Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,10,Mod(1,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.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: | \(50.4735119441\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{4817})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 2411x^{2} + 2412x + 1444802 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 3^{2}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(33.7881\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.0000 | −0.707107 | ||||||||
\(3\) | −102.682 | −0.731893 | −0.365946 | − | 0.930636i | \(-0.619255\pi\) | ||||
−0.365946 | + | 0.930636i | \(0.619255\pi\) | |||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | 2094.80 | 1.49892 | 0.749459 | − | 0.662051i | \(-0.230314\pi\) | ||||
0.749459 | + | 0.662051i | \(0.230314\pi\) | |||||||
\(6\) | 1642.91 | 0.517526 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | −9139.47 | −0.464333 | ||||||||
\(10\) | −33516.8 | −1.05990 | ||||||||
\(11\) | 56314.4 | 1.15972 | 0.579859 | − | 0.814717i | \(-0.303108\pi\) | ||||
0.579859 | + | 0.814717i | \(0.303108\pi\) | |||||||
\(12\) | −26286.5 | −0.365946 | ||||||||
\(13\) | −124915. | −1.21302 | −0.606510 | − | 0.795076i | \(-0.707431\pi\) | ||||
−0.606510 | + | 0.795076i | \(0.707431\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −215098. | −1.09705 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | −388641. | −1.12857 | −0.564285 | − | 0.825580i | \(-0.690848\pi\) | ||||
−0.564285 | + | 0.825580i | \(0.690848\pi\) | |||||||
\(18\) | 146232. | 0.328333 | ||||||||
\(19\) | 246657. | 0.434212 | 0.217106 | − | 0.976148i | \(-0.430338\pi\) | ||||
0.217106 | + | 0.976148i | \(0.430338\pi\) | |||||||
\(20\) | 536269. | 0.749459 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −901030. | −0.820044 | ||||||||
\(23\) | −1.71777e6 | −1.27994 | −0.639971 | − | 0.768399i | \(-0.721054\pi\) | ||||
−0.639971 | + | 0.768399i | \(0.721054\pi\) | |||||||
\(24\) | 420584. | 0.258763 | ||||||||
\(25\) | 2.43507e6 | 1.24676 | ||||||||
\(26\) | 1.99863e6 | 0.857735 | ||||||||
\(27\) | 2.95954e6 | 1.07173 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.75179e6 | 1.51012 | 0.755061 | − | 0.655654i | \(-0.227607\pi\) | ||||
0.755061 | + | 0.655654i | \(0.227607\pi\) | |||||||
\(30\) | 3.44156e6 | 0.775729 | ||||||||
\(31\) | 5.26785e6 | 1.02449 | 0.512243 | − | 0.858841i | \(-0.328815\pi\) | ||||
0.512243 | + | 0.858841i | \(0.328815\pi\) | |||||||
\(32\) | −1.04858e6 | −0.176777 | ||||||||
\(33\) | −5.78246e6 | −0.848789 | ||||||||
\(34\) | 6.21825e6 | 0.798019 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.33970e6 | −0.232167 | ||||||||
\(37\) | −1.23415e7 | −1.08258 | −0.541290 | − | 0.840836i | \(-0.682064\pi\) | ||||
−0.541290 | + | 0.840836i | \(0.682064\pi\) | |||||||
\(38\) | −3.94651e6 | −0.307035 | ||||||||
\(39\) | 1.28264e7 | 0.887801 | ||||||||
\(40\) | −8.58031e6 | −0.529948 | ||||||||
\(41\) | 5.54285e6 | 0.306342 | 0.153171 | − | 0.988200i | \(-0.451052\pi\) | ||||
0.153171 | + | 0.988200i | \(0.451052\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.78833e6 | −0.258193 | −0.129097 | − | 0.991632i | \(-0.541208\pi\) | ||||
−0.129097 | + | 0.991632i | \(0.541208\pi\) | |||||||
\(44\) | 1.44165e7 | 0.579859 | ||||||||
\(45\) | −1.91454e7 | −0.695997 | ||||||||
\(46\) | 2.74843e7 | 0.905055 | ||||||||
\(47\) | −5.11932e7 | −1.53028 | −0.765142 | − | 0.643861i | \(-0.777331\pi\) | ||||
−0.765142 | + | 0.643861i | \(0.777331\pi\) | |||||||
\(48\) | −6.72935e6 | −0.182973 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.89611e7 | −0.881589 | ||||||||
\(51\) | 3.99063e7 | 0.825991 | ||||||||
\(52\) | −3.19782e7 | −0.606510 | ||||||||
\(53\) | −8.14372e7 | −1.41769 | −0.708845 | − | 0.705364i | \(-0.750783\pi\) | ||||
−0.708845 | + | 0.705364i | \(0.750783\pi\) | |||||||
\(54\) | −4.73526e7 | −0.757831 | ||||||||
\(55\) | 1.17967e8 | 1.73832 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.53272e7 | −0.317797 | ||||||||
\(58\) | −9.20287e7 | −1.06782 | ||||||||
\(59\) | 7.85852e7 | 0.844319 | 0.422160 | − | 0.906522i | \(-0.361272\pi\) | ||||
0.422160 | + | 0.906522i | \(0.361272\pi\) | |||||||
\(60\) | −5.50650e7 | −0.548523 | ||||||||
\(61\) | −1.38027e7 | −0.127638 | −0.0638188 | − | 0.997962i | \(-0.520328\pi\) | ||||
−0.0638188 | + | 0.997962i | \(0.520328\pi\) | |||||||
\(62\) | −8.42856e7 | −0.724421 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | −2.61671e8 | −1.81822 | ||||||||
\(66\) | 9.25193e7 | 0.600184 | ||||||||
\(67\) | −1.01717e8 | −0.616678 | −0.308339 | − | 0.951276i | \(-0.599773\pi\) | ||||
−0.308339 | + | 0.951276i | \(0.599773\pi\) | |||||||
\(68\) | −9.94920e7 | −0.564285 | ||||||||
\(69\) | 1.76384e8 | 0.936780 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.75670e8 | −1.75446 | −0.877232 | − | 0.480067i | \(-0.840612\pi\) | ||||
−0.877232 | + | 0.480067i | \(0.840612\pi\) | |||||||
\(72\) | 3.74353e7 | 0.164167 | ||||||||
\(73\) | 4.45945e8 | 1.83793 | 0.918964 | − | 0.394341i | \(-0.129027\pi\) | ||||
0.918964 | + | 0.394341i | \(0.129027\pi\) | |||||||
\(74\) | 1.97464e8 | 0.765499 | ||||||||
\(75\) | −2.50037e8 | −0.912491 | ||||||||
\(76\) | 6.31442e7 | 0.217106 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.05223e8 | −0.627770 | ||||||||
\(79\) | −2.26624e8 | −0.654612 | −0.327306 | − | 0.944918i | \(-0.606141\pi\) | ||||
−0.327306 | + | 0.944918i | \(0.606141\pi\) | |||||||
\(80\) | 1.37285e8 | 0.374730 | ||||||||
\(81\) | −1.23998e8 | −0.320061 | ||||||||
\(82\) | −8.86857e7 | −0.216616 | ||||||||
\(83\) | −5.26823e8 | −1.21847 | −0.609233 | − | 0.792992i | \(-0.708522\pi\) | ||||
−0.609233 | + | 0.792992i | \(0.708522\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.14125e8 | −1.69163 | ||||||||
\(86\) | 9.26132e7 | 0.182570 | ||||||||
\(87\) | −5.90604e8 | −1.10525 | ||||||||
\(88\) | −2.30664e8 | −0.410022 | ||||||||
\(89\) | −5.19381e8 | −0.877468 | −0.438734 | − | 0.898617i | \(-0.644573\pi\) | ||||
−0.438734 | + | 0.898617i | \(0.644573\pi\) | |||||||
\(90\) | 3.06326e8 | 0.492145 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.39750e8 | −0.639971 | ||||||||
\(93\) | −5.40912e8 | −0.749814 | ||||||||
\(94\) | 8.19091e8 | 1.08207 | ||||||||
\(95\) | 5.16697e8 | 0.650849 | ||||||||
\(96\) | 1.07670e8 | 0.129382 | ||||||||
\(97\) | 8.75899e8 | 1.00457 | 0.502286 | − | 0.864701i | \(-0.332492\pi\) | ||||
0.502286 | + | 0.864701i | \(0.332492\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.14684e8 | −0.538495 | ||||||||
\(100\) | 6.23378e8 | 0.623378 | ||||||||
\(101\) | 8.73621e6 | 0.00835366 | 0.00417683 | − | 0.999991i | \(-0.498670\pi\) | ||||
0.00417683 | + | 0.999991i | \(0.498670\pi\) | |||||||
\(102\) | −6.38501e8 | −0.584064 | ||||||||
\(103\) | −9.59029e8 | −0.839584 | −0.419792 | − | 0.907620i | \(-0.637897\pi\) | ||||
−0.419792 | + | 0.907620i | \(0.637897\pi\) | |||||||
\(104\) | 5.11650e8 | 0.428868 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.30299e9 | 1.00246 | ||||||||
\(107\) | −1.48471e9 | −1.09500 | −0.547499 | − | 0.836806i | \(-0.684420\pi\) | ||||
−0.547499 | + | 0.836806i | \(0.684420\pi\) | |||||||
\(108\) | 7.57642e8 | 0.535867 | ||||||||
\(109\) | −1.53530e9 | −1.04178 | −0.520888 | − | 0.853625i | \(-0.674399\pi\) | ||||
−0.520888 | + | 0.853625i | \(0.674399\pi\) | |||||||
\(110\) | −1.88748e9 | −1.22918 | ||||||||
\(111\) | 1.26724e9 | 0.792332 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.29034e9 | 1.89840 | 0.949199 | − | 0.314677i | \(-0.101896\pi\) | ||||
0.949199 | + | 0.314677i | \(0.101896\pi\) | |||||||
\(114\) | 4.05235e8 | 0.224716 | ||||||||
\(115\) | −3.59839e9 | −1.91853 | ||||||||
\(116\) | 1.47246e9 | 0.755061 | ||||||||
\(117\) | 1.14165e9 | 0.563246 | ||||||||
\(118\) | −1.25736e9 | −0.597024 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.81040e8 | 0.387865 | ||||||||
\(121\) | 8.13362e8 | 0.344945 | ||||||||
\(122\) | 2.20843e8 | 0.0902534 | ||||||||
\(123\) | −5.69150e8 | −0.224209 | ||||||||
\(124\) | 1.34857e9 | 0.512243 | ||||||||
\(125\) | 1.00958e9 | 0.369866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.41672e9 | −1.84765 | −0.923826 | − | 0.382814i | \(-0.874955\pi\) | ||||
−0.923826 | + | 0.382814i | \(0.874955\pi\) | |||||||
\(128\) | −2.68435e8 | −0.0883883 | ||||||||
\(129\) | 5.94355e8 | 0.188970 | ||||||||
\(130\) | 4.18674e9 | 1.28567 | ||||||||
\(131\) | 3.38792e9 | 1.00511 | 0.502553 | − | 0.864546i | \(-0.332394\pi\) | ||||
0.502553 | + | 0.864546i | \(0.332394\pi\) | |||||||
\(132\) | −1.48031e9 | −0.424394 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.62748e9 | 0.436057 | ||||||||
\(135\) | 6.19965e9 | 1.60644 | ||||||||
\(136\) | 1.59187e9 | 0.399009 | ||||||||
\(137\) | 4.74729e9 | 1.15134 | 0.575669 | − | 0.817683i | \(-0.304742\pi\) | ||||
0.575669 | + | 0.817683i | \(0.304742\pi\) | |||||||
\(138\) | −2.82214e9 | −0.662403 | ||||||||
\(139\) | −2.17838e9 | −0.494958 | −0.247479 | − | 0.968893i | \(-0.579602\pi\) | ||||
−0.247479 | + | 0.968893i | \(0.579602\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.25661e9 | 1.12000 | ||||||||
\(142\) | 6.01073e9 | 1.24059 | ||||||||
\(143\) | −7.03449e9 | −1.40676 | ||||||||
\(144\) | −5.98964e8 | −0.116083 | ||||||||
\(145\) | 1.20489e10 | 2.26355 | ||||||||
\(146\) | −7.13512e9 | −1.29961 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.15942e9 | −0.541290 | ||||||||
\(149\) | −1.18058e10 | −1.96226 | −0.981129 | − | 0.193354i | \(-0.938064\pi\) | ||||
−0.981129 | + | 0.193354i | \(0.938064\pi\) | |||||||
\(150\) | 4.00059e9 | 0.645228 | ||||||||
\(151\) | −6.31601e9 | −0.988660 | −0.494330 | − | 0.869274i | \(-0.664586\pi\) | ||||
−0.494330 | + | 0.869274i | \(0.664586\pi\) | |||||||
\(152\) | −1.01031e9 | −0.153517 | ||||||||
\(153\) | 3.55197e9 | 0.524032 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.10351e10 | 1.53562 | ||||||||
\(156\) | 3.28357e9 | 0.443900 | ||||||||
\(157\) | 1.03026e9 | 0.135331 | 0.0676655 | − | 0.997708i | \(-0.478445\pi\) | ||||
0.0676655 | + | 0.997708i | \(0.478445\pi\) | |||||||
\(158\) | 3.62598e9 | 0.462881 | ||||||||
\(159\) | 8.36211e9 | 1.03760 | ||||||||
\(160\) | −2.19656e9 | −0.264974 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.98397e9 | 0.226318 | ||||||||
\(163\) | −3.34930e9 | −0.371629 | −0.185814 | − | 0.982585i | \(-0.559492\pi\) | ||||
−0.185814 | + | 0.982585i | \(0.559492\pi\) | |||||||
\(164\) | 1.41897e9 | 0.153171 | ||||||||
\(165\) | −1.21131e10 | −1.27226 | ||||||||
\(166\) | 8.42917e9 | 0.861585 | ||||||||
\(167\) | −1.63487e10 | −1.62652 | −0.813261 | − | 0.581899i | \(-0.802310\pi\) | ||||
−0.813261 | + | 0.581899i | \(0.802310\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.99917e9 | 0.471420 | ||||||||
\(170\) | 1.30260e10 | 1.19616 | ||||||||
\(171\) | −2.25431e9 | −0.201619 | ||||||||
\(172\) | −1.48181e9 | −0.129097 | ||||||||
\(173\) | 7.47099e9 | 0.634119 | 0.317059 | − | 0.948406i | \(-0.397305\pi\) | ||||
0.317059 | + | 0.948406i | \(0.397305\pi\) | |||||||
\(174\) | 9.44966e9 | 0.781528 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.69062e9 | 0.289929 | ||||||||
\(177\) | −8.06926e9 | −0.617951 | ||||||||
\(178\) | 8.31010e9 | 0.620464 | ||||||||
\(179\) | −6.23008e9 | −0.453581 | −0.226790 | − | 0.973944i | \(-0.572823\pi\) | ||||
−0.226790 | + | 0.973944i | \(0.572823\pi\) | |||||||
\(180\) | −4.90122e9 | −0.347999 | ||||||||
\(181\) | −5.46976e9 | −0.378804 | −0.189402 | − | 0.981900i | \(-0.560655\pi\) | ||||
−0.189402 | + | 0.981900i | \(0.560655\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.41728e9 | 0.0934170 | ||||||||
\(184\) | 7.03599e9 | 0.452528 | ||||||||
\(185\) | −2.58530e10 | −1.62270 | ||||||||
\(186\) | 8.65459e9 | 0.530198 | ||||||||
\(187\) | −2.18861e10 | −1.30882 | ||||||||
\(188\) | −1.31055e10 | −0.765142 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.26716e9 | −0.460220 | ||||||||
\(191\) | 6.93485e9 | 0.377039 | 0.188520 | − | 0.982069i | \(-0.439631\pi\) | ||||
0.188520 | + | 0.982069i | \(0.439631\pi\) | |||||||
\(192\) | −1.72271e9 | −0.0914866 | ||||||||
\(193\) | 4.17331e9 | 0.216508 | 0.108254 | − | 0.994123i | \(-0.465474\pi\) | ||||
0.108254 | + | 0.994123i | \(0.465474\pi\) | |||||||
\(194\) | −1.40144e10 | −0.710340 | ||||||||
\(195\) | 2.68689e10 | 1.33074 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.62569e10 | −1.71511 | −0.857556 | − | 0.514391i | \(-0.828018\pi\) | ||||
−0.857556 | + | 0.514391i | \(0.828018\pi\) | |||||||
\(198\) | 8.23494e9 | 0.380774 | ||||||||
\(199\) | −1.79583e10 | −0.811759 | −0.405880 | − | 0.913927i | \(-0.633035\pi\) | ||||
−0.405880 | + | 0.913927i | \(0.633035\pi\) | |||||||
\(200\) | −9.97404e9 | −0.440795 | ||||||||
\(201\) | 1.04445e10 | 0.451342 | ||||||||
\(202\) | −1.39779e8 | −0.00590693 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.02160e10 | 0.412996 | ||||||||
\(205\) | 1.16112e10 | 0.459181 | ||||||||
\(206\) | 1.53445e10 | 0.593675 | ||||||||
\(207\) | 1.56995e10 | 0.594320 | ||||||||
\(208\) | −8.18641e9 | −0.303255 | ||||||||
\(209\) | 1.38903e10 | 0.503564 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.33838e9 | 0.220144 | 0.110072 | − | 0.993924i | \(-0.464892\pi\) | ||||
0.110072 | + | 0.993924i | \(0.464892\pi\) | |||||||
\(212\) | −2.08479e10 | −0.708845 | ||||||||
\(213\) | 3.85745e10 | 1.28408 | ||||||||
\(214\) | 2.37553e10 | 0.774281 | ||||||||
\(215\) | −1.21254e10 | −0.387011 | ||||||||
\(216\) | −1.21223e10 | −0.378915 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.45648e10 | 0.736647 | ||||||||
\(219\) | −4.57904e10 | −1.34517 | ||||||||
\(220\) | 3.01997e10 | 0.869161 | ||||||||
\(221\) | 4.85469e10 | 1.36898 | ||||||||
\(222\) | −2.02759e10 | −0.560263 | ||||||||
\(223\) | 4.34746e10 | 1.17724 | 0.588619 | − | 0.808411i | \(-0.299672\pi\) | ||||
0.588619 | + | 0.808411i | \(0.299672\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.22552e10 | −0.578910 | ||||||||
\(226\) | −5.26454e10 | −1.34237 | ||||||||
\(227\) | 1.89487e10 | 0.473657 | 0.236828 | − | 0.971552i | \(-0.423892\pi\) | ||||
0.236828 | + | 0.971552i | \(0.423892\pi\) | |||||||
\(228\) | −6.48375e9 | −0.158898 | ||||||||
\(229\) | −3.72378e10 | −0.894796 | −0.447398 | − | 0.894335i | \(-0.647649\pi\) | ||||
−0.447398 | + | 0.894335i | \(0.647649\pi\) | |||||||
\(230\) | 5.75743e10 | 1.35660 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.35593e10 | −0.533909 | ||||||||
\(233\) | 1.83837e10 | 0.408632 | 0.204316 | − | 0.978905i | \(-0.434503\pi\) | ||||
0.204316 | + | 0.978905i | \(0.434503\pi\) | |||||||
\(234\) | −1.82665e10 | −0.398275 | ||||||||
\(235\) | −1.07240e11 | −2.29377 | ||||||||
\(236\) | 2.01178e10 | 0.422160 | ||||||||
\(237\) | 2.32701e10 | 0.479106 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.65476e10 | −0.724550 | −0.362275 | − | 0.932071i | \(-0.618000\pi\) | ||||
−0.362275 | + | 0.932071i | \(0.618000\pi\) | |||||||
\(240\) | −1.40966e10 | −0.274262 | ||||||||
\(241\) | −2.85905e10 | −0.545941 | −0.272970 | − | 0.962022i | \(-0.588006\pi\) | ||||
−0.272970 | + | 0.962022i | \(0.588006\pi\) | |||||||
\(242\) | −1.30138e10 | −0.243913 | ||||||||
\(243\) | −4.55203e10 | −0.837484 | ||||||||
\(244\) | −3.53348e9 | −0.0638188 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.10639e9 | 0.158540 | ||||||||
\(247\) | −3.08111e10 | −0.526709 | ||||||||
\(248\) | −2.15771e10 | −0.362210 | ||||||||
\(249\) | 5.40951e10 | 0.891786 | ||||||||
\(250\) | −1.61532e10 | −0.261535 | ||||||||
\(251\) | 1.00172e10 | 0.159300 | 0.0796499 | − | 0.996823i | \(-0.474620\pi\) | ||||
0.0796499 | + | 0.996823i | \(0.474620\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.67353e10 | −1.48437 | ||||||||
\(254\) | 8.66676e10 | 1.30649 | ||||||||
\(255\) | 8.35957e10 | 1.23809 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | 1.69681e10 | 0.242625 | 0.121312 | − | 0.992614i | \(-0.461290\pi\) | ||||
0.121312 | + | 0.992614i | \(0.461290\pi\) | |||||||
\(258\) | −9.50968e9 | −0.133622 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.69879e10 | −0.909109 | ||||||||
\(261\) | −5.25683e10 | −0.701200 | ||||||||
\(262\) | −5.42067e10 | −0.710717 | ||||||||
\(263\) | 7.07192e9 | 0.0911458 | 0.0455729 | − | 0.998961i | \(-0.485489\pi\) | ||||
0.0455729 | + | 0.998961i | \(0.485489\pi\) | |||||||
\(264\) | 2.36849e10 | 0.300092 | ||||||||
\(265\) | −1.70595e11 | −2.12500 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.33310e10 | 0.642212 | ||||||||
\(268\) | −2.60397e10 | −0.308339 | ||||||||
\(269\) | 3.69954e8 | 0.00430787 | 0.00215393 | − | 0.999998i | \(-0.499314\pi\) | ||||
0.00215393 | + | 0.999998i | \(0.499314\pi\) | |||||||
\(270\) | −9.91944e10 | −1.13593 | ||||||||
\(271\) | −1.24288e11 | −1.39981 | −0.699904 | − | 0.714237i | \(-0.746774\pi\) | ||||
−0.699904 | + | 0.714237i | \(0.746774\pi\) | |||||||
\(272\) | −2.54700e10 | −0.282142 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.59566e10 | −0.814119 | ||||||||
\(275\) | 1.37129e11 | 1.44588 | ||||||||
\(276\) | 4.51542e10 | 0.468390 | ||||||||
\(277\) | 1.69613e10 | 0.173101 | 0.0865506 | − | 0.996247i | \(-0.472416\pi\) | ||||
0.0865506 | + | 0.996247i | \(0.472416\pi\) | |||||||
\(278\) | 3.48542e10 | 0.349988 | ||||||||
\(279\) | −4.81454e10 | −0.475703 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.16441e11 | 1.11411 | 0.557053 | − | 0.830477i | \(-0.311932\pi\) | ||||
0.557053 | + | 0.830477i | \(0.311932\pi\) | |||||||
\(282\) | −8.41057e10 | −0.791962 | ||||||||
\(283\) | 2.65533e10 | 0.246082 | 0.123041 | − | 0.992402i | \(-0.460735\pi\) | ||||
0.123041 | + | 0.992402i | \(0.460735\pi\) | |||||||
\(284\) | −9.61716e10 | −0.877232 | ||||||||
\(285\) | −5.30554e10 | −0.476351 | ||||||||
\(286\) | 1.12552e11 | 0.994731 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 9.58343e9 | 0.0820833 | ||||||||
\(289\) | 3.24537e10 | 0.273668 | ||||||||
\(290\) | −1.92782e11 | −1.60057 | ||||||||
\(291\) | −8.99388e10 | −0.735239 | ||||||||
\(292\) | 1.14162e11 | 0.918964 | ||||||||
\(293\) | 9.43424e8 | 0.00747829 | 0.00373915 | − | 0.999993i | \(-0.498810\pi\) | ||||
0.00373915 | + | 0.999993i | \(0.498810\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.64620e11 | 1.26557 | ||||||||
\(296\) | 5.05507e10 | 0.382750 | ||||||||
\(297\) | 1.66665e11 | 1.24291 | ||||||||
\(298\) | 1.88892e11 | 1.38753 | ||||||||
\(299\) | 2.14575e11 | 1.55260 | ||||||||
\(300\) | −6.40095e10 | −0.456245 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.01056e11 | 0.699088 | ||||||||
\(303\) | −8.97049e8 | −0.00611398 | ||||||||
\(304\) | 1.61649e10 | 0.108553 | ||||||||
\(305\) | −2.89139e10 | −0.191318 | ||||||||
\(306\) | −5.68315e10 | −0.370547 | ||||||||
\(307\) | −2.20668e10 | −0.141780 | −0.0708902 | − | 0.997484i | \(-0.522584\pi\) | ||||
−0.0708902 | + | 0.997484i | \(0.522584\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.84747e10 | 0.614485 | ||||||||
\(310\) | −1.76562e11 | −1.08585 | ||||||||
\(311\) | 2.30243e11 | 1.39561 | 0.697805 | − | 0.716288i | \(-0.254160\pi\) | ||||
0.697805 | + | 0.716288i | \(0.254160\pi\) | |||||||
\(312\) | −5.25371e10 | −0.313885 | ||||||||
\(313\) | 1.57588e11 | 0.928055 | 0.464027 | − | 0.885821i | \(-0.346404\pi\) | ||||
0.464027 | + | 0.885821i | \(0.346404\pi\) | |||||||
\(314\) | −1.64841e10 | −0.0956935 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.80158e10 | −0.327306 | ||||||||
\(317\) | 2.41500e11 | 1.34323 | 0.671614 | − | 0.740901i | \(-0.265601\pi\) | ||||
0.671614 | + | 0.740901i | \(0.265601\pi\) | |||||||
\(318\) | −1.33794e11 | −0.733692 | ||||||||
\(319\) | 3.23909e11 | 1.75132 | ||||||||
\(320\) | 3.51449e10 | 0.187365 | ||||||||
\(321\) | 1.52452e11 | 0.801422 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.58610e10 | −0.490039 | ||||||||
\(324\) | −3.17436e10 | −0.160031 | ||||||||
\(325\) | −3.04176e11 | −1.51234 | ||||||||
\(326\) | 5.35887e10 | 0.262781 | ||||||||
\(327\) | 1.57647e11 | 0.762468 | ||||||||
\(328\) | −2.27035e10 | −0.108308 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.93810e11 | 0.899627 | ||||||||
\(331\) | 1.43537e11 | 0.657259 | 0.328630 | − | 0.944459i | \(-0.393413\pi\) | ||||
0.328630 | + | 0.944459i | \(0.393413\pi\) | |||||||
\(332\) | −1.34867e11 | −0.609233 | ||||||||
\(333\) | 1.12795e11 | 0.502678 | ||||||||
\(334\) | 2.61580e11 | 1.15012 | ||||||||
\(335\) | −2.13078e11 | −0.924350 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.35343e11 | 0.571612 | 0.285806 | − | 0.958288i | \(-0.407739\pi\) | ||||
0.285806 | + | 0.958288i | \(0.407739\pi\) | |||||||
\(338\) | −7.99867e10 | −0.333344 | ||||||||
\(339\) | −3.37857e11 | −1.38942 | ||||||||
\(340\) | −2.08416e11 | −0.845816 | ||||||||
\(341\) | 2.96656e11 | 1.18811 | ||||||||
\(342\) | 3.60690e10 | 0.142566 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.37090e10 | 0.0912851 | ||||||||
\(345\) | 3.69489e11 | 1.40416 | ||||||||
\(346\) | −1.19536e11 | −0.448390 | ||||||||
\(347\) | 3.87493e11 | 1.43477 | 0.717383 | − | 0.696679i | \(-0.245340\pi\) | ||||
0.717383 | + | 0.696679i | \(0.245340\pi\) | |||||||
\(348\) | −1.51195e11 | −0.552624 | ||||||||
\(349\) | 1.02561e11 | 0.370056 | 0.185028 | − | 0.982733i | \(-0.440762\pi\) | ||||
0.185028 | + | 0.982733i | \(0.440762\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.69690e11 | −1.30004 | ||||||||
\(352\) | −5.90499e10 | −0.205011 | ||||||||
\(353\) | 1.30016e10 | 0.0445667 | 0.0222834 | − | 0.999752i | \(-0.492906\pi\) | ||||
0.0222834 | + | 0.999752i | \(0.492906\pi\) | |||||||
\(354\) | 1.29108e11 | 0.436957 | ||||||||
\(355\) | −7.86955e11 | −2.62980 | ||||||||
\(356\) | −1.32962e11 | −0.438734 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.96812e10 | 0.320730 | ||||||||
\(359\) | −8.55526e10 | −0.271837 | −0.135918 | − | 0.990720i | \(-0.543398\pi\) | ||||
−0.135918 | + | 0.990720i | \(0.543398\pi\) | |||||||
\(360\) | 7.84195e10 | 0.246072 | ||||||||
\(361\) | −2.61848e11 | −0.811460 | ||||||||
\(362\) | 8.75161e10 | 0.267855 | ||||||||
\(363\) | −8.35174e10 | −0.252463 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.34166e11 | 2.75490 | ||||||||
\(366\) | −2.26765e10 | −0.0660558 | ||||||||
\(367\) | 1.13117e11 | 0.325484 | 0.162742 | − | 0.986669i | \(-0.447966\pi\) | ||||
0.162742 | + | 0.986669i | \(0.447966\pi\) | |||||||
\(368\) | −1.12576e11 | −0.319985 | ||||||||
\(369\) | −5.06588e10 | −0.142245 | ||||||||
\(370\) | 4.13647e11 | 1.14742 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.38473e11 | −0.374907 | ||||||||
\(373\) | −1.94719e11 | −0.520857 | −0.260428 | − | 0.965493i | \(-0.583864\pi\) | ||||
−0.260428 | + | 0.965493i | \(0.583864\pi\) | |||||||
\(374\) | 3.50177e11 | 0.925477 | ||||||||
\(375\) | −1.03665e11 | −0.270702 | ||||||||
\(376\) | 2.09687e11 | 0.541037 | ||||||||
\(377\) | −7.18483e11 | −1.83181 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.22727e11 | −0.554493 | −0.277247 | − | 0.960799i | \(-0.589422\pi\) | ||||
−0.277247 | + | 0.960799i | \(0.589422\pi\) | |||||||
\(380\) | 1.32275e11 | 0.325424 | ||||||||
\(381\) | 5.56198e11 | 1.35228 | ||||||||
\(382\) | −1.10958e11 | −0.266607 | ||||||||
\(383\) | 3.36594e11 | 0.799305 | 0.399652 | − | 0.916667i | \(-0.369131\pi\) | ||||
0.399652 | + | 0.916667i | \(0.369131\pi\) | |||||||
\(384\) | 2.75634e10 | 0.0646908 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.67730e10 | −0.153094 | ||||||||
\(387\) | 5.29023e10 | 0.119888 | ||||||||
\(388\) | 2.24230e11 | 0.502286 | ||||||||
\(389\) | −3.47900e11 | −0.770338 | −0.385169 | − | 0.922846i | \(-0.625857\pi\) | ||||
−0.385169 | + | 0.922846i | \(0.625857\pi\) | |||||||
\(390\) | −4.29902e11 | −0.940976 | ||||||||
\(391\) | 6.67596e11 | 1.44450 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.47877e11 | −0.735630 | ||||||||
\(394\) | 5.80110e11 | 1.21277 | ||||||||
\(395\) | −4.74732e11 | −0.981210 | ||||||||
\(396\) | −1.31759e11 | −0.269248 | ||||||||
\(397\) | −2.75509e10 | −0.0556645 | −0.0278323 | − | 0.999613i | \(-0.508860\pi\) | ||||
−0.0278323 | + | 0.999613i | \(0.508860\pi\) | |||||||
\(398\) | 2.87333e11 | 0.574001 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.59585e11 | 0.311689 | ||||||||
\(401\) | −6.21170e11 | −1.19967 | −0.599834 | − | 0.800124i | \(-0.704767\pi\) | ||||
−0.599834 | + | 0.800124i | \(0.704767\pi\) | |||||||
\(402\) | −1.67112e11 | −0.319147 | ||||||||
\(403\) | −6.58032e11 | −1.24272 | ||||||||
\(404\) | 2.23647e9 | 0.00417683 | ||||||||
\(405\) | −2.59752e11 | −0.479746 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.95003e11 | −1.25549 | ||||||||
\(408\) | −1.63456e11 | −0.292032 | ||||||||
\(409\) | −1.46395e10 | −0.0258686 | −0.0129343 | − | 0.999916i | \(-0.504117\pi\) | ||||
−0.0129343 | + | 0.999916i | \(0.504117\pi\) | |||||||
\(410\) | −1.85779e11 | −0.324690 | ||||||||
\(411\) | −4.87459e11 | −0.842656 | ||||||||
\(412\) | −2.45511e11 | −0.419792 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.51192e11 | −0.420247 | ||||||||
\(415\) | −1.10359e12 | −1.82638 | ||||||||
\(416\) | 1.30983e11 | 0.214434 | ||||||||
\(417\) | 2.23680e11 | 0.362256 | ||||||||
\(418\) | −2.22245e11 | −0.356073 | ||||||||
\(419\) | −1.21505e11 | −0.192589 | −0.0962946 | − | 0.995353i | \(-0.530699\pi\) | ||||
−0.0962946 | + | 0.995353i | \(0.530699\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.61016e11 | −0.870373 | −0.435187 | − | 0.900340i | \(-0.643318\pi\) | ||||
−0.435187 | + | 0.900340i | \(0.643318\pi\) | |||||||
\(422\) | −1.01414e11 | −0.155666 | ||||||||
\(423\) | 4.67879e11 | 0.710562 | ||||||||
\(424\) | 3.33567e11 | 0.501229 | ||||||||
\(425\) | −9.46367e11 | −1.40705 | ||||||||
\(426\) | −6.17192e11 | −0.907981 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.80085e11 | −0.547499 | ||||||||
\(429\) | 7.22313e11 | 1.02960 | ||||||||
\(430\) | 1.94006e11 | 0.273658 | ||||||||
\(431\) | 1.04432e12 | 1.45776 | 0.728878 | − | 0.684644i | \(-0.240042\pi\) | ||||
0.728878 | + | 0.684644i | \(0.240042\pi\) | |||||||
\(432\) | 1.93956e11 | 0.267934 | ||||||||
\(433\) | 1.05446e12 | 1.44156 | 0.720781 | − | 0.693163i | \(-0.243784\pi\) | ||||
0.720781 | + | 0.693163i | \(0.243784\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.23720e12 | −1.65668 | ||||||||
\(436\) | −3.93037e11 | −0.520888 | ||||||||
\(437\) | −4.23700e11 | −0.555767 | ||||||||
\(438\) | 7.32646e11 | 0.951176 | ||||||||
\(439\) | 1.17037e12 | 1.50395 | 0.751973 | − | 0.659194i | \(-0.229103\pi\) | ||||
0.751973 | + | 0.659194i | \(0.229103\pi\) | |||||||
\(440\) | −4.83195e11 | −0.614589 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.76751e11 | −0.968014 | ||||||||
\(443\) | −7.10660e11 | −0.876688 | −0.438344 | − | 0.898807i | \(-0.644435\pi\) | ||||
−0.438344 | + | 0.898807i | \(0.644435\pi\) | |||||||
\(444\) | 3.24415e11 | 0.396166 | ||||||||
\(445\) | −1.08800e12 | −1.31525 | ||||||||
\(446\) | −6.95594e11 | −0.832433 | ||||||||
\(447\) | 1.21224e12 | 1.43616 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.40485e11 | 1.09205 | 0.546026 | − | 0.837768i | \(-0.316140\pi\) | ||||
0.546026 | + | 0.837768i | \(0.316140\pi\) | |||||||
\(450\) | 3.56084e11 | 0.409351 | ||||||||
\(451\) | 3.12142e11 | 0.355270 | ||||||||
\(452\) | 8.42326e11 | 0.949199 | ||||||||
\(453\) | 6.48539e11 | 0.723593 | ||||||||
\(454\) | −3.03180e11 | −0.334926 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.03740e11 | 0.112358 | ||||||||
\(457\) | −1.15083e12 | −1.23420 | −0.617102 | − | 0.786883i | \(-0.711693\pi\) | ||||
−0.617102 | + | 0.786883i | \(0.711693\pi\) | |||||||
\(458\) | 5.95805e11 | 0.632716 | ||||||||
\(459\) | −1.15020e12 | −1.20953 | ||||||||
\(460\) | −9.21188e11 | −0.959264 | ||||||||
\(461\) | 2.66471e11 | 0.274786 | 0.137393 | − | 0.990517i | \(-0.456128\pi\) | ||||
0.137393 | + | 0.990517i | \(0.456128\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.48766e11 | −0.453843 | −0.226921 | − | 0.973913i | \(-0.572866\pi\) | ||||
−0.226921 | + | 0.973913i | \(0.572866\pi\) | |||||||
\(464\) | 3.76949e11 | 0.377531 | ||||||||
\(465\) | −1.13310e12 | −1.12391 | ||||||||
\(466\) | −2.94140e11 | −0.288946 | ||||||||
\(467\) | −1.77815e12 | −1.72999 | −0.864993 | − | 0.501783i | \(-0.832677\pi\) | ||||
−0.864993 | + | 0.501783i | \(0.832677\pi\) | |||||||
\(468\) | 2.92263e11 | 0.281623 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.71583e12 | 1.62194 | ||||||||
\(471\) | −1.05789e11 | −0.0990478 | ||||||||
\(472\) | −3.21885e11 | −0.298512 | ||||||||
\(473\) | −3.25966e11 | −0.299431 | ||||||||
\(474\) | −3.72322e11 | −0.338779 | ||||||||
\(475\) | 6.00627e11 | 0.541357 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.44293e11 | 0.658281 | ||||||||
\(478\) | 5.84762e11 | 0.512334 | ||||||||
\(479\) | 1.98906e12 | 1.72639 | 0.863194 | − | 0.504872i | \(-0.168460\pi\) | ||||
0.863194 | + | 0.504872i | \(0.168460\pi\) | |||||||
\(480\) | 2.25546e11 | 0.193932 | ||||||||
\(481\) | 1.54163e12 | 1.31319 | ||||||||
\(482\) | 4.57448e11 | 0.386038 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.08221e11 | 0.172472 | ||||||||
\(485\) | 1.83484e12 | 1.50577 | ||||||||
\(486\) | 7.28324e11 | 0.592191 | ||||||||
\(487\) | 6.88592e11 | 0.554730 | 0.277365 | − | 0.960765i | \(-0.410539\pi\) | ||||
0.277365 | + | 0.960765i | \(0.410539\pi\) | |||||||
\(488\) | 5.65357e10 | 0.0451267 | ||||||||
\(489\) | 3.43911e11 | 0.271992 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.86881e12 | 1.45111 | 0.725553 | − | 0.688166i | \(-0.241584\pi\) | ||||
0.725553 | + | 0.688166i | \(0.241584\pi\) | |||||||
\(492\) | −1.45702e11 | −0.112105 | ||||||||
\(493\) | −2.23538e12 | −1.70428 | ||||||||
\(494\) | 4.92977e11 | 0.372439 | ||||||||
\(495\) | −1.07816e12 | −0.807161 | ||||||||
\(496\) | 3.45234e11 | 0.256121 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −8.65521e11 | −0.630588 | ||||||||
\(499\) | −8.77411e11 | −0.633506 | −0.316753 | − | 0.948508i | \(-0.602593\pi\) | ||||
−0.316753 | + | 0.948508i | \(0.602593\pi\) | |||||||
\(500\) | 2.58452e11 | 0.184933 | ||||||||
\(501\) | 1.67872e12 | 1.19044 | ||||||||
\(502\) | −1.60275e11 | −0.112642 | ||||||||
\(503\) | 2.12177e11 | 0.147789 | 0.0738945 | − | 0.997266i | \(-0.476457\pi\) | ||||
0.0738945 | + | 0.997266i | \(0.476457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.83006e10 | 0.0125215 | ||||||||
\(506\) | 1.54776e12 | 1.04961 | ||||||||
\(507\) | −5.13323e11 | −0.345029 | ||||||||
\(508\) | −1.38668e12 | −0.923826 | ||||||||
\(509\) | 1.82871e12 | 1.20758 | 0.603790 | − | 0.797144i | \(-0.293657\pi\) | ||||
0.603790 | + | 0.797144i | \(0.293657\pi\) | |||||||
\(510\) | −1.33753e12 | −0.875464 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | 7.29991e11 | 0.465361 | ||||||||
\(514\) | −2.71490e11 | −0.171561 | ||||||||
\(515\) | −2.00897e12 | −1.25847 | ||||||||
\(516\) | 1.52155e11 | 0.0944849 | ||||||||
\(517\) | −2.88291e12 | −1.77470 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.67134e11 | −0.464107 | ||||||||
\(520\) | 1.07181e12 | 0.642837 | ||||||||
\(521\) | −2.68357e12 | −1.59567 | −0.797834 | − | 0.602877i | \(-0.794021\pi\) | ||||
−0.797834 | + | 0.602877i | \(0.794021\pi\) | |||||||
\(522\) | 8.41093e11 | 0.495823 | ||||||||
\(523\) | −9.07444e11 | −0.530349 | −0.265175 | − | 0.964200i | \(-0.585430\pi\) | ||||
−0.265175 | + | 0.964200i | \(0.585430\pi\) | |||||||
\(524\) | 8.67307e11 | 0.502553 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.13151e11 | −0.0644498 | ||||||||
\(527\) | −2.04730e12 | −1.15620 | ||||||||
\(528\) | −3.78959e11 | −0.212197 | ||||||||
\(529\) | 1.14959e12 | 0.638251 | ||||||||
\(530\) | 2.72952e12 | 1.50260 | ||||||||
\(531\) | −7.18227e11 | −0.392046 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.92384e11 | −0.371599 | ||||||||
\(534\) | −8.53295e11 | −0.454113 | ||||||||
\(535\) | −3.11017e12 | −1.64131 | ||||||||
\(536\) | 4.16635e11 | 0.218029 | ||||||||
\(537\) | 6.39715e11 | 0.331972 | ||||||||
\(538\) | −5.91926e9 | −0.00304612 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.58711e12 | 0.803221 | ||||||||
\(541\) | −4.83134e11 | −0.242482 | −0.121241 | − | 0.992623i | \(-0.538687\pi\) | ||||
−0.121241 | + | 0.992623i | \(0.538687\pi\) | |||||||
\(542\) | 1.98861e12 | 0.989814 | ||||||||
\(543\) | 5.61644e11 | 0.277244 | ||||||||
\(544\) | 4.07519e11 | 0.199505 | ||||||||
\(545\) | −3.21615e12 | −1.56154 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.24340e12 | 1.07143 | 0.535716 | − | 0.844398i | \(-0.320042\pi\) | ||||
0.535716 | + | 0.844398i | \(0.320042\pi\) | |||||||
\(548\) | 1.21531e12 | 0.575669 | ||||||||
\(549\) | 1.26149e11 | 0.0592664 | ||||||||
\(550\) | −2.19407e12 | −1.02239 | ||||||||
\(551\) | 1.41872e12 | 0.655714 | ||||||||
\(552\) | −7.22468e11 | −0.331202 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.71381e11 | −0.122401 | ||||||||
\(555\) | 2.65463e12 | 1.18764 | ||||||||
\(556\) | −5.57666e11 | −0.247479 | ||||||||
\(557\) | 7.24610e11 | 0.318974 | 0.159487 | − | 0.987200i | \(-0.449016\pi\) | ||||
0.159487 | + | 0.987200i | \(0.449016\pi\) | |||||||
\(558\) | 7.70326e11 | 0.336373 | ||||||||
\(559\) | 7.23047e11 | 0.313194 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.24730e12 | 0.957917 | ||||||||
\(562\) | −1.86305e12 | −0.787792 | ||||||||
\(563\) | 4.21854e12 | 1.76960 | 0.884799 | − | 0.465973i | \(-0.154296\pi\) | ||||
0.884799 | + | 0.465973i | \(0.154296\pi\) | |||||||
\(564\) | 1.34569e12 | 0.560002 | ||||||||
\(565\) | 6.89260e12 | 2.84554 | ||||||||
\(566\) | −4.24852e11 | −0.174006 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.53875e12 | 0.620297 | ||||||||
\(569\) | 4.34809e12 | 1.73898 | 0.869488 | − | 0.493954i | \(-0.164449\pi\) | ||||
0.869488 | + | 0.493954i | \(0.164449\pi\) | |||||||
\(570\) | 8.48886e11 | 0.336831 | ||||||||
\(571\) | −2.24603e12 | −0.884206 | −0.442103 | − | 0.896964i | \(-0.645767\pi\) | ||||
−0.442103 | + | 0.896964i | \(0.645767\pi\) | |||||||
\(572\) | −1.80083e12 | −0.703381 | ||||||||
\(573\) | −7.12082e11 | −0.275952 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.18289e12 | −1.59577 | ||||||||
\(576\) | −1.53335e11 | −0.0580417 | ||||||||
\(577\) | 2.64828e12 | 0.994655 | 0.497328 | − | 0.867563i | \(-0.334315\pi\) | ||||
0.497328 | + | 0.867563i | \(0.334315\pi\) | |||||||
\(578\) | −5.19260e11 | −0.193513 | ||||||||
\(579\) | −4.28523e11 | −0.158460 | ||||||||
\(580\) | 3.08451e12 | 1.13177 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.43902e12 | 0.519893 | ||||||||
\(583\) | −4.58608e12 | −1.64412 | ||||||||
\(584\) | −1.82659e12 | −0.649806 | ||||||||
\(585\) | 2.39154e12 | 0.844259 | ||||||||
\(586\) | −1.50948e10 | −0.00528795 | ||||||||
\(587\) | 2.72201e12 | 0.946276 | 0.473138 | − | 0.880988i | \(-0.343121\pi\) | ||||
0.473138 | + | 0.880988i | \(0.343121\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.29935e12 | 0.444845 | ||||||||
\(590\) | −2.63393e12 | −0.894890 | ||||||||
\(591\) | 3.72292e12 | 1.25528 | ||||||||
\(592\) | −8.08812e11 | −0.270645 | ||||||||
\(593\) | −2.15619e11 | −0.0716046 | −0.0358023 | − | 0.999359i | \(-0.511399\pi\) | ||||
−0.0358023 | + | 0.999359i | \(0.511399\pi\) | |||||||
\(594\) | −2.66663e12 | −0.878870 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.02228e12 | −0.981129 | ||||||||
\(597\) | 1.84399e12 | 0.594121 | ||||||||
\(598\) | −3.43320e12 | −1.09785 | ||||||||
\(599\) | −1.11903e12 | −0.355156 | −0.177578 | − | 0.984107i | \(-0.556826\pi\) | ||||
−0.177578 | + | 0.984107i | \(0.556826\pi\) | |||||||
\(600\) | 1.02415e12 | 0.322614 | ||||||||
\(601\) | −2.89926e12 | −0.906467 | −0.453234 | − | 0.891392i | \(-0.649730\pi\) | ||||
−0.453234 | + | 0.891392i | \(0.649730\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.29643e11 | 0.286344 | ||||||||
\(604\) | −1.61690e12 | −0.494330 | ||||||||
\(605\) | 1.70383e12 | 0.517044 | ||||||||
\(606\) | 1.43528e10 | 0.00432324 | ||||||||
\(607\) | −1.76725e12 | −0.528384 | −0.264192 | − | 0.964470i | \(-0.585105\pi\) | ||||
−0.264192 | + | 0.964470i | \(0.585105\pi\) | |||||||
\(608\) | −2.58639e11 | −0.0767586 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.62622e11 | 0.135283 | ||||||||
\(611\) | 6.39478e12 | 1.85627 | ||||||||
\(612\) | 9.09305e11 | 0.262016 | ||||||||
\(613\) | −7.94293e11 | −0.227200 | −0.113600 | − | 0.993527i | \(-0.536238\pi\) | ||||
−0.113600 | + | 0.993527i | \(0.536238\pi\) | |||||||
\(614\) | 3.53068e11 | 0.100254 | ||||||||
\(615\) | −1.19226e12 | −0.336071 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.17799e12 | 0.882815 | 0.441407 | − | 0.897307i | \(-0.354479\pi\) | ||||
0.441407 | + | 0.897307i | \(0.354479\pi\) | |||||||
\(618\) | −1.57559e12 | −0.434507 | ||||||||
\(619\) | −6.59526e12 | −1.80561 | −0.902804 | − | 0.430051i | \(-0.858495\pi\) | ||||
−0.902804 | + | 0.430051i | \(0.858495\pi\) | |||||||
\(620\) | 2.82499e12 | 0.767810 | ||||||||
\(621\) | −5.08381e12 | −1.37176 | ||||||||
\(622\) | −3.68388e12 | −0.986845 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.40594e11 | 0.221950 | ||||||||
\(625\) | −2.64113e12 | −0.692357 | ||||||||
\(626\) | −2.52141e12 | −0.656234 | ||||||||
\(627\) | −1.42628e12 | −0.368555 | ||||||||
\(628\) | 2.63746e11 | 0.0676655 | ||||||||
\(629\) | 4.79640e12 | 1.22177 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.22143e12 | −1.31117 | −0.655583 | − | 0.755123i | \(-0.727577\pi\) | ||||
−0.655583 | + | 0.755123i | \(0.727577\pi\) | |||||||
\(632\) | 9.28252e11 | 0.231440 | ||||||||
\(633\) | −6.50836e11 | −0.161122 | ||||||||
\(634\) | −3.86399e12 | −0.949806 | ||||||||
\(635\) | −1.13470e13 | −2.76948 | ||||||||
\(636\) | 2.14070e12 | 0.518798 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.18254e12 | −1.23837 | ||||||||
\(639\) | 3.43343e12 | 0.814656 | ||||||||
\(640\) | −5.62319e11 | −0.132487 | ||||||||
\(641\) | 3.69727e12 | 0.865008 | 0.432504 | − | 0.901632i | \(-0.357630\pi\) | ||||
0.432504 | + | 0.901632i | \(0.357630\pi\) | |||||||
\(642\) | −2.43923e12 | −0.566691 | ||||||||
\(643\) | 5.23082e12 | 1.20676 | 0.603379 | − | 0.797455i | \(-0.293821\pi\) | ||||
0.603379 | + | 0.797455i | \(0.293821\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.24506e12 | 0.283250 | ||||||||
\(646\) | 1.53378e12 | 0.346510 | ||||||||
\(647\) | 2.92473e12 | 0.656170 | 0.328085 | − | 0.944648i | \(-0.393597\pi\) | ||||
0.328085 | + | 0.944648i | \(0.393597\pi\) | |||||||
\(648\) | 5.07897e11 | 0.113159 | ||||||||
\(649\) | 4.42548e12 | 0.979172 | ||||||||
\(650\) | 4.86681e12 | 1.06939 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.57420e11 | −0.185814 | ||||||||
\(653\) | −4.32042e11 | −0.0929859 | −0.0464930 | − | 0.998919i | \(-0.514805\pi\) | ||||
−0.0464930 | + | 0.998919i | \(0.514805\pi\) | |||||||
\(654\) | −2.52236e12 | −0.539146 | ||||||||
\(655\) | 7.09701e12 | 1.50657 | ||||||||
\(656\) | 3.63257e11 | 0.0765854 | ||||||||
\(657\) | −4.07570e12 | −0.853411 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.16777e12 | −1.27393 | −0.636963 | − | 0.770894i | \(-0.719810\pi\) | ||||
−0.636963 | + | 0.770894i | \(0.719810\pi\) | |||||||
\(660\) | −3.10095e12 | −0.636132 | ||||||||
\(661\) | 2.25373e12 | 0.459193 | 0.229596 | − | 0.973286i | \(-0.426259\pi\) | ||||
0.229596 | + | 0.973286i | \(0.426259\pi\) | |||||||
\(662\) | −2.29659e12 | −0.464752 | ||||||||
\(663\) | −4.98488e12 | −1.00194 | ||||||||
\(664\) | 2.15787e12 | 0.430793 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.80471e12 | −0.355447 | ||||||||
\(667\) | −9.88027e12 | −1.93287 | ||||||||
\(668\) | −4.18528e12 | −0.813261 | ||||||||
\(669\) | −4.46405e12 | −0.861611 | ||||||||
\(670\) | 3.40925e12 | 0.653614 | ||||||||
\(671\) | −7.77289e11 | −0.148024 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.91498e12 | 0.923536 | 0.461768 | − | 0.887001i | \(-0.347215\pi\) | ||||
0.461768 | + | 0.887001i | \(0.347215\pi\) | |||||||
\(674\) | −2.16549e12 | −0.404191 | ||||||||
\(675\) | 7.20668e12 | 1.33619 | ||||||||
\(676\) | 1.27979e12 | 0.235710 | ||||||||
\(677\) | −1.00923e12 | −0.184647 | −0.0923233 | − | 0.995729i | \(-0.529429\pi\) | ||||
−0.0923233 | + | 0.995729i | \(0.529429\pi\) | |||||||
\(678\) | 5.40571e12 | 0.982470 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.33466e12 | 0.598082 | ||||||||
\(681\) | −1.94569e12 | −0.346666 | ||||||||
\(682\) | −4.74649e12 | −0.840124 | ||||||||
\(683\) | −2.33611e12 | −0.410772 | −0.205386 | − | 0.978681i | \(-0.565845\pi\) | ||||
−0.205386 | + | 0.978681i | \(0.565845\pi\) | |||||||
\(684\) | −5.77105e11 | −0.100810 | ||||||||
\(685\) | 9.94462e12 | 1.72576 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.82364e12 | 0.654895 | ||||||||
\(688\) | −3.79344e11 | −0.0645483 | ||||||||
\(689\) | 1.01727e13 | 1.71969 | ||||||||
\(690\) | −5.91182e12 | −0.992888 | ||||||||
\(691\) | −1.10788e13 | −1.84860 | −0.924300 | − | 0.381666i | \(-0.875350\pi\) | ||||
−0.924300 | + | 0.381666i | \(0.875350\pi\) | |||||||
\(692\) | 1.91257e12 | 0.317059 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.19989e12 | −1.01453 | ||||||||
\(695\) | −4.56328e12 | −0.741901 | ||||||||
\(696\) | 2.41911e12 | 0.390764 | ||||||||
\(697\) | −2.15418e12 | −0.345728 | ||||||||
\(698\) | −1.64098e12 | −0.261669 | ||||||||
\(699\) | −1.88767e12 | −0.299075 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.11682e11 | 0.126956 | 0.0634782 | − | 0.997983i | \(-0.479781\pi\) | ||||
0.0634782 | + | 0.997983i | \(0.479781\pi\) | |||||||
\(702\) | 5.91504e12 | 0.919265 | ||||||||
\(703\) | −3.04411e12 | −0.470069 | ||||||||
\(704\) | 9.44799e11 | 0.144965 | ||||||||
\(705\) | 1.10115e13 | 1.67879 | ||||||||
\(706\) | −2.08026e11 | −0.0315134 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.06573e12 | −0.308976 | ||||||||
\(709\) | 8.96980e12 | 1.33314 | 0.666568 | − | 0.745444i | \(-0.267762\pi\) | ||||
0.666568 | + | 0.745444i | \(0.267762\pi\) | |||||||
\(710\) | 1.25913e13 | 1.85955 | ||||||||
\(711\) | 2.07122e12 | 0.303958 | ||||||||
\(712\) | 2.12739e12 | 0.310232 | ||||||||
\(713\) | −9.04897e12 | −1.31128 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.47359e13 | −2.10862 | ||||||||
\(716\) | −1.59490e12 | −0.226790 | ||||||||
\(717\) | 3.75277e12 | 0.530293 | ||||||||
\(718\) | 1.36884e12 | 0.192218 | ||||||||
\(719\) | −1.05576e13 | −1.47328 | −0.736638 | − | 0.676287i | \(-0.763588\pi\) | ||||
−0.736638 | + | 0.676287i | \(0.763588\pi\) | |||||||
\(720\) | −1.25471e12 | −0.173999 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.18957e12 | 0.573789 | ||||||||
\(723\) | 2.93572e12 | 0.399570 | ||||||||
\(724\) | −1.40026e12 | −0.189402 | ||||||||
\(725\) | 1.40060e13 | 1.88275 | ||||||||
\(726\) | 1.33628e12 | 0.178518 | ||||||||
\(727\) | −2.48043e12 | −0.329323 | −0.164661 | − | 0.986350i | \(-0.552653\pi\) | ||||
−0.164661 | + | 0.986350i | \(0.552653\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.11476e12 | 0.933010 | ||||||||
\(730\) | −1.49467e13 | −1.94801 | ||||||||
\(731\) | 2.24958e12 | 0.291389 | ||||||||
\(732\) | 3.62824e11 | 0.0467085 | ||||||||
\(733\) | 9.95078e12 | 1.27318 | 0.636589 | − | 0.771203i | \(-0.280345\pi\) | ||||
0.636589 | + | 0.771203i | \(0.280345\pi\) | |||||||
\(734\) | −1.80987e12 | −0.230152 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.80121e12 | 0.226264 | ||||||||
\(737\) | −5.72815e12 | −0.715173 | ||||||||
\(738\) | 8.10540e11 | 0.100582 | ||||||||
\(739\) | −3.52201e12 | −0.434401 | −0.217200 | − | 0.976127i | \(-0.569692\pi\) | ||||
−0.217200 | + | 0.976127i | \(0.569692\pi\) | |||||||
\(740\) | −6.61836e12 | −0.811349 | ||||||||
\(741\) | 3.16373e12 | 0.385494 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.25259e13 | −1.50786 | −0.753930 | − | 0.656955i | \(-0.771844\pi\) | ||||
−0.753930 | + | 0.656955i | \(0.771844\pi\) | |||||||
\(744\) | 2.21558e12 | 0.265099 | ||||||||
\(745\) | −2.47307e13 | −2.94126 | ||||||||
\(746\) | 3.11550e12 | 0.368301 | ||||||||
\(747\) | 4.81488e12 | 0.565774 | ||||||||
\(748\) | −5.60283e12 | −0.654411 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.65864e12 | 0.191415 | ||||||||
\(751\) | 6.91859e12 | 0.793666 | 0.396833 | − | 0.917891i | \(-0.370109\pi\) | ||||
0.396833 | + | 0.917891i | \(0.370109\pi\) | |||||||
\(752\) | −3.35500e12 | −0.382571 | ||||||||
\(753\) | −1.02858e12 | −0.116590 | ||||||||
\(754\) | 1.14957e13 | 1.29529 | ||||||||
\(755\) | −1.32308e13 | −1.48192 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.68669e12 | −0.297362 | −0.148681 | − | 0.988885i | \(-0.547503\pi\) | ||||
−0.148681 | + | 0.988885i | \(0.547503\pi\) | |||||||
\(758\) | 3.56363e12 | 0.392086 | ||||||||
\(759\) | 9.93294e12 | 1.08640 | ||||||||
\(760\) | −2.11639e12 | −0.230110 | ||||||||
\(761\) | −4.54213e12 | −0.490940 | −0.245470 | − | 0.969404i | \(-0.578942\pi\) | ||||
−0.245470 | + | 0.969404i | \(0.578942\pi\) | |||||||
\(762\) | −8.89917e12 | −0.956208 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.77532e12 | 0.188520 | ||||||||
\(765\) | 7.44067e12 | 0.785481 | ||||||||
\(766\) | −5.38551e12 | −0.565194 | ||||||||
\(767\) | −9.81644e12 | −1.02418 | ||||||||
\(768\) | −4.41014e11 | −0.0457433 | ||||||||
\(769\) | 2.34852e12 | 0.242173 | 0.121087 | − | 0.992642i | \(-0.461362\pi\) | ||||
0.121087 | + | 0.992642i | \(0.461362\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.74232e12 | −0.177575 | ||||||||
\(772\) | 1.06837e12 | 0.108254 | ||||||||
\(773\) | −3.78193e11 | −0.0380983 | −0.0190492 | − | 0.999819i | \(-0.506064\pi\) | ||||
−0.0190492 | + | 0.999819i | \(0.506064\pi\) | |||||||
\(774\) | −8.46436e11 | −0.0847734 | ||||||||
\(775\) | 1.28276e13 | 1.27728 | ||||||||
\(776\) | −3.58768e12 | −0.355170 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.56640e12 | 0.544711 | ||||||||
\(779\) | 1.36718e12 | 0.133017 | ||||||||
\(780\) | 6.87843e12 | 0.665370 | ||||||||
\(781\) | −2.11556e13 | −2.03468 | ||||||||
\(782\) | −1.06815e13 | −1.02142 | ||||||||
\(783\) | 1.70227e13 | 1.61845 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.15818e12 | 0.202850 | ||||||||
\(786\) | 5.56603e12 | 0.520169 | ||||||||
\(787\) | −1.21085e13 | −1.12514 | −0.562568 | − | 0.826751i | \(-0.690186\pi\) | ||||
−0.562568 | + | 0.826751i | \(0.690186\pi\) | |||||||
\(788\) | −9.28176e12 | −0.857556 | ||||||||
\(789\) | −7.26157e11 | −0.0667089 | ||||||||
\(790\) | 7.59572e12 | 0.693820 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.10814e12 | 0.190387 | ||||||||
\(793\) | 1.72416e12 | 0.154827 | ||||||||
\(794\) | 4.40815e11 | 0.0393608 | ||||||||
\(795\) | 1.75170e13 | 1.55527 | ||||||||
\(796\) | −4.59733e12 | −0.405880 | ||||||||
\(797\) | −2.16394e13 | −1.89969 | −0.949846 | − | 0.312719i | \(-0.898760\pi\) | ||||
−0.949846 | + | 0.312719i | \(0.898760\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.98958e13 | 1.72703 | ||||||||
\(800\) | −2.55335e12 | −0.220397 | ||||||||
\(801\) | 4.74687e12 | 0.407438 | ||||||||
\(802\) | 9.93873e12 | 0.848293 | ||||||||
\(803\) | 2.51131e13 | 2.13148 | ||||||||
\(804\) | 2.67380e12 | 0.225671 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.05285e13 | 0.878738 | ||||||||
\(807\) | −3.79875e10 | −0.00315289 | ||||||||
\(808\) | −3.57835e10 | −0.00295347 | ||||||||
\(809\) | −4.36869e12 | −0.358578 | −0.179289 | − | 0.983796i | \(-0.557380\pi\) | ||||
−0.179289 | + | 0.983796i | \(0.557380\pi\) | |||||||
\(810\) | 4.15603e12 | 0.339231 | ||||||||
\(811\) | 1.39017e13 | 1.12843 | 0.564215 | − | 0.825628i | \(-0.309179\pi\) | ||||
0.564215 | + | 0.825628i | \(0.309179\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.27621e13 | 1.02451 | ||||||||
\(814\) | 1.11201e13 | 0.887763 | ||||||||
\(815\) | −7.01611e12 | −0.557041 | ||||||||
\(816\) | 2.61530e12 | 0.206498 | ||||||||
\(817\) | −1.42773e12 | −0.112111 | ||||||||
\(818\) | 2.34233e11 | 0.0182919 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.97246e12 | 0.229591 | ||||||||
\(821\) | 8.03927e12 | 0.617551 | 0.308775 | − | 0.951135i | \(-0.400081\pi\) | ||||
0.308775 | + | 0.951135i | \(0.400081\pi\) | |||||||
\(822\) | 7.79935e12 | 0.595848 | ||||||||
\(823\) | −1.95539e13 | −1.48571 | −0.742854 | − | 0.669454i | \(-0.766528\pi\) | ||||
−0.742854 | + | 0.669454i | \(0.766528\pi\) | |||||||
\(824\) | 3.92818e12 | 0.296838 | ||||||||
\(825\) | −1.40807e13 | −1.05823 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.31390e13 | 0.976760 | 0.488380 | − | 0.872631i | \(-0.337588\pi\) | ||||
0.488380 | + | 0.872631i | \(0.337588\pi\) | |||||||
\(828\) | 4.01908e12 | 0.297160 | ||||||||
\(829\) | −2.18347e13 | −1.60565 | −0.802827 | − | 0.596211i | \(-0.796672\pi\) | ||||
−0.802827 | + | 0.596211i | \(0.796672\pi\) | |||||||
\(830\) | 1.76574e13 | 1.29145 | ||||||||
\(831\) | −1.74161e12 | −0.126692 | ||||||||
\(832\) | −2.09572e12 | −0.151628 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.57888e12 | −0.256154 | ||||||||
\(835\) | −3.42474e13 | −2.43802 | ||||||||
\(836\) | 3.55593e12 | 0.251782 | ||||||||
\(837\) | 1.55904e13 | 1.09798 | ||||||||
\(838\) | 1.94408e12 | 0.136181 | ||||||||
\(839\) | 1.23225e13 | 0.858561 | 0.429281 | − | 0.903171i | \(-0.358767\pi\) | ||||
0.429281 | + | 0.903171i | \(0.358767\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.85760e13 | 1.28047 | ||||||||
\(842\) | 8.97625e12 | 0.615447 | ||||||||
\(843\) | −1.19563e13 | −0.815406 | ||||||||
\(844\) | 1.62263e12 | 0.110072 | ||||||||
\(845\) | 1.04723e13 | 0.706620 | ||||||||
\(846\) | −7.48606e12 | −0.502443 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.33707e12 | −0.354423 | ||||||||
\(849\) | −2.72654e12 | −0.180105 | ||||||||
\(850\) | 1.51419e13 | 0.994934 | ||||||||
\(851\) | 2.11999e13 | 1.38564 | ||||||||
\(852\) | 9.87506e12 | 0.642040 | ||||||||
\(853\) | 9.07085e12 | 0.586647 | 0.293324 | − | 0.956013i | \(-0.405239\pi\) | ||||
0.293324 | + | 0.956013i | \(0.405239\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.72234e12 | −0.302211 | ||||||||
\(856\) | 6.08136e12 | 0.387141 | ||||||||
\(857\) | 1.66440e12 | 0.105401 | 0.0527003 | − | 0.998610i | \(-0.483217\pi\) | ||||
0.0527003 | + | 0.998610i | \(0.483217\pi\) | |||||||
\(858\) | −1.15570e13 | −0.728036 | ||||||||
\(859\) | −1.40232e12 | −0.0878775 | −0.0439388 | − | 0.999034i | \(-0.513991\pi\) | ||||
−0.0439388 | + | 0.999034i | \(0.513991\pi\) | |||||||
\(860\) | −3.10410e12 | −0.193505 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.67091e13 | −1.03079 | ||||||||
\(863\) | −2.05982e12 | −0.126410 | −0.0632049 | − | 0.998001i | \(-0.520132\pi\) | ||||
−0.0632049 | + | 0.998001i | \(0.520132\pi\) | |||||||
\(864\) | −3.10330e12 | −0.189458 | ||||||||
\(865\) | 1.56502e13 | 0.950492 | ||||||||
\(866\) | −1.68713e13 | −1.01934 | ||||||||
\(867\) | −3.33240e12 | −0.200296 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.27622e13 | −0.759165 | ||||||||
\(870\) | 1.97952e13 | 1.17145 | ||||||||
\(871\) | 1.27060e13 | 0.748044 | ||||||||
\(872\) | 6.28859e12 | 0.368323 | ||||||||
\(873\) | −8.00526e12 | −0.466457 | ||||||||
\(874\) | 6.77921e12 | 0.392986 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.17223e13 | −0.672583 | ||||||||
\(877\) | 1.74285e13 | 0.994859 | 0.497429 | − | 0.867504i | \(-0.334277\pi\) | ||||
0.497429 | + | 0.867504i | \(0.334277\pi\) | |||||||
\(878\) | −1.87259e13 | −1.06345 | ||||||||
\(879\) | −9.68723e10 | −0.00547331 | ||||||||
\(880\) | 7.73112e12 | 0.434580 | ||||||||
\(881\) | −1.33834e11 | −0.00748471 | −0.00374235 | − | 0.999993i | \(-0.501191\pi\) | ||||
−0.00374235 | + | 0.999993i | \(0.501191\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.44009e12 | 0.135077 | 0.0675386 | − | 0.997717i | \(-0.478485\pi\) | ||||
0.0675386 | + | 0.997717i | \(0.478485\pi\) | |||||||
\(884\) | 1.24280e13 | 0.684489 | ||||||||
\(885\) | −1.69035e13 | −0.926258 | ||||||||
\(886\) | 1.13706e13 | 0.619912 | ||||||||
\(887\) | −1.36032e13 | −0.737877 | −0.368939 | − | 0.929454i | \(-0.620279\pi\) | ||||
−0.368939 | + | 0.929454i | \(0.620279\pi\) | |||||||
\(888\) | −5.19063e12 | −0.280132 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.74080e13 | 0.930024 | ||||||||
\(891\) | −6.98289e12 | −0.371181 | ||||||||
\(892\) | 1.11295e13 | 0.588619 | ||||||||
\(893\) | −1.26272e13 | −0.664468 | ||||||||
\(894\) | −1.93958e13 | −1.01552 | ||||||||
\(895\) | −1.30508e13 | −0.679880 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.20329e13 | −1.13633 | ||||||||
\(898\) | −1.50478e13 | −0.772197 | ||||||||
\(899\) | 3.02996e13 | 1.54710 | ||||||||
\(900\) | −5.69734e12 | −0.289455 | ||||||||
\(901\) | 3.16498e13 | 1.59996 | ||||||||
\(902\) | −4.99428e12 | −0.251214 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.34772e13 | −0.671185 | ||||||||
\(905\) | −1.14581e13 | −0.567796 | ||||||||
\(906\) | −1.03766e13 | −0.511657 | ||||||||
\(907\) | −6.73549e12 | −0.330473 | −0.165237 | − | 0.986254i | \(-0.552839\pi\) | ||||
−0.165237 | + | 0.986254i | \(0.552839\pi\) | |||||||
\(908\) | 4.85087e12 | 0.236828 | ||||||||
\(909\) | −7.98443e10 | −0.00387888 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.74134e12 | 0.324275 | 0.162137 | − | 0.986768i | \(-0.448161\pi\) | ||||
0.162137 | + | 0.986768i | \(0.448161\pi\) | |||||||
\(912\) | −1.65984e12 | −0.0794492 | ||||||||
\(913\) | −2.96677e13 | −1.41308 | ||||||||
\(914\) | 1.84132e13 | 0.872714 | ||||||||
\(915\) | 2.96892e12 | 0.140024 | ||||||||
\(916\) | −9.53287e12 | −0.447398 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.84032e13 | 0.855264 | ||||||||
\(919\) | −2.79444e13 | −1.29233 | −0.646167 | − | 0.763196i | \(-0.723629\pi\) | ||||
−0.646167 | + | 0.763196i | \(0.723629\pi\) | |||||||
\(920\) | 1.47390e13 | 0.678302 | ||||||||
\(921\) | 2.26585e12 | 0.103768 | ||||||||
\(922\) | −4.26353e12 | −0.194303 | ||||||||
\(923\) | 4.69267e13 | 2.12820 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.00524e13 | −1.34971 | ||||||||
\(926\) | 7.18025e12 | 0.320915 | ||||||||
\(927\) | 8.76501e12 | 0.389847 | ||||||||
\(928\) | −6.03119e12 | −0.266954 | ||||||||
\(929\) | −1.03095e13 | −0.454118 | −0.227059 | − | 0.973881i | \(-0.572911\pi\) | ||||
−0.227059 | + | 0.973881i | \(0.572911\pi\) | |||||||
\(930\) | 1.81297e13 | 0.794724 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.70624e12 | 0.204316 | ||||||||
\(933\) | −2.36417e13 | −1.02144 | ||||||||
\(934\) | 2.84504e13 | 1.22329 | ||||||||
\(935\) | −4.58470e13 | −1.96182 | ||||||||
\(936\) | −4.67621e12 | −0.199138 | ||||||||
\(937\) | 2.54975e13 | 1.08061 | 0.540306 | − | 0.841468i | \(-0.318308\pi\) | ||||
0.540306 | + | 0.841468i | \(0.318308\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.61814e13 | −0.679236 | ||||||||
\(940\) | −2.74533e13 | −1.14689 | ||||||||
\(941\) | 1.65839e13 | 0.689498 | 0.344749 | − | 0.938695i | \(-0.387964\pi\) | ||||
0.344749 | + | 0.938695i | \(0.387964\pi\) | |||||||
\(942\) | 1.69262e12 | 0.0700373 | ||||||||
\(943\) | −9.52136e12 | −0.392100 | ||||||||
\(944\) | 5.15016e12 | 0.211080 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.21546e12 | 0.211730 | ||||||||
\(947\) | 2.26232e13 | 0.914067 | 0.457034 | − | 0.889449i | \(-0.348912\pi\) | ||||
0.457034 | + | 0.889449i | \(0.348912\pi\) | |||||||
\(948\) | 5.95716e12 | 0.239553 | ||||||||
\(949\) | −5.57051e13 | −2.22945 | ||||||||
\(950\) | −9.61003e12 | −0.382797 | ||||||||
\(951\) | −2.47976e13 | −0.983099 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.02695e11 | −0.0118874 | −0.00594370 | − | 0.999982i | \(-0.501892\pi\) | ||||
−0.00594370 | + | 0.999982i | \(0.501892\pi\) | |||||||
\(954\) | −1.19087e13 | −0.465475 | ||||||||
\(955\) | 1.45271e13 | 0.565151 | ||||||||
\(956\) | −9.35618e12 | −0.362275 | ||||||||
\(957\) | −3.32595e13 | −1.28177 | ||||||||
\(958\) | −3.18250e13 | −1.22074 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.60874e12 | −0.137131 | ||||||||
\(961\) | 1.31065e12 | 0.0495715 | ||||||||
\(962\) | −2.46661e13 | −0.928566 | ||||||||
\(963\) | 1.35694e13 | 0.508444 | ||||||||
\(964\) | −7.31918e12 | −0.272970 | ||||||||
\(965\) | 8.74227e12 | 0.324527 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.03988e12 | 0.111799 | 0.0558994 | − | 0.998436i | \(-0.482197\pi\) | ||||
0.0558994 | + | 0.998436i | \(0.482197\pi\) | |||||||
\(968\) | −3.33153e12 | −0.121956 | ||||||||
\(969\) | 9.84316e12 | 0.358656 | ||||||||
\(970\) | −2.93574e13 | −1.06474 | ||||||||
\(971\) | 2.15206e13 | 0.776906 | 0.388453 | − | 0.921468i | \(-0.373010\pi\) | ||||
0.388453 | + | 0.921468i | \(0.373010\pi\) | |||||||
\(972\) | −1.16532e13 | −0.418742 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.10175e13 | −0.392254 | ||||||||
\(975\) | 3.12333e13 | 1.10687 | ||||||||
\(976\) | −9.04572e11 | −0.0319094 | ||||||||
\(977\) | −1.56454e13 | −0.549364 | −0.274682 | − | 0.961535i | \(-0.588573\pi\) | ||||
−0.274682 | + | 0.961535i | \(0.588573\pi\) | |||||||
\(978\) | −5.50258e12 | −0.192328 | ||||||||
\(979\) | −2.92486e13 | −1.01762 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.40318e13 | 0.483731 | ||||||||
\(982\) | −2.99010e13 | −1.02609 | ||||||||
\(983\) | −2.28763e13 | −0.781437 | −0.390719 | − | 0.920510i | \(-0.627773\pi\) | ||||
−0.390719 | + | 0.920510i | \(0.627773\pi\) | |||||||
\(984\) | 2.33124e12 | 0.0792699 | ||||||||
\(985\) | −7.59510e13 | −2.57081 | ||||||||
\(986\) | 3.57661e13 | 1.20511 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.88763e12 | −0.263354 | ||||||||
\(989\) | 9.94303e12 | 0.330472 | ||||||||
\(990\) | 1.72506e13 | 0.570749 | ||||||||
\(991\) | 4.47356e13 | 1.47340 | 0.736701 | − | 0.676218i | \(-0.236382\pi\) | ||||
0.736701 | + | 0.676218i | \(0.236382\pi\) | |||||||
\(992\) | −5.52374e12 | −0.181105 | ||||||||
\(993\) | −1.47386e13 | −0.481043 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.76192e13 | −1.21676 | ||||||||
\(996\) | 1.38483e13 | 0.445893 | ||||||||
\(997\) | 3.24564e13 | 1.04033 | 0.520166 | − | 0.854065i | \(-0.325870\pi\) | ||||
0.520166 | + | 0.854065i | \(0.325870\pi\) | |||||||
\(998\) | 1.40386e13 | 0.447956 | ||||||||
\(999\) | −3.65251e13 | −1.16024 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 98.10.a.k.1.2 | ✓ | 4 | |
7.2 | even | 3 | 98.10.c.m.67.3 | 8 | |||
7.3 | odd | 6 | 98.10.c.m.79.2 | 8 | |||
7.4 | even | 3 | 98.10.c.m.79.3 | 8 | |||
7.5 | odd | 6 | 98.10.c.m.67.2 | 8 | |||
7.6 | odd | 2 | inner | 98.10.a.k.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.10.a.k.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
98.10.a.k.1.3 | yes | 4 | 7.6 | odd | 2 | inner | |
98.10.c.m.67.2 | 8 | 7.5 | odd | 6 | |||
98.10.c.m.67.3 | 8 | 7.2 | even | 3 | |||
98.10.c.m.79.2 | 8 | 7.3 | odd | 6 | |||
98.10.c.m.79.3 | 8 | 7.4 | even | 3 |