Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,14,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(211.244930035\) |
Analytic rank: | \(1\) |
Dimension: | \(104\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −130.362 | −1.44031 | −0.720154 | − | 0.693815i | \(-0.755929\pi\) | ||||
−0.720154 | + | 0.693815i | \(0.755929\pi\) | |||||||
\(3\) | −354.130 | −0.280463 | −0.140231 | − | 0.990119i | \(-0.544785\pi\) | ||||
−0.140231 | + | 0.990119i | \(0.544785\pi\) | |||||||
\(4\) | 8802.19 | 1.07449 | ||||||||
\(5\) | 43213.6 | 1.23685 | 0.618423 | − | 0.785845i | \(-0.287772\pi\) | ||||
0.618423 | + | 0.785845i | \(0.287772\pi\) | |||||||
\(6\) | 46165.1 | 0.403953 | ||||||||
\(7\) | −431996. | −1.38785 | −0.693924 | − | 0.720048i | \(-0.744120\pi\) | ||||
−0.693924 | + | 0.720048i | \(0.744120\pi\) | |||||||
\(8\) | −79545.1 | −0.107282 | ||||||||
\(9\) | −1.46891e6 | −0.921341 | ||||||||
\(10\) | −5.63341e6 | −1.78144 | ||||||||
\(11\) | −2.08630e6 | −0.355078 | −0.177539 | − | 0.984114i | \(-0.556814\pi\) | ||||
−0.177539 | + | 0.984114i | \(0.556814\pi\) | |||||||
\(12\) | −3.11712e6 | −0.301353 | ||||||||
\(13\) | −1.11228e7 | −0.639120 | −0.319560 | − | 0.947566i | \(-0.603535\pi\) | ||||
−0.319560 | + | 0.947566i | \(0.603535\pi\) | |||||||
\(14\) | 5.63157e7 | 1.99893 | ||||||||
\(15\) | −1.53033e7 | −0.346889 | ||||||||
\(16\) | −6.17379e7 | −0.919966 | ||||||||
\(17\) | −1.52551e6 | −0.0153284 | −0.00766421 | − | 0.999971i | \(-0.502440\pi\) | ||||
−0.00766421 | + | 0.999971i | \(0.502440\pi\) | |||||||
\(18\) | 1.91490e8 | 1.32701 | ||||||||
\(19\) | −3.65937e8 | −1.78447 | −0.892233 | − | 0.451575i | \(-0.850862\pi\) | ||||
−0.892233 | + | 0.451575i | \(0.850862\pi\) | |||||||
\(20\) | 3.80375e8 | 1.32897 | ||||||||
\(21\) | 1.52983e8 | 0.389240 | ||||||||
\(22\) | 2.71974e8 | 0.511422 | ||||||||
\(23\) | 9.39744e8 | 1.32367 | 0.661833 | − | 0.749651i | \(-0.269779\pi\) | ||||
0.661833 | + | 0.749651i | \(0.269779\pi\) | |||||||
\(24\) | 2.81693e7 | 0.0300887 | ||||||||
\(25\) | 6.46716e8 | 0.529789 | ||||||||
\(26\) | 1.44999e9 | 0.920529 | ||||||||
\(27\) | 1.08479e9 | 0.538864 | ||||||||
\(28\) | −3.80251e9 | −1.49122 | ||||||||
\(29\) | 2.35362e9 | 0.734767 | 0.367383 | − | 0.930070i | \(-0.380254\pi\) | ||||
0.367383 | + | 0.930070i | \(0.380254\pi\) | |||||||
\(30\) | 1.99496e9 | 0.499627 | ||||||||
\(31\) | 3.30404e9 | 0.668644 | 0.334322 | − | 0.942459i | \(-0.391493\pi\) | ||||
0.334322 | + | 0.942459i | \(0.391493\pi\) | |||||||
\(32\) | 8.69989e9 | 1.43232 | ||||||||
\(33\) | 7.38822e8 | 0.0995863 | ||||||||
\(34\) | 1.98868e8 | 0.0220776 | ||||||||
\(35\) | −1.86681e10 | −1.71656 | ||||||||
\(36\) | −1.29297e10 | −0.989967 | ||||||||
\(37\) | 1.67506e10 | 1.07330 | 0.536649 | − | 0.843806i | \(-0.319690\pi\) | ||||
0.536649 | + | 0.843806i | \(0.319690\pi\) | |||||||
\(38\) | 4.77042e10 | 2.57018 | ||||||||
\(39\) | 3.93892e9 | 0.179249 | ||||||||
\(40\) | −3.43743e9 | −0.132692 | ||||||||
\(41\) | 3.16155e10 | 1.03945 | 0.519726 | − | 0.854333i | \(-0.326034\pi\) | ||||
0.519726 | + | 0.854333i | \(0.326034\pi\) | |||||||
\(42\) | −1.99431e10 | −0.560625 | ||||||||
\(43\) | 5.12868e10 | 1.23726 | 0.618630 | − | 0.785683i | \(-0.287688\pi\) | ||||
0.618630 | + | 0.785683i | \(0.287688\pi\) | |||||||
\(44\) | −1.83640e10 | −0.381527 | ||||||||
\(45\) | −6.34771e10 | −1.13956 | ||||||||
\(46\) | −1.22507e11 | −1.90649 | ||||||||
\(47\) | −1.37272e11 | −1.85757 | −0.928785 | − | 0.370620i | \(-0.879145\pi\) | ||||
−0.928785 | + | 0.370620i | \(0.879145\pi\) | |||||||
\(48\) | 2.18633e10 | 0.258016 | ||||||||
\(49\) | 8.97312e10 | 0.926123 | ||||||||
\(50\) | −8.43070e10 | −0.763060 | ||||||||
\(51\) | 5.40230e8 | 0.00429905 | ||||||||
\(52\) | −9.79050e10 | −0.686725 | ||||||||
\(53\) | −2.69141e9 | −0.0166796 | −0.00833981 | − | 0.999965i | \(-0.502655\pi\) | ||||
−0.00833981 | + | 0.999965i | \(0.502655\pi\) | |||||||
\(54\) | −1.41415e11 | −0.776130 | ||||||||
\(55\) | −9.01566e10 | −0.439178 | ||||||||
\(56\) | 3.43631e10 | 0.148892 | ||||||||
\(57\) | 1.29590e11 | 0.500476 | ||||||||
\(58\) | −3.06822e11 | −1.05829 | ||||||||
\(59\) | −5.97819e11 | −1.84515 | −0.922576 | − | 0.385816i | \(-0.873920\pi\) | ||||
−0.922576 | + | 0.385816i | \(0.873920\pi\) | |||||||
\(60\) | −1.34702e11 | −0.372728 | ||||||||
\(61\) | −4.79482e11 | −1.19159 | −0.595797 | − | 0.803135i | \(-0.703164\pi\) | ||||
−0.595797 | + | 0.803135i | \(0.703164\pi\) | |||||||
\(62\) | −4.30721e11 | −0.963053 | ||||||||
\(63\) | 6.34565e11 | 1.27868 | ||||||||
\(64\) | −6.28376e11 | −1.14301 | ||||||||
\(65\) | −4.80657e11 | −0.790493 | ||||||||
\(66\) | −9.63142e10 | −0.143435 | ||||||||
\(67\) | 8.58918e11 | 1.16002 | 0.580010 | − | 0.814609i | \(-0.303049\pi\) | ||||
0.580010 | + | 0.814609i | \(0.303049\pi\) | |||||||
\(68\) | −1.34278e10 | −0.0164702 | ||||||||
\(69\) | −3.32792e11 | −0.371239 | ||||||||
\(70\) | 2.43361e12 | 2.47237 | ||||||||
\(71\) | 9.24785e11 | 0.856765 | 0.428382 | − | 0.903598i | \(-0.359084\pi\) | ||||
0.428382 | + | 0.903598i | \(0.359084\pi\) | |||||||
\(72\) | 1.16845e11 | 0.0988436 | ||||||||
\(73\) | 1.02832e12 | 0.795296 | 0.397648 | − | 0.917538i | \(-0.369827\pi\) | ||||
0.397648 | + | 0.917538i | \(0.369827\pi\) | |||||||
\(74\) | −2.18364e12 | −1.54588 | ||||||||
\(75\) | −2.29022e11 | −0.148586 | ||||||||
\(76\) | −3.22105e12 | −1.91738 | ||||||||
\(77\) | 9.01272e11 | 0.492795 | ||||||||
\(78\) | −5.13485e11 | −0.258174 | ||||||||
\(79\) | 1.12964e12 | 0.522832 | 0.261416 | − | 0.965226i | \(-0.415811\pi\) | ||||
0.261416 | + | 0.965226i | \(0.415811\pi\) | |||||||
\(80\) | −2.66792e12 | −1.13786 | ||||||||
\(81\) | 1.95777e12 | 0.770209 | ||||||||
\(82\) | −4.12145e12 | −1.49713 | ||||||||
\(83\) | 3.36152e12 | 1.12857 | 0.564284 | − | 0.825581i | \(-0.309152\pi\) | ||||
0.564284 | + | 0.825581i | \(0.309152\pi\) | |||||||
\(84\) | 1.34658e12 | 0.418233 | ||||||||
\(85\) | −6.59229e10 | −0.0189589 | ||||||||
\(86\) | −6.68584e12 | −1.78203 | ||||||||
\(87\) | −8.33489e11 | −0.206075 | ||||||||
\(88\) | 1.65955e11 | 0.0380937 | ||||||||
\(89\) | −4.04530e12 | −0.862811 | −0.431406 | − | 0.902158i | \(-0.641982\pi\) | ||||
−0.431406 | + | 0.902158i | \(0.641982\pi\) | |||||||
\(90\) | 8.27499e12 | 1.64131 | ||||||||
\(91\) | 4.80500e12 | 0.887002 | ||||||||
\(92\) | 8.27180e12 | 1.42226 | ||||||||
\(93\) | −1.17006e12 | −0.187530 | ||||||||
\(94\) | 1.78950e13 | 2.67547 | ||||||||
\(95\) | −1.58135e13 | −2.20711 | ||||||||
\(96\) | −3.08090e12 | −0.401711 | ||||||||
\(97\) | 1.29664e13 | 1.58053 | 0.790265 | − | 0.612765i | \(-0.209943\pi\) | ||||
0.790265 | + | 0.612765i | \(0.209943\pi\) | |||||||
\(98\) | −1.16975e13 | −1.33390 | ||||||||
\(99\) | 3.06460e12 | 0.327148 | ||||||||
\(100\) | 5.69251e12 | 0.569251 | ||||||||
\(101\) | 1.69646e13 | 1.59021 | 0.795104 | − | 0.606474i | \(-0.207416\pi\) | ||||
0.795104 | + | 0.606474i | \(0.207416\pi\) | |||||||
\(102\) | −7.04253e10 | −0.00619195 | ||||||||
\(103\) | −6.05853e12 | −0.499949 | −0.249974 | − | 0.968252i | \(-0.580422\pi\) | ||||
−0.249974 | + | 0.968252i | \(0.580422\pi\) | |||||||
\(104\) | 8.84764e11 | 0.0685663 | ||||||||
\(105\) | 6.61094e12 | 0.481430 | ||||||||
\(106\) | 3.50856e11 | 0.0240238 | ||||||||
\(107\) | −2.27509e13 | −1.46556 | −0.732781 | − | 0.680464i | \(-0.761778\pi\) | ||||
−0.732781 | + | 0.680464i | \(0.761778\pi\) | |||||||
\(108\) | 9.54849e12 | 0.579002 | ||||||||
\(109\) | 4.33407e12 | 0.247528 | 0.123764 | − | 0.992312i | \(-0.460503\pi\) | ||||
0.123764 | + | 0.992312i | \(0.460503\pi\) | |||||||
\(110\) | 1.17530e13 | 0.632551 | ||||||||
\(111\) | −5.93191e12 | −0.301020 | ||||||||
\(112\) | 2.66705e13 | 1.27677 | ||||||||
\(113\) | 3.27907e13 | 1.48163 | 0.740816 | − | 0.671708i | \(-0.234439\pi\) | ||||
0.740816 | + | 0.671708i | \(0.234439\pi\) | |||||||
\(114\) | −1.68935e13 | −0.720840 | ||||||||
\(115\) | 4.06098e13 | 1.63717 | ||||||||
\(116\) | 2.07170e13 | 0.789496 | ||||||||
\(117\) | 1.63384e13 | 0.588847 | ||||||||
\(118\) | 7.79328e13 | 2.65759 | ||||||||
\(119\) | 6.59014e11 | 0.0212735 | ||||||||
\(120\) | 1.21730e12 | 0.0372151 | ||||||||
\(121\) | −3.01701e13 | −0.873919 | ||||||||
\(122\) | 6.25061e13 | 1.71626 | ||||||||
\(123\) | −1.11960e13 | −0.291527 | ||||||||
\(124\) | 2.90828e13 | 0.718448 | ||||||||
\(125\) | −2.48041e13 | −0.581578 | ||||||||
\(126\) | −8.27230e13 | −1.84169 | ||||||||
\(127\) | −4.06455e13 | −0.859585 | −0.429792 | − | 0.902928i | \(-0.641413\pi\) | ||||
−0.429792 | + | 0.902928i | \(0.641413\pi\) | |||||||
\(128\) | 1.06467e13 | 0.213970 | ||||||||
\(129\) | −1.81622e13 | −0.347005 | ||||||||
\(130\) | 6.26593e13 | 1.13855 | ||||||||
\(131\) | −4.84077e13 | −0.836856 | −0.418428 | − | 0.908250i | \(-0.637419\pi\) | ||||
−0.418428 | + | 0.908250i | \(0.637419\pi\) | |||||||
\(132\) | 6.50325e12 | 0.107004 | ||||||||
\(133\) | 1.58083e14 | 2.47657 | ||||||||
\(134\) | −1.11970e14 | −1.67079 | ||||||||
\(135\) | 4.68775e13 | 0.666493 | ||||||||
\(136\) | 1.21347e11 | 0.00164447 | ||||||||
\(137\) | −4.02215e13 | −0.519726 | −0.259863 | − | 0.965646i | \(-0.583677\pi\) | ||||
−0.259863 | + | 0.965646i | \(0.583677\pi\) | |||||||
\(138\) | 4.33833e13 | 0.534698 | ||||||||
\(139\) | 4.65542e13 | 0.547473 | 0.273737 | − | 0.961805i | \(-0.411740\pi\) | ||||
0.273737 | + | 0.961805i | \(0.411740\pi\) | |||||||
\(140\) | −1.64320e14 | −1.84441 | ||||||||
\(141\) | 4.86121e13 | 0.520979 | ||||||||
\(142\) | −1.20557e14 | −1.23400 | ||||||||
\(143\) | 2.32055e13 | 0.226938 | ||||||||
\(144\) | 9.06877e13 | 0.847602 | ||||||||
\(145\) | 1.01708e14 | 0.908793 | ||||||||
\(146\) | −1.34053e14 | −1.14547 | ||||||||
\(147\) | −3.17765e13 | −0.259743 | ||||||||
\(148\) | 1.47442e14 | 1.15324 | ||||||||
\(149\) | 1.25126e14 | 0.936778 | 0.468389 | − | 0.883522i | \(-0.344835\pi\) | ||||
0.468389 | + | 0.883522i | \(0.344835\pi\) | |||||||
\(150\) | 2.98557e13 | 0.214010 | ||||||||
\(151\) | 7.35760e13 | 0.505110 | 0.252555 | − | 0.967583i | \(-0.418729\pi\) | ||||
0.252555 | + | 0.967583i | \(0.418729\pi\) | |||||||
\(152\) | 2.91085e13 | 0.191442 | ||||||||
\(153\) | 2.24084e12 | 0.0141227 | ||||||||
\(154\) | −1.17491e14 | −0.709776 | ||||||||
\(155\) | 1.42780e14 | 0.827010 | ||||||||
\(156\) | 3.46711e13 | 0.192601 | ||||||||
\(157\) | 1.87382e13 | 0.0998572 | 0.0499286 | − | 0.998753i | \(-0.484101\pi\) | ||||
0.0499286 | + | 0.998753i | \(0.484101\pi\) | |||||||
\(158\) | −1.47261e14 | −0.753039 | ||||||||
\(159\) | 9.53109e11 | 0.00467801 | ||||||||
\(160\) | 3.75954e14 | 1.77156 | ||||||||
\(161\) | −4.05965e14 | −1.83705 | ||||||||
\(162\) | −2.55218e14 | −1.10934 | ||||||||
\(163\) | −9.17220e13 | −0.383049 | −0.191524 | − | 0.981488i | \(-0.561343\pi\) | ||||
−0.191524 | + | 0.981488i | \(0.561343\pi\) | |||||||
\(164\) | 2.78285e14 | 1.11688 | ||||||||
\(165\) | 3.19272e13 | 0.123173 | ||||||||
\(166\) | −4.38213e14 | −1.62548 | ||||||||
\(167\) | 2.47054e14 | 0.881324 | 0.440662 | − | 0.897673i | \(-0.354744\pi\) | ||||
0.440662 | + | 0.897673i | \(0.354744\pi\) | |||||||
\(168\) | −1.21690e13 | −0.0417586 | ||||||||
\(169\) | −1.79158e14 | −0.591526 | ||||||||
\(170\) | 8.59382e12 | 0.0273066 | ||||||||
\(171\) | 5.37531e14 | 1.64410 | ||||||||
\(172\) | 4.51436e14 | 1.32942 | ||||||||
\(173\) | −1.49888e14 | −0.425076 | −0.212538 | − | 0.977153i | \(-0.568173\pi\) | ||||
−0.212538 | + | 0.977153i | \(0.568173\pi\) | |||||||
\(174\) | 1.08655e14 | 0.296811 | ||||||||
\(175\) | −2.79378e14 | −0.735267 | ||||||||
\(176\) | 1.28804e14 | 0.326660 | ||||||||
\(177\) | 2.11706e14 | 0.517496 | ||||||||
\(178\) | 5.27353e14 | 1.24271 | ||||||||
\(179\) | −3.88315e13 | −0.0882346 | −0.0441173 | − | 0.999026i | \(-0.514048\pi\) | ||||
−0.0441173 | + | 0.999026i | \(0.514048\pi\) | |||||||
\(180\) | −5.58738e14 | −1.22444 | ||||||||
\(181\) | 1.34399e14 | 0.284110 | 0.142055 | − | 0.989859i | \(-0.454629\pi\) | ||||
0.142055 | + | 0.989859i | \(0.454629\pi\) | |||||||
\(182\) | −6.26388e14 | −1.27756 | ||||||||
\(183\) | 1.69799e14 | 0.334198 | ||||||||
\(184\) | −7.47520e13 | −0.142006 | ||||||||
\(185\) | 7.23856e14 | 1.32750 | ||||||||
\(186\) | 1.52531e14 | 0.270100 | ||||||||
\(187\) | 3.18267e12 | 0.00544279 | ||||||||
\(188\) | −1.20829e15 | −1.99593 | ||||||||
\(189\) | −4.68623e14 | −0.747862 | ||||||||
\(190\) | 2.06147e15 | 3.17892 | ||||||||
\(191\) | 1.63251e14 | 0.243299 | 0.121649 | − | 0.992573i | \(-0.461182\pi\) | ||||
0.121649 | + | 0.992573i | \(0.461182\pi\) | |||||||
\(192\) | 2.22527e14 | 0.320572 | ||||||||
\(193\) | 4.52436e14 | 0.630137 | 0.315068 | − | 0.949069i | \(-0.397973\pi\) | ||||
0.315068 | + | 0.949069i | \(0.397973\pi\) | |||||||
\(194\) | −1.69032e15 | −2.27645 | ||||||||
\(195\) | 1.70215e14 | 0.221704 | ||||||||
\(196\) | 7.89831e14 | 0.995106 | ||||||||
\(197\) | −5.84517e13 | −0.0712470 | ||||||||
\(198\) | −3.99506e14 | −0.471194 | ||||||||
\(199\) | −1.12221e15 | −1.28095 | −0.640473 | − | 0.767981i | \(-0.721262\pi\) | ||||
−0.640473 | + | 0.767981i | \(0.721262\pi\) | |||||||
\(200\) | −5.14431e13 | −0.0568371 | ||||||||
\(201\) | −3.04169e14 | −0.325342 | ||||||||
\(202\) | −2.21153e15 | −2.29039 | ||||||||
\(203\) | −1.01675e15 | −1.01974 | ||||||||
\(204\) | 4.75520e12 | 0.00461927 | ||||||||
\(205\) | 1.36622e15 | 1.28564 | ||||||||
\(206\) | 7.89801e14 | 0.720080 | ||||||||
\(207\) | −1.38040e15 | −1.21955 | ||||||||
\(208\) | 6.86698e14 | 0.587969 | ||||||||
\(209\) | 7.63455e14 | 0.633625 | ||||||||
\(210\) | −8.61814e14 | −0.693407 | ||||||||
\(211\) | 3.23786e14 | 0.252593 | 0.126297 | − | 0.991993i | \(-0.459691\pi\) | ||||
0.126297 | + | 0.991993i | \(0.459691\pi\) | |||||||
\(212\) | −2.36903e13 | −0.0179220 | ||||||||
\(213\) | −3.27495e14 | −0.240291 | ||||||||
\(214\) | 2.96585e15 | 2.11086 | ||||||||
\(215\) | 2.21629e15 | 1.53030 | ||||||||
\(216\) | −8.62894e13 | −0.0578107 | ||||||||
\(217\) | −1.42733e15 | −0.927976 | ||||||||
\(218\) | −5.64997e14 | −0.356516 | ||||||||
\(219\) | −3.64159e14 | −0.223051 | ||||||||
\(220\) | −7.93576e14 | −0.471890 | ||||||||
\(221\) | 1.69679e13 | 0.00979669 | ||||||||
\(222\) | 7.73294e14 | 0.433561 | ||||||||
\(223\) | 1.72096e15 | 0.937107 | 0.468554 | − | 0.883435i | \(-0.344775\pi\) | ||||
0.468554 | + | 0.883435i | \(0.344775\pi\) | |||||||
\(224\) | −3.75831e15 | −1.98784 | ||||||||
\(225\) | −9.49970e14 | −0.488117 | ||||||||
\(226\) | −4.27465e15 | −2.13401 | ||||||||
\(227\) | −1.48303e15 | −0.719421 | −0.359710 | − | 0.933064i | \(-0.617124\pi\) | ||||
−0.359710 | + | 0.933064i | \(0.617124\pi\) | |||||||
\(228\) | 1.14067e15 | 0.537755 | ||||||||
\(229\) | 5.64162e14 | 0.258507 | 0.129254 | − | 0.991612i | \(-0.458742\pi\) | ||||
0.129254 | + | 0.991612i | \(0.458742\pi\) | |||||||
\(230\) | −5.29396e15 | −2.35803 | ||||||||
\(231\) | −3.19168e14 | −0.138211 | ||||||||
\(232\) | −1.87219e14 | −0.0788275 | ||||||||
\(233\) | −7.20181e14 | −0.294869 | −0.147434 | − | 0.989072i | \(-0.547101\pi\) | ||||
−0.147434 | + | 0.989072i | \(0.547101\pi\) | |||||||
\(234\) | −2.12991e15 | −0.848121 | ||||||||
\(235\) | −5.93201e15 | −2.29753 | ||||||||
\(236\) | −5.26212e15 | −1.98259 | ||||||||
\(237\) | −4.00039e14 | −0.146635 | ||||||||
\(238\) | −8.59102e13 | −0.0306404 | ||||||||
\(239\) | 8.69155e14 | 0.301655 | 0.150828 | − | 0.988560i | \(-0.451806\pi\) | ||||
0.150828 | + | 0.988560i | \(0.451806\pi\) | |||||||
\(240\) | 9.44791e14 | 0.319126 | ||||||||
\(241\) | −4.72685e15 | −1.55404 | −0.777018 | − | 0.629478i | \(-0.783269\pi\) | ||||
−0.777018 | + | 0.629478i | \(0.783269\pi\) | |||||||
\(242\) | 3.93302e15 | 1.25871 | ||||||||
\(243\) | −2.42280e15 | −0.754879 | ||||||||
\(244\) | −4.22049e15 | −1.28035 | ||||||||
\(245\) | 3.87761e15 | 1.14547 | ||||||||
\(246\) | 1.45953e15 | 0.419889 | ||||||||
\(247\) | 4.07025e15 | 1.14049 | ||||||||
\(248\) | −2.62820e14 | −0.0717337 | ||||||||
\(249\) | −1.19041e15 | −0.316521 | ||||||||
\(250\) | 3.23350e15 | 0.837652 | ||||||||
\(251\) | 1.70080e15 | 0.429314 | 0.214657 | − | 0.976689i | \(-0.431137\pi\) | ||||
0.214657 | + | 0.976689i | \(0.431137\pi\) | |||||||
\(252\) | 5.58556e15 | 1.37392 | ||||||||
\(253\) | −1.96059e15 | −0.470005 | ||||||||
\(254\) | 5.29862e15 | 1.23807 | ||||||||
\(255\) | 2.33453e13 | 0.00531726 | ||||||||
\(256\) | 3.75973e15 | 0.834828 | ||||||||
\(257\) | 2.07760e14 | 0.0449777 | 0.0224888 | − | 0.999747i | \(-0.492841\pi\) | ||||
0.0224888 | + | 0.999747i | \(0.492841\pi\) | |||||||
\(258\) | 2.36766e15 | 0.499794 | ||||||||
\(259\) | −7.23620e15 | −1.48957 | ||||||||
\(260\) | −4.23083e15 | −0.849374 | ||||||||
\(261\) | −3.45727e15 | −0.676970 | ||||||||
\(262\) | 6.31051e15 | 1.20533 | ||||||||
\(263\) | −8.78752e13 | −0.0163740 | −0.00818699 | − | 0.999966i | \(-0.502606\pi\) | ||||
−0.00818699 | + | 0.999966i | \(0.502606\pi\) | |||||||
\(264\) | −5.87697e13 | −0.0106839 | ||||||||
\(265\) | −1.16305e14 | −0.0206301 | ||||||||
\(266\) | −2.06080e16 | −3.56702 | ||||||||
\(267\) | 1.43256e15 | 0.241986 | ||||||||
\(268\) | 7.56036e15 | 1.24642 | ||||||||
\(269\) | −9.58755e15 | −1.54283 | −0.771414 | − | 0.636333i | \(-0.780450\pi\) | ||||
−0.771414 | + | 0.636333i | \(0.780450\pi\) | |||||||
\(270\) | −6.11104e15 | −0.959954 | ||||||||
\(271\) | 6.49098e15 | 0.995429 | 0.497714 | − | 0.867341i | \(-0.334173\pi\) | ||||
0.497714 | + | 0.867341i | \(0.334173\pi\) | |||||||
\(272\) | 9.41818e13 | 0.0141016 | ||||||||
\(273\) | −1.70160e15 | −0.248771 | ||||||||
\(274\) | 5.24334e15 | 0.748565 | ||||||||
\(275\) | −1.34924e15 | −0.188117 | ||||||||
\(276\) | −2.92930e15 | −0.398891 | ||||||||
\(277\) | 1.15861e16 | 1.54105 | 0.770527 | − | 0.637407i | \(-0.219993\pi\) | ||||
0.770527 | + | 0.637407i | \(0.219993\pi\) | |||||||
\(278\) | −6.06889e15 | −0.788530 | ||||||||
\(279\) | −4.85336e15 | −0.616049 | ||||||||
\(280\) | 1.48496e15 | 0.184156 | ||||||||
\(281\) | 1.45285e16 | 1.76047 | 0.880235 | − | 0.474538i | \(-0.157385\pi\) | ||||
0.880235 | + | 0.474538i | \(0.157385\pi\) | |||||||
\(282\) | −6.33716e15 | −0.750370 | ||||||||
\(283\) | −1.50963e16 | −1.74686 | −0.873430 | − | 0.486950i | \(-0.838109\pi\) | ||||
−0.873430 | + | 0.486950i | \(0.838109\pi\) | |||||||
\(284\) | 8.14013e15 | 0.920581 | ||||||||
\(285\) | 5.60004e15 | 0.619012 | ||||||||
\(286\) | −3.02511e15 | −0.326860 | ||||||||
\(287\) | −1.36577e16 | −1.44260 | ||||||||
\(288\) | −1.27794e16 | −1.31965 | ||||||||
\(289\) | −9.90225e15 | −0.999765 | ||||||||
\(290\) | −1.32589e16 | −1.30894 | ||||||||
\(291\) | −4.59179e15 | −0.443280 | ||||||||
\(292\) | 9.05144e15 | 0.854534 | ||||||||
\(293\) | −7.51198e15 | −0.693609 | −0.346805 | − | 0.937937i | \(-0.612733\pi\) | ||||
−0.346805 | + | 0.937937i | \(0.612733\pi\) | |||||||
\(294\) | 4.14245e15 | 0.374110 | ||||||||
\(295\) | −2.58340e16 | −2.28217 | ||||||||
\(296\) | −1.33243e15 | −0.115146 | ||||||||
\(297\) | −2.26319e15 | −0.191339 | ||||||||
\(298\) | −1.63116e16 | −1.34925 | ||||||||
\(299\) | −1.04526e16 | −0.845982 | ||||||||
\(300\) | −2.01589e15 | −0.159654 | ||||||||
\(301\) | −2.21557e16 | −1.71713 | ||||||||
\(302\) | −9.59150e15 | −0.727514 | ||||||||
\(303\) | −6.00767e15 | −0.445994 | ||||||||
\(304\) | 2.25922e16 | 1.64165 | ||||||||
\(305\) | −2.07202e16 | −1.47382 | ||||||||
\(306\) | −2.92120e14 | −0.0203410 | ||||||||
\(307\) | 1.71489e15 | 0.116906 | 0.0584530 | − | 0.998290i | \(-0.481383\pi\) | ||||
0.0584530 | + | 0.998290i | \(0.481383\pi\) | |||||||
\(308\) | 7.93317e15 | 0.529501 | ||||||||
\(309\) | 2.14551e15 | 0.140217 | ||||||||
\(310\) | −1.86130e16 | −1.19115 | ||||||||
\(311\) | 1.38605e16 | 0.868631 | 0.434316 | − | 0.900761i | \(-0.356990\pi\) | ||||
0.434316 | + | 0.900761i | \(0.356990\pi\) | |||||||
\(312\) | −3.13322e14 | −0.0192303 | ||||||||
\(313\) | −2.39233e16 | −1.43808 | −0.719040 | − | 0.694969i | \(-0.755418\pi\) | ||||
−0.719040 | + | 0.694969i | \(0.755418\pi\) | |||||||
\(314\) | −2.44274e15 | −0.143825 | ||||||||
\(315\) | 2.74218e16 | 1.58153 | ||||||||
\(316\) | 9.94327e15 | 0.561776 | ||||||||
\(317\) | −2.31923e16 | −1.28369 | −0.641843 | − | 0.766836i | \(-0.721830\pi\) | ||||
−0.641843 | + | 0.766836i | \(0.721830\pi\) | |||||||
\(318\) | −1.24249e14 | −0.00673777 | ||||||||
\(319\) | −4.91036e15 | −0.260900 | ||||||||
\(320\) | −2.71544e16 | −1.41373 | ||||||||
\(321\) | 8.05679e15 | 0.411036 | ||||||||
\(322\) | 5.29223e16 | 2.64591 | ||||||||
\(323\) | 5.58241e14 | 0.0273530 | ||||||||
\(324\) | 1.72326e16 | 0.827579 | ||||||||
\(325\) | −7.19329e15 | −0.338599 | ||||||||
\(326\) | 1.19570e16 | 0.551708 | ||||||||
\(327\) | −1.53483e15 | −0.0694223 | ||||||||
\(328\) | −2.51485e15 | −0.111515 | ||||||||
\(329\) | 5.93008e16 | 2.57802 | ||||||||
\(330\) | −4.16209e15 | −0.177407 | ||||||||
\(331\) | −1.97820e16 | −0.826775 | −0.413387 | − | 0.910555i | \(-0.635654\pi\) | ||||
−0.413387 | + | 0.910555i | \(0.635654\pi\) | |||||||
\(332\) | 2.95887e16 | 1.21263 | ||||||||
\(333\) | −2.46053e16 | −0.988873 | ||||||||
\(334\) | −3.22064e16 | −1.26938 | ||||||||
\(335\) | 3.71170e16 | 1.43477 | ||||||||
\(336\) | −9.44483e15 | −0.358087 | ||||||||
\(337\) | 4.12798e16 | 1.53512 | 0.767561 | − | 0.640976i | \(-0.221470\pi\) | ||||
0.767561 | + | 0.640976i | \(0.221470\pi\) | |||||||
\(338\) | 2.33554e16 | 0.851979 | ||||||||
\(339\) | −1.16122e16 | −0.415543 | ||||||||
\(340\) | −5.80265e14 | −0.0203711 | ||||||||
\(341\) | −6.89323e15 | −0.237421 | ||||||||
\(342\) | −7.00734e16 | −2.36801 | ||||||||
\(343\) | 3.09216e15 | 0.102530 | ||||||||
\(344\) | −4.07961e15 | −0.132736 | ||||||||
\(345\) | −1.43812e16 | −0.459166 | ||||||||
\(346\) | 1.95397e16 | 0.612241 | ||||||||
\(347\) | −4.98693e16 | −1.53353 | −0.766764 | − | 0.641929i | \(-0.778134\pi\) | ||||
−0.766764 | + | 0.641929i | \(0.778134\pi\) | |||||||
\(348\) | −7.33652e15 | −0.221424 | ||||||||
\(349\) | −8.69199e15 | −0.257486 | −0.128743 | − | 0.991678i | \(-0.541094\pi\) | ||||
−0.128743 | + | 0.991678i | \(0.541094\pi\) | |||||||
\(350\) | 3.64202e16 | 1.05901 | ||||||||
\(351\) | −1.20659e16 | −0.344399 | ||||||||
\(352\) | −1.81506e16 | −0.508585 | ||||||||
\(353\) | 5.78772e16 | 1.59211 | 0.796053 | − | 0.605228i | \(-0.206918\pi\) | ||||
0.796053 | + | 0.605228i | \(0.206918\pi\) | |||||||
\(354\) | −2.75984e16 | −0.745354 | ||||||||
\(355\) | 3.99633e16 | 1.05969 | ||||||||
\(356\) | −3.56075e16 | −0.927078 | ||||||||
\(357\) | −2.33377e14 | −0.00596643 | ||||||||
\(358\) | 5.06214e15 | 0.127085 | ||||||||
\(359\) | −3.73927e16 | −0.921877 | −0.460938 | − | 0.887432i | \(-0.652487\pi\) | ||||
−0.460938 | + | 0.887432i | \(0.652487\pi\) | |||||||
\(360\) | 5.04930e15 | 0.122254 | ||||||||
\(361\) | 9.18571e16 | 2.18432 | ||||||||
\(362\) | −1.75205e16 | −0.409205 | ||||||||
\(363\) | 1.06841e16 | 0.245102 | ||||||||
\(364\) | 4.22945e16 | 0.953071 | ||||||||
\(365\) | 4.44374e16 | 0.983659 | ||||||||
\(366\) | −2.21353e16 | −0.481347 | ||||||||
\(367\) | 6.55093e16 | 1.39950 | 0.699751 | − | 0.714387i | \(-0.253294\pi\) | ||||
0.699751 | + | 0.714387i | \(0.253294\pi\) | |||||||
\(368\) | −5.80178e16 | −1.21773 | ||||||||
\(369\) | −4.64404e16 | −0.957689 | ||||||||
\(370\) | −9.43631e16 | −1.91201 | ||||||||
\(371\) | 1.16268e15 | 0.0231488 | ||||||||
\(372\) | −1.02991e16 | −0.201498 | ||||||||
\(373\) | 6.89000e16 | 1.32468 | 0.662341 | − | 0.749202i | \(-0.269563\pi\) | ||||
0.662341 | + | 0.749202i | \(0.269563\pi\) | |||||||
\(374\) | −4.14899e14 | −0.00783929 | ||||||||
\(375\) | 8.78388e15 | 0.163111 | ||||||||
\(376\) | 1.09193e16 | 0.199284 | ||||||||
\(377\) | −2.61788e16 | −0.469604 | ||||||||
\(378\) | 6.10905e16 | 1.07715 | ||||||||
\(379\) | 7.69091e16 | 1.33298 | 0.666489 | − | 0.745515i | \(-0.267796\pi\) | ||||
0.666489 | + | 0.745515i | \(0.267796\pi\) | |||||||
\(380\) | −1.39193e17 | −2.37151 | ||||||||
\(381\) | 1.43938e16 | 0.241082 | ||||||||
\(382\) | −2.12817e16 | −0.350425 | ||||||||
\(383\) | 7.74236e16 | 1.25338 | 0.626688 | − | 0.779270i | \(-0.284410\pi\) | ||||
0.626688 | + | 0.779270i | \(0.284410\pi\) | |||||||
\(384\) | −3.77034e15 | −0.0600105 | ||||||||
\(385\) | 3.89473e16 | 0.609512 | ||||||||
\(386\) | −5.89804e16 | −0.907590 | ||||||||
\(387\) | −7.53359e16 | −1.13994 | ||||||||
\(388\) | 1.14133e17 | 1.69826 | ||||||||
\(389\) | 2.01646e16 | 0.295065 | 0.147532 | − | 0.989057i | \(-0.452867\pi\) | ||||
0.147532 | + | 0.989057i | \(0.452867\pi\) | |||||||
\(390\) | −2.21896e16 | −0.319322 | ||||||||
\(391\) | −1.43359e15 | −0.0202897 | ||||||||
\(392\) | −7.13767e15 | −0.0993567 | ||||||||
\(393\) | 1.71426e16 | 0.234707 | ||||||||
\(394\) | 7.61987e15 | 0.102618 | ||||||||
\(395\) | 4.88157e16 | 0.646663 | ||||||||
\(396\) | 2.69752e16 | 0.351516 | ||||||||
\(397\) | −9.16217e14 | −0.0117452 | −0.00587259 | − | 0.999983i | \(-0.501869\pi\) | ||||
−0.00587259 | + | 0.999983i | \(0.501869\pi\) | |||||||
\(398\) | 1.46294e17 | 1.84496 | ||||||||
\(399\) | −5.59821e16 | −0.694585 | ||||||||
\(400\) | −3.99269e16 | −0.487388 | ||||||||
\(401\) | −6.44125e16 | −0.773627 | −0.386813 | − | 0.922158i | \(-0.626424\pi\) | ||||
−0.386813 | + | 0.922158i | \(0.626424\pi\) | |||||||
\(402\) | 3.96520e16 | 0.468593 | ||||||||
\(403\) | −3.67502e16 | −0.427344 | ||||||||
\(404\) | 1.49325e17 | 1.70865 | ||||||||
\(405\) | 8.46023e16 | 0.952631 | ||||||||
\(406\) | 1.32546e17 | 1.46875 | ||||||||
\(407\) | −3.49469e16 | −0.381105 | ||||||||
\(408\) | −4.29726e13 | −0.000461212 0 | ||||||||
\(409\) | −5.87064e16 | −0.620132 | −0.310066 | − | 0.950715i | \(-0.600351\pi\) | ||||
−0.310066 | + | 0.950715i | \(0.600351\pi\) | |||||||
\(410\) | −1.78103e17 | −1.85172 | ||||||||
\(411\) | 1.42436e16 | 0.145764 | ||||||||
\(412\) | −5.33283e16 | −0.537188 | ||||||||
\(413\) | 2.58255e17 | 2.56079 | ||||||||
\(414\) | 1.79952e17 | 1.75652 | ||||||||
\(415\) | 1.45263e17 | 1.39586 | ||||||||
\(416\) | −9.67672e16 | −0.915422 | ||||||||
\(417\) | −1.64863e16 | −0.153546 | ||||||||
\(418\) | −9.95253e16 | −0.912616 | ||||||||
\(419\) | −1.69233e17 | −1.52790 | −0.763948 | − | 0.645278i | \(-0.776742\pi\) | ||||
−0.763948 | + | 0.645278i | \(0.776742\pi\) | |||||||
\(420\) | 5.81908e16 | 0.517290 | ||||||||
\(421\) | −1.23495e17 | −1.08098 | −0.540488 | − | 0.841351i | \(-0.681761\pi\) | ||||
−0.540488 | + | 0.841351i | \(0.681761\pi\) | |||||||
\(422\) | −4.22093e16 | −0.363812 | ||||||||
\(423\) | 2.01640e17 | 1.71145 | ||||||||
\(424\) | 2.14088e14 | 0.00178943 | ||||||||
\(425\) | −9.86571e14 | −0.00812083 | ||||||||
\(426\) | 4.26928e16 | 0.346092 | ||||||||
\(427\) | 2.07134e17 | 1.65375 | ||||||||
\(428\) | −2.00258e17 | −1.57473 | ||||||||
\(429\) | −8.21778e15 | −0.0636476 | ||||||||
\(430\) | −2.88919e17 | −2.20410 | ||||||||
\(431\) | −2.22328e16 | −0.167068 | −0.0835338 | − | 0.996505i | \(-0.526621\pi\) | ||||
−0.0835338 | + | 0.996505i | \(0.526621\pi\) | |||||||
\(432\) | −6.69724e16 | −0.495737 | ||||||||
\(433\) | −2.25406e17 | −1.64359 | −0.821796 | − | 0.569782i | \(-0.807028\pi\) | ||||
−0.821796 | + | 0.569782i | \(0.807028\pi\) | |||||||
\(434\) | 1.86070e17 | 1.33657 | ||||||||
\(435\) | −3.60181e16 | −0.254883 | ||||||||
\(436\) | 3.81493e16 | 0.265965 | ||||||||
\(437\) | −3.43887e17 | −2.36204 | ||||||||
\(438\) | 4.74724e16 | 0.321262 | ||||||||
\(439\) | 5.26523e16 | 0.351073 | 0.175537 | − | 0.984473i | \(-0.443834\pi\) | ||||
0.175537 | + | 0.984473i | \(0.443834\pi\) | |||||||
\(440\) | 7.17152e15 | 0.0471160 | ||||||||
\(441\) | −1.31807e17 | −0.853275 | ||||||||
\(442\) | −2.21197e15 | −0.0141103 | ||||||||
\(443\) | 7.62979e16 | 0.479610 | 0.239805 | − | 0.970821i | \(-0.422916\pi\) | ||||
0.239805 | + | 0.970821i | \(0.422916\pi\) | |||||||
\(444\) | −5.22138e16 | −0.323442 | ||||||||
\(445\) | −1.74812e17 | −1.06717 | ||||||||
\(446\) | −2.24347e17 | −1.34972 | ||||||||
\(447\) | −4.43109e16 | −0.262731 | ||||||||
\(448\) | 2.71456e17 | 1.58632 | ||||||||
\(449\) | −7.06286e16 | −0.406799 | −0.203399 | − | 0.979096i | \(-0.565199\pi\) | ||||
−0.203399 | + | 0.979096i | \(0.565199\pi\) | |||||||
\(450\) | 1.23840e17 | 0.703038 | ||||||||
\(451\) | −6.59593e16 | −0.369087 | ||||||||
\(452\) | 2.88630e17 | 1.59199 | ||||||||
\(453\) | −2.60555e16 | −0.141665 | ||||||||
\(454\) | 1.93331e17 | 1.03619 | ||||||||
\(455\) | 2.07642e17 | 1.09708 | ||||||||
\(456\) | −1.03082e16 | −0.0536923 | ||||||||
\(457\) | −1.37388e17 | −0.705497 | −0.352748 | − | 0.935718i | \(-0.614753\pi\) | ||||
−0.352748 | + | 0.935718i | \(0.614753\pi\) | |||||||
\(458\) | −7.35451e16 | −0.372330 | ||||||||
\(459\) | −1.65485e15 | −0.00825994 | ||||||||
\(460\) | 3.57455e17 | 1.75912 | ||||||||
\(461\) | −1.74298e17 | −0.845739 | −0.422869 | − | 0.906191i | \(-0.638977\pi\) | ||||
−0.422869 | + | 0.906191i | \(0.638977\pi\) | |||||||
\(462\) | 4.16073e16 | 0.199066 | ||||||||
\(463\) | 3.38040e17 | 1.59475 | 0.797374 | − | 0.603485i | \(-0.206222\pi\) | ||||
0.797374 | + | 0.603485i | \(0.206222\pi\) | |||||||
\(464\) | −1.45308e17 | −0.675960 | ||||||||
\(465\) | −5.05627e16 | −0.231945 | ||||||||
\(466\) | 9.38841e16 | 0.424701 | ||||||||
\(467\) | −3.13179e17 | −1.39712 | −0.698559 | − | 0.715552i | \(-0.746175\pi\) | ||||
−0.698559 | + | 0.715552i | \(0.746175\pi\) | |||||||
\(468\) | 1.43814e17 | 0.632708 | ||||||||
\(469\) | −3.71049e17 | −1.60993 | ||||||||
\(470\) | 7.73307e17 | 3.30915 | ||||||||
\(471\) | −6.63575e15 | −0.0280062 | ||||||||
\(472\) | 4.75536e16 | 0.197952 | ||||||||
\(473\) | −1.07000e17 | −0.439324 | ||||||||
\(474\) | 5.21497e16 | 0.211199 | ||||||||
\(475\) | −2.36657e17 | −0.945391 | ||||||||
\(476\) | 5.80076e15 | 0.0228581 | ||||||||
\(477\) | 3.95344e15 | 0.0153676 | ||||||||
\(478\) | −1.13305e17 | −0.434476 | ||||||||
\(479\) | −4.95167e17 | −1.87314 | −0.936572 | − | 0.350475i | \(-0.886020\pi\) | ||||
−0.936572 | + | 0.350475i | \(0.886020\pi\) | |||||||
\(480\) | −1.33137e17 | −0.496855 | ||||||||
\(481\) | −1.86314e17 | −0.685966 | ||||||||
\(482\) | 6.16200e17 | 2.23829 | ||||||||
\(483\) | 1.43765e17 | 0.515224 | ||||||||
\(484\) | −2.65563e17 | −0.939014 | ||||||||
\(485\) | 5.60325e17 | 1.95487 | ||||||||
\(486\) | 3.15841e17 | 1.08726 | ||||||||
\(487\) | 2.13238e16 | 0.0724313 | 0.0362156 | − | 0.999344i | \(-0.488470\pi\) | ||||
0.0362156 | + | 0.999344i | \(0.488470\pi\) | |||||||
\(488\) | 3.81404e16 | 0.127837 | ||||||||
\(489\) | 3.24816e16 | 0.107431 | ||||||||
\(490\) | −5.05492e17 | −1.64983 | ||||||||
\(491\) | 2.36164e17 | 0.760649 | 0.380324 | − | 0.924853i | \(-0.375812\pi\) | ||||
0.380324 | + | 0.924853i | \(0.375812\pi\) | |||||||
\(492\) | −9.85492e16 | −0.313242 | ||||||||
\(493\) | −3.59047e15 | −0.0112628 | ||||||||
\(494\) | −5.30605e17 | −1.64265 | ||||||||
\(495\) | 1.32432e17 | 0.404632 | ||||||||
\(496\) | −2.03985e17 | −0.615130 | ||||||||
\(497\) | −3.99503e17 | −1.18906 | ||||||||
\(498\) | 1.55185e17 | 0.455888 | ||||||||
\(499\) | −2.84757e17 | −0.825698 | −0.412849 | − | 0.910799i | \(-0.635466\pi\) | ||||
−0.412849 | + | 0.910799i | \(0.635466\pi\) | |||||||
\(500\) | −2.18330e17 | −0.624898 | ||||||||
\(501\) | −8.74895e16 | −0.247178 | ||||||||
\(502\) | −2.21720e17 | −0.618344 | ||||||||
\(503\) | −4.44490e17 | −1.22369 | −0.611844 | − | 0.790979i | \(-0.709572\pi\) | ||||
−0.611844 | + | 0.790979i | \(0.709572\pi\) | |||||||
\(504\) | −5.04765e16 | −0.137180 | ||||||||
\(505\) | 7.33100e17 | 1.96684 | ||||||||
\(506\) | 2.55586e17 | 0.676952 | ||||||||
\(507\) | 6.34454e16 | 0.165901 | ||||||||
\(508\) | −3.57770e17 | −0.923612 | ||||||||
\(509\) | 2.80337e17 | 0.714519 | 0.357260 | − | 0.934005i | \(-0.383711\pi\) | ||||
0.357260 | + | 0.934005i | \(0.383711\pi\) | |||||||
\(510\) | −3.04333e15 | −0.00765849 | ||||||||
\(511\) | −4.44229e17 | −1.10375 | ||||||||
\(512\) | −5.77343e17 | −1.41638 | ||||||||
\(513\) | −3.96964e17 | −0.961585 | ||||||||
\(514\) | −2.70840e16 | −0.0647817 | ||||||||
\(515\) | −2.61811e17 | −0.618360 | ||||||||
\(516\) | −1.59867e17 | −0.372852 | ||||||||
\(517\) | 2.86390e17 | 0.659583 | ||||||||
\(518\) | 9.43324e17 | 2.14545 | ||||||||
\(519\) | 5.30799e16 | 0.119218 | ||||||||
\(520\) | 3.82339e16 | 0.0848060 | ||||||||
\(521\) | 5.77857e17 | 1.26583 | 0.632915 | − | 0.774221i | \(-0.281858\pi\) | ||||
0.632915 | + | 0.774221i | \(0.281858\pi\) | |||||||
\(522\) | 4.50695e17 | 0.975045 | ||||||||
\(523\) | −8.49227e16 | −0.181452 | −0.0907262 | − | 0.995876i | \(-0.528919\pi\) | ||||
−0.0907262 | + | 0.995876i | \(0.528919\pi\) | |||||||
\(524\) | −4.26093e17 | −0.899190 | ||||||||
\(525\) | 9.89364e16 | 0.206215 | ||||||||
\(526\) | 1.14556e16 | 0.0235836 | ||||||||
\(527\) | −5.04035e15 | −0.0102492 | ||||||||
\(528\) | −4.56133e16 | −0.0916160 | ||||||||
\(529\) | 3.79082e17 | 0.752093 | ||||||||
\(530\) | 1.51618e16 | 0.0297137 | ||||||||
\(531\) | 8.78146e17 | 1.70001 | ||||||||
\(532\) | 1.39148e18 | 2.66104 | ||||||||
\(533\) | −3.51652e17 | −0.664334 | ||||||||
\(534\) | −1.86752e17 | −0.348535 | ||||||||
\(535\) | −9.83150e17 | −1.81268 | ||||||||
\(536\) | −6.83227e16 | −0.124450 | ||||||||
\(537\) | 1.37514e16 | 0.0247465 | ||||||||
\(538\) | 1.24985e18 | 2.22215 | ||||||||
\(539\) | −1.87206e17 | −0.328846 | ||||||||
\(540\) | 4.12625e17 | 0.716137 | ||||||||
\(541\) | −3.20352e17 | −0.549346 | −0.274673 | − | 0.961538i | \(-0.588570\pi\) | ||||
−0.274673 | + | 0.961538i | \(0.588570\pi\) | |||||||
\(542\) | −8.46176e17 | −1.43372 | ||||||||
\(543\) | −4.75949e16 | −0.0796822 | ||||||||
\(544\) | −1.32718e16 | −0.0219551 | ||||||||
\(545\) | 1.87291e17 | 0.306154 | ||||||||
\(546\) | 2.21823e17 | 0.358307 | ||||||||
\(547\) | 8.83411e17 | 1.41008 | 0.705042 | − | 0.709165i | \(-0.250928\pi\) | ||||
0.705042 | + | 0.709165i | \(0.250928\pi\) | |||||||
\(548\) | −3.54037e17 | −0.558438 | ||||||||
\(549\) | 7.04318e17 | 1.09786 | ||||||||
\(550\) | 1.75890e17 | 0.270946 | ||||||||
\(551\) | −8.61277e17 | −1.31117 | ||||||||
\(552\) | 2.64720e16 | 0.0398274 | ||||||||
\(553\) | −4.87998e17 | −0.725612 | ||||||||
\(554\) | −1.51038e18 | −2.21959 | ||||||||
\(555\) | −2.56339e17 | −0.372316 | ||||||||
\(556\) | 4.09779e17 | 0.588252 | ||||||||
\(557\) | 3.21388e17 | 0.456006 | 0.228003 | − | 0.973660i | \(-0.426780\pi\) | ||||
0.228003 | + | 0.973660i | \(0.426780\pi\) | |||||||
\(558\) | 6.32692e17 | 0.887299 | ||||||||
\(559\) | −5.70453e17 | −0.790757 | ||||||||
\(560\) | 1.15253e18 | 1.57917 | ||||||||
\(561\) | −1.12708e15 | −0.00152650 | ||||||||
\(562\) | −1.89396e18 | −2.53562 | ||||||||
\(563\) | −1.00802e18 | −1.33403 | −0.667015 | − | 0.745044i | \(-0.732428\pi\) | ||||
−0.667015 | + | 0.745044i | \(0.732428\pi\) | |||||||
\(564\) | 4.27893e17 | 0.559784 | ||||||||
\(565\) | 1.41700e18 | 1.83255 | ||||||||
\(566\) | 1.96798e18 | 2.51601 | ||||||||
\(567\) | −8.45747e17 | −1.06893 | ||||||||
\(568\) | −7.35621e16 | −0.0919158 | ||||||||
\(569\) | 1.09784e18 | 1.35615 | 0.678077 | − | 0.734991i | \(-0.262813\pi\) | ||||
0.678077 | + | 0.734991i | \(0.262813\pi\) | |||||||
\(570\) | −7.30031e17 | −0.891568 | ||||||||
\(571\) | 4.95212e17 | 0.597938 | 0.298969 | − | 0.954263i | \(-0.403357\pi\) | ||||
0.298969 | + | 0.954263i | \(0.403357\pi\) | |||||||
\(572\) | 2.04259e17 | 0.243841 | ||||||||
\(573\) | −5.78122e16 | −0.0682362 | ||||||||
\(574\) | 1.78045e18 | 2.07779 | ||||||||
\(575\) | 6.07747e17 | 0.701264 | ||||||||
\(576\) | 9.23031e17 | 1.05310 | ||||||||
\(577\) | −4.70532e17 | −0.530819 | −0.265410 | − | 0.964136i | \(-0.585507\pi\) | ||||
−0.265410 | + | 0.964136i | \(0.585507\pi\) | |||||||
\(578\) | 1.29087e18 | 1.43997 | ||||||||
\(579\) | −1.60221e17 | −0.176730 | ||||||||
\(580\) | 8.95257e17 | 0.976486 | ||||||||
\(581\) | −1.45216e18 | −1.56628 | ||||||||
\(582\) | 5.98594e17 | 0.638459 | ||||||||
\(583\) | 5.61508e15 | 0.00592257 | ||||||||
\(584\) | −8.17976e16 | −0.0853212 | ||||||||
\(585\) | 7.06044e17 | 0.728314 | ||||||||
\(586\) | 9.79275e17 | 0.999010 | ||||||||
\(587\) | −1.48009e18 | −1.49327 | −0.746637 | − | 0.665231i | \(-0.768333\pi\) | ||||
−0.746637 | + | 0.665231i | \(0.768333\pi\) | |||||||
\(588\) | −2.79703e17 | −0.279090 | ||||||||
\(589\) | −1.20907e18 | −1.19317 | ||||||||
\(590\) | 3.36776e18 | 3.28702 | ||||||||
\(591\) | 2.06995e16 | 0.0199821 | ||||||||
\(592\) | −1.03415e18 | −0.987397 | ||||||||
\(593\) | −8.73156e17 | −0.824587 | −0.412293 | − | 0.911051i | \(-0.635272\pi\) | ||||
−0.412293 | + | 0.911051i | \(0.635272\pi\) | |||||||
\(594\) | 2.95033e17 | 0.275587 | ||||||||
\(595\) | 2.84784e16 | 0.0263121 | ||||||||
\(596\) | 1.10138e18 | 1.00656 | ||||||||
\(597\) | 3.97410e17 | 0.359258 | ||||||||
\(598\) | 1.36262e18 | 1.21847 | ||||||||
\(599\) | 6.21604e17 | 0.549844 | 0.274922 | − | 0.961466i | \(-0.411348\pi\) | ||||
0.274922 | + | 0.961466i | \(0.411348\pi\) | |||||||
\(600\) | 1.82176e16 | 0.0159407 | ||||||||
\(601\) | 1.31450e18 | 1.13783 | 0.568913 | − | 0.822398i | \(-0.307364\pi\) | ||||
0.568913 | + | 0.822398i | \(0.307364\pi\) | |||||||
\(602\) | 2.88825e18 | 2.47319 | ||||||||
\(603\) | −1.26168e18 | −1.06877 | ||||||||
\(604\) | 6.47630e17 | 0.542733 | ||||||||
\(605\) | −1.30376e18 | −1.08090 | ||||||||
\(606\) | 7.83170e17 | 0.642368 | ||||||||
\(607\) | −6.74618e16 | −0.0547434 | −0.0273717 | − | 0.999625i | \(-0.508714\pi\) | ||||
−0.0273717 | + | 0.999625i | \(0.508714\pi\) | |||||||
\(608\) | −3.18362e18 | −2.55592 | ||||||||
\(609\) | 3.60063e17 | 0.286000 | ||||||||
\(610\) | 2.70112e18 | 2.12275 | ||||||||
\(611\) | 1.52685e18 | 1.18721 | ||||||||
\(612\) | 1.97243e16 | 0.0151746 | ||||||||
\(613\) | −1.81911e18 | −1.38473 | −0.692367 | − | 0.721546i | \(-0.743432\pi\) | ||||
−0.692367 | + | 0.721546i | \(0.743432\pi\) | |||||||
\(614\) | −2.23556e17 | −0.168381 | ||||||||
\(615\) | −4.83820e17 | −0.360575 | ||||||||
\(616\) | −7.16918e16 | −0.0528682 | ||||||||
\(617\) | 1.86705e17 | 0.136239 | 0.0681197 | − | 0.997677i | \(-0.478300\pi\) | ||||
0.0681197 | + | 0.997677i | \(0.478300\pi\) | |||||||
\(618\) | −2.79692e17 | −0.201955 | ||||||||
\(619\) | −8.32368e16 | −0.0594739 | −0.0297369 | − | 0.999558i | \(-0.509467\pi\) | ||||
−0.0297369 | + | 0.999558i | \(0.509467\pi\) | |||||||
\(620\) | 1.25677e18 | 0.888610 | ||||||||
\(621\) | 1.01942e18 | 0.713277 | ||||||||
\(622\) | −1.80688e18 | −1.25110 | ||||||||
\(623\) | 1.74755e18 | 1.19745 | ||||||||
\(624\) | −2.43181e17 | −0.164903 | ||||||||
\(625\) | −1.86132e18 | −1.24911 | ||||||||
\(626\) | 3.11868e18 | 2.07128 | ||||||||
\(627\) | −2.70363e17 | −0.177708 | ||||||||
\(628\) | 1.64937e17 | 0.107295 | ||||||||
\(629\) | −2.55533e16 | −0.0164519 | ||||||||
\(630\) | −3.57476e18 | −2.27789 | ||||||||
\(631\) | −6.61200e17 | −0.417005 | −0.208503 | − | 0.978022i | \(-0.566859\pi\) | ||||
−0.208503 | + | 0.978022i | \(0.566859\pi\) | |||||||
\(632\) | −8.98570e16 | −0.0560907 | ||||||||
\(633\) | −1.14662e17 | −0.0708430 | ||||||||
\(634\) | 3.02339e18 | 1.84890 | ||||||||
\(635\) | −1.75644e18 | −1.06317 | ||||||||
\(636\) | 8.38944e15 | 0.00502645 | ||||||||
\(637\) | −9.98062e17 | −0.591904 | ||||||||
\(638\) | 6.40123e17 | 0.375776 | ||||||||
\(639\) | −1.35843e18 | −0.789372 | ||||||||
\(640\) | 4.60085e17 | 0.264648 | ||||||||
\(641\) | 3.30693e18 | 1.88299 | 0.941495 | − | 0.337027i | \(-0.109421\pi\) | ||||
0.941495 | + | 0.337027i | \(0.109421\pi\) | |||||||
\(642\) | −1.05030e18 | −0.592018 | ||||||||
\(643\) | −2.70105e18 | −1.50717 | −0.753584 | − | 0.657351i | \(-0.771677\pi\) | ||||
−0.753584 | + | 0.657351i | \(0.771677\pi\) | |||||||
\(644\) | −3.57338e18 | −1.97388 | ||||||||
\(645\) | −7.84856e17 | −0.429192 | ||||||||
\(646\) | −7.27733e16 | −0.0393968 | ||||||||
\(647\) | −2.86266e18 | −1.53424 | −0.767118 | − | 0.641507i | \(-0.778310\pi\) | ||||
−0.767118 | + | 0.641507i | \(0.778310\pi\) | |||||||
\(648\) | −1.55731e17 | −0.0826299 | ||||||||
\(649\) | 1.24723e18 | 0.655173 | ||||||||
\(650\) | 9.37730e17 | 0.487687 | ||||||||
\(651\) | 5.05462e17 | 0.260263 | ||||||||
\(652\) | −8.07355e17 | −0.411581 | ||||||||
\(653\) | −3.82428e18 | −1.93025 | −0.965126 | − | 0.261784i | \(-0.915689\pi\) | ||||
−0.965126 | + | 0.261784i | \(0.915689\pi\) | |||||||
\(654\) | 2.00083e17 | 0.0999894 | ||||||||
\(655\) | −2.09187e18 | −1.03506 | ||||||||
\(656\) | −1.95187e18 | −0.956260 | ||||||||
\(657\) | −1.51051e18 | −0.732738 | ||||||||
\(658\) | −7.73055e18 | −3.71315 | ||||||||
\(659\) | −7.48217e17 | −0.355854 | −0.177927 | − | 0.984044i | \(-0.556939\pi\) | ||||
−0.177927 | + | 0.984044i | \(0.556939\pi\) | |||||||
\(660\) | 2.81029e17 | 0.132348 | ||||||||
\(661\) | 2.00527e18 | 0.935110 | 0.467555 | − | 0.883964i | \(-0.345135\pi\) | ||||
0.467555 | + | 0.883964i | \(0.345135\pi\) | |||||||
\(662\) | 2.57881e18 | 1.19081 | ||||||||
\(663\) | −6.00887e15 | −0.00274761 | ||||||||
\(664\) | −2.67392e17 | −0.121075 | ||||||||
\(665\) | 6.83135e18 | 3.06314 | ||||||||
\(666\) | 3.20758e18 | 1.42428 | ||||||||
\(667\) | 2.21180e18 | 0.972586 | ||||||||
\(668\) | 2.17462e18 | 0.946970 | ||||||||
\(669\) | −6.09444e17 | −0.262824 | ||||||||
\(670\) | −4.83863e18 | −2.06651 | ||||||||
\(671\) | 1.00034e18 | 0.423109 | ||||||||
\(672\) | 1.33093e18 | 0.557515 | ||||||||
\(673\) | 9.39797e17 | 0.389885 | 0.194942 | − | 0.980815i | \(-0.437548\pi\) | ||||
0.194942 | + | 0.980815i | \(0.437548\pi\) | |||||||
\(674\) | −5.38130e18 | −2.21105 | ||||||||
\(675\) | 7.01548e17 | 0.285485 | ||||||||
\(676\) | −1.57699e18 | −0.635586 | ||||||||
\(677\) | 7.53077e16 | 0.0300617 | 0.0150308 | − | 0.999887i | \(-0.495215\pi\) | ||||
0.0150308 | + | 0.999887i | \(0.495215\pi\) | |||||||
\(678\) | 1.51378e18 | 0.598509 | ||||||||
\(679\) | −5.60142e18 | −2.19354 | ||||||||
\(680\) | 5.24384e15 | 0.00203396 | ||||||||
\(681\) | 5.25187e17 | 0.201771 | ||||||||
\(682\) | 8.98613e17 | 0.341959 | ||||||||
\(683\) | 3.21238e18 | 1.21085 | 0.605427 | − | 0.795901i | \(-0.293002\pi\) | ||||
0.605427 | + | 0.795901i | \(0.293002\pi\) | |||||||
\(684\) | 4.73145e18 | 1.76656 | ||||||||
\(685\) | −1.73812e18 | −0.642821 | ||||||||
\(686\) | −4.03099e17 | −0.147674 | ||||||||
\(687\) | −1.99787e17 | −0.0725017 | ||||||||
\(688\) | −3.16634e18 | −1.13824 | ||||||||
\(689\) | 2.99360e16 | 0.0106603 | ||||||||
\(690\) | 1.87475e18 | 0.661340 | ||||||||
\(691\) | −1.98052e18 | −0.692105 | −0.346052 | − | 0.938215i | \(-0.612478\pi\) | ||||
−0.346052 | + | 0.938215i | \(0.612478\pi\) | |||||||
\(692\) | −1.31934e18 | −0.456739 | ||||||||
\(693\) | −1.32389e18 | −0.454032 | ||||||||
\(694\) | 6.50105e18 | 2.20875 | ||||||||
\(695\) | 2.01178e18 | 0.677141 | ||||||||
\(696\) | 6.62999e16 | 0.0221082 | ||||||||
\(697\) | −4.82297e16 | −0.0159331 | ||||||||
\(698\) | 1.13310e18 | 0.370859 | ||||||||
\(699\) | 2.55038e17 | 0.0826996 | ||||||||
\(700\) | −2.45914e18 | −0.790034 | ||||||||
\(701\) | −2.04579e18 | −0.651168 | −0.325584 | − | 0.945513i | \(-0.605561\pi\) | ||||
−0.325584 | + | 0.945513i | \(0.605561\pi\) | |||||||
\(702\) | 1.57293e18 | 0.496040 | ||||||||
\(703\) | −6.12968e18 | −1.91526 | ||||||||
\(704\) | 1.31098e18 | 0.405858 | ||||||||
\(705\) | 2.10071e18 | 0.644371 | ||||||||
\(706\) | −7.54497e18 | −2.29312 | ||||||||
\(707\) | −7.32862e18 | −2.20697 | ||||||||
\(708\) | 1.86348e18 | 0.556042 | ||||||||
\(709\) | −2.92951e18 | −0.866151 | −0.433076 | − | 0.901358i | \(-0.642572\pi\) | ||||
−0.433076 | + | 0.901358i | \(0.642572\pi\) | |||||||
\(710\) | −5.20969e18 | −1.52627 | ||||||||
\(711\) | −1.65934e18 | −0.481707 | ||||||||
\(712\) | 3.21784e17 | 0.0925645 | ||||||||
\(713\) | 3.10495e18 | 0.885061 | ||||||||
\(714\) | 3.04234e16 | 0.00859349 | ||||||||
\(715\) | 1.00279e18 | 0.280687 | ||||||||
\(716\) | −3.41802e17 | −0.0948068 | ||||||||
\(717\) | −3.07794e17 | −0.0846031 | ||||||||
\(718\) | 4.87458e18 | 1.32779 | ||||||||
\(719\) | 3.18410e18 | 0.859506 | 0.429753 | − | 0.902946i | \(-0.358601\pi\) | ||||
0.429753 | + | 0.902946i | \(0.358601\pi\) | |||||||
\(720\) | 3.91894e18 | 1.04835 | ||||||||
\(721\) | 2.61726e18 | 0.693853 | ||||||||
\(722\) | −1.19747e19 | −3.14609 | ||||||||
\(723\) | 1.67392e18 | 0.435849 | ||||||||
\(724\) | 1.18301e18 | 0.305272 | ||||||||
\(725\) | 1.52212e18 | 0.389272 | ||||||||
\(726\) | −1.39280e18 | −0.353022 | ||||||||
\(727\) | −5.57646e18 | −1.40083 | −0.700415 | − | 0.713736i | \(-0.747002\pi\) | ||||
−0.700415 | + | 0.713736i | \(0.747002\pi\) | |||||||
\(728\) | −3.82214e17 | −0.0951597 | ||||||||
\(729\) | −2.26333e18 | −0.558494 | ||||||||
\(730\) | −5.79293e18 | −1.41677 | ||||||||
\(731\) | −7.82386e16 | −0.0189652 | ||||||||
\(732\) | 1.49460e18 | 0.359091 | ||||||||
\(733\) | −3.54256e18 | −0.843610 | −0.421805 | − | 0.906687i | \(-0.638603\pi\) | ||||
−0.421805 | + | 0.906687i | \(0.638603\pi\) | |||||||
\(734\) | −8.53990e18 | −2.01571 | ||||||||
\(735\) | −1.37318e18 | −0.321262 | ||||||||
\(736\) | 8.17567e18 | 1.89591 | ||||||||
\(737\) | −1.79196e18 | −0.411898 | ||||||||
\(738\) | 6.05405e18 | 1.37937 | ||||||||
\(739\) | 6.53089e18 | 1.47497 | 0.737486 | − | 0.675363i | \(-0.236013\pi\) | ||||
0.737486 | + | 0.675363i | \(0.236013\pi\) | |||||||
\(740\) | 6.37152e18 | 1.42638 | ||||||||
\(741\) | −1.44140e18 | −0.319864 | ||||||||
\(742\) | −1.51568e17 | −0.0333414 | ||||||||
\(743\) | 1.75730e18 | 0.383193 | 0.191596 | − | 0.981474i | \(-0.438634\pi\) | ||||
0.191596 | + | 0.981474i | \(0.438634\pi\) | |||||||
\(744\) | 9.30727e16 | 0.0201186 | ||||||||
\(745\) | 5.40715e18 | 1.15865 | ||||||||
\(746\) | −8.98193e18 | −1.90795 | ||||||||
\(747\) | −4.93778e18 | −1.03980 | ||||||||
\(748\) | 2.80145e16 | 0.00584820 | ||||||||
\(749\) | 9.82830e18 | 2.03398 | ||||||||
\(750\) | −1.14508e18 | −0.234930 | ||||||||
\(751\) | −1.77683e18 | −0.361399 | −0.180700 | − | 0.983538i | \(-0.557836\pi\) | ||||
−0.180700 | + | 0.983538i | \(0.557836\pi\) | |||||||
\(752\) | 8.47487e18 | 1.70890 | ||||||||
\(753\) | −6.02307e17 | −0.120407 | ||||||||
\(754\) | 3.41272e18 | 0.676374 | ||||||||
\(755\) | 3.17949e18 | 0.624744 | ||||||||
\(756\) | −4.12490e18 | −0.803567 | ||||||||
\(757\) | −8.48499e18 | −1.63881 | −0.819404 | − | 0.573216i | \(-0.805696\pi\) | ||||
−0.819404 | + | 0.573216i | \(0.805696\pi\) | |||||||
\(758\) | −1.00260e19 | −1.91990 | ||||||||
\(759\) | 6.94304e17 | 0.131819 | ||||||||
\(760\) | 1.25788e18 | 0.236784 | ||||||||
\(761\) | 4.01095e18 | 0.748595 | 0.374298 | − | 0.927309i | \(-0.377884\pi\) | ||||
0.374298 | + | 0.927309i | \(0.377884\pi\) | |||||||
\(762\) | −1.87640e18 | −0.347231 | ||||||||
\(763\) | −1.87230e18 | −0.343531 | ||||||||
\(764\) | 1.43697e18 | 0.261421 | ||||||||
\(765\) | 9.68351e16 | 0.0174676 | ||||||||
\(766\) | −1.00931e19 | −1.80525 | ||||||||
\(767\) | 6.64943e18 | 1.17927 | ||||||||
\(768\) | −1.33144e18 | −0.234138 | ||||||||
\(769\) | 4.76798e18 | 0.831406 | 0.415703 | − | 0.909500i | \(-0.363536\pi\) | ||||
0.415703 | + | 0.909500i | \(0.363536\pi\) | |||||||
\(770\) | −5.07723e18 | −0.877885 | ||||||||
\(771\) | −7.35742e16 | −0.0126146 | ||||||||
\(772\) | 3.98243e18 | 0.677073 | ||||||||
\(773\) | −9.55748e16 | −0.0161130 | −0.00805650 | − | 0.999968i | \(-0.502564\pi\) | ||||
−0.00805650 | + | 0.999968i | \(0.502564\pi\) | |||||||
\(774\) | 9.82092e18 | 1.64186 | ||||||||
\(775\) | 2.13678e18 | 0.354240 | ||||||||
\(776\) | −1.03141e18 | −0.169563 | ||||||||
\(777\) | 2.56256e18 | 0.417770 | ||||||||
\(778\) | −2.62869e18 | −0.424984 | ||||||||
\(779\) | −1.15693e19 | −1.85487 | ||||||||
\(780\) | 1.49827e18 | 0.238218 | ||||||||
\(781\) | −1.92938e18 | −0.304219 | ||||||||
\(782\) | 1.86885e17 | 0.0292234 | ||||||||
\(783\) | 2.55317e18 | 0.395940 | ||||||||
\(784\) | −5.53981e18 | −0.852002 | ||||||||
\(785\) | 8.09744e17 | 0.123508 | ||||||||
\(786\) | −2.23474e18 | −0.338050 | ||||||||
\(787\) | −1.89933e18 | −0.284948 | −0.142474 | − | 0.989799i | \(-0.545506\pi\) | ||||
−0.142474 | + | 0.989799i | \(0.545506\pi\) | |||||||
\(788\) | −5.14503e17 | −0.0765539 | ||||||||
\(789\) | 3.11193e16 | 0.00459229 | ||||||||
\(790\) | −6.36370e18 | −0.931394 | ||||||||
\(791\) | −1.41654e19 | −2.05628 | ||||||||
\(792\) | −2.43774e17 | −0.0350972 | ||||||||
\(793\) | 5.33318e18 | 0.761571 | ||||||||
\(794\) | 1.19440e17 | 0.0169167 | ||||||||
\(795\) | 4.11873e16 | 0.00578598 | ||||||||
\(796\) | −9.87794e18 | −1.37636 | ||||||||
\(797\) | −2.00304e18 | −0.276828 | −0.138414 | − | 0.990374i | \(-0.544201\pi\) | ||||
−0.138414 | + | 0.990374i | \(0.544201\pi\) | |||||||
\(798\) | 7.29793e18 | 1.00042 | ||||||||
\(799\) | 2.09409e17 | 0.0284736 | ||||||||
\(800\) | 5.62636e18 | 0.758826 | ||||||||
\(801\) | 5.94220e18 | 0.794943 | ||||||||
\(802\) | 8.39692e18 | 1.11426 | ||||||||
\(803\) | −2.14538e18 | −0.282392 | ||||||||
\(804\) | −2.67735e18 | −0.349576 | ||||||||
\(805\) | −1.75432e19 | −2.27215 | ||||||||
\(806\) | 4.79082e18 | 0.615506 | ||||||||
\(807\) | 3.39524e18 | 0.432706 | ||||||||
\(808\) | −1.34945e18 | −0.170601 | ||||||||
\(809\) | 1.82735e18 | 0.229170 | 0.114585 | − | 0.993413i | \(-0.463446\pi\) | ||||
0.114585 | + | 0.993413i | \(0.463446\pi\) | |||||||
\(810\) | −1.10289e19 | −1.37208 | ||||||||
\(811\) | −9.26601e18 | −1.14356 | −0.571778 | − | 0.820409i | \(-0.693746\pi\) | ||||
−0.571778 | + | 0.820409i | \(0.693746\pi\) | |||||||
\(812\) | −8.94965e18 | −1.09570 | ||||||||
\(813\) | −2.29865e18 | −0.279181 | ||||||||
\(814\) | 4.55573e18 | 0.548908 | ||||||||
\(815\) | −3.96364e18 | −0.473773 | ||||||||
\(816\) | −3.33526e16 | −0.00395498 | ||||||||
\(817\) | −1.87678e19 | −2.20785 | ||||||||
\(818\) | 7.65307e18 | 0.893181 | ||||||||
\(819\) | −7.05814e18 | −0.817231 | ||||||||
\(820\) | 1.20257e19 | 1.38140 | ||||||||
\(821\) | 4.51238e18 | 0.514251 | 0.257125 | − | 0.966378i | \(-0.417225\pi\) | ||||
0.257125 | + | 0.966378i | \(0.417225\pi\) | |||||||
\(822\) | −1.85683e18 | −0.209945 | ||||||||
\(823\) | −1.65659e19 | −1.85830 | −0.929152 | − | 0.369698i | \(-0.879461\pi\) | ||||
−0.929152 | + | 0.369698i | \(0.879461\pi\) | |||||||
\(824\) | 4.81926e17 | 0.0536357 | ||||||||
\(825\) | 4.77808e17 | 0.0527598 | ||||||||
\(826\) | −3.36666e19 | −3.68833 | ||||||||
\(827\) | −7.96052e18 | −0.865278 | −0.432639 | − | 0.901567i | \(-0.642418\pi\) | ||||
−0.432639 | + | 0.901567i | \(0.642418\pi\) | |||||||
\(828\) | −1.21506e19 | −1.31039 | ||||||||
\(829\) | 2.51596e18 | 0.269215 | 0.134608 | − | 0.990899i | \(-0.457023\pi\) | ||||
0.134608 | + | 0.990899i | \(0.457023\pi\) | |||||||
\(830\) | −1.89368e19 | −2.01047 | ||||||||
\(831\) | −4.10298e18 | −0.432208 | ||||||||
\(832\) | 6.98931e18 | 0.730521 | ||||||||
\(833\) | −1.36886e17 | −0.0141960 | ||||||||
\(834\) | 2.14918e18 | 0.221153 | ||||||||
\(835\) | 1.06761e19 | 1.09006 | ||||||||
\(836\) | 6.72007e18 | 0.680822 | ||||||||
\(837\) | 3.58418e18 | 0.360308 | ||||||||
\(838\) | 2.20615e19 | 2.20064 | ||||||||
\(839\) | −1.07160e19 | −1.06067 | −0.530334 | − | 0.847789i | \(-0.677934\pi\) | ||||
−0.530334 | + | 0.847789i | \(0.677934\pi\) | |||||||
\(840\) | −5.25868e17 | −0.0516489 | ||||||||
\(841\) | −4.72110e18 | −0.460118 | ||||||||
\(842\) | 1.60990e19 | 1.55694 | ||||||||
\(843\) | −5.14497e18 | −0.493746 | ||||||||
\(844\) | 2.85002e18 | 0.271408 | ||||||||
\(845\) | −7.74209e18 | −0.731627 | ||||||||
\(846\) | −2.62862e19 | −2.46502 | ||||||||
\(847\) | 1.30333e19 | 1.21287 | ||||||||
\(848\) | 1.66162e17 | 0.0153447 | ||||||||
\(849\) | 5.34605e18 | 0.489929 | ||||||||
\(850\) | 1.28611e17 | 0.0116965 | ||||||||
\(851\) | 1.57413e19 | 1.42069 | ||||||||
\(852\) | −2.88267e18 | −0.258189 | ||||||||
\(853\) | −5.39090e17 | −0.0479174 | −0.0239587 | − | 0.999713i | \(-0.507627\pi\) | ||||
−0.0239587 | + | 0.999713i | \(0.507627\pi\) | |||||||
\(854\) | −2.70024e19 | −2.38191 | ||||||||
\(855\) | 2.32287e19 | 2.03350 | ||||||||
\(856\) | 1.80972e18 | 0.157229 | ||||||||
\(857\) | 1.40302e19 | 1.20973 | 0.604867 | − | 0.796327i | \(-0.293226\pi\) | ||||
0.604867 | + | 0.796327i | \(0.293226\pi\) | |||||||
\(858\) | 1.07128e18 | 0.0916721 | ||||||||
\(859\) | −5.15612e18 | −0.437893 | −0.218946 | − | 0.975737i | \(-0.570262\pi\) | ||||
−0.218946 | + | 0.975737i | \(0.570262\pi\) | |||||||
\(860\) | 1.95082e19 | 1.64429 | ||||||||
\(861\) | 4.83662e18 | 0.404596 | ||||||||
\(862\) | 2.89831e18 | 0.240629 | ||||||||
\(863\) | 7.53893e18 | 0.621212 | 0.310606 | − | 0.950539i | \(-0.399468\pi\) | ||||
0.310606 | + | 0.950539i | \(0.399468\pi\) | |||||||
\(864\) | 9.43752e18 | 0.771824 | ||||||||
\(865\) | −6.47720e18 | −0.525754 | ||||||||
\(866\) | 2.93843e19 | 2.36728 | ||||||||
\(867\) | 3.50669e18 | 0.280397 | ||||||||
\(868\) | −1.25636e19 | −0.997097 | ||||||||
\(869\) | −2.35676e18 | −0.185647 | ||||||||
\(870\) | 4.69538e18 | 0.367109 | ||||||||
\(871\) | −9.55357e18 | −0.741392 | ||||||||
\(872\) | −3.44754e17 | −0.0265553 | ||||||||
\(873\) | −1.90465e19 | −1.45621 | ||||||||
\(874\) | 4.48298e19 | 3.40206 | ||||||||
\(875\) | 1.07153e19 | 0.807143 | ||||||||
\(876\) | −3.20539e18 | −0.239665 | ||||||||
\(877\) | 1.36024e19 | 1.00953 | 0.504766 | − | 0.863256i | \(-0.331579\pi\) | ||||
0.504766 | + | 0.863256i | \(0.331579\pi\) | |||||||
\(878\) | −6.86384e18 | −0.505654 | ||||||||
\(879\) | 2.66022e18 | 0.194531 | ||||||||
\(880\) | 5.56608e18 | 0.404028 | ||||||||
\(881\) | 2.72051e19 | 1.96023 | 0.980113 | − | 0.198438i | \(-0.0635870\pi\) | ||||
0.980113 | + | 0.198438i | \(0.0635870\pi\) | |||||||
\(882\) | 1.71826e19 | 1.22898 | ||||||||
\(883\) | 7.54359e18 | 0.535591 | 0.267796 | − | 0.963476i | \(-0.413705\pi\) | ||||
0.267796 | + | 0.963476i | \(0.413705\pi\) | |||||||
\(884\) | 1.49355e17 | 0.0105264 | ||||||||
\(885\) | 9.14859e18 | 0.640063 | ||||||||
\(886\) | −9.94633e18 | −0.690786 | ||||||||
\(887\) | −1.91787e19 | −1.32225 | −0.661127 | − | 0.750274i | \(-0.729921\pi\) | ||||
−0.661127 | + | 0.750274i | \(0.729921\pi\) | |||||||
\(888\) | 4.71854e17 | 0.0322941 | ||||||||
\(889\) | 1.75587e19 | 1.19297 | ||||||||
\(890\) | 2.27888e19 | 1.53705 | ||||||||
\(891\) | −4.08449e18 | −0.273485 | ||||||||
\(892\) | 1.51482e19 | 1.00691 | ||||||||
\(893\) | 5.02328e19 | 3.31477 | ||||||||
\(894\) | 5.77645e18 | 0.378414 | ||||||||
\(895\) | −1.67805e18 | −0.109133 | ||||||||
\(896\) | −4.59935e18 | −0.296957 | ||||||||
\(897\) | 3.70158e18 | 0.237266 | ||||||||
\(898\) | 9.20727e18 | 0.585915 | ||||||||
\(899\) | 7.77646e18 | 0.491297 | ||||||||
\(900\) | −8.36181e18 | −0.524474 | ||||||||
\(901\) | 4.10577e15 | 0.000255672 0 | ||||||||
\(902\) | 8.59857e18 | 0.531599 | ||||||||
\(903\) | 7.84600e18 | 0.481590 | ||||||||
\(904\) | −2.60834e18 | −0.158953 | ||||||||
\(905\) | 5.80788e18 | 0.351400 | ||||||||
\(906\) | 3.39664e18 | 0.204040 | ||||||||
\(907\) | −2.12971e19 | −1.27021 | −0.635103 | − | 0.772428i | \(-0.719042\pi\) | ||||
−0.635103 | + | 0.772428i | \(0.719042\pi\) | |||||||
\(908\) | −1.30539e19 | −0.773007 | ||||||||
\(909\) | −2.49195e19 | −1.46512 | ||||||||
\(910\) | −2.70685e19 | −1.58014 | ||||||||
\(911\) | −7.70001e18 | −0.446295 | −0.223147 | − | 0.974785i | \(-0.571633\pi\) | ||||
−0.223147 | + | 0.974785i | \(0.571633\pi\) | |||||||
\(912\) | −8.00058e18 | −0.460421 | ||||||||
\(913\) | −7.01313e18 | −0.400730 | ||||||||
\(914\) | 1.79102e19 | 1.01613 | ||||||||
\(915\) | 7.33764e18 | 0.413351 | ||||||||
\(916\) | 4.96586e18 | 0.277763 | ||||||||
\(917\) | 2.09119e19 | 1.16143 | ||||||||
\(918\) | 2.15729e17 | 0.0118968 | ||||||||
\(919\) | −1.27519e19 | −0.698274 | −0.349137 | − | 0.937072i | \(-0.613525\pi\) | ||||
−0.349137 | + | 0.937072i | \(0.613525\pi\) | |||||||
\(920\) | −3.23031e18 | −0.175640 | ||||||||
\(921\) | −6.07295e17 | −0.0327878 | ||||||||
\(922\) | 2.27218e19 | 1.21812 | ||||||||
\(923\) | −1.02862e19 | −0.547575 | ||||||||
\(924\) | −2.80938e18 | −0.148505 | ||||||||
\(925\) | 1.08329e19 | 0.568622 | ||||||||
\(926\) | −4.40675e19 | −2.29693 | ||||||||
\(927\) | 8.89946e18 | 0.460623 | ||||||||
\(928\) | 2.04762e19 | 1.05242 | ||||||||
\(929\) | 1.83918e19 | 0.938690 | 0.469345 | − | 0.883015i | \(-0.344490\pi\) | ||||
0.469345 | + | 0.883015i | \(0.344490\pi\) | |||||||
\(930\) | 6.59144e18 | 0.334073 | ||||||||
\(931\) | −3.28360e19 | −1.65264 | ||||||||
\(932\) | −6.33917e18 | −0.316832 | ||||||||
\(933\) | −4.90841e18 | −0.243619 | ||||||||
\(934\) | 4.08266e19 | 2.01228 | ||||||||
\(935\) | 1.37535e17 | 0.00673190 | ||||||||
\(936\) | −1.29964e18 | −0.0631729 | ||||||||
\(937\) | −2.05015e19 | −0.989644 | −0.494822 | − | 0.868994i | \(-0.664767\pi\) | ||||
−0.494822 | + | 0.868994i | \(0.664767\pi\) | |||||||
\(938\) | 4.83706e19 | 2.31880 | ||||||||
\(939\) | 8.47197e18 | 0.403328 | ||||||||
\(940\) | −5.22147e19 | −2.46866 | ||||||||
\(941\) | −1.54458e19 | −0.725234 | −0.362617 | − | 0.931938i | \(-0.618117\pi\) | ||||
−0.362617 | + | 0.931938i | \(0.618117\pi\) | |||||||
\(942\) | 8.65048e17 | 0.0403376 | ||||||||
\(943\) | 2.97104e19 | 1.37589 | ||||||||
\(944\) | 3.69081e19 | 1.69748 | ||||||||
\(945\) | −2.02509e19 | −0.924991 | ||||||||
\(946\) | 1.39487e19 | 0.632762 | ||||||||
\(947\) | 1.02449e19 | 0.461563 | 0.230782 | − | 0.973006i | \(-0.425872\pi\) | ||||
0.230782 | + | 0.973006i | \(0.425872\pi\) | |||||||
\(948\) | −3.52121e18 | −0.157557 | ||||||||
\(949\) | −1.14378e19 | −0.508289 | ||||||||
\(950\) | 3.08511e19 | 1.36165 | ||||||||
\(951\) | 8.21311e18 | 0.360026 | ||||||||
\(952\) | −5.24213e16 | −0.00228227 | ||||||||
\(953\) | 3.86166e19 | 1.66982 | 0.834911 | − | 0.550385i | \(-0.185519\pi\) | ||||
0.834911 | + | 0.550385i | \(0.185519\pi\) | |||||||
\(954\) | −5.15378e17 | −0.0221341 | ||||||||
\(955\) | 7.05468e18 | 0.300923 | ||||||||
\(956\) | 7.65047e18 | 0.324124 | ||||||||
\(957\) | 1.73891e18 | 0.0731727 | ||||||||
\(958\) | 6.45509e19 | 2.69790 | ||||||||
\(959\) | 1.73755e19 | 0.721301 | ||||||||
\(960\) | 9.61621e18 | 0.396498 | ||||||||
\(961\) | −1.35008e19 | −0.552916 | ||||||||
\(962\) | 2.42882e19 | 0.988002 | ||||||||
\(963\) | 3.34192e19 | 1.35028 | ||||||||
\(964\) | −4.16066e19 | −1.66979 | ||||||||
\(965\) | 1.95514e19 | 0.779382 | ||||||||
\(966\) | −1.87414e19 | −0.742080 | ||||||||
\(967\) | 3.72062e19 | 1.46333 | 0.731667 | − | 0.681662i | \(-0.238742\pi\) | ||||
0.731667 | + | 0.681662i | \(0.238742\pi\) | |||||||
\(968\) | 2.39988e18 | 0.0937562 | ||||||||
\(969\) | −1.97690e17 | −0.00767151 | ||||||||
\(970\) | −7.30449e19 | −2.81562 | ||||||||
\(971\) | 1.13456e19 | 0.434411 | 0.217206 | − | 0.976126i | \(-0.430306\pi\) | ||||
0.217206 | + | 0.976126i | \(0.430306\pi\) | |||||||
\(972\) | −2.13260e19 | −0.811107 | ||||||||
\(973\) | −2.01112e19 | −0.759810 | ||||||||
\(974\) | −2.77981e18 | −0.104323 | ||||||||
\(975\) | 2.54736e18 | 0.0949644 | ||||||||
\(976\) | 2.96022e19 | 1.09623 | ||||||||
\(977\) | −2.40491e19 | −0.884677 | −0.442338 | − | 0.896848i | \(-0.645851\pi\) | ||||
−0.442338 | + | 0.896848i | \(0.645851\pi\) | |||||||
\(978\) | −4.23435e18 | −0.154734 | ||||||||
\(979\) | 8.43971e18 | 0.306366 | ||||||||
\(980\) | 3.41315e19 | 1.23079 | ||||||||
\(981\) | −6.36638e18 | −0.228057 | ||||||||
\(982\) | −3.07868e19 | −1.09557 | ||||||||
\(983\) | −5.06524e19 | −1.79062 | −0.895308 | − | 0.445448i | \(-0.853045\pi\) | ||||
−0.895308 | + | 0.445448i | \(0.853045\pi\) | |||||||
\(984\) | 8.90586e17 | 0.0312758 | ||||||||
\(985\) | −2.52591e18 | −0.0881217 | ||||||||
\(986\) | 4.68060e17 | 0.0162219 | ||||||||
\(987\) | −2.10002e19 | −0.723040 | ||||||||
\(988\) | 3.58271e19 | 1.22544 | ||||||||
\(989\) | 4.81965e19 | 1.63772 | ||||||||
\(990\) | −1.72641e19 | −0.582795 | ||||||||
\(991\) | −9.17044e18 | −0.307547 | −0.153774 | − | 0.988106i | \(-0.549143\pi\) | ||||
−0.153774 | + | 0.988106i | \(0.549143\pi\) | |||||||
\(992\) | 2.87448e19 | 0.957709 | ||||||||
\(993\) | 7.00539e18 | 0.231880 | ||||||||
\(994\) | 5.20799e19 | 1.71261 | ||||||||
\(995\) | −4.84950e19 | −1.58433 | ||||||||
\(996\) | −1.04783e19 | −0.340097 | ||||||||
\(997\) | 1.48626e19 | 0.479267 | 0.239633 | − | 0.970863i | \(-0.422973\pi\) | ||||
0.239633 | + | 0.970863i | \(0.422973\pi\) | |||||||
\(998\) | 3.71215e19 | 1.18926 | ||||||||
\(999\) | 1.81709e19 | 0.578362 |
(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 | 197.14.a.a.1.19 | ✓ | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.14.a.a.1.19 | ✓ | 104 | 1.1 | even | 1 | trivial |