Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,11,Mod(11,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.11");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.7071450535\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + 84 x^{18} - 86 x^{17} - 51565 x^{16} + 188134 x^{15} - 12946328 x^{14} + 95990512 x^{13} + 5401091173 x^{12} - 59241975423 x^{11} + \cdots + 11\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{94}\cdot 3^{4}\cdot 5^{29} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.8 | ||
Root | \(-8.12576 + 14.6168i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.11 |
Dual form | 20.11.b.a.11.7 |
$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −13.0154 | + | 29.2335i | −0.406733 | + | 0.913547i | ||||
\(3\) | 448.707i | 1.84653i | 0.384162 | + | 0.923266i | \(0.374490\pi\) | ||||
−0.384162 | + | 0.923266i | \(0.625510\pi\) | |||||||
\(4\) | −685.197 | − | 760.974i | −0.669137 | − | 0.743139i | ||||
\(5\) | −1397.54 | −0.447214 | ||||||||
\(6\) | −13117.3 | − | 5840.12i | −1.68689 | − | 0.751044i | ||||
\(7\) | − | 19334.7i | − | 1.15040i | −0.818014 | − | 0.575198i | \(-0.804925\pi\) | ||
0.818014 | − | 0.575198i | \(-0.195075\pi\) | |||||||
\(8\) | 31164.1 | − | 10126.3i | 0.951052 | − | 0.309030i | ||||
\(9\) | −142289. | −2.40968 | ||||||||
\(10\) | 18189.6 | − | 40855.1i | 0.181896 | − | 0.408551i | ||||
\(11\) | 207443.i | 1.28806i | 0.765002 | + | 0.644028i | \(0.222738\pi\) | ||||
−0.765002 | + | 0.644028i | \(0.777262\pi\) | |||||||
\(12\) | 341455. | − | 307453.i | 1.37223 | − | 1.23558i | ||||
\(13\) | 65166.8 | 0.175513 | 0.0877565 | − | 0.996142i | \(-0.472030\pi\) | ||||
0.0877565 | + | 0.996142i | \(0.472030\pi\) | |||||||
\(14\) | 565222. | + | 251650.i | 1.05094 | + | 0.467904i | ||||
\(15\) | − | 627087.i | − | 0.825794i | ||||||
\(16\) | −109587. | + | 1.04283e6i | −0.104511 | + | 0.994524i | ||||
\(17\) | −805200. | −0.567099 | −0.283550 | − | 0.958958i | \(-0.591512\pi\) | ||||
−0.283550 | + | 0.958958i | \(0.591512\pi\) | |||||||
\(18\) | 1.85196e6 | − | 4.15961e6i | 0.980094 | − | 2.20135i | ||||
\(19\) | − | 4.08369e6i | − | 1.64924i | −0.565685 | − | 0.824622i | \(-0.691388\pi\) | ||
0.565685 | − | 0.824622i | \(-0.308612\pi\) | |||||||
\(20\) | 957591. | + | 1.06349e6i | 0.299247 | + | 0.332342i | ||||
\(21\) | 8.67562e6 | 2.12424 | ||||||||
\(22\) | −6.06427e6 | − | 2.69996e6i | −1.17670 | − | 0.523894i | ||||
\(23\) | 4.40794e6i | 0.684851i | 0.939545 | + | 0.342426i | \(0.111249\pi\) | ||||
−0.939545 | + | 0.342426i | \(0.888751\pi\) | |||||||
\(24\) | 4.54374e6 | + | 1.39835e7i | 0.570633 | + | 1.75615i | ||||
\(25\) | 1.95312e6 | 0.200000 | ||||||||
\(26\) | −848174. | + | 1.90505e6i | −0.0713869 | + | 0.160339i | ||||
\(27\) | − | 3.73504e7i | − | 2.60301i | ||||||
\(28\) | −1.47132e7 | + | 1.32481e7i | −0.854904 | + | 0.769773i | ||||
\(29\) | −1.06041e7 | −0.516990 | −0.258495 | − | 0.966013i | \(-0.583227\pi\) | ||||
−0.258495 | + | 0.966013i | \(0.583227\pi\) | |||||||
\(30\) | 1.83320e7 | + | 8.16182e6i | 0.754402 | + | 0.335877i | ||||
\(31\) | 2.90491e6i | 0.101467i | 0.998712 | + | 0.0507335i | \(0.0161559\pi\) | ||||
−0.998712 | + | 0.0507335i | \(0.983844\pi\) | |||||||
\(32\) | −2.90594e7 | − | 1.67766e7i | −0.866037 | − | 0.499981i | ||||
\(33\) | −9.30810e7 | −2.37843 | ||||||||
\(34\) | 1.04800e7 | − | 2.35388e7i | 0.230658 | − | 0.518072i | ||||
\(35\) | 2.70211e7i | 0.514473i | ||||||||
\(36\) | 9.74960e7 | + | 1.08278e8i | 1.61241 | + | 1.79073i | ||||
\(37\) | −1.45768e7 | −0.210210 | −0.105105 | − | 0.994461i | \(-0.533518\pi\) | ||||
−0.105105 | + | 0.994461i | \(0.533518\pi\) | |||||||
\(38\) | 1.19381e8 | + | 5.31510e7i | 1.50666 | + | 0.670801i | ||||
\(39\) | 2.92408e7i | 0.324090i | ||||||||
\(40\) | −4.35531e7 | + | 1.41519e7i | −0.425324 | + | 0.138202i | ||||
\(41\) | −6.38483e7 | −0.551099 | −0.275550 | − | 0.961287i | \(-0.588860\pi\) | ||||
−0.275550 | + | 0.961287i | \(0.588860\pi\) | |||||||
\(42\) | −1.12917e8 | + | 2.53619e8i | −0.863999 | + | 1.94060i | ||||
\(43\) | − | 2.40099e8i | − | 1.63323i | −0.577180 | − | 0.816617i | \(-0.695847\pi\) | ||
0.577180 | − | 0.816617i | \(-0.304153\pi\) | |||||||
\(44\) | 1.57858e8 | − | 1.42139e8i | 0.957204 | − | 0.861886i | ||||
\(45\) | 1.98855e8 | 1.07764 | ||||||||
\(46\) | −1.28860e8 | − | 5.73713e7i | −0.625644 | − | 0.278551i | ||||
\(47\) | − | 1.51193e8i | − | 0.659238i | −0.944114 | − | 0.329619i | \(-0.893080\pi\) | ||
0.944114 | − | 0.329619i | \(-0.106920\pi\) | |||||||
\(48\) | −4.67927e8 | − | 4.91727e7i | −1.83642 | − | 0.192982i | ||||
\(49\) | −9.13560e7 | −0.323412 | ||||||||
\(50\) | −2.54208e7 | + | 5.70967e7i | −0.0813465 | + | 0.182709i | ||||
\(51\) | − | 3.61299e8i | − | 1.04717i | ||||||
\(52\) | −4.46520e7 | − | 4.95902e7i | −0.117442 | − | 0.130431i | ||||
\(53\) | −3.71821e8 | −0.889108 | −0.444554 | − | 0.895752i | \(-0.646638\pi\) | ||||
−0.444554 | + | 0.895752i | \(0.646638\pi\) | |||||||
\(54\) | 1.09188e9 | + | 4.86132e8i | 2.37798 | + | 1.05873i | ||||
\(55\) | − | 2.89910e8i | − | 0.576036i | ||||||
\(56\) | −1.95789e8 | − | 6.02549e8i | −0.355507 | − | 1.09409i | ||||
\(57\) | 1.83238e9 | 3.04538 | ||||||||
\(58\) | 1.38017e8 | − | 3.09994e8i | 0.210277 | − | 0.472295i | ||||
\(59\) | 4.69987e8i | 0.657395i | 0.944435 | + | 0.328697i | \(0.106610\pi\) | ||||
−0.944435 | + | 0.328697i | \(0.893390\pi\) | |||||||
\(60\) | −4.77197e8 | + | 4.29678e8i | −0.613680 | + | 0.552569i | ||||
\(61\) | −7.97019e8 | −0.943669 | −0.471835 | − | 0.881687i | \(-0.656408\pi\) | ||||
−0.471835 | + | 0.881687i | \(0.656408\pi\) | |||||||
\(62\) | −8.49209e7 | − | 3.78088e7i | −0.0926949 | − | 0.0412699i | ||||
\(63\) | 2.75112e9i | 2.77209i | ||||||||
\(64\) | 8.68659e8 | − | 6.31153e8i | 0.809001 | − | 0.587807i | ||||
\(65\) | −9.10733e7 | −0.0784918 | ||||||||
\(66\) | 1.21149e9 | − | 2.72108e9i | 0.967387 | − | 2.17281i | ||||
\(67\) | − | 8.39728e8i | − | 0.621963i | −0.950416 | − | 0.310981i | \(-0.899342\pi\) | ||
0.950416 | − | 0.310981i | \(-0.100658\pi\) | |||||||
\(68\) | 5.51720e8 | + | 6.12736e8i | 0.379467 | + | 0.421433i | ||||
\(69\) | −1.97787e9 | −1.26460 | ||||||||
\(70\) | −7.89921e8 | − | 3.51691e8i | −0.469995 | − | 0.209253i | ||||
\(71\) | 4.87774e8i | 0.270350i | 0.990822 | + | 0.135175i | \(0.0431597\pi\) | ||||
−0.990822 | + | 0.135175i | \(0.956840\pi\) | |||||||
\(72\) | −4.43431e9 | + | 1.44086e9i | −2.29173 | + | 0.744662i | ||||
\(73\) | −3.05750e9 | −1.47487 | −0.737433 | − | 0.675421i | \(-0.763962\pi\) | ||||
−0.737433 | + | 0.675421i | \(0.763962\pi\) | |||||||
\(74\) | 1.89723e8 | − | 4.26131e8i | 0.0854993 | − | 0.192037i | ||||
\(75\) | 8.76381e8i | 0.369306i | ||||||||
\(76\) | −3.10758e9 | + | 2.79813e9i | −1.22562 | + | 1.10357i | ||||
\(77\) | 4.01084e9 | 1.48177 | ||||||||
\(78\) | −8.54811e8 | − | 3.80582e8i | −0.296072 | − | 0.131818i | ||||
\(79\) | 4.58675e9i | 1.49063i | 0.666712 | + | 0.745315i | \(0.267701\pi\) | ||||
−0.666712 | + | 0.745315i | \(0.732299\pi\) | |||||||
\(80\) | 1.53153e8 | − | 1.45740e9i | 0.0467386 | − | 0.444765i | ||||
\(81\) | 8.35737e9 | 2.39687 | ||||||||
\(82\) | 8.31014e8 | − | 1.86651e9i | 0.224150 | − | 0.503455i | ||||
\(83\) | − | 2.95392e8i | − | 0.0749909i | −0.999297 | − | 0.0374954i | \(-0.988062\pi\) | ||
0.999297 | − | 0.0374954i | \(-0.0119380\pi\) | |||||||
\(84\) | −5.94451e9 | − | 6.60193e9i | −1.42141 | − | 1.57861i | ||||
\(85\) | 1.12530e9 | 0.253614 | ||||||||
\(86\) | 7.01894e9 | + | 3.12500e9i | 1.49204 | + | 0.664289i | ||||
\(87\) | − | 4.75812e9i | − | 0.954639i | ||||||
\(88\) | 2.10062e9 | + | 6.46476e9i | 0.398047 | + | 1.22501i | ||||
\(89\) | −3.76251e9 | −0.673794 | −0.336897 | − | 0.941541i | \(-0.609377\pi\) | ||||
−0.336897 | + | 0.941541i | \(0.609377\pi\) | |||||||
\(90\) | −2.58819e9 | + | 5.81323e9i | −0.438312 | + | 0.984476i | ||||
\(91\) | − | 1.25998e9i | − | 0.201910i | ||||||
\(92\) | 3.35433e9 | − | 3.02030e9i | 0.508940 | − | 0.458260i | ||||
\(93\) | −1.30346e9 | −0.187362 | ||||||||
\(94\) | 4.41990e9 | + | 1.96784e9i | 0.602245 | + | 0.268134i | ||||
\(95\) | 5.70713e9i | 0.737564i | ||||||||
\(96\) | 7.52777e9 | − | 1.30391e10i | 0.923230 | − | 1.59916i | ||||
\(97\) | −1.37175e10 | −1.59741 | −0.798706 | − | 0.601721i | \(-0.794482\pi\) | ||||
−0.798706 | + | 0.601721i | \(0.794482\pi\) | |||||||
\(98\) | 1.18904e9 | − | 2.67066e9i | 0.131542 | − | 0.295452i | ||||
\(99\) | − | 2.95168e10i | − | 3.10380i | ||||||
\(100\) | −1.33827e9 | − | 1.48628e9i | −0.133827 | − | 0.148628i | ||||
\(101\) | 6.29138e9 | 0.598603 | 0.299301 | − | 0.954159i | \(-0.403246\pi\) | ||||
0.299301 | + | 0.954159i | \(0.403246\pi\) | |||||||
\(102\) | 1.05620e10 | + | 4.70246e9i | 0.956636 | + | 0.425917i | ||||
\(103\) | 1.48493e10i | 1.28091i | 0.767996 | + | 0.640455i | \(0.221254\pi\) | ||||
−0.767996 | + | 0.640455i | \(0.778746\pi\) | |||||||
\(104\) | 2.03086e9 | − | 6.59897e8i | 0.166922 | − | 0.0542387i | ||||
\(105\) | −1.21246e10 | −0.949990 | ||||||||
\(106\) | 4.83941e9 | − | 1.08696e10i | 0.361629 | − | 0.812242i | ||||
\(107\) | − | 7.85004e9i | − | 0.559697i | −0.960044 | − | 0.279848i | \(-0.909716\pi\) | ||
0.960044 | − | 0.279848i | \(-0.0902842\pi\) | |||||||
\(108\) | −2.84227e10 | + | 2.55924e10i | −1.93440 | + | 1.74177i | ||||
\(109\) | 3.49014e9 | 0.226835 | 0.113418 | − | 0.993547i | \(-0.463820\pi\) | ||||
0.113418 | + | 0.993547i | \(0.463820\pi\) | |||||||
\(110\) | 8.47508e9 | + | 3.77330e9i | 0.526236 | + | 0.234293i | ||||
\(111\) | − | 6.54071e9i | − | 0.388159i | ||||||
\(112\) | 2.01629e10 | + | 2.11884e9i | 1.14410 | + | 0.120229i | ||||
\(113\) | 1.37109e10 | 0.744171 | 0.372085 | − | 0.928199i | \(-0.378643\pi\) | ||||
0.372085 | + | 0.928199i | \(0.378643\pi\) | |||||||
\(114\) | −2.38492e10 | + | 5.35669e10i | −1.23865 | + | 2.78210i | ||||
\(115\) | − | 6.16028e9i | − | 0.306275i | ||||||
\(116\) | 7.26587e9 | + | 8.06942e9i | 0.345938 | + | 0.384196i | ||||
\(117\) | −9.27252e9 | −0.422930 | ||||||||
\(118\) | −1.37394e10 | − | 6.11709e9i | −0.600561 | − | 0.267384i | ||||
\(119\) | 1.55683e10i | 0.652389i | ||||||||
\(120\) | −6.35006e9 | − | 1.95426e10i | −0.255195 | − | 0.785373i | ||||
\(121\) | −1.70950e10 | −0.659086 | ||||||||
\(122\) | 1.03736e10 | − | 2.32997e10i | 0.383821 | − | 0.862086i | ||||
\(123\) | − | 2.86492e10i | − | 1.01762i | ||||||
\(124\) | 2.21057e9 | − | 1.99044e9i | 0.0754041 | − | 0.0678954i | ||||
\(125\) | −2.72958e9 | −0.0894427 | ||||||||
\(126\) | −8.04249e10 | − | 3.58070e10i | −2.53243 | − | 1.12750i | ||||
\(127\) | 1.28415e10i | 0.388684i | 0.980934 | + | 0.194342i | \(0.0622571\pi\) | ||||
−0.980934 | + | 0.194342i | \(0.937743\pi\) | |||||||
\(128\) | 7.14484e9 | + | 3.36087e10i | 0.207942 | + | 0.978141i | ||||
\(129\) | 1.07734e11 | 3.01582 | ||||||||
\(130\) | 1.18536e9 | − | 2.66239e9i | 0.0319252 | − | 0.0717060i | ||||
\(131\) | 8.76942e9i | 0.227308i | 0.993520 | + | 0.113654i | \(0.0362555\pi\) | ||||
−0.993520 | + | 0.113654i | \(0.963744\pi\) | |||||||
\(132\) | 6.37787e10 | + | 7.08322e10i | 1.59150 | + | 1.76751i | ||||
\(133\) | −7.89570e10 | −1.89728 | ||||||||
\(134\) | 2.45482e10 | + | 1.09294e10i | 0.568192 | + | 0.252973i | ||||
\(135\) | 5.21988e10i | 1.16410i | ||||||||
\(136\) | −2.50933e10 | + | 8.15368e9i | −0.539341 | + | 0.175250i | ||||
\(137\) | −8.29170e10 | −1.71807 | −0.859034 | − | 0.511918i | \(-0.828935\pi\) | ||||
−0.859034 | + | 0.511918i | \(0.828935\pi\) | |||||||
\(138\) | 2.57429e10 | − | 5.78202e10i | 0.514354 | − | 1.15527i | ||||
\(139\) | 2.53373e10i | 0.488300i | 0.969737 | + | 0.244150i | \(0.0785090\pi\) | ||||
−0.969737 | + | 0.244150i | \(0.921491\pi\) | |||||||
\(140\) | 2.05624e10 | − | 1.85148e10i | 0.382325 | − | 0.344253i | ||||
\(141\) | 6.78414e10 | 1.21730 | ||||||||
\(142\) | −1.42594e10 | − | 6.34860e9i | −0.246978 | − | 0.109960i | ||||
\(143\) | 1.35184e10i | 0.226071i | ||||||||
\(144\) | 1.55931e10 | − | 1.48384e11i | 0.251837 | − | 2.39648i | ||||
\(145\) | 1.48196e10 | 0.231205 | ||||||||
\(146\) | 3.97947e10 | − | 8.93815e10i | 0.599876 | − | 1.34736i | ||||
\(147\) | − | 4.09921e10i | − | 0.597191i | ||||||
\(148\) | 9.98797e9 | + | 1.10926e10i | 0.140659 | + | 0.156215i | ||||
\(149\) | −1.13838e11 | −1.55009 | −0.775045 | − | 0.631906i | \(-0.782273\pi\) | ||||
−0.775045 | + | 0.631906i | \(0.782273\pi\) | |||||||
\(150\) | −2.56197e10 | − | 1.14065e10i | −0.337379 | − | 0.150209i | ||||
\(151\) | 1.22959e11i | 1.56630i | 0.621832 | + | 0.783151i | \(0.286389\pi\) | ||||
−0.621832 | + | 0.783151i | \(0.713611\pi\) | |||||||
\(152\) | −4.13526e10 | − | 1.27264e11i | −0.509665 | − | 1.56852i | ||||
\(153\) | 1.14571e11 | 1.36653 | ||||||||
\(154\) | −5.22029e10 | + | 1.17251e11i | −0.602686 | + | 1.35367i | ||||
\(155\) | − | 4.05974e9i | − | 0.0453774i | ||||||
\(156\) | 2.22515e10 | − | 2.00357e10i | 0.240844 | − | 0.216861i | ||||
\(157\) | 1.38471e11 | 1.45164 | 0.725822 | − | 0.687882i | \(-0.241460\pi\) | ||||
0.725822 | + | 0.687882i | \(0.241460\pi\) | |||||||
\(158\) | −1.34087e11 | − | 5.96986e10i | −1.36176 | − | 0.606288i | ||||
\(159\) | − | 1.66839e11i | − | 1.64177i | ||||||
\(160\) | 4.06117e10 | + | 2.34460e10i | 0.387303 | + | 0.223598i | ||||
\(161\) | 8.52262e10 | 0.787851 | ||||||||
\(162\) | −1.08775e11 | + | 2.44315e11i | −0.974885 | + | 2.18965i | ||||
\(163\) | − | 1.63012e9i | − | 0.0141671i | −0.999975 | − | 0.00708354i | \(-0.997745\pi\) | ||
0.999975 | − | 0.00708354i | \(-0.00225478\pi\) | |||||||
\(164\) | 4.37486e10 | + | 4.85869e10i | 0.368761 | + | 0.409543i | ||||
\(165\) | 1.30085e11 | 1.06367 | ||||||||
\(166\) | 8.63535e9 | + | 3.84466e9i | 0.0685077 | + | 0.0305012i | ||||
\(167\) | − | 2.23725e11i | − | 1.72239i | −0.508271 | − | 0.861197i | \(-0.669715\pi\) | ||
0.508271 | − | 0.861197i | \(-0.330285\pi\) | |||||||
\(168\) | 2.70368e11 | − | 8.78518e10i | 2.02027 | − | 0.656454i | ||||
\(169\) | −1.33612e11 | −0.969195 | ||||||||
\(170\) | −1.46463e10 | + | 3.28965e10i | −0.103153 | + | 0.231689i | ||||
\(171\) | 5.81064e11i | 3.97414i | ||||||||
\(172\) | −1.82709e11 | + | 1.64515e11i | −1.21372 | + | 1.09286i | ||||
\(173\) | 8.02780e10 | 0.518043 | 0.259022 | − | 0.965872i | \(-0.416600\pi\) | ||||
0.259022 | + | 0.965872i | \(0.416600\pi\) | |||||||
\(174\) | 1.39097e11 | + | 6.19290e10i | 0.872108 | + | 0.388283i | ||||
\(175\) | − | 3.77631e10i | − | 0.230079i | ||||||
\(176\) | −2.16328e11 | − | 2.27331e10i | −1.28100 | − | 0.134616i | ||||
\(177\) | −2.10887e11 | −1.21390 | ||||||||
\(178\) | 4.89707e10 | − | 1.09991e11i | 0.274054 | − | 0.615543i | ||||
\(179\) | 6.51569e10i | 0.354565i | 0.984160 | + | 0.177282i | \(0.0567306\pi\) | ||||
−0.984160 | + | 0.177282i | \(0.943269\pi\) | |||||||
\(180\) | −1.36255e11 | − | 1.51324e11i | −0.721089 | − | 0.800837i | ||||
\(181\) | −3.13027e11 | −1.61135 | −0.805673 | − | 0.592360i | \(-0.798196\pi\) | ||||
−0.805673 | + | 0.592360i | \(0.798196\pi\) | |||||||
\(182\) | 3.68337e10 | + | 1.63992e10i | 0.184454 | + | 0.0821232i | ||||
\(183\) | − | 3.57628e11i | − | 1.74251i | ||||||
\(184\) | 4.46360e10 | + | 1.37369e11i | 0.211639 | + | 0.651330i | ||||
\(185\) | 2.03717e10 | 0.0940088 | ||||||||
\(186\) | 1.69651e10 | − | 3.81046e10i | 0.0762062 | − | 0.171164i | ||||
\(187\) | − | 1.67033e11i | − | 0.730455i | ||||||
\(188\) | −1.15054e11 | + | 1.03597e11i | −0.489905 | + | 0.441121i | ||||
\(189\) | −7.22159e11 | −2.99450 | ||||||||
\(190\) | −1.66839e11 | − | 7.42808e10i | −0.673800 | − | 0.299991i | ||||
\(191\) | − | 2.53418e11i | − | 0.996942i | −0.866906 | − | 0.498471i | \(-0.833895\pi\) | ||
0.866906 | − | 0.498471i | \(-0.166105\pi\) | |||||||
\(192\) | 2.83203e11 | + | 3.89773e11i | 1.08540 | + | 1.49385i | ||||
\(193\) | −9.09625e9 | −0.0339684 | −0.0169842 | − | 0.999856i | \(-0.505407\pi\) | ||||
−0.0169842 | + | 0.999856i | \(0.505407\pi\) | |||||||
\(194\) | 1.78540e11 | − | 4.01011e11i | 0.649720 | − | 1.45931i | ||||
\(195\) | − | 4.08653e10i | − | 0.144938i | ||||||
\(196\) | 6.25968e10 | + | 6.95196e10i | 0.216407 | + | 0.240340i | ||||
\(197\) | 3.36881e11 | 1.13539 | 0.567695 | − | 0.823239i | \(-0.307835\pi\) | ||||
0.567695 | + | 0.823239i | \(0.307835\pi\) | |||||||
\(198\) | 8.62880e11 | + | 3.84174e11i | 2.83547 | + | 1.26242i | ||||
\(199\) | 3.33901e11i | 1.06992i | 0.844877 | + | 0.534961i | \(0.179674\pi\) | ||||
−0.844877 | + | 0.534961i | \(0.820326\pi\) | |||||||
\(200\) | 6.08674e10 | − | 1.97779e10i | 0.190210 | − | 0.0618059i | ||||
\(201\) | 3.76792e11 | 1.14847 | ||||||||
\(202\) | −8.18851e10 | + | 1.83919e11i | −0.243471 | + | 0.546852i | ||||
\(203\) | 2.05027e11i | 0.594744i | ||||||||
\(204\) | −2.74939e11 | + | 2.47561e11i | −0.778190 | + | 0.700698i | ||||
\(205\) | 8.92307e10 | 0.246459 | ||||||||
\(206\) | −4.34096e11 | − | 1.93270e11i | −1.17017 | − | 0.520988i | ||||
\(207\) | − | 6.27201e11i | − | 1.65027i | ||||||
\(208\) | −7.14146e9 | + | 6.79581e10i | −0.0183430 | + | 0.174552i | ||||
\(209\) | 8.47131e11 | 2.12432 | ||||||||
\(210\) | 1.57806e11 | − | 3.54443e11i | 0.386392 | − | 0.867861i | ||||
\(211\) | − | 3.03506e9i | − | 0.00725696i | −0.999993 | − | 0.00362848i | \(-0.998845\pi\) | ||
0.999993 | − | 0.00362848i | \(-0.00115498\pi\) | |||||||
\(212\) | 2.54770e11 | + | 2.82946e11i | 0.594935 | + | 0.660731i | ||||
\(213\) | −2.18868e11 | −0.499211 | ||||||||
\(214\) | 2.29484e11 | + | 1.02172e11i | 0.511310 | + | 0.227647i | ||||
\(215\) | 3.35549e11i | 0.730404i | ||||||||
\(216\) | −3.78221e11 | − | 1.16399e12i | −0.804409 | − | 2.47560i | ||||
\(217\) | 5.61657e10 | 0.116727 | ||||||||
\(218\) | −4.54258e10 | + | 1.02029e11i | −0.0922613 | + | 0.207225i | ||||
\(219\) | − | 1.37192e12i | − | 2.72339i | ||||||
\(220\) | −2.20614e11 | + | 1.98645e11i | −0.428075 | + | 0.385447i | ||||
\(221\) | −5.24723e10 | −0.0995333 | ||||||||
\(222\) | 1.91208e11 | + | 8.51302e10i | 0.354602 | + | 0.157877i | ||||
\(223\) | − | 6.58534e11i | − | 1.19414i | −0.802191 | − | 0.597068i | \(-0.796332\pi\) | ||
0.802191 | − | 0.597068i | \(-0.203668\pi\) | |||||||
\(224\) | −3.24370e11 | + | 5.61855e11i | −0.575176 | + | 0.996285i | ||||
\(225\) | −2.77908e11 | −0.481936 | ||||||||
\(226\) | −1.78453e11 | + | 4.00817e11i | −0.302678 | + | 0.679835i | ||||
\(227\) | 8.15148e11i | 1.35241i | 0.736715 | + | 0.676203i | \(0.236376\pi\) | ||||
−0.736715 | + | 0.676203i | \(0.763624\pi\) | |||||||
\(228\) | −1.25554e12 | − | 1.39439e12i | −2.03778 | − | 2.26314i | ||||
\(229\) | 3.19584e11 | 0.507467 | 0.253734 | − | 0.967274i | \(-0.418341\pi\) | ||||
0.253734 | + | 0.967274i | \(0.418341\pi\) | |||||||
\(230\) | 1.80087e11 | + | 8.01788e10i | 0.279797 | + | 0.124572i | ||||
\(231\) | 1.79969e12i | 2.73614i | ||||||||
\(232\) | −3.30466e11 | + | 1.07380e11i | −0.491685 | + | 0.159765i | ||||
\(233\) | 4.24100e11 | 0.617573 | 0.308786 | − | 0.951131i | \(-0.400077\pi\) | ||||
0.308786 | + | 0.951131i | \(0.400077\pi\) | |||||||
\(234\) | 1.20686e11 | − | 2.71068e11i | 0.172019 | − | 0.386366i | ||||
\(235\) | 2.11299e11i | 0.294820i | ||||||||
\(236\) | 3.57648e11 | − | 3.22034e11i | 0.488535 | − | 0.439887i | ||||
\(237\) | −2.05811e12 | −2.75250 | ||||||||
\(238\) | −4.55116e11 | − | 2.02628e11i | −0.595988 | − | 0.265348i | ||||
\(239\) | 5.17807e11i | 0.664016i | 0.943277 | + | 0.332008i | \(0.107726\pi\) | ||||
−0.943277 | + | 0.332008i | \(0.892274\pi\) | |||||||
\(240\) | 6.53948e11 | + | 6.87209e10i | 0.821272 | + | 0.0863044i | ||||
\(241\) | 7.14203e11 | 0.878489 | 0.439244 | − | 0.898368i | \(-0.355246\pi\) | ||||
0.439244 | + | 0.898368i | \(0.355246\pi\) | |||||||
\(242\) | 2.22499e11 | − | 4.99747e11i | 0.268072 | − | 0.602106i | ||||
\(243\) | 1.54451e12i | 1.82288i | ||||||||
\(244\) | 5.46115e11 | + | 6.06511e11i | 0.631444 | + | 0.701277i | ||||
\(245\) | 1.27674e11 | 0.144634 | ||||||||
\(246\) | 8.37516e11 | + | 3.72882e11i | 0.929646 | + | 0.413900i | ||||
\(247\) | − | 2.66121e11i | − | 0.289464i | ||||||
\(248\) | 2.94160e10 | + | 9.05290e10i | 0.0313563 | + | 0.0965005i | ||||
\(249\) | 1.32545e11 | 0.138473 | ||||||||
\(250\) | 3.55266e10 | − | 7.97951e10i | 0.0363793 | − | 0.0817102i | ||||
\(251\) | − | 1.25838e11i | − | 0.126311i | −0.998004 | − | 0.0631557i | \(-0.979884\pi\) | ||
0.998004 | − | 0.0631557i | \(-0.0201165\pi\) | |||||||
\(252\) | 2.09353e12 | − | 1.88506e12i | 2.06004 | − | 1.85491i | ||||
\(253\) | −9.14394e11 | −0.882126 | ||||||||
\(254\) | −3.75401e11 | − | 1.67138e11i | −0.355081 | − | 0.158090i | ||||
\(255\) | 5.04931e11i | 0.468307i | ||||||||
\(256\) | −1.07549e12 | − | 2.28563e11i | −0.978155 | − | 0.207877i | ||||
\(257\) | −9.33845e11 | −0.832931 | −0.416466 | − | 0.909151i | \(-0.636731\pi\) | ||||
−0.416466 | + | 0.909151i | \(0.636731\pi\) | |||||||
\(258\) | −1.40221e12 | + | 3.14945e12i | −1.22663 | + | 2.75509i | ||||
\(259\) | 2.81838e11i | 0.241825i | ||||||||
\(260\) | 6.24031e10 | + | 6.93045e10i | 0.0525218 | + | 0.0583303i | ||||
\(261\) | 1.50884e12 | 1.24578 | ||||||||
\(262\) | −2.56361e11 | − | 1.14138e11i | −0.207656 | − | 0.0924535i | ||||
\(263\) | − | 3.58314e10i | − | 0.0284764i | −0.999899 | − | 0.0142382i | \(-0.995468\pi\) | ||
0.999899 | − | 0.0142382i | \(-0.00453231\pi\) | |||||||
\(264\) | −2.90078e12 | + | 9.42564e11i | −2.26202 | + | 0.735007i | ||||
\(265\) | 5.19636e11 | 0.397621 | ||||||||
\(266\) | 1.02766e12 | − | 2.30819e12i | 0.771687 | − | 1.73326i | ||||
\(267\) | − | 1.68826e12i | − | 1.24418i | ||||||
\(268\) | −6.39011e11 | + | 5.75378e11i | −0.462205 | + | 0.416178i | ||||
\(269\) | 2.26680e12 | 1.60936 | 0.804678 | − | 0.593711i | \(-0.202338\pi\) | ||||
0.804678 | + | 0.593711i | \(0.202338\pi\) | |||||||
\(270\) | −1.52595e12 | − | 6.79390e11i | −1.06346 | − | 0.473479i | ||||
\(271\) | − | 1.16910e12i | − | 0.799845i | −0.916549 | − | 0.399922i | \(-0.869037\pi\) | ||
0.916549 | − | 0.399922i | \(-0.130963\pi\) | |||||||
\(272\) | 8.82398e10 | − | 8.39690e11i | 0.0592680 | − | 0.563994i | ||||
\(273\) | 5.65362e11 | 0.372832 | ||||||||
\(274\) | 1.07920e12 | − | 2.42395e12i | 0.698794 | − | 1.56954i | ||||
\(275\) | 4.05161e11i | 0.257611i | ||||||||
\(276\) | 1.35523e12 | + | 1.50511e12i | 0.846191 | + | 0.939773i | ||||
\(277\) | 5.07340e11 | 0.311100 | 0.155550 | − | 0.987828i | \(-0.450285\pi\) | ||||
0.155550 | + | 0.987828i | \(0.450285\pi\) | |||||||
\(278\) | −7.40700e11 | − | 3.29777e11i | −0.446086 | − | 0.198608i | ||||
\(279\) | − | 4.13338e11i | − | 0.244503i | ||||||
\(280\) | 2.73623e11 | + | 8.42087e11i | 0.158987 | + | 0.489291i | ||||
\(281\) | −3.17014e11 | −0.180945 | −0.0904727 | − | 0.995899i | \(-0.528838\pi\) | ||||
−0.0904727 | + | 0.995899i | \(0.528838\pi\) | |||||||
\(282\) | −8.82985e11 | + | 1.98324e12i | −0.495117 | + | 1.11206i | ||||
\(283\) | − | 1.42234e12i | − | 0.783558i | −0.920059 | − | 0.391779i | \(-0.871860\pi\) | ||
0.920059 | − | 0.391779i | \(-0.128140\pi\) | |||||||
\(284\) | 3.71184e11 | − | 3.34221e11i | 0.200908 | − | 0.180902i | ||||
\(285\) | −2.56083e12 | −1.36193 | ||||||||
\(286\) | −3.95189e11 | − | 1.75947e11i | −0.206526 | − | 0.0919502i | ||||
\(287\) | 1.23449e12i | 0.633983i | ||||||||
\(288\) | 4.13483e12 | + | 2.38712e12i | 2.08687 | + | 1.20479i | ||||
\(289\) | −1.36765e12 | −0.678398 | ||||||||
\(290\) | −1.92884e11 | + | 4.33230e11i | −0.0940387 | + | 0.211217i | ||||
\(291\) | − | 6.15515e12i | − | 2.94967i | ||||||
\(292\) | 2.09499e12 | + | 2.32668e12i | 0.986887 | + | 1.09603i | ||||
\(293\) | −2.22060e12 | −1.02833 | −0.514165 | − | 0.857691i | \(-0.671898\pi\) | ||||
−0.514165 | + | 0.857691i | \(0.671898\pi\) | |||||||
\(294\) | 1.19834e12 | + | 5.33530e11i | 0.545562 | + | 0.242897i | ||||
\(295\) | − | 6.56827e11i | − | 0.293996i | ||||||
\(296\) | −4.54272e11 | + | 1.47609e11i | −0.199921 | + | 0.0649611i | ||||
\(297\) | 7.74806e12 | 3.35283 | ||||||||
\(298\) | 1.48166e12 | − | 3.32789e12i | 0.630472 | − | 1.41608i | ||||
\(299\) | 2.87251e11i | 0.120200i | ||||||||
\(300\) | 6.66903e11 | − | 6.00493e11i | 0.274446 | − | 0.247117i | ||||
\(301\) | −4.64225e12 | −1.87887 | ||||||||
\(302\) | −3.59452e12 | − | 1.60036e12i | −1.43089 | − | 0.637066i | ||||
\(303\) | 2.82299e12i | 1.10534i | ||||||||
\(304\) | 4.25861e12 | + | 4.47521e11i | 1.64021 | + | 0.172364i | ||||
\(305\) | 1.11387e12 | 0.422022 | ||||||||
\(306\) | −1.49119e12 | + | 3.34932e12i | −0.555811 | + | 1.24839i | ||||
\(307\) | 9.58563e11i | 0.351503i | 0.984435 | + | 0.175751i | \(0.0562355\pi\) | ||||
−0.984435 | + | 0.175751i | \(0.943765\pi\) | |||||||
\(308\) | −2.74822e12 | − | 3.05215e12i | −0.991510 | − | 1.10116i | ||||
\(309\) | −6.66297e12 | −2.36524 | ||||||||
\(310\) | 1.18681e11 | + | 5.28393e10i | 0.0414544 | + | 0.0184565i | ||||
\(311\) | 4.11550e12i | 1.41456i | 0.706934 | + | 0.707280i | \(0.250078\pi\) | ||||
−0.706934 | + | 0.707280i | \(0.749922\pi\) | |||||||
\(312\) | 2.96101e11 | + | 9.11263e11i | 0.100154 | + | 0.308227i | ||||
\(313\) | 8.45683e10 | 0.0281505 | 0.0140752 | − | 0.999901i | \(-0.495520\pi\) | ||||
0.0140752 | + | 0.999901i | \(0.495520\pi\) | |||||||
\(314\) | −1.80226e12 | + | 4.04799e12i | −0.590431 | + | 1.32615i | ||||
\(315\) | − | 3.84481e12i | − | 1.23971i | ||||||
\(316\) | 3.49040e12 | − | 3.14283e12i | 1.10775 | − | 0.997436i | ||||
\(317\) | −3.02740e12 | −0.945745 | −0.472872 | − | 0.881131i | \(-0.656783\pi\) | ||||
−0.472872 | + | 0.881131i | \(0.656783\pi\) | |||||||
\(318\) | 4.87728e12 | + | 2.17148e12i | 1.49983 | + | 0.667760i | ||||
\(319\) | − | 2.19974e12i | − | 0.665912i | ||||||
\(320\) | −1.21399e12 | + | 8.82063e11i | −0.361796 | + | 0.262875i | ||||
\(321\) | 3.52237e12 | 1.03350 | ||||||||
\(322\) | −1.10926e12 | + | 2.49146e12i | −0.320445 | + | 0.719739i | ||||
\(323\) | 3.28819e12i | 0.935285i | ||||||||
\(324\) | −5.72644e12 | − | 6.35974e12i | −1.60383 | − | 1.78121i | ||||
\(325\) | 1.27279e11 | 0.0351026 | ||||||||
\(326\) | 4.76540e10 | + | 2.12167e10i | 0.0129423 | + | 0.00576221i | ||||
\(327\) | 1.56605e12i | 0.418859i | ||||||||
\(328\) | −1.98977e12 | + | 6.46546e11i | −0.524124 | + | 0.170306i | ||||
\(329\) | −2.92327e12 | −0.758385 | ||||||||
\(330\) | −1.69311e12 | + | 3.80283e12i | −0.432628 | + | 0.971711i | ||||
\(331\) | − | 3.58363e12i | − | 0.901951i | −0.892536 | − | 0.450975i | \(-0.851076\pi\) | ||
0.892536 | − | 0.450975i | \(-0.148924\pi\) | |||||||
\(332\) | −2.24786e11 | + | 2.02402e11i | −0.0557286 | + | 0.0501792i | ||||
\(333\) | 2.07412e12 | 0.506538 | ||||||||
\(334\) | 6.54028e12 | + | 2.91188e12i | 1.57349 | + | 0.700554i | ||||
\(335\) | 1.17355e12i | 0.278150i | ||||||||
\(336\) | −9.50740e11 | + | 9.04723e12i | −0.222006 | + | 2.11261i | ||||
\(337\) | 7.53391e12 | 1.73329 | 0.866645 | − | 0.498926i | \(-0.166272\pi\) | ||||
0.866645 | + | 0.498926i | \(0.166272\pi\) | |||||||
\(338\) | 1.73902e12 | − | 3.90594e12i | 0.394203 | − | 0.885406i | ||||
\(339\) | 6.15216e12i | 1.37413i | ||||||||
\(340\) | −7.71052e11 | − | 8.56325e11i | −0.169703 | − | 0.188471i | ||||
\(341\) | −6.02603e11 | −0.130695 | ||||||||
\(342\) | −1.69866e13 | − | 7.56281e12i | −3.63057 | − | 1.61641i | ||||
\(343\) | − | 3.69524e12i | − | 0.778344i | ||||||
\(344\) | −2.43131e12 | − | 7.48247e12i | −0.504718 | − | 1.55329i | ||||
\(345\) | 2.76416e12 | 0.565546 | ||||||||
\(346\) | −1.04485e12 | + | 2.34681e12i | −0.210705 | + | 0.473257i | ||||
\(347\) | 3.87583e12i | 0.770401i | 0.922833 | + | 0.385201i | \(0.125868\pi\) | ||||
−0.922833 | + | 0.385201i | \(0.874132\pi\) | |||||||
\(348\) | −3.62081e12 | + | 3.26025e12i | −0.709429 | + | 0.638784i | ||||
\(349\) | 6.88957e12 | 1.33065 | 0.665327 | − | 0.746552i | \(-0.268292\pi\) | ||||
0.665327 | + | 0.746552i | \(0.268292\pi\) | |||||||
\(350\) | 1.10395e12 | + | 4.91504e11i | 0.210188 | + | 0.0935808i | ||||
\(351\) | − | 2.43401e12i | − | 0.456863i | ||||||
\(352\) | 3.48017e12 | − | 6.02815e12i | 0.644003 | − | 1.11550i | ||||
\(353\) | 1.22636e12 | 0.223741 | 0.111870 | − | 0.993723i | \(-0.464316\pi\) | ||||
0.111870 | + | 0.993723i | \(0.464316\pi\) | |||||||
\(354\) | 2.74478e12 | − | 6.16496e12i | 0.493733 | − | 1.10895i | ||||
\(355\) | − | 6.81685e11i | − | 0.120904i | ||||||
\(356\) | 2.57806e12 | + | 2.86317e12i | 0.450861 | + | 0.500723i | ||||
\(357\) | −6.98561e12 | −1.20466 | ||||||||
\(358\) | −1.90477e12 | − | 8.48047e11i | −0.323912 | − | 0.144213i | ||||
\(359\) | 1.09523e13i | 1.83667i | 0.395802 | + | 0.918336i | \(0.370467\pi\) | ||||
−0.395802 | + | 0.918336i | \(0.629533\pi\) | |||||||
\(360\) | 6.19713e12 | − | 2.01366e12i | 1.02489 | − | 0.333023i | ||||
\(361\) | −1.05455e13 | −1.72000 | ||||||||
\(362\) | 4.07419e12 | − | 9.15088e12i | 0.655387 | − | 1.47204i | ||||
\(363\) | − | 7.67065e12i | − | 1.21702i | ||||||
\(364\) | −9.58813e11 | + | 8.63335e11i | −0.150047 | + | 0.135105i | ||||
\(365\) | 4.27299e12 | 0.659580 | ||||||||
\(366\) | 1.04547e13 | + | 4.65469e12i | 1.59187 | + | 0.708737i | ||||
\(367\) | − | 7.38135e12i | − | 1.10868i | −0.832291 | − | 0.554339i | \(-0.812971\pi\) | ||
0.832291 | − | 0.554339i | \(-0.187029\pi\) | |||||||
\(368\) | −4.59675e12 | − | 4.83055e11i | −0.681101 | − | 0.0715744i | ||||
\(369\) | 9.08491e12 | 1.32797 | ||||||||
\(370\) | −2.65147e11 | + | 5.95536e11i | −0.0382364 | + | 0.0858814i | ||||
\(371\) | 7.18905e12i | 1.02283i | ||||||||
\(372\) | 8.93123e11 | + | 9.91896e11i | 0.125371 | + | 0.139236i | ||||
\(373\) | 5.26643e12 | 0.729411 | 0.364705 | − | 0.931123i | \(-0.381170\pi\) | ||||
0.364705 | + | 0.931123i | \(0.381170\pi\) | |||||||
\(374\) | 4.88295e12 | + | 2.17400e12i | 0.667305 | + | 0.297100i | ||||
\(375\) | − | 1.22478e12i | − | 0.165159i | ||||||
\(376\) | −1.53102e12 | − | 4.71179e12i | −0.203724 | − | 0.626970i | ||||
\(377\) | −6.91033e11 | −0.0907386 | ||||||||
\(378\) | 9.39923e12 | − | 2.11113e13i | 1.21796 | − | 2.73562i | ||||
\(379\) | 6.22868e12i | 0.796527i | 0.917271 | + | 0.398263i | \(0.130387\pi\) | ||||
−0.917271 | + | 0.398263i | \(0.869613\pi\) | |||||||
\(380\) | 4.34298e12 | − | 3.91051e12i | 0.548112 | − | 0.493531i | ||||
\(381\) | −5.76206e12 | −0.717717 | ||||||||
\(382\) | 7.40828e12 | + | 3.29834e12i | 0.910754 | + | 0.405489i | ||||
\(383\) | − | 3.30387e12i | − | 0.400893i | −0.979705 | − | 0.200447i | \(-0.935761\pi\) | ||
0.979705 | − | 0.200447i | \(-0.0642394\pi\) | |||||||
\(384\) | −1.50805e13 | + | 3.20594e12i | −1.80617 | + | 0.383972i | ||||
\(385\) | −5.60532e12 | −0.662670 | ||||||||
\(386\) | 1.18392e11 | − | 2.65915e11i | 0.0138161 | − | 0.0310318i | ||||
\(387\) | 3.41635e13i | 3.93557i | ||||||||
\(388\) | 9.39920e12 | + | 1.04387e13i | 1.06889 | + | 1.18710i | ||||
\(389\) | 2.72395e12 | 0.305809 | 0.152905 | − | 0.988241i | \(-0.451137\pi\) | ||||
0.152905 | + | 0.988241i | \(0.451137\pi\) | |||||||
\(390\) | 1.19463e12 | + | 5.31879e11i | 0.132407 | + | 0.0589509i | ||||
\(391\) | − | 3.54927e12i | − | 0.388379i | ||||||
\(392\) | −2.84703e12 | + | 9.25097e11i | −0.307582 | + | 0.0999440i | ||||
\(393\) | −3.93490e12 | −0.419731 | ||||||||
\(394\) | −4.38465e12 | + | 9.84820e12i | −0.461800 | + | 1.03723i | ||||
\(395\) | − | 6.41018e12i | − | 0.666630i | ||||||
\(396\) | −2.24615e13 | + | 2.02248e13i | −2.30655 | + | 2.07687i | ||||
\(397\) | −5.16095e12 | −0.523332 | −0.261666 | − | 0.965158i | \(-0.584272\pi\) | ||||
−0.261666 | + | 0.965158i | \(0.584272\pi\) | |||||||
\(398\) | −9.76110e12 | − | 4.34587e12i | −0.977425 | − | 0.435172i | ||||
\(399\) | − | 3.54286e13i | − | 3.50339i | ||||||
\(400\) | −2.14038e11 | + | 2.03678e12i | −0.0209022 | + | 0.198905i | ||||
\(401\) | 6.09489e12 | 0.587820 | 0.293910 | − | 0.955833i | \(-0.405043\pi\) | ||||
0.293910 | + | 0.955833i | \(0.405043\pi\) | |||||||
\(402\) | −4.90411e12 | + | 1.10149e13i | −0.467122 | + | 1.04919i | ||||
\(403\) | 1.89304e11i | 0.0178088i | ||||||||
\(404\) | −4.31083e12 | − | 4.78758e12i | −0.400547 | − | 0.444845i | ||||
\(405\) | −1.16798e13 | −1.07191 | ||||||||
\(406\) | −5.99365e12 | − | 2.66851e12i | −0.543327 | − | 0.241902i | ||||
\(407\) | − | 3.02385e12i | − | 0.270762i | ||||||
\(408\) | −3.65862e12 | − | 1.12595e13i | −0.323606 | − | 0.995910i | ||||
\(409\) | 8.94937e12 | 0.781944 | 0.390972 | − | 0.920402i | \(-0.372139\pi\) | ||||
0.390972 | + | 0.920402i | \(0.372139\pi\) | |||||||
\(410\) | −1.16138e12 | + | 2.60853e12i | −0.100243 | + | 0.225152i | ||||
\(411\) | − | 3.72054e13i | − | 3.17247i | ||||||
\(412\) | 1.12999e13 | − | 1.01747e13i | 0.951894 | − | 0.857105i | ||||
\(413\) | 9.08707e12 | 0.756264 | ||||||||
\(414\) | 1.83353e13 | + | 8.16330e12i | 1.50760 | + | 0.671219i | ||||
\(415\) | 4.12823e11i | 0.0335369i | ||||||||
\(416\) | −1.89370e12 | − | 1.09327e12i | −0.152001 | − | 0.0877532i | ||||
\(417\) | −1.13690e13 | −0.901662 | ||||||||
\(418\) | −1.10258e13 | + | 2.47646e13i | −0.864029 | + | 1.94066i | ||||
\(419\) | 1.32772e13i | 1.02810i | 0.857759 | + | 0.514052i | \(0.171856\pi\) | ||||
−0.857759 | + | 0.514052i | \(0.828144\pi\) | |||||||
\(420\) | 8.30770e12 | + | 9.22647e12i | 0.635674 | + | 0.705975i | ||||
\(421\) | −1.16418e13 | −0.880258 | −0.440129 | − | 0.897935i | \(-0.645067\pi\) | ||||
−0.440129 | + | 0.897935i | \(0.645067\pi\) | |||||||
\(422\) | 8.87254e10 | + | 3.95026e10i | 0.00662957 | + | 0.00295164i | ||||
\(423\) | 2.15131e13i | 1.58855i | ||||||||
\(424\) | −1.15875e13 | + | 3.76516e12i | −0.845588 | + | 0.274761i | ||||
\(425\) | −1.57266e12 | −0.113420 | ||||||||
\(426\) | 2.84866e12 | − | 6.39827e12i | 0.203045 | − | 0.456052i | ||||
\(427\) | 1.54101e13i | 1.08559i | ||||||||
\(428\) | −5.97368e12 | + | 5.37882e12i | −0.415933 | + | 0.374514i | ||||
\(429\) | −6.06579e12 | −0.417446 | ||||||||
\(430\) | −9.80927e12 | − | 4.36732e12i | −0.667259 | − | 0.297079i | ||||
\(431\) | 1.70572e13i | 1.14689i | 0.819245 | + | 0.573443i | \(0.194393\pi\) | ||||
−0.819245 | + | 0.573443i | \(0.805607\pi\) | |||||||
\(432\) | 3.89503e13 | + | 4.09314e12i | 2.58876 | + | 0.272043i | ||||
\(433\) | 1.59244e13 | 1.04622 | 0.523110 | − | 0.852265i | \(-0.324772\pi\) | ||||
0.523110 | + | 0.852265i | \(0.324772\pi\) | |||||||
\(434\) | −7.31021e11 | + | 1.64192e12i | −0.0474768 | + | 0.106636i | ||||
\(435\) | 6.64968e12i | 0.426928i | ||||||||
\(436\) | −2.39143e12 | − | 2.65591e12i | −0.151784 | − | 0.168570i | ||||
\(437\) | 1.80007e13 | 1.12949 | ||||||||
\(438\) | 4.01061e13 | + | 1.78562e13i | 2.48794 | + | 1.10769i | ||||
\(439\) | − | 6.37376e12i | − | 0.390907i | −0.980713 | − | 0.195453i | \(-0.937382\pi\) | ||
0.980713 | − | 0.195453i | \(-0.0626178\pi\) | |||||||
\(440\) | −2.93571e12 | − | 9.03477e12i | −0.178012 | − | 0.547840i | ||||
\(441\) | 1.29990e13 | 0.779320 | ||||||||
\(442\) | 6.82950e11 | − | 1.53395e12i | 0.0404834 | − | 0.0909284i | ||||
\(443\) | − | 2.35727e13i | − | 1.38163i | −0.723032 | − | 0.690815i | \(-0.757252\pi\) | ||
0.723032 | − | 0.690815i | \(-0.242748\pi\) | |||||||
\(444\) | −4.97731e12 | + | 4.48167e12i | −0.288456 | + | 0.259732i | ||||
\(445\) | 5.25827e12 | 0.301330 | ||||||||
\(446\) | 1.92513e13 | + | 8.57111e12i | 1.09090 | + | 0.485694i | ||||
\(447\) | − | 5.10800e13i | − | 2.86229i | ||||||
\(448\) | −1.22032e13 | − | 1.67953e13i | −0.676211 | − | 0.930672i | ||||
\(449\) | −1.03415e13 | −0.566700 | −0.283350 | − | 0.959017i | \(-0.591446\pi\) | ||||
−0.283350 | + | 0.959017i | \(0.591446\pi\) | |||||||
\(450\) | 3.61710e12 | − | 8.12424e12i | 0.196019 | − | 0.440271i | ||||
\(451\) | − | 1.32449e13i | − | 0.709846i | ||||||
\(452\) | −9.39464e12 | − | 1.04336e13i | −0.497952 | − | 0.553022i | ||||
\(453\) | −5.51725e13 | −2.89222 | ||||||||
\(454\) | −2.38296e13 | − | 1.06095e13i | −1.23549 | − | 0.550068i | ||||
\(455\) | 1.76088e12i | 0.0902967i | ||||||||
\(456\) | 5.71045e13 | − | 1.85552e13i | 2.89631 | − | 0.941113i | ||||
\(457\) | −3.19521e13 | −1.60294 | −0.801471 | − | 0.598033i | \(-0.795949\pi\) | ||||
−0.801471 | + | 0.598033i | \(0.795949\pi\) | |||||||
\(458\) | −4.15953e12 | + | 9.34258e12i | −0.206404 | + | 0.463596i | ||||
\(459\) | 3.00745e13i | 1.47617i | ||||||||
\(460\) | −4.68782e12 | + | 4.22100e12i | −0.227605 | + | 0.204940i | ||||
\(461\) | 1.06085e13 | 0.509508 | 0.254754 | − | 0.967006i | \(-0.418005\pi\) | ||||
0.254754 | + | 0.967006i | \(0.418005\pi\) | |||||||
\(462\) | −5.26114e13 | − | 2.34238e13i | −2.49960 | − | 1.11288i | ||||
\(463\) | − | 1.01429e13i | − | 0.476715i | −0.971178 | − | 0.238357i | \(-0.923391\pi\) | ||
0.971178 | − | 0.238357i | \(-0.0766089\pi\) | |||||||
\(464\) | 1.16207e12 | − | 1.10583e13i | 0.0540311 | − | 0.514159i | ||||
\(465\) | 1.82163e12 | 0.0837908 | ||||||||
\(466\) | −5.51984e12 | + | 1.23979e13i | −0.251187 | + | 0.564182i | ||||
\(467\) | − | 1.20631e13i | − | 0.543094i | −0.962425 | − | 0.271547i | \(-0.912465\pi\) | ||
0.962425 | − | 0.271547i | \(-0.0875353\pi\) | |||||||
\(468\) | 6.35350e12 | + | 7.05615e12i | 0.282998 | + | 0.314296i | ||||
\(469\) | −1.62359e13 | −0.715504 | ||||||||
\(470\) | −6.17700e12 | − | 2.75014e12i | −0.269332 | − | 0.119913i | ||||
\(471\) | 6.21329e13i | 2.68051i | ||||||||
\(472\) | 4.75923e12 | + | 1.46467e13i | 0.203154 | + | 0.625217i | ||||
\(473\) | 4.98068e13 | 2.10370 | ||||||||
\(474\) | 2.67872e13 | − | 6.01658e13i | 1.11953 | − | 2.51454i | ||||
\(475\) | − | 7.97596e12i | − | 0.329849i | ||||||
\(476\) | 1.18471e13 | − | 1.06674e13i | 0.484816 | − | 0.436538i | ||||
\(477\) | 5.29060e13 | 2.14246 | ||||||||
\(478\) | −1.51373e13 | − | 6.73949e12i | −0.606610 | − | 0.270077i | ||||
\(479\) | − | 1.51493e13i | − | 0.600781i | −0.953816 | − | 0.300390i | \(-0.902883\pi\) | ||
0.953816 | − | 0.300390i | \(-0.0971169\pi\) | |||||||
\(480\) | −1.05204e13 | + | 1.82228e13i | −0.412881 | + | 0.715168i | ||||
\(481\) | −9.49923e11 | −0.0368946 | ||||||||
\(482\) | −9.29566e12 | + | 2.08787e13i | −0.357310 | + | 0.802541i | ||||
\(483\) | 3.82416e13i | 1.45479i | ||||||||
\(484\) | 1.17134e13 | + | 1.30089e13i | 0.441019 | + | 0.489792i | ||||
\(485\) | 1.91708e13 | 0.714385 | ||||||||
\(486\) | −4.51513e13 | − | 2.01024e13i | −1.66529 | − | 0.741425i | ||||
\(487\) | 1.23333e13i | 0.450232i | 0.974332 | + | 0.225116i | \(0.0722761\pi\) | ||||
−0.974332 | + | 0.225116i | \(0.927724\pi\) | |||||||
\(488\) | −2.48384e13 | + | 8.07085e12i | −0.897479 | + | 0.291622i | ||||
\(489\) | 7.31444e11 | 0.0261600 | ||||||||
\(490\) | −1.66173e12 | + | 3.73236e12i | −0.0588275 | + | 0.132130i | ||||
\(491\) | − | 2.24401e13i | − | 0.786353i | −0.919463 | − | 0.393176i | \(-0.871376\pi\) | ||
0.919463 | − | 0.393176i | \(-0.128624\pi\) | |||||||
\(492\) | −2.18013e13 | + | 1.96303e13i | −0.756235 | + | 0.680929i | ||||
\(493\) | 8.53839e12 | 0.293185 | ||||||||
\(494\) | 7.77965e12 | + | 3.46368e12i | 0.264439 | + | 0.117734i | ||||
\(495\) | 4.12510e13i | 1.38806i | ||||||||
\(496\) | −3.02934e12 | − | 3.18342e11i | −0.100911 | − | 0.0106044i | ||||
\(497\) | 9.43098e12 | 0.311010 | ||||||||
\(498\) | −1.72513e12 | + | 3.87474e12i | −0.0563215 | + | 0.126502i | ||||
\(499\) | − | 3.09195e13i | − | 0.999378i | −0.866205 | − | 0.499689i | \(-0.833448\pi\) | ||
0.866205 | − | 0.499689i | \(-0.166552\pi\) | |||||||
\(500\) | 1.87030e12 | + | 2.07714e12i | 0.0598495 | + | 0.0664684i | ||||
\(501\) | 1.00387e14 | 3.18046 | ||||||||
\(502\) | 3.67868e12 | + | 1.63784e12i | 0.115391 | + | 0.0513750i | ||||
\(503\) | 5.50005e13i | 1.70815i | 0.520147 | + | 0.854077i | \(0.325877\pi\) | ||||
−0.520147 | + | 0.854077i | \(0.674123\pi\) | |||||||
\(504\) | 2.78586e13 | + | 8.57361e13i | 0.856657 | + | 2.63640i | ||||
\(505\) | −8.79247e12 | −0.267703 | ||||||||
\(506\) | 1.19012e13 | − | 2.67310e13i | 0.358790 | − | 0.805864i | ||||
\(507\) | − | 5.99526e13i | − | 1.78965i | ||||||
\(508\) | 9.77203e12 | − | 8.79894e12i | 0.288846 | − | 0.260083i | ||||
\(509\) | −6.10086e13 | −1.78567 | −0.892836 | − | 0.450381i | \(-0.851288\pi\) | ||||
−0.892836 | + | 0.450381i | \(0.851288\pi\) | |||||||
\(510\) | −1.47609e13 | − | 6.57189e12i | −0.427821 | − | 0.190476i | ||||
\(511\) | 5.91159e13i | 1.69668i | ||||||||
\(512\) | 2.06797e13 | − | 2.84656e13i | 0.587753 | − | 0.809041i | ||||
\(513\) | −1.52527e14 | −4.29300 | ||||||||
\(514\) | 1.21544e13 | − | 2.72996e13i | 0.338780 | − | 0.760922i | ||||
\(515\) | − | 2.07525e13i | − | 0.572840i | ||||||
\(516\) | −7.38191e13 | − | 8.19830e13i | −2.01800 | − | 2.24117i | ||||
\(517\) | 3.13639e13 | 0.849135 | ||||||||
\(518\) | −8.23912e12 | − | 3.66825e12i | −0.220918 | − | 0.0983580i | ||||
\(519\) | 3.60213e13i | 0.956583i | ||||||||
\(520\) | −2.83822e12 | + | 9.22235e11i | −0.0746498 | + | 0.0242563i | ||||
\(521\) | −5.32796e13 | −1.38795 | −0.693973 | − | 0.720001i | \(-0.744141\pi\) | ||||
−0.693973 | + | 0.720001i | \(0.744141\pi\) | |||||||
\(522\) | −1.96383e13 | + | 4.41088e13i | −0.506699 | + | 1.13808i | ||||
\(523\) | 5.41769e13i | 1.38454i | 0.721638 | + | 0.692271i | \(0.243390\pi\) | ||||
−0.721638 | + | 0.692271i | \(0.756610\pi\) | |||||||
\(524\) | 6.67330e12 | − | 6.00878e12i | 0.168921 | − | 0.152100i | ||||
\(525\) | 1.69446e13 | 0.424849 | ||||||||
\(526\) | 1.04748e12 | + | 4.66362e11i | 0.0260145 | + | 0.0115823i | ||||
\(527\) | − | 2.33904e12i | − | 0.0575419i | ||||||
\(528\) | 1.02005e13 | − | 9.70680e13i | 0.248572 | − | 2.36541i | ||||
\(529\) | 2.19966e13 | 0.530978 | ||||||||
\(530\) | −6.76329e12 | + | 1.51908e13i | −0.161725 | + | 0.363246i | ||||
\(531\) | − | 6.68741e13i | − | 1.58411i | ||||||
\(532\) | 5.41010e13 | + | 6.00842e13i | 1.26954 | + | 1.40995i | ||||
\(533\) | −4.16079e12 | −0.0967251 | ||||||||
\(534\) | 4.93539e13 | + | 2.19735e13i | 1.13662 | + | 0.506050i | ||||
\(535\) | 1.09708e13i | 0.250304i | ||||||||
\(536\) | −8.50332e12 | − | 2.61693e13i | −0.192205 | − | 0.591519i | ||||
\(537\) | −2.92364e13 | −0.654715 | ||||||||
\(538\) | −2.95034e13 | + | 6.62666e13i | −0.654578 | + | 1.47022i | ||||
\(539\) | − | 1.89511e13i | − | 0.416573i | ||||||
\(540\) | 3.97219e13 | − | 3.57664e13i | 0.865090 | − | 0.778945i | ||||
\(541\) | −8.90533e13 | −1.92160 | −0.960801 | − | 0.277239i | \(-0.910581\pi\) | ||||
−0.960801 | + | 0.277239i | \(0.910581\pi\) | |||||||
\(542\) | 3.41769e13 | + | 1.52164e13i | 0.730696 | + | 0.325323i | ||||
\(543\) | − | 1.40457e14i | − | 2.97540i | ||||||
\(544\) | 2.33986e13 | + | 1.35085e13i | 0.491129 | + | 0.283539i | ||||
\(545\) | −4.87762e12 | −0.101444 | ||||||||
\(546\) | −7.35844e12 | + | 1.65275e13i | −0.151643 | + | 0.340600i | ||||
\(547\) | 6.79396e13i | 1.38735i | 0.720287 | + | 0.693676i | \(0.244010\pi\) | ||||
−0.720287 | + | 0.693676i | \(0.755990\pi\) | |||||||
\(548\) | 5.68144e13 | + | 6.30977e13i | 1.14962 | + | 1.27676i | ||||
\(549\) | 1.13407e14 | 2.27394 | ||||||||
\(550\) | −1.18443e13 | − | 5.27335e12i | −0.235340 | − | 0.104779i | ||||
\(551\) | 4.33037e13i | 0.852643i | ||||||||
\(552\) | −6.16386e13 | + | 2.00285e13i | −1.20270 | + | 0.390799i | ||||
\(553\) | 8.86836e13 | 1.71482 | ||||||||
\(554\) | −6.60326e12 | + | 1.48313e13i | −0.126535 | + | 0.284205i | ||||
\(555\) | 9.14092e12i | 0.173590i | ||||||||
\(556\) | 1.92811e13 | − | 1.73611e13i | 0.362875 | − | 0.326740i | ||||
\(557\) | −3.38104e13 | −0.630630 | −0.315315 | − | 0.948987i | \(-0.602110\pi\) | ||||
−0.315315 | + | 0.948987i | \(0.602110\pi\) | |||||||
\(558\) | 1.20833e13 | + | 5.37977e12i | 0.223365 | + | 0.0994473i | ||||
\(559\) | − | 1.56465e13i | − | 0.286654i | ||||||
\(560\) | −2.81785e13 | − | 2.96117e12i | −0.511656 | − | 0.0537680i | ||||
\(561\) | 7.49488e13 | 1.34881 | ||||||||
\(562\) | 4.12608e12 | − | 9.26744e12i | 0.0735964 | − | 0.165302i | ||||
\(563\) | − | 8.00894e13i | − | 1.41590i | −0.706262 | − | 0.707951i | \(-0.749620\pi\) | ||
0.706262 | − | 0.707951i | \(-0.250380\pi\) | |||||||
\(564\) | −4.64847e13 | − | 5.16255e13i | −0.814543 | − | 0.904626i | ||||
\(565\) | −1.91615e13 | −0.332803 | ||||||||
\(566\) | 4.15800e13 | + | 1.85124e13i | 0.715817 | + | 0.318699i | ||||
\(567\) | − | 1.61587e14i | − | 2.75735i | ||||||
\(568\) | 4.93934e12 | + | 1.52010e13i | 0.0835463 | + | 0.257117i | ||||
\(569\) | −2.99622e13 | −0.502357 | −0.251178 | − | 0.967941i | \(-0.580818\pi\) | ||||
−0.251178 | + | 0.967941i | \(0.580818\pi\) | |||||||
\(570\) | 3.33303e13 | − | 7.48620e13i | 0.553943 | − | 1.24419i | ||||
\(571\) | 2.15663e13i | 0.355300i | 0.984094 | + | 0.177650i | \(0.0568495\pi\) | ||||
−0.984094 | + | 0.177650i | \(0.943150\pi\) | |||||||
\(572\) | 1.02871e13 | − | 9.26274e12i | 0.168002 | − | 0.151272i | ||||
\(573\) | 1.13710e14 | 1.84088 | ||||||||
\(574\) | −3.60884e13 | − | 1.60674e13i | −0.579173 | − | 0.257861i | ||||
\(575\) | 8.60926e12i | 0.136970i | ||||||||
\(576\) | −1.23601e14 | + | 8.98061e13i | −1.94943 | + | 1.41643i | ||||
\(577\) | −4.63163e13 | −0.724194 | −0.362097 | − | 0.932141i | \(-0.617939\pi\) | ||||
−0.362097 | + | 0.932141i | \(0.617939\pi\) | |||||||
\(578\) | 1.78005e13 | − | 3.99811e13i | 0.275927 | − | 0.619749i | ||||
\(579\) | − | 4.08155e12i | − | 0.0627238i | ||||||
\(580\) | −1.01544e13 | − | 1.12774e13i | −0.154708 | − | 0.171818i | ||||
\(581\) | −5.71132e12 | −0.0862692 | ||||||||
\(582\) | 1.79937e14 | + | 8.01120e13i | 2.69466 | + | 1.19973i | ||||
\(583\) | − | 7.71315e13i | − | 1.14522i | ||||||
\(584\) | −9.52842e13 | + | 3.09611e13i | −1.40267 | + | 0.455777i | ||||
\(585\) | 1.29587e13 | 0.189140 | ||||||||
\(586\) | 2.89021e13 | − | 6.49160e13i | 0.418256 | − | 0.939429i | ||||
\(587\) | − | 1.79638e13i | − | 0.257755i | −0.991660 | − | 0.128878i | \(-0.958863\pi\) | ||
0.991660 | − | 0.128878i | \(-0.0411375\pi\) | |||||||
\(588\) | −3.11939e13 | + | 2.80876e13i | −0.443796 | + | 0.399603i | ||||
\(589\) | 1.18628e13 | 0.167344 | ||||||||
\(590\) | 1.92014e13 | + | 8.54890e12i | 0.268579 | + | 0.119578i | ||||
\(591\) | 1.51161e14i | 2.09653i | ||||||||
\(592\) | 1.59743e12 | − | 1.52012e13i | 0.0219692 | − | 0.209059i | ||||
\(593\) | −4.08145e13 | −0.556597 | −0.278298 | − | 0.960495i | \(-0.589770\pi\) | ||||
−0.278298 | + | 0.960495i | \(0.589770\pi\) | |||||||
\(594\) | −1.00844e14 | + | 2.26503e14i | −1.36370 | + | 3.06296i | ||||
\(595\) | − | 2.17574e13i | − | 0.291757i | ||||||
\(596\) | 7.80016e13 | + | 8.66280e13i | 1.03722 | + | 1.15193i | ||||
\(597\) | −1.49824e14 | −1.97565 | ||||||||
\(598\) | −8.39736e12 | − | 3.73870e12i | −0.109809 | − | 0.0488894i | ||||
\(599\) | − | 8.40892e13i | − | 1.09045i | −0.838289 | − | 0.545226i | \(-0.816444\pi\) | ||
0.838289 | − | 0.545226i | \(-0.183556\pi\) | |||||||
\(600\) | 8.87448e12 | + | 2.73116e13i | 0.114127 | + | 0.351230i | ||||
\(601\) | −4.22110e13 | −0.538336 | −0.269168 | − | 0.963093i | \(-0.586749\pi\) | ||||
−0.269168 | + | 0.963093i | \(0.586749\pi\) | |||||||
\(602\) | 6.04209e13 | − | 1.35709e14i | 0.764196 | − | 1.71643i | ||||
\(603\) | 1.19484e14i | 1.49873i | ||||||||
\(604\) | 9.35686e13 | − | 8.42510e13i | 1.16398 | − | 1.04807i | ||||
\(605\) | 2.38910e13 | 0.294752 | ||||||||
\(606\) | −8.25258e13 | − | 3.67424e13i | −1.00978 | − | 0.449577i | ||||
\(607\) | 2.70801e13i | 0.328630i | 0.986408 | + | 0.164315i | \(0.0525414\pi\) | ||||
−0.986408 | + | 0.164315i | \(0.947459\pi\) | |||||||
\(608\) | −6.85103e13 | + | 1.18669e14i | −0.824590 | + | 1.42830i | ||||
\(609\) | −9.19969e13 | −1.09821 | ||||||||
\(610\) | −1.44975e13 | + | 3.25623e13i | −0.171650 | + | 0.385537i | ||||
\(611\) | − | 9.85276e12i | − | 0.115705i | ||||||
\(612\) | −7.85037e13 | − | 8.71857e13i | −0.914394 | − | 1.01552i | ||||
\(613\) | 9.95572e13 | 1.15019 | 0.575096 | − | 0.818086i | \(-0.304965\pi\) | ||||
0.575096 | + | 0.818086i | \(0.304965\pi\) | |||||||
\(614\) | −2.80222e13 | − | 1.24761e13i | −0.321114 | − | 0.142968i | ||||
\(615\) | 4.00384e13i | 0.455094i | ||||||||
\(616\) | 1.24994e14 | − | 4.06149e13i | 1.40924 | − | 0.457912i | ||||
\(617\) | −1.74652e14 | −1.95320 | −0.976600 | − | 0.215062i | \(-0.931005\pi\) | ||||
−0.976600 | + | 0.215062i | \(0.931005\pi\) | |||||||
\(618\) | 8.67215e13 | − | 1.94782e14i | 0.962020 | − | 2.16076i | ||||
\(619\) | − | 4.05398e13i | − | 0.446096i | −0.974807 | − | 0.223048i | \(-0.928399\pi\) | ||
0.974807 | − | 0.223048i | \(-0.0716007\pi\) | |||||||
\(620\) | −3.08936e12 | + | 2.78172e12i | −0.0337217 | + | 0.0303637i | ||||
\(621\) | 1.64638e14 | 1.78268 | ||||||||
\(622\) | −1.20311e14 | − | 5.35651e13i | −1.29227 | − | 0.575347i | ||||
\(623\) | 7.27470e13i | 0.775131i | ||||||||
\(624\) | −3.04933e13 | − | 3.20443e12i | −0.322316 | − | 0.0338709i | ||||
\(625\) | 3.81470e12 | 0.0400000 | ||||||||
\(626\) | −1.10069e12 | + | 2.47223e12i | −0.0114497 | + | 0.0257168i | ||||
\(627\) | 3.80114e14i | 3.92262i | ||||||||
\(628\) | −9.48798e13 | − | 1.05373e14i | −0.971349 | − | 1.07877i | ||||
\(629\) | 1.17372e13 | 0.119210 | ||||||||
\(630\) | 1.12397e14 | + | 5.00418e13i | 1.13254 | + | 0.504232i | ||||
\(631\) | 7.81000e13i | 0.780737i | 0.920659 | + | 0.390368i | \(0.127652\pi\) | ||||
−0.920659 | + | 0.390368i | \(0.872348\pi\) | |||||||
\(632\) | 4.64468e13 | + | 1.42942e14i | 0.460649 | + | 1.41767i | ||||
\(633\) | 1.36185e12 | 0.0134002 | ||||||||
\(634\) | 3.94030e13 | − | 8.85016e13i | 0.384665 | − | 0.863983i | ||||
\(635\) | − | 1.79465e13i | − | 0.173825i | ||||||
\(636\) | −1.26960e14 | + | 1.14317e14i | −1.22006 | + | 1.09857i | ||||
\(637\) | −5.95337e12 | −0.0567631 | ||||||||
\(638\) | 6.43060e13 | + | 2.86305e13i | 0.608342 | + | 0.270848i | ||||
\(639\) | − | 6.94049e13i | − | 0.651458i | ||||||
\(640\) | −9.98521e12 | − | 4.69695e13i | −0.0929946 | − | 0.437438i | ||||
\(641\) | −6.92002e13 | −0.639466 | −0.319733 | − | 0.947508i | \(-0.603593\pi\) | ||||
−0.319733 | + | 0.947508i | \(0.603593\pi\) | |||||||
\(642\) | −4.58452e13 | + | 1.02971e14i | −0.420357 | + | 0.944149i | ||||
\(643\) | − | 9.07760e13i | − | 0.825878i | −0.910759 | − | 0.412939i | \(-0.864502\pi\) | ||
0.910759 | − | 0.412939i | \(-0.135498\pi\) | |||||||
\(644\) | −5.83967e13 | − | 6.48550e13i | −0.527180 | − | 0.585483i | ||||
\(645\) | −1.50563e14 | −1.34871 | ||||||||
\(646\) | −9.61252e13 | − | 4.27972e13i | −0.854427 | − | 0.380411i | ||||
\(647\) | − | 2.15102e14i | − | 1.89724i | −0.316413 | − | 0.948621i | \(-0.602479\pi\) | ||
0.316413 | − | 0.948621i | \(-0.397521\pi\) | |||||||
\(648\) | 2.60450e14 | − | 8.46291e13i | 2.27955 | − | 0.740704i | ||||
\(649\) | −9.74954e13 | −0.846760 | ||||||||
\(650\) | −1.65659e12 | + | 3.72081e12i | −0.0142774 | + | 0.0320679i | ||||
\(651\) | 2.52019e13i | 0.215541i | ||||||||
\(652\) | −1.24048e12 | + | 1.11695e12i | −0.0105281 | + | 0.00947972i | ||||
\(653\) | 1.02504e14 | 0.863330 | 0.431665 | − | 0.902034i | \(-0.357926\pi\) | ||||
0.431665 | + | 0.902034i | \(0.357926\pi\) | |||||||
\(654\) | −4.57812e13 | − | 2.03829e13i | −0.382647 | − | 0.170363i | ||||
\(655\) | − | 1.22556e13i | − | 0.101655i | ||||||
\(656\) | 6.99697e12 | − | 6.65831e13i | 0.0575958 | − | 0.548081i | ||||
\(657\) | 4.35049e14 | 3.55395 | ||||||||
\(658\) | 3.80477e13 | − | 8.54575e13i | 0.308460 | − | 0.692821i | ||||
\(659\) | 1.36237e14i | 1.09615i | 0.836430 | + | 0.548074i | \(0.184639\pi\) | ||||
−0.836430 | + | 0.548074i | \(0.815361\pi\) | |||||||
\(660\) | −8.91335e13 | − | 9.89910e13i | −0.711740 | − | 0.790453i | ||||
\(661\) | 9.24829e13 | 0.732916 | 0.366458 | − | 0.930435i | \(-0.380570\pi\) | ||||
0.366458 | + | 0.930435i | \(0.380570\pi\) | |||||||
\(662\) | 1.04762e14 | + | 4.66425e13i | 0.823975 | + | 0.366853i | ||||
\(663\) | − | 2.35447e13i | − | 0.183791i | ||||||
\(664\) | −2.99122e12 | − | 9.20562e12i | −0.0231744 | − | 0.0713202i | ||||
\(665\) | 1.10346e14 | 0.848491 | ||||||||
\(666\) | −2.69956e13 | + | 6.06338e13i | −0.206026 | + | 0.462747i | ||||
\(667\) | − | 4.67421e13i | − | 0.354062i | ||||||
\(668\) | −1.70249e14 | + | 1.53296e14i | −1.27998 | + | 1.15252i | ||||
\(669\) | 2.95489e14 | 2.20501 | ||||||||
\(670\) | −3.43071e13 | − | 1.52743e13i | −0.254103 | − | 0.113133i | ||||
\(671\) | − | 1.65336e14i | − | 1.21550i | ||||||
\(672\) | −2.52108e14 | − | 1.45547e14i | −1.83967 | − | 1.06208i | ||||
\(673\) | 1.84677e13 | 0.133763 | 0.0668816 | − | 0.997761i | \(-0.478695\pi\) | ||||
0.0668816 | + | 0.997761i | \(0.478695\pi\) | |||||||
\(674\) | −9.80572e13 | + | 2.20243e14i | −0.704985 | + | 1.58344i | ||||
\(675\) | − | 7.29500e13i | − | 0.520603i | ||||||
\(676\) | 9.15503e13 | + | 1.01675e14i | 0.648525 | + | 0.720247i | ||||
\(677\) | 2.46456e14 | 1.73299 | 0.866497 | − | 0.499183i | \(-0.166366\pi\) | ||||
0.866497 | + | 0.499183i | \(0.166366\pi\) | |||||||
\(678\) | −1.79849e14 | − | 8.00731e13i | −1.25534 | − | 0.558905i | ||||
\(679\) | 2.65224e14i | 1.83766i | ||||||||
\(680\) | 3.50690e13 | − | 1.13951e13i | 0.241201 | − | 0.0783744i | ||||
\(681\) | −3.65763e14 | −2.49726 | ||||||||
\(682\) | 7.84314e12 | − | 1.76162e13i | 0.0531580 | − | 0.119396i | ||||
\(683\) | − | 1.59101e13i | − | 0.107046i | −0.998567 | − | 0.0535228i | \(-0.982955\pi\) | ||
0.998567 | − | 0.0535228i | \(-0.0170450\pi\) | |||||||
\(684\) | 4.42175e14 | − | 3.98143e14i | 2.95334 | − | 2.65925i | ||||
\(685\) | 1.15880e14 | 0.768344 | ||||||||
\(686\) | 1.08025e14 | + | 4.80951e13i | 0.711054 | + | 0.316578i | ||||
\(687\) | 1.43400e14i | 0.937055i | ||||||||
\(688\) | 2.50384e14 | + | 2.63119e13i | 1.62429 | + | 0.170691i | ||||
\(689\) | −2.42304e13 | −0.156050 | ||||||||
\(690\) | −3.59768e13 | + | 8.08062e13i | −0.230026 | + | 0.516653i | ||||
\(691\) | − | 1.99068e14i | − | 1.26360i | −0.775130 | − | 0.631801i | \(-0.782316\pi\) | ||
0.775130 | − | 0.631801i | \(-0.217684\pi\) | |||||||
\(692\) | −5.50062e13 | − | 6.10895e13i | −0.346642 | − | 0.384978i | ||||
\(693\) | −5.70699e14 | −3.57060 | ||||||||
\(694\) | −1.13304e14 | − | 5.04456e13i | −0.703798 | − | 0.313347i | ||||
\(695\) | − | 3.54100e13i | − | 0.218375i | ||||||
\(696\) | −4.81821e13 | − | 1.48282e14i | −0.295012 | − | 0.907912i | ||||
\(697\) | 5.14106e13 | 0.312528 | ||||||||
\(698\) | −8.96708e13 | + | 2.01406e14i | −0.541220 | + | 1.21561i | ||||
\(699\) | 1.90297e14i | 1.14037i | ||||||||
\(700\) | −2.87368e13 | + | 2.58752e13i | −0.170981 | + | 0.153955i | ||||
\(701\) | −2.55726e14 | −1.51072 | −0.755362 | − | 0.655308i | \(-0.772539\pi\) | ||||
−0.755362 | + | 0.655308i | \(0.772539\pi\) | |||||||
\(702\) | 7.11545e13 | + | 3.16797e13i | 0.417366 | + | 0.185821i | ||||
\(703\) | 5.95271e13i | 0.346687i | ||||||||
\(704\) | 1.30928e14 | + | 1.80197e14i | 0.757128 | + | 1.04204i | ||||
\(705\) | −9.48112e13 | −0.544395 | ||||||||
\(706\) | −1.59616e13 | + | 3.58508e13i | −0.0910026 | + | 0.204398i | ||||
\(707\) | − | 1.21642e14i | − | 0.688631i | ||||||
\(708\) | 1.44499e14 | + | 1.60479e14i | 0.812265 | + | 0.902096i | ||||
\(709\) | −1.47763e14 | −0.824774 | −0.412387 | − | 0.911009i | \(-0.635305\pi\) | ||||
−0.412387 | + | 0.911009i | \(0.635305\pi\) | |||||||
\(710\) | 1.99281e13 | + | 8.87244e12i | 0.110452 | + | 0.0491758i | ||||
\(711\) | − | 6.52645e14i | − | 3.59194i | ||||||
\(712\) | −1.17255e14 | + | 3.81002e13i | −0.640814 | + | 0.208222i | ||||
\(713\) | −1.28047e13 | −0.0694898 | ||||||||
\(714\) | 9.09208e13 | − | 2.04214e14i | 0.489973 | − | 1.10051i | ||||
\(715\) | − | 1.88925e13i | − | 0.101102i | ||||||
\(716\) | 4.95828e13 | − | 4.46453e13i | 0.263491 | − | 0.237252i | ||||
\(717\) | −2.32344e14 | −1.22613 | ||||||||
\(718\) | −3.20173e14 | − | 1.42549e14i | −1.67789 | − | 0.747034i | ||||
\(719\) | 1.18505e14i | 0.616724i | 0.951269 | + | 0.308362i | \(0.0997808\pi\) | ||||
−0.951269 | + | 0.308362i | \(0.900219\pi\) | |||||||
\(720\) | −2.17920e13 | + | 2.07373e14i | −0.112625 | + | 1.07174i | ||||
\(721\) | 2.87106e14 | 1.47355 | ||||||||
\(722\) | 1.37254e14 | − | 3.08281e14i | 0.699581 | − | 1.57130i | ||||
\(723\) | 3.20468e14i | 1.62216i | ||||||||
\(724\) | 2.14485e14 | + | 2.38205e14i | 1.07821 | + | 1.19745i | ||||
\(725\) | −2.07111e13 | −0.103398 | ||||||||
\(726\) | 2.24240e14 | + | 9.98368e13i | 1.11181 | + | 0.495003i | ||||
\(727\) | 6.63470e13i | 0.326700i | 0.986568 | + | 0.163350i | \(0.0522300\pi\) | ||||
−0.986568 | + | 0.163350i | \(0.947770\pi\) | |||||||
\(728\) | −1.27589e13 | − | 3.92662e13i | −0.0623961 | − | 0.192027i | ||||
\(729\) | −1.99536e14 | −0.969135 | ||||||||
\(730\) | −5.56148e13 | + | 1.24914e14i | −0.268273 | + | 0.602557i | ||||
\(731\) | 1.93328e14i | 0.926206i | ||||||||
\(732\) | −2.72146e14 | + | 2.45046e14i | −1.29493 | + | 1.16598i | ||||
\(733\) | 8.24457e13 | 0.389626 | 0.194813 | − | 0.980840i | \(-0.437590\pi\) | ||||
0.194813 | + | 0.980840i | \(0.437590\pi\) | |||||||
\(734\) | 2.15783e14 | + | 9.60716e13i | 1.01283 | + | 0.450936i | ||||
\(735\) | 5.72882e13i | 0.267072i | ||||||||
\(736\) | 7.39501e13 | − | 1.28092e14i | 0.342413 | − | 0.593106i | ||||
\(737\) | 1.74195e14 | 0.801122 | ||||||||
\(738\) | −1.18244e14 | + | 2.65584e14i | −0.540129 | + | 1.21317i | ||||
\(739\) | − | 3.99191e14i | − | 1.81117i | −0.424169 | − | 0.905583i | \(-0.639434\pi\) | ||
0.424169 | − | 0.905583i | \(-0.360566\pi\) | |||||||
\(740\) | −1.39586e13 | − | 1.55023e13i | −0.0629048 | − | 0.0698616i | ||||
\(741\) | 1.19410e14 | 0.534504 | ||||||||
\(742\) | −2.10161e14 | − | 9.35687e13i | −0.934401 | − | 0.416017i | ||||
\(743\) | − | 4.95145e13i | − | 0.218669i | −0.994005 | − | 0.109335i | \(-0.965128\pi\) | ||
0.994005 | − | 0.109335i | \(-0.0348720\pi\) | |||||||
\(744\) | −4.06210e13 | + | 1.31992e13i | −0.178191 | + | 0.0579004i | ||||
\(745\) | 1.59094e14 | 0.693221 | ||||||||
\(746\) | −6.85449e13 | + | 1.53956e14i | −0.296675 | + | 0.666351i | ||||
\(747\) | 4.20311e13i | 0.180704i | ||||||||
\(748\) | −1.27108e14 | + | 1.14450e14i | −0.542830 | + | 0.488775i | ||||
\(749\) | −1.51778e14 | −0.643873 | ||||||||
\(750\) | 3.58046e13 | + | 1.59411e13i | 0.150880 | + | 0.0671755i | ||||
\(751\) | 3.40765e14i | 1.42645i | 0.700936 | + | 0.713224i | \(0.252766\pi\) | ||||
−0.700936 | + | 0.713224i | \(0.747234\pi\) | |||||||
\(752\) | 1.57669e14 | + | 1.65689e13i | 0.655628 | + | 0.0688975i | ||||
\(753\) | 5.64643e13 | 0.233238 | ||||||||
\(754\) | 8.99410e12 | − | 2.02013e13i | 0.0369063 | − | 0.0828940i | ||||
\(755\) | − | 1.71840e14i | − | 0.700471i | ||||||
\(756\) | 4.94821e14 | + | 5.49545e14i | 2.00373 | + | 2.22533i | ||||
\(757\) | 1.55318e14 | 0.624801 | 0.312401 | − | 0.949950i | \(-0.398867\pi\) | ||||
0.312401 | + | 0.949950i | \(0.398867\pi\) | |||||||
\(758\) | −1.82086e14 | − | 8.10691e13i | −0.727665 | − | 0.323973i | ||||
\(759\) | − | 4.10295e14i | − | 1.62887i | ||||||
\(760\) | 5.77920e13 | + | 1.77857e14i | 0.227929 | + | 0.701462i | ||||
\(761\) | −3.51812e13 | −0.137844 | −0.0689220 | − | 0.997622i | \(-0.521956\pi\) | ||||
−0.0689220 | + | 0.997622i | \(0.521956\pi\) | |||||||
\(762\) | 7.49958e13 | − | 1.68445e14i | 0.291919 | − | 0.655668i | ||||
\(763\) | − | 6.74809e13i | − | 0.260951i | ||||||
\(764\) | −1.92844e14 | + | 1.73641e14i | −0.740866 | + | 0.667091i | ||||
\(765\) | −1.60118e14 | −0.611129 | ||||||||
\(766\) | 9.65837e13 | + | 4.30013e13i | 0.366235 | + | 0.163056i | ||||
\(767\) | 3.06276e13i | 0.115381i | ||||||||
\(768\) | 1.02558e14 | − | 4.82581e14i | 0.383851 | − | 1.80619i | ||||
\(769\) | 3.92216e14 | 1.45846 | 0.729229 | − | 0.684270i | \(-0.239879\pi\) | ||||
0.729229 | + | 0.684270i | \(0.239879\pi\) | |||||||
\(770\) | 7.29558e13 | − | 1.63863e14i | 0.269529 | − | 0.605380i | ||||
\(771\) | − | 4.19023e14i | − | 1.53803i | ||||||
\(772\) | 6.23272e12 | + | 6.92201e12i | 0.0227295 | + | 0.0252433i | ||||
\(773\) | −7.38440e13 | −0.267558 | −0.133779 | − | 0.991011i | \(-0.542711\pi\) | ||||
−0.133779 | + | 0.991011i | \(0.542711\pi\) | |||||||
\(774\) | −9.98719e14 | − | 4.44653e14i | −3.59533 | − | 1.60072i | ||||
\(775\) | 5.67366e12i | 0.0202934i | ||||||||
\(776\) | −4.27494e14 | + | 1.38908e14i | −1.51922 | + | 0.493648i | ||||
\(777\) | −1.26463e14 | −0.446537 | ||||||||
\(778\) | −3.54534e13 | + | 7.96306e13i | −0.124383 | + | 0.279371i | ||||
\(779\) | 2.60737e14i | 0.908897i | ||||||||
\(780\) | −3.10974e13 | + | 2.80007e13i | −0.107709 | + | 0.0969832i | ||||
\(781\) | −1.01185e14 | −0.348226 | ||||||||
\(782\) | 1.03758e14 | + | 4.61953e13i | 0.354802 | + | 0.157966i | ||||
\(783\) | 3.96066e14i | 1.34573i | ||||||||
\(784\) | 1.00115e13 | − | 9.52691e13i | 0.0338001 | − | 0.321641i | ||||
\(785\) | −1.93519e14 | −0.649195 | ||||||||
\(786\) | 5.12145e13 | − | 1.15031e14i | 0.170718 | − | 0.383444i | ||||
\(787\) | − | 1.87527e14i | − | 0.621142i | −0.950550 | − | 0.310571i | \(-0.899480\pi\) | ||
0.950550 | − | 0.310571i | \(-0.100520\pi\) | |||||||
\(788\) | −2.30829e14 | − | 2.56357e14i | −0.759731 | − | 0.843752i | ||||
\(789\) | 1.60778e13 | 0.0525826 | ||||||||
\(790\) | 1.87392e14 | + | 8.34314e13i | 0.608998 | + | 0.271140i | ||||
\(791\) | − | 2.65096e14i | − | 0.856092i | ||||||
\(792\) | −2.98896e14 | − | 9.19864e14i | −0.959166 | − | 2.95187i | ||||
\(793\) | −5.19392e13 | −0.165626 | ||||||||
\(794\) | 6.71721e13 | − | 1.50873e14i | 0.212856 | − | 0.478089i | ||||
\(795\) | 2.33164e14i | 0.734220i | ||||||||
\(796\) | 2.54090e14 | − | 2.28788e14i | 0.795101 | − | 0.715925i | ||||
\(797\) | 1.76065e14 | 0.547498 | 0.273749 | − | 0.961801i | \(-0.411736\pi\) | ||||
0.273749 | + | 0.961801i | \(0.411736\pi\) | |||||||
\(798\) | 1.03570e15 | + | 4.61118e14i | 3.20052 | + | 1.42494i | ||||
\(799\) | 1.21741e14i | 0.373853i | ||||||||
\(800\) | −5.67566e13 | − | 3.27667e13i | −0.173207 | − | 0.0999961i | ||||
\(801\) | 5.35364e14 | 1.62363 | ||||||||
\(802\) | −7.93278e13 | + | 1.78175e14i | −0.239086 | + | 0.537001i | ||||
\(803\) | − | 6.34256e14i | − | 1.89971i | ||||||
\(804\) | −2.58176e14 | − | 2.86729e14i | −0.768487 | − | 0.853475i | ||||
\(805\) | −1.19107e14 | −0.352338 | ||||||||
\(806\) | −5.53402e12 | − | 2.46387e12i | −0.0162692 | − | 0.00724341i | ||||
\(807\) | 1.01713e15i | 2.97173i | ||||||||
\(808\) | 1.96065e14 | − | 6.37083e13i | 0.569303 | − | 0.184986i | ||||
\(809\) | 3.01803e14 | 0.870925 | 0.435462 | − | 0.900207i | \(-0.356585\pi\) | ||||
0.435462 | + | 0.900207i | \(0.356585\pi\) | |||||||
\(810\) | 1.52017e14 | − | 3.41441e14i | 0.435982 | − | 0.979243i | ||||
\(811\) | − | 1.06911e14i | − | 0.304731i | −0.988324 | − | 0.152366i | \(-0.951311\pi\) | ||
0.988324 | − | 0.152366i | \(-0.0486891\pi\) | |||||||
\(812\) | 1.56020e14 | − | 1.40484e14i | 0.441977 | − | 0.397965i | ||||
\(813\) | 5.24584e14 | 1.47694 | ||||||||
\(814\) | 8.83977e13 | + | 3.93567e13i | 0.247354 | + | 0.110128i | ||||
\(815\) | 2.27816e12i | 0.00633571i | ||||||||
\(816\) | 3.76775e14 | + | 3.95938e13i | 1.04143 | + | 0.109440i | ||||
\(817\) | −9.80490e14 | −2.69360 | ||||||||
\(818\) | −1.16480e14 | + | 2.61621e14i | −0.318042 | + | 0.714343i | ||||
\(819\) | 1.79282e14i | 0.486537i | ||||||||
\(820\) | −6.11406e13 | − | 6.79022e13i | −0.164915 | − | 0.183153i | ||||
\(821\) | −2.26172e13 | −0.0606350 | −0.0303175 | − | 0.999540i | \(-0.509652\pi\) | ||||
−0.0303175 | + | 0.999540i | \(0.509652\pi\) | |||||||
\(822\) | 1.08765e15 | + | 4.84245e14i | 2.89820 | + | 1.29035i | ||||
\(823\) | 4.19066e14i | 1.10990i | 0.831884 | + | 0.554949i | \(0.187262\pi\) | ||||
−0.831884 | + | 0.554949i | \(0.812738\pi\) | |||||||
\(824\) | 1.50368e14 | + | 4.62764e14i | 0.395839 | + | 1.21821i | ||||
\(825\) | −1.81799e14 | −0.475687 | ||||||||
\(826\) | −1.18272e14 | + | 2.65647e14i | −0.307597 | + | 0.690883i | ||||
\(827\) | − | 1.07778e14i | − | 0.278614i | −0.990249 | − | 0.139307i | \(-0.955513\pi\) | ||
0.990249 | − | 0.139307i | \(-0.0444875\pi\) | |||||||
\(828\) | −4.77284e14 | + | 4.29756e14i | −1.22638 | + | 1.10426i | ||||
\(829\) | 1.06061e14 | 0.270883 | 0.135441 | − | 0.990785i | \(-0.456755\pi\) | ||||
0.135441 | + | 0.990785i | \(0.456755\pi\) | |||||||
\(830\) | −1.20683e13 | − | 5.37307e12i | −0.0306376 | − | 0.0136406i | ||||
\(831\) | 2.27647e14i | 0.574456i | ||||||||
\(832\) | 5.66077e13 | − | 4.11302e13i | 0.141990 | − | 0.103168i | ||||
\(833\) | 7.35598e13 | 0.183407 | ||||||||
\(834\) | 1.47973e14 | − | 3.32357e14i | 0.366735 | − | 0.823711i | ||||
\(835\) | 3.12666e14i | 0.770278i | ||||||||
\(836\) | −5.80451e14 | − | 6.44645e14i | −1.42146 | − | 1.57866i | ||||
\(837\) | 1.08500e14 | 0.264120 | ||||||||
\(838\) | −3.88140e14 | − | 1.72809e14i | −0.939221 | − | 0.418163i | ||||
\(839\) | 6.55176e14i | 1.57597i | 0.615694 | + | 0.787985i | \(0.288876\pi\) | ||||
−0.615694 | + | 0.787985i | \(0.711124\pi\) | |||||||
\(840\) | −3.77851e14 | + | 1.22777e14i | −0.903491 | + | 0.293575i | ||||
\(841\) | −3.08261e14 | −0.732721 | ||||||||
\(842\) | 1.51523e14 | − | 3.40331e14i | 0.358030 | − | 0.804157i | ||||
\(843\) | − | 1.42247e14i | − | 0.334121i | ||||||
\(844\) | −2.30960e12 | + | 2.07961e12i | −0.00539293 | + | 0.00485590i | ||||
\(845\) | 1.86728e14 | 0.433437 | ||||||||
\(846\) | −6.28904e14 | − | 2.80003e14i | −1.45122 | − | 0.646116i | ||||
\(847\) | 3.30527e14i | 0.758210i | ||||||||
\(848\) | 4.07469e13 | − | 3.87747e14i | 0.0929213 | − | 0.884239i | ||||
\(849\) | 6.38214e14 | 1.44686 | ||||||||
\(850\) | 2.04688e13 | − | 4.59743e13i | 0.0461315 | − | 0.103614i | ||||
\(851\) | − | 6.42536e13i | − | 0.143963i | ||||||
\(852\) | 1.49967e14 | + | 1.66553e14i | 0.334040 | + | 0.370983i | ||||
\(853\) | −6.23120e14 | −1.37983 | −0.689917 | − | 0.723889i | \(-0.742353\pi\) | ||||
−0.689917 | + | 0.723889i | \(0.742353\pi\) | |||||||
\(854\) | −4.50493e14 | − | 2.00570e14i | −0.991741 | − | 0.441546i | ||||
\(855\) | − | 8.12062e14i | − | 1.77729i | ||||||
\(856\) | −7.94917e13 | − | 2.44639e14i | −0.172963 | − | 0.532301i | ||||
\(857\) | 4.84964e14 | 1.04907 | 0.524537 | − | 0.851388i | \(-0.324239\pi\) | ||||
0.524537 | + | 0.851388i | \(0.324239\pi\) | |||||||
\(858\) | 7.89489e13 | − | 1.77324e14i | 0.169789 | − | 0.381357i | ||||
\(859\) | − | 3.76960e14i | − | 0.805991i | −0.915202 | − | 0.402995i | \(-0.867969\pi\) | ||
0.915202 | − | 0.402995i | \(-0.132031\pi\) | |||||||
\(860\) | 2.55344e14 | − | 2.29917e14i | 0.542792 | − | 0.488741i | ||||
\(861\) | −5.53924e14 | −1.17067 | ||||||||
\(862\) | −4.98641e14 | − | 2.22007e14i | −1.04774 | − | 0.466476i | ||||
\(863\) | 4.17983e14i | 0.873181i | 0.899660 | + | 0.436591i | \(0.143814\pi\) | ||||
−0.899660 | + | 0.436591i | \(0.856186\pi\) | |||||||
\(864\) | −6.26612e14 | + | 1.08538e15i | −1.30146 | + | 2.25431i | ||||
\(865\) | −1.12192e14 | −0.231676 | ||||||||
\(866\) | −2.07263e14 | + | 4.65525e14i | −0.425532 | + | 0.955771i | ||||
\(867\) | − | 6.13673e14i | − | 1.25268i | ||||||
\(868\) | −3.84845e13 | − | 4.27406e13i | −0.0781066 | − | 0.0867446i | ||||
\(869\) | −9.51488e14 | −1.92001 | ||||||||
\(870\) | −1.94393e14 | − | 8.65485e13i | −0.390018 | − | 0.173645i | ||||
\(871\) | − | 5.47223e13i | − | 0.109163i | ||||||
\(872\) | 1.08767e14 | − | 3.53422e13i | 0.215732 | − | 0.0700989i | ||||
\(873\) | 1.95185e15 | 3.84925 | ||||||||
\(874\) | −2.34286e14 | + | 5.26222e14i | −0.459399 | + | 1.03184i | ||||
\(875\) | 5.27756e13i | 0.102895i | ||||||||
\(876\) | −1.04400e15 | + | 9.40037e14i | −2.02385 | + | 1.82232i | ||||
\(877\) | −4.50456e14 | −0.868270 | −0.434135 | − | 0.900848i | \(-0.642946\pi\) | ||||
−0.434135 | + | 0.900848i | \(0.642946\pi\) | |||||||
\(878\) | 1.86327e14 | + | 8.29573e13i | 0.357112 | + | 0.158995i | ||||
\(879\) | − | 9.96400e14i | − | 1.89884i | ||||||
\(880\) | 3.02328e14 | + | 3.17705e13i | 0.572881 | + | 0.0602019i | ||||
\(881\) | −4.00485e14 | −0.754583 | −0.377292 | − | 0.926094i | \(-0.623145\pi\) | ||||
−0.377292 | + | 0.926094i | \(0.623145\pi\) | |||||||
\(882\) | −1.69187e14 | + | 3.80005e14i | −0.316975 | + | 0.711945i | ||||
\(883\) | − | 1.22465e14i | − | 0.228144i | −0.993473 | − | 0.114072i | \(-0.963611\pi\) | ||
0.993473 | − | 0.114072i | \(-0.0363894\pi\) | |||||||
\(884\) | 3.59538e13 | + | 3.99300e13i | 0.0666015 | + | 0.0739671i | ||||
\(885\) | 2.94723e14 | 0.542872 | ||||||||
\(886\) | 6.89114e14 | + | 3.06810e14i | 1.26218 | + | 0.561954i | ||||
\(887\) | 1.37787e14i | 0.250953i | 0.992097 | + | 0.125476i | \(0.0400459\pi\) | ||||
−0.992097 | + | 0.125476i | \(0.959954\pi\) | |||||||
\(888\) | −6.62331e13 | − | 2.03835e14i | −0.119953 | − | 0.369160i | ||||
\(889\) | 2.48286e14 | 0.447140 | ||||||||
\(890\) | −6.84387e13 | + | 1.53718e14i | −0.122561 | + | 0.275279i | ||||
\(891\) | 1.73367e15i | 3.08730i | ||||||||
\(892\) | −5.01127e14 | + | 4.51225e14i | −0.887409 | + | 0.799041i | ||||
\(893\) | −6.17425e14 | −1.08724 | ||||||||
\(894\) | 1.49325e15 | + | 6.64829e14i | 2.61484 | + | 1.16419i | ||||
\(895\) | − | 9.10596e13i | − | 0.158566i | ||||||
\(896\) | 6.49814e14 | − | 1.38143e14i | 1.12525 | − | 0.239216i | ||||
\(897\) | −1.28892e14 | −0.221954 | ||||||||
\(898\) | 1.34600e14 | − | 3.02319e14i | 0.230495 | − | 0.517707i | ||||
\(899\) | − | 3.08039e13i | − | 0.0524575i | ||||||
\(900\) | 1.90422e14 | + | 2.11481e14i | 0.322481 | + | 0.358145i | ||||
\(901\) | 2.99390e14 | 0.504212 | ||||||||
\(902\) | 3.87194e14 | + | 1.72388e14i | 0.648478 | + | 0.288718i | ||||
\(903\) | − | 2.08301e15i | − | 3.46939i | ||||||
\(904\) | 4.27287e14 | − | 1.38840e14i | 0.707745 | − | 0.229971i | ||||
\(905\) | 4.37469e14 | 0.720616 | ||||||||
\(906\) | 7.18095e14 | − | 1.61289e15i | 1.17636 | − | 2.64218i | ||||
\(907\) | 3.75970e14i | 0.612516i | 0.951949 | + | 0.306258i | \(0.0990770\pi\) | ||||
−0.951949 | + | 0.306258i | \(0.900923\pi\) | |||||||
\(908\) | 6.20307e14 | − | 5.58537e14i | 1.00503 | − | 0.904945i | ||||
\(909\) | −8.95194e14 | −1.44244 | ||||||||
\(910\) | −5.14766e13 | − | 2.29186e13i | −0.0824903 | − | 0.0367266i | ||||
\(911\) | 3.99006e14i | 0.635899i | 0.948108 | + | 0.317949i | \(0.102994\pi\) | ||||
−0.948108 | + | 0.317949i | \(0.897006\pi\) | |||||||
\(912\) | −2.00806e14 | + | 1.91087e15i | −0.318275 | + | 3.02870i | ||||
\(913\) | 6.12769e13 | 0.0965924 | ||||||||
\(914\) | 4.15870e14 | − | 9.34071e14i | 0.651969 | − | 1.46436i | ||||
\(915\) | 4.99801e14i | 0.779276i | ||||||||
\(916\) | −2.18978e14 | − | 2.43196e14i | −0.339565 | − | 0.377119i | ||||
\(917\) | 1.69554e14 | 0.261494 | ||||||||
\(918\) | −8.79184e14 | − | 3.91433e14i | −1.34855 | − | 0.600405i | ||||
\(919\) | − | 2.15850e14i | − | 0.329287i | −0.986353 | − | 0.164643i | \(-0.947353\pi\) | ||
0.986353 | − | 0.164643i | \(-0.0526473\pi\) | |||||||
\(920\) | −6.23808e13 | − | 1.91980e14i | −0.0946480 | − | 0.291283i | ||||
\(921\) | −4.30114e14 | −0.649061 | ||||||||
\(922\) | −1.38075e14 | + | 3.10125e14i | −0.207234 | + | 0.465460i | ||||
\(923\) | 3.17867e13i | 0.0474500i | ||||||||
\(924\) | 1.36952e15 | − | 1.23314e15i | 2.03333 | − | 1.83085i | ||||
\(925\) | −2.84703e13 | −0.0420420 | ||||||||
\(926\) | 2.96514e14 | + | 1.32015e14i | 0.435501 | + | 0.193895i | ||||
\(927\) | − | 2.11289e15i | − | 3.08658i | ||||||
\(928\) | 3.08147e14 | + | 1.77900e14i | 0.447733 | + | 0.258485i | ||||
\(929\) | 4.43413e14 | 0.640811 | 0.320406 | − | 0.947280i | \(-0.396181\pi\) | ||||
0.320406 | + | 0.947280i | \(0.396181\pi\) | |||||||
\(930\) | −2.37094e13 | + | 5.32528e13i | −0.0340805 | + | 0.0765469i | ||||
\(931\) | 3.73069e14i | 0.533386i | ||||||||
\(932\) | −2.90592e14 | − | 3.22729e14i | −0.413241 | − | 0.458942i | ||||
\(933\) | −1.84666e15 | −2.61203 | ||||||||
\(934\) | 3.52647e14 | + | 1.57007e14i | 0.496142 | + | 0.220894i | ||||
\(935\) | 2.33435e14i | 0.326669i | ||||||||
\(936\) | −2.88970e14 | + | 9.38962e13i | −0.402229 | + | 0.130698i | ||||
\(937\) | −5.87919e14 | −0.813991 | −0.406996 | − | 0.913430i | \(-0.633424\pi\) | ||||
−0.406996 | + | 0.913430i | \(0.633424\pi\) | |||||||
\(938\) | 2.11317e14 | − | 4.74632e14i | 0.291019 | − | 0.653647i | ||||
\(939\) | 3.79464e13i | 0.0519808i | ||||||||
\(940\) | 1.60793e14 | − | 1.44781e14i | 0.219092 | − | 0.197275i | ||||
\(941\) | 1.28114e15 | 1.73639 | 0.868195 | − | 0.496224i | \(-0.165280\pi\) | ||||
0.868195 | + | 0.496224i | \(0.165280\pi\) | |||||||
\(942\) | −1.81636e15 | − | 8.08687e14i | −2.44877 | − | 1.09025i | ||||
\(943\) | − | 2.81439e14i | − | 0.377421i | ||||||
\(944\) | −4.90119e14 | − | 5.15047e13i | −0.653795 | − | 0.0687048i | ||||
\(945\) | 1.00925e15 | 1.33918 | ||||||||
\(946\) | −6.48257e14 | + | 1.45603e15i | −0.855641 | + | 1.92183i | ||||
\(947\) | − | 1.43625e15i | − | 1.88574i | −0.333166 | − | 0.942868i | \(-0.608117\pi\) | ||
0.333166 | − | 0.942868i | \(-0.391883\pi\) | |||||||
\(948\) | 1.41021e15 | + | 1.56617e15i | 1.84180 | + | 2.04549i | ||||
\(949\) | −1.99248e14 | −0.258858 | ||||||||
\(950\) | 2.33165e14 | + | 1.03811e14i | 0.301332 | + | 0.134160i | ||||
\(951\) | − | 1.35842e15i | − | 1.74635i | ||||||
\(952\) | 1.57649e14 | + | 4.85172e14i | 0.201608 | + | 0.620456i | ||||
\(953\) | −1.10609e15 | −1.40711 | −0.703554 | − | 0.710642i | \(-0.748405\pi\) | ||||
−0.703554 | + | 0.710642i | \(0.748405\pi\) | |||||||
\(954\) | −6.88596e14 | + | 1.54663e15i | −0.871410 | + | 1.95724i | ||||
\(955\) | 3.54162e14i | 0.445846i | ||||||||
\(956\) | 3.94038e14 | − | 3.54800e14i | 0.493456 | − | 0.444318i | ||||
\(957\) | 9.87037e14 | 1.22963 | ||||||||
\(958\) | 4.42868e14 | + | 1.97175e14i | 0.548841 | + | 0.244357i | ||||
\(959\) | 1.60318e15i | 1.97646i | ||||||||
\(960\) | −3.95788e14 | − | 5.44725e14i | −0.485407 | − | 0.668068i | ||||
\(961\) | 8.11190e14 | 0.989704 | ||||||||
\(962\) | 1.23637e13 | − | 2.77696e13i | 0.0150062 | − | 0.0337050i | ||||
\(963\) | 1.11697e15i | 1.34869i | ||||||||
\(964\) | −4.89369e14 | − | 5.43490e14i | −0.587830 | − | 0.652839i | ||||
\(965\) | 1.27124e13 | 0.0151911 | ||||||||
\(966\) | −1.11794e15 | − | 4.97732e14i | −1.32902 | − | 0.591711i | ||||
\(967\) | 5.03424e14i | 0.595390i | 0.954661 | + | 0.297695i | \(0.0962179\pi\) | ||||
−0.954661 | + | 0.297695i | \(0.903782\pi\) | |||||||
\(968\) | −5.32750e14 | + | 1.73109e14i | −0.626825 | + | 0.203677i | ||||
\(969\) | −1.47543e15 | −1.72703 | ||||||||
\(970\) | −2.49517e14 | + | 5.60430e14i | −0.290563 | + | 0.652624i | ||||
\(971\) | 1.45819e15i | 1.68934i | 0.535288 | + | 0.844670i | \(0.320203\pi\) | ||||
−0.535288 | + | 0.844670i | \(0.679797\pi\) | |||||||
\(972\) | 1.17533e15 | − | 1.05829e15i | 1.35465 | − | 1.21976i | ||||
\(973\) | 4.89890e14 | 0.561739 | ||||||||
\(974\) | −3.60547e14 | − | 1.60524e14i | −0.411308 | − | 0.183124i | ||||
\(975\) | 5.71109e13i | 0.0648181i | ||||||||
\(976\) | 8.73434e13 | − | 8.31159e14i | 0.0986236 | − | 0.938501i | ||||
\(977\) | 1.28973e15 | 1.44886 | 0.724431 | − | 0.689348i | \(-0.242103\pi\) | ||||
0.724431 | + | 0.689348i | \(0.242103\pi\) | |||||||
\(978\) | −9.52007e12 | + | 2.13827e13i | −0.0106401 | + | 0.0238984i | ||||
\(979\) | − | 7.80504e14i | − | 0.867884i | ||||||
\(980\) | −8.74817e13 | − | 9.71565e13i | −0.0967803 | − | 0.107483i | ||||
\(981\) | −4.96609e14 | −0.546600 | ||||||||
\(982\) | 6.56003e14 | + | 2.92068e14i | 0.718370 | + | 0.319835i | ||||
\(983\) | 1.23310e15i | 1.34348i | 0.740788 | + | 0.671738i | \(0.234452\pi\) | ||||
−0.740788 | + | 0.671738i | \(0.765548\pi\) | |||||||
\(984\) | −2.90110e14 | − | 8.92825e14i | −0.314475 | − | 0.967812i | ||||
\(985\) | −4.70805e14 | −0.507762 | ||||||||
\(986\) | −1.11131e14 | + | 2.49607e14i | −0.119248 | + | 0.267838i | ||||
\(987\) | − | 1.31169e15i | − | 1.40038i | ||||||
\(988\) | −2.02511e14 | + | 1.82345e14i | −0.215112 | + | 0.193691i | ||||
\(989\) | 1.05834e15 | 1.11852 | ||||||||
\(990\) | −1.20591e15 | − | 5.36900e14i | −1.26806 | − | 0.564569i | ||||
\(991\) | − | 7.76053e14i | − | 0.811938i | −0.913887 | − | 0.405969i | \(-0.866934\pi\) | ||
0.913887 | − | 0.405969i | \(-0.133066\pi\) | |||||||
\(992\) | 4.87345e13 | − | 8.44150e13i | 0.0507316 | − | 0.0878741i | ||||
\(993\) | 1.60800e15 | 1.66548 | ||||||||
\(994\) | −1.22748e14 | + | 2.75701e14i | −0.126498 | + | 0.284123i | ||||
\(995\) | − | 4.66641e14i | − | 0.478484i | ||||||
\(996\) | −9.08190e13 | − | 1.00863e14i | −0.0926574 | − | 0.102905i | ||||
\(997\) | −4.19236e14 | −0.425582 | −0.212791 | − | 0.977098i | \(-0.568255\pi\) | ||||
−0.212791 | + | 0.977098i | \(0.568255\pi\) | |||||||
\(998\) | 9.03886e14 | + | 4.02431e14i | 0.912979 | + | 0.406480i | ||||
\(999\) | 5.44449e14i | 0.547180i |
(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 | 20.11.b.a.11.8 | yes | 20 | |
3.2 | odd | 2 | 180.11.c.a.91.13 | 20 | |||
4.3 | odd | 2 | inner | 20.11.b.a.11.7 | ✓ | 20 | |
5.2 | odd | 4 | 100.11.d.c.99.7 | 40 | |||
5.3 | odd | 4 | 100.11.d.c.99.34 | 40 | |||
5.4 | even | 2 | 100.11.b.e.51.13 | 20 | |||
8.3 | odd | 2 | 320.11.b.d.191.20 | 20 | |||
8.5 | even | 2 | 320.11.b.d.191.1 | 20 | |||
12.11 | even | 2 | 180.11.c.a.91.14 | 20 | |||
20.3 | even | 4 | 100.11.d.c.99.8 | 40 | |||
20.7 | even | 4 | 100.11.d.c.99.33 | 40 | |||
20.19 | odd | 2 | 100.11.b.e.51.14 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.11.b.a.11.7 | ✓ | 20 | 4.3 | odd | 2 | inner | |
20.11.b.a.11.8 | yes | 20 | 1.1 | even | 1 | trivial | |
100.11.b.e.51.13 | 20 | 5.4 | even | 2 | |||
100.11.b.e.51.14 | 20 | 20.19 | odd | 2 | |||
100.11.d.c.99.7 | 40 | 5.2 | odd | 4 | |||
100.11.d.c.99.8 | 40 | 20.3 | even | 4 | |||
100.11.d.c.99.33 | 40 | 20.7 | even | 4 | |||
100.11.d.c.99.34 | 40 | 5.3 | odd | 4 | |||
180.11.c.a.91.13 | 20 | 3.2 | odd | 2 | |||
180.11.c.a.91.14 | 20 | 12.11 | even | 2 | |||
320.11.b.d.191.1 | 20 | 8.5 | even | 2 | |||
320.11.b.d.191.20 | 20 | 8.3 | odd | 2 |