Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,9,Mod(19,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.19");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.n (of order \(6\), degree \(2\), 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: | \(51.3297048677\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} - 26382 x^{18} + 177344 x^{17} + 298653216 x^{16} - 1823810808 x^{15} - 1891249463672 x^{14} + 11806020599312 x^{13} + \cdots + 42\!\cdots\!32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{40}\cdot 3^{18}\cdot 7^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.5 | ||
Root | \(70.5683 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.19 |
Dual form | 126.9.n.d.73.5 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.65685 | + | 9.79796i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −64.0000 | − | 110.851i | −0.250000 | − | 0.433013i | ||||
\(5\) | 814.617 | + | 470.320i | 1.30339 | + | 0.752511i | 0.980984 | − | 0.194091i | \(-0.0621756\pi\) |
0.322404 | + | 0.946602i | \(0.395509\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.7985 | − | 2400.95i | 0.00616349 | − | 0.999981i | ||||
\(8\) | 1448.15 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −9216.34 | + | 5321.06i | −0.921634 | + | 0.532106i | ||||
\(11\) | 522.290 | + | 904.633i | 0.0356731 | + | 0.0617876i | 0.883311 | − | 0.468788i | \(-0.155309\pi\) |
−0.847638 | + | 0.530576i | \(0.821976\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 47076.6i | − | 1.64828i | −0.566385 | − | 0.824141i | \(-0.691658\pi\) | ||
0.566385 | − | 0.824141i | \(-0.308342\pi\) | |||||||
\(14\) | 23440.7 | + | 13726.8i | 0.610182 | + | 0.357321i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8192.00 | + | 14189.0i | −0.125000 | + | 0.216506i | ||||
\(17\) | 55462.6 | − | 32021.4i | 0.664056 | − | 0.383393i | −0.129765 | − | 0.991545i | \(-0.541422\pi\) |
0.793821 | + | 0.608152i | \(0.208089\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −203421. | − | 117445.i | −1.56092 | − | 0.901197i | −0.997164 | − | 0.0752548i | \(-0.976023\pi\) |
−0.563755 | − | 0.825942i | \(-0.690644\pi\) | |||||||
\(20\) | − | 120402.i | − | 0.752511i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −11818.1 | −0.0504494 | ||||||||
\(23\) | −135729. | + | 235089.i | −0.485022 | + | 0.840082i | −0.999852 | − | 0.0172101i | \(-0.994522\pi\) |
0.514830 | + | 0.857292i | \(0.327855\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 247089. | + | 427970.i | 0.632547 | + | 1.09560i | ||||
\(26\) | 461254. | + | 266305.i | 1.00936 | + | 0.582756i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −267096. | + | 152021.i | −0.434545 | + | 0.247326i | ||||
\(29\) | −1.26478e6 | −1.78823 | −0.894116 | − | 0.447836i | \(-0.852195\pi\) | ||||
−0.894116 | + | 0.447836i | \(0.852195\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 143445. | − | 82818.0i | 0.155324 | − | 0.0896764i | −0.420323 | − | 0.907374i | \(-0.638083\pi\) |
0.575647 | + | 0.817698i | \(0.304750\pi\) | |||||||
\(32\) | −92681.9 | − | 160530.i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 724561.i | 0.542200i | ||||||||
\(35\) | 1.14127e6 | − | 1.94890e6i | 0.760530 | − | 1.29873i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.35572e6 | + | 2.34818e6i | −0.723375 | + | 1.25292i | 0.236265 | + | 0.971689i | \(0.424077\pi\) |
−0.959639 | + | 0.281233i | \(0.909257\pi\) | |||||||
\(38\) | 2.30144e6 | − | 1.32874e6i | 1.10374 | − | 0.637243i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.17969e6 | + | 681096.i | 0.460817 | + | 0.266053i | ||||
\(41\) | 1.48329e6i | 0.524917i | 0.964943 | + | 0.262458i | \(0.0845332\pi\) | ||||
−0.964943 | + | 0.262458i | \(0.915467\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −928927. | −0.271711 | −0.135856 | − | 0.990729i | \(-0.543378\pi\) | ||||
−0.135856 | + | 0.990729i | \(0.543378\pi\) | |||||||
\(44\) | 66853.1 | − | 115793.i | 0.0178366 | − | 0.0308938i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.53560e6 | − | 2.65973e6i | −0.342962 | − | 0.594028i | ||||
\(47\) | −8.09682e6 | − | 4.67470e6i | −1.65929 | − | 0.957993i | −0.973042 | − | 0.230628i | \(-0.925922\pi\) |
−0.686251 | − | 0.727365i | \(-0.740745\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.76436e6 | − | 71061.3i | −0.999924 | − | 0.0123268i | ||||
\(50\) | −5.59098e6 | −0.894556 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.21850e6 | + | 3.01290e6i | −0.713727 | + | 0.412070i | ||||
\(53\) | −462964. | − | 801877.i | −0.0586737 | − | 0.101626i | 0.835197 | − | 0.549952i | \(-0.185354\pi\) |
−0.893870 | + | 0.448326i | \(0.852020\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 982573.i | 0.107378i | ||||||||
\(56\) | 21430.6 | − | 3.47695e6i | 0.00217912 | − | 0.353547i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.15469e6 | − | 1.23923e7i | 0.632235 | − | 1.09506i | ||||
\(59\) | 1.14511e7 | − | 6.61132e6i | 0.945019 | − | 0.545607i | 0.0534889 | − | 0.998568i | \(-0.482966\pi\) |
0.891530 | + | 0.452961i | \(0.149632\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.21666e7 | − | 7.02438e6i | −0.878717 | − | 0.507328i | −0.00848188 | − | 0.999964i | \(-0.502700\pi\) |
−0.870235 | + | 0.492636i | \(0.836033\pi\) | |||||||
\(62\) | 1.87396e6i | 0.126822i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.09715e6 | 0.125000 | ||||||||
\(65\) | 2.21410e7 | − | 3.83494e7i | 1.24035 | − | 2.14835i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.70876e6 | + | 1.50840e7i | 0.432172 | + | 0.748544i | 0.997060 | − | 0.0766234i | \(-0.0244139\pi\) |
−0.564888 | + | 0.825168i | \(0.691081\pi\) | |||||||
\(68\) | −7.09922e6 | − | 4.09874e6i | −0.332028 | − | 0.191697i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.26392e7 | + | 2.22068e7i | 0.526415 | + | 0.924897i | ||||
\(71\) | −5.33768e6 | −0.210048 | −0.105024 | − | 0.994470i | \(-0.533492\pi\) | ||||
−0.105024 | + | 0.994470i | \(0.533492\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.95255e7 | − | 1.70466e7i | 1.03970 | − | 0.600268i | 0.119948 | − | 0.992780i | \(-0.461727\pi\) |
0.919747 | + | 0.392512i | \(0.128394\pi\) | |||||||
\(74\) | −1.53382e7 | − | 2.65666e7i | −0.511503 | − | 0.885950i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.00659e7i | 0.901197i | ||||||||
\(77\) | 2.17971e6 | − | 1.24061e6i | 0.0620063 | − | 0.0352916i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.61504e7 | − | 2.79734e7i | 0.414644 | − | 0.718185i | −0.580747 | − | 0.814084i | \(-0.697239\pi\) |
0.995391 | + | 0.0958993i | \(0.0305727\pi\) | |||||||
\(80\) | −1.33467e7 | + | 7.70572e6i | −0.325847 | + | 0.188128i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.45332e7 | − | 8.39075e6i | −0.321444 | − | 0.185586i | ||||
\(83\) | − | 6.53156e7i | − | 1.37627i | −0.725582 | − | 0.688136i | \(-0.758429\pi\) | ||
0.725582 | − | 0.688136i | \(-0.241571\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.02411e7 | 1.15403 | ||||||||
\(86\) | 5.25480e6 | − | 9.10159e6i | 0.0960645 | − | 0.166389i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 756357. | + | 1.31005e6i | 0.0126123 | + | 0.0218452i | ||||
\(89\) | −2.58655e7 | − | 1.49334e7i | −0.412250 | − | 0.238012i | 0.279506 | − | 0.960144i | \(-0.409829\pi\) |
−0.691756 | + | 0.722131i | \(0.743163\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.13029e8 | − | 696665.i | −1.64825 | − | 0.0101592i | ||||
\(92\) | 3.47466e7 | 0.485022 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.16051e7 | − | 5.28882e7i | 1.17330 | − | 0.677403i | ||||
\(95\) | −1.10473e8 | − | 1.91345e8i | −1.35632 | − | 2.34922i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 5.40321e7i | − | 0.610330i | −0.952299 | − | 0.305165i | \(-0.901288\pi\) | ||
0.952299 | − | 0.305165i | \(-0.0987116\pi\) | |||||||
\(98\) | 3.33044e7 | − | 5.60770e7i | 0.361075 | − | 0.607968i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.16273e7 | − | 5.47801e7i | 0.316273 | − | 0.547801i | ||||
\(101\) | −8.47958e7 | + | 4.89569e7i | −0.814871 | + | 0.470466i | −0.848644 | − | 0.528964i | \(-0.822581\pi\) |
0.0337737 | + | 0.999430i | \(0.489247\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.64140e8 | − | 9.47665e7i | −1.45837 | − | 0.841988i | −0.459435 | − | 0.888211i | \(-0.651948\pi\) |
−0.998931 | + | 0.0462234i | \(0.985281\pi\) | |||||||
\(104\) | − | 6.81742e7i | − | 0.582756i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.04757e7 | 0.0829772 | ||||||||
\(107\) | −3.06326e7 | + | 5.30573e7i | −0.233695 | + | 0.404772i | −0.958893 | − | 0.283769i | \(-0.908415\pi\) |
0.725198 | + | 0.688541i | \(0.241748\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.66765e7 | + | 1.15487e8i | 0.472353 | + | 0.818139i | 0.999499 | − | 0.0316350i | \(-0.0100714\pi\) |
−0.527146 | + | 0.849774i | \(0.676738\pi\) | |||||||
\(110\) | −9.62721e6 | − | 5.55827e6i | −0.0657551 | − | 0.0379637i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.39458e7 | + | 1.98786e7i | 0.215732 | + | 0.126332i | ||||
\(113\) | 2.67016e8 | 1.63766 | 0.818831 | − | 0.574035i | \(-0.194623\pi\) | ||||
0.818831 | + | 0.574035i | \(0.194623\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.21134e8 | + | 1.27672e8i | −1.26434 | + | 0.729968i | ||||
\(116\) | 8.09460e7 | + | 1.40203e8i | 0.447058 | + | 0.774327i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.49597e8i | 0.771605i | ||||||||
\(119\) | −7.60611e7 | − | 1.33637e8i | −0.379293 | − | 0.666407i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.06634e8 | − | 1.84695e8i | 0.497455 | − | 0.861617i | ||||
\(122\) | 1.37649e8 | − | 7.94717e7i | 0.621347 | − | 0.358735i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.83610e7 | − | 1.06007e7i | −0.0776620 | − | 0.0448382i | ||||
\(125\) | 9.74051e7i | 0.398971i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.08576e8 | 0.417368 | 0.208684 | − | 0.977983i | \(-0.433082\pi\) | ||||
0.208684 | + | 0.977983i | \(0.433082\pi\) | |||||||
\(128\) | −1.18633e7 | + | 2.05478e7i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.50497e8 | + | 4.33874e8i | 0.877060 | + | 1.51911i | ||||
\(131\) | −1.17441e8 | − | 6.78047e7i | −0.398782 | − | 0.230237i | 0.287176 | − | 0.957878i | \(-0.407283\pi\) |
−0.685958 | + | 0.727641i | \(0.740617\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.84990e8 | + | 4.86665e8i | −0.910801 | + | 1.55533i | ||||
\(134\) | −1.97057e8 | −0.611184 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.03185e7 | − | 4.63719e7i | 0.234779 | − | 0.135550i | ||||
\(137\) | 2.77423e8 | + | 4.80510e8i | 0.787516 | + | 1.36402i | 0.927484 | + | 0.373862i | \(0.121967\pi\) |
−0.139968 | + | 0.990156i | \(0.544700\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.11909e7i | 0.190706i | 0.995444 | + | 0.0953532i | \(0.0303980\pi\) | ||||
−0.995444 | + | 0.0953532i | \(0.969602\pi\) | |||||||
\(140\) | −2.89079e8 | − | 1.78177e6i | −0.752497 | − | 0.00463810i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.01945e7 | − | 5.22984e7i | 0.0742633 | − | 0.128628i | ||||
\(143\) | 4.25870e7 | − | 2.45876e7i | 0.101843 | − | 0.0587993i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.03031e9 | − | 5.94852e8i | −2.33076 | − | 1.34566i | ||||
\(146\) | 3.85720e8i | 0.848908i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.47065e8 | 0.723375 | ||||||||
\(149\) | −1.42326e8 | + | 2.46517e8i | −0.288762 | + | 0.500151i | −0.973515 | − | 0.228625i | \(-0.926577\pi\) |
0.684752 | + | 0.728776i | \(0.259910\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.56501e8 | − | 4.44273e8i | −0.493380 | − | 0.854559i | 0.506591 | − | 0.862187i | \(-0.330905\pi\) |
−0.999971 | + | 0.00762721i | \(0.997572\pi\) | |||||||
\(152\) | −2.94584e8 | − | 1.70078e8i | −0.551868 | − | 0.318621i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −174890. | + | 2.83747e7i | −0.000310945 | + | 0.0504484i | ||||
\(155\) | 1.55804e8 | 0.269930 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.41830e8 | − | 2.55091e8i | 0.727204 | − | 0.419851i | −0.0901944 | − | 0.995924i | \(-0.528749\pi\) |
0.817398 | + | 0.576073i | \(0.195415\pi\) | |||||||
\(158\) | 1.82721e8 | + | 3.16482e8i | 0.293198 | + | 0.507833i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 1.74360e8i | − | 0.266053i | ||||||
\(161\) | 5.62430e8 | + | 3.29358e8i | 0.837077 | + | 0.490190i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.54375e7 | + | 1.65303e8i | −0.135197 | + | 0.234169i | −0.925673 | − | 0.378325i | \(-0.876500\pi\) |
0.790475 | + | 0.612494i | \(0.209834\pi\) | |||||||
\(164\) | 1.64424e8 | − | 9.49305e7i | 0.227296 | − | 0.131229i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.39959e8 | + | 3.69481e8i | 0.842791 | + | 0.486586i | ||||
\(167\) | 1.37420e9i | 1.76678i | 0.468636 | + | 0.883391i | \(0.344746\pi\) | ||||
−0.468636 | + | 0.883391i | \(0.655254\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.40047e9 | −1.71683 | ||||||||
\(170\) | −3.40775e8 | + | 5.90240e8i | −0.408011 | + | 0.706696i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.94513e7 | + | 1.02973e8i | 0.0679278 | + | 0.117654i | ||||
\(173\) | 1.02182e9 | + | 5.89945e8i | 1.14074 | + | 0.658608i | 0.946615 | − | 0.322368i | \(-0.104479\pi\) |
0.194129 | + | 0.980976i | \(0.437812\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.03119e9 | − | 5.86915e8i | 1.09948 | − | 0.625782i | ||||
\(176\) | −1.71144e7 | −0.0178366 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.92634e8 | − | 1.68952e8i | 0.291504 | − | 0.168300i | ||||
\(179\) | −7.26254e8 | − | 1.25791e9i | −0.707419 | − | 1.22529i | −0.965811 | − | 0.259245i | \(-0.916526\pi\) |
0.258393 | − | 0.966040i | \(-0.416807\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.51470e8i | − | 0.327471i | −0.986504 | − | 0.163736i | \(-0.947646\pi\) | ||
0.986504 | − | 0.163736i | \(-0.0523544\pi\) | |||||||
\(182\) | 6.46213e8 | − | 1.10351e9i | 0.588966 | − | 1.00575i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.96556e8 | + | 3.40446e8i | −0.171481 | + | 0.297014i | ||||
\(185\) | −2.20879e9 | + | 1.27524e9i | −1.88568 | + | 1.08870i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.79352e7 | + | 3.34489e7i | 0.0473779 | + | 0.0273536i | ||||
\(188\) | 1.19672e9i | 0.957993i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.49972e9 | 1.91813 | ||||||||
\(191\) | 1.43167e8 | − | 2.47972e8i | 0.107574 | − | 0.186324i | −0.807213 | − | 0.590261i | \(-0.799025\pi\) |
0.914787 | + | 0.403936i | \(0.132358\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.60498e8 | + | 2.77991e8i | 0.115676 | + | 0.200356i | 0.918050 | − | 0.396466i | \(-0.129763\pi\) |
−0.802374 | + | 0.596821i | \(0.796430\pi\) | |||||||
\(194\) | 5.29404e8 | + | 3.05652e8i | 0.373749 | + | 0.215784i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.61042e8 | + | 6.43535e8i | 0.244643 | + | 0.436061i | ||||
\(197\) | 9.97043e8 | 0.661986 | 0.330993 | − | 0.943633i | \(-0.392616\pi\) | ||||
0.330993 | + | 0.943633i | \(0.392616\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.03419e7 | − | 5.21589e7i | 0.0576072 | − | 0.0332595i | −0.470920 | − | 0.882176i | \(-0.656078\pi\) |
0.528527 | + | 0.848917i | \(0.322745\pi\) | |||||||
\(200\) | 3.57822e8 | + | 6.19767e8i | 0.223639 | + | 0.387354i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 1.10777e9i | − | 0.665339i | ||||||
\(203\) | −1.87169e7 | + | 3.03668e9i | −0.0110218 | + | 1.78820i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.97620e8 | + | 1.20831e9i | −0.395006 | + | 0.684170i | ||||
\(206\) | 1.85704e9 | − | 1.07216e9i | 1.03122 | − | 0.595375i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.67968e8 | + | 3.85651e8i | 0.356863 | + | 0.206035i | ||||
\(209\) | − | 2.45361e8i | − | 0.128594i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.58407e8 | −0.281722 | −0.140861 | − | 0.990029i | \(-0.544987\pi\) | ||||
−0.140861 | + | 0.990029i | \(0.544987\pi\) | |||||||
\(212\) | −5.92594e7 | + | 1.02640e8i | −0.0293369 | + | 0.0508129i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.46569e8 | − | 6.00275e8i | −0.165247 | − | 0.286217i | ||||
\(215\) | −7.56720e8 | − | 4.36893e8i | −0.354145 | − | 0.204466i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.96719e8 | − | 3.45630e8i | −0.0887173 | − | 0.155874i | ||||
\(218\) | −1.50872e9 | −0.668008 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.08919e8 | − | 6.28847e7i | 0.0464959 | − | 0.0268444i | ||||
\(221\) | −1.50746e9 | − | 2.61099e9i | −0.631940 | − | 1.09455i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.47205e9i | − | 0.595254i | −0.954682 | − | 0.297627i | \(-0.903805\pi\) | ||
0.954682 | − | 0.297627i | \(-0.0961951\pi\) | |||||||
\(224\) | −3.86796e8 | + | 2.20149e8i | −0.153635 | + | 0.0874431i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.51047e9 | + | 2.61621e9i | −0.579001 | + | 1.00286i | ||||
\(227\) | 1.03779e9 | − | 5.99169e8i | 0.390847 | − | 0.225656i | −0.291680 | − | 0.956516i | \(-0.594214\pi\) |
0.682527 | + | 0.730860i | \(0.260881\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.13100e7 | + | 1.80768e7i | 0.0113852 | + | 0.00657326i | 0.505682 | − | 0.862720i | \(-0.331241\pi\) |
−0.494297 | + | 0.869293i | \(0.664574\pi\) | |||||||
\(230\) | − | 2.88889e9i | − | 1.03233i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.83160e9 | −0.632235 | ||||||||
\(233\) | 1.64329e9 | − | 2.84627e9i | 0.557560 | − | 0.965722i | −0.440140 | − | 0.897929i | \(-0.645071\pi\) |
0.997699 | − | 0.0677924i | \(-0.0215955\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.39721e9 | − | 7.61619e9i | −1.44180 | − | 2.49727i | ||||
\(236\) | −1.46575e9 | − | 8.46249e8i | −0.472510 | − | 0.272803i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.73964e9 | + | 1.07225e7i | 0.542189 | + | 0.00334184i | ||||
\(239\) | 3.73479e9 | 1.14465 | 0.572327 | − | 0.820025i | \(-0.306041\pi\) | ||||
0.572327 | + | 0.820025i | \(0.306041\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.92362e9 | − | 1.11060e9i | 0.570231 | − | 0.329223i | −0.187011 | − | 0.982358i | \(-0.559880\pi\) |
0.757241 | + | 0.653135i | \(0.226547\pi\) | |||||||
\(242\) | 1.20642e9 | + | 2.08959e9i | 0.351754 | + | 0.609255i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.79824e9i | 0.507328i | ||||||||
\(245\) | −4.66233e9 | − | 2.76898e9i | −1.29401 | − | 0.768521i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.52890e9 | + | 9.57634e9i | −1.48543 | + | 2.57283i | ||||
\(248\) | 2.07731e8 | − | 1.19933e8i | 0.0549153 | − | 0.0317054i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.54371e8 | − | 5.51007e8i | −0.244319 | − | 0.141058i | ||||
\(251\) | − | 3.49708e9i | − | 0.881069i | −0.897736 | − | 0.440535i | \(-0.854789\pi\) | ||
0.897736 | − | 0.440535i | \(-0.145211\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.83559e8 | −0.0692089 | ||||||||
\(254\) | −6.14198e8 | + | 1.06382e9i | −0.147562 | + | 0.255584i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.34218e8 | − | 2.32472e8i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −7.77094e8 | − | 4.48656e8i | −0.178132 | − | 0.102844i | 0.408283 | − | 0.912855i | \(-0.366128\pi\) |
−0.586415 | + | 0.810011i | \(0.699461\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.61780e9 | + | 3.28977e9i | 1.24844 | + | 0.731084i | ||||
\(260\) | −5.66810e9 | −1.24035 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.32870e9 | − | 7.67123e8i | 0.281981 | − | 0.162802i | ||||
\(263\) | −1.47398e9 | − | 2.55300e9i | −0.308083 | − | 0.533615i | 0.669860 | − | 0.742487i | \(-0.266354\pi\) |
−0.977943 | + | 0.208872i | \(0.933021\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8.70964e8i | − | 0.176611i | ||||||
\(266\) | −3.15618e9 | − | 5.54532e9i | −0.630428 | − | 1.10764i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.11472e9 | − | 1.93075e9i | 0.216086 | − | 0.374272i | ||||
\(269\) | 3.58685e9 | − | 2.07087e9i | 0.685021 | − | 0.395497i | −0.116723 | − | 0.993164i | \(-0.537239\pi\) |
0.801744 | + | 0.597668i | \(0.203906\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.98614e9 | + | 1.14670e9i | 0.368241 | + | 0.212604i | 0.672690 | − | 0.739925i | \(-0.265139\pi\) |
−0.304449 | + | 0.952529i | \(0.598472\pi\) | |||||||
\(272\) | 1.04928e9i | 0.191697i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.27736e9 | −1.11372 | ||||||||
\(275\) | −2.58104e8 | + | 4.47049e8i | −0.0451298 | + | 0.0781671i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.31629e9 | + | 7.47604e9i | 0.733149 | + | 1.26985i | 0.955531 | + | 0.294891i | \(0.0952833\pi\) |
−0.222382 | + | 0.974960i | \(0.571383\pi\) | |||||||
\(278\) | −6.97525e8 | − | 4.02716e8i | −0.116783 | − | 0.0674249i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.65274e9 | − | 2.82231e9i | 0.268888 | − | 0.459169i | ||||
\(281\) | −1.42076e9 | −0.227874 | −0.113937 | − | 0.993488i | \(-0.536346\pi\) | ||||
−0.113937 | + | 0.993488i | \(0.536346\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.50006e9 | + | 1.44341e9i | −0.389766 | + | 0.225032i | −0.682059 | − | 0.731297i | \(-0.738915\pi\) |
0.292293 | + | 0.956329i | \(0.405582\pi\) | |||||||
\(284\) | 3.41612e8 | + | 5.91689e8i | 0.0525121 | + | 0.0909536i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.56354e8i | 0.0831548i | ||||||||
\(287\) | 3.56131e9 | + | 2.19505e7i | 0.524907 | + | 0.00323532i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.43714e9 | + | 2.48920e9i | −0.206020 | + | 0.356836i | ||||
\(290\) | 1.16567e10 | − | 6.72998e9i | 1.64810 | − | 0.951528i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.77927e9 | − | 2.18196e9i | −0.519848 | − | 0.300134i | ||||
\(293\) | − | 9.77296e9i | − | 1.32604i | −0.748603 | − | 0.663019i | \(-0.769275\pi\) | ||
0.748603 | − | 0.663019i | \(-0.230725\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.24377e10 | 1.64230 | ||||||||
\(296\) | −1.96329e9 | + | 3.40052e9i | −0.255752 | + | 0.442975i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.61024e9 | − | 2.78902e9i | −0.204186 | − | 0.353660i | ||||
\(299\) | 1.10672e10 | + | 6.38965e9i | 1.38469 | + | 0.799452i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.37468e7 | + | 2.23031e9i | −0.00167469 | + | 0.271706i | ||||
\(302\) | 5.80396e9 | 0.697745 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.33284e9 | − | 1.92422e9i | 0.390230 | − | 0.225299i | ||||
\(305\) | −6.60740e9 | − | 1.14444e10i | −0.763539 | − | 1.32249i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.57927e10i | − | 1.77788i | −0.458024 | − | 0.888940i | \(-0.651443\pi\) | ||
0.458024 | − | 0.888940i | \(-0.348557\pi\) | |||||||
\(308\) | −2.77024e8 | − | 1.62225e8i | −0.0307833 | − | 0.0180266i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.81359e8 | + | 1.52656e9i | −0.0954346 | + | 0.165298i | ||||
\(311\) | −4.52636e9 | + | 2.61329e9i | −0.483846 | + | 0.279349i | −0.722018 | − | 0.691874i | \(-0.756785\pi\) |
0.238172 | + | 0.971223i | \(0.423452\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.51493e9 | − | 4.91610e9i | −0.887164 | − | 0.512204i | −0.0141503 | − | 0.999900i | \(-0.504504\pi\) |
−0.873014 | + | 0.487695i | \(0.837838\pi\) | |||||||
\(314\) | 5.77204e9i | 0.593760i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.13451e9 | −0.414644 | ||||||||
\(317\) | −1.96496e9 | + | 3.40341e9i | −0.194588 | + | 0.337036i | −0.946765 | − | 0.321924i | \(-0.895670\pi\) |
0.752177 | + | 0.658961i | \(0.229004\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.60583e8 | − | 1.14416e9i | −0.0637918 | − | 0.110491i | ||||
\(320\) | 1.70838e9 | + | 9.86332e8i | 0.162923 | + | 0.0940639i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.40862e9 | + | 3.64754e9i | −0.596130 | + | 0.339294i | ||||
\(323\) | −1.50430e10 | −1.38205 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.01474e10 | − | 1.16321e10i | 1.80586 | − | 1.04262i | ||||
\(326\) | −1.07975e9 | − | 1.87018e9i | −0.0955990 | − | 0.165582i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.14803e9i | 0.185586i | ||||||||
\(329\) | −1.13436e10 | + | 1.93709e10i | −0.968202 | + | 1.65336i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.65125e9 | − | 1.15203e10i | 0.554104 | − | 0.959736i | −0.443869 | − | 0.896092i | \(-0.646394\pi\) |
0.997973 | − | 0.0636440i | \(-0.0202722\pi\) | |||||||
\(332\) | −7.24031e9 | + | 4.18020e9i | −0.595943 | + | 0.344068i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.34643e10 | − | 7.77363e9i | −1.08193 | − | 0.624652i | ||||
\(335\) | 1.63836e10i | 1.30086i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.53635e10 | 1.19116 | 0.595580 | − | 0.803296i | \(-0.296922\pi\) | ||||
0.595580 | + | 0.803296i | \(0.296922\pi\) | |||||||
\(338\) | 7.92227e9 | − | 1.37218e10i | 0.606992 | − | 1.05134i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.85543e9 | − | 6.67780e9i | −0.288508 | − | 0.499710i | ||||
\(341\) | 1.49840e8 | + | 8.65100e7i | 0.0110818 | + | 0.00639807i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.55919e8 | + | 1.38389e10i | −0.0184895 | + | 0.999829i | ||||
\(344\) | −1.34523e9 | −0.0960645 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.15605e10 | + | 6.67447e9i | −0.806627 | + | 0.465706i | ||||
\(347\) | −1.41386e9 | − | 2.44888e9i | −0.0975191 | − | 0.168908i | 0.813138 | − | 0.582071i | \(-0.197757\pi\) |
−0.910657 | + | 0.413163i | \(0.864424\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.88443e10i | 1.27022i | 0.772423 | + | 0.635109i | \(0.219045\pi\) | ||||
−0.772423 | + | 0.635109i | \(0.780955\pi\) | |||||||
\(350\) | −8.27383e7 | + | 1.34237e10i | −0.00551359 | + | 0.894539i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.68136e7 | − | 1.67686e8i | 0.00630617 | − | 0.0109226i | ||||
\(353\) | 1.19955e10 | − | 6.92562e9i | 0.772539 | − | 0.446026i | −0.0612403 | − | 0.998123i | \(-0.519506\pi\) |
0.833780 | + | 0.552097i | \(0.186172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.34817e9 | − | 2.51042e9i | −0.273775 | − | 0.158064i | ||||
\(356\) | 3.82296e9i | 0.238012i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.64333e10 | 1.00044 | ||||||||
\(359\) | 2.92238e9 | − | 5.06172e9i | 0.175938 | − | 0.304733i | −0.764548 | − | 0.644567i | \(-0.777038\pi\) |
0.940485 | + | 0.339834i | \(0.110371\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.90948e10 | + | 3.30732e10i | 1.12431 | + | 1.94737i | ||||
\(362\) | 3.44368e9 | + | 1.98821e9i | 0.200534 | + | 0.115779i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.15661e9 | + | 1.25740e10i | 0.407664 | + | 0.716253i | ||||
\(365\) | 3.20693e10 | 1.80683 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.52947e9 | − | 2.61509e9i | 0.249680 | − | 0.144153i | −0.369938 | − | 0.929057i | \(-0.620621\pi\) |
0.619618 | + | 0.784904i | \(0.287288\pi\) | |||||||
\(368\) | −2.22378e9 | − | 3.85170e9i | −0.121255 | − | 0.210020i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 2.88555e10i | − | 1.53965i | ||||||
\(371\) | −1.93212e9 | + | 1.09969e9i | −0.101986 | + | 0.0580463i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.35811e9 | + | 1.10126e10i | −0.328468 | + | 0.568922i | −0.982208 | − | 0.187796i | \(-0.939865\pi\) |
0.653740 | + | 0.756719i | \(0.273199\pi\) | |||||||
\(374\) | −6.55461e8 | + | 3.78431e8i | −0.0335012 | + | 0.0193419i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.17254e10 | − | 6.76969e9i | −0.586649 | − | 0.338702i | ||||
\(377\) | 5.95416e10i | 2.94751i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.59283e10 | −0.771991 | −0.385995 | − | 0.922501i | \(-0.626142\pi\) | ||||
−0.385995 | + | 0.922501i | \(0.626142\pi\) | |||||||
\(380\) | −1.41406e10 | + | 2.44922e10i | −0.678161 | + | 1.17461i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.61975e9 | + | 2.80549e9i | 0.0760666 | + | 0.131751i | ||||
\(383\) | 3.16640e9 | + | 1.82812e9i | 0.147154 | + | 0.0849593i | 0.571769 | − | 0.820415i | \(-0.306257\pi\) |
−0.424615 | + | 0.905374i | \(0.639591\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.35911e9 | + | 1.45407e7i | 0.107376 | + | 0.000661822i | ||||
\(386\) | −3.63167e9 | −0.163590 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.98952e9 | + | 3.45805e9i | −0.264281 | + | 0.152583i | ||||
\(389\) | 5.63251e9 | + | 9.75580e9i | 0.245982 | + | 0.426054i | 0.962407 | − | 0.271610i | \(-0.0875561\pi\) |
−0.716425 | + | 0.697664i | \(0.754223\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.73849e10i | 0.743816i | ||||||||
\(392\) | −8.34769e9 | − | 1.02908e8i | −0.353527 | − | 0.00435817i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.64013e9 | + | 9.76898e9i | −0.234047 | + | 0.405382i | ||||
\(395\) | 2.63128e10 | − | 1.51917e10i | 1.08088 | − | 0.624049i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.73124e10 | − | 1.57688e10i | −1.09951 | − | 0.634800i | −0.163415 | − | 0.986557i | \(-0.552251\pi\) |
−0.936091 | + | 0.351757i | \(0.885584\pi\) | |||||||
\(398\) | 1.18022e9i | 0.0470361i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.09660e9 | −0.316273 | ||||||||
\(401\) | −1.90026e10 | + | 3.29135e10i | −0.734914 | + | 1.27291i | 0.219848 | + | 0.975534i | \(0.429444\pi\) |
−0.954761 | + | 0.297373i | \(0.903889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.89879e9 | − | 6.75290e9i | −0.147812 | − | 0.256018i | ||||
\(404\) | 1.08539e10 | + | 6.26648e9i | 0.407435 | + | 0.235233i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.96474e10 | − | 1.73615e10i | −1.09115 | − | 0.638973i | ||||
\(407\) | −2.83232e9 | −0.103220 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.88374e9 | − | 5.70638e9i | 0.353206 | − | 0.203924i | −0.312890 | − | 0.949789i | \(-0.601297\pi\) |
0.666096 | + | 0.745866i | \(0.267964\pi\) | |||||||
\(410\) | −7.89267e9 | − | 1.36705e10i | −0.279311 | − | 0.483781i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.42602e10i | 0.841988i | ||||||||
\(413\) | −1.57040e10 | − | 2.75915e10i | −0.539772 | − | 0.948364i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.07192e10 | − | 5.32072e10i | 1.03566 | − | 1.79382i | ||||
\(416\) | −7.55719e9 | + | 4.36315e9i | −0.252341 | + | 0.145689i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.40404e9 | + | 1.38797e9i | 0.0787474 | + | 0.0454648i | ||||
\(419\) | 7.05049e9i | 0.228751i | 0.993438 | + | 0.114376i | \(0.0364867\pi\) | ||||
−0.993438 | + | 0.114376i | \(0.963513\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.15471e10 | −1.00422 | −0.502112 | − | 0.864803i | \(-0.667444\pi\) | ||||
−0.502112 | + | 0.864803i | \(0.667444\pi\) | |||||||
\(422\) | 3.15883e9 | − | 5.47125e9i | 0.0996038 | − | 0.172519i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.70444e8 | − | 1.16124e9i | −0.0207443 | − | 0.0359302i | ||||
\(425\) | 2.74084e10 | + | 1.58242e10i | 0.840093 | + | 0.485028i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.70453e10 | + | 2.91074e10i | −0.512734 | + | 0.875573i | ||||
\(428\) | 7.84196e9 | 0.233695 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.56131e9 | − | 4.94287e9i | 0.250419 | − | 0.144579i | ||||
\(431\) | −1.60391e10 | − | 2.77805e10i | −0.464805 | − | 0.805066i | 0.534387 | − | 0.845240i | \(-0.320542\pi\) |
−0.999193 | + | 0.0401733i | \(0.987209\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.28833e10i | 0.650979i | 0.945546 | + | 0.325489i | \(0.105529\pi\) | ||||
−0.945546 | + | 0.325489i | \(0.894471\pi\) | |||||||
\(434\) | 4.49929e9 | + | 2.77319e7i | 0.126819 | + | 0.000781664i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.53459e9 | − | 1.47823e10i | 0.236177 | − | 0.409070i | ||||
\(437\) | 5.52201e10 | − | 3.18813e10i | 1.51416 | − | 0.874200i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.93893e9 | − | 1.69679e9i | −0.0791282 | − | 0.0456847i | 0.459914 | − | 0.887964i | \(-0.347880\pi\) |
−0.539042 | + | 0.842279i | \(0.681214\pi\) | |||||||
\(440\) | 1.42292e9i | 0.0379637i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.41098e10 | 0.893698 | ||||||||
\(443\) | −2.58531e10 | + | 4.47789e10i | −0.671271 | + | 1.16268i | 0.306273 | + | 0.951944i | \(0.400918\pi\) |
−0.977544 | + | 0.210732i | \(0.932415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.40470e10 | − | 2.43301e10i | −0.358214 | − | 0.620445i | ||||
\(446\) | 1.44231e10 | + | 8.32715e9i | 0.364517 | + | 0.210454i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.10348e7 | − | 5.03517e9i | 0.000770437 | − | 0.124998i | ||||
\(449\) | −5.01205e10 | −1.23319 | −0.616595 | − | 0.787281i | \(-0.711488\pi\) | ||||
−0.616595 | + | 0.787281i | \(0.711488\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.34183e9 | + | 7.74707e8i | −0.0324334 | + | 0.0187254i | ||||
\(452\) | −1.70890e10 | − | 2.95991e10i | −0.409415 | − | 0.709128i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.35576e10i | 0.319125i | ||||||||
\(455\) | −9.17475e10 | − | 5.37271e10i | −2.14066 | − | 1.25357i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.95560e10 | + | 6.85130e10i | −0.906875 | + | 1.57075i | −0.0884942 | + | 0.996077i | \(0.528205\pi\) |
−0.818381 | + | 0.574677i | \(0.805128\pi\) | |||||||
\(458\) | −3.54232e8 | + | 2.04516e8i | −0.00805056 | + | 0.00464799i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.83052e10 | + | 1.63420e10i | 0.632171 | + | 0.364984i | ||||
\(461\) | − | 1.40115e10i | − | 0.310228i | −0.987897 | − | 0.155114i | \(-0.950426\pi\) | ||
0.987897 | − | 0.155114i | \(-0.0495745\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.61893e10 | 1.44034 | 0.720168 | − | 0.693800i | \(-0.244065\pi\) | ||||
0.720168 | + | 0.693800i | \(0.244065\pi\) | |||||||
\(464\) | 1.03611e10 | − | 1.79459e10i | 0.223529 | − | 0.387163i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.85917e10 | + | 3.22018e10i | 0.394254 | + | 0.682868i | ||||
\(467\) | −3.14542e10 | − | 1.81601e10i | −0.661319 | − | 0.381813i | 0.131460 | − | 0.991321i | \(-0.458033\pi\) |
−0.792780 | + | 0.609509i | \(0.791367\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.63449e10 | − | 2.06861e10i | 0.751194 | − | 0.427550i | ||||
\(470\) | 9.94974e10 | 2.03902 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.65830e10 | − | 9.57421e9i | 0.334115 | − | 0.192901i | ||||
\(473\) | −4.85169e8 | − | 8.40338e8i | −0.00969279 | − | 0.0167884i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.16077e11i | − | 2.28020i | ||||||
\(476\) | −9.94593e9 | + | 1.69842e10i | −0.193739 | + | 0.330840i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.11272e10 | + | 3.65933e10i | −0.404697 | + | 0.700955i | ||||
\(479\) | 6.34734e10 | − | 3.66464e10i | 1.20573 | − | 0.696128i | 0.243906 | − | 0.969799i | \(-0.421571\pi\) |
0.961823 | + | 0.273671i | \(0.0882378\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.10544e11 | + | 6.38227e10i | 2.06517 | + | 1.19233i | ||||
\(482\) | 2.51300e10i | 0.465591i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.72983e10 | −0.497455 | ||||||||
\(485\) | 2.54124e10 | − | 4.40155e10i | 0.459280 | − | 0.795497i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.96063e10 | − | 6.86001e10i | −0.704123 | − | 1.21958i | −0.967007 | − | 0.254749i | \(-0.918007\pi\) |
0.262884 | − | 0.964827i | \(-0.415326\pi\) | |||||||
\(488\) | −1.76191e10 | − | 1.01724e10i | −0.310673 | − | 0.179367i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.35045e10 | − | 3.00176e10i | 0.928124 | − | 0.520705i | ||||
\(491\) | 5.63231e10 | 0.969082 | 0.484541 | − | 0.874769i | \(-0.338987\pi\) | ||||
0.484541 | + | 0.874769i | \(0.338987\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.01481e10 | + | 4.05001e10i | −1.18749 | + | 0.685595i | ||||
\(494\) | −6.25524e10 | − | 1.08344e11i | −1.05036 | − | 1.81927i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.71378e9i | 0.0448382i | ||||||||
\(497\) | −7.89900e7 | + | 1.28155e10i | −0.00129463 | + | 0.210044i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.34346e10 | − | 2.32693e10i | 0.216681 | − | 0.375303i | −0.737110 | − | 0.675773i | \(-0.763810\pi\) |
0.953791 | + | 0.300470i | \(0.0971434\pi\) | |||||||
\(500\) | 1.07975e10 | − | 6.23393e9i | 0.172760 | − | 0.0997428i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.42642e10 | + | 1.97824e10i | 0.539543 | + | 0.311505i | ||||
\(503\) | 4.60200e10i | 0.718910i | 0.933162 | + | 0.359455i | \(0.117037\pi\) | ||||
−0.933162 | + | 0.359455i | \(0.882963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.21015e10 | −1.41612 | ||||||||
\(506\) | 1.60405e9 | − | 2.77830e9i | 0.0244690 | − | 0.0423816i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.94886e9 | − | 1.20358e10i | −0.104342 | − | 0.180725i | ||||
\(509\) | −9.09077e10 | − | 5.24856e10i | −1.35435 | − | 0.781932i | −0.365492 | − | 0.930815i | \(-0.619099\pi\) |
−0.988855 | + | 0.148882i | \(0.952432\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.04911e10 | − | 7.11417e10i | −0.593849 | − | 1.04338i | ||||
\(512\) | 3.03700e9 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.79182e9 | − | 5.07596e9i | 0.125958 | − | 0.0727220i | ||||
\(515\) | −8.91411e10 | − | 1.54397e11i | −1.26721 | − | 2.19487i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9.76620e9i | − | 0.136698i | ||||||
\(518\) | −6.40122e10 | + | 3.64333e10i | −0.889086 | + | 0.506033i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.20636e10 | − | 5.55359e10i | 0.438530 | − | 0.759557i | ||||
\(521\) | 4.56369e10 | − | 2.63485e10i | 0.619391 | − | 0.357606i | −0.157241 | − | 0.987560i | \(-0.550260\pi\) |
0.776632 | + | 0.629955i | \(0.216927\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.74118e10 | − | 2.15997e10i | −0.500037 | − | 0.288697i | 0.228692 | − | 0.973499i | \(-0.426555\pi\) |
−0.728729 | + | 0.684802i | \(0.759889\pi\) | |||||||
\(524\) | 1.73580e10i | 0.230237i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.33523e10 | 0.435695 | ||||||||
\(527\) | 5.30389e9 | − | 9.18661e9i | 0.0687626 | − | 0.119100i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.31081e9 | + | 4.00245e9i | 0.0295082 | + | 0.0511096i | ||||
\(530\) | 8.53367e9 | + | 4.92692e9i | 0.108151 | + | 0.0624413i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.21868e10 | + | 4.44932e8i | 0.901180 | + | 0.00555452i | ||||
\(533\) | 6.98282e10 | 0.865211 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.99078e10 | + | 2.88143e10i | −0.609190 | + | 0.351716i | ||||
\(536\) | 1.26116e10 | + | 2.18440e10i | 0.152796 | + | 0.264650i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.68584e10i | 0.559317i | ||||||||
\(539\) | −2.94638e9 | − | 5.25175e9i | −0.0349088 | − | 0.0622227i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.65828e10 | + | 2.87222e10i | −0.193583 | + | 0.335296i | −0.946435 | − | 0.322894i | \(-0.895344\pi\) |
0.752852 | + | 0.658190i | \(0.228678\pi\) | |||||||
\(542\) | −2.24706e10 | + | 1.29734e10i | −0.260386 | + | 0.150334i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.02808e10 | − | 5.93560e9i | −0.117390 | − | 0.0677750i | ||||
\(545\) | 1.25437e11i | 1.42180i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.44828e11 | −1.61772 | −0.808860 | − | 0.588001i | \(-0.799915\pi\) | ||||
−0.808860 | + | 0.588001i | \(0.799915\pi\) | |||||||
\(548\) | 3.55101e10 | − | 6.15053e10i | 0.393758 | − | 0.682009i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.92011e9 | − | 5.05778e9i | −0.0319116 | − | 0.0552725i | ||||
\(551\) | 2.57283e11 | + | 1.48542e11i | 2.79128 | + | 1.61155i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.69238e10 | − | 3.91904e10i | −0.715616 | − | 0.419063i | ||||
\(554\) | −9.76666e10 | −1.03683 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.89160e9 | − | 4.55622e9i | 0.0825783 | − | 0.0476766i | ||||
\(557\) | −9.10260e10 | − | 1.57662e11i | −0.945682 | − | 1.63797i | −0.754381 | − | 0.656437i | \(-0.772063\pi\) |
−0.191301 | − | 0.981531i | \(-0.561271\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.37307e10i | 0.447857i | ||||||||
\(560\) | 1.83036e10 | + | 3.21588e10i | 0.186116 | + | 0.327000i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.03703e9 | − | 1.39205e10i | 0.0805657 | − | 0.139544i | ||||
\(563\) | 1.36642e11 | − | 7.88902e10i | 1.36003 | − | 0.785216i | 0.370407 | − | 0.928870i | \(-0.379218\pi\) |
0.989628 | + | 0.143653i | \(0.0458850\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.17516e11 | + | 1.25583e11i | 2.13451 | + | 1.23236i | ||||
\(566\) | − | 3.26606e10i | − | 0.318243i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.72979e9 | −0.0742633 | ||||||||
\(569\) | 7.37347e9 | − | 1.27712e10i | 0.0703433 | − | 0.121838i | −0.828708 | − | 0.559680i | \(-0.810924\pi\) |
0.899052 | + | 0.437842i | \(0.144257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.95716e9 | + | 5.12196e9i | 0.0278183 | + | 0.0481828i | 0.879599 | − | 0.475715i | \(-0.157811\pi\) |
−0.851781 | + | 0.523898i | \(0.824477\pi\) | |||||||
\(572\) | −5.45114e9 | − | 3.14722e9i | −0.0509217 | − | 0.0293997i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.03609e10 | + | 3.47694e10i | −0.187564 | + | 0.320295i | ||||
\(575\) | −1.34148e11 | −1.22720 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.08835e10 | + | 3.51511e10i | −0.549283 | + | 0.317129i | −0.748833 | − | 0.662759i | \(-0.769385\pi\) |
0.199549 | + | 0.979888i | \(0.436052\pi\) | |||||||
\(578\) | −1.62594e10 | − | 2.81621e10i | −0.145678 | − | 0.252321i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.52282e11i | 1.34566i | ||||||||
\(581\) | −1.56820e11 | − | 9.66576e8i | −1.37625 | − | 0.00848264i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.83603e8 | − | 8.37625e8i | 0.00418615 | − | 0.00725062i | ||||
\(584\) | 4.27575e10 | − | 2.46861e10i | 0.367588 | − | 0.212227i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.57551e10 | + | 5.52842e10i | 0.812029 | + | 0.468825i | ||||
\(587\) | 1.35170e11i | 1.13849i | 0.822168 | + | 0.569245i | \(0.192764\pi\) | ||||
−0.822168 | + | 0.569245i | \(0.807236\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.89062e10 | −0.323264 | ||||||||
\(590\) | −7.03584e10 | + | 1.21864e11i | −0.580641 | + | 1.00570i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.22121e10 | − | 3.84725e10i | −0.180844 | − | 0.313231i | ||||
\(593\) | −5.35885e10 | − | 3.09393e10i | −0.433364 | − | 0.250203i | 0.267415 | − | 0.963582i | \(-0.413831\pi\) |
−0.700779 | + | 0.713379i | \(0.747164\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.91481e8 | − | 1.44636e11i | 0.00711286 | − | 1.15401i | ||||
\(596\) | 3.64356e10 | 0.288762 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.25211e11 | + | 7.22907e10i | −0.979125 | + | 0.565298i | ||||
\(599\) | 5.68987e9 | + | 9.85515e9i | 0.0441972 | + | 0.0765519i | 0.887278 | − | 0.461235i | \(-0.152594\pi\) |
−0.843081 | + | 0.537787i | \(0.819260\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 4.63889e10i | − | 0.355563i | −0.984070 | − | 0.177781i | \(-0.943108\pi\) | ||
0.984070 | − | 0.177781i | \(-0.0568920\pi\) | |||||||
\(602\) | −2.17747e10 | − | 1.27512e10i | −0.165793 | − | 0.0970882i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.28322e10 | + | 5.68670e10i | −0.246690 | + | 0.427280i | ||||
\(605\) | 1.73732e11 | − | 1.00304e11i | 1.29675 | − | 0.748681i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.52237e11 | − | 8.78940e10i | −1.12141 | − | 0.647447i | −0.179650 | − | 0.983731i | \(-0.557497\pi\) |
−0.941761 | + | 0.336284i | \(0.890830\pi\) | |||||||
\(608\) | 4.35401e10i | 0.318621i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.49508e11 | 1.07981 | ||||||||
\(611\) | −2.20069e11 | + | 3.81171e11i | −1.57904 | + | 2.73498i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.02160e11 | + | 1.76947e11i | 0.723504 | + | 1.25315i | 0.959587 | + | 0.281412i | \(0.0908029\pi\) |
−0.236083 | + | 0.971733i | \(0.575864\pi\) | |||||||
\(614\) | 1.54736e11 | + | 8.93369e10i | 1.08872 | + | 0.628575i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.15656e9 | − | 1.79659e9i | 0.0219225 | − | 0.0124775i | ||||
\(617\) | −1.15941e11 | −0.800009 | −0.400005 | − | 0.916513i | \(-0.630991\pi\) | ||||
−0.400005 | + | 0.916513i | \(0.630991\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.73665e10 | − | 2.15736e10i | 0.254519 | − | 0.146947i | −0.367313 | − | 0.930097i | \(-0.619722\pi\) |
0.621832 | + | 0.783151i | \(0.286389\pi\) | |||||||
\(620\) | −9.97144e9 | − | 1.72710e10i | −0.0674825 | − | 0.116883i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 5.91321e10i | − | 0.395059i | ||||||
\(623\) | −3.62373e10 | + | 6.18808e10i | −0.240549 | + | 0.410775i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.07074e10 | − | 8.78278e10i | 0.332316 | − | 0.575588i | ||||
\(626\) | 9.63355e10 | − | 5.56193e10i | 0.627320 | − | 0.362183i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.65542e10 | − | 3.26516e10i | −0.363602 | − | 0.209926i | ||||
\(629\) | 1.73648e11i | 1.10935i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.09578e11 | −0.691204 | −0.345602 | − | 0.938381i | \(-0.612325\pi\) | ||||
−0.345602 | + | 0.938381i | \(0.612325\pi\) | |||||||
\(632\) | 2.33883e10 | − | 4.05098e10i | 0.146599 | − | 0.253917i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.22310e10 | − | 3.85052e10i | −0.137595 | − | 0.238321i | ||||
\(635\) | 8.84479e10 | + | 5.10654e10i | 0.543992 | + | 0.314074i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.34532e9 | + | 2.71366e11i | −0.0203180 | + | 1.64816i | ||||
\(638\) | 1.49473e10 | 0.0902152 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.93281e10 | + | 1.11591e10i | −0.115204 | + | 0.0665132i | ||||
\(641\) | 1.02428e11 | + | 1.77410e11i | 0.606718 | + | 1.05087i | 0.991778 | + | 0.127974i | \(0.0408474\pi\) |
−0.385060 | + | 0.922892i | \(0.625819\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.78587e11i | − | 1.04474i | −0.852720 | − | 0.522369i | \(-0.825049\pi\) | ||
0.852720 | − | 0.522369i | \(-0.174951\pi\) | |||||||
\(644\) | 5.14199e8 | − | 8.34250e10i | 0.00298943 | − | 0.485012i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.50960e10 | − | 1.47391e11i | 0.488629 | − | 0.846330i | ||||
\(647\) | 1.20405e10 | − | 6.95156e9i | 0.0687109 | − | 0.0396703i | −0.465251 | − | 0.885179i | \(-0.654036\pi\) |
0.533962 | + | 0.845509i | \(0.320703\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.19616e10 | + | 6.90605e9i | 0.0674235 | + | 0.0389270i | ||||
\(650\) | 2.63204e11i | 1.47448i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.44320e10 | 0.135197 | ||||||||
\(653\) | 1.33723e11 | − | 2.31615e11i | 0.735452 | − | 1.27384i | −0.219073 | − | 0.975708i | \(-0.570303\pi\) |
0.954525 | − | 0.298131i | \(-0.0963633\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.37798e10 | − | 1.10470e11i | −0.346512 | − | 0.600176i | ||||
\(656\) | −2.10463e10 | − | 1.21511e10i | −0.113648 | − | 0.0656146i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.25627e11 | − | 2.20722e11i | −0.670159 | − | 1.17745i | ||||
\(659\) | 2.98246e11 | 1.58137 | 0.790684 | − | 0.612225i | \(-0.209725\pi\) | ||||
0.790684 | + | 0.612225i | \(0.209725\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.89538e10 | + | 3.98105e10i | −0.361204 | + | 0.208541i | −0.669609 | − | 0.742714i | \(-0.733538\pi\) |
0.308405 | + | 0.951255i | \(0.400205\pi\) | |||||||
\(662\) | 7.52503e10 | + | 1.30337e11i | 0.391810 | + | 0.678636i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 9.45870e10i | − | 0.486586i | ||||||
\(665\) | −4.61046e11 | + | 2.62410e11i | −2.35753 | + | 1.34182i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.71667e11 | − | 2.97337e11i | 0.867331 | − | 1.50226i | ||||
\(668\) | 1.52331e11 | − | 8.79486e10i | 0.765039 | − | 0.441696i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.60526e11 | − | 9.26796e10i | −0.796610 | − | 0.459923i | ||||
\(671\) | − | 1.46750e10i | − | 0.0723918i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.67506e11 | 1.30398 | 0.651992 | − | 0.758226i | \(-0.273933\pi\) | ||||
0.651992 | + | 0.758226i | \(0.273933\pi\) | |||||||
\(674\) | −8.69089e10 | + | 1.50531e11i | −0.421138 | + | 0.729433i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.96303e10 | + | 1.55244e11i | 0.429208 | + | 0.743410i | ||||
\(677\) | 2.29678e11 | + | 1.32605e11i | 1.09336 | + | 0.631254i | 0.934470 | − | 0.356041i | \(-0.115874\pi\) |
0.158894 | + | 0.987296i | \(0.449207\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.29729e11 | − | 7.99597e8i | −0.610319 | − | 0.00376177i | ||||
\(680\) | 8.72384e10 | 0.408011 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.69524e9 | + | 9.78749e8i | −0.00783600 | + | 0.00452412i | ||||
\(683\) | −1.38922e11 | − | 2.40619e11i | −0.638391 | − | 1.10573i | −0.985786 | − | 0.168007i | \(-0.946267\pi\) |
0.347394 | − | 0.937719i | \(-0.387067\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.21909e11i | 2.37046i | ||||||||
\(686\) | −1.34145e11 | − | 8.07922e10i | −0.605731 | − | 0.364815i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.60977e9 | − | 1.31805e10i | 0.0339639 | − | 0.0588272i | ||||
\(689\) | −3.77496e10 | + | 2.17948e10i | −0.167508 | + | 0.0967108i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.28031e11 | + | 1.31654e11i | 1.00019 | + | 0.577459i | 0.908304 | − | 0.418311i | \(-0.137378\pi\) |
0.0918837 | + | 0.995770i | \(0.470711\pi\) | |||||||
\(692\) | − | 1.51026e11i | − | 0.658608i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.19921e10 | 0.137913 | ||||||||
\(695\) | −3.34825e10 | + | 5.79933e10i | −0.143509 | + | 0.248564i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.74969e10 | + | 8.22671e10i | 0.201249 | + | 0.348574i | ||||
\(698\) | −1.84636e11 | − | 1.06599e11i | −0.777846 | − | 0.449090i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.31057e11 | − | 7.67464e10i | −0.545842 | − | 0.319644i | ||||
\(701\) | 3.04779e11 | 1.26216 | 0.631078 | − | 0.775719i | \(-0.282613\pi\) | ||||
0.631078 | + | 0.775719i | \(0.282613\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.51563e11 | − | 3.18445e11i | 2.25826 | − | 1.30381i | ||||
\(704\) | 1.09532e9 | + | 1.89715e9i | 0.00445914 | + | 0.00772345i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.56709e11i | 0.630776i | ||||||||
\(707\) | 1.16288e11 | + | 2.04315e11i | 0.465434 | + | 0.817755i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.59806e11 | − | 2.76793e11i | 0.632425 | − | 1.09539i | −0.354629 | − | 0.935007i | \(-0.615393\pi\) |
0.987054 | − | 0.160386i | \(-0.0512737\pi\) | |||||||
\(710\) | 4.91939e10 | − | 2.84021e10i | 0.193588 | − | 0.111768i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.74572e10 | − | 2.16259e10i | −0.145752 | − | 0.0841501i | ||||
\(713\) | 4.49632e10i | 0.173980i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.62562e10 | 0.176989 | ||||||||
\(716\) | −9.29606e10 | + | 1.61012e11i | −0.353709 | + | 0.612643i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.30630e10 | + | 5.72668e10i | 0.124407 | + | 0.215479i | ||||
\(719\) | 3.85186e10 | + | 2.22387e10i | 0.144130 | + | 0.0832136i | 0.570331 | − | 0.821415i | \(-0.306815\pi\) |
−0.426201 | + | 0.904629i | \(0.640148\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.29959e11 | + | 3.92691e11i | −0.850961 | + | 1.45315i | ||||
\(722\) | −4.32067e11 | −1.59002 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.89608e10 | + | 2.24940e10i | −0.141799 | + | 0.0818679i | ||||
\(725\) | −3.12513e11 | − | 5.41289e11i | −1.13114 | − | 1.95919i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.83129e10i | − | 0.172952i | −0.996254 | − | 0.0864760i | \(-0.972439\pi\) | ||
0.996254 | − | 0.0864760i | \(-0.0275606\pi\) | |||||||
\(728\) | −1.63683e11 | − | 1.00888e9i | −0.582745 | − | 0.00359181i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.81412e11 | + | 3.14214e11i | −0.638813 | + | 1.10646i | ||||
\(731\) | −5.15207e10 | + | 2.97455e10i | −0.180432 | + | 0.104172i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.14347e10 | − | 4.12428e10i | −0.247453 | − | 0.142867i | 0.371144 | − | 0.928575i | \(-0.378966\pi\) |
−0.618598 | + | 0.785708i | \(0.712299\pi\) | |||||||
\(734\) | 5.91728e10i | 0.203863i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.03185e10 | 0.171481 | ||||||||
\(737\) | −9.09699e9 | + | 1.57564e10i | −0.0308339 | + | 0.0534058i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.42038e11 | + | 4.19222e11i | 0.811532 | + | 1.40561i | 0.911792 | + | 0.410653i | \(0.134699\pi\) |
−0.100260 | + | 0.994961i | \(0.531968\pi\) | |||||||
\(740\) | 2.82725e11 | + | 1.63231e11i | 0.942838 | + | 0.544348i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.55025e8 | − | 2.51516e10i | 0.000511429 | − | 0.0829756i | ||||
\(743\) | −1.64425e11 | −0.539527 | −0.269763 | − | 0.962927i | \(-0.586945\pi\) | ||||
−0.269763 | + | 0.962927i | \(0.586945\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.31883e11 | + | 1.33878e11i | −0.752738 | + | 0.434594i | ||||
\(746\) | −7.19338e10 | − | 1.24593e11i | −0.232262 | − | 0.402289i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 8.56291e9i | − | 0.0273536i | ||||||
\(749\) | 1.26935e11 | + | 7.43327e10i | 0.403323 | + | 0.236185i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.10159e11 | − | 3.64006e11i | 0.660675 | − | 1.14432i | −0.319763 | − | 0.947498i | \(-0.603603\pi\) |
0.980438 | − | 0.196826i | \(-0.0630633\pi\) | |||||||
\(752\) | 1.32658e11 | − | 7.65903e10i | 0.414823 | − | 0.239498i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.83386e11 | − | 3.36818e11i | −1.80497 | − | 1.04210i | ||||
\(755\) | − | 4.82550e11i | − | 1.48510i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.03317e11 | −0.619143 | −0.309572 | − | 0.950876i | \(-0.600186\pi\) | ||||
−0.309572 | + | 0.950876i | \(0.600186\pi\) | |||||||
\(758\) | 9.01040e10 | − | 1.56065e11i | 0.272940 | − | 0.472746i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.59982e11 | − | 2.77098e11i | −0.479532 | − | 0.830574i | ||||
\(761\) | 1.16599e11 | + | 6.73185e10i | 0.347661 | + | 0.200722i | 0.663655 | − | 0.748039i | \(-0.269004\pi\) |
−0.315993 | + | 0.948761i | \(0.602338\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.78266e11 | − | 1.58378e11i | 0.821035 | − | 0.467301i | ||||
\(764\) | −3.66507e10 | −0.107574 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.58238e10 | + | 2.06829e10i | −0.104053 | + | 0.0600753i | ||||
\(767\) | −3.11238e11 | − | 5.39080e11i | −0.899314 | − | 1.55766i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.56622e11i | − | 0.733817i | −0.930257 | − | 0.366909i | \(-0.880416\pi\) | ||
0.930257 | − | 0.366909i | \(-0.119584\pi\) | |||||||
\(770\) | −1.34876e10 | + | 2.30322e10i | −0.0383683 | + | 0.0655199i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.05438e10 | − | 3.55829e10i | 0.0578378 | − | 0.100178i | ||||
\(773\) | 1.03389e11 | − | 5.96919e10i | 0.289573 | − | 0.167185i | −0.348176 | − | 0.937429i | \(-0.613199\pi\) |
0.637749 | + | 0.770244i | \(0.279866\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.08872e10 | + | 4.09268e10i | 0.196499 | + | 0.113449i | ||||
\(776\) | − | 7.82468e10i | − | 0.215784i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.27449e11 | −0.347872 | ||||||||
\(779\) | 1.74205e11 | − | 3.01731e11i | 0.473053 | − | 0.819352i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.78782e9 | − | 4.82864e9i | −0.00749308 | − | 0.0129784i | ||||
\(782\) | −1.70337e11 | − | 9.83439e10i | −0.455492 | − | 0.262979i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.82299e10 | − | 8.12082e10i | 0.127659 | − | 0.214949i | ||||
\(785\) | 4.79896e11 | 1.26377 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.33037e11 | + | 1.34544e11i | −0.607472 | + | 0.350724i | −0.771975 | − | 0.635652i | \(-0.780731\pi\) |
0.164503 | + | 0.986377i | \(0.447398\pi\) | |||||||
\(788\) | −6.38107e10 | − | 1.10523e11i | −0.165497 | − | 0.286648i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.43750e11i | 0.882539i | ||||||||
\(791\) | 3.95145e9 | − | 6.41094e11i | 0.0100937 | − | 1.63763i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.30684e11 | + | 5.72761e11i | −0.836219 | + | 1.44837i | ||||
\(794\) | 3.09004e11 | − | 1.78404e11i | 0.777468 | − | 0.448872i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.15638e10 | − | 6.67634e9i | −0.0288036 | − | 0.0166298i | ||||
\(797\) | 6.65272e11i | 1.64879i | 0.566013 | + | 0.824396i | \(0.308485\pi\) | ||||
−0.566013 | + | 0.824396i | \(0.691515\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.98761e11 | −1.46915 | ||||||||
\(800\) | 4.58013e10 | − | 7.93301e10i | 0.111820 | − | 0.193677i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.14990e11 | − | 3.72374e11i | −0.519662 | − | 0.900082i | ||||
\(803\) | 3.08418e10 | + | 1.78065e10i | 0.0741783 | + | 0.0428269i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.03262e11 | + | 5.32823e11i | 0.722162 | + | 1.26882i | ||||
\(806\) | 8.82195e10 | 0.209038 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.22797e11 | + | 7.08971e10i | −0.288100 | + | 0.166335i | ||||
\(809\) | −5.08703e10 | − | 8.81100e10i | −0.118760 | − | 0.205699i | 0.800516 | − | 0.599311i | \(-0.204559\pi\) |
−0.919277 | + | 0.393612i | \(0.871225\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6.79465e11i | − | 1.57067i | −0.619074 | − | 0.785333i | \(-0.712492\pi\) | ||
0.619074 | − | 0.785333i | \(-0.287508\pi\) | |||||||
\(812\) | 3.37818e11 | − | 1.92273e11i | 0.777068 | − | 0.442277i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.60220e10 | − | 2.77509e10i | 0.0364938 | − | 0.0632092i | ||||
\(815\) | −1.55490e11 | + | 8.97722e10i | −0.352429 | + | 0.203475i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.88963e11 | + | 1.09098e11i | 0.424119 | + | 0.244865i | ||||
\(818\) | 1.29121e11i | 0.288391i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.78591e11 | 0.395006 | ||||||||
\(821\) | 8.29553e10 | − | 1.43683e11i | 0.182588 | − | 0.316251i | −0.760173 | − | 0.649720i | \(-0.774886\pi\) |
0.942761 | + | 0.333469i | \(0.108219\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.01168e11 | − | 3.48433e11i | −0.438489 | − | 0.759485i | 0.559084 | − | 0.829111i | \(-0.311153\pi\) |
−0.997573 | + | 0.0696256i | \(0.977820\pi\) | |||||||
\(824\) | −2.37701e11 | − | 1.37237e11i | −0.515610 | − | 0.297688i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.59176e11 | + | 2.21382e9i | 0.771590 | + | 0.00475578i | ||||
\(827\) | −7.25185e11 | −1.55034 | −0.775170 | − | 0.631753i | \(-0.782336\pi\) | ||||
−0.775170 | + | 0.631753i | \(0.782336\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.13337e11 | − | 2.38640e11i | 0.875158 | − | 0.505273i | 0.00609923 | − | 0.999981i | \(-0.498059\pi\) |
0.869059 | + | 0.494709i | \(0.164725\pi\) | |||||||
\(830\) | 3.47548e11 | + | 6.01971e11i | 0.732322 | + | 1.26842i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 9.87267e10i | − | 0.206035i | ||||||
\(833\) | −3.21982e11 | + | 1.80642e11i | −0.668732 | + | 0.375178i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.46312e11 | + | 1.11944e12i | −1.32952 | + | 2.30280i | ||||
\(836\) | −2.71986e10 | + | 1.57031e10i | −0.0556828 | + | 0.0321485i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.90804e10 | − | 3.98836e10i | −0.140081 | − | 0.0808758i | ||||
\(839\) | 4.84023e11i | 0.976828i | 0.872612 | + | 0.488414i | \(0.162424\pi\) | ||||
−0.872612 | + | 0.488414i | \(0.837576\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.09943e12 | 2.19777 | ||||||||
\(842\) | 1.78457e11 | − | 3.09097e11i | 0.355047 | − | 0.614959i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.57380e10 | + | 6.19001e10i | 0.0704305 | + | 0.121989i | ||||
\(845\) | −1.14085e12 | − | 6.58670e11i | −2.23770 | − | 1.29194i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.41867e11 | − | 2.58756e11i | −0.858535 | − | 0.502756i | ||||
\(848\) | 1.51704e10 | 0.0293369 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.10090e11 | + | 1.79031e11i | −0.594035 | + | 0.342967i | ||||
\(851\) | −3.68021e11 | − | 6.37431e11i | −0.701705 | − | 1.21539i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.15896e10i | 0.0974464i | 0.998812 | + | 0.0487232i | \(0.0155152\pi\) | ||||
−0.998812 | + | 0.0487232i | \(0.984485\pi\) | |||||||
\(854\) | −1.88771e11 | − | 3.31665e11i | −0.354898 | − | 0.623546i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.43608e10 | + | 7.68352e10i | −0.0826236 | + | 0.143108i | ||||
\(857\) | 7.06025e11 | − | 4.07624e11i | 1.30887 | − | 0.755677i | 0.326963 | − | 0.945037i | \(-0.393975\pi\) |
0.981908 | + | 0.189360i | \(0.0606414\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.78407e11 | + | 2.76208e11i | 0.878667 | + | 0.507299i | 0.870219 | − | 0.492666i | \(-0.163977\pi\) |
0.00844851 | + | 0.999964i | \(0.497311\pi\) | |||||||
\(860\) | 1.11844e11i | 0.204466i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.62923e11 | 0.657334 | ||||||||
\(863\) | −1.19370e11 | + | 2.06755e11i | −0.215205 | + | 0.372746i | −0.953336 | − | 0.301912i | \(-0.902375\pi\) |
0.738131 | + | 0.674657i | \(0.235709\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.54926e11 | + | 9.61159e11i | 0.991221 | + | 1.71684i | ||||
\(866\) | −2.24209e11 | − | 1.29447e11i | −0.398641 | − | 0.230156i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.57235e10 | + | 4.39269e10i | −0.0453160 | + | 0.0773842i | ||||
\(869\) | 3.37408e10 | 0.0591666 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.10103e11 | − | 4.09978e11i | 1.23381 | − | 0.712342i | ||||
\(872\) | 9.65579e10 | + | 1.67243e11i | 0.167002 | + | 0.289256i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.21392e11i | 1.23631i | ||||||||
\(875\) | 2.33865e11 | + | 1.44145e9i | 0.398964 | + | 0.00245906i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.70803e10 | − | 6.42249e10i | 0.0626822 | − | 0.108569i | −0.832981 | − | 0.553301i | \(-0.813368\pi\) |
0.895664 | + | 0.444732i | \(0.146701\pi\) | |||||||
\(878\) | 3.32502e10 | − | 1.91970e10i | 0.0559521 | − | 0.0323039i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.39417e10 | − | 8.04924e9i | −0.0232479 | − | 0.0134222i | ||||
\(881\) | − | 1.01123e12i | − | 1.67860i | −0.543669 | − | 0.839300i | \(-0.682965\pi\) | ||
0.543669 | − | 0.839300i | \(-0.317035\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.12397e11 | −1.50086 | −0.750432 | − | 0.660948i | \(-0.770154\pi\) | ||||
−0.750432 | + | 0.660948i | \(0.770154\pi\) | |||||||
\(884\) | −1.92954e11 | + | 3.34207e11i | −0.315970 | + | 0.547276i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.92495e11 | − | 5.06615e11i | −0.474660 | − | 0.822136i | ||||
\(887\) | 8.38886e11 | + | 4.84331e11i | 1.35522 | + | 0.782434i | 0.988974 | − | 0.148086i | \(-0.0473113\pi\) |
0.366241 | + | 0.930520i | \(0.380645\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.60677e9 | − | 2.60686e11i | 0.00257244 | − | 0.417360i | ||||
\(890\) | 3.17847e11 | 0.506591 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.63178e11 | + | 9.42110e10i | −0.257752 | + | 0.148813i | ||||
\(893\) | 1.09804e12 | + | 1.90186e12i | 1.72668 | + | 2.99070i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.36629e12i | − | 2.12936i | ||||||
\(896\) | 4.91588e10 | + | 2.87873e10i | 0.0762727 | + | 0.0446651i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.83524e11 | − | 4.91078e11i | 0.435998 | − | 0.755171i | ||||
\(899\) | −1.81427e11 | + | 1.04747e11i | −0.277755 | + | 0.160362i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.13544e10 | − | 2.96495e10i | −0.0779253 | − | 0.0449902i | ||||
\(902\) | − | 1.75296e10i | − | 0.0264817i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.86681e11 | 0.579001 | ||||||||
\(905\) | 1.65303e11 | − | 2.86313e11i | 0.246426 | − | 0.426822i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.82503e11 | − | 1.00893e12i | −0.860735 | − | 1.49084i | −0.871221 | − | 0.490891i | \(-0.836671\pi\) |
0.0104860 | − | 0.999945i | \(-0.496662\pi\) | |||||||
\(908\) | −1.32837e11 | − | 7.66936e10i | −0.195423 | − | 0.112828i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.04542e12 | − | 5.95012e11i | 1.52449 | − | 0.867681i | ||||
\(911\) | 3.53799e11 | 0.513669 | 0.256835 | − | 0.966455i | \(-0.417320\pi\) | ||||
0.256835 | + | 0.966455i | \(0.417320\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.90866e10 | − | 3.41137e10i | 0.0850366 | − | 0.0490959i | ||||
\(914\) | −4.47525e11 | − | 7.75136e11i | −0.641257 | − | 1.11069i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 4.62767e9i | − | 0.00657326i | ||||||
\(917\) | −1.64534e11 | + | 2.80968e11i | −0.232690 | + | 0.397355i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.37089e11 | + | 4.10651e11i | −0.332392 | + | 0.575719i | −0.982980 | − | 0.183711i | \(-0.941189\pi\) |
0.650589 | + | 0.759430i | \(0.274522\pi\) | |||||||
\(920\) | −3.20237e11 | + | 1.84889e11i | −0.447013 | + | 0.258083i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.37284e11 | + | 7.92610e10i | 0.189975 | + | 0.109682i | ||||
\(923\) | 2.51280e11i | 0.346219i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.33993e12 | −1.83027 | ||||||||
\(926\) | −3.74423e11 | + | 6.48520e11i | −0.509235 | + | 0.882022i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.17222e11 | + | 2.03035e11i | 0.158059 | + | 0.273766i | ||||
\(929\) | −3.72827e11 | − | 2.15252e11i | −0.500546 | − | 0.288990i | 0.228393 | − | 0.973569i | \(-0.426653\pi\) |
−0.728939 | + | 0.684579i | \(0.759986\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.16424e12 | + | 6.91450e11i | 1.54969 | + | 0.920370i | ||||
\(932\) | −4.20683e11 | −0.557560 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.55864e11 | − | 2.05458e11i | 0.467623 | − | 0.269983i | ||||
\(935\) | 3.14633e10 | + | 5.44961e10i | 0.0411678 | + | 0.0713048i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.06322e12i | − | 1.37932i | −0.724134 | − | 0.689659i | \(-0.757760\pi\) | ||
0.724134 | − | 0.689659i | \(-0.242240\pi\) | |||||||
\(938\) | −2.91615e9 | + | 4.73124e11i | −0.00376703 | + | 0.611172i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.62842e11 | + | 9.74872e11i | −0.720901 | + | 1.24864i | ||||
\(941\) | −1.26165e12 | + | 7.28416e11i | −1.60910 | + | 0.929012i | −0.619523 | + | 0.784979i | \(0.712674\pi\) |
−0.989573 | + | 0.144033i | \(0.953993\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.48706e11 | − | 2.01325e11i | −0.440973 | − | 0.254596i | ||||
\(944\) | 2.16640e11i | 0.272803i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.09781e10 | 0.0137077 | ||||||||
\(947\) | −6.32117e11 | + | 1.09486e12i | −0.785954 | + | 1.36131i | 0.142473 | + | 0.989799i | \(0.454495\pi\) |
−0.928427 | + | 0.371514i | \(0.878839\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.02494e11 | − | 1.38996e12i | −0.989411 | − | 1.71371i | ||||
\(950\) | 1.13732e12 | + | 6.56632e11i | 1.39633 | + | 0.806171i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.10148e11 | − | 1.93527e11i | −0.134100 | − | 0.235610i | ||||
\(953\) | 7.86324e11 | 0.953300 | 0.476650 | − | 0.879093i | \(-0.341851\pi\) | ||||
0.476650 | + | 0.879093i | \(0.341851\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.33253e11 | − | 1.34668e11i | 0.280423 | − | 0.161902i | ||||
\(956\) | −2.39027e11 | − | 4.14006e11i | −0.286164 | − | 0.495650i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.29213e11i | 0.984474i | ||||||||
\(959\) | 1.15779e12 | − | 6.58968e11i | 1.36885 | − | 0.779094i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.12728e11 | + | 7.14866e11i | −0.483916 | + | 0.838168i | ||||
\(962\) | −1.25066e12 | + | 7.22071e11i | −1.46029 | + | 0.843102i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.46223e11 | − | 1.42157e11i | −0.285115 | − | 0.164611i | ||||
\(965\) | 3.01942e11i | 0.348189i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.31465e11 | 0.264715 | 0.132358 | − | 0.991202i | \(-0.457745\pi\) | ||||
0.132358 | + | 0.991202i | \(0.457745\pi\) | |||||||
\(968\) | 1.54422e11 | − | 2.67467e11i | 0.175877 | − | 0.304628i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.87508e11 | + | 4.97978e11i | 0.324760 | + | 0.562501i | ||||
\(971\) | 1.04667e12 | + | 6.04295e11i | 1.17742 | + | 0.679786i | 0.955417 | − | 0.295260i | \(-0.0954061\pi\) |
0.222006 | + | 0.975045i | \(0.428739\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.70926e11 | + | 1.05352e9i | 0.190703 | + | 0.00117542i | ||||
\(974\) | 8.96188e11 | 0.995780 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.99337e11 | − | 1.15087e11i | 0.219679 | − | 0.126832i | ||||
\(977\) | 5.07309e11 | + | 8.78684e11i | 0.556793 | + | 0.964394i | 0.997762 | + | 0.0668716i | \(0.0213018\pi\) |
−0.440968 | + | 0.897523i | \(0.645365\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.11983e10i | − | 0.0339626i | ||||||
\(980\) | −8.55591e9 | + | 6.94040e11i | −0.00927602 | + | 0.752454i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.18612e11 | + | 5.51851e11i | −0.342622 | + | 0.593439i | ||||
\(983\) | −2.92626e11 | + | 1.68948e11i | −0.313400 | + | 0.180942i | −0.648447 | − | 0.761260i | \(-0.724581\pi\) |
0.335047 | + | 0.942201i | \(0.391248\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.12208e11 | + | 4.68929e11i | 0.862825 | + | 0.498152i | ||||
\(986\) | − | 9.16412e11i | − | 0.969578i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.41540e12 | 1.48543 | ||||||||
\(989\) | 1.26082e11 | − | 2.18381e11i | 0.131786 | − | 0.228260i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.53859e11 | + | 9.59312e11i | 0.574255 | + | 0.994639i | 0.996122 | + | 0.0879813i | \(0.0280416\pi\) |
−0.421867 | + | 0.906658i | \(0.638625\pi\) | |||||||
\(992\) | −2.65895e10 | − | 1.53515e10i | −0.0274577 | − | 0.0158527i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.25119e11 | − | 7.32695e10i | −0.128168 | − | 0.0750547i | ||||
\(995\) | 9.81254e10 | 0.100113 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.16099e11 | + | 2.40235e11i | −0.421130 | + | 0.243139i | −0.695561 | − | 0.718468i | \(-0.744844\pi\) |
0.274431 | + | 0.961607i | \(0.411511\pi\) | |||||||
\(998\) | 1.51995e11 | + | 2.63263e11i | 0.153217 | + | 0.265379i | ||||
\(999\) | 0 | 0 |
(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 | 126.9.n.d.19.5 | ✓ | 20 | |
3.2 | odd | 2 | inner | 126.9.n.d.19.6 | yes | 20 | |
7.3 | odd | 6 | inner | 126.9.n.d.73.5 | yes | 20 | |
21.17 | even | 6 | inner | 126.9.n.d.73.6 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.9.n.d.19.5 | ✓ | 20 | 1.1 | even | 1 | trivial | |
126.9.n.d.19.6 | yes | 20 | 3.2 | odd | 2 | inner | |
126.9.n.d.73.5 | yes | 20 | 7.3 | odd | 6 | inner | |
126.9.n.d.73.6 | yes | 20 | 21.17 | even | 6 | inner |