Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −73.1261 | −0.807937 | −0.403969 | − | 0.914773i | \(-0.632370\pi\) | ||||
−0.403969 | + | 0.914773i | \(0.632370\pi\) | |||||||
\(3\) | −729.000 | −0.577350 | ||||||||
\(4\) | −2844.57 | −0.347237 | ||||||||
\(5\) | −37898.1 | −1.08471 | −0.542354 | − | 0.840150i | \(-0.682467\pi\) | ||||
−0.542354 | + | 0.840150i | \(0.682467\pi\) | |||||||
\(6\) | 53309.0 | 0.466463 | ||||||||
\(7\) | 370148. | 1.18915 | 0.594577 | − | 0.804038i | \(-0.297319\pi\) | ||||
0.594577 | + | 0.804038i | \(0.297319\pi\) | |||||||
\(8\) | 807062. | 1.08848 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | 2.77134e6 | 0.876375 | ||||||||
\(11\) | −7.88747e6 | −1.34241 | −0.671205 | − | 0.741272i | \(-0.734223\pi\) | ||||
−0.671205 | + | 0.741272i | \(0.734223\pi\) | |||||||
\(12\) | 2.07369e6 | 0.200478 | ||||||||
\(13\) | −2.23192e6 | −0.128247 | −0.0641235 | − | 0.997942i | \(-0.520425\pi\) | ||||
−0.0641235 | + | 0.997942i | \(0.520425\pi\) | |||||||
\(14\) | −2.70675e7 | −0.960762 | ||||||||
\(15\) | 2.76277e7 | 0.626256 | ||||||||
\(16\) | −3.57146e7 | −0.532189 | ||||||||
\(17\) | 6.39279e7 | 0.642351 | 0.321175 | − | 0.947020i | \(-0.395922\pi\) | ||||
0.321175 | + | 0.947020i | \(0.395922\pi\) | |||||||
\(18\) | −3.88622e7 | −0.269312 | ||||||||
\(19\) | 1.32405e8 | 0.645664 | 0.322832 | − | 0.946456i | \(-0.395365\pi\) | ||||
0.322832 | + | 0.946456i | \(0.395365\pi\) | |||||||
\(20\) | 1.07804e8 | 0.376651 | ||||||||
\(21\) | −2.69838e8 | −0.686559 | ||||||||
\(22\) | 5.76780e8 | 1.08458 | ||||||||
\(23\) | −1.21940e9 | −1.71757 | −0.858787 | − | 0.512333i | \(-0.828782\pi\) | ||||
−0.858787 | + | 0.512333i | \(0.828782\pi\) | |||||||
\(24\) | −5.88348e8 | −0.628436 | ||||||||
\(25\) | 2.15563e8 | 0.176590 | ||||||||
\(26\) | 1.63212e8 | 0.103616 | ||||||||
\(27\) | −3.87420e8 | −0.192450 | ||||||||
\(28\) | −1.05291e9 | −0.412919 | ||||||||
\(29\) | 4.50974e9 | 1.40788 | 0.703938 | − | 0.710261i | \(-0.251423\pi\) | ||||
0.703938 | + | 0.710261i | \(0.251423\pi\) | |||||||
\(30\) | −2.02031e9 | −0.505976 | ||||||||
\(31\) | −6.42026e9 | −1.29928 | −0.649639 | − | 0.760243i | \(-0.725080\pi\) | ||||
−0.649639 | + | 0.760243i | \(0.725080\pi\) | |||||||
\(32\) | −3.99978e9 | −0.658508 | ||||||||
\(33\) | 5.74996e9 | 0.775041 | ||||||||
\(34\) | −4.67480e9 | −0.518979 | ||||||||
\(35\) | −1.40279e10 | −1.28988 | ||||||||
\(36\) | −1.51172e9 | −0.115746 | ||||||||
\(37\) | −2.37133e10 | −1.51943 | −0.759715 | − | 0.650256i | \(-0.774662\pi\) | ||||
−0.759715 | + | 0.650256i | \(0.774662\pi\) | |||||||
\(38\) | −9.68228e9 | −0.521656 | ||||||||
\(39\) | 1.62707e9 | 0.0740435 | ||||||||
\(40\) | −3.05861e10 | −1.18069 | ||||||||
\(41\) | 2.80832e10 | 0.923318 | 0.461659 | − | 0.887057i | \(-0.347254\pi\) | ||||
0.461659 | + | 0.887057i | \(0.347254\pi\) | |||||||
\(42\) | 1.97322e10 | 0.554696 | ||||||||
\(43\) | −2.26518e10 | −0.546460 | −0.273230 | − | 0.961949i | \(-0.588092\pi\) | ||||
−0.273230 | + | 0.961949i | \(0.588092\pi\) | |||||||
\(44\) | 2.24364e10 | 0.466135 | ||||||||
\(45\) | −2.01406e10 | −0.361569 | ||||||||
\(46\) | 8.91701e10 | 1.38769 | ||||||||
\(47\) | 6.72298e10 | 0.909758 | 0.454879 | − | 0.890553i | \(-0.349683\pi\) | ||||
0.454879 | + | 0.890553i | \(0.349683\pi\) | |||||||
\(48\) | 2.60359e10 | 0.307260 | ||||||||
\(49\) | 4.01207e10 | 0.414089 | ||||||||
\(50\) | −1.57633e10 | −0.142673 | ||||||||
\(51\) | −4.66034e10 | −0.370861 | ||||||||
\(52\) | 6.34886e9 | 0.0445322 | ||||||||
\(53\) | 1.27588e11 | 0.790709 | 0.395354 | − | 0.918529i | \(-0.370622\pi\) | ||||
0.395354 | + | 0.918529i | \(0.370622\pi\) | |||||||
\(54\) | 2.83306e10 | 0.155488 | ||||||||
\(55\) | 2.98920e11 | 1.45612 | ||||||||
\(56\) | 2.98732e11 | 1.29437 | ||||||||
\(57\) | −9.65234e10 | −0.372774 | ||||||||
\(58\) | −3.29780e11 | −1.13748 | ||||||||
\(59\) | −4.21805e10 | −0.130189 | ||||||||
\(60\) | −7.85889e10 | −0.217459 | ||||||||
\(61\) | 7.06444e11 | 1.75563 | 0.877817 | − | 0.478997i | \(-0.158999\pi\) | ||||
0.877817 | + | 0.478997i | \(0.158999\pi\) | |||||||
\(62\) | 4.69489e11 | 1.04973 | ||||||||
\(63\) | 1.96712e11 | 0.396385 | ||||||||
\(64\) | 5.85062e11 | 1.06422 | ||||||||
\(65\) | 8.45857e10 | 0.139111 | ||||||||
\(66\) | −4.20473e11 | −0.626184 | ||||||||
\(67\) | −9.15774e11 | −1.23681 | −0.618404 | − | 0.785860i | \(-0.712220\pi\) | ||||
−0.618404 | + | 0.785860i | \(0.712220\pi\) | |||||||
\(68\) | −1.81847e11 | −0.223048 | ||||||||
\(69\) | 8.88943e11 | 0.991642 | ||||||||
\(70\) | 1.02581e12 | 1.04215 | ||||||||
\(71\) | 1.48868e12 | 1.37918 | 0.689592 | − | 0.724198i | \(-0.257790\pi\) | ||||
0.689592 | + | 0.724198i | \(0.257790\pi\) | |||||||
\(72\) | 4.28906e11 | 0.362828 | ||||||||
\(73\) | −1.43403e12 | −1.10907 | −0.554536 | − | 0.832159i | \(-0.687104\pi\) | ||||
−0.554536 | + | 0.832159i | \(0.687104\pi\) | |||||||
\(74\) | 1.73406e12 | 1.22760 | ||||||||
\(75\) | −1.57146e11 | −0.101954 | ||||||||
\(76\) | −3.76635e11 | −0.224199 | ||||||||
\(77\) | −2.91953e12 | −1.59633 | ||||||||
\(78\) | −1.18981e11 | −0.0598225 | ||||||||
\(79\) | 9.88310e11 | 0.457422 | 0.228711 | − | 0.973494i | \(-0.426549\pi\) | ||||
0.228711 | + | 0.973494i | \(0.426549\pi\) | |||||||
\(80\) | 1.35352e12 | 0.577269 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | −2.05362e12 | −0.745983 | ||||||||
\(83\) | 7.61608e11 | 0.255696 | 0.127848 | − | 0.991794i | \(-0.459193\pi\) | ||||
0.127848 | + | 0.991794i | \(0.459193\pi\) | |||||||
\(84\) | 7.67572e11 | 0.238399 | ||||||||
\(85\) | −2.42275e12 | −0.696762 | ||||||||
\(86\) | 1.65644e12 | 0.441506 | ||||||||
\(87\) | −3.28760e12 | −0.812838 | ||||||||
\(88\) | −6.36567e12 | −1.46119 | ||||||||
\(89\) | 4.89776e12 | 1.04463 | 0.522315 | − | 0.852753i | \(-0.325069\pi\) | ||||
0.522315 | + | 0.852753i | \(0.325069\pi\) | |||||||
\(90\) | 1.47280e12 | 0.292125 | ||||||||
\(91\) | −8.26142e11 | −0.152506 | ||||||||
\(92\) | 3.46867e12 | 0.596406 | ||||||||
\(93\) | 4.68037e12 | 0.750138 | ||||||||
\(94\) | −4.91626e12 | −0.735027 | ||||||||
\(95\) | −5.01791e12 | −0.700356 | ||||||||
\(96\) | 2.91584e12 | 0.380190 | ||||||||
\(97\) | 1.14572e13 | 1.39657 | 0.698287 | − | 0.715818i | \(-0.253946\pi\) | ||||
0.698287 | + | 0.715818i | \(0.253946\pi\) | |||||||
\(98\) | −2.93387e12 | −0.334558 | ||||||||
\(99\) | −4.19172e12 | −0.447470 | ||||||||
\(100\) | −6.13185e11 | −0.0613185 | ||||||||
\(101\) | 1.57286e13 | 1.47435 | 0.737174 | − | 0.675703i | \(-0.236160\pi\) | ||||
0.737174 | + | 0.675703i | \(0.236160\pi\) | |||||||
\(102\) | 3.40793e12 | 0.299633 | ||||||||
\(103\) | −9.38141e12 | −0.774152 | −0.387076 | − | 0.922048i | \(-0.626515\pi\) | ||||
−0.387076 | + | 0.922048i | \(0.626515\pi\) | |||||||
\(104\) | −1.80130e12 | −0.139595 | ||||||||
\(105\) | 1.02264e13 | 0.744715 | ||||||||
\(106\) | −9.33002e12 | −0.638843 | ||||||||
\(107\) | −1.15569e13 | −0.744472 | −0.372236 | − | 0.928138i | \(-0.621409\pi\) | ||||
−0.372236 | + | 0.928138i | \(0.621409\pi\) | |||||||
\(108\) | 1.10204e12 | 0.0668258 | ||||||||
\(109\) | 1.41881e13 | 0.810313 | 0.405156 | − | 0.914247i | \(-0.367217\pi\) | ||||
0.405156 | + | 0.914247i | \(0.367217\pi\) | |||||||
\(110\) | −2.18589e13 | −1.17646 | ||||||||
\(111\) | 1.72870e13 | 0.877244 | ||||||||
\(112\) | −1.32197e13 | −0.632855 | ||||||||
\(113\) | −4.04064e12 | −0.182574 | −0.0912872 | − | 0.995825i | \(-0.529098\pi\) | ||||
−0.0912872 | + | 0.995825i | \(0.529098\pi\) | |||||||
\(114\) | 7.05838e12 | 0.301178 | ||||||||
\(115\) | 4.62130e13 | 1.86307 | ||||||||
\(116\) | −1.28283e13 | −0.488867 | ||||||||
\(117\) | −1.18614e12 | −0.0427490 | ||||||||
\(118\) | 3.08450e12 | 0.105184 | ||||||||
\(119\) | 2.36628e13 | 0.763854 | ||||||||
\(120\) | 2.22973e13 | 0.681669 | ||||||||
\(121\) | 2.76895e13 | 0.802065 | ||||||||
\(122\) | −5.16595e13 | −1.41844 | ||||||||
\(123\) | −2.04726e13 | −0.533078 | ||||||||
\(124\) | 1.82629e13 | 0.451157 | ||||||||
\(125\) | 3.80929e13 | 0.893159 | ||||||||
\(126\) | −1.43848e13 | −0.320254 | ||||||||
\(127\) | 1.98619e13 | 0.420045 | 0.210023 | − | 0.977697i | \(-0.432646\pi\) | ||||
0.210023 | + | 0.977697i | \(0.432646\pi\) | |||||||
\(128\) | −1.00172e13 | −0.201317 | ||||||||
\(129\) | 1.65132e13 | 0.315499 | ||||||||
\(130\) | −6.18542e12 | −0.112393 | ||||||||
\(131\) | −2.03935e12 | −0.0352556 | −0.0176278 | − | 0.999845i | \(-0.505611\pi\) | ||||
−0.0176278 | + | 0.999845i | \(0.505611\pi\) | |||||||
\(132\) | −1.63562e13 | −0.269123 | ||||||||
\(133\) | 4.90095e13 | 0.767794 | ||||||||
\(134\) | 6.69670e13 | 0.999263 | ||||||||
\(135\) | 1.46825e13 | 0.208752 | ||||||||
\(136\) | 5.15937e13 | 0.699188 | ||||||||
\(137\) | 1.42474e14 | 1.84099 | 0.920496 | − | 0.390753i | \(-0.127785\pi\) | ||||
0.920496 | + | 0.390753i | \(0.127785\pi\) | |||||||
\(138\) | −6.50050e13 | −0.801185 | ||||||||
\(139\) | −1.42860e14 | −1.68002 | −0.840012 | − | 0.542567i | \(-0.817452\pi\) | ||||
−0.840012 | + | 0.542567i | \(0.817452\pi\) | |||||||
\(140\) | 3.99034e13 | 0.447896 | ||||||||
\(141\) | −4.90105e13 | −0.525249 | ||||||||
\(142\) | −1.08862e14 | −1.11429 | ||||||||
\(143\) | 1.76042e13 | 0.172160 | ||||||||
\(144\) | −1.89802e13 | −0.177396 | ||||||||
\(145\) | −1.70911e14 | −1.52713 | ||||||||
\(146\) | 1.04865e14 | 0.896061 | ||||||||
\(147\) | −2.92480e13 | −0.239074 | ||||||||
\(148\) | 6.74541e13 | 0.527603 | ||||||||
\(149\) | 9.36377e13 | 0.701035 | 0.350518 | − | 0.936556i | \(-0.386006\pi\) | ||||
0.350518 | + | 0.936556i | \(0.386006\pi\) | |||||||
\(150\) | 1.14915e13 | 0.0823725 | ||||||||
\(151\) | −1.45031e14 | −0.995657 | −0.497828 | − | 0.867276i | \(-0.665869\pi\) | ||||
−0.497828 | + | 0.867276i | \(0.665869\pi\) | |||||||
\(152\) | 1.06859e14 | 0.702795 | ||||||||
\(153\) | 3.39739e13 | 0.214117 | ||||||||
\(154\) | 2.13494e14 | 1.28974 | ||||||||
\(155\) | 2.43316e14 | 1.40934 | ||||||||
\(156\) | −4.62832e12 | −0.0257107 | ||||||||
\(157\) | 1.86864e14 | 0.995816 | 0.497908 | − | 0.867230i | \(-0.334102\pi\) | ||||
0.497908 | + | 0.867230i | \(0.334102\pi\) | |||||||
\(158\) | −7.22713e13 | −0.369569 | ||||||||
\(159\) | −9.30117e13 | −0.456516 | ||||||||
\(160\) | 1.51584e14 | 0.714288 | ||||||||
\(161\) | −4.51359e14 | −2.04246 | ||||||||
\(162\) | −2.06530e13 | −0.0897708 | ||||||||
\(163\) | −3.54345e14 | −1.47981 | −0.739906 | − | 0.672710i | \(-0.765130\pi\) | ||||
−0.739906 | + | 0.672710i | \(0.765130\pi\) | |||||||
\(164\) | −7.98845e13 | −0.320610 | ||||||||
\(165\) | −2.17913e14 | −0.840692 | ||||||||
\(166\) | −5.56935e13 | −0.206586 | ||||||||
\(167\) | −3.33353e14 | −1.18918 | −0.594590 | − | 0.804029i | \(-0.702686\pi\) | ||||
−0.594590 | + | 0.804029i | \(0.702686\pi\) | |||||||
\(168\) | −2.17776e14 | −0.747308 | ||||||||
\(169\) | −2.97894e14 | −0.983553 | ||||||||
\(170\) | 1.77166e14 | 0.562940 | ||||||||
\(171\) | 7.03655e13 | 0.215221 | ||||||||
\(172\) | 6.44347e13 | 0.189751 | ||||||||
\(173\) | 3.36990e14 | 0.955689 | 0.477845 | − | 0.878444i | \(-0.341418\pi\) | ||||
0.477845 | + | 0.878444i | \(0.341418\pi\) | |||||||
\(174\) | 2.40409e14 | 0.656722 | ||||||||
\(175\) | 7.97904e13 | 0.209992 | ||||||||
\(176\) | 2.81698e14 | 0.714416 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | −3.58154e14 | −0.843995 | ||||||||
\(179\) | −4.84063e14 | −1.09991 | −0.549955 | − | 0.835194i | \(-0.685355\pi\) | ||||
−0.549955 | + | 0.835194i | \(0.685355\pi\) | |||||||
\(180\) | 5.72913e13 | 0.125550 | ||||||||
\(181\) | 6.15655e14 | 1.30145 | 0.650724 | − | 0.759315i | \(-0.274466\pi\) | ||||
0.650724 | + | 0.759315i | \(0.274466\pi\) | |||||||
\(182\) | 6.04126e13 | 0.123215 | ||||||||
\(183\) | −5.14998e14 | −1.01362 | ||||||||
\(184\) | −9.84132e14 | −1.86955 | ||||||||
\(185\) | 8.98689e14 | 1.64814 | ||||||||
\(186\) | −3.42258e14 | −0.606065 | ||||||||
\(187\) | −5.04229e14 | −0.862298 | ||||||||
\(188\) | −1.91240e14 | −0.315902 | ||||||||
\(189\) | −1.43403e14 | −0.228853 | ||||||||
\(190\) | 3.66940e14 | 0.565844 | ||||||||
\(191\) | −1.28312e15 | −1.91228 | −0.956139 | − | 0.292914i | \(-0.905375\pi\) | ||||
−0.956139 | + | 0.292914i | \(0.905375\pi\) | |||||||
\(192\) | −4.26510e14 | −0.614429 | ||||||||
\(193\) | 4.00231e14 | 0.557427 | 0.278714 | − | 0.960374i | \(-0.410092\pi\) | ||||
0.278714 | + | 0.960374i | \(0.410092\pi\) | |||||||
\(194\) | −8.37824e14 | −1.12834 | ||||||||
\(195\) | −6.16630e13 | −0.0803155 | ||||||||
\(196\) | −1.14126e14 | −0.143787 | ||||||||
\(197\) | 7.76732e14 | 0.946761 | 0.473381 | − | 0.880858i | \(-0.343033\pi\) | ||||
0.473381 | + | 0.880858i | \(0.343033\pi\) | |||||||
\(198\) | 3.06525e14 | 0.361528 | ||||||||
\(199\) | 1.14802e15 | 1.31041 | 0.655203 | − | 0.755453i | \(-0.272583\pi\) | ||||
0.655203 | + | 0.755453i | \(0.272583\pi\) | |||||||
\(200\) | 1.73973e14 | 0.192215 | ||||||||
\(201\) | 6.67600e14 | 0.714071 | ||||||||
\(202\) | −1.15017e15 | −1.19118 | ||||||||
\(203\) | 1.66927e15 | 1.67418 | ||||||||
\(204\) | 1.32567e14 | 0.128777 | ||||||||
\(205\) | −1.06430e15 | −1.00153 | ||||||||
\(206\) | 6.86026e14 | 0.625466 | ||||||||
\(207\) | −6.48040e14 | −0.572525 | ||||||||
\(208\) | 7.97123e13 | 0.0682517 | ||||||||
\(209\) | −1.04434e15 | −0.866746 | ||||||||
\(210\) | −7.47814e14 | −0.601683 | ||||||||
\(211\) | 1.48177e15 | 1.15597 | 0.577984 | − | 0.816048i | \(-0.303840\pi\) | ||||
0.577984 | + | 0.816048i | \(0.303840\pi\) | |||||||
\(212\) | −3.62933e14 | −0.274564 | ||||||||
\(213\) | −1.08525e15 | −0.796273 | ||||||||
\(214\) | 8.45114e14 | 0.601487 | ||||||||
\(215\) | 8.58462e14 | 0.592749 | ||||||||
\(216\) | −3.12672e14 | −0.209479 | ||||||||
\(217\) | −2.37645e15 | −1.54504 | ||||||||
\(218\) | −1.03752e15 | −0.654682 | ||||||||
\(219\) | 1.04541e15 | 0.640323 | ||||||||
\(220\) | −8.50298e14 | −0.505620 | ||||||||
\(221\) | −1.42682e14 | −0.0823796 | ||||||||
\(222\) | −1.26413e15 | −0.708758 | ||||||||
\(223\) | 2.27715e15 | 1.23997 | 0.619983 | − | 0.784615i | \(-0.287139\pi\) | ||||
0.619983 | + | 0.784615i | \(0.287139\pi\) | |||||||
\(224\) | −1.48051e15 | −0.783068 | ||||||||
\(225\) | 1.14559e14 | 0.0588632 | ||||||||
\(226\) | 2.95476e14 | 0.147509 | ||||||||
\(227\) | −8.42246e14 | −0.408574 | −0.204287 | − | 0.978911i | \(-0.565488\pi\) | ||||
−0.204287 | + | 0.978911i | \(0.565488\pi\) | |||||||
\(228\) | 2.74567e14 | 0.129441 | ||||||||
\(229\) | −2.08226e15 | −0.954124 | −0.477062 | − | 0.878870i | \(-0.658298\pi\) | ||||
−0.477062 | + | 0.878870i | \(0.658298\pi\) | |||||||
\(230\) | −3.37938e15 | −1.50524 | ||||||||
\(231\) | 2.12834e15 | 0.921643 | ||||||||
\(232\) | 3.63964e15 | 1.53245 | ||||||||
\(233\) | −4.28235e15 | −1.75335 | −0.876674 | − | 0.481084i | \(-0.840243\pi\) | ||||
−0.876674 | + | 0.481084i | \(0.840243\pi\) | |||||||
\(234\) | 8.67375e13 | 0.0345385 | ||||||||
\(235\) | −2.54788e15 | −0.986821 | ||||||||
\(236\) | 1.19985e14 | 0.0452064 | ||||||||
\(237\) | −7.20478e14 | −0.264093 | ||||||||
\(238\) | −1.73037e15 | −0.617146 | ||||||||
\(239\) | 3.50465e14 | 0.121635 | 0.0608175 | − | 0.998149i | \(-0.480629\pi\) | ||||
0.0608175 | + | 0.998149i | \(0.480629\pi\) | |||||||
\(240\) | −9.86713e14 | −0.333287 | ||||||||
\(241\) | −1.02876e15 | −0.338223 | −0.169112 | − | 0.985597i | \(-0.554090\pi\) | ||||
−0.169112 | + | 0.985597i | \(0.554090\pi\) | |||||||
\(242\) | −2.02482e15 | −0.648018 | ||||||||
\(243\) | −2.05891e14 | −0.0641500 | ||||||||
\(244\) | −2.00953e15 | −0.609621 | ||||||||
\(245\) | −1.52050e15 | −0.449165 | ||||||||
\(246\) | 1.49709e15 | 0.430694 | ||||||||
\(247\) | −2.95518e14 | −0.0828045 | ||||||||
\(248\) | −5.18155e15 | −1.41424 | ||||||||
\(249\) | −5.55212e14 | −0.147626 | ||||||||
\(250\) | −2.78559e15 | −0.721617 | ||||||||
\(251\) | 6.11470e15 | 1.54346 | 0.771731 | − | 0.635950i | \(-0.219391\pi\) | ||||
0.771731 | + | 0.635950i | \(0.219391\pi\) | |||||||
\(252\) | −5.59560e14 | −0.137640 | ||||||||
\(253\) | 9.61799e15 | 2.30569 | ||||||||
\(254\) | −1.45242e15 | −0.339370 | ||||||||
\(255\) | 1.76618e15 | 0.402276 | ||||||||
\(256\) | −4.06031e15 | −0.901571 | ||||||||
\(257\) | −3.65987e14 | −0.0792320 | −0.0396160 | − | 0.999215i | \(-0.512613\pi\) | ||||
−0.0396160 | + | 0.999215i | \(0.512613\pi\) | |||||||
\(258\) | −1.20755e15 | −0.254903 | ||||||||
\(259\) | −8.77744e15 | −1.80684 | ||||||||
\(260\) | −2.40610e14 | −0.0483043 | ||||||||
\(261\) | 2.39666e15 | 0.469292 | ||||||||
\(262\) | 1.49130e14 | 0.0284843 | ||||||||
\(263\) | −1.04025e16 | −1.93833 | −0.969164 | − | 0.246417i | \(-0.920747\pi\) | ||||
−0.969164 | + | 0.246417i | \(0.920747\pi\) | |||||||
\(264\) | 4.64058e15 | 0.843619 | ||||||||
\(265\) | −4.83534e15 | −0.857688 | ||||||||
\(266\) | −3.58388e15 | −0.620330 | ||||||||
\(267\) | −3.57047e15 | −0.603117 | ||||||||
\(268\) | 2.60498e15 | 0.429466 | ||||||||
\(269\) | −7.87928e14 | −0.126793 | −0.0633967 | − | 0.997988i | \(-0.520193\pi\) | ||||
−0.0633967 | + | 0.997988i | \(0.520193\pi\) | |||||||
\(270\) | −1.07367e15 | −0.168659 | ||||||||
\(271\) | 8.24265e15 | 1.26406 | 0.632028 | − | 0.774946i | \(-0.282223\pi\) | ||||
0.632028 | + | 0.774946i | \(0.282223\pi\) | |||||||
\(272\) | −2.28316e15 | −0.341852 | ||||||||
\(273\) | 6.02258e14 | 0.0880492 | ||||||||
\(274\) | −1.04186e16 | −1.48741 | ||||||||
\(275\) | −1.70025e15 | −0.237056 | ||||||||
\(276\) | −2.52866e15 | −0.344335 | ||||||||
\(277\) | 1.20923e16 | 1.60838 | 0.804191 | − | 0.594371i | \(-0.202599\pi\) | ||||
0.804191 | + | 0.594371i | \(0.202599\pi\) | |||||||
\(278\) | 1.04468e16 | 1.35735 | ||||||||
\(279\) | −3.41199e15 | −0.433092 | ||||||||
\(280\) | −1.13214e16 | −1.40402 | ||||||||
\(281\) | −6.11128e15 | −0.740527 | −0.370264 | − | 0.928927i | \(-0.620733\pi\) | ||||
−0.370264 | + | 0.928927i | \(0.620733\pi\) | |||||||
\(282\) | 3.58395e15 | 0.424368 | ||||||||
\(283\) | −8.43187e15 | −0.975690 | −0.487845 | − | 0.872930i | \(-0.662217\pi\) | ||||
−0.487845 | + | 0.872930i | \(0.662217\pi\) | |||||||
\(284\) | −4.23465e15 | −0.478904 | ||||||||
\(285\) | 3.65805e15 | 0.404351 | ||||||||
\(286\) | −1.28733e15 | −0.139095 | ||||||||
\(287\) | 1.03949e16 | 1.09797 | ||||||||
\(288\) | −2.12565e15 | −0.219503 | ||||||||
\(289\) | −5.81781e15 | −0.587386 | ||||||||
\(290\) | 1.24980e16 | 1.23383 | ||||||||
\(291\) | −8.35233e15 | −0.806312 | ||||||||
\(292\) | 4.07920e15 | 0.385111 | ||||||||
\(293\) | −1.09076e16 | −1.00714 | −0.503570 | − | 0.863955i | \(-0.667980\pi\) | ||||
−0.503570 | + | 0.863955i | \(0.667980\pi\) | |||||||
\(294\) | 2.13879e15 | 0.193157 | ||||||||
\(295\) | 1.59856e15 | 0.141217 | ||||||||
\(296\) | −1.91381e16 | −1.65387 | ||||||||
\(297\) | 3.05577e15 | 0.258347 | ||||||||
\(298\) | −6.84736e15 | −0.566393 | ||||||||
\(299\) | 2.72161e15 | 0.220274 | ||||||||
\(300\) | 4.47012e14 | 0.0354022 | ||||||||
\(301\) | −8.38454e15 | −0.649826 | ||||||||
\(302\) | 1.06055e16 | 0.804428 | ||||||||
\(303\) | −1.14661e16 | −0.851215 | ||||||||
\(304\) | −4.72880e15 | −0.343615 | ||||||||
\(305\) | −2.67729e16 | −1.90435 | ||||||||
\(306\) | −2.48438e15 | −0.172993 | ||||||||
\(307\) | −5.44084e14 | −0.0370909 | −0.0185454 | − | 0.999828i | \(-0.505904\pi\) | ||||
−0.0185454 | + | 0.999828i | \(0.505904\pi\) | |||||||
\(308\) | 8.30481e15 | 0.554306 | ||||||||
\(309\) | 6.83905e15 | 0.446957 | ||||||||
\(310\) | −1.77927e16 | −1.13865 | ||||||||
\(311\) | 2.81204e16 | 1.76230 | 0.881148 | − | 0.472840i | \(-0.156771\pi\) | ||||
0.881148 | + | 0.472840i | \(0.156771\pi\) | |||||||
\(312\) | 1.31315e15 | 0.0805951 | ||||||||
\(313\) | −2.17471e16 | −1.30726 | −0.653631 | − | 0.756813i | \(-0.726755\pi\) | ||||
−0.653631 | + | 0.756813i | \(0.726755\pi\) | |||||||
\(314\) | −1.36647e16 | −0.804557 | ||||||||
\(315\) | −7.45501e15 | −0.429962 | ||||||||
\(316\) | −2.81132e15 | −0.158834 | ||||||||
\(317\) | 2.25030e16 | 1.24553 | 0.622766 | − | 0.782408i | \(-0.286009\pi\) | ||||
0.622766 | + | 0.782408i | \(0.286009\pi\) | |||||||
\(318\) | 6.80158e15 | 0.368836 | ||||||||
\(319\) | −3.55704e16 | −1.88995 | ||||||||
\(320\) | −2.21728e16 | −1.15437 | ||||||||
\(321\) | 8.42501e15 | 0.429821 | ||||||||
\(322\) | 3.30061e16 | 1.65018 | ||||||||
\(323\) | 8.46438e15 | 0.414743 | ||||||||
\(324\) | −8.03390e14 | −0.0385819 | ||||||||
\(325\) | −4.81121e14 | −0.0226471 | ||||||||
\(326\) | 2.59119e16 | 1.19560 | ||||||||
\(327\) | −1.03431e16 | −0.467834 | ||||||||
\(328\) | 2.26649e16 | 1.00502 | ||||||||
\(329\) | 2.48850e16 | 1.08184 | ||||||||
\(330\) | 1.59351e16 | 0.679227 | ||||||||
\(331\) | 1.11987e16 | 0.468041 | 0.234021 | − | 0.972232i | \(-0.424812\pi\) | ||||
0.234021 | + | 0.972232i | \(0.424812\pi\) | |||||||
\(332\) | −2.16645e15 | −0.0887872 | ||||||||
\(333\) | −1.26022e16 | −0.506477 | ||||||||
\(334\) | 2.43768e16 | 0.960783 | ||||||||
\(335\) | 3.47061e16 | 1.34157 | ||||||||
\(336\) | 9.63716e15 | 0.365379 | ||||||||
\(337\) | −4.82725e15 | −0.179517 | −0.0897584 | − | 0.995964i | \(-0.528609\pi\) | ||||
−0.0897584 | + | 0.995964i | \(0.528609\pi\) | |||||||
\(338\) | 2.17838e16 | 0.794649 | ||||||||
\(339\) | 2.94562e15 | 0.105409 | ||||||||
\(340\) | 6.89166e15 | 0.241942 | ||||||||
\(341\) | 5.06396e16 | 1.74416 | ||||||||
\(342\) | −5.14556e15 | −0.173885 | ||||||||
\(343\) | −2.10127e16 | −0.696739 | ||||||||
\(344\) | −1.82814e16 | −0.594813 | ||||||||
\(345\) | −3.36893e16 | −1.07564 | ||||||||
\(346\) | −2.46427e16 | −0.772137 | ||||||||
\(347\) | 4.80731e16 | 1.47829 | 0.739146 | − | 0.673545i | \(-0.235229\pi\) | ||||
0.739146 | + | 0.673545i | \(0.235229\pi\) | |||||||
\(348\) | 9.35180e15 | 0.282247 | ||||||||
\(349\) | 2.33023e16 | 0.690293 | 0.345146 | − | 0.938549i | \(-0.387829\pi\) | ||||
0.345146 | + | 0.938549i | \(0.387829\pi\) | |||||||
\(350\) | −5.83477e15 | −0.169661 | ||||||||
\(351\) | 8.64693e14 | 0.0246812 | ||||||||
\(352\) | 3.15481e16 | 0.883988 | ||||||||
\(353\) | −2.68573e16 | −0.738799 | −0.369400 | − | 0.929271i | \(-0.620437\pi\) | ||||
−0.369400 | + | 0.929271i | \(0.620437\pi\) | |||||||
\(354\) | −2.24860e15 | −0.0607283 | ||||||||
\(355\) | −5.64182e16 | −1.49601 | ||||||||
\(356\) | −1.39320e16 | −0.362734 | ||||||||
\(357\) | −1.72502e16 | −0.441012 | ||||||||
\(358\) | 3.53977e16 | 0.888659 | ||||||||
\(359\) | −6.33371e16 | −1.56151 | −0.780754 | − | 0.624839i | \(-0.785165\pi\) | ||||
−0.780754 | + | 0.624839i | \(0.785165\pi\) | |||||||
\(360\) | −1.62547e16 | −0.393562 | ||||||||
\(361\) | −2.45218e16 | −0.583118 | ||||||||
\(362\) | −4.50205e16 | −1.05149 | ||||||||
\(363\) | −2.01856e16 | −0.463072 | ||||||||
\(364\) | 2.35002e15 | 0.0529556 | ||||||||
\(365\) | 5.43471e16 | 1.20302 | ||||||||
\(366\) | 3.76598e16 | 0.818938 | ||||||||
\(367\) | −3.87957e16 | −0.828809 | −0.414405 | − | 0.910093i | \(-0.636010\pi\) | ||||
−0.414405 | + | 0.910093i | \(0.636010\pi\) | |||||||
\(368\) | 4.35504e16 | 0.914074 | ||||||||
\(369\) | 1.49246e16 | 0.307773 | ||||||||
\(370\) | −6.57177e16 | −1.33159 | ||||||||
\(371\) | 4.72265e16 | 0.940275 | ||||||||
\(372\) | −1.33136e16 | −0.260476 | ||||||||
\(373\) | −3.10449e16 | −0.596875 | −0.298438 | − | 0.954429i | \(-0.596465\pi\) | ||||
−0.298438 | + | 0.954429i | \(0.596465\pi\) | |||||||
\(374\) | 3.68723e16 | 0.696683 | ||||||||
\(375\) | −2.77697e16 | −0.515666 | ||||||||
\(376\) | 5.42586e16 | 0.990256 | ||||||||
\(377\) | −1.00654e16 | −0.180556 | ||||||||
\(378\) | 1.04865e16 | 0.184899 | ||||||||
\(379\) | −4.11618e16 | −0.713411 | −0.356706 | − | 0.934217i | \(-0.616100\pi\) | ||||
−0.356706 | + | 0.934217i | \(0.616100\pi\) | |||||||
\(380\) | 1.42738e16 | 0.243190 | ||||||||
\(381\) | −1.44793e16 | −0.242513 | ||||||||
\(382\) | 9.38297e16 | 1.54500 | ||||||||
\(383\) | −5.75790e15 | −0.0932120 | −0.0466060 | − | 0.998913i | \(-0.514841\pi\) | ||||
−0.0466060 | + | 0.998913i | \(0.514841\pi\) | |||||||
\(384\) | 7.30252e15 | 0.116230 | ||||||||
\(385\) | 1.10645e17 | 1.73155 | ||||||||
\(386\) | −2.92674e16 | −0.450366 | ||||||||
\(387\) | −1.20381e16 | −0.182153 | ||||||||
\(388\) | −3.25909e16 | −0.484942 | ||||||||
\(389\) | −4.95437e16 | −0.724964 | −0.362482 | − | 0.931991i | \(-0.618071\pi\) | ||||
−0.362482 | + | 0.931991i | \(0.618071\pi\) | |||||||
\(390\) | 4.50917e15 | 0.0648899 | ||||||||
\(391\) | −7.79537e16 | −1.10329 | ||||||||
\(392\) | 3.23798e16 | 0.450729 | ||||||||
\(393\) | 1.48669e15 | 0.0203548 | ||||||||
\(394\) | −5.67994e16 | −0.764924 | ||||||||
\(395\) | −3.74551e16 | −0.496169 | ||||||||
\(396\) | 1.19236e16 | 0.155378 | ||||||||
\(397\) | 1.07289e17 | 1.37536 | 0.687682 | − | 0.726012i | \(-0.258628\pi\) | ||||
0.687682 | + | 0.726012i | \(0.258628\pi\) | |||||||
\(398\) | −8.39505e16 | −1.05873 | ||||||||
\(399\) | −3.57280e16 | −0.443286 | ||||||||
\(400\) | −7.69876e15 | −0.0939791 | ||||||||
\(401\) | 6.02400e16 | 0.723513 | 0.361756 | − | 0.932273i | \(-0.382177\pi\) | ||||
0.361756 | + | 0.932273i | \(0.382177\pi\) | |||||||
\(402\) | −4.88190e16 | −0.576925 | ||||||||
\(403\) | 1.43295e16 | 0.166628 | ||||||||
\(404\) | −4.47410e16 | −0.511949 | ||||||||
\(405\) | −1.07035e16 | −0.120523 | ||||||||
\(406\) | −1.22067e17 | −1.35263 | ||||||||
\(407\) | 1.87038e17 | 2.03970 | ||||||||
\(408\) | −3.76118e16 | −0.403676 | ||||||||
\(409\) | 1.51728e16 | 0.160275 | 0.0801375 | − | 0.996784i | \(-0.474464\pi\) | ||||
0.0801375 | + | 0.996784i | \(0.474464\pi\) | |||||||
\(410\) | 7.78281e16 | 0.809173 | ||||||||
\(411\) | −1.03863e17 | −1.06290 | ||||||||
\(412\) | 2.66861e16 | 0.268814 | ||||||||
\(413\) | −1.56130e16 | −0.154815 | ||||||||
\(414\) | 4.73886e16 | 0.462564 | ||||||||
\(415\) | −2.88635e16 | −0.277355 | ||||||||
\(416\) | 8.92720e15 | 0.0844517 | ||||||||
\(417\) | 1.04145e17 | 0.969963 | ||||||||
\(418\) | 7.63687e16 | 0.700276 | ||||||||
\(419\) | 6.50706e16 | 0.587481 | 0.293740 | − | 0.955885i | \(-0.405100\pi\) | ||||
0.293740 | + | 0.955885i | \(0.405100\pi\) | |||||||
\(420\) | −2.90895e16 | −0.258593 | ||||||||
\(421\) | 4.92680e16 | 0.431253 | 0.215626 | − | 0.976476i | \(-0.430821\pi\) | ||||
0.215626 | + | 0.976476i | \(0.430821\pi\) | |||||||
\(422\) | −1.08356e17 | −0.933949 | ||||||||
\(423\) | 3.57287e16 | 0.303253 | ||||||||
\(424\) | 1.02971e17 | 0.860674 | ||||||||
\(425\) | 1.37805e16 | 0.113432 | ||||||||
\(426\) | 7.93600e16 | 0.643338 | ||||||||
\(427\) | 2.61489e17 | 2.08772 | ||||||||
\(428\) | 3.28745e16 | 0.258508 | ||||||||
\(429\) | −1.28335e16 | −0.0993967 | ||||||||
\(430\) | −6.27760e16 | −0.478904 | ||||||||
\(431\) | 5.82573e16 | 0.437772 | 0.218886 | − | 0.975750i | \(-0.429758\pi\) | ||||
0.218886 | + | 0.975750i | \(0.429758\pi\) | |||||||
\(432\) | 1.38366e16 | 0.102420 | ||||||||
\(433\) | −5.36263e16 | −0.391027 | −0.195513 | − | 0.980701i | \(-0.562637\pi\) | ||||
−0.195513 | + | 0.980701i | \(0.562637\pi\) | |||||||
\(434\) | 1.73781e17 | 1.24830 | ||||||||
\(435\) | 1.24594e17 | 0.881691 | ||||||||
\(436\) | −4.03591e16 | −0.281371 | ||||||||
\(437\) | −1.61455e17 | −1.10898 | ||||||||
\(438\) | −7.64467e16 | −0.517341 | ||||||||
\(439\) | −2.07555e17 | −1.38393 | −0.691964 | − | 0.721932i | \(-0.743254\pi\) | ||||
−0.691964 | + | 0.721932i | \(0.743254\pi\) | |||||||
\(440\) | 2.41247e17 | 1.58496 | ||||||||
\(441\) | 2.13218e16 | 0.138030 | ||||||||
\(442\) | 1.04338e16 | 0.0665576 | ||||||||
\(443\) | −7.36795e15 | −0.0463151 | −0.0231575 | − | 0.999732i | \(-0.507372\pi\) | ||||
−0.0231575 | + | 0.999732i | \(0.507372\pi\) | |||||||
\(444\) | −4.91740e16 | −0.304612 | ||||||||
\(445\) | −1.85616e17 | −1.13312 | ||||||||
\(446\) | −1.66519e17 | −1.00182 | ||||||||
\(447\) | −6.82619e16 | −0.404743 | ||||||||
\(448\) | 2.16560e17 | 1.26552 | ||||||||
\(449\) | 1.54892e17 | 0.892132 | 0.446066 | − | 0.895000i | \(-0.352825\pi\) | ||||
0.446066 | + | 0.895000i | \(0.352825\pi\) | |||||||
\(450\) | −8.37728e15 | −0.0475578 | ||||||||
\(451\) | −2.21505e17 | −1.23947 | ||||||||
\(452\) | 1.14939e16 | 0.0633966 | ||||||||
\(453\) | 1.05727e17 | 0.574843 | ||||||||
\(454\) | 6.15902e16 | 0.330102 | ||||||||
\(455\) | 3.13092e16 | 0.165424 | ||||||||
\(456\) | −7.79003e16 | −0.405759 | ||||||||
\(457\) | −2.59040e17 | −1.33018 | −0.665091 | − | 0.746762i | \(-0.731607\pi\) | ||||
−0.665091 | + | 0.746762i | \(0.731607\pi\) | |||||||
\(458\) | 1.52268e17 | 0.770872 | ||||||||
\(459\) | −2.47670e16 | −0.123620 | ||||||||
\(460\) | −1.31456e17 | −0.646926 | ||||||||
\(461\) | 1.25135e17 | 0.607190 | 0.303595 | − | 0.952801i | \(-0.401813\pi\) | ||||
0.303595 | + | 0.952801i | \(0.401813\pi\) | |||||||
\(462\) | −1.55637e17 | −0.744630 | ||||||||
\(463\) | −6.63878e16 | −0.313193 | −0.156596 | − | 0.987663i | \(-0.550052\pi\) | ||||
−0.156596 | + | 0.987663i | \(0.550052\pi\) | |||||||
\(464\) | −1.61064e17 | −0.749256 | ||||||||
\(465\) | −1.77377e17 | −0.813680 | ||||||||
\(466\) | 3.13151e17 | 1.41660 | ||||||||
\(467\) | 1.40751e17 | 0.627900 | 0.313950 | − | 0.949439i | \(-0.398347\pi\) | ||||
0.313950 | + | 0.949439i | \(0.398347\pi\) | |||||||
\(468\) | 3.37404e15 | 0.0148441 | ||||||||
\(469\) | −3.38972e17 | −1.47076 | ||||||||
\(470\) | 1.86317e17 | 0.797289 | ||||||||
\(471\) | −1.36224e17 | −0.574934 | ||||||||
\(472\) | −3.40423e16 | −0.141708 | ||||||||
\(473\) | 1.78666e17 | 0.733574 | ||||||||
\(474\) | 5.26858e16 | 0.213370 | ||||||||
\(475\) | 2.85417e16 | 0.114018 | ||||||||
\(476\) | −6.73104e16 | −0.265239 | ||||||||
\(477\) | 6.78055e16 | 0.263570 | ||||||||
\(478\) | −2.56282e16 | −0.0982735 | ||||||||
\(479\) | −2.42759e17 | −0.918321 | −0.459161 | − | 0.888353i | \(-0.651850\pi\) | ||||
−0.459161 | + | 0.888353i | \(0.651850\pi\) | |||||||
\(480\) | −1.10505e17 | −0.412394 | ||||||||
\(481\) | 5.29263e16 | 0.194863 | ||||||||
\(482\) | 7.52293e16 | 0.273263 | ||||||||
\(483\) | 3.29041e17 | 1.17922 | ||||||||
\(484\) | −7.87645e16 | −0.278507 | ||||||||
\(485\) | −4.34208e17 | −1.51487 | ||||||||
\(486\) | 1.50560e16 | 0.0518292 | ||||||||
\(487\) | −2.49745e17 | −0.848319 | −0.424160 | − | 0.905587i | \(-0.639430\pi\) | ||||
−0.424160 | + | 0.905587i | \(0.639430\pi\) | |||||||
\(488\) | 5.70144e17 | 1.91098 | ||||||||
\(489\) | 2.58317e17 | 0.854370 | ||||||||
\(490\) | 1.11188e17 | 0.362897 | ||||||||
\(491\) | 5.45019e17 | 1.75542 | 0.877712 | − | 0.479188i | \(-0.159069\pi\) | ||||
0.877712 | + | 0.479188i | \(0.159069\pi\) | |||||||
\(492\) | 5.82358e16 | 0.185105 | ||||||||
\(493\) | 2.88298e17 | 0.904350 | ||||||||
\(494\) | 2.16101e16 | 0.0669009 | ||||||||
\(495\) | 1.58858e17 | 0.485374 | ||||||||
\(496\) | 2.29297e17 | 0.691461 | ||||||||
\(497\) | 5.51033e17 | 1.64006 | ||||||||
\(498\) | 4.06005e16 | 0.119273 | ||||||||
\(499\) | 2.62257e17 | 0.760456 | 0.380228 | − | 0.924893i | \(-0.375846\pi\) | ||||
0.380228 | + | 0.924893i | \(0.375846\pi\) | |||||||
\(500\) | −1.08358e17 | −0.310138 | ||||||||
\(501\) | 2.43015e17 | 0.686574 | ||||||||
\(502\) | −4.47144e17 | −1.24702 | ||||||||
\(503\) | 4.68641e17 | 1.29017 | 0.645087 | − | 0.764109i | \(-0.276821\pi\) | ||||
0.645087 | + | 0.764109i | \(0.276821\pi\) | |||||||
\(504\) | 1.58759e17 | 0.431458 | ||||||||
\(505\) | −5.96083e17 | −1.59924 | ||||||||
\(506\) | −7.03326e17 | −1.86285 | ||||||||
\(507\) | 2.17164e17 | 0.567854 | ||||||||
\(508\) | −5.64985e16 | −0.145855 | ||||||||
\(509\) | −1.26286e17 | −0.321878 | −0.160939 | − | 0.986964i | \(-0.551452\pi\) | ||||
−0.160939 | + | 0.986964i | \(0.551452\pi\) | |||||||
\(510\) | −1.29154e17 | −0.325014 | ||||||||
\(511\) | −5.30804e17 | −1.31886 | ||||||||
\(512\) | 3.78976e17 | 0.929730 | ||||||||
\(513\) | −5.12965e16 | −0.124258 | ||||||||
\(514\) | 2.67632e16 | 0.0640145 | ||||||||
\(515\) | 3.55538e17 | 0.839728 | ||||||||
\(516\) | −4.69729e16 | −0.109553 | ||||||||
\(517\) | −5.30273e17 | −1.22127 | ||||||||
\(518\) | 6.41860e17 | 1.45981 | ||||||||
\(519\) | −2.45665e17 | −0.551767 | ||||||||
\(520\) | 6.82658e16 | 0.151419 | ||||||||
\(521\) | −6.46305e17 | −1.41577 | −0.707884 | − | 0.706329i | \(-0.750350\pi\) | ||||
−0.707884 | + | 0.706329i | \(0.750350\pi\) | |||||||
\(522\) | −1.75259e17 | −0.379159 | ||||||||
\(523\) | 5.52191e17 | 1.17985 | 0.589927 | − | 0.807457i | \(-0.299156\pi\) | ||||
0.589927 | + | 0.807457i | \(0.299156\pi\) | |||||||
\(524\) | 5.80107e15 | 0.0122421 | ||||||||
\(525\) | −5.81672e16 | −0.121239 | ||||||||
\(526\) | 7.60698e17 | 1.56605 | ||||||||
\(527\) | −4.10434e17 | −0.834592 | ||||||||
\(528\) | −2.05358e17 | −0.412468 | ||||||||
\(529\) | 9.82902e17 | 1.95006 | ||||||||
\(530\) | 3.53590e17 | 0.692958 | ||||||||
\(531\) | −2.24165e16 | −0.0433963 | ||||||||
\(532\) | −1.39411e17 | −0.266607 | ||||||||
\(533\) | −6.26795e16 | −0.118413 | ||||||||
\(534\) | 2.61094e17 | 0.487281 | ||||||||
\(535\) | 4.37986e17 | 0.807534 | ||||||||
\(536\) | −7.39086e17 | −1.34624 | ||||||||
\(537\) | 3.52882e17 | 0.635034 | ||||||||
\(538\) | 5.76181e16 | 0.102441 | ||||||||
\(539\) | −3.16450e17 | −0.555877 | ||||||||
\(540\) | −4.17654e16 | −0.0724865 | ||||||||
\(541\) | −2.35160e17 | −0.403257 | −0.201628 | − | 0.979462i | \(-0.564623\pi\) | ||||
−0.201628 | + | 0.979462i | \(0.564623\pi\) | |||||||
\(542\) | −6.02753e17 | −1.02128 | ||||||||
\(543\) | −4.48813e17 | −0.751391 | ||||||||
\(544\) | −2.55697e17 | −0.422993 | ||||||||
\(545\) | −5.37703e17 | −0.878952 | ||||||||
\(546\) | −4.40408e16 | −0.0711382 | ||||||||
\(547\) | 3.58254e17 | 0.571839 | 0.285919 | − | 0.958254i | \(-0.407701\pi\) | ||||
0.285919 | + | 0.958254i | \(0.407701\pi\) | |||||||
\(548\) | −4.05277e17 | −0.639261 | ||||||||
\(549\) | 3.75433e17 | 0.585211 | ||||||||
\(550\) | 1.24333e17 | 0.191526 | ||||||||
\(551\) | 5.97113e17 | 0.909015 | ||||||||
\(552\) | 7.17432e17 | 1.07939 | ||||||||
\(553\) | 3.65821e17 | 0.543946 | ||||||||
\(554\) | −8.84261e17 | −1.29947 | ||||||||
\(555\) | −6.55145e17 | −0.951553 | ||||||||
\(556\) | 4.06376e17 | 0.583367 | ||||||||
\(557\) | −3.00119e17 | −0.425828 | −0.212914 | − | 0.977071i | \(-0.568295\pi\) | ||||
−0.212914 | + | 0.977071i | \(0.568295\pi\) | |||||||
\(558\) | 2.49506e17 | 0.349912 | ||||||||
\(559\) | 5.05572e16 | 0.0700819 | ||||||||
\(560\) | 5.01001e17 | 0.686462 | ||||||||
\(561\) | 3.67583e17 | 0.497848 | ||||||||
\(562\) | 4.46894e17 | 0.598299 | ||||||||
\(563\) | 6.69169e17 | 0.885587 | 0.442794 | − | 0.896624i | \(-0.353987\pi\) | ||||
0.442794 | + | 0.896624i | \(0.353987\pi\) | |||||||
\(564\) | 1.39414e17 | 0.182386 | ||||||||
\(565\) | 1.53133e17 | 0.198040 | ||||||||
\(566\) | 6.16590e17 | 0.788297 | ||||||||
\(567\) | 1.04541e17 | 0.132128 | ||||||||
\(568\) | 1.20146e18 | 1.50122 | ||||||||
\(569\) | −4.72534e17 | −0.583718 | −0.291859 | − | 0.956461i | \(-0.594274\pi\) | ||||
−0.291859 | + | 0.956461i | \(0.594274\pi\) | |||||||
\(570\) | −2.67499e17 | −0.326690 | ||||||||
\(571\) | −5.55849e17 | −0.671154 | −0.335577 | − | 0.942013i | \(-0.608931\pi\) | ||||
−0.335577 | + | 0.942013i | \(0.608931\pi\) | |||||||
\(572\) | −5.00764e16 | −0.0597804 | ||||||||
\(573\) | 9.35396e17 | 1.10405 | ||||||||
\(574\) | −7.60142e17 | −0.887089 | ||||||||
\(575\) | −2.62858e17 | −0.303306 | ||||||||
\(576\) | 3.10926e17 | 0.354741 | ||||||||
\(577\) | −5.61922e16 | −0.0633918 | −0.0316959 | − | 0.999498i | \(-0.510091\pi\) | ||||
−0.0316959 | + | 0.999498i | \(0.510091\pi\) | |||||||
\(578\) | 4.25434e17 | 0.474571 | ||||||||
\(579\) | −2.91768e17 | −0.321831 | ||||||||
\(580\) | 4.86167e17 | 0.530278 | ||||||||
\(581\) | 2.81908e17 | 0.304062 | ||||||||
\(582\) | 6.10774e17 | 0.651450 | ||||||||
\(583\) | −1.00635e18 | −1.06146 | ||||||||
\(584\) | −1.15735e18 | −1.20721 | ||||||||
\(585\) | 4.49523e16 | 0.0463702 | ||||||||
\(586\) | 7.97631e17 | 0.813706 | ||||||||
\(587\) | 1.36912e18 | 1.38131 | 0.690657 | − | 0.723182i | \(-0.257321\pi\) | ||||
0.690657 | + | 0.723182i | \(0.257321\pi\) | |||||||
\(588\) | 8.31978e16 | 0.0830155 | ||||||||
\(589\) | −8.50076e17 | −0.838897 | ||||||||
\(590\) | −1.16897e17 | −0.114094 | ||||||||
\(591\) | −5.66237e17 | −0.546613 | ||||||||
\(592\) | 8.46911e17 | 0.808624 | ||||||||
\(593\) | 1.03680e18 | 0.979128 | 0.489564 | − | 0.871967i | \(-0.337156\pi\) | ||||
0.489564 | + | 0.871967i | \(0.337156\pi\) | |||||||
\(594\) | −2.23456e17 | −0.208728 | ||||||||
\(595\) | −8.96775e17 | −0.828558 | ||||||||
\(596\) | −2.66359e17 | −0.243426 | ||||||||
\(597\) | −8.36909e17 | −0.756563 | ||||||||
\(598\) | −1.99021e17 | −0.177967 | ||||||||
\(599\) | 1.11217e18 | 0.983778 | 0.491889 | − | 0.870658i | \(-0.336307\pi\) | ||||
0.491889 | + | 0.870658i | \(0.336307\pi\) | |||||||
\(600\) | −1.26826e17 | −0.110975 | ||||||||
\(601\) | 3.64114e17 | 0.315176 | 0.157588 | − | 0.987505i | \(-0.449628\pi\) | ||||
0.157588 | + | 0.987505i | \(0.449628\pi\) | |||||||
\(602\) | 6.13129e17 | 0.525018 | ||||||||
\(603\) | −4.86680e17 | −0.412269 | ||||||||
\(604\) | 4.12550e17 | 0.345729 | ||||||||
\(605\) | −1.04938e18 | −0.870005 | ||||||||
\(606\) | 8.38473e17 | 0.687729 | ||||||||
\(607\) | 5.94061e17 | 0.482064 | 0.241032 | − | 0.970517i | \(-0.422514\pi\) | ||||
0.241032 | + | 0.970517i | \(0.422514\pi\) | |||||||
\(608\) | −5.29591e17 | −0.425175 | ||||||||
\(609\) | −1.21690e18 | −0.966590 | ||||||||
\(610\) | 1.95780e18 | 1.53859 | ||||||||
\(611\) | −1.50052e17 | −0.116674 | ||||||||
\(612\) | −9.66410e16 | −0.0743494 | ||||||||
\(613\) | −2.17994e18 | −1.65940 | −0.829702 | − | 0.558206i | \(-0.811490\pi\) | ||||
−0.829702 | + | 0.558206i | \(0.811490\pi\) | |||||||
\(614\) | 3.97868e16 | 0.0299671 | ||||||||
\(615\) | 7.75875e17 | 0.578234 | ||||||||
\(616\) | −2.35624e18 | −1.73758 | ||||||||
\(617\) | −1.76345e18 | −1.28680 | −0.643398 | − | 0.765532i | \(-0.722476\pi\) | ||||
−0.643398 | + | 0.765532i | \(0.722476\pi\) | |||||||
\(618\) | −5.00113e17 | −0.361113 | ||||||||
\(619\) | −5.68471e15 | −0.00406180 | −0.00203090 | − | 0.999998i | \(-0.500646\pi\) | ||||
−0.00203090 | + | 0.999998i | \(0.500646\pi\) | |||||||
\(620\) | −6.92128e17 | −0.489374 | ||||||||
\(621\) | 4.72421e17 | 0.330547 | ||||||||
\(622\) | −2.05634e18 | −1.42383 | ||||||||
\(623\) | 1.81290e18 | 1.24223 | ||||||||
\(624\) | −5.81102e16 | −0.0394051 | ||||||||
\(625\) | −1.70679e18 | −1.14541 | ||||||||
\(626\) | 1.59028e18 | 1.05619 | ||||||||
\(627\) | 7.61325e17 | 0.500416 | ||||||||
\(628\) | −5.31549e17 | −0.345784 | ||||||||
\(629\) | −1.51594e18 | −0.976007 | ||||||||
\(630\) | 5.45156e17 | 0.347382 | ||||||||
\(631\) | −1.13226e18 | −0.714097 | −0.357048 | − | 0.934086i | \(-0.616217\pi\) | ||||
−0.357048 | + | 0.934086i | \(0.616217\pi\) | |||||||
\(632\) | 7.97627e17 | 0.497896 | ||||||||
\(633\) | −1.08021e18 | −0.667398 | ||||||||
\(634\) | −1.64556e18 | −1.00631 | ||||||||
\(635\) | −7.52728e17 | −0.455626 | ||||||||
\(636\) | 2.64578e17 | 0.158519 | ||||||||
\(637\) | −8.95462e16 | −0.0531057 | ||||||||
\(638\) | 2.60113e18 | 1.52696 | ||||||||
\(639\) | 7.91146e17 | 0.459728 | ||||||||
\(640\) | 3.79632e17 | 0.218370 | ||||||||
\(641\) | −1.59725e18 | −0.909483 | −0.454742 | − | 0.890623i | \(-0.650268\pi\) | ||||
−0.454742 | + | 0.890623i | \(0.650268\pi\) | |||||||
\(642\) | −6.16088e17 | −0.347268 | ||||||||
\(643\) | −2.33433e18 | −1.30254 | −0.651269 | − | 0.758847i | \(-0.725763\pi\) | ||||
−0.651269 | + | 0.758847i | \(0.725763\pi\) | |||||||
\(644\) | 1.28392e18 | 0.709219 | ||||||||
\(645\) | −6.25819e17 | −0.342224 | ||||||||
\(646\) | −6.18968e17 | −0.335086 | ||||||||
\(647\) | 2.15674e18 | 1.15590 | 0.577949 | − | 0.816073i | \(-0.303853\pi\) | ||||
0.577949 | + | 0.816073i | \(0.303853\pi\) | |||||||
\(648\) | 2.27938e17 | 0.120943 | ||||||||
\(649\) | 3.32698e17 | 0.174767 | ||||||||
\(650\) | 3.51825e16 | 0.0182974 | ||||||||
\(651\) | 1.73243e18 | 0.892030 | ||||||||
\(652\) | 1.00796e18 | 0.513846 | ||||||||
\(653\) | −2.51576e18 | −1.26979 | −0.634897 | − | 0.772597i | \(-0.718958\pi\) | ||||
−0.634897 | + | 0.772597i | \(0.718958\pi\) | |||||||
\(654\) | 7.56354e17 | 0.377981 | ||||||||
\(655\) | 7.72875e16 | 0.0382420 | ||||||||
\(656\) | −1.00298e18 | −0.491380 | ||||||||
\(657\) | −7.62103e17 | −0.369691 | ||||||||
\(658\) | −1.81974e18 | −0.874061 | ||||||||
\(659\) | −3.59012e18 | −1.70747 | −0.853737 | − | 0.520704i | \(-0.825670\pi\) | ||||
−0.853737 | + | 0.520704i | \(0.825670\pi\) | |||||||
\(660\) | 6.19868e17 | 0.291920 | ||||||||
\(661\) | −1.54091e18 | −0.718569 | −0.359285 | − | 0.933228i | \(-0.616979\pi\) | ||||
−0.359285 | + | 0.933228i | \(0.616979\pi\) | |||||||
\(662\) | −8.18915e17 | −0.378148 | ||||||||
\(663\) | 1.04015e17 | 0.0475619 | ||||||||
\(664\) | 6.14665e17 | 0.278321 | ||||||||
\(665\) | −1.85737e18 | −0.832832 | ||||||||
\(666\) | 9.21552e17 | 0.409202 | ||||||||
\(667\) | −5.49918e18 | −2.41813 | ||||||||
\(668\) | 9.48246e17 | 0.412928 | ||||||||
\(669\) | −1.66004e18 | −0.715895 | ||||||||
\(670\) | −2.53792e18 | −1.08391 | ||||||||
\(671\) | −5.57205e18 | −2.35678 | ||||||||
\(672\) | 1.07929e18 | 0.452104 | ||||||||
\(673\) | −4.27821e18 | −1.77486 | −0.887431 | − | 0.460940i | \(-0.847512\pi\) | ||||
−0.887431 | + | 0.460940i | \(0.847512\pi\) | |||||||
\(674\) | 3.52998e17 | 0.145038 | ||||||||
\(675\) | −8.35137e16 | −0.0339847 | ||||||||
\(676\) | 8.47378e17 | 0.341526 | ||||||||
\(677\) | −2.37034e18 | −0.946201 | −0.473100 | − | 0.881008i | \(-0.656865\pi\) | ||||
−0.473100 | + | 0.881008i | \(0.656865\pi\) | |||||||
\(678\) | −2.15402e17 | −0.0851642 | ||||||||
\(679\) | 4.24088e18 | 1.66074 | ||||||||
\(680\) | −1.95530e18 | −0.758414 | ||||||||
\(681\) | 6.13998e17 | 0.235890 | ||||||||
\(682\) | −3.70308e18 | −1.40917 | ||||||||
\(683\) | −4.83798e18 | −1.82360 | −0.911800 | − | 0.410634i | \(-0.865307\pi\) | ||||
−0.911800 | + | 0.410634i | \(0.865307\pi\) | |||||||
\(684\) | −2.00160e17 | −0.0747329 | ||||||||
\(685\) | −5.39949e18 | −1.99694 | ||||||||
\(686\) | 1.53658e18 | 0.562921 | ||||||||
\(687\) | 1.51797e18 | 0.550864 | ||||||||
\(688\) | 8.09001e17 | 0.290820 | ||||||||
\(689\) | −2.84767e17 | −0.101406 | ||||||||
\(690\) | 2.46357e18 | 0.869051 | ||||||||
\(691\) | −7.71829e17 | −0.269720 | −0.134860 | − | 0.990865i | \(-0.543059\pi\) | ||||
−0.134860 | + | 0.990865i | \(0.543059\pi\) | |||||||
\(692\) | −9.58589e17 | −0.331851 | ||||||||
\(693\) | −1.55156e18 | −0.532111 | ||||||||
\(694\) | −3.51540e18 | −1.19437 | ||||||||
\(695\) | 5.41414e18 | 1.82233 | ||||||||
\(696\) | −2.65330e18 | −0.884760 | ||||||||
\(697\) | 1.79530e18 | 0.593094 | ||||||||
\(698\) | −1.70401e18 | −0.557713 | ||||||||
\(699\) | 3.12183e18 | 1.01230 | ||||||||
\(700\) | −2.26969e17 | −0.0729172 | ||||||||
\(701\) | −3.65953e18 | −1.16482 | −0.582410 | − | 0.812895i | \(-0.697890\pi\) | ||||
−0.582410 | + | 0.812895i | \(0.697890\pi\) | |||||||
\(702\) | −6.32316e16 | −0.0199408 | ||||||||
\(703\) | −3.13976e18 | −0.981042 | ||||||||
\(704\) | −4.61466e18 | −1.42862 | ||||||||
\(705\) | 1.85741e18 | 0.569741 | ||||||||
\(706\) | 1.96397e18 | 0.596904 | ||||||||
\(707\) | 5.82190e18 | 1.75323 | ||||||||
\(708\) | −8.74693e16 | −0.0260999 | ||||||||
\(709\) | 7.72559e17 | 0.228418 | 0.114209 | − | 0.993457i | \(-0.463567\pi\) | ||||
0.114209 | + | 0.993457i | \(0.463567\pi\) | |||||||
\(710\) | 4.12565e18 | 1.20868 | ||||||||
\(711\) | 5.25229e17 | 0.152474 | ||||||||
\(712\) | 3.95279e18 | 1.13706 | ||||||||
\(713\) | 7.82887e18 | 2.23161 | ||||||||
\(714\) | 1.26144e18 | 0.356310 | ||||||||
\(715\) | −6.67167e17 | −0.186743 | ||||||||
\(716\) | 1.37695e18 | 0.381930 | ||||||||
\(717\) | −2.55489e17 | −0.0702260 | ||||||||
\(718\) | 4.63160e18 | 1.26160 | ||||||||
\(719\) | 1.20782e18 | 0.326034 | 0.163017 | − | 0.986623i | \(-0.447877\pi\) | ||||
0.163017 | + | 0.986623i | \(0.447877\pi\) | |||||||
\(720\) | 7.19314e17 | 0.192423 | ||||||||
\(721\) | −3.47251e18 | −0.920586 | ||||||||
\(722\) | 1.79319e18 | 0.471123 | ||||||||
\(723\) | 7.49966e17 | 0.195273 | ||||||||
\(724\) | −1.75127e18 | −0.451911 | ||||||||
\(725\) | 9.72135e17 | 0.248616 | ||||||||
\(726\) | 1.47610e18 | 0.374133 | ||||||||
\(727\) | 1.12668e17 | 0.0283025 | 0.0141513 | − | 0.999900i | \(-0.495495\pi\) | ||||
0.0141513 | + | 0.999900i | \(0.495495\pi\) | |||||||
\(728\) | −6.66748e17 | −0.166000 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −3.97419e18 | −0.971964 | ||||||||
\(731\) | −1.44808e18 | −0.351019 | ||||||||
\(732\) | 1.46495e18 | 0.351965 | ||||||||
\(733\) | 1.73665e18 | 0.413558 | 0.206779 | − | 0.978388i | \(-0.433702\pi\) | ||||
0.206779 | + | 0.978388i | \(0.433702\pi\) | |||||||
\(734\) | 2.83698e18 | 0.669626 | ||||||||
\(735\) | 1.10844e18 | 0.259326 | ||||||||
\(736\) | 4.87733e18 | 1.13104 | ||||||||
\(737\) | 7.22314e18 | 1.66030 | ||||||||
\(738\) | −1.09138e18 | −0.248661 | ||||||||
\(739\) | −2.36418e18 | −0.533938 | −0.266969 | − | 0.963705i | \(-0.586022\pi\) | ||||
−0.266969 | + | 0.963705i | \(0.586022\pi\) | |||||||
\(740\) | −2.55638e18 | −0.572295 | ||||||||
\(741\) | 2.15433e17 | 0.0478072 | ||||||||
\(742\) | −3.45349e18 | −0.759684 | ||||||||
\(743\) | 1.01901e18 | 0.222204 | 0.111102 | − | 0.993809i | \(-0.464562\pi\) | ||||
0.111102 | + | 0.993809i | \(0.464562\pi\) | |||||||
\(744\) | 3.77735e18 | 0.816513 | ||||||||
\(745\) | −3.54869e18 | −0.760418 | ||||||||
\(746\) | 2.27020e18 | 0.482238 | ||||||||
\(747\) | 4.04750e17 | 0.0852320 | ||||||||
\(748\) | 1.43431e18 | 0.299422 | ||||||||
\(749\) | −4.27778e18 | −0.885292 | ||||||||
\(750\) | 2.03069e18 | 0.416626 | ||||||||
\(751\) | 6.47444e18 | 1.31687 | 0.658435 | − | 0.752638i | \(-0.271219\pi\) | ||||
0.658435 | + | 0.752638i | \(0.271219\pi\) | |||||||
\(752\) | −2.40109e18 | −0.484163 | ||||||||
\(753\) | −4.45761e18 | −0.891118 | ||||||||
\(754\) | 7.36043e17 | 0.145878 | ||||||||
\(755\) | 5.49639e18 | 1.08000 | ||||||||
\(756\) | 4.07919e17 | 0.0794663 | ||||||||
\(757\) | 7.01680e17 | 0.135524 | 0.0677620 | − | 0.997702i | \(-0.478414\pi\) | ||||
0.0677620 | + | 0.997702i | \(0.478414\pi\) | |||||||
\(758\) | 3.01001e18 | 0.576392 | ||||||||
\(759\) | −7.01151e18 | −1.33119 | ||||||||
\(760\) | −4.04976e18 | −0.762326 | ||||||||
\(761\) | −2.94718e18 | −0.550055 | −0.275028 | − | 0.961436i | \(-0.588687\pi\) | ||||
−0.275028 | + | 0.961436i | \(0.588687\pi\) | |||||||
\(762\) | 1.05882e18 | 0.195936 | ||||||||
\(763\) | 5.25171e18 | 0.963587 | ||||||||
\(764\) | 3.64993e18 | 0.664014 | ||||||||
\(765\) | −1.28755e18 | −0.232254 | ||||||||
\(766\) | 4.21053e17 | 0.0753095 | ||||||||
\(767\) | 9.41437e16 | 0.0166963 | ||||||||
\(768\) | 2.95997e18 | 0.520522 | ||||||||
\(769\) | 1.14106e17 | 0.0198970 | 0.00994848 | − | 0.999951i | \(-0.496833\pi\) | ||||
0.00994848 | + | 0.999951i | \(0.496833\pi\) | |||||||
\(770\) | −8.09102e18 | −1.39899 | ||||||||
\(771\) | 2.66805e17 | 0.0457446 | ||||||||
\(772\) | −1.13848e18 | −0.193560 | ||||||||
\(773\) | −3.74426e18 | −0.631247 | −0.315624 | − | 0.948884i | \(-0.602214\pi\) | ||||
−0.315624 | + | 0.948884i | \(0.602214\pi\) | |||||||
\(774\) | 8.80301e17 | 0.147169 | ||||||||
\(775\) | −1.38397e18 | −0.229439 | ||||||||
\(776\) | 9.24670e18 | 1.52015 | ||||||||
\(777\) | 6.39875e18 | 1.04318 | ||||||||
\(778\) | 3.62294e18 | 0.585725 | ||||||||
\(779\) | 3.71836e18 | 0.596153 | ||||||||
\(780\) | 1.75404e17 | 0.0278885 | ||||||||
\(781\) | −1.17419e19 | −1.85143 | ||||||||
\(782\) | 5.70045e18 | 0.891385 | ||||||||
\(783\) | −1.74717e18 | −0.270946 | ||||||||
\(784\) | −1.43289e18 | −0.220374 | ||||||||
\(785\) | −7.08181e18 | −1.08017 | ||||||||
\(786\) | −1.08716e17 | −0.0164454 | ||||||||
\(787\) | −6.36658e18 | −0.955147 | −0.477574 | − | 0.878592i | \(-0.658484\pi\) | ||||
−0.477574 | + | 0.878592i | \(0.658484\pi\) | |||||||
\(788\) | −2.20947e18 | −0.328751 | ||||||||
\(789\) | 7.58346e18 | 1.11909 | ||||||||
\(790\) | 2.73895e18 | 0.400874 | ||||||||
\(791\) | −1.49563e18 | −0.217109 | ||||||||
\(792\) | −3.38298e18 | −0.487064 | ||||||||
\(793\) | −1.57673e18 | −0.225155 | ||||||||
\(794\) | −7.84565e18 | −1.11121 | ||||||||
\(795\) | 3.52497e18 | 0.495186 | ||||||||
\(796\) | −3.26563e18 | −0.455022 | ||||||||
\(797\) | −3.45409e18 | −0.477369 | −0.238685 | − | 0.971097i | \(-0.576716\pi\) | ||||
−0.238685 | + | 0.971097i | \(0.576716\pi\) | |||||||
\(798\) | 2.61265e18 | 0.358148 | ||||||||
\(799\) | 4.29786e18 | 0.584383 | ||||||||
\(800\) | −8.62206e17 | −0.116286 | ||||||||
\(801\) | 2.60287e18 | 0.348210 | ||||||||
\(802\) | −4.40512e18 | −0.584553 | ||||||||
\(803\) | 1.13109e19 | 1.48883 | ||||||||
\(804\) | −1.89903e18 | −0.247952 | ||||||||
\(805\) | 1.71057e19 | 2.21547 | ||||||||
\(806\) | −1.04786e18 | −0.134625 | ||||||||
\(807\) | 5.74400e17 | 0.0732042 | ||||||||
\(808\) | 1.26939e19 | 1.60480 | ||||||||
\(809\) | 4.79330e18 | 0.601131 | 0.300565 | − | 0.953761i | \(-0.402825\pi\) | ||||
0.300565 | + | 0.953761i | \(0.402825\pi\) | |||||||
\(810\) | 7.82709e17 | 0.0973750 | ||||||||
\(811\) | −5.15289e17 | −0.0635938 | −0.0317969 | − | 0.999494i | \(-0.510123\pi\) | ||||
−0.0317969 | + | 0.999494i | \(0.510123\pi\) | |||||||
\(812\) | −4.74836e18 | −0.581338 | ||||||||
\(813\) | −6.00889e18 | −0.729803 | ||||||||
\(814\) | −1.36774e19 | −1.64795 | ||||||||
\(815\) | 1.34290e19 | 1.60516 | ||||||||
\(816\) | 1.66442e18 | 0.197368 | ||||||||
\(817\) | −2.99922e18 | −0.352830 | ||||||||
\(818\) | −1.10953e18 | −0.129492 | ||||||||
\(819\) | −4.39046e17 | −0.0508352 | ||||||||
\(820\) | 3.02747e18 | 0.347768 | ||||||||
\(821\) | −1.24790e19 | −1.42217 | −0.711083 | − | 0.703108i | \(-0.751795\pi\) | ||||
−0.711083 | + | 0.703108i | \(0.751795\pi\) | |||||||
\(822\) | 7.59514e18 | 0.858754 | ||||||||
\(823\) | 2.93432e18 | 0.329161 | 0.164580 | − | 0.986364i | \(-0.447373\pi\) | ||||
0.164580 | + | 0.986364i | \(0.447373\pi\) | |||||||
\(824\) | −7.57138e18 | −0.842651 | ||||||||
\(825\) | 1.23948e18 | 0.136864 | ||||||||
\(826\) | 1.14172e18 | 0.125081 | ||||||||
\(827\) | −2.37820e18 | −0.258501 | −0.129251 | − | 0.991612i | \(-0.541257\pi\) | ||||
−0.129251 | + | 0.991612i | \(0.541257\pi\) | |||||||
\(828\) | 1.84339e18 | 0.198802 | ||||||||
\(829\) | 1.36509e19 | 1.46069 | 0.730345 | − | 0.683078i | \(-0.239359\pi\) | ||||
0.730345 | + | 0.683078i | \(0.239359\pi\) | |||||||
\(830\) | 2.11068e18 | 0.224086 | ||||||||
\(831\) | −8.81527e18 | −0.928600 | ||||||||
\(832\) | −1.30581e18 | −0.136483 | ||||||||
\(833\) | 2.56483e18 | 0.265990 | ||||||||
\(834\) | −7.61574e18 | −0.783669 | ||||||||
\(835\) | 1.26335e19 | 1.28991 | ||||||||
\(836\) | 2.97070e18 | 0.300966 | ||||||||
\(837\) | 2.48734e18 | 0.250046 | ||||||||
\(838\) | −4.75836e18 | −0.474648 | ||||||||
\(839\) | −1.24402e19 | −1.23133 | −0.615666 | − | 0.788007i | \(-0.711113\pi\) | ||||
−0.615666 | + | 0.788007i | \(0.711113\pi\) | |||||||
\(840\) | 8.25329e18 | 0.810610 | ||||||||
\(841\) | 1.00771e19 | 0.982115 | ||||||||
\(842\) | −3.60278e18 | −0.348425 | ||||||||
\(843\) | 4.45512e18 | 0.427543 | ||||||||
\(844\) | −4.21500e18 | −0.401395 | ||||||||
\(845\) | 1.12896e19 | 1.06687 | ||||||||
\(846\) | −2.61270e18 | −0.245009 | ||||||||
\(847\) | 1.02492e19 | 0.953779 | ||||||||
\(848\) | −4.55675e18 | −0.420807 | ||||||||
\(849\) | 6.14683e18 | 0.563315 | ||||||||
\(850\) | −1.00772e18 | −0.0916463 | ||||||||
\(851\) | 2.89160e19 | 2.60974 | ||||||||
\(852\) | 3.08706e18 | 0.276496 | ||||||||
\(853\) | 1.46204e19 | 1.29955 | 0.649773 | − | 0.760128i | \(-0.274864\pi\) | ||||
0.649773 | + | 0.760128i | \(0.274864\pi\) | |||||||
\(854\) | −1.91217e19 | −1.68675 | ||||||||
\(855\) | −2.66672e18 | −0.233452 | ||||||||
\(856\) | −9.32716e18 | −0.810345 | ||||||||
\(857\) | −2.56019e18 | −0.220748 | −0.110374 | − | 0.993890i | \(-0.535205\pi\) | ||||
−0.110374 | + | 0.993890i | \(0.535205\pi\) | |||||||
\(858\) | 9.38463e17 | 0.0803063 | ||||||||
\(859\) | −2.08392e19 | −1.76981 | −0.884904 | − | 0.465773i | \(-0.845776\pi\) | ||||
−0.884904 | + | 0.465773i | \(0.845776\pi\) | |||||||
\(860\) | −2.44195e18 | −0.205825 | ||||||||
\(861\) | −7.57791e18 | −0.633912 | ||||||||
\(862\) | −4.26013e18 | −0.353693 | ||||||||
\(863\) | 1.35776e17 | 0.0111880 | 0.00559401 | − | 0.999984i | \(-0.498219\pi\) | ||||
0.00559401 | + | 0.999984i | \(0.498219\pi\) | |||||||
\(864\) | 1.54960e18 | 0.126730 | ||||||||
\(865\) | −1.27713e19 | −1.03664 | ||||||||
\(866\) | 3.92149e18 | 0.315925 | ||||||||
\(867\) | 4.24118e18 | 0.339127 | ||||||||
\(868\) | 6.75997e18 | 0.536496 | ||||||||
\(869\) | −7.79527e18 | −0.614048 | ||||||||
\(870\) | −9.11107e18 | −0.712351 | ||||||||
\(871\) | 2.04394e18 | 0.158617 | ||||||||
\(872\) | 1.14507e19 | 0.882012 | ||||||||
\(873\) | 6.08885e18 | 0.465525 | ||||||||
\(874\) | 1.18066e19 | 0.895983 | ||||||||
\(875\) | 1.41000e19 | 1.06210 | ||||||||
\(876\) | −2.97374e18 | −0.222344 | ||||||||
\(877\) | −1.38538e19 | −1.02819 | −0.514094 | − | 0.857734i | \(-0.671872\pi\) | ||||
−0.514094 | + | 0.857734i | \(0.671872\pi\) | |||||||
\(878\) | 1.51777e19 | 1.11813 | ||||||||
\(879\) | 7.95164e18 | 0.581472 | ||||||||
\(880\) | −1.06758e19 | −0.774932 | ||||||||
\(881\) | 2.39062e19 | 1.72253 | 0.861266 | − | 0.508154i | \(-0.169672\pi\) | ||||
0.861266 | + | 0.508154i | \(0.169672\pi\) | |||||||
\(882\) | −1.55918e18 | −0.111519 | ||||||||
\(883\) | −1.46923e19 | −1.04314 | −0.521572 | − | 0.853207i | \(-0.674654\pi\) | ||||
−0.521572 | + | 0.853207i | \(0.674654\pi\) | |||||||
\(884\) | 4.05869e17 | 0.0286053 | ||||||||
\(885\) | −1.16535e18 | −0.0815316 | ||||||||
\(886\) | 5.38790e17 | 0.0374197 | ||||||||
\(887\) | −1.54616e19 | −1.06598 | −0.532992 | − | 0.846120i | \(-0.678932\pi\) | ||||
−0.532992 | + | 0.846120i | \(0.678932\pi\) | |||||||
\(888\) | 1.39517e19 | 0.954865 | ||||||||
\(889\) | 7.35184e18 | 0.499499 | ||||||||
\(890\) | 1.35734e19 | 0.915488 | ||||||||
\(891\) | −2.22765e18 | −0.149157 | ||||||||
\(892\) | −6.47750e18 | −0.430562 | ||||||||
\(893\) | 8.90157e18 | 0.587398 | ||||||||
\(894\) | 4.99173e18 | 0.327007 | ||||||||
\(895\) | 1.83451e19 | 1.19308 | ||||||||
\(896\) | −3.70784e18 | −0.239397 | ||||||||
\(897\) | −1.98405e18 | −0.127175 | ||||||||
\(898\) | −1.13267e19 | −0.720787 | ||||||||
\(899\) | −2.89537e19 | −1.82922 | ||||||||
\(900\) | −3.25872e17 | −0.0204395 | ||||||||
\(901\) | 8.15643e18 | 0.507912 | ||||||||
\(902\) | 1.61978e19 | 1.00142 | ||||||||
\(903\) | 6.11233e18 | 0.375177 | ||||||||
\(904\) | −3.26104e18 | −0.198729 | ||||||||
\(905\) | −2.33322e19 | −1.41169 | ||||||||
\(906\) | −7.73143e18 | −0.464437 | ||||||||
\(907\) | 5.27965e17 | 0.0314889 | 0.0157445 | − | 0.999876i | \(-0.494988\pi\) | ||||
0.0157445 | + | 0.999876i | \(0.494988\pi\) | |||||||
\(908\) | 2.39583e18 | 0.141872 | ||||||||
\(909\) | 8.35880e18 | 0.491449 | ||||||||
\(910\) | −2.28952e18 | −0.133652 | ||||||||
\(911\) | −1.52230e19 | −0.882328 | −0.441164 | − | 0.897427i | \(-0.645434\pi\) | ||||
−0.441164 | + | 0.897427i | \(0.645434\pi\) | |||||||
\(912\) | 3.44729e18 | 0.198386 | ||||||||
\(913\) | −6.00716e18 | −0.343249 | ||||||||
\(914\) | 1.89426e19 | 1.07470 | ||||||||
\(915\) | 1.95174e19 | 1.09948 | ||||||||
\(916\) | 5.92313e18 | 0.331307 | ||||||||
\(917\) | −7.54862e17 | −0.0419244 | ||||||||
\(918\) | 1.81111e18 | 0.0998776 | ||||||||
\(919\) | −3.07666e19 | −1.68472 | −0.842361 | − | 0.538914i | \(-0.818835\pi\) | ||||
−0.842361 | + | 0.538914i | \(0.818835\pi\) | |||||||
\(920\) | 3.72967e19 | 2.02792 | ||||||||
\(921\) | 3.96638e17 | 0.0214144 | ||||||||
\(922\) | −9.15067e18 | −0.490571 | ||||||||
\(923\) | −3.32262e18 | −0.176876 | ||||||||
\(924\) | −6.05420e18 | −0.320029 | ||||||||
\(925\) | −5.11172e18 | −0.268316 | ||||||||
\(926\) | 4.85468e18 | 0.253040 | ||||||||
\(927\) | −4.98567e18 | −0.258051 | ||||||||
\(928\) | −1.80380e19 | −0.927097 | ||||||||
\(929\) | 2.97721e19 | 1.51952 | 0.759762 | − | 0.650201i | \(-0.225315\pi\) | ||||
0.759762 | + | 0.650201i | \(0.225315\pi\) | |||||||
\(930\) | 1.29709e19 | 0.657403 | ||||||||
\(931\) | 5.31218e18 | 0.267362 | ||||||||
\(932\) | 1.21814e19 | 0.608828 | ||||||||
\(933\) | −2.04998e19 | −1.01746 | ||||||||
\(934\) | −1.02926e19 | −0.507304 | ||||||||
\(935\) | 1.91093e19 | 0.935341 | ||||||||
\(936\) | −9.57284e17 | −0.0465316 | ||||||||
\(937\) | 1.13196e19 | 0.546416 | 0.273208 | − | 0.961955i | \(-0.411915\pi\) | ||||
0.273208 | + | 0.961955i | \(0.411915\pi\) | |||||||
\(938\) | 2.47877e19 | 1.18828 | ||||||||
\(939\) | 1.58536e19 | 0.754748 | ||||||||
\(940\) | 7.24762e18 | 0.342661 | ||||||||
\(941\) | −1.83852e19 | −0.863246 | −0.431623 | − | 0.902054i | \(-0.642059\pi\) | ||||
−0.431623 | + | 0.902054i | \(0.642059\pi\) | |||||||
\(942\) | 9.96155e18 | 0.464511 | ||||||||
\(943\) | −3.42447e19 | −1.58587 | ||||||||
\(944\) | 1.50646e18 | 0.0692851 | ||||||||
\(945\) | 5.43470e18 | 0.248238 | ||||||||
\(946\) | −1.30651e19 | −0.592682 | ||||||||
\(947\) | 9.10215e17 | 0.0410080 | 0.0205040 | − | 0.999790i | \(-0.493473\pi\) | ||||
0.0205040 | + | 0.999790i | \(0.493473\pi\) | |||||||
\(948\) | 2.04945e18 | 0.0917029 | ||||||||
\(949\) | 3.20065e18 | 0.142235 | ||||||||
\(950\) | −2.08715e18 | −0.0921190 | ||||||||
\(951\) | −1.64047e19 | −0.719109 | ||||||||
\(952\) | 1.90973e19 | 0.831443 | ||||||||
\(953\) | −3.11203e19 | −1.34567 | −0.672836 | − | 0.739791i | \(-0.734924\pi\) | ||||
−0.672836 | + | 0.739791i | \(0.734924\pi\) | |||||||
\(954\) | −4.95835e18 | −0.212948 | ||||||||
\(955\) | 4.86279e19 | 2.07426 | ||||||||
\(956\) | −9.96923e17 | −0.0422362 | ||||||||
\(957\) | 2.59308e19 | 1.09116 | ||||||||
\(958\) | 1.77520e19 | 0.741946 | ||||||||
\(959\) | 5.27365e19 | 2.18922 | ||||||||
\(960\) | 1.61639e19 | 0.666475 | ||||||||
\(961\) | 1.68022e19 | 0.688121 | ||||||||
\(962\) | −3.87029e18 | −0.157437 | ||||||||
\(963\) | −6.14183e18 | −0.248157 | ||||||||
\(964\) | 2.92638e18 | 0.117444 | ||||||||
\(965\) | −1.51680e19 | −0.604645 | ||||||||
\(966\) | −2.40615e19 | −0.952732 | ||||||||
\(967\) | −4.19261e19 | −1.64897 | −0.824484 | − | 0.565885i | \(-0.808535\pi\) | ||||
−0.824484 | + | 0.565885i | \(0.808535\pi\) | |||||||
\(968\) | 2.23471e19 | 0.873034 | ||||||||
\(969\) | −6.17053e18 | −0.239452 | ||||||||
\(970\) | 3.17520e19 | 1.22392 | ||||||||
\(971\) | 2.85140e19 | 1.09178 | 0.545888 | − | 0.837858i | \(-0.316193\pi\) | ||||
0.545888 | + | 0.837858i | \(0.316193\pi\) | |||||||
\(972\) | 5.85671e17 | 0.0222753 | ||||||||
\(973\) | −5.28795e19 | −1.99781 | ||||||||
\(974\) | 1.82629e19 | 0.685389 | ||||||||
\(975\) | 3.50737e17 | 0.0130753 | ||||||||
\(976\) | −2.52304e19 | −0.934329 | ||||||||
\(977\) | −3.32048e19 | −1.22148 | −0.610740 | − | 0.791831i | \(-0.709128\pi\) | ||||
−0.610740 | + | 0.791831i | \(0.709128\pi\) | |||||||
\(978\) | −1.88898e19 | −0.690278 | ||||||||
\(979\) | −3.86309e19 | −1.40232 | ||||||||
\(980\) | 4.32516e18 | 0.155967 | ||||||||
\(981\) | 7.54015e18 | 0.270104 | ||||||||
\(982\) | −3.98552e19 | −1.41827 | ||||||||
\(983\) | −1.48141e19 | −0.523695 | −0.261848 | − | 0.965109i | \(-0.584332\pi\) | ||||
−0.261848 | + | 0.965109i | \(0.584332\pi\) | |||||||
\(984\) | −1.65227e19 | −0.580247 | ||||||||
\(985\) | −2.94367e19 | −1.02696 | ||||||||
\(986\) | −2.10821e19 | −0.730658 | ||||||||
\(987\) | −1.81412e19 | −0.624602 | ||||||||
\(988\) | 8.40621e17 | 0.0287528 | ||||||||
\(989\) | 2.76217e19 | 0.938586 | ||||||||
\(990\) | −1.16167e19 | −0.392152 | ||||||||
\(991\) | −2.81327e19 | −0.943479 | −0.471739 | − | 0.881738i | \(-0.656374\pi\) | ||||
−0.471739 | + | 0.881738i | \(0.656374\pi\) | |||||||
\(992\) | 2.56796e19 | 0.855584 | ||||||||
\(993\) | −8.16382e18 | −0.270224 | ||||||||
\(994\) | −4.02949e19 | −1.32507 | ||||||||
\(995\) | −4.35079e19 | −1.42141 | ||||||||
\(996\) | 1.57934e18 | 0.0512613 | ||||||||
\(997\) | 2.19082e19 | 0.706461 | 0.353230 | − | 0.935536i | \(-0.385083\pi\) | ||||
0.353230 | + | 0.935536i | \(0.385083\pi\) | |||||||
\(998\) | −1.91779e19 | −0.614401 | ||||||||
\(999\) | 9.18702e18 | 0.292415 |
(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 | 177.14.a.b.1.10 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.b.1.10 | ✓ | 31 | 1.1 | even | 1 | trivial |