Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,8,Mod(1,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, 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("175.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.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: | \(54.6673794597\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 542x^{4} + 982x^{3} + 69485x^{2} - 187765x - 953200 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.67453\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.67453 | 0.324786 | 0.162393 | − | 0.986726i | \(-0.448079\pi\) | ||||
0.162393 | + | 0.986726i | \(0.448079\pi\) | |||||||
\(3\) | −52.1592 | −1.11534 | −0.557669 | − | 0.830064i | \(-0.688304\pi\) | ||||
−0.557669 | + | 0.830064i | \(0.688304\pi\) | |||||||
\(4\) | −114.498 | −0.894514 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −191.660 | −0.362245 | ||||||||
\(7\) | −343.000 | −0.377964 | ||||||||
\(8\) | −891.065 | −0.615311 | ||||||||
\(9\) | 533.578 | 0.243977 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2402.61 | 0.544262 | 0.272131 | − | 0.962260i | \(-0.412272\pi\) | ||||
0.272131 | + | 0.962260i | \(0.412272\pi\) | |||||||
\(12\) | 5972.11 | 0.997685 | ||||||||
\(13\) | 8971.92 | 1.13262 | 0.566310 | − | 0.824193i | \(-0.308371\pi\) | ||||
0.566310 | + | 0.824193i | \(0.308371\pi\) | |||||||
\(14\) | −1260.36 | −0.122757 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11381.5 | 0.694670 | ||||||||
\(17\) | 16827.7 | 0.830718 | 0.415359 | − | 0.909658i | \(-0.363656\pi\) | ||||
0.415359 | + | 0.909658i | \(0.363656\pi\) | |||||||
\(18\) | 1960.65 | 0.0792402 | ||||||||
\(19\) | 15357.7 | 0.513675 | 0.256838 | − | 0.966455i | \(-0.417319\pi\) | ||||
0.256838 | + | 0.966455i | \(0.417319\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 17890.6 | 0.421558 | ||||||||
\(22\) | 8828.45 | 0.176769 | ||||||||
\(23\) | −81244.7 | −1.39235 | −0.696174 | − | 0.717874i | \(-0.745116\pi\) | ||||
−0.696174 | + | 0.717874i | \(0.745116\pi\) | |||||||
\(24\) | 46477.2 | 0.686279 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 32967.6 | 0.367858 | ||||||||
\(27\) | 86241.1 | 0.843221 | ||||||||
\(28\) | 39272.8 | 0.338095 | ||||||||
\(29\) | −203872. | −1.55226 | −0.776132 | − | 0.630571i | \(-0.782821\pi\) | ||||
−0.776132 | + | 0.630571i | \(0.782821\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 88474.9 | 0.533401 | 0.266701 | − | 0.963779i | \(-0.414067\pi\) | ||||
0.266701 | + | 0.963779i | \(0.414067\pi\) | |||||||
\(32\) | 155878. | 0.840930 | ||||||||
\(33\) | −125318. | −0.607036 | ||||||||
\(34\) | 61833.9 | 0.269805 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −61093.5 | −0.218241 | ||||||||
\(37\) | 261256. | 0.847931 | 0.423965 | − | 0.905678i | \(-0.360638\pi\) | ||||
0.423965 | + | 0.905678i | \(0.360638\pi\) | |||||||
\(38\) | 56432.3 | 0.166834 | ||||||||
\(39\) | −467968. | −1.26325 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 179461. | 0.406655 | 0.203327 | − | 0.979111i | \(-0.434824\pi\) | ||||
0.203327 | + | 0.979111i | \(0.434824\pi\) | |||||||
\(42\) | 65739.5 | 0.136916 | ||||||||
\(43\) | 520767. | 0.998858 | 0.499429 | − | 0.866355i | \(-0.333543\pi\) | ||||
0.499429 | + | 0.866355i | \(0.333543\pi\) | |||||||
\(44\) | −275093. | −0.486851 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −298536. | −0.452214 | ||||||||
\(47\) | −123436. | −0.173420 | −0.0867100 | − | 0.996234i | \(-0.527635\pi\) | ||||
−0.0867100 | + | 0.996234i | \(0.527635\pi\) | |||||||
\(48\) | −593648. | −0.774792 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −877719. | −0.926531 | ||||||||
\(52\) | −1.02727e6 | −1.01314 | ||||||||
\(53\) | −936049. | −0.863641 | −0.431820 | − | 0.901960i | \(-0.642129\pi\) | ||||
−0.431820 | + | 0.901960i | \(0.642129\pi\) | |||||||
\(54\) | 316895. | 0.273866 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 305635. | 0.232566 | ||||||||
\(57\) | −801044. | −0.572921 | ||||||||
\(58\) | −749135. | −0.504153 | ||||||||
\(59\) | −1.77448e6 | −1.12484 | −0.562419 | − | 0.826852i | \(-0.690129\pi\) | ||||
−0.562419 | + | 0.826852i | \(0.690129\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.84579e6 | −1.60527 | −0.802634 | − | 0.596471i | \(-0.796569\pi\) | ||||
−0.802634 | + | 0.596471i | \(0.796569\pi\) | |||||||
\(62\) | 325104. | 0.173241 | ||||||||
\(63\) | −183017. | −0.0922147 | ||||||||
\(64\) | −884051. | −0.421548 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −460485. | −0.197157 | ||||||||
\(67\) | 2.45723e6 | 0.998124 | 0.499062 | − | 0.866566i | \(-0.333678\pi\) | ||||
0.499062 | + | 0.866566i | \(0.333678\pi\) | |||||||
\(68\) | −1.92674e6 | −0.743089 | ||||||||
\(69\) | 4.23765e6 | 1.55294 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.59302e6 | −0.859809 | −0.429905 | − | 0.902874i | \(-0.641453\pi\) | ||||
−0.429905 | + | 0.902874i | \(0.641453\pi\) | |||||||
\(72\) | −475453. | −0.150122 | ||||||||
\(73\) | −1.98548e6 | −0.597360 | −0.298680 | − | 0.954353i | \(-0.596546\pi\) | ||||
−0.298680 | + | 0.954353i | \(0.596546\pi\) | |||||||
\(74\) | 959993. | 0.275396 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.75842e6 | −0.459490 | ||||||||
\(77\) | −824094. | −0.205712 | ||||||||
\(78\) | −1.71956e6 | −0.410286 | ||||||||
\(79\) | −1.13717e6 | −0.259495 | −0.129748 | − | 0.991547i | \(-0.541417\pi\) | ||||
−0.129748 | + | 0.991547i | \(0.541417\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.66520e6 | −1.18445 | ||||||||
\(82\) | 659433. | 0.132076 | ||||||||
\(83\) | −2.32030e6 | −0.445420 | −0.222710 | − | 0.974885i | \(-0.571490\pi\) | ||||
−0.222710 | + | 0.974885i | \(0.571490\pi\) | |||||||
\(84\) | −2.04843e6 | −0.377090 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.91357e6 | 0.324415 | ||||||||
\(87\) | 1.06338e7 | 1.73130 | ||||||||
\(88\) | −2.14088e6 | −0.334891 | ||||||||
\(89\) | −1.88285e6 | −0.283108 | −0.141554 | − | 0.989931i | \(-0.545210\pi\) | ||||
−0.141554 | + | 0.989931i | \(0.545210\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.07737e6 | −0.428090 | ||||||||
\(92\) | 9.30234e6 | 1.24547 | ||||||||
\(93\) | −4.61478e6 | −0.594922 | ||||||||
\(94\) | −453569. | −0.0563243 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.13046e6 | −0.937920 | ||||||||
\(97\) | 5.66884e6 | 0.630656 | 0.315328 | − | 0.948983i | \(-0.397885\pi\) | ||||
0.315328 | + | 0.948983i | \(0.397885\pi\) | |||||||
\(98\) | 432305. | 0.0463979 | ||||||||
\(99\) | 1.28198e6 | 0.132788 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.87704e6 | −0.471012 | −0.235506 | − | 0.971873i | \(-0.575675\pi\) | ||||
−0.235506 | + | 0.971873i | \(0.575675\pi\) | |||||||
\(102\) | −3.22520e6 | −0.300924 | ||||||||
\(103\) | 1.86759e7 | 1.68404 | 0.842019 | − | 0.539447i | \(-0.181367\pi\) | ||||
0.842019 | + | 0.539447i | \(0.181367\pi\) | |||||||
\(104\) | −7.99457e6 | −0.696913 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.43954e6 | −0.280498 | ||||||||
\(107\) | 8.17763e6 | 0.645333 | 0.322667 | − | 0.946513i | \(-0.395421\pi\) | ||||
0.322667 | + | 0.946513i | \(0.395421\pi\) | |||||||
\(108\) | −9.87442e6 | −0.754273 | ||||||||
\(109\) | −1.20799e7 | −0.893452 | −0.446726 | − | 0.894671i | \(-0.647410\pi\) | ||||
−0.446726 | + | 0.894671i | \(0.647410\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.36269e7 | −0.945729 | ||||||||
\(112\) | −3.90385e6 | −0.262561 | ||||||||
\(113\) | 1.08439e7 | 0.706988 | 0.353494 | − | 0.935437i | \(-0.384994\pi\) | ||||
0.353494 | + | 0.935437i | \(0.384994\pi\) | |||||||
\(114\) | −2.94346e6 | −0.186076 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.33430e7 | 1.38852 | ||||||||
\(117\) | 4.78722e6 | 0.276333 | ||||||||
\(118\) | −6.52039e6 | −0.365331 | ||||||||
\(119\) | −5.77190e6 | −0.313982 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.37146e7 | −0.703778 | ||||||||
\(122\) | −1.04569e7 | −0.521368 | ||||||||
\(123\) | −9.36052e6 | −0.453557 | ||||||||
\(124\) | −1.01302e7 | −0.477135 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −672502. | −0.0299500 | ||||||||
\(127\) | 2.76641e7 | 1.19841 | 0.599203 | − | 0.800597i | \(-0.295484\pi\) | ||||
0.599203 | + | 0.800597i | \(0.295484\pi\) | |||||||
\(128\) | −2.32008e7 | −0.977843 | ||||||||
\(129\) | −2.71628e7 | −1.11406 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.60892e7 | −0.625295 | −0.312647 | − | 0.949869i | \(-0.601216\pi\) | ||||
−0.312647 | + | 0.949869i | \(0.601216\pi\) | |||||||
\(132\) | 1.43486e7 | 0.543003 | ||||||||
\(133\) | −5.26769e6 | −0.194151 | ||||||||
\(134\) | 9.02917e6 | 0.324176 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.49946e7 | −0.511150 | ||||||||
\(137\) | −1.69816e7 | −0.564231 | −0.282116 | − | 0.959380i | \(-0.591036\pi\) | ||||
−0.282116 | + | 0.959380i | \(0.591036\pi\) | |||||||
\(138\) | 1.55714e7 | 0.504371 | ||||||||
\(139\) | 3.31021e7 | 1.04545 | 0.522725 | − | 0.852501i | \(-0.324915\pi\) | ||||
0.522725 | + | 0.852501i | \(0.324915\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.43831e6 | 0.193422 | ||||||||
\(142\) | −9.52814e6 | −0.279254 | ||||||||
\(143\) | 2.15560e7 | 0.616442 | ||||||||
\(144\) | 6.07290e6 | 0.169484 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.29571e6 | −0.194014 | ||||||||
\(147\) | −6.13647e6 | −0.159334 | ||||||||
\(148\) | −2.99133e7 | −0.758486 | ||||||||
\(149\) | 6.37347e7 | 1.57843 | 0.789213 | − | 0.614119i | \(-0.210489\pi\) | ||||
0.789213 | + | 0.614119i | \(0.210489\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.83946e6 | −0.232569 | −0.116285 | − | 0.993216i | \(-0.537098\pi\) | ||||
−0.116285 | + | 0.993216i | \(0.537098\pi\) | |||||||
\(152\) | −1.36847e7 | −0.316070 | ||||||||
\(153\) | 8.97889e6 | 0.202676 | ||||||||
\(154\) | −3.02816e6 | −0.0668122 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.35813e7 | 1.13000 | ||||||||
\(157\) | −7.00482e7 | −1.44460 | −0.722301 | − | 0.691578i | \(-0.756916\pi\) | ||||
−0.722301 | + | 0.691578i | \(0.756916\pi\) | |||||||
\(158\) | −4.17856e6 | −0.0842804 | ||||||||
\(159\) | 4.88235e7 | 0.963251 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.78669e7 | 0.526258 | ||||||||
\(162\) | −2.08169e7 | −0.384693 | ||||||||
\(163\) | −9.64289e7 | −1.74402 | −0.872009 | − | 0.489491i | \(-0.837183\pi\) | ||||
−0.872009 | + | 0.489491i | \(0.837183\pi\) | |||||||
\(164\) | −2.05479e7 | −0.363758 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.52599e6 | −0.144666 | ||||||||
\(167\) | −4.58188e7 | −0.761266 | −0.380633 | − | 0.924726i | \(-0.624294\pi\) | ||||
−0.380633 | + | 0.924726i | \(0.624294\pi\) | |||||||
\(168\) | −1.59417e7 | −0.259389 | ||||||||
\(169\) | 1.77469e7 | 0.282826 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.19453e6 | 0.125325 | ||||||||
\(172\) | −5.96267e7 | −0.893493 | ||||||||
\(173\) | 8.69029e7 | 1.27606 | 0.638032 | − | 0.770009i | \(-0.279749\pi\) | ||||
0.638032 | + | 0.770009i | \(0.279749\pi\) | |||||||
\(174\) | 3.90743e7 | 0.562300 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.73452e7 | 0.378083 | ||||||||
\(177\) | 9.25556e7 | 1.25457 | ||||||||
\(178\) | −6.91860e6 | −0.0919493 | ||||||||
\(179\) | −1.48385e8 | −1.93377 | −0.966884 | − | 0.255216i | \(-0.917853\pi\) | ||||
−0.966884 | + | 0.255216i | \(0.917853\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.45089e8 | 1.81869 | 0.909345 | − | 0.416042i | \(-0.136583\pi\) | ||||
0.909345 | + | 0.416042i | \(0.136583\pi\) | |||||||
\(182\) | −1.13079e7 | −0.139037 | ||||||||
\(183\) | 1.48434e8 | 1.79042 | ||||||||
\(184\) | 7.23943e7 | 0.856726 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.69571e7 | −0.193222 | ||||||||
\(187\) | 4.04304e7 | 0.452129 | ||||||||
\(188\) | 1.41331e7 | 0.155127 | ||||||||
\(189\) | −2.95807e7 | −0.318707 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.70854e8 | 1.77422 | 0.887112 | − | 0.461555i | \(-0.152708\pi\) | ||||
0.887112 | + | 0.461555i | \(0.152708\pi\) | |||||||
\(192\) | 4.61114e7 | 0.470169 | ||||||||
\(193\) | 6.73834e6 | 0.0674687 | 0.0337343 | − | 0.999431i | \(-0.489260\pi\) | ||||
0.0337343 | + | 0.999431i | \(0.489260\pi\) | |||||||
\(194\) | 2.08303e7 | 0.204828 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.34706e7 | −0.127788 | ||||||||
\(197\) | −1.11483e8 | −1.03891 | −0.519454 | − | 0.854498i | \(-0.673865\pi\) | ||||
−0.519454 | + | 0.854498i | \(0.673865\pi\) | |||||||
\(198\) | 4.71066e6 | 0.0431275 | ||||||||
\(199\) | −1.57863e8 | −1.42002 | −0.710012 | − | 0.704189i | \(-0.751311\pi\) | ||||
−0.710012 | + | 0.704189i | \(0.751311\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.28167e8 | −1.11324 | ||||||||
\(202\) | −1.79208e7 | −0.152978 | ||||||||
\(203\) | 6.99282e7 | 0.586701 | ||||||||
\(204\) | 1.00497e8 | 0.828795 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.86253e7 | 0.546951 | ||||||||
\(207\) | −4.33504e7 | −0.339701 | ||||||||
\(208\) | 1.02114e8 | 0.786797 | ||||||||
\(209\) | 3.68985e7 | 0.279574 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.19808e7 | 0.674076 | 0.337038 | − | 0.941491i | \(-0.390575\pi\) | ||||
0.337038 | + | 0.941491i | \(0.390575\pi\) | |||||||
\(212\) | 1.07176e8 | 0.772539 | ||||||||
\(213\) | 1.35250e8 | 0.958977 | ||||||||
\(214\) | 3.00489e7 | 0.209595 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.68465e7 | −0.518843 | ||||||||
\(217\) | −3.03469e7 | −0.201607 | ||||||||
\(218\) | −4.43880e7 | −0.290180 | ||||||||
\(219\) | 1.03561e8 | 0.666257 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.50977e8 | 0.940887 | ||||||||
\(222\) | −5.00724e7 | −0.307159 | ||||||||
\(223\) | 6.32103e7 | 0.381699 | 0.190849 | − | 0.981619i | \(-0.438876\pi\) | ||||
0.190849 | + | 0.981619i | \(0.438876\pi\) | |||||||
\(224\) | −5.34661e7 | −0.317842 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.98463e7 | 0.229619 | ||||||||
\(227\) | −1.72910e8 | −0.981138 | −0.490569 | − | 0.871402i | \(-0.663211\pi\) | ||||
−0.490569 | + | 0.871402i | \(0.663211\pi\) | |||||||
\(228\) | 9.17179e7 | 0.512486 | ||||||||
\(229\) | −3.40481e8 | −1.87357 | −0.936784 | − | 0.349909i | \(-0.886212\pi\) | ||||
−0.936784 | + | 0.349909i | \(0.886212\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.29841e7 | 0.229438 | ||||||||
\(232\) | 1.81664e8 | 0.955125 | ||||||||
\(233\) | −9.00565e7 | −0.466412 | −0.233206 | − | 0.972427i | \(-0.574922\pi\) | ||||
−0.233206 | + | 0.972427i | \(0.574922\pi\) | |||||||
\(234\) | 1.75908e7 | 0.0897490 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.03175e8 | 1.00618 | ||||||||
\(237\) | 5.93137e7 | 0.289425 | ||||||||
\(238\) | −2.12090e7 | −0.101977 | ||||||||
\(239\) | 2.50065e8 | 1.18484 | 0.592421 | − | 0.805628i | \(-0.298172\pi\) | ||||
0.592421 | + | 0.805628i | \(0.298172\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.76848e8 | −0.813842 | −0.406921 | − | 0.913463i | \(-0.633397\pi\) | ||||
−0.406921 | + | 0.913463i | \(0.633397\pi\) | |||||||
\(242\) | −5.03949e7 | −0.228577 | ||||||||
\(243\) | 1.06883e8 | 0.477843 | ||||||||
\(244\) | 3.25836e8 | 1.43594 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.43955e7 | −0.147309 | ||||||||
\(247\) | 1.37788e8 | 0.581798 | ||||||||
\(248\) | −7.88369e7 | −0.328208 | ||||||||
\(249\) | 1.21025e8 | 0.496794 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.48482e7 | −0.139098 | −0.0695492 | − | 0.997579i | \(-0.522156\pi\) | ||||
−0.0695492 | + | 0.997579i | \(0.522156\pi\) | |||||||
\(252\) | 2.09551e7 | 0.0824873 | ||||||||
\(253\) | −1.95199e8 | −0.757802 | ||||||||
\(254\) | 1.01653e8 | 0.389225 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.79064e7 | 0.103959 | ||||||||
\(257\) | −2.80632e8 | −1.03127 | −0.515633 | − | 0.856810i | \(-0.672443\pi\) | ||||
−0.515633 | + | 0.856810i | \(0.672443\pi\) | |||||||
\(258\) | −9.98103e7 | −0.361832 | ||||||||
\(259\) | −8.96109e7 | −0.320488 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.08782e8 | −0.378717 | ||||||||
\(262\) | −5.91202e7 | −0.203087 | ||||||||
\(263\) | 1.37112e7 | 0.0464763 | 0.0232381 | − | 0.999730i | \(-0.492602\pi\) | ||||
0.0232381 | + | 0.999730i | \(0.492602\pi\) | |||||||
\(264\) | 1.11666e8 | 0.373516 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.93563e7 | −0.0630574 | ||||||||
\(267\) | 9.82081e7 | 0.315761 | ||||||||
\(268\) | −2.81348e8 | −0.892836 | ||||||||
\(269\) | −1.60114e8 | −0.501530 | −0.250765 | − | 0.968048i | \(-0.580682\pi\) | ||||
−0.250765 | + | 0.968048i | \(0.580682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.68123e8 | −0.513140 | −0.256570 | − | 0.966526i | \(-0.582592\pi\) | ||||
−0.256570 | + | 0.966526i | \(0.582592\pi\) | |||||||
\(272\) | 1.91524e8 | 0.577075 | ||||||||
\(273\) | 1.60513e8 | 0.477464 | ||||||||
\(274\) | −6.23995e7 | −0.183254 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.85202e8 | −1.38912 | ||||||||
\(277\) | −4.17131e8 | −1.17922 | −0.589608 | − | 0.807690i | \(-0.700718\pi\) | ||||
−0.589608 | + | 0.807690i | \(0.700718\pi\) | |||||||
\(278\) | 1.21635e8 | 0.339547 | ||||||||
\(279\) | 4.72082e7 | 0.130138 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.23209e7 | 0.113784 | 0.0568921 | − | 0.998380i | \(-0.481881\pi\) | ||||
0.0568921 | + | 0.998380i | \(0.481881\pi\) | |||||||
\(282\) | 2.36578e7 | 0.0628206 | ||||||||
\(283\) | −4.33200e8 | −1.13615 | −0.568075 | − | 0.822976i | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822976i | \(0.692312\pi\) | |||||||
\(284\) | 2.96895e8 | 0.769112 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.92082e7 | 0.200211 | ||||||||
\(287\) | −6.15550e7 | −0.153701 | ||||||||
\(288\) | 8.31730e7 | 0.205168 | ||||||||
\(289\) | −1.27167e8 | −0.309908 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.95682e8 | −0.703395 | ||||||||
\(292\) | 2.27333e8 | 0.534347 | ||||||||
\(293\) | −7.50146e8 | −1.74224 | −0.871122 | − | 0.491067i | \(-0.836607\pi\) | ||||
−0.871122 | + | 0.491067i | \(0.836607\pi\) | |||||||
\(294\) | −2.25486e7 | −0.0517493 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.32796e8 | −0.521741 | ||||||||
\(297\) | 2.07204e8 | 0.458933 | ||||||||
\(298\) | 2.34195e8 | 0.512650 | ||||||||
\(299\) | −7.28921e8 | −1.57700 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.78623e8 | −0.377533 | ||||||||
\(302\) | −3.61554e7 | −0.0755351 | ||||||||
\(303\) | 2.54382e8 | 0.525337 | ||||||||
\(304\) | 1.74793e8 | 0.356835 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.29932e7 | 0.0658263 | ||||||||
\(307\) | −5.40678e8 | −1.06648 | −0.533242 | − | 0.845963i | \(-0.679027\pi\) | ||||
−0.533242 | + | 0.845963i | \(0.679027\pi\) | |||||||
\(308\) | 9.43570e7 | 0.184012 | ||||||||
\(309\) | −9.74121e8 | −1.87827 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.63814e8 | −0.874344 | −0.437172 | − | 0.899378i | \(-0.644020\pi\) | ||||
−0.437172 | + | 0.899378i | \(0.644020\pi\) | |||||||
\(312\) | 4.16990e8 | 0.777293 | ||||||||
\(313\) | −7.31063e8 | −1.34757 | −0.673783 | − | 0.738930i | \(-0.735332\pi\) | ||||
−0.673783 | + | 0.738930i | \(0.735332\pi\) | |||||||
\(314\) | −2.57394e8 | −0.469186 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.30203e8 | 0.232122 | ||||||||
\(317\) | 7.29343e8 | 1.28595 | 0.642976 | − | 0.765886i | \(-0.277700\pi\) | ||||
0.642976 | + | 0.765886i | \(0.277700\pi\) | |||||||
\(318\) | 1.79403e8 | 0.312850 | ||||||||
\(319\) | −4.89825e8 | −0.844839 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.26538e8 | −0.719764 | ||||||||
\(322\) | 1.02398e8 | 0.170921 | ||||||||
\(323\) | 2.58435e8 | 0.426719 | ||||||||
\(324\) | 6.48653e8 | 1.05951 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.54331e8 | −0.566432 | ||||||||
\(327\) | 6.30079e8 | 0.996501 | ||||||||
\(328\) | −1.59911e8 | −0.250219 | ||||||||
\(329\) | 4.23385e7 | 0.0655466 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.87428e7 | −0.149661 | −0.0748303 | − | 0.997196i | \(-0.523842\pi\) | ||||
−0.0748303 | + | 0.997196i | \(0.523842\pi\) | |||||||
\(332\) | 2.65669e8 | 0.398435 | ||||||||
\(333\) | 1.39400e8 | 0.206876 | ||||||||
\(334\) | −1.68363e8 | −0.247248 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.03621e8 | 0.292844 | ||||||||
\(337\) | −9.26763e7 | −0.131906 | −0.0659529 | − | 0.997823i | \(-0.521009\pi\) | ||||
−0.0659529 | + | 0.997823i | \(0.521009\pi\) | |||||||
\(338\) | 6.52115e7 | 0.0918578 | ||||||||
\(339\) | −5.65610e8 | −0.788530 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.12570e8 | 0.290310 | ||||||||
\(342\) | 3.01110e7 | 0.0407037 | ||||||||
\(343\) | −4.03536e7 | −0.0539949 | ||||||||
\(344\) | −4.64037e8 | −0.614608 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.19327e8 | 0.414447 | ||||||||
\(347\) | −1.42087e8 | −0.182558 | −0.0912792 | − | 0.995825i | \(-0.529096\pi\) | ||||
−0.0912792 | + | 0.995825i | \(0.529096\pi\) | |||||||
\(348\) | −1.21755e9 | −1.54867 | ||||||||
\(349\) | 7.82143e8 | 0.984912 | 0.492456 | − | 0.870337i | \(-0.336099\pi\) | ||||
0.492456 | + | 0.870337i | \(0.336099\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.73749e8 | 0.955048 | ||||||||
\(352\) | 3.74513e8 | 0.457686 | ||||||||
\(353\) | 5.74706e8 | 0.695399 | 0.347700 | − | 0.937606i | \(-0.386963\pi\) | ||||
0.347700 | + | 0.937606i | \(0.386963\pi\) | |||||||
\(354\) | 3.40098e8 | 0.407468 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.15583e8 | 0.253244 | ||||||||
\(357\) | 3.01058e8 | 0.350196 | ||||||||
\(358\) | −5.45245e8 | −0.628060 | ||||||||
\(359\) | −1.42968e9 | −1.63082 | −0.815412 | − | 0.578881i | \(-0.803489\pi\) | ||||
−0.815412 | + | 0.578881i | \(0.803489\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.58013e8 | −0.736138 | ||||||||
\(362\) | 5.33133e8 | 0.590684 | ||||||||
\(363\) | 7.15345e8 | 0.784950 | ||||||||
\(364\) | 3.52352e8 | 0.382932 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.45424e8 | 0.581501 | ||||||||
\(367\) | 8.75438e8 | 0.924473 | 0.462236 | − | 0.886757i | \(-0.347047\pi\) | ||||
0.462236 | + | 0.886757i | \(0.347047\pi\) | |||||||
\(368\) | −9.24684e8 | −0.967222 | ||||||||
\(369\) | 9.57562e7 | 0.0992144 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.21065e8 | 0.326425 | ||||||||
\(372\) | 5.28382e8 | 0.532167 | ||||||||
\(373\) | 7.33357e8 | 0.731703 | 0.365851 | − | 0.930673i | \(-0.380778\pi\) | ||||
0.365851 | + | 0.930673i | \(0.380778\pi\) | |||||||
\(374\) | 1.48563e8 | 0.146845 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.09989e8 | 0.106707 | ||||||||
\(377\) | −1.82913e9 | −1.75812 | ||||||||
\(378\) | −1.08695e8 | −0.103512 | ||||||||
\(379\) | 8.06937e8 | 0.761381 | 0.380691 | − | 0.924702i | \(-0.375686\pi\) | ||||
0.380691 | + | 0.924702i | \(0.375686\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.44294e9 | −1.33663 | ||||||||
\(382\) | 6.27808e8 | 0.576242 | ||||||||
\(383\) | −5.38367e7 | −0.0489647 | −0.0244823 | − | 0.999700i | \(-0.507794\pi\) | ||||
−0.0244823 | + | 0.999700i | \(0.507794\pi\) | |||||||
\(384\) | 1.21014e9 | 1.09062 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.47602e7 | 0.0219129 | ||||||||
\(387\) | 2.77870e8 | 0.243698 | ||||||||
\(388\) | −6.49070e8 | −0.564131 | ||||||||
\(389\) | 1.01850e9 | 0.877278 | 0.438639 | − | 0.898663i | \(-0.355461\pi\) | ||||
0.438639 | + | 0.898663i | \(0.355461\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.36716e9 | −1.15665 | ||||||||
\(392\) | −1.04833e8 | −0.0879016 | ||||||||
\(393\) | 8.39199e8 | 0.697414 | ||||||||
\(394\) | −4.09648e8 | −0.337423 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.46784e8 | −0.118780 | ||||||||
\(397\) | −1.92918e9 | −1.54742 | −0.773708 | − | 0.633543i | \(-0.781600\pi\) | ||||
−0.773708 | + | 0.633543i | \(0.781600\pi\) | |||||||
\(398\) | −5.80074e8 | −0.461203 | ||||||||
\(399\) | 2.74758e8 | 0.216544 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.34586e9 | −1.81676 | −0.908380 | − | 0.418146i | \(-0.862680\pi\) | ||||
−0.908380 | + | 0.418146i | \(0.862680\pi\) | |||||||
\(402\) | −4.70954e8 | −0.361566 | ||||||||
\(403\) | 7.93790e8 | 0.604140 | ||||||||
\(404\) | 5.58411e8 | 0.421327 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.56953e8 | 0.190552 | ||||||||
\(407\) | 6.27696e8 | 0.461497 | ||||||||
\(408\) | 7.82105e8 | 0.570104 | ||||||||
\(409\) | 1.95618e9 | 1.41376 | 0.706882 | − | 0.707332i | \(-0.250101\pi\) | ||||
0.706882 | + | 0.707332i | \(0.250101\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.85747e8 | 0.629308 | ||||||||
\(412\) | −2.13835e9 | −1.50640 | ||||||||
\(413\) | 6.08648e8 | 0.425149 | ||||||||
\(414\) | −1.59292e8 | −0.110330 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.39852e9 | 0.952453 | ||||||||
\(417\) | −1.72658e9 | −1.16603 | ||||||||
\(418\) | 1.35585e8 | 0.0908016 | ||||||||
\(419\) | −2.72762e9 | −1.81149 | −0.905744 | − | 0.423825i | \(-0.860687\pi\) | ||||
−0.905744 | + | 0.423825i | \(0.860687\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.49203e9 | 0.974519 | 0.487260 | − | 0.873257i | \(-0.337997\pi\) | ||||
0.487260 | + | 0.873257i | \(0.337997\pi\) | |||||||
\(422\) | 3.37986e8 | 0.218930 | ||||||||
\(423\) | −6.58627e7 | −0.0423105 | ||||||||
\(424\) | 8.34081e8 | 0.531407 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.96980e8 | 0.311462 | ||||||||
\(427\) | 9.76105e8 | 0.606735 | ||||||||
\(428\) | −9.36321e8 | −0.577260 | ||||||||
\(429\) | −1.12434e9 | −0.687541 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.00007e9 | 1.20330 | 0.601650 | − | 0.798760i | \(-0.294510\pi\) | ||||
0.601650 | + | 0.798760i | \(0.294510\pi\) | |||||||
\(432\) | 9.81551e8 | 0.585760 | ||||||||
\(433\) | 6.56921e8 | 0.388871 | 0.194435 | − | 0.980915i | \(-0.437713\pi\) | ||||
0.194435 | + | 0.980915i | \(0.437713\pi\) | |||||||
\(434\) | −1.11511e8 | −0.0654790 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.38312e9 | 0.799206 | ||||||||
\(437\) | −1.24773e9 | −0.715214 | ||||||||
\(438\) | 3.80538e8 | 0.216391 | ||||||||
\(439\) | 1.07249e9 | 0.605015 | 0.302508 | − | 0.953147i | \(-0.402176\pi\) | ||||
0.302508 | + | 0.953147i | \(0.402176\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.27749e7 | 0.0348539 | ||||||||
\(442\) | 5.54769e8 | 0.305587 | ||||||||
\(443\) | 1.74877e9 | 0.955696 | 0.477848 | − | 0.878443i | \(-0.341417\pi\) | ||||
0.477848 | + | 0.878443i | \(0.341417\pi\) | |||||||
\(444\) | 1.56025e9 | 0.845968 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.32268e8 | 0.123970 | ||||||||
\(447\) | −3.32435e9 | −1.76048 | ||||||||
\(448\) | 3.03230e8 | 0.159330 | ||||||||
\(449\) | −1.66388e9 | −0.867481 | −0.433741 | − | 0.901038i | \(-0.642807\pi\) | ||||
−0.433741 | + | 0.901038i | \(0.642807\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.31174e8 | 0.221327 | ||||||||
\(452\) | −1.24161e9 | −0.632411 | ||||||||
\(453\) | 5.13218e8 | 0.259393 | ||||||||
\(454\) | −6.35364e8 | −0.318659 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.13783e8 | 0.352524 | ||||||||
\(457\) | −2.49377e9 | −1.22222 | −0.611110 | − | 0.791546i | \(-0.709277\pi\) | ||||
−0.611110 | + | 0.791546i | \(0.709277\pi\) | |||||||
\(458\) | −1.25111e9 | −0.608508 | ||||||||
\(459\) | 1.45124e9 | 0.700478 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.96619e9 | −1.88548 | −0.942738 | − | 0.333535i | \(-0.891758\pi\) | ||||
−0.942738 | + | 0.333535i | \(0.891758\pi\) | |||||||
\(462\) | 1.57946e8 | 0.0745182 | ||||||||
\(463\) | 3.38794e9 | 1.58636 | 0.793181 | − | 0.608986i | \(-0.208424\pi\) | ||||
0.793181 | + | 0.608986i | \(0.208424\pi\) | |||||||
\(464\) | −2.32037e9 | −1.07831 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.30915e8 | −0.151484 | ||||||||
\(467\) | 3.18287e9 | 1.44614 | 0.723069 | − | 0.690776i | \(-0.242731\pi\) | ||||
0.723069 | + | 0.690776i | \(0.242731\pi\) | |||||||
\(468\) | −5.48126e8 | −0.247184 | ||||||||
\(469\) | −8.42831e8 | −0.377255 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.65366e9 | 1.61122 | ||||||||
\(472\) | 1.58118e9 | 0.692125 | ||||||||
\(473\) | 1.25120e9 | 0.543641 | ||||||||
\(474\) | 2.17950e8 | 0.0940010 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.60870e8 | 0.280861 | ||||||||
\(477\) | −4.99455e8 | −0.210709 | ||||||||
\(478\) | 9.18872e8 | 0.384820 | ||||||||
\(479\) | 1.47183e9 | 0.611906 | 0.305953 | − | 0.952047i | \(-0.401025\pi\) | ||||
0.305953 | + | 0.952047i | \(0.401025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.34397e9 | 0.960383 | ||||||||
\(482\) | −6.49832e8 | −0.264324 | ||||||||
\(483\) | −1.45352e9 | −0.586955 | ||||||||
\(484\) | 1.57030e9 | 0.629540 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.92743e8 | 0.155197 | ||||||||
\(487\) | −6.97309e8 | −0.273574 | −0.136787 | − | 0.990601i | \(-0.543678\pi\) | ||||
−0.136787 | + | 0.990601i | \(0.543678\pi\) | |||||||
\(488\) | 2.53578e9 | 0.987739 | ||||||||
\(489\) | 5.02965e9 | 1.94517 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.85732e8 | 0.299564 | 0.149782 | − | 0.988719i | \(-0.452143\pi\) | ||||
0.149782 | + | 0.988719i | \(0.452143\pi\) | |||||||
\(492\) | 1.07176e9 | 0.405713 | ||||||||
\(493\) | −3.43070e9 | −1.28949 | ||||||||
\(494\) | 5.06306e8 | 0.188960 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00697e9 | 0.370538 | ||||||||
\(497\) | 8.89407e8 | 0.324977 | ||||||||
\(498\) | 4.44709e8 | 0.161351 | ||||||||
\(499\) | −5.18713e9 | −1.86885 | −0.934427 | − | 0.356155i | \(-0.884088\pi\) | ||||
−0.934427 | + | 0.356155i | \(0.884088\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.38987e9 | 0.849068 | ||||||||
\(502\) | −1.28051e8 | −0.0451771 | ||||||||
\(503\) | 1.10364e9 | 0.386667 | 0.193334 | − | 0.981133i | \(-0.438070\pi\) | ||||
0.193334 | + | 0.981133i | \(0.438070\pi\) | |||||||
\(504\) | 1.63080e8 | 0.0567407 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.17265e8 | −0.246123 | ||||||||
\(507\) | −9.25664e8 | −0.315446 | ||||||||
\(508\) | −3.16748e9 | −1.07199 | ||||||||
\(509\) | −1.13819e9 | −0.382563 | −0.191282 | − | 0.981535i | \(-0.561264\pi\) | ||||
−0.191282 | + | 0.981535i | \(0.561264\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.81020e8 | 0.225781 | ||||||||
\(512\) | 3.07225e9 | 1.01161 | ||||||||
\(513\) | 1.32446e9 | 0.433141 | ||||||||
\(514\) | −1.03119e9 | −0.334940 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.11008e9 | 0.996546 | ||||||||
\(517\) | −2.96568e8 | −0.0943860 | ||||||||
\(518\) | −3.29278e8 | −0.104090 | ||||||||
\(519\) | −4.53278e9 | −1.42324 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.48972e8 | 0.170066 | 0.0850331 | − | 0.996378i | \(-0.472900\pi\) | ||||
0.0850331 | + | 0.996378i | \(0.472900\pi\) | |||||||
\(522\) | −3.99722e8 | −0.123002 | ||||||||
\(523\) | 5.67676e8 | 0.173518 | 0.0867590 | − | 0.996229i | \(-0.472349\pi\) | ||||
0.0867590 | + | 0.996229i | \(0.472349\pi\) | |||||||
\(524\) | 1.84218e9 | 0.559335 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.03823e7 | 0.0150948 | ||||||||
\(527\) | 1.48883e9 | 0.443106 | ||||||||
\(528\) | −1.42630e9 | −0.421690 | ||||||||
\(529\) | 3.19587e9 | 0.938630 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.46825e8 | −0.274435 | ||||||||
\(532\) | 6.03139e8 | 0.173671 | ||||||||
\(533\) | 1.61011e9 | 0.460585 | ||||||||
\(534\) | 3.60868e8 | 0.102554 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.18955e9 | −0.614156 | ||||||||
\(537\) | 7.73964e9 | 2.15680 | ||||||||
\(538\) | −5.88344e8 | −0.162890 | ||||||||
\(539\) | 2.82664e8 | 0.0777518 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.48367e9 | 0.945904 | 0.472952 | − | 0.881088i | \(-0.343188\pi\) | ||||
0.472952 | + | 0.881088i | \(0.343188\pi\) | |||||||
\(542\) | −6.17774e8 | −0.166660 | ||||||||
\(543\) | −7.56771e9 | −2.02845 | ||||||||
\(544\) | 2.62307e9 | 0.698575 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.89810e8 | 0.155074 | ||||||||
\(547\) | 3.85021e8 | 0.100584 | 0.0502920 | − | 0.998735i | \(-0.483985\pi\) | ||||
0.0502920 | + | 0.998735i | \(0.483985\pi\) | |||||||
\(548\) | 1.94436e9 | 0.504713 | ||||||||
\(549\) | −1.51845e9 | −0.391649 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.13101e9 | −0.797359 | ||||||||
\(552\) | −3.77603e9 | −0.955539 | ||||||||
\(553\) | 3.90048e8 | 0.0980800 | ||||||||
\(554\) | −1.53276e9 | −0.382992 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.79012e9 | −0.935170 | ||||||||
\(557\) | −6.31036e9 | −1.54725 | −0.773626 | − | 0.633643i | \(-0.781559\pi\) | ||||
−0.773626 | + | 0.633643i | \(0.781559\pi\) | |||||||
\(558\) | 1.73468e8 | 0.0422668 | ||||||||
\(559\) | 4.67228e9 | 1.13133 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.10881e9 | −0.504276 | ||||||||
\(562\) | 1.55509e8 | 0.0369555 | ||||||||
\(563\) | 5.61957e9 | 1.32716 | 0.663581 | − | 0.748105i | \(-0.269036\pi\) | ||||
0.663581 | + | 0.748105i | \(0.269036\pi\) | |||||||
\(564\) | −7.37173e8 | −0.173018 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.59181e9 | −0.369005 | ||||||||
\(567\) | 1.94316e9 | 0.447681 | ||||||||
\(568\) | 2.31055e9 | 0.529050 | ||||||||
\(569\) | −6.15281e9 | −1.40017 | −0.700085 | − | 0.714059i | \(-0.746855\pi\) | ||||
−0.700085 | + | 0.714059i | \(0.746855\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.39916e9 | −1.66324 | −0.831622 | − | 0.555342i | \(-0.812587\pi\) | ||||
−0.831622 | + | 0.555342i | \(0.812587\pi\) | |||||||
\(572\) | −2.46812e9 | −0.551416 | ||||||||
\(573\) | −8.91160e9 | −1.97886 | ||||||||
\(574\) | −2.26186e8 | −0.0499199 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.71710e8 | −0.102848 | ||||||||
\(577\) | −5.93377e9 | −1.28592 | −0.642962 | − | 0.765898i | \(-0.722295\pi\) | ||||
−0.642962 | + | 0.765898i | \(0.722295\pi\) | |||||||
\(578\) | −4.67279e8 | −0.100653 | ||||||||
\(579\) | −3.51466e8 | −0.0752503 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.95861e8 | 0.168353 | ||||||||
\(582\) | −1.08649e9 | −0.228452 | ||||||||
\(583\) | −2.24896e9 | −0.470047 | ||||||||
\(584\) | 1.76919e9 | 0.367562 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.75643e9 | −0.565855 | ||||||||
\(587\) | −8.51343e9 | −1.73729 | −0.868643 | − | 0.495439i | \(-0.835007\pi\) | ||||
−0.868643 | + | 0.495439i | \(0.835007\pi\) | |||||||
\(588\) | 7.02613e8 | 0.142526 | ||||||||
\(589\) | 1.35877e9 | 0.273995 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.81487e9 | 1.15873 | ||||||||
\(592\) | 2.97348e9 | 0.589032 | ||||||||
\(593\) | 3.13459e9 | 0.617290 | 0.308645 | − | 0.951177i | \(-0.400125\pi\) | ||||
0.308645 | + | 0.951177i | \(0.400125\pi\) | |||||||
\(594\) | 7.61375e8 | 0.149055 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.29749e9 | −1.41192 | ||||||||
\(597\) | 8.23403e9 | 1.58381 | ||||||||
\(598\) | −2.67844e9 | −0.512186 | ||||||||
\(599\) | −4.23565e9 | −0.805241 | −0.402620 | − | 0.915367i | \(-0.631901\pi\) | ||||
−0.402620 | + | 0.915367i | \(0.631901\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.04662e10 | −1.96666 | −0.983328 | − | 0.181843i | \(-0.941794\pi\) | ||||
−0.983328 | + | 0.181843i | \(0.941794\pi\) | |||||||
\(602\) | −6.56355e8 | −0.122617 | ||||||||
\(603\) | 1.31112e9 | 0.243519 | ||||||||
\(604\) | 1.12660e9 | 0.208036 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.34735e8 | 0.170622 | ||||||||
\(607\) | 7.13282e9 | 1.29450 | 0.647248 | − | 0.762279i | \(-0.275920\pi\) | ||||
0.647248 | + | 0.762279i | \(0.275920\pi\) | |||||||
\(608\) | 2.39393e9 | 0.431965 | ||||||||
\(609\) | −3.64740e9 | −0.654369 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.10746e9 | −0.196419 | ||||||||
\(612\) | −1.02806e9 | −0.181297 | ||||||||
\(613\) | −4.63327e9 | −0.812412 | −0.406206 | − | 0.913782i | \(-0.633148\pi\) | ||||
−0.406206 | + | 0.913782i | \(0.633148\pi\) | |||||||
\(614\) | −1.98674e9 | −0.346379 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.34322e8 | 0.126577 | ||||||||
\(617\) | 5.02424e9 | 0.861137 | 0.430568 | − | 0.902558i | \(-0.358313\pi\) | ||||
0.430568 | + | 0.902558i | \(0.358313\pi\) | |||||||
\(618\) | −3.57944e9 | −0.610035 | ||||||||
\(619\) | 5.70730e9 | 0.967194 | 0.483597 | − | 0.875291i | \(-0.339330\pi\) | ||||
0.483597 | + | 0.875291i | \(0.339330\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.00663e9 | −1.17406 | ||||||||
\(622\) | −1.70430e9 | −0.283974 | ||||||||
\(623\) | 6.45819e8 | 0.107005 | ||||||||
\(624\) | −5.32617e9 | −0.877544 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.68631e9 | −0.437670 | ||||||||
\(627\) | −1.92460e9 | −0.311819 | ||||||||
\(628\) | 8.02037e9 | 1.29222 | ||||||||
\(629\) | 4.39634e9 | 0.704392 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.74258e9 | 1.54373 | 0.771865 | − | 0.635787i | \(-0.219324\pi\) | ||||
0.771865 | + | 0.635787i | \(0.219324\pi\) | |||||||
\(632\) | 1.01329e9 | 0.159670 | ||||||||
\(633\) | −4.79764e9 | −0.751822 | ||||||||
\(634\) | 2.67999e9 | 0.417659 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.59019e9 | −0.861641 | ||||||||
\(637\) | 1.05554e9 | 0.161803 | ||||||||
\(638\) | −1.79988e9 | −0.274391 | ||||||||
\(639\) | −1.38358e9 | −0.209774 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.95897e9 | −1.04362 | −0.521809 | − | 0.853062i | \(-0.674743\pi\) | ||||
−0.521809 | + | 0.853062i | \(0.674743\pi\) | |||||||
\(642\) | −1.56733e9 | −0.233769 | ||||||||
\(643\) | −4.05867e9 | −0.602067 | −0.301034 | − | 0.953613i | \(-0.597332\pi\) | ||||
−0.301034 | + | 0.953613i | \(0.597332\pi\) | |||||||
\(644\) | −3.19070e9 | −0.470745 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.49626e8 | 0.138592 | ||||||||
\(647\) | 1.06287e9 | 0.154282 | 0.0771411 | − | 0.997020i | \(-0.475421\pi\) | ||||
0.0771411 | + | 0.997020i | \(0.475421\pi\) | |||||||
\(648\) | 5.04806e9 | 0.728806 | ||||||||
\(649\) | −4.26339e9 | −0.612207 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.58287e9 | 0.224859 | ||||||||
\(652\) | 1.10409e10 | 1.56005 | ||||||||
\(653\) | −4.15262e9 | −0.583615 | −0.291807 | − | 0.956477i | \(-0.594257\pi\) | ||||
−0.291807 | + | 0.956477i | \(0.594257\pi\) | |||||||
\(654\) | 2.31524e9 | 0.323649 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.04253e9 | 0.282491 | ||||||||
\(657\) | −1.05941e9 | −0.145742 | ||||||||
\(658\) | 1.55574e8 | 0.0212886 | ||||||||
\(659\) | 1.98297e9 | 0.269909 | 0.134954 | − | 0.990852i | \(-0.456911\pi\) | ||||
0.134954 | + | 0.990852i | \(0.456911\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.36180e9 | −0.318081 | −0.159041 | − | 0.987272i | \(-0.550840\pi\) | ||||
−0.159041 | + | 0.987272i | \(0.550840\pi\) | |||||||
\(662\) | −3.62833e8 | −0.0486076 | ||||||||
\(663\) | −7.87483e9 | −1.04941 | ||||||||
\(664\) | 2.06754e9 | 0.274072 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.12231e8 | 0.0671902 | ||||||||
\(667\) | 1.65635e10 | 2.16129 | ||||||||
\(668\) | 5.24616e9 | 0.680963 | ||||||||
\(669\) | −3.29700e9 | −0.425723 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.83731e9 | −0.873688 | ||||||||
\(672\) | 2.78875e9 | 0.354501 | ||||||||
\(673\) | −5.23236e9 | −0.661676 | −0.330838 | − | 0.943688i | \(-0.607331\pi\) | ||||
−0.330838 | + | 0.943688i | \(0.607331\pi\) | |||||||
\(674\) | −3.40542e8 | −0.0428411 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.03198e9 | −0.252992 | ||||||||
\(677\) | −5.54225e9 | −0.686476 | −0.343238 | − | 0.939248i | \(-0.611524\pi\) | ||||
−0.343238 | + | 0.939248i | \(0.611524\pi\) | |||||||
\(678\) | −2.07835e9 | −0.256103 | ||||||||
\(679\) | −1.94441e9 | −0.238366 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.01885e9 | 1.09430 | ||||||||
\(682\) | 7.81096e8 | 0.0942886 | ||||||||
\(683\) | 2.76485e9 | 0.332047 | 0.166024 | − | 0.986122i | \(-0.446907\pi\) | ||||
0.166024 | + | 0.986122i | \(0.446907\pi\) | |||||||
\(684\) | −9.38255e8 | −0.112105 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.48280e8 | −0.0175368 | ||||||||
\(687\) | 1.77592e10 | 2.08966 | ||||||||
\(688\) | 5.92710e9 | 0.693877 | ||||||||
\(689\) | −8.39816e9 | −0.978176 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.20041e10 | 1.38406 | 0.692030 | − | 0.721868i | \(-0.256716\pi\) | ||||
0.692030 | + | 0.721868i | \(0.256716\pi\) | |||||||
\(692\) | −9.95019e9 | −1.14146 | ||||||||
\(693\) | −4.39718e8 | −0.0501890 | ||||||||
\(694\) | −5.22104e8 | −0.0592923 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.47542e9 | −1.06529 | ||||||||
\(697\) | 3.01991e9 | 0.337815 | ||||||||
\(698\) | 2.87401e9 | 0.319885 | ||||||||
\(699\) | 4.69727e9 | 0.520206 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.26875e10 | 1.39111 | 0.695557 | − | 0.718471i | \(-0.255158\pi\) | ||||
0.695557 | + | 0.718471i | \(0.255158\pi\) | |||||||
\(702\) | 2.84316e9 | 0.310186 | ||||||||
\(703\) | 4.01229e9 | 0.435561 | ||||||||
\(704\) | −2.12403e9 | −0.229433 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.11177e9 | 0.225856 | ||||||||
\(707\) | 1.67282e9 | 0.178026 | ||||||||
\(708\) | −1.05974e10 | −1.12223 | ||||||||
\(709\) | 1.72658e10 | 1.81939 | 0.909694 | − | 0.415280i | \(-0.136316\pi\) | ||||
0.909694 | + | 0.415280i | \(0.136316\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.06767e8 | −0.0633109 | ||||||||
\(712\) | 1.67775e9 | 0.174199 | ||||||||
\(713\) | −7.18811e9 | −0.742680 | ||||||||
\(714\) | 1.10624e9 | 0.113738 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.69898e10 | 1.72978 | ||||||||
\(717\) | −1.30432e10 | −1.32150 | ||||||||
\(718\) | −5.25339e9 | −0.529668 | ||||||||
\(719\) | −1.23080e10 | −1.23491 | −0.617455 | − | 0.786606i | \(-0.711836\pi\) | ||||
−0.617455 | + | 0.786606i | \(0.711836\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.40585e9 | −0.636507 | ||||||||
\(722\) | −2.41789e9 | −0.239087 | ||||||||
\(723\) | 9.22423e9 | 0.907708 | ||||||||
\(724\) | −1.66124e10 | −1.62684 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.62855e9 | 0.254940 | ||||||||
\(727\) | −1.18757e10 | −1.14628 | −0.573138 | − | 0.819459i | \(-0.694274\pi\) | ||||
−0.573138 | + | 0.819459i | \(0.694274\pi\) | |||||||
\(728\) | 2.74214e9 | 0.263408 | ||||||||
\(729\) | 6.81488e9 | 0.651496 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.76331e9 | 0.829769 | ||||||||
\(732\) | −1.69953e10 | −1.60155 | ||||||||
\(733\) | 3.88675e9 | 0.364521 | 0.182261 | − | 0.983250i | \(-0.441659\pi\) | ||||
0.182261 | + | 0.983250i | \(0.441659\pi\) | |||||||
\(734\) | 3.21682e9 | 0.300255 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.26643e10 | −1.17087 | ||||||||
\(737\) | 5.90376e9 | 0.543241 | ||||||||
\(738\) | 3.51859e8 | 0.0322234 | ||||||||
\(739\) | 1.21007e10 | 1.10295 | 0.551474 | − | 0.834192i | \(-0.314065\pi\) | ||||
0.551474 | + | 0.834192i | \(0.314065\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.18691e9 | −0.648901 | ||||||||
\(742\) | 1.17976e9 | 0.106018 | ||||||||
\(743\) | 1.18364e10 | 1.05867 | 0.529333 | − | 0.848414i | \(-0.322442\pi\) | ||||
0.529333 | + | 0.848414i | \(0.322442\pi\) | |||||||
\(744\) | 4.11207e9 | 0.366062 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.69474e9 | 0.237646 | ||||||||
\(747\) | −1.23806e9 | −0.108672 | ||||||||
\(748\) | −4.62919e9 | −0.404436 | ||||||||
\(749\) | −2.80493e9 | −0.243913 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.53011e8 | 0.0734877 | 0.0367439 | − | 0.999325i | \(-0.488301\pi\) | ||||
0.0367439 | + | 0.999325i | \(0.488301\pi\) | |||||||
\(752\) | −1.40488e9 | −0.120470 | ||||||||
\(753\) | 1.81765e9 | 0.155142 | ||||||||
\(754\) | −6.72118e9 | −0.571013 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.38693e9 | 0.285088 | ||||||||
\(757\) | 8.40844e9 | 0.704498 | 0.352249 | − | 0.935906i | \(-0.385417\pi\) | ||||
0.352249 | + | 0.935906i | \(0.385417\pi\) | |||||||
\(758\) | 2.96511e9 | 0.247286 | ||||||||
\(759\) | 1.01814e10 | 0.845205 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.78648e9 | −0.393704 | −0.196852 | − | 0.980433i | \(-0.563072\pi\) | ||||
−0.196852 | + | 0.980433i | \(0.563072\pi\) | |||||||
\(762\) | −5.30211e9 | −0.434117 | ||||||||
\(763\) | 4.14341e9 | 0.337693 | ||||||||
\(764\) | −1.95624e10 | −1.58707 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.97825e8 | −0.0159030 | ||||||||
\(767\) | −1.59205e10 | −1.27401 | ||||||||
\(768\) | −1.45557e9 | −0.115950 | ||||||||
\(769\) | 1.23304e10 | 0.977764 | 0.488882 | − | 0.872350i | \(-0.337405\pi\) | ||||
0.488882 | + | 0.872350i | \(0.337405\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.46375e10 | 1.15021 | ||||||||
\(772\) | −7.71525e8 | −0.0603517 | ||||||||
\(773\) | 1.65741e10 | 1.29063 | 0.645314 | − | 0.763917i | \(-0.276726\pi\) | ||||
0.645314 | + | 0.763917i | \(0.276726\pi\) | |||||||
\(774\) | 1.02104e9 | 0.0791497 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.05130e9 | −0.388050 | ||||||||
\(777\) | 4.67403e9 | 0.357452 | ||||||||
\(778\) | 3.74251e9 | 0.284927 | ||||||||
\(779\) | 2.75610e9 | 0.208888 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.23001e9 | −0.467962 | ||||||||
\(782\) | −5.02367e9 | −0.375662 | ||||||||
\(783\) | −1.75822e10 | −1.30890 | ||||||||
\(784\) | 1.33902e9 | 0.0992386 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.08366e9 | 0.226510 | ||||||||
\(787\) | −1.49363e10 | −1.09227 | −0.546137 | − | 0.837696i | \(-0.683902\pi\) | ||||
−0.546137 | + | 0.837696i | \(0.683902\pi\) | |||||||
\(788\) | 1.27646e10 | 0.929319 | ||||||||
\(789\) | −7.15166e8 | −0.0518367 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.71947e9 | −0.267216 | ||||||||
\(792\) | −1.14233e9 | −0.0817056 | ||||||||
\(793\) | −2.55322e10 | −1.81816 | ||||||||
\(794\) | −7.08884e9 | −0.502578 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.80750e10 | 1.27023 | ||||||||
\(797\) | −1.31070e10 | −0.917064 | −0.458532 | − | 0.888678i | \(-0.651625\pi\) | ||||
−0.458532 | + | 0.888678i | \(0.651625\pi\) | |||||||
\(798\) | 1.00961e9 | 0.0703303 | ||||||||
\(799\) | −2.07714e9 | −0.144063 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.00465e9 | −0.0690718 | ||||||||
\(802\) | −8.61995e9 | −0.590057 | ||||||||
\(803\) | −4.77033e9 | −0.325120 | ||||||||
\(804\) | 1.46749e10 | 0.995813 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.91680e9 | 0.196216 | ||||||||
\(807\) | 8.35142e9 | 0.559375 | ||||||||
\(808\) | 4.34576e9 | 0.289819 | ||||||||
\(809\) | 5.11703e8 | 0.0339780 | 0.0169890 | − | 0.999856i | \(-0.494592\pi\) | ||||
0.0169890 | + | 0.999856i | \(0.494592\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.98145e9 | 0.459592 | 0.229796 | − | 0.973239i | \(-0.426194\pi\) | ||||
0.229796 | + | 0.973239i | \(0.426194\pi\) | |||||||
\(812\) | −8.00663e9 | −0.524812 | ||||||||
\(813\) | 8.76917e9 | 0.572324 | ||||||||
\(814\) | 2.30649e9 | 0.149888 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −9.98974e9 | −0.643633 | ||||||||
\(817\) | 7.99778e9 | 0.513088 | ||||||||
\(818\) | 7.18803e9 | 0.459170 | ||||||||
\(819\) | −1.64202e9 | −0.104444 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.37608e10 | 0.867848 | 0.433924 | − | 0.900950i | \(-0.357129\pi\) | ||||
0.433924 | + | 0.900950i | \(0.357129\pi\) | |||||||
\(822\) | 3.25470e9 | 0.204390 | ||||||||
\(823\) | 1.36525e10 | 0.853716 | 0.426858 | − | 0.904319i | \(-0.359620\pi\) | ||||
0.426858 | + | 0.904319i | \(0.359620\pi\) | |||||||
\(824\) | −1.66415e10 | −1.03621 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.23650e9 | 0.138082 | ||||||||
\(827\) | −2.97475e10 | −1.82887 | −0.914433 | − | 0.404737i | \(-0.867363\pi\) | ||||
−0.914433 | + | 0.404737i | \(0.867363\pi\) | |||||||
\(828\) | 4.96352e9 | 0.303867 | ||||||||
\(829\) | 2.10898e10 | 1.28567 | 0.642837 | − | 0.766003i | \(-0.277757\pi\) | ||||
0.642837 | + | 0.766003i | \(0.277757\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.17572e10 | 1.31522 | ||||||||
\(832\) | −7.93164e9 | −0.477454 | ||||||||
\(833\) | 1.97976e9 | 0.118674 | ||||||||
\(834\) | −6.34436e9 | −0.378710 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.22480e9 | −0.250083 | ||||||||
\(837\) | 7.63017e9 | 0.449775 | ||||||||
\(838\) | −1.00227e10 | −0.588345 | ||||||||
\(839\) | 2.12030e10 | 1.23945 | 0.619727 | − | 0.784817i | \(-0.287243\pi\) | ||||
0.619727 | + | 0.784817i | \(0.287243\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.43141e10 | 1.40952 | ||||||||
\(842\) | 5.48251e9 | 0.316510 | ||||||||
\(843\) | −2.20742e9 | −0.126908 | ||||||||
\(844\) | −1.05316e10 | −0.602970 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.42014e8 | −0.0137418 | ||||||||
\(847\) | 4.70412e9 | 0.266003 | ||||||||
\(848\) | −1.06536e10 | −0.599945 | ||||||||
\(849\) | 2.25954e10 | 1.26719 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.12257e10 | −1.18061 | ||||||||
\(852\) | −1.54858e10 | −0.857819 | ||||||||
\(853\) | −3.82463e9 | −0.210993 | −0.105496 | − | 0.994420i | \(-0.533643\pi\) | ||||
−0.105496 | + | 0.994420i | \(0.533643\pi\) | |||||||
\(854\) | 3.58672e9 | 0.197059 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.28680e9 | −0.397081 | ||||||||
\(857\) | −1.02342e10 | −0.555417 | −0.277708 | − | 0.960665i | \(-0.589575\pi\) | ||||
−0.277708 | + | 0.960665i | \(0.589575\pi\) | |||||||
\(858\) | −4.13143e9 | −0.223303 | ||||||||
\(859\) | 1.61175e10 | 0.867603 | 0.433801 | − | 0.901009i | \(-0.357172\pi\) | ||||
0.433801 | + | 0.901009i | \(0.357172\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.21066e9 | 0.171428 | ||||||||
\(862\) | 7.34930e9 | 0.390815 | ||||||||
\(863\) | 3.16724e10 | 1.67742 | 0.838712 | − | 0.544575i | \(-0.183309\pi\) | ||||
0.838712 | + | 0.544575i | \(0.183309\pi\) | |||||||
\(864\) | 1.34431e10 | 0.709089 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.41387e9 | 0.126300 | ||||||||
\(867\) | 6.63293e9 | 0.345651 | ||||||||
\(868\) | 3.47465e9 | 0.180340 | ||||||||
\(869\) | −2.73217e9 | −0.141234 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.20461e10 | 1.13049 | ||||||||
\(872\) | 1.07640e10 | 0.549751 | ||||||||
\(873\) | 3.02477e9 | 0.153866 | ||||||||
\(874\) | −4.58482e9 | −0.232291 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.18575e10 | −0.595977 | ||||||||
\(877\) | 3.49078e10 | 1.74753 | 0.873764 | − | 0.486350i | \(-0.161672\pi\) | ||||
0.873764 | + | 0.486350i | \(0.161672\pi\) | |||||||
\(878\) | 3.94089e9 | 0.196500 | ||||||||
\(879\) | 3.91270e10 | 1.94319 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.20797e9 | −0.256598 | −0.128299 | − | 0.991736i | \(-0.540952\pi\) | ||||
−0.128299 | + | 0.991736i | \(0.540952\pi\) | |||||||
\(882\) | 2.30668e8 | 0.0113200 | ||||||||
\(883\) | 1.95840e9 | 0.0957278 | 0.0478639 | − | 0.998854i | \(-0.484759\pi\) | ||||
0.0478639 | + | 0.998854i | \(0.484759\pi\) | |||||||
\(884\) | −1.72865e10 | −0.841637 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.42591e9 | 0.310396 | ||||||||
\(887\) | 1.80819e10 | 0.869985 | 0.434992 | − | 0.900434i | \(-0.356751\pi\) | ||||
0.434992 | + | 0.900434i | \(0.356751\pi\) | |||||||
\(888\) | 1.21425e10 | 0.581917 | ||||||||
\(889\) | −9.48879e9 | −0.452955 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.36112e10 | −0.644653 | ||||||||
\(892\) | −7.23744e9 | −0.341435 | ||||||||
\(893\) | −1.89569e9 | −0.0890815 | ||||||||
\(894\) | −1.22154e10 | −0.571778 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7.95789e9 | 0.369590 | ||||||||
\(897\) | 3.80199e10 | 1.75889 | ||||||||
\(898\) | −6.11398e9 | −0.281745 | ||||||||
\(899\) | −1.80376e10 | −0.827979 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.57516e10 | −0.717442 | ||||||||
\(902\) | 1.58436e9 | 0.0718838 | ||||||||
\(903\) | 9.31683e9 | 0.421076 | ||||||||
\(904\) | −9.66264e9 | −0.435017 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.88583e9 | 0.0842471 | ||||||||
\(907\) | 1.32060e10 | 0.587688 | 0.293844 | − | 0.955853i | \(-0.405065\pi\) | ||||
0.293844 | + | 0.955853i | \(0.405065\pi\) | |||||||
\(908\) | 1.97978e10 | 0.877642 | ||||||||
\(909\) | −2.60228e9 | −0.114916 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.83495e9 | −0.299517 | −0.149758 | − | 0.988723i | \(-0.547850\pi\) | ||||
−0.149758 | + | 0.988723i | \(0.547850\pi\) | |||||||
\(912\) | −9.11707e9 | −0.397991 | ||||||||
\(913\) | −5.57476e9 | −0.242426 | ||||||||
\(914\) | −9.16343e9 | −0.396959 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.89844e10 | 1.67593 | ||||||||
\(917\) | 5.51859e9 | 0.236339 | ||||||||
\(918\) | 5.33262e9 | 0.227505 | ||||||||
\(919\) | −3.96347e10 | −1.68450 | −0.842251 | − | 0.539086i | \(-0.818770\pi\) | ||||
−0.842251 | + | 0.539086i | \(0.818770\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.82013e10 | 1.18949 | ||||||||
\(922\) | −1.45739e10 | −0.612375 | ||||||||
\(923\) | −2.32644e10 | −0.973836 | ||||||||
\(924\) | −4.92158e9 | −0.205236 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.24491e10 | 0.515227 | ||||||||
\(927\) | 9.96506e9 | 0.410867 | ||||||||
\(928\) | −3.17792e10 | −1.30534 | ||||||||
\(929\) | −2.44116e10 | −0.998944 | −0.499472 | − | 0.866330i | \(-0.666473\pi\) | ||||
−0.499472 | + | 0.866330i | \(0.666473\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.80682e9 | 0.0733821 | ||||||||
\(932\) | 1.03113e10 | 0.417212 | ||||||||
\(933\) | 2.41922e10 | 0.975189 | ||||||||
\(934\) | 1.16955e10 | 0.469685 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.26573e9 | −0.170031 | ||||||||
\(937\) | 5.38252e8 | 0.0213745 | 0.0106873 | − | 0.999943i | \(-0.496598\pi\) | ||||
0.0106873 | + | 0.999943i | \(0.496598\pi\) | |||||||
\(938\) | −3.09701e9 | −0.122527 | ||||||||
\(939\) | 3.81316e10 | 1.50299 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.81189e10 | −1.10010 | −0.550052 | − | 0.835130i | \(-0.685392\pi\) | ||||
−0.550052 | + | 0.835130i | \(0.685392\pi\) | |||||||
\(942\) | 1.34255e10 | 0.523301 | ||||||||
\(943\) | −1.45802e10 | −0.566204 | ||||||||
\(944\) | −2.01963e10 | −0.781392 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.59756e9 | 0.176567 | ||||||||
\(947\) | −4.48215e10 | −1.71499 | −0.857495 | − | 0.514492i | \(-0.827980\pi\) | ||||
−0.857495 | + | 0.514492i | \(0.827980\pi\) | |||||||
\(948\) | −6.79129e9 | −0.258895 | ||||||||
\(949\) | −1.78136e10 | −0.676581 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.80419e10 | −1.43427 | ||||||||
\(952\) | 5.14314e9 | 0.193196 | ||||||||
\(953\) | −2.41425e9 | −0.0903561 | −0.0451780 | − | 0.998979i | \(-0.514386\pi\) | ||||
−0.0451780 | + | 0.998979i | \(0.514386\pi\) | |||||||
\(954\) | −1.83526e9 | −0.0684351 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.86319e10 | −1.05986 | ||||||||
\(957\) | 2.55489e10 | 0.942280 | ||||||||
\(958\) | 5.40830e9 | 0.198738 | ||||||||
\(959\) | 5.82470e9 | 0.213259 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.96848e10 | −0.715483 | ||||||||
\(962\) | 8.61299e9 | 0.311918 | ||||||||
\(963\) | 4.36340e9 | 0.157447 | ||||||||
\(964\) | 2.02487e10 | 0.727993 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.34098e9 | −0.190634 | ||||||||
\(967\) | −4.34362e10 | −1.54475 | −0.772377 | − | 0.635164i | \(-0.780932\pi\) | ||||
−0.772377 | + | 0.635164i | \(0.780932\pi\) | |||||||
\(968\) | 1.22206e10 | 0.433042 | ||||||||
\(969\) | −1.34797e10 | −0.475936 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.21172e10 | −1.47636 | −0.738180 | − | 0.674604i | \(-0.764314\pi\) | ||||
−0.738180 | + | 0.674604i | \(0.764314\pi\) | |||||||
\(972\) | −1.22378e10 | −0.427438 | ||||||||
\(973\) | −1.13540e10 | −0.395143 | ||||||||
\(974\) | −2.56228e9 | −0.0888527 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.23892e10 | −1.11513 | ||||||||
\(977\) | −3.57143e10 | −1.22521 | −0.612606 | − | 0.790389i | \(-0.709879\pi\) | ||||
−0.612606 | + | 0.790389i | \(0.709879\pi\) | |||||||
\(978\) | 1.84816e10 | 0.631762 | ||||||||
\(979\) | −4.52376e9 | −0.154085 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.44558e9 | −0.217982 | ||||||||
\(982\) | 2.88719e9 | 0.0972940 | ||||||||
\(983\) | −2.72118e10 | −0.913735 | −0.456868 | − | 0.889535i | \(-0.651029\pi\) | ||||
−0.456868 | + | 0.889535i | \(0.651029\pi\) | |||||||
\(984\) | 8.34083e9 | 0.279079 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.26062e10 | −0.418809 | ||||||||
\(987\) | −2.20834e9 | −0.0731065 | ||||||||
\(988\) | −1.57764e10 | −0.520427 | ||||||||
\(989\) | −4.23095e10 | −1.39076 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.43790e10 | 1.12211 | 0.561055 | − | 0.827778i | \(-0.310396\pi\) | ||||
0.561055 | + | 0.827778i | \(0.310396\pi\) | |||||||
\(992\) | 1.37913e10 | 0.448553 | ||||||||
\(993\) | 5.15034e9 | 0.166922 | ||||||||
\(994\) | 3.26815e9 | 0.105548 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.38571e10 | −0.444389 | ||||||||
\(997\) | 4.40554e10 | 1.40788 | 0.703940 | − | 0.710259i | \(-0.251422\pi\) | ||||
0.703940 | + | 0.710259i | \(0.251422\pi\) | |||||||
\(998\) | −1.90603e10 | −0.606977 | ||||||||
\(999\) | 2.25310e10 | 0.714993 |
(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 | 175.8.a.h.1.4 | yes | 6 | |
5.2 | odd | 4 | 175.8.b.g.99.7 | 12 | |||
5.3 | odd | 4 | 175.8.b.g.99.6 | 12 | |||
5.4 | even | 2 | 175.8.a.g.1.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.8.a.g.1.3 | ✓ | 6 | 5.4 | even | 2 | ||
175.8.a.h.1.4 | yes | 6 | 1.1 | even | 1 | trivial | |
175.8.b.g.99.6 | 12 | 5.3 | odd | 4 | |||
175.8.b.g.99.7 | 12 | 5.2 | odd | 4 |