Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 28.8329 | 1.27425 | 0.637123 | − | 0.770762i | \(-0.280124\pi\) | ||||
0.637123 | + | 0.770762i | \(0.280124\pi\) | |||||||
\(3\) | 253.694 | 1.80827 | 0.904137 | − | 0.427243i | \(-0.140515\pi\) | ||||
0.904137 | + | 0.427243i | \(0.140515\pi\) | |||||||
\(4\) | 319.336 | 0.623703 | ||||||||
\(5\) | −1602.54 | −1.14668 | −0.573342 | − | 0.819316i | \(-0.694353\pi\) | ||||
−0.573342 | + | 0.819316i | \(0.694353\pi\) | |||||||
\(6\) | 7314.73 | 2.30419 | ||||||||
\(7\) | 6961.05 | 1.09581 | 0.547903 | − | 0.836542i | \(-0.315426\pi\) | ||||
0.547903 | + | 0.836542i | \(0.315426\pi\) | |||||||
\(8\) | −5555.06 | −0.479494 | ||||||||
\(9\) | 44677.5 | 2.26985 | ||||||||
\(10\) | −46205.9 | −1.46116 | ||||||||
\(11\) | −63360.1 | −1.30481 | −0.652407 | − | 0.757869i | \(-0.726241\pi\) | ||||
−0.652407 | + | 0.757869i | \(0.726241\pi\) | |||||||
\(12\) | 81013.6 | 1.12783 | ||||||||
\(13\) | −114552. | −1.11239 | −0.556197 | − | 0.831051i | \(-0.687740\pi\) | ||||
−0.556197 | + | 0.831051i | \(0.687740\pi\) | |||||||
\(14\) | 200707. | 1.39633 | ||||||||
\(15\) | −406554. | −2.07352 | ||||||||
\(16\) | −323669. | −1.23470 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 1.28818e6 | 2.89235 | ||||||||
\(19\) | 50488.5 | 0.0888794 | 0.0444397 | − | 0.999012i | \(-0.485850\pi\) | ||||
0.0444397 | + | 0.999012i | \(0.485850\pi\) | |||||||
\(20\) | −511749. | −0.715191 | ||||||||
\(21\) | 1.76597e6 | 1.98152 | ||||||||
\(22\) | −1.82685e6 | −1.66265 | ||||||||
\(23\) | −1.13882e6 | −0.848555 | −0.424278 | − | 0.905532i | \(-0.639472\pi\) | ||||
−0.424278 | + | 0.905532i | \(0.639472\pi\) | |||||||
\(24\) | −1.40928e6 | −0.867057 | ||||||||
\(25\) | 615007. | 0.314884 | ||||||||
\(26\) | −3.30287e6 | −1.41746 | ||||||||
\(27\) | 6.34095e6 | 2.29624 | ||||||||
\(28\) | 2.22291e6 | 0.683458 | ||||||||
\(29\) | −2.03871e6 | −0.535259 | −0.267630 | − | 0.963522i | \(-0.586240\pi\) | ||||
−0.267630 | + | 0.963522i | \(0.586240\pi\) | |||||||
\(30\) | −1.17221e7 | −2.64217 | ||||||||
\(31\) | −1.03910e6 | −0.202083 | −0.101041 | − | 0.994882i | \(-0.532217\pi\) | ||||
−0.101041 | + | 0.994882i | \(0.532217\pi\) | |||||||
\(32\) | −6.48811e6 | −1.09381 | ||||||||
\(33\) | −1.60741e7 | −2.35946 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.11554e7 | −1.25654 | ||||||||
\(36\) | 1.42671e7 | 1.41571 | ||||||||
\(37\) | −1.84413e7 | −1.61765 | −0.808823 | − | 0.588052i | \(-0.799895\pi\) | ||||
−0.808823 | + | 0.588052i | \(0.799895\pi\) | |||||||
\(38\) | 1.45573e6 | 0.113254 | ||||||||
\(39\) | −2.90612e7 | −2.01151 | ||||||||
\(40\) | 8.90220e6 | 0.549829 | ||||||||
\(41\) | 7.96470e6 | 0.440192 | 0.220096 | − | 0.975478i | \(-0.429363\pi\) | ||||
0.220096 | + | 0.975478i | \(0.429363\pi\) | |||||||
\(42\) | 5.09182e7 | 2.52494 | ||||||||
\(43\) | 2.09816e7 | 0.935902 | 0.467951 | − | 0.883755i | \(-0.344992\pi\) | ||||
0.467951 | + | 0.883755i | \(0.344992\pi\) | |||||||
\(44\) | −2.02332e7 | −0.813817 | ||||||||
\(45\) | −7.15974e7 | −2.60280 | ||||||||
\(46\) | −3.28355e7 | −1.08127 | ||||||||
\(47\) | −6.43503e6 | −0.192358 | −0.0961790 | − | 0.995364i | \(-0.530662\pi\) | ||||
−0.0961790 | + | 0.995364i | \(0.530662\pi\) | |||||||
\(48\) | −8.21127e7 | −2.23267 | ||||||||
\(49\) | 8.10258e6 | 0.200789 | ||||||||
\(50\) | 1.77324e7 | 0.401239 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.65807e7 | −0.693803 | ||||||||
\(53\) | 1.61556e7 | 0.281242 | 0.140621 | − | 0.990063i | \(-0.455090\pi\) | ||||
0.140621 | + | 0.990063i | \(0.455090\pi\) | |||||||
\(54\) | 1.82828e8 | 2.92597 | ||||||||
\(55\) | 1.01537e8 | 1.49621 | ||||||||
\(56\) | −3.86690e7 | −0.525433 | ||||||||
\(57\) | 1.28086e7 | 0.160718 | ||||||||
\(58\) | −5.87819e7 | −0.682052 | ||||||||
\(59\) | −1.17489e8 | −1.26230 | −0.631152 | − | 0.775659i | \(-0.717417\pi\) | ||||
−0.631152 | + | 0.775659i | \(0.717417\pi\) | |||||||
\(60\) | −1.29827e8 | −1.29326 | ||||||||
\(61\) | 3.52242e7 | 0.325729 | 0.162865 | − | 0.986648i | \(-0.447927\pi\) | ||||
0.162865 | + | 0.986648i | \(0.447927\pi\) | |||||||
\(62\) | −2.99602e7 | −0.257503 | ||||||||
\(63\) | 3.11002e8 | 2.48732 | ||||||||
\(64\) | −2.13528e7 | −0.159091 | ||||||||
\(65\) | 1.83574e8 | 1.27556 | ||||||||
\(66\) | −4.63462e8 | −3.00653 | ||||||||
\(67\) | 2.32033e8 | 1.40674 | 0.703368 | − | 0.710826i | \(-0.251679\pi\) | ||||
0.703368 | + | 0.710826i | \(0.251679\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.88912e8 | −1.53442 | ||||||||
\(70\) | −3.21641e8 | −1.60114 | ||||||||
\(71\) | 7.20809e6 | 0.0336634 | 0.0168317 | − | 0.999858i | \(-0.494642\pi\) | ||||
0.0168317 | + | 0.999858i | \(0.494642\pi\) | |||||||
\(72\) | −2.48186e8 | −1.08838 | ||||||||
\(73\) | −3.16063e8 | −1.30263 | −0.651314 | − | 0.758808i | \(-0.725782\pi\) | ||||
−0.651314 | + | 0.758808i | \(0.725782\pi\) | |||||||
\(74\) | −5.31716e8 | −2.06128 | ||||||||
\(75\) | 1.56023e8 | 0.569396 | ||||||||
\(76\) | 1.61228e7 | 0.0554344 | ||||||||
\(77\) | −4.41053e8 | −1.42982 | ||||||||
\(78\) | −8.37918e8 | −2.56316 | ||||||||
\(79\) | 5.83535e8 | 1.68556 | 0.842782 | − | 0.538255i | \(-0.180916\pi\) | ||||
0.842782 | + | 0.538255i | \(0.180916\pi\) | |||||||
\(80\) | 5.18692e8 | 1.41581 | ||||||||
\(81\) | 7.29271e8 | 1.88238 | ||||||||
\(82\) | 2.29645e8 | 0.560913 | ||||||||
\(83\) | −2.61757e8 | −0.605407 | −0.302704 | − | 0.953085i | \(-0.597889\pi\) | ||||
−0.302704 | + | 0.953085i | \(0.597889\pi\) | |||||||
\(84\) | 5.63939e8 | 1.23588 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.04960e8 | 1.19257 | ||||||||
\(87\) | −5.17208e8 | −0.967895 | ||||||||
\(88\) | 3.51969e8 | 0.625651 | ||||||||
\(89\) | −8.28097e7 | −0.139903 | −0.0699513 | − | 0.997550i | \(-0.522284\pi\) | ||||
−0.0699513 | + | 0.997550i | \(0.522284\pi\) | |||||||
\(90\) | −2.06436e9 | −3.31661 | ||||||||
\(91\) | −7.97403e8 | −1.21897 | ||||||||
\(92\) | −3.63667e8 | −0.529247 | ||||||||
\(93\) | −2.63613e8 | −0.365421 | ||||||||
\(94\) | −1.85541e8 | −0.245111 | ||||||||
\(95\) | −8.09098e7 | −0.101917 | ||||||||
\(96\) | −1.64599e9 | −1.97791 | ||||||||
\(97\) | −1.66783e8 | −0.191284 | −0.0956422 | − | 0.995416i | \(-0.530490\pi\) | ||||
−0.0956422 | + | 0.995416i | \(0.530490\pi\) | |||||||
\(98\) | 2.33621e8 | 0.255855 | ||||||||
\(99\) | −2.83077e9 | −2.96173 | ||||||||
\(100\) | 1.96394e8 | 0.196394 | ||||||||
\(101\) | −1.93499e9 | −1.85026 | −0.925130 | − | 0.379651i | \(-0.876044\pi\) | ||||
−0.925130 | + | 0.379651i | \(0.876044\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.87339e9 | −1.64006 | −0.820031 | − | 0.572319i | \(-0.806044\pi\) | ||||
−0.820031 | + | 0.572319i | \(0.806044\pi\) | |||||||
\(104\) | 6.36344e8 | 0.533386 | ||||||||
\(105\) | −2.83004e9 | −2.27217 | ||||||||
\(106\) | 4.65812e8 | 0.358372 | ||||||||
\(107\) | 2.10383e9 | 1.55161 | 0.775805 | − | 0.630972i | \(-0.217344\pi\) | ||||
0.775805 | + | 0.630972i | \(0.217344\pi\) | |||||||
\(108\) | 2.02489e9 | 1.43217 | ||||||||
\(109\) | 1.00138e9 | 0.679486 | 0.339743 | − | 0.940518i | \(-0.389660\pi\) | ||||
0.339743 | + | 0.940518i | \(0.389660\pi\) | |||||||
\(110\) | 2.92761e9 | 1.90654 | ||||||||
\(111\) | −4.67844e9 | −2.92515 | ||||||||
\(112\) | −2.25307e9 | −1.35299 | ||||||||
\(113\) | −2.22131e9 | −1.28161 | −0.640806 | − | 0.767703i | \(-0.721400\pi\) | ||||
−0.640806 | + | 0.767703i | \(0.721400\pi\) | |||||||
\(114\) | 3.69310e8 | 0.204795 | ||||||||
\(115\) | 1.82500e9 | 0.973024 | ||||||||
\(116\) | −6.51034e8 | −0.333843 | ||||||||
\(117\) | −5.11790e9 | −2.52497 | ||||||||
\(118\) | −3.38755e9 | −1.60849 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.25843e9 | 0.994240 | ||||||||
\(121\) | 1.65655e9 | 0.702540 | ||||||||
\(122\) | 1.01562e9 | 0.415060 | ||||||||
\(123\) | 2.02059e9 | 0.795987 | ||||||||
\(124\) | −3.31822e8 | −0.126040 | ||||||||
\(125\) | 2.14439e9 | 0.785612 | ||||||||
\(126\) | 8.96710e9 | 3.16945 | ||||||||
\(127\) | −1.88159e9 | −0.641814 | −0.320907 | − | 0.947111i | \(-0.603988\pi\) | ||||
−0.320907 | + | 0.947111i | \(0.603988\pi\) | |||||||
\(128\) | 2.70625e9 | 0.891093 | ||||||||
\(129\) | 5.32290e9 | 1.69237 | ||||||||
\(130\) | 5.29298e9 | 1.62538 | ||||||||
\(131\) | 3.11456e9 | 0.924009 | 0.462005 | − | 0.886878i | \(-0.347130\pi\) | ||||
0.462005 | + | 0.886878i | \(0.347130\pi\) | |||||||
\(132\) | −5.13303e9 | −1.47160 | ||||||||
\(133\) | 3.51453e8 | 0.0973946 | ||||||||
\(134\) | 6.69017e9 | 1.79253 | ||||||||
\(135\) | −1.01616e10 | −2.63306 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.16041e9 | 1.00901 | 0.504503 | − | 0.863410i | \(-0.331676\pi\) | ||||
0.504503 | + | 0.863410i | \(0.331676\pi\) | |||||||
\(138\) | −8.33016e9 | −1.95523 | ||||||||
\(139\) | 8.10754e8 | 0.184214 | 0.0921070 | − | 0.995749i | \(-0.470640\pi\) | ||||
0.0921070 | + | 0.995749i | \(0.470640\pi\) | |||||||
\(140\) | −3.56231e9 | −0.783710 | ||||||||
\(141\) | −1.63253e9 | −0.347836 | ||||||||
\(142\) | 2.07830e8 | 0.0428954 | ||||||||
\(143\) | 7.25803e9 | 1.45147 | ||||||||
\(144\) | −1.44607e10 | −2.80258 | ||||||||
\(145\) | 3.26711e9 | 0.613773 | ||||||||
\(146\) | −9.11301e9 | −1.65987 | ||||||||
\(147\) | 2.05557e9 | 0.363082 | ||||||||
\(148\) | −5.88897e9 | −1.00893 | ||||||||
\(149\) | 1.33926e9 | 0.222601 | 0.111301 | − | 0.993787i | \(-0.464498\pi\) | ||||
0.111301 | + | 0.993787i | \(0.464498\pi\) | |||||||
\(150\) | 4.49861e9 | 0.725550 | ||||||||
\(151\) | −3.62654e9 | −0.567671 | −0.283835 | − | 0.958873i | \(-0.591607\pi\) | ||||
−0.283835 | + | 0.958873i | \(0.591607\pi\) | |||||||
\(152\) | −2.80467e8 | −0.0426172 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.27168e10 | −1.82195 | ||||||||
\(155\) | 1.66520e9 | 0.231725 | ||||||||
\(156\) | −9.28028e9 | −1.25459 | ||||||||
\(157\) | −4.56689e9 | −0.599891 | −0.299945 | − | 0.953956i | \(-0.596968\pi\) | ||||
−0.299945 | + | 0.953956i | \(0.596968\pi\) | |||||||
\(158\) | 1.68250e10 | 2.14782 | ||||||||
\(159\) | 4.09856e9 | 0.508563 | ||||||||
\(160\) | 1.03975e10 | 1.25426 | ||||||||
\(161\) | −7.92738e9 | −0.929851 | ||||||||
\(162\) | 2.10270e10 | 2.39861 | ||||||||
\(163\) | 1.59091e9 | 0.176523 | 0.0882616 | − | 0.996097i | \(-0.471869\pi\) | ||||
0.0882616 | + | 0.996097i | \(0.471869\pi\) | |||||||
\(164\) | 2.54342e9 | 0.274549 | ||||||||
\(165\) | 2.57593e10 | 2.70555 | ||||||||
\(166\) | −7.54723e9 | −0.771438 | ||||||||
\(167\) | 4.47570e9 | 0.445284 | 0.222642 | − | 0.974900i | \(-0.428532\pi\) | ||||
0.222642 | + | 0.974900i | \(0.428532\pi\) | |||||||
\(168\) | −9.81009e9 | −0.950126 | ||||||||
\(169\) | 2.51770e9 | 0.237418 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.25570e9 | 0.201743 | ||||||||
\(172\) | 6.70018e9 | 0.583725 | ||||||||
\(173\) | 4.80503e9 | 0.407839 | 0.203920 | − | 0.978988i | \(-0.434632\pi\) | ||||
0.203920 | + | 0.978988i | \(0.434632\pi\) | |||||||
\(174\) | −1.49126e10 | −1.23334 | ||||||||
\(175\) | 4.28110e9 | 0.345051 | ||||||||
\(176\) | 2.05077e10 | 1.61105 | ||||||||
\(177\) | −2.98063e10 | −2.28259 | ||||||||
\(178\) | −2.38764e9 | −0.178270 | ||||||||
\(179\) | −1.33451e10 | −0.971592 | −0.485796 | − | 0.874072i | \(-0.661470\pi\) | ||||
−0.485796 | + | 0.874072i | \(0.661470\pi\) | |||||||
\(180\) | −2.28637e10 | −1.62338 | ||||||||
\(181\) | −7.08745e9 | −0.490836 | −0.245418 | − | 0.969417i | \(-0.578925\pi\) | ||||
−0.245418 | + | 0.969417i | \(0.578925\pi\) | |||||||
\(182\) | −2.29914e10 | −1.55326 | ||||||||
\(183\) | 8.93616e9 | 0.589008 | ||||||||
\(184\) | 6.32621e9 | 0.406877 | ||||||||
\(185\) | 2.95529e10 | 1.85493 | ||||||||
\(186\) | −7.60072e9 | −0.465636 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.05494e9 | −0.119974 | ||||||||
\(189\) | 4.41396e10 | 2.51623 | ||||||||
\(190\) | −2.33286e9 | −0.129867 | ||||||||
\(191\) | −3.04732e10 | −1.65679 | −0.828396 | − | 0.560143i | \(-0.810746\pi\) | ||||
−0.828396 | + | 0.560143i | \(0.810746\pi\) | |||||||
\(192\) | −5.41708e9 | −0.287680 | ||||||||
\(193\) | −1.05728e10 | −0.548508 | −0.274254 | − | 0.961657i | \(-0.588431\pi\) | ||||
−0.274254 | + | 0.961657i | \(0.588431\pi\) | |||||||
\(194\) | −4.80884e9 | −0.243743 | ||||||||
\(195\) | 4.65717e10 | 2.30657 | ||||||||
\(196\) | 2.58745e9 | 0.125233 | ||||||||
\(197\) | 1.29392e10 | 0.612080 | 0.306040 | − | 0.952019i | \(-0.400996\pi\) | ||||
0.306040 | + | 0.952019i | \(0.400996\pi\) | |||||||
\(198\) | −8.16193e10 | −3.77398 | ||||||||
\(199\) | 1.78277e10 | 0.805854 | 0.402927 | − | 0.915232i | \(-0.367993\pi\) | ||||
0.402927 | + | 0.915232i | \(0.367993\pi\) | |||||||
\(200\) | −3.41640e9 | −0.150985 | ||||||||
\(201\) | 5.88652e10 | 2.54376 | ||||||||
\(202\) | −5.57914e10 | −2.35769 | ||||||||
\(203\) | −1.41916e10 | −0.586540 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.27637e10 | −0.504761 | ||||||||
\(206\) | −5.40152e10 | −2.08984 | ||||||||
\(207\) | −5.08797e10 | −1.92609 | ||||||||
\(208\) | 3.70769e10 | 1.37347 | ||||||||
\(209\) | −3.19896e9 | −0.115971 | ||||||||
\(210\) | −8.15983e10 | −2.89531 | ||||||||
\(211\) | 1.68952e10 | 0.586801 | 0.293401 | − | 0.955990i | \(-0.405213\pi\) | ||||
0.293401 | + | 0.955990i | \(0.405213\pi\) | |||||||
\(212\) | 5.15905e9 | 0.175412 | ||||||||
\(213\) | 1.82865e9 | 0.0608725 | ||||||||
\(214\) | 6.06594e10 | 1.97713 | ||||||||
\(215\) | −3.36238e10 | −1.07318 | ||||||||
\(216\) | −3.52243e10 | −1.10103 | ||||||||
\(217\) | −7.23322e9 | −0.221443 | ||||||||
\(218\) | 2.88728e10 | 0.865833 | ||||||||
\(219\) | −8.01831e10 | −2.35551 | ||||||||
\(220\) | 3.24244e10 | 0.933191 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.34893e11 | −3.72736 | ||||||||
\(223\) | −1.23092e10 | −0.333319 | −0.166659 | − | 0.986015i | \(-0.553298\pi\) | ||||
−0.166659 | + | 0.986015i | \(0.553298\pi\) | |||||||
\(224\) | −4.51641e10 | −1.19861 | ||||||||
\(225\) | 2.74770e10 | 0.714739 | ||||||||
\(226\) | −6.40469e10 | −1.63309 | ||||||||
\(227\) | −1.11999e10 | −0.279962 | −0.139981 | − | 0.990154i | \(-0.544704\pi\) | ||||
−0.139981 | + | 0.990154i | \(0.544704\pi\) | |||||||
\(228\) | 4.09025e9 | 0.100241 | ||||||||
\(229\) | 5.37234e10 | 1.29093 | 0.645467 | − | 0.763788i | \(-0.276663\pi\) | ||||
0.645467 | + | 0.763788i | \(0.276663\pi\) | |||||||
\(230\) | 5.26202e10 | 1.23987 | ||||||||
\(231\) | −1.11892e11 | −2.58551 | ||||||||
\(232\) | 1.13251e10 | 0.256654 | ||||||||
\(233\) | −3.19551e10 | −0.710295 | −0.355147 | − | 0.934810i | \(-0.615569\pi\) | ||||
−0.355147 | + | 0.934810i | \(0.615569\pi\) | |||||||
\(234\) | −1.47564e11 | −3.21743 | ||||||||
\(235\) | 1.03124e10 | 0.220574 | ||||||||
\(236\) | −3.75185e10 | −0.787303 | ||||||||
\(237\) | 1.48039e11 | 3.04796 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.64220e10 | −0.523813 | −0.261906 | − | 0.965093i | \(-0.584351\pi\) | ||||
−0.261906 | + | 0.965093i | \(0.584351\pi\) | |||||||
\(240\) | 1.31589e11 | 2.56017 | ||||||||
\(241\) | 6.13523e10 | 1.17153 | 0.585766 | − | 0.810480i | \(-0.300794\pi\) | ||||
0.585766 | + | 0.810480i | \(0.300794\pi\) | |||||||
\(242\) | 4.77632e10 | 0.895209 | ||||||||
\(243\) | 6.02026e10 | 1.10761 | ||||||||
\(244\) | 1.12484e10 | 0.203159 | ||||||||
\(245\) | −1.29847e10 | −0.230242 | ||||||||
\(246\) | 5.82596e10 | 1.01428 | ||||||||
\(247\) | −5.78357e9 | −0.0988689 | ||||||||
\(248\) | 5.77225e9 | 0.0968976 | ||||||||
\(249\) | −6.64062e10 | −1.09474 | ||||||||
\(250\) | 6.18289e10 | 1.00106 | ||||||||
\(251\) | 1.01008e11 | 1.60629 | 0.803145 | − | 0.595783i | \(-0.203158\pi\) | ||||
0.803145 | + | 0.595783i | \(0.203158\pi\) | |||||||
\(252\) | 9.93142e10 | 1.55135 | ||||||||
\(253\) | 7.21558e10 | 1.10721 | ||||||||
\(254\) | −5.42518e10 | −0.817829 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.89617e10 | 1.29456 | ||||||||
\(257\) | −6.24220e10 | −0.892563 | −0.446282 | − | 0.894893i | \(-0.647252\pi\) | ||||
−0.446282 | + | 0.894893i | \(0.647252\pi\) | |||||||
\(258\) | 1.53475e11 | 2.15649 | ||||||||
\(259\) | −1.28371e11 | −1.77262 | ||||||||
\(260\) | 5.86219e10 | 0.795573 | ||||||||
\(261\) | −9.10844e10 | −1.21496 | ||||||||
\(262\) | 8.98019e10 | 1.17742 | ||||||||
\(263\) | −4.12563e10 | −0.531728 | −0.265864 | − | 0.964010i | \(-0.585657\pi\) | ||||
−0.265864 | + | 0.964010i | \(0.585657\pi\) | |||||||
\(264\) | 8.92923e10 | 1.13135 | ||||||||
\(265\) | −2.58899e10 | −0.322496 | ||||||||
\(266\) | 1.01334e10 | 0.124105 | ||||||||
\(267\) | −2.10083e10 | −0.252982 | ||||||||
\(268\) | 7.40964e10 | 0.877386 | ||||||||
\(269\) | 7.37696e10 | 0.858998 | 0.429499 | − | 0.903067i | \(-0.358690\pi\) | ||||
0.429499 | + | 0.903067i | \(0.358690\pi\) | |||||||
\(270\) | −2.92989e11 | −3.35517 | ||||||||
\(271\) | 6.04771e10 | 0.681128 | 0.340564 | − | 0.940221i | \(-0.389382\pi\) | ||||
0.340564 | + | 0.940221i | \(0.389382\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.02296e11 | −2.20422 | ||||||||
\(274\) | 1.19957e11 | 1.28572 | ||||||||
\(275\) | −3.89669e10 | −0.410865 | ||||||||
\(276\) | −9.22599e10 | −0.957023 | ||||||||
\(277\) | 6.65923e10 | 0.679618 | 0.339809 | − | 0.940494i | \(-0.389638\pi\) | ||||
0.339809 | + | 0.940494i | \(0.389638\pi\) | |||||||
\(278\) | 2.33764e10 | 0.234734 | ||||||||
\(279\) | −4.64243e10 | −0.458698 | ||||||||
\(280\) | 6.19686e10 | 0.602505 | ||||||||
\(281\) | 1.81317e11 | 1.73484 | 0.867419 | − | 0.497578i | \(-0.165777\pi\) | ||||
0.867419 | + | 0.497578i | \(0.165777\pi\) | |||||||
\(282\) | −4.70705e10 | −0.443228 | ||||||||
\(283\) | −3.12027e10 | −0.289170 | −0.144585 | − | 0.989492i | \(-0.546185\pi\) | ||||
−0.144585 | + | 0.989492i | \(0.546185\pi\) | |||||||
\(284\) | 2.30180e9 | 0.0209960 | ||||||||
\(285\) | −2.05263e10 | −0.184293 | ||||||||
\(286\) | 2.09270e11 | 1.84953 | ||||||||
\(287\) | 5.54427e10 | 0.482365 | ||||||||
\(288\) | −2.89873e11 | −2.48280 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 9.42003e10 | 0.782098 | ||||||||
\(291\) | −4.23118e10 | −0.345894 | ||||||||
\(292\) | −1.00930e11 | −0.812454 | ||||||||
\(293\) | −1.41584e11 | −1.12230 | −0.561151 | − | 0.827713i | \(-0.689641\pi\) | ||||
−0.561151 | + | 0.827713i | \(0.689641\pi\) | |||||||
\(294\) | 5.92682e10 | 0.462656 | ||||||||
\(295\) | 1.88281e11 | 1.44746 | ||||||||
\(296\) | 1.02442e11 | 0.775652 | ||||||||
\(297\) | −4.01763e11 | −2.99617 | ||||||||
\(298\) | 3.86149e10 | 0.283649 | ||||||||
\(299\) | 1.30454e11 | 0.943927 | ||||||||
\(300\) | 4.98239e10 | 0.355134 | ||||||||
\(301\) | 1.46054e11 | 1.02557 | ||||||||
\(302\) | −1.04564e11 | −0.723352 | ||||||||
\(303\) | −4.90895e11 | −3.34578 | ||||||||
\(304\) | −1.63415e10 | −0.109739 | ||||||||
\(305\) | −5.64482e10 | −0.373509 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.60774e10 | 0.103299 | 0.0516493 | − | 0.998665i | \(-0.483552\pi\) | ||||
0.0516493 | + | 0.998665i | \(0.483552\pi\) | |||||||
\(308\) | −1.40844e11 | −0.891785 | ||||||||
\(309\) | −4.75267e11 | −2.96568 | ||||||||
\(310\) | 4.80125e10 | 0.295275 | ||||||||
\(311\) | −2.50094e11 | −1.51594 | −0.757969 | − | 0.652291i | \(-0.773808\pi\) | ||||
−0.757969 | + | 0.652291i | \(0.773808\pi\) | |||||||
\(312\) | 1.61436e11 | 0.964508 | ||||||||
\(313\) | −1.83769e11 | −1.08224 | −0.541119 | − | 0.840946i | \(-0.681999\pi\) | ||||
−0.541119 | + | 0.840946i | \(0.681999\pi\) | |||||||
\(314\) | −1.31677e11 | −0.764408 | ||||||||
\(315\) | −4.98393e11 | −2.85217 | ||||||||
\(316\) | 1.86344e11 | 1.05129 | ||||||||
\(317\) | 4.13738e8 | 0.00230122 | 0.00115061 | − | 0.999999i | \(-0.499634\pi\) | ||||
0.00115061 | + | 0.999999i | \(0.499634\pi\) | |||||||
\(318\) | 1.18173e11 | 0.648034 | ||||||||
\(319\) | 1.29173e11 | 0.698414 | ||||||||
\(320\) | 3.42188e10 | 0.182427 | ||||||||
\(321\) | 5.33727e11 | 2.80574 | ||||||||
\(322\) | −2.28569e11 | −1.18486 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.32883e11 | 1.17404 | ||||||||
\(325\) | −7.04504e10 | −0.350274 | ||||||||
\(326\) | 4.58706e10 | 0.224934 | ||||||||
\(327\) | 2.54044e11 | 1.22870 | ||||||||
\(328\) | −4.42444e10 | −0.211070 | ||||||||
\(329\) | −4.47945e10 | −0.210787 | ||||||||
\(330\) | 7.42715e11 | 3.44754 | ||||||||
\(331\) | 2.02135e11 | 0.925586 | 0.462793 | − | 0.886466i | \(-0.346847\pi\) | ||||
0.462793 | + | 0.886466i | \(0.346847\pi\) | |||||||
\(332\) | −8.35886e10 | −0.377595 | ||||||||
\(333\) | −8.23910e11 | −3.67182 | ||||||||
\(334\) | 1.29048e11 | 0.567402 | ||||||||
\(335\) | −3.71841e11 | −1.61308 | ||||||||
\(336\) | −5.71590e11 | −2.44657 | ||||||||
\(337\) | 3.22290e11 | 1.36117 | 0.680585 | − | 0.732669i | \(-0.261726\pi\) | ||||
0.680585 | + | 0.732669i | \(0.261726\pi\) | |||||||
\(338\) | 7.25926e10 | 0.302529 | ||||||||
\(339\) | −5.63533e11 | −2.31750 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.58374e10 | 0.263680 | ||||||||
\(342\) | 6.50384e10 | 0.257070 | ||||||||
\(343\) | −2.24501e11 | −0.875779 | ||||||||
\(344\) | −1.16554e11 | −0.448760 | ||||||||
\(345\) | 4.62992e11 | 1.75949 | ||||||||
\(346\) | 1.38543e11 | 0.519688 | ||||||||
\(347\) | 5.55411e10 | 0.205651 | 0.102826 | − | 0.994699i | \(-0.467212\pi\) | ||||
0.102826 | + | 0.994699i | \(0.467212\pi\) | |||||||
\(348\) | −1.65163e11 | −0.603680 | ||||||||
\(349\) | −1.80693e11 | −0.651968 | −0.325984 | − | 0.945375i | \(-0.605696\pi\) | ||||
−0.325984 | + | 0.945375i | \(0.605696\pi\) | |||||||
\(350\) | 1.23436e11 | 0.439680 | ||||||||
\(351\) | −7.26369e11 | −2.55432 | ||||||||
\(352\) | 4.11087e11 | 1.42722 | ||||||||
\(353\) | 1.18291e11 | 0.405475 | 0.202738 | − | 0.979233i | \(-0.435016\pi\) | ||||
0.202738 | + | 0.979233i | \(0.435016\pi\) | |||||||
\(354\) | −8.59401e11 | −2.90858 | ||||||||
\(355\) | −1.15512e10 | −0.0386012 | ||||||||
\(356\) | −2.64441e10 | −0.0872578 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.84779e11 | −1.23805 | ||||||||
\(359\) | −4.33360e11 | −1.37697 | −0.688484 | − | 0.725251i | \(-0.741724\pi\) | ||||
−0.688484 | + | 0.725251i | \(0.741724\pi\) | |||||||
\(360\) | 3.97728e11 | 1.24803 | ||||||||
\(361\) | −3.20139e11 | −0.992100 | ||||||||
\(362\) | −2.04352e11 | −0.625446 | ||||||||
\(363\) | 4.20257e11 | 1.27038 | ||||||||
\(364\) | −2.54640e11 | −0.760273 | ||||||||
\(365\) | 5.06503e11 | 1.49370 | ||||||||
\(366\) | 2.57655e11 | 0.750541 | ||||||||
\(367\) | 4.17148e11 | 1.20031 | 0.600155 | − | 0.799884i | \(-0.295106\pi\) | ||||
0.600155 | + | 0.799884i | \(0.295106\pi\) | |||||||
\(368\) | 3.68600e11 | 1.04771 | ||||||||
\(369\) | 3.55843e11 | 0.999170 | ||||||||
\(370\) | 8.52095e11 | 2.36364 | ||||||||
\(371\) | 1.12460e11 | 0.308187 | ||||||||
\(372\) | −8.41811e10 | −0.227914 | ||||||||
\(373\) | −3.22658e11 | −0.863083 | −0.431542 | − | 0.902093i | \(-0.642030\pi\) | ||||
−0.431542 | + | 0.902093i | \(0.642030\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.44017e11 | 1.42060 | ||||||||
\(376\) | 3.57469e10 | 0.0922346 | ||||||||
\(377\) | 2.33539e11 | 0.595419 | ||||||||
\(378\) | 1.27267e12 | 3.20630 | ||||||||
\(379\) | 4.31063e11 | 1.07316 | 0.536580 | − | 0.843849i | \(-0.319716\pi\) | ||||
0.536580 | + | 0.843849i | \(0.319716\pi\) | |||||||
\(380\) | −2.58374e10 | −0.0635657 | ||||||||
\(381\) | −4.77349e11 | −1.16058 | ||||||||
\(382\) | −8.78631e11 | −2.11116 | ||||||||
\(383\) | −7.20550e10 | −0.171108 | −0.0855539 | − | 0.996334i | \(-0.527266\pi\) | ||||
−0.0855539 | + | 0.996334i | \(0.527266\pi\) | |||||||
\(384\) | 6.86559e11 | 1.61134 | ||||||||
\(385\) | 7.06804e11 | 1.63955 | ||||||||
\(386\) | −3.04845e11 | −0.698934 | ||||||||
\(387\) | 9.37405e11 | 2.12436 | ||||||||
\(388\) | −5.32599e10 | −0.119305 | ||||||||
\(389\) | −2.81453e11 | −0.623206 | −0.311603 | − | 0.950212i | \(-0.600866\pi\) | ||||
−0.311603 | + | 0.950212i | \(0.600866\pi\) | |||||||
\(390\) | 1.34280e12 | 2.93913 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.50103e10 | −0.0962775 | ||||||||
\(393\) | 7.90145e11 | 1.67086 | ||||||||
\(394\) | 3.73074e11 | 0.779940 | ||||||||
\(395\) | −9.35139e11 | −1.93281 | ||||||||
\(396\) | −9.03967e11 | −1.84724 | ||||||||
\(397\) | −6.13368e11 | −1.23926 | −0.619632 | − | 0.784893i | \(-0.712718\pi\) | ||||
−0.619632 | + | 0.784893i | \(0.712718\pi\) | |||||||
\(398\) | 5.14024e11 | 1.02686 | ||||||||
\(399\) | 8.91614e10 | 0.176116 | ||||||||
\(400\) | −1.99059e11 | −0.388786 | ||||||||
\(401\) | −9.06061e11 | −1.74988 | −0.874939 | − | 0.484233i | \(-0.839099\pi\) | ||||
−0.874939 | + | 0.484233i | \(0.839099\pi\) | |||||||
\(402\) | 1.69725e12 | 3.24138 | ||||||||
\(403\) | 1.19031e11 | 0.224795 | ||||||||
\(404\) | −6.17913e11 | −1.15401 | ||||||||
\(405\) | −1.16869e12 | −2.15849 | ||||||||
\(406\) | −4.09184e11 | −0.747396 | ||||||||
\(407\) | 1.16844e12 | 2.11073 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.05301e11 | 0.892884 | 0.446442 | − | 0.894813i | \(-0.352691\pi\) | ||||
0.446442 | + | 0.894813i | \(0.352691\pi\) | |||||||
\(410\) | −3.68016e11 | −0.643190 | ||||||||
\(411\) | 1.05547e12 | 1.82456 | ||||||||
\(412\) | −5.98241e11 | −1.02291 | ||||||||
\(413\) | −8.17848e11 | −1.38324 | ||||||||
\(414\) | −1.46701e12 | −2.45432 | ||||||||
\(415\) | 4.19477e11 | 0.694211 | ||||||||
\(416\) | 7.43227e11 | 1.21675 | ||||||||
\(417\) | 2.05683e11 | 0.333109 | ||||||||
\(418\) | −9.22352e10 | −0.147776 | ||||||||
\(419\) | −8.55218e11 | −1.35554 | −0.677772 | − | 0.735272i | \(-0.737054\pi\) | ||||
−0.677772 | + | 0.735272i | \(0.737054\pi\) | |||||||
\(420\) | −9.03735e11 | −1.41716 | ||||||||
\(421\) | 1.94096e11 | 0.301125 | 0.150563 | − | 0.988600i | \(-0.451891\pi\) | ||||
0.150563 | + | 0.988600i | \(0.451891\pi\) | |||||||
\(422\) | 4.87136e11 | 0.747730 | ||||||||
\(423\) | −2.87501e11 | −0.436624 | ||||||||
\(424\) | −8.97451e10 | −0.134854 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.27252e10 | 0.0775666 | ||||||||
\(427\) | 2.45197e11 | 0.356936 | ||||||||
\(428\) | 6.71828e11 | 0.967745 | ||||||||
\(429\) | 1.84132e12 | 2.62465 | ||||||||
\(430\) | −9.69472e11 | −1.36750 | ||||||||
\(431\) | 1.88698e11 | 0.263402 | 0.131701 | − | 0.991289i | \(-0.457956\pi\) | ||||
0.131701 | + | 0.991289i | \(0.457956\pi\) | |||||||
\(432\) | −2.05236e12 | −2.83516 | ||||||||
\(433\) | 2.24845e11 | 0.307389 | 0.153694 | − | 0.988118i | \(-0.450883\pi\) | ||||
0.153694 | + | 0.988118i | \(0.450883\pi\) | |||||||
\(434\) | −2.08555e11 | −0.282173 | ||||||||
\(435\) | 8.28846e11 | 1.10987 | ||||||||
\(436\) | 3.19778e11 | 0.423798 | ||||||||
\(437\) | −5.74973e10 | −0.0754191 | ||||||||
\(438\) | −2.31191e12 | −3.00150 | ||||||||
\(439\) | 9.16644e11 | 1.17791 | 0.588953 | − | 0.808168i | \(-0.299540\pi\) | ||||
0.588953 | + | 0.808168i | \(0.299540\pi\) | |||||||
\(440\) | −5.64044e11 | −0.717424 | ||||||||
\(441\) | 3.62003e11 | 0.455762 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.92953e11 | −0.608119 | −0.304060 | − | 0.952653i | \(-0.598342\pi\) | ||||
−0.304060 | + | 0.952653i | \(0.598342\pi\) | |||||||
\(444\) | −1.49399e12 | −1.82442 | ||||||||
\(445\) | 1.32706e11 | 0.160424 | ||||||||
\(446\) | −3.54911e11 | −0.424730 | ||||||||
\(447\) | 3.39763e11 | 0.402524 | ||||||||
\(448\) | −1.48638e11 | −0.174333 | ||||||||
\(449\) | −9.28323e11 | −1.07793 | −0.538965 | − | 0.842328i | \(-0.681185\pi\) | ||||
−0.538965 | + | 0.842328i | \(0.681185\pi\) | |||||||
\(450\) | 7.92241e11 | 0.910754 | ||||||||
\(451\) | −5.04644e11 | −0.574369 | ||||||||
\(452\) | −7.09345e11 | −0.799346 | ||||||||
\(453\) | −9.20031e11 | −1.02650 | ||||||||
\(454\) | −3.22926e11 | −0.356740 | ||||||||
\(455\) | 1.27787e12 | 1.39777 | ||||||||
\(456\) | −7.11526e10 | −0.0770635 | ||||||||
\(457\) | 1.66023e12 | 1.78052 | 0.890258 | − | 0.455456i | \(-0.150524\pi\) | ||||
0.890258 | + | 0.455456i | \(0.150524\pi\) | |||||||
\(458\) | 1.54900e12 | 1.64497 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.82790e11 | 0.606879 | ||||||||
\(461\) | −1.62302e11 | −0.167367 | −0.0836837 | − | 0.996492i | \(-0.526669\pi\) | ||||
−0.0836837 | + | 0.996492i | \(0.526669\pi\) | |||||||
\(462\) | −3.22618e12 | −3.29458 | ||||||||
\(463\) | 7.72644e10 | 0.0781385 | 0.0390692 | − | 0.999237i | \(-0.487561\pi\) | ||||
0.0390692 | + | 0.999237i | \(0.487561\pi\) | |||||||
\(464\) | 6.59866e11 | 0.660883 | ||||||||
\(465\) | 4.22450e11 | 0.419022 | ||||||||
\(466\) | −9.21358e11 | −0.905090 | ||||||||
\(467\) | 6.91956e11 | 0.673213 | 0.336607 | − | 0.941645i | \(-0.390721\pi\) | ||||
0.336607 | + | 0.941645i | \(0.390721\pi\) | |||||||
\(468\) | −1.63433e12 | −1.57483 | ||||||||
\(469\) | 1.61519e12 | 1.54151 | ||||||||
\(470\) | 2.97336e11 | 0.281065 | ||||||||
\(471\) | −1.15859e12 | −1.08477 | ||||||||
\(472\) | 6.52659e11 | 0.605268 | ||||||||
\(473\) | −1.32939e12 | −1.22118 | ||||||||
\(474\) | 4.26840e12 | 3.88385 | ||||||||
\(475\) | 3.10508e10 | 0.0279867 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.21790e11 | 0.638378 | ||||||||
\(478\) | −7.61824e11 | −0.667466 | ||||||||
\(479\) | 1.79976e12 | 1.56208 | 0.781042 | − | 0.624478i | \(-0.214688\pi\) | ||||
0.781042 | + | 0.624478i | \(0.214688\pi\) | |||||||
\(480\) | 2.63777e12 | 2.26804 | ||||||||
\(481\) | 2.11249e12 | 1.79946 | ||||||||
\(482\) | 1.76897e12 | 1.49282 | ||||||||
\(483\) | −2.01113e12 | −1.68143 | ||||||||
\(484\) | 5.28997e11 | 0.438176 | ||||||||
\(485\) | 2.67277e11 | 0.219343 | ||||||||
\(486\) | 1.73582e12 | 1.41137 | ||||||||
\(487\) | −8.60582e11 | −0.693285 | −0.346643 | − | 0.937997i | \(-0.612678\pi\) | ||||
−0.346643 | + | 0.937997i | \(0.612678\pi\) | |||||||
\(488\) | −1.95673e11 | −0.156185 | ||||||||
\(489\) | 4.03604e11 | 0.319202 | ||||||||
\(490\) | −3.74387e11 | −0.293385 | ||||||||
\(491\) | 5.49516e11 | 0.426692 | 0.213346 | − | 0.976977i | \(-0.431564\pi\) | ||||
0.213346 | + | 0.976977i | \(0.431564\pi\) | |||||||
\(492\) | 6.45249e11 | 0.496460 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −1.66757e11 | −0.125983 | ||||||||
\(495\) | 4.53642e12 | 3.39617 | ||||||||
\(496\) | 3.36324e11 | 0.249511 | ||||||||
\(497\) | 5.01758e10 | 0.0368885 | ||||||||
\(498\) | −1.91468e12 | −1.39497 | ||||||||
\(499\) | −1.30212e12 | −0.940150 | −0.470075 | − | 0.882626i | \(-0.655773\pi\) | ||||
−0.470075 | + | 0.882626i | \(0.655773\pi\) | |||||||
\(500\) | 6.84780e11 | 0.489989 | ||||||||
\(501\) | 1.13546e12 | 0.805196 | ||||||||
\(502\) | 2.91235e12 | 2.04681 | ||||||||
\(503\) | 1.54975e12 | 1.07946 | 0.539730 | − | 0.841838i | \(-0.318526\pi\) | ||||
0.539730 | + | 0.841838i | \(0.318526\pi\) | |||||||
\(504\) | −1.72764e12 | −1.19265 | ||||||||
\(505\) | 3.10090e12 | 2.12166 | ||||||||
\(506\) | 2.08046e12 | 1.41085 | ||||||||
\(507\) | 6.38725e11 | 0.429317 | ||||||||
\(508\) | −6.00861e11 | −0.400302 | ||||||||
\(509\) | −1.50541e12 | −0.994091 | −0.497045 | − | 0.867725i | \(-0.665582\pi\) | ||||
−0.497045 | + | 0.867725i | \(0.665582\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.20013e12 | −1.42743 | ||||||||
\(512\) | 1.17942e12 | 0.758499 | ||||||||
\(513\) | 3.20145e11 | 0.204088 | ||||||||
\(514\) | −1.79981e12 | −1.13735 | ||||||||
\(515\) | 3.00218e12 | 1.88063 | ||||||||
\(516\) | 1.69979e12 | 1.05553 | ||||||||
\(517\) | 4.07724e11 | 0.250991 | ||||||||
\(518\) | −3.70130e12 | −2.25876 | ||||||||
\(519\) | 1.21901e12 | 0.737485 | ||||||||
\(520\) | −1.01977e12 | −0.611625 | ||||||||
\(521\) | 2.16632e12 | 1.28811 | 0.644056 | − | 0.764978i | \(-0.277250\pi\) | ||||
0.644056 | + | 0.764978i | \(0.277250\pi\) | |||||||
\(522\) | −2.62623e12 | −1.54816 | ||||||||
\(523\) | −2.82309e12 | −1.64994 | −0.824969 | − | 0.565178i | \(-0.808808\pi\) | ||||
−0.824969 | + | 0.565178i | \(0.808808\pi\) | |||||||
\(524\) | 9.94593e11 | 0.576308 | ||||||||
\(525\) | 1.08609e12 | 0.623947 | ||||||||
\(526\) | −1.18954e12 | −0.677553 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 5.20267e12 | 2.91322 | ||||||||
\(529\) | −5.04240e11 | −0.279954 | ||||||||
\(530\) | −7.46481e11 | −0.410939 | ||||||||
\(531\) | −5.24912e12 | −2.86524 | ||||||||
\(532\) | 1.12232e11 | 0.0607453 | ||||||||
\(533\) | −9.12374e11 | −0.489666 | ||||||||
\(534\) | −6.05730e11 | −0.322362 | ||||||||
\(535\) | −3.37146e12 | −1.77921 | ||||||||
\(536\) | −1.28895e12 | −0.674522 | ||||||||
\(537\) | −3.38557e12 | −1.75690 | ||||||||
\(538\) | 2.12699e12 | 1.09457 | ||||||||
\(539\) | −5.13380e11 | −0.261993 | ||||||||
\(540\) | −3.24497e12 | −1.64225 | ||||||||
\(541\) | 2.38210e11 | 0.119556 | 0.0597782 | − | 0.998212i | \(-0.480961\pi\) | ||||
0.0597782 | + | 0.998212i | \(0.480961\pi\) | |||||||
\(542\) | 1.74373e12 | 0.867925 | ||||||||
\(543\) | −1.79804e12 | −0.887566 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.60475e12 | −0.779156 | ||||||||
\(546\) | −5.83279e12 | −2.80872 | ||||||||
\(547\) | 1.95687e12 | 0.934585 | 0.467293 | − | 0.884103i | \(-0.345229\pi\) | ||||
0.467293 | + | 0.884103i | \(0.345229\pi\) | |||||||
\(548\) | 1.32857e12 | 0.629320 | ||||||||
\(549\) | 1.57373e12 | 0.739358 | ||||||||
\(550\) | −1.12353e12 | −0.523543 | ||||||||
\(551\) | −1.02931e11 | −0.0475735 | ||||||||
\(552\) | 1.60492e12 | 0.735746 | ||||||||
\(553\) | 4.06202e12 | 1.84705 | ||||||||
\(554\) | 1.92005e12 | 0.866001 | ||||||||
\(555\) | 7.49738e12 | 3.35422 | ||||||||
\(556\) | 2.58903e11 | 0.114895 | ||||||||
\(557\) | −5.54013e11 | −0.243877 | −0.121939 | − | 0.992538i | \(-0.538911\pi\) | ||||
−0.121939 | + | 0.992538i | \(0.538911\pi\) | |||||||
\(558\) | −1.33855e12 | −0.584494 | ||||||||
\(559\) | −2.40349e12 | −1.04109 | ||||||||
\(560\) | 3.61064e12 | 1.55145 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.22788e12 | 2.21061 | ||||||||
\(563\) | −6.79128e11 | −0.284881 | −0.142441 | − | 0.989803i | \(-0.545495\pi\) | ||||
−0.142441 | + | 0.989803i | \(0.545495\pi\) | |||||||
\(564\) | −5.21325e11 | −0.216946 | ||||||||
\(565\) | 3.55974e12 | 1.46960 | ||||||||
\(566\) | −8.99665e11 | −0.368474 | ||||||||
\(567\) | 5.07649e12 | 2.06272 | ||||||||
\(568\) | −4.00413e10 | −0.0161414 | ||||||||
\(569\) | −2.62380e12 | −1.04936 | −0.524681 | − | 0.851299i | \(-0.675815\pi\) | ||||
−0.524681 | + | 0.851299i | \(0.675815\pi\) | |||||||
\(570\) | −5.91833e11 | −0.234835 | ||||||||
\(571\) | 2.30932e12 | 0.909123 | 0.454561 | − | 0.890715i | \(-0.349796\pi\) | ||||
0.454561 | + | 0.890715i | \(0.349796\pi\) | |||||||
\(572\) | 2.31775e12 | 0.905284 | ||||||||
\(573\) | −7.73086e12 | −2.99593 | ||||||||
\(574\) | 1.59857e12 | 0.614651 | ||||||||
\(575\) | −7.00383e11 | −0.267196 | ||||||||
\(576\) | −9.53991e11 | −0.361113 | ||||||||
\(577\) | 4.55996e12 | 1.71266 | 0.856328 | − | 0.516432i | \(-0.172740\pi\) | ||||
0.856328 | + | 0.516432i | \(0.172740\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.68226e12 | −0.991852 | ||||||||
\(580\) | 1.04331e12 | 0.382812 | ||||||||
\(581\) | −1.82211e12 | −0.663408 | ||||||||
\(582\) | −1.21997e12 | −0.440755 | ||||||||
\(583\) | −1.02362e12 | −0.366969 | ||||||||
\(584\) | 1.75575e12 | 0.624603 | ||||||||
\(585\) | 8.20164e12 | 2.89534 | ||||||||
\(586\) | −4.08228e12 | −1.43009 | ||||||||
\(587\) | −6.94817e11 | −0.241546 | −0.120773 | − | 0.992680i | \(-0.538537\pi\) | ||||
−0.120773 | + | 0.992680i | \(0.538537\pi\) | |||||||
\(588\) | 6.56419e11 | 0.226456 | ||||||||
\(589\) | −5.24626e10 | −0.0179610 | ||||||||
\(590\) | 5.42869e12 | 1.84442 | ||||||||
\(591\) | 3.28258e12 | 1.10681 | ||||||||
\(592\) | 5.96886e12 | 1.99730 | ||||||||
\(593\) | −3.17510e12 | −1.05441 | −0.527207 | − | 0.849737i | \(-0.676761\pi\) | ||||
−0.527207 | + | 0.849737i | \(0.676761\pi\) | |||||||
\(594\) | −1.15840e13 | −3.81785 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.27675e11 | 0.138837 | ||||||||
\(597\) | 4.52277e12 | 1.45720 | ||||||||
\(598\) | 3.76138e12 | 1.20280 | ||||||||
\(599\) | −2.43909e12 | −0.774119 | −0.387060 | − | 0.922055i | \(-0.626509\pi\) | ||||
−0.387060 | + | 0.922055i | \(0.626509\pi\) | |||||||
\(600\) | −8.66719e11 | −0.273022 | ||||||||
\(601\) | 2.36635e12 | 0.739851 | 0.369925 | − | 0.929061i | \(-0.379383\pi\) | ||||
0.369925 | + | 0.929061i | \(0.379383\pi\) | |||||||
\(602\) | 4.21115e12 | 1.30682 | ||||||||
\(603\) | 1.03666e13 | 3.19308 | ||||||||
\(604\) | −1.15809e12 | −0.354058 | ||||||||
\(605\) | −2.65469e12 | −0.805591 | ||||||||
\(606\) | −1.41539e13 | −4.26334 | ||||||||
\(607\) | 6.01062e12 | 1.79709 | 0.898545 | − | 0.438881i | \(-0.144625\pi\) | ||||
0.898545 | + | 0.438881i | \(0.144625\pi\) | |||||||
\(608\) | −3.27575e11 | −0.0972176 | ||||||||
\(609\) | −3.60031e12 | −1.06062 | ||||||||
\(610\) | −1.62757e12 | −0.475942 | ||||||||
\(611\) | 7.37146e11 | 0.213978 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.01272e12 | −0.861761 | −0.430880 | − | 0.902409i | \(-0.641797\pi\) | ||||
−0.430880 | + | 0.902409i | \(0.641797\pi\) | |||||||
\(614\) | 4.63559e11 | 0.131628 | ||||||||
\(615\) | −3.23808e12 | −0.912746 | ||||||||
\(616\) | 2.45007e12 | 0.685592 | ||||||||
\(617\) | −1.01050e12 | −0.280707 | −0.140354 | − | 0.990101i | \(-0.544824\pi\) | ||||
−0.140354 | + | 0.990101i | \(0.544824\pi\) | |||||||
\(618\) | −1.37033e13 | −3.77901 | ||||||||
\(619\) | −1.82736e11 | −0.0500284 | −0.0250142 | − | 0.999687i | \(-0.507963\pi\) | ||||
−0.0250142 | + | 0.999687i | \(0.507963\pi\) | |||||||
\(620\) | 5.31758e11 | 0.144528 | ||||||||
\(621\) | −7.22120e12 | −1.94849 | ||||||||
\(622\) | −7.21093e12 | −1.93168 | ||||||||
\(623\) | −5.76442e11 | −0.153306 | ||||||||
\(624\) | 9.40618e12 | 2.48361 | ||||||||
\(625\) | −4.63765e12 | −1.21573 | ||||||||
\(626\) | −5.29860e12 | −1.37904 | ||||||||
\(627\) | −8.11555e11 | −0.209708 | ||||||||
\(628\) | −1.45837e12 | −0.374154 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1.43701e13 | −3.63436 | ||||||||
\(631\) | −6.42710e11 | −0.161392 | −0.0806962 | − | 0.996739i | \(-0.525714\pi\) | ||||
−0.0806962 | + | 0.996739i | \(0.525714\pi\) | |||||||
\(632\) | −3.24157e12 | −0.808219 | ||||||||
\(633\) | 4.28620e12 | 1.06110 | ||||||||
\(634\) | 1.19293e10 | 0.00293233 | ||||||||
\(635\) | 3.01533e12 | 0.735958 | ||||||||
\(636\) | 1.30882e12 | 0.317192 | ||||||||
\(637\) | −9.28168e11 | −0.223357 | ||||||||
\(638\) | 3.72443e12 | 0.889951 | ||||||||
\(639\) | 3.22039e11 | 0.0764108 | ||||||||
\(640\) | −4.33687e12 | −1.02180 | ||||||||
\(641\) | −6.42109e12 | −1.50227 | −0.751134 | − | 0.660150i | \(-0.770493\pi\) | ||||
−0.751134 | + | 0.660150i | \(0.770493\pi\) | |||||||
\(642\) | 1.53889e13 | 3.57520 | ||||||||
\(643\) | −7.03016e12 | −1.62187 | −0.810935 | − | 0.585137i | \(-0.801041\pi\) | ||||
−0.810935 | + | 0.585137i | \(0.801041\pi\) | |||||||
\(644\) | −2.53150e12 | −0.579951 | ||||||||
\(645\) | −8.53015e12 | −1.94061 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.41347e12 | 1.43888 | 0.719439 | − | 0.694556i | \(-0.244399\pi\) | ||||
0.719439 | + | 0.694556i | \(0.244399\pi\) | |||||||
\(648\) | −4.05114e12 | −0.902589 | ||||||||
\(649\) | 7.44412e12 | 1.64707 | ||||||||
\(650\) | −2.03129e12 | −0.446336 | ||||||||
\(651\) | −1.83502e12 | −0.400430 | ||||||||
\(652\) | 5.08036e11 | 0.110098 | ||||||||
\(653\) | −4.35666e11 | −0.0937659 | −0.0468829 | − | 0.998900i | \(-0.514929\pi\) | ||||
−0.0468829 | + | 0.998900i | \(0.514929\pi\) | |||||||
\(654\) | 7.32484e12 | 1.56566 | ||||||||
\(655\) | −4.99121e12 | −1.05955 | ||||||||
\(656\) | −2.57792e12 | −0.543504 | ||||||||
\(657\) | −1.41209e13 | −2.95677 | ||||||||
\(658\) | −1.29156e12 | −0.268594 | ||||||||
\(659\) | −1.79536e12 | −0.370823 | −0.185412 | − | 0.982661i | \(-0.559362\pi\) | ||||
−0.185412 | + | 0.982661i | \(0.559362\pi\) | |||||||
\(660\) | 8.22588e12 | 1.68746 | ||||||||
\(661\) | −1.53076e12 | −0.311889 | −0.155945 | − | 0.987766i | \(-0.549842\pi\) | ||||
−0.155945 | + | 0.987766i | \(0.549842\pi\) | |||||||
\(662\) | 5.82815e12 | 1.17942 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.45408e12 | 0.290289 | ||||||||
\(665\) | −5.63217e11 | −0.111681 | ||||||||
\(666\) | −2.37557e13 | −4.67880 | ||||||||
\(667\) | 2.32172e12 | 0.454197 | ||||||||
\(668\) | 1.42925e12 | 0.277725 | ||||||||
\(669\) | −3.12278e12 | −0.602731 | ||||||||
\(670\) | −1.07213e13 | −2.05546 | ||||||||
\(671\) | −2.23181e12 | −0.425016 | ||||||||
\(672\) | −1.14578e13 | −2.16741 | ||||||||
\(673\) | −1.00261e13 | −1.88393 | −0.941965 | − | 0.335710i | \(-0.891024\pi\) | ||||
−0.941965 | + | 0.335710i | \(0.891024\pi\) | |||||||
\(674\) | 9.29256e12 | 1.73447 | ||||||||
\(675\) | 3.89973e12 | 0.723048 | ||||||||
\(676\) | 8.03993e11 | 0.148079 | ||||||||
\(677\) | −1.68851e12 | −0.308926 | −0.154463 | − | 0.987999i | \(-0.549365\pi\) | ||||
−0.154463 | + | 0.987999i | \(0.549365\pi\) | |||||||
\(678\) | −1.62483e13 | −2.95307 | ||||||||
\(679\) | −1.16099e12 | −0.209610 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.84135e12 | −0.506247 | ||||||||
\(682\) | 1.89828e12 | 0.335994 | ||||||||
\(683\) | 9.76584e12 | 1.71718 | 0.858592 | − | 0.512660i | \(-0.171340\pi\) | ||||
0.858592 | + | 0.512660i | \(0.171340\pi\) | |||||||
\(684\) | 7.20327e11 | 0.125828 | ||||||||
\(685\) | −6.66722e12 | −1.15701 | ||||||||
\(686\) | −6.47301e12 | −1.11596 | ||||||||
\(687\) | 1.36293e13 | 2.33436 | ||||||||
\(688\) | −6.79108e12 | −1.15556 | ||||||||
\(689\) | −1.85065e12 | −0.312852 | ||||||||
\(690\) | 1.33494e13 | 2.24203 | ||||||||
\(691\) | 2.34843e12 | 0.391856 | 0.195928 | − | 0.980618i | \(-0.437228\pi\) | ||||
0.195928 | + | 0.980618i | \(0.437228\pi\) | |||||||
\(692\) | 1.53442e12 | 0.254371 | ||||||||
\(693\) | −1.97051e13 | −3.24549 | ||||||||
\(694\) | 1.60141e12 | 0.262051 | ||||||||
\(695\) | −1.29927e12 | −0.211235 | ||||||||
\(696\) | 2.87312e12 | 0.464100 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −5.20989e12 | −0.830767 | ||||||||
\(699\) | −8.10681e12 | −1.28441 | ||||||||
\(700\) | 1.36711e12 | 0.215210 | ||||||||
\(701\) | −9.78498e12 | −1.53048 | −0.765242 | − | 0.643742i | \(-0.777381\pi\) | ||||
−0.765242 | + | 0.643742i | \(0.777381\pi\) | |||||||
\(702\) | −2.09433e13 | −3.25483 | ||||||||
\(703\) | −9.31073e11 | −0.143775 | ||||||||
\(704\) | 1.35292e12 | 0.207584 | ||||||||
\(705\) | 2.61619e12 | 0.398857 | ||||||||
\(706\) | 3.41066e12 | 0.516675 | ||||||||
\(707\) | −1.34696e13 | −2.02752 | ||||||||
\(708\) | −9.51822e12 | −1.42366 | ||||||||
\(709\) | −5.41326e12 | −0.804545 | −0.402273 | − | 0.915520i | \(-0.631780\pi\) | ||||
−0.402273 | + | 0.915520i | \(0.631780\pi\) | |||||||
\(710\) | −3.33056e11 | −0.0491875 | ||||||||
\(711\) | 2.60709e13 | 3.82598 | ||||||||
\(712\) | 4.60012e11 | 0.0670826 | ||||||||
\(713\) | 1.18335e12 | 0.171478 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.16313e13 | −1.66437 | ||||||||
\(716\) | −4.26158e12 | −0.605985 | ||||||||
\(717\) | −6.70311e12 | −0.947196 | ||||||||
\(718\) | −1.24950e13 | −1.75460 | ||||||||
\(719\) | −4.91756e11 | −0.0686229 | −0.0343115 | − | 0.999411i | \(-0.510924\pi\) | ||||
−0.0343115 | + | 0.999411i | \(0.510924\pi\) | |||||||
\(720\) | 2.31738e13 | 3.21367 | ||||||||
\(721\) | −1.30407e13 | −1.79719 | ||||||||
\(722\) | −9.23052e12 | −1.26418 | ||||||||
\(723\) | 1.55647e13 | 2.11845 | ||||||||
\(724\) | −2.26328e12 | −0.306136 | ||||||||
\(725\) | −1.25382e12 | −0.168544 | ||||||||
\(726\) | 1.21172e13 | 1.61878 | ||||||||
\(727\) | 4.85245e11 | 0.0644253 | 0.0322127 | − | 0.999481i | \(-0.489745\pi\) | ||||
0.0322127 | + | 0.999481i | \(0.489745\pi\) | |||||||
\(728\) | 4.42962e12 | 0.584488 | ||||||||
\(729\) | 9.18785e11 | 0.120487 | ||||||||
\(730\) | 1.46040e13 | 1.90334 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 2.85364e12 | 0.367366 | ||||||||
\(733\) | 4.53070e12 | 0.579693 | 0.289846 | − | 0.957073i | \(-0.406396\pi\) | ||||
0.289846 | + | 0.957073i | \(0.406396\pi\) | |||||||
\(734\) | 1.20276e13 | 1.52949 | ||||||||
\(735\) | −3.29414e12 | −0.416341 | ||||||||
\(736\) | 7.38880e12 | 0.928162 | ||||||||
\(737\) | −1.47016e13 | −1.83553 | ||||||||
\(738\) | 1.02600e13 | 1.27319 | ||||||||
\(739\) | −3.39131e12 | −0.418281 | −0.209140 | − | 0.977886i | \(-0.567067\pi\) | ||||
−0.209140 | + | 0.977886i | \(0.567067\pi\) | |||||||
\(740\) | 9.43730e12 | 1.15692 | ||||||||
\(741\) | −1.46725e12 | −0.178782 | ||||||||
\(742\) | 3.24254e12 | 0.392706 | ||||||||
\(743\) | 1.09348e13 | 1.31632 | 0.658161 | − | 0.752877i | \(-0.271335\pi\) | ||||
0.658161 | + | 0.752877i | \(0.271335\pi\) | |||||||
\(744\) | 1.46438e12 | 0.175217 | ||||||||
\(745\) | −2.14622e12 | −0.255253 | ||||||||
\(746\) | −9.30316e12 | −1.09978 | ||||||||
\(747\) | −1.16947e13 | −1.37418 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.46448e13 | 1.70026 | ||||||||
\(750\) | 1.56856e13 | 1.81019 | ||||||||
\(751\) | −5.13831e12 | −0.589441 | −0.294721 | − | 0.955583i | \(-0.595227\pi\) | ||||
−0.294721 | + | 0.955583i | \(0.595227\pi\) | |||||||
\(752\) | 2.08282e12 | 0.237504 | ||||||||
\(753\) | 2.56251e13 | 2.90461 | ||||||||
\(754\) | 6.73359e12 | 0.758710 | ||||||||
\(755\) | 5.81167e12 | 0.650939 | ||||||||
\(756\) | 1.40954e13 | 1.56938 | ||||||||
\(757\) | 8.25749e12 | 0.913938 | 0.456969 | − | 0.889483i | \(-0.348935\pi\) | ||||
0.456969 | + | 0.889483i | \(0.348935\pi\) | |||||||
\(758\) | 1.24288e13 | 1.36747 | ||||||||
\(759\) | 1.83055e13 | 2.00213 | ||||||||
\(760\) | 4.49459e11 | 0.0488685 | ||||||||
\(761\) | 1.37466e13 | 1.48581 | 0.742906 | − | 0.669396i | \(-0.233447\pi\) | ||||
0.742906 | + | 0.669396i | \(0.233447\pi\) | |||||||
\(762\) | −1.37633e13 | −1.47886 | ||||||||
\(763\) | 6.97067e12 | 0.744585 | ||||||||
\(764\) | −9.73119e12 | −1.03335 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.07756e12 | −0.218033 | ||||||||
\(767\) | 1.34586e13 | 1.40418 | ||||||||
\(768\) | 2.25690e13 | 2.34092 | ||||||||
\(769\) | −1.41070e13 | −1.45468 | −0.727338 | − | 0.686280i | \(-0.759243\pi\) | ||||
−0.727338 | + | 0.686280i | \(0.759243\pi\) | |||||||
\(770\) | 2.03792e13 | 2.08920 | ||||||||
\(771\) | −1.58361e13 | −1.61400 | ||||||||
\(772\) | −3.37628e12 | −0.342106 | ||||||||
\(773\) | −3.76516e12 | −0.379294 | −0.189647 | − | 0.981852i | \(-0.560734\pi\) | ||||
−0.189647 | + | 0.981852i | \(0.560734\pi\) | |||||||
\(774\) | 2.70281e13 | 2.70696 | ||||||||
\(775\) | −6.39053e11 | −0.0636326 | ||||||||
\(776\) | 9.26490e11 | 0.0917198 | ||||||||
\(777\) | −3.25668e13 | −3.20539 | ||||||||
\(778\) | −8.11509e12 | −0.794118 | ||||||||
\(779\) | 4.02126e11 | 0.0391240 | ||||||||
\(780\) | 1.48720e13 | 1.43861 | ||||||||
\(781\) | −4.56705e11 | −0.0439244 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.29273e13 | −1.22908 | ||||||||
\(784\) | −2.62255e12 | −0.247914 | ||||||||
\(785\) | 7.31862e12 | 0.687885 | ||||||||
\(786\) | 2.27822e13 | 2.12909 | ||||||||
\(787\) | 5.93405e12 | 0.551397 | 0.275699 | − | 0.961244i | \(-0.411091\pi\) | ||||
0.275699 | + | 0.961244i | \(0.411091\pi\) | |||||||
\(788\) | 4.13194e12 | 0.381756 | ||||||||
\(789\) | −1.04665e13 | −0.961510 | ||||||||
\(790\) | −2.69628e13 | −2.46287 | ||||||||
\(791\) | −1.54627e13 | −1.40440 | ||||||||
\(792\) | 1.57251e13 | 1.42014 | ||||||||
\(793\) | −4.03501e12 | −0.362339 | ||||||||
\(794\) | −1.76852e13 | −1.57913 | ||||||||
\(795\) | −6.56811e12 | −0.583161 | ||||||||
\(796\) | 5.69303e12 | 0.502614 | ||||||||
\(797\) | −1.41517e13 | −1.24235 | −0.621177 | − | 0.783670i | \(-0.713345\pi\) | ||||
−0.621177 | + | 0.783670i | \(0.713345\pi\) | |||||||
\(798\) | 2.57078e12 | 0.224415 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −3.99024e12 | −0.344424 | ||||||||
\(801\) | −3.69973e12 | −0.317558 | ||||||||
\(802\) | −2.61244e13 | −2.22978 | ||||||||
\(803\) | 2.00258e13 | 1.69969 | ||||||||
\(804\) | 1.87978e13 | 1.58655 | ||||||||
\(805\) | 1.27039e13 | 1.06625 | ||||||||
\(806\) | 3.43201e12 | 0.286445 | ||||||||
\(807\) | 1.87149e13 | 1.55330 | ||||||||
\(808\) | 1.07490e13 | 0.887189 | ||||||||
\(809\) | 5.98845e12 | 0.491525 | 0.245763 | − | 0.969330i | \(-0.420962\pi\) | ||||
0.245763 | + | 0.969330i | \(0.420962\pi\) | |||||||
\(810\) | −3.36966e13 | −2.75045 | ||||||||
\(811\) | 1.95715e13 | 1.58865 | 0.794327 | − | 0.607490i | \(-0.207824\pi\) | ||||
0.794327 | + | 0.607490i | \(0.207824\pi\) | |||||||
\(812\) | −4.53188e12 | −0.365827 | ||||||||
\(813\) | 1.53427e13 | 1.23167 | ||||||||
\(814\) | 3.36895e13 | 2.68959 | ||||||||
\(815\) | −2.54950e12 | −0.202416 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.05933e12 | 0.0831824 | ||||||||
\(818\) | 1.45693e13 | 1.13775 | ||||||||
\(819\) | −3.56260e13 | −2.76687 | ||||||||
\(820\) | −4.07593e12 | −0.314821 | ||||||||
\(821\) | 3.53238e12 | 0.271346 | 0.135673 | − | 0.990754i | \(-0.456680\pi\) | ||||
0.135673 | + | 0.990754i | \(0.456680\pi\) | |||||||
\(822\) | 3.04323e13 | 2.32494 | ||||||||
\(823\) | 1.42829e13 | 1.08522 | 0.542609 | − | 0.839986i | \(-0.317437\pi\) | ||||
0.542609 | + | 0.839986i | \(0.317437\pi\) | |||||||
\(824\) | 1.04068e13 | 0.786401 | ||||||||
\(825\) | −9.88566e12 | −0.742956 | ||||||||
\(826\) | −2.35809e13 | −1.76259 | ||||||||
\(827\) | 1.97804e12 | 0.147048 | 0.0735242 | − | 0.997293i | \(-0.476575\pi\) | ||||
0.0735242 | + | 0.997293i | \(0.476575\pi\) | |||||||
\(828\) | −1.62477e13 | −1.20131 | ||||||||
\(829\) | −1.38516e13 | −1.01860 | −0.509301 | − | 0.860588i | \(-0.670096\pi\) | ||||
−0.509301 | + | 0.860588i | \(0.670096\pi\) | |||||||
\(830\) | 1.20947e13 | 0.884595 | ||||||||
\(831\) | 1.68940e13 | 1.22893 | ||||||||
\(832\) | 2.44601e12 | 0.176972 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 5.93044e12 | 0.424463 | ||||||||
\(835\) | −7.17249e12 | −0.510600 | ||||||||
\(836\) | −1.02154e12 | −0.0723316 | ||||||||
\(837\) | −6.58887e12 | −0.464030 | ||||||||
\(838\) | −2.46584e13 | −1.72730 | ||||||||
\(839\) | −1.47221e13 | −1.02575 | −0.512876 | − | 0.858463i | \(-0.671420\pi\) | ||||
−0.512876 | + | 0.858463i | \(0.671420\pi\) | |||||||
\(840\) | 1.57211e13 | 1.08949 | ||||||||
\(841\) | −1.03508e13 | −0.713497 | ||||||||
\(842\) | 5.59635e12 | 0.383708 | ||||||||
\(843\) | 4.59989e13 | 3.13706 | ||||||||
\(844\) | 5.39523e12 | 0.365990 | ||||||||
\(845\) | −4.03472e12 | −0.272244 | ||||||||
\(846\) | −8.28949e12 | −0.556366 | ||||||||
\(847\) | 1.15313e13 | 0.769847 | ||||||||
\(848\) | −5.22905e12 | −0.347249 | ||||||||
\(849\) | −7.91594e12 | −0.522899 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.10013e13 | 1.37266 | ||||||||
\(852\) | 5.83953e11 | 0.0379664 | ||||||||
\(853\) | 1.19185e13 | 0.770817 | 0.385408 | − | 0.922746i | \(-0.374061\pi\) | ||||
0.385408 | + | 0.922746i | \(0.374061\pi\) | |||||||
\(854\) | 7.06975e12 | 0.454825 | ||||||||
\(855\) | −3.61485e12 | −0.231336 | ||||||||
\(856\) | −1.16869e13 | −0.743989 | ||||||||
\(857\) | −2.67712e13 | −1.69533 | −0.847666 | − | 0.530530i | \(-0.821993\pi\) | ||||
−0.847666 | + | 0.530530i | \(0.821993\pi\) | |||||||
\(858\) | 5.30905e13 | 3.34445 | ||||||||
\(859\) | −1.36188e13 | −0.853431 | −0.426716 | − | 0.904386i | \(-0.640329\pi\) | ||||
−0.426716 | + | 0.904386i | \(0.640329\pi\) | |||||||
\(860\) | −1.07373e13 | −0.669348 | ||||||||
\(861\) | 1.40655e13 | 0.872247 | ||||||||
\(862\) | 5.44071e12 | 0.335639 | ||||||||
\(863\) | 1.57643e13 | 0.967446 | 0.483723 | − | 0.875221i | \(-0.339284\pi\) | ||||
0.483723 | + | 0.875221i | \(0.339284\pi\) | |||||||
\(864\) | −4.11408e13 | −2.51166 | ||||||||
\(865\) | −7.70026e12 | −0.467663 | ||||||||
\(866\) | 6.48293e12 | 0.391689 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.30983e12 | −0.138115 | ||||||||
\(869\) | −3.69729e13 | −2.19935 | ||||||||
\(870\) | 2.38980e13 | 1.41425 | ||||||||
\(871\) | −2.65798e13 | −1.56484 | ||||||||
\(872\) | −5.56274e12 | −0.325810 | ||||||||
\(873\) | −7.45146e12 | −0.434187 | ||||||||
\(874\) | −1.65782e12 | −0.0961025 | ||||||||
\(875\) | 1.49272e13 | 0.860878 | ||||||||
\(876\) | −2.56054e13 | −1.46914 | ||||||||
\(877\) | −2.58985e11 | −0.0147835 | −0.00739174 | − | 0.999973i | \(-0.502353\pi\) | ||||
−0.00739174 | + | 0.999973i | \(0.502353\pi\) | |||||||
\(878\) | 2.64295e13 | 1.50094 | ||||||||
\(879\) | −3.59190e13 | −2.02943 | ||||||||
\(880\) | −3.28643e13 | −1.84737 | ||||||||
\(881\) | 7.41674e12 | 0.414784 | 0.207392 | − | 0.978258i | \(-0.433503\pi\) | ||||
0.207392 | + | 0.978258i | \(0.433503\pi\) | |||||||
\(882\) | 1.04376e13 | 0.580754 | ||||||||
\(883\) | 1.94425e13 | 1.07629 | 0.538146 | − | 0.842852i | \(-0.319125\pi\) | ||||
0.538146 | + | 0.842852i | \(0.319125\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.77657e13 | 2.61741 | ||||||||
\(886\) | −1.42133e13 | −0.774893 | ||||||||
\(887\) | −2.94376e13 | −1.59678 | −0.798391 | − | 0.602139i | \(-0.794315\pi\) | ||||
−0.798391 | + | 0.602139i | \(0.794315\pi\) | |||||||
\(888\) | 2.59890e13 | 1.40259 | ||||||||
\(889\) | −1.30979e13 | −0.703303 | ||||||||
\(890\) | 3.82629e12 | 0.204420 | ||||||||
\(891\) | −4.62067e13 | −2.45615 | ||||||||
\(892\) | −3.93079e12 | −0.207892 | ||||||||
\(893\) | −3.24895e11 | −0.0170967 | ||||||||
\(894\) | 9.79635e12 | 0.512915 | ||||||||
\(895\) | 2.13861e13 | 1.11411 | ||||||||
\(896\) | 1.88383e13 | 0.976464 | ||||||||
\(897\) | 3.30955e13 | 1.70688 | ||||||||
\(898\) | −2.67663e13 | −1.37355 | ||||||||
\(899\) | 2.11842e12 | 0.108167 | ||||||||
\(900\) | 8.77440e12 | 0.445785 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −1.45504e13 | −0.731887 | ||||||||
\(903\) | 3.70529e13 | 1.85450 | ||||||||
\(904\) | 1.23395e13 | 0.614526 | ||||||||
\(905\) | 1.13579e13 | 0.562834 | ||||||||
\(906\) | −2.65272e13 | −1.30802 | ||||||||
\(907\) | 3.10008e12 | 0.152104 | 0.0760520 | − | 0.997104i | \(-0.475769\pi\) | ||||
0.0760520 | + | 0.997104i | \(0.475769\pi\) | |||||||
\(908\) | −3.57654e12 | −0.174613 | ||||||||
\(909\) | −8.64505e13 | −4.19982 | ||||||||
\(910\) | 3.68447e13 | 1.78110 | ||||||||
\(911\) | −3.17488e13 | −1.52719 | −0.763597 | − | 0.645693i | \(-0.776569\pi\) | ||||
−0.763597 | + | 0.645693i | \(0.776569\pi\) | |||||||
\(912\) | −4.14575e12 | −0.198438 | ||||||||
\(913\) | 1.65850e13 | 0.789944 | ||||||||
\(914\) | 4.78693e13 | 2.26882 | ||||||||
\(915\) | −1.43206e13 | −0.675406 | ||||||||
\(916\) | 1.71558e13 | 0.805160 | ||||||||
\(917\) | 2.16806e13 | 1.01253 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.86061e13 | −1.78540 | −0.892702 | − | 0.450648i | \(-0.851193\pi\) | ||||
−0.892702 | + | 0.450648i | \(0.851193\pi\) | |||||||
\(920\) | −1.01380e13 | −0.466560 | ||||||||
\(921\) | 4.07875e12 | 0.186792 | ||||||||
\(922\) | −4.67965e12 | −0.213267 | ||||||||
\(923\) | −8.25702e11 | −0.0374469 | ||||||||
\(924\) | −3.57312e13 | −1.61259 | ||||||||
\(925\) | −1.13415e13 | −0.509370 | ||||||||
\(926\) | 2.22776e12 | 0.0995677 | ||||||||
\(927\) | −8.36983e13 | −3.72270 | ||||||||
\(928\) | 1.32274e13 | 0.585474 | ||||||||
\(929\) | −2.55970e13 | −1.12750 | −0.563751 | − | 0.825944i | \(-0.690642\pi\) | ||||
−0.563751 | + | 0.825944i | \(0.690642\pi\) | |||||||
\(930\) | 1.21805e13 | 0.533937 | ||||||||
\(931\) | 4.09087e11 | 0.0178461 | ||||||||
\(932\) | −1.02044e13 | −0.443013 | ||||||||
\(933\) | −6.34472e13 | −2.74123 | ||||||||
\(934\) | 1.99511e13 | 0.857840 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.84303e13 | 1.21071 | ||||||||
\(937\) | 2.65934e12 | 0.112706 | 0.0563529 | − | 0.998411i | \(-0.482053\pi\) | ||||
0.0563529 | + | 0.998411i | \(0.482053\pi\) | |||||||
\(938\) | 4.65706e13 | 1.96426 | ||||||||
\(939\) | −4.66211e13 | −1.95698 | ||||||||
\(940\) | 3.29312e12 | 0.137573 | ||||||||
\(941\) | −4.13336e13 | −1.71850 | −0.859251 | − | 0.511554i | \(-0.829070\pi\) | ||||
−0.859251 | + | 0.511554i | \(0.829070\pi\) | |||||||
\(942\) | −3.34055e13 | −1.38226 | ||||||||
\(943\) | −9.07036e12 | −0.373527 | ||||||||
\(944\) | 3.80275e13 | 1.55856 | ||||||||
\(945\) | −7.07355e13 | −2.88532 | ||||||||
\(946\) | −3.83303e13 | −1.55608 | ||||||||
\(947\) | 2.07199e13 | 0.837166 | 0.418583 | − | 0.908178i | \(-0.362527\pi\) | ||||
0.418583 | + | 0.908178i | \(0.362527\pi\) | |||||||
\(948\) | 4.72743e13 | 1.90102 | ||||||||
\(949\) | 3.62057e13 | 1.44903 | ||||||||
\(950\) | 8.95285e11 | 0.0356619 | ||||||||
\(951\) | 1.04963e11 | 0.00416124 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.21831e13 | −0.871174 | −0.435587 | − | 0.900147i | \(-0.643459\pi\) | ||||
−0.435587 | + | 0.900147i | \(0.643459\pi\) | |||||||
\(954\) | 2.08113e13 | 0.813451 | ||||||||
\(955\) | 4.88345e13 | 1.89982 | ||||||||
\(956\) | −8.43751e12 | −0.326704 | ||||||||
\(957\) | 3.27703e13 | 1.26292 | ||||||||
\(958\) | 5.18923e13 | 1.99048 | ||||||||
\(959\) | 2.89608e13 | 1.10567 | ||||||||
\(960\) | 8.68108e12 | 0.329878 | ||||||||
\(961\) | −2.53599e13 | −0.959163 | ||||||||
\(962\) | 6.09092e13 | 2.29295 | ||||||||
\(963\) | 9.39937e13 | 3.52193 | ||||||||
\(964\) | 1.95920e13 | 0.730689 | ||||||||
\(965\) | 1.69434e13 | 0.628965 | ||||||||
\(966\) | −5.79866e13 | −2.14255 | ||||||||
\(967\) | 2.63617e13 | 0.969514 | 0.484757 | − | 0.874649i | \(-0.338908\pi\) | ||||
0.484757 | + | 0.874649i | \(0.338908\pi\) | |||||||
\(968\) | −9.20224e12 | −0.336864 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.70636e12 | 0.279497 | ||||||||
\(971\) | −3.49050e12 | −0.126009 | −0.0630045 | − | 0.998013i | \(-0.520068\pi\) | ||||
−0.0630045 | + | 0.998013i | \(0.520068\pi\) | |||||||
\(972\) | 1.92249e13 | 0.690821 | ||||||||
\(973\) | 5.64370e12 | 0.201863 | ||||||||
\(974\) | −2.48131e13 | −0.883416 | ||||||||
\(975\) | −1.78728e13 | −0.633392 | ||||||||
\(976\) | −1.14010e13 | −0.402177 | ||||||||
\(977\) | 1.46631e13 | 0.514875 | 0.257437 | − | 0.966295i | \(-0.417122\pi\) | ||||
0.257437 | + | 0.966295i | \(0.417122\pi\) | |||||||
\(978\) | 1.16371e13 | 0.406742 | ||||||||
\(979\) | 5.24683e12 | 0.182547 | ||||||||
\(980\) | −4.14649e12 | −0.143603 | ||||||||
\(981\) | 4.47392e13 | 1.54233 | ||||||||
\(982\) | 1.58442e13 | 0.543710 | ||||||||
\(983\) | −9.90226e12 | −0.338254 | −0.169127 | − | 0.985594i | \(-0.554095\pi\) | ||||
−0.169127 | + | 0.985594i | \(0.554095\pi\) | |||||||
\(984\) | −1.12245e13 | −0.381671 | ||||||||
\(985\) | −2.07355e13 | −0.701862 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.13641e13 | −0.381160 | ||||||||
\(988\) | −1.84690e12 | −0.0616649 | ||||||||
\(989\) | −2.38943e13 | −0.794164 | ||||||||
\(990\) | 1.30798e14 | 4.32756 | ||||||||
\(991\) | −5.12906e13 | −1.68930 | −0.844649 | − | 0.535321i | \(-0.820191\pi\) | ||||
−0.844649 | + | 0.535321i | \(0.820191\pi\) | |||||||
\(992\) | 6.74179e12 | 0.221041 | ||||||||
\(993\) | 5.12805e13 | 1.67371 | ||||||||
\(994\) | 1.44671e12 | 0.0470050 | ||||||||
\(995\) | −2.85696e13 | −0.924060 | ||||||||
\(996\) | −2.12059e13 | −0.682794 | ||||||||
\(997\) | 7.06003e12 | 0.226297 | 0.113148 | − | 0.993578i | \(-0.463906\pi\) | ||||
0.113148 | + | 0.993578i | \(0.463906\pi\) | |||||||
\(998\) | −3.75438e13 | −1.19798 | ||||||||
\(999\) | −1.16935e14 | −3.71450 |
(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 | 289.10.a.f.1.20 | 24 | ||
17.8 | even | 8 | 17.10.c.a.13.3 | yes | 24 | ||
17.15 | even | 8 | 17.10.c.a.4.10 | ✓ | 24 | ||
17.16 | even | 2 | inner | 289.10.a.f.1.19 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.c.a.4.10 | ✓ | 24 | 17.15 | even | 8 | ||
17.10.c.a.13.3 | yes | 24 | 17.8 | even | 8 | ||
289.10.a.f.1.19 | 24 | 17.16 | even | 2 | inner | ||
289.10.a.f.1.20 | 24 | 1.1 | even | 1 | trivial |