Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,15,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(3.72986904456\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.1929141760.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 364x^{2} + 3640 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.4 | ||
Root | \(18.8072i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.15.b.a.2.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 225.686i | 1.76317i | 0.472025 | + | 0.881585i | \(0.343523\pi\) | ||||
−0.472025 | + | 0.881585i | \(0.656477\pi\) | |||||||
\(3\) | 1922.67 | + | 1042.26i | 0.879137 | + | 0.476569i | ||||
\(4\) | −34550.1 | −2.10877 | ||||||||
\(5\) | − | 23159.5i | − | 0.296442i | −0.988954 | − | 0.148221i | \(-0.952645\pi\) | ||
0.988954 | − | 0.148221i | \(-0.0473547\pi\) | |||||||
\(6\) | −235223. | + | 433920.i | −0.840273 | + | 1.55007i | ||||
\(7\) | 478389. | 0.580892 | 0.290446 | − | 0.956891i | \(-0.406196\pi\) | ||||
0.290446 | + | 0.956891i | \(0.406196\pi\) | |||||||
\(8\) | − | 4.09983e6i | − | 1.95495i | ||||||
\(9\) | 2.61037e6 | + | 4.00784e6i | 0.545763 | + | 0.837939i | ||||
\(10\) | 5.22678e6 | 0.522678 | ||||||||
\(11\) | 1.60910e7i | 0.825725i | 0.910793 | + | 0.412862i | \(0.135471\pi\) | ||||
−0.910793 | + | 0.412862i | \(0.864529\pi\) | |||||||
\(12\) | −6.64285e7 | − | 3.60101e7i | −1.85390 | − | 1.00498i | ||||
\(13\) | 3.37094e7 | 0.537214 | 0.268607 | − | 0.963250i | \(-0.413437\pi\) | ||||
0.268607 | + | 0.963250i | \(0.413437\pi\) | |||||||
\(14\) | 1.07966e8i | 1.02421i | ||||||||
\(15\) | 2.41382e7 | − | 4.45282e7i | 0.141275 | − | 0.260613i | ||||
\(16\) | 3.59205e8 | 1.33814 | ||||||||
\(17\) | − | 6.70754e8i | − | 1.63464i | −0.576187 | − | 0.817318i | \(-0.695460\pi\) | ||
0.576187 | − | 0.817318i | \(-0.304540\pi\) | |||||||
\(18\) | −9.04512e8 | + | 5.89124e8i | −1.47743 | + | 0.962274i | ||||
\(19\) | 3.92753e8 | 0.439384 | 0.219692 | − | 0.975569i | \(-0.429495\pi\) | ||||
0.219692 | + | 0.975569i | \(0.429495\pi\) | |||||||
\(20\) | 8.00165e8i | 0.625129i | ||||||||
\(21\) | 9.19786e8 | + | 4.98604e8i | 0.510683 | + | 0.276835i | ||||
\(22\) | −3.63152e9 | −1.45589 | ||||||||
\(23\) | − | 3.24506e7i | − | 0.00953077i | −0.999989 | − | 0.00476539i | \(-0.998483\pi\) | ||
0.999989 | − | 0.00476539i | \(-0.00151688\pi\) | |||||||
\(24\) | 4.27308e9 | − | 7.88264e9i | 0.931670 | − | 1.71867i | ||||
\(25\) | 5.56715e9 | 0.912122 | ||||||||
\(26\) | 7.60773e9i | 0.947200i | ||||||||
\(27\) | 8.41689e8 | + | 1.04264e10i | 0.0804647 | + | 0.996757i | ||||
\(28\) | −1.65284e10 | −1.22497 | ||||||||
\(29\) | − | 2.47510e10i | − | 1.43485i | −0.696637 | − | 0.717424i | \(-0.745321\pi\) | ||
0.696637 | − | 0.717424i | \(-0.254679\pi\) | |||||||
\(30\) | 1.00494e10 | + | 5.44765e9i | 0.459506 | + | 0.249092i | ||||
\(31\) | −3.17682e10 | −1.15468 | −0.577340 | − | 0.816504i | \(-0.695909\pi\) | ||||
−0.577340 | + | 0.816504i | \(0.695909\pi\) | |||||||
\(32\) | 1.38959e10i | 0.404424i | ||||||||
\(33\) | −1.67710e10 | + | 3.09378e10i | −0.393515 | + | 0.725925i | ||||
\(34\) | 1.51380e11 | 2.88214 | ||||||||
\(35\) | − | 1.10793e10i | − | 0.172201i | ||||||
\(36\) | −9.01885e10 | − | 1.38471e11i | −1.15089 | − | 1.76702i | ||||
\(37\) | −4.38690e10 | −0.462111 | −0.231055 | − | 0.972941i | \(-0.574218\pi\) | ||||
−0.231055 | + | 0.972941i | \(0.574218\pi\) | |||||||
\(38\) | 8.86387e10i | 0.774709i | ||||||||
\(39\) | 6.48121e10 | + | 3.51338e10i | 0.472285 | + | 0.256020i | ||||
\(40\) | −9.49502e10 | −0.579530 | ||||||||
\(41\) | 1.11156e11i | 0.570751i | 0.958416 | + | 0.285376i | \(0.0921184\pi\) | ||||
−0.958416 | + | 0.285376i | \(0.907882\pi\) | |||||||
\(42\) | −1.12528e11 | + | 2.07583e11i | −0.488107 | + | 0.900422i | ||||
\(43\) | 1.00533e11 | 0.369853 | 0.184927 | − | 0.982752i | \(-0.440795\pi\) | ||||
0.184927 | + | 0.982752i | \(0.440795\pi\) | |||||||
\(44\) | − | 5.55947e11i | − | 1.74126i | ||||||
\(45\) | 9.28197e10 | − | 6.04550e10i | 0.248401 | − | 0.161787i | ||||
\(46\) | 7.32365e9 | 0.0168044 | ||||||||
\(47\) | − | 2.14354e11i | − | 0.423104i | −0.977367 | − | 0.211552i | \(-0.932148\pi\) | ||
0.977367 | − | 0.211552i | \(-0.0678518\pi\) | |||||||
\(48\) | 6.90634e11 | + | 3.74384e11i | 1.17641 | + | 0.637718i | ||||
\(49\) | −4.49367e11 | −0.662565 | ||||||||
\(50\) | 1.25643e12i | 1.60823i | ||||||||
\(51\) | 6.99098e11 | − | 1.28964e12i | 0.779017 | − | 1.43707i | ||||
\(52\) | −1.16466e12 | −1.13286 | ||||||||
\(53\) | 5.81823e11i | 0.495290i | 0.968851 | + | 0.247645i | \(0.0796567\pi\) | ||||
−0.968851 | + | 0.247645i | \(0.920343\pi\) | |||||||
\(54\) | −2.35310e12 | + | 1.89957e11i | −1.75745 | + | 0.141873i | ||||
\(55\) | 3.72661e11 | 0.244780 | ||||||||
\(56\) | − | 1.96132e12i | − | 1.13562i | ||||||
\(57\) | 7.55135e11 | + | 4.09349e11i | 0.386278 | + | 0.209397i | ||||
\(58\) | 5.58594e12 | 2.52988 | ||||||||
\(59\) | 2.31936e12i | 0.931973i | 0.884792 | + | 0.465986i | \(0.154300\pi\) | ||||
−0.884792 | + | 0.465986i | \(0.845700\pi\) | |||||||
\(60\) | −8.33977e11 | + | 1.53845e12i | −0.297917 | + | 0.549574i | ||||
\(61\) | −4.22999e12 | −1.34595 | −0.672977 | − | 0.739663i | \(-0.734985\pi\) | ||||
−0.672977 | + | 0.739663i | \(0.734985\pi\) | |||||||
\(62\) | − | 7.16964e12i | − | 2.03590i | ||||||
\(63\) | 1.24877e12 | + | 1.91731e12i | 0.317029 | + | 0.486752i | ||||
\(64\) | 2.74911e12 | 0.625076 | ||||||||
\(65\) | − | 7.80694e11i | − | 0.159253i | ||||||
\(66\) | −6.98222e12 | − | 3.78498e12i | −1.27993 | − | 0.693834i | ||||
\(67\) | −2.32014e12 | −0.382817 | −0.191408 | − | 0.981510i | \(-0.561305\pi\) | ||||
−0.191408 | + | 0.981510i | \(0.561305\pi\) | |||||||
\(68\) | 2.31746e13i | 3.44707i | ||||||||
\(69\) | 3.38219e10 | − | 6.23919e10i | 0.00454207 | − | 0.00837886i | ||||
\(70\) | 2.50044e12 | 0.303619 | ||||||||
\(71\) | − | 1.42262e13i | − | 1.56415i | −0.623182 | − | 0.782077i | \(-0.714160\pi\) | ||
0.623182 | − | 0.782077i | \(-0.285840\pi\) | |||||||
\(72\) | 1.64315e13 | − | 1.07021e13i | 1.63813 | − | 1.06694i | ||||
\(73\) | −1.06676e13 | −0.965622 | −0.482811 | − | 0.875725i | \(-0.660384\pi\) | ||||
−0.482811 | + | 0.875725i | \(0.660384\pi\) | |||||||
\(74\) | − | 9.90062e12i | − | 0.814780i | ||||||
\(75\) | 1.07038e13 | + | 5.80240e12i | 0.801880 | + | 0.434689i | ||||
\(76\) | −1.35696e13 | −0.926560 | ||||||||
\(77\) | 7.69778e12i | 0.479656i | ||||||||
\(78\) | −7.92921e12 | + | 1.46272e13i | −0.451406 | + | 0.832718i | ||||
\(79\) | 3.21572e13 | 1.67451 | 0.837256 | − | 0.546812i | \(-0.184159\pi\) | ||||
0.837256 | + | 0.546812i | \(0.184159\pi\) | |||||||
\(80\) | − | 8.31903e12i | − | 0.396682i | ||||||
\(81\) | −9.24873e12 | + | 2.09239e13i | −0.404284 | + | 0.914633i | ||||
\(82\) | −2.50864e13 | −1.00633 | ||||||||
\(83\) | − | 1.21884e13i | − | 0.449159i | −0.974456 | − | 0.224580i | \(-0.927899\pi\) | ||
0.974456 | − | 0.224580i | \(-0.0721009\pi\) | |||||||
\(84\) | −3.17787e13 | − | 1.72268e13i | −1.07691 | − | 0.583782i | ||||
\(85\) | −1.55344e13 | −0.484575 | ||||||||
\(86\) | 2.26889e13i | 0.652114i | ||||||||
\(87\) | 2.57969e13 | − | 4.75880e13i | 0.683805 | − | 1.26143i | ||||
\(88\) | 6.59706e13 | 1.61425 | ||||||||
\(89\) | 3.00312e13i | 0.678957i | 0.940614 | + | 0.339479i | \(0.110251\pi\) | ||||
−0.940614 | + | 0.339479i | \(0.889749\pi\) | |||||||
\(90\) | 1.36438e13 | + | 2.09481e13i | 0.285259 | + | 0.437973i | ||||
\(91\) | 1.61262e13 | 0.312063 | ||||||||
\(92\) | 1.12117e12i | 0.0200982i | ||||||||
\(93\) | −6.10799e13 | − | 3.31107e13i | −1.01512 | − | 0.550285i | ||||
\(94\) | 4.83768e13 | 0.746005 | ||||||||
\(95\) | − | 9.09597e12i | − | 0.130252i | ||||||
\(96\) | −1.44831e13 | + | 2.67173e13i | −0.192736 | + | 0.355544i | ||||
\(97\) | −5.28428e13 | −0.654009 | −0.327004 | − | 0.945023i | \(-0.606039\pi\) | ||||
−0.327004 | + | 0.945023i | \(0.606039\pi\) | |||||||
\(98\) | − | 1.01416e14i | − | 1.16822i | ||||||
\(99\) | −6.44903e13 | + | 4.20035e13i | −0.691907 | + | 0.450650i | ||||
\(100\) | −1.92346e14 | −1.92346 | ||||||||
\(101\) | 9.00471e13i | 0.839886i | 0.907551 | + | 0.419943i | \(0.137950\pi\) | ||||
−0.907551 | + | 0.419943i | \(0.862050\pi\) | |||||||
\(102\) | 2.91054e14 | + | 1.57777e14i | 2.53380 | + | 1.37354i | ||||
\(103\) | 9.84098e13 | 0.800162 | 0.400081 | − | 0.916480i | \(-0.368982\pi\) | ||||
0.400081 | + | 0.916480i | \(0.368982\pi\) | |||||||
\(104\) | − | 1.38203e14i | − | 1.05023i | ||||||
\(105\) | 1.15475e13 | − | 2.13018e13i | 0.0820656 | − | 0.151388i | ||||
\(106\) | −1.31309e14 | −0.873281 | ||||||||
\(107\) | 1.29015e14i | 0.803440i | 0.915763 | + | 0.401720i | \(0.131587\pi\) | ||||
−0.915763 | + | 0.401720i | \(0.868413\pi\) | |||||||
\(108\) | −2.90804e13 | − | 3.60234e14i | −0.169682 | − | 2.10193i | ||||
\(109\) | 1.17591e14 | 0.643265 | 0.321633 | − | 0.946865i | \(-0.395768\pi\) | ||||
0.321633 | + | 0.946865i | \(0.395768\pi\) | |||||||
\(110\) | 8.41043e13i | 0.431588i | ||||||||
\(111\) | −8.43458e13 | − | 4.57228e13i | −0.406259 | − | 0.220228i | ||||
\(112\) | 1.71840e14 | 0.777317 | ||||||||
\(113\) | − | 2.84987e14i | − | 1.21137i | −0.795705 | − | 0.605684i | \(-0.792899\pi\) | ||
0.795705 | − | 0.605684i | \(-0.207101\pi\) | |||||||
\(114\) | −9.23843e13 | + | 1.70423e14i | −0.369202 | + | 0.681075i | ||||
\(115\) | −7.51542e11 | −0.00282532 | ||||||||
\(116\) | 8.55148e14i | 3.02577i | ||||||||
\(117\) | 8.79939e13 | + | 1.35102e14i | 0.293192 | + | 0.450153i | ||||
\(118\) | −5.23446e14 | −1.64323 | ||||||||
\(119\) | − | 3.20882e14i | − | 0.949546i | ||||||
\(120\) | −1.82558e14 | − | 9.89626e13i | −0.509487 | − | 0.276186i | ||||
\(121\) | 1.20828e14 | 0.318179 | ||||||||
\(122\) | − | 9.54649e14i | − | 2.37315i | ||||||
\(123\) | −1.15853e14 | + | 2.13717e14i | −0.272003 | + | 0.501769i | ||||
\(124\) | 1.09760e15 | 2.43495 | ||||||||
\(125\) | − | 2.70287e14i | − | 0.566834i | ||||||
\(126\) | −4.32709e14 | + | 2.81830e14i | −0.858227 | + | 0.558977i | ||||
\(127\) | −1.21233e14 | −0.227506 | −0.113753 | − | 0.993509i | \(-0.536287\pi\) | ||||
−0.113753 | + | 0.993509i | \(0.536287\pi\) | |||||||
\(128\) | 8.48106e14i | 1.50654i | ||||||||
\(129\) | 1.93292e14 | + | 1.04781e14i | 0.325152 | + | 0.176261i | ||||
\(130\) | 1.76192e14 | 0.280790 | ||||||||
\(131\) | 4.29478e14i | 0.648697i | 0.945938 | + | 0.324348i | \(0.105145\pi\) | ||||
−0.945938 | + | 0.324348i | \(0.894855\pi\) | |||||||
\(132\) | 5.79440e14 | − | 1.06890e15i | 0.829833 | − | 1.53081i | ||||
\(133\) | 1.87889e14 | 0.255234 | ||||||||
\(134\) | − | 5.23623e14i | − | 0.674971i | ||||||
\(135\) | 2.41471e14 | − | 1.94931e13i | 0.295481 | − | 0.0238531i | ||||
\(136\) | −2.74998e15 | −3.19564 | ||||||||
\(137\) | 7.44475e14i | 0.821876i | 0.911663 | + | 0.410938i | \(0.134799\pi\) | ||||
−0.911663 | + | 0.410938i | \(0.865201\pi\) | |||||||
\(138\) | 1.40810e13 | + | 7.63312e12i | 0.0147734 | + | 0.00800845i | ||||
\(139\) | −1.29615e15 | −1.29286 | −0.646431 | − | 0.762972i | \(-0.723739\pi\) | ||||
−0.646431 | + | 0.762972i | \(0.723739\pi\) | |||||||
\(140\) | 3.82790e14i | 0.363132i | ||||||||
\(141\) | 2.23412e14 | − | 4.12133e14i | 0.201639 | − | 0.371967i | ||||
\(142\) | 3.21065e15 | 2.75787 | ||||||||
\(143\) | 5.42419e14i | 0.443591i | ||||||||
\(144\) | 9.37659e14 | + | 1.43964e15i | 0.730310 | + | 1.12128i | ||||
\(145\) | −5.73221e14 | −0.425349 | ||||||||
\(146\) | − | 2.40753e15i | − | 1.70256i | ||||||
\(147\) | −8.63985e14 | − | 4.68356e14i | −0.582485 | − | 0.315758i | ||||
\(148\) | 1.51568e15 | 0.974486 | ||||||||
\(149\) | − | 9.69877e14i | − | 0.594857i | −0.954744 | − | 0.297429i | \(-0.903871\pi\) | ||
0.954744 | − | 0.297429i | \(-0.0961290\pi\) | |||||||
\(150\) | −1.30952e15 | + | 2.41570e15i | −0.766432 | + | 1.41385i | ||||
\(151\) | −1.01305e15 | −0.565966 | −0.282983 | − | 0.959125i | \(-0.591324\pi\) | ||||
−0.282983 | + | 0.959125i | \(0.591324\pi\) | |||||||
\(152\) | − | 1.61022e15i | − | 0.858974i | ||||||
\(153\) | 2.68827e15 | − | 1.75092e15i | 1.36973 | − | 0.892125i | ||||
\(154\) | −1.73728e15 | −0.845716 | ||||||||
\(155\) | 7.35738e14i | 0.342296i | ||||||||
\(156\) | −2.23926e15 | − | 1.21388e15i | −0.995940 | − | 0.539887i | ||||
\(157\) | 1.64534e15 | 0.699776 | 0.349888 | − | 0.936792i | \(-0.386220\pi\) | ||||
0.349888 | + | 0.936792i | \(0.386220\pi\) | |||||||
\(158\) | 7.25742e15i | 2.95245i | ||||||||
\(159\) | −6.06409e14 | + | 1.11865e15i | −0.236040 | + | 0.435428i | ||||
\(160\) | 3.21823e14 | 0.119888 | ||||||||
\(161\) | − | 1.55240e13i | − | 0.00553635i | ||||||
\(162\) | −4.72222e15 | − | 2.08731e15i | −1.61265 | − | 0.712823i | ||||
\(163\) | 2.55006e15 | 0.834137 | 0.417068 | − | 0.908875i | \(-0.363058\pi\) | ||||
0.417068 | + | 0.908875i | \(0.363058\pi\) | |||||||
\(164\) | − | 3.84046e15i | − | 1.20358i | ||||||
\(165\) | 7.16505e14 | + | 3.88409e14i | 0.215195 | + | 0.116654i | ||||
\(166\) | 2.75075e15 | 0.791945 | ||||||||
\(167\) | 8.83395e14i | 0.243859i | 0.992539 | + | 0.121930i | \(0.0389082\pi\) | ||||
−0.992539 | + | 0.121930i | \(0.961092\pi\) | |||||||
\(168\) | 2.04419e15 | − | 3.77097e15i | 0.541199 | − | 0.998361i | ||||
\(169\) | −2.80105e15 | −0.711401 | ||||||||
\(170\) | − | 3.50589e15i | − | 0.854388i | ||||||
\(171\) | 1.02523e15 | + | 1.57409e15i | 0.239800 | + | 0.368177i | ||||
\(172\) | −3.47343e15 | −0.779936 | ||||||||
\(173\) | − | 8.97288e14i | − | 0.193468i | −0.995310 | − | 0.0967340i | \(-0.969160\pi\) | ||
0.995310 | − | 0.0967340i | \(-0.0308396\pi\) | |||||||
\(174\) | 1.07399e16 | + | 5.82199e15i | 2.22411 | + | 1.20566i | ||||
\(175\) | 2.66326e15 | 0.529844 | ||||||||
\(176\) | 5.77999e15i | 1.10494i | ||||||||
\(177\) | −2.41736e15 | + | 4.45936e15i | −0.444150 | + | 0.819332i | ||||
\(178\) | −6.77761e15 | −1.19712 | ||||||||
\(179\) | − | 1.09489e16i | − | 1.85951i | −0.368178 | − | 0.929755i | \(-0.620018\pi\) | ||
0.368178 | − | 0.929755i | \(-0.379982\pi\) | |||||||
\(180\) | −3.20693e15 | + | 2.08873e15i | −0.523820 | + | 0.341172i | ||||
\(181\) | −6.47973e15 | −1.01814 | −0.509070 | − | 0.860725i | \(-0.670010\pi\) | ||||
−0.509070 | + | 0.860725i | \(0.670010\pi\) | |||||||
\(182\) | 3.63945e15i | 0.550220i | ||||||||
\(183\) | −8.13289e15 | − | 4.40874e15i | −1.18328 | − | 0.641441i | ||||
\(184\) | −1.33042e14 | −0.0186322 | ||||||||
\(185\) | 1.01599e15i | 0.136989i | ||||||||
\(186\) | 7.47261e15 | − | 1.37849e16i | 0.970246 | − | 1.78983i | ||||
\(187\) | 1.07931e16 | 1.34976 | ||||||||
\(188\) | 7.40597e15i | 0.892230i | ||||||||
\(189\) | 4.02655e14 | + | 4.98789e15i | 0.0467413 | + | 0.579008i | ||||
\(190\) | 2.05283e15 | 0.229656 | ||||||||
\(191\) | 1.10814e16i | 1.19498i | 0.801877 | + | 0.597490i | \(0.203835\pi\) | ||||
−0.801877 | + | 0.597490i | \(0.796165\pi\) | |||||||
\(192\) | 5.28564e15 | + | 2.86528e15i | 0.549527 | + | 0.297892i | ||||
\(193\) | −9.76570e15 | −0.979044 | −0.489522 | − | 0.871991i | \(-0.662829\pi\) | ||||
−0.489522 | + | 0.871991i | \(0.662829\pi\) | |||||||
\(194\) | − | 1.19259e16i | − | 1.15313i | ||||||
\(195\) | 8.13683e14 | − | 1.50102e15i | 0.0758950 | − | 0.140005i | ||||
\(196\) | 1.55257e16 | 1.39720 | ||||||||
\(197\) | 1.03403e16i | 0.897984i | 0.893536 | + | 0.448992i | \(0.148217\pi\) | ||||
−0.893536 | + | 0.448992i | \(0.851783\pi\) | |||||||
\(198\) | −9.47961e15 | − | 1.45545e16i | −0.794573 | − | 1.21995i | ||||
\(199\) | 1.32910e16 | 1.07544 | 0.537721 | − | 0.843123i | \(-0.319285\pi\) | ||||
0.537721 | + | 0.843123i | \(0.319285\pi\) | |||||||
\(200\) | − | 2.28244e16i | − | 1.78316i | ||||||
\(201\) | −4.46087e15 | − | 2.41818e15i | −0.336548 | − | 0.182439i | ||||
\(202\) | −2.03224e16 | −1.48086 | ||||||||
\(203\) | − | 1.18406e16i | − | 0.833491i | ||||||
\(204\) | −2.41539e16 | + | 4.45572e16i | −1.64277 | + | 3.03045i | ||||
\(205\) | 2.57433e15 | 0.169195 | ||||||||
\(206\) | 2.22097e16i | 1.41082i | ||||||||
\(207\) | 1.30057e14 | − | 8.47081e13i | 0.00798621 | − | 0.00520155i | ||||
\(208\) | 1.21086e16 | 0.718870 | ||||||||
\(209\) | 6.31980e15i | 0.362810i | ||||||||
\(210\) | 4.80752e15 | + | 2.60610e15i | 0.266923 | + | 0.144696i | ||||
\(211\) | 1.38905e16 | 0.746003 | 0.373001 | − | 0.927831i | \(-0.378329\pi\) | ||||
0.373001 | + | 0.927831i | \(0.378329\pi\) | |||||||
\(212\) | − | 2.01020e16i | − | 1.04445i | ||||||
\(213\) | 1.48273e16 | − | 2.73523e16i | 0.745428 | − | 1.37511i | ||||
\(214\) | −2.91168e16 | −1.41660 | ||||||||
\(215\) | − | 2.32830e15i | − | 0.109640i | ||||||
\(216\) | 4.27466e16 | − | 3.45078e15i | 1.94861 | − | 0.157305i | ||||
\(217\) | −1.51976e16 | −0.670743 | ||||||||
\(218\) | 2.65387e16i | 1.13419i | ||||||||
\(219\) | −2.05103e16 | − | 1.11184e16i | −0.848914 | − | 0.460186i | ||||
\(220\) | −1.28755e16 | −0.516184 | ||||||||
\(221\) | − | 2.26107e16i | − | 0.878149i | ||||||
\(222\) | 1.03190e16 | − | 1.90357e16i | 0.388299 | − | 0.716303i | ||||
\(223\) | −1.51743e14 | −0.00553317 | −0.00276659 | − | 0.999996i | \(-0.500881\pi\) | ||||
−0.00276659 | + | 0.999996i | \(0.500881\pi\) | |||||||
\(224\) | 6.64765e15i | 0.234926i | ||||||||
\(225\) | 1.45323e16 | + | 2.23122e16i | 0.497803 | + | 0.764303i | ||||
\(226\) | 6.43176e16 | 2.13585 | ||||||||
\(227\) | 5.26622e16i | 1.69558i | 0.530332 | + | 0.847790i | \(0.322067\pi\) | ||||
−0.530332 | + | 0.847790i | \(0.677933\pi\) | |||||||
\(228\) | −2.60900e16 | − | 1.41431e16i | −0.814573 | − | 0.441570i | ||||
\(229\) | −1.16961e16 | −0.354154 | −0.177077 | − | 0.984197i | \(-0.556664\pi\) | ||||
−0.177077 | + | 0.984197i | \(0.556664\pi\) | |||||||
\(230\) | − | 1.69612e14i | − | 0.00498153i | ||||||
\(231\) | −8.02306e15 | + | 1.48003e16i | −0.228589 | + | 0.421684i | ||||
\(232\) | −1.01475e17 | −2.80506 | ||||||||
\(233\) | − | 8.01172e14i | − | 0.0214899i | −0.999942 | − | 0.0107450i | \(-0.996580\pi\) | ||
0.999942 | − | 0.0107450i | \(-0.00342029\pi\) | |||||||
\(234\) | −3.04905e16 | + | 1.98590e16i | −0.793696 | + | 0.516947i | ||||
\(235\) | −4.96435e15 | −0.125426 | ||||||||
\(236\) | − | 8.01340e16i | − | 1.96532i | ||||||
\(237\) | 6.18277e16 | + | 3.35160e16i | 1.47212 | + | 0.798021i | ||||
\(238\) | 7.24184e16 | 1.67421 | ||||||||
\(239\) | − | 6.36561e16i | − | 1.42907i | −0.699598 | − | 0.714536i | \(-0.746638\pi\) | ||
0.699598 | − | 0.714536i | \(-0.253362\pi\) | |||||||
\(240\) | 8.67057e15 | − | 1.59948e16i | 0.189047 | − | 0.348738i | ||||
\(241\) | −6.17574e16 | −1.30789 | −0.653943 | − | 0.756544i | \(-0.726886\pi\) | ||||
−0.653943 | + | 0.756544i | \(0.726886\pi\) | |||||||
\(242\) | 2.72693e16i | 0.561004i | ||||||||
\(243\) | −3.95903e16 | + | 3.05902e16i | −0.791308 | + | 0.611418i | ||||
\(244\) | 1.46147e17 | 2.83831 | ||||||||
\(245\) | 1.04071e16i | 0.196412i | ||||||||
\(246\) | −4.82329e16 | − | 2.61465e16i | −0.884704 | − | 0.479587i | ||||
\(247\) | 1.32394e16 | 0.236043 | ||||||||
\(248\) | 1.30244e17i | 2.25734i | ||||||||
\(249\) | 1.27035e16 | − | 2.34343e16i | 0.214056 | − | 0.394873i | ||||
\(250\) | 6.10000e16 | 0.999424 | ||||||||
\(251\) | − | 3.71900e16i | − | 0.592530i | −0.955106 | − | 0.296265i | \(-0.904259\pi\) | ||
0.955106 | − | 0.296265i | \(-0.0957411\pi\) | |||||||
\(252\) | −4.31452e16 | − | 6.62431e16i | −0.668542 | − | 1.02645i | ||||
\(253\) | 5.22164e14 | 0.00786979 | ||||||||
\(254\) | − | 2.73605e16i | − | 0.401132i | ||||||
\(255\) | −2.98675e16 | − | 1.61908e16i | −0.426008 | − | 0.230934i | ||||
\(256\) | −1.46364e17 | −2.03121 | ||||||||
\(257\) | − | 1.85887e15i | − | 0.0251025i | −0.999921 | − | 0.0125512i | \(-0.996005\pi\) | ||
0.999921 | − | 0.0125512i | \(-0.00399529\pi\) | |||||||
\(258\) | −2.36476e16 | + | 4.36233e16i | −0.310778 | + | 0.573298i | ||||
\(259\) | −2.09865e16 | −0.268436 | ||||||||
\(260\) | 2.69730e16i | 0.335828i | ||||||||
\(261\) | 9.91978e16 | − | 6.46091e16i | 1.20232 | − | 0.783088i | ||||
\(262\) | −9.69271e16 | −1.14376 | ||||||||
\(263\) | 8.73906e16i | 1.00409i | 0.864840 | + | 0.502047i | \(0.167420\pi\) | ||||
−0.864840 | + | 0.502047i | \(0.832580\pi\) | |||||||
\(264\) | 1.26840e17 | + | 6.87583e16i | 1.41915 | + | 0.769303i | ||||
\(265\) | 1.34747e16 | 0.146825 | ||||||||
\(266\) | 4.24038e16i | 0.450022i | ||||||||
\(267\) | −3.13002e16 | + | 5.77401e16i | −0.323570 | + | 0.596896i | ||||
\(268\) | 8.01611e16 | 0.807273 | ||||||||
\(269\) | − | 1.26379e17i | − | 1.23996i | −0.784616 | − | 0.619982i | \(-0.787140\pi\) | ||
0.784616 | − | 0.619982i | \(-0.212860\pi\) | |||||||
\(270\) | 4.39932e15 | + | 5.44967e16i | 0.0420571 | + | 0.520983i | ||||
\(271\) | 5.86413e16 | 0.546284 | 0.273142 | − | 0.961974i | \(-0.411937\pi\) | ||||
0.273142 | + | 0.961974i | \(0.411937\pi\) | |||||||
\(272\) | − | 2.40939e17i | − | 2.18738i | ||||||
\(273\) | 3.10054e16 | + | 1.68076e16i | 0.274346 | + | 0.148720i | ||||
\(274\) | −1.68017e17 | −1.44911 | ||||||||
\(275\) | 8.95812e16i | 0.753162i | ||||||||
\(276\) | −1.16855e15 | + | 2.15565e15i | −0.00957819 | + | 0.0176691i | ||||
\(277\) | 1.76150e17 | 1.40774 | 0.703872 | − | 0.710327i | \(-0.251453\pi\) | ||||
0.703872 | + | 0.710327i | \(0.251453\pi\) | |||||||
\(278\) | − | 2.92523e17i | − | 2.27954i | ||||||
\(279\) | −8.29269e16 | − | 1.27322e17i | −0.630182 | − | 0.967551i | ||||
\(280\) | −4.54232e16 | −0.336644 | ||||||||
\(281\) | 1.87231e17i | 1.35342i | 0.736249 | + | 0.676711i | \(0.236595\pi\) | ||||
−0.736249 | + | 0.676711i | \(0.763405\pi\) | |||||||
\(282\) | 9.30127e16 | + | 5.04210e16i | 0.655841 | + | 0.355523i | ||||
\(283\) | −1.05273e16 | −0.0724121 | −0.0362060 | − | 0.999344i | \(-0.511527\pi\) | ||||
−0.0362060 | + | 0.999344i | \(0.511527\pi\) | |||||||
\(284\) | 4.91516e17i | 3.29844i | ||||||||
\(285\) | 9.48034e15 | − | 1.74886e16i | 0.0620740 | − | 0.114509i | ||||
\(286\) | −1.22416e17 | −0.782126 | ||||||||
\(287\) | 5.31760e16i | 0.331545i | ||||||||
\(288\) | −5.56925e16 | + | 3.62734e16i | −0.338883 | + | 0.220720i | ||||
\(289\) | −2.81534e17 | −1.67203 | ||||||||
\(290\) | − | 1.29368e17i | − | 0.749964i | ||||||
\(291\) | −1.01599e17 | − | 5.50758e16i | −0.574963 | − | 0.311680i | ||||
\(292\) | 3.68567e17 | 2.03627 | ||||||||
\(293\) | − | 2.07675e17i | − | 1.12024i | −0.828411 | − | 0.560121i | \(-0.810755\pi\) | ||
0.828411 | − | 0.560121i | \(-0.189245\pi\) | |||||||
\(294\) | 1.05701e17 | − | 1.94989e17i | 0.556736 | − | 1.02702i | ||||
\(295\) | 5.37152e16 | 0.276276 | ||||||||
\(296\) | 1.79856e17i | 0.903405i | ||||||||
\(297\) | −1.67772e17 | + | 1.35436e16i | −0.823047 | + | 0.0664417i | ||||
\(298\) | 2.18887e17 | 1.04883 | ||||||||
\(299\) | − | 1.09389e15i | − | 0.00512006i | ||||||
\(300\) | −3.69818e17 | − | 2.00474e17i | −1.69098 | − | 0.916660i | ||||
\(301\) | 4.80939e16 | 0.214845 | ||||||||
\(302\) | − | 2.28630e17i | − | 0.997895i | ||||||
\(303\) | −9.38523e16 | + | 1.73131e17i | −0.400264 | + | 0.738375i | ||||
\(304\) | 1.41079e17 | 0.587959 | ||||||||
\(305\) | 9.79646e16i | 0.398998i | ||||||||
\(306\) | 3.95157e17 | + | 6.06706e17i | 1.57297 | + | 2.41506i | ||||
\(307\) | 3.26458e17 | 1.27016 | 0.635081 | − | 0.772446i | \(-0.280967\pi\) | ||||
0.635081 | + | 0.772446i | \(0.280967\pi\) | |||||||
\(308\) | − | 2.65959e17i | − | 1.01149i | ||||||
\(309\) | 1.89210e17 | + | 1.02568e17i | 0.703452 | + | 0.381333i | ||||
\(310\) | −1.66046e17 | −0.603526 | ||||||||
\(311\) | − | 3.94473e17i | − | 1.40183i | −0.713245 | − | 0.700915i | \(-0.752775\pi\) | ||
0.713245 | − | 0.700915i | \(-0.247225\pi\) | |||||||
\(312\) | 1.44043e17 | − | 2.65719e17i | 0.500506 | − | 0.923294i | ||||
\(313\) | −4.19357e17 | −1.42486 | −0.712432 | − | 0.701741i | \(-0.752406\pi\) | ||||
−0.712432 | + | 0.701741i | \(0.752406\pi\) | |||||||
\(314\) | 3.71331e17i | 1.23382i | ||||||||
\(315\) | 4.44039e16 | − | 2.89210e16i | 0.144294 | − | 0.0939809i | ||||
\(316\) | −1.11103e18 | −3.53116 | ||||||||
\(317\) | 3.68072e17i | 1.14424i | 0.820170 | + | 0.572120i | \(0.193879\pi\) | ||||
−0.820170 | + | 0.572120i | \(0.806121\pi\) | |||||||
\(318\) | −2.52465e17 | − | 1.36858e17i | −0.767734 | − | 0.416179i | ||||
\(319\) | 3.98268e17 | 1.18479 | ||||||||
\(320\) | − | 6.36682e16i | − | 0.185299i | ||||||
\(321\) | −1.34467e17 | + | 2.48053e17i | −0.382895 | + | 0.706334i | ||||
\(322\) | 3.50355e15 | 0.00976152 | ||||||||
\(323\) | − | 2.63441e17i | − | 0.718232i | ||||||
\(324\) | 3.19545e17 | − | 7.22922e17i | 0.852543 | − | 1.92875i | ||||
\(325\) | 1.87665e17 | 0.490005 | ||||||||
\(326\) | 5.75513e17i | 1.47073i | ||||||||
\(327\) | 2.26090e17 | + | 1.22561e17i | 0.565518 | + | 0.306561i | ||||
\(328\) | 4.55722e17 | 1.11579 | ||||||||
\(329\) | − | 1.02545e17i | − | 0.245778i | ||||||
\(330\) | −8.76583e16 | + | 1.61705e17i | −0.205682 | + | 0.379425i | ||||
\(331\) | 1.46374e17 | 0.336255 | 0.168127 | − | 0.985765i | \(-0.446228\pi\) | ||||
0.168127 | + | 0.985765i | \(0.446228\pi\) | |||||||
\(332\) | 4.21111e17i | 0.947174i | ||||||||
\(333\) | −1.14514e17 | − | 1.75820e17i | −0.252203 | − | 0.387221i | ||||
\(334\) | −1.99370e17 | −0.429966 | ||||||||
\(335\) | 5.37334e16i | 0.113483i | ||||||||
\(336\) | 3.30392e17 | + | 1.79101e17i | 0.683368 | + | 0.370445i | ||||
\(337\) | −5.56586e17 | −1.12752 | −0.563758 | − | 0.825940i | \(-0.690645\pi\) | ||||
−0.563758 | + | 0.825940i | \(0.690645\pi\) | |||||||
\(338\) | − | 6.32158e17i | − | 1.25432i | ||||||
\(339\) | 2.97030e17 | − | 5.47937e17i | 0.577301 | − | 1.06496i | ||||
\(340\) | 5.36714e17 | 1.02186 | ||||||||
\(341\) | − | 5.11184e17i | − | 0.953447i | ||||||
\(342\) | −3.55250e17 | + | 2.31380e17i | −0.649159 | + | 0.422808i | ||||
\(343\) | −5.39427e17 | −0.965770 | ||||||||
\(344\) | − | 4.12169e17i | − | 0.723046i | ||||||
\(345\) | −1.44497e15 | − | 7.83299e14i | −0.00248385 | − | 0.00134646i | ||||
\(346\) | 2.02505e17 | 0.341117 | ||||||||
\(347\) | − | 5.48397e16i | − | 0.0905292i | −0.998975 | − | 0.0452646i | \(-0.985587\pi\) | ||
0.998975 | − | 0.0452646i | \(-0.0144131\pi\) | |||||||
\(348\) | −8.91284e17 | + | 1.64417e18i | −1.44199 | + | 2.66006i | ||||
\(349\) | 5.77040e17 | 0.915014 | 0.457507 | − | 0.889206i | \(-0.348742\pi\) | ||||
0.457507 | + | 0.889206i | \(0.348742\pi\) | |||||||
\(350\) | 6.01061e17i | 0.934205i | ||||||||
\(351\) | 2.83728e16 | + | 3.51469e17i | 0.0432267 | + | 0.535472i | ||||
\(352\) | −2.23599e17 | −0.333943 | ||||||||
\(353\) | 8.97000e17i | 1.31332i | 0.754188 | + | 0.656658i | \(0.228031\pi\) | ||||
−0.754188 | + | 0.656658i | \(0.771969\pi\) | |||||||
\(354\) | −1.00641e18 | − | 5.45565e17i | −1.44462 | − | 0.783112i | ||||
\(355\) | −3.29472e17 | −0.463681 | ||||||||
\(356\) | − | 1.03758e18i | − | 1.43177i | ||||||
\(357\) | 3.34441e17 | − | 6.16950e17i | 0.452525 | − | 0.834781i | ||||
\(358\) | 2.47101e18 | 3.27863 | ||||||||
\(359\) | 1.18291e18i | 1.53918i | 0.638540 | + | 0.769589i | \(0.279539\pi\) | ||||
−0.638540 | + | 0.769589i | \(0.720461\pi\) | |||||||
\(360\) | −2.47855e17 | − | 3.80545e17i | −0.316286 | − | 0.485611i | ||||
\(361\) | −6.44752e17 | −0.806942 | ||||||||
\(362\) | − | 1.46238e18i | − | 1.79515i | ||||||
\(363\) | 2.32313e17 | + | 1.25934e17i | 0.279723 | + | 0.151634i | ||||
\(364\) | −5.57162e17 | −0.658069 | ||||||||
\(365\) | 2.47057e17i | 0.286251i | ||||||||
\(366\) | 9.94989e17 | − | 1.83548e18i | 1.13097 | − | 2.08632i | ||||
\(367\) | −1.25177e18 | −1.39592 | −0.697962 | − | 0.716135i | \(-0.745909\pi\) | ||||
−0.697962 | + | 0.716135i | \(0.745909\pi\) | |||||||
\(368\) | − | 1.16564e16i | − | 0.0127535i | ||||||
\(369\) | −4.45496e17 | + | 2.90159e17i | −0.478255 | + | 0.311495i | ||||
\(370\) | −2.29294e17 | −0.241535 | ||||||||
\(371\) | 2.78338e17i | 0.287710i | ||||||||
\(372\) | 2.11032e18 | + | 1.14398e18i | 2.14066 | + | 1.16042i | ||||
\(373\) | 1.64900e18 | 1.64157 | 0.820783 | − | 0.571240i | \(-0.193538\pi\) | ||||
0.820783 | + | 0.571240i | \(0.193538\pi\) | |||||||
\(374\) | 2.43586e18i | 2.37986i | ||||||||
\(375\) | 2.81709e17 | − | 5.19674e17i | 0.270135 | − | 0.498324i | ||||
\(376\) | −8.78817e17 | −0.827149 | ||||||||
\(377\) | − | 8.34339e17i | − | 0.770820i | ||||||
\(378\) | −1.12570e18 | + | 9.08735e16i | −1.02089 | + | 0.0824128i | ||||
\(379\) | −2.49403e17 | −0.222038 | −0.111019 | − | 0.993818i | \(-0.535411\pi\) | ||||
−0.111019 | + | 0.993818i | \(0.535411\pi\) | |||||||
\(380\) | 3.14267e17i | 0.274671i | ||||||||
\(381\) | −2.33091e17 | − | 1.26356e17i | −0.200009 | − | 0.108422i | ||||
\(382\) | −2.50091e18 | −2.10695 | ||||||||
\(383\) | − | 7.17438e17i | − | 0.593462i | −0.954961 | − | 0.296731i | \(-0.904104\pi\) | ||
0.954961 | − | 0.296731i | \(-0.0958965\pi\) | |||||||
\(384\) | −8.83944e17 | + | 1.63063e18i | −0.717970 | + | 1.32445i | ||||
\(385\) | 1.78277e17 | 0.142190 | ||||||||
\(386\) | − | 2.20398e18i | − | 1.72622i | ||||||
\(387\) | 2.62428e17 | + | 4.02920e17i | 0.201852 | + | 0.309915i | ||||
\(388\) | 1.82572e18 | 1.37915 | ||||||||
\(389\) | − | 2.36642e18i | − | 1.75568i | −0.478958 | − | 0.877838i | \(-0.658985\pi\) | ||
0.478958 | − | 0.877838i | \(-0.341015\pi\) | |||||||
\(390\) | 3.38759e17 | + | 1.83637e17i | 0.246853 | + | 0.133816i | ||||
\(391\) | −2.17664e16 | −0.0155793 | ||||||||
\(392\) | 1.84233e18i | 1.29528i | ||||||||
\(393\) | −4.47626e17 | + | 8.25745e17i | −0.309149 | + | 0.570293i | ||||
\(394\) | −2.33365e18 | −1.58330 | ||||||||
\(395\) | − | 7.44745e17i | − | 0.496396i | ||||||
\(396\) | 2.22815e18 | − | 1.45123e18i | 1.45907 | − | 0.950318i | ||||
\(397\) | 9.86307e17 | 0.634569 | 0.317284 | − | 0.948330i | \(-0.397229\pi\) | ||||
0.317284 | + | 0.948330i | \(0.397229\pi\) | |||||||
\(398\) | 2.99960e18i | 1.89619i | ||||||||
\(399\) | 3.61248e17 | + | 1.95828e17i | 0.224386 | + | 0.121637i | ||||
\(400\) | 1.99975e18 | 1.22055 | ||||||||
\(401\) | 2.15290e18i | 1.29126i | 0.763651 | + | 0.645629i | \(0.223405\pi\) | ||||
−0.763651 | + | 0.645629i | \(0.776595\pi\) | |||||||
\(402\) | 5.45750e17 | − | 1.00676e18i | 0.321671 | − | 0.593392i | ||||
\(403\) | −1.07089e18 | −0.620310 | ||||||||
\(404\) | − | 3.11114e18i | − | 1.77113i | ||||||
\(405\) | 4.84587e17 | + | 2.14196e17i | 0.271136 | + | 0.119847i | ||||
\(406\) | 2.67225e18 | 1.46959 | ||||||||
\(407\) | − | 7.05898e17i | − | 0.381576i | ||||||
\(408\) | −5.28731e18 | − | 2.86619e18i | −2.80940 | − | 1.52294i | ||||
\(409\) | 3.32383e18 | 1.73610 | 0.868052 | − | 0.496474i | \(-0.165372\pi\) | ||||
0.868052 | + | 0.496474i | \(0.165372\pi\) | |||||||
\(410\) | 5.80990e17i | 0.298319i | ||||||||
\(411\) | −7.75934e17 | + | 1.43138e18i | −0.391681 | + | 0.722541i | ||||
\(412\) | −3.40007e18 | −1.68736 | ||||||||
\(413\) | 1.10955e18i | 0.541375i | ||||||||
\(414\) | 1.91174e16 | + | 2.93520e16i | 0.00917122 | + | 0.0140811i | ||||
\(415\) | −2.82278e17 | −0.133150 | ||||||||
\(416\) | 4.68422e17i | 0.217262i | ||||||||
\(417\) | −2.49208e18 | − | 1.35092e18i | −1.13660 | − | 0.616139i | ||||
\(418\) | −1.42629e18 | −0.639696 | ||||||||
\(419\) | 2.14089e18i | 0.944272i | 0.881526 | + | 0.472136i | \(0.156517\pi\) | ||||
−0.881526 | + | 0.472136i | \(0.843483\pi\) | |||||||
\(420\) | −3.98966e17 | + | 7.35980e17i | −0.173058 | + | 0.319243i | ||||
\(421\) | 8.73440e17 | 0.372613 | 0.186307 | − | 0.982492i | \(-0.440348\pi\) | ||||
0.186307 | + | 0.982492i | \(0.440348\pi\) | |||||||
\(422\) | 3.13489e18i | 1.31533i | ||||||||
\(423\) | 8.59098e17 | − | 5.59544e17i | 0.354536 | − | 0.230915i | ||||
\(424\) | 2.38538e18 | 0.968269 | ||||||||
\(425\) | − | 3.73419e18i | − | 1.49099i | ||||||
\(426\) | 6.17302e18 | + | 3.34632e18i | 2.42455 | + | 1.31432i | ||||
\(427\) | −2.02358e18 | −0.781854 | ||||||||
\(428\) | − | 4.45748e18i | − | 1.69427i | ||||||
\(429\) | −5.65340e17 | + | 1.04289e18i | −0.211402 | + | 0.389977i | ||||
\(430\) | 5.25464e17 | 0.193314 | ||||||||
\(431\) | 5.74588e17i | 0.207977i | 0.994578 | + | 0.103989i | \(0.0331605\pi\) | ||||
−0.994578 | + | 0.103989i | \(0.966839\pi\) | |||||||
\(432\) | 3.02339e17 | + | 3.74523e18i | 0.107673 | + | 1.33381i | ||||
\(433\) | −1.73636e18 | −0.608450 | −0.304225 | − | 0.952600i | \(-0.598398\pi\) | ||||
−0.304225 | + | 0.952600i | \(0.598398\pi\) | |||||||
\(434\) | − | 3.42988e18i | − | 1.18264i | ||||||
\(435\) | −1.10212e18 | − | 5.97443e17i | −0.373940 | − | 0.202708i | ||||
\(436\) | −4.06280e18 | −1.35650 | ||||||||
\(437\) | − | 1.27451e16i | − | 0.00418767i | ||||||
\(438\) | 2.50926e18 | − | 4.62889e18i | 0.811386 | − | 1.49678i | ||||
\(439\) | 2.13182e17 | 0.0678419 | 0.0339209 | − | 0.999425i | \(-0.489201\pi\) | ||||
0.0339209 | + | 0.999425i | \(0.489201\pi\) | |||||||
\(440\) | − | 1.52785e18i | − | 0.478532i | ||||||
\(441\) | −1.17301e18 | − | 1.80099e18i | −0.361604 | − | 0.555189i | ||||
\(442\) | 5.10292e18 | 1.54833 | ||||||||
\(443\) | 1.81656e18i | 0.542530i | 0.962505 | + | 0.271265i | \(0.0874420\pi\) | ||||
−0.962505 | + | 0.271265i | \(0.912558\pi\) | |||||||
\(444\) | 2.91416e18 | + | 1.57973e18i | 0.856707 | + | 0.464410i | ||||
\(445\) | 6.95508e17 | 0.201272 | ||||||||
\(446\) | − | 3.42462e16i | − | 0.00975593i | ||||||
\(447\) | 1.01086e18 | − | 1.86476e18i | 0.283491 | − | 0.522961i | ||||
\(448\) | 1.31515e18 | 0.363101 | ||||||||
\(449\) | 4.45737e18i | 1.21158i | 0.795623 | + | 0.605792i | \(0.207144\pi\) | ||||
−0.795623 | + | 0.605792i | \(0.792856\pi\) | |||||||
\(450\) | −5.03556e18 | + | 3.27974e18i | −1.34760 | + | 0.877711i | ||||
\(451\) | −1.78862e18 | −0.471283 | ||||||||
\(452\) | 9.84634e18i | 2.55450i | ||||||||
\(453\) | −1.94775e18 | − | 1.05585e18i | −0.497562 | − | 0.269722i | ||||
\(454\) | −1.18851e19 | −2.98960 | ||||||||
\(455\) | − | 3.73475e17i | − | 0.0925086i | ||||||
\(456\) | 1.67826e18 | − | 3.09593e18i | 0.409361 | − | 0.755156i | ||||
\(457\) | 1.94241e18 | 0.466581 | 0.233290 | − | 0.972407i | \(-0.425051\pi\) | ||||
0.233290 | + | 0.972407i | \(0.425051\pi\) | |||||||
\(458\) | − | 2.63964e18i | − | 0.624434i | ||||||
\(459\) | 6.99358e18 | − | 5.64567e17i | 1.62934 | − | 0.131530i | ||||
\(460\) | 2.59658e16 | 0.00595796 | ||||||||
\(461\) | 1.12266e18i | 0.253713i | 0.991921 | + | 0.126856i | \(0.0404888\pi\) | ||||
−0.991921 | + | 0.126856i | \(0.959511\pi\) | |||||||
\(462\) | −3.34022e18 | − | 1.81069e18i | −0.743500 | − | 0.403042i | ||||
\(463\) | 3.87736e18 | 0.850098 | 0.425049 | − | 0.905170i | \(-0.360257\pi\) | ||||
0.425049 | + | 0.905170i | \(0.360257\pi\) | |||||||
\(464\) | − | 8.89068e18i | − | 1.92003i | ||||||
\(465\) | −7.66828e17 | + | 1.41458e18i | −0.163128 | + | 0.300925i | ||||
\(466\) | 1.80813e17 | 0.0378904 | ||||||||
\(467\) | − | 2.71349e18i | − | 0.560156i | −0.959977 | − | 0.280078i | \(-0.909640\pi\) | ||
0.959977 | − | 0.280078i | \(-0.0903604\pi\) | |||||||
\(468\) | −3.04020e18 | − | 4.66778e18i | −0.618274 | − | 0.949269i | ||||
\(469\) | −1.10993e18 | −0.222375 | ||||||||
\(470\) | − | 1.12038e18i | − | 0.221147i | ||||||
\(471\) | 3.16346e18 | + | 1.71487e18i | 0.615199 | + | 0.333492i | ||||
\(472\) | 9.50897e18 | 1.82196 | ||||||||
\(473\) | 1.61768e18i | 0.305397i | ||||||||
\(474\) | −7.56409e18 | + | 1.39536e19i | −1.40705 | + | 2.59561i | ||||
\(475\) | 2.18651e18 | 0.400772 | ||||||||
\(476\) | 1.10865e19i | 2.00238i | ||||||||
\(477\) | −2.33185e18 | + | 1.51877e18i | −0.415023 | + | 0.270311i | ||||
\(478\) | 1.43663e19 | 2.51970 | ||||||||
\(479\) | − | 9.98368e18i | − | 1.72561i | −0.505538 | − | 0.862804i | \(-0.668706\pi\) | ||
0.505538 | − | 0.862804i | \(-0.331294\pi\) | |||||||
\(480\) | 6.18760e17 | + | 3.35422e17i | 0.105398 | + | 0.0571351i | ||||
\(481\) | −1.47880e18 | −0.248252 | ||||||||
\(482\) | − | 1.39378e19i | − | 2.30603i | ||||||
\(483\) | 1.61800e16 | − | 2.98476e16i | 0.00263845 | − | 0.00486721i | ||||
\(484\) | −4.17463e18 | −0.670967 | ||||||||
\(485\) | 1.22381e18i | 0.193876i | ||||||||
\(486\) | −6.90378e18 | − | 8.93498e18i | −1.07803 | − | 1.39521i | ||||
\(487\) | −7.04157e18 | −1.08384 | −0.541922 | − | 0.840429i | \(-0.682303\pi\) | ||||
−0.541922 | + | 0.840429i | \(0.682303\pi\) | |||||||
\(488\) | 1.73423e19i | 2.63128i | ||||||||
\(489\) | 4.90293e18 | + | 2.65782e18i | 0.733320 | + | 0.397524i | ||||
\(490\) | −2.34874e18 | −0.346308 | ||||||||
\(491\) | − | 3.57849e18i | − | 0.520151i | −0.965588 | − | 0.260076i | \(-0.916253\pi\) | ||
0.965588 | − | 0.260076i | \(-0.0837475\pi\) | |||||||
\(492\) | 4.00275e18 | − | 7.38395e18i | 0.573591 | − | 1.05812i | ||||
\(493\) | −1.66018e19 | −2.34545 | ||||||||
\(494\) | 2.98796e18i | 0.416184i | ||||||||
\(495\) | 9.72783e17 | + | 1.49356e18i | 0.133592 | + | 0.205110i | ||||
\(496\) | −1.14113e19 | −1.54513 | ||||||||
\(497\) | − | 6.80564e18i | − | 0.908604i | ||||||
\(498\) | 5.28880e18 | + | 2.86699e18i | 0.696228 | + | 0.377416i | ||||
\(499\) | 1.27672e19 | 1.65726 | 0.828629 | − | 0.559797i | \(-0.189121\pi\) | ||||
0.828629 | + | 0.559797i | \(0.189121\pi\) | |||||||
\(500\) | 9.33845e18i | 1.19532i | ||||||||
\(501\) | −9.20724e17 | + | 1.69848e18i | −0.116216 | + | 0.214386i | ||||
\(502\) | 8.39326e18 | 1.04473 | ||||||||
\(503\) | 1.14021e19i | 1.39962i | 0.714330 | + | 0.699809i | \(0.246731\pi\) | ||||
−0.714330 | + | 0.699809i | \(0.753269\pi\) | |||||||
\(504\) | 7.86063e18 | − | 5.11976e18i | 0.951577 | − | 0.619777i | ||||
\(505\) | 2.08545e18 | 0.248978 | ||||||||
\(506\) | 1.17845e17i | 0.0138758i | ||||||||
\(507\) | −5.38551e18 | − | 2.91942e18i | −0.625419 | − | 0.339032i | ||||
\(508\) | 4.18860e18 | 0.479759 | ||||||||
\(509\) | 5.16333e18i | 0.583319i | 0.956522 | + | 0.291659i | \(0.0942073\pi\) | ||||
−0.956522 | + | 0.291659i | \(0.905793\pi\) | |||||||
\(510\) | 3.65403e18 | − | 6.74067e18i | 0.407175 | − | 0.751124i | ||||
\(511\) | −5.10327e18 | −0.560921 | ||||||||
\(512\) | − | 1.91369e19i | − | 2.07483i | ||||||
\(513\) | 3.30576e17 | + | 4.09501e18i | 0.0353549 | + | 0.437959i | ||||
\(514\) | 4.19520e17 | 0.0442599 | ||||||||
\(515\) | − | 2.27913e18i | − | 0.237202i | ||||||
\(516\) | −6.67826e18 | − | 3.62020e18i | −0.685670 | − | 0.371693i | ||||
\(517\) | 3.44919e18 | 0.349368 | ||||||||
\(518\) | − | 4.73635e18i | − | 0.473299i | ||||||
\(519\) | 9.35205e17 | − | 1.72519e18i | 0.0922009 | − | 0.170085i | ||||
\(520\) | −3.20071e18 | −0.311332 | ||||||||
\(521\) | − | 1.00727e19i | − | 0.966675i | −0.875434 | − | 0.483338i | \(-0.839424\pi\) | ||
0.875434 | − | 0.483338i | \(-0.160576\pi\) | |||||||
\(522\) | 1.45814e19 | + | 2.23875e19i | 1.38072 | + | 2.11989i | ||||
\(523\) | −7.35018e18 | −0.686730 | −0.343365 | − | 0.939202i | \(-0.611567\pi\) | ||||
−0.343365 | + | 0.939202i | \(0.611567\pi\) | |||||||
\(524\) | − | 1.48385e19i | − | 1.36795i | ||||||
\(525\) | 5.12059e18 | + | 2.77581e18i | 0.465805 | + | 0.252507i | ||||
\(526\) | −1.97228e19 | −1.77039 | ||||||||
\(527\) | 2.13087e19i | 1.88748i | ||||||||
\(528\) | −6.02423e18 | + | 1.11130e19i | −0.526580 | + | 0.971392i | ||||
\(529\) | 1.15918e19 | 0.999909 | ||||||||
\(530\) | 3.04106e18i | 0.258877i | ||||||||
\(531\) | −9.29560e18 | + | 6.05438e18i | −0.780937 | + | 0.508637i | ||||
\(532\) | −6.49157e18 | −0.538231 | ||||||||
\(533\) | 3.74701e18i | 0.306616i | ||||||||
\(534\) | −1.30311e19 | − | 7.06401e18i | −1.05243 | − | 0.570509i | ||||
\(535\) | 2.98793e18 | 0.238173 | ||||||||
\(536\) | 9.51219e18i | 0.748388i | ||||||||
\(537\) | 1.14115e19 | − | 2.10511e19i | 0.886185 | − | 1.63476i | ||||
\(538\) | 2.85220e19 | 2.18627 | ||||||||
\(539\) | − | 7.23078e18i | − | 0.547096i | ||||||
\(540\) | −8.34286e18 | + | 6.73490e17i | −0.623102 | + | 0.0503008i | ||||
\(541\) | −3.58953e18 | −0.264640 | −0.132320 | − | 0.991207i | \(-0.542243\pi\) | ||||
−0.132320 | + | 0.991207i | \(0.542243\pi\) | |||||||
\(542\) | 1.32345e19i | 0.963192i | ||||||||
\(543\) | −1.24584e19 | − | 6.75355e18i | −0.895084 | − | 0.485214i | ||||
\(544\) | 9.32074e18 | 0.661086 | ||||||||
\(545\) | − | 2.72336e18i | − | 0.190691i | ||||||
\(546\) | −3.79325e18 | + | 6.99748e18i | −0.262218 | + | 0.483719i | ||||
\(547\) | 4.53669e18 | 0.309619 | 0.154809 | − | 0.987944i | \(-0.450524\pi\) | ||||
0.154809 | + | 0.987944i | \(0.450524\pi\) | |||||||
\(548\) | − | 2.57217e19i | − | 1.73315i | ||||||
\(549\) | −1.10418e19 | − | 1.69531e19i | −0.734573 | − | 1.12783i | ||||
\(550\) | −2.02172e19 | −1.32795 | ||||||||
\(551\) | − | 9.72100e18i | − | 0.630449i | ||||||
\(552\) | −2.55796e17 | − | 1.38664e17i | −0.0163803 | − | 0.00887954i | ||||
\(553\) | 1.53836e19 | 0.972709 | ||||||||
\(554\) | 3.97545e19i | 2.48209i | ||||||||
\(555\) | −1.05892e18 | + | 1.95341e18i | −0.0652848 | + | 0.120432i | ||||
\(556\) | 4.47822e19 | 2.72635 | ||||||||
\(557\) | 6.89338e18i | 0.414425i | 0.978296 | + | 0.207212i | \(0.0664391\pi\) | ||||
−0.978296 | + | 0.207212i | \(0.933561\pi\) | |||||||
\(558\) | 2.87348e19 | − | 1.87154e19i | 1.70596 | − | 1.11112i | ||||
\(559\) | 3.38890e18 | 0.198690 | ||||||||
\(560\) | − | 3.97973e18i | − | 0.230429i | ||||||
\(561\) | 2.07517e19 | + | 1.12492e19i | 1.18662 | + | 0.643254i | ||||
\(562\) | −4.22554e19 | −2.38631 | ||||||||
\(563\) | − | 1.45922e18i | − | 0.0813883i | −0.999172 | − | 0.0406942i | \(-0.987043\pi\) | ||
0.999172 | − | 0.0406942i | \(-0.0129569\pi\) | |||||||
\(564\) | −7.71892e18 | + | 1.42393e19i | −0.425210 | + | 0.784393i | ||||
\(565\) | −6.60018e18 | −0.359101 | ||||||||
\(566\) | − | 2.37586e18i | − | 0.127675i | ||||||
\(567\) | −4.42449e18 | + | 1.00098e19i | −0.234845 | + | 0.531303i | ||||
\(568\) | −5.83249e19 | −3.05785 | ||||||||
\(569\) | 4.36385e18i | 0.225987i | 0.993596 | + | 0.112994i | \(0.0360440\pi\) | ||||
−0.993596 | + | 0.112994i | \(0.963956\pi\) | |||||||
\(570\) | 3.94692e18 | + | 2.13958e18i | 0.201899 | + | 0.109447i | ||||
\(571\) | 1.61706e19 | 0.817099 | 0.408549 | − | 0.912736i | \(-0.366035\pi\) | ||||
0.408549 | + | 0.912736i | \(0.366035\pi\) | |||||||
\(572\) | − | 1.87406e19i | − | 0.935431i | ||||||
\(573\) | −1.15496e19 | + | 2.13059e19i | −0.569490 | + | 1.05055i | ||||
\(574\) | −1.20011e19 | −0.584570 | ||||||||
\(575\) | − | 1.80658e17i | − | 0.00869323i | ||||||
\(576\) | 7.17620e18 | + | 1.10180e19i | 0.341143 | + | 0.523775i | ||||
\(577\) | 8.26639e17 | 0.0388227 | 0.0194113 | − | 0.999812i | \(-0.493821\pi\) | ||||
0.0194113 | + | 0.999812i | \(0.493821\pi\) | |||||||
\(578\) | − | 6.35381e19i | − | 2.94808i | ||||||
\(579\) | −1.87762e19 | − | 1.01784e19i | −0.860714 | − | 0.466582i | ||||
\(580\) | 1.98048e19 | 0.896965 | ||||||||
\(581\) | − | 5.83080e18i | − | 0.260913i | ||||||
\(582\) | 1.24298e19 | − | 2.29295e19i | 0.549546 | − | 1.01376i | ||||
\(583\) | −9.36213e18 | −0.408973 | ||||||||
\(584\) | 4.37354e19i | 1.88774i | ||||||||
\(585\) | 3.12889e18 | − | 2.03790e18i | 0.133444 | − | 0.0869144i | ||||
\(586\) | 4.68694e19 | 1.97518 | ||||||||
\(587\) | 3.82350e19i | 1.59219i | 0.605172 | + | 0.796095i | \(0.293104\pi\) | ||||
−0.605172 | + | 0.796095i | \(0.706896\pi\) | |||||||
\(588\) | 2.98508e19 | + | 1.61817e19i | 1.22833 | + | 0.665862i | ||||
\(589\) | −1.24771e19 | −0.507347 | ||||||||
\(590\) | 1.21228e19i | 0.487122i | ||||||||
\(591\) | −1.07772e19 | + | 1.98810e19i | −0.427952 | + | 0.789451i | ||||
\(592\) | −1.57580e19 | −0.618371 | ||||||||
\(593\) | − | 2.10110e19i | − | 0.814826i | −0.913244 | − | 0.407413i | \(-0.866431\pi\) | ||
0.913244 | − | 0.407413i | \(-0.133569\pi\) | |||||||
\(594\) | −3.05661e18 | − | 3.78638e19i | −0.117148 | − | 1.45117i | ||||
\(595\) | −7.43147e18 | −0.281485 | ||||||||
\(596\) | 3.35093e19i | 1.25442i | ||||||||
\(597\) | 2.55543e19 | + | 1.38527e19i | 0.945461 | + | 0.512523i | ||||
\(598\) | 2.46876e17 | 0.00902755 | ||||||||
\(599\) | − | 4.94075e19i | − | 1.78569i | −0.450367 | − | 0.892844i | \(-0.648707\pi\) | ||
0.450367 | − | 0.892844i | \(-0.351293\pi\) | |||||||
\(600\) | 2.37889e19 | − | 4.38838e19i | 0.849797 | − | 1.56764i | ||||
\(601\) | −2.29665e19 | −0.810912 | −0.405456 | − | 0.914115i | \(-0.632887\pi\) | ||||
−0.405456 | + | 0.914115i | \(0.632887\pi\) | |||||||
\(602\) | 1.08541e19i | 0.378808i | ||||||||
\(603\) | −6.05643e18 | − | 9.29875e18i | −0.208927 | − | 0.320777i | ||||
\(604\) | 3.50008e19 | 1.19349 | ||||||||
\(605\) | − | 2.79833e18i | − | 0.0943217i | ||||||
\(606\) | −3.90733e19 | − | 2.11811e19i | −1.30188 | − | 0.705733i | ||||
\(607\) | 2.40723e19 | 0.792862 | 0.396431 | − | 0.918065i | \(-0.370249\pi\) | ||||
0.396431 | + | 0.918065i | \(0.370249\pi\) | |||||||
\(608\) | 5.45765e18i | 0.177697i | ||||||||
\(609\) | 1.23409e19 | − | 2.27656e19i | 0.397216 | − | 0.732753i | ||||
\(610\) | −2.21092e19 | −0.703501 | ||||||||
\(611\) | − | 7.22575e18i | − | 0.227298i | ||||||
\(612\) | −9.28802e19 | + | 6.04944e19i | −2.88844 | + | 1.88129i | ||||
\(613\) | −4.49657e19 | −1.38248 | −0.691239 | − | 0.722626i | \(-0.742935\pi\) | ||||
−0.691239 | + | 0.722626i | \(0.742935\pi\) | |||||||
\(614\) | 7.36770e19i | 2.23951i | ||||||||
\(615\) | 4.94959e18 | + | 2.68311e18i | 0.148745 | + | 0.0806330i | ||||
\(616\) | 3.15596e19 | 0.937705 | ||||||||
\(617\) | 1.15025e18i | 0.0337907i | 0.999857 | + | 0.0168954i | \(0.00537822\pi\) | ||||
−0.999857 | + | 0.0168954i | \(0.994622\pi\) | |||||||
\(618\) | −2.31482e19 | + | 4.27020e19i | −0.672355 | + | 1.24031i | ||||
\(619\) | 1.85323e19 | 0.532224 | 0.266112 | − | 0.963942i | \(-0.414261\pi\) | ||||
0.266112 | + | 0.963942i | \(0.414261\pi\) | |||||||
\(620\) | − | 2.54198e19i | − | 0.721823i | ||||||
\(621\) | 3.38344e17 | − | 2.73133e16i | 0.00949987 | − | 0.000766891i | ||||
\(622\) | 8.90271e19 | 2.47166 | ||||||||
\(623\) | 1.43666e19i | 0.394400i | ||||||||
\(624\) | 2.32808e19 | + | 1.26203e19i | 0.631985 | + | 0.342591i | ||||
\(625\) | 2.77195e19 | 0.744089 | ||||||||
\(626\) | − | 9.46430e19i | − | 2.51228i | ||||||
\(627\) | −6.58685e18 | + | 1.21509e19i | −0.172904 | + | 0.318960i | ||||
\(628\) | −5.68468e19 | −1.47567 | ||||||||
\(629\) | 2.94254e19i | 0.755383i | ||||||||
\(630\) | 6.52706e18 | + | 1.00213e19i | 0.165704 | + | 0.254415i | ||||
\(631\) | 2.33455e18 | 0.0586136 | 0.0293068 | − | 0.999570i | \(-0.490670\pi\) | ||||
0.0293068 | + | 0.999570i | \(0.490670\pi\) | |||||||
\(632\) | − | 1.31839e20i | − | 3.27359i | ||||||
\(633\) | 2.67069e19 | + | 1.44775e19i | 0.655838 | + | 0.355522i | ||||
\(634\) | −8.30685e19 | −2.01749 | ||||||||
\(635\) | 2.80769e18i | 0.0674424i | ||||||||
\(636\) | 2.09515e19 | − | 3.86496e19i | 0.497754 | − | 0.918217i | ||||
\(637\) | −1.51479e19 | −0.355939 | ||||||||
\(638\) | 8.98836e19i | 2.08899i | ||||||||
\(639\) | 5.70162e19 | − | 3.71356e19i | 1.31067 | − | 0.853658i | ||||
\(640\) | 1.96417e19 | 0.446602 | ||||||||
\(641\) | 2.31344e19i | 0.520298i | 0.965568 | + | 0.260149i | \(0.0837717\pi\) | ||||
−0.965568 | + | 0.260149i | \(0.916228\pi\) | |||||||
\(642\) | −5.59821e19 | − | 3.03472e19i | −1.24539 | − | 0.675109i | ||||
\(643\) | 3.27850e19 | 0.721438 | 0.360719 | − | 0.932675i | \(-0.382531\pi\) | ||||
0.360719 | + | 0.932675i | \(0.382531\pi\) | |||||||
\(644\) | 5.36357e17i | 0.0116749i | ||||||||
\(645\) | 2.42669e18 | − | 4.47656e18i | 0.0522511 | − | 0.0963887i | ||||
\(646\) | 5.94548e19 | 1.26637 | ||||||||
\(647\) | 2.52933e19i | 0.532937i | 0.963844 | + | 0.266468i | \(0.0858568\pi\) | ||||
−0.963844 | + | 0.266468i | \(0.914143\pi\) | |||||||
\(648\) | 8.57844e19 | + | 3.79183e19i | 1.78806 | + | 0.790357i | ||||
\(649\) | −3.73208e19 | −0.769553 | ||||||||
\(650\) | 4.23534e19i | 0.863962i | ||||||||
\(651\) | −2.92200e19 | − | 1.58398e19i | −0.589675 | − | 0.319656i | ||||
\(652\) | −8.81048e19 | −1.75900 | ||||||||
\(653\) | − | 2.21595e19i | − | 0.437692i | −0.975759 | − | 0.218846i | \(-0.929771\pi\) | ||
0.975759 | − | 0.218846i | \(-0.0702292\pi\) | |||||||
\(654\) | −2.76602e19 | + | 5.10253e19i | −0.540519 | + | 0.997106i | ||||
\(655\) | 9.94651e18 | 0.192301 | ||||||||
\(656\) | 3.99279e19i | 0.763748i | ||||||||
\(657\) | −2.78464e19 | − | 4.27540e19i | −0.527001 | − | 0.809132i | ||||
\(658\) | 2.31429e19 | 0.433348 | ||||||||
\(659\) | 1.61070e19i | 0.298413i | 0.988806 | + | 0.149207i | \(0.0476719\pi\) | ||||
−0.988806 | + | 0.149207i | \(0.952328\pi\) | |||||||
\(660\) | −2.47553e19 | − | 1.34196e19i | −0.453796 | − | 0.245997i | ||||
\(661\) | −3.88817e19 | −0.705236 | −0.352618 | − | 0.935767i | \(-0.614709\pi\) | ||||
−0.352618 | + | 0.935767i | \(0.614709\pi\) | |||||||
\(662\) | 3.30346e19i | 0.592875i | ||||||||
\(663\) | 2.35662e19 | − | 4.34730e19i | 0.418499 | − | 0.772013i | ||||
\(664\) | −4.99704e19 | −0.878085 | ||||||||
\(665\) | − | 4.35141e18i | − | 0.0756622i | ||||||
\(666\) | 3.96801e19 | − | 2.58443e19i | 0.682736 | − | 0.444677i | ||||
\(667\) | −8.03184e17 | −0.0136752 | ||||||||
\(668\) | − | 3.05214e19i | − | 0.514244i | ||||||
\(669\) | −2.91752e17 | − | 1.58155e17i | −0.00486442 | − | 0.00263694i | ||||
\(670\) | −1.21269e19 | −0.200090 | ||||||||
\(671\) | − | 6.80649e19i | − | 1.11139i | ||||||
\(672\) | −6.92856e18 | + | 1.27813e19i | −0.111959 | + | 0.206533i | ||||
\(673\) | −3.72205e19 | −0.595219 | −0.297609 | − | 0.954688i | \(-0.596189\pi\) | ||||
−0.297609 | + | 0.954688i | \(0.596189\pi\) | |||||||
\(674\) | − | 1.25614e20i | − | 1.98800i | ||||||
\(675\) | 4.68581e18 | + | 5.80455e19i | 0.0733936 | + | 0.909164i | ||||
\(676\) | 9.67767e19 | 1.50018 | ||||||||
\(677\) | 8.23009e19i | 1.26265i | 0.775517 | + | 0.631326i | \(0.217489\pi\) | ||||
−0.775517 | + | 0.631326i | \(0.782511\pi\) | |||||||
\(678\) | 1.23662e20 | + | 6.70355e19i | 1.87770 | + | 1.01788i | ||||
\(679\) | −2.52794e19 | −0.379908 | ||||||||
\(680\) | 6.36883e19i | 0.947321i | ||||||||
\(681\) | −5.48876e19 | + | 1.01252e20i | −0.808061 | + | 1.49065i | ||||
\(682\) | 1.15367e20 | 1.68109 | ||||||||
\(683\) | − | 6.26033e19i | − | 0.902927i | −0.892290 | − | 0.451463i | \(-0.850902\pi\) | ||
0.892290 | − | 0.451463i | \(-0.149098\pi\) | |||||||
\(684\) | −3.54218e19 | − | 5.43849e19i | −0.505682 | − | 0.776401i | ||||
\(685\) | 1.72417e19 | 0.243639 | ||||||||
\(686\) | − | 1.21741e20i | − | 1.70282i | ||||||
\(687\) | −2.24877e19 | − | 1.21903e19i | −0.311350 | − | 0.168779i | ||||
\(688\) | 3.61120e19 | 0.494917 | ||||||||
\(689\) | 1.96129e19i | 0.266077i | ||||||||
\(690\) | 1.76780e17 | − | 3.26109e17i | 0.00237404 | − | 0.00437944i | ||||
\(691\) | 2.70281e19 | 0.359309 | 0.179655 | − | 0.983730i | \(-0.442502\pi\) | ||||
0.179655 | + | 0.983730i | \(0.442502\pi\) | |||||||
\(692\) | 3.10014e19i | 0.407980i | ||||||||
\(693\) | −3.08514e19 | + | 2.00940e19i | −0.401923 | + | 0.261779i | ||||
\(694\) | 1.23765e19 | 0.159618 | ||||||||
\(695\) | 3.00183e19i | 0.383259i | ||||||||
\(696\) | −1.95103e20 | − | 1.05763e20i | −2.46603 | − | 1.33681i | ||||
\(697\) | 7.45586e19 | 0.932971 | ||||||||
\(698\) | 1.30230e20i | 1.61333i | ||||||||
\(699\) | 8.35028e17 | − | 1.54039e18i | 0.0102414 | − | 0.0188926i | ||||
\(700\) | −9.20161e19 | −1.11732 | ||||||||
\(701\) | − | 9.70271e19i | − | 1.16645i | −0.812310 | − | 0.583226i | \(-0.801790\pi\) | ||
0.812310 | − | 0.583226i | \(-0.198210\pi\) | |||||||
\(702\) | −7.93215e19 | + | 6.40334e18i | −0.944128 | + | 0.0762161i | ||||
\(703\) | −1.72297e19 | −0.203044 | ||||||||
\(704\) | 4.42360e19i | 0.516140i | ||||||||
\(705\) | −9.54482e18 | − | 5.17413e18i | −0.110267 | − | 0.0597742i | ||||
\(706\) | −2.02440e20 | −2.31560 | ||||||||
\(707\) | 4.30776e19i | 0.487883i | ||||||||
\(708\) | 8.35202e19 | − | 1.54071e20i | 0.936610 | − | 1.72778i | ||||
\(709\) | 1.02481e20 | 1.13794 | 0.568968 | − | 0.822360i | \(-0.307343\pi\) | ||||
0.568968 | + | 0.822360i | \(0.307343\pi\) | |||||||
\(710\) | − | 7.43571e19i | − | 0.817549i | ||||||
\(711\) | 8.39421e19 | + | 1.28881e20i | 0.913887 | + | 1.40314i | ||||
\(712\) | 1.23123e20 | 1.32733 | ||||||||
\(713\) | 1.03090e18i | 0.0110050i | ||||||||
\(714\) | 1.39237e20 | + | 7.54786e19i | 1.47186 | + | 0.797878i | ||||
\(715\) | 1.25622e19 | 0.131499 | ||||||||
\(716\) | 3.78285e20i | 3.92128i | ||||||||
\(717\) | 6.63460e19 | − | 1.22390e20i | 0.681052 | − | 1.25635i | ||||
\(718\) | −2.66965e20 | −2.71383 | ||||||||
\(719\) | 1.67928e19i | 0.169052i | 0.996421 | + | 0.0845260i | \(0.0269376\pi\) | ||||
−0.996421 | + | 0.0845260i | \(0.973062\pi\) | |||||||
\(720\) | 3.33413e19 | − | 2.17157e19i | 0.332396 | − | 0.216495i | ||||
\(721\) | 4.70782e19 | 0.464807 | ||||||||
\(722\) | − | 1.45511e20i | − | 1.42278i | ||||||
\(723\) | −1.18739e20 | − | 6.43671e19i | −1.14981 | − | 0.623298i | ||||
\(724\) | 2.23875e20 | 2.14702 | ||||||||
\(725\) | − | 1.37792e20i | − | 1.30876i | ||||||
\(726\) | −2.84216e19 | + | 5.24299e19i | −0.267357 | + | 0.493199i | ||||
\(727\) | −1.97576e20 | −1.84074 | −0.920371 | − | 0.391047i | \(-0.872113\pi\) | ||||
−0.920371 | + | 0.391047i | \(0.872113\pi\) | |||||||
\(728\) | − | 6.61147e19i | − | 0.610068i | ||||||
\(729\) | −1.08002e20 | + | 1.75516e19i | −0.987051 | + | 0.160408i | ||||
\(730\) | −5.57572e19 | −0.504709 | ||||||||
\(731\) | − | 6.74329e19i | − | 0.604575i | ||||||
\(732\) | 2.80992e20 | + | 1.52322e20i | 2.49526 | + | 1.35265i | ||||
\(733\) | 2.03135e20 | 1.78672 | 0.893360 | − | 0.449341i | \(-0.148341\pi\) | ||||
0.893360 | + | 0.449341i | \(0.148341\pi\) | |||||||
\(734\) | − | 2.82506e20i | − | 2.46125i | ||||||
\(735\) | −1.08469e19 | + | 2.00095e19i | −0.0936040 | + | 0.172673i | ||||
\(736\) | 4.50931e17 | 0.00385447 | ||||||||
\(737\) | − | 3.73335e19i | − | 0.316101i | ||||||
\(738\) | −6.54848e19 | − | 1.00542e20i | −0.549219 | − | 0.843245i | ||||
\(739\) | 3.77054e19 | 0.313251 | 0.156625 | − | 0.987658i | \(-0.449938\pi\) | ||||
0.156625 | + | 0.987658i | \(0.449938\pi\) | |||||||
\(740\) | − | 3.51025e19i | − | 0.288879i | ||||||
\(741\) | 2.54551e19 | + | 1.37989e19i | 0.207514 | + | 0.112491i | ||||
\(742\) | −6.28169e19 | −0.507282 | ||||||||
\(743\) | 1.51734e20i | 1.21384i | 0.794764 | + | 0.606918i | \(0.207595\pi\) | ||||
−0.794764 | + | 0.606918i | \(0.792405\pi\) | |||||||
\(744\) | −1.35748e20 | + | 2.50417e20i | −1.07578 | + | 1.98451i | ||||
\(745\) | −2.24619e19 | −0.176341 | ||||||||
\(746\) | 3.72156e20i | 2.89436i | ||||||||
\(747\) | 4.88492e19 | − | 3.18163e19i | 0.376368 | − | 0.245135i | ||||
\(748\) | −3.72904e20 | −2.84633 | ||||||||
\(749\) | 6.17193e19i | 0.466711i | ||||||||
\(750\) | 1.17283e20 | + | 6.35777e19i | 0.878631 | + | 0.476295i | ||||
\(751\) | −1.19860e20 | −0.889600 | −0.444800 | − | 0.895630i | \(-0.646725\pi\) | ||||
−0.444800 | + | 0.895630i | \(0.646725\pi\) | |||||||
\(752\) | − | 7.69973e19i | − | 0.566175i | ||||||
\(753\) | 3.87615e19 | − | 7.15042e19i | 0.282381 | − | 0.520915i | ||||
\(754\) | 1.88299e20 | 1.35909 | ||||||||
\(755\) | 2.34617e19i | 0.167776i | ||||||||
\(756\) | −1.39118e19 | − | 1.72332e20i | −0.0985666 | − | 1.22100i | ||||
\(757\) | 6.29864e19 | 0.442156 | 0.221078 | − | 0.975256i | \(-0.429042\pi\) | ||||
0.221078 | + | 0.975256i | \(0.429042\pi\) | |||||||
\(758\) | − | 5.62867e19i | − | 0.391491i | ||||||
\(759\) | 1.00395e18 | + | 5.44229e17i | 0.00691863 | + | 0.00375050i | ||||
\(760\) | −3.72920e19 | −0.254636 | ||||||||
\(761\) | 7.74499e19i | 0.523997i | 0.965068 | + | 0.261998i | \(0.0843815\pi\) | ||||
−0.965068 | + | 0.261998i | \(0.915619\pi\) | |||||||
\(762\) | 2.85167e19 | − | 5.26052e19i | 0.191167 | − | 0.352650i | ||||
\(763\) | 5.62545e19 | 0.373667 | ||||||||
\(764\) | − | 3.82863e20i | − | 2.51994i | ||||||
\(765\) | −4.05504e19 | − | 6.22592e19i | −0.264463 | − | 0.406044i | ||||
\(766\) | 1.61916e20 | 1.04638 | ||||||||
\(767\) | 7.81840e19i | 0.500669i | ||||||||
\(768\) | −2.81410e20 | − | 1.52549e20i | −1.78571 | − | 0.968012i | ||||
\(769\) | −1.63707e20 | −1.02939 | −0.514697 | − | 0.857372i | \(-0.672096\pi\) | ||||
−0.514697 | + | 0.857372i | \(0.672096\pi\) | |||||||
\(770\) | 4.02346e19i | 0.250706i | ||||||||
\(771\) | 1.93742e18 | − | 3.57399e18i | 0.0119631 | − | 0.0220685i | ||||
\(772\) | 3.37406e20 | 2.06458 | ||||||||
\(773\) | 1.95306e20i | 1.18430i | 0.805829 | + | 0.592148i | \(0.201720\pi\) | ||||
−0.805829 | + | 0.592148i | \(0.798280\pi\) | |||||||
\(774\) | −9.09333e19 | + | 5.92264e19i | −0.546432 | + | 0.355900i | ||||
\(775\) | −1.76859e20 | −1.05321 | ||||||||
\(776\) | 2.16647e20i | 1.27856i | ||||||||
\(777\) | −4.03501e19 | − | 2.18733e19i | −0.235992 | − | 0.127928i | ||||
\(778\) | 5.34067e20 | 3.09556 | ||||||||
\(779\) | 4.36569e19i | 0.250779i | ||||||||
\(780\) | −2.81128e19 | + | 5.18603e19i | −0.160045 | + | 0.295239i | ||||
\(781\) | 2.28914e20 | 1.29156 | ||||||||
\(782\) | − | 4.91237e18i | − | 0.0274690i | ||||||
\(783\) | 2.58064e20 | − | 2.08326e19i | 1.43020 | − | 0.115455i | ||||
\(784\) | −1.61415e20 | −0.886608 | ||||||||
\(785\) | − | 3.81054e19i | − | 0.207443i | ||||||
\(786\) | −1.86359e20 | − | 1.01023e20i | −1.00552 | − | 0.545082i | ||||
\(787\) | −1.79888e20 | −0.962007 | −0.481004 | − | 0.876719i | \(-0.659728\pi\) | ||||
−0.481004 | + | 0.876719i | \(0.659728\pi\) | |||||||
\(788\) | − | 3.57258e20i | − | 1.89364i | ||||||
\(789\) | −9.10834e19 | + | 1.68023e20i | −0.478520 | + | 0.882736i | ||||
\(790\) | 1.68078e20 | 0.875230 | ||||||||
\(791\) | − | 1.36335e20i | − | 0.703674i | ||||||
\(792\) | 1.72208e20 | + | 2.64399e20i | 0.881000 | + | 1.35265i | ||||
\(793\) | −1.42590e20 | −0.723066 | ||||||||
\(794\) | 2.22596e20i | 1.11885i | ||||||||
\(795\) | 2.59075e19 | + | 1.40442e19i | 0.129079 | + | 0.0699722i | ||||
\(796\) | −4.59206e20 | −2.26786 | ||||||||
\(797\) | − | 2.77052e20i | − | 1.35629i | −0.734927 | − | 0.678146i | \(-0.762784\pi\) | ||
0.734927 | − | 0.678146i | \(-0.237216\pi\) | |||||||
\(798\) | −4.41957e19 | + | 8.15286e19i | −0.214466 | + | 0.395631i | ||||
\(799\) | −1.43779e20 | −0.691622 | ||||||||
\(800\) | 7.73606e19i | 0.368884i | ||||||||
\(801\) | −1.20360e20 | + | 7.83925e19i | −0.568925 | + | 0.370550i | ||||
\(802\) | −4.85879e20 | −2.27671 | ||||||||
\(803\) | − | 1.71653e20i | − | 0.797337i | ||||||
\(804\) | 1.54124e20 | + | 8.35485e19i | 0.709703 | + | 0.384721i | ||||
\(805\) | −3.59529e17 | −0.00164121 | ||||||||
\(806\) | − | 2.41684e20i | − | 1.09371i | ||||||
\(807\) | 1.31719e20 | − | 2.42985e20i | 0.590929 | − | 1.09010i | ||||
\(808\) | 3.69178e20 | 1.64194 | ||||||||
\(809\) | 1.89882e20i | 0.837229i | 0.908164 | + | 0.418615i | \(0.137484\pi\) | ||||
−0.908164 | + | 0.418615i | \(0.862516\pi\) | |||||||
\(810\) | −4.83411e19 | + | 1.09365e20i | −0.211311 | + | 0.478059i | ||||
\(811\) | 2.25399e20 | 0.976802 | 0.488401 | − | 0.872619i | \(-0.337580\pi\) | ||||
0.488401 | + | 0.872619i | \(0.337580\pi\) | |||||||
\(812\) | 4.09094e20i | 1.75764i | ||||||||
\(813\) | 1.12748e20 | + | 6.11193e19i | 0.480259 | + | 0.260342i | ||||
\(814\) | 1.59311e20 | 0.672784 | ||||||||
\(815\) | − | 5.90582e19i | − | 0.247273i | ||||||
\(816\) | 2.51120e20 | − | 4.63246e20i | 1.04244 | − | 1.92301i | ||||
\(817\) | 3.94846e19 | 0.162508 | ||||||||
\(818\) | 7.50141e20i | 3.06105i | ||||||||
\(819\) | 4.20953e19 | + | 6.46312e19i | 0.170313 | + | 0.261490i | ||||
\(820\) | −8.89433e19 | −0.356793 | ||||||||
\(821\) | − | 4.00570e20i | − | 1.59322i | −0.604492 | − | 0.796611i | \(-0.706624\pi\) | ||
0.604492 | − | 0.796611i | \(-0.293376\pi\) | |||||||
\(822\) | −3.23042e20 | − | 1.75117e20i | −1.27396 | − | 0.690600i | ||||
\(823\) | 1.34324e20 | 0.525235 | 0.262617 | − | 0.964900i | \(-0.415414\pi\) | ||||
0.262617 | + | 0.964900i | \(0.415414\pi\) | |||||||
\(824\) | − | 4.03464e20i | − | 1.56428i | ||||||
\(825\) | −9.33667e19 | + | 1.72235e20i | −0.358934 | + | 0.662132i | ||||
\(826\) | −2.50411e20 | −0.954537 | ||||||||
\(827\) | 9.76761e19i | 0.369190i | 0.982815 | + | 0.184595i | \(0.0590973\pi\) | ||||
−0.982815 | + | 0.184595i | \(0.940903\pi\) | |||||||
\(828\) | −4.49348e18 | + | 2.92667e18i | −0.0168411 | + | 0.0109689i | ||||
\(829\) | 1.39626e20 | 0.518900 | 0.259450 | − | 0.965757i | \(-0.416459\pi\) | ||||
0.259450 | + | 0.965757i | \(0.416459\pi\) | |||||||
\(830\) | − | 6.37062e19i | − | 0.234766i | ||||||
\(831\) | 3.38678e20 | + | 1.83593e20i | 1.23760 | + | 0.670888i | ||||
\(832\) | 9.26708e19 | 0.335799 | ||||||||
\(833\) | 3.01415e20i | 1.08305i | ||||||||
\(834\) | 3.04884e20 | − | 5.62426e20i | 1.08636 | − | 2.00403i | ||||
\(835\) | 2.04590e19 | 0.0722902 | ||||||||
\(836\) | − | 2.18350e20i | − | 0.765083i | ||||||
\(837\) | −2.67390e19 | − | 3.31230e20i | −0.0929109 | − | 1.15094i | ||||
\(838\) | −4.83169e20 | −1.66491 | ||||||||
\(839\) | − | 3.23963e19i | − | 0.110703i | −0.998467 | − | 0.0553517i | \(-0.982372\pi\) | ||
0.998467 | − | 0.0553517i | \(-0.0176280\pi\) | |||||||
\(840\) | −8.73339e19 | − | 4.73426e19i | −0.295956 | − | 0.160434i | ||||
\(841\) | −3.15052e20 | −1.05879 | ||||||||
\(842\) | 1.97123e20i | 0.656981i | ||||||||
\(843\) | −1.95143e20 | + | 3.59984e20i | −0.644999 | + | 1.18984i | ||||
\(844\) | −4.79918e20 | −1.57315 | ||||||||
\(845\) | 6.48711e19i | 0.210889i | ||||||||
\(846\) | 1.26281e20 | + | 1.93886e20i | 0.407142 | + | 0.625107i | ||||
\(847\) | 5.78030e19 | 0.184827 | ||||||||
\(848\) | 2.08994e20i | 0.662770i | ||||||||
\(849\) | −2.02405e19 | − | 1.09721e19i | −0.0636601 | − | 0.0345094i | ||||
\(850\) | 8.42754e20 | 2.62887 | ||||||||
\(851\) | 1.42358e18i | 0.00440427i | ||||||||
\(852\) | −5.12286e20 | + | 9.45024e20i | −1.57194 | + | 2.89978i | ||||
\(853\) | −3.08044e19 | −0.0937495 | −0.0468748 | − | 0.998901i | \(-0.514926\pi\) | ||||
−0.0468748 | + | 0.998901i | \(0.514926\pi\) | |||||||
\(854\) | − | 4.56694e20i | − | 1.37854i | ||||||
\(855\) | 3.64552e19 | − | 2.37439e19i | 0.109143 | − | 0.0710867i | ||||
\(856\) | 5.28940e20 | 1.57069 | ||||||||
\(857\) | − | 4.87680e19i | − | 0.143638i | −0.997418 | − | 0.0718190i | \(-0.977120\pi\) | ||
0.997418 | − | 0.0718190i | \(-0.0228804\pi\) | |||||||
\(858\) | −2.35366e20 | − | 1.27589e20i | −0.687596 | − | 0.372737i | ||||
\(859\) | 1.49706e20 | 0.433799 | 0.216899 | − | 0.976194i | \(-0.430406\pi\) | ||||
0.216899 | + | 0.976194i | \(0.430406\pi\) | |||||||
\(860\) | 8.04430e19i | 0.231206i | ||||||||
\(861\) | −5.54230e19 | + | 1.02240e20i | −0.158004 | + | 0.291473i | ||||
\(862\) | −1.29676e20 | −0.366699 | ||||||||
\(863\) | − | 3.15069e20i | − | 0.883751i | −0.897076 | − | 0.441875i | \(-0.854313\pi\) | ||
0.897076 | − | 0.441875i | \(-0.145687\pi\) | |||||||
\(864\) | −1.44885e20 | + | 1.16960e19i | −0.403113 | + | 0.0325419i | ||||
\(865\) | −2.07808e19 | −0.0573521 | ||||||||
\(866\) | − | 3.91872e20i | − | 1.07280i | ||||||
\(867\) | −5.41297e20 | − | 2.93430e20i | −1.46995 | − | 0.796840i | ||||
\(868\) | 5.25078e20 | 1.41444 | ||||||||
\(869\) | 5.17442e20i | 1.38269i | ||||||||
\(870\) | 1.34835e20 | − | 2.48732e20i | 0.357410 | − | 0.659321i | ||||
\(871\) | −7.82105e19 | −0.205654 | ||||||||
\(872\) | − | 4.82105e20i | − | 1.25755i | ||||||
\(873\) | −1.37939e20 | − | 2.11785e20i | −0.356934 | − | 0.548020i | ||||
\(874\) | 2.87638e18 | 0.00738357 | ||||||||
\(875\) | − | 1.29303e20i | − | 0.329269i | ||||||
\(876\) | 7.08633e20 | + | 3.84141e20i | 1.79016 | + | 0.970426i | ||||
\(877\) | −3.62517e20 | −0.908512 | −0.454256 | − | 0.890871i | \(-0.650095\pi\) | ||||
−0.454256 | + | 0.890871i | \(0.650095\pi\) | |||||||
\(878\) | 4.81121e19i | 0.119617i | ||||||||
\(879\) | 2.16451e20 | − | 3.99292e20i | 0.533873 | − | 0.984846i | ||||
\(880\) | 1.33862e20 | 0.327550 | ||||||||
\(881\) | − | 1.15407e20i | − | 0.280157i | −0.990140 | − | 0.140078i | \(-0.955265\pi\) | ||
0.990140 | − | 0.140078i | \(-0.0447355\pi\) | |||||||
\(882\) | 4.06458e20 | − | 2.64733e20i | 0.978893 | − | 0.637569i | ||||
\(883\) | 3.76570e20 | 0.899748 | 0.449874 | − | 0.893092i | \(-0.351469\pi\) | ||||
0.449874 | + | 0.893092i | \(0.351469\pi\) | |||||||
\(884\) | 7.81202e20i | 1.85182i | ||||||||
\(885\) | 1.03277e20 | + | 5.59851e19i | 0.242884 | + | 0.131665i | ||||
\(886\) | −4.09972e20 | −0.956573 | ||||||||
\(887\) | 4.49245e20i | 1.03996i | 0.854177 | + | 0.519982i | \(0.174061\pi\) | ||||
−0.854177 | + | 0.519982i | \(0.825939\pi\) | |||||||
\(888\) | −1.87456e20 | + | 3.45804e20i | −0.430535 | + | 0.794216i | ||||
\(889\) | −5.79964e19 | −0.132156 | ||||||||
\(890\) | 1.56966e20i | 0.354876i | ||||||||
\(891\) | −3.36687e20 | − | 1.48822e20i | −0.755235 | − | 0.333828i | ||||
\(892\) | 5.24273e18 | 0.0116682 | ||||||||
\(893\) | − | 8.41883e19i | − | 0.185905i | ||||||
\(894\) | 4.20849e20 | + | 2.28137e20i | 0.922069 | + | 0.499842i | ||||
\(895\) | −2.53571e20 | −0.551237 | ||||||||
\(896\) | 4.05725e20i | 0.875136i | ||||||||
\(897\) | 1.14011e18 | − | 2.10319e18i | 0.00244006 | − | 0.00450124i | ||||
\(898\) | −1.00596e21 | −2.13623 | ||||||||
\(899\) | 7.86294e20i | 1.65679i | ||||||||
\(900\) | −5.02093e20 | − | 7.70890e20i | −1.04975 | − | 1.61174i | ||||
\(901\) | 3.90260e20 | 0.809619 | ||||||||
\(902\) | − | 4.03666e20i | − | 0.830953i | ||||||
\(903\) | 9.24688e19 | + | 5.01262e19i | 0.188878 | + | 0.102388i | ||||
\(904\) | −1.16840e21 | −2.36817 | ||||||||
\(905\) | 1.50068e20i | 0.301819i | ||||||||
\(906\) | 2.38291e20 | − | 4.39581e20i | 0.475566 | − | 0.877286i | ||||
\(907\) | 9.99929e20 | 1.98024 | 0.990121 | − | 0.140215i | \(-0.0447794\pi\) | ||||
0.990121 | + | 0.140215i | \(0.0447794\pi\) | |||||||
\(908\) | − | 1.81949e21i | − | 3.57559i | ||||||
\(909\) | −3.60894e20 | + | 2.35056e20i | −0.703773 | + | 0.458379i | ||||
\(910\) | 8.42881e19 | 0.163108 | ||||||||
\(911\) | − | 5.11050e20i | − | 0.981374i | −0.871336 | − | 0.490687i | \(-0.836746\pi\) | ||
0.871336 | − | 0.490687i | \(-0.163254\pi\) | |||||||
\(912\) | 2.71248e20 | + | 1.47040e20i | 0.516896 | + | 0.280203i | ||||
\(913\) | 1.96124e20 | 0.370882 | ||||||||
\(914\) | 4.38374e20i | 0.822661i | ||||||||
\(915\) | −1.02104e20 | + | 1.88354e20i | −0.190150 | + | 0.350774i | ||||
\(916\) | 4.04101e20 | 0.746830 | ||||||||
\(917\) | 2.05458e20i | 0.376822i | ||||||||
\(918\) | 1.27415e20 | + | 1.57835e21i | 0.231911 | + | 2.87280i | ||||
\(919\) | −4.38250e20 | −0.791613 | −0.395807 | − | 0.918334i | \(-0.629535\pi\) | ||||
−0.395807 | + | 0.918334i | \(0.629535\pi\) | |||||||
\(920\) | 3.08119e18i | 0.00552337i | ||||||||
\(921\) | 6.27672e20 | + | 3.40253e20i | 1.11665 | + | 0.605320i | ||||
\(922\) | −2.53369e20 | −0.447339 | ||||||||
\(923\) | − | 4.79555e20i | − | 0.840285i | ||||||
\(924\) | 2.77198e20 | − | 5.11352e20i | 0.482043 | − | 0.889234i | ||||
\(925\) | −2.44226e20 | −0.421501 | ||||||||
\(926\) | 8.75065e20i | 1.49887i | ||||||||
\(927\) | 2.56886e20 | + | 3.94411e20i | 0.436699 | + | 0.670487i | ||||
\(928\) | 3.43937e20 | 0.580287 | ||||||||
\(929\) | − | 6.29570e20i | − | 1.05423i | −0.849795 | − | 0.527113i | \(-0.823274\pi\) | ||
0.849795 | − | 0.527113i | \(-0.176726\pi\) | |||||||
\(930\) | −3.19251e20 | − | 1.73062e20i | −0.530582 | − | 0.287622i | ||||
\(931\) | −1.76490e20 | −0.291120 | ||||||||
\(932\) | 2.76806e19i | 0.0453173i | ||||||||
\(933\) | 4.11143e20 | − | 7.58443e20i | 0.668069 | − | 1.23240i | ||||
\(934\) | 6.12395e20 | 0.987651 | ||||||||
\(935\) | − | 2.49964e20i | − | 0.400125i | ||||||
\(936\) | 5.53894e20 | − | 3.60760e20i | 0.880027 | − | 0.573176i | ||||
\(937\) | 4.29592e20 | 0.677454 | 0.338727 | − | 0.940885i | \(-0.390004\pi\) | ||||
0.338727 | + | 0.940885i | \(0.390004\pi\) | |||||||
\(938\) | − | 2.50496e20i | − | 0.392085i | ||||||
\(939\) | −8.06286e20 | − | 4.37078e20i | −1.25265 | − | 0.679047i | ||||
\(940\) | 1.71519e20 | 0.264495 | ||||||||
\(941\) | − | 2.95757e20i | − | 0.452697i | −0.974046 | − | 0.226349i | \(-0.927321\pi\) | ||
0.974046 | − | 0.226349i | \(-0.0726789\pi\) | |||||||
\(942\) | −3.87022e20 | + | 7.13947e20i | −0.588003 | + | 1.08470i | ||||
\(943\) | 3.60709e18 | 0.00543970 | ||||||||
\(944\) | 8.33125e20i | 1.24711i | ||||||||
\(945\) | 1.15517e20 | − | 9.32530e18i | 0.171642 | − | 0.0138561i | ||||
\(946\) | −3.65088e20 | −0.538467 | ||||||||
\(947\) | 1.58610e20i | 0.232210i | 0.993237 | + | 0.116105i | \(0.0370408\pi\) | ||||
−0.993237 | + | 0.116105i | \(0.962959\pi\) | |||||||
\(948\) | −2.13615e21 | − | 1.15798e21i | −3.10437 | − | 1.68284i | ||||
\(949\) | −3.59598e20 | −0.518745 | ||||||||
\(950\) | 4.93465e20i | 0.706629i | ||||||||
\(951\) | −3.83625e20 | + | 7.07681e20i | −0.545310 | + | 1.00594i | ||||
\(952\) | −1.31556e21 | −1.85632 | ||||||||
\(953\) | − | 8.31966e20i | − | 1.16535i | −0.812707 | − | 0.582673i | \(-0.802007\pi\) | ||
0.812707 | − | 0.582673i | \(-0.197993\pi\) | |||||||
\(954\) | −3.42765e20 | − | 5.26266e20i | −0.476605 | − | 0.731756i | ||||
\(955\) | 2.56640e20 | 0.354242 | ||||||||
\(956\) | 2.19932e21i | 3.01359i | ||||||||
\(957\) | 7.65740e20 | + | 4.15098e20i | 1.04159 | + | 0.564634i | ||||
\(958\) | 2.25318e21 | 3.04254 | ||||||||
\(959\) | 3.56149e20i | 0.477421i | ||||||||
\(960\) | 6.63586e19 | − | 1.22413e20i | 0.0883077 | − | 0.162903i | ||||
\(961\) | 2.52277e20 | 0.333284 | ||||||||
\(962\) | − | 3.33744e20i | − | 0.437711i | ||||||
\(963\) | −5.17071e20 | + | 3.36777e20i | −0.673234 | + | 0.438488i | ||||
\(964\) | 2.13372e21 | 2.75803 | ||||||||
\(965\) | 2.26169e20i | 0.290230i | ||||||||
\(966\) | 6.73618e18 | + | 3.65160e18i | 0.00858171 | + | 0.00465204i | ||||
\(967\) | −1.46184e21 | −1.84890 | −0.924452 | − | 0.381299i | \(-0.875477\pi\) | ||||
−0.924452 | + | 0.381299i | \(0.875477\pi\) | |||||||
\(968\) | − | 4.95376e20i | − | 0.622025i | ||||||
\(969\) | 2.74573e20 | − | 5.06510e20i | 0.342287 | − | 0.631425i | ||||
\(970\) | −2.76198e20 | −0.341836 | ||||||||
\(971\) | 3.08836e20i | 0.379484i | 0.981834 | + | 0.189742i | \(0.0607652\pi\) | ||||
−0.981834 | + | 0.189742i | \(0.939235\pi\) | |||||||
\(972\) | 1.36785e21 | − | 1.05689e21i | 1.66869 | − | 1.28934i | ||||
\(973\) | −6.20065e20 | −0.751013 | ||||||||
\(974\) | − | 1.58918e21i | − | 1.91100i | ||||||
\(975\) | 3.60819e20 | + | 1.95595e20i | 0.430781 | + | 0.233521i | ||||
\(976\) | −1.51943e21 | −1.80108 | ||||||||
\(977\) | 2.08527e20i | 0.245414i | 0.992443 | + | 0.122707i | \(0.0391576\pi\) | ||||
−0.992443 | + | 0.122707i | \(0.960842\pi\) | |||||||
\(978\) | −5.99832e20 | + | 1.10652e21i | −0.700902 | + | 1.29297i | ||||
\(979\) | −4.83233e20 | −0.560632 | ||||||||
\(980\) | − | 3.59567e20i | − | 0.414188i | ||||||
\(981\) | 3.06957e20 | + | 4.71287e20i | 0.351071 | + | 0.539017i | ||||
\(982\) | 8.07615e20 | 0.917115 | ||||||||
\(983\) | 1.09204e21i | 1.23130i | 0.788020 | + | 0.615649i | \(0.211106\pi\) | ||||
−0.788020 | + | 0.615649i | \(0.788894\pi\) | |||||||
\(984\) | 8.76204e20 | + | 4.74980e20i | 0.980934 | + | 0.531752i | ||||
\(985\) | 2.39476e20 | 0.266200 | ||||||||
\(986\) | − | 3.74679e21i | − | 4.13544i | ||||||
\(987\) | 1.06878e20 | − | 1.97160e20i | 0.117130 | − | 0.216072i | ||||
\(988\) | −4.57424e20 | −0.497761 | ||||||||
\(989\) | − | 3.26236e18i | − | 0.00352499i | ||||||
\(990\) | −3.37076e20 | + | 2.19543e20i | −0.361645 | + | 0.235545i | ||||
\(991\) | 5.22556e20 | 0.556695 | 0.278347 | − | 0.960480i | \(-0.410213\pi\) | ||||
0.278347 | + | 0.960480i | \(0.410213\pi\) | |||||||
\(992\) | − | 4.41448e20i | − | 0.466980i | ||||||
\(993\) | 2.81430e20 | + | 1.52559e20i | 0.295614 | + | 0.160249i | ||||
\(994\) | 1.53594e21 | 1.60202 | ||||||||
\(995\) | − | 3.07814e20i | − | 0.318806i | ||||||
\(996\) | −4.38906e20 | + | 8.09658e20i | −0.451394 | + | 0.832696i | ||||
\(997\) | −8.85987e20 | −0.904818 | −0.452409 | − | 0.891811i | \(-0.649435\pi\) | ||||
−0.452409 | + | 0.891811i | \(0.649435\pi\) | |||||||
\(998\) | 2.88137e21i | 2.92203i | ||||||||
\(999\) | −3.69241e19 | − | 4.57398e20i | −0.0371836 | − | 0.460612i |
(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 | 3.15.b.a.2.4 | yes | 4 | |
3.2 | odd | 2 | inner | 3.15.b.a.2.1 | ✓ | 4 | |
4.3 | odd | 2 | 48.15.e.b.17.1 | 4 | |||
5.2 | odd | 4 | 75.15.d.b.74.1 | 8 | |||
5.3 | odd | 4 | 75.15.d.b.74.8 | 8 | |||
5.4 | even | 2 | 75.15.c.d.26.1 | 4 | |||
12.11 | even | 2 | 48.15.e.b.17.2 | 4 | |||
15.2 | even | 4 | 75.15.d.b.74.7 | 8 | |||
15.8 | even | 4 | 75.15.d.b.74.2 | 8 | |||
15.14 | odd | 2 | 75.15.c.d.26.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.15.b.a.2.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
3.15.b.a.2.4 | yes | 4 | 1.1 | even | 1 | trivial | |
48.15.e.b.17.1 | 4 | 4.3 | odd | 2 | |||
48.15.e.b.17.2 | 4 | 12.11 | even | 2 | |||
75.15.c.d.26.1 | 4 | 5.4 | even | 2 | |||
75.15.c.d.26.4 | 4 | 15.14 | odd | 2 | |||
75.15.d.b.74.1 | 8 | 5.2 | odd | 4 | |||
75.15.d.b.74.2 | 8 | 15.8 | even | 4 | |||
75.15.d.b.74.7 | 8 | 15.2 | even | 4 | |||
75.15.d.b.74.8 | 8 | 5.3 | odd | 4 |