Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,82,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 82, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 82);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 82 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(41.5501285538\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3 x^{5} + \cdots - 27\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{58}\cdot 3^{26}\cdot 5^{7}\cdot 7^{3}\cdot 13 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.73117e10\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.41607e12 | 1.55380 | 0.776900 | − | 0.629624i | \(-0.216791\pi\) | ||||
0.776900 | + | 0.629624i | \(0.216791\pi\) | |||||||
\(3\) | −1.10180e19 | −0.523227 | −0.261613 | − | 0.965173i | \(-0.584255\pi\) | ||||
−0.261613 | + | 0.965173i | \(0.584255\pi\) | |||||||
\(4\) | 3.41956e24 | 1.41430 | ||||||||
\(5\) | −1.95525e27 | −0.0961427 | −0.0480713 | − | 0.998844i | \(-0.515307\pi\) | ||||
−0.0480713 | + | 0.998844i | \(0.515307\pi\) | |||||||
\(6\) | −2.66202e31 | −0.812990 | ||||||||
\(7\) | 1.09563e34 | 0.650418 | 0.325209 | − | 0.945642i | \(-0.394565\pi\) | ||||
0.325209 | + | 0.945642i | \(0.394565\pi\) | |||||||
\(8\) | 2.42020e36 | 0.643734 | ||||||||
\(9\) | −3.22031e38 | −0.726234 | ||||||||
\(10\) | −4.72402e39 | −0.149387 | ||||||||
\(11\) | −2.45659e42 | −1.63655 | −0.818275 | − | 0.574827i | \(-0.805069\pi\) | ||||
−0.818275 | + | 0.574827i | \(0.805069\pi\) | |||||||
\(12\) | −3.76765e43 | −0.739998 | ||||||||
\(13\) | 1.04827e45 | 0.804947 | 0.402473 | − | 0.915432i | \(-0.368151\pi\) | ||||
0.402473 | + | 0.915432i | \(0.368151\pi\) | |||||||
\(14\) | 2.64712e46 | 1.01062 | ||||||||
\(15\) | 2.15428e46 | 0.0503044 | ||||||||
\(16\) | −2.42061e48 | −0.414062 | ||||||||
\(17\) | 7.60247e49 | 1.11628 | 0.558140 | − | 0.829747i | \(-0.311515\pi\) | ||||
0.558140 | + | 0.829747i | \(0.311515\pi\) | |||||||
\(18\) | −7.78051e50 | −1.12842 | ||||||||
\(19\) | −5.17134e51 | −0.839620 | −0.419810 | − | 0.907612i | \(-0.637903\pi\) | ||||
−0.419810 | + | 0.907612i | \(0.637903\pi\) | |||||||
\(20\) | −6.68608e51 | −0.135974 | ||||||||
\(21\) | −1.20716e53 | −0.340316 | ||||||||
\(22\) | −5.93531e54 | −2.54287 | ||||||||
\(23\) | −1.96011e55 | −1.38772 | −0.693861 | − | 0.720109i | \(-0.744092\pi\) | ||||
−0.693861 | + | 0.720109i | \(0.744092\pi\) | |||||||
\(24\) | −2.66656e55 | −0.336819 | ||||||||
\(25\) | −4.09767e56 | −0.990757 | ||||||||
\(26\) | 2.53270e57 | 1.25073 | ||||||||
\(27\) | 8.43378e57 | 0.903212 | ||||||||
\(28\) | 3.74656e58 | 0.919884 | ||||||||
\(29\) | −7.07167e58 | −0.419183 | −0.209591 | − | 0.977789i | \(-0.567213\pi\) | ||||
−0.209591 | + | 0.977789i | \(0.567213\pi\) | |||||||
\(30\) | 5.20490e58 | 0.0781631 | ||||||||
\(31\) | −3.03406e60 | −1.20747 | −0.603735 | − | 0.797185i | \(-0.706321\pi\) | ||||
−0.603735 | + | 0.797185i | \(0.706321\pi\) | |||||||
\(32\) | −1.17001e61 | −1.28710 | ||||||||
\(33\) | 2.70666e61 | 0.856287 | ||||||||
\(34\) | 1.83681e62 | 1.73448 | ||||||||
\(35\) | −2.14222e61 | −0.0625329 | ||||||||
\(36\) | −1.10120e63 | −1.02711 | ||||||||
\(37\) | 3.76143e62 | 0.115660 | 0.0578300 | − | 0.998326i | \(-0.481582\pi\) | ||||
0.0578300 | + | 0.998326i | \(0.481582\pi\) | |||||||
\(38\) | −1.24943e64 | −1.30460 | ||||||||
\(39\) | −1.15498e64 | −0.421170 | ||||||||
\(40\) | −4.73208e63 | −0.0618903 | ||||||||
\(41\) | 1.34796e65 | 0.648531 | 0.324266 | − | 0.945966i | \(-0.394883\pi\) | ||||
0.324266 | + | 0.945966i | \(0.394883\pi\) | |||||||
\(42\) | −2.91658e65 | −0.528784 | ||||||||
\(43\) | −2.04430e66 | −1.42913 | −0.714566 | − | 0.699568i | \(-0.753376\pi\) | ||||
−0.714566 | + | 0.699568i | \(0.753376\pi\) | |||||||
\(44\) | −8.40046e66 | −2.31457 | ||||||||
\(45\) | 6.29650e65 | 0.0698220 | ||||||||
\(46\) | −4.73576e67 | −2.15624 | ||||||||
\(47\) | 2.88861e67 | 0.550460 | 0.275230 | − | 0.961378i | \(-0.411246\pi\) | ||||
0.275230 | + | 0.961378i | \(0.411246\pi\) | |||||||
\(48\) | 2.66702e67 | 0.216649 | ||||||||
\(49\) | −1.63713e68 | −0.576956 | ||||||||
\(50\) | −9.90028e68 | −1.53944 | ||||||||
\(51\) | −8.37636e68 | −0.584068 | ||||||||
\(52\) | 3.58462e69 | 1.13843 | ||||||||
\(53\) | 8.48669e69 | 1.24614 | 0.623068 | − | 0.782168i | \(-0.285886\pi\) | ||||
0.623068 | + | 0.782168i | \(0.285886\pi\) | |||||||
\(54\) | 2.03766e70 | 1.40341 | ||||||||
\(55\) | 4.80324e69 | 0.157342 | ||||||||
\(56\) | 2.65164e70 | 0.418696 | ||||||||
\(57\) | 5.69776e70 | 0.439312 | ||||||||
\(58\) | −1.70857e71 | −0.651326 | ||||||||
\(59\) | −4.61708e71 | −0.880767 | −0.440383 | − | 0.897810i | \(-0.645157\pi\) | ||||
−0.440383 | + | 0.897810i | \(0.645157\pi\) | |||||||
\(60\) | 7.36669e70 | 0.0711454 | ||||||||
\(61\) | 2.95815e72 | 1.46272 | 0.731361 | − | 0.681991i | \(-0.238886\pi\) | ||||
0.731361 | + | 0.681991i | \(0.238886\pi\) | |||||||
\(62\) | −7.33052e72 | −1.87617 | ||||||||
\(63\) | −3.52826e72 | −0.472355 | ||||||||
\(64\) | −2.24155e73 | −1.58584 | ||||||||
\(65\) | −2.04962e72 | −0.0773897 | ||||||||
\(66\) | 6.53949e73 | 1.33050 | ||||||||
\(67\) | 1.59714e73 | 0.176731 | 0.0883654 | − | 0.996088i | \(-0.471836\pi\) | ||||
0.0883654 | + | 0.996088i | \(0.471836\pi\) | |||||||
\(68\) | 2.59971e74 | 1.57875 | ||||||||
\(69\) | 2.15964e74 | 0.726094 | ||||||||
\(70\) | −5.17577e73 | −0.0971637 | ||||||||
\(71\) | −7.76456e74 | −0.820641 | −0.410321 | − | 0.911941i | \(-0.634583\pi\) | ||||
−0.410321 | + | 0.911941i | \(0.634583\pi\) | |||||||
\(72\) | −7.79379e74 | −0.467501 | ||||||||
\(73\) | 1.29321e74 | 0.0443705 | 0.0221853 | − | 0.999754i | \(-0.492938\pi\) | ||||
0.0221853 | + | 0.999754i | \(0.492938\pi\) | |||||||
\(74\) | 9.08789e74 | 0.179713 | ||||||||
\(75\) | 4.51480e75 | 0.518391 | ||||||||
\(76\) | −1.76837e76 | −1.18747 | ||||||||
\(77\) | −2.69151e76 | −1.06444 | ||||||||
\(78\) | −2.79051e76 | −0.654414 | ||||||||
\(79\) | 8.99349e76 | 1.25902 | 0.629508 | − | 0.776994i | \(-0.283257\pi\) | ||||
0.629508 | + | 0.776994i | \(0.283257\pi\) | |||||||
\(80\) | 4.73289e75 | 0.0398091 | ||||||||
\(81\) | 4.98742e76 | 0.253649 | ||||||||
\(82\) | 3.25677e77 | 1.00769 | ||||||||
\(83\) | 8.55650e77 | 1.62044 | 0.810221 | − | 0.586125i | \(-0.199347\pi\) | ||||
0.810221 | + | 0.586125i | \(0.199347\pi\) | |||||||
\(84\) | −4.12795e77 | −0.481308 | ||||||||
\(85\) | −1.48647e77 | −0.107322 | ||||||||
\(86\) | −4.93918e78 | −2.22059 | ||||||||
\(87\) | 7.79153e77 | 0.219328 | ||||||||
\(88\) | −5.94544e78 | −1.05350 | ||||||||
\(89\) | 1.10189e79 | 1.23550 | 0.617750 | − | 0.786375i | \(-0.288045\pi\) | ||||
0.617750 | + | 0.786375i | \(0.288045\pi\) | |||||||
\(90\) | 1.52128e78 | 0.108490 | ||||||||
\(91\) | 1.14851e79 | 0.523552 | ||||||||
\(92\) | −6.70270e79 | −1.96265 | ||||||||
\(93\) | 3.34292e79 | 0.631780 | ||||||||
\(94\) | 6.97910e79 | 0.855306 | ||||||||
\(95\) | 1.01112e79 | 0.0807233 | ||||||||
\(96\) | 1.28911e80 | 0.673448 | ||||||||
\(97\) | 3.05910e80 | 1.05036 | 0.525181 | − | 0.850991i | \(-0.323998\pi\) | ||||
0.525181 | + | 0.850991i | \(0.323998\pi\) | |||||||
\(98\) | −3.95544e80 | −0.896475 | ||||||||
\(99\) | 7.91099e80 | 1.18852 | ||||||||
\(100\) | −1.40122e81 | −1.40122 | ||||||||
\(101\) | −2.73530e81 | −1.82806 | −0.914028 | − | 0.405651i | \(-0.867045\pi\) | ||||
−0.914028 | + | 0.405651i | \(0.867045\pi\) | |||||||
\(102\) | −2.02379e81 | −0.907525 | ||||||||
\(103\) | 2.59921e81 | 0.785116 | 0.392558 | − | 0.919727i | \(-0.371590\pi\) | ||||
0.392558 | + | 0.919727i | \(0.371590\pi\) | |||||||
\(104\) | 2.53702e81 | 0.518171 | ||||||||
\(105\) | 2.36029e80 | 0.0327189 | ||||||||
\(106\) | 2.05045e82 | 1.93625 | ||||||||
\(107\) | −2.21960e82 | −1.43296 | −0.716478 | − | 0.697610i | \(-0.754247\pi\) | ||||
−0.716478 | + | 0.697610i | \(0.754247\pi\) | |||||||
\(108\) | 2.88398e82 | 1.27741 | ||||||||
\(109\) | −1.81444e82 | −0.553311 | −0.276656 | − | 0.960969i | \(-0.589226\pi\) | ||||
−0.276656 | + | 0.960969i | \(0.589226\pi\) | |||||||
\(110\) | 1.16050e82 | 0.244478 | ||||||||
\(111\) | −4.14432e81 | −0.0605164 | ||||||||
\(112\) | −2.65209e82 | −0.269314 | ||||||||
\(113\) | −1.03987e83 | −0.736718 | −0.368359 | − | 0.929684i | \(-0.620080\pi\) | ||||
−0.368359 | + | 0.929684i | \(0.620080\pi\) | |||||||
\(114\) | 1.37662e83 | 0.682603 | ||||||||
\(115\) | 3.83249e82 | 0.133419 | ||||||||
\(116\) | −2.41820e83 | −0.592848 | ||||||||
\(117\) | −3.37575e83 | −0.584579 | ||||||||
\(118\) | −1.11552e84 | −1.36854 | ||||||||
\(119\) | 8.32948e83 | 0.726049 | ||||||||
\(120\) | 5.21378e82 | 0.0323827 | ||||||||
\(121\) | 3.78160e84 | 1.67830 | ||||||||
\(122\) | 7.14711e84 | 2.27278 | ||||||||
\(123\) | −1.48518e84 | −0.339329 | ||||||||
\(124\) | −1.03752e85 | −1.70772 | ||||||||
\(125\) | 1.60987e84 | 0.191397 | ||||||||
\(126\) | −8.52455e84 | −0.733946 | ||||||||
\(127\) | −4.55702e84 | −0.284859 | −0.142430 | − | 0.989805i | \(-0.545491\pi\) | ||||
−0.142430 | + | 0.989805i | \(0.545491\pi\) | |||||||
\(128\) | −2.58685e85 | −1.17698 | ||||||||
\(129\) | 2.25240e85 | 0.747760 | ||||||||
\(130\) | −4.95204e84 | −0.120248 | ||||||||
\(131\) | −2.83953e83 | −0.00505544 | −0.00252772 | − | 0.999997i | \(-0.500805\pi\) | ||||
−0.00252772 | + | 0.999997i | \(0.500805\pi\) | |||||||
\(132\) | 9.25559e85 | 1.21104 | ||||||||
\(133\) | −5.66587e85 | −0.546104 | ||||||||
\(134\) | 3.85880e85 | 0.274605 | ||||||||
\(135\) | −1.64901e85 | −0.0868372 | ||||||||
\(136\) | 1.83995e86 | 0.718587 | ||||||||
\(137\) | −4.69797e86 | −1.36373 | −0.681863 | − | 0.731480i | \(-0.738830\pi\) | ||||
−0.681863 | + | 0.731480i | \(0.738830\pi\) | |||||||
\(138\) | 5.21784e86 | 1.12820 | ||||||||
\(139\) | 5.71964e86 | 0.923144 | 0.461572 | − | 0.887103i | \(-0.347286\pi\) | ||||
0.461572 | + | 0.887103i | \(0.347286\pi\) | |||||||
\(140\) | −7.32545e85 | −0.0884401 | ||||||||
\(141\) | −3.18266e86 | −0.288016 | ||||||||
\(142\) | −1.87597e87 | −1.27511 | ||||||||
\(143\) | −2.57517e87 | −1.31734 | ||||||||
\(144\) | 7.79512e86 | 0.300706 | ||||||||
\(145\) | 1.38269e86 | 0.0403013 | ||||||||
\(146\) | 3.12450e86 | 0.0689430 | ||||||||
\(147\) | 1.80379e87 | 0.301879 | ||||||||
\(148\) | 1.28624e87 | 0.163577 | ||||||||
\(149\) | 1.40161e88 | 1.35701 | 0.678506 | − | 0.734595i | \(-0.262628\pi\) | ||||
0.678506 | + | 0.734595i | \(0.262628\pi\) | |||||||
\(150\) | 1.09081e88 | 0.805476 | ||||||||
\(151\) | 1.21103e88 | 0.683263 | 0.341632 | − | 0.939834i | \(-0.389020\pi\) | ||||
0.341632 | + | 0.939834i | \(0.389020\pi\) | |||||||
\(152\) | −1.25157e88 | −0.540491 | ||||||||
\(153\) | −2.44823e88 | −0.810680 | ||||||||
\(154\) | −6.50289e88 | −1.65393 | ||||||||
\(155\) | 5.93234e87 | 0.116089 | ||||||||
\(156\) | −3.94952e88 | −0.595659 | ||||||||
\(157\) | 2.02144e87 | 0.0235355 | 0.0117678 | − | 0.999931i | \(-0.496254\pi\) | ||||
0.0117678 | + | 0.999931i | \(0.496254\pi\) | |||||||
\(158\) | 2.17289e89 | 1.95626 | ||||||||
\(159\) | −9.35059e88 | −0.652012 | ||||||||
\(160\) | 2.28765e88 | 0.123746 | ||||||||
\(161\) | −2.14755e89 | −0.902600 | ||||||||
\(162\) | 1.20500e89 | 0.394119 | ||||||||
\(163\) | −2.86179e89 | −0.729525 | −0.364762 | − | 0.931101i | \(-0.618850\pi\) | ||||
−0.364762 | + | 0.931101i | \(0.618850\pi\) | |||||||
\(164\) | 4.60943e89 | 0.917216 | ||||||||
\(165\) | −5.29219e88 | −0.0823257 | ||||||||
\(166\) | 2.06731e90 | 2.51784 | ||||||||
\(167\) | −1.21974e90 | −1.16480 | −0.582398 | − | 0.812904i | \(-0.697885\pi\) | ||||
−0.582398 | + | 0.812904i | \(0.697885\pi\) | |||||||
\(168\) | −2.92156e89 | −0.219073 | ||||||||
\(169\) | −5.97075e89 | −0.352061 | ||||||||
\(170\) | −3.59142e89 | −0.166757 | ||||||||
\(171\) | 1.66533e90 | 0.609760 | ||||||||
\(172\) | −6.99060e90 | −2.02122 | ||||||||
\(173\) | −2.41069e90 | −0.551155 | −0.275577 | − | 0.961279i | \(-0.588869\pi\) | ||||
−0.275577 | + | 0.961279i | \(0.588869\pi\) | |||||||
\(174\) | 1.88249e90 | 0.340791 | ||||||||
\(175\) | −4.48953e90 | −0.644406 | ||||||||
\(176\) | 5.94645e90 | 0.677634 | ||||||||
\(177\) | 5.08708e90 | 0.460841 | ||||||||
\(178\) | 2.66224e91 | 1.91972 | ||||||||
\(179\) | 1.25746e91 | 0.722681 | 0.361341 | − | 0.932434i | \(-0.382319\pi\) | ||||
0.361341 | + | 0.932434i | \(0.382319\pi\) | |||||||
\(180\) | 2.15313e90 | 0.0987490 | ||||||||
\(181\) | −4.59827e91 | −1.68505 | −0.842523 | − | 0.538660i | \(-0.818931\pi\) | ||||
−0.842523 | + | 0.538660i | \(0.818931\pi\) | |||||||
\(182\) | 2.77489e91 | 0.813495 | ||||||||
\(183\) | −3.25928e91 | −0.765336 | ||||||||
\(184\) | −4.74385e91 | −0.893324 | ||||||||
\(185\) | −7.35452e89 | −0.0111199 | ||||||||
\(186\) | 8.07673e91 | 0.981661 | ||||||||
\(187\) | −1.86762e92 | −1.82685 | ||||||||
\(188\) | 9.87778e91 | 0.778514 | ||||||||
\(189\) | 9.24028e91 | 0.587465 | ||||||||
\(190\) | 2.44295e91 | 0.125428 | ||||||||
\(191\) | −1.78047e92 | −0.739065 | −0.369532 | − | 0.929218i | \(-0.620482\pi\) | ||||
−0.369532 | + | 0.929218i | \(0.620482\pi\) | |||||||
\(192\) | 2.46973e92 | 0.829755 | ||||||||
\(193\) | −5.37925e92 | −1.46437 | −0.732185 | − | 0.681106i | \(-0.761499\pi\) | ||||
−0.732185 | + | 0.681106i | \(0.761499\pi\) | |||||||
\(194\) | 7.39102e92 | 1.63205 | ||||||||
\(195\) | 2.25827e91 | 0.0404924 | ||||||||
\(196\) | −5.59828e92 | −0.815987 | ||||||||
\(197\) | 5.95922e91 | 0.0706817 | 0.0353409 | − | 0.999375i | \(-0.488748\pi\) | ||||
0.0353409 | + | 0.999375i | \(0.488748\pi\) | |||||||
\(198\) | 1.91135e93 | 1.84672 | ||||||||
\(199\) | 1.19376e93 | 0.940522 | 0.470261 | − | 0.882527i | \(-0.344160\pi\) | ||||
0.470261 | + | 0.882527i | \(0.344160\pi\) | |||||||
\(200\) | −9.91718e92 | −0.637783 | ||||||||
\(201\) | −1.75972e92 | −0.0924704 | ||||||||
\(202\) | −6.60869e93 | −2.84043 | ||||||||
\(203\) | −7.74792e92 | −0.272644 | ||||||||
\(204\) | −2.86435e93 | −0.826045 | ||||||||
\(205\) | −2.63559e92 | −0.0623515 | ||||||||
\(206\) | 6.27989e93 | 1.21991 | ||||||||
\(207\) | 6.31216e93 | 1.00781 | ||||||||
\(208\) | −2.53745e93 | −0.333298 | ||||||||
\(209\) | 1.27039e94 | 1.37408 | ||||||||
\(210\) | 5.70263e92 | 0.0508387 | ||||||||
\(211\) | −1.50516e94 | −1.10699 | −0.553496 | − | 0.832852i | \(-0.686706\pi\) | ||||
−0.553496 | + | 0.832852i | \(0.686706\pi\) | |||||||
\(212\) | 2.90207e94 | 1.76241 | ||||||||
\(213\) | 8.55495e93 | 0.429382 | ||||||||
\(214\) | −5.36273e94 | −2.22653 | ||||||||
\(215\) | 3.99711e93 | 0.137401 | ||||||||
\(216\) | 2.04114e94 | 0.581428 | ||||||||
\(217\) | −3.32420e94 | −0.785360 | ||||||||
\(218\) | −4.38382e94 | −0.859736 | ||||||||
\(219\) | −1.42486e93 | −0.0232159 | ||||||||
\(220\) | 1.64250e94 | 0.222529 | ||||||||
\(221\) | 7.96943e94 | 0.898546 | ||||||||
\(222\) | −1.00130e94 | −0.0940304 | ||||||||
\(223\) | 4.43990e94 | 0.347557 | 0.173779 | − | 0.984785i | \(-0.444402\pi\) | ||||
0.173779 | + | 0.984785i | \(0.444402\pi\) | |||||||
\(224\) | −1.28189e95 | −0.837156 | ||||||||
\(225\) | 1.31958e95 | 0.719521 | ||||||||
\(226\) | −2.51240e95 | −1.14471 | ||||||||
\(227\) | −1.64130e93 | −0.00625376 | −0.00312688 | − | 0.999995i | \(-0.500995\pi\) | ||||
−0.00312688 | + | 0.999995i | \(0.500995\pi\) | |||||||
\(228\) | 1.94838e95 | 0.621317 | ||||||||
\(229\) | 5.28950e95 | 1.41279 | 0.706395 | − | 0.707818i | \(-0.250320\pi\) | ||||
0.706395 | + | 0.707818i | \(0.250320\pi\) | |||||||
\(230\) | 9.25958e94 | 0.207307 | ||||||||
\(231\) | 2.96549e95 | 0.556944 | ||||||||
\(232\) | −1.71148e95 | −0.269842 | ||||||||
\(233\) | −4.06009e95 | −0.537800 | −0.268900 | − | 0.963168i | \(-0.586660\pi\) | ||||
−0.268900 | + | 0.963168i | \(0.586660\pi\) | |||||||
\(234\) | −8.15607e95 | −0.908320 | ||||||||
\(235\) | −5.64795e94 | −0.0529227 | ||||||||
\(236\) | −1.57884e96 | −1.24567 | ||||||||
\(237\) | −9.90898e95 | −0.658751 | ||||||||
\(238\) | 2.01246e96 | 1.12813 | ||||||||
\(239\) | −2.21661e96 | −1.04851 | −0.524256 | − | 0.851561i | \(-0.675657\pi\) | ||||
−0.524256 | + | 0.851561i | \(0.675657\pi\) | |||||||
\(240\) | −5.21468e94 | −0.0208292 | ||||||||
\(241\) | 7.77775e95 | 0.262521 | 0.131260 | − | 0.991348i | \(-0.458098\pi\) | ||||
0.131260 | + | 0.991348i | \(0.458098\pi\) | |||||||
\(242\) | 9.13663e96 | 2.60774 | ||||||||
\(243\) | −4.28927e96 | −1.03593 | ||||||||
\(244\) | 1.01156e97 | 2.06872 | ||||||||
\(245\) | 3.20100e95 | 0.0554701 | ||||||||
\(246\) | −3.58830e96 | −0.527250 | ||||||||
\(247\) | −5.42096e96 | −0.675849 | ||||||||
\(248\) | −7.34303e96 | −0.777289 | ||||||||
\(249\) | −9.42751e96 | −0.847859 | ||||||||
\(250\) | 3.88956e96 | 0.297392 | ||||||||
\(251\) | −9.22205e96 | −0.599849 | −0.299924 | − | 0.953963i | \(-0.596961\pi\) | ||||
−0.299924 | + | 0.953963i | \(0.596961\pi\) | |||||||
\(252\) | −1.20651e97 | −0.668050 | ||||||||
\(253\) | 4.81518e97 | 2.27108 | ||||||||
\(254\) | −1.10101e97 | −0.442614 | ||||||||
\(255\) | 1.63778e96 | 0.0561538 | ||||||||
\(256\) | −8.30285e96 | −0.242945 | ||||||||
\(257\) | −6.53948e97 | −1.63400 | −0.816999 | − | 0.576639i | \(-0.804364\pi\) | ||||
−0.816999 | + | 0.576639i | \(0.804364\pi\) | |||||||
\(258\) | 5.44196e97 | 1.16187 | ||||||||
\(259\) | 4.12113e96 | 0.0752273 | ||||||||
\(260\) | −7.00881e96 | −0.109452 | ||||||||
\(261\) | 2.27730e97 | 0.304424 | ||||||||
\(262\) | −6.86051e95 | −0.00785515 | ||||||||
\(263\) | 1.21377e98 | 1.19105 | 0.595524 | − | 0.803337i | \(-0.296944\pi\) | ||||
0.595524 | + | 0.803337i | \(0.296944\pi\) | |||||||
\(264\) | 6.55065e97 | 0.551221 | ||||||||
\(265\) | −1.65936e97 | −0.119807 | ||||||||
\(266\) | −1.36892e98 | −0.848536 | ||||||||
\(267\) | −1.21406e98 | −0.646446 | ||||||||
\(268\) | 5.46150e97 | 0.249950 | ||||||||
\(269\) | 2.83784e98 | 1.11692 | 0.558458 | − | 0.829533i | \(-0.311393\pi\) | ||||
0.558458 | + | 0.829533i | \(0.311393\pi\) | |||||||
\(270\) | −3.98413e97 | −0.134928 | ||||||||
\(271\) | −6.20737e98 | −1.80989 | −0.904944 | − | 0.425531i | \(-0.860087\pi\) | ||||
−0.904944 | + | 0.425531i | \(0.860087\pi\) | |||||||
\(272\) | −1.84026e98 | −0.462210 | ||||||||
\(273\) | −1.26543e98 | −0.273936 | ||||||||
\(274\) | −1.13506e99 | −2.11896 | ||||||||
\(275\) | 1.00663e99 | 1.62142 | ||||||||
\(276\) | 7.38501e98 | 1.02691 | ||||||||
\(277\) | 4.30712e98 | 0.517317 | 0.258658 | − | 0.965969i | \(-0.416720\pi\) | ||||
0.258658 | + | 0.965969i | \(0.416720\pi\) | |||||||
\(278\) | 1.38191e99 | 1.43438 | ||||||||
\(279\) | 9.77063e98 | 0.876905 | ||||||||
\(280\) | −5.18460e97 | −0.0402545 | ||||||||
\(281\) | −8.03373e98 | −0.539897 | −0.269949 | − | 0.962875i | \(-0.587007\pi\) | ||||
−0.269949 | + | 0.962875i | \(0.587007\pi\) | |||||||
\(282\) | −7.68954e98 | −0.447519 | ||||||||
\(283\) | 1.04623e99 | 0.527566 | 0.263783 | − | 0.964582i | \(-0.415030\pi\) | ||||
0.263783 | + | 0.964582i | \(0.415030\pi\) | |||||||
\(284\) | −2.65513e99 | −1.16063 | ||||||||
\(285\) | −1.11405e98 | −0.0422366 | ||||||||
\(286\) | −6.22180e99 | −2.04688 | ||||||||
\(287\) | 1.47686e99 | 0.421817 | ||||||||
\(288\) | 3.76778e99 | 0.934738 | ||||||||
\(289\) | 1.14141e99 | 0.246082 | ||||||||
\(290\) | 3.34067e98 | 0.0626202 | ||||||||
\(291\) | −3.37051e99 | −0.549578 | ||||||||
\(292\) | 4.42222e98 | 0.0627531 | ||||||||
\(293\) | 1.88779e99 | 0.233247 | 0.116623 | − | 0.993176i | \(-0.462793\pi\) | ||||
0.116623 | + | 0.993176i | \(0.462793\pi\) | |||||||
\(294\) | 4.35808e99 | 0.469060 | ||||||||
\(295\) | 9.02753e98 | 0.0846793 | ||||||||
\(296\) | 9.10340e98 | 0.0744542 | ||||||||
\(297\) | −2.07183e100 | −1.47815 | ||||||||
\(298\) | 3.38640e100 | 2.10853 | ||||||||
\(299\) | −2.05472e100 | −1.11704 | ||||||||
\(300\) | 1.54386e100 | 0.733158 | ||||||||
\(301\) | −2.23979e100 | −0.929533 | ||||||||
\(302\) | 2.92594e100 | 1.06166 | ||||||||
\(303\) | 3.01374e100 | 0.956488 | ||||||||
\(304\) | 1.25178e100 | 0.347655 | ||||||||
\(305\) | −5.78391e99 | −0.140630 | ||||||||
\(306\) | −5.91511e100 | −1.25964 | ||||||||
\(307\) | −3.44926e100 | −0.643609 | −0.321804 | − | 0.946806i | \(-0.604289\pi\) | ||||
−0.321804 | + | 0.946806i | \(0.604289\pi\) | |||||||
\(308\) | −9.20378e100 | −1.50544 | ||||||||
\(309\) | −2.86380e100 | −0.410794 | ||||||||
\(310\) | 1.43330e100 | 0.180380 | ||||||||
\(311\) | 9.09772e99 | 0.100493 | 0.0502466 | − | 0.998737i | \(-0.483999\pi\) | ||||
0.0502466 | + | 0.998737i | \(0.483999\pi\) | |||||||
\(312\) | −2.79528e100 | −0.271121 | ||||||||
\(313\) | 2.21518e101 | 1.88740 | 0.943699 | − | 0.330804i | \(-0.107320\pi\) | ||||
0.943699 | + | 0.330804i | \(0.107320\pi\) | |||||||
\(314\) | 4.88394e99 | 0.0365695 | ||||||||
\(315\) | 6.89862e99 | 0.0454135 | ||||||||
\(316\) | 3.07538e101 | 1.78062 | ||||||||
\(317\) | −5.44905e100 | −0.277601 | −0.138800 | − | 0.990320i | \(-0.544325\pi\) | ||||
−0.138800 | + | 0.990320i | \(0.544325\pi\) | |||||||
\(318\) | −2.25917e101 | −1.01310 | ||||||||
\(319\) | 1.73722e101 | 0.686013 | ||||||||
\(320\) | 4.38278e100 | 0.152467 | ||||||||
\(321\) | 2.44555e101 | 0.749761 | ||||||||
\(322\) | −5.18864e101 | −1.40246 | ||||||||
\(323\) | −3.93150e101 | −0.937251 | ||||||||
\(324\) | 1.70548e101 | 0.358734 | ||||||||
\(325\) | −4.29547e101 | −0.797506 | ||||||||
\(326\) | −6.91430e101 | −1.13354 | ||||||||
\(327\) | 1.99914e101 | 0.289507 | ||||||||
\(328\) | 3.26233e101 | 0.417482 | ||||||||
\(329\) | 3.16485e101 | 0.358029 | ||||||||
\(330\) | −1.27863e101 | −0.127918 | ||||||||
\(331\) | 4.31900e101 | 0.382252 | 0.191126 | − | 0.981566i | \(-0.438786\pi\) | ||||
0.191126 | + | 0.981566i | \(0.438786\pi\) | |||||||
\(332\) | 2.92594e102 | 2.29178 | ||||||||
\(333\) | −1.21130e101 | −0.0839961 | ||||||||
\(334\) | −2.94698e102 | −1.80986 | ||||||||
\(335\) | −3.12279e100 | −0.0169914 | ||||||||
\(336\) | 2.92206e101 | 0.140912 | ||||||||
\(337\) | −1.76336e101 | −0.0753930 | −0.0376965 | − | 0.999289i | \(-0.512002\pi\) | ||||
−0.0376965 | + | 0.999289i | \(0.512002\pi\) | |||||||
\(338\) | −1.44258e102 | −0.547032 | ||||||||
\(339\) | 1.14572e102 | 0.385471 | ||||||||
\(340\) | −5.08307e101 | −0.151785 | ||||||||
\(341\) | 7.45345e102 | 1.97608 | ||||||||
\(342\) | 4.02357e102 | 0.947445 | ||||||||
\(343\) | −4.90257e102 | −1.02568 | ||||||||
\(344\) | −4.94761e102 | −0.919980 | ||||||||
\(345\) | −4.22262e101 | −0.0698086 | ||||||||
\(346\) | −5.82439e102 | −0.856384 | ||||||||
\(347\) | −6.69404e102 | −0.875678 | −0.437839 | − | 0.899053i | \(-0.644256\pi\) | ||||
−0.437839 | + | 0.899053i | \(0.644256\pi\) | |||||||
\(348\) | 2.66436e102 | 0.310194 | ||||||||
\(349\) | −5.08612e102 | −0.527177 | −0.263589 | − | 0.964635i | \(-0.584906\pi\) | ||||
−0.263589 | + | 0.964635i | \(0.584906\pi\) | |||||||
\(350\) | −1.08470e103 | −1.00128 | ||||||||
\(351\) | 8.84087e102 | 0.727038 | ||||||||
\(352\) | 2.87423e103 | 2.10641 | ||||||||
\(353\) | −2.29436e103 | −1.49895 | −0.749473 | − | 0.662035i | \(-0.769693\pi\) | ||||
−0.749473 | + | 0.662035i | \(0.769693\pi\) | |||||||
\(354\) | 1.22908e103 | 0.716055 | ||||||||
\(355\) | 1.51816e102 | 0.0788987 | ||||||||
\(356\) | 3.76797e103 | 1.74736 | ||||||||
\(357\) | −9.17738e102 | −0.379888 | ||||||||
\(358\) | 3.03812e103 | 1.12290 | ||||||||
\(359\) | 4.04753e102 | 0.133618 | 0.0668090 | − | 0.997766i | \(-0.478718\pi\) | ||||
0.0668090 | + | 0.997766i | \(0.478718\pi\) | |||||||
\(360\) | 1.52388e102 | 0.0449468 | ||||||||
\(361\) | −1.11923e103 | −0.295039 | ||||||||
\(362\) | −1.11097e104 | −2.61823 | ||||||||
\(363\) | −4.16655e103 | −0.878129 | ||||||||
\(364\) | 3.92741e103 | 0.740457 | ||||||||
\(365\) | −2.52855e101 | −0.00426590 | ||||||||
\(366\) | −7.87465e103 | −1.18918 | ||||||||
\(367\) | 5.19277e103 | 0.702139 | 0.351070 | − | 0.936349i | \(-0.385818\pi\) | ||||
0.351070 | + | 0.936349i | \(0.385818\pi\) | |||||||
\(368\) | 4.74466e103 | 0.574604 | ||||||||
\(369\) | −4.34085e103 | −0.470985 | ||||||||
\(370\) | −1.77691e102 | −0.0172780 | ||||||||
\(371\) | 9.29825e103 | 0.810509 | ||||||||
\(372\) | 1.14313e104 | 0.893525 | ||||||||
\(373\) | 2.75979e104 | 1.93494 | 0.967471 | − | 0.252983i | \(-0.0814116\pi\) | ||||
0.967471 | + | 0.252983i | \(0.0814116\pi\) | |||||||
\(374\) | −4.51230e104 | −2.83856 | ||||||||
\(375\) | −1.77374e103 | −0.100144 | ||||||||
\(376\) | 6.99101e103 | 0.354350 | ||||||||
\(377\) | −7.41302e103 | −0.337420 | ||||||||
\(378\) | 2.23252e104 | 0.912804 | ||||||||
\(379\) | 1.08706e104 | 0.399360 | 0.199680 | − | 0.979861i | \(-0.436010\pi\) | ||||
0.199680 | + | 0.979861i | \(0.436010\pi\) | |||||||
\(380\) | 3.45760e103 | 0.114167 | ||||||||
\(381\) | 5.02090e103 | 0.149046 | ||||||||
\(382\) | −4.30174e104 | −1.14836 | ||||||||
\(383\) | −1.96036e103 | −0.0470744 | −0.0235372 | − | 0.999723i | \(-0.507493\pi\) | ||||
−0.0235372 | + | 0.999723i | \(0.507493\pi\) | |||||||
\(384\) | 2.85018e104 | 0.615826 | ||||||||
\(385\) | 5.26256e103 | 0.102338 | ||||||||
\(386\) | −1.29967e105 | −2.27534 | ||||||||
\(387\) | 6.58328e104 | 1.03788 | ||||||||
\(388\) | 1.04608e105 | 1.48552 | ||||||||
\(389\) | −6.50767e104 | −0.832658 | −0.416329 | − | 0.909214i | \(-0.636684\pi\) | ||||
−0.416329 | + | 0.909214i | \(0.636684\pi\) | |||||||
\(390\) | 5.45614e103 | 0.0629171 | ||||||||
\(391\) | −1.49017e105 | −1.54909 | ||||||||
\(392\) | −3.96219e104 | −0.371406 | ||||||||
\(393\) | 3.12858e102 | 0.00264514 | ||||||||
\(394\) | 1.43979e104 | 0.109825 | ||||||||
\(395\) | −1.75845e104 | −0.121045 | ||||||||
\(396\) | 2.70521e105 | 1.68092 | ||||||||
\(397\) | 3.42316e104 | 0.192049 | 0.0960244 | − | 0.995379i | \(-0.469387\pi\) | ||||
0.0960244 | + | 0.995379i | \(0.469387\pi\) | |||||||
\(398\) | 2.88422e105 | 1.46138 | ||||||||
\(399\) | 6.24263e104 | 0.285736 | ||||||||
\(400\) | 9.91888e104 | 0.410235 | ||||||||
\(401\) | 1.64711e105 | 0.615709 | 0.307855 | − | 0.951433i | \(-0.400389\pi\) | ||||
0.307855 | + | 0.951433i | \(0.400389\pi\) | |||||||
\(402\) | −4.25161e104 | −0.143681 | ||||||||
\(403\) | −3.18052e105 | −0.971948 | ||||||||
\(404\) | −9.35352e105 | −2.58541 | ||||||||
\(405\) | −9.75163e103 | −0.0243865 | ||||||||
\(406\) | −1.87195e105 | −0.423634 | ||||||||
\(407\) | −9.24029e104 | −0.189283 | ||||||||
\(408\) | −2.02724e105 | −0.375984 | ||||||||
\(409\) | 8.09693e104 | 0.135996 | 0.0679980 | − | 0.997685i | \(-0.478339\pi\) | ||||
0.0679980 | + | 0.997685i | \(0.478339\pi\) | |||||||
\(410\) | −6.36779e104 | −0.0968819 | ||||||||
\(411\) | 5.17620e105 | 0.713539 | ||||||||
\(412\) | 8.88816e105 | 1.11039 | ||||||||
\(413\) | −5.05860e105 | −0.572867 | ||||||||
\(414\) | 1.52506e106 | 1.56594 | ||||||||
\(415\) | −1.67301e105 | −0.155794 | ||||||||
\(416\) | −1.22648e106 | −1.03605 | ||||||||
\(417\) | −6.30188e105 | −0.483014 | ||||||||
\(418\) | 3.06935e106 | 2.13505 | ||||||||
\(419\) | −1.32493e106 | −0.836611 | −0.418306 | − | 0.908306i | \(-0.637376\pi\) | ||||
−0.418306 | + | 0.908306i | \(0.637376\pi\) | |||||||
\(420\) | 8.07115e104 | 0.0462742 | ||||||||
\(421\) | 2.12938e106 | 1.10874 | 0.554369 | − | 0.832271i | \(-0.312960\pi\) | ||||
0.554369 | + | 0.832271i | \(0.312960\pi\) | |||||||
\(422\) | −3.63658e106 | −1.72004 | ||||||||
\(423\) | −9.30223e105 | −0.399763 | ||||||||
\(424\) | 2.05395e106 | 0.802180 | ||||||||
\(425\) | −3.11524e106 | −1.10596 | ||||||||
\(426\) | 2.06694e106 | 0.667174 | ||||||||
\(427\) | 3.24103e106 | 0.951381 | ||||||||
\(428\) | −7.59007e106 | −2.02662 | ||||||||
\(429\) | 2.83731e106 | 0.689265 | ||||||||
\(430\) | 9.65731e105 | 0.213493 | ||||||||
\(431\) | 5.23722e106 | 1.05383 | 0.526916 | − | 0.849918i | \(-0.323348\pi\) | ||||
0.526916 | + | 0.849918i | \(0.323348\pi\) | |||||||
\(432\) | −2.04149e106 | −0.373986 | ||||||||
\(433\) | −5.09355e106 | −0.849690 | −0.424845 | − | 0.905266i | \(-0.639671\pi\) | ||||
−0.424845 | + | 0.905266i | \(0.639671\pi\) | |||||||
\(434\) | −8.03152e106 | −1.22029 | ||||||||
\(435\) | −1.52344e105 | −0.0210867 | ||||||||
\(436\) | −6.20459e106 | −0.782546 | ||||||||
\(437\) | 1.01364e107 | 1.16516 | ||||||||
\(438\) | −3.44256e105 | −0.0360728 | ||||||||
\(439\) | 1.41527e107 | 1.35216 | 0.676078 | − | 0.736830i | \(-0.263678\pi\) | ||||
0.676078 | + | 0.736830i | \(0.263678\pi\) | |||||||
\(440\) | 1.16248e106 | 0.101287 | ||||||||
\(441\) | 5.27208e106 | 0.419005 | ||||||||
\(442\) | 1.92547e107 | 1.39616 | ||||||||
\(443\) | −8.09669e106 | −0.535743 | −0.267871 | − | 0.963455i | \(-0.586320\pi\) | ||||
−0.267871 | + | 0.963455i | \(0.586320\pi\) | |||||||
\(444\) | −1.41718e106 | −0.0855881 | ||||||||
\(445\) | −2.15446e106 | −0.118784 | ||||||||
\(446\) | 1.07271e107 | 0.540034 | ||||||||
\(447\) | −1.54429e107 | −0.710026 | ||||||||
\(448\) | −2.45591e107 | −1.03146 | ||||||||
\(449\) | −1.78149e107 | −0.683606 | −0.341803 | − | 0.939772i | \(-0.611038\pi\) | ||||
−0.341803 | + | 0.939772i | \(0.611038\pi\) | |||||||
\(450\) | 3.18820e107 | 1.11799 | ||||||||
\(451\) | −3.31139e107 | −1.06135 | ||||||||
\(452\) | −3.55589e107 | −1.04194 | ||||||||
\(453\) | −1.33431e107 | −0.357502 | ||||||||
\(454\) | −3.96550e105 | −0.00971709 | ||||||||
\(455\) | −2.24563e106 | −0.0503357 | ||||||||
\(456\) | 1.37897e107 | 0.282800 | ||||||||
\(457\) | −3.94961e107 | −0.741221 | −0.370611 | − | 0.928788i | \(-0.620852\pi\) | ||||
−0.370611 | + | 0.928788i | \(0.620852\pi\) | |||||||
\(458\) | 1.27798e108 | 2.19519 | ||||||||
\(459\) | 6.41175e107 | 1.00824 | ||||||||
\(460\) | 1.31054e107 | 0.188694 | ||||||||
\(461\) | −2.95679e106 | −0.0389882 | −0.0194941 | − | 0.999810i | \(-0.506206\pi\) | ||||
−0.0194941 | + | 0.999810i | \(0.506206\pi\) | |||||||
\(462\) | 7.16485e107 | 0.865381 | ||||||||
\(463\) | −1.31699e107 | −0.145731 | −0.0728655 | − | 0.997342i | \(-0.523214\pi\) | ||||
−0.0728655 | + | 0.997342i | \(0.523214\pi\) | |||||||
\(464\) | 1.71178e107 | 0.173568 | ||||||||
\(465\) | −6.53622e106 | −0.0607410 | ||||||||
\(466\) | −9.80948e107 | −0.835635 | ||||||||
\(467\) | −1.31297e108 | −1.02546 | −0.512732 | − | 0.858549i | \(-0.671367\pi\) | ||||
−0.512732 | + | 0.858549i | \(0.671367\pi\) | |||||||
\(468\) | −1.15436e108 | −0.826768 | ||||||||
\(469\) | 1.74987e107 | 0.114949 | ||||||||
\(470\) | −1.36459e107 | −0.0822314 | ||||||||
\(471\) | −2.22721e106 | −0.0123144 | ||||||||
\(472\) | −1.11742e108 | −0.566979 | ||||||||
\(473\) | 5.02201e108 | 2.33885 | ||||||||
\(474\) | −2.39408e108 | −1.02357 | ||||||||
\(475\) | 2.11905e108 | 0.831859 | ||||||||
\(476\) | 2.84831e108 | 1.02685 | ||||||||
\(477\) | −2.73298e108 | −0.904986 | ||||||||
\(478\) | −5.35548e108 | −1.62918 | ||||||||
\(479\) | −3.75891e108 | −1.05069 | −0.525344 | − | 0.850890i | \(-0.676063\pi\) | ||||
−0.525344 | + | 0.850890i | \(0.676063\pi\) | |||||||
\(480\) | −2.52052e107 | −0.0647470 | ||||||||
\(481\) | 3.94299e107 | 0.0931001 | ||||||||
\(482\) | 1.87916e108 | 0.407905 | ||||||||
\(483\) | 2.36616e108 | 0.472264 | ||||||||
\(484\) | 1.29314e109 | 2.37361 | ||||||||
\(485\) | −5.98130e107 | −0.100985 | ||||||||
\(486\) | −1.03632e109 | −1.60963 | ||||||||
\(487\) | 1.64053e108 | 0.234456 | 0.117228 | − | 0.993105i | \(-0.462599\pi\) | ||||
0.117228 | + | 0.993105i | \(0.462599\pi\) | |||||||
\(488\) | 7.15930e108 | 0.941603 | ||||||||
\(489\) | 3.15311e108 | 0.381707 | ||||||||
\(490\) | 7.73385e107 | 0.0861895 | ||||||||
\(491\) | 6.82374e108 | 0.700200 | 0.350100 | − | 0.936712i | \(-0.386148\pi\) | ||||
0.350100 | + | 0.936712i | \(0.386148\pi\) | |||||||
\(492\) | −5.07865e108 | −0.479912 | ||||||||
\(493\) | −5.37621e108 | −0.467925 | ||||||||
\(494\) | −1.30974e109 | −1.05013 | ||||||||
\(495\) | −1.54679e108 | −0.114267 | ||||||||
\(496\) | 7.34429e108 | 0.499968 | ||||||||
\(497\) | −8.50707e108 | −0.533760 | ||||||||
\(498\) | −2.27776e109 | −1.31740 | ||||||||
\(499\) | −1.45297e109 | −0.774791 | −0.387396 | − | 0.921914i | \(-0.626625\pi\) | ||||
−0.387396 | + | 0.921914i | \(0.626625\pi\) | |||||||
\(500\) | 5.50503e108 | 0.270692 | ||||||||
\(501\) | 1.34390e109 | 0.609453 | ||||||||
\(502\) | −2.22811e109 | −0.932045 | ||||||||
\(503\) | 1.78726e109 | 0.689739 | 0.344869 | − | 0.938651i | \(-0.387923\pi\) | ||||
0.344869 | + | 0.938651i | \(0.387923\pi\) | |||||||
\(504\) | −8.53909e108 | −0.304071 | ||||||||
\(505\) | 5.34818e108 | 0.175754 | ||||||||
\(506\) | 1.16338e110 | 3.52880 | ||||||||
\(507\) | 6.57855e108 | 0.184208 | ||||||||
\(508\) | −1.55830e109 | −0.402875 | ||||||||
\(509\) | −6.63065e108 | −0.158302 | −0.0791510 | − | 0.996863i | \(-0.525221\pi\) | ||||
−0.0791510 | + | 0.996863i | \(0.525221\pi\) | |||||||
\(510\) | 3.95701e108 | 0.0872519 | ||||||||
\(511\) | 1.41688e108 | 0.0288594 | ||||||||
\(512\) | 4.24859e109 | 0.799487 | ||||||||
\(513\) | −4.36140e109 | −0.758354 | ||||||||
\(514\) | −1.57999e110 | −2.53891 | ||||||||
\(515\) | −5.08210e108 | −0.0754832 | ||||||||
\(516\) | 7.70222e109 | 1.05755 | ||||||||
\(517\) | −7.09614e109 | −0.900856 | ||||||||
\(518\) | 9.95695e108 | 0.116888 | ||||||||
\(519\) | 2.65608e109 | 0.288379 | ||||||||
\(520\) | −4.96049e108 | −0.0498184 | ||||||||
\(521\) | −2.32219e109 | −0.215760 | −0.107880 | − | 0.994164i | \(-0.534406\pi\) | ||||
−0.107880 | + | 0.994164i | \(0.534406\pi\) | |||||||
\(522\) | 5.50212e109 | 0.473015 | ||||||||
\(523\) | −1.15930e110 | −0.922311 | −0.461155 | − | 0.887319i | \(-0.652565\pi\) | ||||
−0.461155 | + | 0.887319i | \(0.652565\pi\) | |||||||
\(524\) | −9.70994e107 | −0.00714989 | ||||||||
\(525\) | 4.94654e109 | 0.337171 | ||||||||
\(526\) | 2.93256e110 | 1.85065 | ||||||||
\(527\) | −2.30664e110 | −1.34787 | ||||||||
\(528\) | −6.55178e109 | −0.354556 | ||||||||
\(529\) | 1.84697e110 | 0.925773 | ||||||||
\(530\) | −4.00912e109 | −0.186156 | ||||||||
\(531\) | 1.48684e110 | 0.639642 | ||||||||
\(532\) | −1.93748e110 | −0.772352 | ||||||||
\(533\) | 1.41303e110 | 0.522033 | ||||||||
\(534\) | −2.93325e110 | −1.00445 | ||||||||
\(535\) | 4.33987e109 | 0.137768 | ||||||||
\(536\) | 3.86538e109 | 0.113768 | ||||||||
\(537\) | −1.38546e110 | −0.378126 | ||||||||
\(538\) | 6.85643e110 | 1.73547 | ||||||||
\(539\) | 4.02177e110 | 0.944218 | ||||||||
\(540\) | −5.63889e109 | −0.122814 | ||||||||
\(541\) | 6.02154e110 | 1.21680 | 0.608399 | − | 0.793631i | \(-0.291812\pi\) | ||||
0.608399 | + | 0.793631i | \(0.291812\pi\) | |||||||
\(542\) | −1.49975e111 | −2.81220 | ||||||||
\(543\) | 5.06635e110 | 0.881661 | ||||||||
\(544\) | −8.89493e110 | −1.43677 | ||||||||
\(545\) | 3.54768e109 | 0.0531968 | ||||||||
\(546\) | −3.05736e110 | −0.425643 | ||||||||
\(547\) | −5.44322e110 | −0.703670 | −0.351835 | − | 0.936062i | \(-0.614442\pi\) | ||||
−0.351835 | + | 0.936062i | \(0.614442\pi\) | |||||||
\(548\) | −1.60650e111 | −1.92871 | ||||||||
\(549\) | −9.52616e110 | −1.06228 | ||||||||
\(550\) | 2.43209e111 | 2.51937 | ||||||||
\(551\) | 3.65700e110 | 0.351954 | ||||||||
\(552\) | 5.22675e110 | 0.467411 | ||||||||
\(553\) | 9.85352e110 | 0.818886 | ||||||||
\(554\) | 1.04063e111 | 0.803807 | ||||||||
\(555\) | 8.10317e108 | 0.00581821 | ||||||||
\(556\) | 1.95587e111 | 1.30560 | ||||||||
\(557\) | −1.37636e111 | −0.854275 | −0.427137 | − | 0.904187i | \(-0.640478\pi\) | ||||
−0.427137 | + | 0.904187i | \(0.640478\pi\) | |||||||
\(558\) | 2.36066e111 | 1.36253 | ||||||||
\(559\) | −2.14298e111 | −1.15037 | ||||||||
\(560\) | 5.18549e109 | 0.0258925 | ||||||||
\(561\) | 2.05773e111 | 0.955856 | ||||||||
\(562\) | −1.94101e111 | −0.838893 | ||||||||
\(563\) | −4.54012e111 | −1.82590 | −0.912950 | − | 0.408070i | \(-0.866202\pi\) | ||||
−0.912950 | + | 0.408070i | \(0.866202\pi\) | |||||||
\(564\) | −1.08833e111 | −0.407340 | ||||||||
\(565\) | 2.03320e110 | 0.0708300 | ||||||||
\(566\) | 2.52777e111 | 0.819733 | ||||||||
\(567\) | 5.46436e110 | 0.164978 | ||||||||
\(568\) | −1.87918e111 | −0.528275 | ||||||||
\(569\) | −4.78435e111 | −1.25250 | −0.626248 | − | 0.779624i | \(-0.715410\pi\) | ||||
−0.626248 | + | 0.779624i | \(0.715410\pi\) | |||||||
\(570\) | −2.69163e110 | −0.0656272 | ||||||||
\(571\) | 5.09517e111 | 1.15717 | 0.578584 | − | 0.815623i | \(-0.303605\pi\) | ||||
0.578584 | + | 0.815623i | \(0.303605\pi\) | |||||||
\(572\) | −8.80594e111 | −1.86310 | ||||||||
\(573\) | 1.96171e111 | 0.386699 | ||||||||
\(574\) | 3.56821e111 | 0.655419 | ||||||||
\(575\) | 8.03188e111 | 1.37489 | ||||||||
\(576\) | 7.21849e111 | 1.15169 | ||||||||
\(577\) | −1.02672e112 | −1.52698 | −0.763488 | − | 0.645822i | \(-0.776515\pi\) | ||||
−0.763488 | + | 0.645822i | \(0.776515\pi\) | |||||||
\(578\) | 2.75773e111 | 0.382362 | ||||||||
\(579\) | 5.92683e111 | 0.766198 | ||||||||
\(580\) | 4.72817e110 | 0.0569980 | ||||||||
\(581\) | 9.37474e111 | 1.05396 | ||||||||
\(582\) | −8.14339e111 | −0.853934 | ||||||||
\(583\) | −2.08483e112 | −2.03936 | ||||||||
\(584\) | 3.12983e110 | 0.0285628 | ||||||||
\(585\) | 6.60043e110 | 0.0562030 | ||||||||
\(586\) | 4.56104e111 | 0.362419 | ||||||||
\(587\) | 5.68440e111 | 0.421543 | 0.210771 | − | 0.977535i | \(-0.432402\pi\) | ||||
0.210771 | + | 0.977535i | \(0.432402\pi\) | |||||||
\(588\) | 6.16815e111 | 0.426947 | ||||||||
\(589\) | 1.56902e112 | 1.01381 | ||||||||
\(590\) | 2.18112e111 | 0.131575 | ||||||||
\(591\) | −6.56584e110 | −0.0369826 | ||||||||
\(592\) | −9.10496e110 | −0.0478904 | ||||||||
\(593\) | −1.19671e112 | −0.587858 | −0.293929 | − | 0.955827i | \(-0.594963\pi\) | ||||
−0.293929 | + | 0.955827i | \(0.594963\pi\) | |||||||
\(594\) | −5.00570e112 | −2.29675 | ||||||||
\(595\) | −1.62862e111 | −0.0698043 | ||||||||
\(596\) | 4.79289e112 | 1.91922 | ||||||||
\(597\) | −1.31528e112 | −0.492106 | ||||||||
\(598\) | −4.96436e112 | −1.73566 | ||||||||
\(599\) | −1.71608e112 | −0.560725 | −0.280363 | − | 0.959894i | \(-0.590455\pi\) | ||||
−0.280363 | + | 0.959894i | \(0.590455\pi\) | |||||||
\(600\) | 1.09267e112 | 0.333705 | ||||||||
\(601\) | 6.36761e112 | 1.81786 | 0.908930 | − | 0.416948i | \(-0.136900\pi\) | ||||
0.908930 | + | 0.416948i | \(0.136900\pi\) | |||||||
\(602\) | −5.41150e112 | −1.44431 | ||||||||
\(603\) | −5.14328e111 | −0.128348 | ||||||||
\(604\) | 4.14118e112 | 0.966337 | ||||||||
\(605\) | −7.39396e111 | −0.161356 | ||||||||
\(606\) | 7.28142e112 | 1.48619 | ||||||||
\(607\) | 1.92645e112 | 0.367804 | 0.183902 | − | 0.982945i | \(-0.441127\pi\) | ||||
0.183902 | + | 0.982945i | \(0.441127\pi\) | |||||||
\(608\) | 6.05050e112 | 1.08068 | ||||||||
\(609\) | 8.53662e111 | 0.142655 | ||||||||
\(610\) | −1.39743e112 | −0.218511 | ||||||||
\(611\) | 3.02804e112 | 0.443091 | ||||||||
\(612\) | −8.37187e112 | −1.14654 | ||||||||
\(613\) | 6.29200e112 | 0.806565 | 0.403282 | − | 0.915076i | \(-0.367869\pi\) | ||||
0.403282 | + | 0.915076i | \(0.367869\pi\) | |||||||
\(614\) | −8.33367e112 | −1.00004 | ||||||||
\(615\) | 2.90389e111 | 0.0326240 | ||||||||
\(616\) | −6.51399e112 | −0.685217 | ||||||||
\(617\) | −2.13054e112 | −0.209865 | −0.104933 | − | 0.994479i | \(-0.533463\pi\) | ||||
−0.104933 | + | 0.994479i | \(0.533463\pi\) | |||||||
\(618\) | −6.91915e112 | −0.638292 | ||||||||
\(619\) | −1.80351e113 | −1.55829 | −0.779143 | − | 0.626846i | \(-0.784345\pi\) | ||||
−0.779143 | + | 0.626846i | \(0.784345\pi\) | |||||||
\(620\) | 2.02860e112 | 0.164185 | ||||||||
\(621\) | −1.65311e113 | −1.25341 | ||||||||
\(622\) | 2.19808e112 | 0.156146 | ||||||||
\(623\) | 1.20726e113 | 0.803591 | ||||||||
\(624\) | 2.79575e112 | 0.174391 | ||||||||
\(625\) | 1.66328e113 | 0.972355 | ||||||||
\(626\) | 5.35204e113 | 2.93264 | ||||||||
\(627\) | −1.39971e113 | −0.718955 | ||||||||
\(628\) | 6.91242e111 | 0.0332862 | ||||||||
\(629\) | 2.85961e112 | 0.129109 | ||||||||
\(630\) | 1.66676e112 | 0.0705635 | ||||||||
\(631\) | −4.77991e113 | −1.89771 | −0.948856 | − | 0.315709i | \(-0.897758\pi\) | ||||
−0.948856 | + | 0.315709i | \(0.897758\pi\) | |||||||
\(632\) | 2.17660e113 | 0.810470 | ||||||||
\(633\) | 1.65838e113 | 0.579208 | ||||||||
\(634\) | −1.31653e113 | −0.431336 | ||||||||
\(635\) | 8.91009e111 | 0.0273871 | ||||||||
\(636\) | −3.19749e113 | −0.922138 | ||||||||
\(637\) | −1.71616e113 | −0.464419 | ||||||||
\(638\) | 4.19725e113 | 1.06593 | ||||||||
\(639\) | 2.50043e113 | 0.595977 | ||||||||
\(640\) | 5.05793e112 | 0.113158 | ||||||||
\(641\) | −2.57522e113 | −0.540833 | −0.270417 | − | 0.962743i | \(-0.587161\pi\) | ||||
−0.270417 | + | 0.962743i | \(0.587161\pi\) | |||||||
\(642\) | 5.90863e113 | 1.16498 | ||||||||
\(643\) | −1.67597e113 | −0.310258 | −0.155129 | − | 0.987894i | \(-0.549579\pi\) | ||||
−0.155129 | + | 0.987894i | \(0.549579\pi\) | |||||||
\(644\) | −7.34367e113 | −1.27654 | ||||||||
\(645\) | −4.40400e112 | −0.0718917 | ||||||||
\(646\) | −9.49878e113 | −1.45630 | ||||||||
\(647\) | 3.03414e113 | 0.436931 | 0.218465 | − | 0.975845i | \(-0.429895\pi\) | ||||
0.218465 | + | 0.975845i | \(0.429895\pi\) | |||||||
\(648\) | 1.20705e113 | 0.163282 | ||||||||
\(649\) | 1.13423e114 | 1.44142 | ||||||||
\(650\) | −1.03782e114 | −1.23917 | ||||||||
\(651\) | 3.66259e113 | 0.410921 | ||||||||
\(652\) | −9.78607e113 | −1.03176 | ||||||||
\(653\) | 4.88486e113 | 0.484026 | 0.242013 | − | 0.970273i | \(-0.422192\pi\) | ||||
0.242013 | + | 0.970273i | \(0.422192\pi\) | |||||||
\(654\) | 4.83008e113 | 0.449837 | ||||||||
\(655\) | 5.55198e110 | 0.000486044 0 | ||||||||
\(656\) | −3.26289e113 | −0.268533 | ||||||||
\(657\) | −4.16455e112 | −0.0322234 | ||||||||
\(658\) | 7.64650e113 | 0.556306 | ||||||||
\(659\) | −1.18985e113 | −0.0814013 | −0.0407007 | − | 0.999171i | \(-0.512959\pi\) | ||||
−0.0407007 | + | 0.999171i | \(0.512959\pi\) | |||||||
\(660\) | −1.80969e113 | −0.116433 | ||||||||
\(661\) | 2.33519e114 | 1.41307 | 0.706535 | − | 0.707678i | \(-0.250257\pi\) | ||||
0.706535 | + | 0.707678i | \(0.250257\pi\) | |||||||
\(662\) | 1.04350e114 | 0.593943 | ||||||||
\(663\) | −8.78069e113 | −0.470144 | ||||||||
\(664\) | 2.07084e114 | 1.04313 | ||||||||
\(665\) | 1.10782e113 | 0.0525039 | ||||||||
\(666\) | −2.92658e113 | −0.130513 | ||||||||
\(667\) | 1.38612e114 | 0.581709 | ||||||||
\(668\) | −4.17097e114 | −1.64737 | ||||||||
\(669\) | −4.89186e113 | −0.181851 | ||||||||
\(670\) | −7.54490e112 | −0.0264012 | ||||||||
\(671\) | −7.26696e114 | −2.39382 | ||||||||
\(672\) | 1.41238e114 | 0.438022 | ||||||||
\(673\) | −3.17725e114 | −0.927771 | −0.463885 | − | 0.885895i | \(-0.653545\pi\) | ||||
−0.463885 | + | 0.885895i | \(0.653545\pi\) | |||||||
\(674\) | −4.26042e113 | −0.117146 | ||||||||
\(675\) | −3.45589e114 | −0.894863 | ||||||||
\(676\) | −2.04173e114 | −0.497918 | ||||||||
\(677\) | 7.91759e114 | 1.81866 | 0.909331 | − | 0.416074i | \(-0.136594\pi\) | ||||
0.909331 | + | 0.416074i | \(0.136594\pi\) | |||||||
\(678\) | 2.76815e114 | 0.598944 | ||||||||
\(679\) | 3.35164e114 | 0.683174 | ||||||||
\(680\) | −3.59755e113 | −0.0690869 | ||||||||
\(681\) | 1.80838e112 | 0.00327213 | ||||||||
\(682\) | 1.80081e115 | 3.07044 | ||||||||
\(683\) | −7.97601e114 | −1.28159 | −0.640793 | − | 0.767714i | \(-0.721394\pi\) | ||||
−0.640793 | + | 0.767714i | \(0.721394\pi\) | |||||||
\(684\) | 5.69471e114 | 0.862381 | ||||||||
\(685\) | 9.18569e113 | 0.131112 | ||||||||
\(686\) | −1.18450e115 | −1.59370 | ||||||||
\(687\) | −5.82794e114 | −0.739209 | ||||||||
\(688\) | 4.94846e114 | 0.591750 | ||||||||
\(689\) | 8.89633e114 | 1.00307 | ||||||||
\(690\) | −1.02022e114 | −0.108469 | ||||||||
\(691\) | −6.85346e114 | −0.687146 | −0.343573 | − | 0.939126i | \(-0.611637\pi\) | ||||
−0.343573 | + | 0.939126i | \(0.611637\pi\) | |||||||
\(692\) | −8.24348e114 | −0.779496 | ||||||||
\(693\) | 8.66750e114 | 0.773033 | ||||||||
\(694\) | −1.61733e115 | −1.36063 | ||||||||
\(695\) | −1.11833e114 | −0.0887535 | ||||||||
\(696\) | 1.88570e114 | 0.141189 | ||||||||
\(697\) | 1.02478e115 | 0.723943 | ||||||||
\(698\) | −1.22884e115 | −0.819128 | ||||||||
\(699\) | 4.47339e114 | 0.281392 | ||||||||
\(700\) | −1.53522e115 | −0.911381 | ||||||||
\(701\) | −4.43843e114 | −0.248685 | −0.124342 | − | 0.992239i | \(-0.539682\pi\) | ||||
−0.124342 | + | 0.992239i | \(0.539682\pi\) | |||||||
\(702\) | 2.13602e115 | 1.12967 | ||||||||
\(703\) | −1.94516e114 | −0.0971104 | ||||||||
\(704\) | 5.50657e115 | 2.59531 | ||||||||
\(705\) | 6.22288e113 | 0.0276906 | ||||||||
\(706\) | −5.54334e115 | −2.32906 | ||||||||
\(707\) | −2.99687e115 | −1.18900 | ||||||||
\(708\) | 1.73956e115 | 0.651766 | ||||||||
\(709\) | −9.80069e114 | −0.346804 | −0.173402 | − | 0.984851i | \(-0.555476\pi\) | ||||
−0.173402 | + | 0.984851i | \(0.555476\pi\) | |||||||
\(710\) | 3.66799e114 | 0.122593 | ||||||||
\(711\) | −2.89618e115 | −0.914339 | ||||||||
\(712\) | 2.66679e115 | 0.795332 | ||||||||
\(713\) | 5.94709e115 | 1.67563 | ||||||||
\(714\) | −2.21732e115 | −0.590271 | ||||||||
\(715\) | 5.03509e114 | 0.126652 | ||||||||
\(716\) | 4.29996e115 | 1.02209 | ||||||||
\(717\) | 2.44225e115 | 0.548610 | ||||||||
\(718\) | 9.77913e114 | 0.207616 | ||||||||
\(719\) | 2.77664e114 | 0.0557186 | 0.0278593 | − | 0.999612i | \(-0.491131\pi\) | ||||
0.0278593 | + | 0.999612i | \(0.491131\pi\) | |||||||
\(720\) | −1.52414e114 | −0.0289107 | ||||||||
\(721\) | 2.84777e115 | 0.510654 | ||||||||
\(722\) | −2.70415e115 | −0.458432 | ||||||||
\(723\) | −8.56949e114 | −0.137358 | ||||||||
\(724\) | −1.57240e116 | −2.38315 | ||||||||
\(725\) | 2.89774e115 | 0.415308 | ||||||||
\(726\) | −1.00667e116 | −1.36444 | ||||||||
\(727\) | −2.96271e114 | −0.0379792 | −0.0189896 | − | 0.999820i | \(-0.506045\pi\) | ||||
−0.0189896 | + | 0.999820i | \(0.506045\pi\) | |||||||
\(728\) | 2.77963e115 | 0.337028 | ||||||||
\(729\) | 2.51435e115 | 0.288377 | ||||||||
\(730\) | −6.10917e113 | −0.00662836 | ||||||||
\(731\) | −1.55417e116 | −1.59531 | ||||||||
\(732\) | −1.11453e116 | −1.08241 | ||||||||
\(733\) | 1.99971e116 | 1.83762 | 0.918812 | − | 0.394695i | \(-0.129150\pi\) | ||||
0.918812 | + | 0.394695i | \(0.129150\pi\) | |||||||
\(734\) | 1.25461e116 | 1.09098 | ||||||||
\(735\) | −3.52685e114 | −0.0290235 | ||||||||
\(736\) | 2.29334e116 | 1.78614 | ||||||||
\(737\) | −3.92351e115 | −0.289229 | ||||||||
\(738\) | −1.04878e116 | −0.731817 | ||||||||
\(739\) | 2.00957e115 | 0.132740 | 0.0663701 | − | 0.997795i | \(-0.478858\pi\) | ||||
0.0663701 | + | 0.997795i | \(0.478858\pi\) | |||||||
\(740\) | −2.51492e114 | −0.0157268 | ||||||||
\(741\) | 5.97279e115 | 0.353622 | ||||||||
\(742\) | 2.24653e116 | 1.25937 | ||||||||
\(743\) | −1.11989e116 | −0.594466 | −0.297233 | − | 0.954805i | \(-0.596064\pi\) | ||||
−0.297233 | + | 0.954805i | \(0.596064\pi\) | |||||||
\(744\) | 8.09052e115 | 0.406698 | ||||||||
\(745\) | −2.74050e115 | −0.130467 | ||||||||
\(746\) | 6.66785e116 | 3.00651 | ||||||||
\(747\) | −2.75546e116 | −1.17682 | ||||||||
\(748\) | −6.38642e116 | −2.58370 | ||||||||
\(749\) | −2.43186e116 | −0.932020 | ||||||||
\(750\) | −4.28549e115 | −0.155604 | ||||||||
\(751\) | −4.00717e116 | −1.37854 | −0.689271 | − | 0.724504i | \(-0.742069\pi\) | ||||
−0.689271 | + | 0.724504i | \(0.742069\pi\) | |||||||
\(752\) | −6.99221e115 | −0.227925 | ||||||||
\(753\) | 1.01608e116 | 0.313857 | ||||||||
\(754\) | −1.79104e116 | −0.524283 | ||||||||
\(755\) | −2.36786e115 | −0.0656908 | ||||||||
\(756\) | 3.15977e116 | 0.830850 | ||||||||
\(757\) | 4.95196e116 | 1.23422 | 0.617112 | − | 0.786876i | \(-0.288303\pi\) | ||||
0.617112 | + | 0.786876i | \(0.288303\pi\) | |||||||
\(758\) | 2.62641e116 | 0.620525 | ||||||||
\(759\) | −5.30535e116 | −1.18829 | ||||||||
\(760\) | 2.44712e115 | 0.0519643 | ||||||||
\(761\) | 9.13010e116 | 1.83822 | 0.919109 | − | 0.394004i | \(-0.128910\pi\) | ||||
0.919109 | + | 0.394004i | \(0.128910\pi\) | |||||||
\(762\) | 1.21309e116 | 0.231588 | ||||||||
\(763\) | −1.98795e116 | −0.359884 | ||||||||
\(764\) | −6.08841e116 | −1.04526 | ||||||||
\(765\) | 4.78689e115 | 0.0779409 | ||||||||
\(766\) | −4.73637e115 | −0.0731442 | ||||||||
\(767\) | −4.83994e116 | −0.708970 | ||||||||
\(768\) | 9.14804e115 | 0.127116 | ||||||||
\(769\) | 3.66597e116 | 0.483251 | 0.241625 | − | 0.970370i | \(-0.422319\pi\) | ||||
0.241625 | + | 0.970370i | \(0.422319\pi\) | |||||||
\(770\) | 1.27147e116 | 0.159013 | ||||||||
\(771\) | 7.20517e116 | 0.854952 | ||||||||
\(772\) | −1.83947e117 | −2.07105 | ||||||||
\(773\) | 1.65148e116 | 0.176442 | 0.0882212 | − | 0.996101i | \(-0.471882\pi\) | ||||
0.0882212 | + | 0.996101i | \(0.471882\pi\) | |||||||
\(774\) | 1.59057e117 | 1.61266 | ||||||||
\(775\) | 1.24326e117 | 1.19631 | ||||||||
\(776\) | 7.40363e116 | 0.676153 | ||||||||
\(777\) | −4.54064e115 | −0.0393610 | ||||||||
\(778\) | −1.57230e117 | −1.29378 | ||||||||
\(779\) | −6.97077e116 | −0.544520 | ||||||||
\(780\) | 7.72227e115 | 0.0572682 | ||||||||
\(781\) | 1.90743e117 | 1.34302 | ||||||||
\(782\) | −3.60035e117 | −2.40697 | ||||||||
\(783\) | −5.96409e116 | −0.378611 | ||||||||
\(784\) | 3.96287e116 | 0.238896 | ||||||||
\(785\) | −3.95241e114 | −0.00226277 | ||||||||
\(786\) | 7.55888e114 | 0.00411003 | ||||||||
\(787\) | −1.71855e117 | −0.887535 | −0.443767 | − | 0.896142i | \(-0.646358\pi\) | ||||
−0.443767 | + | 0.896142i | \(0.646358\pi\) | |||||||
\(788\) | 2.03779e116 | 0.0999649 | ||||||||
\(789\) | −1.33733e117 | −0.623189 | ||||||||
\(790\) | −4.24854e116 | −0.188080 | ||||||||
\(791\) | −1.13931e117 | −0.479175 | ||||||||
\(792\) | 1.91462e117 | 0.765089 | ||||||||
\(793\) | 3.10094e117 | 1.17741 | ||||||||
\(794\) | 8.27060e116 | 0.298406 | ||||||||
\(795\) | 1.82827e116 | 0.0626862 | ||||||||
\(796\) | 4.08215e117 | 1.33018 | ||||||||
\(797\) | −2.22332e117 | −0.688556 | −0.344278 | − | 0.938868i | \(-0.611876\pi\) | ||||
−0.344278 | + | 0.938868i | \(0.611876\pi\) | |||||||
\(798\) | 1.50826e117 | 0.443977 | ||||||||
\(799\) | 2.19606e117 | 0.614468 | ||||||||
\(800\) | 4.79430e117 | 1.27521 | ||||||||
\(801\) | −3.54843e117 | −0.897261 | ||||||||
\(802\) | 3.97954e117 | 0.956689 | ||||||||
\(803\) | −3.17690e116 | −0.0726146 | ||||||||
\(804\) | −6.01746e116 | −0.130780 | ||||||||
\(805\) | 4.19899e116 | 0.0867783 | ||||||||
\(806\) | −7.68436e117 | −1.51021 | ||||||||
\(807\) | −3.12672e117 | −0.584401 | ||||||||
\(808\) | −6.61997e117 | −1.17678 | ||||||||
\(809\) | −9.77019e117 | −1.65192 | −0.825958 | − | 0.563732i | \(-0.809365\pi\) | ||||
−0.825958 | + | 0.563732i | \(0.809365\pi\) | |||||||
\(810\) | −2.35607e116 | −0.0378917 | ||||||||
\(811\) | 4.27401e117 | 0.653870 | 0.326935 | − | 0.945047i | \(-0.393984\pi\) | ||||
0.326935 | + | 0.945047i | \(0.393984\pi\) | |||||||
\(812\) | −2.64945e117 | −0.385599 | ||||||||
\(813\) | 6.83925e117 | 0.946982 | ||||||||
\(814\) | −2.23252e117 | −0.294108 | ||||||||
\(815\) | 5.59551e116 | 0.0701385 | ||||||||
\(816\) | 2.02759e117 | 0.241841 | ||||||||
\(817\) | 1.05718e118 | 1.19993 | ||||||||
\(818\) | 1.95628e117 | 0.211311 | ||||||||
\(819\) | −3.69857e117 | −0.380221 | ||||||||
\(820\) | −9.01257e116 | −0.0881835 | ||||||||
\(821\) | −2.83374e117 | −0.263914 | −0.131957 | − | 0.991255i | \(-0.542126\pi\) | ||||
−0.131957 | + | 0.991255i | \(0.542126\pi\) | |||||||
\(822\) | 1.25061e118 | 1.10870 | ||||||||
\(823\) | −2.15540e117 | −0.181901 | −0.0909504 | − | 0.995855i | \(-0.528990\pi\) | ||||
−0.0909504 | + | 0.995855i | \(0.528990\pi\) | |||||||
\(824\) | 6.29060e117 | 0.505406 | ||||||||
\(825\) | −1.10910e118 | −0.848372 | ||||||||
\(826\) | −1.22220e118 | −0.890121 | ||||||||
\(827\) | 9.73580e116 | 0.0675147 | 0.0337574 | − | 0.999430i | \(-0.489253\pi\) | ||||
0.0337574 | + | 0.999430i | \(0.489253\pi\) | |||||||
\(828\) | 2.15848e118 | 1.42534 | ||||||||
\(829\) | 2.64408e118 | 1.66271 | 0.831355 | − | 0.555741i | \(-0.187565\pi\) | ||||
0.831355 | + | 0.555741i | \(0.187565\pi\) | |||||||
\(830\) | −4.04210e117 | −0.242072 | ||||||||
\(831\) | −4.74557e117 | −0.270674 | ||||||||
\(832\) | −2.34975e118 | −1.27652 | ||||||||
\(833\) | −1.24463e118 | −0.644045 | ||||||||
\(834\) | −1.52258e118 | −0.750507 | ||||||||
\(835\) | 2.38489e117 | 0.111987 | ||||||||
\(836\) | 4.34417e118 | 1.94335 | ||||||||
\(837\) | −2.55886e118 | −1.09060 | ||||||||
\(838\) | −3.20112e118 | −1.29993 | ||||||||
\(839\) | 3.19388e118 | 1.23583 | 0.617915 | − | 0.786245i | \(-0.287978\pi\) | ||||
0.617915 | + | 0.786245i | \(0.287978\pi\) | |||||||
\(840\) | 5.71237e116 | 0.0210623 | ||||||||
\(841\) | −2.34593e118 | −0.824286 | ||||||||
\(842\) | 5.14475e118 | 1.72276 | ||||||||
\(843\) | 8.85152e117 | 0.282489 | ||||||||
\(844\) | −5.14699e118 | −1.56561 | ||||||||
\(845\) | 1.16743e117 | 0.0338480 | ||||||||
\(846\) | −2.24749e118 | −0.621152 | ||||||||
\(847\) | 4.14323e118 | 1.09159 | ||||||||
\(848\) | −2.05430e118 | −0.515978 | ||||||||
\(849\) | −1.15273e118 | −0.276037 | ||||||||
\(850\) | −7.52665e118 | −1.71844 | ||||||||
\(851\) | −7.37280e117 | −0.160504 | ||||||||
\(852\) | 2.92542e118 | 0.607273 | ||||||||
\(853\) | −8.55794e117 | −0.169408 | −0.0847039 | − | 0.996406i | \(-0.526994\pi\) | ||||
−0.0847039 | + | 0.996406i | \(0.526994\pi\) | |||||||
\(854\) | 7.83057e118 | 1.47826 | ||||||||
\(855\) | −3.25614e117 | −0.0586239 | ||||||||
\(856\) | −5.37188e118 | −0.922442 | ||||||||
\(857\) | 7.27197e118 | 1.19105 | 0.595523 | − | 0.803338i | \(-0.296945\pi\) | ||||
0.595523 | + | 0.803338i | \(0.296945\pi\) | |||||||
\(858\) | 6.85515e118 | 1.07098 | ||||||||
\(859\) | 9.35991e118 | 1.39492 | 0.697459 | − | 0.716625i | \(-0.254314\pi\) | ||||
0.697459 | + | 0.716625i | \(0.254314\pi\) | |||||||
\(860\) | 1.36683e118 | 0.194325 | ||||||||
\(861\) | −1.62720e118 | −0.220706 | ||||||||
\(862\) | 1.26535e119 | 1.63744 | ||||||||
\(863\) | −9.13910e117 | −0.112841 | −0.0564204 | − | 0.998407i | \(-0.517969\pi\) | ||||
−0.0564204 | + | 0.998407i | \(0.517969\pi\) | |||||||
\(864\) | −9.86756e118 | −1.16253 | ||||||||
\(865\) | 4.71348e117 | 0.0529895 | ||||||||
\(866\) | −1.23064e119 | −1.32025 | ||||||||
\(867\) | −1.25760e118 | −0.128756 | ||||||||
\(868\) | −1.13673e119 | −1.11073 | ||||||||
\(869\) | −2.20933e119 | −2.06044 | ||||||||
\(870\) | −3.68073e117 | −0.0327646 | ||||||||
\(871\) | 1.67423e118 | 0.142259 | ||||||||
\(872\) | −4.39130e118 | −0.356185 | ||||||||
\(873\) | −9.85127e118 | −0.762808 | ||||||||
\(874\) | 2.44903e119 | 1.81042 | ||||||||
\(875\) | 1.76381e118 | 0.124488 | ||||||||
\(876\) | −4.87238e117 | −0.0328341 | ||||||||
\(877\) | −1.18082e119 | −0.759802 | −0.379901 | − | 0.925027i | \(-0.624042\pi\) | ||||
−0.379901 | + | 0.925027i | \(0.624042\pi\) | |||||||
\(878\) | 3.41940e119 | 2.10098 | ||||||||
\(879\) | −2.07996e118 | −0.122041 | ||||||||
\(880\) | −1.16268e118 | −0.0651495 | ||||||||
\(881\) | −3.61720e119 | −1.93575 | −0.967873 | − | 0.251440i | \(-0.919096\pi\) | ||||
−0.967873 | + | 0.251440i | \(0.919096\pi\) | |||||||
\(882\) | 1.27377e119 | 0.651050 | ||||||||
\(883\) | 3.73604e119 | 1.82391 | 0.911954 | − | 0.410291i | \(-0.134573\pi\) | ||||
0.911954 | + | 0.410291i | \(0.134573\pi\) | |||||||
\(884\) | 2.72519e119 | 1.27081 | ||||||||
\(885\) | −9.94649e117 | −0.0443065 | ||||||||
\(886\) | −1.95622e119 | −0.832438 | ||||||||
\(887\) | 1.97664e119 | 0.803566 | 0.401783 | − | 0.915735i | \(-0.368391\pi\) | ||||
0.401783 | + | 0.915735i | \(0.368391\pi\) | |||||||
\(888\) | −1.00301e118 | −0.0389565 | ||||||||
\(889\) | −4.99280e118 | −0.185278 | ||||||||
\(890\) | −5.20534e118 | −0.184567 | ||||||||
\(891\) | −1.22521e119 | −0.415109 | ||||||||
\(892\) | 1.51825e119 | 0.491549 | ||||||||
\(893\) | −1.49380e119 | −0.462177 | ||||||||
\(894\) | −3.73112e119 | −1.10324 | ||||||||
\(895\) | −2.45864e118 | −0.0694805 | ||||||||
\(896\) | −2.83423e119 | −0.765526 | ||||||||
\(897\) | 2.26388e119 | 0.584467 | ||||||||
\(898\) | −4.30420e119 | −1.06219 | ||||||||
\(899\) | 2.14559e119 | 0.506150 | ||||||||
\(900\) | 4.51238e119 | 1.01762 | ||||||||
\(901\) | 6.45198e119 | 1.39104 | ||||||||
\(902\) | −8.00056e119 | −1.64913 | ||||||||
\(903\) | 2.46779e119 | 0.486357 | ||||||||
\(904\) | −2.51668e119 | −0.474250 | ||||||||
\(905\) | 8.99074e118 | 0.162005 | ||||||||
\(906\) | −3.22378e119 | −0.555487 | ||||||||
\(907\) | −3.42004e119 | −0.563555 | −0.281777 | − | 0.959480i | \(-0.590924\pi\) | ||||
−0.281777 | + | 0.959480i | \(0.590924\pi\) | |||||||
\(908\) | −5.61252e117 | −0.00884466 | ||||||||
\(909\) | 8.80852e119 | 1.32760 | ||||||||
\(910\) | −5.42560e118 | −0.0782116 | ||||||||
\(911\) | 6.98876e119 | 0.963620 | 0.481810 | − | 0.876276i | \(-0.339979\pi\) | ||||
0.481810 | + | 0.876276i | \(0.339979\pi\) | |||||||
\(912\) | −1.37921e119 | −0.181902 | ||||||||
\(913\) | −2.10198e120 | −2.65193 | ||||||||
\(914\) | −9.54254e119 | −1.15171 | ||||||||
\(915\) | 6.37268e118 | 0.0735814 | ||||||||
\(916\) | 1.80877e120 | 1.99810 | ||||||||
\(917\) | −3.11107e117 | −0.00328815 | ||||||||
\(918\) | 1.54913e120 | 1.56660 | ||||||||
\(919\) | 7.46775e119 | 0.722623 | 0.361311 | − | 0.932445i | \(-0.382329\pi\) | ||||
0.361311 | + | 0.932445i | \(0.382329\pi\) | |||||||
\(920\) | 9.27538e118 | 0.0858865 | ||||||||
\(921\) | 3.80038e119 | 0.336754 | ||||||||
\(922\) | −7.14383e118 | −0.0605799 | ||||||||
\(923\) | −8.13935e119 | −0.660573 | ||||||||
\(924\) | 1.01407e120 | 0.787684 | ||||||||
\(925\) | −1.54131e119 | −0.114591 | ||||||||
\(926\) | −3.18194e119 | −0.226437 | ||||||||
\(927\) | −8.37027e119 | −0.570178 | ||||||||
\(928\) | 8.27389e119 | 0.539532 | ||||||||
\(929\) | −1.75314e120 | −1.09441 | −0.547205 | − | 0.836999i | \(-0.684308\pi\) | ||||
−0.547205 | + | 0.836999i | \(0.684308\pi\) | |||||||
\(930\) | −1.57920e119 | −0.0943795 | ||||||||
\(931\) | 8.46618e119 | 0.484424 | ||||||||
\(932\) | −1.38837e120 | −0.760609 | ||||||||
\(933\) | −1.00238e119 | −0.0525808 | ||||||||
\(934\) | −3.17223e120 | −1.59337 | ||||||||
\(935\) | 3.65165e119 | 0.175638 | ||||||||
\(936\) | −8.16999e119 | −0.376313 | ||||||||
\(937\) | 7.97609e119 | 0.351833 | 0.175917 | − | 0.984405i | \(-0.443711\pi\) | ||||
0.175917 | + | 0.984405i | \(0.443711\pi\) | |||||||
\(938\) | 4.22781e119 | 0.178608 | ||||||||
\(939\) | −2.44068e120 | −0.987538 | ||||||||
\(940\) | −1.93135e119 | −0.0748484 | ||||||||
\(941\) | 2.31142e120 | 0.858024 | 0.429012 | − | 0.903299i | \(-0.358862\pi\) | ||||
0.429012 | + | 0.903299i | \(0.358862\pi\) | |||||||
\(942\) | −5.38110e118 | −0.0191342 | ||||||||
\(943\) | −2.64215e120 | −0.899982 | ||||||||
\(944\) | 1.11762e120 | 0.364692 | ||||||||
\(945\) | −1.80670e119 | −0.0564805 | ||||||||
\(946\) | 1.21335e121 | 3.63410 | ||||||||
\(947\) | 2.94297e120 | 0.844522 | 0.422261 | − | 0.906474i | \(-0.361237\pi\) | ||||
0.422261 | + | 0.906474i | \(0.361237\pi\) | |||||||
\(948\) | −3.38843e120 | −0.931668 | ||||||||
\(949\) | 1.35564e119 | 0.0357159 | ||||||||
\(950\) | 5.11977e120 | 1.29254 | ||||||||
\(951\) | 6.00374e119 | 0.145248 | ||||||||
\(952\) | 2.01590e120 | 0.467382 | ||||||||
\(953\) | −1.72509e118 | −0.00383309 | −0.00191654 | − | 0.999998i | \(-0.500610\pi\) | ||||
−0.00191654 | + | 0.999998i | \(0.500610\pi\) | |||||||
\(954\) | −6.60307e120 | −1.40617 | ||||||||
\(955\) | 3.48125e119 | 0.0710557 | ||||||||
\(956\) | −7.57981e120 | −1.48291 | ||||||||
\(957\) | −1.91406e120 | −0.358941 | ||||||||
\(958\) | −9.08181e120 | −1.63256 | ||||||||
\(959\) | −5.14723e120 | −0.886992 | ||||||||
\(960\) | −4.82893e119 | −0.0797748 | ||||||||
\(961\) | 2.89165e120 | 0.457982 | ||||||||
\(962\) | 9.52656e119 | 0.144659 | ||||||||
\(963\) | 7.14782e120 | 1.04066 | ||||||||
\(964\) | 2.65965e120 | 0.371282 | ||||||||
\(965\) | 1.05178e120 | 0.140788 | ||||||||
\(966\) | 5.71681e120 | 0.733805 | ||||||||
\(967\) | −1.30973e121 | −1.61217 | −0.806083 | − | 0.591802i | \(-0.798417\pi\) | ||||
−0.806083 | + | 0.591802i | \(0.798417\pi\) | |||||||
\(968\) | 9.15222e120 | 1.08038 | ||||||||
\(969\) | 4.33170e120 | 0.490395 | ||||||||
\(970\) | −1.44513e120 | −0.156910 | ||||||||
\(971\) | 1.50046e119 | 0.0156260 | 0.00781298 | − | 0.999969i | \(-0.497513\pi\) | ||||
0.00781298 | + | 0.999969i | \(0.497513\pi\) | |||||||
\(972\) | −1.46674e121 | −1.46511 | ||||||||
\(973\) | 6.26660e120 | 0.600430 | ||||||||
\(974\) | 3.96365e120 | 0.364298 | ||||||||
\(975\) | 4.73272e120 | 0.417277 | ||||||||
\(976\) | −7.16053e120 | −0.605658 | ||||||||
\(977\) | 2.74062e120 | 0.222392 | 0.111196 | − | 0.993799i | \(-0.464532\pi\) | ||||
0.111196 | + | 0.993799i | \(0.464532\pi\) | |||||||
\(978\) | 7.61814e120 | 0.593097 | ||||||||
\(979\) | −2.70689e121 | −2.02196 | ||||||||
\(980\) | 1.09460e120 | 0.0784512 | ||||||||
\(981\) | 5.84307e120 | 0.401833 | ||||||||
\(982\) | 1.64867e121 | 1.08797 | ||||||||
\(983\) | 2.98161e121 | 1.88814 | 0.944068 | − | 0.329751i | \(-0.106965\pi\) | ||||
0.944068 | + | 0.329751i | \(0.106965\pi\) | |||||||
\(984\) | −3.59442e120 | −0.218438 | ||||||||
\(985\) | −1.16517e119 | −0.00679553 | ||||||||
\(986\) | −1.29893e121 | −0.727062 | ||||||||
\(987\) | −3.48701e120 | −0.187331 | ||||||||
\(988\) | −1.85373e121 | −0.955851 | ||||||||
\(989\) | 4.00705e121 | 1.98324 | ||||||||
\(990\) | −3.73717e120 | −0.177548 | ||||||||
\(991\) | −3.44828e121 | −1.57261 | −0.786303 | − | 0.617841i | \(-0.788008\pi\) | ||||
−0.786303 | + | 0.617841i | \(0.788008\pi\) | |||||||
\(992\) | 3.54987e121 | 1.55414 | ||||||||
\(993\) | −4.75866e120 | −0.200004 | ||||||||
\(994\) | −2.05537e121 | −0.829357 | ||||||||
\(995\) | −2.33410e120 | −0.0904243 | ||||||||
\(996\) | −3.22379e121 | −1.19912 | ||||||||
\(997\) | 2.95661e121 | 1.05594 | 0.527972 | − | 0.849262i | \(-0.322953\pi\) | ||||
0.527972 | + | 0.849262i | \(0.322953\pi\) | |||||||
\(998\) | −3.51048e121 | −1.20387 | ||||||||
\(999\) | 3.17231e120 | 0.104465 |
(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 | 1.82.a.a.1.6 | ✓ | 6 | |
3.2 | odd | 2 | 9.82.a.b.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.82.a.a.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial | |
9.82.a.b.1.1 | 6 | 3.2 | odd | 2 |