Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,10,Mod(67,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.67");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(50.4735119441\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4 x^{7} - 4806 x^{6} + 14432 x^{5} + 8678459 x^{4} - 17380976 x^{3} - 6978412850 x^{2} + \cdots + 2108388231292 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.1 | ||
Root | \(-33.4952 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.79 |
Dual form | 98.10.c.m.67.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | − | 13.8564i | 0.353553 | − | 0.612372i | ||||
\(3\) | −95.8886 | − | 166.084i | −0.683473 | − | 1.18381i | −0.973914 | − | 0.226917i | \(-0.927135\pi\) |
0.290441 | − | 0.956893i | \(-0.406198\pi\) | |||||||
\(4\) | −128.000 | − | 221.703i | −0.250000 | − | 0.433013i | ||||
\(5\) | −16.7949 | + | 29.0896i | −0.0120175 | + | 0.0208148i | −0.871972 | − | 0.489556i | \(-0.837159\pi\) |
0.859954 | + | 0.510371i | \(0.170492\pi\) | |||||||
\(6\) | −3068.43 | −0.966576 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | −8547.74 | + | 14805.1i | −0.434270 | + | 0.752178i | ||||
\(10\) | 268.719 | + | 465.434i | 0.00849763 | + | 0.0147183i | ||||
\(11\) | 25770.2 | + | 44635.3i | 0.530702 | + | 0.919202i | 0.999358 | + | 0.0358219i | \(0.0114049\pi\) |
−0.468656 | + | 0.883381i | \(0.655262\pi\) | |||||||
\(12\) | −24547.5 | + | 42517.5i | −0.341736 | + | 0.591905i | ||||
\(13\) | 113303. | 1.10026 | 0.550129 | − | 0.835080i | \(-0.314579\pi\) | ||||
0.550129 | + | 0.835080i | \(0.314579\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6441.76 | 0.0328544 | ||||||||
\(16\) | −32768.0 | + | 56755.8i | −0.125000 | + | 0.216506i | ||||
\(17\) | 230833. | + | 399815.i | 0.670314 | + | 1.16102i | 0.977815 | + | 0.209470i | \(0.0671739\pi\) |
−0.307501 | + | 0.951548i | \(0.599493\pi\) | |||||||
\(18\) | 136764. | + | 236882.i | 0.307075 | + | 0.531870i | ||||
\(19\) | 418329. | − | 724566.i | 0.736421 | − | 1.27552i | −0.217676 | − | 0.976021i | \(-0.569848\pi\) |
0.954097 | − | 0.299498i | \(-0.0968191\pi\) | |||||||
\(20\) | 8598.99 | 0.0120175 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 824646. | 0.750526 | ||||||||
\(23\) | −149702. | + | 259291.i | −0.111546 | + | 0.193202i | −0.916394 | − | 0.400278i | \(-0.868913\pi\) |
0.804848 | + | 0.593481i | \(0.202247\pi\) | |||||||
\(24\) | 392760. | + | 680280.i | 0.241644 | + | 0.418540i | ||||
\(25\) | 975998. | + | 1.69048e6i | 0.499711 | + | 0.865525i | ||||
\(26\) | 906420. | − | 1.56997e6i | 0.389000 | − | 0.673768i | ||||
\(27\) | −496229. | −0.179699 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.58319e6 | 0.678213 | 0.339106 | − | 0.940748i | \(-0.389875\pi\) | ||||
0.339106 | + | 0.940748i | \(0.389875\pi\) | |||||||
\(30\) | 51534.1 | − | 89259.6i | 0.0116158 | − | 0.0201191i | ||||
\(31\) | 3.42162e6 | + | 5.92642e6i | 0.665433 | + | 1.15256i | 0.979168 | + | 0.203053i | \(0.0650862\pi\) |
−0.313735 | + | 0.949511i | \(0.601580\pi\) | |||||||
\(32\) | 524288. | + | 908093.i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 4.94213e6 | − | 8.56003e6i | 0.725440 | − | 1.25650i | ||||
\(34\) | 7.38666e6 | 0.947967 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.37644e6 | 0.434270 | ||||||||
\(37\) | −6.97734e6 | + | 1.20851e7i | −0.612043 | + | 1.06009i | 0.378853 | + | 0.925457i | \(0.376319\pi\) |
−0.990896 | + | 0.134632i | \(0.957015\pi\) | |||||||
\(38\) | −6.69326e6 | − | 1.15931e7i | −0.520728 | − | 0.901928i | ||||
\(39\) | −1.08644e7 | − | 1.88177e7i | −0.751996 | − | 1.30250i | ||||
\(40\) | 68791.9 | − | 119151.i | 0.00424881 | − | 0.00735916i | ||||
\(41\) | 2.22245e7 | 1.22830 | 0.614151 | − | 0.789188i | \(-0.289498\pi\) | ||||
0.614151 | + | 0.789188i | \(0.289498\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.24518e7 | −1.44754 | −0.723770 | − | 0.690042i | \(-0.757592\pi\) | ||||
−0.723770 | + | 0.690042i | \(0.757592\pi\) | |||||||
\(44\) | 6.59717e6 | − | 1.14266e7i | 0.265351 | − | 0.459601i | ||||
\(45\) | −287117. | − | 497301.i | −0.0104376 | − | 0.0180785i | ||||
\(46\) | 2.39523e6 | + | 4.14866e6i | 0.0788746 | + | 0.136615i | ||||
\(47\) | 1.59026e6 | − | 2.75442e6i | 0.0475367 | − | 0.0823360i | −0.841278 | − | 0.540603i | \(-0.818196\pi\) |
0.888815 | + | 0.458267i | \(0.151530\pi\) | |||||||
\(48\) | 1.25683e7 | 0.341736 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.12319e7 | 0.706698 | ||||||||
\(51\) | 4.42685e7 | − | 7.66754e7i | 0.916283 | − | 1.58705i | ||||
\(52\) | −1.45027e7 | − | 2.51195e7i | −0.275065 | − | 0.476426i | ||||
\(53\) | −4.41456e7 | − | 7.64625e7i | −0.768504 | − | 1.33109i | −0.938374 | − | 0.345622i | \(-0.887668\pi\) |
0.169870 | − | 0.985467i | \(-0.445665\pi\) | |||||||
\(54\) | −3.96983e6 | + | 6.87595e6i | −0.0635331 | + | 0.110043i | ||||
\(55\) | −1.73123e6 | −0.0255107 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.60452e8 | −2.01330 | ||||||||
\(58\) | 2.06656e7 | − | 3.57938e7i | 0.239784 | − | 0.415319i | ||||
\(59\) | 6.99559e6 | + | 1.21167e7i | 0.0751606 | + | 0.130182i | 0.901156 | − | 0.433495i | \(-0.142720\pi\) |
−0.825995 | + | 0.563677i | \(0.809386\pi\) | |||||||
\(60\) | −824545. | − | 1.42815e6i | −0.00821360 | − | 0.0142264i | ||||
\(61\) | 5.69654e7 | − | 9.86669e7i | 0.526777 | − | 0.912404i | −0.472736 | − | 0.881204i | \(-0.656734\pi\) |
0.999513 | − | 0.0312003i | \(-0.00993298\pi\) | |||||||
\(62\) | 1.09492e8 | 0.941064 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | −1.90291e6 | + | 3.29593e6i | −0.0132223 | + | 0.0229017i | ||||
\(66\) | −7.90741e7 | − | 1.36960e8i | −0.512964 | − | 0.888479i | ||||
\(67\) | 1.52746e8 | + | 2.64565e8i | 0.926050 | + | 1.60397i | 0.789863 | + | 0.613283i | \(0.210152\pi\) |
0.136187 | + | 0.990683i | \(0.456515\pi\) | |||||||
\(68\) | 5.90933e7 | − | 1.02353e8i | 0.335157 | − | 0.580509i | ||||
\(69\) | 5.74188e7 | 0.304953 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.86664e8 | −1.33878 | −0.669392 | − | 0.742909i | \(-0.733445\pi\) | ||||
−0.669392 | + | 0.742909i | \(0.733445\pi\) | |||||||
\(72\) | 3.50115e7 | − | 6.06417e7i | 0.153538 | − | 0.265935i | ||||
\(73\) | −2.39428e7 | − | 4.14702e7i | −0.0986785 | − | 0.170916i | 0.812459 | − | 0.583018i | \(-0.198128\pi\) |
−0.911138 | + | 0.412102i | \(0.864795\pi\) | |||||||
\(74\) | 1.11637e8 | + | 1.93362e8i | 0.432780 | + | 0.749596i | ||||
\(75\) | 1.87174e8 | − | 3.24195e8i | 0.683078 | − | 1.18313i | ||||
\(76\) | −2.14184e8 | −0.736421 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.47661e8 | −1.06348 | ||||||||
\(79\) | 5.37908e7 | − | 9.31683e7i | 0.155377 | − | 0.269120i | −0.777819 | − | 0.628488i | \(-0.783674\pi\) |
0.933196 | + | 0.359367i | \(0.117008\pi\) | |||||||
\(80\) | −1.10067e6 | − | 1.90642e6i | −0.00300436 | − | 0.00520371i | ||||
\(81\) | 2.15828e8 | + | 3.73825e8i | 0.557089 | + | 0.964907i | ||||
\(82\) | 1.77796e8 | − | 3.07952e8i | 0.434271 | − | 0.752179i | ||||
\(83\) | 5.67595e7 | 0.131277 | 0.0656383 | − | 0.997843i | \(-0.479092\pi\) | ||||
0.0656383 | + | 0.997843i | \(0.479092\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.55073e7 | −0.0322219 | ||||||||
\(86\) | −2.59614e8 | + | 4.49665e8i | −0.511782 | + | 0.886433i | ||||
\(87\) | −2.47699e8 | − | 4.29027e8i | −0.463540 | − | 0.802875i | ||||
\(88\) | −1.05555e8 | − | 1.82826e8i | −0.187631 | − | 0.324987i | ||||
\(89\) | 4.24334e8 | − | 7.34969e8i | 0.716891 | − | 1.24169i | −0.245334 | − | 0.969438i | \(-0.578898\pi\) |
0.962226 | − | 0.272253i | \(-0.0877689\pi\) | |||||||
\(90\) | −9.18774e6 | −0.0147611 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.66474e7 | 0.111546 | ||||||||
\(93\) | 6.56188e8 | − | 1.13655e9i | 0.909610 | − | 1.57549i | ||||
\(94\) | −2.54442e7 | − | 4.40707e7i | −0.0336135 | − | 0.0582203i | ||||
\(95\) | 1.40516e7 | + | 2.43380e7i | 0.0176998 | + | 0.0306570i | ||||
\(96\) | 1.00546e8 | − | 1.74152e8i | 0.120822 | − | 0.209270i | ||||
\(97\) | 8.99384e8 | 1.03151 | 0.515754 | − | 0.856737i | \(-0.327512\pi\) | ||||
0.515754 | + | 0.856737i | \(0.327512\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.81107e8 | −0.921871 | ||||||||
\(100\) | 2.49856e8 | − | 4.32763e8i | 0.249856 | − | 0.432763i | ||||
\(101\) | −3.16101e7 | − | 5.47503e7i | −0.0302259 | − | 0.0523529i | 0.850517 | − | 0.525948i | \(-0.176289\pi\) |
−0.880743 | + | 0.473595i | \(0.842956\pi\) | |||||||
\(102\) | −7.08297e8 | − | 1.22681e9i | −0.647910 | − | 1.12221i | ||||
\(103\) | −6.07898e8 | + | 1.05291e9i | −0.532185 | + | 0.921772i | 0.467108 | + | 0.884200i | \(0.345296\pi\) |
−0.999294 | + | 0.0375722i | \(0.988038\pi\) | |||||||
\(104\) | −4.64087e8 | −0.389000 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.41266e9 | −1.08683 | ||||||||
\(107\) | 6.41212e8 | − | 1.11061e9i | 0.472906 | − | 0.819097i | −0.526613 | − | 0.850105i | \(-0.676538\pi\) |
0.999519 | + | 0.0310082i | \(0.00987180\pi\) | |||||||
\(108\) | 6.35173e7 | + | 1.10015e8i | 0.0449247 | + | 0.0778118i | ||||
\(109\) | 2.53284e8 | + | 4.38700e8i | 0.171865 | + | 0.297679i | 0.939072 | − | 0.343721i | \(-0.111687\pi\) |
−0.767207 | + | 0.641400i | \(0.778354\pi\) | |||||||
\(110\) | −1.38499e7 | + | 2.39887e7i | −0.00901941 | + | 0.0156221i | ||||
\(111\) | 2.67619e9 | 1.67326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.15512e9 | 0.666462 | 0.333231 | − | 0.942845i | \(-0.391861\pi\) | ||||
0.333231 | + | 0.942845i | \(0.391861\pi\) | |||||||
\(114\) | −1.28361e9 | + | 2.22328e9i | −0.711807 | + | 1.23289i | ||||
\(115\) | −5.02846e6 | − | 8.70955e6i | −0.00268099 | − | 0.00464361i | ||||
\(116\) | −3.30649e8 | − | 5.72701e8i | −0.169553 | − | 0.293675i | ||||
\(117\) | −9.68480e8 | + | 1.67746e9i | −0.477809 | + | 0.827590i | ||||
\(118\) | 2.23859e8 | 0.106293 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.63854e7 | −0.0116158 | ||||||||
\(121\) | −1.49232e8 | + | 2.58477e8i | −0.0632888 | + | 0.109619i | ||||
\(122\) | −9.11446e8 | − | 1.57867e9i | −0.372487 | − | 0.645167i | ||||
\(123\) | −2.13108e9 | − | 3.69114e9i | −0.839511 | − | 1.45408i | ||||
\(124\) | 8.75935e8 | − | 1.51716e9i | 0.332716 | − | 0.576282i | ||||
\(125\) | −1.31172e8 | −0.0480559 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.41280e9 | 1.16411 | 0.582055 | − | 0.813150i | \(-0.302249\pi\) | ||||
0.582055 | + | 0.813150i | \(0.302249\pi\) | |||||||
\(128\) | 1.34218e8 | − | 2.32472e8i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 3.11175e9 | + | 5.38972e9i | 0.989354 | + | 1.71361i | ||||
\(130\) | 3.04465e7 | + | 5.27349e7i | 0.00934958 | + | 0.0161940i | ||||
\(131\) | −3.58994e8 | + | 6.21795e8i | −0.106504 | + | 0.184470i | −0.914352 | − | 0.404921i | \(-0.867299\pi\) |
0.807848 | + | 0.589391i | \(0.200632\pi\) | |||||||
\(132\) | −2.53037e9 | −0.725440 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.88789e9 | 1.30963 | ||||||||
\(135\) | 8.33412e6 | − | 1.44351e7i | 0.00215952 | − | 0.00374040i | ||||
\(136\) | −9.45493e8 | − | 1.63764e9i | −0.236992 | − | 0.410482i | ||||
\(137\) | 3.65685e9 | + | 6.33385e9i | 0.886880 | + | 1.53612i | 0.843544 | + | 0.537061i | \(0.180465\pi\) |
0.0433362 | + | 0.999061i | \(0.486201\pi\) | |||||||
\(138\) | 4.59350e8 | − | 7.95618e8i | 0.107817 | − | 0.186745i | ||||
\(139\) | −4.88666e9 | −1.11031 | −0.555157 | − | 0.831746i | \(-0.687342\pi\) | ||||
−0.555157 | + | 0.831746i | \(0.687342\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.09953e8 | −0.129960 | ||||||||
\(142\) | −2.29331e9 | + | 3.97213e9i | −0.473332 | + | 0.819834i | ||||
\(143\) | 2.91983e9 | + | 5.05729e9i | 0.583909 | + | 1.01136i | ||||
\(144\) | −5.60184e8 | − | 9.70268e8i | −0.108567 | − | 0.188044i | ||||
\(145\) | −4.33845e7 | + | 7.51442e7i | −0.00815039 | + | 0.0141169i | ||||
\(146\) | −7.66170e8 | −0.139552 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.57240e9 | 0.612043 | ||||||||
\(149\) | −3.45145e9 | + | 5.97808e9i | −0.573671 | + | 0.993627i | 0.422514 | + | 0.906356i | \(0.361148\pi\) |
−0.996185 | + | 0.0872706i | \(0.972186\pi\) | |||||||
\(150\) | −2.99479e9 | − | 5.18712e9i | −0.483009 | − | 0.836596i | ||||
\(151\) | 2.82774e9 | + | 4.89778e9i | 0.442632 | + | 0.766660i | 0.997884 | − | 0.0650215i | \(-0.0207116\pi\) |
−0.555252 | + | 0.831682i | \(0.687378\pi\) | |||||||
\(152\) | −1.71347e9 | + | 2.96782e9i | −0.260364 | + | 0.450964i | ||||
\(153\) | −7.89241e9 | −1.16439 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.29863e8 | −0.0319872 | ||||||||
\(156\) | −2.78129e9 | + | 4.81734e9i | −0.375998 | + | 0.651248i | ||||
\(157\) | 3.29987e9 | + | 5.71555e9i | 0.433460 | + | 0.750775i | 0.997169 | − | 0.0751991i | \(-0.0239592\pi\) |
−0.563709 | + | 0.825974i | \(0.690626\pi\) | |||||||
\(158\) | −8.60652e8 | − | 1.49069e9i | −0.109868 | − | 0.190297i | ||||
\(159\) | −8.46612e9 | + | 1.46638e10i | −1.05050 | + | 1.81952i | ||||
\(160\) | −3.52215e7 | −0.00424881 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 6.90649e9 | 0.787843 | ||||||||
\(163\) | 3.99398e9 | − | 6.91778e9i | 0.443162 | − | 0.767578i | −0.554761 | − | 0.832010i | \(-0.687190\pi\) |
0.997922 | + | 0.0644317i | \(0.0205235\pi\) | |||||||
\(164\) | −2.84474e9 | − | 4.92724e9i | −0.307076 | − | 0.531871i | ||||
\(165\) | 1.66005e8 | + | 2.87530e8i | 0.0174359 | + | 0.0301999i | ||||
\(166\) | 4.54076e8 | − | 7.86483e8i | 0.0464133 | − | 0.0803902i | ||||
\(167\) | 4.34905e9 | 0.432683 | 0.216342 | − | 0.976318i | \(-0.430588\pi\) | ||||
0.216342 | + | 0.976318i | \(0.430588\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.23297e9 | 0.210568 | ||||||||
\(170\) | −1.24058e8 | + | 2.14875e8i | −0.0113922 | + | 0.0197318i | ||||
\(171\) | 7.15152e9 | + | 1.23868e10i | 0.639611 | + | 1.10784i | ||||
\(172\) | 4.15383e9 | + | 7.19464e9i | 0.361885 | + | 0.626803i | ||||
\(173\) | −6.92455e9 | + | 1.19937e10i | −0.587739 | + | 1.01799i | 0.406789 | + | 0.913522i | \(0.366648\pi\) |
−0.994528 | + | 0.104471i | \(0.966685\pi\) | |||||||
\(174\) | −7.92636e9 | −0.655545 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.37775e9 | −0.265351 | ||||||||
\(177\) | 1.34159e9 | − | 2.32371e9i | 0.102740 | − | 0.177952i | ||||
\(178\) | −6.78935e9 | − | 1.17595e10i | −0.506919 | − | 0.878009i | ||||
\(179\) | −9.97712e9 | − | 1.72809e10i | −0.726384 | − | 1.25813i | −0.958402 | − | 0.285423i | \(-0.907866\pi\) |
0.232017 | − | 0.972712i | \(-0.425467\pi\) | |||||||
\(180\) | −7.35019e7 | + | 1.27309e8i | −0.00521882 | + | 0.00903926i | ||||
\(181\) | −3.33705e9 | −0.231105 | −0.115552 | − | 0.993301i | \(-0.536864\pi\) | ||||
−0.115552 | + | 0.993301i | \(0.536864\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.18493e10 | −1.44015 | ||||||||
\(184\) | 6.13179e8 | − | 1.06206e9i | 0.0394373 | − | 0.0683074i | ||||
\(185\) | −2.34367e8 | − | 4.05936e8i | −0.0147104 | − | 0.0254792i | ||||
\(186\) | −1.04990e10 | − | 1.81848e10i | −0.643191 | − | 1.11404i | ||||
\(187\) | −1.18972e10 | + | 2.06066e10i | −0.711474 | + | 1.23231i | ||||
\(188\) | −8.14216e8 | −0.0475367 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.49650e8 | 0.0250313 | ||||||||
\(191\) | 1.22946e10 | − | 2.12948e10i | 0.668441 | − | 1.15777i | −0.309899 | − | 0.950770i | \(-0.600295\pi\) |
0.978340 | − | 0.207005i | \(-0.0663716\pi\) | |||||||
\(192\) | −1.60874e9 | − | 2.78643e9i | −0.0854341 | − | 0.147976i | ||||
\(193\) | 9.00593e9 | + | 1.55987e10i | 0.467219 | + | 0.809247i | 0.999299 | − | 0.0374471i | \(-0.0119226\pi\) |
−0.532079 | + | 0.846694i | \(0.678589\pi\) | |||||||
\(194\) | 7.19507e9 | − | 1.24622e10i | 0.364693 | − | 0.631666i | ||||
\(195\) | 7.29868e8 | 0.0361483 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.02716e10 | 1.90503 | 0.952514 | − | 0.304496i | \(-0.0984880\pi\) | ||||
0.952514 | + | 0.304496i | \(0.0984880\pi\) | |||||||
\(198\) | −7.04886e9 | + | 1.22090e10i | −0.325931 | + | 0.564529i | ||||
\(199\) | −1.88426e10 | − | 3.26363e10i | −0.851730 | − | 1.47524i | −0.879646 | − | 0.475630i | \(-0.842220\pi\) |
0.0279153 | − | 0.999610i | \(-0.491113\pi\) | |||||||
\(200\) | −3.99769e9 | − | 6.92420e9i | −0.176675 | − | 0.306009i | ||||
\(201\) | 2.92933e10 | − | 5.07375e10i | 1.26586 | − | 2.19253i | ||||
\(202\) | −1.01152e9 | −0.0427459 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.26655e10 | −0.916283 | ||||||||
\(205\) | −3.73259e8 | + | 6.46504e8i | −0.0147611 | + | 0.0255669i | ||||
\(206\) | 9.72636e9 | + | 1.68466e10i | 0.376312 | + | 0.651791i | ||||
\(207\) | −2.55922e9 | − | 4.43271e9i | −0.0968817 | − | 0.167804i | ||||
\(208\) | −3.71270e9 | + | 6.43058e9i | −0.137532 | + | 0.238213i | ||||
\(209\) | 4.31216e10 | 1.56328 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.57268e10 | −0.546223 | −0.273111 | − | 0.961982i | \(-0.588053\pi\) | ||||
−0.273111 | + | 0.961982i | \(0.588053\pi\) | |||||||
\(212\) | −1.13013e10 | + | 1.95744e10i | −0.384252 | + | 0.665544i | ||||
\(213\) | 2.74878e10 | + | 4.76103e10i | 0.915022 | + | 1.58487i | ||||
\(214\) | −1.02594e10 | − | 1.77698e10i | −0.334395 | − | 0.579189i | ||||
\(215\) | 5.45025e8 | − | 9.44010e8i | 0.0173957 | − | 0.0301303i | ||||
\(216\) | 2.03255e9 | 0.0635331 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.10508e9 | 0.243054 | ||||||||
\(219\) | −4.59169e9 | + | 7.95303e9i | −0.134888 | + | 0.233633i | ||||
\(220\) | 2.21598e8 | + | 3.83818e8i | 0.00637769 | + | 0.0110465i | ||||
\(221\) | 2.61540e10 | + | 4.53000e10i | 0.737518 | + | 1.27742i | ||||
\(222\) | 2.14095e10 | − | 3.70823e10i | 0.591586 | − | 1.02466i | ||||
\(223\) | 6.29667e10 | 1.70506 | 0.852528 | − | 0.522681i | \(-0.175068\pi\) | ||||
0.852528 | + | 0.522681i | \(0.175068\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.33703e10 | −0.868038 | ||||||||
\(226\) | 9.24098e9 | − | 1.60058e10i | 0.235630 | − | 0.408123i | ||||
\(227\) | −2.74005e10 | − | 4.74591e10i | −0.684925 | − | 1.18632i | −0.973460 | − | 0.228855i | \(-0.926502\pi\) |
0.288536 | − | 0.957469i | \(-0.406832\pi\) | |||||||
\(228\) | 2.05378e10 | + | 3.55725e10i | 0.503324 | + | 0.871782i | ||||
\(229\) | 3.07059e10 | − | 5.31842e10i | 0.737840 | − | 1.27798i | −0.215627 | − | 0.976476i | \(-0.569179\pi\) |
0.953466 | − | 0.301500i | \(-0.0974872\pi\) | |||||||
\(230\) | −1.60911e8 | −0.00379149 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.05808e10 | −0.239784 | ||||||||
\(233\) | 4.21455e9 | − | 7.29981e9i | 0.0936806 | − | 0.162259i | −0.815377 | − | 0.578931i | \(-0.803470\pi\) |
0.909057 | + | 0.416671i | \(0.136803\pi\) | |||||||
\(234\) | 1.54957e10 | + | 2.68393e10i | 0.337862 | + | 0.585194i | ||||
\(235\) | 5.34167e7 | + | 9.25204e7i | 0.00114254 | + | 0.00197894i | ||||
\(236\) | 1.79087e9 | − | 3.10188e9i | 0.0375803 | − | 0.0650910i | ||||
\(237\) | −2.06317e10 | −0.424783 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.13951e10 | 0.622402 | 0.311201 | − | 0.950344i | \(-0.399269\pi\) | ||||
0.311201 | + | 0.950344i | \(0.399269\pi\) | |||||||
\(240\) | −2.11084e8 | + | 3.65607e8i | −0.00410680 | + | 0.00711319i | ||||
\(241\) | −7.29330e9 | − | 1.26324e10i | −0.139267 | − | 0.241217i | 0.787953 | − | 0.615736i | \(-0.211141\pi\) |
−0.927219 | + | 0.374519i | \(0.877808\pi\) | |||||||
\(242\) | 2.38771e9 | + | 4.13563e9i | 0.0447519 | + | 0.0775126i | ||||
\(243\) | 3.65072e10 | − | 6.32323e10i | 0.671661 | − | 1.16335i | ||||
\(244\) | −2.91663e10 | −0.526777 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.81945e10 | −1.18725 | ||||||||
\(247\) | 4.73977e10 | − | 8.20952e10i | 0.810253 | − | 1.40340i | ||||
\(248\) | −1.40150e10 | − | 2.42746e10i | −0.235266 | − | 0.407493i | ||||
\(249\) | −5.44259e9 | − | 9.42684e9i | −0.0897240 | − | 0.155406i | ||||
\(250\) | −1.04938e9 | + | 1.81758e9i | −0.0169903 | + | 0.0294281i | ||||
\(251\) | −3.56389e10 | −0.566752 | −0.283376 | − | 0.959009i | \(-0.591454\pi\) | ||||
−0.283376 | + | 0.959009i | \(0.591454\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.54314e10 | −0.236790 | ||||||||
\(254\) | 2.73024e10 | − | 4.72891e10i | 0.411575 | − | 0.712869i | ||||
\(255\) | 1.48697e9 | + | 2.57551e9i | 0.0220228 | + | 0.0381446i | ||||
\(256\) | −2.14748e9 | − | 3.71955e9i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −3.47285e10 | + | 6.01515e10i | −0.496577 | + | 0.860096i | −0.999992 | − | 0.00394818i | \(-0.998743\pi\) |
0.503415 | + | 0.864045i | \(0.332077\pi\) | |||||||
\(258\) | 9.95761e10 | 1.39916 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9.74288e8 | 0.0132223 | ||||||||
\(261\) | −2.20805e10 | + | 3.82445e10i | −0.294527 | + | 0.510137i | ||||
\(262\) | 5.74390e9 | + | 9.94873e9i | 0.0753097 | + | 0.130440i | ||||
\(263\) | −3.61510e10 | − | 6.26154e10i | −0.465929 | − | 0.807012i | 0.533314 | − | 0.845917i | \(-0.320946\pi\) |
−0.999243 | + | 0.0389051i | \(0.987613\pi\) | |||||||
\(264\) | −2.02430e10 | + | 3.50619e10i | −0.256482 | + | 0.444240i | ||||
\(265\) | 2.96569e9 | 0.0369419 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.62755e11 | −1.95990 | ||||||||
\(268\) | 3.91031e10 | − | 6.77286e10i | 0.463025 | − | 0.801983i | ||||
\(269\) | −4.51533e10 | − | 7.82078e10i | −0.525780 | − | 0.910678i | −0.999549 | − | 0.0300285i | \(-0.990440\pi\) |
0.473769 | − | 0.880649i | \(-0.342893\pi\) | |||||||
\(270\) | −1.33346e8 | − | 2.30962e8i | −0.00152701 | − | 0.00264486i | ||||
\(271\) | −2.01115e10 | + | 3.48341e10i | −0.226507 | + | 0.392322i | −0.956771 | − | 0.290844i | \(-0.906064\pi\) |
0.730264 | + | 0.683166i | \(0.239397\pi\) | |||||||
\(272\) | −3.02558e10 | −0.335157 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.17019e11 | 1.25424 | ||||||||
\(275\) | −5.03033e10 | + | 8.71279e10i | −0.530395 | + | 0.918671i | ||||
\(276\) | −7.34961e9 | − | 1.27299e10i | −0.0762383 | − | 0.132049i | ||||
\(277\) | 1.03358e10 | + | 1.79022e10i | 0.105484 | + | 0.182704i | 0.913936 | − | 0.405859i | \(-0.133027\pi\) |
−0.808452 | + | 0.588562i | \(0.799694\pi\) | |||||||
\(278\) | −3.90933e10 | + | 6.77116e10i | −0.392555 | + | 0.679926i | ||||
\(279\) | −1.16988e11 | −1.15591 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.46833e10 | −0.331850 | −0.165925 | − | 0.986138i | \(-0.553061\pi\) | ||||
−0.165925 | + | 0.986138i | \(0.553061\pi\) | |||||||
\(282\) | −4.87962e9 | + | 8.45175e9i | −0.0459479 | + | 0.0795840i | ||||
\(283\) | −5.23196e10 | − | 9.06203e10i | −0.484870 | − | 0.839820i | 0.514978 | − | 0.857203i | \(-0.327800\pi\) |
−0.999849 | + | 0.0173829i | \(0.994467\pi\) | |||||||
\(284\) | 3.66930e10 | + | 6.35541e10i | 0.334696 | + | 0.579711i | ||||
\(285\) | 2.69477e9 | − | 4.66748e9i | 0.0241947 | − | 0.0419064i | ||||
\(286\) | 9.34345e10 | 0.825772 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.79259e10 | −0.153538 | ||||||||
\(289\) | −4.72740e10 | + | 8.18810e10i | −0.398641 | + | 0.690467i | ||||
\(290\) | 6.94152e8 | + | 1.20231e9i | 0.00576320 | + | 0.00998215i | ||||
\(291\) | −8.62406e10 | − | 1.49373e11i | −0.705007 | − | 1.22111i | ||||
\(292\) | −6.12936e9 | + | 1.06164e10i | −0.0493392 | + | 0.0854581i | ||||
\(293\) | −1.60760e11 | −1.27431 | −0.637153 | − | 0.770737i | \(-0.719888\pi\) | ||||
−0.637153 | + | 0.770737i | \(0.719888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.69961e8 | −0.00361296 | ||||||||
\(296\) | 2.85792e10 | − | 4.95006e10i | 0.216390 | − | 0.374798i | ||||
\(297\) | −1.27879e10 | − | 2.21493e10i | −0.0953664 | − | 0.165180i | ||||
\(298\) | 5.52231e10 | + | 9.56493e10i | 0.405647 | + | 0.702600i | ||||
\(299\) | −1.69616e10 | + | 2.93784e10i | −0.122729 | + | 0.212573i | ||||
\(300\) | −9.58332e10 | −0.683078 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.04875e10 | 0.625976 | ||||||||
\(303\) | −6.06210e9 | + | 1.04999e10i | −0.0413172 | + | 0.0715635i | ||||
\(304\) | 2.74156e10 | + | 4.74852e10i | 0.184105 | + | 0.318880i | ||||
\(305\) | 1.91346e9 | + | 3.31420e9i | 0.0126610 | + | 0.0219296i | ||||
\(306\) | −6.31393e10 | + | 1.09360e11i | −0.411674 | + | 0.713040i | ||||
\(307\) | 1.45170e11 | 0.932725 | 0.466362 | − | 0.884594i | \(-0.345564\pi\) | ||||
0.466362 | + | 0.884594i | \(0.345564\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.33162e11 | 1.45494 | ||||||||
\(310\) | −1.83891e9 | + | 3.18508e9i | −0.0113092 | + | 0.0195881i | ||||
\(311\) | 1.31545e11 | + | 2.27842e11i | 0.797356 | + | 1.38106i | 0.921333 | + | 0.388775i | \(0.127102\pi\) |
−0.123977 | + | 0.992285i | \(0.539565\pi\) | |||||||
\(312\) | 4.45007e10 | + | 7.70774e10i | 0.265871 | + | 0.460502i | ||||
\(313\) | 4.19102e10 | − | 7.25905e10i | 0.246814 | − | 0.427495i | −0.715826 | − | 0.698279i | \(-0.753950\pi\) |
0.962640 | + | 0.270784i | \(0.0872830\pi\) | |||||||
\(314\) | 1.05596e11 | 0.613005 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.75409e10 | −0.155377 | ||||||||
\(317\) | −1.35358e11 | + | 2.34447e11i | −0.752865 | + | 1.30400i | 0.193564 | + | 0.981088i | \(0.437995\pi\) |
−0.946429 | + | 0.322913i | \(0.895338\pi\) | |||||||
\(318\) | 1.35458e11 | + | 2.34620e11i | 0.742818 | + | 1.28660i | ||||
\(319\) | 6.65694e10 | + | 1.15302e11i | 0.359929 | + | 0.623415i | ||||
\(320\) | −2.81772e8 | + | 4.88043e8i | −0.00150218 | + | 0.00260186i | ||||
\(321\) | −2.45940e11 | −1.29287 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.86257e11 | 1.97453 | ||||||||
\(324\) | 5.52519e10 | − | 9.56991e10i | 0.278545 | − | 0.482453i | ||||
\(325\) | 1.10583e11 | + | 1.91536e11i | 0.549811 | + | 0.952301i | ||||
\(326\) | −6.39037e10 | − | 1.10685e11i | −0.313363 | − | 0.542760i | ||||
\(327\) | 4.85740e10 | − | 8.41327e10i | 0.234930 | − | 0.406911i | ||||
\(328\) | −9.10317e10 | −0.434271 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.31217e9 | 0.0246581 | ||||||||
\(331\) | −9.68704e10 | + | 1.67784e11i | −0.443573 | + | 0.768291i | −0.997952 | − | 0.0639738i | \(-0.979623\pi\) |
0.554379 | + | 0.832265i | \(0.312956\pi\) | |||||||
\(332\) | −7.26522e9 | − | 1.25837e10i | −0.0328191 | − | 0.0568444i | ||||
\(333\) | −1.19281e11 | − | 2.06600e11i | −0.531584 | − | 0.920730i | ||||
\(334\) | 3.47924e10 | − | 6.02622e10i | 0.152977 | − | 0.264963i | ||||
\(335\) | −1.02615e10 | −0.0445151 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.23909e11 | 0.945665 | 0.472832 | − | 0.881152i | \(-0.343232\pi\) | ||||
0.472832 | + | 0.881152i | \(0.343232\pi\) | |||||||
\(338\) | 1.78637e10 | − | 3.09409e10i | 0.0744470 | − | 0.128946i | ||||
\(339\) | −1.10763e11 | − | 1.91847e11i | −0.455508 | − | 0.788964i | ||||
\(340\) | 1.98493e9 | + | 3.43801e9i | 0.00805547 | + | 0.0139525i | ||||
\(341\) | −1.76352e11 | + | 3.05450e11i | −0.706293 | + | 1.22333i | ||||
\(342\) | 2.28849e11 | 0.904547 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.32922e11 | 0.511782 | ||||||||
\(345\) | −9.64344e8 | + | 1.67029e9i | −0.00366476 | + | 0.00634756i | ||||
\(346\) | 1.10793e11 | + | 1.91899e11i | 0.415594 | + | 0.719830i | ||||
\(347\) | 1.28864e11 | + | 2.23200e11i | 0.477145 | + | 0.826439i | 0.999657 | − | 0.0261929i | \(-0.00833841\pi\) |
−0.522512 | + | 0.852632i | \(0.675005\pi\) | |||||||
\(348\) | −6.34109e10 | + | 1.09831e11i | −0.231770 | + | 0.401437i | ||||
\(349\) | 1.38744e11 | 0.500609 | 0.250304 | − | 0.968167i | \(-0.419469\pi\) | ||||
0.250304 | + | 0.968167i | \(0.419469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.62240e10 | −0.197715 | ||||||||
\(352\) | −2.70220e10 | + | 4.68035e10i | −0.0938157 | + | 0.162494i | ||||
\(353\) | −9.34902e10 | − | 1.61930e11i | −0.320464 | − | 0.555061i | 0.660119 | − | 0.751161i | \(-0.270506\pi\) |
−0.980584 | + | 0.196100i | \(0.937172\pi\) | |||||||
\(354\) | −2.14655e10 | − | 3.71794e10i | −0.0726485 | − | 0.125831i | ||||
\(355\) | 4.81450e9 | − | 8.33895e9i | 0.0160888 | − | 0.0278666i | ||||
\(356\) | −2.17259e11 | −0.716891 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.19268e11 | −1.02726 | ||||||||
\(359\) | −1.03782e11 | + | 1.79755e11i | −0.329758 | + | 0.571157i | −0.982464 | − | 0.186454i | \(-0.940300\pi\) |
0.652706 | + | 0.757611i | \(0.273634\pi\) | |||||||
\(360\) | 1.17603e9 | + | 2.03694e9i | 0.00369026 | + | 0.00639172i | ||||
\(361\) | −1.88654e11 | − | 3.26758e11i | −0.584632 | − | 1.01261i | ||||
\(362\) | −2.66964e10 | + | 4.62395e10i | −0.0817079 | + | 0.141522i | ||||
\(363\) | 5.72384e10 | 0.173025 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.60847e9 | 0.00474346 | ||||||||
\(366\) | −1.74794e11 | + | 3.02753e11i | −0.509170 | + | 0.881908i | ||||
\(367\) | −8.96653e10 | − | 1.55305e11i | −0.258004 | − | 0.446877i | 0.707703 | − | 0.706510i | \(-0.249732\pi\) |
−0.965707 | + | 0.259634i | \(0.916398\pi\) | |||||||
\(368\) | −9.81086e9 | − | 1.69929e10i | −0.0278864 | − | 0.0483006i | ||||
\(369\) | −1.89969e11 | + | 3.29037e11i | −0.533415 | + | 0.923902i | ||||
\(370\) | −7.49976e9 | −0.0208036 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.35968e11 | −0.909610 | ||||||||
\(373\) | 2.72418e11 | − | 4.71842e11i | 0.728696 | − | 1.26214i | −0.228738 | − | 0.973488i | \(-0.573460\pi\) |
0.957434 | − | 0.288651i | \(-0.0932066\pi\) | |||||||
\(374\) | 1.90356e11 | + | 3.29706e11i | 0.503088 | + | 0.871374i | ||||
\(375\) | 1.25779e10 | + | 2.17856e10i | 0.0328449 | + | 0.0568891i | ||||
\(376\) | −6.51372e9 | + | 1.12821e10i | −0.0168068 | + | 0.0291102i | ||||
\(377\) | 2.92682e11 | 0.746209 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.24662e11 | −0.310353 | −0.155177 | − | 0.987887i | \(-0.549595\pi\) | ||||
−0.155177 | + | 0.987887i | \(0.549595\pi\) | |||||||
\(380\) | 3.59720e9 | − | 6.23054e9i | 0.00884991 | − | 0.0153285i | ||||
\(381\) | −3.27248e11 | − | 5.66811e11i | −0.795637 | − | 1.37808i | ||||
\(382\) | −1.96713e11 | − | 3.40717e11i | −0.472659 | − | 0.818670i | ||||
\(383\) | 2.04123e11 | − | 3.53551e11i | 0.484726 | − | 0.839571i | −0.515120 | − | 0.857118i | \(-0.672253\pi\) |
0.999846 | + | 0.0175476i | \(0.00558586\pi\) | |||||||
\(384\) | −5.14798e10 | −0.120822 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.88190e11 | 0.660748 | ||||||||
\(387\) | 2.77389e11 | − | 4.80452e11i | 0.628623 | − | 1.08881i | ||||
\(388\) | −1.15121e11 | − | 1.99396e11i | −0.257877 | − | 0.446656i | ||||
\(389\) | −2.56820e11 | − | 4.44825e11i | −0.568663 | − | 0.984954i | −0.996698 | − | 0.0811919i | \(-0.974127\pi\) |
0.428035 | − | 0.903762i | \(-0.359206\pi\) | |||||||
\(390\) | 5.83894e9 | − | 1.01133e10i | 0.0127804 | − | 0.0221362i | ||||
\(391\) | −1.38225e11 | −0.299082 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.37694e11 | 0.291170 | ||||||||
\(394\) | 3.22173e11 | − | 5.58020e11i | 0.673529 | − | 1.16659i | ||||
\(395\) | 1.80682e9 | + | 3.12951e9i | 0.00373447 | + | 0.00646828i | ||||
\(396\) | 1.12782e11 | + | 1.95344e11i | 0.230468 | + | 0.399182i | ||||
\(397\) | −1.80407e11 | + | 3.12474e11i | −0.364499 | + | 0.631331i | −0.988696 | − | 0.149936i | \(-0.952093\pi\) |
0.624197 | + | 0.781267i | \(0.285426\pi\) | |||||||
\(398\) | −6.02963e11 | −1.20453 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.27926e11 | −0.249856 | ||||||||
\(401\) | −1.19297e11 | + | 2.06629e11i | −0.230399 | + | 0.399062i | −0.957925 | − | 0.287017i | \(-0.907336\pi\) |
0.727527 | + | 0.686079i | \(0.240670\pi\) | |||||||
\(402\) | −4.68693e11 | − | 8.11799e11i | −0.895098 | − | 1.55036i | ||||
\(403\) | 3.87678e11 | + | 6.71478e11i | 0.732148 | + | 1.26812i | ||||
\(404\) | −8.09219e9 | + | 1.40161e10i | −0.0151130 | + | 0.0261764i | ||||
\(405\) | −1.44992e10 | −0.0267792 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.19229e11 | −1.29925 | ||||||||
\(408\) | −1.81324e11 | + | 3.14062e11i | −0.323955 | + | 0.561106i | ||||
\(409\) | 3.87345e11 | + | 6.70901e11i | 0.684452 | + | 1.18551i | 0.973609 | + | 0.228224i | \(0.0732919\pi\) |
−0.289157 | + | 0.957282i | \(0.593375\pi\) | |||||||
\(410\) | 5.97214e9 | + | 1.03441e10i | 0.0104377 | + | 0.0180785i | ||||
\(411\) | 7.01301e11 | − | 1.21469e12i | 1.21232 | − | 2.09979i | ||||
\(412\) | 3.11244e11 | 0.532185 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.18952e10 | −0.137011 | ||||||||
\(415\) | −9.53271e8 | + | 1.65111e9i | −0.00157761 | + | 0.00273250i | ||||
\(416\) | 5.94032e10 | + | 1.02889e11i | 0.0972500 | + | 0.168442i | ||||
\(417\) | 4.68575e11 | + | 8.11596e11i | 0.758869 | + | 1.31440i | ||||
\(418\) | 3.44973e11 | − | 5.97511e11i | 0.552703 | − | 0.957310i | ||||
\(419\) | −5.87231e11 | −0.930777 | −0.465389 | − | 0.885106i | \(-0.654085\pi\) | ||||
−0.465389 | + | 0.885106i | \(0.654085\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.12541e12 | −1.74599 | −0.872993 | − | 0.487733i | \(-0.837824\pi\) | ||||
−0.872993 | + | 0.487733i | \(0.837824\pi\) | |||||||
\(422\) | −1.25815e11 | + | 2.17917e11i | −0.193119 | + | 0.334492i | ||||
\(423\) | 2.71863e10 | + | 4.70881e10i | 0.0412875 | + | 0.0715121i | ||||
\(424\) | 1.80820e11 | + | 3.13190e11i | 0.271707 | + | 0.470611i | ||||
\(425\) | −4.50586e11 | + | 7.80437e11i | −0.669927 | + | 1.16035i | ||||
\(426\) | 8.79610e11 | 1.29404 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.28300e11 | −0.472906 | ||||||||
\(429\) | 5.59956e11 | − | 9.69873e11i | 0.798172 | − | 1.38247i | ||||
\(430\) | −8.72039e9 | − | 1.51042e10i | −0.0123006 | − | 0.0213053i | ||||
\(431\) | 3.38834e11 | + | 5.86878e11i | 0.472976 | + | 0.819219i | 0.999522 | − | 0.0309282i | \(-0.00984632\pi\) |
−0.526545 | + | 0.850147i | \(0.676513\pi\) | |||||||
\(432\) | 1.62604e10 | − | 2.81639e10i | 0.0224623 | − | 0.0389059i | ||||
\(433\) | 5.66584e11 | 0.774585 | 0.387292 | − | 0.921957i | \(-0.373410\pi\) | ||||
0.387292 | + | 0.921957i | \(0.373410\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.66403e10 | 0.0222823 | ||||||||
\(436\) | 6.48406e10 | − | 1.12307e11i | 0.0859326 | − | 0.148840i | ||||
\(437\) | 1.25249e11 | + | 2.16938e11i | 0.164289 | + | 0.284557i | ||||
\(438\) | 7.34670e10 | + | 1.27249e11i | 0.0953803 | + | 0.165203i | ||||
\(439\) | 3.70618e11 | − | 6.41930e11i | 0.476252 | − | 0.824892i | −0.523378 | − | 0.852100i | \(-0.675329\pi\) |
0.999630 | + | 0.0272086i | \(0.00866184\pi\) | |||||||
\(440\) | 7.09113e9 | 0.00901941 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.36928e11 | 1.04301 | ||||||||
\(443\) | −4.62603e10 | + | 8.01252e10i | −0.0570679 | + | 0.0988445i | −0.893148 | − | 0.449763i | \(-0.851508\pi\) |
0.836080 | + | 0.548607i | \(0.184842\pi\) | |||||||
\(444\) | −3.42552e11 | − | 5.93317e11i | −0.418315 | − | 0.724542i | ||||
\(445\) | 1.42533e10 | + | 2.46875e10i | 0.0172304 | + | 0.0298440i | ||||
\(446\) | 5.03733e11 | − | 8.72492e11i | 0.602828 | − | 1.04413i | ||||
\(447\) | 1.32382e12 | 1.56835 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.26884e11 | −0.147333 | −0.0736664 | − | 0.997283i | \(-0.523470\pi\) | ||||
−0.0736664 | + | 0.997283i | \(0.523470\pi\) | |||||||
\(450\) | −2.66962e11 | + | 4.62392e11i | −0.306898 | + | 0.531563i | ||||
\(451\) | 5.72731e11 | + | 9.91998e11i | 0.651862 | + | 1.12906i | ||||
\(452\) | −1.47856e11 | − | 2.56094e11i | −0.166615 | − | 0.288586i | ||||
\(453\) | 5.42295e11 | − | 9.39282e11i | 0.605053 | − | 1.04798i | ||||
\(454\) | −8.76817e11 | −0.968630 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.57210e11 | 0.711807 | ||||||||
\(457\) | −5.14076e11 | + | 8.90406e11i | −0.551321 | + | 0.954916i | 0.446858 | + | 0.894605i | \(0.352543\pi\) |
−0.998180 | + | 0.0603116i | \(0.980791\pi\) | |||||||
\(458\) | −4.91294e11 | − | 8.50946e11i | −0.521731 | − | 0.903665i | ||||
\(459\) | −1.14546e11 | − | 1.98400e11i | −0.120455 | − | 0.208633i | ||||
\(460\) | −1.28729e9 | + | 2.22964e9i | −0.00134049 | + | 0.00232180i | ||||
\(461\) | −8.10233e11 | −0.835518 | −0.417759 | − | 0.908558i | \(-0.637184\pi\) | ||||
−0.417759 | + | 0.908558i | \(0.637184\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.44793e12 | −1.46431 | −0.732155 | − | 0.681139i | \(-0.761485\pi\) | ||||
−0.732155 | + | 0.681139i | \(0.761485\pi\) | |||||||
\(464\) | −8.46461e10 | + | 1.46611e11i | −0.0847766 | + | 0.146837i | ||||
\(465\) | 2.20412e10 | + | 3.81766e10i | 0.0218624 | + | 0.0378668i | ||||
\(466\) | −6.74328e10 | − | 1.16797e11i | −0.0662422 | − | 0.114735i | ||||
\(467\) | 2.23517e11 | − | 3.87143e11i | 0.217463 | − | 0.376657i | −0.736569 | − | 0.676363i | \(-0.763555\pi\) |
0.954032 | + | 0.299706i | \(0.0968886\pi\) | |||||||
\(468\) | 4.95862e11 | 0.477809 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.70933e9 | 0.00161580 | ||||||||
\(471\) | 6.32840e11 | − | 1.09611e12i | 0.592516 | − | 1.02627i | ||||
\(472\) | −2.86539e10 | − | 4.96301e10i | −0.0265733 | − | 0.0460263i | ||||
\(473\) | −8.36288e11 | − | 1.44849e12i | −0.768212 | − | 1.33058i | ||||
\(474\) | −1.65053e11 | + | 2.85881e11i | −0.150183 | + | 0.260125i | ||||
\(475\) | 1.63315e12 | 1.47199 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.50938e12 | 1.33495 | ||||||||
\(478\) | 2.51161e11 | − | 4.35023e11i | 0.220052 | − | 0.381142i | ||||
\(479\) | 4.34776e10 | + | 7.53054e10i | 0.0377360 | + | 0.0653606i | 0.884277 | − | 0.466964i | \(-0.154652\pi\) |
−0.846541 | + | 0.532324i | \(0.821319\pi\) | |||||||
\(480\) | 3.37734e9 | + | 5.84972e9i | 0.00290395 | + | 0.00502979i | ||||
\(481\) | −7.90550e11 | + | 1.36927e12i | −0.673405 | + | 1.16637i | ||||
\(482\) | −2.33386e11 | −0.196953 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.64066e10 | 0.0632888 | ||||||||
\(485\) | −1.51051e10 | + | 2.61627e10i | −0.0123961 | + | 0.0214707i | ||||
\(486\) | −5.84115e11 | − | 1.01172e12i | −0.474936 | − | 0.822614i | ||||
\(487\) | 2.40968e8 | + | 4.17368e8i | 0.000194124 | + | 0.000336232i | 0.866122 | − | 0.499832i | \(-0.166605\pi\) |
−0.865928 | + | 0.500168i | \(0.833272\pi\) | |||||||
\(488\) | −2.33330e11 | + | 4.04140e11i | −0.186244 | + | 0.322584i | ||||
\(489\) | −1.53191e12 | −1.21156 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.88640e11 | −0.457070 | −0.228535 | − | 0.973536i | \(-0.573394\pi\) | ||||
−0.228535 | + | 0.973536i | \(0.573394\pi\) | |||||||
\(492\) | −5.45556e11 | + | 9.44931e11i | −0.419756 | + | 0.727038i | ||||
\(493\) | 5.96287e11 | + | 1.03280e12i | 0.454616 | + | 0.787417i | ||||
\(494\) | −7.58363e11 | − | 1.31352e12i | −0.572936 | − | 0.992354i | ||||
\(495\) | 1.47981e10 | − | 2.56311e10i | 0.0110786 | − | 0.0191886i | ||||
\(496\) | −4.48478e11 | −0.332716 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.74163e11 | −0.126889 | ||||||||
\(499\) | 1.23973e12 | − | 2.14728e12i | 0.895107 | − | 1.55037i | 0.0614341 | − | 0.998111i | \(-0.480433\pi\) |
0.833673 | − | 0.552259i | \(-0.186234\pi\) | |||||||
\(500\) | 1.67901e10 | + | 2.90812e10i | 0.0120140 | + | 0.0208088i | ||||
\(501\) | −4.17024e11 | − | 7.22307e11i | −0.295727 | − | 0.512214i | ||||
\(502\) | −2.85111e11 | + | 4.93828e11i | −0.200377 | + | 0.347063i | ||||
\(503\) | 1.35604e12 | 0.944530 | 0.472265 | − | 0.881457i | \(-0.343437\pi\) | ||||
0.472265 | + | 0.881457i | \(0.343437\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.12356e9 | 0.00145296 | ||||||||
\(506\) | −1.23451e11 | + | 2.13824e11i | −0.0837178 | + | 0.145003i | ||||
\(507\) | −2.14116e11 | − | 3.70860e11i | −0.143917 | − | 0.249272i | ||||
\(508\) | −4.36838e11 | − | 7.56626e11i | −0.291027 | − | 0.504074i | ||||
\(509\) | −8.44120e11 | + | 1.46206e12i | −0.557409 | + | 0.965461i | 0.440303 | + | 0.897849i | \(0.354871\pi\) |
−0.997712 | + | 0.0676115i | \(0.978462\pi\) | |||||||
\(510\) | 4.75831e10 | 0.0311449 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | −2.07587e11 | + | 3.59551e11i | −0.132334 | + | 0.229209i | ||||
\(514\) | 5.55655e11 | + | 9.62423e11i | 0.351133 | + | 0.608180i | ||||
\(515\) | −2.04192e10 | − | 3.53670e10i | −0.0127910 | − | 0.0221547i | ||||
\(516\) | 7.96609e11 | − | 1.37977e12i | 0.494677 | − | 0.856805i | ||||
\(517\) | 1.63926e11 | 0.100911 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.65594e12 | 1.60681 | ||||||||
\(520\) | 7.79430e9 | − | 1.35001e10i | 0.00467479 | − | 0.00809698i | ||||
\(521\) | −4.71068e11 | − | 8.15913e11i | −0.280100 | − | 0.485148i | 0.691309 | − | 0.722559i | \(-0.257034\pi\) |
−0.971409 | + | 0.237411i | \(0.923701\pi\) | |||||||
\(522\) | 3.53287e11 | + | 6.11912e11i | 0.208262 | + | 0.360721i | ||||
\(523\) | −1.22203e12 | + | 2.11661e12i | −0.714206 | + | 1.23704i | 0.249060 | + | 0.968488i | \(0.419879\pi\) |
−0.963265 | + | 0.268552i | \(0.913455\pi\) | |||||||
\(524\) | 1.83805e11 | 0.106504 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.15683e12 | −0.658923 | ||||||||
\(527\) | −1.57965e12 | + | 2.73603e12i | −0.892097 | + | 1.54516i | ||||
\(528\) | 3.23888e11 | + | 5.60990e11i | 0.181360 | + | 0.314125i | ||||
\(529\) | 8.55755e11 | + | 1.48221e12i | 0.475115 | + | 0.822924i | ||||
\(530\) | 2.37255e10 | − | 4.10938e10i | 0.0130609 | − | 0.0226222i | ||||
\(531\) | −2.39186e11 | −0.130560 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.51810e12 | 1.35145 | ||||||||
\(534\) | −1.30204e12 | + | 2.25520e12i | −0.692930 | + | 1.20019i | ||||
\(535\) | 2.15382e10 | + | 3.73052e10i | 0.0113662 | + | 0.0196869i | ||||
\(536\) | −6.25650e11 | − | 1.08366e12i | −0.327408 | − | 0.567088i | ||||
\(537\) | −1.91338e12 | + | 3.31408e12i | −0.992928 | + | 1.71980i | ||||
\(538\) | −1.44490e12 | −0.743565 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.26707e9 | −0.00215952 | ||||||||
\(541\) | 3.29098e11 | − | 5.70014e11i | 0.165172 | − | 0.286087i | −0.771544 | − | 0.636176i | \(-0.780515\pi\) |
0.936716 | + | 0.350089i | \(0.113849\pi\) | |||||||
\(542\) | 3.21783e11 | + | 5.57345e11i | 0.160165 | + | 0.277413i | ||||
\(543\) | 3.19985e11 | + | 5.54230e11i | 0.157954 | + | 0.273584i | ||||
\(544\) | −2.42046e11 | + | 4.19236e11i | −0.118496 | + | 0.205241i | ||||
\(545\) | −1.70155e10 | −0.00826153 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.50775e12 | −1.19768 | −0.598840 | − | 0.800869i | \(-0.704372\pi\) | ||||
−0.598840 | + | 0.800869i | \(0.704372\pi\) | |||||||
\(548\) | 9.36154e11 | − | 1.62147e12i | 0.443440 | − | 0.768061i | ||||
\(549\) | 9.73850e11 | + | 1.68676e12i | 0.457527 | + | 0.792460i | ||||
\(550\) | 8.04853e11 | + | 1.39405e12i | 0.375046 | + | 0.649599i | ||||
\(551\) | 1.08062e12 | − | 1.87170e12i | 0.499450 | − | 0.865073i | ||||
\(552\) | −2.35187e11 | −0.107817 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.30747e11 | 0.149177 | ||||||||
\(555\) | −4.49463e10 | + | 7.78493e10i | −0.0201083 | + | 0.0348286i | ||||
\(556\) | 6.25493e11 | + | 1.08339e12i | 0.277578 | + | 0.480780i | ||||
\(557\) | 1.30253e12 | + | 2.25604e12i | 0.573375 | + | 0.993114i | 0.996216 | + | 0.0869103i | \(0.0276993\pi\) |
−0.422842 | + | 0.906204i | \(0.638967\pi\) | |||||||
\(558\) | −9.35907e11 | + | 1.62104e12i | −0.408676 | + | 0.707847i | ||||
\(559\) | −3.67687e12 | −1.59267 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.56324e12 | 1.94509 | ||||||||
\(562\) | −2.77467e11 | + | 4.80586e11i | −0.117327 | + | 0.203216i | ||||
\(563\) | −1.29701e11 | − | 2.24649e11i | −0.0544071 | − | 0.0942359i | 0.837539 | − | 0.546377i | \(-0.183994\pi\) |
−0.891946 | + | 0.452141i | \(0.850660\pi\) | |||||||
\(564\) | 7.80740e10 | + | 1.35228e11i | 0.0324900 | + | 0.0562744i | ||||
\(565\) | −1.94002e10 | + | 3.36021e10i | −0.00800917 | + | 0.0138723i | ||||
\(566\) | −1.67423e12 | −0.685710 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.17418e12 | 0.473332 | ||||||||
\(569\) | −1.32166e12 | + | 2.28918e12i | −0.528585 | + | 0.915536i | 0.470860 | + | 0.882208i | \(0.343944\pi\) |
−0.999444 | + | 0.0333277i | \(0.989389\pi\) | |||||||
\(570\) | −4.31163e10 | − | 7.46797e10i | −0.0171082 | − | 0.0296323i | ||||
\(571\) | 1.03397e12 | + | 1.79089e12i | 0.407049 | + | 0.705029i | 0.994558 | − | 0.104189i | \(-0.0332246\pi\) |
−0.587509 | + | 0.809218i | \(0.699891\pi\) | |||||||
\(572\) | 7.47476e11 | − | 1.29467e12i | 0.291954 | − | 0.505680i | ||||
\(573\) | −4.71564e12 | −1.82745 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.84435e11 | −0.222962 | ||||||||
\(576\) | −1.43407e11 | + | 2.48389e11i | −0.0542837 | + | 0.0940222i | ||||
\(577\) | 1.28250e12 | + | 2.22135e12i | 0.481688 | + | 0.834309i | 0.999779 | − | 0.0210170i | \(-0.00669040\pi\) |
−0.518091 | + | 0.855326i | \(0.673357\pi\) | |||||||
\(578\) | 7.56385e11 | + | 1.31010e12i | 0.281882 | + | 0.488234i | ||||
\(579\) | 1.72713e12 | − | 2.99148e12i | 0.638663 | − | 1.10620i | ||||
\(580\) | 2.22129e10 | 0.00815039 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.75970e12 | −0.997030 | ||||||||
\(583\) | 2.27528e12 | − | 3.94090e12i | 0.815693 | − | 1.41282i | ||||
\(584\) | 9.80698e10 | + | 1.69862e11i | 0.0348881 | + | 0.0604280i | ||||
\(585\) | −3.25311e10 | − | 5.63455e10i | −0.0114841 | − | 0.0198910i | ||||
\(586\) | −1.28608e12 | + | 2.22756e12i | −0.450535 | + | 0.780350i | ||||
\(587\) | 1.59591e12 | 0.554800 | 0.277400 | − | 0.960755i | \(-0.410527\pi\) | ||||
0.277400 | + | 0.960755i | \(0.410527\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.72544e12 | 1.96015 | ||||||||
\(590\) | −3.75969e9 | + | 6.51197e9i | −0.00127737 | + | 0.00221248i | ||||
\(591\) | −3.86159e12 | − | 6.68847e12i | −1.30203 | − | 2.25519i | ||||
\(592\) | −4.57267e11 | − | 7.92009e11i | −0.153011 | − | 0.265022i | ||||
\(593\) | 9.85581e11 | − | 1.70708e12i | 0.327300 | − | 0.566900i | −0.654675 | − | 0.755910i | \(-0.727195\pi\) |
0.981975 | + | 0.189010i | \(0.0605279\pi\) | |||||||
\(594\) | −4.09213e11 | −0.134869 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.76714e12 | 0.573671 | ||||||||
\(597\) | −3.61358e12 | + | 6.25891e12i | −1.16427 | + | 2.01657i | ||||
\(598\) | 2.71386e11 | + | 4.70054e11i | 0.0867824 | + | 0.150312i | ||||
\(599\) | −2.48539e12 | − | 4.30483e12i | −0.788814 | − | 1.36627i | −0.926694 | − | 0.375817i | \(-0.877362\pi\) |
0.137880 | − | 0.990449i | \(-0.455971\pi\) | |||||||
\(600\) | −7.66665e11 | + | 1.32790e12i | −0.241505 | + | 0.418298i | ||||
\(601\) | 4.73669e12 | 1.48095 | 0.740475 | − | 0.672084i | \(-0.234601\pi\) | ||||
0.740475 | + | 0.672084i | \(0.234601\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.22255e12 | −1.60862 | ||||||||
\(604\) | 7.23900e11 | − | 1.25383e12i | 0.221316 | − | 0.383330i | ||||
\(605\) | −5.01266e9 | − | 8.68219e9i | −0.00152114 | − | 0.00263469i | ||||
\(606\) | 9.69935e10 | + | 1.67998e11i | 0.0292157 | + | 0.0506030i | ||||
\(607\) | −1.63452e12 | + | 2.83106e12i | −0.488697 | + | 0.846449i | −0.999915 | − | 0.0130024i | \(-0.995861\pi\) |
0.511218 | + | 0.859451i | \(0.329194\pi\) | |||||||
\(608\) | 8.77298e11 | 0.260364 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.12306e10 | 0.0179054 | ||||||||
\(611\) | 1.80181e11 | − | 3.12083e11i | 0.0523026 | − | 0.0905908i | ||||
\(612\) | 1.01023e12 | + | 1.74977e12i | 0.291097 | + | 0.504195i | ||||
\(613\) | 3.26789e11 | + | 5.66014e11i | 0.0934748 | + | 0.161903i | 0.908971 | − | 0.416859i | \(-0.136869\pi\) |
−0.815496 | + | 0.578762i | \(0.803536\pi\) | |||||||
\(614\) | 1.16136e12 | − | 2.01153e12i | 0.329768 | − | 0.571175i | ||||
\(615\) | 1.43165e11 | 0.0403552 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.63823e12 | −1.84404 | −0.922018 | − | 0.387148i | \(-0.873460\pi\) | ||||
−0.922018 | + | 0.387148i | \(0.873460\pi\) | |||||||
\(618\) | 1.86529e12 | − | 3.23078e12i | 0.514398 | − | 0.890963i | ||||
\(619\) | −3.62687e10 | − | 6.28193e10i | −0.00992943 | − | 0.0171983i | 0.861018 | − | 0.508574i | \(-0.169827\pi\) |
−0.870947 | + | 0.491376i | \(0.836494\pi\) | |||||||
\(620\) | 2.94225e10 | + | 5.09612e10i | 0.00799681 | + | 0.0138509i | ||||
\(621\) | 7.42864e10 | − | 1.28668e11i | 0.0200446 | − | 0.0347182i | ||||
\(622\) | 4.20943e12 | 1.12763 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.42402e12 | 0.375998 | ||||||||
\(625\) | −1.90404e12 | + | 3.29790e12i | −0.499134 | + | 0.864525i | ||||
\(626\) | −6.70563e11 | − | 1.16145e12i | −0.174524 | − | 0.302284i | ||||
\(627\) | −4.13487e12 | − | 7.16181e12i | −1.06846 | − | 1.85063i | ||||
\(628\) | 8.44768e11 | − | 1.46318e12i | 0.216730 | − | 0.375387i | ||||
\(629\) | −6.44240e12 | −1.64104 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.35325e12 | −0.590930 | −0.295465 | − | 0.955354i | \(-0.595475\pi\) | ||||
−0.295465 | + | 0.955354i | \(0.595475\pi\) | |||||||
\(632\) | −2.20327e11 | + | 3.81618e11i | −0.0549340 | + | 0.0951484i | ||||
\(633\) | 1.50802e12 | + | 2.61197e12i | 0.373328 | + | 0.646624i | ||||
\(634\) | 2.16573e12 | + | 3.75115e12i | 0.532356 | + | 0.922068i | ||||
\(635\) | −5.73176e10 | + | 9.92770e10i | −0.0139896 | + | 0.0242308i | ||||
\(636\) | 4.33465e12 | 1.05050 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.13022e12 | 0.509016 | ||||||||
\(639\) | 2.45033e12 | − | 4.24409e12i | 0.581394 | − | 1.00700i | ||||
\(640\) | 4.50835e9 | + | 7.80869e9i | 0.00106220 | + | 0.00183979i | ||||
\(641\) | 3.76444e11 | + | 6.52019e11i | 0.0880722 | + | 0.152546i | 0.906696 | − | 0.421784i | \(-0.138596\pi\) |
−0.818624 | + | 0.574330i | \(0.805263\pi\) | |||||||
\(642\) | −1.96752e12 | + | 3.40784e12i | −0.457099 | + | 0.791719i | ||||
\(643\) | 4.82355e12 | 1.11280 | 0.556400 | − | 0.830915i | \(-0.312182\pi\) | ||||
0.556400 | + | 0.830915i | \(0.312182\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.09047e11 | −0.0475581 | ||||||||
\(646\) | 3.09005e12 | − | 5.35213e12i | 0.698103 | − | 1.20915i | ||||
\(647\) | −4.09586e12 | − | 7.09424e12i | −0.918916 | − | 1.59161i | −0.801065 | − | 0.598578i | \(-0.795733\pi\) |
−0.117851 | − | 0.993031i | \(-0.537601\pi\) | |||||||
\(648\) | −8.84030e11 | − | 1.53119e12i | −0.196961 | − | 0.341146i | ||||
\(649\) | −3.60555e11 | + | 6.24500e11i | −0.0797758 | + | 0.138176i | ||||
\(650\) | 3.53866e12 | 0.777551 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.04492e12 | −0.443162 | ||||||||
\(653\) | 2.90609e12 | − | 5.03349e12i | 0.625460 | − | 1.08333i | −0.362992 | − | 0.931792i | \(-0.618245\pi\) |
0.988452 | − | 0.151536i | \(-0.0484218\pi\) | |||||||
\(654\) | −7.77184e11 | − | 1.34612e12i | −0.166121 | − | 0.287730i | ||||
\(655\) | −1.20585e10 | − | 2.08860e10i | −0.00255982 | − | 0.00443373i | ||||
\(656\) | −7.28254e11 | + | 1.26137e12i | −0.153538 | + | 0.265935i | ||||
\(657\) | 8.18628e11 | 0.171412 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.45418e12 | −0.713446 | −0.356723 | − | 0.934210i | \(-0.616106\pi\) | ||||
−0.356723 | + | 0.934210i | \(0.616106\pi\) | |||||||
\(660\) | 4.24974e10 | − | 7.36076e10i | 0.00871795 | − | 0.0150999i | ||||
\(661\) | 2.72790e12 | + | 4.72487e12i | 0.555805 | + | 0.962683i | 0.997840 | + | 0.0656852i | \(0.0209233\pi\) |
−0.442035 | + | 0.896998i | \(0.645743\pi\) | |||||||
\(662\) | 1.54993e12 | + | 2.68455e12i | 0.313653 | + | 0.543264i | ||||
\(663\) | 5.01574e12 | − | 8.68751e12i | 1.00815 | − | 1.74616i | ||||
\(664\) | −2.32487e11 | −0.0464133 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.81699e12 | −0.751773 | ||||||||
\(667\) | −3.86709e11 | + | 6.69800e11i | −0.0756516 | + | 0.131032i | ||||
\(668\) | −5.56678e11 | − | 9.64195e11i | −0.108171 | − | 0.187357i | ||||
\(669\) | −6.03778e12 | − | 1.04577e13i | −1.16536 | − | 2.01846i | ||||
\(670\) | −8.20916e10 | + | 1.42187e11i | −0.0157385 | + | 0.0272598i | ||||
\(671\) | 5.87203e12 | 1.11825 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.93782e12 | 0.927828 | 0.463914 | − | 0.885880i | \(-0.346445\pi\) | ||||
0.463914 | + | 0.885880i | \(0.346445\pi\) | |||||||
\(674\) | 1.79127e12 | − | 3.10258e12i | 0.334343 | − | 0.579099i | ||||
\(675\) | −4.84319e11 | − | 8.38864e11i | −0.0897975 | − | 0.155534i | ||||
\(676\) | −2.85820e11 | − | 4.95054e11i | −0.0526420 | − | 0.0911785i | ||||
\(677\) | 4.53949e12 | − | 7.86262e12i | 0.830535 | − | 1.43853i | −0.0670798 | − | 0.997748i | \(-0.521368\pi\) |
0.897615 | − | 0.440781i | \(-0.145298\pi\) | |||||||
\(678\) | −3.54442e12 | −0.644186 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.35179e10 | 0.0113922 | ||||||||
\(681\) | −5.25480e12 | + | 9.10158e12i | −0.936255 | + | 1.62164i | ||||
\(682\) | 2.82163e12 | + | 4.88720e12i | 0.499424 | + | 0.865028i | ||||
\(683\) | 2.54958e12 | + | 4.41601e12i | 0.448308 | + | 0.776492i | 0.998276 | − | 0.0586939i | \(-0.0186936\pi\) |
−0.549968 | + | 0.835185i | \(0.685360\pi\) | |||||||
\(684\) | 1.83079e12 | − | 3.17102e12i | 0.319806 | − | 0.553920i | ||||
\(685\) | −2.45666e11 | −0.0426322 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.17774e13 | −2.01717 | ||||||||
\(688\) | 1.06338e12 | − | 1.84183e12i | 0.180942 | − | 0.313401i | ||||
\(689\) | −5.00181e12 | − | 8.66339e12i | −0.845553 | − | 1.46454i | ||||
\(690\) | 1.54295e10 | + | 2.67247e10i | 0.00259138 | + | 0.00448840i | ||||
\(691\) | 3.42055e12 | − | 5.92457e12i | 0.570748 | − | 0.988565i | −0.425741 | − | 0.904845i | \(-0.639986\pi\) |
0.996489 | − | 0.0837201i | \(-0.0266802\pi\) | |||||||
\(692\) | 3.54537e12 | 0.587739 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.12366e12 | 0.674785 | ||||||||
\(695\) | 8.20710e10 | − | 1.42151e11i | 0.0133431 | − | 0.0231110i | ||||
\(696\) | 1.01457e12 | + | 1.75729e12i | 0.163886 | + | 0.283859i | ||||
\(697\) | 5.13016e12 | + | 8.88570e12i | 0.823348 | + | 1.42608i | ||||
\(698\) | 1.10995e12 | − | 1.92249e12i | 0.176992 | − | 0.306559i | ||||
\(699\) | −1.61651e12 | −0.256112 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.89108e12 | 1.54708 | 0.773539 | − | 0.633748i | \(-0.218484\pi\) | ||||
0.773539 | + | 0.633748i | \(0.218484\pi\) | |||||||
\(702\) | −4.49792e11 | + | 7.79062e11i | −0.0699028 | + | 0.121075i | ||||
\(703\) | 5.83764e12 | + | 1.01111e13i | 0.901443 | + | 1.56134i | ||||
\(704\) | 4.32352e11 | + | 7.48856e11i | 0.0663377 | + | 0.114900i | ||||
\(705\) | 1.02441e10 | − | 1.77433e10i | 0.00156179 | − | 0.00270510i | ||||
\(706\) | −2.99169e12 | −0.453205 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.86896e11 | −0.102740 | ||||||||
\(709\) | 5.72156e12 | − | 9.91004e12i | 0.850368 | − | 1.47288i | −0.0305092 | − | 0.999534i | \(-0.509713\pi\) |
0.880877 | − | 0.473345i | \(-0.156954\pi\) | |||||||
\(710\) | −7.70319e10 | − | 1.33423e11i | −0.0113765 | − | 0.0197047i | ||||
\(711\) | 9.19579e11 | + | 1.59276e12i | 0.134951 | + | 0.233742i | ||||
\(712\) | −1.73807e12 | + | 3.01043e12i | −0.253459 | + | 0.439004i | ||||
\(713\) | −2.04889e12 | −0.296904 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.96153e11 | −0.0280684 | ||||||||
\(716\) | −2.55414e12 | + | 4.42390e12i | −0.363192 | + | 0.629067i | ||||
\(717\) | −3.01043e12 | − | 5.21422e12i | −0.425395 | − | 0.736806i | ||||
\(718\) | 1.66050e12 | + | 2.87608e12i | 0.233174 | + | 0.403869i | ||||
\(719\) | 3.60225e12 | − | 6.23928e12i | 0.502683 | − | 0.870672i | −0.497313 | − | 0.867571i | \(-0.665680\pi\) |
0.999995 | − | 0.00310036i | \(-0.000986878\pi\) | |||||||
\(720\) | 3.76330e10 | 0.00521882 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.03692e12 | −0.826795 | ||||||||
\(723\) | −1.39869e12 | + | 2.42260e12i | −0.190370 | + | 0.329730i | ||||
\(724\) | 4.27142e11 | + | 7.39832e11i | 0.0577762 | + | 0.100071i | ||||
\(725\) | 2.52119e12 | + | 4.36683e12i | 0.338911 | + | 0.587010i | ||||
\(726\) | 4.57908e11 | − | 7.93119e11i | 0.0611735 | − | 0.105956i | ||||
\(727\) | 7.27861e12 | 0.966371 | 0.483185 | − | 0.875518i | \(-0.339480\pi\) | ||||
0.483185 | + | 0.875518i | \(0.339480\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.50621e12 | −0.722070 | ||||||||
\(730\) | 1.28678e10 | − | 2.22876e10i | 0.00167707 | − | 0.00290476i | ||||
\(731\) | −7.49095e12 | − | 1.29747e13i | −0.970306 | − | 1.68062i | ||||
\(732\) | 2.79671e12 | + | 4.84405e12i | 0.360038 | + | 0.623603i | ||||
\(733\) | −6.84727e12 | + | 1.18598e13i | −0.876092 | + | 1.51744i | −0.0204976 | + | 0.999790i | \(0.506525\pi\) |
−0.855595 | + | 0.517646i | \(0.826808\pi\) | |||||||
\(734\) | −2.86929e12 | −0.364873 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.13948e11 | −0.0394373 | ||||||||
\(737\) | −7.87261e12 | + | 1.36358e13i | −0.982913 | + | 1.70246i | ||||
\(738\) | 3.03951e12 | + | 5.26459e12i | 0.377181 | + | 0.653297i | ||||
\(739\) | 8.29933e11 | + | 1.43749e12i | 0.102363 | + | 0.177298i | 0.912658 | − | 0.408725i | \(-0.134026\pi\) |
−0.810295 | + | 0.586023i | \(0.800693\pi\) | |||||||
\(740\) | −5.99981e10 | + | 1.03920e11i | −0.00735520 | + | 0.0127396i | ||||
\(741\) | −1.81796e13 | −2.21514 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.66431e11 | −0.0561484 | −0.0280742 | − | 0.999606i | \(-0.508937\pi\) | ||||
−0.0280742 | + | 0.999606i | \(0.508937\pi\) | |||||||
\(744\) | −2.68775e12 | + | 4.65532e12i | −0.321596 | + | 0.557020i | ||||
\(745\) | −1.15933e11 | − | 2.00803e11i | −0.0137881 | − | 0.0238817i | ||||
\(746\) | −4.35869e12 | − | 7.54948e12i | −0.515266 | − | 0.892467i | ||||
\(747\) | −4.85165e11 | + | 8.40331e11i | −0.0570095 | + | 0.0987433i | ||||
\(748\) | 6.09138e12 | 0.711474 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.02494e11 | 0.0464497 | ||||||||
\(751\) | 2.66801e12 | − | 4.62113e12i | 0.306061 | − | 0.530113i | −0.671436 | − | 0.741063i | \(-0.734322\pi\) |
0.977497 | + | 0.210949i | \(0.0676555\pi\) | |||||||
\(752\) | 1.04220e11 | + | 1.80514e11i | 0.0118842 | + | 0.0205840i | ||||
\(753\) | 3.41737e12 | + | 5.91905e12i | 0.387359 | + | 0.670926i | ||||
\(754\) | 2.34146e12 | − | 4.05553e12i | 0.263825 | − | 0.456958i | ||||
\(755\) | −1.89966e11 | −0.0212772 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.40938e12 | 0.930748 | 0.465374 | − | 0.885114i | \(-0.345920\pi\) | ||||
0.465374 | + | 0.885114i | \(0.345920\pi\) | |||||||
\(758\) | −9.97292e11 | + | 1.72736e12i | −0.109726 | + | 0.190052i | ||||
\(759\) | 1.47969e12 | + | 2.56290e12i | 0.161839 | + | 0.280314i | ||||
\(760\) | −5.75553e10 | − | 9.96886e10i | −0.00625783 | − | 0.0108389i | ||||
\(761\) | −3.08193e12 | + | 5.33806e12i | −0.333113 | + | 0.576969i | −0.983121 | − | 0.182959i | \(-0.941433\pi\) |
0.650007 | + | 0.759928i | \(0.274766\pi\) | |||||||
\(762\) | −1.04719e13 | −1.12520 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.29482e12 | −0.668441 | ||||||||
\(765\) | 1.32552e11 | − | 2.29587e11i | 0.0139930 | − | 0.0242366i | ||||
\(766\) | −3.26596e12 | − | 5.65681e12i | −0.342753 | − | 0.593666i | ||||
\(767\) | 7.92618e11 | + | 1.37286e12i | 0.0826961 | + | 0.143234i | ||||
\(768\) | −4.11838e11 | + | 7.13325e11i | −0.0427170 | + | 0.0739881i | ||||
\(769\) | 9.39193e12 | 0.968470 | 0.484235 | − | 0.874938i | \(-0.339098\pi\) | ||||
0.484235 | + | 0.874938i | \(0.339098\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.33203e13 | 1.35759 | ||||||||
\(772\) | 2.30552e12 | − | 3.99327e12i | 0.233610 | − | 0.404624i | ||||
\(773\) | 2.11318e12 | + | 3.66014e12i | 0.212877 | + | 0.368714i | 0.952614 | − | 0.304182i | \(-0.0983832\pi\) |
−0.739737 | + | 0.672897i | \(0.765050\pi\) | |||||||
\(774\) | −4.43823e12 | − | 7.68723e12i | −0.444504 | − | 0.769903i | ||||
\(775\) | −6.67899e12 | + | 1.15683e13i | −0.665048 | + | 1.15190i | ||||
\(776\) | −3.68388e12 | −0.364693 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.21823e12 | −0.804212 | ||||||||
\(779\) | 9.29716e12 | − | 1.61031e13i | 0.904548 | − | 1.56672i | ||||
\(780\) | −9.34231e10 | − | 1.61813e11i | −0.00903709 | − | 0.0156527i | ||||
\(781\) | −7.38739e12 | − | 1.27953e13i | −0.710495 | − | 1.23061i | ||||
\(782\) | −1.10580e12 | + | 1.91530e12i | −0.105741 | + | 0.183150i | ||||
\(783\) | −1.28186e12 | −0.121874 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.21684e11 | −0.0208363 | ||||||||
\(786\) | 1.10155e12 | − | 1.90794e12i | 0.102944 | − | 0.178305i | ||||
\(787\) | 2.94913e11 | + | 5.10804e11i | 0.0274036 | + | 0.0474644i | 0.879402 | − | 0.476080i | \(-0.157943\pi\) |
−0.851998 | + | 0.523544i | \(0.824609\pi\) | |||||||
\(788\) | −5.15477e12 | − | 8.92832e12i | −0.476257 | − | 0.824901i | ||||
\(789\) | −6.93293e12 | + | 1.20082e13i | −0.636899 | + | 1.10314i | ||||
\(790\) | 5.78183e10 | 0.00528133 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.60901e12 | 0.325931 | ||||||||
\(793\) | 6.45432e12 | − | 1.11792e13i | 0.579590 | − | 1.00388i | ||||
\(794\) | 2.88651e12 | + | 4.99959e12i | 0.257740 | + | 0.446418i | ||||
\(795\) | −2.84375e11 | − | 4.92553e11i | −0.0252488 | − | 0.0437321i | ||||
\(796\) | −4.82371e12 | + | 8.35490e12i | −0.425865 | + | 0.737620i | ||||
\(797\) | −2.83029e12 | −0.248467 | −0.124233 | − | 0.992253i | \(-0.539647\pi\) | ||||
−0.124233 | + | 0.992253i | \(0.539647\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.46834e12 | 0.127458 | ||||||||
\(800\) | −1.02341e12 | + | 1.77260e12i | −0.0883373 | + | 0.153005i | ||||
\(801\) | 7.25420e12 | + | 1.25646e13i | 0.622649 | + | 1.07846i | ||||
\(802\) | 1.90875e12 | + | 3.30606e12i | 0.162916 | + | 0.282180i | ||||
\(803\) | 1.23402e12 | − | 2.13739e12i | 0.104738 | − | 0.181411i | ||||
\(804\) | −1.49982e13 | −1.26586 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.24057e13 | 1.03541 | ||||||||
\(807\) | −8.65937e12 | + | 1.49985e13i | −0.718713 | + | 1.24485i | ||||
\(808\) | 1.29475e11 | + | 2.24257e11i | 0.0106865 | + | 0.0185095i | ||||
\(809\) | −5.80166e12 | − | 1.00488e13i | −0.476194 | − | 0.824793i | 0.523434 | − | 0.852066i | \(-0.324651\pi\) |
−0.999628 | + | 0.0272738i | \(0.991317\pi\) | |||||||
\(810\) | −1.15994e11 | + | 2.00907e11i | −0.00946787 | + | 0.0163988i | ||||
\(811\) | −4.13817e12 | −0.335903 | −0.167952 | − | 0.985795i | \(-0.553715\pi\) | ||||
−0.167952 | + | 0.985795i | \(0.553715\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.71383e12 | 0.619245 | ||||||||
\(814\) | −5.75383e12 | + | 9.96593e12i | −0.459354 | + | 0.795624i | ||||
\(815\) | 1.34157e11 | + | 2.32367e11i | 0.0106514 | + | 0.0184487i | ||||
\(816\) | 2.90118e12 | + | 5.02500e12i | 0.229071 | + | 0.396762i | ||||
\(817\) | −1.35755e13 | + | 2.35135e13i | −1.06600 | + | 1.84636i | ||||
\(818\) | 1.23950e13 | 0.967961 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.91109e11 | 0.0147611 | ||||||||
\(821\) | 9.78514e10 | − | 1.69484e11i | 0.00751662 | − | 0.0130192i | −0.862243 | − | 0.506495i | \(-0.830941\pi\) |
0.869759 | + | 0.493476i | \(0.164274\pi\) | |||||||
\(822\) | −1.12208e13 | − | 1.94350e13i | −0.857237 | − | 1.48478i | ||||
\(823\) | 4.25699e12 | + | 7.37333e12i | 0.323447 | + | 0.560227i | 0.981197 | − | 0.193009i | \(-0.0618248\pi\) |
−0.657750 | + | 0.753237i | \(0.728491\pi\) | |||||||
\(824\) | 2.48995e12 | − | 4.31272e12i | 0.188156 | − | 0.325896i | ||||
\(825\) | 1.92941e13 | 1.45004 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.19931e12 | −0.0891576 | −0.0445788 | − | 0.999006i | \(-0.514195\pi\) | ||||
−0.0445788 | + | 0.999006i | \(0.514195\pi\) | |||||||
\(828\) | −6.55161e11 | + | 1.13477e12i | −0.0484409 | + | 0.0839020i | ||||
\(829\) | 8.20420e12 | + | 1.42101e13i | 0.603311 | + | 1.04496i | 0.992316 | + | 0.123729i | \(0.0394855\pi\) |
−0.389005 | + | 0.921236i | \(0.627181\pi\) | |||||||
\(830\) | 1.52523e10 | + | 2.64178e10i | 0.00111554 | + | 0.00193217i | ||||
\(831\) | 1.98218e12 | − | 3.43323e12i | 0.144191 | − | 0.249746i | ||||
\(832\) | 1.90090e12 | 0.137532 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.49944e13 | 1.07320 | ||||||||
\(835\) | −7.30418e10 | + | 1.26512e11i | −0.00519975 | + | 0.00900623i | ||||
\(836\) | −5.51957e12 | − | 9.56017e12i | −0.390820 | − | 0.676920i | ||||
\(837\) | −1.69791e12 | − | 2.94086e12i | −0.119577 | − | 0.207114i | ||||
\(838\) | −4.69785e12 | + | 8.13691e12i | −0.329080 | + | 0.569982i | ||||
\(839\) | −1.67670e13 | −1.16822 | −0.584111 | − | 0.811674i | \(-0.698557\pi\) | ||||
−0.584111 | + | 0.811674i | \(0.698557\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.83425e12 | −0.540027 | ||||||||
\(842\) | −9.00327e12 | + | 1.55941e13i | −0.617299 | + | 1.06919i | ||||
\(843\) | 3.32574e12 | + | 5.76034e12i | 0.226811 | + | 0.392848i | ||||
\(844\) | 2.01303e12 | + | 3.48668e12i | 0.136556 | + | 0.236521i | ||||
\(845\) | −3.75025e10 | + | 6.49562e10i | −0.00253049 | + | 0.00438294i | ||||
\(846\) | 8.69962e11 | 0.0583894 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.78625e12 | 0.384252 | ||||||||
\(849\) | −1.00337e13 | + | 1.73789e13i | −0.662791 | + | 1.14799i | ||||
\(850\) | 7.20937e12 | + | 1.24870e13i | 0.473710 | + | 0.820489i | ||||
\(851\) | −2.08904e12 | − | 3.61833e12i | −0.136541 | − | 0.236496i | ||||
\(852\) | 7.03688e12 | − | 1.21882e13i | 0.457511 | − | 0.792433i | ||||
\(853\) | −6.93277e12 | −0.448370 | −0.224185 | − | 0.974547i | \(-0.571972\pi\) | ||||
−0.224185 | + | 0.974547i | \(0.571972\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.80437e11 | −0.0307460 | ||||||||
\(856\) | −2.62640e12 | + | 4.54906e12i | −0.167197 | + | 0.289594i | ||||
\(857\) | 1.30460e11 | + | 2.25963e11i | 0.00826158 | + | 0.0143095i | 0.870127 | − | 0.492828i | \(-0.164037\pi\) |
−0.861865 | + | 0.507138i | \(0.830704\pi\) | |||||||
\(858\) | −8.95930e12 | − | 1.55180e13i | −0.564393 | − | 0.977557i | ||||
\(859\) | 1.27103e13 | − | 2.20149e13i | 0.796502 | − | 1.37958i | −0.125379 | − | 0.992109i | \(-0.540015\pi\) |
0.921881 | − | 0.387473i | \(-0.126652\pi\) | |||||||
\(860\) | −2.79053e11 | −0.0173957 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.08427e13 | 0.668889 | ||||||||
\(863\) | −3.59309e12 | + | 6.22342e12i | −0.220506 | + | 0.381927i | −0.954962 | − | 0.296729i | \(-0.904104\pi\) |
0.734456 | + | 0.678656i | \(0.237437\pi\) | |||||||
\(864\) | −2.60167e11 | − | 4.50622e11i | −0.0158833 | − | 0.0275106i | ||||
\(865\) | −2.32594e11 | − | 4.02865e11i | −0.0141262 | − | 0.0244674i | ||||
\(866\) | 4.53267e12 | − | 7.85082e12i | 0.273857 | − | 0.474334i | ||||
\(867\) | 1.81322e13 | 1.08984 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.54479e12 | 0.329835 | ||||||||
\(870\) | 1.33122e11 | − | 2.30575e11i | 0.00787798 | − | 0.0136451i | ||||
\(871\) | 1.73066e13 | + | 2.99758e13i | 1.01889 | + | 1.76478i | ||||
\(872\) | −1.03745e12 | − | 1.79692e12i | −0.0607635 | − | 0.105245i | ||||
\(873\) | −7.68769e12 | + | 1.33155e13i | −0.447953 | + | 0.775877i | ||||
\(874\) | 4.00797e12 | 0.232340 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.35094e12 | 0.134888 | ||||||||
\(877\) | 1.34403e13 | − | 2.32793e13i | 0.767205 | − | 1.32884i | −0.171868 | − | 0.985120i | \(-0.554980\pi\) |
0.939073 | − | 0.343718i | \(-0.111686\pi\) | |||||||
\(878\) | −5.92989e12 | − | 1.02709e13i | −0.336761 | − | 0.583287i | ||||
\(879\) | 1.54151e13 | + | 2.66997e13i | 0.870954 | + | 1.50854i | ||||
\(880\) | 5.67290e10 | − | 9.82575e10i | 0.00318884 | − | 0.00552324i | ||||
\(881\) | 5.33553e11 | 0.0298391 | 0.0149195 | − | 0.999889i | \(-0.495251\pi\) | ||||
0.0149195 | + | 0.999889i | \(0.495251\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.42561e12 | 0.355706 | 0.177853 | − | 0.984057i | \(-0.443085\pi\) | ||||
0.177853 | + | 0.984057i | \(0.443085\pi\) | |||||||
\(884\) | 6.69542e12 | − | 1.15968e13i | 0.368759 | − | 0.638710i | ||||
\(885\) | 4.50639e10 | + | 7.80530e10i | 0.00246936 | + | 0.00427705i | ||||
\(886\) | 7.40165e11 | + | 1.28200e12i | 0.0403531 | + | 0.0698936i | ||||
\(887\) | 1.44219e12 | − | 2.49794e12i | 0.0782285 | − | 0.135496i | −0.824257 | − | 0.566216i | \(-0.808407\pi\) |
0.902486 | + | 0.430720i | \(0.141740\pi\) | |||||||
\(888\) | −1.09617e13 | −0.591586 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.56106e11 | 0.0243675 | ||||||||
\(891\) | −1.11238e13 | + | 1.92671e13i | −0.591296 | + | 1.02416i | ||||
\(892\) | −8.05973e12 | − | 1.39599e13i | −0.426264 | − | 0.738311i | ||||
\(893\) | −1.33051e12 | − | 2.30450e12i | −0.0700141 | − | 0.121268i | ||||
\(894\) | 1.05905e13 | − | 1.83433e13i | 0.554497 | − | 0.960416i | ||||
\(895\) | 6.70259e11 | 0.0349172 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.50570e12 | 0.335527 | ||||||||
\(898\) | −1.01507e12 | + | 1.75816e12i | −0.0520900 | + | 0.0902225i | ||||
\(899\) | 8.83871e12 | + | 1.53091e13i | 0.451305 | + | 0.781683i | ||||
\(900\) | 4.27140e12 | + | 7.39828e12i | 0.217010 | + | 0.375872i | ||||
\(901\) | 2.03806e13 | − | 3.53002e13i | 1.03028 | − | 1.78449i | ||||
\(902\) | 1.83274e13 | 0.921873 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.73138e12 | −0.235630 | ||||||||
\(905\) | 5.60454e10 | − | 9.70735e10i | 0.00277729 | − | 0.00481041i | ||||
\(906\) | −8.67672e12 | − | 1.50285e13i | −0.427837 | − | 0.741036i | ||||
\(907\) | 8.74404e12 | + | 1.51451e13i | 0.429022 | + | 0.743088i | 0.996787 | − | 0.0801031i | \(-0.0255249\pi\) |
−0.567765 | + | 0.823191i | \(0.692192\pi\) | |||||||
\(908\) | −7.01454e12 | + | 1.21495e13i | −0.342462 | + | 0.593162i | ||||
\(909\) | 1.08078e12 | 0.0525049 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.68088e13 | −0.808543 | −0.404271 | − | 0.914639i | \(-0.632475\pi\) | ||||
−0.404271 | + | 0.914639i | \(0.632475\pi\) | |||||||
\(912\) | 5.25768e12 | − | 9.10657e12i | 0.251662 | − | 0.435891i | ||||
\(913\) | 1.46270e12 | + | 2.53348e12i | 0.0696687 | + | 0.120670i | ||||
\(914\) | 8.22522e12 | + | 1.42465e13i | 0.389843 | + | 0.675228i | ||||
\(915\) | 3.66957e11 | − | 6.35588e11i | 0.0173069 | − | 0.0299765i | ||||
\(916\) | −1.57214e13 | −0.737840 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.66548e12 | −0.170348 | ||||||||
\(919\) | 1.24473e13 | − | 2.15594e13i | 0.575648 | − | 0.997051i | −0.420323 | − | 0.907374i | \(-0.638083\pi\) |
0.995971 | − | 0.0896768i | \(-0.0285834\pi\) | |||||||
\(920\) | 2.05966e10 | + | 3.56743e10i | 0.000947872 | + | 0.00164176i | ||||
\(921\) | −1.39201e13 | − | 2.41104e13i | −0.637492 | − | 1.10417i | ||||
\(922\) | −6.48186e12 | + | 1.12269e13i | −0.295400 | + | 0.511648i | ||||
\(923\) | −3.24798e13 | −1.47301 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.72395e13 | −1.22338 | ||||||||
\(926\) | −1.15834e13 | + | 2.00631e13i | −0.517711 | + | 0.896703i | ||||
\(927\) | −1.03923e13 | − | 1.80000e13i | −0.462224 | − | 0.800596i | ||||
\(928\) | 1.35434e12 | + | 2.34578e12i | 0.0599461 | + | 0.103830i | ||||
\(929\) | −1.92243e13 | + | 3.32975e13i | −0.846799 | + | 1.46670i | 0.0372516 | + | 0.999306i | \(0.488140\pi\) |
−0.884050 | + | 0.467392i | \(0.845194\pi\) | |||||||
\(930\) | 7.05320e11 | 0.0309181 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.15785e12 | −0.0936806 | ||||||||
\(933\) | 2.52273e13 | − | 4.36950e13i | 1.08994 | − | 1.88783i | ||||
\(934\) | −3.57627e12 | − | 6.19429e12i | −0.153769 | − | 0.266336i | ||||
\(935\) | −3.99626e11 | − | 6.92172e11i | −0.0171002 | − | 0.0296184i | ||||
\(936\) | 3.96689e12 | − | 6.87086e12i | 0.168931 | − | 0.292597i | ||||
\(937\) | −4.89574e11 | −0.0207486 | −0.0103743 | − | 0.999946i | \(-0.503302\pi\) | ||||
−0.0103743 | + | 0.999946i | \(0.503302\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.60748e13 | −0.674763 | ||||||||
\(940\) | 1.36747e10 | − | 2.36852e10i | 0.000571270 | − | 0.000989469i | ||||
\(941\) | −1.10361e13 | − | 1.91150e13i | −0.458840 | − | 0.794734i | 0.540060 | − | 0.841626i | \(-0.318401\pi\) |
−0.998900 | + | 0.0468926i | \(0.985068\pi\) | |||||||
\(942\) | −1.01254e13 | − | 1.75378e13i | −0.418972 | − | 0.725681i | ||||
\(943\) | −3.32706e12 | + | 5.76263e12i | −0.137012 | + | 0.237311i | ||||
\(944\) | −9.16926e11 | −0.0375803 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.67612e13 | −1.08642 | ||||||||
\(947\) | −2.43071e11 | + | 4.21012e11i | −0.00982108 | + | 0.0170106i | −0.870894 | − | 0.491471i | \(-0.836460\pi\) |
0.861073 | + | 0.508481i | \(0.169793\pi\) | |||||||
\(948\) | 2.64086e12 | + | 4.57410e12i | 0.106196 | + | 0.183936i | ||||
\(949\) | −2.71278e12 | − | 4.69868e12i | −0.108572 | − | 0.188052i | ||||
\(950\) | 1.30652e13 | − | 2.26296e13i | 0.520428 | − | 0.901407i | ||||
\(951\) | 5.19171e13 | 2.05825 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.77682e13 | −1.09051 | −0.545254 | − | 0.838271i | \(-0.683567\pi\) | ||||
−0.545254 | + | 0.838271i | \(0.683567\pi\) | |||||||
\(954\) | 1.20750e13 | − | 2.09146e13i | 0.471977 | − | 0.817488i | ||||
\(955\) | 4.12972e11 | + | 7.15289e11i | 0.0160659 | + | 0.0278270i | ||||
\(956\) | −4.01857e12 | − | 6.96037e12i | −0.155601 | − | 0.269508i | ||||
\(957\) | 1.27665e13 | − | 2.21122e13i | 0.492003 | − | 0.852174i | ||||
\(958\) | 1.39128e12 | 0.0533667 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.08075e11 | 0.00410680 | ||||||||
\(961\) | −1.01951e13 | + | 1.76585e13i | −0.385601 | + | 0.667881i | ||||
\(962\) | 1.26488e13 | + | 2.19084e13i | 0.476169 | + | 0.824750i | ||||
\(963\) | 1.09618e13 | + | 1.89864e13i | 0.410737 | + | 0.711418i | ||||
\(964\) | −1.86708e12 | + | 3.23388e12i | −0.0696333 | + | 0.120608i | ||||
\(965\) | −6.05015e11 | −0.0224591 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.53282e12 | −0.0931505 | −0.0465752 | − | 0.998915i | \(-0.514831\pi\) | ||||
−0.0465752 | + | 0.998915i | \(0.514831\pi\) | |||||||
\(968\) | 6.11253e11 | − | 1.05872e12i | 0.0223760 | − | 0.0387563i | ||||
\(969\) | −3.70376e13 | − | 6.41510e13i | −1.34954 | − | 2.33747i | ||||
\(970\) | 2.41681e11 | + | 4.18604e11i | 0.00876536 | + | 0.0151821i | ||||
\(971\) | −4.26211e12 | + | 7.38219e12i | −0.153864 | + | 0.266501i | −0.932645 | − | 0.360795i | \(-0.882505\pi\) |
0.778781 | + | 0.627296i | \(0.215839\pi\) | |||||||
\(972\) | −1.86917e13 | −0.671661 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 7.71096e9 | 0.000274532 | ||||||||
\(975\) | 2.12073e13 | − | 3.67321e13i | 0.751562 | − | 1.30174i | ||||
\(976\) | 3.73328e12 | + | 6.46624e12i | 0.131694 | + | 0.228101i | ||||
\(977\) | 1.68588e13 | + | 2.92003e13i | 0.591972 | + | 1.02533i | 0.993967 | + | 0.109684i | \(0.0349839\pi\) |
−0.401994 | + | 0.915642i | \(0.631683\pi\) | |||||||
\(978\) | −1.22553e13 | + | 2.12268e13i | −0.428350 | + | 0.741923i | ||||
\(979\) | 4.37407e13 | 1.52182 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.66001e12 | −0.298544 | ||||||||
\(982\) | −4.70912e12 | + | 8.15643e12i | −0.161599 | + | 0.279897i | ||||
\(983\) | −1.63952e12 | − | 2.83973e12i | −0.0560049 | − | 0.0970033i | 0.836664 | − | 0.547717i | \(-0.184503\pi\) |
−0.892669 | + | 0.450714i | \(0.851170\pi\) | |||||||
\(984\) | 8.72890e12 | + | 1.51189e13i | 0.296812 | + | 0.514094i | ||||
\(985\) | −6.76358e11 | + | 1.17149e12i | −0.0228936 | + | 0.0396529i | ||||
\(986\) | 1.90812e13 | 0.642923 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.42676e13 | −0.810253 | ||||||||
\(989\) | 4.85809e12 | − | 8.41446e12i | 0.161467 | − | 0.279668i | ||||
\(990\) | −2.36770e11 | − | 4.10097e11i | −0.00783372 | − | 0.0135684i | ||||
\(991\) | −1.14647e13 | − | 1.98575e13i | −0.377600 | − | 0.654023i | 0.613112 | − | 0.789996i | \(-0.289917\pi\) |
−0.990713 | + | 0.135973i | \(0.956584\pi\) | |||||||
\(992\) | −3.58783e12 | + | 6.21430e12i | −0.117633 | + | 0.203746i | ||||
\(993\) | 3.71550e13 | 1.21268 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.26584e12 | 0.0409425 | ||||||||
\(996\) | −1.39330e12 | + | 2.41327e12i | −0.0448620 | + | 0.0777032i | ||||
\(997\) | −6.27545e12 | − | 1.08694e13i | −0.201148 | − | 0.348399i | 0.747750 | − | 0.663980i | \(-0.231134\pi\) |
−0.948899 | + | 0.315581i | \(0.897801\pi\) | |||||||
\(998\) | −1.98357e13 | − | 3.43564e13i | −0.632936 | − | 1.09628i | ||||
\(999\) | 3.46236e12 | − | 5.99698e12i | 0.109983 | − | 0.190497i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 98.10.c.m.79.1 | 8 | ||
7.2 | even | 3 | 98.10.a.k.1.4 | yes | 4 | ||
7.3 | odd | 6 | inner | 98.10.c.m.67.4 | 8 | ||
7.4 | even | 3 | inner | 98.10.c.m.67.1 | 8 | ||
7.5 | odd | 6 | 98.10.a.k.1.1 | ✓ | 4 | ||
7.6 | odd | 2 | inner | 98.10.c.m.79.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.10.a.k.1.1 | ✓ | 4 | 7.5 | odd | 6 | ||
98.10.a.k.1.4 | yes | 4 | 7.2 | even | 3 | ||
98.10.c.m.67.1 | 8 | 7.4 | even | 3 | inner | ||
98.10.c.m.67.4 | 8 | 7.3 | odd | 6 | inner | ||
98.10.c.m.79.1 | 8 | 1.1 | even | 1 | trivial | ||
98.10.c.m.79.4 | 8 | 7.6 | odd | 2 | inner |