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 | 5.5 | ||
Root | \(85.4804 - 88.2031i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.5 |
Dual form | 6.19.b.a.5.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
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 | ||||||||
\(3\) | −3612.02 | + | 19348.7i | −0.183510 | + | 0.983018i | ||||
\(4\) | −131072. | −0.500000 | ||||||||
\(5\) | − | 3.69488e6i | − | 1.89178i | −0.324492 | − | 0.945889i | \(-0.605193\pi\) | ||
0.324492 | − | 0.945889i | \(-0.394807\pi\) | |||||||
\(6\) | −7.00499e6 | − | 1.30769e6i | −0.695099 | − | 0.129761i | ||||
\(7\) | 3.18077e7 | 0.788224 | 0.394112 | − | 0.919062i | \(-0.371052\pi\) | ||||
0.394112 | + | 0.919062i | \(0.371052\pi\) | |||||||
\(8\) | − | 4.74531e7i | − | 0.353553i | ||||||
\(9\) | −3.61327e8 | − | 1.39776e8i | −0.932648 | − | 0.360787i | ||||
\(10\) | 1.33769e9 | 1.33769 | ||||||||
\(11\) | 7.02311e8i | 0.297848i | 0.988849 | + | 0.148924i | \(0.0475810\pi\) | ||||
−0.988849 | + | 0.148924i | \(0.952419\pi\) | |||||||
\(12\) | 4.73435e8 | − | 2.53608e9i | 0.0917549 | − | 0.491509i | ||||
\(13\) | 8.10908e9 | 0.764683 | 0.382342 | − | 0.924021i | \(-0.375118\pi\) | ||||
0.382342 | + | 0.924021i | \(0.375118\pi\) | |||||||
\(14\) | 1.15156e10i | 0.557359i | ||||||||
\(15\) | 7.14912e10 | + | 1.33460e10i | 1.85965 | + | 0.347160i | ||||
\(16\) | 1.71799e10 | 0.250000 | ||||||||
\(17\) | − | 1.82909e11i | − | 1.54239i | −0.636596 | − | 0.771197i | \(-0.719658\pi\) | ||
0.636596 | − | 0.771197i | \(-0.280342\pi\) | |||||||
\(18\) | 5.06044e10 | − | 1.30814e11i | 0.255115 | − | 0.659482i | ||||
\(19\) | 2.50983e11 | 0.777789 | 0.388894 | − | 0.921282i | \(-0.372857\pi\) | ||||
0.388894 | + | 0.921282i | \(0.372857\pi\) | |||||||
\(20\) | 4.84295e11i | 0.945889i | ||||||||
\(21\) | −1.14890e11 | + | 6.15439e11i | −0.144647 | + | 0.774838i | ||||
\(22\) | −2.54264e11 | −0.210611 | ||||||||
\(23\) | − | 9.32089e11i | − | 0.517496i | −0.965945 | − | 0.258748i | \(-0.916690\pi\) | ||
0.965945 | − | 0.258748i | \(-0.0833099\pi\) | |||||||
\(24\) | 9.18158e11 | + | 1.71402e11i | 0.347549 | + | 0.0648805i | ||||
\(25\) | −9.83742e12 | −2.57882 | ||||||||
\(26\) | 2.93580e12i | 0.540713i | ||||||||
\(27\) | 4.00962e12 | − | 6.48635e12i | 0.525810 | − | 0.850602i | ||||
\(28\) | −4.16910e12 | −0.394112 | ||||||||
\(29\) | − | 8.17010e12i | − | 0.563178i | −0.959535 | − | 0.281589i | \(-0.909139\pi\) | ||
0.959535 | − | 0.281589i | \(-0.0908614\pi\) | |||||||
\(30\) | −4.83176e12 | + | 2.58826e13i | −0.245479 | + | 1.31497i | ||||
\(31\) | 2.87019e13 | 1.08557 | 0.542783 | − | 0.839873i | \(-0.317371\pi\) | ||||
0.542783 | + | 0.839873i | \(0.317371\pi\) | |||||||
\(32\) | 6.21978e12i | 0.176777i | ||||||||
\(33\) | −1.35888e13 | − | 2.53676e12i | −0.292790 | − | 0.0546581i | ||||
\(34\) | 6.62202e13 | 1.09064 | ||||||||
\(35\) | − | 1.17525e14i | − | 1.49114i | ||||||
\(36\) | 4.73599e13 | + | 1.83207e13i | 0.466324 | + | 0.180393i | ||||
\(37\) | 3.99953e13 | 0.307747 | 0.153874 | − | 0.988091i | \(-0.450825\pi\) | ||||
0.153874 | + | 0.988091i | \(0.450825\pi\) | |||||||
\(38\) | 9.08655e13i | 0.549980i | ||||||||
\(39\) | −2.92902e13 | + | 1.56900e14i | −0.140327 | + | 0.751697i | ||||
\(40\) | −1.75333e14 | −0.668844 | ||||||||
\(41\) | − | 3.68995e14i | − | 1.12711i | −0.826079 | − | 0.563554i | \(-0.809434\pi\) | ||
0.826079 | − | 0.563554i | \(-0.190566\pi\) | |||||||
\(42\) | −2.22813e14 | − | 4.15947e13i | −0.547893 | − | 0.102281i | ||||
\(43\) | −2.11773e14 | −0.421361 | −0.210680 | − | 0.977555i | \(-0.567568\pi\) | ||||
−0.210680 | + | 0.977555i | \(0.567568\pi\) | |||||||
\(44\) | − | 9.20533e13i | − | 0.148924i | ||||||
\(45\) | −5.16456e14 | + | 1.33506e15i | −0.682528 | + | 1.76436i | ||||
\(46\) | 3.37452e14 | 0.365925 | ||||||||
\(47\) | − | 2.53857e14i | − | 0.226834i | −0.993547 | − | 0.113417i | \(-0.963820\pi\) | ||
0.993547 | − | 0.113417i | \(-0.0361796\pi\) | |||||||
\(48\) | −6.20541e13 | + | 3.32409e14i | −0.0458774 | + | 0.245754i | ||||
\(49\) | −6.16685e14 | −0.378703 | ||||||||
\(50\) | − | 3.56153e15i | − | 1.82350i | ||||||
\(51\) | 3.53906e15 | + | 6.60673e14i | 1.51620 | + | 0.283044i | ||||
\(52\) | −1.06287e15 | −0.382342 | ||||||||
\(53\) | − | 2.48752e14i | − | 0.0753848i | −0.999289 | − | 0.0376924i | \(-0.987999\pi\) | ||
0.999289 | − | 0.0376924i | \(-0.0120007\pi\) | |||||||
\(54\) | 2.34831e15 | + | 1.45164e15i | 0.601466 | + | 0.371804i | ||||
\(55\) | 2.59495e15 | 0.563463 | ||||||||
\(56\) | − | 1.50937e15i | − | 0.278679i | ||||||
\(57\) | −9.06556e14 | + | 4.85620e15i | −0.142732 | + | 0.764580i | ||||
\(58\) | 2.95789e15 | 0.398227 | ||||||||
\(59\) | 1.21495e14i | 0.0140246i | 0.999975 | + | 0.00701231i | \(0.00223211\pi\) | ||||
−0.999975 | + | 0.00701231i | \(0.997768\pi\) | |||||||
\(60\) | −9.37050e15 | − | 1.74928e15i | −0.929825 | − | 0.173580i | ||||
\(61\) | 7.62514e14 | 0.0652047 | 0.0326024 | − | 0.999468i | \(-0.489621\pi\) | ||||
0.0326024 | + | 0.999468i | \(0.489621\pi\) | |||||||
\(62\) | 1.03912e16i | 0.767611i | ||||||||
\(63\) | −1.14930e16 | − | 4.44596e15i | −0.735136 | − | 0.284381i | ||||
\(64\) | −2.25180e15 | −0.125000 | ||||||||
\(65\) | − | 2.99621e16i | − | 1.44661i | ||||||
\(66\) | 9.18406e14 | − | 4.91968e15i | 0.0386491 | − | 0.207034i | ||||
\(67\) | −4.78338e16 | −1.75817 | −0.879086 | − | 0.476663i | \(-0.841846\pi\) | ||||
−0.879086 | + | 0.476663i | \(0.841846\pi\) | |||||||
\(68\) | 2.39743e16i | 0.771197i | ||||||||
\(69\) | 1.80347e16 | + | 3.36673e15i | 0.508707 | + | 0.0949655i | ||||
\(70\) | 4.25488e16 | 1.05440 | ||||||||
\(71\) | 6.41967e16i | 1.40019i | 0.714048 | + | 0.700096i | \(0.246860\pi\) | ||||
−0.714048 | + | 0.700096i | \(0.753140\pi\) | |||||||
\(72\) | −6.63282e15 | + | 1.71461e16i | −0.127557 | + | 0.329741i | ||||
\(73\) | 7.57613e16 | 1.28689 | 0.643446 | − | 0.765492i | \(-0.277504\pi\) | ||||
0.643446 | + | 0.765492i | \(0.277504\pi\) | |||||||
\(74\) | 1.44799e16i | 0.217610i | ||||||||
\(75\) | 3.55330e16 | − | 1.90342e17i | 0.473239 | − | 2.53503i | ||||
\(76\) | −3.28968e16 | −0.388894 | ||||||||
\(77\) | 2.23389e16i | 0.234771i | ||||||||
\(78\) | −5.68040e16 | − | 1.06042e16i | −0.531530 | − | 0.0992260i | ||||
\(79\) | 1.35483e16 | 0.113042 | 0.0565209 | − | 0.998401i | \(-0.481999\pi\) | ||||
0.0565209 | + | 0.998401i | \(0.481999\pi\) | |||||||
\(80\) | − | 6.34775e16i | − | 0.472944i | ||||||
\(81\) | 1.11020e17 | + | 1.01010e17i | 0.739666 | + | 0.672974i | ||||
\(82\) | 1.33590e17 | 0.796986 | ||||||||
\(83\) | 2.11746e17i | 1.13269i | 0.824168 | + | 0.566346i | \(0.191643\pi\) | ||||
−0.824168 | + | 0.566346i | \(0.808357\pi\) | |||||||
\(84\) | 1.50589e16 | − | 8.06668e16i | 0.0723234 | − | 0.387419i | ||||
\(85\) | −6.75827e17 | −2.91787 | ||||||||
\(86\) | − | 7.66699e16i | − | 0.297947i | ||||||
\(87\) | 1.58081e17 | + | 2.95106e16i | 0.553614 | + | 0.103349i | ||||
\(88\) | 3.33268e16 | 0.105305 | ||||||||
\(89\) | 1.30497e17i | 0.372470i | 0.982505 | + | 0.186235i | \(0.0596285\pi\) | ||||
−0.982505 | + | 0.186235i | \(0.940371\pi\) | |||||||
\(90\) | −4.83343e17 | − | 1.86977e17i | −1.24759 | − | 0.482620i | ||||
\(91\) | 2.57931e17 | 0.602742 | ||||||||
\(92\) | 1.22171e17i | 0.258748i | ||||||||
\(93\) | −1.03672e17 | + | 5.55346e17i | −0.199212 | + | 1.06713i | ||||
\(94\) | 9.19059e16 | 0.160396 | ||||||||
\(95\) | − | 9.27351e17i | − | 1.47140i | ||||||
\(96\) | −1.20345e17 | − | 2.24660e16i | −0.173775 | − | 0.0324403i | ||||
\(97\) | 9.26791e17 | 1.21909 | 0.609545 | − | 0.792751i | \(-0.291352\pi\) | ||||
0.609545 | + | 0.792751i | \(0.291352\pi\) | |||||||
\(98\) | − | 2.23264e17i | − | 0.267783i | ||||||
\(99\) | 9.81663e16 | − | 2.53764e17i | 0.107460 | − | 0.277788i | ||||
\(100\) | 1.28941e18 | 1.28941 | ||||||||
\(101\) | 4.46291e16i | 0.0408062i | 0.999792 | + | 0.0204031i | \(0.00649495\pi\) | ||||
−0.999792 | + | 0.0204031i | \(0.993505\pi\) | |||||||
\(102\) | −2.39189e17 | + | 1.28128e18i | −0.200143 | + | 1.07212i | ||||
\(103\) | −1.64674e18 | −1.26209 | −0.631043 | − | 0.775747i | \(-0.717373\pi\) | ||||
−0.631043 | + | 0.775747i | \(0.717373\pi\) | |||||||
\(104\) | − | 3.84801e17i | − | 0.270356i | ||||||
\(105\) | 2.27397e18 | + | 4.24505e17i | 1.46582 | + | 0.273640i | ||||
\(106\) | 9.00579e16 | 0.0533051 | ||||||||
\(107\) | − | 2.30785e18i | − | 1.25532i | −0.778488 | − | 0.627660i | \(-0.784013\pi\) | ||
0.778488 | − | 0.627660i | \(-0.215987\pi\) | |||||||
\(108\) | −5.25548e17 | + | 8.50179e17i | −0.262905 | + | 0.425301i | ||||
\(109\) | −1.97197e18 | −0.907951 | −0.453975 | − | 0.891014i | \(-0.649995\pi\) | ||||
−0.453975 | + | 0.891014i | \(0.649995\pi\) | |||||||
\(110\) | 9.39473e17i | 0.398428i | ||||||||
\(111\) | −1.44464e17 | + | 7.73860e17i | −0.0564746 | + | 0.302521i | ||||
\(112\) | 5.46452e17 | 0.197056 | ||||||||
\(113\) | 1.28812e18i | 0.428794i | 0.976747 | + | 0.214397i | \(0.0687787\pi\) | ||||
−0.976747 | + | 0.214397i | \(0.931221\pi\) | |||||||
\(114\) | −1.75813e18 | − | 3.28208e17i | −0.540640 | − | 0.100927i | ||||
\(115\) | −3.44395e18 | −0.978986 | ||||||||
\(116\) | 1.07087e18i | 0.281589i | ||||||||
\(117\) | −2.93003e18 | − | 1.13346e18i | −0.713180 | − | 0.275888i | ||||
\(118\) | −4.39860e16 | −0.00991691 | ||||||||
\(119\) | − | 5.81792e18i | − | 1.21575i | ||||||
\(120\) | 6.33309e17 | − | 3.39248e18i | 0.122739 | − | 0.657486i | ||||
\(121\) | 5.06668e18 | 0.911286 | ||||||||
\(122\) | 2.76059e17i | 0.0461067i | ||||||||
\(123\) | 7.13958e18 | + | 1.33282e18i | 1.10797 | + | 0.206835i | ||||
\(124\) | −3.76202e18 | −0.542783 | ||||||||
\(125\) | 2.22532e19i | 2.98678i | ||||||||
\(126\) | 1.60961e18 | − | 4.16090e18i | 0.201088 | − | 0.519820i | ||||
\(127\) | 2.56743e18 | 0.298721 | 0.149360 | − | 0.988783i | \(-0.452279\pi\) | ||||
0.149360 | + | 0.988783i | \(0.452279\pi\) | |||||||
\(128\) | − | 8.15239e17i | − | 0.0883883i | ||||||
\(129\) | 7.64928e17 | − | 4.09754e18i | 0.0773238 | − | 0.414205i | ||||
\(130\) | 1.08474e19 | 1.02291 | ||||||||
\(131\) | − | 9.70264e18i | − | 0.853981i | −0.904256 | − | 0.426990i | \(-0.859574\pi\) | ||
0.904256 | − | 0.426990i | \(-0.140426\pi\) | |||||||
\(132\) | 1.78112e18 | + | 3.32499e17i | 0.146395 | + | 0.0273290i | ||||
\(133\) | 7.98318e18 | 0.613072 | ||||||||
\(134\) | − | 1.73177e19i | − | 1.24322i | ||||||
\(135\) | −2.39663e19 | − | 1.48150e19i | −1.60915 | − | 0.994715i | ||||
\(136\) | −8.67962e18 | −0.545319 | ||||||||
\(137\) | 2.13367e19i | 1.25500i | 0.778618 | + | 0.627498i | \(0.215921\pi\) | ||||
−0.778618 | + | 0.627498i | \(0.784079\pi\) | |||||||
\(138\) | −1.21888e18 | + | 6.52927e18i | −0.0671508 | + | 0.359710i | ||||
\(139\) | 1.11915e19 | 0.577770 | 0.288885 | − | 0.957364i | \(-0.406716\pi\) | ||||
0.288885 | + | 0.957364i | \(0.406716\pi\) | |||||||
\(140\) | 1.54043e19i | 0.745572i | ||||||||
\(141\) | 4.91181e18 | + | 9.16936e17i | 0.222982 | + | 0.0416262i | ||||
\(142\) | −2.32417e19 | −0.990086 | ||||||||
\(143\) | 5.69509e18i | 0.227760i | ||||||||
\(144\) | −6.20755e18 | − | 2.40134e18i | −0.233162 | − | 0.0901967i | ||||
\(145\) | −3.01875e19 | −1.06541 | ||||||||
\(146\) | 2.74285e19i | 0.909969i | ||||||||
\(147\) | 2.22748e18 | − | 1.19321e19i | 0.0694957 | − | 0.372272i | ||||
\(148\) | −5.24227e18 | −0.153874 | ||||||||
\(149\) | − | 3.51402e19i | − | 0.970796i | −0.874293 | − | 0.485398i | \(-0.838675\pi\) | ||
0.874293 | − | 0.485398i | \(-0.161325\pi\) | |||||||
\(150\) | 6.89111e19 | + | 1.28643e19i | 1.79253 | + | 0.334630i | ||||
\(151\) | −1.32025e19 | −0.323491 | −0.161746 | − | 0.986832i | \(-0.551712\pi\) | ||||
−0.161746 | + | 0.986832i | \(0.551712\pi\) | |||||||
\(152\) | − | 1.19099e19i | − | 0.274990i | ||||||
\(153\) | −2.55664e19 | + | 6.60901e19i | −0.556476 | + | 1.43851i | ||||
\(154\) | −8.08754e18 | −0.166008 | ||||||||
\(155\) | − | 1.06050e20i | − | 2.05365i | ||||||
\(156\) | 3.83912e18 | − | 2.05653e19i | 0.0701634 | − | 0.375849i | ||||
\(157\) | 6.77852e19 | 1.16960 | 0.584801 | − | 0.811177i | \(-0.301173\pi\) | ||||
0.584801 | + | 0.811177i | \(0.301173\pi\) | |||||||
\(158\) | 4.90499e18i | 0.0799327i | ||||||||
\(159\) | 4.81304e18 | + | 8.98498e17i | 0.0741046 | + | 0.0138338i | ||||
\(160\) | 2.29813e19 | 0.334422 | ||||||||
\(161\) | − | 2.96476e19i | − | 0.407902i | ||||||
\(162\) | −3.65695e19 | + | 4.01935e19i | −0.475865 | + | 0.523023i | ||||
\(163\) | 1.40045e20 | 1.72416 | 0.862081 | − | 0.506770i | \(-0.169161\pi\) | ||||
0.862081 | + | 0.506770i | \(0.169161\pi\) | |||||||
\(164\) | 4.83649e19i | 0.563554i | ||||||||
\(165\) | −9.37303e18 | + | 5.02091e19i | −0.103401 | + | 0.553894i | ||||
\(166\) | −7.66601e19 | −0.800934 | ||||||||
\(167\) | 1.49329e20i | 1.47808i | 0.673664 | + | 0.739038i | \(0.264720\pi\) | ||||
−0.673664 | + | 0.739038i | \(0.735280\pi\) | |||||||
\(168\) | 2.92045e19 | + | 5.45189e18i | 0.273947 | + | 0.0511404i | ||||
\(169\) | −4.66982e19 | −0.415260 | ||||||||
\(170\) | − | 2.44676e20i | − | 2.06324i | ||||||
\(171\) | −9.06869e19 | − | 3.50814e19i | −0.725403 | − | 0.280616i | ||||
\(172\) | 2.77575e19 | 0.210680 | ||||||||
\(173\) | − | 6.62161e19i | − | 0.477033i | −0.971138 | − | 0.238517i | \(-0.923339\pi\) | ||
0.971138 | − | 0.238517i | \(-0.0766611\pi\) | |||||||
\(174\) | −1.06840e19 | + | 5.72315e19i | −0.0730785 | + | 0.391464i | ||||
\(175\) | −3.12906e20 | −2.03269 | ||||||||
\(176\) | 1.20656e19i | 0.0744621i | ||||||||
\(177\) | −2.35078e18 | − | 4.38844e17i | −0.0137865 | − | 0.00257366i | ||||
\(178\) | −4.72450e19 | −0.263376 | ||||||||
\(179\) | 3.08840e20i | 1.63703i | 0.574485 | + | 0.818515i | \(0.305202\pi\) | ||||
−0.574485 | + | 0.818515i | \(0.694798\pi\) | |||||||
\(180\) | 6.76929e19 | − | 1.74989e20i | 0.341264 | − | 0.882181i | ||||
\(181\) | 2.66841e20 | 1.27981 | 0.639904 | − | 0.768455i | \(-0.278974\pi\) | ||||
0.639904 | + | 0.768455i | \(0.278974\pi\) | |||||||
\(182\) | 9.33810e19i | 0.426203i | ||||||||
\(183\) | −2.75422e18 | + | 1.47537e19i | −0.0119657 | + | 0.0640974i | ||||
\(184\) | −4.42305e19 | −0.182962 | ||||||||
\(185\) | − | 1.47778e20i | − | 0.582189i | ||||||
\(186\) | −2.01057e20 | − | 3.75333e19i | −0.754575 | − | 0.140864i | ||||
\(187\) | 1.28459e20 | 0.459400 | ||||||||
\(188\) | 3.32735e19i | 0.113417i | ||||||||
\(189\) | 1.27537e20 | − | 2.06316e20i | 0.414456 | − | 0.670465i | ||||
\(190\) | 3.35737e20 | 1.04044 | ||||||||
\(191\) | − | 7.13917e19i | − | 0.211032i | −0.994418 | − | 0.105516i | \(-0.966351\pi\) | ||
0.994418 | − | 0.105516i | \(-0.0336494\pi\) | |||||||
\(192\) | 8.13355e18 | − | 4.35695e19i | 0.0229387 | − | 0.122877i | ||||
\(193\) | −3.84509e20 | −1.03488 | −0.517441 | − | 0.855719i | \(-0.673115\pi\) | ||||
−0.517441 | + | 0.855719i | \(0.673115\pi\) | |||||||
\(194\) | 3.35534e20i | 0.862027i | ||||||||
\(195\) | 5.79728e20 | + | 1.08224e20i | 1.42204 | + | 0.265467i | ||||
\(196\) | 8.08301e19 | 0.189351 | ||||||||
\(197\) | 1.85603e20i | 0.415325i | 0.978201 | + | 0.207663i | \(0.0665856\pi\) | ||||
−0.978201 | + | 0.207663i | \(0.933414\pi\) | |||||||
\(198\) | 9.18723e19 | + | 3.55400e19i | 0.196426 | + | 0.0759855i | ||||
\(199\) | 2.31039e20 | 0.472071 | 0.236035 | − | 0.971744i | \(-0.424152\pi\) | ||||
0.236035 | + | 0.971744i | \(0.424152\pi\) | |||||||
\(200\) | 4.66816e20i | 0.911751i | ||||||||
\(201\) | 1.72777e20 | − | 9.25523e20i | 0.322642 | − | 1.72831i | ||||
\(202\) | −1.61575e19 | −0.0288543 | ||||||||
\(203\) | − | 2.59872e20i | − | 0.443910i | ||||||
\(204\) | −4.63872e20 | − | 8.65957e19i | −0.758101 | − | 0.141522i | ||||
\(205\) | −1.36339e21 | −2.13224 | ||||||||
\(206\) | − | 5.96183e20i | − | 0.892430i | ||||||
\(207\) | −1.30284e20 | + | 3.36789e20i | −0.186706 | + | 0.482641i | ||||
\(208\) | 1.39313e20 | 0.191171 | ||||||||
\(209\) | 1.76268e20i | 0.231663i | ||||||||
\(210\) | −1.53687e20 | + | 8.23265e20i | −0.193492 | + | 1.03649i | ||||
\(211\) | 2.14795e20 | 0.259108 | 0.129554 | − | 0.991572i | \(-0.458645\pi\) | ||||
0.129554 | + | 0.991572i | \(0.458645\pi\) | |||||||
\(212\) | 3.26044e19i | 0.0376924i | ||||||||
\(213\) | −1.24213e21 | − | 2.31880e20i | −1.37641 | − | 0.256949i | ||||
\(214\) | 8.35533e20 | 0.887645 | ||||||||
\(215\) | 7.82474e20i | 0.797120i | ||||||||
\(216\) | −3.07798e20 | − | 1.90269e20i | −0.300733 | − | 0.185902i | ||||
\(217\) | 9.12942e20 | 0.855669 | ||||||||
\(218\) | − | 7.13930e20i | − | 0.642018i | ||||||
\(219\) | −2.73652e20 | + | 1.46589e21i | −0.236157 | + | 1.26504i | ||||
\(220\) | −3.40126e20 | −0.281731 | ||||||||
\(221\) | − | 1.48323e21i | − | 1.17944i | ||||||
\(222\) | −2.80167e20 | − | 5.23016e19i | −0.213915 | − | 0.0399336i | ||||
\(223\) | −3.18670e20 | −0.233667 | −0.116833 | − | 0.993152i | \(-0.537274\pi\) | ||||
−0.116833 | + | 0.993152i | \(0.537274\pi\) | |||||||
\(224\) | 1.97837e20i | 0.139340i | ||||||||
\(225\) | 3.55453e21 | + | 1.37504e21i | 2.40513 | + | 0.930404i | ||||
\(226\) | −4.66348e20 | −0.303203 | ||||||||
\(227\) | − | 6.91420e20i | − | 0.432025i | −0.976391 | − | 0.216013i | \(-0.930695\pi\) | ||
0.976391 | − | 0.216013i | \(-0.0693052\pi\) | |||||||
\(228\) | 1.18824e20 | − | 6.36512e20i | 0.0713659 | − | 0.382290i | ||||
\(229\) | 9.82621e20 | 0.567371 | 0.283685 | − | 0.958917i | \(-0.408443\pi\) | ||||
0.283685 | + | 0.958917i | \(0.408443\pi\) | |||||||
\(230\) | − | 1.24684e21i | − | 0.692248i | ||||||
\(231\) | −4.32229e20 | − | 8.06885e19i | −0.230784 | − | 0.0430828i | ||||
\(232\) | −3.87697e20 | −0.199113 | ||||||||
\(233\) | − | 1.17159e21i | − | 0.578856i | −0.957200 | − | 0.289428i | \(-0.906535\pi\) | ||
0.957200 | − | 0.289428i | \(-0.0934651\pi\) | |||||||
\(234\) | 4.10355e20 | − | 1.06078e21i | 0.195082 | − | 0.504295i | ||||
\(235\) | −9.37969e20 | −0.429119 | ||||||||
\(236\) | − | 1.59246e19i | − | 0.00701231i | ||||||
\(237\) | −4.89366e19 | + | 2.62142e20i | −0.0207443 | + | 0.111122i | ||||
\(238\) | 2.10631e21 | 0.859667 | ||||||||
\(239\) | 1.92312e21i | 0.755832i | 0.925840 | + | 0.377916i | \(0.123359\pi\) | ||||
−0.925840 | + | 0.377916i | \(0.876641\pi\) | |||||||
\(240\) | 1.22821e21 | + | 2.29282e20i | 0.464913 | + | 0.0867899i | ||||
\(241\) | −1.72968e21 | −0.630685 | −0.315342 | − | 0.948978i | \(-0.602119\pi\) | ||||
−0.315342 | + | 0.948978i | \(0.602119\pi\) | |||||||
\(242\) | 1.83433e21i | 0.644377i | ||||||||
\(243\) | −2.35542e21 | + | 1.78324e21i | −0.797282 | + | 0.603607i | ||||
\(244\) | −9.99442e19 | −0.0326024 | ||||||||
\(245\) | 2.27858e21i | 0.716421i | ||||||||
\(246\) | −4.82531e20 | + | 2.58481e21i | −0.146255 | + | 0.783451i | ||||
\(247\) | 2.03524e21 | 0.594762 | ||||||||
\(248\) | − | 1.36200e21i | − | 0.383805i | ||||||
\(249\) | −4.09701e21 | − | 7.64830e20i | −1.11346 | − | 0.207860i | ||||
\(250\) | −8.05653e21 | −2.11197 | ||||||||
\(251\) | − | 4.72980e21i | − | 1.19613i | −0.801447 | − | 0.598066i | \(-0.795936\pi\) | ||
0.801447 | − | 0.598066i | \(-0.204064\pi\) | |||||||
\(252\) | 1.50641e21 | + | 5.82740e20i | 0.367568 | + | 0.142190i | ||||
\(253\) | 6.54616e20 | 0.154135 | ||||||||
\(254\) | 9.29510e20i | 0.211228i | ||||||||
\(255\) | 2.44110e21 | − | 1.30764e22i | 0.535457 | − | 2.86831i | ||||
\(256\) | 2.95148e20 | 0.0625000 | ||||||||
\(257\) | 1.96395e21i | 0.401543i | 0.979638 | + | 0.200771i | \(0.0643449\pi\) | ||||
−0.979638 | + | 0.200771i | \(0.935655\pi\) | |||||||
\(258\) | 1.48347e21 | + | 2.76934e20i | 0.292887 | + | 0.0546762i | ||||
\(259\) | 1.27216e21 | 0.242574 | ||||||||
\(260\) | 3.92719e21i | 0.723305i | ||||||||
\(261\) | −1.14199e21 | + | 2.95208e21i | −0.203187 | + | 0.525247i | ||||
\(262\) | 3.51273e21 | 0.603856 | ||||||||
\(263\) | 7.44618e21i | 1.23689i | 0.785827 | + | 0.618446i | \(0.212238\pi\) | ||||
−0.785827 | + | 0.618446i | \(0.787762\pi\) | |||||||
\(264\) | −1.20377e20 | + | 6.44833e20i | −0.0193246 | + | 0.103517i | ||||
\(265\) | −9.19108e20 | −0.142611 | ||||||||
\(266\) | 2.89022e21i | 0.433507i | ||||||||
\(267\) | −2.52495e21 | − | 4.71358e20i | −0.366144 | − | 0.0683518i | ||||
\(268\) | 6.26967e21 | 0.879086 | ||||||||
\(269\) | − | 1.76444e21i | − | 0.239241i | −0.992820 | − | 0.119621i | \(-0.961832\pi\) | ||
0.992820 | − | 0.119621i | \(-0.0381678\pi\) | |||||||
\(270\) | 5.36362e21 | − | 8.67671e21i | 0.703370 | − | 1.13784i | ||||
\(271\) | 1.35817e22 | 1.72279 | 0.861394 | − | 0.507937i | \(-0.169592\pi\) | ||||
0.861394 | + | 0.507937i | \(0.169592\pi\) | |||||||
\(272\) | − | 3.14236e21i | − | 0.385599i | ||||||
\(273\) | −9.31653e20 | + | 4.99064e21i | −0.110609 | + | 0.592506i | ||||
\(274\) | −7.72472e21 | −0.887417 | ||||||||
\(275\) | − | 6.90893e21i | − | 0.768097i | ||||||
\(276\) | −2.36385e21 | − | 4.41283e20i | −0.254354 | − | 0.0474828i | ||||
\(277\) | 9.98253e21 | 1.03973 | 0.519867 | − | 0.854247i | \(-0.325981\pi\) | ||||
0.519867 | + | 0.854247i | \(0.325981\pi\) | |||||||
\(278\) | 4.05175e21i | 0.408545i | ||||||||
\(279\) | −1.03708e22 | − | 4.01185e21i | −1.01245 | − | 0.391658i | ||||
\(280\) | −5.57695e21 | −0.527199 | ||||||||
\(281\) | 1.38066e22i | 1.26395i | 0.774988 | + | 0.631976i | \(0.217756\pi\) | ||||
−0.774988 | + | 0.631976i | \(0.782244\pi\) | |||||||
\(282\) | −3.31966e20 | + | 1.77826e21i | −0.0294342 | + | 0.157672i | ||||
\(283\) | −1.74078e22 | −1.49509 | −0.747543 | − | 0.664213i | \(-0.768767\pi\) | ||||
−0.747543 | + | 0.664213i | \(0.768767\pi\) | |||||||
\(284\) | − | 8.41439e21i | − | 0.700096i | ||||||
\(285\) | 1.79431e22 | + | 3.34961e21i | 1.44642 | + | 0.270017i | ||||
\(286\) | −2.06184e21 | −0.161050 | ||||||||
\(287\) | − | 1.17369e22i | − | 0.888413i | ||||||
\(288\) | 8.69377e20 | − | 2.24737e21i | 0.0637787 | − | 0.164870i | ||||
\(289\) | −1.93927e22 | −1.37898 | ||||||||
\(290\) | − | 1.09290e22i | − | 0.753356i | ||||||
\(291\) | −3.34759e21 | + | 1.79322e22i | −0.223715 | + | 1.19839i | ||||
\(292\) | −9.93019e21 | −0.643446 | ||||||||
\(293\) | 9.25225e21i | 0.581352i | 0.956822 | + | 0.290676i | \(0.0938801\pi\) | ||||
−0.956822 | + | 0.290676i | \(0.906120\pi\) | |||||||
\(294\) | 4.31987e21 | + | 8.06434e20i | 0.263236 | + | 0.0491409i | ||||
\(295\) | 4.48910e20 | 0.0265315 | ||||||||
\(296\) | − | 1.89790e21i | − | 0.108805i | ||||||
\(297\) | 4.55543e21 | + | 2.81600e21i | 0.253350 | + | 0.156612i | ||||
\(298\) | 1.27221e22 | 0.686456 | ||||||||
\(299\) | − | 7.55838e21i | − | 0.395720i | ||||||
\(300\) | −4.65738e21 | + | 2.49485e22i | −0.236619 | + | 1.26751i | ||||
\(301\) | −6.73600e21 | −0.332127 | ||||||||
\(302\) | − | 4.77980e21i | − | 0.228743i | ||||||
\(303\) | −8.63517e20 | − | 1.61201e20i | −0.0401132 | − | 0.00748833i | ||||
\(304\) | 4.31185e21 | 0.194447 | ||||||||
\(305\) | − | 2.81739e21i | − | 0.123353i | ||||||
\(306\) | −2.39272e22 | − | 9.25601e21i | −1.01718 | − | 0.393488i | ||||
\(307\) | 3.43877e22 | 1.41957 | 0.709787 | − | 0.704416i | \(-0.248791\pi\) | ||||
0.709787 | + | 0.704416i | \(0.248791\pi\) | |||||||
\(308\) | − | 2.92800e21i | − | 0.117386i | ||||||
\(309\) | 5.94805e21 | − | 3.18623e22i | 0.231605 | − | 1.24065i | ||||
\(310\) | 3.83942e22 | 1.45215 | ||||||||
\(311\) | − | 1.60564e22i | − | 0.589934i | −0.955507 | − | 0.294967i | \(-0.904691\pi\) | ||
0.955507 | − | 0.294967i | \(-0.0953086\pi\) | |||||||
\(312\) | 7.44542e21 | + | 1.38991e21i | 0.265765 | + | 0.0496130i | ||||
\(313\) | 2.72444e21 | 0.0944884 | 0.0472442 | − | 0.998883i | \(-0.484956\pi\) | ||||
0.0472442 | + | 0.998883i | \(0.484956\pi\) | |||||||
\(314\) | 2.45409e22i | 0.827033i | ||||||||
\(315\) | −1.64273e22 | + | 4.24651e22i | −0.537985 | + | 1.39071i | ||||
\(316\) | −1.77580e21 | −0.0565209 | ||||||||
\(317\) | − | 2.47426e22i | − | 0.765440i | −0.923864 | − | 0.382720i | \(-0.874987\pi\) | ||
0.923864 | − | 0.382720i | \(-0.125013\pi\) | |||||||
\(318\) | −3.25291e20 | + | 1.74251e21i | −0.00978201 | + | 0.0523999i | ||||
\(319\) | 5.73795e21 | 0.167741 | ||||||||
\(320\) | 8.32012e21i | 0.236472i | ||||||||
\(321\) | 4.46541e22 | + | 8.33602e21i | 1.23400 | + | 0.230363i | ||||
\(322\) | 1.07336e22 | 0.288431 | ||||||||
\(323\) | − | 4.59071e22i | − | 1.19966i | ||||||
\(324\) | −1.45516e22 | − | 1.32396e22i | −0.369833 | − | 0.336487i | ||||
\(325\) | −7.97724e22 | −1.97198 | ||||||||
\(326\) | 5.07016e22i | 1.21917i | ||||||||
\(327\) | 7.12281e21 | − | 3.81552e22i | 0.166618 | − | 0.892532i | ||||
\(328\) | −1.75100e22 | −0.398493 | ||||||||
\(329\) | − | 8.07459e21i | − | 0.178796i | ||||||
\(330\) | −1.81776e22 | − | 3.39340e21i | −0.391662 | − | 0.0731155i | ||||
\(331\) | −1.10986e22 | −0.232711 | −0.116356 | − | 0.993208i | \(-0.537121\pi\) | ||||
−0.116356 | + | 0.993208i | \(0.537121\pi\) | |||||||
\(332\) | − | 2.77539e22i | − | 0.566346i | ||||||
\(333\) | −1.44514e22 | − | 5.59040e21i | −0.287020 | − | 0.111031i | ||||
\(334\) | −5.40630e22 | −1.04516 | ||||||||
\(335\) | 1.76740e23i | 3.32607i | ||||||||
\(336\) | −1.97380e21 | + | 1.05732e22i | −0.0361617 | + | 0.193710i | ||||
\(337\) | 4.70594e22 | 0.839415 | 0.419708 | − | 0.907659i | \(-0.362133\pi\) | ||||
0.419708 | + | 0.907659i | \(0.362133\pi\) | |||||||
\(338\) | − | 1.69066e22i | − | 0.293633i | ||||||
\(339\) | −2.49234e22 | − | 4.65270e21i | −0.421512 | − | 0.0786879i | ||||
\(340\) | 8.85820e22 | 1.45893 | ||||||||
\(341\) | 2.01577e22i | 0.323334i | ||||||||
\(342\) | 1.27008e22 | − | 3.28322e22i | 0.198425 | − | 0.512938i | ||||
\(343\) | −7.14114e22 | −1.08673 | ||||||||
\(344\) | 1.00493e22i | 0.148973i | ||||||||
\(345\) | 1.24396e22 | − | 6.66362e22i | 0.179654 | − | 0.962361i | ||||
\(346\) | 2.39728e22 | 0.337313 | ||||||||
\(347\) | − | 2.23558e22i | − | 0.306496i | −0.988188 | − | 0.153248i | \(-0.951027\pi\) | ||
0.988188 | − | 0.153248i | \(-0.0489733\pi\) | |||||||
\(348\) | −2.07200e22 | − | 3.86801e21i | −0.276807 | − | 0.0516743i | ||||
\(349\) | −9.63172e22 | −1.25394 | −0.626968 | − | 0.779045i | \(-0.715704\pi\) | ||||
−0.626968 | + | 0.779045i | \(0.715704\pi\) | |||||||
\(350\) | − | 1.13284e23i | − | 1.43733i | ||||||
\(351\) | 3.25143e22 | − | 5.25983e22i | 0.402078 | − | 0.650441i | ||||
\(352\) | −4.36822e21 | −0.0526526 | ||||||||
\(353\) | 2.12429e22i | 0.249599i | 0.992182 | + | 0.124799i | \(0.0398287\pi\) | ||||
−0.992182 | + | 0.124799i | \(0.960171\pi\) | |||||||
\(354\) | 1.58878e20 | − | 8.51073e20i | 0.00181985 | − | 0.00974850i | ||||
\(355\) | 2.37199e23 | 2.64885 | ||||||||
\(356\) | − | 1.71045e22i | − | 0.186235i | ||||||
\(357\) | 1.12569e23 | + | 2.10145e22i | 1.19511 | + | 0.223102i | ||||
\(358\) | −1.11812e23 | −1.15756 | ||||||||
\(359\) | 1.79251e23i | 1.80972i | 0.425705 | + | 0.904862i | \(0.360026\pi\) | ||||
−0.425705 | + | 0.904862i | \(0.639974\pi\) | |||||||
\(360\) | 6.33527e22 | + | 2.45075e22i | 0.623796 | + | 0.241310i | ||||
\(361\) | −4.11350e22 | −0.395045 | ||||||||
\(362\) | 9.66066e22i | 0.904961i | ||||||||
\(363\) | −1.83010e22 | + | 9.80338e22i | −0.167230 | + | 0.895811i | ||||
\(364\) | −3.38075e22 | −0.301371 | ||||||||
\(365\) | − | 2.79929e23i | − | 2.43451i | ||||||
\(366\) | −5.34140e21 | − | 9.97133e20i | −0.0453237 | − | 0.00846103i | ||||
\(367\) | 2.02891e23 | 1.67984 | 0.839922 | − | 0.542706i | \(-0.182600\pi\) | ||||
0.839922 | + | 0.542706i | \(0.182600\pi\) | |||||||
\(368\) | − | 1.60132e22i | − | 0.129374i | ||||||
\(369\) | −5.15767e22 | + | 1.33328e23i | −0.406646 | + | 1.05120i | ||||
\(370\) | 5.35013e22 | 0.411670 | ||||||||
\(371\) | − | 7.91223e21i | − | 0.0594201i | ||||||
\(372\) | 1.35885e22 | − | 7.27904e22i | 0.0996059 | − | 0.533565i | ||||
\(373\) | −1.15346e23 | −0.825319 | −0.412659 | − | 0.910885i | \(-0.635400\pi\) | ||||
−0.412659 | + | 0.910885i | \(0.635400\pi\) | |||||||
\(374\) | 4.65072e22i | 0.324845i | ||||||||
\(375\) | −4.30572e23 | − | 8.03792e22i | −2.93606 | − | 0.548103i | ||||
\(376\) | −1.20463e22 | −0.0801979 | ||||||||
\(377\) | − | 6.62520e22i | − | 0.430652i | ||||||
\(378\) | 7.46943e22 | + | 4.61732e22i | 0.474090 | + | 0.293065i | ||||
\(379\) | −1.01983e23 | −0.632086 | −0.316043 | − | 0.948745i | \(-0.602354\pi\) | ||||
−0.316043 | + | 0.948745i | \(0.602354\pi\) | |||||||
\(380\) | 1.21550e23i | 0.735701i | ||||||||
\(381\) | −9.27363e21 | + | 4.96766e22i | −0.0548182 | + | 0.293648i | ||||
\(382\) | 2.58466e22 | 0.149222 | ||||||||
\(383\) | − | 2.38227e23i | − | 1.34339i | −0.740828 | − | 0.671695i | \(-0.765567\pi\) | ||
0.740828 | − | 0.671695i | \(-0.234433\pi\) | |||||||
\(384\) | 1.57738e22 | + | 2.94466e21i | 0.0868873 | + | 0.0162201i | ||||
\(385\) | 8.25394e22 | 0.444135 | ||||||||
\(386\) | − | 1.39207e23i | − | 0.731773i | ||||||
\(387\) | 7.65192e22 | + | 2.96008e22i | 0.392981 | + | 0.152021i | ||||
\(388\) | −1.21476e23 | −0.609545 | ||||||||
\(389\) | − | 8.49618e20i | − | 0.00416560i | −0.999998 | − | 0.00208280i | \(-0.999337\pi\) | ||
0.999998 | − | 0.00208280i | \(-0.000662976\pi\) | |||||||
\(390\) | −3.91811e22 | + | 2.09884e23i | −0.187714 | + | 1.00554i | ||||
\(391\) | −1.70488e23 | −0.798182 | ||||||||
\(392\) | 2.92636e22i | 0.133892i | ||||||||
\(393\) | 1.87734e23 | + | 3.50461e22i | 0.839478 | + | 0.156714i | ||||
\(394\) | −6.71954e22 | −0.293679 | ||||||||
\(395\) | − | 5.00591e22i | − | 0.213850i | ||||||
\(396\) | −1.28669e22 | + | 3.32613e22i | −0.0537299 | + | 0.138894i | ||||
\(397\) | 2.52796e23 | 1.03194 | 0.515971 | − | 0.856606i | \(-0.327431\pi\) | ||||
0.515971 | + | 0.856606i | \(0.327431\pi\) | |||||||
\(398\) | 8.36450e22i | 0.333804i | ||||||||
\(399\) | −2.88354e22 | + | 1.54465e23i | −0.112505 | + | 0.602660i | ||||
\(400\) | −1.69006e23 | −0.644705 | ||||||||
\(401\) | 2.33535e23i | 0.871068i | 0.900172 | + | 0.435534i | \(0.143440\pi\) | ||||
−0.900172 | + | 0.435534i | \(0.856560\pi\) | |||||||
\(402\) | 3.35075e23 | + | 6.25518e22i | 1.22210 | + | 0.228142i | ||||
\(403\) | 2.32746e23 | 0.830113 | ||||||||
\(404\) | − | 5.84963e21i | − | 0.0204031i | ||||||
\(405\) | 3.73219e23 | − | 4.10205e23i | 1.27312 | − | 1.39928i | ||||
\(406\) | 9.40837e22 | 0.313892 | ||||||||
\(407\) | 2.80892e22i | 0.0916620i | ||||||||
\(408\) | 3.13510e22 | − | 1.67940e23i | 0.100071 | − | 0.536058i | ||||
\(409\) | −4.91082e23 | −1.53336 | −0.766680 | − | 0.642029i | \(-0.778093\pi\) | ||||
−0.766680 | + | 0.642029i | \(0.778093\pi\) | |||||||
\(410\) | − | 4.93600e23i | − | 1.50772i | ||||||
\(411\) | −4.12839e23 | − | 7.70687e22i | −1.23368 | − | 0.230304i | ||||
\(412\) | 2.15841e23 | 0.631043 | ||||||||
\(413\) | 3.86448e21i | 0.0110545i | ||||||||
\(414\) | −1.21931e23 | − | 4.71678e22i | −0.341279 | − | 0.132021i | ||||
\(415\) | 7.82374e23 | 2.14280 | ||||||||
\(416\) | 5.04367e22i | 0.135178i | ||||||||
\(417\) | −4.04239e22 | + | 2.16541e23i | −0.106026 | + | 0.567958i | ||||
\(418\) | −6.38158e22 | −0.163811 | ||||||||
\(419\) | − | 2.92094e23i | − | 0.733832i | −0.930254 | − | 0.366916i | \(-0.880414\pi\) | ||
0.930254 | − | 0.366916i | \(-0.119586\pi\) | |||||||
\(420\) | −2.98054e23 | − | 5.56407e22i | −0.732911 | − | 0.136820i | ||||
\(421\) | −3.49420e23 | −0.841026 | −0.420513 | − | 0.907287i | \(-0.638150\pi\) | ||||
−0.420513 | + | 0.907287i | \(0.638150\pi\) | |||||||
\(422\) | 7.77640e22i | 0.183217i | ||||||||
\(423\) | −3.54831e22 | + | 9.17253e22i | −0.0818387 | + | 0.211556i | ||||
\(424\) | −1.18041e22 | −0.0266526 | ||||||||
\(425\) | 1.79936e24i | 3.97756i | ||||||||
\(426\) | 8.39496e22 | − | 4.49698e23i | 0.181690 | − | 0.973272i | ||||
\(427\) | 2.42538e22 | 0.0513959 | ||||||||
\(428\) | 3.02495e23i | 0.627660i | ||||||||
\(429\) | −1.10193e23 | − | 2.05708e22i | −0.223892 | − | 0.0417961i | ||||
\(430\) | −2.83286e23 | −0.563649 | ||||||||
\(431\) | − | 8.50240e23i | − | 1.65671i | −0.560205 | − | 0.828354i | \(-0.689277\pi\) | ||
0.560205 | − | 0.828354i | \(-0.310723\pi\) | |||||||
\(432\) | 6.88847e22 | − | 1.11435e23i | 0.131452 | − | 0.212651i | ||||
\(433\) | −6.80853e23 | −1.27251 | −0.636257 | − | 0.771477i | \(-0.719518\pi\) | ||||
−0.636257 | + | 0.771477i | \(0.719518\pi\) | |||||||
\(434\) | 3.30520e23i | 0.605049i | ||||||||
\(435\) | 1.09038e23 | − | 5.84090e23i | 0.195513 | − | 1.04731i | ||||
\(436\) | 2.58470e23 | 0.453975 | ||||||||
\(437\) | − | 2.33938e23i | − | 0.402502i | ||||||
\(438\) | −5.30707e23 | − | 9.90725e22i | −0.894516 | − | 0.166988i | ||||
\(439\) | −6.56128e23 | −1.08345 | −0.541724 | − | 0.840556i | \(-0.682228\pi\) | ||||
−0.541724 | + | 0.840556i | \(0.682228\pi\) | |||||||
\(440\) | − | 1.23139e23i | − | 0.199214i | ||||||
\(441\) | 2.22825e23 | + | 8.61979e22i | 0.353197 | + | 0.136631i | ||||
\(442\) | 5.36985e23 | 0.833992 | ||||||||
\(443\) | 9.77752e23i | 1.48797i | 0.668194 | + | 0.743987i | \(0.267068\pi\) | ||||
−0.668194 | + | 0.743987i | \(0.732932\pi\) | |||||||
\(444\) | 1.89352e22 | − | 1.01431e23i | 0.0282373 | − | 0.151260i | ||||
\(445\) | 4.82171e23 | 0.704629 | ||||||||
\(446\) | − | 1.15371e23i | − | 0.165227i | ||||||
\(447\) | 6.79919e23 | + | 1.26927e23i | 0.954310 | + | 0.178151i | ||||
\(448\) | −7.16245e22 | −0.0985280 | ||||||||
\(449\) | − | 8.18355e23i | − | 1.10338i | −0.834050 | − | 0.551689i | \(-0.813983\pi\) | ||
0.834050 | − | 0.551689i | \(-0.186017\pi\) | |||||||
\(450\) | −4.97817e23 | + | 1.28688e24i | −0.657895 | + | 1.70069i | ||||
\(451\) | 2.59149e23 | 0.335707 | ||||||||
\(452\) | − | 1.68836e23i | − | 0.214397i | ||||||
\(453\) | 4.76876e22 | − | 2.55451e23i | 0.0593638 | − | 0.317998i | ||||
\(454\) | 2.50321e23 | 0.305488 | ||||||||
\(455\) | − | 9.53024e23i | − | 1.14025i | ||||||
\(456\) | 2.30442e23 | + | 4.30189e22i | 0.270320 | + | 0.0504633i | ||||
\(457\) | 9.22885e23 | 1.06146 | 0.530728 | − | 0.847542i | \(-0.321919\pi\) | ||||
0.530728 | + | 0.847542i | \(0.321919\pi\) | |||||||
\(458\) | 3.55747e23i | 0.401192i | ||||||||
\(459\) | −1.18641e24 | − | 7.33396e23i | −1.31196 | − | 0.811006i | ||||
\(460\) | 4.51406e23 | 0.489493 | ||||||||
\(461\) | − | 2.88458e23i | − | 0.306743i | −0.988169 | − | 0.153371i | \(-0.950987\pi\) | ||
0.988169 | − | 0.153371i | \(-0.0490130\pi\) | |||||||
\(462\) | 2.92124e22 | − | 1.56484e23i | 0.0304641 | − | 0.163189i | ||||
\(463\) | 1.02160e22 | 0.0104485 | 0.00522423 | − | 0.999986i | \(-0.498337\pi\) | ||||
0.00522423 | + | 0.999986i | \(0.498337\pi\) | |||||||
\(464\) | − | 1.40361e23i | − | 0.140794i | ||||||
\(465\) | 2.05194e24 | + | 3.83056e23i | 2.01877 | + | 0.376864i | ||||
\(466\) | 4.24159e23 | 0.409313 | ||||||||
\(467\) | 3.70628e23i | 0.350822i | 0.984495 | + | 0.175411i | \(0.0561254\pi\) | ||||
−0.984495 | + | 0.175411i | \(0.943875\pi\) | |||||||
\(468\) | 3.84045e23 | + | 1.48564e23i | 0.356590 | + | 0.137944i | ||||
\(469\) | −1.52148e24 | −1.38583 | ||||||||
\(470\) | − | 3.39581e23i | − | 0.303433i | ||||||
\(471\) | −2.44842e23 | + | 1.31156e24i | −0.214633 | + | 1.14974i | ||||
\(472\) | 5.76533e21 | 0.00495845 | ||||||||
\(473\) | − | 1.48730e23i | − | 0.125502i | ||||||
\(474\) | −9.49054e22 | − | 1.77169e22i | −0.0785753 | − | 0.0146684i | ||||
\(475\) | −2.46902e24 | −2.00578 | ||||||||
\(476\) | 7.62566e23i | 0.607876i | ||||||||
\(477\) | −3.47696e22 | + | 8.98808e22i | −0.0271978 | + | 0.0703075i | ||||
\(478\) | −6.96243e23 | −0.534454 | ||||||||
\(479\) | 6.56672e23i | 0.494685i | 0.968928 | + | 0.247343i | \(0.0795573\pi\) | ||||
−0.968928 | + | 0.247343i | \(0.920443\pi\) | |||||||
\(480\) | −8.30090e22 | + | 4.44659e23i | −0.0613697 | + | 0.328743i | ||||
\(481\) | 3.24325e23 | 0.235329 | ||||||||
\(482\) | − | 6.26211e23i | − | 0.445961i | ||||||
\(483\) | 5.73643e23 | + | 1.07088e23i | 0.400975 | + | 0.0748541i | ||||
\(484\) | −6.64099e23 | −0.455643 | ||||||||
\(485\) | − | 3.42438e24i | − | 2.30625i | ||||||
\(486\) | −6.45604e23 | − | 8.52753e23i | −0.426815 | − | 0.563763i | ||||
\(487\) | 2.28426e24 | 1.48247 | 0.741233 | − | 0.671248i | \(-0.234242\pi\) | ||||
0.741233 | + | 0.671248i | \(0.234242\pi\) | |||||||
\(488\) | − | 3.61837e22i | − | 0.0230534i | ||||||
\(489\) | −5.05845e23 | + | 2.70969e24i | −0.316401 | + | 1.69488i | ||||
\(490\) | −8.24932e23 | −0.506586 | ||||||||
\(491\) | 2.05495e23i | 0.123899i | 0.998079 | + | 0.0619496i | \(0.0197318\pi\) | ||||
−0.998079 | + | 0.0619496i | \(0.980268\pi\) | |||||||
\(492\) | −9.35799e23 | − | 1.74695e23i | −0.553984 | − | 0.103418i | ||||
\(493\) | −1.49439e24 | −0.868642 | ||||||||
\(494\) | 7.36836e23i | 0.420560i | ||||||||
\(495\) | −9.37626e23 | − | 3.62713e23i | −0.525512 | − | 0.203290i | ||||
\(496\) | 4.93096e23 | 0.271391 | ||||||||
\(497\) | 2.04195e24i | 1.10367i | ||||||||
\(498\) | 2.76898e23 | − | 1.48328e24i | 0.146979 | − | 0.787332i | ||||
\(499\) | 2.98859e24 | 1.55798 | 0.778989 | − | 0.627037i | \(-0.215733\pi\) | ||||
0.778989 | + | 0.627037i | \(0.215733\pi\) | |||||||
\(500\) | − | 2.91677e24i | − | 1.49339i | ||||||
\(501\) | −2.88933e24 | − | 5.39381e23i | −1.45298 | − | 0.271241i | ||||
\(502\) | 1.71237e24 | 0.845793 | ||||||||
\(503\) | 1.72827e24i | 0.838494i | 0.907872 | + | 0.419247i | \(0.137706\pi\) | ||||
−0.907872 | + | 0.419247i | \(0.862294\pi\) | |||||||
\(504\) | −2.10975e23 | + | 5.45378e23i | −0.100544 | + | 0.259910i | ||||
\(505\) | 1.64899e23 | 0.0771962 | ||||||||
\(506\) | 2.36996e23i | 0.108990i | ||||||||
\(507\) | 1.68675e23 | − | 9.03552e23i | 0.0762043 | − | 0.408208i | ||||
\(508\) | −3.36519e23 | −0.149360 | ||||||||
\(509\) | − | 1.92080e24i | − | 0.837574i | −0.908084 | − | 0.418787i | \(-0.862455\pi\) | ||
0.908084 | − | 0.418787i | \(-0.137545\pi\) | |||||||
\(510\) | 4.73417e24 | + | 8.83774e23i | 2.02820 | + | 0.378625i | ||||
\(511\) | 2.40979e24 | 1.01436 | ||||||||
\(512\) | 1.06855e23i | 0.0441942i | ||||||||
\(513\) | 1.00634e24 | − | 1.62796e24i | 0.408969 | − | 0.661589i | ||||
\(514\) | −7.11025e23 | −0.283934 | ||||||||
\(515\) | 6.08449e24i | 2.38759i | ||||||||
\(516\) | −1.00261e23 | + | 5.37072e23i | −0.0386619 | + | 0.207103i | ||||
\(517\) | 1.78286e23 | 0.0675621 | ||||||||
\(518\) | 4.60571e23i | 0.171525i | ||||||||
\(519\) | 1.28120e24 | + | 2.39174e23i | 0.468932 | + | 0.0875402i | ||||
\(520\) | −1.42179e24 | −0.511454 | ||||||||
\(521\) | 2.22359e24i | 0.786166i | 0.919503 | + | 0.393083i | \(0.128592\pi\) | ||||
−0.919503 | + | 0.393083i | \(0.871408\pi\) | |||||||
\(522\) | −1.06877e24 | − | 4.13443e23i | −0.371405 | − | 0.143675i | ||||
\(523\) | −4.28781e23 | −0.146461 | −0.0732303 | − | 0.997315i | \(-0.523331\pi\) | ||||
−0.0732303 | + | 0.997315i | \(0.523331\pi\) | |||||||
\(524\) | 1.27174e24i | 0.426990i | ||||||||
\(525\) | 1.13022e24 | − | 6.05433e24i | 0.373018 | − | 1.99817i | ||||
\(526\) | −2.69581e24 | −0.874615 | ||||||||
\(527\) | − | 5.24985e24i | − | 1.67437i | ||||||
\(528\) | −2.33454e23 | − | 4.35813e22i | −0.0731976 | − | 0.0136645i | ||||
\(529\) | 2.37536e24 | 0.732198 | ||||||||
\(530\) | − | 3.32753e23i | − | 0.100841i | ||||||
\(531\) | 1.69821e22 | − | 4.38995e22i | 0.00505990 | − | 0.0130800i | ||||
\(532\) | −1.04637e24 | −0.306536 | ||||||||
\(533\) | − | 2.99221e24i | − | 0.861880i | ||||||
\(534\) | 1.70650e23 | − | 9.14131e23i | 0.0483320 | − | 0.258903i | ||||
\(535\) | −8.52724e24 | −2.37479 | ||||||||
\(536\) | 2.26986e24i | 0.621608i | ||||||||
\(537\) | −5.97567e24 | − | 1.11554e24i | −1.60923 | − | 0.300411i | ||||
\(538\) | 6.38795e23 | 0.169169 | ||||||||
\(539\) | − | 4.33104e23i | − | 0.112796i | ||||||
\(540\) | 3.14131e24 | + | 1.94184e24i | 0.804575 | + | 0.497358i | ||||
\(541\) | 3.73835e24 | 0.941683 | 0.470842 | − | 0.882218i | \(-0.343950\pi\) | ||||
0.470842 | + | 0.882218i | \(0.343950\pi\) | |||||||
\(542\) | 4.91712e24i | 1.21820i | ||||||||
\(543\) | −9.63834e23 | + | 5.16303e24i | −0.234857 | + | 1.25807i | ||||
\(544\) | 1.13765e24 | 0.272659 | ||||||||
\(545\) | 7.28619e24i | 1.71764i | ||||||||
\(546\) | −1.80681e24 | − | 3.37294e23i | −0.418965 | − | 0.0782124i | ||||
\(547\) | −1.53228e24 | −0.349503 | −0.174752 | − | 0.984613i | \(-0.555912\pi\) | ||||
−0.174752 | + | 0.984613i | \(0.555912\pi\) | |||||||
\(548\) | − | 2.79665e24i | − | 0.627498i | ||||||
\(549\) | −2.75517e23 | − | 1.06581e23i | −0.0608131 | − | 0.0235250i | ||||
\(550\) | 2.50130e24 | 0.543127 | ||||||||
\(551\) | − | 2.05055e24i | − | 0.438033i | ||||||
\(552\) | 1.59762e23 | − | 8.55805e23i | 0.0335754 | − | 0.179855i | ||||
\(553\) | 4.30938e23 | 0.0891023 | ||||||||
\(554\) | 3.61406e24i | 0.735204i | ||||||||
\(555\) | 2.85932e24 | + | 5.33777e23i | 0.572302 | + | 0.106837i | ||||
\(556\) | −1.46689e24 | −0.288885 | ||||||||
\(557\) | − | 5.08097e24i | − | 0.984578i | −0.870432 | − | 0.492289i | \(-0.836160\pi\) | ||
0.870432 | − | 0.492289i | \(-0.163840\pi\) | |||||||
\(558\) | 1.45244e24 | − | 3.75463e24i | 0.276944 | − | 0.715911i | ||||
\(559\) | −1.71728e24 | −0.322207 | ||||||||
\(560\) | − | 2.01907e24i | − | 0.372786i | ||||||
\(561\) | −4.63997e23 | + | 2.48552e24i | −0.0843043 | + | 0.451598i | ||||
\(562\) | −4.99853e24 | −0.893749 | ||||||||
\(563\) | − | 6.50158e24i | − | 1.14405i | −0.820238 | − | 0.572023i | \(-0.806159\pi\) | ||
0.820238 | − | 0.572023i | \(-0.193841\pi\) | |||||||
\(564\) | −6.43800e23 | − | 1.20185e23i | −0.111491 | − | 0.0208131i | ||||
\(565\) | 4.75943e24 | 0.811183 | ||||||||
\(566\) | − | 6.30230e24i | − | 1.05719i | ||||||
\(567\) | 3.53128e24 | + | 3.21289e24i | 0.583022 | + | 0.530455i | ||||
\(568\) | 3.04634e24 | 0.495043 | ||||||||
\(569\) | − | 2.38767e24i | − | 0.381913i | −0.981598 | − | 0.190957i | \(-0.938841\pi\) | ||
0.981598 | − | 0.190957i | \(-0.0611590\pi\) | |||||||
\(570\) | −1.21269e24 | + | 6.49608e24i | −0.190931 | + | 1.02277i | ||||
\(571\) | 9.17508e24 | 1.42195 | 0.710976 | − | 0.703216i | \(-0.248253\pi\) | ||||
0.710976 | + | 0.703216i | \(0.248253\pi\) | |||||||
\(572\) | − | 7.46467e23i | − | 0.113880i | ||||||
\(573\) | 1.38134e24 | + | 2.57869e23i | 0.207448 | + | 0.0387264i | ||||
\(574\) | 4.24920e24 | 0.628203 | ||||||||
\(575\) | 9.16935e24i | 1.33453i | ||||||||
\(576\) | 8.13636e23 | + | 3.14748e23i | 0.116581 | + | 0.0450984i | ||||
\(577\) | −4.46121e24 | −0.629318 | −0.314659 | − | 0.949205i | \(-0.601890\pi\) | ||||
−0.314659 | + | 0.949205i | \(0.601890\pi\) | |||||||
\(578\) | − | 7.02091e24i | − | 0.975087i | ||||||
\(579\) | 1.38886e24 | − | 7.43977e24i | 0.189911 | − | 1.01731i | ||||
\(580\) | 3.95674e24 | 0.532703 | ||||||||
\(581\) | 6.73514e24i | 0.892815i | ||||||||
\(582\) | −6.49216e24 | − | 1.21196e24i | −0.847388 | − | 0.158190i | ||||
\(583\) | 1.74701e23 | 0.0224532 | ||||||||
\(584\) | − | 3.59511e24i | − | 0.454985i | ||||||
\(585\) | −4.18798e24 | + | 1.08261e25i | −0.521918 | + | 1.34918i | ||||
\(586\) | −3.34967e24 | −0.411078 | ||||||||
\(587\) | − | 5.98733e24i | − | 0.723586i | −0.932258 | − | 0.361793i | \(-0.882165\pi\) | ||
0.932258 | − | 0.361793i | \(-0.117835\pi\) | |||||||
\(588\) | −2.91960e23 | + | 1.56396e24i | −0.0347478 | + | 0.186136i | ||||
\(589\) | 7.20369e24 | 0.844340 | ||||||||
\(590\) | 1.62523e23i | 0.0187606i | ||||||||
\(591\) | −3.59118e24 | − | 6.70401e23i | −0.408272 | − | 0.0762162i | ||||
\(592\) | 6.87115e23 | 0.0769368 | ||||||||
\(593\) | 9.26339e24i | 1.02159i | 0.859702 | + | 0.510796i | \(0.170649\pi\) | ||||
−0.859702 | + | 0.510796i | \(0.829351\pi\) | |||||||
\(594\) | −1.01950e24 | + | 1.64924e24i | −0.110741 | + | 0.179146i | ||||
\(595\) | −2.14965e25 | −2.29993 | ||||||||
\(596\) | 4.60590e24i | 0.485398i | ||||||||
\(597\) | −8.34517e23 | + | 4.47031e24i | −0.0866296 | + | 0.464054i | ||||
\(598\) | 2.73643e24 | 0.279816 | ||||||||
\(599\) | − | 7.25144e24i | − | 0.730437i | −0.930922 | − | 0.365219i | \(-0.880994\pi\) | ||
0.930922 | − | 0.365219i | \(-0.119006\pi\) | |||||||
\(600\) | −9.03231e24 | − | 1.68615e24i | −0.896267 | − | 0.167315i | ||||
\(601\) | −8.01360e23 | −0.0783352 | −0.0391676 | − | 0.999233i | \(-0.512471\pi\) | ||||
−0.0391676 | + | 0.999233i | \(0.512471\pi\) | |||||||
\(602\) | − | 2.43869e24i | − | 0.234849i | ||||||
\(603\) | 1.72836e25 | + | 6.68602e24i | 1.63976 | + | 0.634325i | ||||
\(604\) | 1.73047e24 | 0.161746 | ||||||||
\(605\) | − | 1.87207e25i | − | 1.72395i | ||||||
\(606\) | 5.83611e22 | − | 3.12627e23i | 0.00529505 | − | 0.0283643i | ||||
\(607\) | −1.52554e25 | −1.36372 | −0.681861 | − | 0.731482i | \(-0.738829\pi\) | ||||
−0.681861 | + | 0.731482i | \(0.738829\pi\) | |||||||
\(608\) | 1.56106e24i | 0.137495i | ||||||||
\(609\) | 5.02819e24 | + | 9.38663e23i | 0.436372 | + | 0.0814618i | ||||
\(610\) | 1.02001e24 | 0.0872236 | ||||||||
\(611\) | − | 2.05854e24i | − | 0.173456i | ||||||
\(612\) | 3.35103e24 | − | 8.66256e24i | 0.278238 | − | 0.719256i | ||||
\(613\) | −2.34840e25 | −1.92145 | −0.960723 | − | 0.277509i | \(-0.910491\pi\) | ||||
−0.960723 | + | 0.277509i | \(0.910491\pi\) | |||||||
\(614\) | 1.24497e25i | 1.00379i | ||||||||
\(615\) | 4.92460e24 | − | 2.63799e25i | 0.391286 | − | 2.09603i | ||||
\(616\) | 1.06005e24 | 0.0830042 | ||||||||
\(617\) | 2.25430e25i | 1.73958i | 0.493421 | + | 0.869790i | \(0.335746\pi\) | ||||
−0.493421 | + | 0.869790i | \(0.664254\pi\) | |||||||
\(618\) | 1.15354e25 | + | 2.15343e24i | 0.877275 | + | 0.163770i | ||||
\(619\) | 3.04763e24 | 0.228427 | 0.114213 | − | 0.993456i | \(-0.463565\pi\) | ||||
0.114213 | + | 0.993456i | \(0.463565\pi\) | |||||||
\(620\) | 1.39002e25i | 1.02682i | ||||||||
\(621\) | −6.04585e24 | − | 3.73732e24i | −0.440183 | − | 0.272104i | ||||
\(622\) | 5.81302e24 | 0.417146 | ||||||||
\(623\) | 4.15081e24i | 0.293589i | ||||||||
\(624\) | −5.03202e23 | + | 2.69553e24i | −0.0350817 | + | 0.187924i | ||||
\(625\) | 4.46961e25 | 3.07150 | ||||||||
\(626\) | 9.86353e23i | 0.0668134i | ||||||||
\(627\) | −3.41056e24 | − | 6.36684e23i | −0.227729 | − | 0.0425124i | ||||
\(628\) | −8.88474e24 | −0.584801 | ||||||||
\(629\) | − | 7.31552e24i | − | 0.474667i | ||||||
\(630\) | −1.53740e25 | − | 5.94731e24i | −0.983383 | − | 0.380413i | ||||
\(631\) | 1.65170e25 | 1.04152 | 0.520760 | − | 0.853703i | \(-0.325649\pi\) | ||||
0.520760 | + | 0.853703i | \(0.325649\pi\) | |||||||
\(632\) | − | 6.42907e23i | − | 0.0399663i | ||||||
\(633\) | −7.75844e23 | + | 4.15601e24i | −0.0475489 | + | 0.254708i | ||||
\(634\) | 8.95776e24 | 0.541248 | ||||||||
\(635\) | − | 9.48635e24i | − | 0.565113i | ||||||
\(636\) | −6.30855e23 | − | 1.17768e23i | −0.0370523 | − | 0.00691692i | ||||
\(637\) | −5.00075e24 | −0.289588 | ||||||||
\(638\) | 2.07736e24i | 0.118611i | ||||||||
\(639\) | 8.97318e24 | − | 2.31960e25i | 0.505171 | − | 1.30589i | ||||
\(640\) | −3.01221e24 | −0.167211 | ||||||||
\(641\) | − | 1.10098e25i | − | 0.602636i | −0.953524 | − | 0.301318i | \(-0.902573\pi\) | ||
0.953524 | − | 0.301318i | \(-0.0974266\pi\) | |||||||
\(642\) | −3.01796e24 | + | 1.61665e25i | −0.162892 | + | 0.872571i | ||||
\(643\) | 1.18166e24 | 0.0628920 | 0.0314460 | − | 0.999505i | \(-0.489989\pi\) | ||||
0.0314460 | + | 0.999505i | \(0.489989\pi\) | |||||||
\(644\) | 3.88597e24i | 0.203951i | ||||||||
\(645\) | −1.51399e25 | − | 2.82632e24i | −0.783584 | − | 0.146279i | ||||
\(646\) | 1.66201e25 | 0.848285 | ||||||||
\(647\) | 3.86630e25i | 1.94606i | 0.230674 | + | 0.973031i | \(0.425907\pi\) | ||||
−0.230674 | + | 0.973031i | \(0.574093\pi\) | |||||||
\(648\) | 4.79323e24 | − | 5.26824e24i | 0.237932 | − | 0.261511i | ||||
\(649\) | −8.53274e22 | −0.00417721 | ||||||||
\(650\) | − | 2.88807e25i | − | 1.39440i | ||||||
\(651\) | −3.29757e24 | + | 1.76643e25i | −0.157024 | + | 0.841138i | ||||
\(652\) | −1.83559e25 | −0.862081 | ||||||||
\(653\) | 3.72586e25i | 1.72587i | 0.505315 | + | 0.862935i | \(0.331376\pi\) | ||||
−0.505315 | + | 0.862935i | \(0.668624\pi\) | |||||||
\(654\) | 1.38136e25 | + | 2.57873e24i | 0.631115 | + | 0.117817i | ||||
\(655\) | −3.58501e25 | −1.61554 | ||||||||
\(656\) | − | 6.33928e24i | − | 0.281777i | ||||||
\(657\) | −2.73746e25 | − | 1.05896e25i | −1.20022 | − | 0.464293i | ||||
\(658\) | 2.92331e24 | 0.126428 | ||||||||
\(659\) | − | 1.32111e25i | − | 0.563597i | −0.959474 | − | 0.281799i | \(-0.909069\pi\) | ||
0.959474 | − | 0.281799i | \(-0.0909310\pi\) | |||||||
\(660\) | 1.22854e24 | − | 6.58100e24i | 0.0517005 | − | 0.276947i | ||||
\(661\) | −1.10139e25 | −0.457222 | −0.228611 | − | 0.973518i | \(-0.573418\pi\) | ||||
−0.228611 | + | 0.973518i | \(0.573418\pi\) | |||||||
\(662\) | − | 4.01814e24i | − | 0.164552i | ||||||
\(663\) | 2.86986e25 | + | 5.35745e24i | 1.15941 | + | 0.216439i | ||||
\(664\) | 1.00480e25 | 0.400467 | ||||||||
\(665\) | − | 2.94969e25i | − | 1.15979i | ||||||
\(666\) | 2.02394e24 | − | 5.23197e24i | 0.0785108 | − | 0.202954i | ||||
\(667\) | −7.61526e24 | −0.291442 | ||||||||
\(668\) | − | 1.95729e25i | − | 0.739038i | ||||||
\(669\) | 1.15104e24 | − | 6.16586e24i | 0.0428802 | − | 0.229699i | ||||
\(670\) | −6.39867e25 | −2.35189 | ||||||||
\(671\) | 5.35522e23i | 0.0194211i | ||||||||
\(672\) | −3.82789e24 | − | 7.14591e23i | −0.136973 | − | 0.0255702i | ||||
\(673\) | 2.97930e25 | 1.05191 | 0.525955 | − | 0.850513i | \(-0.323708\pi\) | ||||
0.525955 | + | 0.850513i | \(0.323708\pi\) | |||||||
\(674\) | 1.70373e25i | 0.593556i | ||||||||
\(675\) | −3.94443e25 | + | 6.38089e25i | −1.35597 | + | 2.19355i | ||||
\(676\) | 6.12083e24 | 0.207630 | ||||||||
\(677\) | − | 4.34240e24i | − | 0.145356i | −0.997355 | − | 0.0726778i | \(-0.976846\pi\) | ||
0.997355 | − | 0.0726778i | \(-0.0231545\pi\) | |||||||
\(678\) | 1.68446e24 | − | 9.02324e24i | 0.0556408 | − | 0.298054i | ||||
\(679\) | 2.94791e25 | 0.960917 | ||||||||
\(680\) | 3.20701e25i | 1.03162i | ||||||||
\(681\) | 1.33781e25 | + | 2.49742e24i | 0.424689 | + | 0.0792809i | ||||
\(682\) | −7.29786e24 | −0.228632 | ||||||||
\(683\) | − | 2.86178e24i | − | 0.0884810i | −0.999021 | − | 0.0442405i | \(-0.985913\pi\) | ||
0.999021 | − | 0.0442405i | \(-0.0140868\pi\) | |||||||
\(684\) | 1.18865e25 | + | 4.59819e24i | 0.362702 | + | 0.140308i | ||||
\(685\) | 7.88366e25 | 2.37417 | ||||||||
\(686\) | − | 2.58537e25i | − | 0.768432i | ||||||
\(687\) | −3.54925e24 | + | 1.90125e25i | −0.104118 | + | 0.557736i | ||||
\(688\) | −3.63823e24 | −0.105340 | ||||||||
\(689\) | − | 2.01715e24i | − | 0.0576455i | ||||||
\(690\) | 2.41249e25 | + | 4.50363e24i | 0.680492 | + | 0.127034i | ||||
\(691\) | −1.68395e25 | −0.468842 | −0.234421 | − | 0.972135i | \(-0.575319\pi\) | ||||
−0.234421 | + | 0.972135i | \(0.575319\pi\) | |||||||
\(692\) | 8.67907e24i | 0.238517i | ||||||||
\(693\) | 3.12244e24 | − | 8.07164e24i | 0.0847024 | − | 0.218959i | ||||
\(694\) | 8.09366e24 | 0.216725 | ||||||||
\(695\) | − | 4.13512e25i | − | 1.09301i | ||||||
\(696\) | 1.40037e24 | − | 7.50144e24i | 0.0365392 | − | 0.195732i | ||||
\(697\) | −6.74926e25 | −1.73844 | ||||||||
\(698\) | − | 3.48706e25i | − | 0.886666i | ||||||
\(699\) | 2.26687e25 | + | 4.23179e24i | 0.569026 | + | 0.106226i | ||||
\(700\) | 4.10132e25 | 1.01634 | ||||||||
\(701\) | − | 4.96096e25i | − | 1.21368i | −0.794825 | − | 0.606839i | \(-0.792437\pi\) | ||
0.794825 | − | 0.606839i | \(-0.207563\pi\) | |||||||
\(702\) | 1.90426e25 | + | 1.17714e25i | 0.459931 | + | 0.284312i | ||||
\(703\) | 1.00381e25 | 0.239362 | ||||||||
\(704\) | − | 1.58146e24i | − | 0.0372310i | ||||||
\(705\) | 3.38797e24 | − | 1.81485e25i | 0.0787476 | − | 0.421832i | ||||
\(706\) | −7.69076e24 | −0.176493 | ||||||||
\(707\) | 1.41955e24i | 0.0321644i | ||||||||
\(708\) | 3.08121e23 | + | 5.75201e22i | 0.00689323 | + | 0.00128683i | ||||
\(709\) | −1.44322e25 | −0.318799 | −0.159400 | − | 0.987214i | \(-0.550956\pi\) | ||||
−0.159400 | + | 0.987214i | \(0.550956\pi\) | |||||||
\(710\) | 8.58752e25i | 1.87302i | ||||||||
\(711\) | −4.89535e24 | − | 1.89372e24i | −0.105428 | − | 0.0407840i | ||||
\(712\) | 6.19250e24 | 0.131688 | ||||||||
\(713\) | − | 2.67527e25i | − | 0.561775i | ||||||
\(714\) | −7.60805e24 | + | 4.07545e25i | −0.157757 | + | 0.845068i | ||||
\(715\) | 2.10427e25 | 0.430870 | ||||||||
\(716\) | − | 4.04803e25i | − | 0.818515i | ||||||
\(717\) | −3.72099e25 | − | 6.94635e24i | −0.742996 | − | 0.138702i | ||||
\(718\) | −6.48959e25 | −1.27967 | ||||||||
\(719\) | 5.43271e25i | 1.05793i | 0.848644 | + | 0.528965i | \(0.177420\pi\) | ||||
−0.848644 | + | 0.528965i | \(0.822580\pi\) | |||||||
\(720\) | −8.87264e24 | + | 2.29361e25i | −0.170632 | + | 0.441091i | ||||
\(721\) | −5.23789e25 | −0.994807 | ||||||||
\(722\) | − | 1.48925e25i | − | 0.279339i | ||||||
\(723\) | 6.24764e24 | − | 3.34671e25i | 0.115737 | − | 0.619974i | ||||
\(724\) | −3.49753e25 | −0.639904 | ||||||||
\(725\) | 8.03727e25i | 1.45233i | ||||||||
\(726\) | −3.54920e25 | − | 6.62565e24i | −0.633434 | − | 0.118249i | ||||
\(727\) | 6.60270e25 | 1.16389 | 0.581945 | − | 0.813228i | \(-0.302292\pi\) | ||||
0.581945 | + | 0.813228i | \(0.302292\pi\) | |||||||
\(728\) | − | 1.22396e25i | − | 0.213101i | ||||||
\(729\) | −2.59957e25 | − | 5.20155e25i | −0.447048 | − | 0.894510i | ||||
\(730\) | 1.01345e26 | 1.72146 | ||||||||
\(731\) | 3.87352e25i | 0.649904i | ||||||||
\(732\) | 3.61001e23 | − | 1.93379e24i | 0.00598285 | − | 0.0320487i | ||||
\(733\) | 2.07863e25 | 0.340284 | 0.170142 | − | 0.985420i | \(-0.445577\pi\) | ||||
0.170142 | + | 0.985420i | \(0.445577\pi\) | |||||||
\(734\) | 7.34546e25i | 1.18783i | ||||||||
\(735\) | −4.40876e25 | − | 8.23027e24i | −0.704255 | − | 0.131470i | ||||
\(736\) | 5.79738e24 | 0.0914812 | ||||||||
\(737\) | − | 3.35942e25i | − | 0.523669i | ||||||
\(738\) | −4.82698e25 | − | 1.86728e25i | −0.743307 | − | 0.287542i | ||||
\(739\) | −2.13791e25 | −0.325229 | −0.162614 | − | 0.986690i | \(-0.551993\pi\) | ||||
−0.162614 | + | 0.986690i | \(0.551993\pi\) | |||||||
\(740\) | 1.93695e25i | 0.291094i | ||||||||
\(741\) | −7.35133e24 | + | 3.93793e25i | −0.109145 | + | 0.584661i | ||||
\(742\) | 2.86453e24 | 0.0420164 | ||||||||
\(743\) | 1.95124e25i | 0.282756i | 0.989956 | + | 0.141378i | \(0.0451534\pi\) | ||||
−0.989956 | + | 0.141378i | \(0.954847\pi\) | |||||||
\(744\) | 2.63529e25 | + | 4.91956e24i | 0.377287 | + | 0.0704320i | ||||
\(745\) | −1.29839e26 | −1.83653 | ||||||||
\(746\) | − | 4.17596e25i | − | 0.583588i | ||||||
\(747\) | 2.95970e25 | − | 7.65094e25i | 0.408660 | − | 1.05640i | ||||
\(748\) | −1.68374e25 | −0.229700 | ||||||||
\(749\) | − | 7.34075e25i | − | 0.989473i | ||||||
\(750\) | 2.91004e25 | − | 1.55884e26i | 0.387567 | − | 2.07610i | ||||
\(751\) | 8.83451e25 | 1.16258 | 0.581290 | − | 0.813696i | \(-0.302548\pi\) | ||||
0.581290 | + | 0.813696i | \(0.302548\pi\) | |||||||
\(752\) | − | 4.36122e24i | − | 0.0567085i | ||||||
\(753\) | 9.15157e25 | + | 1.70841e25i | 1.17582 | + | 0.219502i | ||||
\(754\) | 2.39858e25 | 0.304517 | ||||||||
\(755\) | 4.87815e25i | 0.611973i | ||||||||
\(756\) | −1.67165e25 | + | 2.70422e25i | −0.207228 | + | 0.335232i | ||||
\(757\) | 4.11022e25 | 0.503504 | 0.251752 | − | 0.967792i | \(-0.418993\pi\) | ||||
0.251752 | + | 0.967792i | \(0.418993\pi\) | |||||||
\(758\) | − | 3.69219e25i | − | 0.446953i | ||||||
\(759\) | −2.36449e24 | + | 1.26660e25i | −0.0282853 | + | 0.151518i | ||||
\(760\) | −4.40057e25 | −0.520219 | ||||||||
\(761\) | 9.29992e25i | 1.08647i | 0.839581 | + | 0.543235i | \(0.182801\pi\) | ||||
−0.839581 | + | 0.543235i | \(0.817199\pi\) | |||||||
\(762\) | −1.79848e25 | − | 3.35741e24i | −0.207640 | − | 0.0387623i | ||||
\(763\) | −6.27239e25 | −0.715668 | ||||||||
\(764\) | 9.35746e24i | 0.105516i | ||||||||
\(765\) | 2.44195e26 | + | 9.44646e25i | 2.72134 | + | 1.05273i | ||||
\(766\) | 8.62474e25 | 0.949920 | ||||||||
\(767\) | 9.85215e23i | 0.0107244i | ||||||||
\(768\) | −1.06608e24 | + | 5.71074e24i | −0.0114694 | + | 0.0614386i | ||||
\(769\) | 1.12638e26 | 1.19770 | 0.598850 | − | 0.800861i | \(-0.295624\pi\) | ||||
0.598850 | + | 0.800861i | \(0.295624\pi\) | |||||||
\(770\) | 2.98825e25i | 0.314051i | ||||||||
\(771\) | −3.79999e25 | − | 7.09383e24i | −0.394724 | − | 0.0736871i | ||||
\(772\) | 5.03984e25 | 0.517441 | ||||||||
\(773\) | 1.32815e26i | 1.34782i | 0.738815 | + | 0.673908i | \(0.235386\pi\) | ||||
−0.738815 | + | 0.673908i | \(0.764614\pi\) | |||||||
\(774\) | −1.07166e25 | + | 2.77029e25i | −0.107495 | + | 0.277880i | ||||
\(775\) | −2.82353e26 | −2.79948 | ||||||||
\(776\) | − | 4.39791e25i | − | 0.431014i | ||||||
\(777\) | −4.59507e24 | + | 2.46147e25i | −0.0445146 | + | 0.238454i | ||||
\(778\) | 3.07594e23 | 0.00294552 | ||||||||
\(779\) | − | 9.26113e25i | − | 0.876652i | ||||||
\(780\) | −7.59861e25 | − | 1.41851e25i | −0.711022 | − | 0.132734i | ||||
\(781\) | −4.50861e25 | −0.417045 | ||||||||
\(782\) | − | 6.17231e25i | − | 0.564400i | ||||||
\(783\) | −5.29941e25 | − | 3.27590e25i | −0.479040 | − | 0.296124i | ||||
\(784\) | −1.05946e25 | −0.0946757 | ||||||||
\(785\) | − | 2.50458e26i | − | 2.21263i | ||||||
\(786\) | −1.26881e25 | + | 6.79669e25i | −0.110813 | + | 0.593601i | ||||
\(787\) | 1.65188e26 | 1.42628 | 0.713140 | − | 0.701022i | \(-0.247273\pi\) | ||||
0.713140 | + | 0.701022i | \(0.247273\pi\) | |||||||
\(788\) | − | 2.43273e25i | − | 0.207663i | ||||||
\(789\) | −1.44074e26 | − | 2.68958e25i | −1.21589 | − | 0.226982i | ||||
\(790\) | 1.81233e25 | 0.151215 | ||||||||
\(791\) | 4.09720e25i | 0.337986i | ||||||||
\(792\) | −1.20419e25 | − | 4.65830e24i | −0.0982128 | − | 0.0379928i | ||||
\(793\) | 6.18328e24 | 0.0498610 | ||||||||
\(794\) | 9.15218e25i | 0.729692i | ||||||||
\(795\) | 3.31984e24 | − | 1.77836e25i | 0.0261706 | − | 0.140189i | ||||
\(796\) | −3.02827e25 | −0.236035 | ||||||||
\(797\) | 1.75243e26i | 1.35057i | 0.737557 | + | 0.675285i | \(0.235979\pi\) | ||||
−0.737557 | + | 0.675285i | \(0.764021\pi\) | |||||||
\(798\) | −5.59221e25 | − | 1.04395e25i | −0.426145 | − | 0.0795528i | ||||
\(799\) | −4.64327e25 | −0.349867 | ||||||||
\(800\) | − | 6.11866e25i | − | 0.455875i | ||||||
\(801\) | 1.82404e25 | − | 4.71521e25i | 0.134382 | − | 0.347383i | ||||
\(802\) | −8.45486e25 | −0.615938 | ||||||||
\(803\) | 5.32080e25i | 0.383298i | ||||||||
\(804\) | −2.26462e25 | + | 1.21310e26i | −0.161321 | + | 0.864157i | ||||
\(805\) | −1.09544e26 | −0.771661 | ||||||||
\(806\) | 8.42632e25i | 0.586979i | ||||||||
\(807\) | 3.41396e25 | + | 6.37319e24i | 0.235178 | + | 0.0439031i | ||||
\(808\) | 2.11779e24 | 0.0144272 | ||||||||
\(809\) | − | 1.81052e26i | − | 1.21974i | −0.792503 | − | 0.609869i | \(-0.791222\pi\) | ||
0.792503 | − | 0.609869i | \(-0.208778\pi\) | |||||||
\(810\) | 1.48510e26 | + | 1.35120e26i | 0.989442 | + | 0.900230i | ||||
\(811\) | 1.11663e26 | 0.735733 | 0.367867 | − | 0.929879i | \(-0.380088\pi\) | ||||
0.367867 | + | 0.929879i | \(0.380088\pi\) | |||||||
\(812\) | 3.40619e25i | 0.221955i | ||||||||
\(813\) | −4.90576e25 | + | 2.62790e26i | −0.316148 | + | 1.69353i | ||||
\(814\) | −1.01694e25 | −0.0648148 | ||||||||
\(815\) | − | 5.17448e26i | − | 3.26173i | ||||||
\(816\) | 6.08007e25 | + | 1.13503e25i | 0.379050 | + | 0.0707611i | ||||
\(817\) | −5.31513e25 | −0.327730 | ||||||||
\(818\) | − | 1.77791e26i | − | 1.08425i | ||||||
\(819\) | −9.31975e25 | − | 3.60526e25i | −0.562146 | − | 0.217461i | ||||
\(820\) | 1.78702e26 | 1.06612 | ||||||||
\(821\) | 2.31975e26i | 1.36884i | 0.729088 | + | 0.684420i | \(0.239944\pi\) | ||||
−0.729088 | + | 0.684420i | \(0.760056\pi\) | |||||||
\(822\) | 2.79019e25 | − | 1.49464e26i | 0.162850 | − | 0.872347i | ||||
\(823\) | 1.29059e26 | 0.745057 | 0.372528 | − | 0.928021i | \(-0.378491\pi\) | ||||
0.372528 | + | 0.928021i | \(0.378491\pi\) | |||||||
\(824\) | 7.81428e25i | 0.446215i | ||||||||
\(825\) | 1.33679e26 | + | 2.49552e25i | 0.755054 | + | 0.140953i | ||||
\(826\) | −1.39909e24 | −0.00781674 | ||||||||
\(827\) | − | 9.14427e25i | − | 0.505358i | −0.967550 | − | 0.252679i | \(-0.918688\pi\) | ||
0.967550 | − | 0.252679i | \(-0.0813117\pi\) | |||||||
\(828\) | 1.70766e25 | − | 4.41436e25i | 0.0933528 | − | 0.241321i | ||||
\(829\) | −2.88476e26 | −1.55998 | −0.779989 | − | 0.625793i | \(-0.784776\pi\) | ||||
−0.779989 | + | 0.625793i | \(0.784776\pi\) | |||||||
\(830\) | 2.83250e26i | 1.51519i | ||||||||
\(831\) | −3.60571e25 | + | 1.93149e26i | −0.190802 | + | 1.02208i | ||||
\(832\) | −1.82600e25 | −0.0955854 | ||||||||
\(833\) | 1.12797e26i | 0.584109i | ||||||||
\(834\) | −7.83963e25 | − | 1.46350e25i | −0.401607 | − | 0.0749720i | ||||
\(835\) | 5.51754e26 | 2.79619 | ||||||||
\(836\) | − | 2.31038e25i | − | 0.115832i | ||||||
\(837\) | 1.15084e26 | − | 1.86171e26i | 0.570801 | − | 0.923384i | ||||
\(838\) | 1.05749e26 | 0.518898 | ||||||||
\(839\) | − | 1.27722e26i | − | 0.620021i | −0.950733 | − | 0.310011i | \(-0.899667\pi\) | ||
0.950733 | − | 0.310011i | \(-0.100333\pi\) | |||||||
\(840\) | 2.01441e25 | − | 1.07907e26i | 0.0967462 | − | 0.518246i | ||||
\(841\) | 1.43707e26 | 0.682831 | ||||||||
\(842\) | − | 1.26504e26i | − | 0.594695i | ||||||
\(843\) | −2.67141e26 | − | 4.98699e25i | −1.24249 | − | 0.231948i | ||||
\(844\) | −2.81536e25 | −0.129554 | ||||||||
\(845\) | 1.72544e26i | 0.785579i | ||||||||
\(846\) | −3.32081e25 | − | 1.28463e25i | −0.149593 | − | 0.0578687i | ||||
\(847\) | 1.61159e26 | 0.718298 | ||||||||
\(848\) | − | 4.27353e24i | − | 0.0188462i | ||||||
\(849\) | 6.28774e25 | − | 3.36819e26i | 0.274363 | − | 1.46970i | ||||
\(850\) | −6.51436e26 | −2.81256 | ||||||||
\(851\) | − | 3.72792e25i | − | 0.159258i | ||||||
\(852\) | 1.62808e26 | + | 3.03930e25i | 0.688207 | + | 0.128475i | ||||
\(853\) | −3.33058e25 | −0.139309 | −0.0696545 | − | 0.997571i | \(-0.522190\pi\) | ||||
−0.0696545 | + | 0.997571i | \(0.522190\pi\) | |||||||
\(854\) | 8.78081e24i | 0.0363424i | ||||||||
\(855\) | −1.29622e26 | + | 3.35077e26i | −0.530863 | + | 1.37230i | ||||
\(856\) | −1.09515e26 | −0.443823 | ||||||||
\(857\) | 1.96913e26i | 0.789672i | 0.918752 | + | 0.394836i | \(0.129199\pi\) | ||||
−0.918752 | + | 0.394836i | \(0.870801\pi\) | |||||||
\(858\) | 7.44743e24 | − | 3.98941e25i | 0.0295543 | − | 0.158315i | ||||
\(859\) | −4.72996e26 | −1.85746 | −0.928728 | − | 0.370761i | \(-0.879097\pi\) | ||||
−0.928728 | + | 0.370761i | \(0.879097\pi\) | |||||||
\(860\) | − | 1.02560e26i | − | 0.398560i | ||||||
\(861\) | 2.27094e26 | + | 4.23938e25i | 0.873326 | + | 0.163033i | ||||
\(862\) | 3.07820e26 | 1.17147 | ||||||||
\(863\) | 4.83906e26i | 1.82249i | 0.411870 | + | 0.911243i | \(0.364876\pi\) | ||||
−0.411870 | + | 0.911243i | \(0.635124\pi\) | |||||||
\(864\) | 4.03436e25 | + | 2.49389e25i | 0.150367 | + | 0.0929510i | ||||
\(865\) | −2.44660e26 | −0.902440 | ||||||||
\(866\) | − | 2.46495e26i | − | 0.899803i | ||||||
\(867\) | 7.00470e25 | − | 3.75225e26i | 0.253056 | − | 1.35556i | ||||
\(868\) | −1.19661e26 | −0.427834 | ||||||||
\(869\) | 9.51508e24i | 0.0336693i | ||||||||
\(870\) | 2.11463e26 | + | 3.94760e25i | 0.740563 | + | 0.138248i | ||||
\(871\) | −3.87888e26 | −1.34444 | ||||||||
\(872\) | 9.35762e25i | 0.321009i | ||||||||
\(873\) | −3.34875e26 | − | 1.29543e26i | −1.13698 | − | 0.439832i | ||||
\(874\) | 8.46947e25 | 0.284612 | ||||||||
\(875\) | 7.07823e26i | 2.35425i | ||||||||
\(876\) | 3.58681e25 | − | 1.92137e26i | 0.118079 | − | 0.632518i | ||||
\(877\) | 4.82462e26 | 1.57205 | 0.786026 | − | 0.618193i | \(-0.212135\pi\) | ||||
0.786026 | + | 0.618193i | \(0.212135\pi\) | |||||||
\(878\) | − | 2.37544e26i | − | 0.766114i | ||||||
\(879\) | −1.79019e26 | − | 3.34194e25i | −0.571479 | − | 0.106684i | ||||
\(880\) | 4.45809e25 | 0.140866 | ||||||||
\(881\) | − | 3.32122e26i | − | 1.03876i | −0.854544 | − | 0.519379i | \(-0.826163\pi\) | ||
0.854544 | − | 0.519379i | \(-0.173837\pi\) | |||||||
\(882\) | −3.12070e25 | + | 8.06713e25i | −0.0966127 | + | 0.249748i | ||||
\(883\) | −1.07959e25 | −0.0330837 | −0.0165418 | − | 0.999863i | \(-0.505266\pi\) | ||||
−0.0165418 | + | 0.999863i | \(0.505266\pi\) | |||||||
\(884\) | 1.94409e26i | 0.589721i | ||||||||
\(885\) | −1.62147e24 | + | 8.68584e24i | −0.00486878 | + | 0.0260809i | ||||
\(886\) | −3.53984e26 | −1.05216 | ||||||||
\(887\) | − | 1.13579e24i | − | 0.00334183i | −0.999999 | − | 0.00167091i | \(-0.999468\pi\) | ||
0.999999 | − | 0.00167091i | \(-0.000531869\pi\) | |||||||
\(888\) | 3.67221e25 | + | 6.85528e24i | 0.106957 | + | 0.0199668i | ||||
\(889\) | 8.16641e25 | 0.235459 | ||||||||
\(890\) | 1.74564e26i | 0.498248i | ||||||||
\(891\) | −7.09403e25 | + | 7.79704e25i | −0.200444 | + | 0.220308i | ||||
\(892\) | 4.17687e25 | 0.116833 | ||||||||
\(893\) | − | 6.37137e25i | − | 0.176429i | ||||||
\(894\) | −4.59526e25 | + | 2.46157e26i | −0.125971 | + | 0.674799i | ||||
\(895\) | 1.14113e27 | 3.09690 | ||||||||
\(896\) | − | 2.59309e25i | − | 0.0696698i | ||||||
\(897\) | 1.46245e26 | + | 2.73010e25i | 0.389000 | + | 0.0726185i | ||||
\(898\) | 2.96276e26 | 0.780206 | ||||||||
\(899\) | − | 2.34498e26i | − | 0.611366i | ||||||
\(900\) | −4.65899e26 | − | 1.80229e26i | −1.20257 | − | 0.465202i | ||||
\(901\) | −4.54991e25 | −0.116273 | ||||||||
\(902\) | 9.38220e25i | 0.237381i | ||||||||
\(903\) | 2.43306e25 | − | 1.30333e26i | 0.0609485 | − | 0.326486i | ||||
\(904\) | 6.11251e25 | 0.151602 | ||||||||
\(905\) | − | 9.85943e26i | − | 2.42111i | ||||||
\(906\) | 9.24831e25 | + | 1.72648e25i | 0.224858 | + | 0.0419765i | ||||
\(907\) | 3.78188e25 | 0.0910421 | 0.0455210 | − | 0.998963i | \(-0.485505\pi\) | ||||
0.0455210 | + | 0.998963i | \(0.485505\pi\) | |||||||
\(908\) | 9.06258e25i | 0.216013i | ||||||||
\(909\) | 6.23809e24 | − | 1.61257e25i | 0.0147223 | − | 0.0380578i | ||||
\(910\) | 3.45031e26 | 0.806280 | ||||||||
\(911\) | − | 1.76798e26i | − | 0.409083i | −0.978858 | − | 0.204542i | \(-0.934430\pi\) | ||
0.978858 | − | 0.204542i | \(-0.0655704\pi\) | |||||||
\(912\) | −1.55745e25 | + | 8.34289e25i | −0.0356830 | + | 0.191145i | ||||
\(913\) | −1.48711e26 | −0.337370 | ||||||||
\(914\) | 3.34120e26i | 0.750562i | ||||||||
\(915\) | 5.45130e25 | + | 1.01765e25i | 0.121258 | + | 0.0226364i | ||||
\(916\) | −1.28794e26 | −0.283685 | ||||||||
\(917\) | − | 3.08618e26i | − | 0.673128i | ||||||
\(918\) | 2.65518e26 | − | 4.29528e26i | 0.573468 | − | 0.927699i | ||||
\(919\) | −6.28949e26 | −1.34517 | −0.672583 | − | 0.740022i | \(-0.734815\pi\) | ||||
−0.672583 | + | 0.740022i | \(0.734815\pi\) | |||||||
\(920\) | 1.63426e26i | 0.346124i | ||||||||
\(921\) | −1.24209e26 | + | 6.65359e26i | −0.260506 | + | 1.39547i | ||||
\(922\) | 1.04433e26 | 0.216900 | ||||||||
\(923\) | 5.20576e26i | 1.07070i | ||||||||
\(924\) | 5.66531e25 | + | 1.05760e25i | 0.115392 | + | 0.0215414i | ||||
\(925\) | −3.93451e26 | −0.793625 | ||||||||
\(926\) | 3.69859e24i | 0.00738818i | ||||||||
\(927\) | 5.95011e26 | + | 2.30175e26i | 1.17708 | + | 0.455344i | ||||
\(928\) | 5.08162e25 | 0.0995567 | ||||||||
\(929\) | 5.88758e26i | 1.14234i | 0.820832 | + | 0.571170i | \(0.193510\pi\) | ||||
−0.820832 | + | 0.571170i | \(0.806490\pi\) | |||||||
\(930\) | −1.38681e26 | + | 7.42880e26i | −0.266483 | + | 1.42749i | ||||
\(931\) | −1.54777e26 | −0.294551 | ||||||||
\(932\) | 1.53562e26i | 0.289428i | ||||||||
\(933\) | 3.10670e26 | + | 5.79959e25i | 0.579916 | + | 0.108259i | ||||
\(934\) | −1.34182e26 | −0.248068 | ||||||||
\(935\) | − | 4.74641e26i | − | 0.869082i | ||||||
\(936\) | −5.37861e25 | + | 1.39039e26i | −0.0975410 | + | 0.252147i | ||||
\(937\) | −7.68660e26 | −1.38063 | −0.690316 | − | 0.723508i | \(-0.742528\pi\) | ||||
−0.690316 | + | 0.723508i | \(0.742528\pi\) | |||||||
\(938\) | − | 5.50835e26i | − | 0.979932i | ||||||
\(939\) | −9.84074e24 | + | 5.27145e25i | −0.0173395 | + | 0.0928838i | ||||
\(940\) | 1.22941e26 | 0.214560 | ||||||||
\(941\) | − | 9.90911e26i | − | 1.71288i | −0.516243 | − | 0.856442i | \(-0.672670\pi\) | ||
0.516243 | − | 0.856442i | \(-0.327330\pi\) | |||||||
\(942\) | −4.74835e26 | − | 8.86422e25i | −0.812989 | − | 0.151769i | ||||
\(943\) | −3.43936e26 | −0.583273 | ||||||||
\(944\) | 2.08727e24i | 0.00350616i | ||||||||
\(945\) | −7.62311e26 | − | 4.71232e26i | −1.26837 | − | 0.784058i | ||||
\(946\) | 5.38461e25 | 0.0887430 | ||||||||
\(947\) | 5.98010e26i | 0.976244i | 0.872775 | + | 0.488122i | \(0.162318\pi\) | ||||
−0.872775 | + | 0.488122i | \(0.837682\pi\) | |||||||
\(948\) | 6.41422e24 | − | 3.43594e25i | 0.0103721 | − | 0.0555611i | ||||
\(949\) | 6.14355e26 | 0.984064 | ||||||||
\(950\) | − | 8.93882e26i | − | 1.41830i | ||||||
\(951\) | 4.78737e26 | + | 8.93707e25i | 0.752441 | + | 0.140466i | ||||
\(952\) | −2.76079e26 | −0.429833 | ||||||||
\(953\) | − | 6.89203e26i | − | 1.06295i | −0.847075 | − | 0.531473i | \(-0.821639\pi\) | ||
0.847075 | − | 0.531473i | \(-0.178361\pi\) | |||||||
\(954\) | −3.25403e25 | − | 1.25879e25i | −0.0497149 | − | 0.0192318i | ||||
\(955\) | −2.63784e26 | −0.399225 | ||||||||
\(956\) | − | 2.52067e26i | − | 0.377916i | ||||||
\(957\) | −2.07256e25 | + | 1.11022e26i | −0.0307822 | + | 0.164893i | ||||
\(958\) | −2.37741e26 | −0.349795 | ||||||||
\(959\) | 6.78672e26i | 0.989219i | ||||||||
\(960\) | −1.60984e26 | − | 3.00525e25i | −0.232456 | − | 0.0433950i | ||||
\(961\) | 1.24748e26 | 0.178452 | ||||||||
\(962\) | 1.17418e26i | 0.166403i | ||||||||
\(963\) | −3.22583e26 | + | 8.33890e26i | −0.452903 | + | 1.17077i | ||||
\(964\) | 2.26713e26 | 0.315342 | ||||||||
\(965\) | 1.42072e27i | 1.95777i | ||||||||
\(966\) | −3.87699e25 | + | 2.07681e26i | −0.0529298 | + | 0.283532i | ||||
\(967\) | 2.57739e26 | 0.348612 | 0.174306 | − | 0.984692i | \(-0.444232\pi\) | ||||
0.174306 | + | 0.984692i | \(0.444232\pi\) | |||||||
\(968\) | − | 2.40430e26i | − | 0.322188i | ||||||
\(969\) | 8.88244e26 | + | 1.65817e26i | 1.17928 | + | 0.220149i | ||||
\(970\) | 1.23976e27 | 1.63076 | ||||||||
\(971\) | − | 1.25582e27i | − | 1.63665i | −0.574756 | − | 0.818325i | \(-0.694903\pi\) | ||
0.574756 | − | 0.818325i | \(-0.305097\pi\) | |||||||
\(972\) | 3.08730e26 | − | 2.33733e26i | 0.398641 | − | 0.301804i | ||||
\(973\) | 3.55975e26 | 0.455412 | ||||||||
\(974\) | 8.26990e26i | 1.04826i | ||||||||
\(975\) | 2.88140e26 | − | 1.54350e27i | 0.361878 | − | 1.93849i | ||||
\(976\) | 1.30999e25 | 0.0163012 | ||||||||
\(977\) | 1.20250e27i | 1.48264i | 0.671153 | + | 0.741319i | \(0.265799\pi\) | ||||
−0.671153 | + | 0.741319i | \(0.734201\pi\) | |||||||
\(978\) | −9.81012e26 | − | 1.83135e26i | −1.19846 | − | 0.223729i | ||||
\(979\) | −9.16495e25 | −0.110939 | ||||||||
\(980\) | − | 2.98657e26i | − | 0.358211i | ||||||
\(981\) | 7.12527e26 | + | 2.75635e26i | 0.846799 | + | 0.327577i | ||||
\(982\) | −7.43972e25 | −0.0876099 | ||||||||
\(983\) | 6.46717e26i | 0.754627i | 0.926086 | + | 0.377314i | \(0.123152\pi\) | ||||
−0.926086 | + | 0.377314i | \(0.876848\pi\) | |||||||
\(984\) | 6.32464e25 | − | 3.38796e26i | 0.0731273 | − | 0.391726i | ||||
\(985\) | 6.85779e26 | 0.785703 | ||||||||
\(986\) | − | 5.41026e26i | − | 0.614223i | ||||||
\(987\) | 1.56233e26 | + | 2.91656e25i | 0.175760 | + | 0.0328108i | ||||
\(988\) | −2.66763e26 | −0.297381 | ||||||||
\(989\) | 1.97391e26i | 0.218052i | ||||||||
\(990\) | 1.31316e26 | − | 3.39457e26i | 0.143748 | − | 0.371593i | ||||
\(991\) | −4.68254e25 | −0.0507948 | −0.0253974 | − | 0.999677i | \(-0.508085\pi\) | ||||
−0.0253974 | + | 0.999677i | \(0.508085\pi\) | |||||||
\(992\) | 1.78520e26i | 0.191903i | ||||||||
\(993\) | 4.00885e25 | − | 2.14745e26i | 0.0427048 | − | 0.228759i | ||||
\(994\) | −7.39265e26 | −0.780409 | ||||||||
\(995\) | − | 8.53660e26i | − | 0.893053i | ||||||
\(996\) | 5.37003e26 | + | 1.00248e26i | 0.556728 | + | 0.103930i | ||||
\(997\) | −9.85361e26 | −1.01237 | −0.506185 | − | 0.862425i | \(-0.668945\pi\) | ||||
−0.506185 | + | 0.862425i | \(0.668945\pi\) | |||||||
\(998\) | 1.08199e27i | 1.10166i | ||||||||
\(999\) | 1.60366e26 | − | 2.59424e26i | 0.161816 | − | 0.261770i |
(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.5.5 | yes | 6 | |
3.2 | odd | 2 | inner | 6.19.b.a.5.2 | ✓ | 6 | |
4.3 | odd | 2 | 48.19.e.d.17.3 | 6 | |||
12.11 | even | 2 | 48.19.e.d.17.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.19.b.a.5.2 | ✓ | 6 | 3.2 | odd | 2 | inner | |
6.19.b.a.5.5 | yes | 6 | 1.1 | even | 1 | trivial | |
48.19.e.d.17.3 | 6 | 4.3 | odd | 2 | |||
48.19.e.d.17.4 | 6 | 12.11 | even | 2 |