Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,14,Mod(67,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.67");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.c (of order \(3\), degree \(2\), not 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: | \(105.086310373\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 209077 x^{6} - 47718852 x^{5} + 40973427094 x^{4} - 4988457209802 x^{3} + \cdots + 75\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{2}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.4 | ||
Root | \(-35.6648 - 61.7733i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.79 |
Dual form | 98.14.c.o.67.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 32.0000 | − | 55.4256i | 0.353553 | − | 0.612372i | ||||
\(3\) | 746.854 | + | 1293.59i | 0.591490 | + | 1.02449i | 0.994032 | + | 0.109090i | \(0.0347935\pi\) |
−0.402542 | + | 0.915402i | \(0.631873\pi\) | |||||||
\(4\) | −2048.00 | − | 3547.24i | −0.250000 | − | 0.433013i | ||||
\(5\) | 7178.20 | − | 12433.0i | 0.205452 | − | 0.355853i | −0.744825 | − | 0.667260i | \(-0.767467\pi\) |
0.950277 | + | 0.311407i | \(0.100800\pi\) | |||||||
\(6\) | 95597.3 | 0.836494 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −262144. | −0.353553 | ||||||||
\(9\) | −318420. | + | 551520.i | −0.199721 | + | 0.345928i | ||||
\(10\) | −459405. | − | 795712.i | −0.145276 | − | 0.251626i | ||||
\(11\) | 2.14272e6 | + | 3.71130e6i | 0.364681 | + | 0.631645i | 0.988725 | − | 0.149744i | \(-0.0478449\pi\) |
−0.624044 | + | 0.781389i | \(0.714512\pi\) | |||||||
\(12\) | 3.05911e6 | − | 5.29854e6i | 0.295745 | − | 0.512246i | ||||
\(13\) | −5.50861e6 | −0.316527 | −0.158263 | − | 0.987397i | \(-0.550589\pi\) | ||||
−0.158263 | + | 0.987397i | \(0.550589\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.14443e7 | 0.486091 | ||||||||
\(16\) | −8.38861e6 | + | 1.45295e7i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.98554e7 | − | 3.43905e7i | −0.199508 | − | 0.345558i | 0.748861 | − | 0.662727i | \(-0.230601\pi\) |
−0.948369 | + | 0.317169i | \(0.897268\pi\) | |||||||
\(18\) | 2.03789e7 | + | 3.52973e7i | 0.141224 | + | 0.244608i | ||||
\(19\) | 2.25114e7 | − | 3.89910e7i | 0.109775 | − | 0.190137i | −0.805904 | − | 0.592046i | \(-0.798320\pi\) |
0.915679 | + | 0.401910i | \(0.131654\pi\) | |||||||
\(20\) | −5.88038e7 | −0.205452 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.74268e8 | 0.515736 | ||||||||
\(23\) | −3.77343e8 | + | 6.53577e8i | −0.531502 | + | 0.920589i | 0.467822 | + | 0.883823i | \(0.345039\pi\) |
−0.999324 | + | 0.0367661i | \(0.988294\pi\) | |||||||
\(24\) | −1.95783e8 | − | 3.39107e8i | −0.209123 | − | 0.362212i | ||||
\(25\) | 5.07299e8 | + | 8.78667e8i | 0.415579 | + | 0.719804i | ||||
\(26\) | −1.76275e8 | + | 3.05318e8i | −0.111909 | + | 0.193832i | ||||
\(27\) | 1.43020e9 | 0.710447 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.46353e9 | −0.769078 | −0.384539 | − | 0.923109i | \(-0.625640\pi\) | ||||
−0.384539 | + | 0.923109i | \(0.625640\pi\) | |||||||
\(30\) | 6.86216e8 | − | 1.18856e9i | 0.171859 | − | 0.297669i | ||||
\(31\) | 3.06703e9 | + | 5.31225e9i | 0.620679 | + | 1.07505i | 0.989360 | + | 0.145491i | \(0.0464762\pi\) |
−0.368681 | + | 0.929556i | \(0.620190\pi\) | |||||||
\(32\) | 5.36871e8 | + | 9.29888e8i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −3.20060e9 | + | 5.54359e9i | −0.431410 | + | 0.747224i | ||||
\(34\) | −2.54149e9 | −0.282147 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.60850e9 | 0.199721 | ||||||||
\(37\) | 9.52417e9 | − | 1.64963e10i | 0.610261 | − | 1.05700i | −0.380935 | − | 0.924602i | \(-0.624398\pi\) |
0.991196 | − | 0.132401i | \(-0.0422688\pi\) | |||||||
\(38\) | −1.44073e9 | − | 2.49542e9i | −0.0776229 | − | 0.134447i | ||||
\(39\) | −4.11413e9 | − | 7.12588e9i | −0.187222 | − | 0.324279i | ||||
\(40\) | −1.88172e9 | + | 3.25924e9i | −0.0726382 | + | 0.125813i | ||||
\(41\) | 4.23093e10 | 1.39104 | 0.695522 | − | 0.718505i | \(-0.255173\pi\) | ||||
0.695522 | + | 0.718505i | \(0.255173\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.42867e10 | −1.79212 | −0.896058 | − | 0.443937i | \(-0.853581\pi\) | ||||
−0.896058 | + | 0.443937i | \(0.853581\pi\) | |||||||
\(44\) | 8.77657e9 | − | 1.52015e10i | 0.182340 | − | 0.315823i | ||||
\(45\) | 4.57137e9 | + | 7.91784e9i | 0.0820663 | + | 0.142143i | ||||
\(46\) | 2.41499e10 | + | 4.18289e10i | 0.375829 | + | 0.650955i | ||||
\(47\) | 4.03508e10 | − | 6.98897e10i | 0.546030 | − | 0.945751i | −0.452512 | − | 0.891758i | \(-0.649472\pi\) |
0.998541 | − | 0.0539926i | \(-0.0171947\pi\) | |||||||
\(48\) | −2.50603e10 | −0.295745 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.49342e10 | 0.587717 | ||||||||
\(51\) | 2.96581e10 | − | 5.13694e10i | 0.236014 | − | 0.408788i | ||||
\(52\) | 1.12816e10 | + | 1.95404e10i | 0.0791316 | + | 0.137060i | ||||
\(53\) | 1.10539e11 | + | 1.91459e11i | 0.685049 | + | 1.18654i | 0.973421 | + | 0.229021i | \(0.0735526\pi\) |
−0.288372 | + | 0.957518i | \(0.593114\pi\) | |||||||
\(54\) | 4.57664e10 | − | 7.92697e10i | 0.251181 | − | 0.435058i | ||||
\(55\) | 6.15234e10 | 0.299697 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.72511e10 | 0.259724 | ||||||||
\(58\) | −7.88329e10 | + | 1.36543e11i | −0.271910 | + | 0.470962i | ||||
\(59\) | 2.29890e11 | + | 3.98181e11i | 0.709548 | + | 1.22897i | 0.965025 | + | 0.262158i | \(0.0844342\pi\) |
−0.255477 | + | 0.966815i | \(0.582233\pi\) | |||||||
\(60\) | −4.39178e10 | − | 7.60679e10i | −0.121523 | − | 0.210484i | ||||
\(61\) | 3.23925e10 | − | 5.61055e10i | 0.0805009 | − | 0.139432i | −0.822964 | − | 0.568093i | \(-0.807681\pi\) |
0.903465 | + | 0.428661i | \(0.141015\pi\) | |||||||
\(62\) | 3.92580e11 | 0.877772 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.87195e10 | 0.125000 | ||||||||
\(65\) | −3.95419e10 | + | 6.84885e10i | −0.0650310 | + | 0.112637i | ||||
\(66\) | 2.04838e11 | + | 3.54790e11i | 0.305053 | + | 0.528367i | ||||
\(67\) | 2.07214e11 | + | 3.58905e11i | 0.279855 | + | 0.484722i | 0.971348 | − | 0.237660i | \(-0.0763804\pi\) |
−0.691494 | + | 0.722382i | \(0.743047\pi\) | |||||||
\(68\) | −8.13276e10 | + | 1.40864e11i | −0.0997540 | + | 0.172779i | ||||
\(69\) | −1.12728e12 | −1.25751 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.38110e11 | −0.591175 | −0.295588 | − | 0.955316i | \(-0.595515\pi\) | ||||
−0.295588 | + | 0.955316i | \(0.595515\pi\) | |||||||
\(72\) | 8.34720e10 | − | 1.44578e11i | 0.0706122 | − | 0.122304i | ||||
\(73\) | 2.92998e11 | + | 5.07488e11i | 0.226603 | + | 0.392488i | 0.956799 | − | 0.290749i | \(-0.0939046\pi\) |
−0.730196 | + | 0.683238i | \(0.760571\pi\) | |||||||
\(74\) | −6.09547e11 | − | 1.05577e12i | −0.431520 | − | 0.747414i | ||||
\(75\) | −7.57756e11 | + | 1.31247e12i | −0.491622 | + | 0.851514i | ||||
\(76\) | −1.84414e11 | −0.109775 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.26608e11 | −0.264772 | ||||||||
\(79\) | −1.22943e12 | + | 2.12943e12i | −0.569019 | + | 0.985571i | 0.427644 | + | 0.903947i | \(0.359344\pi\) |
−0.996663 | + | 0.0816233i | \(0.973990\pi\) | |||||||
\(80\) | 1.20430e11 | + | 2.08591e11i | 0.0513630 | + | 0.0889633i | ||||
\(81\) | 1.57581e12 | + | 2.72939e12i | 0.619944 | + | 1.07377i | ||||
\(82\) | 1.35390e12 | − | 2.34502e12i | 0.491808 | − | 0.851837i | ||||
\(83\) | −3.32114e12 | −1.11501 | −0.557506 | − | 0.830173i | \(-0.688242\pi\) | ||||
−0.557506 | + | 0.830173i | \(0.688242\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.70103e11 | −0.163957 | ||||||||
\(86\) | −2.37717e12 | + | 4.11739e12i | −0.633609 | + | 1.09744i | ||||
\(87\) | −1.83990e12 | − | 3.18679e12i | −0.454902 | − | 0.787913i | ||||
\(88\) | −5.61701e11 | − | 9.72894e11i | −0.128934 | − | 0.223320i | ||||
\(89\) | −1.39203e12 | + | 2.41106e12i | −0.296902 | + | 0.514249i | −0.975426 | − | 0.220329i | \(-0.929287\pi\) |
0.678523 | + | 0.734579i | \(0.262620\pi\) | |||||||
\(90\) | 5.85135e11 | 0.116059 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.09119e12 | 0.531502 | ||||||||
\(93\) | −4.58125e12 | + | 7.93495e12i | −0.734251 | + | 1.27176i | ||||
\(94\) | −2.58245e12 | − | 4.47294e12i | −0.386101 | − | 0.668747i | ||||
\(95\) | −3.23183e11 | − | 5.59770e11i | −0.0451071 | − | 0.0781279i | ||||
\(96\) | −8.01928e11 | + | 1.38898e12i | −0.104562 | + | 0.181106i | ||||
\(97\) | 7.80467e12 | 0.951345 | 0.475672 | − | 0.879622i | \(-0.342205\pi\) | ||||
0.475672 | + | 0.879622i | \(0.342205\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.72914e12 | −0.291338 | ||||||||
\(100\) | 2.07789e12 | − | 3.59902e12i | 0.207789 | − | 0.359902i | ||||
\(101\) | 6.58305e12 | + | 1.14022e13i | 0.617076 | + | 1.06881i | 0.990017 | + | 0.140951i | \(0.0450160\pi\) |
−0.372941 | + | 0.927855i | \(0.621651\pi\) | |||||||
\(102\) | −1.89812e12 | − | 3.28764e12i | −0.166887 | − | 0.289057i | ||||
\(103\) | −8.84393e12 | + | 1.53181e13i | −0.729799 | + | 1.26405i | 0.227168 | + | 0.973855i | \(0.427053\pi\) |
−0.956968 | + | 0.290194i | \(0.906280\pi\) | |||||||
\(104\) | 1.44405e12 | 0.111909 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.41490e13 | 0.968806 | ||||||||
\(107\) | 7.23079e12 | − | 1.25241e13i | 0.465791 | − | 0.806774i | −0.533446 | − | 0.845834i | \(-0.679103\pi\) |
0.999237 | + | 0.0390602i | \(0.0124364\pi\) | |||||||
\(108\) | −2.92905e12 | − | 5.07326e12i | −0.177612 | − | 0.307633i | ||||
\(109\) | 7.96586e12 | + | 1.37973e13i | 0.454947 | + | 0.787991i | 0.998685 | − | 0.0512639i | \(-0.0163250\pi\) |
−0.543738 | + | 0.839255i | \(0.682992\pi\) | |||||||
\(110\) | 1.96875e12 | − | 3.40997e12i | 0.105959 | − | 0.183526i | ||||
\(111\) | 2.84526e13 | 1.44385 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.86885e12 | 0.219997 | 0.109998 | − | 0.993932i | \(-0.464915\pi\) | ||||
0.109998 | + | 0.993932i | \(0.464915\pi\) | |||||||
\(114\) | 2.15203e12 | − | 3.72743e12i | 0.0918264 | − | 0.159048i | ||||
\(115\) | 5.41728e12 | + | 9.38301e12i | 0.218396 | + | 0.378274i | ||||
\(116\) | 5.04530e12 | + | 8.73872e12i | 0.192269 | + | 0.333020i | ||||
\(117\) | 1.75405e12 | − | 3.03811e12i | 0.0632171 | − | 0.109495i | ||||
\(118\) | 2.94259e13 | 1.00345 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −5.62148e12 | −0.171859 | ||||||||
\(121\) | 8.07887e12 | − | 1.39930e13i | 0.234016 | − | 0.405328i | ||||
\(122\) | −2.07312e12 | − | 3.59075e12i | −0.0569227 | − | 0.0985930i | ||||
\(123\) | 3.15989e13 | + | 5.47309e13i | 0.822789 | + | 1.42511i | ||||
\(124\) | 1.25626e13 | − | 2.17590e13i | 0.310339 | − | 0.537524i | ||||
\(125\) | 3.20908e13 | 0.752430 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.02773e12 | 0.0217347 | 0.0108674 | − | 0.999941i | \(-0.496541\pi\) | ||||
0.0108674 | + | 0.999941i | \(0.496541\pi\) | |||||||
\(128\) | 2.19902e12 | − | 3.80882e12i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −5.54813e13 | − | 9.60965e13i | −1.06002 | − | 1.83601i | ||||
\(130\) | 2.53068e12 | + | 4.38327e12i | 0.0459839 | + | 0.0796464i | ||||
\(131\) | −3.08691e13 | + | 5.34668e13i | −0.533654 | + | 0.924317i | 0.465573 | + | 0.885010i | \(0.345848\pi\) |
−0.999227 | + | 0.0393070i | \(0.987485\pi\) | |||||||
\(132\) | 2.62193e13 | 0.431410 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.65234e13 | 0.395774 | ||||||||
\(135\) | 1.02662e13 | − | 1.77817e13i | 0.145963 | − | 0.252815i | ||||
\(136\) | 5.20497e12 | + | 9.01527e12i | 0.0705367 | + | 0.122173i | ||||
\(137\) | 6.61761e13 | + | 1.14620e14i | 0.855102 | + | 1.48108i | 0.876551 | + | 0.481310i | \(0.159839\pi\) |
−0.0214489 | + | 0.999770i | \(0.506828\pi\) | |||||||
\(138\) | −3.60730e13 | + | 6.24802e13i | −0.444598 | + | 0.770067i | ||||
\(139\) | 1.66284e14 | 1.95548 | 0.977742 | − | 0.209810i | \(-0.0672845\pi\) | ||||
0.977742 | + | 0.209810i | \(0.0672845\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.20545e14 | 1.29188 | ||||||||
\(142\) | −2.04195e13 | + | 3.53676e13i | −0.209012 | + | 0.362019i | ||||
\(143\) | −1.18034e13 | − | 2.04441e13i | −0.115431 | − | 0.199932i | ||||
\(144\) | −5.34221e12 | − | 9.25298e12i | −0.0499304 | − | 0.0864819i | ||||
\(145\) | −1.76837e13 | + | 3.06290e13i | −0.158009 | + | 0.273679i | ||||
\(146\) | 3.75038e13 | 0.320465 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.80220e13 | −0.610261 | ||||||||
\(149\) | −8.54482e13 | + | 1.48001e14i | −0.639723 | + | 1.10803i | 0.345770 | + | 0.938319i | \(0.387618\pi\) |
−0.985493 | + | 0.169714i | \(0.945716\pi\) | |||||||
\(150\) | 4.84964e13 | + | 8.39982e13i | 0.347629 | + | 0.602111i | ||||
\(151\) | −1.34805e14 | − | 2.33490e14i | −0.925458 | − | 1.60294i | −0.790823 | − | 0.612045i | \(-0.790347\pi\) |
−0.134635 | − | 0.990895i | \(-0.542986\pi\) | |||||||
\(152\) | −5.90124e12 | + | 1.02212e13i | −0.0388115 | + | 0.0672234i | ||||
\(153\) | 2.52894e13 | 0.159384 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.80630e13 | 0.510079 | ||||||||
\(156\) | −1.68515e13 | + | 2.91876e13i | −0.0936112 | + | 0.162139i | ||||
\(157\) | −2.65409e13 | − | 4.59702e13i | −0.141439 | − | 0.244979i | 0.786600 | − | 0.617463i | \(-0.211839\pi\) |
−0.928039 | + | 0.372484i | \(0.878506\pi\) | |||||||
\(158\) | 7.86834e13 | + | 1.36284e14i | 0.402358 | + | 0.696904i | ||||
\(159\) | −1.65113e14 | + | 2.85984e14i | −0.810400 | + | 1.40365i | ||||
\(160\) | 1.54151e13 | 0.0726382 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.01704e14 | 0.876733 | ||||||||
\(163\) | −1.25923e14 | + | 2.18105e14i | −0.525878 | + | 0.910847i | 0.473668 | + | 0.880704i | \(0.342930\pi\) |
−0.999546 | + | 0.0301433i | \(0.990404\pi\) | |||||||
\(164\) | −8.66495e13 | − | 1.50081e14i | −0.347761 | − | 0.602340i | ||||
\(165\) | 4.59490e13 | + | 7.95860e13i | 0.177268 | + | 0.307037i | ||||
\(166\) | −1.06277e14 | + | 1.84076e14i | −0.394216 | + | 0.682803i | ||||
\(167\) | 5.21452e12 | 0.0186019 | 0.00930095 | − | 0.999957i | \(-0.497039\pi\) | ||||
0.00930095 | + | 0.999957i | \(0.497039\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.72530e14 | −0.899811 | ||||||||
\(170\) | −1.82433e13 | + | 3.15983e13i | −0.0579676 | + | 0.100403i | ||||
\(171\) | 1.43362e13 | + | 2.48310e13i | 0.0438490 | + | 0.0759487i | ||||
\(172\) | 1.52139e14 | + | 2.63513e14i | 0.448029 | + | 0.776009i | ||||
\(173\) | 1.31565e14 | − | 2.27877e14i | 0.373113 | − | 0.646251i | −0.616929 | − | 0.787019i | \(-0.711624\pi\) |
0.990043 | + | 0.140767i | \(0.0449569\pi\) | |||||||
\(174\) | −2.35507e14 | −0.643329 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.18977e13 | −0.182340 | ||||||||
\(177\) | −3.43388e14 | + | 5.94766e14i | −0.839381 | + | 1.45385i | ||||
\(178\) | 8.90899e13 | + | 1.54308e14i | 0.209941 | + | 0.363629i | ||||
\(179\) | 1.81035e14 | + | 3.13562e14i | 0.411357 | + | 0.712490i | 0.995038 | − | 0.0994921i | \(-0.0317218\pi\) |
−0.583682 | + | 0.811982i | \(0.698388\pi\) | |||||||
\(180\) | 1.87243e13 | − | 3.24315e13i | 0.0410332 | − | 0.0710715i | ||||
\(181\) | 6.76438e14 | 1.42994 | 0.714969 | − | 0.699156i | \(-0.246441\pi\) | ||||
0.714969 | + | 0.699156i | \(0.246441\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.67699e13 | 0.190462 | ||||||||
\(184\) | 9.89182e13 | − | 1.71331e14i | 0.187914 | − | 0.325477i | ||||
\(185\) | −1.36733e14 | − | 2.36828e14i | −0.250759 | − | 0.434327i | ||||
\(186\) | 2.93200e14 | + | 5.07837e14i | 0.519194 | + | 0.899270i | ||||
\(187\) | 8.50890e13 | − | 1.47378e14i | 0.145513 | − | 0.252037i | ||||
\(188\) | −3.30554e14 | −0.546030 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.13674e13 | −0.0637911 | ||||||||
\(191\) | 3.80180e14 | − | 6.58492e14i | 0.566595 | − | 0.981372i | −0.430304 | − | 0.902684i | \(-0.641594\pi\) |
0.996899 | − | 0.0786877i | \(-0.0250730\pi\) | |||||||
\(192\) | 5.13234e13 | + | 8.88948e13i | 0.0739363 | + | 0.128061i | ||||
\(193\) | 3.21102e12 | + | 5.56164e12i | 0.00447219 | + | 0.00774605i | 0.868253 | − | 0.496122i | \(-0.165243\pi\) |
−0.863781 | + | 0.503868i | \(0.831910\pi\) | |||||||
\(194\) | 2.49749e14 | − | 4.32578e14i | 0.336351 | − | 0.582577i | ||||
\(195\) | −1.18128e14 | −0.153861 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.19711e14 | 0.511588 | 0.255794 | − | 0.966731i | \(-0.417663\pi\) | ||||
0.255794 | + | 0.966731i | \(0.417663\pi\) | |||||||
\(198\) | −8.73325e13 | + | 1.51264e14i | −0.103004 | + | 0.178407i | ||||
\(199\) | 7.53847e14 | + | 1.30570e15i | 0.860475 | + | 1.49039i | 0.871471 | + | 0.490447i | \(0.163166\pi\) |
−0.0109964 | + | 0.999940i | \(0.503500\pi\) | |||||||
\(200\) | −1.32985e14 | − | 2.30337e14i | −0.146929 | − | 0.254489i | ||||
\(201\) | −3.09517e14 | + | 5.36099e14i | −0.331062 | + | 0.573417i | ||||
\(202\) | 8.42631e14 | 0.872677 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.42960e14 | −0.236014 | ||||||||
\(205\) | 3.03705e14 | − | 5.26032e14i | 0.285793 | − | 0.495008i | ||||
\(206\) | 5.66012e14 | + | 9.80361e14i | 0.516046 | + | 0.893818i | ||||
\(207\) | −2.40307e14 | − | 4.16225e14i | −0.212305 | − | 0.367723i | ||||
\(208\) | 4.62096e13 | − | 8.00373e13i | 0.0395658 | − | 0.0685300i | ||||
\(209\) | 1.92943e14 | 0.160132 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.49543e14 | −0.740762 | −0.370381 | − | 0.928880i | \(-0.620773\pi\) | ||||
−0.370381 | + | 0.928880i | \(0.620773\pi\) | |||||||
\(212\) | 4.52767e14 | − | 7.84215e14i | 0.342525 | − | 0.593270i | ||||
\(213\) | −4.76575e14 | − | 8.25452e14i | −0.349674 | − | 0.605654i | ||||
\(214\) | −4.62771e14 | − | 8.01543e14i | −0.329364 | − | 0.570476i | ||||
\(215\) | −5.33245e14 | + | 9.23607e14i | −0.368194 | + | 0.637730i | ||||
\(216\) | −3.74918e14 | −0.251181 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.01963e15 | 0.643392 | ||||||||
\(219\) | −4.37654e14 | + | 7.58038e14i | −0.268067 | + | 0.464306i | ||||
\(220\) | −1.26000e14 | − | 2.18238e14i | −0.0749243 | − | 0.129773i | ||||
\(221\) | 1.09376e14 | + | 1.89444e14i | 0.0631496 | + | 0.109378i | ||||
\(222\) | 9.10485e14 | − | 1.57701e15i | 0.510479 | − | 0.884176i | ||||
\(223\) | −6.07949e14 | −0.331044 | −0.165522 | − | 0.986206i | \(-0.552931\pi\) | ||||
−0.165522 | + | 0.986206i | \(0.552931\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.46137e14 | −0.332000 | ||||||||
\(226\) | 1.55803e14 | − | 2.69859e14i | 0.0777806 | − | 0.134720i | ||||
\(227\) | −1.39309e15 | − | 2.41290e15i | −0.675788 | − | 1.17050i | −0.976238 | − | 0.216702i | \(-0.930470\pi\) |
0.300450 | − | 0.953798i | \(-0.402863\pi\) | |||||||
\(228\) | −1.37730e14 | − | 2.38556e14i | −0.0649311 | − | 0.112464i | ||||
\(229\) | 5.67556e14 | − | 9.83036e14i | 0.260063 | − | 0.450442i | −0.706196 | − | 0.708017i | \(-0.749590\pi\) |
0.966258 | + | 0.257575i | \(0.0829235\pi\) | |||||||
\(230\) | 6.93412e14 | 0.308859 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.45799e14 | 0.271910 | ||||||||
\(233\) | 1.01995e15 | − | 1.76660e15i | 0.417604 | − | 0.723312i | −0.578094 | − | 0.815970i | \(-0.696203\pi\) |
0.995698 | + | 0.0926588i | \(0.0295366\pi\) | |||||||
\(234\) | −1.12259e14 | − | 1.94439e14i | −0.0447013 | − | 0.0774249i | ||||
\(235\) | −5.79292e14 | − | 1.00336e15i | −0.224366 | − | 0.388613i | ||||
\(236\) | 9.41629e14 | − | 1.63095e15i | 0.354774 | − | 0.614487i | ||||
\(237\) | −3.67281e15 | −1.34628 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.57648e15 | −1.24128 | −0.620639 | − | 0.784096i | \(-0.713127\pi\) | ||||
−0.620639 | + | 0.784096i | \(0.713127\pi\) | |||||||
\(240\) | −1.79888e14 | + | 3.11574e14i | −0.0607614 | + | 0.105242i | ||||
\(241\) | −9.08192e14 | − | 1.57304e15i | −0.298584 | − | 0.517163i | 0.677228 | − | 0.735773i | \(-0.263181\pi\) |
−0.975812 | + | 0.218610i | \(0.929848\pi\) | |||||||
\(242\) | −5.17048e14 | − | 8.95553e14i | −0.165474 | − | 0.286610i | ||||
\(243\) | −1.21371e15 | + | 2.10220e15i | −0.378158 | + | 0.654989i | ||||
\(244\) | −2.65359e14 | −0.0805009 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.04466e15 | 1.16360 | ||||||||
\(247\) | −1.24007e14 | + | 2.14786e14i | −0.0347468 | + | 0.0601833i | ||||
\(248\) | −8.04003e14 | − | 1.39257e15i | −0.219443 | − | 0.380087i | ||||
\(249\) | −2.48041e15 | − | 4.29619e15i | −0.659519 | − | 1.14232i | ||||
\(250\) | 1.02691e15 | − | 1.77866e15i | 0.266024 | − | 0.460767i | ||||
\(251\) | −5.30330e15 | −1.33865 | −0.669325 | − | 0.742970i | \(-0.733417\pi\) | ||||
−0.669325 | + | 0.742970i | \(0.733417\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.23416e15 | −0.775314 | ||||||||
\(254\) | 3.28873e13 | − | 5.69625e13i | 0.00768439 | − | 0.0133098i | ||||
\(255\) | −4.25784e14 | − | 7.37479e14i | −0.0969791 | − | 0.167973i | ||||
\(256\) | −1.40737e14 | − | 2.43764e14i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.07805e15 | + | 1.86724e15i | −0.233385 | + | 0.404235i | −0.958802 | − | 0.284074i | \(-0.908314\pi\) |
0.725417 | + | 0.688310i | \(0.241647\pi\) | |||||||
\(258\) | −7.10161e15 | −1.49909 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.23927e14 | 0.0650310 | ||||||||
\(261\) | 7.84437e14 | − | 1.35869e15i | 0.153601 | − | 0.266045i | ||||
\(262\) | 1.97562e15 | + | 3.42188e15i | 0.377351 | + | 0.653591i | ||||
\(263\) | −2.88067e15 | − | 4.98946e15i | −0.536761 | − | 0.929697i | −0.999076 | − | 0.0429812i | \(-0.986314\pi\) |
0.462315 | − | 0.886716i | \(-0.347019\pi\) | |||||||
\(264\) | 8.39017e14 | − | 1.45322e15i | 0.152526 | − | 0.264184i | ||||
\(265\) | 3.17388e15 | 0.562979 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.15857e15 | −0.702459 | ||||||||
\(268\) | 8.48748e14 | − | 1.47007e15i | 0.139927 | − | 0.242361i | ||||
\(269\) | 4.23859e15 | + | 7.34146e15i | 0.682074 | + | 1.18139i | 0.974347 | + | 0.225052i | \(0.0722553\pi\) |
−0.292272 | + | 0.956335i | \(0.594411\pi\) | |||||||
\(270\) | −6.57040e14 | − | 1.13803e15i | −0.103211 | − | 0.178767i | ||||
\(271\) | −4.24299e14 | + | 7.34908e14i | −0.0650687 | + | 0.112702i | −0.896724 | − | 0.442589i | \(-0.854060\pi\) |
0.831656 | + | 0.555292i | \(0.187393\pi\) | |||||||
\(272\) | 6.66236e14 | 0.0997540 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.47055e15 | 1.20930 | ||||||||
\(275\) | −2.17400e15 | + | 3.76547e15i | −0.303107 | + | 0.524997i | ||||
\(276\) | 2.30867e15 | + | 3.99873e15i | 0.314378 | + | 0.544519i | ||||
\(277\) | −3.47520e15 | − | 6.01923e15i | −0.462234 | − | 0.800613i | 0.536838 | − | 0.843685i | \(-0.319619\pi\) |
−0.999072 | + | 0.0430726i | \(0.986285\pi\) | |||||||
\(278\) | 5.32109e15 | − | 9.21640e15i | 0.691368 | − | 1.19748i | ||||
\(279\) | −3.90642e15 | −0.495851 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.13665e15 | −0.137732 | −0.0688661 | − | 0.997626i | \(-0.521938\pi\) | ||||
−0.0688661 | + | 0.997626i | \(0.521938\pi\) | |||||||
\(282\) | 3.85743e15 | − | 6.68126e15i | 0.456750 | − | 0.791115i | ||||
\(283\) | −5.46610e15 | − | 9.46756e15i | −0.632508 | − | 1.09554i | −0.987037 | − | 0.160491i | \(-0.948692\pi\) |
0.354530 | − | 0.935045i | \(-0.384641\pi\) | |||||||
\(284\) | 1.30685e15 | + | 2.26353e15i | 0.147794 | + | 0.255986i | ||||
\(285\) | 4.82741e14 | − | 8.36133e14i | 0.0533609 | − | 0.0924237i | ||||
\(286\) | −1.51083e15 | −0.163244 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −6.83803e14 | −0.0706122 | ||||||||
\(289\) | 4.16382e15 | − | 7.21194e15i | 0.420393 | − | 0.728142i | ||||
\(290\) | 1.13176e15 | + | 1.96026e15i | 0.111729 | + | 0.193520i | ||||
\(291\) | 5.82895e15 | + | 1.00960e16i | 0.562711 | + | 0.974644i | ||||
\(292\) | 1.20012e15 | − | 2.07867e15i | 0.113302 | − | 0.196244i | ||||
\(293\) | 1.63957e15 | 0.151388 | 0.0756940 | − | 0.997131i | \(-0.475883\pi\) | ||||
0.0756940 | + | 0.997131i | \(0.475883\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.60078e15 | 0.583112 | ||||||||
\(296\) | −2.49670e15 | + | 4.32442e15i | −0.215760 | + | 0.373707i | ||||
\(297\) | 3.06451e15 | + | 5.30789e15i | 0.259086 | + | 0.448751i | ||||
\(298\) | 5.46868e15 | + | 9.47204e15i | 0.452352 | + | 0.783497i | ||||
\(299\) | 2.07863e15 | − | 3.60030e15i | 0.168235 | − | 0.291391i | ||||
\(300\) | 6.20754e15 | 0.491622 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.72551e16 | −1.30880 | ||||||||
\(303\) | −9.83316e15 | + | 1.70315e16i | −0.729988 | + | 1.26438i | ||||
\(304\) | 3.77679e14 | + | 6.54160e14i | 0.0274438 | + | 0.0475341i | ||||
\(305\) | −4.65040e14 | − | 8.05472e14i | −0.0330781 | − | 0.0572930i | ||||
\(306\) | 8.09262e14 | − | 1.40168e15i | 0.0563508 | − | 0.0976024i | ||||
\(307\) | −5.69931e15 | −0.388528 | −0.194264 | − | 0.980949i | \(-0.562232\pi\) | ||||
−0.194264 | + | 0.980949i | \(0.562232\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.64205e16 | −1.72668 | ||||||||
\(310\) | 2.81801e15 | − | 4.88094e15i | 0.180340 | − | 0.312358i | ||||
\(311\) | −4.65552e15 | − | 8.06360e15i | −0.291760 | − | 0.505343i | 0.682466 | − | 0.730917i | \(-0.260907\pi\) |
−0.974226 | + | 0.225574i | \(0.927574\pi\) | |||||||
\(312\) | 1.07849e15 | + | 1.86801e15i | 0.0661931 | + | 0.114650i | ||||
\(313\) | −2.82191e15 | + | 4.88770e15i | −0.169631 | + | 0.293810i | −0.938290 | − | 0.345849i | \(-0.887591\pi\) |
0.768659 | + | 0.639659i | \(0.220924\pi\) | |||||||
\(314\) | −3.39724e15 | −0.200024 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.00715e16 | 0.569019 | ||||||||
\(317\) | 6.10586e15 | − | 1.05757e16i | 0.337957 | − | 0.585359i | −0.646091 | − | 0.763260i | \(-0.723597\pi\) |
0.984048 | + | 0.177901i | \(0.0569308\pi\) | |||||||
\(318\) | 1.05672e16 | + | 1.83030e16i | 0.573039 | + | 0.992533i | ||||
\(319\) | −5.27864e15 | − | 9.14288e15i | −0.280468 | − | 0.485784i | ||||
\(320\) | 4.93282e14 | − | 8.54389e14i | 0.0256815 | − | 0.0444817i | ||||
\(321\) | 2.16014e16 | 1.10204 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.78789e15 | −0.0876043 | ||||||||
\(324\) | 6.45454e15 | − | 1.11796e16i | 0.309972 | − | 0.536887i | ||||
\(325\) | −2.79451e15 | − | 4.84023e15i | −0.131542 | − | 0.227837i | ||||
\(326\) | 8.05906e15 | + | 1.39587e16i | 0.371852 | + | 0.644066i | ||||
\(327\) | −1.18987e16 | + | 2.06091e16i | −0.538193 | + | 0.932178i | ||||
\(328\) | −1.10911e16 | −0.491808 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.88147e15 | 0.250695 | ||||||||
\(331\) | −6.64365e15 | + | 1.15071e16i | −0.277667 | + | 0.480934i | −0.970805 | − | 0.239872i | \(-0.922895\pi\) |
0.693137 | + | 0.720806i | \(0.256228\pi\) | |||||||
\(332\) | 6.80170e15 | + | 1.17809e16i | 0.278753 | + | 0.482815i | ||||
\(333\) | 6.06538e15 | + | 1.05055e16i | 0.243764 | + | 0.422212i | ||||
\(334\) | 1.66865e14 | − | 2.89018e14i | 0.00657676 | − | 0.0113913i | ||||
\(335\) | 5.94968e15 | 0.229987 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.83215e16 | 1.05323 | 0.526614 | − | 0.850105i | \(-0.323461\pi\) | ||||
0.526614 | + | 0.850105i | \(0.323461\pi\) | |||||||
\(338\) | −8.72097e15 | + | 1.51052e16i | −0.318131 | + | 0.551019i | ||||
\(339\) | 3.63632e15 | + | 6.29829e15i | 0.130126 | + | 0.225385i | ||||
\(340\) | 1.16757e15 | + | 2.02229e15i | 0.0409893 | + | 0.0709956i | ||||
\(341\) | −1.31436e16 | + | 2.27653e16i | −0.452699 | + | 0.784098i | ||||
\(342\) | 1.83504e15 | 0.0620118 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.94738e16 | 0.633609 | ||||||||
\(345\) | −8.09184e15 | + | 1.40155e16i | −0.258359 | + | 0.447490i | ||||
\(346\) | −8.42016e15 | − | 1.45841e16i | −0.263831 | − | 0.456969i | ||||
\(347\) | −2.42080e16 | − | 4.19294e16i | −0.744417 | − | 1.28937i | −0.950467 | − | 0.310827i | \(-0.899394\pi\) |
0.206049 | − | 0.978542i | \(-0.433939\pi\) | |||||||
\(348\) | −7.53621e15 | + | 1.30531e16i | −0.227451 | + | 0.393957i | ||||
\(349\) | 3.92608e16 | 1.16304 | 0.581519 | − | 0.813533i | \(-0.302459\pi\) | ||||
0.581519 | + | 0.813533i | \(0.302459\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.87840e15 | −0.224875 | ||||||||
\(352\) | −2.30073e15 | + | 3.98497e15i | −0.0644670 | + | 0.111660i | ||||
\(353\) | −1.09539e16 | − | 1.89728e16i | −0.301325 | − | 0.521909i | 0.675112 | − | 0.737716i | \(-0.264095\pi\) |
−0.976436 | + | 0.215806i | \(0.930762\pi\) | |||||||
\(354\) | 2.19769e16 | + | 3.80650e16i | 0.593532 | + | 1.02803i | ||||
\(355\) | −4.58048e15 | + | 7.93362e15i | −0.121458 | + | 0.210372i | ||||
\(356\) | 1.14035e16 | 0.296902 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.31725e16 | 0.581746 | ||||||||
\(359\) | −2.51750e16 | + | 4.36043e16i | −0.620662 | + | 1.07502i | 0.368701 | + | 0.929548i | \(0.379803\pi\) |
−0.989363 | + | 0.145470i | \(0.953531\pi\) | |||||||
\(360\) | −1.19836e15 | − | 2.07562e15i | −0.0290148 | − | 0.0502552i | ||||
\(361\) | 2.00130e16 | + | 3.46635e16i | 0.475899 | + | 0.824281i | ||||
\(362\) | 2.16460e16 | − | 3.74920e16i | 0.505559 | − | 0.875655i | ||||
\(363\) | 2.41350e16 | 0.553673 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.41279e15 | 0.186224 | ||||||||
\(366\) | 3.09664e15 | − | 5.36353e15i | 0.0673385 | − | 0.116634i | ||||
\(367\) | −4.30705e16 | − | 7.46002e16i | −0.920132 | − | 1.59372i | −0.799209 | − | 0.601053i | \(-0.794748\pi\) |
−0.120923 | − | 0.992662i | \(-0.538585\pi\) | |||||||
\(368\) | −6.33076e15 | − | 1.09652e16i | −0.132876 | − | 0.230147i | ||||
\(369\) | −1.34722e16 | + | 2.33345e16i | −0.277821 | + | 0.481201i | ||||
\(370\) | −1.75018e16 | −0.354626 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.75296e16 | 0.734251 | ||||||||
\(373\) | −1.65426e16 | + | 2.86526e16i | −0.318051 | + | 0.550880i | −0.980081 | − | 0.198597i | \(-0.936362\pi\) |
0.662030 | + | 0.749477i | \(0.269695\pi\) | |||||||
\(374\) | −5.44569e15 | − | 9.43222e15i | −0.102893 | − | 0.178217i | ||||
\(375\) | 2.39672e16 | + | 4.15124e16i | 0.445055 | + | 0.770858i | ||||
\(376\) | −1.05777e16 | + | 1.83212e16i | −0.193051 | + | 0.334373i | ||||
\(377\) | 1.35706e16 | 0.243434 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.13699e16 | 0.370380 | 0.185190 | − | 0.982703i | \(-0.440710\pi\) | ||||
0.185190 | + | 0.982703i | \(0.440710\pi\) | |||||||
\(380\) | −1.32376e15 | + | 2.29282e15i | −0.0225536 | + | 0.0390639i | ||||
\(381\) | 7.67564e14 | + | 1.32946e15i | 0.0128559 | + | 0.0222670i | ||||
\(382\) | −2.43315e16 | − | 4.21435e16i | −0.400643 | − | 0.693935i | ||||
\(383\) | −1.11443e16 | + | 1.93025e16i | −0.180410 | + | 0.312479i | −0.942020 | − | 0.335556i | \(-0.891076\pi\) |
0.761610 | + | 0.648035i | \(0.224409\pi\) | |||||||
\(384\) | 6.56940e15 | 0.104562 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.11010e14 | 0.00632463 | ||||||||
\(387\) | 2.36544e16 | − | 4.09706e16i | 0.357924 | − | 0.619943i | ||||
\(388\) | −1.59840e16 | − | 2.76850e16i | −0.237836 | − | 0.411944i | ||||
\(389\) | 1.09136e16 | + | 1.89028e16i | 0.159696 | + | 0.276602i | 0.934759 | − | 0.355282i | \(-0.115615\pi\) |
−0.775063 | + | 0.631884i | \(0.782282\pi\) | |||||||
\(390\) | −3.78010e15 | + | 6.54732e15i | −0.0543980 | + | 0.0942201i | ||||
\(391\) | 2.99691e16 | 0.424156 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.22188e16 | −1.26261 | ||||||||
\(394\) | 1.34308e16 | − | 2.32628e16i | 0.180874 | − | 0.313282i | ||||
\(395\) | 1.76502e16 | + | 3.05710e16i | 0.233812 | + | 0.404975i | ||||
\(396\) | 5.58928e15 | + | 9.68092e15i | 0.0728345 | + | 0.126153i | ||||
\(397\) | 1.31629e16 | − | 2.27988e16i | 0.168738 | − | 0.292263i | −0.769238 | − | 0.638962i | \(-0.779364\pi\) |
0.937977 | + | 0.346699i | \(0.112697\pi\) | |||||||
\(398\) | 9.64924e16 | 1.21690 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.70221e16 | −0.207789 | ||||||||
\(401\) | 8.00434e16 | − | 1.38639e17i | 0.961362 | − | 1.66513i | 0.242276 | − | 0.970207i | \(-0.422106\pi\) |
0.719086 | − | 0.694921i | \(-0.244561\pi\) | |||||||
\(402\) | 1.98091e16 | + | 3.43103e16i | 0.234097 | + | 0.405467i | ||||
\(403\) | −1.68951e16 | − | 2.92631e16i | −0.196461 | − | 0.340281i | ||||
\(404\) | 2.69642e16 | − | 4.67033e16i | 0.308538 | − | 0.534403i | ||||
\(405\) | 4.52460e16 | 0.509475 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.16304e16 | 0.890202 | ||||||||
\(408\) | −7.77470e15 | + | 1.34662e16i | −0.0834436 | + | 0.144528i | ||||
\(409\) | 9.81791e15 | + | 1.70051e16i | 0.103709 | + | 0.179630i | 0.913210 | − | 0.407489i | \(-0.133596\pi\) |
−0.809501 | + | 0.587119i | \(0.800262\pi\) | |||||||
\(410\) | −1.94371e16 | − | 3.36660e16i | −0.202086 | − | 0.350023i | ||||
\(411\) | −9.88478e16 | + | 1.71209e17i | −1.01157 | + | 1.75209i | ||||
\(412\) | 7.24495e16 | 0.729799 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.07593e16 | −0.300244 | ||||||||
\(415\) | −2.38398e16 | + | 4.12917e16i | −0.229081 | + | 0.396781i | ||||
\(416\) | −2.95741e15 | − | 5.12239e15i | −0.0279773 | − | 0.0484580i | ||||
\(417\) | 1.24190e17 | + | 2.15103e17i | 1.15665 | + | 2.00338i | ||||
\(418\) | 6.17417e15 | − | 1.06940e16i | 0.0566151 | − | 0.0980603i | ||||
\(419\) | −1.22382e17 | −1.10491 | −0.552454 | − | 0.833544i | \(-0.686308\pi\) | ||||
−0.552454 | + | 0.833544i | \(0.686308\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.43087e16 | −0.212778 | −0.106389 | − | 0.994325i | \(-0.533929\pi\) | ||||
−0.106389 | + | 0.994325i | \(0.533929\pi\) | |||||||
\(422\) | −3.03854e16 | + | 5.26290e16i | −0.261899 | + | 0.453622i | ||||
\(423\) | 2.56971e16 | + | 4.45086e16i | 0.218108 | + | 0.377774i | ||||
\(424\) | −2.89771e16 | − | 5.01898e16i | −0.242201 | − | 0.419505i | ||||
\(425\) | 2.01452e16 | − | 3.48925e16i | 0.165823 | − | 0.287213i | ||||
\(426\) | −6.10016e16 | −0.494514 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.92347e16 | −0.465791 | ||||||||
\(429\) | 1.76308e16 | − | 3.05375e16i | 0.136553 | − | 0.236516i | ||||
\(430\) | 3.41277e16 | + | 5.91108e16i | 0.260352 | + | 0.450943i | ||||
\(431\) | −6.14438e16 | − | 1.06424e17i | −0.461717 | − | 0.799717i | 0.537330 | − | 0.843372i | \(-0.319433\pi\) |
−0.999047 | + | 0.0436554i | \(0.986100\pi\) | |||||||
\(432\) | −1.19974e16 | + | 2.07801e16i | −0.0888059 | + | 0.153816i | ||||
\(433\) | 1.41055e17 | 1.02853 | 0.514267 | − | 0.857630i | \(-0.328064\pi\) | ||||
0.514267 | + | 0.857630i | \(0.328064\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.28285e16 | −0.373842 | ||||||||
\(436\) | 3.26282e16 | − | 5.65136e16i | 0.227473 | − | 0.393995i | ||||
\(437\) | 1.69891e16 | + | 2.94259e16i | 0.116692 | + | 0.202116i | ||||
\(438\) | 2.80098e16 | + | 4.85145e16i | 0.189552 | + | 0.328314i | ||||
\(439\) | 7.34941e16 | − | 1.27296e17i | 0.490042 | − | 0.848777i | −0.509893 | − | 0.860238i | \(-0.670315\pi\) |
0.999934 | + | 0.0114609i | \(0.00364820\pi\) | |||||||
\(440\) | −1.61280e16 | −0.105959 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.40001e16 | 0.0893070 | ||||||||
\(443\) | −9.34433e16 | + | 1.61849e17i | −0.587386 | + | 1.01738i | 0.407187 | + | 0.913345i | \(0.366510\pi\) |
−0.994573 | + | 0.104038i | \(0.966824\pi\) | |||||||
\(444\) | −5.82710e16 | − | 1.00928e17i | −0.360964 | − | 0.625207i | ||||
\(445\) | 1.99845e16 | + | 3.46142e16i | 0.121998 | + | 0.211307i | ||||
\(446\) | −1.94544e16 | + | 3.36959e16i | −0.117042 | + | 0.202722i | ||||
\(447\) | −2.55269e17 | −1.51356 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.15477e17 | 1.24108 | 0.620540 | − | 0.784175i | \(-0.286913\pi\) | ||||
0.620540 | + | 0.784175i | \(0.286913\pi\) | |||||||
\(450\) | −2.06764e16 | + | 3.58125e16i | −0.117380 | + | 0.203308i | ||||
\(451\) | 9.06570e16 | + | 1.57022e17i | 0.507287 | + | 0.878647i | ||||
\(452\) | −9.97141e15 | − | 1.72710e16i | −0.0549992 | − | 0.0952614i | ||||
\(453\) | 2.01360e17 | − | 3.48765e17i | 1.09480 | − | 1.89625i | ||||
\(454\) | −1.78315e17 | −0.955709 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.76295e16 | −0.0918264 | ||||||||
\(457\) | 1.91954e16 | − | 3.32474e16i | 0.0985694 | − | 0.170727i | −0.812523 | − | 0.582929i | \(-0.801907\pi\) |
0.911093 | + | 0.412201i | \(0.135240\pi\) | |||||||
\(458\) | −3.63236e16 | − | 6.29143e16i | −0.183892 | − | 0.318510i | ||||
\(459\) | −2.83971e16 | − | 4.91853e16i | −0.141740 | − | 0.245501i | ||||
\(460\) | 2.21892e16 | − | 3.84328e16i | 0.109198 | − | 0.189137i | ||||
\(461\) | −3.15284e17 | −1.52984 | −0.764921 | − | 0.644124i | \(-0.777222\pi\) | ||||
−0.764921 | + | 0.644124i | \(0.777222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.28642e17 | −1.07865 | −0.539323 | − | 0.842099i | \(-0.681320\pi\) | ||||
−0.539323 | + | 0.842099i | \(0.681320\pi\) | |||||||
\(464\) | 2.06656e16 | − | 3.57938e16i | 0.0961347 | − | 0.166510i | ||||
\(465\) | 6.57702e16 | + | 1.13917e17i | 0.301707 | + | 0.522571i | ||||
\(466\) | −6.52767e16 | − | 1.13063e17i | −0.295291 | − | 0.511458i | ||||
\(467\) | 1.06511e17 | − | 1.84482e17i | 0.475153 | − | 0.822989i | −0.524442 | − | 0.851446i | \(-0.675726\pi\) |
0.999595 | + | 0.0284570i | \(0.00905938\pi\) | |||||||
\(468\) | −1.43692e16 | −0.0632171 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7.41494e16 | −0.317301 | ||||||||
\(471\) | 3.96444e16 | − | 6.86661e16i | 0.167319 | − | 0.289805i | ||||
\(472\) | −6.02643e16 | − | 1.04381e17i | −0.250863 | − | 0.434508i | ||||
\(473\) | −1.59175e17 | − | 2.75700e17i | −0.653550 | − | 1.13198i | ||||
\(474\) | −1.17530e17 | + | 2.03568e17i | −0.475981 | + | 0.824424i | ||||
\(475\) | 4.56801e16 | 0.182481 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.40791e17 | −0.547276 | ||||||||
\(478\) | −1.14447e17 | + | 1.98228e17i | −0.438858 | + | 0.760124i | ||||
\(479\) | 1.57833e16 | + | 2.73374e16i | 0.0597058 | + | 0.103413i | 0.894333 | − | 0.447401i | \(-0.147650\pi\) |
−0.834628 | + | 0.550815i | \(0.814317\pi\) | |||||||
\(480\) | 1.15128e16 | + | 1.99408e16i | 0.0429648 | + | 0.0744172i | ||||
\(481\) | −5.24649e16 | + | 9.08719e16i | −0.193164 | + | 0.334570i | ||||
\(482\) | −1.16249e17 | −0.422262 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.61821e16 | −0.234016 | ||||||||
\(485\) | 5.60234e16 | − | 9.70354e16i | 0.195456 | − | 0.338539i | ||||
\(486\) | 7.76773e16 | + | 1.34541e17i | 0.267398 | + | 0.463147i | ||||
\(487\) | −2.71494e17 | − | 4.70241e17i | −0.922193 | − | 1.59729i | −0.796014 | − | 0.605278i | \(-0.793062\pi\) |
−0.126179 | − | 0.992008i | \(-0.540271\pi\) | |||||||
\(488\) | −8.49150e15 | + | 1.47077e16i | −0.0284614 | + | 0.0492965i | ||||
\(489\) | −3.76184e17 | −1.24421 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.87085e17 | 0.924658 | 0.462329 | − | 0.886708i | \(-0.347014\pi\) | ||||
0.462329 | + | 0.886708i | \(0.347014\pi\) | |||||||
\(492\) | 1.29429e17 | − | 2.24178e17i | 0.411395 | − | 0.712556i | ||||
\(493\) | 4.89143e16 | + | 8.47220e16i | 0.153437 | + | 0.265761i | ||||
\(494\) | 7.93643e15 | + | 1.37463e16i | 0.0245697 | + | 0.0425560i | ||||
\(495\) | −1.95903e16 | + | 3.39314e16i | −0.0598560 | + | 0.103674i | ||||
\(496\) | −1.02912e17 | −0.310339 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.17492e17 | −0.932701 | ||||||||
\(499\) | −2.64712e15 | + | 4.58495e15i | −0.00767575 | + | 0.0132948i | −0.869838 | − | 0.493338i | \(-0.835777\pi\) |
0.862162 | + | 0.506633i | \(0.169110\pi\) | |||||||
\(500\) | −6.57221e16 | − | 1.13834e17i | −0.188108 | − | 0.325812i | ||||
\(501\) | 3.89449e15 | + | 6.74545e15i | 0.0110028 | + | 0.0190575i | ||||
\(502\) | −1.69706e17 | + | 2.93939e17i | −0.473284 | + | 0.819753i | ||||
\(503\) | −9.65557e16 | −0.265819 | −0.132909 | − | 0.991128i | \(-0.542432\pi\) | ||||
−0.132909 | + | 0.991128i | \(0.542432\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.89018e17 | 0.507118 | ||||||||
\(506\) | −1.03493e17 | + | 1.79255e17i | −0.274115 | + | 0.474781i | ||||
\(507\) | −2.03540e17 | − | 3.52542e17i | −0.532229 | − | 0.921848i | ||||
\(508\) | −2.10479e15 | − | 3.64560e15i | −0.00543369 | − | 0.00941142i | ||||
\(509\) | 2.70435e17 | − | 4.68407e17i | 0.689283 | − | 1.19387i | −0.282787 | − | 0.959183i | \(-0.591259\pi\) |
0.972070 | − | 0.234691i | \(-0.0754077\pi\) | |||||||
\(510\) | −5.45003e16 | −0.137149 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.80144e16 | −0.0441942 | ||||||||
\(513\) | 3.21958e16 | − | 5.57648e16i | 0.0779896 | − | 0.135082i | ||||
\(514\) | 6.89952e16 | + | 1.19503e17i | 0.165028 | + | 0.285838i | ||||
\(515\) | 1.26967e17 | + | 2.19913e17i | 0.299877 | + | 0.519403i | ||||
\(516\) | −2.27252e17 | + | 3.93611e17i | −0.530010 | + | 0.918004i | ||||
\(517\) | 3.45842e17 | 0.796506 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.93040e17 | 0.882772 | ||||||||
\(520\) | 1.03657e16 | − | 1.79539e16i | 0.0229919 | − | 0.0398232i | ||||
\(521\) | 6.51595e16 | + | 1.12860e17i | 0.142736 | + | 0.247225i | 0.928526 | − | 0.371268i | \(-0.121077\pi\) |
−0.785790 | + | 0.618493i | \(0.787743\pi\) | |||||||
\(522\) | −5.02040e16 | − | 8.69559e16i | −0.108613 | − | 0.188122i | ||||
\(523\) | 4.34304e17 | − | 7.52237e17i | 0.927969 | − | 1.60729i | 0.141253 | − | 0.989974i | \(-0.454887\pi\) |
0.786716 | − | 0.617315i | \(-0.211780\pi\) | |||||||
\(524\) | 2.52879e17 | 0.533654 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.68725e17 | −0.759094 | ||||||||
\(527\) | 1.21794e17 | − | 2.10954e17i | 0.247661 | − | 0.428961i | ||||
\(528\) | −5.36971e16 | − | 9.30061e16i | −0.107853 | − | 0.186806i | ||||
\(529\) | −3.27570e16 | − | 5.67368e16i | −0.0649894 | − | 0.112565i | ||||
\(530\) | 1.01564e17 | − | 1.75914e17i | 0.199043 | − | 0.344753i | ||||
\(531\) | −2.92807e17 | −0.566848 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.33065e17 | −0.440302 | ||||||||
\(534\) | −1.33074e17 | + | 2.30491e17i | −0.248357 | + | 0.430166i | ||||
\(535\) | −1.03808e17 | − | 1.79801e17i | −0.191396 | − | 0.331507i | ||||
\(536\) | −5.43198e16 | − | 9.40847e16i | −0.0989435 | − | 0.171375i | ||||
\(537\) | −2.70414e17 | + | 4.68370e17i | −0.486627 | + | 0.842862i | ||||
\(538\) | 5.42540e17 | 0.964599 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −8.41011e16 | −0.145963 | ||||||||
\(541\) | 2.99150e17 | − | 5.18143e17i | 0.512988 | − | 0.888520i | −0.486899 | − | 0.873458i | \(-0.661872\pi\) |
0.999887 | − | 0.0150622i | \(-0.00479462\pi\) | |||||||
\(542\) | 2.71552e16 | + | 4.70341e16i | 0.0460105 | + | 0.0796925i | ||||
\(543\) | 5.05200e17 | + | 8.75033e17i | 0.845794 | + | 1.46496i | ||||
\(544\) | 2.13196e16 | − | 3.69265e16i | 0.0352684 | − | 0.0610866i | ||||
\(545\) | 2.28722e17 | 0.373879 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.94479e17 | 1.10851 | 0.554257 | − | 0.832345i | \(-0.313002\pi\) | ||||
0.554257 | + | 0.832345i | \(0.313002\pi\) | |||||||
\(548\) | 2.71057e17 | − | 4.69485e17i | 0.427551 | − | 0.740540i | ||||
\(549\) | 2.06289e16 | + | 3.57303e16i | 0.0321555 | + | 0.0556950i | ||||
\(550\) | 1.39136e17 | + | 2.40990e17i | 0.214329 | + | 0.371229i | ||||
\(551\) | −5.54576e16 | + | 9.60553e16i | −0.0844258 | + | 0.146230i | ||||
\(552\) | 2.95510e17 | 0.444598 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.44826e17 | −0.653698 | ||||||||
\(555\) | 2.04239e17 | − | 3.53752e17i | 0.296643 | − | 0.513800i | ||||
\(556\) | −3.40550e17 | − | 5.89849e17i | −0.488871 | − | 0.846750i | ||||
\(557\) | −4.32451e17 | − | 7.49027e17i | −0.613590 | − | 1.06277i | −0.990630 | − | 0.136572i | \(-0.956391\pi\) |
0.377040 | − | 0.926197i | \(-0.376942\pi\) | |||||||
\(558\) | −1.25005e17 | + | 2.16516e17i | −0.175310 | + | 0.303646i | ||||
\(559\) | 4.09216e17 | 0.567252 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.54196e17 | 0.344279 | ||||||||
\(562\) | −3.63728e16 | + | 6.29995e16i | −0.0486957 | + | 0.0843434i | ||||
\(563\) | 6.04730e16 | + | 1.04742e17i | 0.0800307 | + | 0.138617i | 0.903263 | − | 0.429088i | \(-0.141165\pi\) |
−0.823232 | + | 0.567705i | \(0.807831\pi\) | |||||||
\(564\) | −2.46875e17 | − | 4.27601e17i | −0.322971 | − | 0.559403i | ||||
\(565\) | 3.49496e16 | − | 6.05344e16i | 0.0451988 | − | 0.0782866i | ||||
\(566\) | −6.99661e17 | −0.894501 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.67277e17 | 0.209012 | ||||||||
\(569\) | 3.13843e17 | − | 5.43592e17i | 0.387688 | − | 0.671496i | −0.604450 | − | 0.796643i | \(-0.706607\pi\) |
0.992138 | + | 0.125147i | \(0.0399404\pi\) | |||||||
\(570\) | −3.08954e16 | − | 5.35125e16i | −0.0377318 | − | 0.0653535i | ||||
\(571\) | 6.18567e17 | + | 1.07139e18i | 0.746882 | + | 1.29364i | 0.949310 | + | 0.314340i | \(0.101783\pi\) |
−0.202428 | + | 0.979297i | \(0.564883\pi\) | |||||||
\(572\) | −4.83467e16 | + | 8.37390e16i | −0.0577155 | + | 0.0999662i | ||||
\(573\) | 1.13576e18 | 1.34054 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.65702e17 | −0.883525 | ||||||||
\(576\) | −2.18817e16 | + | 3.79002e16i | −0.0249652 | + | 0.0432410i | ||||
\(577\) | 4.22370e17 | + | 7.31566e17i | 0.476486 | + | 0.825298i | 0.999637 | − | 0.0269418i | \(-0.00857688\pi\) |
−0.523151 | + | 0.852240i | \(0.675244\pi\) | |||||||
\(578\) | −2.66484e17 | − | 4.61564e17i | −0.297263 | − | 0.514874i | ||||
\(579\) | −4.79632e15 | + | 8.30747e15i | −0.00529051 | + | 0.00916343i | ||||
\(580\) | 1.44865e17 | 0.158009 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.46105e17 | 0.795794 | ||||||||
\(583\) | −4.73707e17 | + | 8.20485e17i | −0.499648 | + | 0.865416i | ||||
\(584\) | −7.68077e16 | − | 1.33035e17i | −0.0801164 | − | 0.138766i | ||||
\(585\) | −2.51819e16 | − | 4.36163e16i | −0.0259762 | − | 0.0449920i | ||||
\(586\) | 5.24663e16 | − | 9.08744e16i | 0.0535237 | − | 0.0927058i | ||||
\(587\) | 9.19950e17 | 0.928146 | 0.464073 | − | 0.885797i | \(-0.346387\pi\) | ||||
0.464073 | + | 0.885797i | \(0.346387\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.76173e17 | 0.272541 | ||||||||
\(590\) | 2.11225e17 | − | 3.65852e17i | 0.206161 | − | 0.357082i | ||||
\(591\) | 3.13463e17 | + | 5.42934e17i | 0.302599 | + | 0.524117i | ||||
\(592\) | 1.59789e17 | + | 2.76763e17i | 0.152565 | + | 0.264251i | ||||
\(593\) | −3.65725e16 | + | 6.33454e16i | −0.0345381 | + | 0.0598218i | −0.882778 | − | 0.469791i | \(-0.844329\pi\) |
0.848240 | + | 0.529613i | \(0.177663\pi\) | |||||||
\(594\) | 3.92258e17 | 0.366403 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.99991e17 | 0.639723 | ||||||||
\(597\) | −1.12603e18 | + | 1.95034e18i | −1.01792 | + | 1.76310i | ||||
\(598\) | −1.33033e17 | − | 2.30419e17i | −0.118960 | − | 0.206044i | ||||
\(599\) | 1.99308e17 | + | 3.45212e17i | 0.176299 | + | 0.305360i | 0.940610 | − | 0.339489i | \(-0.110254\pi\) |
−0.764311 | + | 0.644848i | \(0.776921\pi\) | |||||||
\(600\) | 1.98641e17 | − | 3.44057e17i | 0.173815 | − | 0.301056i | ||||
\(601\) | −2.02331e18 | −1.75137 | −0.875686 | − | 0.482882i | \(-0.839590\pi\) | ||||
−0.875686 | + | 0.482882i | \(0.839590\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.63924e17 | −0.223572 | ||||||||
\(604\) | −5.52162e17 | + | 9.56373e17i | −0.462729 | + | 0.801470i | ||||
\(605\) | −1.15983e17 | − | 2.00889e17i | −0.0961582 | − | 0.166551i | ||||
\(606\) | 6.29322e17 | + | 1.09002e18i | 0.516180 | + | 0.894049i | ||||
\(607\) | −9.11136e17 | + | 1.57813e18i | −0.739361 | + | 1.28061i | 0.213422 | + | 0.976960i | \(0.431539\pi\) |
−0.952783 | + | 0.303651i | \(0.901794\pi\) | |||||||
\(608\) | 4.83430e16 | 0.0388115 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.95251e16 | −0.0467795 | ||||||||
\(611\) | −2.22277e17 | + | 3.84995e17i | −0.172833 | + | 0.299355i | ||||
\(612\) | −5.17928e16 | − | 8.97077e16i | −0.0398460 | − | 0.0690153i | ||||
\(613\) | 8.93380e17 | + | 1.54738e18i | 0.680054 | + | 1.17789i | 0.974964 | + | 0.222363i | \(0.0713769\pi\) |
−0.294910 | + | 0.955525i | \(0.595290\pi\) | |||||||
\(614\) | −1.82378e17 | + | 3.15888e17i | −0.137366 | + | 0.237924i | ||||
\(615\) | 9.07292e17 | 0.676175 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.80000e17 | 0.642139 | 0.321070 | − | 0.947056i | \(-0.395958\pi\) | ||||
0.321070 | + | 0.947056i | \(0.395958\pi\) | |||||||
\(618\) | −8.45456e17 | + | 1.46437e18i | −0.610472 | + | 1.05737i | ||||
\(619\) | −4.84990e16 | − | 8.40027e16i | −0.0346532 | − | 0.0600211i | 0.848179 | − | 0.529710i | \(-0.177699\pi\) |
−0.882832 | + | 0.469689i | \(0.844366\pi\) | |||||||
\(620\) | −1.80353e17 | − | 3.12380e17i | −0.127520 | − | 0.220871i | ||||
\(621\) | −5.39675e17 | + | 9.34745e17i | −0.377604 | + | 0.654030i | ||||
\(622\) | −5.95906e17 | −0.412611 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.38047e17 | 0.0936112 | ||||||||
\(625\) | −3.88906e17 | + | 6.73606e17i | −0.260991 | + | 0.452049i | ||||
\(626\) | 1.80602e17 | + | 3.12813e17i | 0.119947 | + | 0.207755i | ||||
\(627\) | 1.44100e17 | + | 2.49589e17i | 0.0947164 | + | 0.164054i | ||||
\(628\) | −1.08712e17 | + | 1.88294e17i | −0.0707193 | + | 0.122489i | ||||
\(629\) | −7.56424e17 | −0.487008 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.85605e15 | −0.00558533 | −0.00279267 | − | 0.999996i | \(-0.500889\pi\) | ||||
−0.00279267 | + | 0.999996i | \(0.500889\pi\) | |||||||
\(632\) | 3.22287e17 | − | 5.58218e17i | 0.201179 | − | 0.348452i | ||||
\(633\) | −7.09170e17 | − | 1.22832e18i | −0.438153 | − | 0.758904i | ||||
\(634\) | −3.90775e17 | − | 6.76842e17i | −0.238972 | − | 0.413911i | ||||
\(635\) | 7.37724e15 | − | 1.27778e16i | 0.00446545 | − | 0.00773438i | ||||
\(636\) | 1.35260e18 | 0.810400 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.75666e17 | −0.396641 | ||||||||
\(639\) | 2.03187e17 | − | 3.51931e17i | 0.118070 | − | 0.204504i | ||||
\(640\) | −3.15700e16 | − | 5.46809e16i | −0.0181596 | − | 0.0314533i | ||||
\(641\) | −3.07694e17 | − | 5.32941e17i | −0.175203 | − | 0.303460i | 0.765029 | − | 0.643996i | \(-0.222725\pi\) |
−0.940232 | + | 0.340536i | \(0.889392\pi\) | |||||||
\(642\) | 6.91244e17 | − | 1.19727e18i | 0.389631 | − | 0.674861i | ||||
\(643\) | 9.48803e17 | 0.529425 | 0.264713 | − | 0.964327i | \(-0.414723\pi\) | ||||
0.264713 | + | 0.964327i | \(0.414723\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.59302e18 | −0.871132 | ||||||||
\(646\) | −5.72126e16 | + | 9.90951e16i | −0.0309728 | + | 0.0536464i | ||||
\(647\) | 9.09981e16 | + | 1.57613e17i | 0.0487702 | + | 0.0844725i | 0.889380 | − | 0.457169i | \(-0.151136\pi\) |
−0.840610 | + | 0.541641i | \(0.817803\pi\) | |||||||
\(648\) | −4.13090e17 | − | 7.15494e17i | −0.219183 | − | 0.379637i | ||||
\(649\) | −9.85178e17 | + | 1.70638e18i | −0.517517 | + | 0.896365i | ||||
\(650\) | −3.57697e17 | −0.186028 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.03156e18 | 0.525878 | ||||||||
\(653\) | −1.38478e18 | + | 2.39851e18i | −0.698947 | + | 1.21061i | 0.269884 | + | 0.962893i | \(0.413015\pi\) |
−0.968832 | + | 0.247720i | \(0.920319\pi\) | |||||||
\(654\) | 7.61515e17 | + | 1.31898e18i | 0.380560 | + | 0.659149i | ||||
\(655\) | 4.43169e17 | + | 7.67590e17i | 0.219281 | + | 0.379805i | ||||
\(656\) | −3.54916e17 | + | 6.14733e17i | −0.173881 | + | 0.301170i | ||||
\(657\) | −3.73186e17 | −0.181030 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.98995e18 | −0.946427 | −0.473213 | − | 0.880948i | \(-0.656906\pi\) | ||||
−0.473213 | + | 0.880948i | \(0.656906\pi\) | |||||||
\(660\) | 1.88207e17 | − | 3.25984e17i | 0.0886340 | − | 0.153519i | ||||
\(661\) | −5.81844e17 | − | 1.00778e18i | −0.271330 | − | 0.469957i | 0.697873 | − | 0.716222i | \(-0.254130\pi\) |
−0.969203 | + | 0.246265i | \(0.920797\pi\) | |||||||
\(662\) | 4.25194e17 | + | 7.36457e17i | 0.196340 | + | 0.340072i | ||||
\(663\) | −1.63375e17 | + | 2.82974e17i | −0.0747047 | + | 0.129392i | ||||
\(664\) | 8.70617e17 | 0.394216 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.76368e17 | 0.344735 | ||||||||
\(667\) | 9.29594e17 | − | 1.61010e18i | 0.408767 | − | 0.708005i | ||||
\(668\) | −1.06793e16 | − | 1.84972e16i | −0.00465047 | − | 0.00805486i | ||||
\(669\) | −4.54049e17 | − | 7.86436e17i | −0.195809 | − | 0.339151i | ||||
\(670\) | 1.90390e17 | − | 3.29765e17i | 0.0813126 | − | 0.140837i | ||||
\(671\) | 2.77632e17 | 0.117428 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.44542e18 | 0.599650 | 0.299825 | − | 0.953994i | \(-0.403072\pi\) | ||||
0.299825 | + | 0.953994i | \(0.403072\pi\) | |||||||
\(674\) | 9.06289e17 | − | 1.56974e18i | 0.372372 | − | 0.644967i | ||||
\(675\) | 7.25538e17 | + | 1.25667e18i | 0.295247 | + | 0.511383i | ||||
\(676\) | 5.58142e17 | + | 9.66731e17i | 0.224953 | + | 0.389630i | ||||
\(677\) | 1.90818e18 | − | 3.30507e18i | 0.761716 | − | 1.31933i | −0.180249 | − | 0.983621i | \(-0.557690\pi\) |
0.941965 | − | 0.335710i | \(-0.108976\pi\) | |||||||
\(678\) | 4.65449e17 | 0.184026 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.49449e17 | 0.0579676 | ||||||||
\(681\) | 2.08087e18 | − | 3.60417e18i | 0.799444 | − | 1.38468i | ||||
\(682\) | 8.41188e17 | + | 1.45698e18i | 0.320107 | + | 0.554441i | ||||
\(683\) | −1.14349e17 | − | 1.98058e17i | −0.0431019 | − | 0.0746547i | 0.843670 | − | 0.536863i | \(-0.180391\pi\) |
−0.886772 | + | 0.462208i | \(0.847057\pi\) | |||||||
\(684\) | 5.87211e16 | − | 1.01708e17i | 0.0219245 | − | 0.0379743i | ||||
\(685\) | 1.90010e18 | 0.702729 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.69553e18 | 0.615298 | ||||||||
\(688\) | 6.23162e17 | − | 1.07935e18i | 0.224015 | − | 0.388005i | ||||
\(689\) | −6.08915e17 | − | 1.05467e18i | −0.216836 | − | 0.375571i | ||||
\(690\) | 5.17878e17 | + | 8.96990e17i | 0.182687 | + | 0.316423i | ||||
\(691\) | −1.65297e18 | + | 2.86303e18i | −0.577642 | + | 1.00051i | 0.418107 | + | 0.908398i | \(0.362694\pi\) |
−0.995749 | + | 0.0921074i | \(0.970640\pi\) | |||||||
\(692\) | −1.07778e18 | −0.373113 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.09862e18 | −1.05276 | ||||||||
\(695\) | 1.19362e18 | − | 2.06741e18i | 0.401758 | − | 0.695866i | ||||
\(696\) | 4.82317e17 | + | 8.35398e17i | 0.160832 | + | 0.278569i | ||||
\(697\) | −8.40068e17 | − | 1.45504e18i | −0.277524 | − | 0.480686i | ||||
\(698\) | 1.25634e18 | − | 2.17605e18i | 0.411196 | − | 0.712212i | ||||
\(699\) | 3.04701e18 | 0.988035 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.97078e18 | −0.627293 | −0.313647 | − | 0.949540i | \(-0.601551\pi\) | ||||
−0.313647 | + | 0.949540i | \(0.601551\pi\) | |||||||
\(702\) | −2.52109e17 | + | 4.36666e17i | −0.0795055 | + | 0.137708i | ||||
\(703\) | −4.28805e17 | − | 7.42713e17i | −0.133983 | − | 0.232066i | ||||
\(704\) | 1.47246e17 | + | 2.55038e17i | 0.0455851 | + | 0.0789557i | ||||
\(705\) | 8.65293e17 | − | 1.49873e18i | 0.265420 | − | 0.459721i | ||||
\(706\) | −1.40210e18 | −0.426137 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.81304e18 | 0.839381 | ||||||||
\(709\) | −1.90872e18 | + | 3.30601e18i | −0.564342 | + | 0.977470i | 0.432768 | + | 0.901505i | \(0.357537\pi\) |
−0.997111 | + | 0.0759644i | \(0.975796\pi\) | |||||||
\(710\) | 2.93151e17 | + | 5.07752e17i | 0.0858839 | + | 0.148755i | ||||
\(711\) | −7.82950e17 | − | 1.35611e18i | −0.227291 | − | 0.393679i | ||||
\(712\) | 3.64912e17 | − | 6.32046e17i | 0.104971 | − | 0.181815i | ||||
\(713\) | −4.62929e18 | −1.31957 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.38908e17 | −0.0948622 | ||||||||
\(716\) | 7.41520e17 | − | 1.28435e18i | 0.205678 | − | 0.356245i | ||||
\(717\) | −2.67111e18 | − | 4.62649e18i | −0.734204 | − | 1.27168i | ||||
\(718\) | 1.61120e18 | + | 2.79068e18i | 0.438874 | + | 0.760152i | ||||
\(719\) | 1.80548e18 | − | 3.12718e18i | 0.487365 | − | 0.844141i | −0.512529 | − | 0.858670i | \(-0.671291\pi\) |
0.999894 | + | 0.0145287i | \(0.00462480\pi\) | |||||||
\(720\) | −1.53390e17 | −0.0410332 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.56166e18 | 0.673022 | ||||||||
\(723\) | 1.35657e18 | − | 2.34966e18i | 0.353219 | − | 0.611794i | ||||
\(724\) | −1.38534e18 | − | 2.39949e18i | −0.357484 | − | 0.619181i | ||||
\(725\) | −1.24974e18 | − | 2.16462e18i | −0.319613 | − | 0.553585i | ||||
\(726\) | 7.72319e17 | − | 1.33769e18i | 0.195753 | − | 0.339054i | ||||
\(727\) | 3.60755e18 | 0.906230 | 0.453115 | − | 0.891452i | \(-0.350313\pi\) | ||||
0.453115 | + | 0.891452i | \(0.350313\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.39886e18 | 0.345181 | ||||||||
\(730\) | 2.69209e17 | − | 4.66284e17i | 0.0658403 | − | 0.114039i | ||||
\(731\) | 1.47499e18 | + | 2.55476e18i | 0.357541 | + | 0.619280i | ||||
\(732\) | −1.98185e17 | − | 3.43266e17i | −0.0476155 | − | 0.0824724i | ||||
\(733\) | −5.46187e17 | + | 9.46024e17i | −0.130067 | + | 0.225282i | −0.923702 | − | 0.383112i | \(-0.874852\pi\) |
0.793635 | + | 0.608394i | \(0.208186\pi\) | |||||||
\(734\) | −5.51302e18 | −1.30126 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.10337e17 | −0.187914 | ||||||||
\(737\) | −8.88001e17 | + | 1.53806e18i | −0.204115 | + | 0.353538i | ||||
\(738\) | 8.62218e17 | + | 1.49341e18i | 0.196449 | + | 0.340260i | ||||
\(739\) | −2.64348e18 | − | 4.57864e18i | −0.597018 | − | 1.03407i | −0.993259 | − | 0.115919i | \(-0.963019\pi\) |
0.396241 | − | 0.918147i | \(-0.370315\pi\) | |||||||
\(740\) | −5.60057e17 | + | 9.70047e17i | −0.125379 | + | 0.217163i | ||||
\(741\) | −3.70460e17 | −0.0822096 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.06272e18 | −0.231736 | −0.115868 | − | 0.993265i | \(-0.536965\pi\) | ||||
−0.115868 | + | 0.993265i | \(0.536965\pi\) | |||||||
\(744\) | 1.20095e18 | − | 2.08010e18i | 0.259597 | − | 0.449635i | ||||
\(745\) | 1.22673e18 | + | 2.12475e18i | 0.262865 | + | 0.455295i | ||||
\(746\) | 1.05873e18 | + | 1.83377e18i | 0.224896 | + | 0.389531i | ||||
\(747\) | 1.05752e18 | − | 1.83168e18i | 0.222692 | − | 0.385714i | ||||
\(748\) | −6.97049e17 | −0.145513 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.06780e18 | 0.629403 | ||||||||
\(751\) | −4.48188e17 | + | 7.76285e17i | −0.0911593 | + | 0.157892i | −0.907999 | − | 0.418972i | \(-0.862391\pi\) |
0.816840 | + | 0.576864i | \(0.195724\pi\) | |||||||
\(752\) | 6.76974e17 | + | 1.17255e18i | 0.136507 | + | 0.236438i | ||||
\(753\) | −3.96079e18 | − | 6.86029e18i | −0.791799 | − | 1.37144i | ||||
\(754\) | 4.34259e17 | − | 7.52159e17i | 0.0860668 | − | 0.149072i | ||||
\(755\) | −3.87063e18 | −0.760549 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.71607e18 | −1.29716 | −0.648578 | − | 0.761148i | \(-0.724636\pi\) | ||||
−0.648578 | + | 0.761148i | \(0.724636\pi\) | |||||||
\(758\) | 6.83837e17 | − | 1.18444e18i | 0.130949 | − | 0.226811i | ||||
\(759\) | −2.41544e18 | − | 4.18367e18i | −0.458591 | − | 0.794303i | ||||
\(760\) | 8.47205e16 | + | 1.46740e17i | 0.0159478 | + | 0.0276224i | ||||
\(761\) | −3.56938e18 | + | 6.18234e18i | −0.666181 | + | 1.15386i | 0.312783 | + | 0.949825i | \(0.398739\pi\) |
−0.978964 | + | 0.204034i | \(0.934595\pi\) | |||||||
\(762\) | 9.82481e16 | 0.0181810 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.11444e18 | −0.566595 | ||||||||
\(765\) | 1.81533e17 | − | 3.14424e17i | 0.0327458 | − | 0.0567173i | ||||
\(766\) | 7.13234e17 | + | 1.23536e18i | 0.127569 | + | 0.220956i | ||||
\(767\) | −1.26637e18 | − | 2.19342e18i | −0.224591 | − | 0.389003i | ||||
\(768\) | 2.10221e17 | − | 3.64113e17i | 0.0369681 | − | 0.0640307i | ||||
\(769\) | −9.57731e18 | −1.67002 | −0.835011 | − | 0.550233i | \(-0.814539\pi\) | ||||
−0.835011 | + | 0.550233i | \(0.814539\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.22059e18 | −0.552181 | ||||||||
\(772\) | 1.31523e16 | − | 2.27805e16i | 0.00223609 | − | 0.00387303i | ||||
\(773\) | 1.07825e18 | + | 1.86758e18i | 0.181783 | + | 0.314857i | 0.942488 | − | 0.334241i | \(-0.108480\pi\) |
−0.760705 | + | 0.649098i | \(0.775147\pi\) | |||||||
\(774\) | −1.51388e18 | − | 2.62212e18i | −0.253090 | − | 0.438366i | ||||
\(775\) | −3.11180e18 | + | 5.38979e18i | −0.515882 | + | 0.893534i | ||||
\(776\) | −2.04595e18 | −0.336351 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.39694e18 | 0.225844 | ||||||||
\(779\) | 9.52444e17 | − | 1.64968e18i | 0.152702 | − | 0.264488i | ||||
\(780\) | 2.41926e17 | + | 4.19029e17i | 0.0384652 | + | 0.0666237i | ||||
\(781\) | −1.36729e18 | − | 2.36822e18i | −0.215590 | − | 0.373413i | ||||
\(782\) | 9.59012e17 | − | 1.66106e18i | 0.149962 | − | 0.259741i | ||||
\(783\) | −3.52333e18 | −0.546389 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.62063e17 | −0.116235 | ||||||||
\(786\) | −2.95100e18 | + | 5.11128e18i | −0.446398 | + | 0.773185i | ||||
\(787\) | −1.41242e18 | − | 2.44639e18i | −0.211899 | − | 0.367020i | 0.740410 | − | 0.672156i | \(-0.234631\pi\) |
−0.952309 | + | 0.305136i | \(0.901298\pi\) | |||||||
\(788\) | −8.59569e17 | − | 1.48882e18i | −0.127897 | − | 0.221524i | ||||
\(789\) | 4.30288e18 | − | 7.45280e18i | 0.634977 | − | 1.09981i | ||||
\(790\) | 2.25922e18 | 0.330661 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.15428e17 | 0.103004 | ||||||||
\(793\) | −1.78438e17 | + | 3.09063e17i | −0.0254807 | + | 0.0441338i | ||||
\(794\) | −8.42427e17 | − | 1.45913e18i | −0.119316 | − | 0.206661i | ||||
\(795\) | 2.37042e18 | + | 4.10569e18i | 0.332996 | + | 0.576767i | ||||
\(796\) | 3.08776e18 | − | 5.34815e18i | 0.430237 | − | 0.745193i | ||||
\(797\) | −8.37611e18 | −1.15761 | −0.578806 | − | 0.815465i | \(-0.696481\pi\) | ||||
−0.578806 | + | 0.815465i | \(0.696481\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.20472e18 | −0.435749 | ||||||||
\(800\) | −5.44708e17 | + | 9.43461e17i | −0.0734647 | + | 0.127245i | ||||
\(801\) | −8.86501e17 | − | 1.53546e18i | −0.118595 | − | 0.205413i | ||||
\(802\) | −5.12278e18 | − | 8.87291e18i | −0.679786 | − | 1.17742i | ||||
\(803\) | −1.25562e18 | + | 2.17481e18i | −0.165276 | + | 0.286266i | ||||
\(804\) | 2.53556e18 | 0.331062 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.16257e18 | −0.277838 | ||||||||
\(807\) | −6.33122e18 | + | 1.09660e19i | −0.806881 | + | 1.39756i | ||||
\(808\) | −1.72571e18 | − | 2.98901e18i | −0.218169 | − | 0.377880i | ||||
\(809\) | 1.08897e18 | + | 1.88615e18i | 0.136569 | + | 0.236544i | 0.926196 | − | 0.377043i | \(-0.123059\pi\) |
−0.789627 | + | 0.613587i | \(0.789726\pi\) | |||||||
\(810\) | 1.44787e18 | − | 2.50779e18i | 0.180127 | − | 0.311988i | ||||
\(811\) | 1.05998e19 | 1.30817 | 0.654084 | − | 0.756422i | \(-0.273054\pi\) | ||||
0.654084 | + | 0.756422i | \(0.273054\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.26756e18 | −0.153950 | ||||||||
\(814\) | 2.61217e18 | − | 4.52442e18i | 0.314734 | − | 0.545135i | ||||
\(815\) | 1.80780e18 | + | 3.13120e18i | 0.216085 | + | 0.374271i | ||||
\(816\) | 4.97581e17 | + | 8.61836e17i | 0.0590035 | + | 0.102197i | ||||
\(817\) | −1.67230e18 | + | 2.89651e18i | −0.196730 | + | 0.340747i | ||||
\(818\) | 1.25669e18 | 0.146667 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.48795e18 | −0.285793 | ||||||||
\(821\) | −5.15388e16 | + | 8.92679e16i | −0.00587360 | + | 0.0101734i | −0.868947 | − | 0.494905i | \(-0.835203\pi\) |
0.863074 | + | 0.505078i | \(0.168536\pi\) | |||||||
\(822\) | 6.32626e18 | + | 1.09574e19i | 0.715287 | + | 1.23891i | ||||
\(823\) | 5.26006e18 | + | 9.11070e18i | 0.590054 | + | 1.02200i | 0.994224 | + | 0.107320i | \(0.0342271\pi\) |
−0.404170 | + | 0.914684i | \(0.632440\pi\) | |||||||
\(824\) | 2.31838e18 | − | 4.01556e18i | 0.258023 | − | 0.446909i | ||||
\(825\) | −6.49463e18 | −0.717140 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.20216e19 | 1.30670 | 0.653350 | − | 0.757056i | \(-0.273363\pi\) | ||||
0.653350 | + | 0.757056i | \(0.273363\pi\) | |||||||
\(828\) | −9.84299e17 | + | 1.70486e18i | −0.106152 | + | 0.183861i | ||||
\(829\) | 1.57256e18 | + | 2.72375e18i | 0.168268 | + | 0.291449i | 0.937811 | − | 0.347146i | \(-0.112849\pi\) |
−0.769543 | + | 0.638595i | \(0.779516\pi\) | |||||||
\(830\) | 1.52575e18 | + | 2.64267e18i | 0.161985 | + | 0.280566i | ||||
\(831\) | 5.19094e18 | − | 8.99097e18i | 0.546814 | − | 0.947109i | ||||
\(832\) | −3.78549e17 | −0.0395658 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.58963e19 | 1.63575 | ||||||||
\(835\) | 3.74308e16 | − | 6.48321e16i | 0.00382180 | − | 0.00661955i | ||||
\(836\) | −3.95147e17 | − | 6.84414e17i | −0.0400330 | − | 0.0693391i | ||||
\(837\) | 4.38646e18 | + | 7.59757e18i | 0.440960 | + | 0.763765i | ||||
\(838\) | −3.91622e18 | + | 6.78309e18i | −0.390644 | + | 0.676615i | ||||
\(839\) | −5.05894e18 | −0.500734 | −0.250367 | − | 0.968151i | \(-0.580551\pi\) | ||||
−0.250367 | + | 0.968151i | \(0.580551\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.19166e18 | −0.408519 | ||||||||
\(842\) | −7.77878e17 | + | 1.34732e18i | −0.0752286 | + | 0.130300i | ||||
\(843\) | −8.48911e17 | − | 1.47036e18i | −0.0814672 | − | 0.141105i | ||||
\(844\) | 1.94466e18 | + | 3.36826e18i | 0.185190 | + | 0.320759i | ||||
\(845\) | −1.95628e18 | + | 3.38837e18i | −0.184868 | + | 0.320201i | ||||
\(846\) | 3.28922e18 | 0.308451 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.70907e18 | −0.342525 | ||||||||
\(849\) | 8.16476e18 | − | 1.41418e19i | 0.748244 | − | 1.29600i | ||||
\(850\) | −1.28929e18 | − | 2.23312e18i | −0.117254 | − | 0.203090i | ||||
\(851\) | 7.18775e18 | + | 1.24495e19i | 0.648710 | + | 1.12360i | ||||
\(852\) | −1.95205e18 | + | 3.38105e18i | −0.174837 | + | 0.302827i | ||||
\(853\) | 1.27122e19 | 1.12993 | 0.564967 | − | 0.825114i | \(-0.308889\pi\) | ||||
0.564967 | + | 0.825114i | \(0.308889\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.11633e17 | 0.0360355 | ||||||||
\(856\) | −1.89551e18 | + | 3.28312e18i | −0.164682 | + | 0.285238i | ||||
\(857\) | 9.91400e18 | + | 1.71715e19i | 0.854818 | + | 1.48059i | 0.876814 | + | 0.480830i | \(0.159664\pi\) |
−0.0219964 | + | 0.999758i | \(0.507002\pi\) | |||||||
\(858\) | −1.12837e18 | − | 1.95440e18i | −0.0965573 | − | 0.167242i | ||||
\(859\) | −3.16105e18 | + | 5.47510e18i | −0.268458 | + | 0.464982i | −0.968464 | − | 0.249155i | \(-0.919847\pi\) |
0.700006 | + | 0.714137i | \(0.253181\pi\) | |||||||
\(860\) | 4.36834e18 | 0.368194 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.86480e18 | −0.652966 | ||||||||
\(863\) | 3.01615e18 | − | 5.22413e18i | 0.248532 | − | 0.430471i | −0.714586 | − | 0.699547i | \(-0.753385\pi\) |
0.963119 | + | 0.269076i | \(0.0867184\pi\) | |||||||
\(864\) | 7.67832e17 | + | 1.32992e18i | 0.0627953 | + | 0.108765i | ||||
\(865\) | −1.88880e18 | − | 3.27150e18i | −0.153314 | − | 0.265547i | ||||
\(866\) | 4.51377e18 | − | 7.81808e18i | 0.363641 | − | 0.629845i | ||||
\(867\) | 1.24391e19 | 0.994634 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.05373e19 | −0.830041 | ||||||||
\(870\) | −1.69051e18 | + | 2.92805e18i | −0.132173 | + | 0.228931i | ||||
\(871\) | −1.14146e18 | − | 1.97707e18i | −0.0885814 | − | 0.153427i | ||||
\(872\) | −2.08820e18 | − | 3.61687e18i | −0.160848 | − | 0.278597i | ||||
\(873\) | −2.48517e18 | + | 4.30443e18i | −0.190004 | + | 0.329097i | ||||
\(874\) | 2.17460e18 | 0.165027 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.58526e18 | 0.268067 | ||||||||
\(877\) | 1.59022e18 | − | 2.75435e18i | 0.118021 | − | 0.204419i | −0.800962 | − | 0.598715i | \(-0.795678\pi\) |
0.918984 | + | 0.394296i | \(0.129012\pi\) | |||||||
\(878\) | −4.70362e18 | − | 8.14691e18i | −0.346512 | − | 0.600176i | ||||
\(879\) | 1.22452e18 | + | 2.12093e18i | 0.0895445 | + | 0.155096i | ||||
\(880\) | −5.16096e17 | + | 8.93904e17i | −0.0374622 | + | 0.0648864i | ||||
\(881\) | 2.33099e19 | 1.67956 | 0.839782 | − | 0.542924i | \(-0.182683\pi\) | ||||
0.839782 | + | 0.542924i | \(0.182683\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.95630e18 | −0.138896 | −0.0694482 | − | 0.997586i | \(-0.522124\pi\) | ||||
−0.0694482 | + | 0.997586i | \(0.522124\pi\) | |||||||
\(884\) | 4.48002e17 | − | 7.75962e17i | 0.0315748 | − | 0.0546891i | ||||
\(885\) | 4.92982e18 | + | 8.53870e18i | 0.344905 | + | 0.597393i | ||||
\(886\) | 5.98037e18 | + | 1.03583e19i | 0.415345 | + | 0.719399i | ||||
\(887\) | −5.03283e18 | + | 8.71712e18i | −0.346983 | + | 0.600993i | −0.985712 | − | 0.168439i | \(-0.946127\pi\) |
0.638729 | + | 0.769432i | \(0.279461\pi\) | |||||||
\(888\) | −7.45869e18 | −0.510479 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.55802e18 | 0.172532 | ||||||||
\(891\) | −6.75305e18 | + | 1.16966e19i | −0.452163 | + | 0.783170i | ||||
\(892\) | 1.24508e18 | + | 2.15654e18i | 0.0827609 | + | 0.143346i | ||||
\(893\) | −1.81671e18 | − | 3.14663e18i | −0.119881 | − | 0.207640i | ||||
\(894\) | −8.16862e18 | + | 1.41485e19i | −0.535124 | + | 0.926862i | ||||
\(895\) | 5.19803e18 | 0.338056 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.20974e18 | 0.398036 | ||||||||
\(898\) | 6.89527e18 | − | 1.19430e19i | 0.438788 | − | 0.760003i | ||||
\(899\) | −7.55571e18 | − | 1.30869e19i | −0.477350 | − | 0.826795i | ||||
\(900\) | 1.32329e18 | + | 2.29200e18i | 0.0830000 | + | 0.143760i | ||||
\(901\) | 4.38958e18 | − | 7.60298e18i | 0.273345 | − | 0.473448i | ||||
\(902\) | 1.16041e19 | 0.717412 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.27634e18 | −0.0777806 | ||||||||
\(905\) | 4.85560e18 | − | 8.41015e18i | 0.293784 | − | 0.508848i | ||||
\(906\) | −1.28870e19 | − | 2.23210e19i | −0.774140 | − | 1.34085i | ||||
\(907\) | 6.24089e18 | + | 1.08095e19i | 0.372220 | + | 0.644703i | 0.989907 | − | 0.141721i | \(-0.0452635\pi\) |
−0.617687 | + | 0.786424i | \(0.711930\pi\) | |||||||
\(908\) | −5.70609e18 | + | 9.88324e18i | −0.337894 | + | 0.585250i | ||||
\(909\) | −8.38471e18 | −0.492973 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.22935e19 | 1.29214 | 0.646068 | − | 0.763280i | \(-0.276412\pi\) | ||||
0.646068 | + | 0.763280i | \(0.276412\pi\) | |||||||
\(912\) | −5.64143e17 | + | 9.77124e17i | −0.0324655 | + | 0.0562320i | ||||
\(913\) | −7.11627e18 | − | 1.23257e19i | −0.406623 | − | 0.704292i | ||||
\(914\) | −1.22851e18 | − | 2.12784e18i | −0.0696991 | − | 0.120722i | ||||
\(915\) | 6.94633e17 | − | 1.20314e18i | 0.0391308 | − | 0.0677765i | ||||
\(916\) | −4.64942e18 | −0.260063 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.63483e18 | −0.200451 | ||||||||
\(919\) | −1.24631e19 | + | 2.15867e19i | −0.682455 | + | 1.18205i | 0.291774 | + | 0.956487i | \(0.405754\pi\) |
−0.974229 | + | 0.225560i | \(0.927579\pi\) | |||||||
\(920\) | −1.42011e18 | − | 2.45970e18i | −0.0772148 | − | 0.133740i | ||||
\(921\) | −4.25655e18 | − | 7.37256e18i | −0.229811 | − | 0.398044i | ||||
\(922\) | −1.00891e19 | + | 1.74748e19i | −0.540881 | + | 0.936833i | ||||
\(923\) | 3.51510e18 | 0.187123 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.93264e19 | 1.01445 | ||||||||
\(926\) | −7.31653e18 | + | 1.26726e19i | −0.381359 | + | 0.660533i | ||||
\(927\) | −5.63218e18 | − | 9.75522e18i | −0.291513 | − | 0.504916i | ||||
\(928\) | −1.32260e18 | − | 2.29080e18i | −0.0679775 | − | 0.117741i | ||||
\(929\) | 1.55121e19 | − | 2.68677e19i | 0.791713 | − | 1.37129i | −0.133193 | − | 0.991090i | \(-0.542523\pi\) |
0.924906 | − | 0.380197i | \(-0.124144\pi\) | |||||||
\(930\) | 8.41858e18 | 0.426678 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8.35542e18 | −0.417604 | ||||||||
\(933\) | 6.95399e18 | − | 1.20447e19i | 0.345146 | − | 0.597811i | ||||
\(934\) | −6.81668e18 | − | 1.18068e19i | −0.335984 | − | 0.581941i | ||||
\(935\) | −1.22157e18 | − | 2.11582e18i | −0.0597920 | − | 0.103563i | ||||
\(936\) | −4.59815e17 | + | 7.96422e17i | −0.0223506 | + | 0.0387124i | ||||
\(937\) | −4.17037e17 | −0.0201311 | −0.0100655 | − | 0.999949i | \(-0.503204\pi\) | ||||
−0.0100655 | + | 0.999949i | \(0.503204\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.43023e18 | −0.401340 | ||||||||
\(940\) | −2.37278e18 | + | 4.10978e18i | −0.112183 | + | 0.194306i | ||||
\(941\) | −9.59391e17 | − | 1.66171e18i | −0.0450467 | − | 0.0780232i | 0.842623 | − | 0.538504i | \(-0.181010\pi\) |
−0.887670 | + | 0.460481i | \(0.847677\pi\) | |||||||
\(942\) | −2.53724e18 | − | 4.39463e18i | −0.118312 | − | 0.204923i | ||||
\(943\) | −1.59651e19 | + | 2.76524e19i | −0.739343 | + | 1.28058i | ||||
\(944\) | −7.71382e18 | −0.354774 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.03745e19 | −0.924259 | ||||||||
\(947\) | −1.75162e19 | + | 3.03389e19i | −0.789158 | + | 1.36686i | 0.137325 | + | 0.990526i | \(0.456150\pi\) |
−0.926483 | + | 0.376336i | \(0.877184\pi\) | |||||||
\(948\) | 7.52192e18 | + | 1.30284e19i | 0.336569 | + | 0.582955i | ||||
\(949\) | −1.61401e18 | − | 2.79555e18i | −0.0717260 | − | 0.124233i | ||||
\(950\) | 1.46176e18 | − | 2.53185e18i | 0.0645169 | − | 0.111747i | ||||
\(951\) | 1.82407e19 | 0.799593 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.82110e19 | 1.65228 | 0.826142 | − | 0.563462i | \(-0.190531\pi\) | ||||
0.826142 | + | 0.563462i | \(0.190531\pi\) | |||||||
\(954\) | −4.50532e18 | + | 7.80345e18i | −0.193491 | + | 0.335137i | ||||
\(955\) | −5.45802e18 | − | 9.45357e18i | −0.232816 | − | 0.403250i | ||||
\(956\) | 7.32462e18 | + | 1.26866e19i | 0.310320 | + | 0.537489i | ||||
\(957\) | 7.88475e18 | − | 1.36568e19i | 0.331788 | − | 0.574673i | ||||
\(958\) | 2.02026e18 | 0.0844368 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.47364e18 | 0.0607614 | ||||||||
\(961\) | −6.60457e18 | + | 1.14394e19i | −0.270484 | + | 0.468493i | ||||
\(962\) | 3.35775e18 | + | 5.81580e18i | 0.136587 | + | 0.236576i | ||||
\(963\) | 4.60487e18 | + | 7.97586e18i | 0.186057 | + | 0.322260i | ||||
\(964\) | −3.71996e18 | + | 6.44315e18i | −0.149292 | + | 0.258582i | ||||
\(965\) | 9.21972e16 | 0.00367528 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.71357e19 | 1.46056 | 0.730281 | − | 0.683147i | \(-0.239389\pi\) | ||||
0.730281 | + | 0.683147i | \(0.239389\pi\) | |||||||
\(968\) | −2.11783e18 | + | 3.66819e18i | −0.0827372 | + | 0.143305i | ||||
\(969\) | −1.33530e18 | − | 2.31280e18i | −0.0518171 | − | 0.0897498i | ||||
\(970\) | −3.58550e18 | − | 6.21027e18i | −0.138208 | − | 0.239383i | ||||
\(971\) | −5.96924e18 | + | 1.03390e19i | −0.228557 | + | 0.395872i | −0.957381 | − | 0.288829i | \(-0.906734\pi\) |
0.728824 | + | 0.684701i | \(0.240067\pi\) | |||||||
\(972\) | 9.94270e18 | 0.378158 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.47512e19 | −1.30418 | ||||||||
\(975\) | 4.17418e18 | − | 7.22989e18i | 0.155611 | − | 0.269527i | ||||
\(976\) | 5.43456e17 | + | 9.41293e17i | 0.0201252 | + | 0.0348579i | ||||
\(977\) | 4.03279e18 | + | 6.98499e18i | 0.148351 | + | 0.256952i | 0.930618 | − | 0.365992i | \(-0.119270\pi\) |
−0.782267 | + | 0.622943i | \(0.785937\pi\) | |||||||
\(978\) | −1.20379e19 | + | 2.08502e19i | −0.439893 | + | 0.761918i | ||||
\(979\) | −1.19309e19 | −0.433098 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.01460e19 | −0.363450 | ||||||||
\(982\) | 9.18673e18 | − | 1.59119e19i | 0.326916 | − | 0.566235i | ||||
\(983\) | 1.32814e19 | + | 2.30040e19i | 0.469511 | + | 0.813216i | 0.999392 | − | 0.0348552i | \(-0.0110970\pi\) |
−0.529882 | + | 0.848072i | \(0.677764\pi\) | |||||||
\(984\) | −8.28346e18 | − | 1.43474e19i | −0.290900 | − | 0.503853i | ||||
\(985\) | 3.01277e18 | − | 5.21827e18i | 0.105107 | − | 0.182050i | ||||
\(986\) | 6.26103e18 | 0.216993 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.01586e18 | 0.0347468 | ||||||||
\(989\) | 2.80316e19 | − | 4.85521e19i | 0.952514 | − | 1.64980i | ||||
\(990\) | 1.25378e18 | + | 2.17161e18i | 0.0423246 | + | 0.0733083i | ||||
\(991\) | −1.86864e19 | − | 3.23658e19i | −0.626682 | − | 1.08544i | −0.988213 | − | 0.153085i | \(-0.951079\pi\) |
0.361531 | − | 0.932360i | \(-0.382254\pi\) | |||||||
\(992\) | −3.29320e18 | + | 5.70399e18i | −0.109722 | + | 0.190043i | ||||
\(993\) | −1.98473e19 | −0.656950 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.16450e19 | 0.707145 | ||||||||
\(996\) | −1.01597e19 | + | 1.75972e19i | −0.329759 | + | 0.571160i | ||||
\(997\) | 7.48500e17 | + | 1.29644e18i | 0.0241364 | + | 0.0418055i | 0.877841 | − | 0.478952i | \(-0.158983\pi\) |
−0.853705 | + | 0.520757i | \(0.825650\pi\) | |||||||
\(998\) | 1.69416e17 | + | 2.93437e17i | 0.00542757 | + | 0.00940083i | ||||
\(999\) | 1.36214e19 | − | 2.35930e19i | 0.433558 | − | 0.750945i |
(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 | 98.14.c.o.79.4 | 8 | ||
7.2 | even | 3 | 98.14.a.j.1.1 | 4 | |||
7.3 | odd | 6 | 14.14.c.b.11.1 | yes | 8 | ||
7.4 | even | 3 | inner | 98.14.c.o.67.4 | 8 | ||
7.5 | odd | 6 | 98.14.a.h.1.4 | 4 | |||
7.6 | odd | 2 | 14.14.c.b.9.1 | ✓ | 8 | ||
21.17 | even | 6 | 126.14.g.b.109.2 | 8 | |||
21.20 | even | 2 | 126.14.g.b.37.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.14.c.b.9.1 | ✓ | 8 | 7.6 | odd | 2 | ||
14.14.c.b.11.1 | yes | 8 | 7.3 | odd | 6 | ||
98.14.a.h.1.4 | 4 | 7.5 | odd | 6 | |||
98.14.a.j.1.1 | 4 | 7.2 | even | 3 | |||
98.14.c.o.67.4 | 8 | 7.4 | even | 3 | inner | ||
98.14.c.o.79.4 | 8 | 1.1 | even | 1 | trivial | ||
126.14.g.b.37.2 | 8 | 21.20 | even | 2 | |||
126.14.g.b.109.2 | 8 | 21.17 | even | 6 |