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 | 1.5 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −167.056 | −1.84573 | −0.922863 | − | 0.385129i | \(-0.874157\pi\) | ||||
−0.922863 | + | 0.385129i | \(0.874157\pi\) | |||||||
\(3\) | 2054.37 | 1.62701 | 0.813505 | − | 0.581557i | \(-0.197556\pi\) | ||||
0.813505 | + | 0.581557i | \(0.197556\pi\) | |||||||
\(4\) | 19715.7 | 2.40670 | ||||||||
\(5\) | 12824.5 | 0.367060 | 0.183530 | − | 0.983014i | \(-0.441248\pi\) | ||||
0.183530 | + | 0.983014i | \(0.441248\pi\) | |||||||
\(6\) | −343195. | −3.00302 | ||||||||
\(7\) | 34898.6 | 0.112117 | 0.0560583 | − | 0.998427i | \(-0.482147\pi\) | ||||
0.0560583 | + | 0.998427i | \(0.482147\pi\) | |||||||
\(8\) | −1.92511e6 | −2.59639 | ||||||||
\(9\) | 2.62611e6 | 1.64716 | ||||||||
\(10\) | −2.14242e6 | −0.677492 | ||||||||
\(11\) | 5.93755e6 | 1.01054 | 0.505271 | − | 0.862960i | \(-0.331392\pi\) | ||||
0.505271 | + | 0.862960i | \(0.331392\pi\) | |||||||
\(12\) | 4.05034e7 | 3.91573 | ||||||||
\(13\) | −1.86151e7 | −1.06963 | −0.534816 | − | 0.844968i | \(-0.679619\pi\) | ||||
−0.534816 | + | 0.844968i | \(0.679619\pi\) | |||||||
\(14\) | −5.83001e6 | −0.206937 | ||||||||
\(15\) | 2.63464e7 | 0.597210 | ||||||||
\(16\) | 1.60089e8 | 2.38552 | ||||||||
\(17\) | −1.38966e8 | −1.39633 | −0.698167 | − | 0.715935i | \(-0.746001\pi\) | ||||
−0.698167 | + | 0.715935i | \(0.746001\pi\) | |||||||
\(18\) | −4.38708e8 | −3.04021 | ||||||||
\(19\) | 7.18692e7 | 0.350465 | 0.175232 | − | 0.984527i | \(-0.443932\pi\) | ||||
0.175232 | + | 0.984527i | \(0.443932\pi\) | |||||||
\(20\) | 2.52845e8 | 0.883404 | ||||||||
\(21\) | 7.16945e7 | 0.182415 | ||||||||
\(22\) | −9.91903e8 | −1.86518 | ||||||||
\(23\) | −3.24279e8 | −0.456760 | −0.228380 | − | 0.973572i | \(-0.573343\pi\) | ||||
−0.228380 | + | 0.973572i | \(0.573343\pi\) | |||||||
\(24\) | −3.95488e9 | −4.22435 | ||||||||
\(25\) | −1.05623e9 | −0.865267 | ||||||||
\(26\) | 3.10977e9 | 1.97425 | ||||||||
\(27\) | 2.11968e9 | 1.05294 | ||||||||
\(28\) | 6.88050e8 | 0.269832 | ||||||||
\(29\) | −4.79502e8 | −0.149694 | −0.0748468 | − | 0.997195i | \(-0.523847\pi\) | ||||
−0.0748468 | + | 0.997195i | \(0.523847\pi\) | |||||||
\(30\) | −4.40132e9 | −1.10229 | ||||||||
\(31\) | 2.49742e9 | 0.505407 | 0.252703 | − | 0.967544i | \(-0.418680\pi\) | ||||
0.252703 | + | 0.967544i | \(0.418680\pi\) | |||||||
\(32\) | −1.09734e10 | −1.80662 | ||||||||
\(33\) | 1.21979e10 | 1.64416 | ||||||||
\(34\) | 2.32150e10 | 2.57725 | ||||||||
\(35\) | 4.47558e8 | 0.0411535 | ||||||||
\(36\) | 5.17757e10 | 3.96424 | ||||||||
\(37\) | 1.94028e9 | 0.124323 | 0.0621617 | − | 0.998066i | \(-0.480201\pi\) | ||||
0.0621617 | + | 0.998066i | \(0.480201\pi\) | |||||||
\(38\) | −1.20062e10 | −0.646862 | ||||||||
\(39\) | −3.82424e10 | −1.74030 | ||||||||
\(40\) | −2.46886e10 | −0.953030 | ||||||||
\(41\) | 2.36739e10 | 0.778348 | 0.389174 | − | 0.921164i | \(-0.372760\pi\) | ||||
0.389174 | + | 0.921164i | \(0.372760\pi\) | |||||||
\(42\) | −1.19770e10 | −0.336688 | ||||||||
\(43\) | 3.90451e10 | 0.941936 | 0.470968 | − | 0.882150i | \(-0.343905\pi\) | ||||
0.470968 | + | 0.882150i | \(0.343905\pi\) | |||||||
\(44\) | 1.17063e11 | 2.43208 | ||||||||
\(45\) | 3.36787e10 | 0.604608 | ||||||||
\(46\) | 5.41727e10 | 0.843053 | ||||||||
\(47\) | 7.26691e10 | 0.983363 | 0.491682 | − | 0.870775i | \(-0.336382\pi\) | ||||
0.491682 | + | 0.870775i | \(0.336382\pi\) | |||||||
\(48\) | 3.28883e11 | 3.88126 | ||||||||
\(49\) | −9.56711e10 | −0.987430 | ||||||||
\(50\) | 1.76450e11 | 1.59705 | ||||||||
\(51\) | −2.85487e11 | −2.27185 | ||||||||
\(52\) | −3.67011e11 | −2.57429 | ||||||||
\(53\) | −7.11782e10 | −0.441117 | −0.220559 | − | 0.975374i | \(-0.570788\pi\) | ||||
−0.220559 | + | 0.975374i | \(0.570788\pi\) | |||||||
\(54\) | −3.54105e11 | −1.94344 | ||||||||
\(55\) | 7.61463e10 | 0.370930 | ||||||||
\(56\) | −6.71834e10 | −0.291098 | ||||||||
\(57\) | 1.47646e11 | 0.570210 | ||||||||
\(58\) | 8.01036e10 | 0.276293 | ||||||||
\(59\) | −5.26765e11 | −1.62584 | −0.812922 | − | 0.582372i | \(-0.802125\pi\) | ||||
−0.812922 | + | 0.582372i | \(0.802125\pi\) | |||||||
\(60\) | 5.19437e11 | 1.43731 | ||||||||
\(61\) | 1.73926e11 | 0.432235 | 0.216117 | − | 0.976367i | \(-0.430661\pi\) | ||||
0.216117 | + | 0.976367i | \(0.430661\pi\) | |||||||
\(62\) | −4.17210e11 | −0.932842 | ||||||||
\(63\) | 9.16475e10 | 0.184675 | ||||||||
\(64\) | 5.21724e11 | 0.949010 | ||||||||
\(65\) | −2.38731e11 | −0.392619 | ||||||||
\(66\) | −2.03774e12 | −3.03468 | ||||||||
\(67\) | −6.11862e11 | −0.826356 | −0.413178 | − | 0.910650i | \(-0.635581\pi\) | ||||
−0.413178 | + | 0.910650i | \(0.635581\pi\) | |||||||
\(68\) | −2.73980e12 | −3.36056 | ||||||||
\(69\) | −6.66189e11 | −0.743153 | ||||||||
\(70\) | −7.47673e10 | −0.0759581 | ||||||||
\(71\) | −1.18757e12 | −1.10022 | −0.550111 | − | 0.835092i | \(-0.685415\pi\) | ||||
−0.550111 | + | 0.835092i | \(0.685415\pi\) | |||||||
\(72\) | −5.05554e12 | −4.27668 | ||||||||
\(73\) | 1.79915e12 | 1.39145 | 0.695726 | − | 0.718307i | \(-0.255083\pi\) | ||||
0.695726 | + | 0.718307i | \(0.255083\pi\) | |||||||
\(74\) | −3.24135e11 | −0.229467 | ||||||||
\(75\) | −2.16990e12 | −1.40780 | ||||||||
\(76\) | 1.41695e12 | 0.843464 | ||||||||
\(77\) | 2.07212e11 | 0.113299 | ||||||||
\(78\) | 6.38862e12 | 3.21212 | ||||||||
\(79\) | −4.18373e12 | −1.93637 | −0.968183 | − | 0.250243i | \(-0.919489\pi\) | ||||
−0.968183 | + | 0.250243i | \(0.919489\pi\) | |||||||
\(80\) | 2.05307e12 | 0.875627 | ||||||||
\(81\) | 1.67728e11 | 0.0659861 | ||||||||
\(82\) | −3.95486e12 | −1.43662 | ||||||||
\(83\) | 2.99732e12 | 1.00630 | 0.503148 | − | 0.864200i | \(-0.332175\pi\) | ||||
0.503148 | + | 0.864200i | \(0.332175\pi\) | |||||||
\(84\) | 1.41351e12 | 0.439019 | ||||||||
\(85\) | −1.78217e12 | −0.512538 | ||||||||
\(86\) | −6.52272e12 | −1.73856 | ||||||||
\(87\) | −9.85073e11 | −0.243553 | ||||||||
\(88\) | −1.14304e13 | −2.62376 | ||||||||
\(89\) | −9.94142e11 | −0.212038 | −0.106019 | − | 0.994364i | \(-0.533810\pi\) | ||||
−0.106019 | + | 0.994364i | \(0.533810\pi\) | |||||||
\(90\) | −5.62623e12 | −1.11594 | ||||||||
\(91\) | −6.49642e11 | −0.119924 | ||||||||
\(92\) | −6.39339e12 | −1.09929 | ||||||||
\(93\) | 5.13063e12 | 0.822302 | ||||||||
\(94\) | −1.21398e13 | −1.81502 | ||||||||
\(95\) | 9.21689e11 | 0.128641 | ||||||||
\(96\) | −2.25435e13 | −2.93939 | ||||||||
\(97\) | −3.98983e12 | −0.486338 | −0.243169 | − | 0.969984i | \(-0.578187\pi\) | ||||
−0.243169 | + | 0.969984i | \(0.578187\pi\) | |||||||
\(98\) | 1.59824e13 | 1.82252 | ||||||||
\(99\) | 1.55927e13 | 1.66453 | ||||||||
\(100\) | −2.08244e13 | −2.08244 | ||||||||
\(101\) | 4.40567e12 | 0.412974 | 0.206487 | − | 0.978449i | \(-0.433797\pi\) | ||||
0.206487 | + | 0.978449i | \(0.433797\pi\) | |||||||
\(102\) | 4.76922e13 | 4.19321 | ||||||||
\(103\) | −4.67850e12 | −0.386069 | −0.193035 | − | 0.981192i | \(-0.561833\pi\) | ||||
−0.193035 | + | 0.981192i | \(0.561833\pi\) | |||||||
\(104\) | 3.58361e13 | 2.77718 | ||||||||
\(105\) | 9.19450e11 | 0.0669572 | ||||||||
\(106\) | 1.18908e13 | 0.814182 | ||||||||
\(107\) | −2.54486e13 | −1.63934 | −0.819669 | − | 0.572837i | \(-0.805843\pi\) | ||||
−0.819669 | + | 0.572837i | \(0.805843\pi\) | |||||||
\(108\) | 4.17909e13 | 2.53412 | ||||||||
\(109\) | 1.07009e13 | 0.611149 | 0.305575 | − | 0.952168i | \(-0.401151\pi\) | ||||
0.305575 | + | 0.952168i | \(0.401151\pi\) | |||||||
\(110\) | −1.27207e13 | −0.684634 | ||||||||
\(111\) | 3.98605e12 | 0.202276 | ||||||||
\(112\) | 5.58689e12 | 0.267456 | ||||||||
\(113\) | −1.48463e13 | −0.670825 | −0.335412 | − | 0.942071i | \(-0.608876\pi\) | ||||
−0.335412 | + | 0.942071i | \(0.608876\pi\) | |||||||
\(114\) | −2.46651e13 | −1.05245 | ||||||||
\(115\) | −4.15873e12 | −0.167658 | ||||||||
\(116\) | −9.45371e12 | −0.360268 | ||||||||
\(117\) | −4.88855e13 | −1.76186 | ||||||||
\(118\) | 8.79993e13 | 3.00086 | ||||||||
\(119\) | −4.84970e12 | −0.156552 | ||||||||
\(120\) | −5.07195e13 | −1.55059 | ||||||||
\(121\) | 7.31770e11 | 0.0211968 | ||||||||
\(122\) | −2.90553e13 | −0.797787 | ||||||||
\(123\) | 4.86349e13 | 1.26638 | ||||||||
\(124\) | 4.92385e13 | 1.21636 | ||||||||
\(125\) | −2.92007e13 | −0.684665 | ||||||||
\(126\) | −1.53103e13 | −0.340859 | ||||||||
\(127\) | −2.02281e13 | −0.427791 | −0.213896 | − | 0.976857i | \(-0.568615\pi\) | ||||
−0.213896 | + | 0.976857i | \(0.568615\pi\) | |||||||
\(128\) | 2.73713e12 | 0.0550085 | ||||||||
\(129\) | 8.02131e13 | 1.53254 | ||||||||
\(130\) | 3.98814e13 | 0.724667 | ||||||||
\(131\) | 7.46222e13 | 1.29004 | 0.645022 | − | 0.764164i | \(-0.276848\pi\) | ||||
0.645022 | + | 0.764164i | \(0.276848\pi\) | |||||||
\(132\) | 2.40491e14 | 3.95701 | ||||||||
\(133\) | 2.50813e12 | 0.0392929 | ||||||||
\(134\) | 1.02215e14 | 1.52523 | ||||||||
\(135\) | 2.71839e13 | 0.386493 | ||||||||
\(136\) | 2.67523e14 | 3.62542 | ||||||||
\(137\) | −3.22732e13 | −0.417021 | −0.208511 | − | 0.978020i | \(-0.566862\pi\) | ||||
−0.208511 | + | 0.978020i | \(0.566862\pi\) | |||||||
\(138\) | 1.11291e14 | 1.37166 | ||||||||
\(139\) | −4.96884e13 | −0.584331 | −0.292166 | − | 0.956368i | \(-0.594376\pi\) | ||||
−0.292166 | + | 0.956368i | \(0.594376\pi\) | |||||||
\(140\) | 8.82392e12 | 0.0990443 | ||||||||
\(141\) | 1.49289e14 | 1.59994 | ||||||||
\(142\) | 1.98391e14 | 2.03071 | ||||||||
\(143\) | −1.10528e14 | −1.08091 | ||||||||
\(144\) | 4.20412e14 | 3.92934 | ||||||||
\(145\) | −6.14939e12 | −0.0549465 | ||||||||
\(146\) | −3.00559e14 | −2.56824 | ||||||||
\(147\) | −1.96544e14 | −1.60656 | ||||||||
\(148\) | 3.82540e13 | 0.299210 | ||||||||
\(149\) | −6.11378e13 | −0.457719 | −0.228860 | − | 0.973459i | \(-0.573500\pi\) | ||||
−0.228860 | + | 0.973459i | \(0.573500\pi\) | |||||||
\(150\) | 3.62494e14 | 2.59841 | ||||||||
\(151\) | −1.40643e14 | −0.965533 | −0.482767 | − | 0.875749i | \(-0.660368\pi\) | ||||
−0.482767 | + | 0.875749i | \(0.660368\pi\) | |||||||
\(152\) | −1.38356e14 | −0.909942 | ||||||||
\(153\) | −3.64939e14 | −2.29999 | ||||||||
\(154\) | −3.46160e13 | −0.209118 | ||||||||
\(155\) | 3.20283e13 | 0.185515 | ||||||||
\(156\) | −7.53976e14 | −4.18839 | ||||||||
\(157\) | −2.45848e14 | −1.31015 | −0.655073 | − | 0.755566i | \(-0.727362\pi\) | ||||
−0.655073 | + | 0.755566i | \(0.727362\pi\) | |||||||
\(158\) | 6.98917e14 | 3.57400 | ||||||||
\(159\) | −1.46226e14 | −0.717703 | ||||||||
\(160\) | −1.40729e14 | −0.663138 | ||||||||
\(161\) | −1.13169e13 | −0.0512104 | ||||||||
\(162\) | −2.80199e13 | −0.121792 | ||||||||
\(163\) | −2.61548e14 | −1.09227 | −0.546137 | − | 0.837696i | \(-0.683902\pi\) | ||||
−0.546137 | + | 0.837696i | \(0.683902\pi\) | |||||||
\(164\) | 4.66747e14 | 1.87325 | ||||||||
\(165\) | 1.56433e14 | 0.603507 | ||||||||
\(166\) | −5.00720e14 | −1.85735 | ||||||||
\(167\) | 2.72969e14 | 0.973771 | 0.486885 | − | 0.873466i | \(-0.338133\pi\) | ||||
0.486885 | + | 0.873466i | \(0.338133\pi\) | |||||||
\(168\) | −1.38020e14 | −0.473620 | ||||||||
\(169\) | 4.36485e13 | 0.144114 | ||||||||
\(170\) | 2.97722e14 | 0.946004 | ||||||||
\(171\) | 1.88736e14 | 0.577273 | ||||||||
\(172\) | 7.69802e14 | 2.26696 | ||||||||
\(173\) | −3.14109e14 | −0.890800 | −0.445400 | − | 0.895332i | \(-0.646938\pi\) | ||||
−0.445400 | + | 0.895332i | \(0.646938\pi\) | |||||||
\(174\) | 1.64562e14 | 0.449532 | ||||||||
\(175\) | −3.68611e13 | −0.0970109 | ||||||||
\(176\) | 9.50538e14 | 2.41067 | ||||||||
\(177\) | −1.08217e15 | −2.64527 | ||||||||
\(178\) | 1.66077e14 | 0.391364 | ||||||||
\(179\) | −1.35863e14 | −0.308713 | −0.154357 | − | 0.988015i | \(-0.549331\pi\) | ||||
−0.154357 | + | 0.988015i | \(0.549331\pi\) | |||||||
\(180\) | 6.63999e14 | 1.45511 | ||||||||
\(181\) | 2.81928e14 | 0.595974 | 0.297987 | − | 0.954570i | \(-0.403685\pi\) | ||||
0.297987 | + | 0.954570i | \(0.403685\pi\) | |||||||
\(182\) | 1.08527e14 | 0.221346 | ||||||||
\(183\) | 3.57307e14 | 0.703250 | ||||||||
\(184\) | 6.24271e14 | 1.18593 | ||||||||
\(185\) | 2.48832e13 | 0.0456341 | ||||||||
\(186\) | −8.57103e14 | −1.51774 | ||||||||
\(187\) | −8.25115e14 | −1.41105 | ||||||||
\(188\) | 1.43272e15 | 2.36666 | ||||||||
\(189\) | 7.39736e13 | 0.118053 | ||||||||
\(190\) | −1.53974e14 | −0.237437 | ||||||||
\(191\) | 1.04777e15 | 1.56153 | 0.780764 | − | 0.624825i | \(-0.214830\pi\) | ||||
0.780764 | + | 0.624825i | \(0.214830\pi\) | |||||||
\(192\) | 1.07181e15 | 1.54405 | ||||||||
\(193\) | 6.68990e14 | 0.931745 | 0.465873 | − | 0.884852i | \(-0.345740\pi\) | ||||
0.465873 | + | 0.884852i | \(0.345740\pi\) | |||||||
\(194\) | 6.66526e14 | 0.897647 | ||||||||
\(195\) | −4.90441e14 | −0.638796 | ||||||||
\(196\) | −1.88622e15 | −2.37645 | ||||||||
\(197\) | −5.84517e13 | −0.0712470 | ||||||||
\(198\) | −2.60485e15 | −3.07227 | ||||||||
\(199\) | 4.00401e14 | 0.457036 | 0.228518 | − | 0.973540i | \(-0.426612\pi\) | ||||
0.228518 | + | 0.973540i | \(0.426612\pi\) | |||||||
\(200\) | 2.03336e15 | 2.24657 | ||||||||
\(201\) | −1.25699e15 | −1.34449 | ||||||||
\(202\) | −7.35994e14 | −0.762238 | ||||||||
\(203\) | −1.67339e13 | −0.0167831 | ||||||||
\(204\) | −5.62857e15 | −5.46767 | ||||||||
\(205\) | 3.03606e14 | 0.285700 | ||||||||
\(206\) | 7.81572e14 | 0.712578 | ||||||||
\(207\) | −8.51593e14 | −0.752358 | ||||||||
\(208\) | −2.98009e15 | −2.55163 | ||||||||
\(209\) | 4.26727e14 | 0.354160 | ||||||||
\(210\) | −1.53600e14 | −0.123585 | ||||||||
\(211\) | 8.38249e14 | 0.653939 | 0.326969 | − | 0.945035i | \(-0.393973\pi\) | ||||
0.326969 | + | 0.945035i | \(0.393973\pi\) | |||||||
\(212\) | −1.40333e15 | −1.06164 | ||||||||
\(213\) | −2.43971e15 | −1.79007 | ||||||||
\(214\) | 4.25133e15 | 3.02577 | ||||||||
\(215\) | 5.00736e14 | 0.345747 | ||||||||
\(216\) | −4.08060e15 | −2.73385 | ||||||||
\(217\) | 8.71565e13 | 0.0566645 | ||||||||
\(218\) | −1.78765e15 | −1.12801 | ||||||||
\(219\) | 3.69612e15 | 2.26391 | ||||||||
\(220\) | 1.50128e15 | 0.892718 | ||||||||
\(221\) | 2.58686e15 | 1.49356 | ||||||||
\(222\) | −6.65894e14 | −0.373345 | ||||||||
\(223\) | −5.40493e14 | −0.294312 | −0.147156 | − | 0.989113i | \(-0.547012\pi\) | ||||
−0.147156 | + | 0.989113i | \(0.547012\pi\) | |||||||
\(224\) | −3.82956e14 | −0.202552 | ||||||||
\(225\) | −2.77379e15 | −1.42524 | ||||||||
\(226\) | 2.48017e15 | 1.23816 | ||||||||
\(227\) | 1.45466e15 | 0.705655 | 0.352828 | − | 0.935688i | \(-0.385220\pi\) | ||||
0.352828 | + | 0.935688i | \(0.385220\pi\) | |||||||
\(228\) | 2.91094e15 | 1.37233 | ||||||||
\(229\) | 9.69711e14 | 0.444336 | 0.222168 | − | 0.975008i | \(-0.428687\pi\) | ||||
0.222168 | + | 0.975008i | \(0.428687\pi\) | |||||||
\(230\) | 6.94741e14 | 0.309451 | ||||||||
\(231\) | 4.25690e14 | 0.184338 | ||||||||
\(232\) | 9.23091e14 | 0.388662 | ||||||||
\(233\) | −3.68613e15 | −1.50923 | −0.754617 | − | 0.656165i | \(-0.772177\pi\) | ||||
−0.754617 | + | 0.656165i | \(0.772177\pi\) | |||||||
\(234\) | 8.16661e15 | 3.25191 | ||||||||
\(235\) | 9.31949e14 | 0.360953 | ||||||||
\(236\) | −1.03856e16 | −3.91293 | ||||||||
\(237\) | −8.59493e15 | −3.15049 | ||||||||
\(238\) | 8.10171e14 | 0.288952 | ||||||||
\(239\) | 3.14117e15 | 1.09020 | 0.545098 | − | 0.838372i | \(-0.316492\pi\) | ||||
0.545098 | + | 0.838372i | \(0.316492\pi\) | |||||||
\(240\) | 4.21777e15 | 1.42465 | ||||||||
\(241\) | −2.69521e15 | −0.886099 | −0.443050 | − | 0.896497i | \(-0.646103\pi\) | ||||
−0.443050 | + | 0.896497i | \(0.646103\pi\) | |||||||
\(242\) | −1.22247e14 | −0.0391234 | ||||||||
\(243\) | −3.03487e15 | −0.945583 | ||||||||
\(244\) | 3.42907e15 | 1.04026 | ||||||||
\(245\) | −1.22694e15 | −0.362446 | ||||||||
\(246\) | −8.12475e15 | −2.33739 | ||||||||
\(247\) | −1.33785e15 | −0.374868 | ||||||||
\(248\) | −4.80780e15 | −1.31223 | ||||||||
\(249\) | 6.15761e15 | 1.63725 | ||||||||
\(250\) | 4.87815e15 | 1.26370 | ||||||||
\(251\) | 1.68949e15 | 0.426457 | 0.213229 | − | 0.977002i | \(-0.431602\pi\) | ||||
0.213229 | + | 0.977002i | \(0.431602\pi\) | |||||||
\(252\) | 1.80690e15 | 0.444457 | ||||||||
\(253\) | −1.92542e15 | −0.461575 | ||||||||
\(254\) | 3.37923e15 | 0.789585 | ||||||||
\(255\) | −3.66123e15 | −0.833905 | ||||||||
\(256\) | −4.73122e15 | −1.05054 | ||||||||
\(257\) | 3.59727e15 | 0.778767 | 0.389383 | − | 0.921076i | \(-0.372688\pi\) | ||||
0.389383 | + | 0.921076i | \(0.372688\pi\) | |||||||
\(258\) | −1.34001e16 | −2.82865 | ||||||||
\(259\) | 6.77130e13 | 0.0139387 | ||||||||
\(260\) | −4.70675e15 | −0.944918 | ||||||||
\(261\) | −1.25922e15 | −0.246570 | ||||||||
\(262\) | −1.24661e16 | −2.38107 | ||||||||
\(263\) | −2.07601e15 | −0.386828 | −0.193414 | − | 0.981117i | \(-0.561956\pi\) | ||||
−0.193414 | + | 0.981117i | \(0.561956\pi\) | |||||||
\(264\) | −2.34823e16 | −4.26889 | ||||||||
\(265\) | −9.12828e14 | −0.161916 | ||||||||
\(266\) | −4.18998e14 | −0.0725240 | ||||||||
\(267\) | −2.04234e15 | −0.344988 | ||||||||
\(268\) | −1.20633e16 | −1.98879 | ||||||||
\(269\) | −8.87878e15 | −1.42877 | −0.714387 | − | 0.699751i | \(-0.753294\pi\) | ||||
−0.714387 | + | 0.699751i | \(0.753294\pi\) | |||||||
\(270\) | −4.54123e15 | −0.713360 | ||||||||
\(271\) | −1.70109e15 | −0.260872 | −0.130436 | − | 0.991457i | \(-0.541638\pi\) | ||||
−0.130436 | + | 0.991457i | \(0.541638\pi\) | |||||||
\(272\) | −2.22469e16 | −3.33098 | ||||||||
\(273\) | −1.33460e15 | −0.195117 | ||||||||
\(274\) | 5.39143e15 | 0.769707 | ||||||||
\(275\) | −6.27144e15 | −0.874389 | ||||||||
\(276\) | −1.31344e16 | −1.78855 | ||||||||
\(277\) | 1.01913e15 | 0.135554 | 0.0677771 | − | 0.997700i | \(-0.478409\pi\) | ||||
0.0677771 | + | 0.997700i | \(0.478409\pi\) | |||||||
\(278\) | 8.30075e15 | 1.07852 | ||||||||
\(279\) | 6.55851e15 | 0.832488 | ||||||||
\(280\) | −8.61596e14 | −0.106851 | ||||||||
\(281\) | 1.98891e15 | 0.241004 | 0.120502 | − | 0.992713i | \(-0.461550\pi\) | ||||
0.120502 | + | 0.992713i | \(0.461550\pi\) | |||||||
\(282\) | −2.49397e16 | −2.95306 | ||||||||
\(283\) | 4.15226e15 | 0.480477 | 0.240238 | − | 0.970714i | \(-0.422774\pi\) | ||||
0.240238 | + | 0.970714i | \(0.422774\pi\) | |||||||
\(284\) | −2.34138e16 | −2.64791 | ||||||||
\(285\) | 1.89349e15 | 0.209301 | ||||||||
\(286\) | 1.84644e16 | 1.99506 | ||||||||
\(287\) | 8.26184e14 | 0.0872658 | ||||||||
\(288\) | −2.88174e16 | −2.97580 | ||||||||
\(289\) | 9.40684e15 | 0.949746 | ||||||||
\(290\) | 1.02729e15 | 0.101416 | ||||||||
\(291\) | −8.19659e15 | −0.791278 | ||||||||
\(292\) | 3.54715e16 | 3.34881 | ||||||||
\(293\) | −1.84819e16 | −1.70651 | −0.853254 | − | 0.521496i | \(-0.825374\pi\) | ||||
−0.853254 | + | 0.521496i | \(0.825374\pi\) | |||||||
\(294\) | 3.28338e16 | 2.96527 | ||||||||
\(295\) | −6.75552e15 | −0.596782 | ||||||||
\(296\) | −3.73524e15 | −0.322792 | ||||||||
\(297\) | 1.25857e16 | 1.06404 | ||||||||
\(298\) | 1.02134e16 | 0.844824 | ||||||||
\(299\) | 6.03650e15 | 0.488565 | ||||||||
\(300\) | −4.27810e16 | −3.38815 | ||||||||
\(301\) | 1.36262e15 | 0.105607 | ||||||||
\(302\) | 2.34952e16 | 1.78211 | ||||||||
\(303\) | 9.05088e15 | 0.671914 | ||||||||
\(304\) | 1.15055e16 | 0.836039 | ||||||||
\(305\) | 2.23052e15 | 0.158656 | ||||||||
\(306\) | 6.09653e16 | 4.24515 | ||||||||
\(307\) | −1.04629e16 | −0.713270 | −0.356635 | − | 0.934244i | \(-0.616076\pi\) | ||||
−0.356635 | + | 0.934244i | \(0.616076\pi\) | |||||||
\(308\) | 4.08533e15 | 0.272676 | ||||||||
\(309\) | −9.61138e15 | −0.628139 | ||||||||
\(310\) | −5.35052e15 | −0.342409 | ||||||||
\(311\) | 1.46522e16 | 0.918248 | 0.459124 | − | 0.888372i | \(-0.348163\pi\) | ||||
0.459124 | + | 0.888372i | \(0.348163\pi\) | |||||||
\(312\) | 7.36206e16 | 4.51850 | ||||||||
\(313\) | −1.21812e16 | −0.732235 | −0.366118 | − | 0.930569i | \(-0.619313\pi\) | ||||
−0.366118 | + | 0.930569i | \(0.619313\pi\) | |||||||
\(314\) | 4.10704e16 | 2.41817 | ||||||||
\(315\) | 1.17534e15 | 0.0677866 | ||||||||
\(316\) | −8.24852e16 | −4.66026 | ||||||||
\(317\) | −1.44293e16 | −0.798655 | −0.399328 | − | 0.916808i | \(-0.630756\pi\) | ||||
−0.399328 | + | 0.916808i | \(0.630756\pi\) | |||||||
\(318\) | 2.44280e16 | 1.32468 | ||||||||
\(319\) | −2.84706e15 | −0.151272 | ||||||||
\(320\) | 6.69087e15 | 0.348344 | ||||||||
\(321\) | −5.22807e16 | −2.66722 | ||||||||
\(322\) | 1.89055e15 | 0.0945203 | ||||||||
\(323\) | −9.98734e15 | −0.489365 | ||||||||
\(324\) | 3.30687e15 | 0.158809 | ||||||||
\(325\) | 1.96620e16 | 0.925518 | ||||||||
\(326\) | 4.36931e16 | 2.01604 | ||||||||
\(327\) | 2.19836e16 | 0.994346 | ||||||||
\(328\) | −4.55747e16 | −2.02089 | ||||||||
\(329\) | 2.53605e15 | 0.110251 | ||||||||
\(330\) | −2.61330e16 | −1.11391 | ||||||||
\(331\) | 1.86828e16 | 0.780835 | 0.390418 | − | 0.920638i | \(-0.372331\pi\) | ||||
0.390418 | + | 0.920638i | \(0.372331\pi\) | |||||||
\(332\) | 5.90943e16 | 2.42186 | ||||||||
\(333\) | 5.09539e15 | 0.204781 | ||||||||
\(334\) | −4.56012e16 | −1.79731 | ||||||||
\(335\) | −7.84685e15 | −0.303322 | ||||||||
\(336\) | 1.14775e16 | 0.435154 | ||||||||
\(337\) | 2.95110e16 | 1.09746 | 0.548731 | − | 0.835999i | \(-0.315111\pi\) | ||||
0.548731 | + | 0.835999i | \(0.315111\pi\) | |||||||
\(338\) | −7.29174e15 | −0.265994 | ||||||||
\(339\) | −3.04998e16 | −1.09144 | ||||||||
\(340\) | −3.51367e16 | −1.23353 | ||||||||
\(341\) | 1.48286e16 | 0.510735 | ||||||||
\(342\) | −3.15296e16 | −1.06549 | ||||||||
\(343\) | −6.72007e15 | −0.222824 | ||||||||
\(344\) | −7.51659e16 | −2.44563 | ||||||||
\(345\) | −8.54357e15 | −0.272782 | ||||||||
\(346\) | 5.24737e16 | 1.64417 | ||||||||
\(347\) | 4.68700e16 | 1.44130 | 0.720648 | − | 0.693301i | \(-0.243845\pi\) | ||||
0.720648 | + | 0.693301i | \(0.243845\pi\) | |||||||
\(348\) | −1.94214e16 | −0.586160 | ||||||||
\(349\) | −1.98624e16 | −0.588392 | −0.294196 | − | 0.955745i | \(-0.595052\pi\) | ||||
−0.294196 | + | 0.955745i | \(0.595052\pi\) | |||||||
\(350\) | 6.15786e15 | 0.179055 | ||||||||
\(351\) | −3.94581e16 | −1.12626 | ||||||||
\(352\) | −6.51552e16 | −1.82567 | ||||||||
\(353\) | 1.12512e16 | 0.309502 | 0.154751 | − | 0.987953i | \(-0.450542\pi\) | ||||
0.154751 | + | 0.987953i | \(0.450542\pi\) | |||||||
\(354\) | 1.80783e17 | 4.88244 | ||||||||
\(355\) | −1.52301e16 | −0.403847 | ||||||||
\(356\) | −1.96002e16 | −0.510312 | ||||||||
\(357\) | −9.96307e15 | −0.254712 | ||||||||
\(358\) | 2.26967e16 | 0.569800 | ||||||||
\(359\) | 3.80413e16 | 0.937867 | 0.468933 | − | 0.883234i | \(-0.344638\pi\) | ||||
0.468933 | + | 0.883234i | \(0.344638\pi\) | |||||||
\(360\) | −6.48350e16 | −1.56980 | ||||||||
\(361\) | −3.68878e16 | −0.877175 | ||||||||
\(362\) | −4.70978e16 | −1.10001 | ||||||||
\(363\) | 1.50333e15 | 0.0344874 | ||||||||
\(364\) | −1.28081e16 | −0.288621 | ||||||||
\(365\) | 2.30732e16 | 0.510746 | ||||||||
\(366\) | −5.96904e16 | −1.29801 | ||||||||
\(367\) | 5.13474e14 | 0.0109696 | 0.00548478 | − | 0.999985i | \(-0.498254\pi\) | ||||
0.00548478 | + | 0.999985i | \(0.498254\pi\) | |||||||
\(368\) | −5.19136e16 | −1.08961 | ||||||||
\(369\) | 6.21702e16 | 1.28207 | ||||||||
\(370\) | −4.15689e15 | −0.0842281 | ||||||||
\(371\) | −2.48402e15 | −0.0494566 | ||||||||
\(372\) | 1.01154e17 | 1.97904 | ||||||||
\(373\) | −4.59511e16 | −0.883463 | −0.441731 | − | 0.897147i | \(-0.645636\pi\) | ||||
−0.441731 | + | 0.897147i | \(0.645636\pi\) | |||||||
\(374\) | 1.37840e17 | 2.60442 | ||||||||
\(375\) | −5.99890e16 | −1.11396 | ||||||||
\(376\) | −1.39896e17 | −2.55319 | ||||||||
\(377\) | 8.92599e15 | 0.160117 | ||||||||
\(378\) | −1.23577e16 | −0.217893 | ||||||||
\(379\) | −2.47235e16 | −0.428504 | −0.214252 | − | 0.976778i | \(-0.568731\pi\) | ||||
−0.214252 | + | 0.976778i | \(0.568731\pi\) | |||||||
\(380\) | 1.81718e16 | 0.309602 | ||||||||
\(381\) | −4.15561e16 | −0.696021 | ||||||||
\(382\) | −1.75037e17 | −2.88215 | ||||||||
\(383\) | 6.98369e16 | 1.13056 | 0.565279 | − | 0.824900i | \(-0.308768\pi\) | ||||
0.565279 | + | 0.824900i | \(0.308768\pi\) | |||||||
\(384\) | 5.62307e15 | 0.0894995 | ||||||||
\(385\) | 2.65740e15 | 0.0415874 | ||||||||
\(386\) | −1.11759e17 | −1.71975 | ||||||||
\(387\) | 1.02537e17 | 1.55152 | ||||||||
\(388\) | −7.86624e16 | −1.17047 | ||||||||
\(389\) | −3.13101e16 | −0.458154 | −0.229077 | − | 0.973408i | \(-0.573571\pi\) | ||||
−0.229077 | + | 0.973408i | \(0.573571\pi\) | |||||||
\(390\) | 8.19311e16 | 1.17904 | ||||||||
\(391\) | 4.50636e16 | 0.637789 | ||||||||
\(392\) | 1.84177e17 | 2.56375 | ||||||||
\(393\) | 1.53302e17 | 2.09892 | ||||||||
\(394\) | 9.76471e15 | 0.131503 | ||||||||
\(395\) | −5.36544e16 | −0.710762 | ||||||||
\(396\) | 3.07421e17 | 4.00603 | ||||||||
\(397\) | 4.10001e16 | 0.525589 | 0.262794 | − | 0.964852i | \(-0.415356\pi\) | ||||
0.262794 | + | 0.964852i | \(0.415356\pi\) | |||||||
\(398\) | −6.68895e16 | −0.843563 | ||||||||
\(399\) | 5.15263e15 | 0.0639300 | ||||||||
\(400\) | −1.69092e17 | −2.06411 | ||||||||
\(401\) | 2.99900e16 | 0.360196 | 0.180098 | − | 0.983649i | \(-0.442359\pi\) | ||||
0.180098 | + | 0.983649i | \(0.442359\pi\) | |||||||
\(402\) | 2.09988e17 | 2.48156 | ||||||||
\(403\) | −4.64899e16 | −0.540600 | ||||||||
\(404\) | 8.68610e16 | 0.993907 | ||||||||
\(405\) | 2.15103e15 | 0.0242208 | ||||||||
\(406\) | 2.79550e15 | 0.0309771 | ||||||||
\(407\) | 1.15205e16 | 0.125634 | ||||||||
\(408\) | 5.49592e17 | 5.89860 | ||||||||
\(409\) | −3.01326e16 | −0.318299 | −0.159149 | − | 0.987255i | \(-0.550875\pi\) | ||||
−0.159149 | + | 0.987255i | \(0.550875\pi\) | |||||||
\(410\) | −5.07193e16 | −0.527325 | ||||||||
\(411\) | −6.63011e16 | −0.678498 | ||||||||
\(412\) | −9.22400e16 | −0.929154 | ||||||||
\(413\) | −1.83834e16 | −0.182284 | ||||||||
\(414\) | 1.42264e17 | 1.38865 | ||||||||
\(415\) | 3.84393e16 | 0.369371 | ||||||||
\(416\) | 2.04272e17 | 1.93242 | ||||||||
\(417\) | −1.02078e17 | −0.950713 | ||||||||
\(418\) | −7.12873e16 | −0.653681 | ||||||||
\(419\) | 1.39179e17 | 1.25656 | 0.628278 | − | 0.777989i | \(-0.283760\pi\) | ||||
0.628278 | + | 0.777989i | \(0.283760\pi\) | |||||||
\(420\) | 1.81276e16 | 0.161146 | ||||||||
\(421\) | −1.85777e17 | −1.62614 | −0.813072 | − | 0.582163i | \(-0.802207\pi\) | ||||
−0.813072 | + | 0.582163i | \(0.802207\pi\) | |||||||
\(422\) | −1.40035e17 | −1.20699 | ||||||||
\(423\) | 1.90837e17 | 1.61976 | ||||||||
\(424\) | 1.37026e17 | 1.14531 | ||||||||
\(425\) | 1.46780e17 | 1.20820 | ||||||||
\(426\) | 4.07568e17 | 3.30398 | ||||||||
\(427\) | 6.06975e15 | 0.0484607 | ||||||||
\(428\) | −5.01736e17 | −3.94540 | ||||||||
\(429\) | −2.27066e17 | −1.75865 | ||||||||
\(430\) | −8.36509e16 | −0.638154 | ||||||||
\(431\) | 1.48837e17 | 1.11843 | 0.559217 | − | 0.829022i | \(-0.311102\pi\) | ||||
0.559217 | + | 0.829022i | \(0.311102\pi\) | |||||||
\(432\) | 3.39337e17 | 2.51181 | ||||||||
\(433\) | −1.54076e17 | −1.12348 | −0.561739 | − | 0.827314i | \(-0.689868\pi\) | ||||
−0.561739 | + | 0.827314i | \(0.689868\pi\) | |||||||
\(434\) | −1.45600e16 | −0.104587 | ||||||||
\(435\) | −1.26331e16 | −0.0893985 | ||||||||
\(436\) | 2.10975e17 | 1.47085 | ||||||||
\(437\) | −2.33057e16 | −0.160078 | ||||||||
\(438\) | −6.17458e17 | −4.17855 | ||||||||
\(439\) | −2.35755e17 | −1.57196 | −0.785981 | − | 0.618251i | \(-0.787842\pi\) | ||||
−0.785981 | + | 0.618251i | \(0.787842\pi\) | |||||||
\(440\) | −1.46590e17 | −0.963077 | ||||||||
\(441\) | −2.51243e17 | −1.62646 | ||||||||
\(442\) | −4.32151e17 | −2.75671 | ||||||||
\(443\) | −1.61027e17 | −1.01222 | −0.506108 | − | 0.862470i | \(-0.668916\pi\) | ||||
−0.506108 | + | 0.862470i | \(0.668916\pi\) | |||||||
\(444\) | 7.85878e16 | 0.486817 | ||||||||
\(445\) | −1.27494e16 | −0.0778306 | ||||||||
\(446\) | 9.02926e16 | 0.543220 | ||||||||
\(447\) | −1.25600e17 | −0.744714 | ||||||||
\(448\) | 1.82074e16 | 0.106400 | ||||||||
\(449\) | −1.74061e17 | −1.00254 | −0.501268 | − | 0.865292i | \(-0.667133\pi\) | ||||
−0.501268 | + | 0.865292i | \(0.667133\pi\) | |||||||
\(450\) | 4.63378e17 | 2.63060 | ||||||||
\(451\) | 1.40565e17 | 0.786554 | ||||||||
\(452\) | −2.92706e17 | −1.61448 | ||||||||
\(453\) | −2.88932e17 | −1.57093 | ||||||||
\(454\) | −2.43009e17 | −1.30245 | ||||||||
\(455\) | −8.33136e15 | −0.0440192 | ||||||||
\(456\) | −2.84234e17 | −1.48049 | ||||||||
\(457\) | −3.08125e17 | −1.58224 | −0.791119 | − | 0.611662i | \(-0.790501\pi\) | ||||
−0.791119 | + | 0.611662i | \(0.790501\pi\) | |||||||
\(458\) | −1.61996e17 | −0.820123 | ||||||||
\(459\) | −2.94562e17 | −1.47026 | ||||||||
\(460\) | −8.19923e16 | −0.403503 | ||||||||
\(461\) | 1.77805e17 | 0.862755 | 0.431378 | − | 0.902171i | \(-0.358028\pi\) | ||||
0.431378 | + | 0.902171i | \(0.358028\pi\) | |||||||
\(462\) | −7.11140e16 | −0.340238 | ||||||||
\(463\) | −4.07934e17 | −1.92448 | −0.962239 | − | 0.272204i | \(-0.912247\pi\) | ||||
−0.962239 | + | 0.272204i | \(0.912247\pi\) | |||||||
\(464\) | −7.67631e16 | −0.357096 | ||||||||
\(465\) | 6.57980e16 | 0.301834 | ||||||||
\(466\) | 6.15789e17 | 2.78563 | ||||||||
\(467\) | −1.30093e17 | −0.580356 | −0.290178 | − | 0.956973i | \(-0.593715\pi\) | ||||
−0.290178 | + | 0.956973i | \(0.593715\pi\) | |||||||
\(468\) | −9.63811e17 | −4.24028 | ||||||||
\(469\) | −2.13531e16 | −0.0926483 | ||||||||
\(470\) | −1.55688e17 | −0.666220 | ||||||||
\(471\) | −5.05063e17 | −2.13162 | ||||||||
\(472\) | 1.01408e18 | 4.22132 | ||||||||
\(473\) | 2.31832e17 | 0.951867 | ||||||||
\(474\) | 1.43583e18 | 5.81494 | ||||||||
\(475\) | −7.59107e16 | −0.303246 | ||||||||
\(476\) | −9.56152e16 | −0.376775 | ||||||||
\(477\) | −1.86922e17 | −0.726593 | ||||||||
\(478\) | −5.24751e17 | −2.01220 | ||||||||
\(479\) | −4.32104e16 | −0.163459 | −0.0817293 | − | 0.996655i | \(-0.526044\pi\) | ||||
−0.0817293 | + | 0.996655i | \(0.526044\pi\) | |||||||
\(480\) | −2.89110e17 | −1.07893 | ||||||||
\(481\) | −3.61186e16 | −0.132980 | ||||||||
\(482\) | 4.50252e17 | 1.63550 | ||||||||
\(483\) | −2.32490e16 | −0.0833199 | ||||||||
\(484\) | 1.44274e16 | 0.0510143 | ||||||||
\(485\) | −5.11678e16 | −0.178515 | ||||||||
\(486\) | 5.06994e17 | 1.74529 | ||||||||
\(487\) | −4.32949e17 | −1.47061 | −0.735307 | − | 0.677734i | \(-0.762962\pi\) | ||||
−0.735307 | + | 0.677734i | \(0.762962\pi\) | |||||||
\(488\) | −3.34825e17 | −1.12225 | ||||||||
\(489\) | −5.37316e17 | −1.77714 | ||||||||
\(490\) | 2.04967e17 | 0.668976 | ||||||||
\(491\) | 3.56642e17 | 1.14869 | 0.574344 | − | 0.818614i | \(-0.305257\pi\) | ||||
0.574344 | + | 0.818614i | \(0.305257\pi\) | |||||||
\(492\) | 9.58871e17 | 3.04780 | ||||||||
\(493\) | 6.66342e16 | 0.209022 | ||||||||
\(494\) | 2.23497e17 | 0.691904 | ||||||||
\(495\) | 1.99969e17 | 0.610982 | ||||||||
\(496\) | 3.99811e17 | 1.20566 | ||||||||
\(497\) | −4.14445e16 | −0.123353 | ||||||||
\(498\) | −1.02866e18 | −3.02192 | ||||||||
\(499\) | −4.88532e17 | −1.41657 | −0.708287 | − | 0.705925i | \(-0.750532\pi\) | ||||
−0.708287 | + | 0.705925i | \(0.750532\pi\) | |||||||
\(500\) | −5.75712e17 | −1.64778 | ||||||||
\(501\) | 5.60780e17 | 1.58434 | ||||||||
\(502\) | −2.82239e17 | −0.787123 | ||||||||
\(503\) | −5.63176e17 | −1.55043 | −0.775216 | − | 0.631697i | \(-0.782359\pi\) | ||||
−0.775216 | + | 0.631697i | \(0.782359\pi\) | |||||||
\(504\) | −1.76431e17 | −0.479487 | ||||||||
\(505\) | 5.65007e16 | 0.151586 | ||||||||
\(506\) | 3.21653e17 | 0.851941 | ||||||||
\(507\) | 8.96701e16 | 0.234475 | ||||||||
\(508\) | −3.98812e17 | −1.02957 | ||||||||
\(509\) | 4.10438e17 | 1.04612 | 0.523060 | − | 0.852296i | \(-0.324790\pi\) | ||||
0.523060 | + | 0.852296i | \(0.324790\pi\) | |||||||
\(510\) | 6.11631e17 | 1.53916 | ||||||||
\(511\) | 6.27877e16 | 0.156005 | ||||||||
\(512\) | 7.67955e17 | 1.88400 | ||||||||
\(513\) | 1.52339e17 | 0.369019 | ||||||||
\(514\) | −6.00945e17 | −1.43739 | ||||||||
\(515\) | −5.99997e16 | −0.141710 | ||||||||
\(516\) | 1.58146e18 | 3.68837 | ||||||||
\(517\) | 4.31477e17 | 0.993731 | ||||||||
\(518\) | −1.13119e16 | −0.0257271 | ||||||||
\(519\) | −6.45295e17 | −1.44934 | ||||||||
\(520\) | 4.59582e17 | 1.01939 | ||||||||
\(521\) | −6.11645e16 | −0.133984 | −0.0669922 | − | 0.997753i | \(-0.521340\pi\) | ||||
−0.0669922 | + | 0.997753i | \(0.521340\pi\) | |||||||
\(522\) | 2.10361e17 | 0.455100 | ||||||||
\(523\) | 1.69083e17 | 0.361275 | 0.180638 | − | 0.983550i | \(-0.442184\pi\) | ||||
0.180638 | + | 0.983550i | \(0.442184\pi\) | |||||||
\(524\) | 1.47123e18 | 3.10475 | ||||||||
\(525\) | −7.57262e16 | −0.157838 | ||||||||
\(526\) | 3.46810e17 | 0.713977 | ||||||||
\(527\) | −3.47056e17 | −0.705716 | ||||||||
\(528\) | 1.95276e18 | 3.92218 | ||||||||
\(529\) | −3.98880e17 | −0.791371 | ||||||||
\(530\) | 1.52493e17 | 0.298853 | ||||||||
\(531\) | −1.38334e18 | −2.67803 | ||||||||
\(532\) | 4.94496e16 | 0.0945664 | ||||||||
\(533\) | −4.40692e17 | −0.832547 | ||||||||
\(534\) | 3.41185e17 | 0.636753 | ||||||||
\(535\) | −3.26366e17 | −0.601735 | ||||||||
\(536\) | 1.17790e18 | 2.14554 | ||||||||
\(537\) | −2.79112e17 | −0.502280 | ||||||||
\(538\) | 1.48325e18 | 2.63713 | ||||||||
\(539\) | −5.68052e17 | −0.997840 | ||||||||
\(540\) | 5.35949e17 | 0.930174 | ||||||||
\(541\) | 1.02602e18 | 1.75943 | 0.879715 | − | 0.475501i | \(-0.157733\pi\) | ||||
0.879715 | + | 0.475501i | \(0.157733\pi\) | |||||||
\(542\) | 2.84177e17 | 0.481497 | ||||||||
\(543\) | 5.79184e17 | 0.969657 | ||||||||
\(544\) | 1.52493e18 | 2.52264 | ||||||||
\(545\) | 1.37234e17 | 0.224328 | ||||||||
\(546\) | 2.22954e17 | 0.360133 | ||||||||
\(547\) | −4.33635e17 | −0.692160 | −0.346080 | − | 0.938205i | \(-0.612487\pi\) | ||||
−0.346080 | + | 0.938205i | \(0.612487\pi\) | |||||||
\(548\) | −6.36289e17 | −1.00365 | ||||||||
\(549\) | 4.56748e17 | 0.711962 | ||||||||
\(550\) | 1.04768e18 | 1.61388 | ||||||||
\(551\) | −3.44614e16 | −0.0524623 | ||||||||
\(552\) | 1.28248e18 | 1.92951 | ||||||||
\(553\) | −1.46006e17 | −0.217099 | ||||||||
\(554\) | −1.70252e17 | −0.250196 | ||||||||
\(555\) | 5.11193e16 | 0.0742472 | ||||||||
\(556\) | −9.79643e17 | −1.40631 | ||||||||
\(557\) | 7.45475e17 | 1.05773 | 0.528864 | − | 0.848706i | \(-0.322618\pi\) | ||||
0.528864 | + | 0.848706i | \(0.322618\pi\) | |||||||
\(558\) | −1.09564e18 | −1.53654 | ||||||||
\(559\) | −7.26830e17 | −1.00753 | ||||||||
\(560\) | 7.16492e16 | 0.0981724 | ||||||||
\(561\) | −1.69509e18 | −2.29580 | ||||||||
\(562\) | −3.32259e17 | −0.444827 | ||||||||
\(563\) | −1.01184e18 | −1.33908 | −0.669541 | − | 0.742775i | \(-0.733509\pi\) | ||||
−0.669541 | + | 0.742775i | \(0.733509\pi\) | |||||||
\(564\) | 2.94334e18 | 3.85059 | ||||||||
\(565\) | −1.90397e17 | −0.246233 | ||||||||
\(566\) | −6.93660e17 | −0.886828 | ||||||||
\(567\) | 5.85346e15 | 0.00739814 | ||||||||
\(568\) | 2.28620e18 | 2.85660 | ||||||||
\(569\) | −3.05533e17 | −0.377422 | −0.188711 | − | 0.982033i | \(-0.560431\pi\) | ||||
−0.188711 | + | 0.982033i | \(0.560431\pi\) | |||||||
\(570\) | −3.16319e17 | −0.386312 | ||||||||
\(571\) | −2.76855e17 | −0.334285 | −0.167143 | − | 0.985933i | \(-0.553454\pi\) | ||||
−0.167143 | + | 0.985933i | \(0.553454\pi\) | |||||||
\(572\) | −2.17914e18 | −2.60143 | ||||||||
\(573\) | 2.15251e18 | 2.54062 | ||||||||
\(574\) | −1.38019e17 | −0.161069 | ||||||||
\(575\) | 3.42515e17 | 0.395219 | ||||||||
\(576\) | 1.37011e18 | 1.56318 | ||||||||
\(577\) | 6.16642e17 | 0.695650 | 0.347825 | − | 0.937560i | \(-0.386920\pi\) | ||||
0.347825 | + | 0.937560i | \(0.386920\pi\) | |||||||
\(578\) | −1.57147e18 | −1.75297 | ||||||||
\(579\) | 1.37435e18 | 1.51596 | ||||||||
\(580\) | −1.21240e17 | −0.132240 | ||||||||
\(581\) | 1.04602e17 | 0.112823 | ||||||||
\(582\) | 1.36929e18 | 1.46048 | ||||||||
\(583\) | −4.22624e17 | −0.445768 | ||||||||
\(584\) | −3.46355e18 | −3.61275 | ||||||||
\(585\) | −6.26934e17 | −0.646708 | ||||||||
\(586\) | 3.08752e18 | 3.14974 | ||||||||
\(587\) | 6.29563e17 | 0.635172 | 0.317586 | − | 0.948229i | \(-0.397128\pi\) | ||||
0.317586 | + | 0.948229i | \(0.397128\pi\) | |||||||
\(588\) | −3.87500e18 | −3.86651 | ||||||||
\(589\) | 1.79488e17 | 0.177127 | ||||||||
\(590\) | 1.12855e18 | 1.10150 | ||||||||
\(591\) | −1.20081e17 | −0.115920 | ||||||||
\(592\) | 3.10618e17 | 0.296576 | ||||||||
\(593\) | −2.72242e17 | −0.257099 | −0.128549 | − | 0.991703i | \(-0.541032\pi\) | ||||
−0.128549 | + | 0.991703i | \(0.541032\pi\) | |||||||
\(594\) | −2.10251e18 | −1.96393 | ||||||||
\(595\) | −6.21951e16 | −0.0574640 | ||||||||
\(596\) | −1.20538e18 | −1.10159 | ||||||||
\(597\) | 8.22572e17 | 0.743603 | ||||||||
\(598\) | −1.00843e18 | −0.901757 | ||||||||
\(599\) | 1.71240e18 | 1.51472 | 0.757360 | − | 0.652998i | \(-0.226489\pi\) | ||||
0.757360 | + | 0.652998i | \(0.226489\pi\) | |||||||
\(600\) | 4.17728e18 | 3.65519 | ||||||||
\(601\) | −4.70950e17 | −0.407653 | −0.203826 | − | 0.979007i | \(-0.565338\pi\) | ||||
−0.203826 | + | 0.979007i | \(0.565338\pi\) | |||||||
\(602\) | −2.27633e17 | −0.194921 | ||||||||
\(603\) | −1.60682e18 | −1.36114 | ||||||||
\(604\) | −2.77287e18 | −2.32375 | ||||||||
\(605\) | 9.38461e15 | 0.00778048 | ||||||||
\(606\) | −1.51200e18 | −1.24017 | ||||||||
\(607\) | 3.83443e17 | 0.311153 | 0.155576 | − | 0.987824i | \(-0.450276\pi\) | ||||
0.155576 | + | 0.987824i | \(0.450276\pi\) | |||||||
\(608\) | −7.88650e17 | −0.633157 | ||||||||
\(609\) | −3.43776e16 | −0.0273064 | ||||||||
\(610\) | −3.72621e17 | −0.292835 | ||||||||
\(611\) | −1.35275e18 | −1.05184 | ||||||||
\(612\) | −7.19503e18 | −5.53539 | ||||||||
\(613\) | 4.81387e16 | 0.0366439 | 0.0183219 | − | 0.999832i | \(-0.494168\pi\) | ||||
0.0183219 | + | 0.999832i | \(0.494168\pi\) | |||||||
\(614\) | 1.74790e18 | 1.31650 | ||||||||
\(615\) | 6.23720e17 | 0.464838 | ||||||||
\(616\) | −3.98905e17 | −0.294167 | ||||||||
\(617\) | 1.06313e17 | 0.0775772 | 0.0387886 | − | 0.999247i | \(-0.487650\pi\) | ||||
0.0387886 | + | 0.999247i | \(0.487650\pi\) | |||||||
\(618\) | 1.60564e18 | 1.15937 | ||||||||
\(619\) | −2.28357e18 | −1.63164 | −0.815820 | − | 0.578305i | \(-0.803714\pi\) | ||||
−0.815820 | + | 0.578305i | \(0.803714\pi\) | |||||||
\(620\) | 6.31461e17 | 0.446478 | ||||||||
\(621\) | −6.87366e17 | −0.480942 | ||||||||
\(622\) | −2.44774e18 | −1.69483 | ||||||||
\(623\) | −3.46941e16 | −0.0237730 | ||||||||
\(624\) | −6.12220e18 | −4.15152 | ||||||||
\(625\) | 9.14863e17 | 0.613954 | ||||||||
\(626\) | 2.03494e18 | 1.35151 | ||||||||
\(627\) | 8.76654e17 | 0.576221 | ||||||||
\(628\) | −4.84707e18 | −3.15313 | ||||||||
\(629\) | −2.69632e17 | −0.173597 | ||||||||
\(630\) | −1.96347e17 | −0.125116 | ||||||||
\(631\) | 2.54479e18 | 1.60495 | 0.802474 | − | 0.596688i | \(-0.203517\pi\) | ||||
0.802474 | + | 0.596688i | \(0.203517\pi\) | |||||||
\(632\) | 8.05412e18 | 5.02756 | ||||||||
\(633\) | 1.72207e18 | 1.06397 | ||||||||
\(634\) | 2.41050e18 | 1.47410 | ||||||||
\(635\) | −2.59417e17 | −0.157025 | ||||||||
\(636\) | −2.88296e18 | −1.72730 | ||||||||
\(637\) | 1.78093e18 | 1.05619 | ||||||||
\(638\) | 4.75619e17 | 0.279206 | ||||||||
\(639\) | −3.11869e18 | −1.81225 | ||||||||
\(640\) | 3.51024e16 | 0.0201914 | ||||||||
\(641\) | −2.72353e18 | −1.55080 | −0.775399 | − | 0.631471i | \(-0.782451\pi\) | ||||
−0.775399 | + | 0.631471i | \(0.782451\pi\) | |||||||
\(642\) | 8.73381e18 | 4.92296 | ||||||||
\(643\) | −7.92017e17 | −0.441940 | −0.220970 | − | 0.975281i | \(-0.570922\pi\) | ||||
−0.220970 | + | 0.975281i | \(0.570922\pi\) | |||||||
\(644\) | −2.23120e17 | −0.123248 | ||||||||
\(645\) | 1.02870e18 | 0.562534 | ||||||||
\(646\) | 1.66844e18 | 0.903234 | ||||||||
\(647\) | −6.42858e17 | −0.344538 | −0.172269 | − | 0.985050i | \(-0.555110\pi\) | ||||
−0.172269 | + | 0.985050i | \(0.555110\pi\) | |||||||
\(648\) | −3.22894e17 | −0.171325 | ||||||||
\(649\) | −3.12769e18 | −1.64299 | ||||||||
\(650\) | −3.28465e18 | −1.70825 | ||||||||
\(651\) | 1.79052e17 | 0.0921938 | ||||||||
\(652\) | −5.15660e18 | −2.62878 | ||||||||
\(653\) | −6.71995e17 | −0.339180 | −0.169590 | − | 0.985515i | \(-0.554244\pi\) | ||||
−0.169590 | + | 0.985515i | \(0.554244\pi\) | |||||||
\(654\) | −3.67249e18 | −1.83529 | ||||||||
\(655\) | 9.56996e17 | 0.473524 | ||||||||
\(656\) | 3.78993e18 | 1.85676 | ||||||||
\(657\) | 4.72476e18 | 2.29195 | ||||||||
\(658\) | −4.23662e17 | −0.203494 | ||||||||
\(659\) | 3.36471e18 | 1.60027 | 0.800133 | − | 0.599822i | \(-0.204762\pi\) | ||||
0.800133 | + | 0.599822i | \(0.204762\pi\) | |||||||
\(660\) | 3.08418e18 | 1.45246 | ||||||||
\(661\) | −5.83150e17 | −0.271939 | −0.135969 | − | 0.990713i | \(-0.543415\pi\) | ||||
−0.135969 | + | 0.990713i | \(0.543415\pi\) | |||||||
\(662\) | −3.12107e18 | −1.44121 | ||||||||
\(663\) | 5.31437e18 | 2.43004 | ||||||||
\(664\) | −5.77016e18 | −2.61273 | ||||||||
\(665\) | 3.21656e16 | 0.0144229 | ||||||||
\(666\) | −8.51216e17 | −0.377970 | ||||||||
\(667\) | 1.55492e17 | 0.0683740 | ||||||||
\(668\) | 5.38178e18 | 2.34358 | ||||||||
\(669\) | −1.11037e18 | −0.478850 | ||||||||
\(670\) | 1.31086e18 | 0.559849 | ||||||||
\(671\) | 1.03269e18 | 0.436792 | ||||||||
\(672\) | −7.86734e17 | −0.329555 | ||||||||
\(673\) | −1.96018e18 | −0.813202 | −0.406601 | − | 0.913606i | \(-0.633286\pi\) | ||||
−0.406601 | + | 0.913606i | \(0.633286\pi\) | |||||||
\(674\) | −4.92999e18 | −2.02561 | ||||||||
\(675\) | −2.23887e18 | −0.911077 | ||||||||
\(676\) | 8.60561e17 | 0.346839 | ||||||||
\(677\) | 2.44960e18 | 0.977842 | 0.488921 | − | 0.872328i | \(-0.337391\pi\) | ||||
0.488921 | + | 0.872328i | \(0.337391\pi\) | |||||||
\(678\) | 5.09518e18 | 2.01450 | ||||||||
\(679\) | −1.39239e17 | −0.0545266 | ||||||||
\(680\) | 3.43086e18 | 1.33075 | ||||||||
\(681\) | 2.98840e18 | 1.14811 | ||||||||
\(682\) | −2.47720e18 | −0.942677 | ||||||||
\(683\) | 3.28820e18 | 1.23944 | 0.619718 | − | 0.784824i | \(-0.287247\pi\) | ||||
0.619718 | + | 0.784824i | \(0.287247\pi\) | |||||||
\(684\) | 3.72107e18 | 1.38932 | ||||||||
\(685\) | −4.13889e17 | −0.153072 | ||||||||
\(686\) | 1.12263e18 | 0.411272 | ||||||||
\(687\) | 1.99215e18 | 0.722940 | ||||||||
\(688\) | 6.25070e18 | 2.24700 | ||||||||
\(689\) | 1.32499e18 | 0.471833 | ||||||||
\(690\) | 1.42725e18 | 0.503480 | ||||||||
\(691\) | 4.97808e18 | 1.73962 | 0.869810 | − | 0.493387i | \(-0.164242\pi\) | ||||
0.869810 | + | 0.493387i | \(0.164242\pi\) | |||||||
\(692\) | −6.19287e18 | −2.14389 | ||||||||
\(693\) | 5.44162e17 | 0.186622 | ||||||||
\(694\) | −7.82991e18 | −2.66024 | ||||||||
\(695\) | −6.37231e17 | −0.214485 | ||||||||
\(696\) | 1.89637e18 | 0.632358 | ||||||||
\(697\) | −3.28985e18 | −1.08683 | ||||||||
\(698\) | 3.31814e18 | 1.08601 | ||||||||
\(699\) | −7.57266e18 | −2.45554 | ||||||||
\(700\) | −7.26742e17 | −0.233476 | ||||||||
\(701\) | 2.36642e17 | 0.0753225 | 0.0376613 | − | 0.999291i | \(-0.488009\pi\) | ||||
0.0376613 | + | 0.999291i | \(0.488009\pi\) | |||||||
\(702\) | 6.59171e18 | 2.07877 | ||||||||
\(703\) | 1.39446e17 | 0.0435710 | ||||||||
\(704\) | 3.09776e18 | 0.959015 | ||||||||
\(705\) | 1.91457e18 | 0.587275 | ||||||||
\(706\) | −1.87958e18 | −0.571257 | ||||||||
\(707\) | 1.53752e17 | 0.0463013 | ||||||||
\(708\) | −2.13358e19 | −6.36637 | ||||||||
\(709\) | −3.99621e18 | −1.18154 | −0.590769 | − | 0.806840i | \(-0.701176\pi\) | ||||
−0.590769 | + | 0.806840i | \(0.701176\pi\) | |||||||
\(710\) | 2.54427e18 | 0.745391 | ||||||||
\(711\) | −1.09869e19 | −3.18951 | ||||||||
\(712\) | 1.91383e18 | 0.550533 | ||||||||
\(713\) | −8.09862e17 | −0.230850 | ||||||||
\(714\) | 1.66439e18 | 0.470129 | ||||||||
\(715\) | −1.41748e18 | −0.396758 | ||||||||
\(716\) | −2.67863e18 | −0.742982 | ||||||||
\(717\) | 6.45312e18 | 1.77376 | ||||||||
\(718\) | −6.35502e18 | −1.73104 | ||||||||
\(719\) | 5.57196e18 | 1.50408 | 0.752038 | − | 0.659120i | \(-0.229071\pi\) | ||||
0.752038 | + | 0.659120i | \(0.229071\pi\) | |||||||
\(720\) | 5.39160e18 | 1.44230 | ||||||||
\(721\) | −1.63273e17 | −0.0432848 | ||||||||
\(722\) | 6.16233e18 | 1.61902 | ||||||||
\(723\) | −5.53696e18 | −1.44169 | ||||||||
\(724\) | 5.55841e18 | 1.43433 | ||||||||
\(725\) | 5.06466e17 | 0.129525 | ||||||||
\(726\) | −2.51140e17 | −0.0636542 | ||||||||
\(727\) | −3.91166e18 | −0.982625 | −0.491313 | − | 0.870983i | \(-0.663483\pi\) | ||||
−0.491313 | + | 0.870983i | \(0.663483\pi\) | |||||||
\(728\) | 1.25063e18 | 0.311368 | ||||||||
\(729\) | −6.50216e18 | −1.60446 | ||||||||
\(730\) | −3.85453e18 | −0.942697 | ||||||||
\(731\) | −5.42592e18 | −1.31526 | ||||||||
\(732\) | 7.04457e18 | 1.69252 | ||||||||
\(733\) | −1.03950e18 | −0.247542 | −0.123771 | − | 0.992311i | \(-0.539499\pi\) | ||||
−0.123771 | + | 0.992311i | \(0.539499\pi\) | |||||||
\(734\) | −8.57789e16 | −0.0202468 | ||||||||
\(735\) | −2.52058e18 | −0.589703 | ||||||||
\(736\) | 3.55845e18 | 0.825192 | ||||||||
\(737\) | −3.63296e18 | −0.835068 | ||||||||
\(738\) | −1.03859e19 | −2.36634 | ||||||||
\(739\) | 3.88010e18 | 0.876303 | 0.438152 | − | 0.898901i | \(-0.355633\pi\) | ||||
0.438152 | + | 0.898901i | \(0.355633\pi\) | |||||||
\(740\) | 4.90590e17 | 0.109828 | ||||||||
\(741\) | −2.74845e18 | −0.609915 | ||||||||
\(742\) | 4.14970e17 | 0.0912833 | ||||||||
\(743\) | −6.89829e18 | −1.50423 | −0.752115 | − | 0.659032i | \(-0.770966\pi\) | ||||
−0.752115 | + | 0.659032i | \(0.770966\pi\) | |||||||
\(744\) | −9.87700e18 | −2.13502 | ||||||||
\(745\) | −7.84064e17 | −0.168010 | ||||||||
\(746\) | 7.67640e18 | 1.63063 | ||||||||
\(747\) | 7.87130e18 | 1.65753 | ||||||||
\(748\) | −1.62677e19 | −3.39599 | ||||||||
\(749\) | −8.88118e17 | −0.183797 | ||||||||
\(750\) | 1.00215e19 | 2.05606 | ||||||||
\(751\) | 8.43457e18 | 1.71555 | 0.857775 | − | 0.514025i | \(-0.171846\pi\) | ||||
0.857775 | + | 0.514025i | \(0.171846\pi\) | |||||||
\(752\) | 1.16336e19 | 2.34583 | ||||||||
\(753\) | 3.47083e18 | 0.693850 | ||||||||
\(754\) | −1.49114e18 | −0.295532 | ||||||||
\(755\) | −1.80368e18 | −0.354408 | ||||||||
\(756\) | 1.45844e18 | 0.284117 | ||||||||
\(757\) | 2.82123e18 | 0.544898 | 0.272449 | − | 0.962170i | \(-0.412166\pi\) | ||||
0.272449 | + | 0.962170i | \(0.412166\pi\) | |||||||
\(758\) | 4.13021e18 | 0.790902 | ||||||||
\(759\) | −3.95553e18 | −0.750988 | ||||||||
\(760\) | −1.77435e18 | −0.334003 | ||||||||
\(761\) | 3.49050e18 | 0.651459 | 0.325730 | − | 0.945463i | \(-0.394390\pi\) | ||||
0.325730 | + | 0.945463i | \(0.394390\pi\) | |||||||
\(762\) | 6.94219e18 | 1.28466 | ||||||||
\(763\) | 3.73445e17 | 0.0685200 | ||||||||
\(764\) | 2.06576e19 | 3.75814 | ||||||||
\(765\) | −4.68018e18 | −0.844234 | ||||||||
\(766\) | −1.16667e19 | −2.08670 | ||||||||
\(767\) | 9.80581e18 | 1.73906 | ||||||||
\(768\) | −9.71967e18 | −1.70924 | ||||||||
\(769\) | 1.08383e19 | 1.88991 | 0.944956 | − | 0.327197i | \(-0.106104\pi\) | ||||
0.944956 | + | 0.327197i | \(0.106104\pi\) | |||||||
\(770\) | −4.43934e17 | −0.0767589 | ||||||||
\(771\) | 7.39012e18 | 1.26706 | ||||||||
\(772\) | 1.31896e19 | 2.24243 | ||||||||
\(773\) | −5.87557e18 | −0.990566 | −0.495283 | − | 0.868732i | \(-0.664936\pi\) | ||||
−0.495283 | + | 0.868732i | \(0.664936\pi\) | |||||||
\(774\) | −1.71294e19 | −2.86369 | ||||||||
\(775\) | −2.63786e18 | −0.437312 | ||||||||
\(776\) | 7.68085e18 | 1.26272 | ||||||||
\(777\) | 1.39107e17 | 0.0226785 | ||||||||
\(778\) | 5.23053e18 | 0.845627 | ||||||||
\(779\) | 1.70142e18 | 0.272784 | ||||||||
\(780\) | −9.66940e18 | −1.53739 | ||||||||
\(781\) | −7.05126e18 | −1.11182 | ||||||||
\(782\) | −7.52814e18 | −1.17718 | ||||||||
\(783\) | −1.01639e18 | −0.157619 | ||||||||
\(784\) | −1.53159e19 | −2.35553 | ||||||||
\(785\) | −3.15289e18 | −0.480902 | ||||||||
\(786\) | −2.56100e19 | −3.87402 | ||||||||
\(787\) | 1.16087e19 | 1.74160 | 0.870798 | − | 0.491642i | \(-0.163603\pi\) | ||||
0.870798 | + | 0.491642i | \(0.163603\pi\) | |||||||
\(788\) | −1.15242e18 | −0.171470 | ||||||||
\(789\) | −4.26490e18 | −0.629373 | ||||||||
\(790\) | 8.96329e18 | 1.31187 | ||||||||
\(791\) | −5.18115e17 | −0.0752107 | ||||||||
\(792\) | −3.00175e19 | −4.32177 | ||||||||
\(793\) | −3.23765e18 | −0.462332 | ||||||||
\(794\) | −6.84931e18 | −0.970093 | ||||||||
\(795\) | −1.87529e18 | −0.263440 | ||||||||
\(796\) | 7.89420e18 | 1.09995 | ||||||||
\(797\) | −6.97871e17 | −0.0964486 | −0.0482243 | − | 0.998837i | \(-0.515356\pi\) | ||||
−0.0482243 | + | 0.998837i | \(0.515356\pi\) | |||||||
\(798\) | −8.60777e17 | −0.117997 | ||||||||
\(799\) | −1.00985e19 | −1.37310 | ||||||||
\(800\) | 1.15905e19 | 1.56321 | ||||||||
\(801\) | −2.61073e18 | −0.349261 | ||||||||
\(802\) | −5.01002e18 | −0.664823 | ||||||||
\(803\) | 1.06825e19 | 1.40612 | ||||||||
\(804\) | −2.47825e19 | −3.23579 | ||||||||
\(805\) | −1.45134e17 | −0.0187973 | ||||||||
\(806\) | 7.76642e18 | 0.997799 | ||||||||
\(807\) | −1.82403e19 | −2.32463 | ||||||||
\(808\) | −8.48138e18 | −1.07224 | ||||||||
\(809\) | −4.03649e18 | −0.506219 | −0.253109 | − | 0.967438i | \(-0.581453\pi\) | ||||
−0.253109 | + | 0.967438i | \(0.581453\pi\) | |||||||
\(810\) | −3.59343e17 | −0.0447050 | ||||||||
\(811\) | −1.94069e18 | −0.239508 | −0.119754 | − | 0.992804i | \(-0.538211\pi\) | ||||
−0.119754 | + | 0.992804i | \(0.538211\pi\) | |||||||
\(812\) | −3.29921e17 | −0.0403920 | ||||||||
\(813\) | −3.49467e18 | −0.424441 | ||||||||
\(814\) | −1.92457e18 | −0.231886 | ||||||||
\(815\) | −3.35423e18 | −0.400930 | ||||||||
\(816\) | −4.57033e19 | −5.41953 | ||||||||
\(817\) | 2.80614e18 | 0.330115 | ||||||||
\(818\) | 5.03383e18 | 0.587492 | ||||||||
\(819\) | −1.70603e18 | −0.197534 | ||||||||
\(820\) | 5.98582e18 | 0.687596 | ||||||||
\(821\) | −5.70883e18 | −0.650604 | −0.325302 | − | 0.945610i | \(-0.605466\pi\) | ||||
−0.325302 | + | 0.945610i | \(0.605466\pi\) | |||||||
\(822\) | 1.10760e19 | 1.25232 | ||||||||
\(823\) | 1.09771e19 | 1.23137 | 0.615683 | − | 0.787994i | \(-0.288880\pi\) | ||||
0.615683 | + | 0.787994i | \(0.288880\pi\) | |||||||
\(824\) | 9.00661e18 | 1.00239 | ||||||||
\(825\) | −1.28839e19 | −1.42264 | ||||||||
\(826\) | 3.07105e18 | 0.336447 | ||||||||
\(827\) | −1.38129e19 | −1.50141 | −0.750706 | − | 0.660637i | \(-0.770286\pi\) | ||||
−0.750706 | + | 0.660637i | \(0.770286\pi\) | |||||||
\(828\) | −1.67898e19 | −1.81070 | ||||||||
\(829\) | −4.07843e18 | −0.436404 | −0.218202 | − | 0.975904i | \(-0.570019\pi\) | ||||
−0.218202 | + | 0.975904i | \(0.570019\pi\) | |||||||
\(830\) | −6.42151e18 | −0.681757 | ||||||||
\(831\) | 2.09368e18 | 0.220548 | ||||||||
\(832\) | −9.71197e18 | −1.01509 | ||||||||
\(833\) | 1.32950e19 | 1.37878 | ||||||||
\(834\) | 1.70528e19 | 1.75476 | ||||||||
\(835\) | 3.50071e18 | 0.357432 | ||||||||
\(836\) | 8.41322e18 | 0.852357 | ||||||||
\(837\) | 5.29373e18 | 0.532165 | ||||||||
\(838\) | −2.32506e19 | −2.31926 | ||||||||
\(839\) | 1.78304e18 | 0.176486 | 0.0882428 | − | 0.996099i | \(-0.471875\pi\) | ||||
0.0882428 | + | 0.996099i | \(0.471875\pi\) | |||||||
\(840\) | −1.77004e18 | −0.173847 | ||||||||
\(841\) | −1.00307e19 | −0.977592 | ||||||||
\(842\) | 3.10352e19 | 3.00142 | ||||||||
\(843\) | 4.08595e18 | 0.392116 | ||||||||
\(844\) | 1.65267e19 | 1.57384 | ||||||||
\(845\) | 5.59772e17 | 0.0528984 | ||||||||
\(846\) | −3.18805e19 | −2.98963 | ||||||||
\(847\) | 2.55377e16 | 0.00237651 | ||||||||
\(848\) | −1.13949e19 | −1.05229 | ||||||||
\(849\) | 8.53027e18 | 0.781741 | ||||||||
\(850\) | −2.45205e19 | −2.23001 | ||||||||
\(851\) | −6.29192e17 | −0.0567859 | ||||||||
\(852\) | −4.81006e19 | −4.30817 | ||||||||
\(853\) | 3.94325e17 | 0.0350498 | 0.0175249 | − | 0.999846i | \(-0.494421\pi\) | ||||
0.0175249 | + | 0.999846i | \(0.494421\pi\) | |||||||
\(854\) | −1.01399e18 | −0.0894452 | ||||||||
\(855\) | 2.42046e18 | 0.211894 | ||||||||
\(856\) | 4.89912e19 | 4.25636 | ||||||||
\(857\) | 1.99892e19 | 1.72353 | 0.861767 | − | 0.507305i | \(-0.169358\pi\) | ||||
0.861767 | + | 0.507305i | \(0.169358\pi\) | |||||||
\(858\) | 3.79327e19 | 3.24599 | ||||||||
\(859\) | −1.78398e18 | −0.151508 | −0.0757539 | − | 0.997127i | \(-0.524136\pi\) | ||||
−0.0757539 | + | 0.997127i | \(0.524136\pi\) | |||||||
\(860\) | 9.87236e18 | 0.832110 | ||||||||
\(861\) | 1.69729e18 | 0.141982 | ||||||||
\(862\) | −2.48642e19 | −2.06432 | ||||||||
\(863\) | −1.46602e19 | −1.20801 | −0.604004 | − | 0.796982i | \(-0.706429\pi\) | ||||
−0.604004 | + | 0.796982i | \(0.706429\pi\) | |||||||
\(864\) | −2.32601e19 | −1.90227 | ||||||||
\(865\) | −4.02830e18 | −0.326977 | ||||||||
\(866\) | 2.57394e19 | 2.07363 | ||||||||
\(867\) | 1.93251e19 | 1.54525 | ||||||||
\(868\) | 1.71835e18 | 0.136375 | ||||||||
\(869\) | −2.48411e19 | −1.95678 | ||||||||
\(870\) | 2.11044e18 | 0.165005 | ||||||||
\(871\) | 1.13899e19 | 0.883897 | ||||||||
\(872\) | −2.06003e19 | −1.58678 | ||||||||
\(873\) | −1.04777e19 | −0.801079 | ||||||||
\(874\) | 3.89335e18 | 0.295460 | ||||||||
\(875\) | −1.01906e18 | −0.0767623 | ||||||||
\(876\) | 7.28715e19 | 5.44855 | ||||||||
\(877\) | −1.83740e19 | −1.36366 | −0.681830 | − | 0.731511i | \(-0.738816\pi\) | ||||
−0.681830 | + | 0.731511i | \(0.738816\pi\) | |||||||
\(878\) | 3.93843e19 | 2.90141 | ||||||||
\(879\) | −3.79688e19 | −2.77651 | ||||||||
\(880\) | 1.21902e19 | 0.884859 | ||||||||
\(881\) | 9.20911e17 | 0.0663551 | 0.0331776 | − | 0.999449i | \(-0.489437\pi\) | ||||
0.0331776 | + | 0.999449i | \(0.489437\pi\) | |||||||
\(882\) | 4.19717e19 | 3.00200 | ||||||||
\(883\) | 3.66478e18 | 0.260198 | 0.130099 | − | 0.991501i | \(-0.458471\pi\) | ||||
0.130099 | + | 0.991501i | \(0.458471\pi\) | |||||||
\(884\) | 5.10018e19 | 3.59456 | ||||||||
\(885\) | −1.38783e19 | −0.970971 | ||||||||
\(886\) | 2.69005e19 | 1.86827 | ||||||||
\(887\) | −1.17105e19 | −0.807371 | −0.403685 | − | 0.914898i | \(-0.632271\pi\) | ||||
−0.403685 | + | 0.914898i | \(0.632271\pi\) | |||||||
\(888\) | −7.67357e18 | −0.525186 | ||||||||
\(889\) | −7.05933e17 | −0.0479625 | ||||||||
\(890\) | 2.12987e18 | 0.143654 | ||||||||
\(891\) | 9.95892e17 | 0.0666818 | ||||||||
\(892\) | −1.06562e19 | −0.708323 | ||||||||
\(893\) | 5.22267e18 | 0.344634 | ||||||||
\(894\) | 2.09822e19 | 1.37454 | ||||||||
\(895\) | −1.74238e18 | −0.113316 | ||||||||
\(896\) | 9.55218e16 | 0.00616737 | ||||||||
\(897\) | 1.24012e19 | 0.794901 | ||||||||
\(898\) | 2.90779e19 | 1.85041 | ||||||||
\(899\) | −1.19752e18 | −0.0756561 | ||||||||
\(900\) | −5.46872e19 | −3.43012 | ||||||||
\(901\) | 9.89132e18 | 0.615947 | ||||||||
\(902\) | −2.34822e19 | −1.45176 | ||||||||
\(903\) | 2.79932e18 | 0.171823 | ||||||||
\(904\) | 2.85807e19 | 1.74172 | ||||||||
\(905\) | 3.61560e18 | 0.218758 | ||||||||
\(906\) | 4.82679e19 | 2.89951 | ||||||||
\(907\) | −1.17036e19 | −0.698028 | −0.349014 | − | 0.937118i | \(-0.613483\pi\) | ||||
−0.349014 | + | 0.937118i | \(0.613483\pi\) | |||||||
\(908\) | 2.86796e19 | 1.69830 | ||||||||
\(909\) | 1.15698e19 | 0.680237 | ||||||||
\(910\) | 1.39180e18 | 0.0812473 | ||||||||
\(911\) | 2.36394e19 | 1.37014 | 0.685072 | − | 0.728475i | \(-0.259771\pi\) | ||||
0.685072 | + | 0.728475i | \(0.259771\pi\) | |||||||
\(912\) | 2.36365e19 | 1.36024 | ||||||||
\(913\) | 1.77967e19 | 1.01690 | ||||||||
\(914\) | 5.14742e19 | 2.92038 | ||||||||
\(915\) | 4.58230e18 | 0.258135 | ||||||||
\(916\) | 1.91185e19 | 1.06939 | ||||||||
\(917\) | 2.60421e18 | 0.144636 | ||||||||
\(918\) | 4.92083e19 | 2.71370 | ||||||||
\(919\) | 2.18682e19 | 1.19746 | 0.598731 | − | 0.800950i | \(-0.295672\pi\) | ||||
0.598731 | + | 0.800950i | \(0.295672\pi\) | |||||||
\(920\) | 8.00599e18 | 0.435306 | ||||||||
\(921\) | −2.14947e19 | −1.16050 | ||||||||
\(922\) | −2.97034e19 | −1.59241 | ||||||||
\(923\) | 2.21068e19 | 1.17683 | ||||||||
\(924\) | 8.39278e18 | 0.443647 | ||||||||
\(925\) | −2.04939e18 | −0.107573 | ||||||||
\(926\) | 6.81478e19 | 3.55206 | ||||||||
\(927\) | −1.22863e19 | −0.635919 | ||||||||
\(928\) | 5.26177e18 | 0.270439 | ||||||||
\(929\) | −2.63865e19 | −1.34673 | −0.673364 | − | 0.739311i | \(-0.735151\pi\) | ||||
−0.673364 | + | 0.739311i | \(0.735151\pi\) | |||||||
\(930\) | −1.09919e19 | −0.557103 | ||||||||
\(931\) | −6.87580e18 | −0.346059 | ||||||||
\(932\) | −7.26746e19 | −3.63228 | ||||||||
\(933\) | 3.01010e19 | 1.49400 | ||||||||
\(934\) | 2.17328e19 | 1.07118 | ||||||||
\(935\) | −1.05817e19 | −0.517941 | ||||||||
\(936\) | 9.41096e19 | 4.57447 | ||||||||
\(937\) | −1.73731e19 | −0.838627 | −0.419313 | − | 0.907842i | \(-0.637729\pi\) | ||||
−0.419313 | + | 0.907842i | \(0.637729\pi\) | |||||||
\(938\) | 3.56716e18 | 0.171003 | ||||||||
\(939\) | −2.50246e19 | −1.19135 | ||||||||
\(940\) | 1.83740e19 | 0.868707 | ||||||||
\(941\) | 2.45945e19 | 1.15480 | 0.577398 | − | 0.816463i | \(-0.304068\pi\) | ||||
0.577398 | + | 0.816463i | \(0.304068\pi\) | |||||||
\(942\) | 8.43739e19 | 3.93439 | ||||||||
\(943\) | −7.67693e18 | −0.355518 | ||||||||
\(944\) | −8.43295e19 | −3.87848 | ||||||||
\(945\) | 9.48678e17 | 0.0433323 | ||||||||
\(946\) | −3.87290e19 | −1.75689 | ||||||||
\(947\) | 2.67363e19 | 1.20456 | 0.602278 | − | 0.798287i | \(-0.294260\pi\) | ||||
0.602278 | + | 0.798287i | \(0.294260\pi\) | |||||||
\(948\) | −1.69455e20 | −7.58229 | ||||||||
\(949\) | −3.34914e19 | −1.48834 | ||||||||
\(950\) | 1.26813e19 | 0.559708 | ||||||||
\(951\) | −2.96431e19 | −1.29942 | ||||||||
\(952\) | 9.33618e18 | 0.406470 | ||||||||
\(953\) | 1.30292e19 | 0.563394 | 0.281697 | − | 0.959503i | \(-0.409103\pi\) | ||||
0.281697 | + | 0.959503i | \(0.409103\pi\) | |||||||
\(954\) | 3.12265e19 | 1.34109 | ||||||||
\(955\) | 1.34372e19 | 0.573175 | ||||||||
\(956\) | 6.19304e19 | 2.62378 | ||||||||
\(957\) | −5.84892e18 | −0.246121 | ||||||||
\(958\) | 7.21856e18 | 0.301700 | ||||||||
\(959\) | −1.12629e18 | −0.0467551 | ||||||||
\(960\) | 1.37455e19 | 0.566759 | ||||||||
\(961\) | −1.81804e19 | −0.744564 | ||||||||
\(962\) | 6.03383e18 | 0.245445 | ||||||||
\(963\) | −6.68308e19 | −2.70026 | ||||||||
\(964\) | −5.31380e19 | −2.13258 | ||||||||
\(965\) | 8.57949e18 | 0.342006 | ||||||||
\(966\) | 3.88389e18 | 0.153786 | ||||||||
\(967\) | −1.57944e18 | −0.0621198 | −0.0310599 | − | 0.999518i | \(-0.509888\pi\) | ||||
−0.0310599 | + | 0.999518i | \(0.509888\pi\) | |||||||
\(968\) | −1.40873e18 | −0.0550350 | ||||||||
\(969\) | −2.05177e19 | −0.796203 | ||||||||
\(970\) | 8.54789e18 | 0.329490 | ||||||||
\(971\) | 3.02093e19 | 1.15668 | 0.578342 | − | 0.815794i | \(-0.303700\pi\) | ||||
0.578342 | + | 0.815794i | \(0.303700\pi\) | |||||||
\(972\) | −5.98347e19 | −2.27574 | ||||||||
\(973\) | −1.73405e18 | −0.0655133 | ||||||||
\(974\) | 7.23268e19 | 2.71435 | ||||||||
\(975\) | 4.03929e19 | 1.50583 | ||||||||
\(976\) | 2.78436e19 | 1.03110 | ||||||||
\(977\) | −1.37769e19 | −0.506802 | −0.253401 | − | 0.967361i | \(-0.581549\pi\) | ||||
−0.253401 | + | 0.967361i | \(0.581549\pi\) | |||||||
\(978\) | 8.97619e19 | 3.28012 | ||||||||
\(979\) | −5.90277e18 | −0.214273 | ||||||||
\(980\) | −2.41900e19 | −0.872299 | ||||||||
\(981\) | 2.81017e19 | 1.00666 | ||||||||
\(982\) | −5.95791e19 | −2.12016 | ||||||||
\(983\) | −2.41783e19 | −0.854727 | −0.427363 | − | 0.904080i | \(-0.640558\pi\) | ||||
−0.427363 | + | 0.904080i | \(0.640558\pi\) | |||||||
\(984\) | −9.36272e19 | −3.28802 | ||||||||
\(985\) | −7.49617e17 | −0.0261519 | ||||||||
\(986\) | −1.11316e19 | −0.385797 | ||||||||
\(987\) | 5.20998e18 | 0.179380 | ||||||||
\(988\) | −2.63768e19 | −0.902197 | ||||||||
\(989\) | −1.26615e19 | −0.430239 | ||||||||
\(990\) | −3.34060e19 | −1.12771 | ||||||||
\(991\) | 3.20449e19 | 1.07468 | 0.537341 | − | 0.843365i | \(-0.319429\pi\) | ||||
0.537341 | + | 0.843365i | \(0.319429\pi\) | |||||||
\(992\) | −2.74053e19 | −0.913079 | ||||||||
\(993\) | 3.83813e19 | 1.27043 | ||||||||
\(994\) | 6.92355e18 | 0.227676 | ||||||||
\(995\) | 5.13496e18 | 0.167760 | ||||||||
\(996\) | 1.21402e20 | 3.94038 | ||||||||
\(997\) | 4.68142e19 | 1.50959 | 0.754795 | − | 0.655961i | \(-0.227737\pi\) | ||||
0.754795 | + | 0.655961i | \(0.227737\pi\) | |||||||
\(998\) | 8.16122e19 | 2.61461 | ||||||||
\(999\) | 4.11276e18 | 0.130906 |
(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.1.5 | ✓ | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.14.a.a.1.5 | ✓ | 104 | 1.1 | even | 1 | trivial |