 5 x^{9} + 752 x^{8} + 708 x^{7} - 743866 x^{6} + 96647426 x^{5} + 2540283092 x^{4} + \cdots + 31\!\cdots\!68 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{48}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.10 | ||
Root | \(37.4606 + 15.6556i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.14.b.b.5.9 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 84.9212 | + | 31.3112i | 0.938255 | + | 0.345944i | ||||
\(3\) | 1415.71i | 1.12120i | 0.828085 | + | 0.560602i | \(0.189430\pi\) | ||||
−0.828085 | + | 0.560602i | \(0.810570\pi\) | |||||||
\(4\) | 6231.21 | + | 5317.98i | 0.760646 | + | 0.649167i | ||||
\(5\) | 2384.10i | 0.0682368i | 0.999418 | + | 0.0341184i | \(0.0108623\pi\) | ||||
−0.999418 | + | 0.0341184i | \(0.989138\pi\) | |||||||
\(6\) | −44327.5 | + | 120223.i | −0.387873 | + | 1.05198i | ||||
\(7\) | −317448. | −1.01985 | −0.509924 | − | 0.860220i | \(-0.670326\pi\) | ||||
−0.509924 | + | 0.860220i | \(0.670326\pi\) | |||||||
\(8\) | 362649. | + | 646716.i | 0.489105 | + | 0.872225i | ||||
\(9\) | −409898. | −0.257098 | ||||||||
\(10\) | −74649.0 | + | 202460.i | −0.0236061 | + | 0.0640236i | ||||
\(11\) | − | 1.40906e6i | − | 0.239815i | −0.992785 | − | 0.119908i | \(-0.961740\pi\) | ||
0.992785 | − | 0.119908i | \(-0.0382598\pi\) | |||||||
\(12\) | −7.52869e6 | + | 8.82156e6i | −0.727849 | + | 0.852839i | ||||
\(13\) | 2.51242e7i | 1.44364i | 0.692079 | + | 0.721822i | \(0.256695\pi\) | ||||
−0.692079 | + | 0.721822i | \(0.743305\pi\) | |||||||
\(14\) | −2.69581e7 | − | 9.93969e6i | −0.956877 | − | 0.352810i | ||||
\(15\) | −3.37518e6 | −0.0765074 | ||||||||
\(16\) | 1.05471e7 | + | 6.62749e7i | 0.157164 | + | 0.987572i | ||||
\(17\) | 1.11400e8 | 1.11936 | 0.559678 | − | 0.828710i | \(-0.310925\pi\) | ||||
0.559678 | + | 0.828710i | \(0.310925\pi\) | |||||||
\(18\) | −3.48090e7 | − | 1.28344e7i | −0.241224 | − | 0.0889416i | ||||
\(19\) | − | 3.64846e8i | − | 1.77915i | −0.456792 | − | 0.889573i | \(-0.651002\pi\) | ||
0.456792 | − | 0.889573i | \(-0.348998\pi\) | |||||||
\(20\) | −1.26786e7 | + | 1.48558e7i | −0.0442971 | + | 0.0519041i | ||||
\(21\) | − | 4.49413e8i | − | 1.14346i | ||||||
\(22\) | 4.41194e7 | − | 1.19659e8i | 0.0829625 | − | 0.225008i | ||||
\(23\) | 7.49063e8 | 1.05509 | 0.527543 | − | 0.849528i | \(-0.323113\pi\) | ||||
0.527543 | + | 0.849528i | \(0.323113\pi\) | |||||||
\(24\) | −9.15559e8 | + | 5.13405e8i | −0.977942 | + | 0.548386i | ||||
\(25\) | 1.21502e9 | 0.995344 | ||||||||
\(26\) | −7.86670e8 | + | 2.13358e9i | −0.499420 | + | 1.35451i | ||||
\(27\) | 1.67680e9i | 0.832944i | ||||||||
\(28\) | −1.97809e9 | − | 1.68818e9i | −0.775743 | − | 0.662051i | ||||
\(29\) | − | 2.83628e9i | − | 0.885446i | −0.896659 | − | 0.442723i | \(-0.854013\pi\) | ||
0.896659 | − | 0.442723i | \(-0.145987\pi\) | |||||||
\(30\) | −2.86624e8 | − | 1.05681e8i | −0.0717835 | − | 0.0264672i | ||||
\(31\) | −2.93414e9 | −0.593786 | −0.296893 | − | 0.954911i | \(-0.595950\pi\) | ||||
−0.296893 | + | 0.954911i | \(0.595950\pi\) | |||||||
\(32\) | −1.17947e9 | + | 5.95838e9i | −0.194184 | + | 0.980965i | ||||
\(33\) | 1.99481e9 | 0.268882 | ||||||||
\(34\) | 9.46024e9 | + | 3.48808e9i | 1.05024 | + | 0.387234i | ||||
\(35\) | − | 7.56826e8i | − | 0.0695912i | ||||||
\(36\) | −2.55416e9 | − | 2.17983e9i | −0.195561 | − | 0.166900i | ||||
\(37\) | 8.46017e9i | 0.542086i | 0.962567 | + | 0.271043i | \(0.0873685\pi\) | ||||
−0.962567 | + | 0.271043i | \(0.912631\pi\) | |||||||
\(38\) | 1.14238e10 | − | 3.09832e10i | 0.615485 | − | 1.66929i | ||||
\(39\) | −3.55684e10 | −1.61862 | ||||||||
\(40\) | −1.54183e9 | + | 8.64591e8i | −0.0595179 | + | 0.0333750i | ||||
\(41\) | 3.90644e10 | 1.28436 | 0.642180 | − | 0.766554i | \(-0.278030\pi\) | ||||
0.642180 | + | 0.766554i | \(0.278030\pi\) | |||||||
\(42\) | 1.40717e10 | − | 3.81647e10i | 0.395572 | − | 1.07285i | ||||
\(43\) | 2.17473e10i | 0.524639i | 0.964981 | + | 0.262319i | \(0.0844874\pi\) | ||||
−0.964981 | + | 0.262319i | \(0.915513\pi\) | |||||||
\(44\) | 7.49334e9 | − | 8.78014e9i | 0.155680 | − | 0.182414i | ||||
\(45\) | − | 9.77236e8i | − | 0.0175436i | ||||||
\(46\) | 6.36113e10 | + | 2.34541e10i | 0.989940 | + | 0.365000i | ||||
\(47\) | −1.15068e11 | −1.55711 | −0.778557 | − | 0.627574i | \(-0.784048\pi\) | ||||
−0.778557 | + | 0.627574i | \(0.784048\pi\) | |||||||
\(48\) | −9.38257e10 | + | 1.49316e10i | −1.10727 | + | 0.176213i | ||||
\(49\) | 3.88420e9 | 0.0400892 | ||||||||
\(50\) | 1.03181e11 | + | 3.80438e10i | 0.933887 | + | 0.344333i | ||||
\(51\) | 1.57710e11i | 1.25503i | ||||||||
\(52\) | −1.33610e11 | + | 1.56554e11i | −0.937166 | + | 1.09810i | ||||
\(53\) | − | 1.71179e11i | − | 1.06086i | −0.847729 | − | 0.530430i | \(-0.822030\pi\) | ||
0.847729 | − | 0.530430i | \(-0.177970\pi\) | |||||||
\(54\) | −5.25026e10 | + | 1.42396e11i | −0.288152 | + | 0.781514i | ||||
\(55\) | 3.35933e9 | 0.0163642 | ||||||||
\(56\) | −1.15122e11 | − | 2.05299e11i | −0.498812 | − | 0.889537i | ||||
\(57\) | 5.16515e11 | 1.99479 | ||||||||
\(58\) | 8.88074e10 | − | 2.40860e11i | 0.306314 | − | 0.830774i | ||||
\(59\) | − | 2.45442e11i | − | 0.757549i | −0.925489 | − | 0.378774i | \(-0.876346\pi\) | ||
0.925489 | − | 0.378774i | \(-0.123654\pi\) | |||||||
\(60\) | −2.10314e10 | − | 1.79491e10i | −0.0581950 | − | 0.0496661i | ||||
\(61\) | − | 2.71473e11i | − | 0.674657i | −0.941387 | − | 0.337328i | \(-0.890477\pi\) | ||
0.941387 | − | 0.337328i | \(-0.109523\pi\) | |||||||
\(62\) | −2.49170e11 | − | 9.18715e10i | −0.557122 | − | 0.205416i | ||||
\(63\) | 1.30121e11 | 0.262201 | ||||||||
\(64\) | −2.86727e11 | + | 4.69062e11i | −0.521553 | + | 0.853219i | ||||
\(65\) | −5.98985e10 | −0.0985097 | ||||||||
\(66\) | 1.69402e11 | + | 6.24600e10i | 0.252280 | + | 0.0930179i | ||||
\(67\) | − | 6.82198e11i | − | 0.921350i | −0.887569 | − | 0.460675i | \(-0.847607\pi\) | ||
0.887569 | − | 0.460675i | \(-0.152393\pi\) | |||||||
\(68\) | 6.94158e11 | + | 5.92424e11i | 0.851433 | + | 0.726649i | ||||
\(69\) | 1.06045e12i | 1.18297i | ||||||||
\(70\) | 2.36972e10 | − | 6.42706e10i | 0.0240746 | − | 0.0652943i | ||||
\(71\) | −2.90719e11 | −0.269336 | −0.134668 | − | 0.990891i | \(-0.542997\pi\) | ||||
−0.134668 | + | 0.990891i | \(0.542997\pi\) | |||||||
\(72\) | −1.48649e11 | − | 2.65088e11i | −0.125748 | − | 0.224248i | ||||
\(73\) | −1.48745e12 | −1.15039 | −0.575194 | − | 0.818017i | \(-0.695073\pi\) | ||||
−0.575194 | + | 0.818017i | \(0.695073\pi\) | |||||||
\(74\) | −2.64899e11 | + | 7.18448e11i | −0.187531 | + | 0.508615i | ||||
\(75\) | 1.72011e12i | 1.11598i | ||||||||
\(76\) | 1.94024e12 | − | 2.27344e12i | 1.15496 | − | 1.35330i | ||||
\(77\) | 4.47303e11i | 0.244575i | ||||||||
\(78\) | −3.02051e12 | − | 1.11369e12i | −1.51868 | − | 0.559951i | ||||
\(79\) | 1.58653e12 | 0.734296 | 0.367148 | − | 0.930162i | \(-0.380334\pi\) | ||||
0.367148 | + | 0.930162i | \(0.380334\pi\) | |||||||
\(80\) | −1.58006e11 | + | 2.51454e10i | −0.0673888 | + | 0.0107244i | ||||
\(81\) | −3.02736e12 | −1.19100 | ||||||||
\(82\) | 3.31740e12 | + | 1.22316e12i | 1.20506 | + | 0.444316i | ||||
\(83\) | 7.79952e11i | 0.261855i | 0.991392 | + | 0.130927i | \(0.0417955\pi\) | ||||
−0.991392 | + | 0.130927i | \(0.958205\pi\) | |||||||
\(84\) | 2.38997e12 | − | 2.80039e12i | 0.742295 | − | 0.869766i | ||||
\(85\) | 2.65589e11i | 0.0763812i | ||||||||
\(86\) | −6.80935e11 | + | 1.84681e12i | −0.181495 | + | 0.492245i | ||||
\(87\) | 4.01533e12 | 0.992765 | ||||||||
\(88\) | 9.11260e11 | − | 5.10994e11i | 0.209173 | − | 0.117295i | ||||
\(89\) | −4.10498e12 | −0.875540 | −0.437770 | − | 0.899087i | \(-0.644232\pi\) | ||||
−0.437770 | + | 0.899087i | \(0.644232\pi\) | |||||||
\(90\) | 3.05985e10 | − | 8.29881e10i | 0.00606909 | − | 0.0164604i | ||||
\(91\) | − | 7.97562e12i | − | 1.47230i | ||||||
\(92\) | 4.66757e12 | + | 3.98350e12i | 0.802546 | + | 0.684927i | ||||
\(93\) | − | 4.15387e12i | − | 0.665755i | ||||||
\(94\) | −9.77175e12 | − | 3.60294e12i | −1.46097 | − | 0.538673i | ||||
\(95\) | 8.69829e11 | 0.121403 | ||||||||
\(96\) | −8.43531e12 | − | 1.66979e12i | −1.09986 | − | 0.217720i | ||||
\(97\) | 1.11567e13 | 1.35994 | 0.679971 | − | 0.733239i | \(-0.261992\pi\) | ||||
0.679971 | + | 0.733239i | \(0.261992\pi\) | |||||||
\(98\) | 3.29851e11 | + | 1.21619e11i | 0.0376139 | + | 0.0138686i | ||||
\(99\) | 5.77570e11i | 0.0616561i | ||||||||
\(100\) | 7.57104e12 | + | 6.46144e12i | 0.757104 | + | 0.646144i | ||||
\(101\) | 1.76850e13i | 1.65774i | 0.559444 | + | 0.828868i | \(0.311015\pi\) | ||||
−0.559444 | + | 0.828868i | \(0.688985\pi\) | |||||||
\(102\) | −4.93809e12 | + | 1.33929e13i | −0.434168 | + | 1.17753i | ||||
\(103\) | 1.25010e11 | 0.0103158 | 0.00515790 | − | 0.999987i | \(-0.498358\pi\) | ||||
0.00515790 | + | 0.999987i | \(0.498358\pi\) | |||||||
\(104\) | −1.62482e13 | + | 9.11127e12i | −1.25918 | + | 0.706094i | ||||
\(105\) | 1.07144e12 | 0.0780259 | ||||||||
\(106\) | 5.35984e12 | − | 1.45368e13i | 0.366998 | − | 0.995358i | ||||
\(107\) | 5.03372e12i | 0.324261i | 0.986769 | + | 0.162130i | \(0.0518365\pi\) | ||||
−0.986769 | + | 0.162130i | \(0.948164\pi\) | |||||||
\(108\) | −8.91716e12 | + | 1.04485e13i | −0.540720 | + | 0.633576i | ||||
\(109\) | − | 3.05175e13i | − | 1.74291i | −0.490472 | − | 0.871457i | \(-0.663175\pi\) | ||
0.490472 | − | 0.871457i | \(-0.336825\pi\) | |||||||
\(110\) | 2.85278e11 | + | 1.05185e11i | 0.0153538 | + | 0.00566110i | ||||
\(111\) | −1.19771e13 | −0.607789 | ||||||||
\(112\) | −3.34816e12 | − | 2.10388e13i | −0.160284 | − | 1.00717i | ||||
\(113\) | 5.08544e12 | 0.229783 | 0.114892 | − | 0.993378i | \(-0.463348\pi\) | ||||
0.114892 | + | 0.993378i | \(0.463348\pi\) | |||||||
\(114\) | 4.38631e13 | + | 1.61727e13i | 1.87162 | + | 0.690084i | ||||
\(115\) | 1.78584e12i | 0.0719957i | ||||||||
\(116\) | 1.50833e13 | − | 1.76735e13i | 0.574802 | − | 0.673511i | ||||
\(117\) | − | 1.02984e13i | − | 0.371159i | ||||||
\(118\) | 7.68509e12 | − | 2.08432e13i | 0.262069 | − | 0.710774i | ||||
\(119\) | −3.53638e13 | −1.14157 | ||||||||
\(120\) | −1.22401e12 | − | 2.18278e12i | −0.0374201 | − | 0.0667317i | ||||
\(121\) | 3.25373e13 | 0.942489 | ||||||||
\(122\) | 8.50016e12 | − | 2.30538e13i | 0.233393 | − | 0.633000i | ||||
\(123\) | 5.53037e13i | 1.44003i | ||||||||
\(124\) | −1.82832e13 | − | 1.56037e13i | −0.451661 | − | 0.385466i | ||||
\(125\) | 5.80700e12i | 0.136156i | ||||||||
\(126\) | 1.10501e13 | + | 4.07426e12i | 0.246012 | + | 0.0907069i | ||||
\(127\) | −2.64256e13 | −0.558858 | −0.279429 | − | 0.960166i | \(-0.590145\pi\) | ||||
−0.279429 | + | 0.960166i | \(0.590145\pi\) | |||||||
\(128\) | −3.90361e13 | + | 3.08555e13i | −0.784515 | + | 0.620109i | ||||
\(129\) | −3.07878e13 | −0.588227 | ||||||||
\(130\) | −5.08665e12 | − | 1.87550e12i | −0.0924272 | − | 0.0340788i | ||||
\(131\) | − | 7.50964e12i | − | 0.129824i | −0.997891 | − | 0.0649121i | \(-0.979323\pi\) | ||
0.997891 | − | 0.0649121i | \(-0.0206767\pi\) | |||||||
\(132\) | 1.24301e13 | + | 1.06084e13i | 0.204524 | + | 0.174549i | ||||
\(133\) | 1.15820e14i | 1.81446i | ||||||||
\(134\) | 2.13605e13 | − | 5.79331e13i | 0.318735 | − | 0.864461i | ||||
\(135\) | −3.99764e12 | −0.0568375 | ||||||||
\(136\) | 4.03992e13 | + | 7.20443e13i | 0.547482 | + | 0.976330i | ||||
\(137\) | 2.25954e13 | 0.291969 | 0.145985 | − | 0.989287i | \(-0.453365\pi\) | ||||
0.145985 | + | 0.989287i | \(0.453365\pi\) | |||||||
\(138\) | −3.32041e13 | + | 9.00549e13i | −0.409240 | + | 1.10992i | ||||
\(139\) | − | 1.14864e14i | − | 1.35079i | −0.737458 | − | 0.675393i | \(-0.763974\pi\) | ||
0.737458 | − | 0.675393i | \(-0.236026\pi\) | |||||||
\(140\) | 4.02478e12 | − | 4.71595e12i | 0.0451763 | − | 0.0529342i | ||||
\(141\) | − | 1.62903e14i | − | 1.74584i | ||||||
\(142\) | −2.46882e13 | − | 9.10278e12i | −0.252706 | − | 0.0931750i | ||||
\(143\) | 3.54014e13 | 0.346208 | ||||||||
\(144\) | −4.32325e12 | − | 2.71659e13i | −0.0404067 | − | 0.253903i | ||||
\(145\) | 6.76196e12 | 0.0604200 | ||||||||
\(146\) | −1.26316e14 | − | 4.65740e13i | −1.07936 | − | 0.397969i | ||||
\(147\) | 5.49888e12i | 0.0449482i | ||||||||
\(148\) | −4.49910e13 | + | 5.27171e13i | −0.351904 | + | 0.412335i | ||||
\(149\) | 6.70523e13i | 0.501999i | 0.967987 | + | 0.251000i | \(0.0807593\pi\) | ||||
−0.967987 | + | 0.251000i | \(0.919241\pi\) | |||||||
\(150\) | −5.38588e13 | + | 1.46074e14i | −0.386067 | + | 1.04708i | ||||
\(151\) | 2.60422e14 | 1.78784 | 0.893918 | − | 0.448231i | \(-0.147946\pi\) | ||||
0.893918 | + | 0.448231i | \(0.147946\pi\) | |||||||
\(152\) | 2.35952e14 | − | 1.32311e14i | 1.55182 | − | 0.870189i | ||||
\(153\) | −4.56627e13 | −0.287785 | ||||||||
\(154\) | −1.40056e13 | + | 3.79855e13i | −0.0846091 | + | 0.229474i | ||||
\(155\) | − | 6.99527e12i | − | 0.0405180i | ||||||
\(156\) | −2.21634e14 | − | 1.89152e14i | −1.23120 | − | 1.05075i | ||||
\(157\) | − | 8.89796e13i | − | 0.474179i | −0.971488 | − | 0.237090i | \(-0.923806\pi\) | ||
0.971488 | − | 0.237090i | \(-0.0761935\pi\) | |||||||
\(158\) | 1.34730e14 | + | 4.96761e13i | 0.688958 | + | 0.254025i | ||||
\(159\) | 2.42340e14 | 1.18944 | ||||||||
\(160\) | −1.42054e13 | − | 2.81198e12i | −0.0669379 | − | 0.0132505i | ||||
\(161\) | −2.37789e14 | −1.07603 | ||||||||
\(162\) | −2.57087e14 | − | 9.47904e13i | −1.11746 | − | 0.412019i | ||||
\(163\) | − | 1.43591e13i | − | 0.0599664i | −0.999550 | − | 0.0299832i | \(-0.990455\pi\) | ||
0.999550 | − | 0.0299832i | \(-0.00954538\pi\) | |||||||
\(164\) | 2.43419e14 | + | 2.07744e14i | 0.976943 | + | 0.833764i | ||||
\(165\) | 4.75582e12i | 0.0183476i | ||||||||
\(166\) | −2.44213e13 | + | 6.62345e13i | −0.0905870 | + | 0.245687i | ||||
\(167\) | −3.16007e14 | −1.12730 | −0.563650 | − | 0.826014i | \(-0.690603\pi\) | ||||
−0.563650 | + | 0.826014i | \(0.690603\pi\) | |||||||
\(168\) | 2.90642e14 | − | 1.62979e14i | 0.997352 | − | 0.559270i | ||||
\(169\) | −3.28350e14 | −1.08411 | ||||||||
\(170\) | −8.31592e12 | + | 2.25541e13i | −0.0264236 | + | 0.0716651i | ||||
\(171\) | 1.49550e14i | 0.457416i | ||||||||
\(172\) | −1.15652e14 | + | 1.35512e14i | −0.340578 | + | 0.399064i | ||||
\(173\) | 5.70549e14i | 1.61805i | 0.587771 | + | 0.809027i | \(0.300006\pi\) | ||||
−0.587771 | + | 0.809027i | \(0.699994\pi\) | |||||||
\(174\) | 3.40987e14 | + | 1.25725e14i | 0.931467 | + | 0.343441i | ||||
\(175\) | −3.85705e14 | −1.01510 | ||||||||
\(176\) | 9.33851e13 | − | 1.48615e13i | 0.236835 | − | 0.0376904i | ||||
\(177\) | 3.47473e14 | 0.849367 | ||||||||
\(178\) | −3.48600e14 | − | 1.28532e14i | −0.821480 | − | 0.302888i | ||||
\(179\) | − | 3.77361e13i | − | 0.0857456i | −0.999081 | − | 0.0428728i | \(-0.986349\pi\) | ||
0.999081 | − | 0.0428728i | \(-0.0136510\pi\) | |||||||
\(180\) | 5.19692e12 | − | 6.08937e12i | 0.0113887 | − | 0.0133445i | ||||
\(181\) | 1.46717e14i | 0.310148i | 0.987903 | + | 0.155074i | \(0.0495616\pi\) | ||||
−0.987903 | + | 0.155074i | \(0.950438\pi\) | |||||||
\(182\) | 2.49727e14 | − | 6.77299e14i | 0.509332 | − | 1.38139i | ||||
\(183\) | 3.84326e14 | 0.756428 | ||||||||
\(184\) | 2.71647e14 | + | 4.84431e14i | 0.516047 | + | 0.920272i | ||||
\(185\) | −2.01699e13 | −0.0369902 | ||||||||
\(186\) | 1.30063e14 | − | 3.52752e14i | 0.230314 | − | 0.624648i | ||||
\(187\) | − | 1.56969e14i | − | 0.268438i | ||||||
\(188\) | −7.17016e14 | − | 6.11931e14i | −1.18441 | − | 1.01083i | ||||
\(189\) | − | 5.32296e14i | − | 0.849476i | ||||||
\(190\) | 7.38669e13 | + | 2.72354e13i | 0.113907 | + | 0.0419987i | ||||
\(191\) | −5.17437e14 | −0.771153 | −0.385576 | − | 0.922676i | \(-0.625997\pi\) | ||||
−0.385576 | + | 0.922676i | \(0.625997\pi\) | |||||||
\(192\) | −6.64054e14 | − | 4.05921e14i | −0.956633 | − | 0.584767i | ||||
\(193\) | 8.13631e14 | 1.13320 | 0.566598 | − | 0.823995i | \(-0.308259\pi\) | ||||
0.566598 | + | 0.823995i | \(0.308259\pi\) | |||||||
\(194\) | 9.47443e14 | + | 3.49331e14i | 1.27597 | + | 0.470464i | ||||
\(195\) | − | 8.47986e13i | − | 0.110449i | ||||||
\(196\) | 2.42033e13 | + | 2.06561e13i | 0.0304937 | + | 0.0260246i | ||||
\(197\) | − | 1.27500e15i | − | 1.55410i | −0.629439 | − | 0.777050i | \(-0.716715\pi\) | ||
0.629439 | − | 0.777050i | \(-0.283285\pi\) | |||||||
\(198\) | −1.80844e13 | + | 4.90479e13i | −0.0213295 | + | 0.0578491i | ||||
\(199\) | −1.93695e14 | −0.221092 | −0.110546 | − | 0.993871i | \(-0.535260\pi\) | ||||
−0.110546 | + | 0.993871i | \(0.535260\pi\) | |||||||
\(200\) | 4.40626e14 | + | 7.85772e14i | 0.486827 | + | 0.868164i | ||||
\(201\) | 9.65792e14 | 1.03302 | ||||||||
\(202\) | −5.53739e14 | + | 1.50183e15i | −0.573484 | + | 1.55538i | ||||
\(203\) | 9.00371e14i | 0.903020i | ||||||||
\(204\) | −8.38697e14 | + | 9.82723e14i | −0.814721 | + | 0.954630i | ||||
\(205\) | 9.31334e13i | 0.0876406i | ||||||||
\(206\) | 1.06160e13 | + | 3.91422e12i | 0.00967886 | + | 0.00356869i | ||||
\(207\) | −3.07040e14 | −0.271261 | ||||||||
\(208\) | −1.66510e15 | + | 2.64988e14i | −1.42570 | + | 0.226890i | ||||
\(209\) | −5.14090e14 | −0.426666 | ||||||||
\(210\) | 9.09882e13 | + | 3.35482e13i | 0.0732082 | + | 0.0269926i | ||||
\(211\) | 7.41305e14i | 0.578310i | 0.957282 | + | 0.289155i | \(0.0933743\pi\) | ||||
−0.957282 | + | 0.289155i | \(0.906626\pi\) | |||||||
\(212\) | 9.10328e14 | − | 1.06666e15i | 0.688676 | − | 0.806939i | ||||
\(213\) | − | 4.11572e14i | − | 0.301980i | ||||||
\(214\) | −1.57612e14 | + | 4.27469e14i | −0.112176 | + | 0.304239i | ||||
\(215\) | −5.18477e13 | −0.0357997 | ||||||||
\(216\) | −1.08441e15 | + | 6.08089e14i | −0.726515 | + | 0.407397i | ||||
\(217\) | 9.31436e14 | 0.605571 | ||||||||
\(218\) | 9.55540e14 | − | 2.59158e15i | 0.602950 | − | 1.63530i | ||||
\(219\) | − | 2.10579e15i | − | 1.28982i | ||||||
\(220\) | 2.09327e13 | + | 1.78648e13i | 0.0124474 | + | 0.0106231i | ||||
\(221\) | 2.79884e15i | 1.61595i | ||||||||
\(222\) | −1.01711e15 | − | 3.75018e14i | −0.570261 | − | 0.210261i | ||||
\(223\) | 7.76195e14 | 0.422658 | 0.211329 | − | 0.977415i | \(-0.432221\pi\) | ||||
0.211329 | + | 0.977415i | \(0.432221\pi\) | |||||||
\(224\) | 3.74422e14 | − | 1.89148e15i | 0.198038 | − | 1.00043i | ||||
\(225\) | −4.98034e14 | −0.255901 | ||||||||
\(226\) | 4.31862e14 | + | 1.59231e14i | 0.215595 | + | 0.0794921i | ||||
\(227\) | 2.58078e14i | 0.125194i | 0.998039 | + | 0.0625968i | \(0.0199382\pi\) | ||||
−0.998039 | + | 0.0625968i | \(0.980062\pi\) | |||||||
\(228\) | 3.21851e15 | + | 2.74681e15i | 1.51733 | + | 1.29495i | ||||
\(229\) | − | 1.51272e15i | − | 0.693151i | −0.938022 | − | 0.346575i | \(-0.887344\pi\) | ||
0.938022 | − | 0.346575i | \(-0.112656\pi\) | |||||||
\(230\) | −5.59169e13 | + | 1.51656e14i | −0.0249064 | + | 0.0675503i | ||||
\(231\) | −6.33249e14 | −0.274218 | ||||||||
\(232\) | 1.83427e15 | − | 1.02857e15i | 0.772308 | − | 0.433076i | ||||
\(233\) | −2.03207e15 | −0.832002 | −0.416001 | − | 0.909364i | \(-0.636569\pi\) | ||||
−0.416001 | + | 0.909364i | \(0.636569\pi\) | |||||||
\(234\) | 3.22454e14 | − | 8.74548e14i | 0.128400 | − | 0.348242i | ||||
\(235\) | − | 2.74334e14i | − | 0.106252i | ||||||
\(236\) | 1.30525e15 | − | 1.52940e15i | 0.491776 | − | 0.576227i | ||||
\(237\) | 2.24605e15i | 0.823296i | ||||||||
\(238\) | −3.00313e15 | − | 1.10728e15i | −1.07109 | − | 0.394920i | ||||
\(239\) | −2.38480e15 | −0.827687 | −0.413844 | − | 0.910348i | \(-0.635814\pi\) | ||||
−0.413844 | + | 0.910348i | \(0.635814\pi\) | |||||||
\(240\) | −3.55984e13 | − | 2.23689e14i | −0.0120242 | − | 0.0755566i | ||||
\(241\) | −3.98380e15 | −1.30975 | −0.654873 | − | 0.755739i | \(-0.727278\pi\) | ||||
−0.654873 | + | 0.755739i | \(0.727278\pi\) | |||||||
\(242\) | 2.76310e15 | + | 1.01878e15i | 0.884295 | + | 0.326048i | ||||
\(243\) | − | 1.61249e15i | − | 0.502409i | ||||||
\(244\) | 1.44369e15 | − | 1.69161e15i | 0.437965 | − | 0.513175i | ||||
\(245\) | 9.26031e12i | 0.00273556i | ||||||||
\(246\) | −1.73163e15 | + | 4.69646e15i | −0.498169 | + | 1.35111i | ||||
\(247\) | 9.16647e15 | 2.56846 | ||||||||
\(248\) | −1.06406e15 | − | 1.89755e15i | −0.290423 | − | 0.517915i | ||||
\(249\) | −1.10418e15 | −0.293593 | ||||||||
\(250\) | −1.81824e14 | + | 4.93137e14i | −0.0471023 | + | 0.127749i | ||||
\(251\) | 6.79110e15i | 1.71420i | 0.515151 | + | 0.857099i | \(0.327736\pi\) | ||||
−0.515151 | + | 0.857099i | \(0.672264\pi\) | |||||||
\(252\) | 8.10813e14 | + | 6.91982e14i | 0.199442 | + | 0.170212i | ||||
\(253\) | − | 1.05547e15i | − | 0.253025i | ||||||
\(254\) | −2.24410e15 | − | 8.27420e14i | −0.524351 | − | 0.193333i | ||||
\(255\) | −3.75995e14 | −0.0856390 | ||||||||
\(256\) | −4.28112e15 | + | 1.39802e15i | −0.950599 | + | 0.310423i | ||||
\(257\) | −7.36721e14 | −0.159492 | −0.0797458 | − | 0.996815i | \(-0.525411\pi\) | ||||
−0.0797458 | + | 0.996815i | \(0.525411\pi\) | |||||||
\(258\) | −2.61453e15 | − | 9.64003e14i | −0.551907 | − | 0.203493i | ||||
\(259\) | − | 2.68567e15i | − | 0.552845i | ||||||
\(260\) | −3.73240e14 | − | 3.18539e14i | −0.0749310 | − | 0.0639492i | ||||
\(261\) | 1.16258e15i | 0.227647i | ||||||||
\(262\) | 2.35136e14 | − | 6.37728e14i | 0.0449119 | − | 0.121808i | ||||
\(263\) | 4.33694e14 | 0.0808110 | 0.0404055 | − | 0.999183i | \(-0.487135\pi\) | ||||
0.0404055 | + | 0.999183i | \(0.487135\pi\) | |||||||
\(264\) | 7.23417e14 | + | 1.29008e15i | 0.131511 | + | 0.234525i | ||||
\(265\) | 4.08108e14 | 0.0723898 | ||||||||
\(266\) | −3.62646e15 | + | 9.83555e15i | −0.627700 | + | 1.70243i | ||||
\(267\) | − | 5.81144e15i | − | 0.981660i | ||||||
\(268\) | 3.62791e15 | − | 4.25092e15i | 0.598110 | − | 0.700821i | ||||
\(269\) | − | 3.36599e15i | − | 0.541655i | −0.962628 | − | 0.270827i | \(-0.912703\pi\) | ||
0.962628 | − | 0.270827i | \(-0.0872973\pi\) | |||||||
\(270\) | −3.39485e14 | − | 1.25171e14i | −0.0533280 | − | 0.0196626i | ||||
\(271\) | −8.64352e14 | −0.132553 | −0.0662766 | − | 0.997801i | \(-0.521112\pi\) | ||||
−0.0662766 | + | 0.997801i | \(0.521112\pi\) | |||||||
\(272\) | 1.17495e15 | + | 7.38303e15i | 0.175923 | + | 1.10544i | ||||
\(273\) | 1.12911e16 | 1.65075 | ||||||||
\(274\) | 1.91883e15 | + | 7.07491e14i | 0.273942 | + | 0.101005i | ||||
\(275\) | − | 1.71203e15i | − | 0.238698i | ||||||
\(276\) | −5.63946e15 | + | 6.60791e15i | −0.767943 | + | 0.899818i | ||||
\(277\) | − | 4.29153e15i | − | 0.570813i | −0.958407 | − | 0.285407i | \(-0.907871\pi\) | ||
0.958407 | − | 0.285407i | \(-0.0921286\pi\) | |||||||
\(278\) | 3.59653e15 | − | 9.75436e15i | 0.467296 | − | 1.26738i | ||||
\(279\) | 1.20270e15 | 0.152661 | ||||||||
\(280\) | 4.89452e14 | − | 2.74463e14i | 0.0606991 | − | 0.0340374i | ||||
\(281\) | −1.75304e14 | −0.0212422 | −0.0106211 | − | 0.999944i | \(-0.503381\pi\) | ||||
−0.0106211 | + | 0.999944i | \(0.503381\pi\) | |||||||
\(282\) | 5.10070e15 | − | 1.38339e16i | 0.603963 | − | 1.63805i | ||||
\(283\) | − | 1.04579e16i | − | 1.21013i | −0.796177 | − | 0.605064i | \(-0.793147\pi\) | ||
0.796177 | − | 0.605064i | \(-0.206853\pi\) | |||||||
\(284\) | −1.81153e15 | − | 1.54604e15i | −0.204869 | − | 0.174844i | ||||
\(285\) | 1.23142e15i | 0.136118i | ||||||||
\(286\) | 3.00633e15 | + | 1.10846e15i | 0.324831 | + | 0.119768i | ||||
\(287\) | −1.24009e16 | −1.30985 | ||||||||
\(288\) | 4.83464e14 | − | 2.44233e15i | 0.0499244 | − | 0.252205i | ||||
\(289\) | 2.50543e15 | 0.252956 | ||||||||
\(290\) | 5.74234e14 | + | 2.11725e14i | 0.0566894 | + | 0.0209019i | ||||
\(291\) | 1.57946e16i | 1.52477i | ||||||||
\(292\) | −9.26862e15 | − | 7.91023e15i | −0.875038 | − | 0.746794i | ||||
\(293\) | 1.28392e16i | 1.18549i | 0.805390 | + | 0.592745i | \(0.201956\pi\) | ||||
−0.805390 | + | 0.592745i | \(0.798044\pi\) | |||||||
\(294\) | −1.72177e14 | + | 4.66972e14i | −0.0155495 | + | 0.0421729i | ||||
\(295\) | 5.85157e14 | 0.0516927 | ||||||||
\(296\) | −5.47133e15 | + | 3.06808e15i | −0.472821 | + | 0.265137i | ||||
\(297\) | 2.36270e15 | 0.199753 | ||||||||
\(298\) | −2.09949e15 | + | 5.69416e15i | −0.173664 | + | 0.471004i | ||||
\(299\) | 1.88196e16i | 1.52317i | ||||||||
\(300\) | −9.14750e15 | + | 1.07184e16i | −0.724460 | + | 0.848868i | ||||
\(301\) | − | 6.90364e15i | − | 0.535052i | ||||||
\(302\) | 2.21153e16 | + | 8.15414e15i | 1.67745 | + | 0.618490i | ||||
\(303\) | −2.50367e16 | −1.85866 | ||||||||
\(304\) | 2.41802e16 | − | 3.84808e15i | 1.75704 | − | 0.279619i | ||||
\(305\) | 6.47218e14 | 0.0460364 | ||||||||
\(306\) | −3.87773e15 | − | 1.42976e15i | −0.270015 | − | 0.0995572i | ||||
\(307\) | 8.53937e15i | 0.582139i | 0.956702 | + | 0.291069i | \(0.0940110\pi\) | ||||
−0.956702 | + | 0.291069i | \(0.905989\pi\) | |||||||
\(308\) | −2.37874e15 | + | 2.78724e15i | −0.158770 | + | 0.186035i | ||||
\(309\) | 1.76977e14i | 0.0115661i | ||||||||
\(310\) | 2.19031e14 | − | 5.94046e14i | 0.0140170 | − | 0.0380163i | ||||
\(311\) | 3.52686e15 | 0.221027 | 0.110513 | − | 0.993875i | \(-0.464750\pi\) | ||||
0.110513 | + | 0.993875i | \(0.464750\pi\) | |||||||
\(312\) | −1.28989e16 | − | 2.30027e16i | −0.791675 | − | 1.41180i | ||||
\(313\) | −1.00518e16 | −0.604234 | −0.302117 | − | 0.953271i | \(-0.597693\pi\) | ||||
−0.302117 | + | 0.953271i | \(0.597693\pi\) | |||||||
\(314\) | 2.78606e15 | − | 7.55625e15i | 0.164039 | − | 0.444901i | ||||
\(315\) | 3.10222e14i | 0.0178918i | ||||||||
\(316\) | 9.88599e15 | + | 8.43711e15i | 0.558540 | + | 0.476681i | ||||
\(317\) | − | 3.13051e16i | − | 1.73273i | −0.499414 | − | 0.866363i | \(-0.666451\pi\) | ||
0.499414 | − | 0.866363i | \(-0.333549\pi\) | |||||||
\(318\) | 2.05798e16 | + | 7.58795e15i | 1.11600 | + | 0.411480i | ||||
\(319\) | −3.99648e15 | −0.212343 | ||||||||
\(320\) | −1.11829e15 | − | 6.83584e14i | −0.0582209 | − | 0.0355891i | ||||
\(321\) | −7.12626e15 | −0.363562 | ||||||||
\(322\) | −2.01933e16 | − | 7.44546e15i | −1.00959 | − | 0.372245i | ||||
\(323\) | − | 4.06440e16i | − | 1.99150i | ||||||
\(324\) | −1.88641e16 | − | 1.60994e16i | −0.905928 | − | 0.773157i | ||||
\(325\) | 3.05264e16i | 1.43692i | ||||||||
\(326\) | 4.49602e14 | − | 1.21939e15i | 0.0207450 | − | 0.0562638i | ||||
\(327\) | 4.32037e16 | 1.95416 | ||||||||
\(328\) | 1.41667e16 | + | 2.52636e16i | 0.628186 | + | 1.12025i | ||||
\(329\) | 3.65282e16 | 1.58802 | ||||||||
\(330\) | −1.48911e14 | + | 4.03870e14i | −0.00634724 | + | 0.0172148i | ||||
\(331\) | 4.89913e15i | 0.204756i | 0.994746 | + | 0.102378i | \(0.0326452\pi\) | ||||
−0.994746 | + | 0.102378i | \(0.967355\pi\) | |||||||
\(332\) | −4.14777e15 | + | 4.86005e15i | −0.169987 | + | 0.199179i | ||||
\(333\) | − | 3.46781e15i | − | 0.139369i | ||||||
\(334\) | −2.68357e16 | − | 9.89457e15i | −1.05770 | − | 0.389982i | ||||
\(335\) | 1.62643e15 | 0.0628700 | ||||||||
\(336\) | 2.97848e16 | − | 4.74001e15i | 1.12925 | − | 0.179711i | ||||
\(337\) | −2.53208e16 | −0.941636 | −0.470818 | − | 0.882230i | \(-0.656041\pi\) | ||||
−0.470818 | + | 0.882230i | \(0.656041\pi\) | |||||||
\(338\) | −2.78838e16 | − | 1.02810e16i | −1.01717 | − | 0.375041i | ||||
\(339\) | 7.19948e15i | 0.257634i | ||||||||
\(340\) | −1.41239e15 | + | 1.65494e15i | −0.0495842 | + | 0.0580991i | ||||
\(341\) | 4.13437e15i | 0.142399i | ||||||||
\(342\) | −4.68259e15 | + | 1.26999e16i | −0.158240 | + | 0.429173i | ||||
\(343\) | 2.95242e16 | 0.978963 | ||||||||
\(344\) | −1.40643e16 | + | 7.88664e15i | −0.457603 | + | 0.256603i | ||||
\(345\) | −2.52822e15 | −0.0807218 | ||||||||
\(346\) | −1.78646e16 | + | 4.84517e16i | −0.559756 | + | 1.51815i | ||||
\(347\) | − | 5.14894e16i | − | 1.58335i | −0.610943 | − | 0.791674i | \(-0.709210\pi\) | ||
0.610943 | − | 0.791674i | \(-0.290790\pi\) | |||||||
\(348\) | 2.50204e16 | + | 2.13534e16i | 0.755143 | + | 0.644470i | ||||
\(349\) | 3.91636e16i | 1.16016i | 0.814560 | + | 0.580079i | \(0.196978\pi\) | ||||
−0.814560 | + | 0.580079i | \(0.803022\pi\) | |||||||
\(350\) | −3.27546e16 | − | 1.20769e16i | −0.952422 | − | 0.351167i | ||||
\(351\) | −4.21282e16 | −1.20248 | ||||||||
\(352\) | 8.39571e15 | + | 1.66195e15i | 0.235250 | + | 0.0465683i | ||||
\(353\) | 1.84699e15 | 0.0508077 | 0.0254038 | − | 0.999677i | \(-0.491913\pi\) | ||||
0.0254038 | + | 0.999677i | \(0.491913\pi\) | |||||||
\(354\) | 2.95079e16 | + | 1.08798e16i | 0.796923 | + | 0.293833i | ||||
\(355\) | − | 6.93102e14i | − | 0.0183786i | ||||||
\(356\) | −2.55790e16 | − | 2.18302e16i | −0.665976 | − | 0.568372i | ||||
\(357\) | − | 5.00647e16i | − | 1.27994i | ||||||
\(358\) | 1.18156e15 | − | 3.20459e15i | 0.0296631 | − | 0.0804512i | ||||
\(359\) | 6.56490e16 | 1.61850 | 0.809252 | − | 0.587461i | \(-0.199872\pi\) | ||||
0.809252 | + | 0.587461i | \(0.199872\pi\) | |||||||
\(360\) | 6.31994e14 | − | 3.54394e14i | 0.0153019 | − | 0.00858065i | ||||
\(361\) | −9.10600e16 | −2.16536 | ||||||||
\(362\) | −4.59389e15 | + | 1.24594e16i | −0.107294 | + | 0.290998i | ||||
\(363\) | 4.60632e16i | 1.05672i | ||||||||
\(364\) | 4.24142e16 | − | 4.96978e16i | 0.955767 | − | 1.11990i | ||||
\(365\) | − | 3.54623e15i | − | 0.0784988i | ||||||
\(366\) | 3.26374e16 | + | 1.20337e16i | 0.709723 | + | 0.261682i | ||||
\(367\) | 6.75272e15 | 0.144261 | 0.0721305 | − | 0.997395i | \(-0.477020\pi\) | ||||
0.0721305 | + | 0.997395i | \(0.477020\pi\) | |||||||
\(368\) | 7.90047e15 | + | 4.96441e16i | 0.165822 | + | 1.04197i | ||||
\(369\) | −1.60124e16 | −0.330207 | ||||||||
\(370\) | −1.71285e15 | − | 6.31544e14i | −0.0347063 | − | 0.0127965i | ||||
\(371\) | 5.43406e16i | 1.08192i | ||||||||
\(372\) | 2.20902e16 | − | 2.58837e16i | 0.432186 | − | 0.506404i | ||||
\(373\) | 6.35460e16i | 1.22175i | 0.791729 | + | 0.610873i | \(0.209181\pi\) | ||||
−0.791729 | + | 0.610873i | \(0.790819\pi\) | |||||||
\(374\) | 4.91491e15 | − | 1.33300e16i | 0.0928645 | − | 0.251864i | ||||
\(375\) | −8.22099e15 | −0.152659 | ||||||||
\(376\) | −4.17295e16 | − | 7.44166e16i | −0.761592 | − | 1.35815i | ||||
\(377\) | 7.12592e16 | 1.27827 | ||||||||
\(378\) | 1.66668e16 | − | 4.52032e16i | 0.293871 | − | 0.797025i | ||||
\(379\) | − | 1.76761e16i | − | 0.306360i | −0.988198 | − | 0.153180i | \(-0.951048\pi\) | ||
0.988198 | − | 0.153180i | \(-0.0489515\pi\) | |||||||
\(380\) | 5.42009e15 | + | 4.62573e15i | 0.0923449 | + | 0.0788110i | ||||
\(381\) | − | 3.74109e16i | − | 0.626594i | ||||||
\(382\) | −4.39413e16 | − | 1.62016e16i | −0.723538 | − | 0.266775i | ||||
\(383\) | −1.13626e17 | −1.83944 | −0.919718 | − | 0.392580i | \(-0.871583\pi\) | ||||
−0.919718 | + | 0.392580i | \(0.871583\pi\) | |||||||
\(384\) | −4.36823e16 | − | 5.52636e16i | −0.695269 | − | 0.879602i | ||||
\(385\) | −1.06641e15 | −0.0166890 | ||||||||
\(386\) | 6.90945e16 | + | 2.54758e16i | 1.06323 | + | 0.392022i | ||||
\(387\) | − | 8.91417e15i | − | 0.134884i | ||||||
\(388\) | 6.95199e16 | + | 5.93312e16i | 1.03444 | + | 0.882830i | ||||
\(389\) | − | 5.13314e16i | − | 0.751122i | −0.926798 | − | 0.375561i | \(-0.877450\pi\) | ||
0.926798 | − | 0.375561i | \(-0.122550\pi\) | |||||||
\(390\) | 2.65515e15 | − | 7.20120e15i | 0.0382093 | − | 0.103630i | ||||
\(391\) | 8.34458e16 | 1.18102 | ||||||||
\(392\) | 1.40860e15 | + | 2.51197e15i | 0.0196078 | + | 0.0349668i | ||||
\(393\) | 1.06314e16 | 0.145560 | ||||||||
\(394\) | 3.99218e16 | − | 1.08274e17i | 0.537631 | − | 1.45814i | ||||
\(395\) | 3.78243e15i | 0.0501061i | ||||||||
\(396\) | −3.07150e15 | + | 3.59896e15i | −0.0400251 | + | 0.0468984i | ||||
\(397\) | 6.00314e16i | 0.769556i | 0.923009 | + | 0.384778i | \(0.125722\pi\) | ||||
−0.923009 | + | 0.384778i | \(0.874278\pi\) | |||||||
\(398\) | −1.64488e16 | − | 6.06484e15i | −0.207441 | − | 0.0764855i | ||||
\(399\) | −1.63967e17 | −2.03438 | ||||||||
\(400\) | 1.28150e16 | + | 8.05252e16i | 0.156433 | + | 0.982974i | ||||
\(401\) | 1.01141e17 | 1.21475 | 0.607376 | − | 0.794415i | \(-0.292222\pi\) | ||||
0.607376 | + | 0.794415i | \(0.292222\pi\) | |||||||
\(402\) | 8.20162e16 | + | 3.02401e16i | 0.969237 | + | 0.357367i | ||||
\(403\) | − | 7.37178e16i | − | 0.857215i | ||||||
\(404\) | −9.40483e16 | + | 1.10199e17i | −1.07615 | + | 1.26095i | ||||
\(405\) | − | 7.21752e15i | − | 0.0812700i | ||||||
\(406\) | −2.81917e16 | + | 7.64605e16i | −0.312394 | + | 0.847263i | ||||
\(407\) | 1.19209e16 | 0.130000 | ||||||||
\(408\) | −1.01993e17 | + | 5.71934e16i | −1.09466 | + | 0.613839i | ||||
\(409\) | −7.36411e16 | −0.777891 | −0.388945 | − | 0.921261i | \(-0.627161\pi\) | ||||
−0.388945 | + | 0.921261i | \(0.627161\pi\) | |||||||
\(410\) | −2.91612e15 | + | 7.90899e15i | −0.0303187 | + | 0.0822292i | ||||
\(411\) | 3.19885e16i | 0.327357i | ||||||||
\(412\) | 7.78964e14 | + | 6.64801e14i | 0.00784667 | + | 0.00669668i | ||||
\(413\) | 7.79151e16i | 0.772585i | ||||||||
\(414\) | −2.60742e16 | − | 9.61379e15i | −0.254512 | − | 0.0938410i | ||||
\(415\) | −1.85948e15 | −0.0178681 | ||||||||
\(416\) | −1.49700e17 | − | 2.96333e16i | −1.41616 | − | 0.280333i | ||||
\(417\) | 1.62613e17 | 1.51451 | ||||||||
\(418\) | −4.36571e16 | − | 1.60968e16i | −0.400322 | − | 0.147602i | ||||
\(419\) | 2.79559e16i | 0.252396i | 0.992005 | + | 0.126198i | \(0.0402775\pi\) | ||||
−0.992005 | + | 0.126198i | \(0.959723\pi\) | |||||||
\(420\) | 6.67639e15 | + | 5.69791e15i | 0.0593501 | + | 0.0506518i | ||||
\(421\) | − | 1.82667e17i | − | 1.59892i | −0.600718 | − | 0.799461i | \(-0.705118\pi\) | ||
0.600718 | − | 0.799461i | \(-0.294882\pi\) | |||||||
\(422\) | −2.32112e16 | + | 6.29525e16i | −0.200063 | + | 0.542602i | ||||
\(423\) | 4.71663e16 | 0.400331 | ||||||||
\(424\) | 1.10704e17 | − | 6.20781e16i | 0.925309 | − | 0.518872i | ||||
\(425\) | 1.35353e17 | 1.11414 | ||||||||
\(426\) | 1.28868e16 | − | 3.49512e16i | 0.104468 | − | 0.283335i | ||||
\(427\) | 8.61786e16i | 0.688047i | ||||||||
\(428\) | −2.67692e16 | + | 3.13661e16i | −0.210499 | + | 0.246647i | ||||
\(429\) | 5.01180e16i | 0.388169i | ||||||||
\(430\) | −4.40296e15 | − | 1.62341e15i | −0.0335892 | − | 0.0123847i | ||||
\(431\) | −3.02335e16 | −0.227189 | −0.113594 | − | 0.993527i | \(-0.536236\pi\) | ||||
−0.113594 | + | 0.993527i | \(0.536236\pi\) | |||||||
\(432\) | −1.11129e17 | + | 1.76854e16i | −0.822593 | + | 0.130909i | ||||
\(433\) | −8.25641e16 | −0.602033 | −0.301016 | − | 0.953619i | \(-0.597326\pi\) | ||||
−0.301016 | + | 0.953619i | \(0.597326\pi\) | |||||||
\(434\) | 7.90987e16 | + | 2.91644e16i | 0.568180 | + | 0.209493i | ||||
\(435\) | 9.57294e15i | 0.0677431i | ||||||||
\(436\) | 1.62291e17 | − | 1.90161e17i | 1.13144 | − | 1.32574i | ||||
\(437\) | − | 2.73293e17i | − | 1.87715i | ||||||
\(438\) | 6.59350e16 | − | 1.78826e17i | 0.446205 | − | 1.21018i | ||||
\(439\) | 1.89165e17 | 1.26131 | 0.630653 | − | 0.776065i | \(-0.282787\pi\) | ||||
0.630653 | + | 0.776065i | \(0.282787\pi\) | |||||||
\(440\) | 1.21826e15 | + | 2.17253e15i | 0.00800382 | + | 0.0142733i | ||||
\(441\) | −1.59213e15 | −0.0103069 | ||||||||
\(442\) | −8.76352e16 | + | 2.37681e17i | −0.559028 | + | 1.51617i | ||||
\(443\) | − | 1.83331e17i | − | 1.15242i | −0.817301 | − | 0.576210i | \(-0.804531\pi\) | ||
0.817301 | − | 0.576210i | \(-0.195469\pi\) | |||||||
\(444\) | −7.46319e16 | − | 6.36940e16i | −0.462312 | − | 0.394556i | ||||
\(445\) | − | 9.78667e15i | − | 0.0597441i | ||||||
\(446\) | 6.59154e16 | + | 2.43036e16i | 0.396561 | + | 0.146216i | ||||
\(447\) | −9.49263e16 | −0.562844 | ||||||||
\(448\) | 9.10208e16 | − | 1.48903e17i | 0.531904 | − | 0.870153i | ||||
\(449\) | −3.31235e17 | −1.90781 | −0.953904 | − | 0.300111i | \(-0.902976\pi\) | ||||
−0.953904 | + | 0.300111i | \(0.902976\pi\) | |||||||
\(450\) | −4.22936e16 | − | 1.55941e16i | −0.240101 | − | 0.0885275i | ||||
\(451\) | − | 5.50441e16i | − | 0.308009i | ||||||
\(452\) | 3.16884e16 | + | 2.70442e16i | 0.174784 | + | 0.149168i | ||||
\(453\) | 3.68681e17i | 2.00453i | ||||||||
\(454\) | −8.08073e15 | + | 2.19163e16i | −0.0433100 | + | 0.117464i | ||||
\(455\) | 1.90147e16 | 0.100465 | ||||||||
\(456\) | 1.87314e17 | + | 3.34038e17i | 0.975660 | + | 1.73990i | ||||
\(457\) | −1.50721e17 | −0.773961 | −0.386980 | − | 0.922088i | \(-0.626482\pi\) | ||||
−0.386980 | + | 0.922088i | \(0.626482\pi\) | |||||||
\(458\) | 4.73651e16 | − | 1.28462e17i | 0.239791 | − | 0.650352i | ||||
\(459\) | 1.86795e17i | 0.932361i | ||||||||
\(460\) | −9.49705e15 | + | 1.11279e16i | −0.0467372 | + | 0.0547632i | ||||
\(461\) | 1.21235e17i | 0.588261i | 0.955765 | + | 0.294131i | \(0.0950301\pi\) | ||||
−0.955765 | + | 0.294131i | \(0.904970\pi\) | |||||||
\(462\) | −5.37762e16 | − | 1.98278e16i | −0.257287 | − | 0.0948641i | ||||
\(463\) | −8.74764e15 | −0.0412681 | −0.0206340 | − | 0.999787i | \(-0.506568\pi\) | ||||
−0.0206340 | + | 0.999787i | \(0.506568\pi\) | |||||||
\(464\) | 1.87974e17 | − | 2.99146e16i | 0.874442 | − | 0.139161i | ||||
\(465\) | 9.90324e15 | 0.0454290 | ||||||||
\(466\) | −1.72565e17 | − | 6.36265e16i | −0.780630 | − | 0.287826i | ||||
\(467\) | 2.95016e17i | 1.31609i | 0.752978 | + | 0.658045i | \(0.228617\pi\) | ||||
−0.752978 | + | 0.658045i | \(0.771383\pi\) | |||||||
\(468\) | 5.47664e16 | − | 6.41712e16i | 0.240944 | − | 0.282320i | ||||
\(469\) | 2.16562e17i | 0.939636i | ||||||||
\(470\) | 8.58975e15 | − | 2.32968e16i | 0.0367574 | − | 0.0996919i | ||||
\(471\) | 1.25969e17 | 0.531652 | ||||||||
\(472\) | 1.58731e17 | − | 8.90094e16i | 0.660753 | − | 0.370521i | ||||
\(473\) | 3.06432e16 | 0.125816 | ||||||||
\(474\) | −7.03268e16 | + | 1.90738e17i | −0.284814 | + | 0.772462i | ||||
\(475\) | − | 4.43295e17i | − | 1.77086i | ||||||
\(476\) | −2.20359e17 | − | 1.88064e17i | −0.868332 | − | 0.741071i | ||||
\(477\) | 7.01661e16i | 0.272746i | ||||||||
\(478\) | −2.02520e17 | − | 7.46712e16i | −0.776582 | − | 0.286333i | ||||
\(479\) | −2.73322e17 | −1.03394 | −0.516969 | − | 0.856004i | \(-0.672940\pi\) | ||||
−0.516969 | + | 0.856004i | \(0.672940\pi\) | |||||||
\(480\) | 3.98093e15 | − | 2.01106e16i | 0.0148565 | − | 0.0750511i | ||||
\(481\) | −2.12555e17 | −0.782579 | ||||||||
\(482\) | −3.38309e17 | − | 1.24738e17i | −1.22888 | − | 0.453098i | ||||
\(483\) | − | 3.36639e17i | − | 1.20645i | ||||||
\(484\) | 2.02747e17 | + | 1.73032e17i | 0.716900 | + | 0.611833i | ||||
\(485\) | 2.65987e16i | 0.0927982i | ||||||||
\(486\) | 5.04892e16 | − | 1.36935e17i | 0.173805 | − | 0.471387i | ||||
\(487\) | 5.51673e17 | 1.87389 | 0.936943 | − | 0.349482i | \(-0.113642\pi\) | ||||
0.936943 | + | 0.349482i | \(0.113642\pi\) | |||||||
\(488\) | 1.75566e17 | − | 9.84496e16i | 0.588453 | − | 0.329978i | ||||
\(489\) | 2.03283e16 | 0.0672346 | ||||||||
\(490\) | −2.89952e14 | + | 7.86397e14i | −0.000946349 | + | 0.00256665i | ||||
\(491\) | 4.05694e17i | 1.30668i | 0.757065 | + | 0.653340i | \(0.226633\pi\) | ||||
−0.757065 | + | 0.653340i | \(0.773367\pi\) | |||||||
\(492\) | −2.94104e17 | + | 3.44609e17i | −0.934819 | + | 1.09535i | ||||
\(493\) | − | 3.15962e17i | − | 0.991128i | ||||||
\(494\) | 7.78428e17 | + | 2.87014e17i | 2.40987 | + | 0.888541i | ||||
\(495\) | −1.37698e15 | −0.00420721 | ||||||||
\(496\) | −3.09467e16 | − | 1.94460e17i | −0.0933220 | − | 0.586406i | ||||
\(497\) | 9.22882e16 | 0.274682 | ||||||||
\(498\) | −9.37685e16 | − | 3.45733e16i | −0.275465 | − | 0.101567i | ||||
\(499\) | 4.14431e16i | 0.120171i | 0.998193 | + | 0.0600853i | \(0.0191373\pi\) | ||||
−0.998193 | + | 0.0600853i | \(0.980863\pi\) | |||||||
\(500\) | −3.08815e16 | + | 3.61846e16i | −0.0883879 | + | 0.103566i | ||||
\(501\) | − | 4.47373e17i | − | 1.26393i | ||||||
\(502\) | −2.12638e17 | + | 5.76709e17i | −0.593016 | + | 1.60836i | ||||
\(503\) | −2.67191e16 | −0.0735579 | −0.0367789 | − | 0.999323i | \(-0.511710\pi\) | ||||
−0.0367789 | + | 0.999323i | \(0.511710\pi\) | |||||||
\(504\) | 4.71884e16 | + | 8.41515e16i | 0.128244 | + | 0.228698i | ||||
\(505\) | −4.21627e16 | −0.113119 | ||||||||
\(506\) | 3.30482e16 | − | 8.96321e16i | 0.0875325 | − | 0.237402i | ||||
\(507\) | − | 4.64846e17i | − | 1.21551i | ||||||
\(508\) | −1.64664e17 | − | 1.40531e17i | −0.425093 | − | 0.362792i | ||||
\(509\) | − | 2.27992e17i | − | 0.581104i | −0.956859 | − | 0.290552i | \(-0.906161\pi\) | ||
0.956859 | − | 0.290552i | \(-0.0938389\pi\) | |||||||
\(510\) | −3.19300e16 | − | 1.17729e16i | −0.0803512 | − | 0.0296263i | ||||
\(511\) | 4.72188e17 | 1.17322 | ||||||||
\(512\) | −4.07331e17 | − | 1.53257e16i | −0.999293 | − | 0.0375980i | ||||
\(513\) | 6.11773e17 | 1.48193 | ||||||||
\(514\) | −6.25632e16 | − | 2.30676e16i | −0.149644 | − | 0.0551751i | ||||
\(515\) | 2.98036e14i | 0.000703918i | ||||||||
\(516\) | −1.91845e17 | − | 1.63729e17i | −0.447433 | − | 0.381858i | ||||
\(517\) | 1.62138e17i | 0.373419i | ||||||||
\(518\) | 8.40915e16 | − | 2.28070e17i | 0.191253 | − | 0.518710i | ||||
\(519\) | −8.07729e17 | −1.81417 | ||||||||
\(520\) | −2.17221e16 | − | 3.87373e16i | −0.0481816 | − | 0.0859226i | ||||
\(521\) | 2.69956e17 | 0.591355 | 0.295678 | − | 0.955288i | \(-0.404455\pi\) | ||||
0.295678 | + | 0.955288i | \(0.404455\pi\) | |||||||
\(522\) | −3.64020e16 | + | 9.87281e16i | −0.0787529 | + | 0.213591i | ||||
\(523\) | 8.10541e17i | 1.73187i | 0.500161 | + | 0.865933i | \(0.333274\pi\) | ||||
−0.500161 | + | 0.865933i | \(0.666726\pi\) | |||||||
\(524\) | 3.99361e16 | − | 4.67942e16i | 0.0842776 | − | 0.0987503i | ||||
\(525\) | − | 5.46045e17i | − | 1.13813i | ||||||
\(526\) | 3.68298e16 | + | 1.35795e16i | 0.0758214 | + | 0.0279561i | ||||
\(527\) | −3.26864e17 | −0.664657 | ||||||||
\(528\) | 2.10395e16 | + | 1.32206e17i | 0.0422586 | + | 0.265540i | ||||
\(529\) | 5.70597e16 | 0.113205 | ||||||||
\(530\) | 3.46570e16 | + | 1.27784e16i | 0.0679201 | + | 0.0250428i | ||||
\(531\) | 1.00606e17i | 0.194765i | ||||||||
\(532\) | −6.15927e17 | + | 7.21698e17i | −1.17789 | + | 1.38016i | ||||
\(533\) | 9.81462e17i | 1.85416i | ||||||||
\(534\) | 1.81964e17 | − | 4.93515e17i | 0.339599 | − | 0.921047i | ||||
\(535\) | −1.20009e16 | −0.0221265 | ||||||||
\(536\) | 4.41188e17 | − | 2.47399e17i | 0.803624 | − | 0.450637i | ||||
\(537\) | 5.34231e16 | 0.0961383 | ||||||||
\(538\) | 1.05393e17 | − | 2.85844e17i | 0.187382 | − | 0.508210i | ||||
\(539\) | − | 5.47307e15i | − | 0.00961399i | ||||||
\(540\) | −2.49102e16 | − | 2.12594e16i | −0.0432332 | − | 0.0368970i | ||||
\(541\) | 3.09047e17i | 0.529959i | 0.964254 | + | 0.264980i | \(0.0853653\pi\) | ||||
−0.964254 | + | 0.264980i | \(0.914635\pi\) | |||||||
\(542\) | −7.34018e16 | − | 2.70639e16i | −0.124369 | − | 0.0458559i | ||||
\(543\) | −2.07708e17 | −0.347739 | ||||||||
\(544\) | −1.31394e17 | + | 6.63765e17i | −0.217361 | + | 1.09805i | ||||
\(545\) | 7.27565e16 | 0.118931 | ||||||||
\(546\) | 9.58856e17 | + | 3.53539e17i | 1.54882 | + | 0.571065i | ||||
\(547\) | − | 4.33397e17i | − | 0.691780i | −0.938275 | − | 0.345890i | \(-0.887577\pi\) | ||
0.938275 | − | 0.345890i | \(-0.112423\pi\) | |||||||
\(548\) | 1.40797e17 | + | 1.20162e17i | 0.222085 | + | 0.189537i | ||||
\(549\) | 1.11276e17i | 0.173453i | ||||||||
\(550\) | 5.36059e16 | − | 1.45388e17i | 0.0825762 | − | 0.223960i | ||||
\(551\) | −1.03481e18 | −1.57534 | ||||||||
\(552\) | −6.85812e17 | + | 3.84573e17i | −1.03181 | + | 0.578594i | ||||
\(553\) | −5.03640e17 | −0.748871 | ||||||||
\(554\) | 1.34373e17 | − | 3.64442e17i | 0.197469 | − | 0.535568i | ||||
\(555\) | − | 2.85546e16i | − | 0.0414736i | ||||||
\(556\) | 6.10843e17 | − | 7.15740e17i | 0.876886 | − | 1.02747i | ||||
\(557\) | − | 3.35954e17i | − | 0.476674i | −0.971183 | − | 0.238337i | \(-0.923398\pi\) | ||
0.971183 | − | 0.238337i | \(-0.0766022\pi\) | |||||||
\(558\) | 1.02134e17 | + | 3.76580e16i | 0.143235 | + | 0.0528122i | ||||
\(559\) | −5.46383e17 | −0.757392 | ||||||||
\(560\) | 5.01586e16 | − | 7.98235e15i | 0.0687263 | − | 0.0109373i | ||||
\(561\) | 2.22222e17 | 0.300974 | ||||||||
\(562\) | −1.48870e16 | − | 5.48898e15i | −0.0199306 | − | 0.00734861i | ||||
\(563\) | 4.77847e17i | 0.632389i | 0.948694 | + | 0.316195i | \(0.102405\pi\) | ||||
−0.948694 | + | 0.316195i | \(0.897595\pi\) | |||||||
\(564\) | 8.66314e17 | − | 1.01508e18i | 1.13334 | − | 1.32797i | ||||
\(565\) | 1.21242e16i | 0.0156797i | ||||||||
\(566\) | 3.27449e17 | − | 8.88095e17i | 0.418636 | − | 1.13541i | ||||
\(567\) | 9.61029e17 | 1.21464 | ||||||||
\(568\) | −1.05429e17 | − | 1.88013e17i | −0.131733 | − | 0.234921i | ||||
\(569\) | −3.86358e16 | −0.0477265 | −0.0238633 | − | 0.999715i | \(-0.507597\pi\) | ||||
−0.0238633 | + | 0.999715i | \(0.507597\pi\) | |||||||
\(570\) | −3.85573e16 | + | 1.04574e17i | −0.0470891 | + | 0.127713i | ||||
\(571\) | − | 8.78096e17i | − | 1.06025i | −0.847920 | − | 0.530124i | \(-0.822145\pi\) | ||
0.847920 | − | 0.530124i | \(-0.177855\pi\) | |||||||
\(572\) | 2.20594e17 | + | 1.88264e17i | 0.263341 | + | 0.224747i | ||||
\(573\) | − | 7.32538e17i | − | 0.864619i | ||||||
\(574\) | −1.05310e18 | − | 3.88288e17i | −1.22897 | − | 0.453135i | ||||
\(575\) | 9.10126e17 | 1.05017 | ||||||||
\(576\) | 1.17529e17 | − | 1.92268e17i | 0.134090 | − | 0.219361i | ||||
\(577\) | 3.37219e17 | 0.380425 | 0.190213 | − | 0.981743i | \(-0.439082\pi\) | ||||
0.190213 | + | 0.981743i | \(0.439082\pi\) | |||||||
\(578\) | 2.12764e17 | + | 7.84480e16i | 0.237338 | + | 0.0875087i | ||||
\(579\) | 1.15186e18i | 1.27054i | ||||||||
\(580\) | 4.21352e16 | + | 3.59599e16i | 0.0459582 | + | 0.0392227i | ||||
\(581\) | − | 2.47594e17i | − | 0.267052i | ||||||
\(582\) | −4.94550e17 | + | 1.34130e18i | −0.527486 | + | 1.43063i | ||||
\(583\) | −2.41202e17 | −0.254410 | ||||||||
\(584\) | −5.39423e17 | − | 9.61958e17i | −0.562660 | − | 1.00340i | ||||
\(585\) | 2.45523e16 | 0.0253267 | ||||||||
\(586\) | −4.02011e17 | + | 1.09032e18i | −0.410113 | + | 1.11229i | ||||
\(587\) | − | 5.59350e16i | − | 0.0564334i | −0.999602 | − | 0.0282167i | \(-0.991017\pi\) | ||
0.999602 | − | 0.0282167i | \(-0.00898284\pi\) | |||||||
\(588\) | −2.92429e16 | + | 3.42647e16i | −0.0291789 | + | 0.0341896i | ||||
\(589\) | 1.07051e18i | 1.05643i | ||||||||
\(590\) | 4.96922e16 | + | 1.83220e16i | 0.0485010 | + | 0.0178828i | ||||
\(591\) | 1.80502e18 | 1.74246 | ||||||||
\(592\) | −5.60697e17 | + | 8.92305e16i | −0.535349 | + | 0.0851966i | ||||
\(593\) | −1.85096e18 | −1.74800 | −0.874000 | − | 0.485927i | \(-0.838482\pi\) | ||||
−0.874000 | + | 0.485927i | \(0.838482\pi\) | |||||||
\(594\) | 2.00644e17 | + | 7.39792e16i | 0.187419 | + | 0.0691031i | ||||
\(595\) | − | 8.43106e16i | − | 0.0778972i | ||||||
\(596\) | −3.56583e17 | + | 4.17817e17i | −0.325881 | + | 0.381844i | ||||
\(597\) | − | 2.74215e17i | − | 0.247890i | ||||||
\(598\) | −5.89265e17 | + | 1.59818e18i | −0.526930 | + | 1.42912i | ||||
\(599\) | −5.05656e17 | −0.447281 | −0.223641 | − | 0.974672i | \(-0.571794\pi\) | ||||
−0.223641 | + | 0.974672i | \(0.571794\pi\) | |||||||
\(600\) | −1.11242e18 | + | 6.23796e17i | −0.973389 | + | 0.545833i | ||||
\(601\) | 1.45684e16 | 0.0126103 | 0.00630517 | − | 0.999980i | \(-0.497993\pi\) | ||||
0.00630517 | + | 0.999980i | \(0.497993\pi\) | |||||||
\(602\) | 2.16161e17 | − | 5.86265e17i | 0.185098 | − | 0.502015i | ||||
\(603\) | 2.79632e17i | 0.236878i | ||||||||
\(604\) | 1.62274e18 | + | 1.38492e18i | 1.35991 | + | 1.16060i | ||||
\(605\) | 7.75720e16i | 0.0643124i | ||||||||
\(606\) | −2.12615e18 | − | 7.83931e17i | −1.74390 | − | 0.642992i | ||||
\(607\) | 1.20617e18 | 0.978772 | 0.489386 | − | 0.872067i | \(-0.337221\pi\) | ||||
0.489386 | + | 0.872067i | \(0.337221\pi\) | |||||||
\(608\) | 2.17390e18 | + | 4.30327e17i | 1.74528 | + | 0.345482i | ||||
\(609\) | −1.27466e18 | −1.01247 | ||||||||
\(610\) | 5.49625e16 | + | 2.02652e16i | 0.0431939 | + | 0.0159260i | ||||
\(611\) | − | 2.89100e18i | − | 2.24792i | ||||||
\(612\) | −2.84534e17 | − | 2.42833e17i | −0.218902 | − | 0.186820i | ||||
\(613\) | − | 1.01082e18i | − | 0.769450i | −0.923031 | − | 0.384725i | \(-0.874296\pi\) | ||
0.923031 | − | 0.384725i | \(-0.125704\pi\) | |||||||
\(614\) | −2.67378e17 | + | 7.25173e17i | −0.201387 | + | 0.546195i | ||||
\(615\) | −1.31849e17 | −0.0982630 | ||||||||
\(616\) | −2.89278e17 | + | 1.62214e17i | −0.213324 | + | 0.119623i | ||||
\(617\) | 1.35500e18 | 0.988751 | 0.494376 | − | 0.869248i | \(-0.335397\pi\) | ||||
0.494376 | + | 0.869248i | \(0.335397\pi\) | |||||||
\(618\) | −5.54138e15 | + | 1.50291e16i | −0.00400123 | + | 0.0108520i | ||||
\(619\) | 3.64418e17i | 0.260382i | 0.991489 | + | 0.130191i | \(0.0415590\pi\) | ||||
−0.991489 | + | 0.130191i | \(0.958441\pi\) | |||||||
\(620\) | 3.72007e16 | − | 4.35890e16i | 0.0263030 | − | 0.0308199i | ||||
\(621\) | 1.25603e18i | 0.878827i | ||||||||
\(622\) | 2.99505e17 | + | 1.10430e17i | 0.207380 | + | 0.0764629i | ||||
\(623\) | 1.30312e18 | 0.892918 | ||||||||
\(624\) | −3.75145e17 | − | 2.35729e18i | −0.254390 | − | 1.59850i | ||||
\(625\) | 1.46933e18 | 0.986053 | ||||||||
\(626\) | −8.53610e17 | − | 3.14734e17i | −0.566926 | − | 0.209031i | ||||
\(627\) | − | 7.27800e17i | − | 0.478380i | ||||||
\(628\) | 4.73191e17 | − | 5.54451e17i | 0.307822 | − | 0.360683i | ||||
\(629\) | 9.42465e17i | 0.606787i | ||||||||
\(630\) | −9.71343e15 | + | 2.63444e16i | −0.00618955 | + | 0.0167871i | ||||
\(631\) | −2.16455e18 | −1.36514 | −0.682571 | − | 0.730819i | \(-0.739138\pi\) | ||||
−0.682571 | + | 0.730819i | \(0.739138\pi\) | |||||||
\(632\) | 5.75353e17 | + | 1.02603e18i | 0.359148 | + | 0.640472i | ||||
\(633\) | −1.04947e18 | −0.648404 | ||||||||
\(634\) | 9.80202e17 | − | 2.65847e18i | 0.599426 | − | 1.62574i | ||||
\(635\) | − | 6.30013e16i | − | 0.0381347i | ||||||
\(636\) | 1.51007e18 | + | 1.28876e18i | 0.904744 | + | 0.772146i | ||||
\(637\) | 9.75874e16i | 0.0578745i | ||||||||
\(638\) | −3.39386e17 | − | 1.25135e17i | −0.199232 | − | 0.0734588i | ||||
\(639\) | 1.19165e17 | 0.0692458 | ||||||||
\(640\) | −7.35626e16 | − | 9.30658e16i | −0.0423143 | − | 0.0535328i | ||||
\(641\) | −6.48038e17 | −0.368997 | −0.184499 | − | 0.982833i | \(-0.559066\pi\) | ||||
−0.184499 | + | 0.982833i | \(0.559066\pi\) | |||||||
\(642\) | −6.05170e17 | − | 2.23132e17i | −0.341114 | − | 0.125772i | ||||
\(643\) | 1.13754e18i | 0.634738i | 0.948302 | + | 0.317369i | \(0.102799\pi\) | ||||
−0.948302 | + | 0.317369i | \(0.897201\pi\) | |||||||
\(644\) | −1.48171e18 | − | 1.26455e18i | −0.818475 | − | 0.698521i | ||||
\(645\) | − | 7.34010e16i | − | 0.0401387i | ||||||
\(646\) | 1.27261e18 | − | 3.45153e18i | 0.688946 | − | 1.86853i | ||||
\(647\) | 4.00139e17 | 0.214453 | 0.107227 | − | 0.994235i | \(-0.465803\pi\) | ||||
0.107227 | + | 0.994235i | \(0.465803\pi\) | |||||||
\(648\) | −1.09787e18 | − | 1.95784e18i | −0.582523 | − | 1.03882i | ||||
\(649\) | −3.45842e17 | −0.181672 | ||||||||
\(650\) | −9.55819e17 | + | 2.59234e18i | −0.497094 | + | 1.34820i | ||||
\(651\) | 1.31864e18i | 0.678968i | ||||||||
\(652\) | 7.63614e16 | − | 8.94747e16i | 0.0389282 | − | 0.0456132i | ||||
\(653\) | 5.15814e17i | 0.260350i | 0.991491 | + | 0.130175i | \(0.0415539\pi\) | ||||
−0.991491 | + | 0.130175i | \(0.958446\pi\) | |||||||
\(654\) | 3.66891e18 | + | 1.35276e18i | 1.83350 | + | 0.676030i | ||||
\(655\) | 1.79037e16 | 0.00885880 | ||||||||
\(656\) | 4.12018e17 | + | 2.58899e18i | 0.201856 | + | 1.26840i | ||||
\(657\) | 6.09703e17 | 0.295763 | ||||||||
\(658\) | 3.10202e18 | + | 1.14374e18i | 1.48997 | + | 0.549365i | ||||
\(659\) | 2.76356e18i | 1.31436i | 0.753734 | + | 0.657180i | \(0.228251\pi\) | ||||
−0.753734 | + | 0.657180i | \(0.771749\pi\) | |||||||
\(660\) | −2.52913e16 | + | 2.96345e16i | −0.0119107 | + | 0.0139560i | ||||
\(661\) | − | 2.27112e18i | − | 1.05909i | −0.848283 | − | 0.529543i | \(-0.822364\pi\) | ||
0.848283 | − | 0.529543i | \(-0.177636\pi\) | |||||||
\(662\) | −1.53398e17 | + | 4.16040e17i | −0.0708341 | + | 0.192114i | ||||
\(663\) | −3.96233e18 | −1.81181 | ||||||||
\(664\) | −5.04408e17 | + | 2.82849e17i | −0.228396 | + | 0.128074i | ||||
\(665\) | −2.76125e17 | −0.123813 | ||||||||
\(666\) | 1.08581e17 | − | 2.94490e17i | 0.0482140 | − | 0.130764i | ||||
\(667\) | − | 2.12455e18i | − | 0.934221i | ||||||
\(668\) | −1.96911e18 | − | 1.68052e18i | −0.857476 | − | 0.731806i | ||||
\(669\) | 1.09886e18i | 0.473886i | ||||||||
\(670\) | 1.38118e17 | + | 5.09254e16i | 0.0589881 | + | 0.0217495i | ||||
\(671\) | −3.82521e17 | −0.161793 | ||||||||
\(672\) | 2.67777e18 | + | 5.30071e17i | 1.12169 | + | 0.222041i | ||||
\(673\) | 3.76617e17 | 0.156243 | 0.0781217 | − | 0.996944i | \(-0.475108\pi\) | ||||
0.0781217 | + | 0.996944i | \(0.475108\pi\) | |||||||
\(674\) | −2.15027e18 | − | 7.92826e17i | −0.883495 | − | 0.325753i | ||||
\(675\) | 2.03734e18i | 0.829066i | ||||||||
\(676\) | −2.04602e18 | − | 1.74616e18i | −0.824623 | − | 0.703768i | ||||
\(677\) | − | 2.97834e18i | − | 1.18891i | −0.804130 | − | 0.594453i | \(-0.797369\pi\) | ||
0.804130 | − | 0.594453i | \(-0.202631\pi\) | |||||||
\(678\) | −2.25425e17 | + | 6.11389e17i | −0.0891269 | + | 0.241727i | ||||
\(679\) | −3.54168e18 | −1.38693 | ||||||||
\(680\) | −1.71760e17 | + | 9.63156e16i | −0.0666216 | + | 0.0373584i | ||||
\(681\) | −3.65362e17 | −0.140368 | ||||||||
\(682\) | −1.29452e17 | + | 3.51096e17i | −0.0492619 | + | 0.133606i | ||||
\(683\) | 1.79679e18i | 0.677270i | 0.940918 | + | 0.338635i | \(0.109965\pi\) | ||||
−0.940918 | + | 0.338635i | \(0.890035\pi\) | |||||||
\(684\) | −7.95302e17 | + | 9.31877e17i | −0.296939 | + | 0.347932i | ||||
\(685\) | 5.38697e16i | 0.0199231i | ||||||||
\(686\) | 2.50723e18 | + | 9.24439e17i | 0.918517 | + | 0.338666i | ||||
\(687\) | 2.14156e18 | 0.777163 | ||||||||
\(688\) | −1.44130e18 | + | 2.29372e17i | −0.518119 | + | 0.0824546i | ||||
\(689\) | 4.30074e18 | 1.53151 | ||||||||
\(690\) | −2.14700e17 | − | 7.91618e16i | −0.0757377 | − | 0.0279252i | ||||
\(691\) | 8.70716e17i | 0.304277i | 0.988359 | + | 0.152139i | \(0.0486160\pi\) | ||||
−0.988359 | + | 0.152139i | \(0.951384\pi\) | |||||||
\(692\) | −3.03417e18 | + | 3.55521e18i | −1.05039 | + | 1.23077i | ||||
\(693\) | − | 1.83348e17i | − | 0.0628798i | ||||||
\(694\) | 1.61220e18 | − | 4.37254e18i | 0.547750 | − | 1.48559i | ||||
\(695\) | 2.73846e17 | 0.0921734 | ||||||||
\(696\) | 1.45616e18 | + | 2.59678e18i | 0.485566 | + | 0.865915i | ||||
\(697\) | 4.35179e18 | 1.43765 | ||||||||
\(698\) | −1.22626e18 | + | 3.32582e18i | −0.401349 | + | 1.08852i | ||||
\(699\) | − | 2.87681e18i | − | 0.932844i | ||||||
\(700\) | −2.40341e18 | − | 2.05117e18i | −0.772131 | − | 0.658969i | ||||
\(701\) | 3.25269e18i | 1.03532i | 0.855586 | + | 0.517661i | \(0.173197\pi\) | ||||
−0.855586 | + | 0.517661i | \(0.826803\pi\) | |||||||
\(702\) | −3.57757e18 | − | 1.31909e18i | −1.12823 | − | 0.415989i | ||||
\(703\) | 3.08666e18 | 0.964450 | ||||||||
\(704\) | 6.60936e17 | + | 4.04015e17i | 0.204615 | + | 0.125076i | ||||
\(705\) | 3.88376e17 | 0.119131 | ||||||||
\(706\) | 1.56849e17 | + | 5.78316e16i | 0.0476706 | + | 0.0175766i | ||||
\(707\) | − | 5.61406e18i | − | 1.69064i | ||||||
\(708\) | 2.16518e18 | + | 1.84786e18i | 0.646068 | + | 0.551381i | ||||
\(709\) | 6.65027e17i | 0.196625i | 0.995156 | + | 0.0983125i | \(0.0313445\pi\) | ||||
−0.995156 | + | 0.0983125i | \(0.968656\pi\) | |||||||
\(710\) | 2.17019e16 | − | 5.88590e16i | 0.00635797 | − | 0.0172438i | ||||
\(711\) | −6.50314e17 | −0.188786 | ||||||||
\(712\) | −1.48867e18 | − | 2.65476e18i | −0.428231 | − | 0.763668i | ||||
\(713\) | −2.19786e18 | −0.626494 | ||||||||
\(714\) | 1.56759e18 | − | 4.25155e18i | 0.442785 | − | 1.20091i | ||||
\(715\) | 8.44004e16i | 0.0236241i | ||||||||
\(716\) | 2.00679e17 | − | 2.35141e17i | 0.0556632 | − | 0.0652220i | ||||
\(717\) | − | 3.37618e18i | − | 0.928006i | ||||||
\(718\) | 5.57499e18 | + | 2.05555e18i | 1.51857 | + | 0.559911i | ||||
\(719\) | 3.90552e18 | 1.05424 | 0.527122 | − | 0.849790i | \(-0.323271\pi\) | ||||
0.527122 | + | 0.849790i | \(0.323271\pi\) | |||||||
\(720\) | 6.47662e16 | − | 1.03070e16i | 0.0173256 | − | 0.00275723i | ||||
\(721\) | −3.96842e16 | −0.0105205 | ||||||||
\(722\) | −7.73292e18 | − | 2.85120e18i | −2.03166 | − | 0.749094i | ||||
\(723\) | − | 5.63989e18i | − | 1.46849i | ||||||
\(724\) | −7.80237e17 | + | 9.14224e17i | −0.201338 | + | 0.235913i | ||||
\(725\) | − | 3.44613e18i | − | 0.881323i | ||||||
\(726\) | −1.44230e18 | + | 3.91174e18i | −0.365566 | + | 0.991475i | ||||
\(727\) | −5.10127e18 | −1.28146 | −0.640730 | − | 0.767766i | \(-0.721368\pi\) | ||||
−0.640730 | + | 0.767766i | \(0.721368\pi\) | |||||||
\(728\) | 5.15796e18 | − | 2.89235e18i | 1.28417 | − | 0.720108i | ||||
\(729\) | −2.54377e18 | −0.627696 | ||||||||
\(730\) | 1.11037e17 | − | 3.01150e17i | 0.0271562 | − | 0.0736519i | ||||
\(731\) | 2.42265e18i | 0.587257i | ||||||||
\(732\) | 2.39482e18 | + | 2.04384e18i | 0.575374 | + | 0.491048i | ||||
\(733\) | − | 3.11289e18i | − | 0.741289i | −0.928775 | − | 0.370645i | \(-0.879137\pi\) | ||
0.928775 | − | 0.370645i | \(-0.120863\pi\) | |||||||
\(734\) | 5.73449e17 | + | 2.11436e17i | 0.135354 | + | 0.0499062i | ||||
\(735\) | −1.31099e16 | −0.00306712 | ||||||||
\(736\) | −8.83501e17 | + | 4.46321e18i | −0.204881 | + | 1.03500i | ||||
\(737\) | −9.61257e17 | −0.220953 | ||||||||
\(738\) | −1.35979e18 | − | 5.01369e17i | −0.309818 | − | 0.114233i | ||||
\(739\) | 7.69864e18i | 1.73870i | 0.494195 | + | 0.869351i | \(0.335463\pi\) | ||||
−0.494195 | + | 0.869351i | \(0.664537\pi\) | |||||||
\(740\) | −1.25683e17 | − | 1.07263e17i | −0.0281365 | − | 0.0240128i | ||||
\(741\) | 1.29770e19i | 2.87976i | ||||||||
\(742\) | −1.70147e18 | + | 4.61466e18i | −0.374282 | + | 1.01511i | ||||
\(743\) | 6.25892e18 | 1.36481 | 0.682405 | − | 0.730974i | \(-0.260934\pi\) | ||||
0.682405 | + | 0.730974i | \(0.260934\pi\) | |||||||
\(744\) | 2.68638e18 | − | 1.50640e18i | 0.580688 | − | 0.325624i | ||||
\(745\) | −1.59859e17 | −0.0342548 | ||||||||
\(746\) | −1.98970e18 | + | 5.39640e18i | −0.422655 | + | 1.14631i | ||||
\(747\) | − | 3.19701e17i | − | 0.0673225i | ||||||
\(748\) | 8.34759e17 | − | 9.78109e17i | 0.174261 | − | 0.204186i | ||||
\(749\) | − | 1.59794e18i | − | 0.330696i | ||||||
\(750\) | −6.98136e17 | − | 2.57410e17i | −0.143233 | − | 0.0528113i | ||||
\(751\) | −2.41477e18 | −0.491153 | −0.245577 | − | 0.969377i | \(-0.578977\pi\) | ||||
−0.245577 | + | 0.969377i | \(0.578977\pi\) | |||||||
\(752\) | −1.21364e18 | − | 7.62615e18i | −0.244723 | − | 1.53776i | ||||
\(753\) | −9.61420e18 | −1.92197 | ||||||||
\(754\) | 6.05141e18 | + | 2.23121e18i | 1.19934 | + | 0.442209i | ||||
\(755\) | 6.20871e17i | 0.121996i | ||||||||
\(756\) | 2.83074e18 | − | 3.31685e18i | 0.551452 | − | 0.646151i | ||||
\(757\) | 3.19891e18i | 0.617844i | 0.951087 | + | 0.308922i | \(0.0999682\pi\) | ||||
−0.951087 | + | 0.308922i | \(0.900032\pi\) | |||||||
\(758\) | 5.53462e17 | − | 1.50108e18i | 0.105983 | − | 0.287444i | ||||
\(759\) | 1.49424e18 | 0.283693 | ||||||||
\(760\) | 3.15443e17 | + | 5.62532e17i | 0.0593789 | + | 0.105891i | ||||
\(761\) | −5.76395e18 | −1.07577 | −0.537886 | − | 0.843018i | \(-0.680777\pi\) | ||||
−0.537886 | + | 0.843018i | \(0.680777\pi\) | |||||||
\(762\) | 1.17138e18 | − | 3.17698e18i | 0.216766 | − | 0.587905i | ||||
\(763\) | 9.68770e18i | 1.77751i | ||||||||
\(764\) | −3.22426e18 | − | 2.75172e18i | −0.586574 | − | 0.500607i | ||||
\(765\) | − | 1.08864e17i | − | 0.0196375i | ||||||
\(766\) | −9.64923e18 | − | 3.55776e18i | −1.72586 | − | 0.636341i | ||||
\(767\) | 6.16653e18 | 1.09363 | ||||||||
\(768\) | −1.97918e18 | − | 6.06080e18i | −0.348047 | − | 1.06582i | ||||
\(769\) | −2.49093e18 | −0.434351 | −0.217176 | − | 0.976133i | \(-0.569684\pi\) | ||||
−0.217176 | + | 0.976133i | \(0.569684\pi\) | |||||||
\(770\) | −9.05610e16 | − | 3.33907e16i | −0.0156585 | − | 0.00577346i | ||||
\(771\) | − | 1.04298e18i | − | 0.178823i | ||||||
\(772\) | 5.06991e18 | + | 4.32687e18i | 0.861961 | + | 0.735633i | ||||
\(773\) | − | 3.96232e18i | − | 0.668009i | −0.942571 | − | 0.334005i | \(-0.891600\pi\) | ||
0.942571 | − | 0.334005i | \(-0.108400\pi\) | |||||||
\(774\) | 2.79114e17 | − | 7.57002e17i | 0.0466622 | − | 0.126555i | ||||
\(775\) | −3.56503e18 | −0.591021 | ||||||||
\(776\) | 4.04598e18 | + | 7.21523e18i | 0.665155 | + | 1.18618i | ||||
\(777\) | 3.80211e18 | 0.619852 | ||||||||
\(778\) | 1.60725e18 | − | 4.35912e18i | 0.259846 | − | 0.704744i | ||||
\(779\) | − | 1.42525e19i | − | 2.28506i | ||||||
\(780\) | 4.50957e17 | − | 5.28398e17i | 0.0717001 | − | 0.0840129i | ||||
\(781\) | 4.09640e17i | 0.0645908i | ||||||||
\(782\) | 7.08632e18 | + | 2.61279e18i | 1.10809 | + | 0.408565i | ||||
\(783\) | 4.75586e18 | 0.737527 | ||||||||
\(784\) | 4.09672e16 | + | 2.57425e17i | 0.00630060 | + | 0.0395910i | ||||
\(785\) | 2.12136e17 | 0.0323565 | ||||||||
\(786\) | 9.02834e17 | + | 3.32884e17i | 0.136572 | + | 0.0503554i | ||||
\(787\) | − | 4.01666e18i | − | 0.602600i | −0.953529 | − | 0.301300i | \(-0.902579\pi\) | ||
0.953529 | − | 0.301300i | \(-0.0974205\pi\) | |||||||
\(788\) | 6.78040e18 | − | 7.94478e18i | 1.00887 | − | 1.18212i | ||||
\(789\) | 6.13982e17i | 0.0906057i | ||||||||
\(790\) | −1.18433e17 | + | 3.21209e17i | −0.0173339 | + | 0.0470123i | ||||
\(791\) | −1.61436e18 | −0.234344 | ||||||||
\(792\) | −3.73524e17 | + | 2.09455e17i | −0.0537780 | + | 0.0301563i | ||||
\(793\) | 6.82054e18 | 0.973965 | ||||||||
\(794\) | −1.87966e18 | + | 5.09794e18i | −0.266223 | + | 0.722040i | ||||
\(795\) | 5.77761e17i | 0.0811637i | ||||||||
\(796\) | −1.20696e18 | − | 1.03007e18i | −0.168173 | − | 0.143526i | ||||
\(797\) | − | 1.33185e18i | − | 0.184068i | −0.995756 | − | 0.0920338i | \(-0.970663\pi\) | ||
0.995756 | − | 0.0920338i | \(-0.0293368\pi\) | |||||||
\(798\) | −1.39242e19 | − | 5.13400e18i | −1.90877 | − | 0.703780i | ||||
\(799\) | −1.28186e19 | −1.74296 | ||||||||
\(800\) | −1.43308e18 | + | 7.23955e18i | −0.193280 | + | 0.976397i | ||||
\(801\) | 1.68262e18 | 0.225100 | ||||||||
\(802\) | 8.58899e18 | + | 3.16684e18i | 1.13975 | + | 0.420236i | ||||
\(803\) | 2.09591e18i | 0.275880i | ||||||||
\(804\) | 6.01805e18 | + | 5.13606e18i | 0.785763 | + | 0.670603i | ||||
\(805\) | − | 5.66911e17i | − | 0.0734246i | ||||||
\(806\) | 2.30820e18 | − | 6.26021e18i | 0.296548 | − | 0.804287i | ||||
\(807\) | 4.76525e18 | 0.607306 | ||||||||
\(808\) | −1.14372e19 | + | 6.41344e18i | −1.44592 | + | 0.810807i | ||||
\(809\) | 2.65212e18 | 0.332604 | 0.166302 | − | 0.986075i | \(-0.446817\pi\) | ||||
0.166302 | + | 0.986075i | \(0.446817\pi\) | |||||||
\(810\) | 2.25989e17 | − | 6.12920e17i | 0.0281148 | − | 0.0762520i | ||||
\(811\) | − | 5.40937e18i | − | 0.667592i | −0.942645 | − | 0.333796i | \(-0.891670\pi\) | ||
0.942645 | − | 0.333796i | \(-0.108330\pi\) | |||||||
\(812\) | −4.78815e18 | + | 5.61040e18i | −0.586210 | + | 0.686878i | ||||
\(813\) | − | 1.22367e18i | − | 0.148619i | ||||||
\(814\) | 1.01233e18 | + | 3.73258e17i | 0.121974 | + | 0.0449728i | ||||
\(815\) | 3.42335e16 | 0.00409192 | ||||||||
\(816\) | −1.04522e19 | + | 1.66339e18i | −1.23943 | + | 0.197245i | ||||
\(817\) | 7.93443e18 | 0.933409 | ||||||||
\(818\) | −6.25369e18 | − | 2.30579e18i | −0.729860 | − | 0.269106i | ||||
\(819\) | 3.26919e18i | 0.378525i | ||||||||
\(820\) | −4.95281e17 | + | 5.80334e17i | −0.0568934 | + | 0.0666634i | ||||
\(821\) | 9.60867e18i | 1.09505i | 0.836790 | + | 0.547523i | \(0.184429\pi\) | ||||
−0.836790 | + | 0.547523i | \(0.815571\pi\) | |||||||
\(822\) | −1.00160e18 | + | 2.71650e18i | −0.113247 | + | 0.307145i | ||||
\(823\) | 4.48399e18 | 0.502997 | 0.251498 | − | 0.967858i | \(-0.419077\pi\) | ||||
0.251498 | + | 0.967858i | \(0.419077\pi\) | |||||||
\(824\) | 4.53348e16 | + | 8.08460e16i | 0.00504551 | + | 0.00899770i | ||||
\(825\) | 2.42373e18 | 0.267630 | ||||||||
\(826\) | −2.43962e18 | + | 6.61664e18i | −0.267271 | + | 0.724882i | ||||
\(827\) | 9.62703e18i | 1.04642i | 0.852203 | + | 0.523211i | \(0.175266\pi\) | ||||
−0.852203 | + | 0.523211i | \(0.824734\pi\) | |||||||
\(828\) | −1.91323e18 | − | 1.63283e18i | −0.206333 | − | 0.176094i | ||||
\(829\) | − | 1.12704e19i | − | 1.20597i | −0.797753 | − | 0.602984i | \(-0.793978\pi\) | ||
0.797753 | − | 0.602984i | \(-0.206022\pi\) | |||||||
\(830\) | −1.57909e17 | − | 5.82227e16i | −0.0167649 | − | 0.00618137i | ||||
\(831\) | 6.07555e18 | 0.639998 | ||||||||
\(832\) | −1.17848e19 | − | 7.20378e18i | −1.23174 | − | 0.752937i | ||||
\(833\) | 4.32701e17 | 0.0448741 | ||||||||
\(834\) | 1.38093e19 | + | 5.09162e18i | 1.42099 | + | 0.523934i | ||||
\(835\) | − | 7.53391e17i | − | 0.0769234i | ||||||
\(836\) | −3.20340e18 | − | 2.73392e18i | −0.324542 | − | 0.276978i | ||||
\(837\) | − | 4.91995e18i | − | 0.494590i | ||||||
\(838\) | −8.75334e17 | + | 2.37405e18i | −0.0873148 | + | 0.236812i | ||||
\(839\) | −1.51849e19 | −1.50300 | −0.751501 | − | 0.659732i | \(-0.770670\pi\) | ||||
−0.751501 | + | 0.659732i | \(0.770670\pi\) | |||||||
\(840\) | 3.88558e17 | + | 6.92919e17i | 0.0381628 | + | 0.0680561i | ||||
\(841\) | 2.21615e18 | 0.215986 | ||||||||
\(842\) | 5.71954e18 | − | 1.55123e19i | 0.553137 | − | 1.50020i | ||||
\(843\) | − | 2.48178e17i | − | 0.0238169i | ||||||
\(844\) | −3.94224e18 | + | 4.61923e18i | −0.375420 | + | 0.439889i | ||||
\(845\) | − | 7.82817e17i | − | 0.0739762i | ||||||
\(846\) | 4.00542e18 | + | 1.47684e18i | 0.375613 | + | 0.138492i | ||||
\(847\) | −1.03289e19 | −0.961195 | ||||||||
\(848\) | 1.13449e19 | − | 1.80545e18i | 1.04768 | − | 0.166730i | ||||
\(849\) | 1.48053e19 | 1.35680 | ||||||||
\(850\) | 1.14944e19 | + | 4.23808e18i | 1.04535 | + | 0.385431i | ||||
\(851\) | 6.33721e18i | 0.571947i | ||||||||
\(852\) | 2.18873e18 | − | 2.56459e18i | 0.196036 | − | 0.229700i | ||||
\(853\) | − | 1.75981e17i | − | 0.0156422i | −0.999969 | − | 0.00782111i | \(-0.997510\pi\) | ||
0.999969 | − | 0.00782111i | \(-0.00248956\pi\) | |||||||
\(854\) | −2.69836e18 | + | 7.31839e18i | −0.238026 | + | 0.645564i | ||||
\(855\) | −3.56541e17 | −0.0312126 | ||||||||
\(856\) | −3.25538e18 | + | 1.82547e18i | −0.282828 | + | 0.158597i | ||||
\(857\) | −1.54615e19 | −1.33314 | −0.666571 | − | 0.745442i | \(-0.732239\pi\) | ||||
−0.666571 | + | 0.745442i | \(0.732239\pi\) | |||||||
\(858\) | −1.56926e18 | + | 4.25608e18i | −0.134285 | + | 0.364202i | ||||
\(859\) | 7.20321e18i | 0.611745i | 0.952072 | + | 0.305873i | \(0.0989482\pi\) | ||||
−0.952072 | + | 0.305873i | \(0.901052\pi\) | |||||||
\(860\) | −3.23074e17 | − | 2.75725e17i | −0.0272309 | − | 0.0232400i | ||||
\(861\) | − | 1.75561e19i | − | 1.46861i | ||||||
\(862\) | −2.56747e18 | − | 9.46650e17i | −0.213161 | − | 0.0785945i | ||||
\(863\) | −1.11261e19 | −0.916797 | −0.458398 | − | 0.888747i | \(-0.651577\pi\) | ||||
−0.458398 | + | 0.888747i | \(0.651577\pi\) | |||||||
\(864\) | −9.99100e18 | − | 1.97774e18i | −0.817089 | − | 0.161744i | ||||
\(865\) | −1.36024e18 | −0.110411 | ||||||||
\(866\) | −7.01144e18 | − | 2.58519e18i | −0.564860 | − | 0.208269i | ||||
\(867\) | 3.54695e18i | 0.283616i | ||||||||
\(868\) | 5.80398e18 | + | 4.95336e18i | 0.460625 | + | 0.393117i | ||||
\(869\) | − | 2.23551e18i | − | 0.176095i | ||||||
\(870\) | −2.99741e17 | + | 8.12945e17i | −0.0234353 | + | 0.0635603i | ||||
\(871\) | 1.71397e19 | 1.33010 | ||||||||
\(872\) | 1.97361e19 | − | 1.10671e19i | 1.52021 | − | 0.852468i | ||||
\(873\) | −4.57312e18 | −0.349639 | ||||||||
\(874\) | 8.55715e18 | − | 2.32084e19i | 0.649389 | − | 1.76125i | ||||
\(875\) | − | 1.84342e18i | − | 0.138858i | ||||||
\(876\) | 1.11986e19 | − | 1.31216e19i | 0.837308 | − | 0.981096i | ||||
\(877\) | 2.17444e19i | 1.61380i | 0.590688 | + | 0.806900i | \(0.298856\pi\) | ||||
−0.590688 | + | 0.806900i | \(0.701144\pi\) | |||||||
\(878\) | 1.60641e19 | + | 5.92298e18i | 1.18343 | + | 0.436341i | ||||
\(879\) | −1.81765e19 | −1.32918 | ||||||||
\(880\) | 3.54313e16 | + | 2.22639e17i | 0.00257187 | + | 0.0161608i | ||||
\(881\) | 2.54349e18 | 0.183268 | 0.0916338 | − | 0.995793i | \(-0.470791\pi\) | ||||
0.0916338 | + | 0.995793i | \(0.470791\pi\) | |||||||
\(882\) | −1.35205e17 | − | 4.98515e16i | −0.00967047 | − | 0.00356560i | ||||
\(883\) | − | 2.29535e19i | − | 1.62969i | −0.579681 | − | 0.814844i | \(-0.696823\pi\) | ||
0.579681 | − | 0.814844i | \(-0.303177\pi\) | |||||||
\(884\) | −1.48842e19 | + | 1.74402e19i | −1.04902 | + | 1.22917i | ||||
\(885\) | 8.28410e17i | 0.0579581i | ||||||||
\(886\) | 5.74031e18 | − | 1.55687e19i | 0.398673 | − | 1.08126i | ||||
\(887\) | 1.69166e19 | 1.16630 | 0.583149 | − | 0.812365i | \(-0.301820\pi\) | ||||
0.583149 | + | 0.812365i | \(0.301820\pi\) | |||||||
\(888\) | −4.34349e18 | − | 7.74579e18i | −0.297272 | − | 0.530129i | ||||
\(889\) | 8.38877e18 | 0.569950 | ||||||||
\(890\) | 3.06433e17 | − | 8.31096e17i | 0.0206681 | − | 0.0560552i | ||||
\(891\) | 4.26572e18i | 0.285619i | ||||||||
\(892\) | 4.83664e18 | + | 4.12779e18i | 0.321493 | + | 0.274376i | ||||
\(893\) | 4.19823e19i | 2.77033i | ||||||||
\(894\) | −8.06126e18 | − | 2.97226e18i | −0.528091 | − | 0.194712i | ||||
\(895\) | 8.99664e16 | 0.00585101 | ||||||||
\(896\) | 1.23919e19 | − | 9.79503e18i | 0.800086 | − | 0.632417i | ||||
\(897\) | −2.66430e19 | −1.70778 | ||||||||
\(898\) | −2.81288e19 | − | 1.03714e19i | −1.79001 | − | 0.659994i | ||||
\(899\) | 8.32203e18i | 0.525765i | ||||||||
\(900\) | −3.10335e18 | − | 2.64853e18i | −0.194650 | − | 0.166123i | ||||
\(901\) | − | 1.90694e19i | − | 1.18748i | ||||||
\(902\) | 1.72350e18 | − | 4.67441e18i | 0.106554 | − | 0.288991i | ||||
\(903\) | 9.77351e18 | 0.599902 | ||||||||
\(904\) | 1.84423e18 | + | 3.28883e18i | 0.112388 | + | 0.200423i | ||||
\(905\) | −3.49787e17 | −0.0211635 | ||||||||
\(906\) | −1.15439e19 | + | 3.13088e19i | −0.693454 | + | 1.88076i | ||||
\(907\) | − | 6.80309e18i | − | 0.405750i | −0.979205 | − | 0.202875i | \(-0.934971\pi\) | ||
0.979205 | − | 0.202875i | \(-0.0650285\pi\) | |||||||
\(908\) | −1.37245e18 | + | 1.60814e18i | −0.0812716 | + | 0.0952280i | ||||
\(909\) | − | 7.24904e18i | − | 0.426202i | ||||||
\(910\) | 1.61475e18 | + | 5.95372e17i | 0.0942617 | + | 0.0347552i | ||||
\(911\) | −1.18952e19 | −0.689447 | −0.344724 | − | 0.938704i | \(-0.612027\pi\) | ||||
−0.344724 | + | 0.938704i | \(0.612027\pi\) | |||||||
\(912\) | 5.44775e18 | + | 3.42320e19i | 0.313510 | + | 1.97000i | ||||
\(913\) | 1.09900e18 | 0.0627967 | ||||||||
\(914\) | −1.27994e19 | − | 4.71927e18i | −0.726173 | − | 0.267747i | ||||
\(915\) | 9.16270e17i | 0.0516162i | ||||||||
\(916\) | 8.04460e18 | − | 9.42607e18i | 0.449971 | − | 0.527242i | ||||
\(917\) | 2.38392e18i | 0.132401i | ||||||||
\(918\) | −5.84880e18 | + | 1.58629e19i | −0.322544 | + | 0.874792i | ||||
\(919\) | 2.12090e19 | 1.16137 | 0.580683 | − | 0.814130i | \(-0.302786\pi\) | ||||
0.580683 | + | 0.814130i | \(0.302786\pi\) | |||||||
\(920\) | −1.15493e18 | + | 6.47633e17i | −0.0627964 | + | 0.0352134i | ||||
\(921\) | −1.20892e19 | −0.652696 | ||||||||
\(922\) | −3.79600e18 | + | 1.02954e19i | −0.203505 | + | 0.551939i | ||||
\(923\) | − | 7.30408e18i | − | 0.388825i | ||||||
\(924\) | −3.94591e18 | − | 3.36760e18i | −0.208583 | − | 0.178013i | ||||
\(925\) | 1.02793e19i | 0.539562i | ||||||||
\(926\) | −7.42860e17 | − | 2.73900e17i | −0.0387200 | − | 0.0142764i | ||||
\(927\) | −5.12414e16 | −0.00265218 | ||||||||
\(928\) | 1.68996e19 | + | 3.34532e18i | 0.868591 | + | 0.171939i | ||||
\(929\) | 4.89201e18 | 0.249681 | 0.124841 | − | 0.992177i | \(-0.460158\pi\) | ||||
0.124841 | + | 0.992177i | \(0.460158\pi\) | |||||||
\(930\) | 8.40995e17 | + | 3.10083e17i | 0.0426240 | + | 0.0157159i | ||||
\(931\) | − | 1.41714e18i | − | 0.0713246i | ||||||
\(932\) | −1.26622e19 | − | 1.08065e19i | −0.632859 | − | 0.540108i | ||||
\(933\) | 4.99299e18i | 0.247816i | ||||||||
\(934\) | −9.23732e18 | + | 2.50531e19i | −0.455293 | + | 1.23483i | ||||
\(935\) | 3.74230e17 | 0.0183174 | ||||||||
\(936\) | 6.66011e18 | − | 3.73469e18i | 0.323734 | − | 0.181536i | ||||
\(937\) | −3.82987e18 | −0.184874 | −0.0924372 | − | 0.995719i | \(-0.529466\pi\) | ||||
−0.0924372 | + | 0.995719i | \(0.529466\pi\) | |||||||
\(938\) | −6.78084e18 | + | 1.83907e19i | −0.325061 | + | 0.881619i | ||||
\(939\) | − | 1.42304e19i | − | 0.677470i | ||||||
\(940\) | 1.45890e18 | − | 1.70943e18i | 0.0689756 | − | 0.0808205i | ||||
\(941\) | − | 2.73101e19i | − | 1.28231i | −0.767413 | − | 0.641153i | \(-0.778457\pi\) | ||
0.767413 | − | 0.641153i | \(-0.221543\pi\) | |||||||
\(942\) | 1.06974e19 | + | 3.94424e18i | 0.498825 | + | 0.183922i | ||||
\(943\) | 2.92617e19 | 1.35511 | ||||||||
\(944\) | 1.62666e19 | − | 2.58871e18i | 0.748135 | − | 0.119060i | ||||
\(945\) | 1.26904e18 | 0.0579655 | ||||||||
\(946\) | 2.60226e18 | + | 9.59477e17i | 0.118048 | + | 0.0435253i | ||||
\(947\) | 8.00635e18i | 0.360711i | 0.983601 | + | 0.180356i | \(0.0577248\pi\) | ||||
−0.983601 | + | 0.180356i | \(0.942275\pi\) | |||||||
\(948\) | −1.19445e19 | + | 1.39956e19i | −0.534457 | + | 0.626237i | ||||
\(949\) | − | 3.73710e19i | − | 1.66075i | ||||||
\(950\) | 1.38801e19 | − | 3.76452e19i | 0.612619 | − | 1.66152i | ||||
\(951\) | 4.43188e19 | 1.94274 | ||||||||
\(952\) | −1.28246e19 | − | 2.28703e19i | −0.558348 | − | 0.995708i | ||||
\(953\) | −9.72737e18 | −0.420622 | −0.210311 | − | 0.977635i | \(-0.567448\pi\) | ||||
−0.210311 | + | 0.977635i | \(0.567448\pi\) | |||||||
\(954\) | −2.19699e18 | + | 5.95859e18i | −0.0943546 | + | 0.255905i | ||||
\(955\) | − | 1.23362e18i | − | 0.0526210i | ||||||
\(956\) | −1.48602e19 | − | 1.26823e19i | −0.629577 | − | 0.537307i | ||||
\(957\) | − | 5.65784e18i | − | 0.238080i | ||||||
\(958\) | −2.32109e19 | − | 8.55806e18i | −0.970097 | − | 0.357684i | ||||
\(959\) | −7.17288e18 | −0.297764 | ||||||||
\(960\) | 9.67754e17 | − | 1.58317e18i | 0.0399027 | − | 0.0652776i | ||||
\(961\) | −1.58084e19 | −0.647419 | ||||||||
\(962\) | −1.80504e19 | − | 6.65536e18i | −0.734259 | − | 0.270728i | ||||
\(963\) | − | 2.06331e18i | − | 0.0833669i | ||||||
\(964\) | −2.48239e19 | − | 2.11858e19i | −0.996253 | − | 0.850244i | ||||
\(965\) | 1.93977e18i | 0.0773256i | ||||||||
\(966\) | 1.05406e19 | − | 2.85877e19i | 0.417362 | − | 1.13195i | ||||
\(967\) | −1.20531e19 | −0.474054 | −0.237027 | − | 0.971503i | \(-0.576173\pi\) | ||||
−0.237027 | + | 0.971503i | \(0.576173\pi\) | |||||||
\(968\) | 1.17996e19 | + | 2.10424e19i | 0.460976 | + | 0.822062i | ||||
\(969\) | 5.75399e19 | 2.23287 | ||||||||
\(970\) | −8.32839e17 | + | 2.25879e18i | −0.0321029 | + | 0.0870684i | ||||
\(971\) | − | 7.69872e18i | − | 0.294777i | −0.989079 | − | 0.147388i | \(-0.952913\pi\) | ||
0.989079 | − | 0.147388i | \(-0.0470867\pi\) | |||||||
\(972\) | 8.57520e18 | − | 1.00478e19i | 0.326147 | − | 0.382155i | ||||
\(973\) | 3.64633e19i | 1.37760i | ||||||||
\(974\) | 4.68487e19 | + | 1.72736e19i | 1.75818 | + | 0.648259i | ||||
\(975\) | −4.32163e19 | −1.61108 | ||||||||
\(976\) | 1.79918e19 | − | 2.86326e18i | 0.666273 | − | 0.106032i | ||||
\(977\) | −1.13281e19 | −0.416716 | −0.208358 | − | 0.978053i | \(-0.566812\pi\) | ||||
−0.208358 | + | 0.978053i | \(0.566812\pi\) | |||||||
\(978\) | 1.72630e18 | + | 6.36503e17i | 0.0630832 | + | 0.0232594i | ||||
\(979\) | 5.78416e18i | 0.209968i | ||||||||
\(980\) | −4.92461e16 | + | 5.77030e16i | −0.00177583 | + | 0.00208079i | ||||
\(981\) | 1.25090e19i | 0.448101i | ||||||||
\(982\) | −1.27028e19 | + | 3.44520e19i | −0.452038 | + | 1.22600i | ||||
\(983\) | −2.86975e17 | −0.0101449 | −0.00507243 | − | 0.999987i | \(-0.501615\pi\) | ||||
−0.00507243 | + | 0.999987i | \(0.501615\pi\) | |||||||
\(984\) | −3.57658e19 | + | 2.00559e19i | −1.25603 | + | 0.704325i | ||||
\(985\) | 3.03972e18 | 0.106047 | ||||||||
\(986\) | 9.89316e18 | − | 2.68319e19i | 0.342875 | − | 0.929931i | ||||
\(987\) | 5.17132e19i | 1.78049i | ||||||||
\(988\) | 5.71182e19 | + | 4.87471e19i | 1.95369 | + | 1.66736i | ||||
\(989\) | 1.62901e19i | 0.553539i | ||||||||
\(990\) | −1.16935e17 | − | 4.31150e16i | −0.00394744 | − | 0.00145546i | ||||
\(991\) | −3.67463e19 | −1.23235 | −0.616176 | − | 0.787609i | \(-0.711319\pi\) | ||||
−0.616176 | + | 0.787609i | \(0.711319\pi\) | |||||||
\(992\) | 3.46074e18 | − | 1.74827e19i | 0.115304 | − | 0.582483i | ||||
\(993\) | −6.93573e18 | −0.229573 | ||||||||
\(994\) | 7.83722e18 | + | 2.88966e18i | 0.257721 | + | 0.0950243i | ||||
\(995\) | − | 4.61788e17i | − | 0.0150866i | ||||||
\(996\) | −6.88040e18 | − | 5.87202e18i | −0.223320 | − | 0.190591i | ||||
\(997\) | 1.28091e19i | 0.413047i | 0.978442 | + | 0.206523i | \(0.0662149\pi\) | ||||
−0.978442 | + | 0.206523i | \(0.933785\pi\) | |||||||
\(998\) | −1.29763e18 | + | 3.51939e18i | −0.0415723 | + | 0.112751i | ||||
\(999\) | −1.41860e19 | −0.451527 |
(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 | 8.14.b.b.5.10 | yes | 10 | |
3.2 | odd | 2 | 72.14.d.c.37.1 | 10 | |||
4.3 | odd | 2 | 32.14.b.b.17.2 | 10 | |||
8.3 | odd | 2 | 32.14.b.b.17.9 | 10 | |||
8.5 | even | 2 | inner | 8.14.b.b.5.9 | ✓ | 10 | |
24.5 | odd | 2 | 72.14.d.c.37.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.14.b.b.5.9 | ✓ | 10 | 8.5 | even | 2 | inner | |
8.14.b.b.5.10 | yes | 10 | 1.1 | even | 1 | trivial | |
32.14.b.b.17.2 | 10 | 4.3 | odd | 2 | |||
32.14.b.b.17.9 | 10 | 8.3 | odd | 2 | |||
72.14.d.c.37.1 | 10 | 3.2 | odd | 2 | |||
72.14.d.c.37.2 | 10 | 24.5 | odd | 2 |