Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,9,Mod(97,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.97");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(136.879212981\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 14312 x^{8} - 30343 x^{7} + 170123918 x^{6} - 875537263 x^{5} + 496509566533 x^{4} + \cdots + 39\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{15}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.7 | ||
Root | \(10.9569 - 18.9779i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.97 |
Dual form | 336.9.f.a.97.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 46.7654i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 307.159i | − | 0.491455i | −0.969339 | − | 0.245727i | \(-0.920973\pi\) | ||
0.969339 | − | 0.245727i | \(-0.0790268\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −222.189 | − | 2390.70i | −0.0925400 | − | 0.995709i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2187.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5381.78 | −0.367583 | −0.183791 | − | 0.982965i | \(-0.558837\pi\) | ||||
−0.183791 | + | 0.982965i | \(0.558837\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 48978.5i | − | 1.71487i | −0.514589 | − | 0.857437i | \(-0.672056\pi\) | ||
0.514589 | − | 0.857437i | \(-0.327944\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 14364.4 | 0.283742 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 55408.7i | − | 0.663411i | −0.943383 | − | 0.331705i | \(-0.892376\pi\) | ||
0.943383 | − | 0.331705i | \(-0.107624\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 67798.4i | − | 0.520242i | −0.965576 | − | 0.260121i | \(-0.916238\pi\) | ||
0.965576 | − | 0.260121i | \(-0.0837624\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 111802. | − | 10390.7i | 0.574873 | − | 0.0534280i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 344567. | 1.23130 | 0.615648 | − | 0.788021i | \(-0.288894\pi\) | ||||
0.615648 | + | 0.788021i | \(0.288894\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 296278. | 0.758472 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 102276.i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.17408e6 | −1.65999 | −0.829995 | − | 0.557771i | \(-0.811657\pi\) | ||||
−0.829995 | + | 0.557771i | \(0.811657\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 125625.i | − | 0.136029i | −0.997684 | − | 0.0680144i | \(-0.978334\pi\) | ||
0.997684 | − | 0.0680144i | \(-0.0216664\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 251681.i | − | 0.212224i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −734325. | + | 68247.3i | −0.489346 | + | 0.0454793i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −734456. | −0.391885 | −0.195943 | − | 0.980615i | \(-0.562777\pi\) | ||||
−0.195943 | + | 0.980615i | \(0.562777\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.29050e6 | 0.990083 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.18960e6i | − | 0.420984i | −0.977596 | − | 0.210492i | \(-0.932493\pi\) | ||
0.977596 | − | 0.210492i | \(-0.0675065\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.84354e6 | 1.12424 | 0.562119 | − | 0.827057i | \(-0.309986\pi\) | ||||
0.562119 | + | 0.827057i | \(0.309986\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 671757.i | 0.163818i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.82991e6i | − | 0.989799i | −0.868950 | − | 0.494900i | \(-0.835205\pi\) | ||
0.868950 | − | 0.494900i | \(-0.164795\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.66607e6 | + | 1.06237e6i | −0.982873 | + | 0.184286i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.59121e6 | 0.383020 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.19800e7 | −1.51829 | −0.759143 | − | 0.650924i | \(-0.774382\pi\) | ||||
−0.759143 | + | 0.650924i | \(0.774382\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.65306e6i | 0.180650i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.17062e6 | 0.300362 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.90443e7i | 1.57165i | 0.618448 | + | 0.785826i | \(0.287762\pi\) | ||||
−0.618448 | + | 0.785826i | \(0.712238\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.11077e7i | − | 0.802242i | −0.916025 | − | 0.401121i | \(-0.868621\pi\) | ||
0.916025 | − | 0.401121i | \(-0.131379\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 485927. | + | 5.22845e6i | 0.0308467 | + | 0.331903i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.50442e7 | −0.842783 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.92913e7 | 1.45358 | 0.726792 | − | 0.686858i | \(-0.241011\pi\) | ||||
0.726792 | + | 0.686858i | \(0.241011\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.61138e7i | 0.710889i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.79462e6 | −0.109974 | −0.0549869 | − | 0.998487i | \(-0.517512\pi\) | ||||
−0.0549869 | + | 0.998487i | \(0.517512\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.34290e7i | 1.17715i | 0.808443 | + | 0.588574i | \(0.200311\pi\) | ||||
−0.808443 | + | 0.588574i | \(0.799689\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.38556e7i | 0.437904i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.19577e6 | + | 1.28662e7i | 0.0340161 | + | 0.366006i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.96171e6 | 0.127386 | 0.0636932 | − | 0.997970i | \(-0.479712\pi\) | ||||
0.0636932 | + | 0.997970i | \(0.479712\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.78297e6 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.33137e7i | 0.701957i | 0.936384 | + | 0.350978i | \(0.114151\pi\) | ||||
−0.936384 | + | 0.350978i | \(0.885849\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.70193e7 | −0.326036 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 5.49063e7i | − | 0.958396i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.09244e7i | 0.492879i | 0.969158 | + | 0.246440i | \(0.0792607\pi\) | ||||
−0.969158 | + | 0.246440i | \(0.920739\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.17093e8 | + | 1.08825e7i | −1.70751 | + | 0.158694i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.87492e6 | 0.0785362 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.08249e7 | −0.255675 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.05301e7i | 0.570773i | 0.958413 | + | 0.285386i | \(0.0921220\pi\) | ||||
−0.958413 | + | 0.285386i | \(0.907878\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.17700e7 | 0.122528 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.90888e8i | − | 1.83439i | −0.398434 | − | 0.917197i | \(-0.630446\pi\) | ||
0.398434 | − | 0.917197i | \(-0.369554\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.51846e6i | 0.0401459i | 0.999799 | + | 0.0200730i | \(0.00638985\pi\) | ||||
−0.999799 | + | 0.0200730i | \(0.993610\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.19161e6 | − | 3.43410e7i | −0.0262575 | − | 0.282524i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.12055e8 | −0.854861 | −0.427431 | − | 0.904048i | \(-0.640581\pi\) | ||||
−0.427431 | + | 0.904048i | \(0.640581\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.56777e8 | 1.11065 | 0.555325 | − | 0.831634i | \(-0.312594\pi\) | ||||
0.555325 | + | 0.831634i | \(0.312594\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.43471e7i | − | 0.226255i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.97902e8 | 1.21377 | 0.606885 | − | 0.794790i | \(-0.292419\pi\) | ||||
0.606885 | + | 0.794790i | \(0.292419\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.05837e8i | − | 0.605127i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.07116e8i | 0.571625i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.32466e8 | + | 1.23112e7i | −0.660564 | + | 0.0613921i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.85395e8 | −0.864883 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.56320e7 | 0.243055 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2.10989e8i | − | 0.864210i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.18632e8 | −1.60923 | −0.804614 | − | 0.593799i | \(-0.797628\pi\) | ||||
−0.804614 | + | 0.593799i | \(0.797628\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.79745e8i | 0.649079i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.79773e8i | 0.949994i | 0.879988 | + | 0.474997i | \(0.157551\pi\) | ||||
−0.879988 | + | 0.474997i | \(0.842449\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.62086e8 | + | 1.50640e7i | −0.518009 | + | 0.0481432i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.14150e7 | −0.0945805 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.92940e7 | −0.196704 | −0.0983521 | − | 0.995152i | \(-0.531357\pi\) | ||||
−0.0983521 | + | 0.995152i | \(0.531357\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.57712e8i | − | 1.22612i | −0.790036 | − | 0.613060i | \(-0.789938\pi\) | ||
0.790036 | − | 0.613060i | \(-0.210062\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.25872e8 | 0.571461 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.63592e8i | 0.630358i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.60629e8i | 0.815810i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.96822e7 | − | 2.64976e8i | −0.106398 | − | 0.567462i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.29858e8 | −1.48079 | −0.740395 | − | 0.672172i | \(-0.765361\pi\) | ||||
−0.740395 | + | 0.672172i | \(0.765361\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.20692e8 | 0.424501 | 0.212250 | − | 0.977215i | \(-0.431921\pi\) | ||||
0.212250 | + | 0.977215i | \(0.431921\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.21179e8i | 0.221137i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.85870e7 | −0.0668520 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.57190e8i | − | 0.752485i | −0.926521 | − | 0.376243i | \(-0.877216\pi\) | ||
0.926521 | − | 0.376243i | \(-0.122784\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 5.60249e8i | − | 0.876583i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.65589e7 | − | 8.23756e8i | −0.113944 | − | 1.22601i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.58414e8 | 0.224411 | 0.112205 | − | 0.993685i | \(-0.464209\pi\) | ||||
0.112205 | + | 0.993685i | \(0.464209\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.73062e7 | −0.104299 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.55510e8i | 0.714210i | 0.934064 | + | 0.357105i | \(0.116236\pi\) | ||||
−0.934064 | + | 0.357105i | \(0.883764\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.58316e9 | −1.94079 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.48275e8i | 0.173414i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1.42883e9i | − | 1.59513i | −0.603231 | − | 0.797566i | \(-0.706120\pi\) | ||
0.603231 | − | 0.797566i | \(-0.293880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.58296e7 | − | 7.08311e8i | −0.0701890 | − | 0.755218i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.90613e8 | −0.907394 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.76429e8 | −0.658886 | −0.329443 | − | 0.944175i | \(-0.606861\pi\) | ||||
−0.329443 | + | 0.944175i | \(0.606861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.05179e8i | 0.843374i | 0.906742 | + | 0.421687i | \(0.138562\pi\) | ||||
−0.906742 | + | 0.421687i | \(0.861438\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.19457e8 | 0.463175 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.25595e8i | 0.192594i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.98198e8i | 0.243858i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.44511e8 | + | 2.27245e7i | −0.191624 | + | 0.0178093i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.71513e8 | 0.204013 | 0.102006 | − | 0.994784i | \(-0.467474\pi\) | ||||
0.102006 | + | 0.994784i | \(0.467474\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.48364e8 | −0.539366 | −0.269683 | − | 0.962949i | \(-0.586919\pi\) | ||||
−0.269683 | + | 0.962949i | \(0.586919\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 7.03548e8i | − | 0.486581i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.09695e9 | −0.728320 | −0.364160 | − | 0.931336i | \(-0.618644\pi\) | ||||
−0.364160 | + | 0.931336i | \(0.618644\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.37706e8i | − | 0.0878094i | −0.999036 | − | 0.0439047i | \(-0.986020\pi\) | ||
0.999036 | − | 0.0439047i | \(-0.0139798\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.36982e9i | 0.839227i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.60867e8 | + | 2.80687e9i | 0.153616 | + | 1.65287i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.65396e8 | −0.206894 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.53569e8 | −0.410432 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.64876e8i | 0.191232i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.35246e9 | −1.69135 | −0.845676 | − | 0.533696i | \(-0.820803\pi\) | ||||
−0.845676 | + | 0.533696i | \(0.820803\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 1.30691e8i | − | 0.0634934i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.18058e9i | − | 0.552512i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00332e8 | + | 2.79125e7i | −0.135445 | + | 0.0125881i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.56332e9 | −0.679627 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.71384e9 | −1.13767 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.34771e9i | − | 0.949348i | −0.880162 | − | 0.474674i | \(-0.842566\pi\) | ||
0.880162 | − | 0.474674i | \(-0.157434\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.47960e8 | −0.252824 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.87854e9i | 1.08410i | 0.840347 | + | 0.542049i | \(0.182351\pi\) | ||||
−0.840347 | + | 0.542049i | \(0.817649\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.05735e8i | 0.256625i | 0.991734 | + | 0.128313i | \(0.0409561\pi\) | ||||
−0.991734 | + | 0.128313i | \(0.959044\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.01693e8 | + | 5.59207e7i | −0.211313 | + | 0.0196392i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.01041e9 | 1.70000 | 0.850002 | − | 0.526780i | \(-0.176601\pi\) | ||||
0.850002 | + | 0.526780i | \(0.176601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.48355e9 | −0.486442 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.32036e8i | 0.0735465i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.19477e9 | −0.979147 | −0.489574 | − | 0.871962i | \(-0.662848\pi\) | ||||
−0.489574 | + | 0.871962i | \(0.662848\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1.70613e9i | − | 0.505759i | −0.967498 | − | 0.252879i | \(-0.918622\pi\) | ||
0.967498 | − | 0.252879i | \(-0.0813776\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.23677e8i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.26317e8 | + | 1.74038e9i | 0.0905682 | + | 0.483038i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.32067e9 | −0.892149 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.55793e9 | −0.405275 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.60073e9i | − | 0.655239i | −0.944810 | − | 0.327620i | \(-0.893754\pi\) | ||
0.944810 | − | 0.327620i | \(-0.106246\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.85439e9 | −0.452603 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 7.95914e8i | − | 0.188237i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.84643e9i | 0.423252i | 0.977351 | + | 0.211626i | \(0.0678759\pi\) | ||||
−0.977351 | + | 0.211626i | \(0.932124\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.63188e8 | + | 1.75586e9i | 0.0362651 | + | 0.390204i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.56771e9 | 0.553330 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.63329e9 | −1.38646 | −0.693228 | − | 0.720718i | \(-0.743812\pi\) | ||||
−0.693228 | + | 0.720718i | \(0.743812\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.67977e9i | 0.746169i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.44619e9 | −0.284564 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 5.20298e9i | − | 0.993673i | −0.867844 | − | 0.496836i | \(-0.834495\pi\) | ||
0.867844 | − | 0.496836i | \(-0.165505\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.27608e9i | 0.978215i | 0.872224 | + | 0.489107i | \(0.162677\pi\) | ||||
−0.872224 | + | 0.489107i | \(0.837323\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.08923e8 | − | 5.47589e9i | −0.0916223 | − | 0.985834i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.59450e9 | −0.278801 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.54281e9 | 0.262055 | 0.131027 | − | 0.991379i | \(-0.458172\pi\) | ||||
0.131027 | + | 0.991379i | \(0.458172\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.74743e8i | 0.0453429i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.16602e9 | −1.47013 | −0.735065 | − | 0.677997i | \(-0.762848\pi\) | ||||
−0.735065 | + | 0.677997i | \(0.762848\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.15888e9i | 0.648381i | 0.945992 | + | 0.324191i | \(0.105092\pi\) | ||||
−0.945992 | + | 0.324191i | \(0.894908\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 9.73885e8i | − | 0.147614i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.84397e9 | + | 2.64315e8i | −0.419177 | + | 0.0389578i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.90563e9 | 0.559886 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.36306e9 | −0.329536 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.30089e10i | 1.76511i | 0.470210 | + | 0.882554i | \(0.344178\pi\) | ||||
−0.470210 | + | 0.882554i | \(0.655822\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.84963e9 | 0.772396 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.50426e8i | 0.0707414i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.68764e10i | − | 2.11152i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.53992e8 | − | 9.18875e9i | −0.104037 | − | 1.11941i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.92694e9 | 1.05909 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.41184e9 | −0.394266 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.60817e10i | − | 1.81042i | −0.424966 | − | 0.905209i | \(-0.639714\pi\) | ||
0.424966 | − | 0.905209i | \(-0.360286\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.11307e8 | −0.0231783 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.74219e9i | 0.400022i | 0.979794 | + | 0.200011i | \(0.0640978\pi\) | ||||
−0.979794 | + | 0.200011i | \(0.935902\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.81712e8i | 0.0293514i | 0.999892 | + | 0.0146757i | \(0.00467158\pi\) | ||||
−0.999892 | + | 0.0146757i | \(0.995328\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.60597e9 | − | 1.49257e8i | 0.163115 | − | 0.0151598i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.18485e10 | −1.17335 | −0.586675 | − | 0.809822i | \(-0.699564\pi\) | ||||
−0.586675 | + | 0.809822i | \(0.699564\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.31864e9 | 0.610184 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 5.24029e9i | − | 0.493554i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.75662e9 | −0.345134 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.45113e10i | − | 1.30068i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.33175e9i | 0.641234i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.15468e10 | + | 1.07315e9i | −0.985552 | + | 0.0915961i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.46682e9 | 0.205507 | 0.102753 | − | 0.994707i | \(-0.467235\pi\) | ||||
0.102753 | + | 0.994707i | \(0.467235\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.60625e9 | 0.130628 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 8.99711e9i | − | 0.714371i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.20989e9 | −0.0938051 | −0.0469025 | − | 0.998899i | \(-0.514935\pi\) | ||||
−0.0469025 | + | 0.998899i | \(0.514935\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.25496e9i | 0.700770i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.76088e8i | 0.0500018i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.79874e9 | + | 1.33098e10i | 0.274450 | + | 0.961601i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.94951e9 | 0.349370 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.61251e10 | 1.80194 | 0.900971 | − | 0.433880i | \(-0.142856\pi\) | ||||
0.900971 | + | 0.433880i | \(0.142856\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.46730e9i | − | 0.166311i | −0.996537 | − | 0.0831555i | \(-0.973500\pi\) | ||
0.996537 | − | 0.0831555i | \(-0.0264998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00932e9 | −0.330028 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.27283e9i | 0.597191i | 0.954380 | + | 0.298596i | \(0.0965182\pi\) | ||||
−0.954380 | + | 0.298596i | \(0.903482\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.58394e8i | 0.0540472i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.75737e8 | − | 6.19480e9i | −0.0354447 | − | 0.381377i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.76277e9 | 0.106125 | 0.0530624 | − | 0.998591i | \(-0.483102\pi\) | ||||
0.0530624 | + | 0.998591i | \(0.483102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.23869e10 | 0.729349 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 8.67008e9i | − | 0.499340i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.02680e10 | 0.578516 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.47281e10i | 0.811862i | 0.913904 | + | 0.405931i | \(0.133053\pi\) | ||||
−0.913904 | + | 0.405931i | \(0.866947\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.60165e9i | 0.140328i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.66182e9 | + | 2.86406e10i | 0.140502 | + | 1.51177i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.99301e10 | −1.54623 | −0.773114 | − | 0.634268i | \(-0.781302\pi\) | ||||
−0.773114 | + | 0.634268i | \(0.781302\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.86696e9 | 0.498952 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.75047e10i | 2.84667i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.21942e9 | −0.301435 | −0.150717 | − | 0.988577i | \(-0.548158\pi\) | ||||
−0.150717 | + | 0.988577i | \(0.548158\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 1.95775e10i | − | 0.929088i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 1.42959e10i | − | 0.664378i | −0.943213 | − | 0.332189i | \(-0.892213\pi\) | ||
0.943213 | − | 0.332189i | \(-0.107787\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.95198e9 | − | 3.67292e8i | 0.179875 | − | 0.0167174i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.40583e9 | −0.374746 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.15618e10 | 1.81508 | 0.907541 | − | 0.419964i | \(-0.137957\pi\) | ||||
0.907541 | + | 0.419964i | \(0.137957\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.90920e10i | − | 0.816855i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.30837e10 | −0.548479 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1.52403e9i | − | 0.0626046i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.59996e10i | 0.644091i | 0.946724 | + | 0.322045i | \(0.104370\pi\) | ||||
−0.946724 | + | 0.322045i | \(0.895630\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.04475e8 | − | 7.57999e9i | −0.0277955 | − | 0.299073i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.03741e10 | 0.787953 | 0.393976 | − | 0.919121i | \(-0.371099\pi\) | ||||
0.393976 | + | 0.919121i | \(0.371099\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.15294e9 | −0.233272 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.46913e9i | − | 0.0546061i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.95268e9 | 0.144050 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.77473e10i | − | 1.34894i | −0.738302 | − | 0.674471i | \(-0.764372\pi\) | ||
0.738302 | − | 0.674471i | \(-0.235628\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 3.24056e9i | − | 0.113567i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.55291e10 | − | 4.23142e9i | 1.56491 | − | 0.145441i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.02326e10 | 0.344980 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.14051e10 | 0.707901 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 5.28934e9i | − | 0.171611i | −0.996312 | − | 0.0858056i | \(-0.972654\pi\) | ||
0.996312 | − | 0.0858056i | \(-0.0273464\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.20225e10 | 1.01936 | 0.509679 | − | 0.860364i | \(-0.329764\pi\) | ||||
0.509679 | + | 0.860364i | \(0.329764\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.05630e10i | 0.329933i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.64164e10i | − | 0.503179i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.65552e10 | + | 2.46801e9i | −0.798800 | + | 0.0742395i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.23270e10 | −0.363937 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.05036e10 | 0.883978 | 0.441989 | − | 0.897021i | \(-0.354273\pi\) | ||||
0.441989 | + | 0.897021i | \(0.354273\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.62208e10i | 0.745924i | 0.927847 | + | 0.372962i | \(0.121658\pi\) | ||||
−0.927847 | + | 0.372962i | \(0.878342\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.68650e10 | −0.471008 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.33611e10i | − | 0.640572i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 3.44122e10i | − | 0.926519i | −0.886223 | − | 0.463259i | \(-0.846680\pi\) | ||
0.886223 | − | 0.463259i | \(-0.153320\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.23917e10 | − | 2.32341e9i | 0.327624 | − | 0.0614286i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.61747e10 | 0.419974 | 0.209987 | − | 0.977704i | \(-0.432658\pi\) | ||||
0.209987 | + | 0.977704i | \(0.432658\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.49870e9 | 0.242228 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 3.41321e10i | − | 0.854934i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.25204e9 | −0.178433 | −0.0892165 | − | 0.996012i | \(-0.528436\pi\) | ||||
−0.0892165 | + | 0.996012i | \(0.528436\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.40216e9i | 0.154746i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.03207e10i | 0.245086i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.34265e9 | + | 3.59661e10i | 0.0779912 | + | 0.839167i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.99631e10 | 1.83326 | 0.916632 | − | 0.399733i | \(-0.130897\pi\) | ||||
0.916632 | + | 0.399733i | \(0.130897\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.66698e9 | −0.127673 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.61132e10i | 1.24240i | 0.783652 | + | 0.621200i | \(0.213354\pi\) | ||||
−0.783652 | + | 0.621200i | \(0.786646\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.32046e10 | −0.287344 | −0.143672 | − | 0.989625i | \(-0.545891\pi\) | ||||
−0.143672 | + | 0.989625i | \(0.545891\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 1.80454e9i | − | 0.0385970i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.17464e10i | 1.29821i | 0.760700 | + | 0.649104i | \(0.224856\pi\) | ||||
−0.760700 | + | 0.649104i | \(0.775144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.50820e9 | − | 7.00267e10i | −0.134515 | − | 1.44735i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.13807e10 | 0.434448 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.06851e10 | −0.413250 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.00872e10i | − | 0.394589i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.62003e10 | 0.506095 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.70479e10i | 1.46359i | 0.681526 | + | 0.731794i | \(0.261317\pi\) | ||||
−0.681526 | + | 0.731794i | \(0.738683\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.59725e10i | 0.672033i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.85233e10 | − | 3.58031e9i | 0.707839 | − | 0.0657857i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.55208e10 | 0.280509 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.33487e10 | 1.48178 | 0.740889 | − | 0.671627i | \(-0.234404\pi\) | ||||
0.740889 | + | 0.671627i | \(0.234404\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.40830e9i | 0.129564i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.56139e10 | −0.612764 | −0.306382 | − | 0.951909i | \(-0.599119\pi\) | ||||
−0.306382 | + | 0.951909i | \(0.599119\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.50543e10i | 1.10126i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 3.61525e9i | − | 0.0602168i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.20933e8 | + | 6.68109e9i | 0.0101770 | + | 0.109502i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.49153e10 | 0.401851 | 0.200925 | − | 0.979607i | \(-0.435605\pi\) | ||||
0.200925 | + | 0.979607i | \(0.435605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.59786e10 | −0.412349 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.27049e10i | 0.979557i | 0.871847 | + | 0.489778i | \(0.162922\pi\) | ||||
−0.871847 | + | 0.489778i | \(0.837078\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.86330e10 | −0.901522 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 7.40372e10i | − | 1.12052i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.00554e10i | 0.894707i | 0.894357 | + | 0.447353i | \(0.147633\pi\) | ||||
−0.894357 | + | 0.447353i | \(0.852367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.99185e10 | − | 7.42754e9i | 1.17210 | − | 0.108933i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.93414e9 | −0.100121 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.38789e9 | 0.0197299 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.59935e10i | 0.363833i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.68199e10 | 0.920950 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9.52594e10i | − | 1.29288i | −0.762966 | − | 0.646438i | \(-0.776258\pi\) | ||
0.762966 | − | 0.646438i | \(-0.223742\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.86838e10i | − | 0.383381i | −0.981455 | − | 0.191690i | \(-0.938603\pi\) | ||
0.981455 | − | 0.191690i | \(-0.0613969\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.31244e10 | − | 3.07855e9i | 0.436025 | − | 0.0405237i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.96074e9 | −0.0902429 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.04156e10 | 0.516091 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 4.16498e10i | − | 0.523884i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.82648e10 | −0.721934 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.44187e10i | 0.420126i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 3.16335e10i | − | 0.380408i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.04935e10 | − | 5.71745e9i | 0.361287 | − | 0.0677403i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.73664e10 | −1.01990 | −0.509948 | − | 0.860205i | \(-0.670335\pi\) | ||||
−0.509948 | + | 0.860205i | \(0.670335\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.23310e10 | −0.486922 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 4.81556e10i | − | 0.545834i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.69144e10 | 0.524030 | 0.262015 | − | 0.965064i | \(-0.415613\pi\) | ||||
0.262015 | + | 0.965064i | \(0.415613\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.42926e10i | 0.267414i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.96007e10i | 0.863596i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.10244e9 | − | 1.18619e10i | −0.0117883 | − | 0.126840i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.05500e10 | −0.111194 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.29283e11 | −1.34314 | −0.671569 | − | 0.740942i | \(-0.734379\pi\) | ||||
−0.671569 | + | 0.740942i | \(0.734379\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.88251e11i | − | 1.92793i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.39453e10 | −0.140792 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.05189e11i | 1.04698i | 0.852032 | + | 0.523490i | \(0.175370\pi\) | ||||
−0.852032 | + | 0.523490i | \(0.824630\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 6.07874e10i | − | 0.596513i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.06272e9 | − | 1.14346e10i | −0.0102822 | − | 0.110634i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.55660e10 | 0.434703 | 0.217351 | − | 0.976093i | \(-0.430258\pi\) | ||||
0.217351 | + | 0.976093i | \(0.430258\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.10385e11 | −1.03840 | −0.519202 | − | 0.854652i | \(-0.673771\pi\) | ||||
−0.519202 | + | 0.854652i | \(0.673771\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.26974e10i | 0.117787i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.02088e11 | 0.933904 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 7.38745e9i | − | 0.0666487i | −0.999445 | − | 0.0333243i | \(-0.989391\pi\) | ||
0.999445 | − | 0.0333243i | \(-0.0106094\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 3.49975e10i | − | 0.311403i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.96429e10 | − | 7.40192e9i | 0.698945 | − | 0.0649591i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.44738e10 | 0.558096 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.29017e10 | 0.280928 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.31559e10i | 0.700391i | 0.936677 | + | 0.350196i | \(0.113885\pi\) | ||||
−0.936677 | + | 0.350196i | \(0.886115\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.51720e9 | −0.0707678 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 5.12993e10i | − | 0.420496i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.67065e10i | 0.539447i | 0.962938 | + | 0.269724i | \(0.0869324\pi\) | ||||
−0.962938 | + | 0.269724i | \(0.913068\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.78150e9 | + | 4.06880e10i | 0.0301714 | + | 0.324637i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.43988e9 | 0.0506968 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.85940e10 | −0.610495 | −0.305247 | − | 0.952273i | \(-0.598739\pi\) | ||||
−0.305247 | + | 0.952273i | \(0.598739\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.40655e11i | − | 1.84458i | −0.386497 | − | 0.922291i | \(-0.626315\pi\) | ||
0.386497 | − | 0.922291i | \(-0.373685\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.40602e10 | −0.484528 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.69459e10i | 0.425051i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.02833e10i | − | 0.517723i | −0.965914 | − | 0.258862i | \(-0.916653\pi\) | ||
0.965914 | − | 0.258862i | \(-0.0833473\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.31264e11 | + | 1.21995e10i | −0.954283 | + | 0.0886900i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.36562e11 | −1.69738 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.51121e11 | 1.07024 | 0.535121 | − | 0.844776i | \(-0.320266\pi\) | ||||
0.535121 | + | 0.844776i | \(0.320266\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 1.70879e10i | − | 0.119451i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.18283e10 | −0.0816175 | −0.0408088 | − | 0.999167i | \(-0.512993\pi\) | ||||
−0.0408088 | + | 0.999167i | \(0.512993\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 2.21107e11i | − | 1.50605i | −0.657992 | − | 0.753025i | \(-0.728594\pi\) | ||
0.657992 | − | 0.753025i | \(-0.271406\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 3.52409e10i | − | 0.236963i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.39308e10 | − | 6.87104e9i | 0.490764 | − | 0.0456111i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.09265e10 | 0.333752 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.70636e10 | −0.110408 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.06953e10i | 0.259981i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.03138e11 | −1.28137 | −0.640685 | − | 0.767804i | \(-0.721350\pi\) | ||||
−0.640685 | + | 0.767804i | \(0.721350\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.56779e11i | − | 0.976503i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.28587e11i | 0.790863i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.20334e10 | + | 2.77515e11i | 0.316027 | + | 1.68550i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.11183e9 | 0.0366579 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.41763e8 | −0.00143205 | −0.000716023 | − | 1.00000i | \(-0.500228\pi\) | ||||
−0.000716023 | 1.00000i | \(0.500228\pi\) | ||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.17705e11i | 0.688577i | 0.938864 | + | 0.344288i | \(0.111880\pi\) | ||||
−0.938864 | + | 0.344288i | \(0.888120\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.52103e10 | 0.318993 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.63521e11i | − | 0.933163i | −0.884478 | − | 0.466581i | \(-0.845485\pi\) | ||
0.884478 | − | 0.466581i | \(-0.154515\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.02492e11i | − | 0.577712i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.30534e9 | − | 1.40452e10i | −0.00726775 | − | 0.0781992i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.14460e10 | −0.392939 | −0.196470 | − | 0.980510i | \(-0.562948\pi\) | ||||
−0.196470 | + | 0.980510i | \(0.562948\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.59349e10 | 0.466879 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 7.31091e10i | − | 0.392383i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.87788e11 | −1.52592 | −0.762959 | − | 0.646447i | \(-0.776254\pi\) | ||||
−0.762959 | + | 0.646447i | \(0.776254\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.81369e11i | − | 0.950073i | −0.879966 | − | 0.475036i | \(-0.842435\pi\) | ||
0.879966 | − | 0.475036i | \(-0.157565\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 1.26914e11i | − | 0.656832i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.62706e9 | + | 4.97861e10i | 0.0236602 | + | 0.254578i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.04549e11 | −2.04394 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.09792e11 | 0.548107 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.97793e10i | 0.294890i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.10534e10 | −0.346358 | −0.173179 | − | 0.984890i | \(-0.555404\pi\) | ||||
−0.173179 | + | 0.984890i | \(0.555404\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 3.03021e10i | − | 0.145968i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.56950e11i | 1.22319i | 0.791171 | + | 0.611595i | \(0.209472\pi\) | ||||
−0.791171 | + | 0.611595i | \(0.790528\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.20802e11 | − | 1.12272e10i | 0.568324 | − | 0.0528194i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.34616e11 | −0.625904 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.54657e10 | 0.392744 | 0.196372 | − | 0.980530i | \(-0.437084\pi\) | ||||
0.196372 | + | 0.980530i | \(0.437084\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.12843e10i | 0.0966712i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.30039e10 | −0.148163 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.86763e11i | 2.60367i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.41062e10i | 0.149596i | 0.997199 | + | 0.0747981i | \(0.0238312\pi\) | ||||
−0.997199 | + | 0.0747981i | \(0.976169\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.61515e9 | − | 2.81384e10i | −0.0113387 | − | 0.122002i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.40591e11 | −0.602583 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.59142e10 | −0.279285 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.34314e11i | 0.981498i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.13882e10 | −0.378458 | −0.189229 | − | 0.981933i | \(-0.560599\pi\) | ||||
−0.189229 | + | 0.981933i | \(0.560599\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.97949e10i | 0.203875i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 6.93788e10i | − | 0.280847i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.56355e11 | + | 4.24131e10i | −1.82652 | + | 0.169755i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.31905e11 | −1.70924 | −0.854620 | − | 0.519254i | \(-0.826210\pi\) | ||||
−0.854620 | + | 0.519254i | \(0.826210\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.08513e10 | −0.0424621 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4.32864e10i | − | 0.167492i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.09646e10 | 0.309793 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 1.49405e11i | − | 0.565311i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.56445e11i | 1.70794i | 0.520322 | + | 0.853970i | \(0.325812\pi\) | ||||
−0.520322 | + | 0.853970i | \(0.674188\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.08023e10 | − | 1.00395e9i | 0.0399737 | − | 0.00371511i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.97877e10 | 0.292000 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.47854e11 | −1.25906 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.00871e11i | 1.79303i | 0.443012 | + | 0.896516i | \(0.353910\pi\) | ||||
−0.443012 | + | 0.896516i | \(0.646090\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.04604e10 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 2.12966e11i | − | 0.745831i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 3.92835e11i | − | 1.36080i | −0.732841 | − | 0.680400i | \(-0.761806\pi\) | ||
0.732841 | − | 0.680400i | \(-0.238194\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.13897e10 | + | 1.52603e10i | −0.278882 | + | 0.0522896i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.57640e11 | −0.534312 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.54424e11 | −1.18835 | −0.594176 | − | 0.804335i | \(-0.702522\pi\) | ||||
−0.594176 | + | 0.804335i | \(0.702522\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 1.55292e11i | − | 0.515082i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.28146e11 | 1.40487 | 0.702436 | − | 0.711747i | \(-0.252096\pi\) | ||||
0.702436 | + | 0.711747i | \(0.252096\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.24183e11i | 0.727741i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 7.28570e10i | − | 0.233986i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.48973e10 | + | 2.67889e11i | 0.0791089 | + | 0.851193i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.38599e11 | 0.750082 | 0.375041 | − | 0.927008i | \(-0.377629\pi\) | ||||
0.375041 | + | 0.927008i | \(0.377629\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.21624e11 | 0.378303 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 6.77876e10i | − | 0.208623i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.86981e11 | −0.569395 | −0.284697 | − | 0.958617i | \(-0.591893\pi\) | ||||
−0.284697 | + | 0.958617i | \(0.591893\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 8.67210e10i | − | 0.261311i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.41696e11i | 1.31700i | 0.752582 | + | 0.658498i | \(0.228808\pi\) | ||||
−0.752582 | + | 0.658498i | \(0.771192\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.48341e10 | − | 3.74807e11i | −0.102780 | − | 1.10588i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.72212e10 | 0.108679 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.32760e11 | 2.69518 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3.57622e11i | − | 1.02263i | −0.859393 | − | 0.511315i | \(-0.829158\pi\) | ||
0.859393 | − | 0.511315i | \(-0.170842\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.63488e10 | −0.244365 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.35131e11i | 0.658555i | 0.944233 | + | 0.329277i | \(0.106805\pi\) | ||||
−0.944233 | + | 0.329277i | \(0.893195\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.72201e10i | − | 0.103174i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.21135e10 | + | 7.63154e9i | −0.225284 | + | 0.0209376i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.06529e10 | −0.219013 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.50400e10 | 0.0404245 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.20080e11i | 0.319465i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.40430e11 | −0.369813 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.15901e11i | − | 0.302125i | −0.988524 | − | 0.151063i | \(-0.951730\pi\) | ||
0.988524 | − | 0.151063i | \(-0.0482695\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 3.10208e11i | − | 0.800471i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.39716e10 | − | 4.73124e11i | −0.112322 | − | 1.20856i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.44039e11 | −1.37574 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.72086e11 | −0.430801 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 3.96381e11i | − | 0.982381i | −0.871052 | − | 0.491190i | \(-0.836562\pi\) | ||
0.871052 | − | 0.491190i | \(-0.163438\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.67619e11 | −0.656644 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 6.76316e10i | − | 0.164293i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.79907e11i | − | 0.432700i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.53024e11 | + | 2.35158e10i | −0.602530 | + | 0.0559984i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.43320e11 | 0.573697 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.29402e11 | −0.302098 | −0.151049 | − | 0.988526i | \(-0.548265\pi\) | ||||
−0.151049 | + | 0.988526i | \(0.548265\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4.80667e11i | − | 1.11112i | −0.831476 | − | 0.555560i | \(-0.812504\pi\) | ||
0.831476 | − | 0.555560i | \(-0.187496\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.46738e11 | −0.564773 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 4.86584e10i | − | 0.110288i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.60586e11i | − | 0.584875i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.56082e11 | − | 2.38000e10i | 0.569172 | − | 0.0528982i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.26912e11 | 1.37986 | 0.689929 | − | 0.723877i | \(-0.257642\pi\) | ||||
0.689929 | + | 0.723877i | \(0.257642\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.14176e10 | 0.199265 | 0.0996324 | − | 0.995024i | \(-0.468233\pi\) | ||||
0.0996324 | + | 0.995024i | \(0.468233\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 7.45676e10i | − | 0.160966i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.29762e11 | −0.918769 | −0.459384 | − | 0.888238i | \(-0.651930\pi\) | ||||
−0.459384 | + | 0.888238i | \(0.651930\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.66115e11i | − | 0.775174i | −0.921833 | − | 0.387587i | \(-0.873309\pi\) | ||
0.921833 | − | 0.387587i | \(-0.126691\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.21499e10i | 0.151297i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.88647e10 | + | 3.13950e11i | 0.122257 | + | 0.652048i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.70630e11 | 0.351002 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.28484e10 | −0.0261787 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.61714e11i | 1.73906i | 0.493878 | + | 0.869531i | \(0.335579\pi\) | ||||
−0.493878 | + | 0.869531i | \(0.664421\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.78216e11 | 1.75557 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 4.28652e11i | − | 0.848780i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.86283e11i | 0.953811i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.11927e10 | + | 4.43224e11i | 0.0800363 | + | 0.861172i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.94492e11 | −0.374343 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.53069e11 | −0.482527 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 7.23327e11i | − | 1.36628i | −0.730289 | − | 0.683138i | \(-0.760615\pi\) | ||
0.730289 | − | 0.683138i | \(-0.239385\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.55441e10 | 0.0852251 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.28445e11i | − | 0.238119i | −0.992887 | − | 0.119059i | \(-0.962012\pi\) | ||
0.992887 | − | 0.119059i | \(-0.0379879\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.59898e11i | 1.21200i | 0.795463 | + | 0.606002i | \(0.207228\pi\) | ||||
−0.795463 | + | 0.606002i | \(0.792772\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.23608e10 | − | 1.32999e11i | −0.0224923 | − | 0.242012i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.41184e11 | 0.254532 | 0.127266 | − | 0.991869i | \(-0.459380\pi\) | ||||
0.127266 | + | 0.991869i | \(0.459380\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.38879e11 | −0.783936 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.82648e11i | 0.323250i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.67028e10 | −0.0468250 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.43465e12i | − | 2.49271i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1.10509e11i | − | 0.190258i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.04410e11 | + | 4.68793e10i | −0.860501 | + | 0.0799740i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.05924e12 | 1.79059 | 0.895294 | − | 0.445476i | \(-0.146965\pi\) | ||||
0.895294 | + | 0.445476i | \(0.146965\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.08368e11 | −1.01909 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.11273e11i | − | 0.184709i | −0.995726 | − | 0.0923543i | \(-0.970561\pi\) | ||
0.995726 | − | 0.0923543i | \(-0.0294392\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.74127e10 | −0.0944420 | −0.0472210 | − | 0.998884i | \(-0.515037\pi\) | ||||
−0.0472210 | + | 0.998884i | \(0.515037\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.73560e11i | 0.445943i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.33977e11i | 0.377989i | 0.981978 | + | 0.188995i | \(0.0605228\pi\) | ||||
−0.981978 | + | 0.188995i | \(0.939477\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.30153e10 | + | 1.00082e12i | 0.148918 | + | 1.60232i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.57409e10 | −0.0408425 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.27460e11 | −0.514935 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.07771e11i | 0.323813i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.89230e11 | 1.21909 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.47494e11i | 0.225806i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.63797e11i | 1.00725i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.29715e11 | − | 3.99372e10i | 0.646294 | − | 0.0600658i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.78034e11 | 0.414480 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.28107e12 | −1.89297 | −0.946485 | − | 0.322747i | \(-0.895394\pi\) | ||||
−0.946485 | + | 0.322747i | \(0.895394\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.17472e11i | 0.611465i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.60592e11 | 1.10428 | 0.552139 | − | 0.833752i | \(-0.313812\pi\) | ||||
0.552139 | + | 0.833752i | \(0.313812\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.79287e11i | − | 0.258027i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 1.59556e11i | − | 0.227629i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.68853e11 | − | 6.21624e10i | 0.945917 | − | 0.0879124i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.16164e12 | 1.62859 | 0.814293 | − | 0.580454i | \(-0.197125\pi\) | ||||
0.814293 | + | 0.580454i | \(0.197125\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.52068e11 | 1.04525 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.36876e11i | 0.188591i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.17603e11 | −0.297234 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 9.88187e9i | − | 0.0133820i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 4.81419e11i | − | 0.646339i | −0.946341 | − | 0.323169i | \(-0.895252\pi\) | ||
0.946341 | − | 0.323169i | \(-0.104748\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.20271e10 | + | 3.84150e11i | 0.0958732 | + | 0.511331i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.75005e11 | −0.230953 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.15942e10 | 0.119845 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.25575e10i | 0.0422370i | 0.999777 | + | 0.0211185i | \(0.00672272\pi\) | ||||
−0.999777 | + | 0.0211185i | \(0.993277\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.31744e10 | −0.0169460 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 9.07253e11i | − | 1.15710i | −0.815648 | − | 0.578549i | \(-0.803619\pi\) | ||
0.815648 | − | 0.578549i | \(-0.196381\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.09897e11i | − | 0.518356i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.98005e9 | + | 7.51037e10i | 0.00875249 | + | 0.0941747i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.39273e12 | −1.73168 | −0.865838 | − | 0.500325i | \(-0.833214\pi\) | ||||
−0.865838 | + | 0.500325i | \(0.833214\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.63730e12 | 2.01866 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 5.54102e11i | − | 0.677434i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.43413e11 | 0.295102 | 0.147551 | − | 0.989054i | \(-0.452861\pi\) | ||||
0.147551 | + | 0.989054i | \(0.452861\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 8.33978e10i | − | 0.100263i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.95493e11i | 0.352290i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.53964e10 | + | 1.65661e11i | 0.0182030 | + | 0.195860i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.37109e11 | 0.981496 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.45064e11 | 0.284954 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.29867e11i | 0.265074i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.61333e12 | 1.84509 | 0.922545 | − | 0.385890i | \(-0.126106\pi\) | ||||
0.922545 | + | 0.385890i | \(0.126106\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1.75680e11i | − | 0.199263i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.23466e11i | 1.03883i | 0.854523 | + | 0.519414i | \(0.173850\pi\) | ||||
−0.854523 | + | 0.519414i | \(0.826150\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.09425e12 | + | 1.01698e11i | −1.22086 | + | 0.113465i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.78625e11 | 0.750950 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.47197e12 | −1.61555 | −0.807775 | − | 0.589491i | \(-0.799328\pi\) | ||||
−0.807775 | + | 0.589491i | \(0.799328\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.66428e11i | − | 0.181174i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.42872e11 | −0.370216 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 6.45672e11i | − | 0.691509i | −0.938325 | − | 0.345754i | \(-0.887623\pi\) | ||
0.938325 | − | 0.345754i | \(-0.112377\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.36939e11i | 0.357937i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.01863e10 | − | 5.39992e11i | −0.0528830 | − | 0.569009i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.32436e12 | 1.38427 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.11657e11 | −0.426816 | −0.213408 | − | 0.976963i | \(-0.568456\pi\) | ||||
−0.213408 | + | 0.976963i | \(0.568456\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.15362e11i | 0.118649i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.22977e10 | −0.0431543 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.26600e12i | 1.28131i | 0.767831 | + | 0.640653i | \(0.221336\pi\) | ||||
−0.767831 | + | 0.640653i | \(0.778664\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.51171e10i | 0.0754183i |
(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 | 336.9.f.a.97.7 | 10 | ||
4.3 | odd | 2 | 84.9.d.a.13.2 | ✓ | 10 | ||
7.6 | odd | 2 | inner | 336.9.f.a.97.4 | 10 | ||
12.11 | even | 2 | 252.9.d.d.181.7 | 10 | |||
28.27 | even | 2 | 84.9.d.a.13.9 | yes | 10 | ||
84.83 | odd | 2 | 252.9.d.d.181.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.9.d.a.13.2 | ✓ | 10 | 4.3 | odd | 2 | ||
84.9.d.a.13.9 | yes | 10 | 28.27 | even | 2 | ||
252.9.d.d.181.4 | 10 | 84.83 | odd | 2 | |||
252.9.d.d.181.7 | 10 | 12.11 | even | 2 | |||
336.9.f.a.97.4 | 10 | 7.6 | odd | 2 | inner | ||
336.9.f.a.97.7 | 10 | 1.1 | even | 1 | trivial |