Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,8,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.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: | \(28.4270373191\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4 x^{8} - 764 x^{7} + 1562 x^{6} + 176422 x^{5} + 56746 x^{4} - 13204236 x^{3} - 22500802 x^{2} + 176026849 x + 176334338 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-5.28525\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.28525 | −0.555542 | −0.277771 | − | 0.960647i | \(-0.589596\pi\) | ||||
−0.277771 | + | 0.960647i | \(0.589596\pi\) | |||||||
\(3\) | 79.3185 | 1.69610 | 0.848048 | − | 0.529920i | \(-0.177778\pi\) | ||||
0.848048 | + | 0.529920i | \(0.177778\pi\) | |||||||
\(4\) | −88.4957 | −0.691373 | ||||||||
\(5\) | −293.470 | −1.04995 | −0.524976 | − | 0.851117i | \(-0.675926\pi\) | ||||
−0.524976 | + | 0.851117i | \(0.675926\pi\) | |||||||
\(6\) | −498.536 | −0.942253 | ||||||||
\(7\) | −343.000 | −0.377964 | ||||||||
\(8\) | 1360.73 | 0.939629 | ||||||||
\(9\) | 4104.43 | 1.87674 | ||||||||
\(10\) | 1844.53 | 0.583293 | ||||||||
\(11\) | 5225.54 | 1.18374 | 0.591870 | − | 0.806033i | \(-0.298390\pi\) | ||||
0.591870 | + | 0.806033i | \(0.298390\pi\) | |||||||
\(12\) | −7019.35 | −1.17263 | ||||||||
\(13\) | 2197.00 | 0.277350 | ||||||||
\(14\) | 2155.84 | 0.209975 | ||||||||
\(15\) | −23277.6 | −1.78082 | ||||||||
\(16\) | 2774.93 | 0.169369 | ||||||||
\(17\) | −35943.3 | −1.77438 | −0.887190 | − | 0.461405i | \(-0.847346\pi\) | ||||
−0.887190 | + | 0.461405i | \(0.847346\pi\) | |||||||
\(18\) | −25797.4 | −1.04261 | ||||||||
\(19\) | −15900.9 | −0.531845 | −0.265923 | − | 0.963994i | \(-0.585677\pi\) | ||||
−0.265923 | + | 0.963994i | \(0.585677\pi\) | |||||||
\(20\) | 25970.9 | 0.725908 | ||||||||
\(21\) | −27206.3 | −0.641064 | ||||||||
\(22\) | −32843.8 | −0.657618 | ||||||||
\(23\) | −54319.2 | −0.930906 | −0.465453 | − | 0.885073i | \(-0.654109\pi\) | ||||
−0.465453 | + | 0.885073i | \(0.654109\pi\) | |||||||
\(24\) | 107931. | 1.59370 | ||||||||
\(25\) | 7999.90 | 0.102399 | ||||||||
\(26\) | −13808.7 | −0.154080 | ||||||||
\(27\) | 152088. | 1.48703 | ||||||||
\(28\) | 30354.0 | 0.261314 | ||||||||
\(29\) | −11069.5 | −0.0842818 | −0.0421409 | − | 0.999112i | \(-0.513418\pi\) | ||||
−0.0421409 | + | 0.999112i | \(0.513418\pi\) | |||||||
\(30\) | 146306. | 0.989320 | ||||||||
\(31\) | −196401. | −1.18407 | −0.592035 | − | 0.805912i | \(-0.701675\pi\) | ||||
−0.592035 | + | 0.805912i | \(0.701675\pi\) | |||||||
\(32\) | −191614. | −1.03372 | ||||||||
\(33\) | 414482. | 2.00774 | ||||||||
\(34\) | 225912. | 0.985743 | ||||||||
\(35\) | 100660. | 0.396844 | ||||||||
\(36\) | −363224. | −1.29753 | ||||||||
\(37\) | −569532. | −1.84847 | −0.924234 | − | 0.381826i | \(-0.875295\pi\) | ||||
−0.924234 | + | 0.381826i | \(0.875295\pi\) | |||||||
\(38\) | 99941.3 | 0.295463 | ||||||||
\(39\) | 174263. | 0.470412 | ||||||||
\(40\) | −399334. | −0.986565 | ||||||||
\(41\) | 18430.8 | 0.0417640 | 0.0208820 | − | 0.999782i | \(-0.493353\pi\) | ||||
0.0208820 | + | 0.999782i | \(0.493353\pi\) | |||||||
\(42\) | 170998. | 0.356138 | ||||||||
\(43\) | −23342.0 | −0.0447711 | −0.0223855 | − | 0.999749i | \(-0.507126\pi\) | ||||
−0.0223855 | + | 0.999749i | \(0.507126\pi\) | |||||||
\(44\) | −462438. | −0.818406 | ||||||||
\(45\) | −1.20453e6 | −1.97049 | ||||||||
\(46\) | 341410. | 0.517158 | ||||||||
\(47\) | 956732. | 1.34415 | 0.672075 | − | 0.740483i | \(-0.265403\pi\) | ||||
0.672075 | + | 0.740483i | \(0.265403\pi\) | |||||||
\(48\) | 220104. | 0.287265 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | −50281.4 | −0.0568869 | ||||||||
\(51\) | −2.85097e6 | −3.00952 | ||||||||
\(52\) | −194425. | −0.191752 | ||||||||
\(53\) | −933786. | −0.861553 | −0.430776 | − | 0.902459i | \(-0.641760\pi\) | ||||
−0.430776 | + | 0.902459i | \(0.641760\pi\) | |||||||
\(54\) | −955909. | −0.826111 | ||||||||
\(55\) | −1.53354e6 | −1.24287 | ||||||||
\(56\) | −466730. | −0.355146 | ||||||||
\(57\) | −1.26124e6 | −0.902060 | ||||||||
\(58\) | 69574.3 | 0.0468221 | ||||||||
\(59\) | −1.11153e6 | −0.704595 | −0.352298 | − | 0.935888i | \(-0.614600\pi\) | ||||
−0.352298 | + | 0.935888i | \(0.614600\pi\) | |||||||
\(60\) | 2.05997e6 | 1.23121 | ||||||||
\(61\) | −609277. | −0.343685 | −0.171842 | − | 0.985124i | \(-0.554972\pi\) | ||||
−0.171842 | + | 0.985124i | \(0.554972\pi\) | |||||||
\(62\) | 1.23443e6 | 0.657802 | ||||||||
\(63\) | −1.40782e6 | −0.709341 | ||||||||
\(64\) | 849152. | 0.404907 | ||||||||
\(65\) | −644755. | −0.291204 | ||||||||
\(66\) | −2.60512e6 | −1.11538 | ||||||||
\(67\) | 121784. | 0.0494687 | 0.0247343 | − | 0.999694i | \(-0.492126\pi\) | ||||
0.0247343 | + | 0.999694i | \(0.492126\pi\) | |||||||
\(68\) | 3.18083e6 | 1.22676 | ||||||||
\(69\) | −4.30852e6 | −1.57891 | ||||||||
\(70\) | −632675. | −0.220464 | ||||||||
\(71\) | 1.39633e6 | 0.463004 | 0.231502 | − | 0.972834i | \(-0.425636\pi\) | ||||
0.231502 | + | 0.972834i | \(0.425636\pi\) | |||||||
\(72\) | 5.58502e6 | 1.76344 | ||||||||
\(73\) | 2.85451e6 | 0.858818 | 0.429409 | − | 0.903110i | \(-0.358722\pi\) | ||||
0.429409 | + | 0.903110i | \(0.358722\pi\) | |||||||
\(74\) | 3.57965e6 | 1.02690 | ||||||||
\(75\) | 634541. | 0.173678 | ||||||||
\(76\) | 1.40716e6 | 0.367703 | ||||||||
\(77\) | −1.79236e6 | −0.447412 | ||||||||
\(78\) | −1.09528e6 | −0.261334 | ||||||||
\(79\) | −477949. | −0.109065 | −0.0545326 | − | 0.998512i | \(-0.517367\pi\) | ||||
−0.0545326 | + | 0.998512i | \(0.517367\pi\) | |||||||
\(80\) | −814361. | −0.177829 | ||||||||
\(81\) | 3.08699e6 | 0.645413 | ||||||||
\(82\) | −115842. | −0.0232017 | ||||||||
\(83\) | 7.53259e6 | 1.44601 | 0.723005 | − | 0.690843i | \(-0.242760\pi\) | ||||
0.723005 | + | 0.690843i | \(0.242760\pi\) | |||||||
\(84\) | 2.40764e6 | 0.443214 | ||||||||
\(85\) | 1.05483e7 | 1.86301 | ||||||||
\(86\) | 146710. | 0.0248722 | ||||||||
\(87\) | −878014. | −0.142950 | ||||||||
\(88\) | 7.11054e6 | 1.11228 | ||||||||
\(89\) | −9.23609e6 | −1.38875 | −0.694374 | − | 0.719615i | \(-0.744319\pi\) | ||||
−0.694374 | + | 0.719615i | \(0.744319\pi\) | |||||||
\(90\) | 7.57076e6 | 1.09469 | ||||||||
\(91\) | −753571. | −0.104828 | ||||||||
\(92\) | 4.80701e6 | 0.643603 | ||||||||
\(93\) | −1.55782e7 | −2.00830 | ||||||||
\(94\) | −6.01329e6 | −0.746732 | ||||||||
\(95\) | 4.66646e6 | 0.558412 | ||||||||
\(96\) | −1.51986e7 | −1.75329 | ||||||||
\(97\) | 1.58162e7 | 1.75955 | 0.879776 | − | 0.475389i | \(-0.157693\pi\) | ||||
0.879776 | + | 0.475389i | \(0.157693\pi\) | |||||||
\(98\) | −739453. | −0.0793632 | ||||||||
\(99\) | 2.14479e7 | 2.22157 | ||||||||
\(100\) | −707957. | −0.0707957 | ||||||||
\(101\) | −1.94673e7 | −1.88010 | −0.940048 | − | 0.341042i | \(-0.889220\pi\) | ||||
−0.940048 | + | 0.341042i | \(0.889220\pi\) | |||||||
\(102\) | 1.79190e7 | 1.67191 | ||||||||
\(103\) | −9.38945e6 | −0.846661 | −0.423331 | − | 0.905975i | \(-0.639139\pi\) | ||||
−0.423331 | + | 0.905975i | \(0.639139\pi\) | |||||||
\(104\) | 2.98952e6 | 0.260606 | ||||||||
\(105\) | 7.98423e6 | 0.673086 | ||||||||
\(106\) | 5.86907e6 | 0.478629 | ||||||||
\(107\) | −1.46471e7 | −1.15587 | −0.577935 | − | 0.816083i | \(-0.696141\pi\) | ||||
−0.577935 | + | 0.816083i | \(0.696141\pi\) | |||||||
\(108\) | −1.34591e7 | −1.02809 | ||||||||
\(109\) | −641790. | −0.0474679 | −0.0237339 | − | 0.999718i | \(-0.507555\pi\) | ||||
−0.0237339 | + | 0.999718i | \(0.507555\pi\) | |||||||
\(110\) | 9.63868e6 | 0.690468 | ||||||||
\(111\) | −4.51744e7 | −3.13518 | ||||||||
\(112\) | −951802. | −0.0640153 | ||||||||
\(113\) | 1.24089e6 | 0.0809019 | 0.0404509 | − | 0.999182i | \(-0.487121\pi\) | ||||
0.0404509 | + | 0.999182i | \(0.487121\pi\) | |||||||
\(114\) | 7.92720e6 | 0.501133 | ||||||||
\(115\) | 1.59411e7 | 0.977407 | ||||||||
\(116\) | 979600. | 0.0582701 | ||||||||
\(117\) | 9.01743e6 | 0.520514 | ||||||||
\(118\) | 6.98625e6 | 0.391433 | ||||||||
\(119\) | 1.23285e7 | 0.670652 | ||||||||
\(120\) | −3.16746e7 | −1.67331 | ||||||||
\(121\) | 7.81909e6 | 0.401243 | ||||||||
\(122\) | 3.82945e6 | 0.190931 | ||||||||
\(123\) | 1.46191e6 | 0.0708357 | ||||||||
\(124\) | 1.73806e7 | 0.818634 | ||||||||
\(125\) | 2.05796e7 | 0.942438 | ||||||||
\(126\) | 8.84849e6 | 0.394069 | ||||||||
\(127\) | −3.18169e7 | −1.37831 | −0.689153 | − | 0.724616i | \(-0.742017\pi\) | ||||
−0.689153 | + | 0.724616i | \(0.742017\pi\) | |||||||
\(128\) | 1.91895e7 | 0.808778 | ||||||||
\(129\) | −1.85145e6 | −0.0759361 | ||||||||
\(130\) | 4.05244e6 | 0.161776 | ||||||||
\(131\) | −1.22654e7 | −0.476685 | −0.238343 | − | 0.971181i | \(-0.576604\pi\) | ||||
−0.238343 | + | 0.971181i | \(0.576604\pi\) | |||||||
\(132\) | −3.66799e7 | −1.38809 | ||||||||
\(133\) | 5.45402e6 | 0.201019 | ||||||||
\(134\) | −765445. | −0.0274819 | ||||||||
\(135\) | −4.46333e7 | −1.56131 | ||||||||
\(136\) | −4.89091e7 | −1.66726 | ||||||||
\(137\) | 2.63318e7 | 0.874902 | 0.437451 | − | 0.899242i | \(-0.355881\pi\) | ||||
0.437451 | + | 0.899242i | \(0.355881\pi\) | |||||||
\(138\) | 2.70801e7 | 0.877149 | ||||||||
\(139\) | 5.57051e7 | 1.75931 | 0.879657 | − | 0.475609i | \(-0.157772\pi\) | ||||
0.879657 | + | 0.475609i | \(0.157772\pi\) | |||||||
\(140\) | −8.90801e6 | −0.274367 | ||||||||
\(141\) | 7.58866e7 | 2.27981 | ||||||||
\(142\) | −8.77629e6 | −0.257218 | ||||||||
\(143\) | 1.14805e7 | 0.328311 | ||||||||
\(144\) | 1.13895e7 | 0.317861 | ||||||||
\(145\) | 3.24856e6 | 0.0884918 | ||||||||
\(146\) | −1.79413e7 | −0.477110 | ||||||||
\(147\) | 9.33175e6 | 0.242299 | ||||||||
\(148\) | 5.04011e7 | 1.27798 | ||||||||
\(149\) | 3.77273e7 | 0.934337 | 0.467168 | − | 0.884168i | \(-0.345274\pi\) | ||||
0.467168 | + | 0.884168i | \(0.345274\pi\) | |||||||
\(150\) | −3.98824e6 | −0.0964856 | ||||||||
\(151\) | 3.00307e6 | 0.0709816 | 0.0354908 | − | 0.999370i | \(-0.488701\pi\) | ||||
0.0354908 | + | 0.999370i | \(0.488701\pi\) | |||||||
\(152\) | −2.16369e7 | −0.499737 | ||||||||
\(153\) | −1.47527e8 | −3.33005 | ||||||||
\(154\) | 1.12654e7 | 0.248556 | ||||||||
\(155\) | 5.76379e7 | 1.24322 | ||||||||
\(156\) | −1.54215e7 | −0.325230 | ||||||||
\(157\) | −9.46951e6 | −0.195290 | −0.0976448 | − | 0.995221i | \(-0.531131\pi\) | ||||
−0.0976448 | + | 0.995221i | \(0.531131\pi\) | |||||||
\(158\) | 3.00402e6 | 0.0605904 | ||||||||
\(159\) | −7.40665e7 | −1.46128 | ||||||||
\(160\) | 5.62332e7 | 1.08536 | ||||||||
\(161\) | 1.86315e7 | 0.351849 | ||||||||
\(162\) | −1.94025e7 | −0.358554 | ||||||||
\(163\) | 1.72034e6 | 0.0311142 | 0.0155571 | − | 0.999879i | \(-0.495048\pi\) | ||||
0.0155571 | + | 0.999879i | \(0.495048\pi\) | |||||||
\(164\) | −1.63105e6 | −0.0288745 | ||||||||
\(165\) | −1.21638e8 | −2.10803 | ||||||||
\(166\) | −4.73442e7 | −0.803320 | ||||||||
\(167\) | −1.00841e8 | −1.67544 | −0.837718 | − | 0.546103i | \(-0.816111\pi\) | ||||
−0.837718 | + | 0.546103i | \(0.816111\pi\) | |||||||
\(168\) | −3.70203e7 | −0.602362 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | −6.62986e7 | −1.03498 | ||||||||
\(171\) | −6.52643e7 | −0.998135 | ||||||||
\(172\) | 2.06566e6 | 0.0309535 | ||||||||
\(173\) | 1.04816e8 | 1.53910 | 0.769550 | − | 0.638586i | \(-0.220480\pi\) | ||||
0.769550 | + | 0.638586i | \(0.220480\pi\) | |||||||
\(174\) | 5.51853e6 | 0.0794148 | ||||||||
\(175\) | −2.74397e6 | −0.0387031 | ||||||||
\(176\) | 1.45005e7 | 0.200488 | ||||||||
\(177\) | −8.81651e7 | −1.19506 | ||||||||
\(178\) | 5.80511e7 | 0.771508 | ||||||||
\(179\) | −5.81700e7 | −0.758077 | −0.379038 | − | 0.925381i | \(-0.623745\pi\) | ||||
−0.379038 | + | 0.925381i | \(0.623745\pi\) | |||||||
\(180\) | 1.06596e8 | 1.36234 | ||||||||
\(181\) | 1.19705e8 | 1.50051 | 0.750255 | − | 0.661149i | \(-0.229931\pi\) | ||||
0.750255 | + | 0.661149i | \(0.229931\pi\) | |||||||
\(182\) | 4.73638e6 | 0.0582367 | ||||||||
\(183\) | −4.83269e7 | −0.582922 | ||||||||
\(184\) | −7.39137e7 | −0.874707 | ||||||||
\(185\) | 1.67141e8 | 1.94080 | ||||||||
\(186\) | 9.79130e7 | 1.11569 | ||||||||
\(187\) | −1.87823e8 | −2.10041 | ||||||||
\(188\) | −8.46666e7 | −0.929308 | ||||||||
\(189\) | −5.21661e7 | −0.562046 | ||||||||
\(190\) | −2.93298e7 | −0.310222 | ||||||||
\(191\) | −1.09441e8 | −1.13648 | −0.568240 | − | 0.822863i | \(-0.692375\pi\) | ||||
−0.568240 | + | 0.822863i | \(0.692375\pi\) | |||||||
\(192\) | 6.73535e7 | 0.686761 | ||||||||
\(193\) | 5.00461e7 | 0.501094 | 0.250547 | − | 0.968104i | \(-0.419390\pi\) | ||||
0.250547 | + | 0.968104i | \(0.419390\pi\) | |||||||
\(194\) | −9.94089e7 | −0.977506 | ||||||||
\(195\) | −5.11410e7 | −0.493910 | ||||||||
\(196\) | −1.04114e7 | −0.0987675 | ||||||||
\(197\) | 1.05766e7 | 0.0985627 | 0.0492814 | − | 0.998785i | \(-0.484307\pi\) | ||||
0.0492814 | + | 0.998785i | \(0.484307\pi\) | |||||||
\(198\) | −1.34805e8 | −1.23418 | ||||||||
\(199\) | 1.76419e8 | 1.58693 | 0.793466 | − | 0.608614i | \(-0.208274\pi\) | ||||
0.793466 | + | 0.608614i | \(0.208274\pi\) | |||||||
\(200\) | 1.08857e7 | 0.0962169 | ||||||||
\(201\) | 9.65976e6 | 0.0839036 | ||||||||
\(202\) | 1.22357e8 | 1.04447 | ||||||||
\(203\) | 3.79683e6 | 0.0318555 | ||||||||
\(204\) | 2.52298e8 | 2.08070 | ||||||||
\(205\) | −5.40891e6 | −0.0438501 | ||||||||
\(206\) | 5.90150e7 | 0.470356 | ||||||||
\(207\) | −2.22949e8 | −1.74707 | ||||||||
\(208\) | 6.09653e6 | 0.0469744 | ||||||||
\(209\) | −8.30910e7 | −0.629567 | ||||||||
\(210\) | −5.01829e7 | −0.373928 | ||||||||
\(211\) | −2.13989e8 | −1.56820 | −0.784102 | − | 0.620632i | \(-0.786876\pi\) | ||||
−0.784102 | + | 0.620632i | \(0.786876\pi\) | |||||||
\(212\) | 8.26360e7 | 0.595654 | ||||||||
\(213\) | 1.10755e8 | 0.785299 | ||||||||
\(214\) | 9.20607e7 | 0.642135 | ||||||||
\(215\) | 6.85018e6 | 0.0470075 | ||||||||
\(216\) | 2.06950e8 | 1.39726 | ||||||||
\(217\) | 6.73655e7 | 0.447537 | ||||||||
\(218\) | 4.03381e6 | 0.0263704 | ||||||||
\(219\) | 2.26415e8 | 1.45664 | ||||||||
\(220\) | 1.35712e8 | 0.859287 | ||||||||
\(221\) | −7.89674e7 | −0.492124 | ||||||||
\(222\) | 2.83932e8 | 1.74172 | ||||||||
\(223\) | −1.09968e8 | −0.664048 | −0.332024 | − | 0.943271i | \(-0.607731\pi\) | ||||
−0.332024 | + | 0.943271i | \(0.607731\pi\) | |||||||
\(224\) | 6.57237e7 | 0.390710 | ||||||||
\(225\) | 3.28350e7 | 0.192176 | ||||||||
\(226\) | −7.79929e6 | −0.0449444 | ||||||||
\(227\) | 1.55040e8 | 0.879735 | 0.439868 | − | 0.898063i | \(-0.355025\pi\) | ||||
0.439868 | + | 0.898063i | \(0.355025\pi\) | |||||||
\(228\) | 1.11614e8 | 0.623660 | ||||||||
\(229\) | 3.45066e8 | 1.89879 | 0.949397 | − | 0.314078i | \(-0.101695\pi\) | ||||
0.949397 | + | 0.314078i | \(0.101695\pi\) | |||||||
\(230\) | −1.00194e8 | −0.542991 | ||||||||
\(231\) | −1.42167e8 | −0.758854 | ||||||||
\(232\) | −1.50625e7 | −0.0791936 | ||||||||
\(233\) | −6.20447e7 | −0.321336 | −0.160668 | − | 0.987009i | \(-0.551365\pi\) | ||||
−0.160668 | + | 0.987009i | \(0.551365\pi\) | |||||||
\(234\) | −5.66768e7 | −0.289168 | ||||||||
\(235\) | −2.80773e8 | −1.41129 | ||||||||
\(236\) | 9.83658e7 | 0.487138 | ||||||||
\(237\) | −3.79102e7 | −0.184985 | ||||||||
\(238\) | −7.74879e7 | −0.372576 | ||||||||
\(239\) | −2.61194e8 | −1.23757 | −0.618787 | − | 0.785559i | \(-0.712376\pi\) | ||||
−0.618787 | + | 0.785559i | \(0.712376\pi\) | |||||||
\(240\) | −6.45939e7 | −0.301615 | ||||||||
\(241\) | −1.02075e8 | −0.469741 | −0.234870 | − | 0.972027i | \(-0.575467\pi\) | ||||
−0.234870 | + | 0.972027i | \(0.575467\pi\) | |||||||
\(242\) | −4.91449e7 | −0.222907 | ||||||||
\(243\) | −8.77605e7 | −0.392353 | ||||||||
\(244\) | 5.39184e7 | 0.237614 | ||||||||
\(245\) | −3.45265e7 | −0.149993 | ||||||||
\(246\) | −9.18845e6 | −0.0393522 | ||||||||
\(247\) | −3.49344e7 | −0.147507 | ||||||||
\(248\) | −2.67248e8 | −1.11259 | ||||||||
\(249\) | 5.97474e8 | 2.45257 | ||||||||
\(250\) | −1.29348e8 | −0.523564 | ||||||||
\(251\) | −2.93524e7 | −0.117162 | −0.0585809 | − | 0.998283i | \(-0.518658\pi\) | ||||
−0.0585809 | + | 0.998283i | \(0.518658\pi\) | |||||||
\(252\) | 1.24586e8 | 0.490419 | ||||||||
\(253\) | −2.83847e8 | −1.10195 | ||||||||
\(254\) | 1.99977e8 | 0.765707 | ||||||||
\(255\) | 8.36675e8 | 3.15985 | ||||||||
\(256\) | −2.29302e8 | −0.854218 | ||||||||
\(257\) | −3.72786e8 | −1.36992 | −0.684958 | − | 0.728583i | \(-0.740179\pi\) | ||||
−0.684958 | + | 0.728583i | \(0.740179\pi\) | |||||||
\(258\) | 1.16368e7 | 0.0421857 | ||||||||
\(259\) | 1.95349e8 | 0.698655 | ||||||||
\(260\) | 5.70580e7 | 0.201331 | ||||||||
\(261\) | −4.54339e7 | −0.158175 | ||||||||
\(262\) | 7.70910e7 | 0.264819 | ||||||||
\(263\) | −2.46625e8 | −0.835972 | −0.417986 | − | 0.908453i | \(-0.637264\pi\) | ||||
−0.417986 | + | 0.908453i | \(0.637264\pi\) | |||||||
\(264\) | 5.63998e8 | 1.88653 | ||||||||
\(265\) | 2.74039e8 | 0.904589 | ||||||||
\(266\) | −3.42799e7 | −0.111674 | ||||||||
\(267\) | −7.32593e8 | −2.35545 | ||||||||
\(268\) | −1.07774e7 | −0.0342013 | ||||||||
\(269\) | −4.40801e8 | −1.38073 | −0.690367 | − | 0.723459i | \(-0.742551\pi\) | ||||
−0.690367 | + | 0.723459i | \(0.742551\pi\) | |||||||
\(270\) | 2.80531e8 | 0.867377 | ||||||||
\(271\) | 4.61850e8 | 1.40964 | 0.704821 | − | 0.709386i | \(-0.251028\pi\) | ||||
0.704821 | + | 0.709386i | \(0.251028\pi\) | |||||||
\(272\) | −9.97403e7 | −0.300524 | ||||||||
\(273\) | −5.97721e7 | −0.177799 | ||||||||
\(274\) | −1.65502e8 | −0.486045 | ||||||||
\(275\) | 4.18038e7 | 0.121214 | ||||||||
\(276\) | 3.81285e8 | 1.09161 | ||||||||
\(277\) | 5.21353e8 | 1.47385 | 0.736924 | − | 0.675976i | \(-0.236278\pi\) | ||||
0.736924 | + | 0.675976i | \(0.236278\pi\) | |||||||
\(278\) | −3.50120e8 | −0.977373 | ||||||||
\(279\) | −8.06114e8 | −2.22219 | ||||||||
\(280\) | 1.36971e8 | 0.372887 | ||||||||
\(281\) | 2.46808e8 | 0.663571 | 0.331785 | − | 0.943355i | \(-0.392349\pi\) | ||||
0.331785 | + | 0.943355i | \(0.392349\pi\) | |||||||
\(282\) | −4.76966e8 | −1.26653 | ||||||||
\(283\) | 5.37098e8 | 1.40864 | 0.704321 | − | 0.709881i | \(-0.251251\pi\) | ||||
0.704321 | + | 0.709881i | \(0.251251\pi\) | |||||||
\(284\) | −1.23569e8 | −0.320108 | ||||||||
\(285\) | 3.70137e8 | 0.947120 | ||||||||
\(286\) | −7.21578e7 | −0.182391 | ||||||||
\(287\) | −6.32178e6 | −0.0157853 | ||||||||
\(288\) | −7.86468e8 | −1.94002 | ||||||||
\(289\) | 8.81581e8 | 2.14842 | ||||||||
\(290\) | −2.04180e7 | −0.0491610 | ||||||||
\(291\) | 1.25452e9 | 2.98437 | ||||||||
\(292\) | −2.52612e8 | −0.593763 | ||||||||
\(293\) | −7.71723e8 | −1.79236 | −0.896179 | − | 0.443693i | \(-0.853668\pi\) | ||||
−0.896179 | + | 0.443693i | \(0.853668\pi\) | |||||||
\(294\) | −5.86523e7 | −0.134608 | ||||||||
\(295\) | 3.26202e8 | 0.739791 | ||||||||
\(296\) | −7.74978e8 | −1.73687 | ||||||||
\(297\) | 7.94740e8 | 1.76026 | ||||||||
\(298\) | −2.37125e8 | −0.519064 | ||||||||
\(299\) | −1.19339e8 | −0.258187 | ||||||||
\(300\) | −5.61541e7 | −0.120076 | ||||||||
\(301\) | 8.00629e6 | 0.0169219 | ||||||||
\(302\) | −1.88750e7 | −0.0394333 | ||||||||
\(303\) | −1.54411e9 | −3.18882 | ||||||||
\(304\) | −4.41241e7 | −0.0900779 | ||||||||
\(305\) | 1.78805e8 | 0.360852 | ||||||||
\(306\) | 9.27242e8 | 1.84998 | ||||||||
\(307\) | 1.30784e8 | 0.257971 | 0.128986 | − | 0.991646i | \(-0.458828\pi\) | ||||
0.128986 | + | 0.991646i | \(0.458828\pi\) | |||||||
\(308\) | 1.58616e8 | 0.309328 | ||||||||
\(309\) | −7.44757e8 | −1.43602 | ||||||||
\(310\) | −3.62268e8 | −0.690660 | ||||||||
\(311\) | −5.05719e8 | −0.953340 | −0.476670 | − | 0.879082i | \(-0.658156\pi\) | ||||
−0.476670 | + | 0.879082i | \(0.658156\pi\) | |||||||
\(312\) | 2.37124e8 | 0.442013 | ||||||||
\(313\) | 3.25829e8 | 0.600599 | 0.300299 | − | 0.953845i | \(-0.402913\pi\) | ||||
0.300299 | + | 0.953845i | \(0.402913\pi\) | |||||||
\(314\) | 5.95182e7 | 0.108492 | ||||||||
\(315\) | 4.13153e8 | 0.744774 | ||||||||
\(316\) | 4.22964e7 | 0.0754047 | ||||||||
\(317\) | 2.83996e8 | 0.500732 | 0.250366 | − | 0.968151i | \(-0.419449\pi\) | ||||
0.250366 | + | 0.968151i | \(0.419449\pi\) | |||||||
\(318\) | 4.65526e8 | 0.811801 | ||||||||
\(319\) | −5.78439e7 | −0.0997678 | ||||||||
\(320\) | −2.49201e8 | −0.425133 | ||||||||
\(321\) | −1.16179e9 | −1.96047 | ||||||||
\(322\) | −1.17103e8 | −0.195467 | ||||||||
\(323\) | 5.71532e8 | 0.943695 | ||||||||
\(324\) | −2.73185e8 | −0.446221 | ||||||||
\(325\) | 1.75758e7 | 0.0284003 | ||||||||
\(326\) | −1.08128e7 | −0.0172852 | ||||||||
\(327\) | −5.09058e7 | −0.0805101 | ||||||||
\(328\) | 2.50794e7 | 0.0392426 | ||||||||
\(329\) | −3.28159e8 | −0.508041 | ||||||||
\(330\) | 7.64526e8 | 1.17110 | ||||||||
\(331\) | −9.22687e8 | −1.39848 | −0.699241 | − | 0.714886i | \(-0.746478\pi\) | ||||
−0.699241 | + | 0.714886i | \(0.746478\pi\) | |||||||
\(332\) | −6.66602e8 | −0.999731 | ||||||||
\(333\) | −2.33760e9 | −3.46909 | ||||||||
\(334\) | 6.33808e8 | 0.930776 | ||||||||
\(335\) | −3.57401e7 | −0.0519397 | ||||||||
\(336\) | −7.54956e7 | −0.108576 | ||||||||
\(337\) | 6.01648e7 | 0.0856323 | 0.0428161 | − | 0.999083i | \(-0.486367\pi\) | ||||
0.0428161 | + | 0.999083i | \(0.486367\pi\) | |||||||
\(338\) | −3.03377e7 | −0.0427340 | ||||||||
\(339\) | 9.84255e7 | 0.137217 | ||||||||
\(340\) | −9.33478e8 | −1.28804 | ||||||||
\(341\) | −1.02630e9 | −1.40163 | ||||||||
\(342\) | 4.10202e8 | 0.554506 | ||||||||
\(343\) | −4.03536e7 | −0.0539949 | ||||||||
\(344\) | −3.17621e7 | −0.0420682 | ||||||||
\(345\) | 1.26442e9 | 1.65777 | ||||||||
\(346\) | −6.58795e8 | −0.855036 | ||||||||
\(347\) | 1.08011e9 | 1.38776 | 0.693881 | − | 0.720090i | \(-0.255900\pi\) | ||||
0.693881 | + | 0.720090i | \(0.255900\pi\) | |||||||
\(348\) | 7.77005e7 | 0.0988317 | ||||||||
\(349\) | −6.96677e8 | −0.877288 | −0.438644 | − | 0.898661i | \(-0.644541\pi\) | ||||
−0.438644 | + | 0.898661i | \(0.644541\pi\) | |||||||
\(350\) | 1.72465e7 | 0.0215012 | ||||||||
\(351\) | 3.34137e8 | 0.412429 | ||||||||
\(352\) | −1.00129e9 | −1.22366 | ||||||||
\(353\) | −2.15539e7 | −0.0260804 | −0.0130402 | − | 0.999915i | \(-0.504151\pi\) | ||||
−0.0130402 | + | 0.999915i | \(0.504151\pi\) | |||||||
\(354\) | 5.54139e8 | 0.663907 | ||||||||
\(355\) | −4.09782e8 | −0.486132 | ||||||||
\(356\) | 8.17354e8 | 0.960142 | ||||||||
\(357\) | 9.77882e8 | 1.13749 | ||||||||
\(358\) | 3.65613e8 | 0.421144 | ||||||||
\(359\) | −1.02429e9 | −1.16840 | −0.584200 | − | 0.811609i | \(-0.698592\pi\) | ||||
−0.584200 | + | 0.811609i | \(0.698592\pi\) | |||||||
\(360\) | −1.63904e9 | −1.85153 | ||||||||
\(361\) | −6.41032e8 | −0.717141 | ||||||||
\(362\) | −7.52378e8 | −0.833597 | ||||||||
\(363\) | 6.20198e8 | 0.680546 | ||||||||
\(364\) | 6.66878e7 | 0.0724755 | ||||||||
\(365\) | −8.37714e8 | −0.901717 | ||||||||
\(366\) | 3.03747e8 | 0.323838 | ||||||||
\(367\) | −746813. | −0.000788643 0 | −0.000394321 | − | 1.00000i | \(-0.500126\pi\) | ||||
−0.000394321 | 1.00000i | \(0.500126\pi\) | ||||||||
\(368\) | −1.50732e8 | −0.157666 | ||||||||
\(369\) | 7.56481e7 | 0.0783801 | ||||||||
\(370\) | −1.05052e9 | −1.07820 | ||||||||
\(371\) | 3.20289e8 | 0.325636 | ||||||||
\(372\) | 1.37861e9 | 1.38848 | ||||||||
\(373\) | 1.07550e9 | 1.07307 | 0.536535 | − | 0.843878i | \(-0.319733\pi\) | ||||
0.536535 | + | 0.843878i | \(0.319733\pi\) | |||||||
\(374\) | 1.18051e9 | 1.16686 | ||||||||
\(375\) | 1.63235e9 | 1.59846 | ||||||||
\(376\) | 1.30185e9 | 1.26300 | ||||||||
\(377\) | −2.43196e7 | −0.0233756 | ||||||||
\(378\) | 3.27877e8 | 0.312241 | ||||||||
\(379\) | 1.61102e9 | 1.52007 | 0.760037 | − | 0.649880i | \(-0.225181\pi\) | ||||
0.760037 | + | 0.649880i | \(0.225181\pi\) | |||||||
\(380\) | −4.12961e8 | −0.386071 | ||||||||
\(381\) | −2.52367e9 | −2.33774 | ||||||||
\(382\) | 6.87861e8 | 0.631362 | ||||||||
\(383\) | 7.52684e8 | 0.684568 | 0.342284 | − | 0.939596i | \(-0.388799\pi\) | ||||
0.342284 | + | 0.939596i | \(0.388799\pi\) | |||||||
\(384\) | 1.52208e9 | 1.37176 | ||||||||
\(385\) | 5.26005e8 | 0.469761 | ||||||||
\(386\) | −3.14552e8 | −0.278379 | ||||||||
\(387\) | −9.58054e7 | −0.0840237 | ||||||||
\(388\) | −1.39967e9 | −1.21651 | ||||||||
\(389\) | 1.42901e9 | 1.23087 | 0.615434 | − | 0.788188i | \(-0.288981\pi\) | ||||
0.615434 | + | 0.788188i | \(0.288981\pi\) | |||||||
\(390\) | 3.21434e8 | 0.274388 | ||||||||
\(391\) | 1.95241e9 | 1.65178 | ||||||||
\(392\) | 1.60088e8 | 0.134233 | ||||||||
\(393\) | −9.72872e8 | −0.808504 | ||||||||
\(394\) | −6.64763e7 | −0.0547558 | ||||||||
\(395\) | 1.40264e8 | 0.114513 | ||||||||
\(396\) | −1.89804e9 | −1.53594 | ||||||||
\(397\) | 1.04601e9 | 0.839017 | 0.419509 | − | 0.907751i | \(-0.362202\pi\) | ||||
0.419509 | + | 0.907751i | \(0.362202\pi\) | |||||||
\(398\) | −1.10883e9 | −0.881609 | ||||||||
\(399\) | 4.32605e8 | 0.340947 | ||||||||
\(400\) | 2.21992e7 | 0.0173431 | ||||||||
\(401\) | 6.70774e7 | 0.0519483 | 0.0259741 | − | 0.999663i | \(-0.491731\pi\) | ||||
0.0259741 | + | 0.999663i | \(0.491731\pi\) | |||||||
\(402\) | −6.07140e7 | −0.0466120 | ||||||||
\(403\) | −4.31493e8 | −0.328402 | ||||||||
\(404\) | 1.72277e9 | 1.29985 | ||||||||
\(405\) | −9.05940e8 | −0.677652 | ||||||||
\(406\) | −2.38640e7 | −0.0176971 | ||||||||
\(407\) | −2.97611e9 | −2.18811 | ||||||||
\(408\) | −3.87939e9 | −2.82783 | ||||||||
\(409\) | −1.12516e9 | −0.813173 | −0.406587 | − | 0.913612i | \(-0.633281\pi\) | ||||
−0.406587 | + | 0.913612i | \(0.633281\pi\) | |||||||
\(410\) | 3.39963e7 | 0.0243606 | ||||||||
\(411\) | 2.08860e9 | 1.48392 | ||||||||
\(412\) | 8.30926e8 | 0.585358 | ||||||||
\(413\) | 3.81255e8 | 0.266312 | ||||||||
\(414\) | 1.40129e9 | 0.970571 | ||||||||
\(415\) | −2.21059e9 | −1.51824 | ||||||||
\(416\) | −4.20977e8 | −0.286703 | ||||||||
\(417\) | 4.41845e9 | 2.98396 | ||||||||
\(418\) | 5.22247e8 | 0.349751 | ||||||||
\(419\) | 2.20420e9 | 1.46387 | 0.731933 | − | 0.681377i | \(-0.238619\pi\) | ||||
0.731933 | + | 0.681377i | \(0.238619\pi\) | |||||||
\(420\) | −7.06570e8 | −0.465353 | ||||||||
\(421\) | −1.40920e9 | −0.920418 | −0.460209 | − | 0.887811i | \(-0.652226\pi\) | ||||
−0.460209 | + | 0.887811i | \(0.652226\pi\) | |||||||
\(422\) | 1.34497e9 | 0.871204 | ||||||||
\(423\) | 3.92684e9 | 2.52262 | ||||||||
\(424\) | −1.27063e9 | −0.809540 | ||||||||
\(425\) | −2.87543e8 | −0.181694 | ||||||||
\(426\) | −6.96123e8 | −0.436267 | ||||||||
\(427\) | 2.08982e8 | 0.129901 | ||||||||
\(428\) | 1.29621e9 | 0.799137 | ||||||||
\(429\) | 9.10617e8 | 0.556846 | ||||||||
\(430\) | −4.30550e7 | −0.0261147 | ||||||||
\(431\) | 2.63366e9 | 1.58449 | 0.792245 | − | 0.610204i | \(-0.208912\pi\) | ||||
0.792245 | + | 0.610204i | \(0.208912\pi\) | |||||||
\(432\) | 4.22033e8 | 0.251857 | ||||||||
\(433\) | 2.83906e9 | 1.68061 | 0.840306 | − | 0.542112i | \(-0.182375\pi\) | ||||
0.840306 | + | 0.542112i | \(0.182375\pi\) | |||||||
\(434\) | −4.23409e8 | −0.248626 | ||||||||
\(435\) | 2.57671e8 | 0.150091 | ||||||||
\(436\) | 5.67956e7 | 0.0328180 | ||||||||
\(437\) | 8.63726e8 | 0.495098 | ||||||||
\(438\) | −1.42308e9 | −0.809224 | ||||||||
\(439\) | −1.92343e9 | −1.08505 | −0.542527 | − | 0.840039i | \(-0.682532\pi\) | ||||
−0.542527 | + | 0.840039i | \(0.682532\pi\) | |||||||
\(440\) | −2.08673e9 | −1.16784 | ||||||||
\(441\) | 4.82882e8 | 0.268106 | ||||||||
\(442\) | 4.96330e8 | 0.273396 | ||||||||
\(443\) | −3.37999e9 | −1.84715 | −0.923575 | − | 0.383417i | \(-0.874747\pi\) | ||||
−0.923575 | + | 0.383417i | \(0.874747\pi\) | |||||||
\(444\) | 3.99774e9 | 2.16758 | ||||||||
\(445\) | 2.71052e9 | 1.45812 | ||||||||
\(446\) | 6.91176e8 | 0.368907 | ||||||||
\(447\) | 2.99247e9 | 1.58472 | ||||||||
\(448\) | −2.91259e8 | −0.153041 | ||||||||
\(449\) | −7.47706e8 | −0.389824 | −0.194912 | − | 0.980821i | \(-0.562442\pi\) | ||||
−0.194912 | + | 0.980821i | \(0.562442\pi\) | |||||||
\(450\) | −2.06376e8 | −0.106762 | ||||||||
\(451\) | 9.63111e7 | 0.0494377 | ||||||||
\(452\) | −1.09813e8 | −0.0559333 | ||||||||
\(453\) | 2.38199e8 | 0.120392 | ||||||||
\(454\) | −9.74462e8 | −0.488730 | ||||||||
\(455\) | 2.21151e8 | 0.110065 | ||||||||
\(456\) | −1.71620e9 | −0.847602 | ||||||||
\(457\) | 1.37231e9 | 0.672582 | 0.336291 | − | 0.941758i | \(-0.390827\pi\) | ||||
0.336291 | + | 0.941758i | \(0.390827\pi\) | |||||||
\(458\) | −2.16882e9 | −1.05486 | ||||||||
\(459\) | −5.46653e9 | −2.63856 | ||||||||
\(460\) | −1.41072e9 | −0.675752 | ||||||||
\(461\) | −2.64939e9 | −1.25948 | −0.629741 | − | 0.776805i | \(-0.716839\pi\) | ||||
−0.629741 | + | 0.776805i | \(0.716839\pi\) | |||||||
\(462\) | 8.93557e8 | 0.421575 | ||||||||
\(463\) | −2.32553e9 | −1.08890 | −0.544451 | − | 0.838793i | \(-0.683262\pi\) | ||||
−0.544451 | + | 0.838793i | \(0.683262\pi\) | |||||||
\(464\) | −3.07170e7 | −0.0142747 | ||||||||
\(465\) | 4.57175e9 | 2.10862 | ||||||||
\(466\) | 3.89966e8 | 0.178516 | ||||||||
\(467\) | −2.60290e9 | −1.18263 | −0.591315 | − | 0.806440i | \(-0.701391\pi\) | ||||
−0.591315 | + | 0.806440i | \(0.701391\pi\) | |||||||
\(468\) | −7.98004e8 | −0.359869 | ||||||||
\(469\) | −4.17721e7 | −0.0186974 | ||||||||
\(470\) | 1.76472e9 | 0.784033 | ||||||||
\(471\) | −7.51108e8 | −0.331230 | ||||||||
\(472\) | −1.51249e9 | −0.662058 | ||||||||
\(473\) | −1.21974e8 | −0.0529974 | ||||||||
\(474\) | 2.38275e8 | 0.102767 | ||||||||
\(475\) | −1.27206e8 | −0.0544603 | ||||||||
\(476\) | −1.09102e9 | −0.463671 | ||||||||
\(477\) | −3.83266e9 | −1.61691 | ||||||||
\(478\) | 1.64167e9 | 0.687525 | ||||||||
\(479\) | 9.63575e8 | 0.400600 | 0.200300 | − | 0.979735i | \(-0.435808\pi\) | ||||
0.200300 | + | 0.979735i | \(0.435808\pi\) | |||||||
\(480\) | 4.46033e9 | 1.84087 | ||||||||
\(481\) | −1.25126e9 | −0.512673 | ||||||||
\(482\) | 6.41564e8 | 0.260961 | ||||||||
\(483\) | 1.47782e9 | 0.596770 | ||||||||
\(484\) | −6.91955e8 | −0.277408 | ||||||||
\(485\) | −4.64160e9 | −1.84744 | ||||||||
\(486\) | 5.51596e8 | 0.217969 | ||||||||
\(487\) | −3.27359e9 | −1.28432 | −0.642159 | − | 0.766572i | \(-0.721961\pi\) | ||||
−0.642159 | + | 0.766572i | \(0.721961\pi\) | |||||||
\(488\) | −8.29060e8 | −0.322936 | ||||||||
\(489\) | 1.36455e8 | 0.0527726 | ||||||||
\(490\) | 2.17008e8 | 0.0833275 | ||||||||
\(491\) | 1.73467e9 | 0.661351 | 0.330675 | − | 0.943745i | \(-0.392723\pi\) | ||||
0.330675 | + | 0.943745i | \(0.392723\pi\) | |||||||
\(492\) | −1.29372e8 | −0.0489738 | ||||||||
\(493\) | 3.97873e8 | 0.149548 | ||||||||
\(494\) | 2.19571e8 | 0.0819466 | ||||||||
\(495\) | −6.29431e9 | −2.33255 | ||||||||
\(496\) | −5.45000e8 | −0.200544 | ||||||||
\(497\) | −4.78942e8 | −0.174999 | ||||||||
\(498\) | −3.75527e9 | −1.36251 | ||||||||
\(499\) | −1.21566e9 | −0.437987 | −0.218994 | − | 0.975726i | \(-0.570277\pi\) | ||||
−0.218994 | + | 0.975726i | \(0.570277\pi\) | |||||||
\(500\) | −1.82121e9 | −0.651576 | ||||||||
\(501\) | −7.99853e9 | −2.84170 | ||||||||
\(502\) | 1.84487e8 | 0.0650884 | ||||||||
\(503\) | −1.95400e9 | −0.684600 | −0.342300 | − | 0.939591i | \(-0.611206\pi\) | ||||
−0.342300 | + | 0.939591i | \(0.611206\pi\) | |||||||
\(504\) | −1.91566e9 | −0.666518 | ||||||||
\(505\) | 5.71307e9 | 1.97401 | ||||||||
\(506\) | 1.78405e9 | 0.612181 | ||||||||
\(507\) | 3.82855e8 | 0.130469 | ||||||||
\(508\) | 2.81566e9 | 0.952923 | ||||||||
\(509\) | 8.35731e8 | 0.280902 | 0.140451 | − | 0.990088i | \(-0.455145\pi\) | ||||
0.140451 | + | 0.990088i | \(0.455145\pi\) | |||||||
\(510\) | −5.25871e9 | −1.75543 | ||||||||
\(511\) | −9.79096e8 | −0.324603 | ||||||||
\(512\) | −1.01504e9 | −0.334223 | ||||||||
\(513\) | −2.41834e9 | −0.790872 | ||||||||
\(514\) | 2.34305e9 | 0.761046 | ||||||||
\(515\) | 2.75553e9 | 0.888954 | ||||||||
\(516\) | 1.63845e8 | 0.0525001 | ||||||||
\(517\) | 4.99944e9 | 1.59113 | ||||||||
\(518\) | −1.22782e9 | −0.388133 | ||||||||
\(519\) | 8.31387e9 | 2.61046 | ||||||||
\(520\) | −8.77336e8 | −0.273624 | ||||||||
\(521\) | −3.99708e8 | −0.123826 | −0.0619128 | − | 0.998082i | \(-0.519720\pi\) | ||||
−0.0619128 | + | 0.998082i | \(0.519720\pi\) | |||||||
\(522\) | 2.85563e8 | 0.0878729 | ||||||||
\(523\) | 1.45373e9 | 0.444354 | 0.222177 | − | 0.975006i | \(-0.428684\pi\) | ||||
0.222177 | + | 0.975006i | \(0.428684\pi\) | |||||||
\(524\) | 1.08543e9 | 0.329567 | ||||||||
\(525\) | −2.17647e8 | −0.0656441 | ||||||||
\(526\) | 1.55010e9 | 0.464418 | ||||||||
\(527\) | 7.05930e9 | 2.10099 | ||||||||
\(528\) | 1.15016e9 | 0.340048 | ||||||||
\(529\) | −4.54250e8 | −0.133414 | ||||||||
\(530\) | −1.72240e9 | −0.502537 | ||||||||
\(531\) | −4.56220e9 | −1.32234 | ||||||||
\(532\) | −4.82658e8 | −0.138979 | ||||||||
\(533\) | 4.04926e7 | 0.0115832 | ||||||||
\(534\) | 4.60453e9 | 1.30855 | ||||||||
\(535\) | 4.29850e9 | 1.21361 | ||||||||
\(536\) | 1.65716e8 | 0.0464822 | ||||||||
\(537\) | −4.61396e9 | −1.28577 | ||||||||
\(538\) | 2.77054e9 | 0.767056 | ||||||||
\(539\) | 6.14779e8 | 0.169106 | ||||||||
\(540\) | 3.94985e9 | 1.07945 | ||||||||
\(541\) | −1.35141e9 | −0.366940 | −0.183470 | − | 0.983025i | \(-0.558733\pi\) | ||||
−0.183470 | + | 0.983025i | \(0.558733\pi\) | |||||||
\(542\) | −2.90284e9 | −0.783115 | ||||||||
\(543\) | 9.49486e9 | 2.54501 | ||||||||
\(544\) | 6.88725e9 | 1.83421 | ||||||||
\(545\) | 1.88346e8 | 0.0498390 | ||||||||
\(546\) | 3.75683e8 | 0.0987750 | ||||||||
\(547\) | 3.27852e9 | 0.856491 | 0.428245 | − | 0.903662i | \(-0.359132\pi\) | ||||
0.428245 | + | 0.903662i | \(0.359132\pi\) | |||||||
\(548\) | −2.33025e9 | −0.604883 | ||||||||
\(549\) | −2.50073e9 | −0.645007 | ||||||||
\(550\) | −2.62747e8 | −0.0673393 | ||||||||
\(551\) | 1.76015e8 | 0.0448249 | ||||||||
\(552\) | −5.86273e9 | −1.48359 | ||||||||
\(553\) | 1.63936e8 | 0.0412228 | ||||||||
\(554\) | −3.27683e9 | −0.818785 | ||||||||
\(555\) | 1.32574e10 | 3.29179 | ||||||||
\(556\) | −4.92966e9 | −1.21634 | ||||||||
\(557\) | −4.62141e9 | −1.13313 | −0.566567 | − | 0.824016i | \(-0.691729\pi\) | ||||
−0.566567 | + | 0.824016i | \(0.691729\pi\) | |||||||
\(558\) | 5.06662e9 | 1.23452 | ||||||||
\(559\) | −5.12823e7 | −0.0124173 | ||||||||
\(560\) | 2.79326e8 | 0.0672130 | ||||||||
\(561\) | −1.48978e10 | −3.56249 | ||||||||
\(562\) | −1.55125e9 | −0.368642 | ||||||||
\(563\) | 4.93762e9 | 1.16611 | 0.583054 | − | 0.812434i | \(-0.301858\pi\) | ||||
0.583054 | + | 0.812434i | \(0.301858\pi\) | |||||||
\(564\) | −6.71563e9 | −1.57620 | ||||||||
\(565\) | −3.64164e8 | −0.0849430 | ||||||||
\(566\) | −3.37579e9 | −0.782561 | ||||||||
\(567\) | −1.05884e9 | −0.243943 | ||||||||
\(568\) | 1.90003e9 | 0.435052 | ||||||||
\(569\) | −6.57550e7 | −0.0149636 | −0.00748180 | − | 0.999972i | \(-0.502382\pi\) | ||||
−0.00748180 | + | 0.999972i | \(0.502382\pi\) | |||||||
\(570\) | −2.32640e9 | −0.526165 | ||||||||
\(571\) | 2.78142e9 | 0.625231 | 0.312615 | − | 0.949880i | \(-0.398795\pi\) | ||||
0.312615 | + | 0.949880i | \(0.398795\pi\) | |||||||
\(572\) | −1.01598e9 | −0.226985 | ||||||||
\(573\) | −8.68066e9 | −1.92758 | ||||||||
\(574\) | 3.97339e7 | 0.00876940 | ||||||||
\(575\) | −4.34548e8 | −0.0953236 | ||||||||
\(576\) | 3.48529e9 | 0.759906 | ||||||||
\(577\) | 1.91932e9 | 0.415940 | 0.207970 | − | 0.978135i | \(-0.433314\pi\) | ||||
0.207970 | + | 0.978135i | \(0.433314\pi\) | |||||||
\(578\) | −5.54095e9 | −1.19354 | ||||||||
\(579\) | 3.96958e9 | 0.849903 | ||||||||
\(580\) | −2.87484e8 | −0.0611808 | ||||||||
\(581\) | −2.58368e9 | −0.546540 | ||||||||
\(582\) | −7.88497e9 | −1.65794 | ||||||||
\(583\) | −4.87954e9 | −1.01986 | ||||||||
\(584\) | 3.88421e9 | 0.806971 | ||||||||
\(585\) | −2.64635e9 | −0.546515 | ||||||||
\(586\) | 4.85047e9 | 0.995731 | ||||||||
\(587\) | −3.65483e9 | −0.745820 | −0.372910 | − | 0.927868i | \(-0.621640\pi\) | ||||
−0.372910 | + | 0.927868i | \(0.621640\pi\) | |||||||
\(588\) | −8.25819e8 | −0.167519 | ||||||||
\(589\) | 3.12296e9 | 0.629742 | ||||||||
\(590\) | −2.05026e9 | −0.410985 | ||||||||
\(591\) | 8.38917e8 | 0.167172 | ||||||||
\(592\) | −1.58041e9 | −0.313072 | ||||||||
\(593\) | −5.54651e9 | −1.09227 | −0.546133 | − | 0.837698i | \(-0.683901\pi\) | ||||
−0.546133 | + | 0.837698i | \(0.683901\pi\) | |||||||
\(594\) | −4.99514e9 | −0.977901 | ||||||||
\(595\) | −3.61806e9 | −0.704153 | ||||||||
\(596\) | −3.33870e9 | −0.645975 | ||||||||
\(597\) | 1.39933e10 | 2.69159 | ||||||||
\(598\) | 7.50077e8 | 0.143434 | ||||||||
\(599\) | −4.44815e9 | −0.845641 | −0.422820 | − | 0.906214i | \(-0.638960\pi\) | ||||
−0.422820 | + | 0.906214i | \(0.638960\pi\) | |||||||
\(600\) | 8.63438e8 | 0.163193 | ||||||||
\(601\) | −2.18830e9 | −0.411194 | −0.205597 | − | 0.978637i | \(-0.565914\pi\) | ||||
−0.205597 | + | 0.978637i | \(0.565914\pi\) | |||||||
\(602\) | −5.03215e7 | −0.00940083 | ||||||||
\(603\) | 4.99856e8 | 0.0928398 | ||||||||
\(604\) | −2.65759e8 | −0.0490748 | ||||||||
\(605\) | −2.29467e9 | −0.421286 | ||||||||
\(606\) | 9.70514e9 | 1.77153 | ||||||||
\(607\) | 3.10528e9 | 0.563561 | 0.281780 | − | 0.959479i | \(-0.409075\pi\) | ||||
0.281780 | + | 0.959479i | \(0.409075\pi\) | |||||||
\(608\) | 3.04685e9 | 0.549779 | ||||||||
\(609\) | 3.01159e8 | 0.0540300 | ||||||||
\(610\) | −1.12383e9 | −0.200469 | ||||||||
\(611\) | 2.10194e9 | 0.372800 | ||||||||
\(612\) | 1.30555e10 | 2.30230 | ||||||||
\(613\) | −4.84819e9 | −0.850096 | −0.425048 | − | 0.905171i | \(-0.639743\pi\) | ||||
−0.425048 | + | 0.905171i | \(0.639743\pi\) | |||||||
\(614\) | −8.22012e8 | −0.143314 | ||||||||
\(615\) | −4.29027e8 | −0.0743740 | ||||||||
\(616\) | −2.43892e9 | −0.420401 | ||||||||
\(617\) | 4.98963e9 | 0.855206 | 0.427603 | − | 0.903967i | \(-0.359358\pi\) | ||||
0.427603 | + | 0.903967i | \(0.359358\pi\) | |||||||
\(618\) | 4.68098e9 | 0.797769 | ||||||||
\(619\) | −3.67596e9 | −0.622951 | −0.311475 | − | 0.950254i | \(-0.600823\pi\) | ||||
−0.311475 | + | 0.950254i | \(0.600823\pi\) | |||||||
\(620\) | −5.10070e9 | −0.859526 | ||||||||
\(621\) | −8.26128e9 | −1.38429 | ||||||||
\(622\) | 3.17857e9 | 0.529621 | ||||||||
\(623\) | 3.16798e9 | 0.524897 | ||||||||
\(624\) | 4.83568e8 | 0.0796730 | ||||||||
\(625\) | −6.66451e9 | −1.09191 | ||||||||
\(626\) | −2.04791e9 | −0.333658 | ||||||||
\(627\) | −6.59066e9 | −1.06781 | ||||||||
\(628\) | 8.38011e8 | 0.135018 | ||||||||
\(629\) | 2.04708e10 | 3.27988 | ||||||||
\(630\) | −2.59677e9 | −0.413754 | ||||||||
\(631\) | −1.78403e9 | −0.282682 | −0.141341 | − | 0.989961i | \(-0.545141\pi\) | ||||
−0.141341 | + | 0.989961i | \(0.545141\pi\) | |||||||
\(632\) | −6.50358e8 | −0.102481 | ||||||||
\(633\) | −1.69733e10 | −2.65982 | ||||||||
\(634\) | −1.78499e9 | −0.278178 | ||||||||
\(635\) | 9.33733e9 | 1.44715 | ||||||||
\(636\) | 6.55457e9 | 1.01029 | ||||||||
\(637\) | 2.58475e8 | 0.0396214 | ||||||||
\(638\) | 3.63563e8 | 0.0554253 | ||||||||
\(639\) | 5.73115e9 | 0.868938 | ||||||||
\(640\) | −5.63156e9 | −0.849177 | ||||||||
\(641\) | 5.61163e9 | 0.841562 | 0.420781 | − | 0.907162i | \(-0.361756\pi\) | ||||
0.420781 | + | 0.907162i | \(0.361756\pi\) | |||||||
\(642\) | 7.30212e9 | 1.08912 | ||||||||
\(643\) | 2.13249e9 | 0.316337 | 0.158168 | − | 0.987412i | \(-0.449441\pi\) | ||||
0.158168 | + | 0.987412i | \(0.449441\pi\) | |||||||
\(644\) | −1.64881e9 | −0.243259 | ||||||||
\(645\) | 5.43346e8 | 0.0797292 | ||||||||
\(646\) | −3.59222e9 | −0.524263 | ||||||||
\(647\) | −6.37987e9 | −0.926077 | −0.463038 | − | 0.886338i | \(-0.653241\pi\) | ||||
−0.463038 | + | 0.886338i | \(0.653241\pi\) | |||||||
\(648\) | 4.20055e9 | 0.606449 | ||||||||
\(649\) | −5.80835e9 | −0.834058 | ||||||||
\(650\) | −1.10468e8 | −0.0157776 | ||||||||
\(651\) | 5.34333e9 | 0.759065 | ||||||||
\(652\) | −1.52243e8 | −0.0215115 | ||||||||
\(653\) | −4.54878e9 | −0.639292 | −0.319646 | − | 0.947537i | \(-0.603564\pi\) | ||||
−0.319646 | + | 0.947537i | \(0.603564\pi\) | |||||||
\(654\) | 3.19956e8 | 0.0447268 | ||||||||
\(655\) | 3.59953e9 | 0.500497 | ||||||||
\(656\) | 5.11444e7 | 0.00707350 | ||||||||
\(657\) | 1.17161e10 | 1.61178 | ||||||||
\(658\) | 2.06256e9 | 0.282238 | ||||||||
\(659\) | 3.40787e9 | 0.463857 | 0.231928 | − | 0.972733i | \(-0.425497\pi\) | ||||
0.231928 | + | 0.972733i | \(0.425497\pi\) | |||||||
\(660\) | 1.07645e10 | 1.45743 | ||||||||
\(661\) | 2.52665e9 | 0.340283 | 0.170142 | − | 0.985420i | \(-0.445577\pi\) | ||||
0.170142 | + | 0.985420i | \(0.445577\pi\) | |||||||
\(662\) | 5.79932e9 | 0.776916 | ||||||||
\(663\) | −6.26358e9 | −0.834690 | ||||||||
\(664\) | 1.02498e10 | 1.35871 | ||||||||
\(665\) | −1.60059e9 | −0.211060 | ||||||||
\(666\) | 1.46924e10 | 1.92723 | ||||||||
\(667\) | 6.01285e8 | 0.0784585 | ||||||||
\(668\) | 8.92396e9 | 1.15835 | ||||||||
\(669\) | −8.72250e9 | −1.12629 | ||||||||
\(670\) | 2.24636e8 | 0.0288547 | ||||||||
\(671\) | −3.18380e9 | −0.406834 | ||||||||
\(672\) | 5.21311e9 | 0.662681 | ||||||||
\(673\) | 2.92213e9 | 0.369528 | 0.184764 | − | 0.982783i | \(-0.440848\pi\) | ||||
0.184764 | + | 0.982783i | \(0.440848\pi\) | |||||||
\(674\) | −3.78150e8 | −0.0475724 | ||||||||
\(675\) | 1.21669e9 | 0.152270 | ||||||||
\(676\) | −4.27152e8 | −0.0531825 | ||||||||
\(677\) | −1.57979e10 | −1.95676 | −0.978382 | − | 0.206807i | \(-0.933693\pi\) | ||||
−0.978382 | + | 0.206807i | \(0.933693\pi\) | |||||||
\(678\) | −6.18629e8 | −0.0762300 | ||||||||
\(679\) | −5.42497e9 | −0.665048 | ||||||||
\(680\) | 1.43534e10 | 1.75054 | ||||||||
\(681\) | 1.22975e10 | 1.49212 | ||||||||
\(682\) | 6.45055e9 | 0.778667 | ||||||||
\(683\) | 1.12352e10 | 1.34930 | 0.674648 | − | 0.738140i | \(-0.264296\pi\) | ||||
0.674648 | + | 0.738140i | \(0.264296\pi\) | |||||||
\(684\) | 5.77561e9 | 0.690083 | ||||||||
\(685\) | −7.72762e9 | −0.918604 | ||||||||
\(686\) | 2.53632e8 | 0.0299965 | ||||||||
\(687\) | 2.73701e10 | 3.22054 | ||||||||
\(688\) | −6.47724e7 | −0.00758282 | ||||||||
\(689\) | −2.05153e9 | −0.238952 | ||||||||
\(690\) | −7.94721e9 | −0.920964 | ||||||||
\(691\) | 3.86818e9 | 0.445999 | 0.223000 | − | 0.974819i | \(-0.428415\pi\) | ||||
0.223000 | + | 0.974819i | \(0.428415\pi\) | |||||||
\(692\) | −9.27578e9 | −1.06409 | ||||||||
\(693\) | −7.35662e9 | −0.839676 | ||||||||
\(694\) | −6.78876e9 | −0.770960 | ||||||||
\(695\) | −1.63478e10 | −1.84719 | ||||||||
\(696\) | −1.19474e9 | −0.134320 | ||||||||
\(697\) | −6.62465e8 | −0.0741051 | ||||||||
\(698\) | 4.37878e9 | 0.487371 | ||||||||
\(699\) | −4.92130e9 | −0.545016 | ||||||||
\(700\) | 2.42829e8 | 0.0267583 | ||||||||
\(701\) | −1.21215e10 | −1.32906 | −0.664529 | − | 0.747263i | \(-0.731368\pi\) | ||||
−0.664529 | + | 0.747263i | \(0.731368\pi\) | |||||||
\(702\) | −2.10013e9 | −0.229122 | ||||||||
\(703\) | 9.05609e9 | 0.983099 | ||||||||
\(704\) | 4.43728e9 | 0.479305 | ||||||||
\(705\) | −2.22705e10 | −2.39369 | ||||||||
\(706\) | 1.35471e8 | 0.0144888 | ||||||||
\(707\) | 6.67727e9 | 0.710610 | ||||||||
\(708\) | 7.80223e9 | 0.826232 | ||||||||
\(709\) | 1.05985e10 | 1.11682 | 0.558410 | − | 0.829565i | \(-0.311412\pi\) | ||||
0.558410 | + | 0.829565i | \(0.311412\pi\) | |||||||
\(710\) | 2.57558e9 | 0.270067 | ||||||||
\(711\) | −1.96171e9 | −0.204687 | ||||||||
\(712\) | −1.25678e10 | −1.30491 | ||||||||
\(713\) | 1.06683e10 | 1.10226 | ||||||||
\(714\) | −6.14623e9 | −0.631924 | ||||||||
\(715\) | −3.36919e9 | −0.344710 | ||||||||
\(716\) | 5.14779e9 | 0.524114 | ||||||||
\(717\) | −2.07176e10 | −2.09904 | ||||||||
\(718\) | 6.43791e9 | 0.649096 | ||||||||
\(719\) | −1.13284e10 | −1.13663 | −0.568313 | − | 0.822813i | \(-0.692404\pi\) | ||||
−0.568313 | + | 0.822813i | \(0.692404\pi\) | |||||||
\(720\) | −3.34249e9 | −0.333738 | ||||||||
\(721\) | 3.22058e9 | 0.320008 | ||||||||
\(722\) | 4.02904e9 | 0.398402 | ||||||||
\(723\) | −8.09641e9 | −0.796725 | ||||||||
\(724\) | −1.05934e10 | −1.03741 | ||||||||
\(725\) | −8.85547e7 | −0.00863035 | ||||||||
\(726\) | −3.89810e9 | −0.378072 | ||||||||
\(727\) | 1.01385e9 | 0.0978594 | 0.0489297 | − | 0.998802i | \(-0.484419\pi\) | ||||
0.0489297 | + | 0.998802i | \(0.484419\pi\) | |||||||
\(728\) | −1.02541e9 | −0.0984999 | ||||||||
\(729\) | −1.37123e10 | −1.31088 | ||||||||
\(730\) | 5.26524e9 | 0.500942 | ||||||||
\(731\) | 8.38987e8 | 0.0794409 | ||||||||
\(732\) | 4.27673e9 | 0.403016 | ||||||||
\(733\) | 6.74736e9 | 0.632805 | 0.316403 | − | 0.948625i | \(-0.397525\pi\) | ||||
0.316403 | + | 0.948625i | \(0.397525\pi\) | |||||||
\(734\) | 4.69390e6 | 0.000438125 0 | ||||||||
\(735\) | −2.73859e9 | −0.254403 | ||||||||
\(736\) | 1.04083e10 | 0.962297 | ||||||||
\(737\) | 6.36389e8 | 0.0585581 | ||||||||
\(738\) | −4.75467e8 | −0.0435435 | ||||||||
\(739\) | −1.61384e10 | −1.47097 | −0.735486 | − | 0.677540i | \(-0.763046\pi\) | ||||
−0.735486 | + | 0.677540i | \(0.763046\pi\) | |||||||
\(740\) | −1.47912e10 | −1.34182 | ||||||||
\(741\) | −2.77094e9 | −0.250187 | ||||||||
\(742\) | −2.01309e9 | −0.180905 | ||||||||
\(743\) | −1.55945e10 | −1.39479 | −0.697397 | − | 0.716685i | \(-0.745659\pi\) | ||||
−0.697397 | + | 0.716685i | \(0.745659\pi\) | |||||||
\(744\) | −2.11978e10 | −1.88705 | ||||||||
\(745\) | −1.10718e10 | −0.981008 | ||||||||
\(746\) | −6.75976e9 | −0.596136 | ||||||||
\(747\) | 3.09170e10 | 2.71378 | ||||||||
\(748\) | 1.66215e10 | 1.45216 | ||||||||
\(749\) | 5.02396e9 | 0.436878 | ||||||||
\(750\) | −1.02597e10 | −0.888015 | ||||||||
\(751\) | −7.60712e9 | −0.655361 | −0.327680 | − | 0.944789i | \(-0.606267\pi\) | ||||
−0.327680 | + | 0.944789i | \(0.606267\pi\) | |||||||
\(752\) | 2.65487e9 | 0.227657 | ||||||||
\(753\) | −2.32819e9 | −0.198718 | ||||||||
\(754\) | 1.52855e8 | 0.0129861 | ||||||||
\(755\) | −8.81312e8 | −0.0745273 | ||||||||
\(756\) | 4.61647e9 | 0.388583 | ||||||||
\(757\) | 1.29750e10 | 1.08711 | 0.543554 | − | 0.839374i | \(-0.317078\pi\) | ||||
0.543554 | + | 0.839374i | \(0.317078\pi\) | |||||||
\(758\) | −1.01257e10 | −0.844465 | ||||||||
\(759\) | −2.25143e10 | −1.86902 | ||||||||
\(760\) | 6.34978e9 | 0.524700 | ||||||||
\(761\) | −1.26415e10 | −1.03981 | −0.519903 | − | 0.854225i | \(-0.674032\pi\) | ||||
−0.519903 | + | 0.854225i | \(0.674032\pi\) | |||||||
\(762\) | 1.58619e10 | 1.29871 | ||||||||
\(763\) | 2.20134e8 | 0.0179412 | ||||||||
\(764\) | 9.68502e9 | 0.785731 | ||||||||
\(765\) | 4.32947e10 | 3.49639 | ||||||||
\(766\) | −4.73080e9 | −0.380307 | ||||||||
\(767\) | −2.44203e9 | −0.195420 | ||||||||
\(768\) | −1.81879e10 | −1.44883 | ||||||||
\(769\) | −7.25075e9 | −0.574964 | −0.287482 | − | 0.957786i | \(-0.592818\pi\) | ||||
−0.287482 | + | 0.957786i | \(0.592818\pi\) | |||||||
\(770\) | −3.30607e9 | −0.260972 | ||||||||
\(771\) | −2.95689e10 | −2.32351 | ||||||||
\(772\) | −4.42886e9 | −0.346443 | ||||||||
\(773\) | 1.23442e10 | 0.961249 | 0.480625 | − | 0.876926i | \(-0.340410\pi\) | ||||
0.480625 | + | 0.876926i | \(0.340410\pi\) | |||||||
\(774\) | 6.02161e8 | 0.0466787 | ||||||||
\(775\) | −1.57119e9 | −0.121247 | ||||||||
\(776\) | 2.15216e10 | 1.65333 | ||||||||
\(777\) | 1.54948e10 | 1.18499 | ||||||||
\(778\) | −8.98168e9 | −0.683800 | ||||||||
\(779\) | −2.93068e8 | −0.0222120 | ||||||||
\(780\) | 4.52576e9 | 0.341476 | ||||||||
\(781\) | 7.29659e9 | 0.548077 | ||||||||
\(782\) | −1.22714e10 | −0.917635 | ||||||||
\(783\) | −1.68353e9 | −0.125330 | ||||||||
\(784\) | 3.26468e8 | 0.0241955 | ||||||||
\(785\) | 2.77902e9 | 0.205045 | ||||||||
\(786\) | 6.11474e9 | 0.449158 | ||||||||
\(787\) | −1.07484e10 | −0.786019 | −0.393009 | − | 0.919534i | \(-0.628566\pi\) | ||||
−0.393009 | + | 0.919534i | \(0.628566\pi\) | |||||||
\(788\) | −9.35980e8 | −0.0681436 | ||||||||
\(789\) | −1.95619e10 | −1.41789 | ||||||||
\(790\) | −8.81593e8 | −0.0636170 | ||||||||
\(791\) | −4.25625e8 | −0.0305780 | ||||||||
\(792\) | 2.91847e10 | 2.08746 | ||||||||
\(793\) | −1.33858e9 | −0.0953210 | ||||||||
\(794\) | −6.57446e9 | −0.466110 | ||||||||
\(795\) | 2.17363e10 | 1.53427 | ||||||||
\(796\) | −1.56123e10 | −1.09716 | ||||||||
\(797\) | 9.45263e9 | 0.661376 | 0.330688 | − | 0.943740i | \(-0.392719\pi\) | ||||
0.330688 | + | 0.943740i | \(0.392719\pi\) | |||||||
\(798\) | −2.71903e9 | −0.189410 | ||||||||
\(799\) | −3.43881e10 | −2.38503 | ||||||||
\(800\) | −1.53290e9 | −0.105852 | ||||||||
\(801\) | −3.79089e10 | −2.60632 | ||||||||
\(802\) | −4.21598e8 | −0.0288595 | ||||||||
\(803\) | 1.49163e10 | 1.01662 | ||||||||
\(804\) | −8.54848e8 | −0.0580086 | ||||||||
\(805\) | −5.46779e9 | −0.369425 | ||||||||
\(806\) | 2.71204e9 | 0.182441 | ||||||||
\(807\) | −3.49637e10 | −2.34186 | ||||||||
\(808\) | −2.64897e10 | −1.76659 | ||||||||
\(809\) | −5.07982e9 | −0.337309 | −0.168655 | − | 0.985675i | \(-0.553942\pi\) | ||||
−0.168655 | + | 0.985675i | \(0.553942\pi\) | |||||||
\(810\) | 5.69406e9 | 0.376465 | ||||||||
\(811\) | 7.47602e9 | 0.492150 | 0.246075 | − | 0.969251i | \(-0.420859\pi\) | ||||
0.246075 | + | 0.969251i | \(0.420859\pi\) | |||||||
\(812\) | −3.36003e8 | −0.0220240 | ||||||||
\(813\) | 3.66333e10 | 2.39089 | ||||||||
\(814\) | 1.87056e10 | 1.21559 | ||||||||
\(815\) | −5.04869e8 | −0.0326684 | ||||||||
\(816\) | −7.91125e9 | −0.509718 | ||||||||
\(817\) | 3.71159e8 | 0.0238113 | ||||||||
\(818\) | 7.07191e9 | 0.451752 | ||||||||
\(819\) | −3.09298e9 | −0.196736 | ||||||||
\(820\) | 4.78665e8 | 0.0303168 | ||||||||
\(821\) | −3.77573e9 | −0.238122 | −0.119061 | − | 0.992887i | \(-0.537988\pi\) | ||||
−0.119061 | + | 0.992887i | \(0.537988\pi\) | |||||||
\(822\) | −1.31274e10 | −0.824379 | ||||||||
\(823\) | −8.24136e8 | −0.0515347 | −0.0257673 | − | 0.999668i | \(-0.508203\pi\) | ||||
−0.0257673 | + | 0.999668i | \(0.508203\pi\) | |||||||
\(824\) | −1.27765e10 | −0.795548 | ||||||||
\(825\) | 3.31582e9 | 0.205590 | ||||||||
\(826\) | −2.39628e9 | −0.147948 | ||||||||
\(827\) | 1.28403e10 | 0.789418 | 0.394709 | − | 0.918806i | \(-0.370845\pi\) | ||||
0.394709 | + | 0.918806i | \(0.370845\pi\) | |||||||
\(828\) | 1.97301e10 | 1.20788 | ||||||||
\(829\) | −2.31484e10 | −1.41117 | −0.705587 | − | 0.708623i | \(-0.749317\pi\) | ||||
−0.705587 | + | 0.708623i | \(0.749317\pi\) | |||||||
\(830\) | 1.38941e10 | 0.843447 | ||||||||
\(831\) | 4.13530e10 | 2.49979 | ||||||||
\(832\) | 1.86559e9 | 0.112301 | ||||||||
\(833\) | −4.22869e9 | −0.253483 | ||||||||
\(834\) | −2.77710e10 | −1.65772 | ||||||||
\(835\) | 2.95937e10 | 1.75913 | ||||||||
\(836\) | 7.35319e9 | 0.435265 | ||||||||
\(837\) | −2.98702e10 | −1.76075 | ||||||||
\(838\) | −1.38539e10 | −0.813239 | ||||||||
\(839\) | 2.21972e9 | 0.129757 | 0.0648785 | − | 0.997893i | \(-0.479334\pi\) | ||||
0.0648785 | + | 0.997893i | \(0.479334\pi\) | |||||||
\(840\) | 1.08644e10 | 0.632451 | ||||||||
\(841\) | −1.71273e10 | −0.992897 | ||||||||
\(842\) | 8.85717e9 | 0.511331 | ||||||||
\(843\) | 1.95765e10 | 1.12548 | ||||||||
\(844\) | 1.89371e10 | 1.08421 | ||||||||
\(845\) | −1.41653e9 | −0.0807655 | ||||||||
\(846\) | −2.46811e10 | −1.40142 | ||||||||
\(847\) | −2.68195e9 | −0.151655 | ||||||||
\(848\) | −2.59119e9 | −0.145920 | ||||||||
\(849\) | 4.26018e10 | 2.38919 | ||||||||
\(850\) | 1.80728e9 | 0.100939 | ||||||||
\(851\) | 3.09365e10 | 1.72075 | ||||||||
\(852\) | −9.80134e9 | −0.542934 | ||||||||
\(853\) | 2.82906e10 | 1.56070 | 0.780351 | − | 0.625341i | \(-0.215040\pi\) | ||||
0.780351 | + | 0.625341i | \(0.215040\pi\) | |||||||
\(854\) | −1.31350e9 | −0.0721653 | ||||||||
\(855\) | 1.91531e10 | 1.04799 | ||||||||
\(856\) | −1.99307e10 | −1.08609 | ||||||||
\(857\) | 1.67394e10 | 0.908461 | 0.454231 | − | 0.890884i | \(-0.349914\pi\) | ||||
0.454231 | + | 0.890884i | \(0.349914\pi\) | |||||||
\(858\) | −5.72345e9 | −0.309352 | ||||||||
\(859\) | 2.85605e10 | 1.53741 | 0.768704 | − | 0.639604i | \(-0.220902\pi\) | ||||
0.768704 | + | 0.639604i | \(0.220902\pi\) | |||||||
\(860\) | −6.06211e8 | −0.0324997 | ||||||||
\(861\) | −5.01434e8 | −0.0267734 | ||||||||
\(862\) | −1.65532e10 | −0.880251 | ||||||||
\(863\) | 2.80980e10 | 1.48812 | 0.744060 | − | 0.668113i | \(-0.232898\pi\) | ||||
0.744060 | + | 0.668113i | \(0.232898\pi\) | |||||||
\(864\) | −2.91422e10 | −1.53718 | ||||||||
\(865\) | −3.07604e10 | −1.61598 | ||||||||
\(866\) | −1.78442e10 | −0.933652 | ||||||||
\(867\) | 6.99257e10 | 3.64393 | ||||||||
\(868\) | −5.96156e9 | −0.309415 | ||||||||
\(869\) | −2.49754e9 | −0.129105 | ||||||||
\(870\) | −1.61953e9 | −0.0833817 | ||||||||
\(871\) | 2.67560e8 | 0.0137201 | ||||||||
\(872\) | −8.73301e8 | −0.0446022 | ||||||||
\(873\) | 6.49166e10 | 3.30222 | ||||||||
\(874\) | −5.42873e9 | −0.275048 | ||||||||
\(875\) | −7.05882e9 | −0.356208 | ||||||||
\(876\) | −2.00368e10 | −1.00708 | ||||||||
\(877\) | −1.76094e10 | −0.881550 | −0.440775 | − | 0.897618i | \(-0.645296\pi\) | ||||
−0.440775 | + | 0.897618i | \(0.645296\pi\) | |||||||
\(878\) | 1.20892e10 | 0.602793 | ||||||||
\(879\) | −6.12119e10 | −3.04001 | ||||||||
\(880\) | −4.25548e9 | −0.210503 | ||||||||
\(881\) | −6.36370e9 | −0.313541 | −0.156770 | − | 0.987635i | \(-0.550108\pi\) | ||||
−0.156770 | + | 0.987635i | \(0.550108\pi\) | |||||||
\(882\) | −3.03503e9 | −0.148944 | ||||||||
\(883\) | −9.91576e9 | −0.484689 | −0.242345 | − | 0.970190i | \(-0.577916\pi\) | ||||
−0.242345 | + | 0.970190i | \(0.577916\pi\) | |||||||
\(884\) | 6.98827e9 | 0.340241 | ||||||||
\(885\) | 2.58738e10 | 1.25476 | ||||||||
\(886\) | 2.12441e10 | 1.02617 | ||||||||
\(887\) | 1.93540e10 | 0.931192 | 0.465596 | − | 0.884998i | \(-0.345840\pi\) | ||||
0.465596 | + | 0.884998i | \(0.345840\pi\) | |||||||
\(888\) | −6.14701e10 | −2.94591 | ||||||||
\(889\) | 1.09132e10 | 0.520951 | ||||||||
\(890\) | −1.70363e10 | −0.810047 | ||||||||
\(891\) | 1.61312e10 | 0.764001 | ||||||||
\(892\) | 9.73170e9 | 0.459104 | ||||||||
\(893\) | −1.52129e10 | −0.714880 | ||||||||
\(894\) | −1.88084e10 | −0.880382 | ||||||||
\(895\) | 1.70712e10 | 0.795944 | ||||||||
\(896\) | −6.58200e9 | −0.305689 | ||||||||
\(897\) | −9.46582e9 | −0.437910 | ||||||||
\(898\) | 4.69952e9 | 0.216564 | ||||||||
\(899\) | 2.17405e9 | 0.0997956 | ||||||||
\(900\) | −2.90576e9 | −0.132865 | ||||||||
\(901\) | 3.35633e10 | 1.52872 | ||||||||
\(902\) | −6.05339e8 | −0.0274647 | ||||||||
\(903\) | 6.35047e8 | 0.0287011 | ||||||||
\(904\) | 1.68851e9 | 0.0760177 | ||||||||
\(905\) | −3.51300e10 | −1.57546 | ||||||||
\(906\) | −1.49714e9 | −0.0668827 | ||||||||
\(907\) | −3.78862e10 | −1.68599 | −0.842996 | − | 0.537920i | \(-0.819210\pi\) | ||||
−0.842996 | + | 0.537920i | \(0.819210\pi\) | |||||||
\(908\) | −1.37203e10 | −0.608225 | ||||||||
\(909\) | −7.99020e10 | −3.52845 | ||||||||
\(910\) | −1.38999e9 | −0.0611457 | ||||||||
\(911\) | 2.34375e10 | 1.02706 | 0.513531 | − | 0.858071i | \(-0.328337\pi\) | ||||
0.513531 | + | 0.858071i | \(0.328337\pi\) | |||||||
\(912\) | −3.49986e9 | −0.152781 | ||||||||
\(913\) | 3.93619e10 | 1.71170 | ||||||||
\(914\) | −8.62530e9 | −0.373648 | ||||||||
\(915\) | 1.41825e10 | 0.612040 | ||||||||
\(916\) | −3.05369e10 | −1.31277 | ||||||||
\(917\) | 4.20703e9 | 0.180170 | ||||||||
\(918\) | 3.43585e10 | 1.46583 | ||||||||
\(919\) | −1.82970e10 | −0.777634 | −0.388817 | − | 0.921315i | \(-0.627116\pi\) | ||||
−0.388817 | + | 0.921315i | \(0.627116\pi\) | |||||||
\(920\) | 2.16915e10 | 0.918400 | ||||||||
\(921\) | 1.03736e10 | 0.437544 | ||||||||
\(922\) | 1.66521e10 | 0.699696 | ||||||||
\(923\) | 3.06774e9 | 0.128414 | ||||||||
\(924\) | 1.25812e10 | 0.524651 | ||||||||
\(925\) | −4.55620e9 | −0.189281 | ||||||||
\(926\) | 1.46165e10 | 0.604931 | ||||||||
\(927\) | −3.85383e10 | −1.58896 | ||||||||
\(928\) | 2.12107e9 | 0.0871238 | ||||||||
\(929\) | 1.45900e10 | 0.597036 | 0.298518 | − | 0.954404i | \(-0.403508\pi\) | ||||
0.298518 | + | 0.954404i | \(0.403508\pi\) | |||||||
\(930\) | −2.87346e10 | −1.17143 | ||||||||
\(931\) | −1.87073e9 | −0.0759779 | ||||||||
\(932\) | 5.49069e9 | 0.222163 | ||||||||
\(933\) | −4.01129e10 | −1.61696 | ||||||||
\(934\) | 1.63599e10 | 0.657002 | ||||||||
\(935\) | 5.51205e10 | 2.20533 | ||||||||
\(936\) | 1.22703e10 | 0.489090 | ||||||||
\(937\) | 1.07037e10 | 0.425054 | 0.212527 | − | 0.977155i | \(-0.431831\pi\) | ||||
0.212527 | + | 0.977155i | \(0.431831\pi\) | |||||||
\(938\) | 2.62548e8 | 0.0103872 | ||||||||
\(939\) | 2.58443e10 | 1.01867 | ||||||||
\(940\) | 2.48472e10 | 0.975729 | ||||||||
\(941\) | 2.17259e10 | 0.849990 | 0.424995 | − | 0.905196i | \(-0.360276\pi\) | ||||
0.424995 | + | 0.905196i | \(0.360276\pi\) | |||||||
\(942\) | 4.72090e9 | 0.184012 | ||||||||
\(943\) | −1.00115e9 | −0.0388783 | ||||||||
\(944\) | −3.08443e9 | −0.119336 | ||||||||
\(945\) | 1.53092e10 | 0.590121 | ||||||||
\(946\) | 7.66639e8 | 0.0294423 | ||||||||
\(947\) | −1.79648e10 | −0.687379 | −0.343690 | − | 0.939083i | \(-0.611677\pi\) | ||||
−0.343690 | + | 0.939083i | \(0.611677\pi\) | |||||||
\(948\) | 3.35489e9 | 0.127894 | ||||||||
\(949\) | 6.27135e9 | 0.238193 | ||||||||
\(950\) | 7.99521e8 | 0.0302550 | ||||||||
\(951\) | 2.25262e10 | 0.849290 | ||||||||
\(952\) | 1.67758e10 | 0.630165 | ||||||||
\(953\) | 2.28823e10 | 0.856395 | 0.428197 | − | 0.903685i | \(-0.359149\pi\) | ||||
0.428197 | + | 0.903685i | \(0.359149\pi\) | |||||||
\(954\) | 2.40892e10 | 0.898262 | ||||||||
\(955\) | 3.21176e10 | 1.19325 | ||||||||
\(956\) | 2.31146e10 | 0.855625 | ||||||||
\(957\) | −4.58810e9 | −0.169216 | ||||||||
\(958\) | −6.05631e9 | −0.222551 | ||||||||
\(959\) | −9.03182e9 | −0.330682 | ||||||||
\(960\) | −1.97663e10 | −0.721066 | ||||||||
\(961\) | 1.10607e10 | 0.402024 | ||||||||
\(962\) | 7.86449e9 | 0.284812 | ||||||||
\(963\) | −6.01181e10 | −2.16927 | ||||||||
\(964\) | 9.03317e9 | 0.324766 | ||||||||
\(965\) | −1.46870e10 | −0.526125 | ||||||||
\(966\) | −9.28848e9 | −0.331531 | ||||||||
\(967\) | 7.85972e9 | 0.279521 | 0.139761 | − | 0.990185i | \(-0.455367\pi\) | ||||
0.139761 | + | 0.990185i | \(0.455367\pi\) | |||||||
\(968\) | 1.06397e10 | 0.377019 | ||||||||
\(969\) | 4.53331e10 | 1.60060 | ||||||||
\(970\) | 2.91736e10 | 1.02633 | ||||||||
\(971\) | 1.00666e10 | 0.352872 | 0.176436 | − | 0.984312i | \(-0.443543\pi\) | ||||
0.176436 | + | 0.984312i | \(0.443543\pi\) | |||||||
\(972\) | 7.76642e9 | 0.271262 | ||||||||
\(973\) | −1.91068e10 | −0.664958 | ||||||||
\(974\) | 2.05753e10 | 0.713493 | ||||||||
\(975\) | 1.39409e9 | 0.0481696 | ||||||||
\(976\) | −1.69070e9 | −0.0582094 | ||||||||
\(977\) | 1.20709e10 | 0.414103 | 0.207051 | − | 0.978330i | \(-0.433613\pi\) | ||||
0.207051 | + | 0.978330i | \(0.433613\pi\) | |||||||
\(978\) | −8.57653e8 | −0.0293174 | ||||||||
\(979\) | −4.82636e10 | −1.64392 | ||||||||
\(980\) | 3.05545e9 | 0.103701 | ||||||||
\(981\) | −2.63418e9 | −0.0890849 | ||||||||
\(982\) | −1.09028e10 | −0.367409 | ||||||||
\(983\) | −8.83111e9 | −0.296536 | −0.148268 | − | 0.988947i | \(-0.547370\pi\) | ||||
−0.148268 | + | 0.988947i | \(0.547370\pi\) | |||||||
\(984\) | 1.98926e9 | 0.0665593 | ||||||||
\(985\) | −3.10391e9 | −0.103486 | ||||||||
\(986\) | −2.50073e9 | −0.0830802 | ||||||||
\(987\) | −2.60291e10 | −0.861686 | ||||||||
\(988\) | 3.09154e9 | 0.101983 | ||||||||
\(989\) | 1.26792e9 | 0.0416777 | ||||||||
\(990\) | 3.95613e10 | 1.29583 | ||||||||
\(991\) | 5.59892e10 | 1.82745 | 0.913727 | − | 0.406329i | \(-0.133191\pi\) | ||||
0.913727 | + | 0.406329i | \(0.133191\pi\) | |||||||
\(992\) | 3.76332e10 | 1.22400 | ||||||||
\(993\) | −7.31862e10 | −2.37196 | ||||||||
\(994\) | 3.01027e9 | 0.0972194 | ||||||||
\(995\) | −5.17736e10 | −1.66620 | ||||||||
\(996\) | −5.28739e10 | −1.69564 | ||||||||
\(997\) | 1.14701e9 | 0.0366549 | 0.0183275 | − | 0.999832i | \(-0.494166\pi\) | ||||
0.0183275 | + | 0.999832i | \(0.494166\pi\) | |||||||
\(998\) | 7.64074e9 | 0.243320 | ||||||||
\(999\) | −8.66188e10 | −2.74874 |
(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 | 91.8.a.b.1.4 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.8.a.b.1.4 | ✓ | 9 | 1.1 | even | 1 | trivial |