Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,10,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.a (trivial) |
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: | yes |
Analytic conductor: | \(22.1465409550\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} + \cdots + 52\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.220103\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.77990 | −0.0786611 | −0.0393305 | − | 0.999226i | \(-0.512523\pi\) | ||||
−0.0393305 | + | 0.999226i | \(0.512523\pi\) | |||||||
\(3\) | −203.939 | −1.45363 | −0.726816 | − | 0.686832i | \(-0.759001\pi\) | ||||
−0.726816 | + | 0.686832i | \(0.759001\pi\) | |||||||
\(4\) | −508.832 | −0.993812 | ||||||||
\(5\) | 1139.29 | 0.815209 | 0.407604 | − | 0.913159i | \(-0.366364\pi\) | ||||
0.407604 | + | 0.913159i | \(0.366364\pi\) | |||||||
\(6\) | 362.990 | 0.114344 | ||||||||
\(7\) | 4324.96 | 0.680833 | 0.340417 | − | 0.940275i | \(-0.389432\pi\) | ||||
0.340417 | + | 0.940275i | \(0.389432\pi\) | |||||||
\(8\) | 1816.98 | 0.156835 | ||||||||
\(9\) | 21908.1 | 1.11305 | ||||||||
\(10\) | −2027.82 | −0.0641252 | ||||||||
\(11\) | 30380.9 | 0.625652 | 0.312826 | − | 0.949810i | \(-0.398724\pi\) | ||||
0.312826 | + | 0.949810i | \(0.398724\pi\) | |||||||
\(12\) | 103771. | 1.44464 | ||||||||
\(13\) | 34108.8 | 0.331224 | 0.165612 | − | 0.986191i | \(-0.447040\pi\) | ||||
0.165612 | + | 0.986191i | \(0.447040\pi\) | |||||||
\(14\) | −7697.98 | −0.0535551 | ||||||||
\(15\) | −232345. | −1.18501 | ||||||||
\(16\) | 257288. | 0.981476 | ||||||||
\(17\) | −566042. | −1.64372 | −0.821861 | − | 0.569688i | \(-0.807064\pi\) | ||||
−0.821861 | + | 0.569688i | \(0.807064\pi\) | |||||||
\(18\) | −38994.1 | −0.0875534 | ||||||||
\(19\) | 246718. | 0.434319 | 0.217160 | − | 0.976136i | \(-0.430321\pi\) | ||||
0.217160 | + | 0.976136i | \(0.430321\pi\) | |||||||
\(20\) | −579707. | −0.810165 | ||||||||
\(21\) | −882027. | −0.989681 | ||||||||
\(22\) | −54074.8 | −0.0492145 | ||||||||
\(23\) | −1.19112e6 | −0.887523 | −0.443761 | − | 0.896145i | \(-0.646356\pi\) | ||||
−0.443761 | + | 0.896145i | \(0.646356\pi\) | |||||||
\(24\) | −370552. | −0.227981 | ||||||||
\(25\) | −655146. | −0.335435 | ||||||||
\(26\) | −60710.1 | −0.0260544 | ||||||||
\(27\) | −453781. | −0.164327 | ||||||||
\(28\) | −2.20068e6 | −0.676621 | ||||||||
\(29\) | 7.14721e6 | 1.87649 | 0.938243 | − | 0.345976i | \(-0.112452\pi\) | ||||
0.938243 | + | 0.345976i | \(0.112452\pi\) | |||||||
\(30\) | 413551. | 0.0932144 | ||||||||
\(31\) | −5.75774e6 | −1.11976 | −0.559879 | − | 0.828574i | \(-0.689152\pi\) | ||||
−0.559879 | + | 0.828574i | \(0.689152\pi\) | |||||||
\(32\) | −1.38824e6 | −0.234039 | ||||||||
\(33\) | −6.19584e6 | −0.909468 | ||||||||
\(34\) | 1.00750e6 | 0.129297 | ||||||||
\(35\) | 4.92738e6 | 0.555021 | ||||||||
\(36\) | −1.11475e7 | −1.10616 | ||||||||
\(37\) | −8.31491e6 | −0.729374 | −0.364687 | − | 0.931130i | \(-0.618824\pi\) | ||||
−0.364687 | + | 0.931130i | \(0.618824\pi\) | |||||||
\(38\) | −439132. | −0.0341640 | ||||||||
\(39\) | −6.95611e6 | −0.481477 | ||||||||
\(40\) | 2.07006e6 | 0.127854 | ||||||||
\(41\) | −4.50031e6 | −0.248723 | −0.124361 | − | 0.992237i | \(-0.539688\pi\) | ||||
−0.124361 | + | 0.992237i | \(0.539688\pi\) | |||||||
\(42\) | 1.56992e6 | 0.0778494 | ||||||||
\(43\) | −3.41880e6 | −0.152499 | ||||||||
\(44\) | −1.54588e7 | −0.621781 | ||||||||
\(45\) | 2.49596e7 | 0.907365 | ||||||||
\(46\) | 2.12007e6 | 0.0698135 | ||||||||
\(47\) | −2.85694e7 | −0.854006 | −0.427003 | − | 0.904250i | \(-0.640431\pi\) | ||||
−0.427003 | + | 0.904250i | \(0.640431\pi\) | |||||||
\(48\) | −5.24710e7 | −1.42670 | ||||||||
\(49\) | −2.16483e7 | −0.536466 | ||||||||
\(50\) | 1.16609e6 | 0.0263856 | ||||||||
\(51\) | 1.15438e8 | 2.38937 | ||||||||
\(52\) | −1.73556e7 | −0.329174 | ||||||||
\(53\) | 2.07892e7 | 0.361907 | 0.180953 | − | 0.983492i | \(-0.442082\pi\) | ||||
0.180953 | + | 0.983492i | \(0.442082\pi\) | |||||||
\(54\) | 807684. | 0.0129262 | ||||||||
\(55\) | 3.46126e7 | 0.510037 | ||||||||
\(56\) | 7.85834e6 | 0.106779 | ||||||||
\(57\) | −5.03154e7 | −0.631341 | ||||||||
\(58\) | −1.27213e7 | −0.147606 | ||||||||
\(59\) | −3.59484e6 | −0.0386229 | −0.0193115 | − | 0.999814i | \(-0.506147\pi\) | ||||
−0.0193115 | + | 0.999814i | \(0.506147\pi\) | |||||||
\(60\) | 1.18225e8 | 1.17768 | ||||||||
\(61\) | −5.73421e7 | −0.530261 | −0.265130 | − | 0.964213i | \(-0.585415\pi\) | ||||
−0.265130 | + | 0.964213i | \(0.585415\pi\) | |||||||
\(62\) | 1.02482e7 | 0.0880813 | ||||||||
\(63\) | 9.47516e7 | 0.757799 | ||||||||
\(64\) | −1.29261e8 | −0.963066 | ||||||||
\(65\) | 3.88598e7 | 0.270016 | ||||||||
\(66\) | 1.10280e7 | 0.0715397 | ||||||||
\(67\) | 1.95331e8 | 1.18422 | 0.592111 | − | 0.805856i | \(-0.298295\pi\) | ||||
0.592111 | + | 0.805856i | \(0.298295\pi\) | |||||||
\(68\) | 2.88020e8 | 1.63355 | ||||||||
\(69\) | 2.42915e8 | 1.29013 | ||||||||
\(70\) | −8.77022e6 | −0.0436586 | ||||||||
\(71\) | −4.27590e6 | −0.0199694 | −0.00998471 | − | 0.999950i | \(-0.503178\pi\) | ||||
−0.00998471 | + | 0.999950i | \(0.503178\pi\) | |||||||
\(72\) | 3.98064e7 | 0.174565 | ||||||||
\(73\) | −1.36748e8 | −0.563595 | −0.281798 | − | 0.959474i | \(-0.590931\pi\) | ||||
−0.281798 | + | 0.959474i | \(0.590931\pi\) | |||||||
\(74\) | 1.47997e7 | 0.0573733 | ||||||||
\(75\) | 1.33610e8 | 0.487599 | ||||||||
\(76\) | −1.25538e8 | −0.431632 | ||||||||
\(77\) | 1.31396e8 | 0.425965 | ||||||||
\(78\) | 1.23812e7 | 0.0378735 | ||||||||
\(79\) | −3.21883e8 | −0.929770 | −0.464885 | − | 0.885371i | \(-0.653904\pi\) | ||||
−0.464885 | + | 0.885371i | \(0.653904\pi\) | |||||||
\(80\) | 2.93125e8 | 0.800108 | ||||||||
\(81\) | −3.38673e8 | −0.874175 | ||||||||
\(82\) | 8.01009e6 | 0.0195648 | ||||||||
\(83\) | −5.39331e8 | −1.24739 | −0.623697 | − | 0.781666i | \(-0.714370\pi\) | ||||
−0.623697 | + | 0.781666i | \(0.714370\pi\) | |||||||
\(84\) | 4.48804e8 | 0.983557 | ||||||||
\(85\) | −6.44885e8 | −1.33998 | ||||||||
\(86\) | 6.08511e6 | 0.0119957 | ||||||||
\(87\) | −1.45759e9 | −2.72772 | ||||||||
\(88\) | 5.52013e7 | 0.0981244 | ||||||||
\(89\) | 2.05645e8 | 0.347426 | 0.173713 | − | 0.984796i | \(-0.444423\pi\) | ||||
0.173713 | + | 0.984796i | \(0.444423\pi\) | |||||||
\(90\) | −4.44256e7 | −0.0713743 | ||||||||
\(91\) | 1.47519e8 | 0.225508 | ||||||||
\(92\) | 6.06079e8 | 0.882031 | ||||||||
\(93\) | 1.17423e9 | 1.62772 | ||||||||
\(94\) | 5.08506e7 | 0.0671770 | ||||||||
\(95\) | 2.81083e8 | 0.354061 | ||||||||
\(96\) | 2.83116e8 | 0.340207 | ||||||||
\(97\) | −1.10879e9 | −1.27168 | −0.635840 | − | 0.771821i | \(-0.719346\pi\) | ||||
−0.635840 | + | 0.771821i | \(0.719346\pi\) | |||||||
\(98\) | 3.85318e7 | 0.0421990 | ||||||||
\(99\) | 6.65587e8 | 0.696380 | ||||||||
\(100\) | 3.33359e8 | 0.333359 | ||||||||
\(101\) | −1.88058e9 | −1.79823 | −0.899117 | − | 0.437709i | \(-0.855790\pi\) | ||||
−0.899117 | + | 0.437709i | \(0.855790\pi\) | |||||||
\(102\) | −2.05468e8 | −0.187950 | ||||||||
\(103\) | 9.90610e8 | 0.867232 | 0.433616 | − | 0.901098i | \(-0.357237\pi\) | ||||
0.433616 | + | 0.901098i | \(0.357237\pi\) | |||||||
\(104\) | 6.19748e7 | 0.0519476 | ||||||||
\(105\) | −1.00488e9 | −0.806797 | ||||||||
\(106\) | −3.70027e7 | −0.0284680 | ||||||||
\(107\) | 1.83523e6 | 0.00135352 | 0.000676759 | − | 1.00000i | \(-0.499785\pi\) | ||||
0.000676759 | 1.00000i | \(0.499785\pi\) | ||||||||
\(108\) | 2.30898e8 | 0.163311 | ||||||||
\(109\) | −1.28953e9 | −0.875007 | −0.437503 | − | 0.899217i | \(-0.644137\pi\) | ||||
−0.437503 | + | 0.899217i | \(0.644137\pi\) | |||||||
\(110\) | −6.16068e7 | −0.0401201 | ||||||||
\(111\) | 1.69573e9 | 1.06024 | ||||||||
\(112\) | 1.11276e9 | 0.668221 | ||||||||
\(113\) | −1.37637e9 | −0.794115 | −0.397057 | − | 0.917794i | \(-0.629969\pi\) | ||||
−0.397057 | + | 0.917794i | \(0.629969\pi\) | |||||||
\(114\) | 8.95561e7 | 0.0496619 | ||||||||
\(115\) | −1.35703e9 | −0.723517 | ||||||||
\(116\) | −3.63673e9 | −1.86488 | ||||||||
\(117\) | 7.47258e8 | 0.368667 | ||||||||
\(118\) | 6.39844e6 | 0.00303812 | ||||||||
\(119\) | −2.44811e9 | −1.11910 | ||||||||
\(120\) | −4.22166e8 | −0.185852 | ||||||||
\(121\) | −1.43495e9 | −0.608559 | ||||||||
\(122\) | 1.02063e8 | 0.0417109 | ||||||||
\(123\) | 9.17789e8 | 0.361551 | ||||||||
\(124\) | 2.92972e9 | 1.11283 | ||||||||
\(125\) | −2.97157e9 | −1.08866 | ||||||||
\(126\) | −1.68648e8 | −0.0596092 | ||||||||
\(127\) | −1.41410e9 | −0.482352 | −0.241176 | − | 0.970481i | \(-0.577533\pi\) | ||||
−0.241176 | + | 0.970481i | \(0.577533\pi\) | |||||||
\(128\) | 9.40848e8 | 0.309795 | ||||||||
\(129\) | 6.97227e8 | 0.221677 | ||||||||
\(130\) | −6.91664e7 | −0.0212398 | ||||||||
\(131\) | 6.55771e9 | 1.94550 | 0.972750 | − | 0.231857i | \(-0.0744800\pi\) | ||||
0.972750 | + | 0.231857i | \(0.0744800\pi\) | |||||||
\(132\) | 3.15264e9 | 0.903841 | ||||||||
\(133\) | 1.06704e9 | 0.295699 | ||||||||
\(134\) | −3.47668e8 | −0.0931522 | ||||||||
\(135\) | −5.16988e8 | −0.133961 | ||||||||
\(136\) | −1.02848e9 | −0.257794 | ||||||||
\(137\) | 8.93137e8 | 0.216609 | 0.108304 | − | 0.994118i | \(-0.465458\pi\) | ||||
0.108304 | + | 0.994118i | \(0.465458\pi\) | |||||||
\(138\) | −4.32364e8 | −0.101483 | ||||||||
\(139\) | 4.97678e9 | 1.13079 | 0.565395 | − | 0.824820i | \(-0.308724\pi\) | ||||
0.565395 | + | 0.824820i | \(0.308724\pi\) | |||||||
\(140\) | −2.50721e9 | −0.551587 | ||||||||
\(141\) | 5.82642e9 | 1.24141 | ||||||||
\(142\) | 7.61067e6 | 0.00157082 | ||||||||
\(143\) | 1.03625e9 | 0.207231 | ||||||||
\(144\) | 5.63669e9 | 1.09243 | ||||||||
\(145\) | 8.14273e9 | 1.52973 | ||||||||
\(146\) | 2.43397e8 | 0.0443330 | ||||||||
\(147\) | 4.41494e9 | 0.779824 | ||||||||
\(148\) | 4.23089e9 | 0.724861 | ||||||||
\(149\) | −3.83286e9 | −0.637066 | −0.318533 | − | 0.947912i | \(-0.603190\pi\) | ||||
−0.318533 | + | 0.947912i | \(0.603190\pi\) | |||||||
\(150\) | −2.37812e8 | −0.0383550 | ||||||||
\(151\) | 6.11983e9 | 0.957951 | 0.478975 | − | 0.877828i | \(-0.341008\pi\) | ||||
0.478975 | + | 0.877828i | \(0.341008\pi\) | |||||||
\(152\) | 4.48280e8 | 0.0681166 | ||||||||
\(153\) | −1.24009e10 | −1.82954 | ||||||||
\(154\) | −2.33871e8 | −0.0335069 | ||||||||
\(155\) | −6.55972e9 | −0.912836 | ||||||||
\(156\) | 3.53949e9 | 0.478498 | ||||||||
\(157\) | −1.04568e10 | −1.37357 | −0.686783 | − | 0.726863i | \(-0.740978\pi\) | ||||
−0.686783 | + | 0.726863i | \(0.740978\pi\) | |||||||
\(158\) | 5.72918e8 | 0.0731367 | ||||||||
\(159\) | −4.23973e9 | −0.526079 | ||||||||
\(160\) | −1.58160e9 | −0.190791 | ||||||||
\(161\) | −5.15154e9 | −0.604255 | ||||||||
\(162\) | 6.02803e8 | 0.0687635 | ||||||||
\(163\) | 8.35163e9 | 0.926674 | 0.463337 | − | 0.886182i | \(-0.346652\pi\) | ||||
0.463337 | + | 0.886182i | \(0.346652\pi\) | |||||||
\(164\) | 2.28990e9 | 0.247184 | ||||||||
\(165\) | −7.05885e9 | −0.741407 | ||||||||
\(166\) | 9.59953e8 | 0.0981213 | ||||||||
\(167\) | −8.28252e9 | −0.824021 | −0.412011 | − | 0.911179i | \(-0.635173\pi\) | ||||
−0.412011 | + | 0.911179i | \(0.635173\pi\) | |||||||
\(168\) | −1.60262e9 | −0.155217 | ||||||||
\(169\) | −9.44109e9 | −0.890291 | ||||||||
\(170\) | 1.14783e9 | 0.105404 | ||||||||
\(171\) | 5.40511e9 | 0.483417 | ||||||||
\(172\) | 1.73960e9 | 0.151555 | ||||||||
\(173\) | 6.37085e9 | 0.540742 | 0.270371 | − | 0.962756i | \(-0.412854\pi\) | ||||
0.270371 | + | 0.962756i | \(0.412854\pi\) | |||||||
\(174\) | 2.59437e9 | 0.214565 | ||||||||
\(175\) | −2.83348e9 | −0.228375 | ||||||||
\(176\) | 7.81663e9 | 0.614063 | ||||||||
\(177\) | 7.33127e8 | 0.0561435 | ||||||||
\(178\) | −3.66026e8 | −0.0273289 | ||||||||
\(179\) | −1.73831e10 | −1.26558 | −0.632789 | − | 0.774325i | \(-0.718090\pi\) | ||||
−0.632789 | + | 0.774325i | \(0.718090\pi\) | |||||||
\(180\) | −1.27003e10 | −0.901750 | ||||||||
\(181\) | −1.20834e10 | −0.836826 | −0.418413 | − | 0.908257i | \(-0.637414\pi\) | ||||
−0.418413 | + | 0.908257i | \(0.637414\pi\) | |||||||
\(182\) | −2.62569e8 | −0.0177387 | ||||||||
\(183\) | 1.16943e10 | 0.770804 | ||||||||
\(184\) | −2.16423e9 | −0.139195 | ||||||||
\(185\) | −9.47309e9 | −0.594592 | ||||||||
\(186\) | −2.09000e9 | −0.128038 | ||||||||
\(187\) | −1.71969e10 | −1.02840 | ||||||||
\(188\) | 1.45370e10 | 0.848722 | ||||||||
\(189\) | −1.96259e9 | −0.111879 | ||||||||
\(190\) | −5.00298e8 | −0.0278508 | ||||||||
\(191\) | 2.09279e10 | 1.13782 | 0.568912 | − | 0.822398i | \(-0.307365\pi\) | ||||
0.568912 | + | 0.822398i | \(0.307365\pi\) | |||||||
\(192\) | 2.63612e10 | 1.39994 | ||||||||
\(193\) | 2.13946e10 | 1.10993 | 0.554965 | − | 0.831874i | \(-0.312732\pi\) | ||||
0.554965 | + | 0.831874i | \(0.312732\pi\) | |||||||
\(194\) | 1.97354e9 | 0.100032 | ||||||||
\(195\) | −7.92502e9 | −0.392504 | ||||||||
\(196\) | 1.10154e10 | 0.533147 | ||||||||
\(197\) | −2.74114e10 | −1.29668 | −0.648340 | − | 0.761351i | \(-0.724536\pi\) | ||||
−0.648340 | + | 0.761351i | \(0.724536\pi\) | |||||||
\(198\) | −1.18468e9 | −0.0547780 | ||||||||
\(199\) | 4.11872e9 | 0.186176 | 0.0930880 | − | 0.995658i | \(-0.470326\pi\) | ||||
0.0930880 | + | 0.995658i | \(0.470326\pi\) | |||||||
\(200\) | −1.19038e9 | −0.0526080 | ||||||||
\(201\) | −3.98355e10 | −1.72142 | ||||||||
\(202\) | 3.34724e9 | 0.141451 | ||||||||
\(203\) | 3.09114e10 | 1.27757 | ||||||||
\(204\) | −5.87386e10 | −2.37458 | ||||||||
\(205\) | −5.12716e9 | −0.202761 | ||||||||
\(206\) | −1.76318e9 | −0.0682174 | ||||||||
\(207\) | −2.60951e10 | −0.987854 | ||||||||
\(208\) | 8.77578e9 | 0.325088 | ||||||||
\(209\) | 7.49550e9 | 0.271733 | ||||||||
\(210\) | 1.78859e9 | 0.0634635 | ||||||||
\(211\) | 3.83930e10 | 1.33346 | 0.666732 | − | 0.745298i | \(-0.267693\pi\) | ||||
0.666732 | + | 0.745298i | \(0.267693\pi\) | |||||||
\(212\) | −1.05782e10 | −0.359667 | ||||||||
\(213\) | 8.72023e8 | 0.0290282 | ||||||||
\(214\) | −3.26653e6 | −0.000106469 0 | ||||||||
\(215\) | −3.89500e9 | −0.124318 | ||||||||
\(216\) | −8.24510e8 | −0.0257723 | ||||||||
\(217\) | −2.49020e10 | −0.762368 | ||||||||
\(218\) | 2.29523e9 | 0.0688290 | ||||||||
\(219\) | 2.78882e10 | 0.819260 | ||||||||
\(220\) | −1.76120e10 | −0.506881 | ||||||||
\(221\) | −1.93070e10 | −0.544440 | ||||||||
\(222\) | −3.01823e9 | −0.0833997 | ||||||||
\(223\) | 3.85620e10 | 1.04421 | 0.522105 | − | 0.852881i | \(-0.325147\pi\) | ||||
0.522105 | + | 0.852881i | \(0.325147\pi\) | |||||||
\(224\) | −6.00407e9 | −0.159342 | ||||||||
\(225\) | −1.43530e10 | −0.373354 | ||||||||
\(226\) | 2.44980e9 | 0.0624659 | ||||||||
\(227\) | −1.12890e10 | −0.282188 | −0.141094 | − | 0.989996i | \(-0.545062\pi\) | ||||
−0.141094 | + | 0.989996i | \(0.545062\pi\) | |||||||
\(228\) | 2.56021e10 | 0.627434 | ||||||||
\(229\) | 3.48087e10 | 0.836428 | 0.418214 | − | 0.908349i | \(-0.362656\pi\) | ||||
0.418214 | + | 0.908349i | \(0.362656\pi\) | |||||||
\(230\) | 2.41537e9 | 0.0569126 | ||||||||
\(231\) | −2.67968e10 | −0.619196 | ||||||||
\(232\) | 1.29863e10 | 0.294299 | ||||||||
\(233\) | 2.66211e10 | 0.591730 | 0.295865 | − | 0.955230i | \(-0.404392\pi\) | ||||
0.295865 | + | 0.955230i | \(0.404392\pi\) | |||||||
\(234\) | −1.33004e9 | −0.0289997 | ||||||||
\(235\) | −3.25488e10 | −0.696193 | ||||||||
\(236\) | 1.82917e9 | 0.0383839 | ||||||||
\(237\) | 6.56444e10 | 1.35154 | ||||||||
\(238\) | 4.35738e9 | 0.0880297 | ||||||||
\(239\) | 5.93716e10 | 1.17703 | 0.588516 | − | 0.808485i | \(-0.299712\pi\) | ||||
0.588516 | + | 0.808485i | \(0.299712\pi\) | |||||||
\(240\) | −5.97797e10 | −1.16306 | ||||||||
\(241\) | 5.18516e10 | 0.990114 | 0.495057 | − | 0.868860i | \(-0.335147\pi\) | ||||
0.495057 | + | 0.868860i | \(0.335147\pi\) | |||||||
\(242\) | 2.55406e9 | 0.0478699 | ||||||||
\(243\) | 7.80004e10 | 1.43506 | ||||||||
\(244\) | 2.91775e10 | 0.526980 | ||||||||
\(245\) | −2.46637e10 | −0.437332 | ||||||||
\(246\) | −1.63357e9 | −0.0284400 | ||||||||
\(247\) | 8.41524e9 | 0.143857 | ||||||||
\(248\) | −1.04617e10 | −0.175618 | ||||||||
\(249\) | 1.09991e11 | 1.81325 | ||||||||
\(250\) | 5.28909e9 | 0.0856350 | ||||||||
\(251\) | −7.95240e10 | −1.26464 | −0.632320 | − | 0.774708i | \(-0.717897\pi\) | ||||
−0.632320 | + | 0.774708i | \(0.717897\pi\) | |||||||
\(252\) | −4.82126e10 | −0.753110 | ||||||||
\(253\) | −3.61872e10 | −0.555281 | ||||||||
\(254\) | 2.51695e9 | 0.0379423 | ||||||||
\(255\) | 1.31517e11 | 1.94783 | ||||||||
\(256\) | 6.45068e10 | 0.938697 | ||||||||
\(257\) | −1.13156e10 | −0.161800 | −0.0808999 | − | 0.996722i | \(-0.525779\pi\) | ||||
−0.0808999 | + | 0.996722i | \(0.525779\pi\) | |||||||
\(258\) | −1.24099e9 | −0.0174373 | ||||||||
\(259\) | −3.59617e10 | −0.496582 | ||||||||
\(260\) | −1.97731e10 | −0.268346 | ||||||||
\(261\) | 1.56582e11 | 2.08862 | ||||||||
\(262\) | −1.16720e10 | −0.153035 | ||||||||
\(263\) | −1.29655e11 | −1.67105 | −0.835525 | − | 0.549452i | \(-0.814837\pi\) | ||||
−0.835525 | + | 0.549452i | \(0.814837\pi\) | |||||||
\(264\) | −1.12577e10 | −0.142637 | ||||||||
\(265\) | 2.36849e10 | 0.295030 | ||||||||
\(266\) | −1.89923e9 | −0.0232600 | ||||||||
\(267\) | −4.19389e10 | −0.505030 | ||||||||
\(268\) | −9.93904e10 | −1.17690 | ||||||||
\(269\) | 2.31009e10 | 0.268995 | 0.134497 | − | 0.990914i | \(-0.457058\pi\) | ||||
0.134497 | + | 0.990914i | \(0.457058\pi\) | |||||||
\(270\) | 9.20185e8 | 0.0105375 | ||||||||
\(271\) | 8.96402e10 | 1.00958 | 0.504790 | − | 0.863242i | \(-0.331570\pi\) | ||||
0.504790 | + | 0.863242i | \(0.331570\pi\) | |||||||
\(272\) | −1.45636e11 | −1.61327 | ||||||||
\(273\) | −3.00849e10 | −0.327806 | ||||||||
\(274\) | −1.58969e9 | −0.0170387 | ||||||||
\(275\) | −1.99039e10 | −0.209866 | ||||||||
\(276\) | −1.23603e11 | −1.28215 | ||||||||
\(277\) | −9.97287e10 | −1.01780 | −0.508899 | − | 0.860826i | \(-0.669947\pi\) | ||||
−0.508899 | + | 0.860826i | \(0.669947\pi\) | |||||||
\(278\) | −8.85815e9 | −0.0889491 | ||||||||
\(279\) | −1.26141e11 | −1.24634 | ||||||||
\(280\) | 8.95292e9 | 0.0870470 | ||||||||
\(281\) | 1.31117e10 | 0.125453 | 0.0627265 | − | 0.998031i | \(-0.480020\pi\) | ||||
0.0627265 | + | 0.998031i | \(0.480020\pi\) | |||||||
\(282\) | −1.03704e10 | −0.0976507 | ||||||||
\(283\) | −9.75983e10 | −0.904489 | −0.452245 | − | 0.891894i | \(-0.649377\pi\) | ||||
−0.452245 | + | 0.891894i | \(0.649377\pi\) | |||||||
\(284\) | 2.17572e9 | 0.0198459 | ||||||||
\(285\) | −5.73237e10 | −0.514674 | ||||||||
\(286\) | −1.84443e9 | −0.0163010 | ||||||||
\(287\) | −1.94637e10 | −0.169339 | ||||||||
\(288\) | −3.04136e10 | −0.260497 | ||||||||
\(289\) | 2.01816e11 | 1.70182 | ||||||||
\(290\) | −1.44932e10 | −0.120330 | ||||||||
\(291\) | 2.26126e11 | 1.84855 | ||||||||
\(292\) | 6.95816e10 | 0.560108 | ||||||||
\(293\) | −9.70939e10 | −0.769640 | −0.384820 | − | 0.922992i | \(-0.625736\pi\) | ||||
−0.384820 | + | 0.922992i | \(0.625736\pi\) | |||||||
\(294\) | −7.85814e9 | −0.0613418 | ||||||||
\(295\) | −4.09556e9 | −0.0314857 | ||||||||
\(296\) | −1.51080e10 | −0.114392 | ||||||||
\(297\) | −1.37863e10 | −0.102812 | ||||||||
\(298\) | 6.82209e9 | 0.0501123 | ||||||||
\(299\) | −4.06276e10 | −0.293969 | ||||||||
\(300\) | −6.79849e10 | −0.484582 | ||||||||
\(301\) | −1.47862e10 | −0.103826 | ||||||||
\(302\) | −1.08927e10 | −0.0753534 | ||||||||
\(303\) | 3.83524e11 | 2.61397 | ||||||||
\(304\) | 6.34775e10 | 0.426274 | ||||||||
\(305\) | −6.53293e10 | −0.432273 | ||||||||
\(306\) | 2.20723e10 | 0.143913 | ||||||||
\(307\) | −2.39809e11 | −1.54079 | −0.770393 | − | 0.637569i | \(-0.779940\pi\) | ||||
−0.770393 | + | 0.637569i | \(0.779940\pi\) | |||||||
\(308\) | −6.68585e10 | −0.423329 | ||||||||
\(309\) | −2.02024e11 | −1.26064 | ||||||||
\(310\) | 1.16756e10 | 0.0718047 | ||||||||
\(311\) | −5.16196e10 | −0.312891 | −0.156445 | − | 0.987687i | \(-0.550004\pi\) | ||||
−0.156445 | + | 0.987687i | \(0.550004\pi\) | |||||||
\(312\) | −1.26391e10 | −0.0755127 | ||||||||
\(313\) | 9.12143e10 | 0.537172 | 0.268586 | − | 0.963256i | \(-0.413444\pi\) | ||||
0.268586 | + | 0.963256i | \(0.413444\pi\) | |||||||
\(314\) | 1.86120e10 | 0.108046 | ||||||||
\(315\) | 1.07949e11 | 0.617764 | ||||||||
\(316\) | 1.63784e11 | 0.924017 | ||||||||
\(317\) | −3.41738e11 | −1.90076 | −0.950378 | − | 0.311099i | \(-0.899303\pi\) | ||||
−0.950378 | + | 0.311099i | \(0.899303\pi\) | |||||||
\(318\) | 7.54628e9 | 0.0413819 | ||||||||
\(319\) | 2.17138e11 | 1.17403 | ||||||||
\(320\) | −1.47265e11 | −0.785100 | ||||||||
\(321\) | −3.74276e8 | −0.00196752 | ||||||||
\(322\) | 9.16920e9 | 0.0475313 | ||||||||
\(323\) | −1.39653e11 | −0.713901 | ||||||||
\(324\) | 1.72328e11 | 0.868766 | ||||||||
\(325\) | −2.23462e10 | −0.111104 | ||||||||
\(326\) | −1.48650e10 | −0.0728932 | ||||||||
\(327\) | 2.62985e11 | 1.27194 | ||||||||
\(328\) | −8.17696e9 | −0.0390085 | ||||||||
\(329\) | −1.23562e11 | −0.581436 | ||||||||
\(330\) | 1.25640e10 | 0.0583198 | ||||||||
\(331\) | −3.21682e11 | −1.47299 | −0.736497 | − | 0.676441i | \(-0.763521\pi\) | ||||
−0.736497 | + | 0.676441i | \(0.763521\pi\) | |||||||
\(332\) | 2.74429e11 | 1.23968 | ||||||||
\(333\) | −1.82164e11 | −0.811826 | ||||||||
\(334\) | 1.47420e10 | 0.0648184 | ||||||||
\(335\) | 2.22538e11 | 0.965389 | ||||||||
\(336\) | −2.26935e11 | −0.971348 | ||||||||
\(337\) | −4.05004e11 | −1.71051 | −0.855253 | − | 0.518211i | \(-0.826598\pi\) | ||||
−0.855253 | + | 0.518211i | \(0.826598\pi\) | |||||||
\(338\) | 1.68042e10 | 0.0700312 | ||||||||
\(339\) | 2.80696e11 | 1.15435 | ||||||||
\(340\) | 3.28138e11 | 1.33169 | ||||||||
\(341\) | −1.74925e11 | −0.700579 | ||||||||
\(342\) | −9.62054e9 | −0.0380261 | ||||||||
\(343\) | −2.68156e11 | −1.04608 | ||||||||
\(344\) | −6.21188e9 | −0.0239172 | ||||||||
\(345\) | 2.76751e11 | 1.05173 | ||||||||
\(346\) | −1.13395e10 | −0.0425353 | ||||||||
\(347\) | −8.23031e10 | −0.304743 | −0.152371 | − | 0.988323i | \(-0.548691\pi\) | ||||
−0.152371 | + | 0.988323i | \(0.548691\pi\) | |||||||
\(348\) | 7.41670e11 | 2.71084 | ||||||||
\(349\) | 3.73070e11 | 1.34610 | 0.673048 | − | 0.739599i | \(-0.264985\pi\) | ||||
0.673048 | + | 0.739599i | \(0.264985\pi\) | |||||||
\(350\) | 5.04330e9 | 0.0179642 | ||||||||
\(351\) | −1.54779e10 | −0.0544291 | ||||||||
\(352\) | −4.21759e10 | −0.146427 | ||||||||
\(353\) | 1.33171e11 | 0.456483 | 0.228242 | − | 0.973605i | \(-0.426702\pi\) | ||||
0.228242 | + | 0.973605i | \(0.426702\pi\) | |||||||
\(354\) | −1.30489e9 | −0.00441631 | ||||||||
\(355\) | −4.87149e9 | −0.0162792 | ||||||||
\(356\) | −1.04639e11 | −0.345276 | ||||||||
\(357\) | 4.99265e11 | 1.62676 | ||||||||
\(358\) | 3.09401e10 | 0.0995517 | ||||||||
\(359\) | −2.99339e11 | −0.951125 | −0.475563 | − | 0.879682i | \(-0.657755\pi\) | ||||
−0.475563 | + | 0.879682i | \(0.657755\pi\) | |||||||
\(360\) | 4.53510e10 | 0.142307 | ||||||||
\(361\) | −2.61818e11 | −0.811367 | ||||||||
\(362\) | 2.15072e10 | 0.0658256 | ||||||||
\(363\) | 2.92642e11 | 0.884621 | ||||||||
\(364\) | −7.50624e10 | −0.224113 | ||||||||
\(365\) | −1.55795e11 | −0.459448 | ||||||||
\(366\) | −2.08146e10 | −0.0606323 | ||||||||
\(367\) | −4.71753e11 | −1.35743 | −0.678716 | − | 0.734401i | \(-0.737463\pi\) | ||||
−0.678716 | + | 0.734401i | \(0.737463\pi\) | |||||||
\(368\) | −3.06460e11 | −0.871082 | ||||||||
\(369\) | −9.85933e10 | −0.276840 | ||||||||
\(370\) | 1.68611e10 | 0.0467712 | ||||||||
\(371\) | 8.99125e10 | 0.246398 | ||||||||
\(372\) | −5.97484e11 | −1.61764 | ||||||||
\(373\) | 5.78431e11 | 1.54725 | 0.773627 | − | 0.633641i | \(-0.218441\pi\) | ||||
0.773627 | + | 0.633641i | \(0.218441\pi\) | |||||||
\(374\) | 3.06086e10 | 0.0808950 | ||||||||
\(375\) | 6.06020e11 | 1.58251 | ||||||||
\(376\) | −5.19099e10 | −0.133938 | ||||||||
\(377\) | 2.43783e11 | 0.621536 | ||||||||
\(378\) | 3.49320e9 | 0.00880056 | ||||||||
\(379\) | 2.82375e11 | 0.702990 | 0.351495 | − | 0.936190i | \(-0.385673\pi\) | ||||
0.351495 | + | 0.936190i | \(0.385673\pi\) | |||||||
\(380\) | −1.43024e11 | −0.351870 | ||||||||
\(381\) | 2.88390e11 | 0.701162 | ||||||||
\(382\) | −3.72495e10 | −0.0895024 | ||||||||
\(383\) | 1.02581e11 | 0.243596 | 0.121798 | − | 0.992555i | \(-0.461134\pi\) | ||||
0.121798 | + | 0.992555i | \(0.461134\pi\) | |||||||
\(384\) | −1.91875e11 | −0.450328 | ||||||||
\(385\) | 1.49698e11 | 0.347250 | ||||||||
\(386\) | −3.80801e10 | −0.0873083 | ||||||||
\(387\) | −7.48994e10 | −0.169738 | ||||||||
\(388\) | 5.64189e11 | 1.26381 | ||||||||
\(389\) | 3.65492e11 | 0.809290 | 0.404645 | − | 0.914474i | \(-0.367395\pi\) | ||||
0.404645 | + | 0.914474i | \(0.367395\pi\) | |||||||
\(390\) | 1.41057e10 | 0.0308748 | ||||||||
\(391\) | 6.74223e11 | 1.45884 | ||||||||
\(392\) | −3.93345e10 | −0.0841369 | ||||||||
\(393\) | −1.33737e12 | −2.82804 | ||||||||
\(394\) | 4.87894e10 | 0.101998 | ||||||||
\(395\) | −3.66717e11 | −0.757957 | ||||||||
\(396\) | −3.38672e11 | −0.692071 | ||||||||
\(397\) | 7.94172e11 | 1.60457 | 0.802283 | − | 0.596944i | \(-0.203619\pi\) | ||||
0.802283 | + | 0.596944i | \(0.203619\pi\) | |||||||
\(398\) | −7.33090e9 | −0.0146448 | ||||||||
\(399\) | −2.17612e11 | −0.429838 | ||||||||
\(400\) | −1.68561e11 | −0.329221 | ||||||||
\(401\) | −6.31476e11 | −1.21957 | −0.609786 | − | 0.792566i | \(-0.708744\pi\) | ||||
−0.609786 | + | 0.792566i | \(0.708744\pi\) | |||||||
\(402\) | 7.09031e10 | 0.135409 | ||||||||
\(403\) | −1.96389e11 | −0.370890 | ||||||||
\(404\) | 9.56900e11 | 1.78711 | ||||||||
\(405\) | −3.85847e11 | −0.712635 | ||||||||
\(406\) | −5.50191e10 | −0.100495 | ||||||||
\(407\) | −2.52614e11 | −0.456334 | ||||||||
\(408\) | 2.09748e11 | 0.374737 | ||||||||
\(409\) | −1.73599e11 | −0.306755 | −0.153377 | − | 0.988168i | \(-0.549015\pi\) | ||||
−0.153377 | + | 0.988168i | \(0.549015\pi\) | |||||||
\(410\) | 9.12581e9 | 0.0159494 | ||||||||
\(411\) | −1.82145e11 | −0.314869 | ||||||||
\(412\) | −5.04054e11 | −0.861866 | ||||||||
\(413\) | −1.55475e10 | −0.0262958 | ||||||||
\(414\) | 4.64466e10 | 0.0777056 | ||||||||
\(415\) | −6.14453e11 | −1.01689 | ||||||||
\(416\) | −4.73511e10 | −0.0775193 | ||||||||
\(417\) | −1.01496e12 | −1.64375 | ||||||||
\(418\) | −1.33412e10 | −0.0213748 | ||||||||
\(419\) | −7.33980e11 | −1.16338 | −0.581689 | − | 0.813411i | \(-0.697608\pi\) | ||||
−0.581689 | + | 0.813411i | \(0.697608\pi\) | |||||||
\(420\) | 5.11317e11 | 0.801805 | ||||||||
\(421\) | 9.33067e11 | 1.44758 | 0.723791 | − | 0.690019i | \(-0.242398\pi\) | ||||
0.723791 | + | 0.690019i | \(0.242398\pi\) | |||||||
\(422\) | −6.83356e10 | −0.104892 | ||||||||
\(423\) | −6.25901e11 | −0.950548 | ||||||||
\(424\) | 3.77735e10 | 0.0567598 | ||||||||
\(425\) | 3.70840e11 | 0.551362 | ||||||||
\(426\) | −1.55211e9 | −0.00228339 | ||||||||
\(427\) | −2.48002e11 | −0.361019 | ||||||||
\(428\) | −9.33825e8 | −0.00134514 | ||||||||
\(429\) | −2.11333e11 | −0.301237 | ||||||||
\(430\) | 6.93270e9 | 0.00977900 | ||||||||
\(431\) | 6.98145e11 | 0.974536 | 0.487268 | − | 0.873252i | \(-0.337993\pi\) | ||||
0.487268 | + | 0.873252i | \(0.337993\pi\) | |||||||
\(432\) | −1.16752e11 | −0.161283 | ||||||||
\(433\) | 5.56024e11 | 0.760147 | 0.380074 | − | 0.924956i | \(-0.375899\pi\) | ||||
0.380074 | + | 0.924956i | \(0.375899\pi\) | |||||||
\(434\) | 4.43229e10 | 0.0599687 | ||||||||
\(435\) | −1.66062e12 | −2.22366 | ||||||||
\(436\) | 6.56153e11 | 0.869593 | ||||||||
\(437\) | −2.93870e11 | −0.385468 | ||||||||
\(438\) | −4.96381e10 | −0.0644439 | ||||||||
\(439\) | −1.04816e12 | −1.34691 | −0.673456 | − | 0.739228i | \(-0.735191\pi\) | ||||
−0.673456 | + | 0.739228i | \(0.735191\pi\) | |||||||
\(440\) | 6.28902e10 | 0.0799919 | ||||||||
\(441\) | −4.74274e11 | −0.597111 | ||||||||
\(442\) | 3.43645e10 | 0.0428262 | ||||||||
\(443\) | 5.51262e11 | 0.680051 | 0.340026 | − | 0.940416i | \(-0.389564\pi\) | ||||
0.340026 | + | 0.940416i | \(0.389564\pi\) | |||||||
\(444\) | −8.62844e11 | −1.05368 | ||||||||
\(445\) | 2.34289e11 | 0.283225 | ||||||||
\(446\) | −6.86364e10 | −0.0821387 | ||||||||
\(447\) | 7.81668e11 | 0.926059 | ||||||||
\(448\) | −5.59046e11 | −0.655687 | ||||||||
\(449\) | −1.10157e12 | −1.27910 | −0.639550 | − | 0.768749i | \(-0.720879\pi\) | ||||
−0.639550 | + | 0.768749i | \(0.720879\pi\) | |||||||
\(450\) | 2.55468e10 | 0.0293684 | ||||||||
\(451\) | −1.36723e11 | −0.155614 | ||||||||
\(452\) | 7.00343e11 | 0.789201 | ||||||||
\(453\) | −1.24807e12 | −1.39251 | ||||||||
\(454\) | 2.00932e10 | 0.0221972 | ||||||||
\(455\) | 1.68067e11 | 0.183836 | ||||||||
\(456\) | −9.14218e10 | −0.0990165 | ||||||||
\(457\) | −7.85228e11 | −0.842118 | −0.421059 | − | 0.907033i | \(-0.638341\pi\) | ||||
−0.421059 | + | 0.907033i | \(0.638341\pi\) | |||||||
\(458\) | −6.19559e10 | −0.0657943 | ||||||||
\(459\) | 2.56859e11 | 0.270109 | ||||||||
\(460\) | 6.90499e11 | 0.719040 | ||||||||
\(461\) | 1.57045e12 | 1.61946 | 0.809728 | − | 0.586806i | \(-0.199615\pi\) | ||||
0.809728 | + | 0.586806i | \(0.199615\pi\) | |||||||
\(462\) | 4.76955e10 | 0.0487066 | ||||||||
\(463\) | 1.25678e11 | 0.127100 | 0.0635501 | − | 0.997979i | \(-0.479758\pi\) | ||||
0.0635501 | + | 0.997979i | \(0.479758\pi\) | |||||||
\(464\) | 1.83889e12 | 1.84173 | ||||||||
\(465\) | 1.33778e12 | 1.32693 | ||||||||
\(466\) | −4.73827e10 | −0.0465461 | ||||||||
\(467\) | −7.17571e11 | −0.698134 | −0.349067 | − | 0.937098i | \(-0.613501\pi\) | ||||
−0.349067 | + | 0.937098i | \(0.613501\pi\) | |||||||
\(468\) | −3.80229e11 | −0.366386 | ||||||||
\(469\) | 8.44796e11 | 0.806258 | ||||||||
\(470\) | 5.79335e10 | 0.0547633 | ||||||||
\(471\) | 2.13254e12 | 1.99666 | ||||||||
\(472\) | −6.53173e9 | −0.00605744 | ||||||||
\(473\) | −1.03866e11 | −0.0954111 | ||||||||
\(474\) | −1.16840e11 | −0.106314 | ||||||||
\(475\) | −1.61636e11 | −0.145686 | ||||||||
\(476\) | 1.24568e12 | 1.11218 | ||||||||
\(477\) | 4.55452e11 | 0.402819 | ||||||||
\(478\) | −1.05675e11 | −0.0925866 | ||||||||
\(479\) | 1.77215e12 | 1.53812 | 0.769062 | − | 0.639174i | \(-0.220724\pi\) | ||||
0.769062 | + | 0.639174i | \(0.220724\pi\) | |||||||
\(480\) | 3.22550e11 | 0.277340 | ||||||||
\(481\) | −2.83612e11 | −0.241586 | ||||||||
\(482\) | −9.22904e10 | −0.0778834 | ||||||||
\(483\) | 1.05060e12 | 0.878365 | ||||||||
\(484\) | 7.30149e11 | 0.604794 | ||||||||
\(485\) | −1.26324e12 | −1.03668 | ||||||||
\(486\) | −1.38833e11 | −0.112883 | ||||||||
\(487\) | 2.21711e12 | 1.78610 | 0.893051 | − | 0.449956i | \(-0.148560\pi\) | ||||
0.893051 | + | 0.449956i | \(0.148560\pi\) | |||||||
\(488\) | −1.04189e11 | −0.0831637 | ||||||||
\(489\) | −1.70322e12 | −1.34704 | ||||||||
\(490\) | 4.38989e10 | 0.0344010 | ||||||||
\(491\) | −1.36110e12 | −1.05688 | −0.528438 | − | 0.848972i | \(-0.677222\pi\) | ||||
−0.528438 | + | 0.848972i | \(0.677222\pi\) | |||||||
\(492\) | −4.67000e11 | −0.359314 | ||||||||
\(493\) | −4.04562e12 | −3.08442 | ||||||||
\(494\) | −1.49783e10 | −0.0113159 | ||||||||
\(495\) | 7.58296e11 | 0.567695 | ||||||||
\(496\) | −1.48140e12 | −1.09902 | ||||||||
\(497\) | −1.84931e10 | −0.0135958 | ||||||||
\(498\) | −1.95772e11 | −0.142632 | ||||||||
\(499\) | 2.40786e12 | 1.73852 | 0.869258 | − | 0.494359i | \(-0.164597\pi\) | ||||
0.869258 | + | 0.494359i | \(0.164597\pi\) | |||||||
\(500\) | 1.51203e12 | 1.08192 | ||||||||
\(501\) | 1.68913e12 | 1.19782 | ||||||||
\(502\) | 1.41545e11 | 0.0994778 | ||||||||
\(503\) | −2.31596e12 | −1.61315 | −0.806576 | − | 0.591130i | \(-0.798682\pi\) | ||||
−0.806576 | + | 0.591130i | \(0.798682\pi\) | |||||||
\(504\) | 1.72161e11 | 0.118850 | ||||||||
\(505\) | −2.14253e12 | −1.46594 | ||||||||
\(506\) | 6.44095e10 | 0.0436790 | ||||||||
\(507\) | 1.92541e12 | 1.29416 | ||||||||
\(508\) | 7.19540e11 | 0.479367 | ||||||||
\(509\) | 8.58304e10 | 0.0566776 | 0.0283388 | − | 0.999598i | \(-0.490978\pi\) | ||||
0.0283388 | + | 0.999598i | \(0.490978\pi\) | |||||||
\(510\) | −2.34087e11 | −0.153219 | ||||||||
\(511\) | −5.91428e11 | −0.383714 | ||||||||
\(512\) | −5.96529e11 | −0.383634 | ||||||||
\(513\) | −1.11956e11 | −0.0713705 | ||||||||
\(514\) | 2.01406e10 | 0.0127273 | ||||||||
\(515\) | 1.12859e12 | 0.706975 | ||||||||
\(516\) | −3.54771e11 | −0.220305 | ||||||||
\(517\) | −8.67964e11 | −0.534311 | ||||||||
\(518\) | 6.40080e10 | 0.0390616 | ||||||||
\(519\) | −1.29926e12 | −0.786040 | ||||||||
\(520\) | 7.06072e10 | 0.0423481 | ||||||||
\(521\) | −1.42834e12 | −0.849301 | −0.424650 | − | 0.905357i | \(-0.639603\pi\) | ||||
−0.424650 | + | 0.905357i | \(0.639603\pi\) | |||||||
\(522\) | −2.78699e11 | −0.164293 | ||||||||
\(523\) | 2.06838e12 | 1.20885 | 0.604426 | − | 0.796661i | \(-0.293403\pi\) | ||||
0.604426 | + | 0.796661i | \(0.293403\pi\) | |||||||
\(524\) | −3.33677e12 | −1.93346 | ||||||||
\(525\) | 5.77857e11 | 0.331973 | ||||||||
\(526\) | 2.30773e11 | 0.131447 | ||||||||
\(527\) | 3.25912e12 | 1.84057 | ||||||||
\(528\) | −1.59412e12 | −0.892621 | ||||||||
\(529\) | −3.82390e11 | −0.212303 | ||||||||
\(530\) | −4.21567e10 | −0.0232073 | ||||||||
\(531\) | −7.87560e10 | −0.0429891 | ||||||||
\(532\) | −5.42946e11 | −0.293869 | ||||||||
\(533\) | −1.53500e11 | −0.0823828 | ||||||||
\(534\) | 7.46470e10 | 0.0397262 | ||||||||
\(535\) | 2.09086e9 | 0.00110340 | ||||||||
\(536\) | 3.54911e11 | 0.185728 | ||||||||
\(537\) | 3.54509e12 | 1.83968 | ||||||||
\(538\) | −4.11172e10 | −0.0211594 | ||||||||
\(539\) | −6.57695e11 | −0.335641 | ||||||||
\(540\) | 2.63060e11 | 0.133132 | ||||||||
\(541\) | 1.23040e11 | 0.0617529 | 0.0308764 | − | 0.999523i | \(-0.490170\pi\) | ||||
0.0308764 | + | 0.999523i | \(0.490170\pi\) | |||||||
\(542\) | −1.59550e11 | −0.0794147 | ||||||||
\(543\) | 2.46427e12 | 1.21644 | ||||||||
\(544\) | 7.85801e11 | 0.384696 | ||||||||
\(545\) | −1.46914e12 | −0.713313 | ||||||||
\(546\) | 5.35480e10 | 0.0257855 | ||||||||
\(547\) | 1.80654e12 | 0.862787 | 0.431393 | − | 0.902164i | \(-0.358022\pi\) | ||||
0.431393 | + | 0.902164i | \(0.358022\pi\) | |||||||
\(548\) | −4.54457e11 | −0.215268 | ||||||||
\(549\) | −1.25626e12 | −0.590205 | ||||||||
\(550\) | 3.54269e10 | 0.0165082 | ||||||||
\(551\) | 1.76334e12 | 0.814994 | ||||||||
\(552\) | 4.41371e11 | 0.202338 | ||||||||
\(553\) | −1.39213e12 | −0.633019 | ||||||||
\(554\) | 1.77507e11 | 0.0800610 | ||||||||
\(555\) | 1.93193e12 | 0.864318 | ||||||||
\(556\) | −2.53234e12 | −1.12379 | ||||||||
\(557\) | −6.38748e11 | −0.281178 | −0.140589 | − | 0.990068i | \(-0.544900\pi\) | ||||
−0.140589 | + | 0.990068i | \(0.544900\pi\) | |||||||
\(558\) | 2.24518e11 | 0.0980386 | ||||||||
\(559\) | −1.16611e11 | −0.0505111 | ||||||||
\(560\) | 1.26775e12 | 0.544740 | ||||||||
\(561\) | 3.50711e12 | 1.49491 | ||||||||
\(562\) | −2.33375e10 | −0.00986827 | ||||||||
\(563\) | 1.90057e12 | 0.797252 | 0.398626 | − | 0.917114i | \(-0.369487\pi\) | ||||
0.398626 | + | 0.917114i | \(0.369487\pi\) | |||||||
\(564\) | −2.96467e12 | −1.23373 | ||||||||
\(565\) | −1.56809e12 | −0.647369 | ||||||||
\(566\) | 1.73715e11 | 0.0711481 | ||||||||
\(567\) | −1.46475e12 | −0.595167 | ||||||||
\(568\) | −7.76921e9 | −0.00313191 | ||||||||
\(569\) | 1.34358e12 | 0.537353 | 0.268677 | − | 0.963230i | \(-0.413414\pi\) | ||||
0.268677 | + | 0.963230i | \(0.413414\pi\) | |||||||
\(570\) | 1.02030e11 | 0.0404848 | ||||||||
\(571\) | 1.95896e12 | 0.771193 | 0.385597 | − | 0.922667i | \(-0.373996\pi\) | ||||
0.385597 | + | 0.922667i | \(0.373996\pi\) | |||||||
\(572\) | −5.27279e11 | −0.205949 | ||||||||
\(573\) | −4.26801e12 | −1.65398 | ||||||||
\(574\) | 3.46433e10 | 0.0133204 | ||||||||
\(575\) | 7.80356e11 | 0.297706 | ||||||||
\(576\) | −2.83185e12 | −1.07194 | ||||||||
\(577\) | −2.94220e12 | −1.10505 | −0.552523 | − | 0.833497i | \(-0.686335\pi\) | ||||
−0.552523 | + | 0.833497i | \(0.686335\pi\) | |||||||
\(578\) | −3.59211e11 | −0.133867 | ||||||||
\(579\) | −4.36319e12 | −1.61343 | ||||||||
\(580\) | −4.14328e12 | −1.52026 | ||||||||
\(581\) | −2.33258e12 | −0.849267 | ||||||||
\(582\) | −4.02481e11 | −0.145409 | ||||||||
\(583\) | 6.31594e11 | 0.226428 | ||||||||
\(584\) | −2.48467e11 | −0.0883917 | ||||||||
\(585\) | 8.51343e11 | 0.300541 | ||||||||
\(586\) | 1.72817e11 | 0.0605407 | ||||||||
\(587\) | −5.99434e11 | −0.208387 | −0.104193 | − | 0.994557i | \(-0.533226\pi\) | ||||
−0.104193 | + | 0.994557i | \(0.533226\pi\) | |||||||
\(588\) | −2.24646e12 | −0.774999 | ||||||||
\(589\) | −1.42054e12 | −0.486333 | ||||||||
\(590\) | 7.28967e9 | 0.00247670 | ||||||||
\(591\) | 5.59024e12 | 1.88490 | ||||||||
\(592\) | −2.13933e12 | −0.715862 | ||||||||
\(593\) | 5.53945e11 | 0.183959 | 0.0919794 | − | 0.995761i | \(-0.470681\pi\) | ||||
0.0919794 | + | 0.995761i | \(0.470681\pi\) | |||||||
\(594\) | 2.45381e10 | 0.00808728 | ||||||||
\(595\) | −2.78910e12 | −0.912301 | ||||||||
\(596\) | 1.95028e12 | 0.633124 | ||||||||
\(597\) | −8.39968e11 | −0.270631 | ||||||||
\(598\) | 7.23129e10 | 0.0231239 | ||||||||
\(599\) | −1.23783e12 | −0.392864 | −0.196432 | − | 0.980517i | \(-0.562935\pi\) | ||||
−0.196432 | + | 0.980517i | \(0.562935\pi\) | |||||||
\(600\) | 2.42766e11 | 0.0764727 | ||||||||
\(601\) | −4.88544e12 | −1.52745 | −0.763727 | − | 0.645539i | \(-0.776633\pi\) | ||||
−0.763727 | + | 0.645539i | \(0.776633\pi\) | |||||||
\(602\) | 2.63179e10 | 0.00816707 | ||||||||
\(603\) | 4.27932e12 | 1.31809 | ||||||||
\(604\) | −3.11397e12 | −0.952024 | ||||||||
\(605\) | −1.63482e12 | −0.496103 | ||||||||
\(606\) | −6.82633e11 | −0.205618 | ||||||||
\(607\) | 1.73678e12 | 0.519272 | 0.259636 | − | 0.965707i | \(-0.416397\pi\) | ||||
0.259636 | + | 0.965707i | \(0.416397\pi\) | |||||||
\(608\) | −3.42503e11 | −0.101648 | ||||||||
\(609\) | −6.30403e12 | −1.85712 | ||||||||
\(610\) | 1.16279e11 | 0.0340031 | ||||||||
\(611\) | −9.74468e11 | −0.282867 | ||||||||
\(612\) | 6.30997e12 | 1.81822 | ||||||||
\(613\) | 5.18063e12 | 1.48187 | 0.740936 | − | 0.671575i | \(-0.234382\pi\) | ||||
0.740936 | + | 0.671575i | \(0.234382\pi\) | |||||||
\(614\) | 4.26835e11 | 0.121200 | ||||||||
\(615\) | 1.04563e12 | 0.294740 | ||||||||
\(616\) | 2.38743e11 | 0.0668064 | ||||||||
\(617\) | 4.99397e12 | 1.38728 | 0.693638 | − | 0.720324i | \(-0.256007\pi\) | ||||
0.693638 | + | 0.720324i | \(0.256007\pi\) | |||||||
\(618\) | 3.59582e11 | 0.0991630 | ||||||||
\(619\) | 1.19615e11 | 0.0327475 | 0.0163738 | − | 0.999866i | \(-0.494788\pi\) | ||||
0.0163738 | + | 0.999866i | \(0.494788\pi\) | |||||||
\(620\) | 3.33780e12 | 0.907188 | ||||||||
\(621\) | 5.40507e11 | 0.145844 | ||||||||
\(622\) | 9.18775e10 | 0.0246123 | ||||||||
\(623\) | 8.89404e11 | 0.236539 | ||||||||
\(624\) | −1.78972e12 | −0.472558 | ||||||||
\(625\) | −2.10590e12 | −0.552049 | ||||||||
\(626\) | −1.62352e11 | −0.0422545 | ||||||||
\(627\) | −1.52862e12 | −0.395000 | ||||||||
\(628\) | 5.32074e12 | 1.36507 | ||||||||
\(629\) | 4.70659e12 | 1.19889 | ||||||||
\(630\) | −1.92139e11 | −0.0485940 | ||||||||
\(631\) | 6.27030e12 | 1.57455 | 0.787275 | − | 0.616602i | \(-0.211491\pi\) | ||||
0.787275 | + | 0.616602i | \(0.211491\pi\) | |||||||
\(632\) | −5.84853e11 | −0.145821 | ||||||||
\(633\) | −7.82983e12 | −1.93837 | ||||||||
\(634\) | 6.08258e11 | 0.149515 | ||||||||
\(635\) | −1.61107e12 | −0.393217 | ||||||||
\(636\) | 2.15731e12 | 0.522824 | ||||||||
\(637\) | −7.38399e11 | −0.177690 | ||||||||
\(638\) | −3.86484e11 | −0.0923503 | ||||||||
\(639\) | −9.36769e10 | −0.0222269 | ||||||||
\(640\) | 1.07190e12 | 0.252548 | ||||||||
\(641\) | 8.09157e12 | 1.89309 | 0.946546 | − | 0.322570i | \(-0.104547\pi\) | ||||
0.946546 | + | 0.322570i | \(0.104547\pi\) | |||||||
\(642\) | 6.66172e8 | 0.000154767 0 | ||||||||
\(643\) | 8.41338e11 | 0.194098 | 0.0970490 | − | 0.995280i | \(-0.469060\pi\) | ||||
0.0970490 | + | 0.995280i | \(0.469060\pi\) | |||||||
\(644\) | 2.62127e12 | 0.600516 | ||||||||
\(645\) | 7.94343e11 | 0.180713 | ||||||||
\(646\) | 2.48567e11 | 0.0561562 | ||||||||
\(647\) | 2.04314e12 | 0.458384 | 0.229192 | − | 0.973381i | \(-0.426392\pi\) | ||||
0.229192 | + | 0.973381i | \(0.426392\pi\) | |||||||
\(648\) | −6.15361e11 | −0.137102 | ||||||||
\(649\) | −1.09214e11 | −0.0241645 | ||||||||
\(650\) | 3.97740e10 | 0.00873955 | ||||||||
\(651\) | 5.07848e12 | 1.10820 | ||||||||
\(652\) | −4.24958e12 | −0.920941 | ||||||||
\(653\) | 9.39158e11 | 0.202129 | 0.101065 | − | 0.994880i | \(-0.467775\pi\) | ||||
0.101065 | + | 0.994880i | \(0.467775\pi\) | |||||||
\(654\) | −4.68086e11 | −0.100052 | ||||||||
\(655\) | 7.47112e12 | 1.58599 | ||||||||
\(656\) | −1.15788e12 | −0.244115 | ||||||||
\(657\) | −2.99588e12 | −0.627307 | ||||||||
\(658\) | 2.19927e11 | 0.0457364 | ||||||||
\(659\) | −4.13790e12 | −0.854664 | −0.427332 | − | 0.904095i | \(-0.640546\pi\) | ||||
−0.427332 | + | 0.904095i | \(0.640546\pi\) | |||||||
\(660\) | 3.59177e12 | 0.736819 | ||||||||
\(661\) | 1.12840e12 | 0.229909 | 0.114954 | − | 0.993371i | \(-0.463328\pi\) | ||||
0.114954 | + | 0.993371i | \(0.463328\pi\) | |||||||
\(662\) | 5.72561e11 | 0.115867 | ||||||||
\(663\) | 3.93745e12 | 0.791415 | ||||||||
\(664\) | −9.79950e11 | −0.195636 | ||||||||
\(665\) | 1.21567e12 | 0.241056 | ||||||||
\(666\) | 3.24233e11 | 0.0638591 | ||||||||
\(667\) | −8.51317e12 | −1.66542 | ||||||||
\(668\) | 4.21441e12 | 0.818923 | ||||||||
\(669\) | −7.86430e12 | −1.51790 | ||||||||
\(670\) | −3.96094e11 | −0.0759385 | ||||||||
\(671\) | −1.74210e12 | −0.331759 | ||||||||
\(672\) | 1.22446e12 | 0.231624 | ||||||||
\(673\) | −3.96514e12 | −0.745059 | −0.372529 | − | 0.928020i | \(-0.621509\pi\) | ||||
−0.372529 | + | 0.928020i | \(0.621509\pi\) | |||||||
\(674\) | 7.20865e11 | 0.134550 | ||||||||
\(675\) | 2.97293e11 | 0.0551211 | ||||||||
\(676\) | 4.80393e12 | 0.884782 | ||||||||
\(677\) | 5.57988e11 | 0.102088 | 0.0510442 | − | 0.998696i | \(-0.483745\pi\) | ||||
0.0510442 | + | 0.998696i | \(0.483745\pi\) | |||||||
\(678\) | −4.99610e11 | −0.0908024 | ||||||||
\(679\) | −4.79548e12 | −0.865802 | ||||||||
\(680\) | −1.17174e12 | −0.210156 | ||||||||
\(681\) | 2.30227e12 | 0.410198 | ||||||||
\(682\) | 3.11348e11 | 0.0551083 | ||||||||
\(683\) | 1.00796e13 | 1.77236 | 0.886178 | − | 0.463344i | \(-0.153351\pi\) | ||||
0.886178 | + | 0.463344i | \(0.153351\pi\) | |||||||
\(684\) | −2.75029e12 | −0.480426 | ||||||||
\(685\) | 1.01754e12 | 0.176581 | ||||||||
\(686\) | 4.77290e11 | 0.0822855 | ||||||||
\(687\) | −7.09885e12 | −1.21586 | ||||||||
\(688\) | −8.79616e11 | −0.149674 | ||||||||
\(689\) | 7.09095e11 | 0.119872 | ||||||||
\(690\) | −4.92588e11 | −0.0827299 | ||||||||
\(691\) | −1.07053e13 | −1.78626 | −0.893132 | − | 0.449794i | \(-0.851497\pi\) | ||||
−0.893132 | + | 0.449794i | \(0.851497\pi\) | |||||||
\(692\) | −3.24169e12 | −0.537396 | ||||||||
\(693\) | 2.87863e12 | 0.474119 | ||||||||
\(694\) | 1.46491e11 | 0.0239714 | ||||||||
\(695\) | 5.66999e12 | 0.921830 | ||||||||
\(696\) | −2.64841e12 | −0.427803 | ||||||||
\(697\) | 2.54737e12 | 0.408831 | ||||||||
\(698\) | −6.64026e11 | −0.105885 | ||||||||
\(699\) | −5.42907e12 | −0.860158 | ||||||||
\(700\) | 1.44176e12 | 0.226962 | ||||||||
\(701\) | 9.07245e12 | 1.41904 | 0.709518 | − | 0.704687i | \(-0.248913\pi\) | ||||
0.709518 | + | 0.704687i | \(0.248913\pi\) | |||||||
\(702\) | 2.75491e10 | 0.00428145 | ||||||||
\(703\) | −2.05144e12 | −0.316781 | ||||||||
\(704\) | −3.92705e12 | −0.602544 | ||||||||
\(705\) | 6.63797e12 | 1.01201 | ||||||||
\(706\) | −2.37031e11 | −0.0359074 | ||||||||
\(707\) | −8.13344e12 | −1.22430 | ||||||||
\(708\) | −3.73039e11 | −0.0557961 | ||||||||
\(709\) | 1.23204e12 | 0.183112 | 0.0915559 | − | 0.995800i | \(-0.470816\pi\) | ||||
0.0915559 | + | 0.995800i | \(0.470816\pi\) | |||||||
\(710\) | 8.67075e9 | 0.00128054 | ||||||||
\(711\) | −7.05183e12 | −1.03488 | ||||||||
\(712\) | 3.73651e11 | 0.0544887 | ||||||||
\(713\) | 6.85814e12 | 0.993811 | ||||||||
\(714\) | −8.88639e11 | −0.127963 | ||||||||
\(715\) | 1.18059e12 | 0.168936 | ||||||||
\(716\) | 8.84508e12 | 1.25775 | ||||||||
\(717\) | −1.21082e13 | −1.71097 | ||||||||
\(718\) | 5.32792e11 | 0.0748165 | ||||||||
\(719\) | −7.74691e12 | −1.08106 | −0.540528 | − | 0.841326i | \(-0.681776\pi\) | ||||
−0.540528 | + | 0.841326i | \(0.681776\pi\) | |||||||
\(720\) | 6.42181e12 | 0.890556 | ||||||||
\(721\) | 4.28435e12 | 0.590440 | ||||||||
\(722\) | 4.66009e11 | 0.0638230 | ||||||||
\(723\) | −1.05746e13 | −1.43926 | ||||||||
\(724\) | 6.14841e12 | 0.831648 | ||||||||
\(725\) | −4.68246e12 | −0.629439 | ||||||||
\(726\) | −5.20873e11 | −0.0695852 | ||||||||
\(727\) | 3.08284e12 | 0.409304 | 0.204652 | − | 0.978835i | \(-0.434394\pi\) | ||||
0.204652 | + | 0.978835i | \(0.434394\pi\) | |||||||
\(728\) | 2.68039e11 | 0.0353676 | ||||||||
\(729\) | −9.24122e12 | −1.21187 | ||||||||
\(730\) | 2.77299e11 | 0.0361406 | ||||||||
\(731\) | 1.93519e12 | 0.250665 | ||||||||
\(732\) | −5.95043e12 | −0.766035 | ||||||||
\(733\) | −8.15400e12 | −1.04328 | −0.521642 | − | 0.853164i | \(-0.674680\pi\) | ||||
−0.521642 | + | 0.853164i | \(0.674680\pi\) | |||||||
\(734\) | 8.39672e11 | 0.106777 | ||||||||
\(735\) | 5.02989e12 | 0.635720 | ||||||||
\(736\) | 1.65355e12 | 0.207715 | ||||||||
\(737\) | 5.93431e12 | 0.740912 | ||||||||
\(738\) | 1.75486e11 | 0.0217765 | ||||||||
\(739\) | 1.08477e13 | 1.33794 | 0.668969 | − | 0.743291i | \(-0.266736\pi\) | ||||
0.668969 | + | 0.743291i | \(0.266736\pi\) | |||||||
\(740\) | 4.82021e12 | 0.590913 | ||||||||
\(741\) | −1.71620e12 | −0.209115 | ||||||||
\(742\) | −1.60035e11 | −0.0193819 | ||||||||
\(743\) | −6.60935e12 | −0.795626 | −0.397813 | − | 0.917467i | \(-0.630231\pi\) | ||||
−0.397813 | + | 0.917467i | \(0.630231\pi\) | |||||||
\(744\) | 2.13354e12 | 0.255283 | ||||||||
\(745\) | −4.36673e12 | −0.519342 | ||||||||
\(746\) | −1.02955e12 | −0.121709 | ||||||||
\(747\) | −1.18157e13 | −1.38841 | ||||||||
\(748\) | 8.75031e12 | 1.02204 | ||||||||
\(749\) | 7.93731e9 | 0.000921521 0 | ||||||||
\(750\) | −1.07865e12 | −0.124482 | ||||||||
\(751\) | 1.03430e13 | 1.18650 | 0.593248 | − | 0.805020i | \(-0.297845\pi\) | ||||
0.593248 | + | 0.805020i | \(0.297845\pi\) | |||||||
\(752\) | −7.35057e12 | −0.838186 | ||||||||
\(753\) | 1.62180e13 | 1.83832 | ||||||||
\(754\) | −4.33908e11 | −0.0488907 | ||||||||
\(755\) | 6.97226e12 | 0.780930 | ||||||||
\(756\) | 9.98626e11 | 0.111187 | ||||||||
\(757\) | 7.48200e12 | 0.828107 | 0.414054 | − | 0.910253i | \(-0.364113\pi\) | ||||
0.414054 | + | 0.910253i | \(0.364113\pi\) | |||||||
\(758\) | −5.02598e11 | −0.0552979 | ||||||||
\(759\) | 7.37998e12 | 0.807174 | ||||||||
\(760\) | 5.10720e11 | 0.0555293 | ||||||||
\(761\) | −8.49259e12 | −0.917929 | −0.458965 | − | 0.888455i | \(-0.651780\pi\) | ||||
−0.458965 | + | 0.888455i | \(0.651780\pi\) | |||||||
\(762\) | −5.13305e11 | −0.0551541 | ||||||||
\(763\) | −5.57715e12 | −0.595734 | ||||||||
\(764\) | −1.06488e13 | −1.13078 | ||||||||
\(765\) | −1.41282e13 | −1.49146 | ||||||||
\(766\) | −1.82583e11 | −0.0191615 | ||||||||
\(767\) | −1.22616e11 | −0.0127928 | ||||||||
\(768\) | −1.31554e13 | −1.36452 | ||||||||
\(769\) | −1.35879e13 | −1.40115 | −0.700573 | − | 0.713581i | \(-0.747072\pi\) | ||||
−0.700573 | + | 0.713581i | \(0.747072\pi\) | |||||||
\(770\) | −2.66447e11 | −0.0273151 | ||||||||
\(771\) | 2.30769e12 | 0.235197 | ||||||||
\(772\) | −1.08862e13 | −1.10306 | ||||||||
\(773\) | −1.48951e13 | −1.50050 | −0.750251 | − | 0.661153i | \(-0.770067\pi\) | ||||
−0.750251 | + | 0.661153i | \(0.770067\pi\) | |||||||
\(774\) | 1.33313e11 | 0.0133518 | ||||||||
\(775\) | 3.77216e12 | 0.375606 | ||||||||
\(776\) | −2.01465e12 | −0.199444 | ||||||||
\(777\) | 7.33398e12 | 0.721847 | ||||||||
\(778\) | −6.50537e11 | −0.0636596 | ||||||||
\(779\) | −1.11031e12 | −0.108025 | ||||||||
\(780\) | 4.03250e12 | 0.390076 | ||||||||
\(781\) | −1.29906e11 | −0.0124939 | ||||||||
\(782\) | −1.20005e12 | −0.114754 | ||||||||
\(783\) | −3.24327e12 | −0.308358 | ||||||||
\(784\) | −5.56986e12 | −0.526528 | ||||||||
\(785\) | −1.19133e13 | −1.11974 | ||||||||
\(786\) | 2.38038e12 | 0.222457 | ||||||||
\(787\) | −1.79246e13 | −1.66558 | −0.832788 | − | 0.553592i | \(-0.813257\pi\) | ||||
−0.832788 | + | 0.553592i | \(0.813257\pi\) | |||||||
\(788\) | 1.39478e13 | 1.28866 | ||||||||
\(789\) | 2.64418e13 | 2.42909 | ||||||||
\(790\) | 6.52719e11 | 0.0596217 | ||||||||
\(791\) | −5.95276e12 | −0.540660 | ||||||||
\(792\) | 1.20935e12 | 0.109217 | ||||||||
\(793\) | −1.95587e12 | −0.175635 | ||||||||
\(794\) | −1.41354e12 | −0.126217 | ||||||||
\(795\) | −4.83028e12 | −0.428864 | ||||||||
\(796\) | −2.09574e12 | −0.185024 | ||||||||
\(797\) | 1.38729e13 | 1.21788 | 0.608940 | − | 0.793216i | \(-0.291595\pi\) | ||||
0.608940 | + | 0.793216i | \(0.291595\pi\) | |||||||
\(798\) | 3.87326e11 | 0.0338115 | ||||||||
\(799\) | 1.61715e13 | 1.40375 | ||||||||
\(800\) | 9.09498e11 | 0.0785049 | ||||||||
\(801\) | 4.50528e12 | 0.386701 | ||||||||
\(802\) | 1.12396e12 | 0.0959327 | ||||||||
\(803\) | −4.15452e12 | −0.352615 | ||||||||
\(804\) | 2.02696e13 | 1.71077 | ||||||||
\(805\) | −5.86909e12 | −0.492594 | ||||||||
\(806\) | 3.49553e11 | 0.0291746 | ||||||||
\(807\) | −4.71117e12 | −0.391019 | ||||||||
\(808\) | −3.41697e12 | −0.282027 | ||||||||
\(809\) | 9.79702e12 | 0.804129 | 0.402064 | − | 0.915611i | \(-0.368293\pi\) | ||||
0.402064 | + | 0.915611i | \(0.368293\pi\) | |||||||
\(810\) | 6.86767e11 | 0.0560566 | ||||||||
\(811\) | 1.11554e13 | 0.905508 | 0.452754 | − | 0.891635i | \(-0.350442\pi\) | ||||
0.452754 | + | 0.891635i | \(0.350442\pi\) | |||||||
\(812\) | −1.57287e13 | −1.26967 | ||||||||
\(813\) | −1.82811e13 | −1.46756 | ||||||||
\(814\) | 4.49627e11 | 0.0358957 | ||||||||
\(815\) | 9.51492e12 | 0.755433 | ||||||||
\(816\) | 2.97008e13 | 2.34511 | ||||||||
\(817\) | −8.43479e11 | −0.0662331 | ||||||||
\(818\) | 3.08988e11 | 0.0241297 | ||||||||
\(819\) | 3.23186e12 | 0.251001 | ||||||||
\(820\) | 2.60886e12 | 0.201506 | ||||||||
\(821\) | −1.94239e13 | −1.49208 | −0.746039 | − | 0.665902i | \(-0.768047\pi\) | ||||
−0.746039 | + | 0.665902i | \(0.768047\pi\) | |||||||
\(822\) | 3.24200e11 | 0.0247679 | ||||||||
\(823\) | −1.46781e13 | −1.11524 | −0.557622 | − | 0.830095i | \(-0.688286\pi\) | ||||
−0.557622 | + | 0.830095i | \(0.688286\pi\) | |||||||
\(824\) | 1.79991e12 | 0.136013 | ||||||||
\(825\) | 4.05918e12 | 0.305067 | ||||||||
\(826\) | 2.76730e10 | 0.00206845 | ||||||||
\(827\) | −1.77714e13 | −1.32114 | −0.660568 | − | 0.750766i | \(-0.729684\pi\) | ||||
−0.660568 | + | 0.750766i | \(0.729684\pi\) | |||||||
\(828\) | 1.32780e13 | 0.981742 | ||||||||
\(829\) | 1.08538e13 | 0.798151 | 0.399075 | − | 0.916918i | \(-0.369331\pi\) | ||||
0.399075 | + | 0.916918i | \(0.369331\pi\) | |||||||
\(830\) | 1.09366e12 | 0.0799894 | ||||||||
\(831\) | 2.03386e13 | 1.47950 | ||||||||
\(832\) | −4.40892e12 | −0.318990 | ||||||||
\(833\) | 1.22539e13 | 0.881802 | ||||||||
\(834\) | 1.80652e12 | 0.129299 | ||||||||
\(835\) | −9.43618e12 | −0.671749 | ||||||||
\(836\) | −3.81395e12 | −0.270052 | ||||||||
\(837\) | 2.61275e12 | 0.184007 | ||||||||
\(838\) | 1.30641e12 | 0.0915126 | ||||||||
\(839\) | 9.83099e12 | 0.684965 | 0.342482 | − | 0.939524i | \(-0.388732\pi\) | ||||
0.342482 | + | 0.939524i | \(0.388732\pi\) | |||||||
\(840\) | −1.82585e12 | −0.126534 | ||||||||
\(841\) | 3.65754e13 | 2.52120 | ||||||||
\(842\) | −1.66076e12 | −0.113868 | ||||||||
\(843\) | −2.67399e12 | −0.182363 | ||||||||
\(844\) | −1.95356e13 | −1.32521 | ||||||||
\(845\) | −1.07561e13 | −0.725773 | ||||||||
\(846\) | 1.11404e12 | 0.0747711 | ||||||||
\(847\) | −6.20610e12 | −0.414327 | ||||||||
\(848\) | 5.34881e12 | 0.355203 | ||||||||
\(849\) | 1.99041e13 | 1.31479 | ||||||||
\(850\) | −6.60057e11 | −0.0433707 | ||||||||
\(851\) | 9.90405e12 | 0.647336 | ||||||||
\(852\) | −4.43713e11 | −0.0288486 | ||||||||
\(853\) | 2.22566e13 | 1.43942 | 0.719712 | − | 0.694273i | \(-0.244274\pi\) | ||||
0.719712 | + | 0.694273i | \(0.244274\pi\) | |||||||
\(854\) | 4.41419e11 | 0.0283982 | ||||||||
\(855\) | 6.15799e12 | 0.394086 | ||||||||
\(856\) | 3.33457e9 | 0.000212280 0 | ||||||||
\(857\) | 6.93260e12 | 0.439018 | 0.219509 | − | 0.975610i | \(-0.429554\pi\) | ||||
0.219509 | + | 0.975610i | \(0.429554\pi\) | |||||||
\(858\) | 3.76150e11 | 0.0236956 | ||||||||
\(859\) | 3.01241e13 | 1.88775 | 0.943875 | − | 0.330303i | \(-0.107151\pi\) | ||||
0.943875 | + | 0.330303i | \(0.107151\pi\) | |||||||
\(860\) | 1.98190e12 | 0.123549 | ||||||||
\(861\) | 3.96940e12 | 0.246156 | ||||||||
\(862\) | −1.24263e12 | −0.0766581 | ||||||||
\(863\) | −2.10193e13 | −1.28994 | −0.644971 | − | 0.764207i | \(-0.723131\pi\) | ||||
−0.644971 | + | 0.764207i | \(0.723131\pi\) | |||||||
\(864\) | 6.29956e11 | 0.0384590 | ||||||||
\(865\) | 7.25824e12 | 0.440818 | ||||||||
\(866\) | −9.89664e11 | −0.0597940 | ||||||||
\(867\) | −4.11581e13 | −2.47383 | ||||||||
\(868\) | 1.26709e13 | 0.757651 | ||||||||
\(869\) | −9.77908e12 | −0.581713 | ||||||||
\(870\) | 2.95573e12 | 0.174916 | ||||||||
\(871\) | 6.66249e12 | 0.392243 | ||||||||
\(872\) | −2.34304e12 | −0.137232 | ||||||||
\(873\) | −2.42915e13 | −1.41544 | ||||||||
\(874\) | 5.23058e11 | 0.0303214 | ||||||||
\(875\) | −1.28519e13 | −0.741195 | ||||||||
\(876\) | −1.41904e13 | −0.814191 | ||||||||
\(877\) | 1.39399e13 | 0.795720 | 0.397860 | − | 0.917446i | \(-0.369753\pi\) | ||||
0.397860 | + | 0.917446i | \(0.369753\pi\) | |||||||
\(878\) | 1.86562e12 | 0.105949 | ||||||||
\(879\) | 1.98012e13 | 1.11877 | ||||||||
\(880\) | 8.90540e12 | 0.500589 | ||||||||
\(881\) | 3.43345e12 | 0.192017 | 0.0960083 | − | 0.995381i | \(-0.469392\pi\) | ||||
0.0960083 | + | 0.995381i | \(0.469392\pi\) | |||||||
\(882\) | 8.44158e11 | 0.0469694 | ||||||||
\(883\) | 1.64420e13 | 0.910189 | 0.455095 | − | 0.890443i | \(-0.349605\pi\) | ||||
0.455095 | + | 0.890443i | \(0.349605\pi\) | |||||||
\(884\) | 9.82402e12 | 0.541071 | ||||||||
\(885\) | 8.35244e11 | 0.0457687 | ||||||||
\(886\) | −9.81190e11 | −0.0534935 | ||||||||
\(887\) | −2.76514e13 | −1.49990 | −0.749949 | − | 0.661496i | \(-0.769922\pi\) | ||||
−0.749949 | + | 0.661496i | \(0.769922\pi\) | |||||||
\(888\) | 3.08111e12 | 0.166283 | ||||||||
\(889\) | −6.11593e12 | −0.328401 | ||||||||
\(890\) | −4.17010e11 | −0.0222788 | ||||||||
\(891\) | −1.02892e13 | −0.546929 | ||||||||
\(892\) | −1.96216e13 | −1.03775 | ||||||||
\(893\) | −7.04858e12 | −0.370911 | ||||||||
\(894\) | −1.39129e12 | −0.0728448 | ||||||||
\(895\) | −1.98044e13 | −1.03171 | ||||||||
\(896\) | 4.06913e12 | 0.210919 | ||||||||
\(897\) | 8.28555e12 | 0.427322 | ||||||||
\(898\) | 1.96069e12 | 0.100615 | ||||||||
\(899\) | −4.11517e13 | −2.10121 | ||||||||
\(900\) | 7.30326e12 | 0.371044 | ||||||||
\(901\) | −1.17676e13 | −0.594874 | ||||||||
\(902\) | 2.43354e11 | 0.0122408 | ||||||||
\(903\) | 3.01548e12 | 0.150925 | ||||||||
\(904\) | −2.50084e12 | −0.124545 | ||||||||
\(905\) | −1.37665e13 | −0.682188 | ||||||||
\(906\) | 2.22144e12 | 0.109536 | ||||||||
\(907\) | −1.33233e13 | −0.653699 | −0.326850 | − | 0.945076i | \(-0.605987\pi\) | ||||
−0.326850 | + | 0.945076i | \(0.605987\pi\) | |||||||
\(908\) | 5.74420e12 | 0.280442 | ||||||||
\(909\) | −4.12000e13 | −2.00152 | ||||||||
\(910\) | −2.99142e11 | −0.0144607 | ||||||||
\(911\) | −2.44420e11 | −0.0117572 | −0.00587860 | − | 0.999983i | \(-0.501871\pi\) | ||||
−0.00587860 | + | 0.999983i | \(0.501871\pi\) | |||||||
\(912\) | −1.29455e13 | −0.619645 | ||||||||
\(913\) | −1.63853e13 | −0.780435 | ||||||||
\(914\) | 1.39763e12 | 0.0662419 | ||||||||
\(915\) | 1.33232e13 | 0.628366 | ||||||||
\(916\) | −1.77118e13 | −0.831252 | ||||||||
\(917\) | 2.83618e13 | 1.32456 | ||||||||
\(918\) | −4.57183e11 | −0.0212470 | ||||||||
\(919\) | 1.75324e13 | 0.810813 | 0.405407 | − | 0.914136i | \(-0.367130\pi\) | ||||
0.405407 | + | 0.914136i | \(0.367130\pi\) | |||||||
\(920\) | −2.46569e12 | −0.113473 | ||||||||
\(921\) | 4.89063e13 | 2.23974 | ||||||||
\(922\) | −2.79523e12 | −0.127388 | ||||||||
\(923\) | −1.45846e11 | −0.00661434 | ||||||||
\(924\) | 1.36350e13 | 0.615365 | ||||||||
\(925\) | 5.44748e12 | 0.244657 | ||||||||
\(926\) | −2.23695e11 | −0.00999784 | ||||||||
\(927\) | 2.17024e13 | 0.965269 | ||||||||
\(928\) | −9.92202e12 | −0.439172 | ||||||||
\(929\) | −1.10334e13 | −0.486004 | −0.243002 | − | 0.970026i | \(-0.578132\pi\) | ||||
−0.243002 | + | 0.970026i | \(0.578132\pi\) | |||||||
\(930\) | −2.38112e12 | −0.104378 | ||||||||
\(931\) | −5.34103e12 | −0.232998 | ||||||||
\(932\) | −1.35457e13 | −0.588069 | ||||||||
\(933\) | 1.05272e13 | 0.454828 | ||||||||
\(934\) | 1.27720e12 | 0.0549159 | ||||||||
\(935\) | −1.95922e13 | −0.838360 | ||||||||
\(936\) | 1.35775e12 | 0.0578200 | ||||||||
\(937\) | −2.57249e13 | −1.09025 | −0.545124 | − | 0.838356i | \(-0.683517\pi\) | ||||
−0.545124 | + | 0.838356i | \(0.683517\pi\) | |||||||
\(938\) | −1.50365e12 | −0.0634211 | ||||||||
\(939\) | −1.86022e13 | −0.780851 | ||||||||
\(940\) | 1.65619e13 | 0.691886 | ||||||||
\(941\) | −8.89212e12 | −0.369702 | −0.184851 | − | 0.982767i | \(-0.559180\pi\) | ||||
−0.184851 | + | 0.982767i | \(0.559180\pi\) | |||||||
\(942\) | −3.79571e12 | −0.157059 | ||||||||
\(943\) | 5.36041e12 | 0.220747 | ||||||||
\(944\) | −9.24908e11 | −0.0379075 | ||||||||
\(945\) | −2.23595e12 | −0.0912051 | ||||||||
\(946\) | 1.84871e11 | 0.00750514 | ||||||||
\(947\) | −5.49551e12 | −0.222041 | −0.111020 | − | 0.993818i | \(-0.535412\pi\) | ||||
−0.111020 | + | 0.993818i | \(0.535412\pi\) | |||||||
\(948\) | −3.34020e13 | −1.34318 | ||||||||
\(949\) | −4.66430e12 | −0.186676 | ||||||||
\(950\) | 2.87696e11 | 0.0114598 | ||||||||
\(951\) | 6.96936e13 | 2.76300 | ||||||||
\(952\) | −4.44815e12 | −0.175515 | ||||||||
\(953\) | 1.44013e13 | 0.565565 | 0.282783 | − | 0.959184i | \(-0.408742\pi\) | ||||
0.282783 | + | 0.959184i | \(0.408742\pi\) | |||||||
\(954\) | −8.10657e11 | −0.0316862 | ||||||||
\(955\) | 2.38429e13 | 0.927564 | ||||||||
\(956\) | −3.02102e13 | −1.16975 | ||||||||
\(957\) | −4.42830e13 | −1.70661 | ||||||||
\(958\) | −3.15425e12 | −0.120990 | ||||||||
\(959\) | 3.86278e12 | 0.147474 | ||||||||
\(960\) | 3.00331e13 | 1.14125 | ||||||||
\(961\) | 6.71190e12 | 0.253858 | ||||||||
\(962\) | 5.04799e11 | 0.0190034 | ||||||||
\(963\) | 4.02064e10 | 0.00150653 | ||||||||
\(964\) | −2.63837e13 | −0.983988 | ||||||||
\(965\) | 2.43746e13 | 0.904825 | ||||||||
\(966\) | −1.86996e12 | −0.0690931 | ||||||||
\(967\) | 1.72578e13 | 0.634698 | 0.317349 | − | 0.948309i | \(-0.397207\pi\) | ||||
0.317349 | + | 0.948309i | \(0.397207\pi\) | |||||||
\(968\) | −2.60727e12 | −0.0954436 | ||||||||
\(969\) | 2.84806e13 | 1.03775 | ||||||||
\(970\) | 2.24843e12 | 0.0815467 | ||||||||
\(971\) | 1.22438e13 | 0.442007 | 0.221003 | − | 0.975273i | \(-0.429067\pi\) | ||||
0.221003 | + | 0.975273i | \(0.429067\pi\) | |||||||
\(972\) | −3.96891e13 | −1.42618 | ||||||||
\(973\) | 2.15244e13 | 0.769879 | ||||||||
\(974\) | −3.94622e12 | −0.140497 | ||||||||
\(975\) | 4.55727e12 | 0.161504 | ||||||||
\(976\) | −1.47534e13 | −0.520438 | ||||||||
\(977\) | −5.34352e13 | −1.87630 | −0.938149 | − | 0.346231i | \(-0.887461\pi\) | ||||
−0.938149 | + | 0.346231i | \(0.887461\pi\) | |||||||
\(978\) | 3.03156e12 | 0.105960 | ||||||||
\(979\) | 6.24766e12 | 0.217368 | ||||||||
\(980\) | 1.25497e13 | 0.434626 | ||||||||
\(981\) | −2.82511e13 | −0.973923 | ||||||||
\(982\) | 2.42262e12 | 0.0831350 | ||||||||
\(983\) | −5.98058e12 | −0.204293 | −0.102146 | − | 0.994769i | \(-0.532571\pi\) | ||||
−0.102146 | + | 0.994769i | \(0.532571\pi\) | |||||||
\(984\) | 1.66760e12 | 0.0567040 | ||||||||
\(985\) | −3.12295e13 | −1.05706 | ||||||||
\(986\) | 7.20079e12 | 0.242624 | ||||||||
\(987\) | 2.51990e13 | 0.845194 | ||||||||
\(988\) | −4.28194e12 | −0.142967 | ||||||||
\(989\) | 4.07220e12 | 0.135346 | ||||||||
\(990\) | −1.34969e12 | −0.0446555 | ||||||||
\(991\) | −1.53735e13 | −0.506340 | −0.253170 | − | 0.967422i | \(-0.581473\pi\) | ||||
−0.253170 | + | 0.967422i | \(0.581473\pi\) | |||||||
\(992\) | 7.99310e12 | 0.262067 | ||||||||
\(993\) | 6.56035e13 | 2.14119 | ||||||||
\(994\) | 3.29158e10 | 0.00106946 | ||||||||
\(995\) | 4.69241e12 | 0.151772 | ||||||||
\(996\) | −5.59667e13 | −1.80203 | ||||||||
\(997\) | −1.18916e12 | −0.0381165 | −0.0190583 | − | 0.999818i | \(-0.506067\pi\) | ||||
−0.0190583 | + | 0.999818i | \(0.506067\pi\) | |||||||
\(998\) | −4.28574e12 | −0.136754 | ||||||||
\(999\) | 3.77315e12 | 0.119856 |
(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 | 43.10.a.a.1.9 | ✓ | 15 | |
3.2 | odd | 2 | 387.10.a.c.1.7 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.10.a.a.1.9 | ✓ | 15 | 1.1 | even | 1 | trivial | |
387.10.a.c.1.7 | 15 | 3.2 | odd | 2 |