Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,19,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, 19, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.5");
S:= CuspForms(chi, 19);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 19 \) |
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: | \(12.3231682626\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 8797x^{4} + 1809980x^{3} + 107861490x^{2} - 7180095600x + 788142376800 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{31}\cdot 3^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(27.6459 - 55.6125i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.5 |
Dual form | 6.19.b.a.5.4 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 362.039i | − | 0.707107i | ||||||
\(3\) | −19019.3 | − | 5068.08i | −0.966282 | − | 0.257485i | ||||
\(4\) | −131072. | −0.500000 | ||||||||
\(5\) | − | 2.98937e6i | − | 1.53056i | −0.643699 | − | 0.765278i | \(-0.722601\pi\) | ||
0.643699 | − | 0.765278i | \(-0.277399\pi\) | |||||||
\(6\) | −1.83484e6 | + | 6.88573e6i | −0.182070 | + | 0.683265i | ||||
\(7\) | −4.92752e7 | −1.22109 | −0.610543 | − | 0.791983i | \(-0.709049\pi\) | ||||
−0.610543 | + | 0.791983i | \(0.709049\pi\) | |||||||
\(8\) | 4.74531e7i | 0.353553i | ||||||||
\(9\) | 3.36050e8 | + | 1.92783e8i | 0.867403 | + | 0.497607i | ||||
\(10\) | −1.08227e9 | −1.08227 | ||||||||
\(11\) | 5.85405e8i | 0.248269i | 0.992265 | + | 0.124134i | \(0.0396154\pi\) | ||||
−0.992265 | + | 0.124134i | \(0.960385\pi\) | |||||||
\(12\) | 2.49290e9 | + | 6.64284e8i | 0.483141 | + | 0.128743i | ||||
\(13\) | 1.21786e10 | 1.14844 | 0.574218 | − | 0.818703i | \(-0.305306\pi\) | ||||
0.574218 | + | 0.818703i | \(0.305306\pi\) | |||||||
\(14\) | 1.78395e10i | 0.863439i | ||||||||
\(15\) | −1.51504e10 | + | 5.68558e10i | −0.394096 | + | 1.47895i | ||||
\(16\) | 1.71799e10 | 0.250000 | ||||||||
\(17\) | 1.49631e11i | 1.26178i | 0.775874 | + | 0.630888i | \(0.217309\pi\) | ||||
−0.775874 | + | 0.630888i | \(0.782691\pi\) | |||||||
\(18\) | 6.97949e10 | − | 1.21663e11i | 0.351861 | − | 0.613346i | ||||
\(19\) | −3.13905e11 | −0.972783 | −0.486391 | − | 0.873741i | \(-0.661687\pi\) | ||||
−0.486391 | + | 0.873741i | \(0.661687\pi\) | |||||||
\(20\) | 3.91823e11i | 0.765278i | ||||||||
\(21\) | 9.37182e11 | + | 2.49731e11i | 1.17991 | + | 0.314412i | ||||
\(22\) | 2.11939e11 | 0.175553 | ||||||||
\(23\) | − | 2.41974e12i | − | 1.34344i | −0.740805 | − | 0.671721i | \(-0.765556\pi\) | ||
0.740805 | − | 0.671721i | \(-0.234444\pi\) | |||||||
\(24\) | 2.40496e11 | − | 9.02527e11i | 0.0910348 | − | 0.341632i | ||||
\(25\) | −5.12163e12 | −1.34260 | ||||||||
\(26\) | − | 4.40912e12i | − | 0.812066i | ||||||
\(27\) | −5.41440e12 | − | 5.36973e12i | −0.710029 | − | 0.704172i | ||||
\(28\) | 6.45860e12 | 0.610543 | ||||||||
\(29\) | 1.39605e13i | 0.962319i | 0.876633 | + | 0.481159i | \(0.159784\pi\) | ||||
−0.876633 | + | 0.481159i | \(0.840216\pi\) | |||||||
\(30\) | 2.05840e13 | + | 5.48502e12i | 1.04578 | + | 0.278668i | ||||
\(31\) | −2.16303e13 | −0.818101 | −0.409050 | − | 0.912512i | \(-0.634140\pi\) | ||||
−0.409050 | + | 0.912512i | \(0.634140\pi\) | |||||||
\(32\) | − | 6.21978e12i | − | 0.176777i | ||||||
\(33\) | 2.96688e12 | − | 1.11340e13i | 0.0639256 | − | 0.239898i | ||||
\(34\) | 5.41723e13 | 0.892210 | ||||||||
\(35\) | 1.47302e14i | 1.86894i | ||||||||
\(36\) | −4.40467e13 | − | 2.52685e13i | −0.433701 | − | 0.248803i | ||||
\(37\) | 2.89041e13 | 0.222404 | 0.111202 | − | 0.993798i | \(-0.464530\pi\) | ||||
0.111202 | + | 0.993798i | \(0.464530\pi\) | |||||||
\(38\) | 1.13646e14i | 0.687861i | ||||||||
\(39\) | −2.31628e14 | − | 6.17220e13i | −1.10971 | − | 0.295705i | ||||
\(40\) | 1.41855e14 | 0.541134 | ||||||||
\(41\) | − | 2.60395e14i | − | 0.795384i | −0.917519 | − | 0.397692i | \(-0.869811\pi\) | ||
0.917519 | − | 0.397692i | \(-0.130189\pi\) | |||||||
\(42\) | 9.04123e13 | − | 3.39296e14i | 0.222323 | − | 0.834325i | ||||
\(43\) | −9.12102e13 | −0.181479 | −0.0907397 | − | 0.995875i | \(-0.528923\pi\) | ||||
−0.0907397 | + | 0.995875i | \(0.528923\pi\) | |||||||
\(44\) | − | 7.67302e13i | − | 0.124134i | ||||||
\(45\) | 5.76300e14 | − | 1.00458e15i | 0.761616 | − | 1.32761i | ||||
\(46\) | −8.76040e14 | −0.949956 | ||||||||
\(47\) | 1.34983e15i | 1.20615i | 0.797686 | + | 0.603073i | \(0.206057\pi\) | ||||
−0.797686 | + | 0.603073i | \(0.793943\pi\) | |||||||
\(48\) | −3.26750e14 | − | 8.70690e13i | −0.241571 | − | 0.0643713i | ||||
\(49\) | 7.99636e14 | 0.491052 | ||||||||
\(50\) | 1.85423e15i | 0.949365i | ||||||||
\(51\) | 7.58344e14 | − | 2.84589e15i | 0.324889 | − | 1.21923i | ||||
\(52\) | −1.59627e15 | −0.574218 | ||||||||
\(53\) | 4.92446e15i | 1.49237i | 0.665740 | + | 0.746183i | \(0.268116\pi\) | ||||
−0.665740 | + | 0.746183i | \(0.731884\pi\) | |||||||
\(54\) | −1.94405e15 | + | 1.96022e15i | −0.497925 | + | 0.502067i | ||||
\(55\) | 1.74999e15 | 0.379989 | ||||||||
\(56\) | − | 2.33826e15i | − | 0.431719i | ||||||
\(57\) | 5.97026e15 | + | 1.59090e15i | 0.939983 | + | 0.250477i | ||||
\(58\) | 5.05424e15 | 0.680462 | ||||||||
\(59\) | 1.63011e15i | 0.188170i | 0.995564 | + | 0.0940848i | \(0.0299925\pi\) | ||||
−0.995564 | + | 0.0940848i | \(0.970008\pi\) | |||||||
\(60\) | 1.98579e15 | − | 7.45220e15i | 0.197048 | − | 0.739475i | ||||
\(61\) | −1.27764e16 | −1.09255 | −0.546275 | − | 0.837606i | \(-0.683955\pi\) | ||||
−0.546275 | + | 0.837606i | \(0.683955\pi\) | |||||||
\(62\) | 7.83100e15i | 0.578485i | ||||||||
\(63\) | −1.65589e16 | − | 9.49943e15i | −1.05917 | − | 0.607621i | ||||
\(64\) | −2.25180e15 | −0.125000 | ||||||||
\(65\) | − | 3.64063e16i | − | 1.75775i | ||||||
\(66\) | −4.03094e15 | − | 1.07413e15i | −0.169633 | − | 0.0452022i | ||||
\(67\) | 1.62992e16 | 0.599091 | 0.299545 | − | 0.954082i | \(-0.403165\pi\) | ||||
0.299545 | + | 0.954082i | \(0.403165\pi\) | |||||||
\(68\) | − | 1.96125e16i | − | 0.630888i | ||||||
\(69\) | −1.22635e16 | + | 4.60219e16i | −0.345916 | + | 1.29814i | ||||
\(70\) | 5.33290e16 | 1.32154 | ||||||||
\(71\) | 3.19301e16i | 0.696425i | 0.937416 | + | 0.348213i | \(0.113211\pi\) | ||||
−0.937416 | + | 0.348213i | \(0.886789\pi\) | |||||||
\(72\) | −9.14816e15 | + | 1.59466e16i | −0.175931 | + | 0.306673i | ||||
\(73\) | −6.00948e16 | −1.02078 | −0.510389 | − | 0.859944i | \(-0.670499\pi\) | ||||
−0.510389 | + | 0.859944i | \(0.670499\pi\) | |||||||
\(74\) | − | 1.04644e16i | − | 0.157264i | ||||||
\(75\) | 9.74100e16 | + | 2.59568e16i | 1.29733 | + | 0.345701i | ||||
\(76\) | 4.11442e16 | 0.486391 | ||||||||
\(77\) | − | 2.88460e16i | − | 0.303158i | ||||||
\(78\) | −2.23458e16 | + | 8.38585e16i | −0.209095 | + | 0.784685i | ||||
\(79\) | −1.80165e17 | −1.50323 | −0.751616 | − | 0.659600i | \(-0.770726\pi\) | ||||
−0.751616 | + | 0.659600i | \(0.770726\pi\) | |||||||
\(80\) | − | 5.13570e16i | − | 0.382639i | ||||||
\(81\) | 7.57640e16 | + | 1.29569e17i | 0.504775 | + | 0.863251i | ||||
\(82\) | −9.42729e16 | −0.562422 | ||||||||
\(83\) | − | 8.49190e16i | − | 0.454257i | −0.973865 | − | 0.227129i | \(-0.927066\pi\) | ||
0.973865 | − | 0.227129i | \(-0.0729338\pi\) | |||||||
\(84\) | −1.22838e17 | − | 3.27327e16i | −0.589957 | − | 0.157206i | ||||
\(85\) | 4.47303e17 | 1.93122 | ||||||||
\(86\) | 3.30216e16i | 0.128325i | ||||||||
\(87\) | 7.07530e16 | − | 2.65519e17i | 0.247783 | − | 0.929872i | ||||
\(88\) | −2.77793e16 | −0.0877763 | ||||||||
\(89\) | − | 5.84125e17i | − | 1.66723i | −0.552345 | − | 0.833616i | \(-0.686267\pi\) | ||
0.552345 | − | 0.833616i | \(-0.313733\pi\) | |||||||
\(90\) | −3.63695e17 | − | 2.08643e17i | −0.938761 | − | 0.538544i | ||||
\(91\) | −6.00102e17 | −1.40234 | ||||||||
\(92\) | 3.17160e17i | 0.671721i | ||||||||
\(93\) | 4.11393e17 | + | 1.09624e17i | 0.790516 | + | 0.210649i | ||||
\(94\) | 4.88692e17 | 0.852874 | ||||||||
\(95\) | 9.38378e17i | 1.48890i | ||||||||
\(96\) | −3.15223e16 | + | 1.18296e17i | −0.0455174 | + | 0.170816i | ||||
\(97\) | −1.70517e17 | −0.224296 | −0.112148 | − | 0.993692i | \(-0.535773\pi\) | ||||
−0.112148 | + | 0.993692i | \(0.535773\pi\) | |||||||
\(98\) | − | 2.89499e17i | − | 0.347226i | ||||||
\(99\) | −1.12856e17 | + | 1.96725e17i | −0.123540 | + | 0.215349i | ||||
\(100\) | 6.71302e17 | 0.671302 | ||||||||
\(101\) | 1.55698e18i | 1.42361i | 0.702375 | + | 0.711807i | \(0.252123\pi\) | ||||
−0.702375 | + | 0.711807i | \(0.747877\pi\) | |||||||
\(102\) | −1.03032e18 | − | 2.74550e17i | −0.862127 | − | 0.229731i | ||||
\(103\) | −3.33880e17 | −0.255891 | −0.127945 | − | 0.991781i | \(-0.540838\pi\) | ||||
−0.127945 | + | 0.991781i | \(0.540838\pi\) | |||||||
\(104\) | 5.77912e17i | 0.406033i | ||||||||
\(105\) | 7.46538e17 | − | 2.80158e18i | 0.481225 | − | 1.80593i | ||||
\(106\) | 1.78284e18 | 1.05526 | ||||||||
\(107\) | 8.24602e17i | 0.448529i | 0.974528 | + | 0.224265i | \(0.0719980\pi\) | ||||
−0.974528 | + | 0.224265i | \(0.928002\pi\) | |||||||
\(108\) | 7.09676e17 | + | 7.03822e17i | 0.355015 | + | 0.352086i | ||||
\(109\) | −1.02433e18 | −0.471630 | −0.235815 | − | 0.971798i | \(-0.575776\pi\) | ||||
−0.235815 | + | 0.971798i | \(0.575776\pi\) | |||||||
\(110\) | − | 6.33564e17i | − | 0.268693i | ||||||
\(111\) | −5.49736e17 | − | 1.46488e17i | −0.214905 | − | 0.0572659i | ||||
\(112\) | −8.46542e17 | −0.305272 | ||||||||
\(113\) | − | 7.20059e17i | − | 0.239697i | −0.992792 | − | 0.119848i | \(-0.961759\pi\) | ||
0.992792 | − | 0.119848i | \(-0.0382409\pi\) | |||||||
\(114\) | 5.75966e17 | − | 2.16147e18i | 0.177114 | − | 0.664668i | ||||
\(115\) | −7.23350e18 | −2.05621 | ||||||||
\(116\) | − | 1.82983e18i | − | 0.481159i | ||||||
\(117\) | 4.09261e18 | + | 2.34782e18i | 0.996156 | + | 0.571469i | ||||
\(118\) | 5.90164e17 | 0.133056 | ||||||||
\(119\) | − | 7.37312e18i | − | 1.54074i | ||||||
\(120\) | −2.69799e18 | − | 7.18932e17i | −0.522888 | − | 0.139334i | ||||
\(121\) | 5.21722e18 | 0.938363 | ||||||||
\(122\) | 4.62557e18i | 0.772550i | ||||||||
\(123\) | −1.31970e18 | + | 4.95253e18i | −0.204800 | + | 0.768566i | ||||
\(124\) | 2.83512e18 | 0.409050 | ||||||||
\(125\) | 3.90690e18i | 0.524375i | ||||||||
\(126\) | −3.43916e18 | + | 5.99497e18i | −0.429653 | + | 0.748949i | ||||
\(127\) | 1.18563e19 | 1.37948 | 0.689741 | − | 0.724056i | \(-0.257724\pi\) | ||||
0.689741 | + | 0.724056i | \(0.257724\pi\) | |||||||
\(128\) | 8.15239e17i | 0.0883883i | ||||||||
\(129\) | 1.73476e18 | + | 4.62261e17i | 0.175360 | + | 0.0467283i | ||||
\(130\) | −1.31805e19 | −1.24291 | ||||||||
\(131\) | 8.83199e17i | 0.0777350i | 0.999244 | + | 0.0388675i | \(0.0123750\pi\) | ||||
−0.999244 | + | 0.0388675i | \(0.987625\pi\) | |||||||
\(132\) | −3.88875e17 | + | 1.45936e18i | −0.0319628 | + | 0.119949i | ||||
\(133\) | 1.54677e19 | 1.18785 | ||||||||
\(134\) | − | 5.90094e18i | − | 0.423621i | ||||||
\(135\) | −1.60521e19 | + | 1.61856e19i | −1.07778 | + | 1.08674i | ||||
\(136\) | −7.10047e18 | −0.446105 | ||||||||
\(137\) | − | 1.83132e19i | − | 1.07716i | −0.842575 | − | 0.538579i | \(-0.818961\pi\) | ||
0.842575 | − | 0.538579i | \(-0.181039\pi\) | |||||||
\(138\) | 1.66617e19 | + | 4.43984e18i | 0.917926 | + | 0.244600i | ||||
\(139\) | −3.64973e19 | −1.88420 | −0.942102 | − | 0.335327i | \(-0.891153\pi\) | ||||
−0.942102 | + | 0.335327i | \(0.891153\pi\) | |||||||
\(140\) | − | 1.93072e19i | − | 0.934471i | ||||||
\(141\) | 6.84107e18 | − | 2.56729e19i | 0.310565 | − | 1.16548i | ||||
\(142\) | 1.15599e19 | 0.492447 | ||||||||
\(143\) | 7.12940e18i | 0.285121i | ||||||||
\(144\) | 5.77329e18 | + | 3.31199e18i | 0.216851 | + | 0.124402i | ||||
\(145\) | 4.17331e19 | 1.47288 | ||||||||
\(146\) | 2.17567e19i | 0.721799i | ||||||||
\(147\) | −1.52085e19 | − | 4.05262e18i | −0.474495 | − | 0.126439i | ||||
\(148\) | −3.78851e18 | −0.111202 | ||||||||
\(149\) | − | 2.58816e19i | − | 0.715015i | −0.933910 | − | 0.357507i | \(-0.883627\pi\) | ||
0.933910 | − | 0.357507i | \(-0.116373\pi\) | |||||||
\(150\) | 9.39738e18 | − | 3.52662e19i | 0.244447 | − | 0.917354i | ||||
\(151\) | −4.24973e19 | −1.04128 | −0.520642 | − | 0.853775i | \(-0.674307\pi\) | ||||
−0.520642 | + | 0.853775i | \(0.674307\pi\) | |||||||
\(152\) | − | 1.48958e19i | − | 0.343931i | ||||||
\(153\) | −2.88464e19 | + | 5.02835e19i | −0.627868 | + | 1.09447i | ||||
\(154\) | −1.04434e19 | −0.214365 | ||||||||
\(155\) | 6.46609e19i | 1.25215i | ||||||||
\(156\) | 3.03600e19 | + | 8.09003e18i | 0.554856 | + | 0.147853i | ||||
\(157\) | 6.25624e18 | 0.107949 | 0.0539743 | − | 0.998542i | \(-0.482811\pi\) | ||||
0.0539743 | + | 0.998542i | \(0.482811\pi\) | |||||||
\(158\) | 6.52266e19i | 1.06295i | ||||||||
\(159\) | 2.49576e19 | − | 9.36599e19i | 0.384262 | − | 1.44205i | ||||
\(160\) | −1.85932e19 | −0.270567 | ||||||||
\(161\) | 1.19233e20i | 1.64046i | ||||||||
\(162\) | 4.69091e19 | − | 2.74295e19i | 0.610411 | − | 0.356930i | ||||
\(163\) | 6.37578e19 | 0.784955 | 0.392478 | − | 0.919762i | \(-0.371618\pi\) | ||||
0.392478 | + | 0.919762i | \(0.371618\pi\) | |||||||
\(164\) | 3.41304e19i | 0.397692i | ||||||||
\(165\) | −3.32837e19 | − | 8.86910e18i | −0.367177 | − | 0.0978417i | ||||
\(166\) | −3.07439e19 | −0.321208 | ||||||||
\(167\) | − | 7.24036e18i | − | 0.0716658i | −0.999358 | − | 0.0358329i | \(-0.988592\pi\) | ||
0.999358 | − | 0.0358329i | \(-0.0114084\pi\) | |||||||
\(168\) | −1.18505e19 | + | 4.44722e19i | −0.111161 | + | 0.417163i | ||||
\(169\) | 3.58624e19 | 0.318903 | ||||||||
\(170\) | − | 1.61941e20i | − | 1.36558i | ||||||
\(171\) | −1.05488e20 | − | 6.05156e19i | −0.843794 | − | 0.484063i | ||||
\(172\) | 1.19551e19 | 0.0907397 | ||||||||
\(173\) | − | 1.82274e20i | − | 1.31314i | −0.754267 | − | 0.656568i | \(-0.772008\pi\) | ||
0.754267 | − | 0.656568i | \(-0.227992\pi\) | |||||||
\(174\) | −9.61283e19 | − | 2.56153e19i | −0.657518 | − | 0.175209i | ||||
\(175\) | 2.52370e20 | 1.63944 | ||||||||
\(176\) | 1.00572e19i | 0.0620672i | ||||||||
\(177\) | 8.26154e18 | − | 3.10036e19i | 0.0484509 | − | 0.181825i | ||||
\(178\) | −2.11476e20 | −1.17891 | ||||||||
\(179\) | 1.02672e19i | 0.0544221i | 0.999630 | + | 0.0272111i | \(0.00866262\pi\) | ||||
−0.999630 | + | 0.0272111i | \(0.991337\pi\) | |||||||
\(180\) | −7.55368e19 | + | 1.31672e20i | −0.380808 | + | 0.663805i | ||||
\(181\) | −2.72470e20 | −1.30681 | −0.653403 | − | 0.757010i | \(-0.726659\pi\) | ||||
−0.653403 | + | 0.757010i | \(0.726659\pi\) | |||||||
\(182\) | 2.17260e20i | 0.991603i | ||||||||
\(183\) | 2.42999e20 | + | 6.47521e19i | 1.05571 | + | 0.281316i | ||||
\(184\) | 1.14824e20 | 0.474978 | ||||||||
\(185\) | − | 8.64049e19i | − | 0.340403i | ||||||
\(186\) | 3.96881e19 | − | 1.48940e20i | 0.148951 | − | 0.558979i | ||||
\(187\) | −8.75949e19 | −0.313259 | ||||||||
\(188\) | − | 1.76925e20i | − | 0.603073i | ||||||
\(189\) | 2.66796e20 | + | 2.64595e20i | 0.867007 | + | 0.859855i | ||||
\(190\) | 3.39729e20 | 1.05281 | ||||||||
\(191\) | − | 1.79319e20i | − | 0.530062i | −0.964240 | − | 0.265031i | \(-0.914618\pi\) | ||
0.964240 | − | 0.265031i | \(-0.0853822\pi\) | |||||||
\(192\) | 4.28277e19 | + | 1.14123e19i | 0.120785 | + | 0.0321857i | ||||
\(193\) | −3.54201e20 | −0.953309 | −0.476654 | − | 0.879091i | \(-0.658151\pi\) | ||||
−0.476654 | + | 0.879091i | \(0.658151\pi\) | |||||||
\(194\) | 6.17336e19i | 0.158601i | ||||||||
\(195\) | −1.84510e20 | + | 6.92423e20i | −0.452593 | + | 1.69848i | ||||
\(196\) | −1.04810e20 | −0.245526 | ||||||||
\(197\) | 4.40628e20i | 0.985997i | 0.870030 | + | 0.492999i | \(0.164099\pi\) | ||||
−0.870030 | + | 0.492999i | \(0.835901\pi\) | |||||||
\(198\) | 7.12221e19 | + | 4.08583e19i | 0.152275 | + | 0.0873561i | ||||
\(199\) | 2.86891e20 | 0.586191 | 0.293096 | − | 0.956083i | \(-0.405315\pi\) | ||||
0.293096 | + | 0.956083i | \(0.405315\pi\) | |||||||
\(200\) | − | 2.43037e20i | − | 0.474682i | ||||||
\(201\) | −3.10000e20 | − | 8.26056e19i | −0.578891 | − | 0.154257i | ||||
\(202\) | 5.63689e20 | 1.00665 | ||||||||
\(203\) | − | 6.87907e20i | − | 1.17507i | ||||||
\(204\) | −9.93976e19 | + | 3.73016e20i | −0.162444 | + | 0.609616i | ||||
\(205\) | −7.78415e20 | −1.21738 | ||||||||
\(206\) | 1.20877e20i | 0.180942i | ||||||||
\(207\) | 4.66485e20 | − | 8.13153e20i | 0.668505 | − | 1.16530i | ||||
\(208\) | 2.09226e20 | 0.287109 | ||||||||
\(209\) | − | 1.83761e20i | − | 0.241512i | ||||||
\(210\) | −1.01428e21 | − | 2.70276e20i | −1.27698 | − | 0.340278i | ||||
\(211\) | −7.22932e20 | −0.872078 | −0.436039 | − | 0.899928i | \(-0.643619\pi\) | ||||
−0.436039 | + | 0.899928i | \(0.643619\pi\) | |||||||
\(212\) | − | 6.45458e20i | − | 0.746183i | ||||||
\(213\) | 1.61824e20 | − | 6.07288e20i | 0.179319 | − | 0.672943i | ||||
\(214\) | 2.98538e20 | 0.317158 | ||||||||
\(215\) | 2.72661e20i | 0.277764i | ||||||||
\(216\) | 2.54811e20 | − | 2.56930e20i | 0.248962 | − | 0.251033i | ||||
\(217\) | 1.06584e21 | 0.998972 | ||||||||
\(218\) | 3.70847e20i | 0.333493i | ||||||||
\(219\) | 1.14296e21 | + | 3.04566e20i | 0.986360 | + | 0.262835i | ||||
\(220\) | −2.29375e20 | −0.189995 | ||||||||
\(221\) | 1.82230e21i | 1.44907i | ||||||||
\(222\) | −5.30344e19 | + | 1.99026e20i | −0.0404931 | + | 0.151961i | ||||
\(223\) | 8.51613e20 | 0.624451 | 0.312226 | − | 0.950008i | \(-0.398926\pi\) | ||||
0.312226 | + | 0.950008i | \(0.398926\pi\) | |||||||
\(224\) | 3.06481e20i | 0.215860i | ||||||||
\(225\) | −1.72112e21 | − | 9.87363e20i | −1.16458 | − | 0.668089i | ||||
\(226\) | −2.60689e20 | −0.169491 | ||||||||
\(227\) | 3.23696e20i | 0.202257i | 0.994873 | + | 0.101129i | \(0.0322454\pi\) | ||||
−0.994873 | + | 0.101129i | \(0.967755\pi\) | |||||||
\(228\) | −7.82534e20 | − | 2.08522e20i | −0.469991 | − | 0.125239i | ||||
\(229\) | −1.50827e21 | −0.870880 | −0.435440 | − | 0.900218i | \(-0.643407\pi\) | ||||
−0.435440 | + | 0.900218i | \(0.643407\pi\) | |||||||
\(230\) | 2.61881e21i | 1.45396i | ||||||||
\(231\) | −1.46194e20 | + | 5.48631e20i | −0.0780586 | + | 0.292936i | ||||
\(232\) | −6.62469e20 | −0.340231 | ||||||||
\(233\) | − | 5.01578e20i | − | 0.247820i | −0.992293 | − | 0.123910i | \(-0.960457\pi\) | ||
0.992293 | − | 0.123910i | \(-0.0395433\pi\) | |||||||
\(234\) | 8.50003e20 | − | 1.48168e21i | 0.404090 | − | 0.704388i | ||||
\(235\) | 4.03515e21 | 1.84607 | ||||||||
\(236\) | − | 2.13662e20i | − | 0.0940848i | ||||||
\(237\) | 3.42662e21 | + | 9.13090e20i | 1.45255 | + | 0.387060i | ||||
\(238\) | −2.66935e21 | −1.08947 | ||||||||
\(239\) | 1.43956e21i | 0.565781i | 0.959152 | + | 0.282891i | \(0.0912933\pi\) | ||||
−0.959152 | + | 0.282891i | \(0.908707\pi\) | |||||||
\(240\) | −2.60281e20 | + | 9.76775e20i | −0.0985240 | + | 0.369737i | ||||
\(241\) | −2.26560e21 | −0.826094 | −0.413047 | − | 0.910710i | \(-0.635535\pi\) | ||||
−0.413047 | + | 0.910710i | \(0.635535\pi\) | |||||||
\(242\) | − | 1.88883e21i | − | 0.663523i | ||||||
\(243\) | −7.84313e20 | − | 2.84830e21i | −0.265481 | − | 0.964116i | ||||
\(244\) | 1.67463e21 | 0.546275 | ||||||||
\(245\) | − | 2.39041e21i | − | 0.751583i | ||||||
\(246\) | 1.79301e21 | + | 4.77783e20i | 0.543458 | + | 0.144815i | ||||
\(247\) | −3.82292e21 | −1.11718 | ||||||||
\(248\) | − | 1.02642e21i | − | 0.289242i | ||||||
\(249\) | −4.30376e20 | + | 1.61510e21i | −0.116965 | + | 0.438941i | ||||
\(250\) | 1.41445e21 | 0.370789 | ||||||||
\(251\) | − | 3.32950e21i | − | 0.842006i | −0.907059 | − | 0.421003i | \(-0.861678\pi\) | ||
0.907059 | − | 0.421003i | \(-0.138322\pi\) | |||||||
\(252\) | 2.17041e21 | + | 1.24511e21i | 0.529587 | + | 0.303811i | ||||
\(253\) | 1.41653e21 | 0.333534 | ||||||||
\(254\) | − | 4.29244e21i | − | 0.975441i | ||||||
\(255\) | −8.50741e21 | − | 2.26697e21i | −1.86610 | − | 0.497260i | ||||
\(256\) | 2.95148e20 | 0.0625000 | ||||||||
\(257\) | 5.49052e20i | 0.112258i | 0.998424 | + | 0.0561288i | \(0.0178757\pi\) | ||||
−0.998424 | + | 0.0561288i | \(0.982124\pi\) | |||||||
\(258\) | 1.67356e20 | − | 6.28049e20i | 0.0330419 | − | 0.123998i | ||||
\(259\) | −1.42426e21 | −0.271575 | ||||||||
\(260\) | 4.77184e21i | 0.878873i | ||||||||
\(261\) | −2.69135e21 | + | 4.69142e21i | −0.478856 | + | 0.834718i | ||||
\(262\) | 3.19752e20 | 0.0549670 | ||||||||
\(263\) | 7.16927e21i | 1.19089i | 0.803394 | + | 0.595447i | \(0.203025\pi\) | ||||
−0.803394 | + | 0.595447i | \(0.796975\pi\) | |||||||
\(264\) | 5.28344e20 | + | 1.40788e20i | 0.0848167 | + | 0.0226011i | ||||
\(265\) | 1.47210e22 | 2.28415 | ||||||||
\(266\) | − | 5.59992e21i | − | 0.839938i | ||||||
\(267\) | −2.96039e21 | + | 1.11097e22i | −0.429288 | + | 1.61102i | ||||
\(268\) | −2.13637e21 | −0.299545 | ||||||||
\(269\) | − | 1.07660e22i | − | 1.45977i | −0.683571 | − | 0.729884i | \(-0.739574\pi\) | ||
0.683571 | − | 0.729884i | \(-0.260426\pi\) | |||||||
\(270\) | 5.85983e21 | + | 5.81149e21i | 0.768441 | + | 0.762102i | ||||
\(271\) | −1.13119e21 | −0.143487 | −0.0717435 | − | 0.997423i | \(-0.522856\pi\) | ||||
−0.0717435 | + | 0.997423i | \(0.522856\pi\) | |||||||
\(272\) | 2.57065e21i | 0.315444i | ||||||||
\(273\) | 1.14135e22 | + | 3.04137e21i | 1.35505 | + | 0.361082i | ||||
\(274\) | −6.63009e21 | −0.761665 | ||||||||
\(275\) | − | 2.99823e21i | − | 0.333327i | ||||||
\(276\) | 1.60740e21 | − | 6.03218e21i | 0.172958 | − | 0.649072i | ||||
\(277\) | −3.46171e21 | −0.360556 | −0.180278 | − | 0.983616i | \(-0.557700\pi\) | ||||
−0.180278 | + | 0.983616i | \(0.557700\pi\) | |||||||
\(278\) | 1.32134e22i | 1.33233i | ||||||||
\(279\) | −7.26884e21 | − | 4.16995e21i | −0.709623 | − | 0.407093i | ||||
\(280\) | −6.98994e21 | −0.660771 | ||||||||
\(281\) | − | 3.67928e21i | − | 0.336826i | −0.985717 | − | 0.168413i | \(-0.946136\pi\) | ||
0.985717 | − | 0.168413i | \(-0.0538642\pi\) | |||||||
\(282\) | −9.29460e21 | − | 2.47673e21i | −0.824117 | − | 0.219602i | ||||
\(283\) | 2.56879e21 | 0.220623 | 0.110311 | − | 0.993897i | \(-0.464815\pi\) | ||||
0.110311 | + | 0.993897i | \(0.464815\pi\) | |||||||
\(284\) | − | 4.18514e21i | − | 0.348213i | ||||||
\(285\) | 4.75578e21 | − | 1.78473e22i | 0.383370 | − | 1.43870i | ||||
\(286\) | 2.58112e21 | 0.201611 | ||||||||
\(287\) | 1.28310e22i | 0.971233i | ||||||||
\(288\) | 1.19907e21 | − | 2.09015e21i | 0.0879653 | − | 0.153337i | ||||
\(289\) | −8.32643e21 | −0.592077 | ||||||||
\(290\) | − | 1.51090e22i | − | 1.04149i | ||||||
\(291\) | 3.24311e21 | + | 8.64192e20i | 0.216733 | + | 0.0577528i | ||||
\(292\) | 7.87675e21 | 0.510389 | ||||||||
\(293\) | 9.92864e21i | 0.623852i | 0.950106 | + | 0.311926i | \(0.100974\pi\) | ||||
−0.950106 | + | 0.311926i | \(0.899026\pi\) | |||||||
\(294\) | −1.46721e21 | + | 5.50608e21i | −0.0894057 | + | 0.335519i | ||||
\(295\) | 4.87301e21 | 0.288004 | ||||||||
\(296\) | 1.37159e21i | 0.0786319i | ||||||||
\(297\) | 3.14347e21 | − | 3.16961e21i | 0.174824 | − | 0.176278i | ||||
\(298\) | −9.37014e21 | −0.505592 | ||||||||
\(299\) | − | 2.94690e22i | − | 1.54285i | ||||||
\(300\) | −1.27677e22 | − | 3.40221e21i | −0.648667 | − | 0.172850i | ||||
\(301\) | 4.49440e21 | 0.221602 | ||||||||
\(302\) | 1.53857e22i | 0.736298i | ||||||||
\(303\) | 7.89093e21 | − | 2.96128e22i | 0.366559 | − | 1.37561i | ||||
\(304\) | −5.39285e21 | −0.243196 | ||||||||
\(305\) | 3.81935e22i | 1.67221i | ||||||||
\(306\) | 1.82046e22 | + | 1.04435e22i | 0.773905 | + | 0.443970i | ||||
\(307\) | −6.75725e21 | −0.278949 | −0.139474 | − | 0.990226i | \(-0.544541\pi\) | ||||
−0.139474 | + | 0.990226i | \(0.544541\pi\) | |||||||
\(308\) | 3.78090e21i | 0.151579i | ||||||||
\(309\) | 6.35017e21 | + | 1.69213e21i | 0.247263 | + | 0.0658881i | ||||
\(310\) | 2.34097e22 | 0.885403 | ||||||||
\(311\) | 3.33646e22i | 1.22587i | 0.790135 | + | 0.612933i | \(0.210010\pi\) | ||||
−0.790135 | + | 0.612933i | \(0.789990\pi\) | |||||||
\(312\) | 2.92890e21 | − | 1.09915e22i | 0.104548 | − | 0.392343i | ||||
\(313\) | −1.44873e22 | −0.502444 | −0.251222 | − | 0.967929i | \(-0.580832\pi\) | ||||
−0.251222 | + | 0.967929i | \(0.580832\pi\) | |||||||
\(314\) | − | 2.26500e21i | − | 0.0763311i | ||||||
\(315\) | −2.83973e22 | + | 4.95007e22i | −0.929998 | + | 1.62113i | ||||
\(316\) | 2.36146e22 | 0.751616 | ||||||||
\(317\) | 2.47089e22i | 0.764400i | 0.924080 | + | 0.382200i | \(0.124833\pi\) | ||||
−0.924080 | + | 0.382200i | \(0.875167\pi\) | |||||||
\(318\) | −3.39085e22 | − | 9.03560e21i | −1.01968 | − | 0.271715i | ||||
\(319\) | −8.17254e21 | −0.238914 | ||||||||
\(320\) | 6.73146e21i | 0.191320i | ||||||||
\(321\) | 4.17915e21 | − | 1.56834e22i | 0.115490 | − | 0.433406i | ||||
\(322\) | 4.31671e22 | 1.15998 | ||||||||
\(323\) | − | 4.69700e22i | − | 1.22743i | ||||||
\(324\) | −9.93054e21 | − | 1.69829e22i | −0.252387 | − | 0.431626i | ||||
\(325\) | −6.23742e22 | −1.54189 | ||||||||
\(326\) | − | 2.30828e22i | − | 0.555047i | ||||||
\(327\) | 1.94821e22 | + | 5.19139e21i | 0.455728 | + | 0.121438i | ||||
\(328\) | 1.23565e22 | 0.281211 | ||||||||
\(329\) | − | 6.65134e22i | − | 1.47281i | ||||||
\(330\) | −3.21096e21 | + | 1.20500e22i | −0.0691845 | + | 0.259633i | ||||
\(331\) | 7.51986e22 | 1.57673 | 0.788366 | − | 0.615206i | \(-0.210927\pi\) | ||||
0.788366 | + | 0.615206i | \(0.210927\pi\) | |||||||
\(332\) | 1.11305e22i | 0.227129i | ||||||||
\(333\) | 9.71320e21 | + | 5.57222e21i | 0.192914 | + | 0.110670i | ||||
\(334\) | −2.62129e21 | −0.0506754 | ||||||||
\(335\) | − | 4.87243e22i | − | 0.916943i | ||||||
\(336\) | 1.61007e22 | + | 4.29035e21i | 0.294979 | + | 0.0786029i | ||||
\(337\) | −8.71788e22 | −1.55504 | −0.777521 | − | 0.628857i | \(-0.783523\pi\) | ||||
−0.777521 | + | 0.628857i | \(0.783523\pi\) | |||||||
\(338\) | − | 1.29836e22i | − | 0.225499i | ||||||
\(339\) | −3.64932e21 | + | 1.36951e22i | −0.0617184 | + | 0.231615i | ||||
\(340\) | −5.86289e22 | −0.965609 | ||||||||
\(341\) | − | 1.26625e22i | − | 0.203109i | ||||||
\(342\) | −2.19090e22 | + | 3.81906e22i | −0.342284 | + | 0.596653i | ||||
\(343\) | 4.08382e22 | 0.621469 | ||||||||
\(344\) | − | 4.32821e21i | − | 0.0641626i | ||||||
\(345\) | 1.37576e23 | + | 3.66600e22i | 1.98688 | + | 0.529445i | ||||
\(346\) | −6.59902e22 | −0.928527 | ||||||||
\(347\) | 1.05432e23i | 1.44547i | 0.691126 | + | 0.722734i | \(0.257115\pi\) | ||||
−0.691126 | + | 0.722734i | \(0.742885\pi\) | |||||||
\(348\) | −9.27373e21 | + | 3.48022e22i | −0.123891 | + | 0.464936i | ||||
\(349\) | −2.03959e22 | −0.265530 | −0.132765 | − | 0.991148i | \(-0.542386\pi\) | ||||
−0.132765 | + | 0.991148i | \(0.542386\pi\) | |||||||
\(350\) | − | 9.13675e22i | − | 1.15926i | ||||||
\(351\) | −6.59397e22 | − | 6.53957e22i | −0.815423 | − | 0.808696i | ||||
\(352\) | 3.64109e21 | 0.0438881 | ||||||||
\(353\) | − | 1.27972e23i | − | 1.50364i | −0.659368 | − | 0.751821i | \(-0.729176\pi\) | ||
0.659368 | − | 0.751821i | \(-0.270824\pi\) | |||||||
\(354\) | −1.12245e22 | − | 2.99100e21i | −0.128570 | − | 0.0342600i | ||||
\(355\) | 9.54507e22 | 1.06592 | ||||||||
\(356\) | 7.65625e22i | 0.833616i | ||||||||
\(357\) | −3.73676e22 | + | 1.40232e23i | −0.396717 | + | 1.48879i | ||||
\(358\) | 3.71713e21 | 0.0384822 | ||||||||
\(359\) | 8.56995e22i | 0.865224i | 0.901580 | + | 0.432612i | \(0.142408\pi\) | ||||
−0.901580 | + | 0.432612i | \(0.857592\pi\) | |||||||
\(360\) | 4.76703e22 | + | 2.73472e22i | 0.469381 | + | 0.269272i | ||||
\(361\) | −5.59102e21 | −0.0536941 | ||||||||
\(362\) | 9.86446e22i | 0.924052i | ||||||||
\(363\) | −9.92280e22 | − | 2.64413e22i | −0.906723 | − | 0.241615i | ||||
\(364\) | 7.86566e22 | 0.701169 | ||||||||
\(365\) | 1.79646e23i | 1.56236i | ||||||||
\(366\) | 2.34428e22 | − | 8.79752e22i | 0.198920 | − | 0.746501i | ||||
\(367\) | 2.32847e23 | 1.92786 | 0.963930 | − | 0.266156i | \(-0.0857537\pi\) | ||||
0.963930 | + | 0.266156i | \(0.0857537\pi\) | |||||||
\(368\) | − | 4.15709e22i | − | 0.335860i | ||||||
\(369\) | 5.01997e22 | − | 8.75055e22i | 0.395789 | − | 0.689919i | ||||
\(370\) | −3.12819e22 | −0.240701 | ||||||||
\(371\) | − | 2.42654e23i | − | 1.82231i | ||||||
\(372\) | −5.39222e22 | − | 1.43686e22i | −0.395258 | − | 0.105324i | ||||
\(373\) | −1.73285e23 | −1.23989 | −0.619944 | − | 0.784646i | \(-0.712845\pi\) | ||||
−0.619944 | + | 0.784646i | \(0.712845\pi\) | |||||||
\(374\) | 3.17127e22i | 0.221508i | ||||||||
\(375\) | 1.98005e22 | − | 7.43066e22i | 0.135019 | − | 0.506695i | ||||
\(376\) | −6.40539e22 | −0.426437 | ||||||||
\(377\) | 1.70019e23i | 1.10516i | ||||||||
\(378\) | 9.57936e22 | − | 9.65904e22i | 0.608009 | − | 0.613067i | ||||
\(379\) | −1.45667e23 | −0.902837 | −0.451419 | − | 0.892312i | \(-0.649082\pi\) | ||||
−0.451419 | + | 0.892312i | \(0.649082\pi\) | |||||||
\(380\) | − | 1.22995e23i | − | 0.744450i | ||||||
\(381\) | −2.25499e23 | − | 6.00888e22i | −1.33297 | − | 0.355196i | ||||
\(382\) | −6.49205e22 | −0.374811 | ||||||||
\(383\) | − | 2.92179e22i | − | 0.164763i | −0.996601 | − | 0.0823816i | \(-0.973747\pi\) | ||
0.996601 | − | 0.0823816i | \(-0.0262526\pi\) | |||||||
\(384\) | 4.13170e21 | − | 1.55053e22i | 0.0227587 | − | 0.0854081i | ||||
\(385\) | −8.62312e22 | −0.464000 | ||||||||
\(386\) | 1.28234e23i | 0.674091i | ||||||||
\(387\) | −3.06511e22 | − | 1.75838e22i | −0.157416 | − | 0.0903054i | ||||
\(388\) | 2.23499e22 | 0.112148 | ||||||||
\(389\) | − | 3.53662e23i | − | 1.73397i | −0.498333 | − | 0.866986i | \(-0.666054\pi\) | ||
0.498333 | − | 0.866986i | \(-0.333946\pi\) | |||||||
\(390\) | 2.50684e23 | + | 6.67997e22i | 1.20101 | + | 0.320032i | ||||
\(391\) | 3.62069e23 | 1.69512 | ||||||||
\(392\) | 3.79452e22i | 0.173613i | ||||||||
\(393\) | 4.47612e21 | − | 1.67978e22i | 0.0200156 | − | 0.0751140i | ||||
\(394\) | 1.59524e23 | 0.697205 | ||||||||
\(395\) | 5.38579e23i | 2.30078i | ||||||||
\(396\) | 1.47923e22 | − | 2.57851e22i | 0.0617701 | − | 0.107675i | ||||
\(397\) | 4.85574e22 | 0.198217 | 0.0991086 | − | 0.995077i | \(-0.468401\pi\) | ||||
0.0991086 | + | 0.995077i | \(0.468401\pi\) | |||||||
\(398\) | − | 1.03866e23i | − | 0.414500i | ||||||
\(399\) | −2.94186e23 | − | 7.83918e22i | −1.14780 | − | 0.305854i | ||||
\(400\) | −8.79889e22 | −0.335651 | ||||||||
\(401\) | 3.96506e23i | 1.47894i | 0.673190 | + | 0.739469i | \(0.264923\pi\) | ||||
−0.673190 | + | 0.739469i | \(0.735077\pi\) | |||||||
\(402\) | −2.99064e22 | + | 1.12232e23i | −0.109076 | + | 0.409338i | ||||
\(403\) | −2.63426e23 | −0.939536 | ||||||||
\(404\) | − | 2.04077e23i | − | 0.711807i | ||||||
\(405\) | 3.87331e23 | − | 2.26487e23i | 1.32125 | − | 0.772587i | ||||
\(406\) | −2.49049e23 | −0.830903 | ||||||||
\(407\) | 1.69206e22i | 0.0552161i | ||||||||
\(408\) | 1.35046e23 | + | 3.59858e22i | 0.431063 | + | 0.114865i | ||||
\(409\) | 3.36745e23 | 1.05146 | 0.525728 | − | 0.850653i | \(-0.323793\pi\) | ||||
0.525728 | + | 0.850653i | \(0.323793\pi\) | |||||||
\(410\) | 2.81816e23i | 0.860818i | ||||||||
\(411\) | −9.28128e22 | + | 3.48305e23i | −0.277352 | + | 1.04084i | ||||
\(412\) | 4.37623e22 | 0.127945 | ||||||||
\(413\) | − | 8.03242e22i | − | 0.229771i | ||||||
\(414\) | −2.94393e23 | − | 1.68886e23i | −0.823995 | − | 0.472705i | ||||
\(415\) | −2.53854e23 | −0.695266 | ||||||||
\(416\) | − | 7.57480e22i | − | 0.203017i | ||||||
\(417\) | 6.94155e23 | + | 1.84971e23i | 1.82067 | + | 0.485155i | ||||
\(418\) | −6.65288e22 | −0.170774 | ||||||||
\(419\) | − | 5.91207e23i | − | 1.48530i | −0.669681 | − | 0.742648i | \(-0.733569\pi\) | ||
0.669681 | − | 0.742648i | \(-0.266431\pi\) | |||||||
\(420\) | −9.78502e22 | + | 3.67209e23i | −0.240613 | + | 0.902963i | ||||
\(421\) | −4.25919e23 | −1.02515 | −0.512576 | − | 0.858642i | \(-0.671309\pi\) | ||||
−0.512576 | + | 0.858642i | \(0.671309\pi\) | |||||||
\(422\) | 2.61729e23i | 0.616652i | ||||||||
\(423\) | −2.60225e23 | + | 4.53611e23i | −0.600186 | + | 1.04621i | ||||
\(424\) | −2.33681e23 | −0.527631 | ||||||||
\(425\) | − | 7.66356e23i | − | 1.69406i | ||||||
\(426\) | −2.19862e23 | − | 5.85866e22i | −0.475843 | − | 0.126798i | ||||
\(427\) | 6.29562e23 | 1.33410 | ||||||||
\(428\) | − | 1.08082e23i | − | 0.224265i | ||||||
\(429\) | 3.61324e22 | − | 1.35596e23i | 0.0734143 | − | 0.275507i | ||||
\(430\) | 9.87138e22 | 0.196409 | ||||||||
\(431\) | − | 7.33628e23i | − | 1.42949i | −0.699386 | − | 0.714744i | \(-0.746543\pi\) | ||
0.699386 | − | 0.714744i | \(-0.253457\pi\) | |||||||
\(432\) | −9.30187e22 | − | 9.22513e22i | −0.177507 | − | 0.176043i | ||||
\(433\) | 1.04893e24 | 1.96045 | 0.980223 | − | 0.197896i | \(-0.0634107\pi\) | ||||
0.980223 | + | 0.197896i | \(0.0634107\pi\) | |||||||
\(434\) | − | 3.85874e23i | − | 0.706380i | ||||||
\(435\) | −7.93735e23 | − | 2.11507e23i | −1.42322 | − | 0.379246i | ||||
\(436\) | 1.34261e23 | 0.235815 | ||||||||
\(437\) | 7.59569e23i | 1.30688i | ||||||||
\(438\) | 1.10265e23 | − | 4.13797e23i | 0.185853 | − | 0.697462i | ||||
\(439\) | −3.99418e23 | −0.659549 | −0.329774 | − | 0.944060i | \(-0.606973\pi\) | ||||
−0.329774 | + | 0.944060i | \(0.606973\pi\) | |||||||
\(440\) | 8.30426e22i | 0.134347i | ||||||||
\(441\) | 2.68717e23 | + | 1.54156e23i | 0.425940 | + | 0.244351i | ||||
\(442\) | 6.59742e23 | 1.02465 | ||||||||
\(443\) | − | 8.28371e22i | − | 0.126064i | −0.998012 | − | 0.0630320i | \(-0.979923\pi\) | ||
0.998012 | − | 0.0630320i | \(-0.0200770\pi\) | |||||||
\(444\) | 7.20550e22 | + | 1.92005e22i | 0.107453 | + | 0.0286329i | ||||
\(445\) | −1.74617e24 | −2.55179 | ||||||||
\(446\) | − | 3.08317e23i | − | 0.441554i | ||||||
\(447\) | −1.31170e23 | + | 4.92251e23i | −0.184106 | + | 0.690906i | ||||
\(448\) | 1.10958e23 | 0.152636 | ||||||||
\(449\) | − | 1.61666e23i | − | 0.217973i | −0.994043 | − | 0.108986i | \(-0.965240\pi\) | ||
0.994043 | − | 0.108986i | \(-0.0347605\pi\) | |||||||
\(450\) | −3.57464e23 | + | 6.23112e23i | −0.472410 | + | 0.823481i | ||||
\(451\) | 1.52436e23 | 0.197469 | ||||||||
\(452\) | 9.43796e22i | 0.119848i | ||||||||
\(453\) | 8.08270e23 | + | 2.15380e23i | 1.00617 | + | 0.268115i | ||||
\(454\) | 1.17190e23 | 0.143018 | ||||||||
\(455\) | 1.79393e24i | 2.14636i | ||||||||
\(456\) | −7.54930e22 | + | 2.83308e23i | −0.0885571 | + | 0.332334i | ||||
\(457\) | 5.79280e22 | 0.0666259 | 0.0333129 | − | 0.999445i | \(-0.489394\pi\) | ||||
0.0333129 | + | 0.999445i | \(0.489394\pi\) | |||||||
\(458\) | 5.46050e23i | 0.615805i | ||||||||
\(459\) | 8.03480e23 | − | 8.10163e23i | 0.888507 | − | 0.895898i | ||||
\(460\) | 9.48110e23 | 1.02811 | ||||||||
\(461\) | − | 1.63337e23i | − | 0.173691i | −0.996222 | − | 0.0868454i | \(-0.972321\pi\) | ||
0.996222 | − | 0.0868454i | \(-0.0276786\pi\) | |||||||
\(462\) | 1.98626e23 | + | 5.29278e22i | 0.207137 | + | 0.0551958i | ||||
\(463\) | −1.28649e24 | −1.31576 | −0.657880 | − | 0.753122i | \(-0.728547\pi\) | ||||
−0.657880 | + | 0.753122i | \(0.728547\pi\) | |||||||
\(464\) | 2.39840e23i | 0.240580i | ||||||||
\(465\) | 3.27707e23 | − | 1.22981e24i | 0.322410 | − | 1.20993i | ||||
\(466\) | −1.81591e23 | −0.175235 | ||||||||
\(467\) | 1.31844e24i | 1.24798i | 0.781433 | + | 0.623989i | \(0.214489\pi\) | ||||
−0.781433 | + | 0.623989i | \(0.785511\pi\) | |||||||
\(468\) | −5.36426e23 | − | 3.07734e23i | −0.498078 | − | 0.285735i | ||||
\(469\) | −8.03146e23 | −0.731542 | ||||||||
\(470\) | − | 1.46088e24i | − | 1.30537i | ||||||
\(471\) | −1.18990e23 | − | 3.17072e22i | −0.104309 | − | 0.0277952i | ||||
\(472\) | −7.73539e22 | −0.0665280 | ||||||||
\(473\) | − | 5.33949e22i | − | 0.0450557i | ||||||
\(474\) | 3.30574e23 | − | 1.24057e24i | 0.273693 | − | 1.02711i | ||||
\(475\) | 1.60770e24 | 1.30606 | ||||||||
\(476\) | 9.66409e23i | 0.770368i | ||||||||
\(477\) | −9.49352e23 | + | 1.65486e24i | −0.742612 | + | 1.29448i | ||||
\(478\) | 5.21176e23 | 0.400068 | ||||||||
\(479\) | − | 2.24990e24i | − | 1.69490i | −0.530874 | − | 0.847451i | \(-0.678136\pi\) | ||
0.530874 | − | 0.847451i | \(-0.321864\pi\) | |||||||
\(480\) | 3.53630e23 | + | 9.42319e22i | 0.261444 | + | 0.0696670i | ||||
\(481\) | 3.52011e23 | 0.255417 | ||||||||
\(482\) | 8.20234e23i | 0.584136i | ||||||||
\(483\) | 6.04285e23 | − | 2.26774e24i | 0.422394 | − | 1.58515i | ||||
\(484\) | −6.83831e23 | −0.469181 | ||||||||
\(485\) | 5.09737e23i | 0.343297i | ||||||||
\(486\) | −1.03120e24 | + | 2.83951e23i | −0.681733 | + | 0.187723i | ||||
\(487\) | 3.43498e23 | 0.222927 | 0.111464 | − | 0.993769i | \(-0.464446\pi\) | ||||
0.111464 | + | 0.993769i | \(0.464446\pi\) | |||||||
\(488\) | − | 6.06282e23i | − | 0.386275i | ||||||
\(489\) | −1.21263e24 | − | 3.23130e23i | −0.758488 | − | 0.202114i | ||||
\(490\) | −8.65420e23 | −0.531450 | ||||||||
\(491\) | 7.44341e23i | 0.448785i | 0.974499 | + | 0.224393i | \(0.0720398\pi\) | ||||
−0.974499 | + | 0.224393i | \(0.927960\pi\) | |||||||
\(492\) | 1.72976e23 | − | 6.49138e23i | 0.102400 | − | 0.384283i | ||||
\(493\) | −2.08893e24 | −1.21423 | ||||||||
\(494\) | 1.38404e24i | 0.789964i | ||||||||
\(495\) | 5.88084e23 | + | 3.37369e23i | 0.329604 | + | 0.189085i | ||||
\(496\) | −3.71605e23 | −0.204525 | ||||||||
\(497\) | − | 1.57336e24i | − | 0.850396i | ||||||
\(498\) | 5.84729e23 | + | 1.55813e23i | 0.310378 | + | 0.0827064i | ||||
\(499\) | 1.18713e24 | 0.618863 | 0.309432 | − | 0.950922i | \(-0.399861\pi\) | ||||
0.309432 | + | 0.950922i | \(0.399861\pi\) | |||||||
\(500\) | − | 5.12085e23i | − | 0.262188i | ||||||
\(501\) | −3.66947e22 | + | 1.37707e23i | −0.0184529 | + | 0.0692494i | ||||
\(502\) | −1.20541e24 | −0.595388 | ||||||||
\(503\) | − | 3.10476e23i | − | 0.150631i | −0.997160 | − | 0.0753157i | \(-0.976004\pi\) | ||
0.997160 | − | 0.0753157i | \(-0.0239965\pi\) | |||||||
\(504\) | 4.50778e23 | − | 7.85773e23i | 0.214826 | − | 0.374474i | ||||
\(505\) | 4.65440e24 | 2.17892 | ||||||||
\(506\) | − | 5.12838e23i | − | 0.235844i | ||||||
\(507\) | −6.82079e23 | − | 1.81754e23i | −0.308151 | − | 0.0821129i | ||||
\(508\) | −1.55403e24 | −0.689741 | ||||||||
\(509\) | 3.15226e24i | 1.37456i | 0.726394 | + | 0.687278i | \(0.241195\pi\) | ||||
−0.726394 | + | 0.687278i | \(0.758805\pi\) | |||||||
\(510\) | −8.20730e23 | + | 3.08001e24i | −0.351616 | + | 1.31953i | ||||
\(511\) | 2.96119e24 | 1.24646 | ||||||||
\(512\) | − | 1.06855e23i | − | 0.0441942i | ||||||
\(513\) | 1.69961e24 | + | 1.68559e24i | 0.690704 | + | 0.685006i | ||||
\(514\) | 1.98778e23 | 0.0793781 | ||||||||
\(515\) | 9.98089e23i | 0.391656i | ||||||||
\(516\) | −2.27378e23 | − | 6.05894e22i | −0.0876801 | − | 0.0233641i | ||||
\(517\) | −7.90200e23 | −0.299448 | ||||||||
\(518\) | 5.15635e23i | 0.192033i | ||||||||
\(519\) | −9.23779e23 | + | 3.46673e24i | −0.338113 | + | 1.26886i | ||||
\(520\) | 1.72759e24 | 0.621457 | ||||||||
\(521\) | − | 2.05204e24i | − | 0.725515i | −0.931884 | − | 0.362757i | \(-0.881835\pi\) | ||
0.931884 | − | 0.362757i | \(-0.118165\pi\) | |||||||
\(522\) | 1.69848e24 | + | 9.74372e23i | 0.590235 | + | 0.338603i | ||||
\(523\) | −4.10015e24 | −1.40050 | −0.700252 | − | 0.713895i | \(-0.746929\pi\) | ||||
−0.700252 | + | 0.713895i | \(0.746929\pi\) | |||||||
\(524\) | − | 1.15763e23i | − | 0.0388675i | ||||||
\(525\) | −4.79990e24 | − | 1.27903e24i | −1.58416 | − | 0.422131i | ||||
\(526\) | 2.59555e24 | 0.842089 | ||||||||
\(527\) | − | 3.23656e24i | − | 1.03226i | ||||||
\(528\) | 5.09706e22 | − | 1.91281e23i | 0.0159814 | − | 0.0599744i | ||||
\(529\) | −2.61100e24 | −0.804834 | ||||||||
\(530\) | − | 5.32958e24i | − | 1.61514i | ||||||
\(531\) | −3.14258e23 | + | 5.47798e23i | −0.0936345 | + | 0.163219i | ||||
\(532\) | −2.02739e24 | −0.593926 | ||||||||
\(533\) | − | 3.17124e24i | − | 0.913447i | ||||||
\(534\) | 4.02213e24 | + | 1.07178e24i | 1.13916 | + | 0.303552i | ||||
\(535\) | 2.46504e24 | 0.686499 | ||||||||
\(536\) | 7.73447e23i | 0.211811i | ||||||||
\(537\) | 5.20351e22 | − | 1.95276e23i | 0.0140129 | − | 0.0525871i | ||||
\(538\) | −3.89771e24 | −1.03221 | ||||||||
\(539\) | 4.68111e23i | 0.121913i | ||||||||
\(540\) | 2.10398e24 | − | 2.12148e24i | 0.538888 | − | 0.543370i | ||||
\(541\) | −5.58057e24 | −1.40573 | −0.702867 | − | 0.711322i | \(-0.748097\pi\) | ||||
−0.702867 | + | 0.711322i | \(0.748097\pi\) | |||||||
\(542\) | 4.09535e23i | 0.101461i | ||||||||
\(543\) | 5.18220e24 | + | 1.38090e24i | 1.26274 | + | 0.336483i | ||||
\(544\) | 9.30673e23 | 0.223052 | ||||||||
\(545\) | 3.06210e24i | 0.721856i | ||||||||
\(546\) | 1.10109e24 | − | 4.13215e24i | 0.255323 | − | 0.958169i | ||||
\(547\) | 3.61075e23 | 0.0823591 | 0.0411795 | − | 0.999152i | \(-0.486888\pi\) | ||||
0.0411795 | + | 0.999152i | \(0.486888\pi\) | |||||||
\(548\) | 2.40035e24i | 0.538579i | ||||||||
\(549\) | −4.29352e24 | − | 2.46308e24i | −0.947681 | − | 0.543660i | ||||
\(550\) | −1.08547e24 | −0.235698 | ||||||||
\(551\) | − | 4.38227e24i | − | 0.936127i | ||||||
\(552\) | −2.18388e24 | − | 5.81939e23i | −0.458963 | − | 0.122300i | ||||
\(553\) | 8.87767e24 | 1.83558 | ||||||||
\(554\) | 1.25327e24i | 0.254952i | ||||||||
\(555\) | −4.37907e23 | + | 1.64336e24i | −0.0876487 | + | 0.328925i | ||||
\(556\) | 4.78378e24 | 0.942102 | ||||||||
\(557\) | 1.15019e24i | 0.222880i | 0.993771 | + | 0.111440i | \(0.0355463\pi\) | ||||
−0.993771 | + | 0.111440i | \(0.964454\pi\) | |||||||
\(558\) | −1.50968e24 | + | 2.63160e24i | −0.287858 | + | 0.501779i | ||||
\(559\) | −1.11081e24 | −0.208417 | ||||||||
\(560\) | 2.53063e24i | 0.467236i | ||||||||
\(561\) | 1.66600e24 | + | 4.43938e23i | 0.302697 | + | 0.0806597i | ||||
\(562\) | −1.33204e24 | −0.238172 | ||||||||
\(563\) | − | 3.27424e24i | − | 0.576149i | −0.957608 | − | 0.288075i | \(-0.906985\pi\) | ||
0.957608 | − | 0.288075i | \(-0.0930151\pi\) | |||||||
\(564\) | −8.96673e23 | + | 3.36500e24i | −0.155282 | + | 0.582739i | ||||
\(565\) | −2.15252e24 | −0.366870 | ||||||||
\(566\) | − | 9.30000e23i | − | 0.156004i | ||||||
\(567\) | −3.73329e24 | − | 6.38456e24i | −0.616374 | − | 1.05410i | ||||
\(568\) | −1.51518e24 | −0.246224 | ||||||||
\(569\) | 1.03001e25i | 1.64752i | 0.566936 | + | 0.823762i | \(0.308129\pi\) | ||||
−0.566936 | + | 0.823762i | \(0.691871\pi\) | |||||||
\(570\) | −6.46142e24 | − | 1.72177e24i | −1.01731 | − | 0.271083i | ||||
\(571\) | 8.56464e23 | 0.132735 | 0.0663673 | − | 0.997795i | \(-0.478859\pi\) | ||||
0.0663673 | + | 0.997795i | \(0.478859\pi\) | |||||||
\(572\) | − | 9.34465e23i | − | 0.142560i | ||||||
\(573\) | −9.08805e23 | + | 3.41053e24i | −0.136483 | + | 0.512190i | ||||
\(574\) | 4.64532e24 | 0.686766 | ||||||||
\(575\) | 1.23930e25i | 1.80371i | ||||||||
\(576\) | −7.56716e23 | − | 4.34109e23i | −0.108425 | − | 0.0622009i | ||||
\(577\) | 5.51272e24 | 0.777650 | 0.388825 | − | 0.921312i | \(-0.372881\pi\) | ||||
0.388825 | + | 0.921312i | \(0.372881\pi\) | |||||||
\(578\) | 3.01449e24i | 0.418662i | ||||||||
\(579\) | 6.73666e24 | + | 1.79512e24i | 0.921165 | + | 0.245463i | ||||
\(580\) | −5.47004e24 | −0.736442 | ||||||||
\(581\) | 4.18440e24i | 0.554687i | ||||||||
\(582\) | 3.12871e23 | − | 1.17413e24i | 0.0408374 | − | 0.153253i | ||||
\(583\) | −2.88280e24 | −0.370508 | ||||||||
\(584\) | − | 2.85169e24i | − | 0.360900i | ||||||
\(585\) | 7.01851e24 | − | 1.22343e25i | 0.874666 | − | 1.52467i | ||||
\(586\) | 3.59455e24 | 0.441130 | ||||||||
\(587\) | 3.57180e23i | 0.0431662i | 0.999767 | + | 0.0215831i | \(0.00687065\pi\) | ||||
−0.999767 | + | 0.0215831i | \(0.993129\pi\) | |||||||
\(588\) | 1.99341e24 | + | 5.31185e23i | 0.237248 | + | 0.0632194i | ||||
\(589\) | 6.78985e24 | 0.795834 | ||||||||
\(590\) | − | 1.76422e24i | − | 0.203650i | ||||||
\(591\) | 2.23314e24 | − | 8.38044e24i | 0.253880 | − | 0.952752i | ||||
\(592\) | 4.96568e23 | 0.0556011 | ||||||||
\(593\) | − | 1.13918e25i | − | 1.25632i | −0.778084 | − | 0.628160i | \(-0.783808\pi\) | ||
0.778084 | − | 0.628160i | \(-0.216192\pi\) | |||||||
\(594\) | −1.14752e24 | − | 1.13806e24i | −0.124647 | − | 0.123619i | ||||
\(595\) | −2.20410e25 | −2.35819 | ||||||||
\(596\) | 3.39235e24i | 0.357507i | ||||||||
\(597\) | −5.45648e24 | − | 1.45399e24i | −0.566426 | − | 0.150936i | ||||
\(598\) | −1.06689e25 | −1.09096 | ||||||||
\(599\) | − | 7.81570e24i | − | 0.787275i | −0.919266 | − | 0.393638i | \(-0.871217\pi\) | ||
0.919266 | − | 0.393638i | \(-0.128783\pi\) | |||||||
\(600\) | −1.23173e24 | + | 4.62241e24i | −0.122224 | + | 0.458677i | ||||
\(601\) | 1.73207e25 | 1.69315 | 0.846576 | − | 0.532267i | \(-0.178660\pi\) | ||||
0.846576 | + | 0.532267i | \(0.178660\pi\) | |||||||
\(602\) | − | 1.62715e24i | − | 0.156696i | ||||||
\(603\) | 5.47733e24 | + | 3.14221e24i | 0.519653 | + | 0.298112i | ||||
\(604\) | 5.57021e24 | 0.520642 | ||||||||
\(605\) | − | 1.55962e25i | − | 1.43622i | ||||||
\(606\) | −1.07210e25 | − | 2.85682e24i | −0.972705 | − | 0.259197i | ||||
\(607\) | −1.95831e25 | −1.75058 | −0.875291 | − | 0.483597i | \(-0.839330\pi\) | ||||
−0.875291 | + | 0.483597i | \(0.839330\pi\) | |||||||
\(608\) | 1.95242e24i | 0.171965i | ||||||||
\(609\) | −3.48637e24 | + | 1.30835e25i | −0.302564 | + | 1.13545i | ||||
\(610\) | 1.38275e25 | 1.18243 | ||||||||
\(611\) | 1.64391e25i | 1.38518i | ||||||||
\(612\) | 3.78095e24 | − | 6.59076e24i | 0.313934 | − | 0.547234i | ||||
\(613\) | 5.56489e24 | 0.455315 | 0.227658 | − | 0.973741i | \(-0.426893\pi\) | ||||
0.227658 | + | 0.973741i | \(0.426893\pi\) | |||||||
\(614\) | 2.44638e24i | 0.197247i | ||||||||
\(615\) | 1.48049e25 | + | 3.94507e24i | 1.17633 | + | 0.313458i | ||||
\(616\) | 1.36883e24 | 0.107182 | ||||||||
\(617\) | − | 1.88574e25i | − | 1.45518i | −0.686014 | − | 0.727589i | \(-0.740641\pi\) | ||
0.686014 | − | 0.727589i | \(-0.259359\pi\) | |||||||
\(618\) | 6.12616e23 | − | 2.29901e24i | 0.0465899 | − | 0.174841i | ||||
\(619\) | −1.74654e25 | −1.30907 | −0.654536 | − | 0.756031i | \(-0.727136\pi\) | ||||
−0.654536 | + | 0.756031i | \(0.727136\pi\) | |||||||
\(620\) | − | 8.47523e24i | − | 0.626075i | ||||||
\(621\) | −1.29934e25 | + | 1.31014e25i | −0.946014 | + | 0.953883i | ||||
\(622\) | 1.20793e25 | 0.866818 | ||||||||
\(623\) | 2.87829e25i | 2.03583i | ||||||||
\(624\) | −3.97935e24 | − | 1.06038e24i | −0.277428 | − | 0.0739263i | ||||
\(625\) | −7.85830e24 | −0.540018 | ||||||||
\(626\) | 5.24496e24i | 0.355282i | ||||||||
\(627\) | −9.31318e23 | + | 3.49502e24i | −0.0621857 | + | 0.233368i | ||||
\(628\) | −8.20018e23 | −0.0539743 | ||||||||
\(629\) | 4.32495e24i | 0.280624i | ||||||||
\(630\) | 1.79212e25 | + | 1.02809e25i | 1.14631 | + | 0.657608i | ||||
\(631\) | −4.13411e24 | −0.260686 | −0.130343 | − | 0.991469i | \(-0.541608\pi\) | ||||
−0.130343 | + | 0.991469i | \(0.541608\pi\) | |||||||
\(632\) | − | 8.54939e24i | − | 0.531473i | ||||||
\(633\) | 1.37497e25 | + | 3.66388e24i | 0.842674 | + | 0.224547i | ||||
\(634\) | 8.94559e24 | 0.540512 | ||||||||
\(635\) | − | 3.54429e25i | − | 2.11138i | ||||||
\(636\) | −3.27124e24 | + | 1.22762e25i | −0.192131 | + | 0.721024i | ||||
\(637\) | 9.73843e24 | 0.563942 | ||||||||
\(638\) | 2.95878e24i | 0.168938i | ||||||||
\(639\) | −6.15558e24 | + | 1.07301e25i | −0.346546 | + | 0.604081i | ||||
\(640\) | 2.43705e24 | 0.135283 | ||||||||
\(641\) | 1.36929e25i | 0.749501i | 0.927126 | + | 0.374750i | \(0.122272\pi\) | ||||
−0.927126 | + | 0.374750i | \(0.877728\pi\) | |||||||
\(642\) | −5.67799e24 | − | 1.51301e24i | −0.306464 | − | 0.0816635i | ||||
\(643\) | 2.29390e25 | 1.22089 | 0.610444 | − | 0.792059i | \(-0.290991\pi\) | ||||
0.610444 | + | 0.792059i | \(0.290991\pi\) | |||||||
\(644\) | − | 1.56282e25i | − | 0.820229i | ||||||
\(645\) | 1.38187e24 | − | 5.18583e24i | 0.0715202 | − | 0.268399i | ||||
\(646\) | −1.70050e25 | −0.867926 | ||||||||
\(647\) | − | 2.73672e25i | − | 1.37750i | −0.724999 | − | 0.688749i | \(-0.758160\pi\) | ||
0.724999 | − | 0.688749i | \(-0.241840\pi\) | |||||||
\(648\) | −6.14847e24 | + | 3.59524e24i | −0.305205 | + | 0.178465i | ||||
\(649\) | −9.54275e23 | −0.0467166 | ||||||||
\(650\) | 2.25819e25i | 1.09028i | ||||||||
\(651\) | −2.02715e25 | − | 5.40175e24i | −0.965289 | − | 0.257220i | ||||
\(652\) | −8.35686e24 | −0.392478 | ||||||||
\(653\) | 4.03759e25i | 1.87026i | 0.354299 | + | 0.935132i | \(0.384720\pi\) | ||||
−0.354299 | + | 0.935132i | \(0.615280\pi\) | |||||||
\(654\) | 1.87948e24 | − | 7.05326e24i | 0.0858695 | − | 0.322248i | ||||
\(655\) | 2.64021e24 | 0.118978 | ||||||||
\(656\) | − | 4.47354e24i | − | 0.198846i | ||||||
\(657\) | −2.01948e25 | − | 1.15853e25i | −0.885426 | − | 0.507946i | ||||
\(658\) | −2.40804e25 | −1.04143 | ||||||||
\(659\) | 1.20317e25i | 0.513286i | 0.966506 | + | 0.256643i | \(0.0826164\pi\) | ||||
−0.966506 | + | 0.256643i | \(0.917384\pi\) | |||||||
\(660\) | 4.36256e24 | + | 1.16249e24i | 0.183589 | + | 0.0489208i | ||||
\(661\) | 2.12057e25 | 0.880318 | 0.440159 | − | 0.897920i | \(-0.354922\pi\) | ||||
0.440159 | + | 0.897920i | \(0.354922\pi\) | |||||||
\(662\) | − | 2.72248e25i | − | 1.11492i | ||||||
\(663\) | 9.23555e24 | − | 3.46589e25i | 0.373113 | − | 1.40021i | ||||
\(664\) | 4.02967e24 | 0.160604 | ||||||||
\(665\) | − | 4.62388e25i | − | 1.81807i | ||||||
\(666\) | 2.01736e24 | − | 3.51655e24i | 0.0782555 | − | 0.136411i | ||||
\(667\) | 3.37808e25 | 1.29282 | ||||||||
\(668\) | 9.49009e23i | 0.0358329i | ||||||||
\(669\) | −1.61971e25 | − | 4.31604e24i | −0.603396 | − | 0.160787i | ||||
\(670\) | −1.76401e25 | −0.648376 | ||||||||
\(671\) | − | 7.47939e24i | − | 0.271246i | ||||||
\(672\) | 1.55327e24 | − | 5.82906e24i | 0.0555807 | − | 0.208581i | ||||
\(673\) | −2.12038e25 | −0.748650 | −0.374325 | − | 0.927298i | \(-0.622126\pi\) | ||||
−0.374325 | + | 0.927298i | \(0.622126\pi\) | |||||||
\(674\) | 3.15621e25i | 1.09958i | ||||||||
\(675\) | 2.77305e25 | + | 2.75018e25i | 0.953288 | + | 0.945424i | ||||
\(676\) | −4.70056e24 | −0.159452 | ||||||||
\(677\) | 7.94323e24i | 0.265888i | 0.991124 | + | 0.132944i | \(0.0424431\pi\) | ||||
−0.991124 | + | 0.132944i | \(0.957557\pi\) | |||||||
\(678\) | 4.95814e24 | + | 1.32120e24i | 0.163776 | + | 0.0436415i | ||||
\(679\) | 8.40224e24 | 0.273884 | ||||||||
\(680\) | 2.12259e25i | 0.682789i | ||||||||
\(681\) | 1.64052e24 | − | 6.15648e24i | 0.0520783 | − | 0.195438i | ||||
\(682\) | −4.58430e24 | −0.143620 | ||||||||
\(683\) | − | 2.16897e25i | − | 0.670607i | −0.942110 | − | 0.335303i | \(-0.891161\pi\) | ||
0.942110 | − | 0.335303i | \(-0.108839\pi\) | |||||||
\(684\) | 1.38265e25 | + | 7.93190e24i | 0.421897 | + | 0.242032i | ||||
\(685\) | −5.47449e25 | −1.64865 | ||||||||
\(686\) | − | 1.47850e25i | − | 0.439445i | ||||||
\(687\) | 2.86862e25 | + | 7.64401e24i | 0.841516 | + | 0.224239i | ||||
\(688\) | −1.56698e24 | −0.0453698 | ||||||||
\(689\) | 5.99729e25i | 1.71389i | ||||||||
\(690\) | 1.32723e25 | − | 4.98080e25i | 0.374374 | − | 1.40494i | ||||
\(691\) | 1.13295e25 | 0.315435 | 0.157717 | − | 0.987484i | \(-0.449586\pi\) | ||||
0.157717 | + | 0.987484i | \(0.449586\pi\) | |||||||
\(692\) | 2.38910e25i | 0.656568i | ||||||||
\(693\) | 5.56101e24 | − | 9.69367e24i | 0.150853 | − | 0.262960i | ||||
\(694\) | 3.81706e25 | 1.02210 | ||||||||
\(695\) | 1.09104e26i | 2.88388i | ||||||||
\(696\) | 1.25997e25 | + | 3.35745e24i | 0.328759 | + | 0.0876045i | ||||
\(697\) | 3.89632e25 | 1.00360 | ||||||||
\(698\) | 7.38410e24i | 0.187758i | ||||||||
\(699\) | −2.54204e24 | + | 9.53969e24i | −0.0638099 | + | 0.239464i | ||||
\(700\) | −3.30786e25 | −0.819718 | ||||||||
\(701\) | − | 1.73460e25i | − | 0.424364i | −0.977230 | − | 0.212182i | \(-0.931943\pi\) | ||
0.977230 | − | 0.212182i | \(-0.0680569\pi\) | |||||||
\(702\) | −2.36758e25 | + | 2.38727e25i | −0.571834 | + | 0.576591i | ||||
\(703\) | −9.07313e24 | −0.216351 | ||||||||
\(704\) | − | 1.31821e24i | − | 0.0310336i | ||||||
\(705\) | −7.67459e25 | − | 2.04505e25i | −1.78383 | − | 0.475337i | ||||
\(706\) | −4.63310e25 | −1.06323 | ||||||||
\(707\) | − | 7.67208e25i | − | 1.73836i | ||||||
\(708\) | −1.08286e24 | + | 4.06371e24i | −0.0242254 | + | 0.0909124i | ||||
\(709\) | 8.17517e24 | 0.180585 | 0.0902923 | − | 0.995915i | \(-0.471220\pi\) | ||||
0.0902923 | + | 0.995915i | \(0.471220\pi\) | |||||||
\(710\) | − | 3.45569e25i | − | 0.753718i | ||||||
\(711\) | −6.05443e25 | − | 3.47327e25i | −1.30391 | − | 0.748019i | ||||
\(712\) | 2.77186e25 | 0.589455 | ||||||||
\(713\) | 5.23397e25i | 1.09907i | ||||||||
\(714\) | 5.07693e25 | + | 1.35285e25i | 1.05273 | + | 0.280521i | ||||
\(715\) | 2.13124e25 | 0.436393 | ||||||||
\(716\) | − | 1.34574e24i | − | 0.0272111i | ||||||
\(717\) | 7.29580e24 | − | 2.73795e25i | 0.145680 | − | 0.546704i | ||||
\(718\) | 3.10265e25 | 0.611806 | ||||||||
\(719\) | − | 1.53732e25i | − | 0.299368i | −0.988734 | − | 0.149684i | \(-0.952174\pi\) | ||
0.988734 | − | 0.149684i | \(-0.0478256\pi\) | |||||||
\(720\) | 9.90075e24 | − | 1.72585e25i | 0.190404 | − | 0.331902i | ||||
\(721\) | 1.64520e25 | 0.312465 | ||||||||
\(722\) | 2.02417e24i | 0.0379675i | ||||||||
\(723\) | 4.30901e25 | + | 1.14822e25i | 0.798240 | + | 0.212707i | ||||
\(724\) | 3.57132e25 | 0.653403 | ||||||||
\(725\) | − | 7.15005e25i | − | 1.29201i | ||||||
\(726\) | −9.57277e24 | + | 3.59244e25i | −0.170847 | + | 0.641150i | ||||
\(727\) | −6.79047e25 | −1.19699 | −0.598495 | − | 0.801127i | \(-0.704234\pi\) | ||||
−0.598495 | + | 0.801127i | \(0.704234\pi\) | |||||||
\(728\) | − | 2.84767e25i | − | 0.495802i | ||||||
\(729\) | 4.81680e23 | + | 5.81477e25i | 0.00828344 | + | 0.999966i | ||||
\(730\) | 6.50387e25 | 1.10475 | ||||||||
\(731\) | − | 1.36479e25i | − | 0.228986i | ||||||
\(732\) | −3.18504e25 | − | 8.48718e24i | −0.527856 | − | 0.140658i | ||||
\(733\) | −2.21096e25 | −0.361947 | −0.180974 | − | 0.983488i | \(-0.557925\pi\) | ||||
−0.180974 | + | 0.983488i | \(0.557925\pi\) | |||||||
\(734\) | − | 8.42995e25i | − | 1.36320i | ||||||
\(735\) | −1.21148e25 | + | 4.54640e25i | −0.193522 | + | 0.726242i | ||||
\(736\) | −1.50503e25 | −0.237489 | ||||||||
\(737\) | 9.54162e24i | 0.148736i | ||||||||
\(738\) | −3.16804e25 | − | 1.81742e25i | −0.487846 | − | 0.279865i | ||||
\(739\) | −3.66121e25 | −0.556960 | −0.278480 | − | 0.960442i | \(-0.589831\pi\) | ||||
−0.278480 | + | 0.960442i | \(0.589831\pi\) | |||||||
\(740\) | 1.13253e25i | 0.170201i | ||||||||
\(741\) | 7.27093e25 | + | 1.93749e25i | 1.07951 | + | 0.287657i | ||||
\(742\) | −8.78501e25 | −1.28857 | ||||||||
\(743\) | − | 9.48611e25i | − | 1.37464i | −0.726355 | − | 0.687320i | \(-0.758787\pi\) | ||
0.726355 | − | 0.687320i | \(-0.241213\pi\) | |||||||
\(744\) | −5.20200e24 | + | 1.95219e25i | −0.0744756 | + | 0.279490i | ||||
\(745\) | −7.73697e25 | −1.09437 | ||||||||
\(746\) | 6.27360e25i | 0.876733i | ||||||||
\(747\) | 1.63709e25 | − | 2.85370e25i | 0.226041 | − | 0.394024i | ||||
\(748\) | 1.14812e25 | 0.156630 | ||||||||
\(749\) | − | 4.06325e25i | − | 0.547693i | ||||||
\(750\) | −2.69019e25 | − | 7.16854e24i | −0.358287 | − | 0.0954728i | ||||
\(751\) | 1.23146e26 | 1.62054 | 0.810269 | − | 0.586058i | \(-0.199321\pi\) | ||||
0.810269 | + | 0.586058i | \(0.199321\pi\) | |||||||
\(752\) | 2.31900e25i | 0.301536i | ||||||||
\(753\) | −1.68742e25 | + | 6.33248e25i | −0.216804 | + | 0.813615i | ||||
\(754\) | 6.15535e25 | 0.781467 | ||||||||
\(755\) | 1.27040e26i | 1.59374i | ||||||||
\(756\) | −3.49695e25 | − | 3.46810e25i | −0.433504 | − | 0.429927i | ||||
\(757\) | 5.73956e25 | 0.703098 | 0.351549 | − | 0.936170i | \(-0.385655\pi\) | ||||
0.351549 | + | 0.936170i | \(0.385655\pi\) | |||||||
\(758\) | 5.27372e25i | 0.638402i | ||||||||
\(759\) | −2.69414e25 | − | 7.17908e24i | −0.322288 | − | 0.0858802i | ||||
\(760\) | −4.45290e25 | −0.526405 | ||||||||
\(761\) | − | 2.63148e25i | − | 0.307424i | −0.988116 | − | 0.153712i | \(-0.950877\pi\) | ||
0.988116 | − | 0.153712i | \(-0.0491228\pi\) | |||||||
\(762\) | −2.17545e25 | + | 8.16394e25i | −0.251162 | + | 0.942552i | ||||
\(763\) | 5.04741e25 | 0.575901 | ||||||||
\(764\) | 2.35037e25i | 0.265031i | ||||||||
\(765\) | 1.50316e26 | + | 8.62325e25i | 1.67514 | + | 0.960988i | ||||
\(766\) | −1.05780e25 | −0.116505 | ||||||||
\(767\) | 1.98524e25i | 0.216101i | ||||||||
\(768\) | −5.61352e24 | − | 1.49583e24i | −0.0603926 | − | 0.0160928i | ||||
\(769\) | −1.31028e26 | −1.39325 | −0.696624 | − | 0.717436i | \(-0.745316\pi\) | ||||
−0.696624 | + | 0.717436i | \(0.745316\pi\) | |||||||
\(770\) | 3.12190e25i | 0.328098i | ||||||||
\(771\) | 2.78264e24 | − | 1.04426e25i | 0.0289047 | − | 0.108472i | ||||
\(772\) | 4.64258e25 | 0.476654 | ||||||||
\(773\) | − | 1.14653e26i | − | 1.16351i | −0.813365 | − | 0.581753i | \(-0.802367\pi\) | ||
0.813365 | − | 0.581753i | \(-0.197633\pi\) | |||||||
\(774\) | −6.36601e24 | + | 1.10969e25i | −0.0638555 | + | 0.111310i | ||||
\(775\) | 1.10782e26 | 1.09839 | ||||||||
\(776\) | − | 8.09154e24i | − | 0.0793005i | ||||||
\(777\) | 2.70884e25 | + | 7.21824e24i | 0.262418 | + | 0.0699266i | ||||
\(778\) | −1.28039e26 | −1.22610 | ||||||||
\(779\) | 8.17391e25i | 0.773736i | ||||||||
\(780\) | 2.41841e25 | − | 9.07573e25i | 0.226297 | − | 0.849239i | ||||
\(781\) | −1.86920e25 | −0.172901 | ||||||||
\(782\) | − | 1.31083e26i | − | 1.19863i | ||||||
\(783\) | 7.49642e25 | − | 7.55877e25i | 0.677638 | − | 0.683275i | ||||
\(784\) | 1.37376e25 | 0.122763 | ||||||||
\(785\) | − | 1.87022e25i | − | 0.165221i | ||||||
\(786\) | −6.08147e24 | − | 1.62053e24i | −0.0531136 | − | 0.0141532i | ||||
\(787\) | −1.71713e26 | −1.48262 | −0.741311 | − | 0.671162i | \(-0.765795\pi\) | ||||
−0.741311 | + | 0.671162i | \(0.765795\pi\) | |||||||
\(788\) | − | 5.77539e25i | − | 0.492999i | ||||||
\(789\) | 3.63345e25 | − | 1.36355e26i | 0.306638 | − | 1.15074i | ||||
\(790\) | 1.94986e26 | 1.62690 | ||||||||
\(791\) | 3.54811e25i | 0.292691i | ||||||||
\(792\) | −9.33522e24 | − | 5.35538e24i | −0.0761374 | − | 0.0436781i | ||||
\(793\) | −1.55599e26 | −1.25472 | ||||||||
\(794\) | − | 1.75797e25i | − | 0.140161i | ||||||
\(795\) | −2.79984e26 | − | 7.46073e25i | −2.20714 | − | 0.588135i | ||||
\(796\) | −3.76034e25 | −0.293096 | ||||||||
\(797\) | 1.93866e26i | 1.49409i | 0.664775 | + | 0.747043i | \(0.268527\pi\) | ||||
−0.664775 | + | 0.747043i | \(0.731473\pi\) | |||||||
\(798\) | −2.83809e25 | + | 1.06507e26i | −0.216272 | + | 0.811617i | ||||
\(799\) | −2.01977e26 | −1.52188 | ||||||||
\(800\) | 3.18554e25i | 0.237341i | ||||||||
\(801\) | 1.12609e26 | − | 1.96295e26i | 0.829626 | − | 1.44616i | ||||
\(802\) | 1.43550e26 | 1.04577 | ||||||||
\(803\) | − | 3.51798e25i | − | 0.253427i | ||||||
\(804\) | 4.06323e25 | + | 1.08273e25i | 0.289445 | + | 0.0771285i | ||||
\(805\) | 3.56433e26 | 2.51081 | ||||||||
\(806\) | 9.53704e25i | 0.664352i | ||||||||
\(807\) | −5.45629e25 | + | 2.04762e26i | −0.375869 | + | 1.41055i | ||||
\(808\) | −7.38838e25 | −0.503323 | ||||||||
\(809\) | − | 4.32769e25i | − | 0.291554i | −0.989317 | − | 0.145777i | \(-0.953432\pi\) | ||
0.989317 | − | 0.145777i | \(-0.0465683\pi\) | |||||||
\(810\) | −8.19969e25 | − | 1.40229e26i | −0.546301 | − | 0.934268i | ||||
\(811\) | 1.62792e25 | 0.107262 | 0.0536311 | − | 0.998561i | \(-0.482921\pi\) | ||||
0.0536311 | + | 0.998561i | \(0.482921\pi\) | |||||||
\(812\) | 9.01654e25i | 0.587537i | ||||||||
\(813\) | 2.15145e25 | + | 5.73297e24i | 0.138649 | + | 0.0369458i | ||||
\(814\) | 6.12591e24 | 0.0390437 | ||||||||
\(815\) | − | 1.90596e26i | − | 1.20142i | ||||||
\(816\) | 1.30282e25 | − | 4.88920e25i | 0.0812221 | − | 0.304808i | ||||
\(817\) | 2.86313e25 | 0.176540 | ||||||||
\(818\) | − | 1.21915e26i | − | 0.743492i | ||||||
\(819\) | −2.01664e26 | − | 1.15690e26i | −1.21639 | − | 0.697813i | ||||
\(820\) | 1.02028e26 | 0.608691 | ||||||||
\(821\) | 1.85553e26i | 1.09491i | 0.836834 | + | 0.547456i | \(0.184404\pi\) | ||||
−0.836834 | + | 0.547456i | \(0.815596\pi\) | |||||||
\(822\) | 1.26100e26 | + | 3.36018e25i | 0.735984 | + | 0.196118i | ||||
\(823\) | 2.90394e26 | 1.67644 | 0.838221 | − | 0.545331i | \(-0.183596\pi\) | ||||
0.838221 | + | 0.545331i | \(0.183596\pi\) | |||||||
\(824\) | − | 1.58436e25i | − | 0.0904711i | ||||||
\(825\) | −1.51953e25 | + | 5.70243e25i | −0.0858267 | + | 0.322088i | ||||
\(826\) | −2.90805e25 | −0.162473 | ||||||||
\(827\) | 3.58168e26i | 1.97941i | 0.143108 | + | 0.989707i | \(0.454290\pi\) | ||||
−0.143108 | + | 0.989707i | \(0.545710\pi\) | |||||||
\(828\) | −6.11432e25 | + | 1.06582e26i | −0.334253 | + | 0.582652i | ||||
\(829\) | −2.67635e26 | −1.44728 | −0.723638 | − | 0.690180i | \(-0.757531\pi\) | ||||
−0.723638 | + | 0.690180i | \(0.757531\pi\) | |||||||
\(830\) | 9.19050e25i | 0.491628i | ||||||||
\(831\) | 6.58394e25 | + | 1.75442e25i | 0.348399 | + | 0.0928378i | ||||
\(832\) | −2.74237e25 | −0.143554 | ||||||||
\(833\) | 1.19651e26i | 0.619598i | ||||||||
\(834\) | 6.69668e25 | − | 2.51311e26i | 0.343056 | − | 1.28741i | ||||
\(835\) | −2.16441e25 | −0.109689 | ||||||||
\(836\) | 2.40860e25i | 0.120756i | ||||||||
\(837\) | 1.17115e26 | + | 1.16149e26i | 0.580876 | + | 0.576084i | ||||
\(838\) | −2.14040e26 | −1.05026 | ||||||||
\(839\) | − | 2.02874e26i | − | 0.984848i | −0.870355 | − | 0.492424i | \(-0.836111\pi\) | ||
0.870355 | − | 0.492424i | \(-0.163889\pi\) | |||||||
\(840\) | 1.32944e26 | + | 3.54256e25i | 0.638491 | + | 0.170139i | ||||
\(841\) | 1.55617e25 | 0.0739425 | ||||||||
\(842\) | 1.54199e26i | 0.724893i | ||||||||
\(843\) | −1.86469e25 | + | 6.99774e25i | −0.0867277 | + | 0.325469i | ||||
\(844\) | 9.47561e25 | 0.436039 | ||||||||
\(845\) | − | 1.07206e26i | − | 0.488100i | ||||||
\(846\) | 1.64225e26 | + | 9.42116e25i | 0.739785 | + | 0.424396i | ||||
\(847\) | −2.57080e26 | −1.14582 | ||||||||
\(848\) | 8.46015e25i | 0.373092i | ||||||||
\(849\) | −4.88566e25 | − | 1.30188e25i | −0.213184 | − | 0.0568071i | ||||
\(850\) | −2.77450e26 | −1.19788 | ||||||||
\(851\) | − | 6.99404e25i | − | 0.298787i | ||||||
\(852\) | −2.12106e25 | + | 7.95985e25i | −0.0896596 | + | 0.336472i | ||||
\(853\) | 4.59452e26 | 1.92176 | 0.960880 | − | 0.276964i | \(-0.0893282\pi\) | ||||
0.960880 | + | 0.276964i | \(0.0893282\pi\) | |||||||
\(854\) | − | 2.27926e26i | − | 0.943350i | ||||||
\(855\) | −1.80903e26 | + | 3.15341e26i | −0.740886 | + | 1.29148i | ||||
\(856\) | −3.91300e25 | −0.158579 | ||||||||
\(857\) | − | 4.61993e26i | − | 1.85271i | −0.376650 | − | 0.926356i | \(-0.622924\pi\) | ||
0.376650 | − | 0.926356i | \(-0.377076\pi\) | |||||||
\(858\) | −4.90911e25 | − | 1.30813e25i | −0.194813 | − | 0.0519118i | ||||
\(859\) | 3.25676e26 | 1.27893 | 0.639466 | − | 0.768819i | \(-0.279155\pi\) | ||||
0.639466 | + | 0.768819i | \(0.279155\pi\) | |||||||
\(860\) | − | 3.57382e25i | − | 0.138882i | ||||||
\(861\) | 6.50286e25 | − | 2.44037e26i | 0.250078 | − | 0.938485i | ||||
\(862\) | −2.65602e26 | −1.01080 | ||||||||
\(863\) | − | 1.89055e26i | − | 0.712017i | −0.934483 | − | 0.356009i | \(-0.884137\pi\) | ||
0.934483 | − | 0.356009i | \(-0.115863\pi\) | |||||||
\(864\) | −3.33985e25 | + | 3.36763e25i | −0.124481 | + | 0.125517i | ||||
\(865\) | −5.44884e26 | −2.00983 | ||||||||
\(866\) | − | 3.79753e26i | − | 1.38624i | ||||||
\(867\) | 1.58363e26 | + | 4.21990e25i | 0.572113 | + | 0.152451i | ||||
\(868\) | −1.39701e26 | −0.499486 | ||||||||
\(869\) | − | 1.05469e26i | − | 0.373206i | ||||||
\(870\) | −7.65736e25 | + | 2.87363e26i | −0.268167 | + | 1.00637i | ||||
\(871\) | 1.98501e26 | 0.688017 | ||||||||
\(872\) | − | 4.86077e25i | − | 0.166746i | ||||||
\(873\) | −5.73020e25 | − | 3.28727e25i | −0.194555 | − | 0.111611i | ||||
\(874\) | 2.74993e26 | 0.924101 | ||||||||
\(875\) | − | 1.92513e26i | − | 0.640308i | ||||||
\(876\) | −1.49811e26 | − | 3.99200e25i | −0.493180 | − | 0.131418i | ||||
\(877\) | 4.72794e26 | 1.54055 | 0.770275 | − | 0.637712i | \(-0.220119\pi\) | ||||
0.770275 | + | 0.637712i | \(0.220119\pi\) | |||||||
\(878\) | 1.44605e26i | 0.466371i | ||||||||
\(879\) | 5.03192e25 | − | 1.88836e26i | 0.160633 | − | 0.602817i | ||||
\(880\) | 3.00646e25 | 0.0949974 | ||||||||
\(881\) | 5.32633e26i | 1.66589i | 0.553359 | + | 0.832943i | \(0.313346\pi\) | ||||
−0.553359 | + | 0.832943i | \(0.686654\pi\) | |||||||
\(882\) | 5.58106e25 | − | 9.72861e25i | 0.172782 | − | 0.301185i | ||||
\(883\) | 4.09902e26 | 1.25613 | 0.628064 | − | 0.778162i | \(-0.283848\pi\) | ||||
0.628064 | + | 0.778162i | \(0.283848\pi\) | |||||||
\(884\) | − | 2.38852e26i | − | 0.724534i | ||||||
\(885\) | −9.26813e25 | − | 2.46968e25i | −0.278293 | − | 0.0741568i | ||||
\(886\) | −2.99902e25 | −0.0891408 | ||||||||
\(887\) | 3.32555e26i | 0.978477i | 0.872150 | + | 0.489238i | \(0.162725\pi\) | ||||
−0.872150 | + | 0.489238i | \(0.837275\pi\) | |||||||
\(888\) | 6.95132e24 | − | 2.60867e25i | 0.0202465 | − | 0.0759806i | ||||
\(889\) | −5.84223e26 | −1.68447 | ||||||||
\(890\) | 6.32180e26i | 1.80439i | ||||||||
\(891\) | −7.58505e25 | + | 4.43526e25i | −0.214318 | + | 0.125320i | ||||
\(892\) | −1.11623e26 | −0.312226 | ||||||||
\(893\) | − | 4.23720e26i | − | 1.17332i | ||||||
\(894\) | 1.78214e26 | + | 4.74887e25i | 0.488544 | + | 0.130182i | ||||
\(895\) | 3.06925e25 | 0.0832961 | ||||||||
\(896\) | − | 4.01711e25i | − | 0.107930i | ||||||
\(897\) | −1.49351e26 | + | 5.60481e26i | −0.397262 | + | 1.49083i | ||||
\(898\) | −5.85294e25 | −0.154130 | ||||||||
\(899\) | − | 3.01969e26i | − | 0.787274i | ||||||
\(900\) | 2.25591e26 | + | 1.29416e26i | 0.582289 | + | 0.334045i | ||||
\(901\) | −7.36853e26 | −1.88303 | ||||||||
\(902\) | − | 5.51878e25i | − | 0.139632i | ||||||
\(903\) | −8.54806e25 | − | 2.27780e25i | −0.214130 | − | 0.0570592i | ||||
\(904\) | 3.41691e25 | 0.0847456 | ||||||||
\(905\) | 8.14513e26i | 2.00014i | ||||||||
\(906\) | 7.79758e25 | − | 2.92625e26i | 0.189586 | − | 0.711472i | ||||
\(907\) | 4.44460e26 | 1.06996 | 0.534980 | − | 0.844865i | \(-0.320319\pi\) | ||||
0.534980 | + | 0.844865i | \(0.320319\pi\) | |||||||
\(908\) | − | 4.24275e25i | − | 0.101129i | ||||||
\(909\) | −3.00160e26 | + | 5.23224e26i | −0.708400 | + | 1.23485i | ||||
\(910\) | 6.49471e26 | 1.51771 | ||||||||
\(911\) | 2.91261e25i | 0.0673934i | 0.999432 | + | 0.0336967i | \(0.0107280\pi\) | ||||
−0.999432 | + | 0.0336967i | \(0.989272\pi\) | |||||||
\(912\) | 1.02568e26 | + | 2.73314e25i | 0.234996 | + | 0.0626193i | ||||
\(913\) | 4.97120e25 | 0.112778 | ||||||||
\(914\) | − | 2.09722e25i | − | 0.0471116i | ||||||
\(915\) | 1.93568e26 | − | 7.26415e26i | 0.430569 | − | 1.61583i | ||||
\(916\) | 1.97691e26 | 0.435440 | ||||||||
\(917\) | − | 4.35198e25i | − | 0.0949212i | ||||||
\(918\) | −2.93310e26 | − | 2.90891e26i | −0.633495 | − | 0.628269i | ||||
\(919\) | 8.66408e25 | 0.185303 | 0.0926516 | − | 0.995699i | \(-0.470466\pi\) | ||||
0.0926516 | + | 0.995699i | \(0.470466\pi\) | |||||||
\(920\) | − | 3.43252e26i | − | 0.726981i | ||||||
\(921\) | 1.28518e26 | + | 3.42463e25i | 0.269543 | + | 0.0718252i | ||||
\(922\) | −5.91344e25 | −0.122818 | ||||||||
\(923\) | 3.88863e26i | 0.799799i | ||||||||
\(924\) | 1.91619e25 | − | 7.19102e25i | 0.0390293 | − | 0.146468i | ||||
\(925\) | −1.48036e26 | −0.298601 | ||||||||
\(926\) | 4.65759e26i | 0.930383i | ||||||||
\(927\) | −1.12200e26 | − | 6.43663e25i | −0.221960 | − | 0.127333i | ||||
\(928\) | 8.68312e25 | 0.170116 | ||||||||
\(929\) | − | 3.57006e26i | − | 0.692683i | −0.938109 | − | 0.346341i | \(-0.887424\pi\) | ||
0.938109 | − | 0.346341i | \(-0.112576\pi\) | |||||||
\(930\) | −4.45238e26 | − | 1.18642e26i | −0.855550 | − | 0.227978i | ||||
\(931\) | −2.51010e26 | −0.477687 | ||||||||
\(932\) | 6.57429e25i | 0.123910i | ||||||||
\(933\) | 1.69095e26 | − | 6.34573e26i | 0.315642 | − | 1.18453i | ||||
\(934\) | 4.77325e26 | 0.882454 | ||||||||
\(935\) | 2.61853e26i | 0.479461i | ||||||||
\(936\) | −1.11412e26 | + | 1.94207e26i | −0.202045 | + | 0.352194i | ||||
\(937\) | 2.10500e26 | 0.378091 | 0.189045 | − | 0.981968i | \(-0.439461\pi\) | ||||
0.189045 | + | 0.981968i | \(0.439461\pi\) | |||||||
\(938\) | 2.90770e26i | 0.517278i | ||||||||
\(939\) | 2.75539e26 | + | 7.34228e25i | 0.485503 | + | 0.129372i | ||||
\(940\) | −5.28896e26 | −0.923037 | ||||||||
\(941\) | − | 3.39348e26i | − | 0.586595i | −0.956021 | − | 0.293298i | \(-0.905247\pi\) | ||
0.956021 | − | 0.293298i | \(-0.0947527\pi\) | |||||||
\(942\) | −1.14792e25 | + | 4.30788e25i | −0.0196541 | + | 0.0737574i | ||||
\(943\) | −6.30088e26 | −1.06855 | ||||||||
\(944\) | 2.80051e25i | 0.0470424i | ||||||||
\(945\) | 7.90972e26 | − | 7.97551e26i | 1.31606 | − | 1.32700i | ||||
\(946\) | −1.93310e25 | −0.0318592 | ||||||||
\(947\) | − | 1.07609e26i | − | 0.175671i | −0.996135 | − | 0.0878354i | \(-0.972005\pi\) | ||
0.996135 | − | 0.0878354i | \(-0.0279950\pi\) | |||||||
\(948\) | −4.49133e26 | − | 1.19681e26i | −0.726274 | − | 0.193530i | ||||
\(949\) | −7.31870e26 | −1.17230 | ||||||||
\(950\) | − | 5.82051e26i | − | 0.923525i | ||||||
\(951\) | 1.25227e26 | − | 4.69947e26i | 0.196822 | − | 0.738626i | ||||
\(952\) | 3.49877e26 | 0.544733 | ||||||||
\(953\) | − | 3.76958e26i | − | 0.581375i | −0.956818 | − | 0.290688i | \(-0.906116\pi\) | ||
0.956818 | − | 0.290688i | \(-0.0938840\pi\) | |||||||
\(954\) | 5.99124e26 | + | 3.43702e26i | 0.915338 | + | 0.525106i | ||||
\(955\) | −5.36052e26 | −0.811290 | ||||||||
\(956\) | − | 1.88686e26i | − | 0.282891i | ||||||
\(957\) | 1.55436e26 | + | 4.14191e25i | 0.230858 | + | 0.0615168i | ||||
\(958\) | −8.14552e26 | −1.19848 | ||||||||
\(959\) | 9.02388e26i | 1.31530i | ||||||||
\(960\) | 3.41156e25 | − | 1.28028e26i | 0.0492620 | − | 0.184869i | ||||
\(961\) | −2.31185e26 | −0.330711 | ||||||||
\(962\) | − | 1.27441e26i | − | 0.180607i | ||||||
\(963\) | −1.58969e26 | + | 2.77107e26i | −0.223191 | + | 0.389055i | ||||
\(964\) | 2.96956e26 | 0.413047 | ||||||||
\(965\) | 1.05884e27i | 1.45909i | ||||||||
\(966\) | −8.21010e26 | − | 2.18774e26i | −1.12087 | − | 0.298677i | ||||
\(967\) | 5.32227e26 | 0.719878 | 0.359939 | − | 0.932976i | \(-0.382798\pi\) | ||||
0.359939 | + | 0.932976i | \(0.382798\pi\) | |||||||
\(968\) | 2.47573e26i | 0.331761i | ||||||||
\(969\) | −2.38048e26 | + | 8.93338e26i | −0.316046 | + | 1.18605i | ||||
\(970\) | 1.84544e26 | 0.242748 | ||||||||
\(971\) | 1.07664e26i | 0.140312i | 0.997536 | + | 0.0701562i | \(0.0223498\pi\) | ||||
−0.997536 | + | 0.0701562i | \(0.977650\pi\) | |||||||
\(972\) | 1.02801e26 | + | 3.73332e26i | 0.132740 | + | 0.482058i | ||||
\(973\) | 1.79841e27 | 2.30078 | ||||||||
\(974\) | − | 1.24359e26i | − | 0.157633i | ||||||
\(975\) | 1.18632e27 | + | 3.16117e26i | 1.48990 | + | 0.397015i | ||||
\(976\) | −2.19498e26 | −0.273138 | ||||||||
\(977\) | − | 8.28828e26i | − | 1.02191i | −0.859607 | − | 0.510956i | \(-0.829292\pi\) | ||
0.859607 | − | 0.510956i | \(-0.170708\pi\) | |||||||
\(978\) | −1.16985e26 | + | 4.39019e26i | −0.142916 | + | 0.536332i | ||||
\(979\) | 3.41950e26 | 0.413922 | ||||||||
\(980\) | 3.13315e26i | 0.375792i | ||||||||
\(981\) | −3.44226e26 | − | 1.97473e26i | −0.409093 | − | 0.234686i | ||||
\(982\) | 2.69480e26 | 0.317339 | ||||||||
\(983\) | − | 7.43114e26i | − | 0.867110i | −0.901127 | − | 0.433555i | \(-0.857259\pi\) | ||
0.901127 | − | 0.433555i | \(-0.142741\pi\) | |||||||
\(984\) | −2.35013e26 | − | 6.26239e25i | −0.271729 | − | 0.0724077i | ||||
\(985\) | 1.31720e27 | 1.50912 | ||||||||
\(986\) | 7.56272e26i | 0.858590i | ||||||||
\(987\) | −3.37095e26 | + | 1.26504e27i | −0.379226 | + | 1.42315i | ||||
\(988\) | 5.01077e26 | 0.558589 | ||||||||
\(989\) | 2.20705e26i | 0.243807i | ||||||||
\(990\) | 1.22140e26 | − | 2.12909e26i | 0.133704 | − | 0.233065i | ||||
\(991\) | −1.22159e27 | −1.32514 | −0.662569 | − | 0.749000i | \(-0.730534\pi\) | ||||
−0.662569 | + | 0.749000i | \(0.730534\pi\) | |||||||
\(992\) | 1.34535e26i | 0.144621i | ||||||||
\(993\) | −1.43023e27 | − | 3.81113e26i | −1.52357 | − | 0.405985i | ||||
\(994\) | −5.69618e26 | −0.601321 | ||||||||
\(995\) | − | 8.57623e26i | − | 0.897199i | ||||||
\(996\) | 5.64103e25 | − | 2.11695e26i | 0.0584823 | − | 0.219470i | ||||
\(997\) | −9.45525e26 | −0.971442 | −0.485721 | − | 0.874114i | \(-0.661443\pi\) | ||||
−0.485721 | + | 0.874114i | \(0.661443\pi\) | |||||||
\(998\) | − | 4.29788e26i | − | 0.437602i | ||||||
\(999\) | −1.56498e26 | − | 1.55207e26i | −0.157914 | − | 0.156611i |
(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 | 6.19.b.a.5.1 | ✓ | 6 | |
3.2 | odd | 2 | inner | 6.19.b.a.5.4 | yes | 6 | |
4.3 | odd | 2 | 48.19.e.d.17.6 | 6 | |||
12.11 | even | 2 | 48.19.e.d.17.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.19.b.a.5.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
6.19.b.a.5.4 | yes | 6 | 3.2 | odd | 2 | inner | |
48.19.e.d.17.5 | 6 | 12.11 | even | 2 | |||
48.19.e.d.17.6 | 6 | 4.3 | odd | 2 |