Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 9.64157 | 0.106525 | 0.0532627 | − | 0.998581i | \(-0.483038\pi\) | ||||
0.0532627 | + | 0.998581i | \(0.483038\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | −8099.04 | −0.988652 | ||||||||
\(5\) | −58650.0 | −1.67866 | −0.839330 | − | 0.543622i | \(-0.817053\pi\) | ||||
−0.839330 | + | 0.543622i | \(0.817053\pi\) | |||||||
\(6\) | 7028.71 | 0.0615024 | ||||||||
\(7\) | −68208.9 | −0.219131 | −0.109566 | − | 0.993980i | \(-0.534946\pi\) | ||||
−0.109566 | + | 0.993980i | \(0.534946\pi\) | |||||||
\(8\) | −157071. | −0.211842 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −565478. | −0.178820 | ||||||||
\(11\) | −8.19627e6 | −1.39497 | −0.697484 | − | 0.716601i | \(-0.745697\pi\) | ||||
−0.697484 | + | 0.716601i | \(0.745697\pi\) | |||||||
\(12\) | −5.90420e6 | −0.570799 | ||||||||
\(13\) | −4.22126e6 | −0.242555 | −0.121277 | − | 0.992619i | \(-0.538699\pi\) | ||||
−0.121277 | + | 0.992619i | \(0.538699\pi\) | |||||||
\(14\) | −657641. | −0.0233430 | ||||||||
\(15\) | −4.27558e7 | −0.969175 | ||||||||
\(16\) | 6.48329e7 | 0.966086 | ||||||||
\(17\) | 1.28115e8 | 1.28730 | 0.643652 | − | 0.765318i | \(-0.277418\pi\) | ||||
0.643652 | + | 0.765318i | \(0.277418\pi\) | |||||||
\(18\) | 5.12393e6 | 0.0355084 | ||||||||
\(19\) | −5.29427e7 | −0.258171 | −0.129085 | − | 0.991633i | \(-0.541204\pi\) | ||||
−0.129085 | + | 0.991633i | \(0.541204\pi\) | |||||||
\(20\) | 4.75009e8 | 1.65961 | ||||||||
\(21\) | −4.97243e7 | −0.126515 | ||||||||
\(22\) | −7.90250e7 | −0.148599 | ||||||||
\(23\) | −8.07458e7 | −0.113734 | −0.0568669 | − | 0.998382i | \(-0.518111\pi\) | ||||
−0.0568669 | + | 0.998382i | \(0.518111\pi\) | |||||||
\(24\) | −1.14505e8 | −0.122307 | ||||||||
\(25\) | 2.21912e9 | 1.81790 | ||||||||
\(26\) | −4.06996e7 | −0.0258382 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | 5.52427e8 | 0.216644 | ||||||||
\(29\) | 1.70394e9 | 0.531947 | 0.265974 | − | 0.963980i | \(-0.414307\pi\) | ||||
0.265974 | + | 0.963980i | \(0.414307\pi\) | |||||||
\(30\) | −4.12233e8 | −0.103242 | ||||||||
\(31\) | 5.22860e9 | 1.05812 | 0.529059 | − | 0.848585i | \(-0.322545\pi\) | ||||
0.529059 | + | 0.848585i | \(0.322545\pi\) | |||||||
\(32\) | 1.91182e9 | 0.314754 | ||||||||
\(33\) | −5.97508e9 | −0.805385 | ||||||||
\(34\) | 1.23523e9 | 0.137130 | ||||||||
\(35\) | 4.00045e9 | 0.367847 | ||||||||
\(36\) | −4.30416e9 | −0.329551 | ||||||||
\(37\) | −2.22190e10 | −1.42368 | −0.711841 | − | 0.702341i | \(-0.752138\pi\) | ||||
−0.711841 | + | 0.702341i | \(0.752138\pi\) | |||||||
\(38\) | −5.10450e8 | −0.0275017 | ||||||||
\(39\) | −3.07730e9 | −0.140039 | ||||||||
\(40\) | 9.21223e9 | 0.355611 | ||||||||
\(41\) | −1.90946e10 | −0.627791 | −0.313895 | − | 0.949458i | \(-0.601634\pi\) | ||||
−0.313895 | + | 0.949458i | \(0.601634\pi\) | |||||||
\(42\) | −4.79421e8 | −0.0134771 | ||||||||
\(43\) | 5.00370e10 | 1.20711 | 0.603554 | − | 0.797322i | \(-0.293751\pi\) | ||||
0.603554 | + | 0.797322i | \(0.293751\pi\) | |||||||
\(44\) | 6.63820e10 | 1.37914 | ||||||||
\(45\) | −3.11690e10 | −0.559553 | ||||||||
\(46\) | −7.78517e8 | −0.0121155 | ||||||||
\(47\) | 1.40679e11 | 1.90367 | 0.951837 | − | 0.306606i | \(-0.0991934\pi\) | ||||
0.951837 | + | 0.306606i | \(0.0991934\pi\) | |||||||
\(48\) | 4.72632e10 | 0.557770 | ||||||||
\(49\) | −9.22366e10 | −0.951982 | ||||||||
\(50\) | 2.13958e10 | 0.193652 | ||||||||
\(51\) | 9.33956e10 | 0.743225 | ||||||||
\(52\) | 3.41881e10 | 0.239802 | ||||||||
\(53\) | 2.75197e10 | 0.170549 | 0.0852747 | − | 0.996357i | \(-0.472823\pi\) | ||||
0.0852747 | + | 0.996357i | \(0.472823\pi\) | |||||||
\(54\) | 3.73534e9 | 0.0205008 | ||||||||
\(55\) | 4.80711e11 | 2.34168 | ||||||||
\(56\) | 1.07137e10 | 0.0464211 | ||||||||
\(57\) | −3.85952e10 | −0.149055 | ||||||||
\(58\) | 1.64287e10 | 0.0566658 | ||||||||
\(59\) | 4.21805e10 | 0.130189 | ||||||||
\(60\) | 3.46281e11 | 0.958177 | ||||||||
\(61\) | 8.31120e10 | 0.206547 | 0.103274 | − | 0.994653i | \(-0.467068\pi\) | ||||
0.103274 | + | 0.994653i | \(0.467068\pi\) | |||||||
\(62\) | 5.04119e10 | 0.112716 | ||||||||
\(63\) | −3.62490e10 | −0.0730437 | ||||||||
\(64\) | −5.12678e11 | −0.932557 | ||||||||
\(65\) | 2.47577e11 | 0.407167 | ||||||||
\(66\) | −5.76092e10 | −0.0857939 | ||||||||
\(67\) | 1.44720e12 | 1.95453 | 0.977263 | − | 0.212029i | \(-0.0680070\pi\) | ||||
0.977263 | + | 0.212029i | \(0.0680070\pi\) | |||||||
\(68\) | −1.03761e12 | −1.27270 | ||||||||
\(69\) | −5.88637e10 | −0.0656642 | ||||||||
\(70\) | 3.85707e10 | 0.0391850 | ||||||||
\(71\) | −8.00672e11 | −0.741781 | −0.370890 | − | 0.928677i | \(-0.620947\pi\) | ||||
−0.370890 | + | 0.928677i | \(0.620947\pi\) | |||||||
\(72\) | −8.34741e10 | −0.0706139 | ||||||||
\(73\) | −1.15447e12 | −0.892859 | −0.446430 | − | 0.894819i | \(-0.647305\pi\) | ||||
−0.446430 | + | 0.894819i | \(0.647305\pi\) | |||||||
\(74\) | −2.14226e11 | −0.151658 | ||||||||
\(75\) | 1.61774e12 | 1.04957 | ||||||||
\(76\) | 4.28785e11 | 0.255241 | ||||||||
\(77\) | 5.59059e11 | 0.305681 | ||||||||
\(78\) | −2.96700e10 | −0.0149177 | ||||||||
\(79\) | 3.68729e12 | 1.70660 | 0.853299 | − | 0.521421i | \(-0.174598\pi\) | ||||
0.853299 | + | 0.521421i | \(0.174598\pi\) | |||||||
\(80\) | −3.80245e12 | −1.62173 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | −1.84102e11 | −0.0668756 | ||||||||
\(83\) | −2.67410e12 | −0.897781 | −0.448890 | − | 0.893587i | \(-0.648181\pi\) | ||||
−0.448890 | + | 0.893587i | \(0.648181\pi\) | |||||||
\(84\) | 4.02719e11 | 0.125080 | ||||||||
\(85\) | −7.51393e12 | −2.16095 | ||||||||
\(86\) | 4.82435e11 | 0.128588 | ||||||||
\(87\) | 1.24218e12 | 0.307120 | ||||||||
\(88\) | 1.28740e12 | 0.295512 | ||||||||
\(89\) | −7.91226e12 | −1.68759 | −0.843793 | − | 0.536669i | \(-0.819682\pi\) | ||||
−0.843793 | + | 0.536669i | \(0.819682\pi\) | |||||||
\(90\) | −3.00518e11 | −0.0596066 | ||||||||
\(91\) | 2.87927e11 | 0.0531513 | ||||||||
\(92\) | 6.53964e11 | 0.112443 | ||||||||
\(93\) | 3.81165e12 | 0.610905 | ||||||||
\(94\) | 1.35636e12 | 0.202789 | ||||||||
\(95\) | 3.10509e12 | 0.433381 | ||||||||
\(96\) | 1.39372e12 | 0.181724 | ||||||||
\(97\) | −1.18233e13 | −1.44119 | −0.720596 | − | 0.693355i | \(-0.756132\pi\) | ||||
−0.720596 | + | 0.693355i | \(0.756132\pi\) | |||||||
\(98\) | −8.89305e11 | −0.101410 | ||||||||
\(99\) | −4.35584e12 | −0.464989 | ||||||||
\(100\) | −1.79727e13 | −1.79727 | ||||||||
\(101\) | −1.94509e11 | −0.0182327 | −0.00911634 | − | 0.999958i | \(-0.502902\pi\) | ||||
−0.00911634 | + | 0.999958i | \(0.502902\pi\) | |||||||
\(102\) | 9.00481e11 | 0.0791723 | ||||||||
\(103\) | 6.43127e12 | 0.530707 | 0.265354 | − | 0.964151i | \(-0.414511\pi\) | ||||
0.265354 | + | 0.964151i | \(0.414511\pi\) | |||||||
\(104\) | 6.63038e11 | 0.0513833 | ||||||||
\(105\) | 2.91633e12 | 0.212376 | ||||||||
\(106\) | 2.65333e11 | 0.0181678 | ||||||||
\(107\) | 1.47405e13 | 0.949553 | 0.474776 | − | 0.880106i | \(-0.342529\pi\) | ||||
0.474776 | + | 0.880106i | \(0.342529\pi\) | |||||||
\(108\) | −3.13773e12 | −0.190266 | ||||||||
\(109\) | −1.33568e13 | −0.762835 | −0.381418 | − | 0.924403i | \(-0.624564\pi\) | ||||
−0.381418 | + | 0.924403i | \(0.624564\pi\) | |||||||
\(110\) | 4.63481e12 | 0.249448 | ||||||||
\(111\) | −1.61976e13 | −0.821963 | ||||||||
\(112\) | −4.42218e12 | −0.211699 | ||||||||
\(113\) | −2.20014e13 | −0.994125 | −0.497063 | − | 0.867715i | \(-0.665588\pi\) | ||||
−0.497063 | + | 0.867715i | \(0.665588\pi\) | |||||||
\(114\) | −3.72118e11 | −0.0158781 | ||||||||
\(115\) | 4.73574e12 | 0.190920 | ||||||||
\(116\) | −1.38003e13 | −0.525911 | ||||||||
\(117\) | −2.24335e12 | −0.0808516 | ||||||||
\(118\) | 4.06687e11 | 0.0138684 | ||||||||
\(119\) | −8.73857e12 | −0.282088 | ||||||||
\(120\) | 6.71571e12 | 0.205312 | ||||||||
\(121\) | 3.26562e13 | 0.945934 | ||||||||
\(122\) | 8.01330e11 | 0.0220025 | ||||||||
\(123\) | −1.39199e13 | −0.362455 | ||||||||
\(124\) | −4.23466e13 | −1.04611 | ||||||||
\(125\) | −5.85570e13 | −1.37298 | ||||||||
\(126\) | −3.49498e11 | −0.00778100 | ||||||||
\(127\) | 7.50480e13 | 1.58714 | 0.793569 | − | 0.608480i | \(-0.208221\pi\) | ||||
0.793569 | + | 0.608480i | \(0.208221\pi\) | |||||||
\(128\) | −2.06046e13 | −0.414095 | ||||||||
\(129\) | 3.64769e13 | 0.696924 | ||||||||
\(130\) | 2.38703e12 | 0.0433736 | ||||||||
\(131\) | 3.13397e12 | 0.0541791 | 0.0270895 | − | 0.999633i | \(-0.491376\pi\) | ||||
0.0270895 | + | 0.999633i | \(0.491376\pi\) | |||||||
\(132\) | 4.83924e13 | 0.796246 | ||||||||
\(133\) | 3.61116e12 | 0.0565733 | ||||||||
\(134\) | 1.39533e13 | 0.208207 | ||||||||
\(135\) | −2.27222e13 | −0.323058 | ||||||||
\(136\) | −2.01231e13 | −0.272705 | ||||||||
\(137\) | 3.73904e13 | 0.483143 | 0.241572 | − | 0.970383i | \(-0.422337\pi\) | ||||
0.241572 | + | 0.970383i | \(0.422337\pi\) | |||||||
\(138\) | −5.67539e11 | −0.00699490 | ||||||||
\(139\) | 9.33477e12 | 0.109776 | 0.0548880 | − | 0.998493i | \(-0.482520\pi\) | ||||
0.0548880 | + | 0.998493i | \(0.482520\pi\) | |||||||
\(140\) | −3.23998e13 | −0.363672 | ||||||||
\(141\) | 1.02555e14 | 1.09909 | ||||||||
\(142\) | −7.71974e12 | −0.0790185 | ||||||||
\(143\) | 3.45986e13 | 0.338356 | ||||||||
\(144\) | 3.44549e13 | 0.322029 | ||||||||
\(145\) | −9.99363e13 | −0.892959 | ||||||||
\(146\) | −1.11309e13 | −0.0951121 | ||||||||
\(147\) | −6.72404e13 | −0.549627 | ||||||||
\(148\) | 1.79952e14 | 1.40753 | ||||||||
\(149\) | 1.77393e14 | 1.32809 | 0.664043 | − | 0.747695i | \(-0.268839\pi\) | ||||
0.664043 | + | 0.747695i | \(0.268839\pi\) | |||||||
\(150\) | 1.55975e13 | 0.111805 | ||||||||
\(151\) | −3.83684e13 | −0.263405 | −0.131702 | − | 0.991289i | \(-0.542044\pi\) | ||||
−0.131702 | + | 0.991289i | \(0.542044\pi\) | |||||||
\(152\) | 8.31577e12 | 0.0546914 | ||||||||
\(153\) | 6.80854e13 | 0.429101 | ||||||||
\(154\) | 5.39021e12 | 0.0325627 | ||||||||
\(155\) | −3.06657e14 | −1.77622 | ||||||||
\(156\) | 2.49232e13 | 0.138450 | ||||||||
\(157\) | 1.79121e14 | 0.954550 | 0.477275 | − | 0.878754i | \(-0.341625\pi\) | ||||
0.477275 | + | 0.878754i | \(0.341625\pi\) | |||||||
\(158\) | 3.55513e13 | 0.181796 | ||||||||
\(159\) | 2.00619e13 | 0.0984668 | ||||||||
\(160\) | −1.12128e14 | −0.528366 | ||||||||
\(161\) | 5.50759e12 | 0.0249226 | ||||||||
\(162\) | 2.72306e12 | 0.0118361 | ||||||||
\(163\) | 3.30232e14 | 1.37911 | 0.689557 | − | 0.724231i | \(-0.257805\pi\) | ||||
0.689557 | + | 0.724231i | \(0.257805\pi\) | |||||||
\(164\) | 1.54648e14 | 0.620667 | ||||||||
\(165\) | 3.50439e14 | 1.35197 | ||||||||
\(166\) | −2.57825e13 | −0.0956364 | ||||||||
\(167\) | −5.52806e14 | −1.97204 | −0.986020 | − | 0.166627i | \(-0.946712\pi\) | ||||
−0.986020 | + | 0.166627i | \(0.946712\pi\) | |||||||
\(168\) | 7.81026e12 | 0.0268013 | ||||||||
\(169\) | −2.85056e14 | −0.941167 | ||||||||
\(170\) | −7.24461e13 | −0.230196 | ||||||||
\(171\) | −2.81359e13 | −0.0860570 | ||||||||
\(172\) | −4.05251e14 | −1.19341 | ||||||||
\(173\) | 2.12008e14 | 0.601246 | 0.300623 | − | 0.953743i | \(-0.402805\pi\) | ||||
0.300623 | + | 0.953743i | \(0.402805\pi\) | |||||||
\(174\) | 1.19765e13 | 0.0327160 | ||||||||
\(175\) | −1.51364e14 | −0.398359 | ||||||||
\(176\) | −5.31388e14 | −1.34766 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | −7.62867e13 | −0.179771 | ||||||||
\(179\) | −7.03233e14 | −1.59792 | −0.798959 | − | 0.601385i | \(-0.794616\pi\) | ||||
−0.798959 | + | 0.601385i | \(0.794616\pi\) | |||||||
\(180\) | 2.52439e14 | 0.553204 | ||||||||
\(181\) | −7.40089e14 | −1.56449 | −0.782246 | − | 0.622970i | \(-0.785926\pi\) | ||||
−0.782246 | + | 0.622970i | \(0.785926\pi\) | |||||||
\(182\) | 2.77607e12 | 0.00566196 | ||||||||
\(183\) | 6.05886e13 | 0.119250 | ||||||||
\(184\) | 1.26828e13 | 0.0240936 | ||||||||
\(185\) | 1.30314e15 | 2.38988 | ||||||||
\(186\) | 3.67503e13 | 0.0650768 | ||||||||
\(187\) | −1.05006e15 | −1.79575 | ||||||||
\(188\) | −1.13936e15 | −1.88207 | ||||||||
\(189\) | −2.64255e13 | −0.0421718 | ||||||||
\(190\) | 2.99379e13 | 0.0461661 | ||||||||
\(191\) | −3.02452e14 | −0.450754 | −0.225377 | − | 0.974272i | \(-0.572361\pi\) | ||||
−0.225377 | + | 0.974272i | \(0.572361\pi\) | |||||||
\(192\) | −3.73743e14 | −0.538412 | ||||||||
\(193\) | −6.36959e14 | −0.887134 | −0.443567 | − | 0.896241i | \(-0.646287\pi\) | ||||
−0.443567 | + | 0.896241i | \(0.646287\pi\) | |||||||
\(194\) | −1.13995e14 | −0.153524 | ||||||||
\(195\) | 1.80483e14 | 0.235078 | ||||||||
\(196\) | 7.47028e14 | 0.941179 | ||||||||
\(197\) | 4.40983e13 | 0.0537517 | 0.0268758 | − | 0.999639i | \(-0.491444\pi\) | ||||
0.0268758 | + | 0.999639i | \(0.491444\pi\) | |||||||
\(198\) | −4.19971e13 | −0.0495331 | ||||||||
\(199\) | 1.34227e15 | 1.53212 | 0.766062 | − | 0.642767i | \(-0.222213\pi\) | ||||
0.766062 | + | 0.642767i | \(0.222213\pi\) | |||||||
\(200\) | −3.48559e14 | −0.385107 | ||||||||
\(201\) | 1.05501e15 | 1.12845 | ||||||||
\(202\) | −1.87537e12 | −0.00194224 | ||||||||
\(203\) | −1.16224e14 | −0.116566 | ||||||||
\(204\) | −7.56415e14 | −0.734791 | ||||||||
\(205\) | 1.11990e15 | 1.05385 | ||||||||
\(206\) | 6.20076e13 | 0.0565337 | ||||||||
\(207\) | −4.29116e13 | −0.0379112 | ||||||||
\(208\) | −2.73676e14 | −0.234329 | ||||||||
\(209\) | 4.33933e14 | 0.360140 | ||||||||
\(210\) | 2.81180e13 | 0.0226235 | ||||||||
\(211\) | 2.47246e15 | 1.92883 | 0.964415 | − | 0.264392i | \(-0.0851711\pi\) | ||||
0.964415 | + | 0.264392i | \(0.0851711\pi\) | |||||||
\(212\) | −2.22883e14 | −0.168614 | ||||||||
\(213\) | −5.83690e14 | −0.428267 | ||||||||
\(214\) | 1.42122e14 | 0.101151 | ||||||||
\(215\) | −2.93467e15 | −2.02632 | ||||||||
\(216\) | −6.08526e13 | −0.0407690 | ||||||||
\(217\) | −3.56637e14 | −0.231867 | ||||||||
\(218\) | −1.28781e14 | −0.0812613 | ||||||||
\(219\) | −8.41607e14 | −0.515493 | ||||||||
\(220\) | −3.89330e15 | −2.31510 | ||||||||
\(221\) | −5.40805e14 | −0.312242 | ||||||||
\(222\) | −1.56171e14 | −0.0875599 | ||||||||
\(223\) | −2.32661e15 | −1.26690 | −0.633450 | − | 0.773784i | \(-0.718362\pi\) | ||||
−0.633450 | + | 0.773784i | \(0.718362\pi\) | |||||||
\(224\) | −1.30403e14 | −0.0689725 | ||||||||
\(225\) | 1.17933e15 | 0.605967 | ||||||||
\(226\) | −2.12128e14 | −0.105900 | ||||||||
\(227\) | 2.41884e15 | 1.17338 | 0.586690 | − | 0.809812i | \(-0.300431\pi\) | ||||
0.586690 | + | 0.809812i | \(0.300431\pi\) | |||||||
\(228\) | 3.12584e14 | 0.147364 | ||||||||
\(229\) | −3.06398e15 | −1.40396 | −0.701980 | − | 0.712197i | \(-0.747700\pi\) | ||||
−0.701980 | + | 0.712197i | \(0.747700\pi\) | |||||||
\(230\) | 4.56600e13 | 0.0203378 | ||||||||
\(231\) | 4.07554e14 | 0.176485 | ||||||||
\(232\) | −2.67641e14 | −0.112689 | ||||||||
\(233\) | −8.83877e14 | −0.361892 | −0.180946 | − | 0.983493i | \(-0.557916\pi\) | ||||
−0.180946 | + | 0.983493i | \(0.557916\pi\) | |||||||
\(234\) | −2.16294e13 | −0.00861275 | ||||||||
\(235\) | −8.25080e15 | −3.19562 | ||||||||
\(236\) | −3.41622e14 | −0.128712 | ||||||||
\(237\) | 2.68804e15 | 0.985305 | ||||||||
\(238\) | −8.42536e13 | −0.0300496 | ||||||||
\(239\) | 3.76341e15 | 1.30616 | 0.653078 | − | 0.757290i | \(-0.273477\pi\) | ||||
0.653078 | + | 0.757290i | \(0.273477\pi\) | |||||||
\(240\) | −2.77199e15 | −0.936306 | ||||||||
\(241\) | −7.53466e14 | −0.247715 | −0.123858 | − | 0.992300i | \(-0.539527\pi\) | ||||
−0.123858 | + | 0.992300i | \(0.539527\pi\) | |||||||
\(242\) | 3.14857e14 | 0.100766 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | −6.73127e14 | −0.204204 | ||||||||
\(245\) | 5.40967e15 | 1.59805 | ||||||||
\(246\) | −1.34210e14 | −0.0386107 | ||||||||
\(247\) | 2.23485e14 | 0.0626206 | ||||||||
\(248\) | −8.21262e14 | −0.224154 | ||||||||
\(249\) | −1.94942e15 | −0.518334 | ||||||||
\(250\) | −5.64581e14 | −0.146257 | ||||||||
\(251\) | −1.71704e15 | −0.433412 | −0.216706 | − | 0.976237i | \(-0.569531\pi\) | ||||
−0.216706 | + | 0.976237i | \(0.569531\pi\) | |||||||
\(252\) | 2.93582e14 | 0.0722148 | ||||||||
\(253\) | 6.61815e14 | 0.158655 | ||||||||
\(254\) | 7.23580e14 | 0.169070 | ||||||||
\(255\) | −5.47765e15 | −1.24762 | ||||||||
\(256\) | 4.00120e15 | 0.888445 | ||||||||
\(257\) | −1.48391e15 | −0.321250 | −0.160625 | − | 0.987016i | \(-0.551351\pi\) | ||||
−0.160625 | + | 0.987016i | \(0.551351\pi\) | |||||||
\(258\) | 3.51695e14 | 0.0742400 | ||||||||
\(259\) | 1.51553e15 | 0.311973 | ||||||||
\(260\) | −2.00513e15 | −0.402547 | ||||||||
\(261\) | 9.05546e14 | 0.177316 | ||||||||
\(262\) | 3.02164e13 | 0.00577144 | ||||||||
\(263\) | 4.26432e15 | 0.794579 | 0.397290 | − | 0.917693i | \(-0.369951\pi\) | ||||
0.397290 | + | 0.917693i | \(0.369951\pi\) | |||||||
\(264\) | 9.38514e14 | 0.170614 | ||||||||
\(265\) | −1.61403e15 | −0.286295 | ||||||||
\(266\) | 3.48173e13 | 0.00602649 | ||||||||
\(267\) | −5.76804e15 | −0.974328 | ||||||||
\(268\) | −1.17209e16 | −1.93235 | ||||||||
\(269\) | −1.93843e15 | −0.311932 | −0.155966 | − | 0.987762i | \(-0.549849\pi\) | ||||
−0.155966 | + | 0.987762i | \(0.549849\pi\) | |||||||
\(270\) | −2.19078e14 | −0.0344139 | ||||||||
\(271\) | −5.34540e15 | −0.819747 | −0.409874 | − | 0.912142i | \(-0.634427\pi\) | ||||
−0.409874 | + | 0.912142i | \(0.634427\pi\) | |||||||
\(272\) | 8.30605e15 | 1.24365 | ||||||||
\(273\) | 2.09899e14 | 0.0306869 | ||||||||
\(274\) | 3.60502e14 | 0.0514670 | ||||||||
\(275\) | −1.81885e16 | −2.53591 | ||||||||
\(276\) | 4.76740e14 | 0.0649191 | ||||||||
\(277\) | −4.81951e15 | −0.641039 | −0.320519 | − | 0.947242i | \(-0.603857\pi\) | ||||
−0.320519 | + | 0.947242i | \(0.603857\pi\) | |||||||
\(278\) | 9.00018e13 | 0.0116939 | ||||||||
\(279\) | 2.77869e15 | 0.352706 | ||||||||
\(280\) | −6.28356e14 | −0.0779253 | ||||||||
\(281\) | −6.76285e15 | −0.819480 | −0.409740 | − | 0.912202i | \(-0.634381\pi\) | ||||
−0.409740 | + | 0.912202i | \(0.634381\pi\) | |||||||
\(282\) | 9.88789e14 | 0.117081 | ||||||||
\(283\) | −1.07639e15 | −0.124554 | −0.0622772 | − | 0.998059i | \(-0.519836\pi\) | ||||
−0.0622772 | + | 0.998059i | \(0.519836\pi\) | |||||||
\(284\) | 6.48468e15 | 0.733363 | ||||||||
\(285\) | 2.26361e15 | 0.250213 | ||||||||
\(286\) | 3.33585e14 | 0.0360435 | ||||||||
\(287\) | 1.30242e15 | 0.137568 | ||||||||
\(288\) | 1.01602e15 | 0.104918 | ||||||||
\(289\) | 6.50881e15 | 0.657152 | ||||||||
\(290\) | −9.63543e14 | −0.0951227 | ||||||||
\(291\) | −8.61918e15 | −0.832073 | ||||||||
\(292\) | 9.35008e15 | 0.882728 | ||||||||
\(293\) | −2.35706e15 | −0.217637 | −0.108818 | − | 0.994062i | \(-0.534707\pi\) | ||||
−0.108818 | + | 0.994062i | \(0.534707\pi\) | |||||||
\(294\) | −6.48304e14 | −0.0585492 | ||||||||
\(295\) | −2.47389e15 | −0.218543 | ||||||||
\(296\) | 3.48996e15 | 0.301595 | ||||||||
\(297\) | −3.17540e15 | −0.268462 | ||||||||
\(298\) | 1.71035e15 | 0.141475 | ||||||||
\(299\) | 3.40849e14 | 0.0275867 | ||||||||
\(300\) | −1.31021e16 | −1.03766 | ||||||||
\(301\) | −3.41297e15 | −0.264515 | ||||||||
\(302\) | −3.69932e14 | −0.0280593 | ||||||||
\(303\) | −1.41797e14 | −0.0105266 | ||||||||
\(304\) | −3.43243e15 | −0.249415 | ||||||||
\(305\) | −4.87452e15 | −0.346723 | ||||||||
\(306\) | 6.56451e14 | 0.0457102 | ||||||||
\(307\) | 1.61698e16 | 1.10231 | 0.551155 | − | 0.834403i | \(-0.314187\pi\) | ||||
0.551155 | + | 0.834403i | \(0.314187\pi\) | |||||||
\(308\) | −4.52784e15 | −0.302212 | ||||||||
\(309\) | 4.68840e15 | 0.306404 | ||||||||
\(310\) | −2.95666e15 | −0.189212 | ||||||||
\(311\) | 1.16381e16 | 0.729353 | 0.364677 | − | 0.931134i | \(-0.381180\pi\) | ||||
0.364677 | + | 0.931134i | \(0.381180\pi\) | |||||||
\(312\) | 4.83355e14 | 0.0296662 | ||||||||
\(313\) | 1.98768e16 | 1.19484 | 0.597419 | − | 0.801929i | \(-0.296193\pi\) | ||||
0.597419 | + | 0.801929i | \(0.296193\pi\) | |||||||
\(314\) | 1.72701e15 | 0.101684 | ||||||||
\(315\) | 2.12600e15 | 0.122616 | ||||||||
\(316\) | −2.98635e16 | −1.68723 | ||||||||
\(317\) | −1.50701e15 | −0.0834124 | −0.0417062 | − | 0.999130i | \(-0.513279\pi\) | ||||
−0.0417062 | + | 0.999130i | \(0.513279\pi\) | |||||||
\(318\) | 1.93428e14 | 0.0104892 | ||||||||
\(319\) | −1.39660e16 | −0.742049 | ||||||||
\(320\) | 3.00686e16 | 1.56545 | ||||||||
\(321\) | 1.07459e16 | 0.548225 | ||||||||
\(322\) | 5.31018e13 | 0.00265489 | ||||||||
\(323\) | −6.78274e15 | −0.332344 | ||||||||
\(324\) | −2.28741e15 | −0.109850 | ||||||||
\(325\) | −9.36746e15 | −0.440941 | ||||||||
\(326\) | 3.18396e15 | 0.146911 | ||||||||
\(327\) | −9.73712e15 | −0.440423 | ||||||||
\(328\) | 2.99921e15 | 0.132992 | ||||||||
\(329\) | −9.59555e15 | −0.417154 | ||||||||
\(330\) | 3.37878e15 | 0.144019 | ||||||||
\(331\) | −1.09728e16 | −0.458602 | −0.229301 | − | 0.973356i | \(-0.573644\pi\) | ||||
−0.229301 | + | 0.973356i | \(0.573644\pi\) | |||||||
\(332\) | 2.16577e16 | 0.887593 | ||||||||
\(333\) | −1.18081e16 | −0.474561 | ||||||||
\(334\) | −5.32992e15 | −0.210072 | ||||||||
\(335\) | −8.48781e16 | −3.28099 | ||||||||
\(336\) | −3.22377e15 | −0.122225 | ||||||||
\(337\) | 8.21434e15 | 0.305477 | 0.152738 | − | 0.988267i | \(-0.451191\pi\) | ||||
0.152738 | + | 0.988267i | \(0.451191\pi\) | |||||||
\(338\) | −2.74839e15 | −0.100258 | ||||||||
\(339\) | −1.60390e16 | −0.573959 | ||||||||
\(340\) | 6.08556e16 | 2.13642 | ||||||||
\(341\) | −4.28550e16 | −1.47604 | ||||||||
\(342\) | −2.71274e14 | −0.00916725 | ||||||||
\(343\) | 1.29001e16 | 0.427740 | ||||||||
\(344\) | −7.85937e15 | −0.255716 | ||||||||
\(345\) | 3.45236e15 | 0.110228 | ||||||||
\(346\) | 2.04409e15 | 0.0640480 | ||||||||
\(347\) | 2.78219e16 | 0.855550 | 0.427775 | − | 0.903885i | \(-0.359298\pi\) | ||||
0.427775 | + | 0.903885i | \(0.359298\pi\) | |||||||
\(348\) | −1.00604e16 | −0.303635 | ||||||||
\(349\) | −5.73304e15 | −0.169832 | −0.0849161 | − | 0.996388i | \(-0.527062\pi\) | ||||
−0.0849161 | + | 0.996388i | \(0.527062\pi\) | |||||||
\(350\) | −1.45938e15 | −0.0424353 | ||||||||
\(351\) | −1.63540e15 | −0.0466797 | ||||||||
\(352\) | −1.56698e16 | −0.439072 | ||||||||
\(353\) | −6.74015e16 | −1.85410 | −0.927052 | − | 0.374932i | \(-0.877666\pi\) | ||||
−0.927052 | + | 0.374932i | \(0.877666\pi\) | |||||||
\(354\) | 2.96475e14 | 0.00800693 | ||||||||
\(355\) | 4.69594e16 | 1.24520 | ||||||||
\(356\) | 6.40817e16 | 1.66844 | ||||||||
\(357\) | −6.37042e15 | −0.162864 | ||||||||
\(358\) | −6.78027e15 | −0.170219 | ||||||||
\(359\) | −1.09186e16 | −0.269186 | −0.134593 | − | 0.990901i | \(-0.542973\pi\) | ||||
−0.134593 | + | 0.990901i | \(0.542973\pi\) | |||||||
\(360\) | 4.89575e15 | 0.118537 | ||||||||
\(361\) | −3.92501e16 | −0.933348 | ||||||||
\(362\) | −7.13562e15 | −0.166658 | ||||||||
\(363\) | 2.38064e16 | 0.546135 | ||||||||
\(364\) | −2.33194e15 | −0.0525482 | ||||||||
\(365\) | 6.77095e16 | 1.49881 | ||||||||
\(366\) | 5.84170e14 | 0.0127032 | ||||||||
\(367\) | −4.53053e16 | −0.967876 | −0.483938 | − | 0.875102i | \(-0.660794\pi\) | ||||
−0.483938 | + | 0.875102i | \(0.660794\pi\) | |||||||
\(368\) | −5.23499e15 | −0.109877 | ||||||||
\(369\) | −1.01476e16 | −0.209264 | ||||||||
\(370\) | 1.25643e16 | 0.254583 | ||||||||
\(371\) | −1.87709e15 | −0.0373727 | ||||||||
\(372\) | −3.08707e16 | −0.603972 | ||||||||
\(373\) | 4.49231e16 | 0.863699 | 0.431849 | − | 0.901946i | \(-0.357861\pi\) | ||||
0.431849 | + | 0.901946i | \(0.357861\pi\) | |||||||
\(374\) | −1.01243e16 | −0.191293 | ||||||||
\(375\) | −4.26880e16 | −0.792689 | ||||||||
\(376\) | −2.20966e16 | −0.403278 | ||||||||
\(377\) | −7.19279e15 | −0.129026 | ||||||||
\(378\) | −2.54784e14 | −0.00449236 | ||||||||
\(379\) | −4.51749e16 | −0.782965 | −0.391483 | − | 0.920185i | \(-0.628038\pi\) | ||||
−0.391483 | + | 0.920185i | \(0.628038\pi\) | |||||||
\(380\) | −2.51482e16 | −0.428463 | ||||||||
\(381\) | 5.47100e16 | 0.916335 | ||||||||
\(382\) | −2.91612e15 | −0.0480168 | ||||||||
\(383\) | −5.58141e16 | −0.903550 | −0.451775 | − | 0.892132i | \(-0.649209\pi\) | ||||
−0.451775 | + | 0.892132i | \(0.649209\pi\) | |||||||
\(384\) | −1.50208e16 | −0.239078 | ||||||||
\(385\) | −3.27888e16 | −0.513134 | ||||||||
\(386\) | −6.14129e15 | −0.0945022 | ||||||||
\(387\) | 2.65917e16 | 0.402369 | ||||||||
\(388\) | 9.57573e16 | 1.42484 | ||||||||
\(389\) | −5.09688e16 | −0.745817 | −0.372908 | − | 0.927868i | \(-0.621639\pi\) | ||||
−0.372908 | + | 0.927868i | \(0.621639\pi\) | |||||||
\(390\) | 1.74014e15 | 0.0250418 | ||||||||
\(391\) | −1.03447e16 | −0.146410 | ||||||||
\(392\) | 1.44877e16 | 0.201670 | ||||||||
\(393\) | 2.28466e15 | 0.0312803 | ||||||||
\(394\) | 4.25177e14 | 0.00572591 | ||||||||
\(395\) | −2.16260e17 | −2.86480 | ||||||||
\(396\) | 3.52781e16 | 0.459713 | ||||||||
\(397\) | 2.51770e16 | 0.322749 | 0.161375 | − | 0.986893i | \(-0.448407\pi\) | ||||
0.161375 | + | 0.986893i | \(0.448407\pi\) | |||||||
\(398\) | 1.29416e16 | 0.163210 | ||||||||
\(399\) | 2.63254e15 | 0.0326626 | ||||||||
\(400\) | 1.43872e17 | 1.75625 | ||||||||
\(401\) | 5.25786e16 | 0.631496 | 0.315748 | − | 0.948843i | \(-0.397745\pi\) | ||||
0.315748 | + | 0.948843i | \(0.397745\pi\) | |||||||
\(402\) | 1.01719e16 | 0.120208 | ||||||||
\(403\) | −2.20712e16 | −0.256652 | ||||||||
\(404\) | 1.57533e15 | 0.0180258 | ||||||||
\(405\) | −1.65645e16 | −0.186518 | ||||||||
\(406\) | −1.12058e15 | −0.0124172 | ||||||||
\(407\) | 1.82113e17 | 1.98599 | ||||||||
\(408\) | −1.46698e16 | −0.157446 | ||||||||
\(409\) | −4.41135e16 | −0.465983 | −0.232991 | − | 0.972479i | \(-0.574851\pi\) | ||||
−0.232991 | + | 0.972479i | \(0.574851\pi\) | |||||||
\(410\) | 1.07976e16 | 0.112261 | ||||||||
\(411\) | 2.72576e16 | 0.278943 | ||||||||
\(412\) | −5.20871e16 | −0.524685 | ||||||||
\(413\) | −2.87709e15 | −0.0285284 | ||||||||
\(414\) | −4.13736e14 | −0.00403851 | ||||||||
\(415\) | 1.56836e17 | 1.50707 | ||||||||
\(416\) | −8.07028e15 | −0.0763452 | ||||||||
\(417\) | 6.80505e15 | 0.0633792 | ||||||||
\(418\) | 4.18379e15 | 0.0383640 | ||||||||
\(419\) | −1.19723e16 | −0.108090 | −0.0540452 | − | 0.998538i | \(-0.517212\pi\) | ||||
−0.0540452 | + | 0.998538i | \(0.517212\pi\) | |||||||
\(420\) | −2.36195e16 | −0.209966 | ||||||||
\(421\) | 5.96941e16 | 0.522513 | 0.261257 | − | 0.965269i | \(-0.415863\pi\) | ||||
0.261257 | + | 0.965269i | \(0.415863\pi\) | |||||||
\(422\) | 2.38384e16 | 0.205469 | ||||||||
\(423\) | 7.47624e16 | 0.634558 | ||||||||
\(424\) | −4.32255e15 | −0.0361295 | ||||||||
\(425\) | 2.84302e17 | 2.34019 | ||||||||
\(426\) | −5.62769e15 | −0.0456213 | ||||||||
\(427\) | −5.66898e15 | −0.0452610 | ||||||||
\(428\) | −1.19384e17 | −0.938778 | ||||||||
\(429\) | 2.52224e16 | 0.195350 | ||||||||
\(430\) | −2.82948e16 | −0.215855 | ||||||||
\(431\) | −2.08470e17 | −1.56654 | −0.783271 | − | 0.621680i | \(-0.786450\pi\) | ||||
−0.783271 | + | 0.621680i | \(0.786450\pi\) | |||||||
\(432\) | 2.51176e16 | 0.185923 | ||||||||
\(433\) | 2.48092e17 | 1.80901 | 0.904506 | − | 0.426461i | \(-0.140240\pi\) | ||||
0.904506 | + | 0.426461i | \(0.140240\pi\) | |||||||
\(434\) | −3.43854e15 | −0.0246997 | ||||||||
\(435\) | −7.28536e16 | −0.515550 | ||||||||
\(436\) | 1.08177e17 | 0.754179 | ||||||||
\(437\) | 4.27490e15 | 0.0293627 | ||||||||
\(438\) | −8.11441e15 | −0.0549130 | ||||||||
\(439\) | 1.78467e17 | 1.18997 | 0.594987 | − | 0.803735i | \(-0.297157\pi\) | ||||
0.594987 | + | 0.803735i | \(0.297157\pi\) | |||||||
\(440\) | −7.55059e16 | −0.496065 | ||||||||
\(441\) | −4.90183e16 | −0.317327 | ||||||||
\(442\) | −5.21421e15 | −0.0332617 | ||||||||
\(443\) | 2.84466e17 | 1.78816 | 0.894080 | − | 0.447907i | \(-0.147831\pi\) | ||||
0.894080 | + | 0.447907i | \(0.147831\pi\) | |||||||
\(444\) | 1.31185e17 | 0.812636 | ||||||||
\(445\) | 4.64054e17 | 2.83288 | ||||||||
\(446\) | −2.24322e16 | −0.134957 | ||||||||
\(447\) | 1.29320e17 | 0.766770 | ||||||||
\(448\) | 3.49692e16 | 0.204352 | ||||||||
\(449\) | 2.60812e17 | 1.50219 | 0.751096 | − | 0.660193i | \(-0.229525\pi\) | ||||
0.751096 | + | 0.660193i | \(0.229525\pi\) | |||||||
\(450\) | 1.13706e16 | 0.0645508 | ||||||||
\(451\) | 1.56504e17 | 0.875748 | ||||||||
\(452\) | 1.78191e17 | 0.982844 | ||||||||
\(453\) | −2.79706e16 | −0.152077 | ||||||||
\(454\) | 2.33214e16 | 0.124995 | ||||||||
\(455\) | −1.68869e16 | −0.0892230 | ||||||||
\(456\) | 6.06220e15 | 0.0315761 | ||||||||
\(457\) | −3.35212e17 | −1.72133 | −0.860664 | − | 0.509173i | \(-0.829951\pi\) | ||||
−0.860664 | + | 0.509173i | \(0.829951\pi\) | |||||||
\(458\) | −2.95416e16 | −0.149557 | ||||||||
\(459\) | 4.96343e16 | 0.247742 | ||||||||
\(460\) | −3.83550e16 | −0.188754 | ||||||||
\(461\) | −1.13139e17 | −0.548978 | −0.274489 | − | 0.961590i | \(-0.588509\pi\) | ||||
−0.274489 | + | 0.961590i | \(0.588509\pi\) | |||||||
\(462\) | 3.92946e15 | 0.0188001 | ||||||||
\(463\) | −2.11615e17 | −0.998320 | −0.499160 | − | 0.866510i | \(-0.666358\pi\) | ||||
−0.499160 | + | 0.866510i | \(0.666358\pi\) | |||||||
\(464\) | 1.10472e17 | 0.513907 | ||||||||
\(465\) | −2.23553e17 | −1.02550 | ||||||||
\(466\) | −8.52197e15 | −0.0385506 | ||||||||
\(467\) | −2.87406e16 | −0.128214 | −0.0641071 | − | 0.997943i | \(-0.520420\pi\) | ||||
−0.0641071 | + | 0.997943i | \(0.520420\pi\) | |||||||
\(468\) | 1.81690e16 | 0.0799342 | ||||||||
\(469\) | −9.87118e16 | −0.428298 | ||||||||
\(470\) | −7.95507e16 | −0.340415 | ||||||||
\(471\) | 1.30579e17 | 0.551110 | ||||||||
\(472\) | −6.62535e15 | −0.0275795 | ||||||||
\(473\) | −4.10117e17 | −1.68388 | ||||||||
\(474\) | 2.59169e16 | 0.104960 | ||||||||
\(475\) | −1.17486e17 | −0.469329 | ||||||||
\(476\) | 7.07740e16 | 0.278887 | ||||||||
\(477\) | 1.46251e16 | 0.0568498 | ||||||||
\(478\) | 3.62852e16 | 0.139139 | ||||||||
\(479\) | 8.32682e16 | 0.314991 | 0.157496 | − | 0.987520i | \(-0.449658\pi\) | ||||
0.157496 | + | 0.987520i | \(0.449658\pi\) | |||||||
\(480\) | −8.17414e16 | −0.305052 | ||||||||
\(481\) | 9.37920e16 | 0.345321 | ||||||||
\(482\) | −7.26460e15 | −0.0263880 | ||||||||
\(483\) | 4.01503e15 | 0.0143891 | ||||||||
\(484\) | −2.64484e17 | −0.935200 | ||||||||
\(485\) | 6.93436e17 | 2.41927 | ||||||||
\(486\) | 1.98511e15 | 0.00683360 | ||||||||
\(487\) | −1.73796e17 | −0.590341 | −0.295170 | − | 0.955445i | \(-0.595376\pi\) | ||||
−0.295170 | + | 0.955445i | \(0.595376\pi\) | |||||||
\(488\) | −1.30545e16 | −0.0437554 | ||||||||
\(489\) | 2.40739e17 | 0.796232 | ||||||||
\(490\) | 5.21577e16 | 0.170233 | ||||||||
\(491\) | 2.48205e17 | 0.799430 | 0.399715 | − | 0.916640i | \(-0.369109\pi\) | ||||
0.399715 | + | 0.916640i | \(0.369109\pi\) | |||||||
\(492\) | 1.12738e17 | 0.358342 | ||||||||
\(493\) | 2.18300e17 | 0.684778 | ||||||||
\(494\) | 2.15474e15 | 0.00667068 | ||||||||
\(495\) | 2.55470e17 | 0.780559 | ||||||||
\(496\) | 3.38985e17 | 1.02223 | ||||||||
\(497\) | 5.46130e16 | 0.162547 | ||||||||
\(498\) | −1.87955e16 | −0.0552157 | ||||||||
\(499\) | −3.12341e17 | −0.905682 | −0.452841 | − | 0.891591i | \(-0.649589\pi\) | ||||
−0.452841 | + | 0.891591i | \(0.649589\pi\) | |||||||
\(500\) | 4.74255e17 | 1.35740 | ||||||||
\(501\) | −4.02996e17 | −1.13856 | ||||||||
\(502\) | −1.65550e16 | −0.0461694 | ||||||||
\(503\) | −1.11461e17 | −0.306853 | −0.153426 | − | 0.988160i | \(-0.549031\pi\) | ||||
−0.153426 | + | 0.988160i | \(0.549031\pi\) | |||||||
\(504\) | 5.69368e15 | 0.0154737 | ||||||||
\(505\) | 1.14079e16 | 0.0306065 | ||||||||
\(506\) | 6.38094e15 | 0.0169008 | ||||||||
\(507\) | −2.07806e17 | −0.543383 | ||||||||
\(508\) | −6.07816e17 | −1.56913 | ||||||||
\(509\) | −3.12980e17 | −0.797721 | −0.398860 | − | 0.917012i | \(-0.630594\pi\) | ||||
−0.398860 | + | 0.917012i | \(0.630594\pi\) | |||||||
\(510\) | −5.28132e16 | −0.132903 | ||||||||
\(511\) | 7.87450e16 | 0.195653 | ||||||||
\(512\) | 2.07371e17 | 0.508737 | ||||||||
\(513\) | −2.05111e16 | −0.0496850 | ||||||||
\(514\) | −1.43072e16 | −0.0342212 | ||||||||
\(515\) | −3.77194e17 | −0.890877 | ||||||||
\(516\) | −2.95428e17 | −0.689015 | ||||||||
\(517\) | −1.15304e18 | −2.65556 | ||||||||
\(518\) | 1.46121e16 | 0.0332330 | ||||||||
\(519\) | 1.54554e17 | 0.347130 | ||||||||
\(520\) | −3.88872e16 | −0.0862551 | ||||||||
\(521\) | 1.61559e17 | 0.353905 | 0.176953 | − | 0.984219i | \(-0.443376\pi\) | ||||
0.176953 | + | 0.984219i | \(0.443376\pi\) | |||||||
\(522\) | 8.73089e15 | 0.0188886 | ||||||||
\(523\) | 8.32128e17 | 1.77799 | 0.888994 | − | 0.457918i | \(-0.151405\pi\) | ||||
0.888994 | + | 0.457918i | \(0.151405\pi\) | |||||||
\(524\) | −2.53822e16 | −0.0535643 | ||||||||
\(525\) | −1.10344e17 | −0.229992 | ||||||||
\(526\) | 4.11147e16 | 0.0846428 | ||||||||
\(527\) | 6.69860e17 | 1.36212 | ||||||||
\(528\) | −3.87382e17 | −0.778071 | ||||||||
\(529\) | −4.97516e17 | −0.987065 | ||||||||
\(530\) | −1.55618e16 | −0.0304976 | ||||||||
\(531\) | 2.24165e16 | 0.0433963 | ||||||||
\(532\) | −2.92469e16 | −0.0559313 | ||||||||
\(533\) | 8.06031e16 | 0.152274 | ||||||||
\(534\) | −5.56130e16 | −0.103791 | ||||||||
\(535\) | −8.64533e17 | −1.59398 | ||||||||
\(536\) | −2.27313e17 | −0.414051 | ||||||||
\(537\) | −5.12657e17 | −0.922558 | ||||||||
\(538\) | −1.86895e16 | −0.0332286 | ||||||||
\(539\) | 7.55996e17 | 1.32798 | ||||||||
\(540\) | 1.84028e17 | 0.319392 | ||||||||
\(541\) | 6.73090e17 | 1.15423 | 0.577113 | − | 0.816664i | \(-0.304179\pi\) | ||||
0.577113 | + | 0.816664i | \(0.304179\pi\) | |||||||
\(542\) | −5.15381e16 | −0.0873238 | ||||||||
\(543\) | −5.39525e17 | −0.903260 | ||||||||
\(544\) | 2.44932e17 | 0.405185 | ||||||||
\(545\) | 7.83377e17 | 1.28054 | ||||||||
\(546\) | 2.02376e15 | 0.00326894 | ||||||||
\(547\) | 7.45578e17 | 1.19008 | 0.595039 | − | 0.803697i | \(-0.297137\pi\) | ||||
0.595039 | + | 0.803697i | \(0.297137\pi\) | |||||||
\(548\) | −3.02826e17 | −0.477661 | ||||||||
\(549\) | 4.41691e16 | 0.0688491 | ||||||||
\(550\) | −1.75366e17 | −0.270139 | ||||||||
\(551\) | −9.02114e16 | −0.137333 | ||||||||
\(552\) | 9.24580e15 | 0.0139104 | ||||||||
\(553\) | −2.51506e17 | −0.373969 | ||||||||
\(554\) | −4.64676e16 | −0.0682868 | ||||||||
\(555\) | 9.49991e17 | 1.37980 | ||||||||
\(556\) | −7.56027e16 | −0.108530 | ||||||||
\(557\) | −8.10150e17 | −1.14949 | −0.574747 | − | 0.818331i | \(-0.694899\pi\) | ||||
−0.574747 | + | 0.818331i | \(0.694899\pi\) | |||||||
\(558\) | 2.67909e16 | 0.0375721 | ||||||||
\(559\) | −2.11219e17 | −0.292790 | ||||||||
\(560\) | 2.59361e17 | 0.355371 | ||||||||
\(561\) | −7.65496e17 | −1.03678 | ||||||||
\(562\) | −6.52045e16 | −0.0872954 | ||||||||
\(563\) | 1.05610e17 | 0.139766 | 0.0698829 | − | 0.997555i | \(-0.477737\pi\) | ||||
0.0698829 | + | 0.997555i | \(0.477737\pi\) | |||||||
\(564\) | −8.30595e17 | −1.08661 | ||||||||
\(565\) | 1.29038e18 | 1.66880 | ||||||||
\(566\) | −1.03781e16 | −0.0132682 | ||||||||
\(567\) | −1.92642e16 | −0.0243479 | ||||||||
\(568\) | 1.25763e17 | 0.157140 | ||||||||
\(569\) | −3.06846e17 | −0.379045 | −0.189522 | − | 0.981876i | \(-0.560694\pi\) | ||||
−0.189522 | + | 0.981876i | \(0.560694\pi\) | |||||||
\(570\) | 2.18247e16 | 0.0266540 | ||||||||
\(571\) | 1.14639e18 | 1.38420 | 0.692098 | − | 0.721803i | \(-0.256686\pi\) | ||||
0.692098 | + | 0.721803i | \(0.256686\pi\) | |||||||
\(572\) | −2.80215e17 | −0.334517 | ||||||||
\(573\) | −2.20488e17 | −0.260243 | ||||||||
\(574\) | 1.25574e16 | 0.0146545 | ||||||||
\(575\) | −1.79184e17 | −0.206757 | ||||||||
\(576\) | −2.72458e17 | −0.310852 | ||||||||
\(577\) | 1.19316e18 | 1.34604 | 0.673018 | − | 0.739626i | \(-0.264998\pi\) | ||||
0.673018 | + | 0.739626i | \(0.264998\pi\) | |||||||
\(578\) | 6.27552e16 | 0.0700033 | ||||||||
\(579\) | −4.64343e17 | −0.512187 | ||||||||
\(580\) | 8.09388e17 | 0.882826 | ||||||||
\(581\) | 1.82398e17 | 0.196732 | ||||||||
\(582\) | −8.31024e16 | −0.0886368 | ||||||||
\(583\) | −2.25559e17 | −0.237911 | ||||||||
\(584\) | 1.81334e17 | 0.189145 | ||||||||
\(585\) | 1.31572e17 | 0.135722 | ||||||||
\(586\) | −2.27258e16 | −0.0231838 | ||||||||
\(587\) | 9.85683e17 | 0.994466 | 0.497233 | − | 0.867617i | \(-0.334349\pi\) | ||||
0.497233 | + | 0.867617i | \(0.334349\pi\) | |||||||
\(588\) | 5.44583e17 | 0.543390 | ||||||||
\(589\) | −2.76816e17 | −0.273175 | ||||||||
\(590\) | −2.38522e16 | −0.0232804 | ||||||||
\(591\) | 3.21477e16 | 0.0310335 | ||||||||
\(592\) | −1.44052e18 | −1.37540 | ||||||||
\(593\) | −1.79969e17 | −0.169958 | −0.0849791 | − | 0.996383i | \(-0.527082\pi\) | ||||
−0.0849791 | + | 0.996383i | \(0.527082\pi\) | |||||||
\(594\) | −3.06159e16 | −0.0285980 | ||||||||
\(595\) | 5.12517e17 | 0.473530 | ||||||||
\(596\) | −1.43671e18 | −1.31301 | ||||||||
\(597\) | 9.78513e17 | 0.884572 | ||||||||
\(598\) | 3.28632e15 | 0.00293868 | ||||||||
\(599\) | −2.00606e18 | −1.77447 | −0.887237 | − | 0.461314i | \(-0.847378\pi\) | ||||
−0.887237 | + | 0.461314i | \(0.847378\pi\) | |||||||
\(600\) | −2.54100e17 | −0.222342 | ||||||||
\(601\) | 1.45050e18 | 1.25555 | 0.627773 | − | 0.778397i | \(-0.283967\pi\) | ||||
0.627773 | + | 0.778397i | \(0.283967\pi\) | |||||||
\(602\) | −3.29064e16 | −0.0281775 | ||||||||
\(603\) | 7.69100e17 | 0.651509 | ||||||||
\(604\) | 3.10747e17 | 0.260416 | ||||||||
\(605\) | −1.91529e18 | −1.58790 | ||||||||
\(606\) | −1.36715e15 | −0.00112135 | ||||||||
\(607\) | −1.28727e17 | −0.104459 | −0.0522293 | − | 0.998635i | \(-0.516633\pi\) | ||||
−0.0522293 | + | 0.998635i | \(0.516633\pi\) | |||||||
\(608\) | −1.01217e17 | −0.0812604 | ||||||||
\(609\) | −8.47275e16 | −0.0672995 | ||||||||
\(610\) | −4.69980e16 | −0.0369348 | ||||||||
\(611\) | −5.93841e17 | −0.461745 | ||||||||
\(612\) | −5.51427e17 | −0.424232 | ||||||||
\(613\) | 6.07943e17 | 0.462775 | 0.231387 | − | 0.972862i | \(-0.425674\pi\) | ||||
0.231387 | + | 0.972862i | \(0.425674\pi\) | |||||||
\(614\) | 1.55902e17 | 0.117424 | ||||||||
\(615\) | 8.16405e17 | 0.608439 | ||||||||
\(616\) | −8.78121e16 | −0.0647560 | ||||||||
\(617\) | 1.43747e17 | 0.104892 | 0.0524462 | − | 0.998624i | \(-0.483298\pi\) | ||||
0.0524462 | + | 0.998624i | \(0.483298\pi\) | |||||||
\(618\) | 4.52035e16 | 0.0326398 | ||||||||
\(619\) | 1.14313e18 | 0.816782 | 0.408391 | − | 0.912807i | \(-0.366090\pi\) | ||||
0.408391 | + | 0.912807i | \(0.366090\pi\) | |||||||
\(620\) | 2.48363e18 | 1.75606 | ||||||||
\(621\) | −3.12826e16 | −0.0218881 | ||||||||
\(622\) | 1.12209e17 | 0.0776946 | ||||||||
\(623\) | 5.39687e17 | 0.369802 | ||||||||
\(624\) | −1.99510e17 | −0.135290 | ||||||||
\(625\) | 7.25481e17 | 0.486862 | ||||||||
\(626\) | 1.91644e17 | 0.127281 | ||||||||
\(627\) | 3.16337e17 | 0.207927 | ||||||||
\(628\) | −1.45071e18 | −0.943718 | ||||||||
\(629\) | −2.84658e18 | −1.83271 | ||||||||
\(630\) | 2.04980e16 | 0.0130617 | ||||||||
\(631\) | 1.01303e18 | 0.638899 | 0.319449 | − | 0.947603i | \(-0.396502\pi\) | ||||
0.319449 | + | 0.947603i | \(0.396502\pi\) | |||||||
\(632\) | −5.79168e17 | −0.361529 | ||||||||
\(633\) | 1.80243e18 | 1.11361 | ||||||||
\(634\) | −1.45299e16 | −0.00888553 | ||||||||
\(635\) | −4.40156e18 | −2.66427 | ||||||||
\(636\) | −1.62482e17 | −0.0973494 | ||||||||
\(637\) | 3.89354e17 | 0.230908 | ||||||||
\(638\) | −1.34654e17 | −0.0790470 | ||||||||
\(639\) | −4.25510e17 | −0.247260 | ||||||||
\(640\) | 1.20846e18 | 0.695125 | ||||||||
\(641\) | −2.11979e18 | −1.20702 | −0.603512 | − | 0.797354i | \(-0.706233\pi\) | ||||
−0.603512 | + | 0.797354i | \(0.706233\pi\) | |||||||
\(642\) | 1.03607e17 | 0.0583998 | ||||||||
\(643\) | 3.23198e17 | 0.180342 | 0.0901712 | − | 0.995926i | \(-0.471259\pi\) | ||||
0.0901712 | + | 0.995926i | \(0.471259\pi\) | |||||||
\(644\) | −4.46062e16 | −0.0246398 | ||||||||
\(645\) | −2.13937e18 | −1.16990 | ||||||||
\(646\) | −6.53962e16 | −0.0354031 | ||||||||
\(647\) | −1.95948e18 | −1.05018 | −0.525089 | − | 0.851047i | \(-0.675968\pi\) | ||||
−0.525089 | + | 0.851047i | \(0.675968\pi\) | |||||||
\(648\) | −4.43616e16 | −0.0235380 | ||||||||
\(649\) | −3.45723e17 | −0.181609 | ||||||||
\(650\) | −9.03171e16 | −0.0469714 | ||||||||
\(651\) | −2.59988e17 | −0.133868 | ||||||||
\(652\) | −2.67456e18 | −1.36346 | ||||||||
\(653\) | −2.43779e18 | −1.23044 | −0.615219 | − | 0.788356i | \(-0.710933\pi\) | ||||
−0.615219 | + | 0.788356i | \(0.710933\pi\) | |||||||
\(654\) | −9.38811e16 | −0.0469162 | ||||||||
\(655\) | −1.83807e17 | −0.0909483 | ||||||||
\(656\) | −1.23796e18 | −0.606500 | ||||||||
\(657\) | −6.13531e17 | −0.297620 | ||||||||
\(658\) | −9.25161e16 | −0.0444375 | ||||||||
\(659\) | −4.07046e18 | −1.93592 | −0.967962 | − | 0.251098i | \(-0.919208\pi\) | ||||
−0.967962 | + | 0.251098i | \(0.919208\pi\) | |||||||
\(660\) | −2.83822e18 | −1.33663 | ||||||||
\(661\) | −5.99794e17 | −0.279700 | −0.139850 | − | 0.990173i | \(-0.544662\pi\) | ||||
−0.139850 | + | 0.990173i | \(0.544662\pi\) | |||||||
\(662\) | −1.05795e17 | −0.0488528 | ||||||||
\(663\) | −3.94247e17 | −0.180273 | ||||||||
\(664\) | 4.20025e17 | 0.190188 | ||||||||
\(665\) | −2.11795e17 | −0.0949673 | ||||||||
\(666\) | −1.13848e17 | −0.0505527 | ||||||||
\(667\) | −1.37586e17 | −0.0605003 | ||||||||
\(668\) | 4.47720e18 | 1.94966 | ||||||||
\(669\) | −1.69610e18 | −0.731445 | ||||||||
\(670\) | −8.18359e17 | −0.349508 | ||||||||
\(671\) | −6.81209e17 | −0.288127 | ||||||||
\(672\) | −9.50639e16 | −0.0398213 | ||||||||
\(673\) | 3.61261e18 | 1.49873 | 0.749364 | − | 0.662158i | \(-0.230359\pi\) | ||||
0.749364 | + | 0.662158i | \(0.230359\pi\) | |||||||
\(674\) | 7.91992e16 | 0.0325410 | ||||||||
\(675\) | 8.59731e17 | 0.349855 | ||||||||
\(676\) | 2.30868e18 | 0.930487 | ||||||||
\(677\) | −3.17569e18 | −1.26769 | −0.633843 | − | 0.773462i | \(-0.718523\pi\) | ||||
−0.633843 | + | 0.773462i | \(0.718523\pi\) | |||||||
\(678\) | −1.54642e17 | −0.0611411 | ||||||||
\(679\) | 8.06454e17 | 0.315810 | ||||||||
\(680\) | 1.18022e18 | 0.457779 | ||||||||
\(681\) | 1.76333e18 | 0.677451 | ||||||||
\(682\) | −4.13190e17 | −0.157236 | ||||||||
\(683\) | −7.70288e17 | −0.290348 | −0.145174 | − | 0.989406i | \(-0.546374\pi\) | ||||
−0.145174 | + | 0.989406i | \(0.546374\pi\) | |||||||
\(684\) | 2.27874e17 | 0.0850804 | ||||||||
\(685\) | −2.19294e18 | −0.811034 | ||||||||
\(686\) | 1.24377e17 | 0.0455651 | ||||||||
\(687\) | −2.23364e18 | −0.810577 | ||||||||
\(688\) | 3.24404e18 | 1.16617 | ||||||||
\(689\) | −1.16168e17 | −0.0413676 | ||||||||
\(690\) | 3.32861e16 | 0.0117421 | ||||||||
\(691\) | 2.10103e18 | 0.734218 | 0.367109 | − | 0.930178i | \(-0.380348\pi\) | ||||
0.367109 | + | 0.930178i | \(0.380348\pi\) | |||||||
\(692\) | −1.71706e18 | −0.594424 | ||||||||
\(693\) | 2.97107e17 | 0.101894 | ||||||||
\(694\) | 2.68247e17 | 0.0911378 | ||||||||
\(695\) | −5.47484e17 | −0.184277 | ||||||||
\(696\) | −1.95110e17 | −0.0650608 | ||||||||
\(697\) | −2.44630e18 | −0.808158 | ||||||||
\(698\) | −5.52755e16 | −0.0180914 | ||||||||
\(699\) | −6.44347e17 | −0.208938 | ||||||||
\(700\) | 1.22590e18 | 0.393838 | ||||||||
\(701\) | −8.89194e16 | −0.0283028 | −0.0141514 | − | 0.999900i | \(-0.504505\pi\) | ||||
−0.0141514 | + | 0.999900i | \(0.504505\pi\) | |||||||
\(702\) | −1.57678e16 | −0.00497257 | ||||||||
\(703\) | 1.17633e18 | 0.367553 | ||||||||
\(704\) | 4.20205e18 | 1.30089 | ||||||||
\(705\) | −6.01484e18 | −1.84499 | ||||||||
\(706\) | −6.49857e17 | −0.197509 | ||||||||
\(707\) | 1.32672e16 | 0.00399535 | ||||||||
\(708\) | −2.49042e17 | −0.0743117 | ||||||||
\(709\) | −1.89281e18 | −0.559636 | −0.279818 | − | 0.960053i | \(-0.590274\pi\) | ||||
−0.279818 | + | 0.960053i | \(0.590274\pi\) | |||||||
\(710\) | 4.52763e17 | 0.132645 | ||||||||
\(711\) | 1.95958e18 | 0.568866 | ||||||||
\(712\) | 1.24279e18 | 0.357501 | ||||||||
\(713\) | −4.22187e17 | −0.120344 | ||||||||
\(714\) | −6.14208e16 | −0.0173491 | ||||||||
\(715\) | −2.02921e18 | −0.567985 | ||||||||
\(716\) | 5.69551e18 | 1.57979 | ||||||||
\(717\) | 2.74353e18 | 0.754110 | ||||||||
\(718\) | −1.05272e17 | −0.0286751 | ||||||||
\(719\) | −3.76891e18 | −1.01737 | −0.508684 | − | 0.860954i | \(-0.669868\pi\) | ||||
−0.508684 | + | 0.860954i | \(0.669868\pi\) | |||||||
\(720\) | −2.02078e18 | −0.540577 | ||||||||
\(721\) | −4.38670e17 | −0.116294 | ||||||||
\(722\) | −3.78432e17 | −0.0994252 | ||||||||
\(723\) | −5.49277e17 | −0.143019 | ||||||||
\(724\) | 5.99401e18 | 1.54674 | ||||||||
\(725\) | 3.78125e18 | 0.967027 | ||||||||
\(726\) | 2.29531e17 | 0.0581772 | ||||||||
\(727\) | 6.27024e17 | 0.157511 | 0.0787555 | − | 0.996894i | \(-0.474905\pi\) | ||||
0.0787555 | + | 0.996894i | \(0.474905\pi\) | |||||||
\(728\) | −4.52251e16 | −0.0112597 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 6.52826e17 | 0.159661 | ||||||||
\(731\) | 6.41047e18 | 1.55391 | ||||||||
\(732\) | −4.90710e17 | −0.117897 | ||||||||
\(733\) | 5.32014e18 | 1.26691 | 0.633457 | − | 0.773778i | \(-0.281635\pi\) | ||||
0.633457 | + | 0.773778i | \(0.281635\pi\) | |||||||
\(734\) | −4.36814e17 | −0.103103 | ||||||||
\(735\) | 3.94365e18 | 0.922637 | ||||||||
\(736\) | −1.54371e17 | −0.0357982 | ||||||||
\(737\) | −1.18616e19 | −2.72650 | ||||||||
\(738\) | −9.78392e16 | −0.0222919 | ||||||||
\(739\) | 2.25320e18 | 0.508875 | 0.254437 | − | 0.967089i | \(-0.418110\pi\) | ||||
0.254437 | + | 0.967089i | \(0.418110\pi\) | |||||||
\(740\) | −1.05542e19 | −2.36276 | ||||||||
\(741\) | 1.62920e17 | 0.0361540 | ||||||||
\(742\) | −1.80981e16 | −0.00398114 | ||||||||
\(743\) | −6.81639e18 | −1.48637 | −0.743186 | − | 0.669085i | \(-0.766686\pi\) | ||||
−0.743186 | + | 0.669085i | \(0.766686\pi\) | |||||||
\(744\) | −5.98700e17 | −0.129415 | ||||||||
\(745\) | −1.04041e19 | −2.22940 | ||||||||
\(746\) | 4.33129e17 | 0.0920058 | ||||||||
\(747\) | −1.42113e18 | −0.299260 | ||||||||
\(748\) | 8.50451e18 | 1.77537 | ||||||||
\(749\) | −1.00544e18 | −0.208077 | ||||||||
\(750\) | −4.11580e17 | −0.0844415 | ||||||||
\(751\) | −2.67406e18 | −0.543890 | −0.271945 | − | 0.962313i | \(-0.587667\pi\) | ||||
−0.271945 | + | 0.962313i | \(0.587667\pi\) | |||||||
\(752\) | 9.12061e18 | 1.83911 | ||||||||
\(753\) | −1.25172e18 | −0.250231 | ||||||||
\(754\) | −6.93498e16 | −0.0137446 | ||||||||
\(755\) | 2.25031e18 | 0.442167 | ||||||||
\(756\) | 2.14021e17 | 0.0416932 | ||||||||
\(757\) | −2.22413e18 | −0.429573 | −0.214786 | − | 0.976661i | \(-0.568906\pi\) | ||||
−0.214786 | + | 0.976661i | \(0.568906\pi\) | |||||||
\(758\) | −4.35557e17 | −0.0834056 | ||||||||
\(759\) | 4.82463e17 | 0.0915994 | ||||||||
\(760\) | −4.87720e17 | −0.0918083 | ||||||||
\(761\) | 8.42640e17 | 0.157269 | 0.0786343 | − | 0.996904i | \(-0.474944\pi\) | ||||
0.0786343 | + | 0.996904i | \(0.474944\pi\) | |||||||
\(762\) | 5.27490e17 | 0.0976128 | ||||||||
\(763\) | 9.11054e17 | 0.167161 | ||||||||
\(764\) | 2.44957e18 | 0.445639 | ||||||||
\(765\) | −3.99321e18 | −0.720315 | ||||||||
\(766\) | −5.38136e17 | −0.0962510 | ||||||||
\(767\) | −1.78055e17 | −0.0315780 | ||||||||
\(768\) | 2.91687e18 | 0.512944 | ||||||||
\(769\) | 4.49983e18 | 0.784648 | 0.392324 | − | 0.919827i | \(-0.371671\pi\) | ||||
0.392324 | + | 0.919827i | \(0.371671\pi\) | |||||||
\(770\) | −3.16136e17 | −0.0546618 | ||||||||
\(771\) | −1.08177e18 | −0.185474 | ||||||||
\(772\) | 5.15876e18 | 0.877067 | ||||||||
\(773\) | 5.85877e18 | 0.987734 | 0.493867 | − | 0.869537i | \(-0.335583\pi\) | ||||
0.493867 | + | 0.869537i | \(0.335583\pi\) | |||||||
\(774\) | 2.56386e17 | 0.0428625 | ||||||||
\(775\) | 1.16029e19 | 1.92355 | ||||||||
\(776\) | 1.85710e18 | 0.305305 | ||||||||
\(777\) | 1.10482e18 | 0.180118 | ||||||||
\(778\) | −4.91420e17 | −0.0794484 | ||||||||
\(779\) | 1.01092e18 | 0.162077 | ||||||||
\(780\) | −1.46174e18 | −0.232411 | ||||||||
\(781\) | 6.56253e18 | 1.03476 | ||||||||
\(782\) | −9.97395e16 | −0.0155964 | ||||||||
\(783\) | 6.60143e17 | 0.102373 | ||||||||
\(784\) | −5.97997e18 | −0.919696 | ||||||||
\(785\) | −1.05054e19 | −1.60237 | ||||||||
\(786\) | 2.20278e16 | 0.00333214 | ||||||||
\(787\) | −4.70812e18 | −0.706336 | −0.353168 | − | 0.935560i | \(-0.614896\pi\) | ||||
−0.353168 | + | 0.935560i | \(0.614896\pi\) | |||||||
\(788\) | −3.57154e17 | −0.0531417 | ||||||||
\(789\) | 3.10869e18 | 0.458751 | ||||||||
\(790\) | −2.08508e18 | −0.305174 | ||||||||
\(791\) | 1.50069e18 | 0.217844 | ||||||||
\(792\) | 6.84177e17 | 0.0985042 | ||||||||
\(793\) | −3.50837e17 | −0.0500991 | ||||||||
\(794\) | 2.42745e17 | 0.0343809 | ||||||||
\(795\) | −1.17663e18 | −0.165292 | ||||||||
\(796\) | −1.08711e19 | −1.51474 | ||||||||
\(797\) | 5.53101e18 | 0.764408 | 0.382204 | − | 0.924078i | \(-0.375165\pi\) | ||||
0.382204 | + | 0.924078i | \(0.375165\pi\) | |||||||
\(798\) | 2.53818e16 | 0.00347939 | ||||||||
\(799\) | 1.80230e19 | 2.45061 | ||||||||
\(800\) | 4.24255e18 | 0.572192 | ||||||||
\(801\) | −4.20490e18 | −0.562528 | ||||||||
\(802\) | 5.06940e17 | 0.0672703 | ||||||||
\(803\) | 9.46233e18 | 1.24551 | ||||||||
\(804\) | −8.54455e18 | −1.11564 | ||||||||
\(805\) | −3.23020e17 | −0.0418366 | ||||||||
\(806\) | −2.12802e17 | −0.0273399 | ||||||||
\(807\) | −1.41311e18 | −0.180094 | ||||||||
\(808\) | 3.05517e16 | 0.00386244 | ||||||||
\(809\) | 2.45656e18 | 0.308078 | 0.154039 | − | 0.988065i | \(-0.450772\pi\) | ||||
0.154039 | + | 0.988065i | \(0.450772\pi\) | |||||||
\(810\) | −1.59708e17 | −0.0198689 | ||||||||
\(811\) | 1.09964e19 | 1.35711 | 0.678557 | − | 0.734548i | \(-0.262606\pi\) | ||||
0.678557 | + | 0.734548i | \(0.262606\pi\) | |||||||
\(812\) | 9.41305e17 | 0.115243 | ||||||||
\(813\) | −3.89680e18 | −0.473281 | ||||||||
\(814\) | 1.75585e18 | 0.211558 | ||||||||
\(815\) | −1.93681e19 | −2.31506 | ||||||||
\(816\) | 6.05511e18 | 0.718019 | ||||||||
\(817\) | −2.64909e18 | −0.311640 | ||||||||
\(818\) | −4.25323e17 | −0.0496390 | ||||||||
\(819\) | 1.53016e17 | 0.0177171 | ||||||||
\(820\) | −9.07009e18 | −1.04189 | ||||||||
\(821\) | −9.81346e18 | −1.11839 | −0.559193 | − | 0.829038i | \(-0.688889\pi\) | ||||
−0.559193 | + | 0.829038i | \(0.688889\pi\) | |||||||
\(822\) | 2.62806e17 | 0.0297145 | ||||||||
\(823\) | −6.00216e18 | −0.673300 | −0.336650 | − | 0.941630i | \(-0.609294\pi\) | ||||
−0.336650 | + | 0.941630i | \(0.609294\pi\) | |||||||
\(824\) | −1.01017e18 | −0.112426 | ||||||||
\(825\) | −1.32594e19 | −1.46411 | ||||||||
\(826\) | −2.77397e16 | −0.00303900 | ||||||||
\(827\) | 1.52307e19 | 1.65552 | 0.827760 | − | 0.561082i | \(-0.189615\pi\) | ||||
0.827760 | + | 0.561082i | \(0.189615\pi\) | |||||||
\(828\) | 3.47543e17 | 0.0374810 | ||||||||
\(829\) | −5.90352e18 | −0.631694 | −0.315847 | − | 0.948810i | \(-0.602289\pi\) | ||||
−0.315847 | + | 0.948810i | \(0.602289\pi\) | |||||||
\(830\) | 1.51215e18 | 0.160541 | ||||||||
\(831\) | −3.51342e18 | −0.370104 | ||||||||
\(832\) | 2.16415e18 | 0.226196 | ||||||||
\(833\) | −1.18169e19 | −1.22549 | ||||||||
\(834\) | 6.56113e16 | 0.00675149 | ||||||||
\(835\) | 3.24221e19 | 3.31039 | ||||||||
\(836\) | −3.51444e18 | −0.356053 | ||||||||
\(837\) | 2.02566e18 | 0.203635 | ||||||||
\(838\) | −1.15432e17 | −0.0115144 | ||||||||
\(839\) | 8.92085e18 | 0.882985 | 0.441492 | − | 0.897265i | \(-0.354449\pi\) | ||||
0.441492 | + | 0.897265i | \(0.354449\pi\) | |||||||
\(840\) | −4.58072e17 | −0.0449902 | ||||||||
\(841\) | −7.35720e18 | −0.717032 | ||||||||
\(842\) | 5.75545e17 | 0.0556609 | ||||||||
\(843\) | −4.93012e18 | −0.473127 | ||||||||
\(844\) | −2.00246e19 | −1.90694 | ||||||||
\(845\) | 1.67185e19 | 1.57990 | ||||||||
\(846\) | 7.20828e17 | 0.0675965 | ||||||||
\(847\) | −2.22745e18 | −0.207284 | ||||||||
\(848\) | 1.78418e18 | 0.164765 | ||||||||
\(849\) | −7.84690e17 | −0.0719115 | ||||||||
\(850\) | 2.74111e18 | 0.249290 | ||||||||
\(851\) | 1.79409e18 | 0.161921 | ||||||||
\(852\) | 4.72733e18 | 0.423408 | ||||||||
\(853\) | −1.92943e19 | −1.71499 | −0.857495 | − | 0.514493i | \(-0.827980\pi\) | ||||
−0.857495 | + | 0.514493i | \(0.827980\pi\) | |||||||
\(854\) | −5.46579e16 | −0.00482144 | ||||||||
\(855\) | 1.65017e18 | 0.144460 | ||||||||
\(856\) | −2.31532e18 | −0.201155 | ||||||||
\(857\) | 1.88539e19 | 1.62565 | 0.812825 | − | 0.582508i | \(-0.197929\pi\) | ||||
0.812825 | + | 0.582508i | \(0.197929\pi\) | |||||||
\(858\) | 2.43183e17 | 0.0208097 | ||||||||
\(859\) | 1.17967e19 | 1.00185 | 0.500927 | − | 0.865490i | \(-0.332993\pi\) | ||||
0.500927 | + | 0.865490i | \(0.332993\pi\) | |||||||
\(860\) | 2.37680e19 | 2.00333 | ||||||||
\(861\) | 9.49465e17 | 0.0794252 | ||||||||
\(862\) | −2.00998e18 | −0.166876 | ||||||||
\(863\) | −1.91621e18 | −0.157896 | −0.0789482 | − | 0.996879i | \(-0.525156\pi\) | ||||
−0.0789482 | + | 0.996879i | \(0.525156\pi\) | |||||||
\(864\) | 7.40678e17 | 0.0605745 | ||||||||
\(865\) | −1.24343e19 | −1.00929 | ||||||||
\(866\) | 2.39200e18 | 0.192706 | ||||||||
\(867\) | 4.74492e18 | 0.379407 | ||||||||
\(868\) | 2.88842e18 | 0.229235 | ||||||||
\(869\) | −3.02221e19 | −2.38065 | ||||||||
\(870\) | −7.02423e17 | −0.0549191 | ||||||||
\(871\) | −6.10899e18 | −0.474080 | ||||||||
\(872\) | 2.09797e18 | 0.161600 | ||||||||
\(873\) | −6.28338e18 | −0.480398 | ||||||||
\(874\) | 4.12167e16 | 0.00312788 | ||||||||
\(875\) | 3.99411e18 | 0.300862 | ||||||||
\(876\) | 6.81621e18 | 0.509643 | ||||||||
\(877\) | 2.28743e19 | 1.69766 | 0.848828 | − | 0.528669i | \(-0.177309\pi\) | ||||
0.848828 | + | 0.528669i | \(0.177309\pi\) | |||||||
\(878\) | 1.72070e18 | 0.126762 | ||||||||
\(879\) | −1.71830e18 | −0.125653 | ||||||||
\(880\) | 3.11659e19 | 2.26226 | ||||||||
\(881\) | −1.62894e19 | −1.17371 | −0.586855 | − | 0.809692i | \(-0.699634\pi\) | ||||
−0.586855 | + | 0.809692i | \(0.699634\pi\) | |||||||
\(882\) | −4.72613e17 | −0.0338034 | ||||||||
\(883\) | −1.24079e19 | −0.880956 | −0.440478 | − | 0.897763i | \(-0.645191\pi\) | ||||
−0.440478 | + | 0.897763i | \(0.645191\pi\) | |||||||
\(884\) | 4.38000e18 | 0.308699 | ||||||||
\(885\) | −1.80346e18 | −0.126176 | ||||||||
\(886\) | 2.74270e18 | 0.190484 | ||||||||
\(887\) | −2.85771e19 | −1.97022 | −0.985110 | − | 0.171926i | \(-0.945001\pi\) | ||||
−0.985110 | + | 0.171926i | \(0.945001\pi\) | |||||||
\(888\) | 2.54418e18 | 0.174126 | ||||||||
\(889\) | −5.11894e18 | −0.347791 | ||||||||
\(890\) | 4.47421e18 | 0.301774 | ||||||||
\(891\) | −2.31487e18 | −0.154996 | ||||||||
\(892\) | 1.88433e19 | 1.25252 | ||||||||
\(893\) | −7.44791e18 | −0.491473 | ||||||||
\(894\) | 1.24684e18 | 0.0816805 | ||||||||
\(895\) | 4.12446e19 | 2.68236 | ||||||||
\(896\) | 1.40542e18 | 0.0907412 | ||||||||
\(897\) | 2.48479e17 | 0.0159272 | ||||||||
\(898\) | 2.51463e18 | 0.160022 | ||||||||
\(899\) | 8.90924e18 | 0.562863 | ||||||||
\(900\) | −9.55144e18 | −0.599091 | ||||||||
\(901\) | 3.52568e18 | 0.219549 | ||||||||
\(902\) | 1.50895e18 | 0.0932893 | ||||||||
\(903\) | −2.48805e18 | −0.152718 | ||||||||
\(904\) | 3.45579e18 | 0.210597 | ||||||||
\(905\) | 4.34062e19 | 2.62625 | ||||||||
\(906\) | −2.69680e17 | −0.0162000 | ||||||||
\(907\) | 6.87747e18 | 0.410186 | 0.205093 | − | 0.978742i | \(-0.434250\pi\) | ||||
0.205093 | + | 0.978742i | \(0.434250\pi\) | |||||||
\(908\) | −1.95903e19 | −1.16007 | ||||||||
\(909\) | −1.03370e17 | −0.00607756 | ||||||||
\(910\) | −1.62817e17 | −0.00950451 | ||||||||
\(911\) | −7.71382e18 | −0.447095 | −0.223548 | − | 0.974693i | \(-0.571764\pi\) | ||||
−0.223548 | + | 0.974693i | \(0.571764\pi\) | |||||||
\(912\) | −2.50224e18 | −0.144000 | ||||||||
\(913\) | 2.19177e19 | 1.25238 | ||||||||
\(914\) | −3.23197e18 | −0.183365 | ||||||||
\(915\) | −3.55352e18 | −0.200181 | ||||||||
\(916\) | 2.48153e19 | 1.38803 | ||||||||
\(917\) | −2.13765e17 | −0.0118723 | ||||||||
\(918\) | 4.78552e17 | 0.0263908 | ||||||||
\(919\) | −9.11680e18 | −0.499220 | −0.249610 | − | 0.968347i | \(-0.580302\pi\) | ||||
−0.249610 | + | 0.968347i | \(0.580302\pi\) | |||||||
\(920\) | −7.43849e17 | −0.0404449 | ||||||||
\(921\) | 1.17878e19 | 0.636419 | ||||||||
\(922\) | −1.09084e18 | −0.0584801 | ||||||||
\(923\) | 3.37984e18 | 0.179923 | ||||||||
\(924\) | −3.30080e18 | −0.174482 | ||||||||
\(925\) | −4.93065e19 | −2.58811 | ||||||||
\(926\) | −2.04030e18 | −0.106346 | ||||||||
\(927\) | 3.41784e18 | 0.176902 | ||||||||
\(928\) | 3.25763e18 | 0.167433 | ||||||||
\(929\) | −1.07094e17 | −0.00546590 | −0.00273295 | − | 0.999996i | \(-0.500870\pi\) | ||||
−0.00273295 | + | 0.999996i | \(0.500870\pi\) | |||||||
\(930\) | −2.15540e18 | −0.109242 | ||||||||
\(931\) | 4.88325e18 | 0.245774 | ||||||||
\(932\) | 7.15856e18 | 0.357785 | ||||||||
\(933\) | 8.48414e18 | 0.421092 | ||||||||
\(934\) | −2.77104e17 | −0.0136581 | ||||||||
\(935\) | 6.15862e19 | 3.01445 | ||||||||
\(936\) | 3.52366e17 | 0.0171278 | ||||||||
\(937\) | 5.74239e18 | 0.277195 | 0.138597 | − | 0.990349i | \(-0.455741\pi\) | ||||
0.138597 | + | 0.990349i | \(0.455741\pi\) | |||||||
\(938\) | −9.51737e17 | −0.0456245 | ||||||||
\(939\) | 1.44902e19 | 0.689840 | ||||||||
\(940\) | 6.68236e19 | 3.15936 | ||||||||
\(941\) | 4.99015e18 | 0.234305 | 0.117152 | − | 0.993114i | \(-0.462623\pi\) | ||||
0.117152 | + | 0.993114i | \(0.462623\pi\) | |||||||
\(942\) | 1.25899e18 | 0.0587071 | ||||||||
\(943\) | 1.54181e18 | 0.0714010 | ||||||||
\(944\) | 2.73469e18 | 0.125774 | ||||||||
\(945\) | 1.54986e18 | 0.0707921 | ||||||||
\(946\) | −3.95417e18 | −0.179375 | ||||||||
\(947\) | −2.93709e19 | −1.32325 | −0.661626 | − | 0.749834i | \(-0.730133\pi\) | ||||
−0.661626 | + | 0.749834i | \(0.730133\pi\) | |||||||
\(948\) | −2.17705e19 | −0.974124 | ||||||||
\(949\) | 4.87330e18 | 0.216567 | ||||||||
\(950\) | −1.13275e18 | −0.0499954 | ||||||||
\(951\) | −1.09861e18 | −0.0481582 | ||||||||
\(952\) | 1.37258e18 | 0.0597581 | ||||||||
\(953\) | 1.23577e19 | 0.534360 | 0.267180 | − | 0.963647i | \(-0.413908\pi\) | ||||
0.267180 | + | 0.963647i | \(0.413908\pi\) | |||||||
\(954\) | 1.41009e17 | 0.00605595 | ||||||||
\(955\) | 1.77388e19 | 0.756664 | ||||||||
\(956\) | −3.04800e19 | −1.29133 | ||||||||
\(957\) | −1.01812e19 | −0.428422 | ||||||||
\(958\) | 8.02836e17 | 0.0335545 | ||||||||
\(959\) | −2.55036e18 | −0.105872 | ||||||||
\(960\) | 2.19200e19 | 0.903810 | ||||||||
\(961\) | 2.92066e18 | 0.119613 | ||||||||
\(962\) | 9.04303e17 | 0.0367854 | ||||||||
\(963\) | 7.83373e18 | 0.316518 | ||||||||
\(964\) | 6.10236e18 | 0.244904 | ||||||||
\(965\) | 3.73577e19 | 1.48920 | ||||||||
\(966\) | 3.87112e16 | 0.00153280 | ||||||||
\(967\) | −4.45933e19 | −1.75387 | −0.876936 | − | 0.480608i | \(-0.840416\pi\) | ||||
−0.876936 | + | 0.480608i | \(0.840416\pi\) | |||||||
\(968\) | −5.12935e18 | −0.200388 | ||||||||
\(969\) | −4.94461e18 | −0.191879 | ||||||||
\(970\) | 6.68581e18 | 0.257714 | ||||||||
\(971\) | −2.67149e19 | −1.02289 | −0.511444 | − | 0.859317i | \(-0.670889\pi\) | ||||
−0.511444 | + | 0.859317i | \(0.670889\pi\) | |||||||
\(972\) | −1.66752e18 | −0.0634221 | ||||||||
\(973\) | −6.36715e17 | −0.0240553 | ||||||||
\(974\) | −1.67567e18 | −0.0628862 | ||||||||
\(975\) | −6.82888e18 | −0.254577 | ||||||||
\(976\) | 5.38839e18 | 0.199543 | ||||||||
\(977\) | −1.10744e19 | −0.407387 | −0.203693 | − | 0.979035i | \(-0.565295\pi\) | ||||
−0.203693 | + | 0.979035i | \(0.565295\pi\) | |||||||
\(978\) | 2.32111e18 | 0.0848188 | ||||||||
\(979\) | 6.48511e19 | 2.35413 | ||||||||
\(980\) | −4.38132e19 | −1.57992 | ||||||||
\(981\) | −7.09836e18 | −0.254278 | ||||||||
\(982\) | 2.39308e18 | 0.0851595 | ||||||||
\(983\) | 1.41399e18 | 0.0499860 | 0.0249930 | − | 0.999688i | \(-0.492044\pi\) | ||||
0.0249930 | + | 0.999688i | \(0.492044\pi\) | |||||||
\(984\) | 2.18642e18 | 0.0767832 | ||||||||
\(985\) | −2.58637e18 | −0.0902308 | ||||||||
\(986\) | 2.10476e18 | 0.0729462 | ||||||||
\(987\) | −6.99515e18 | −0.240844 | ||||||||
\(988\) | −1.81001e18 | −0.0619100 | ||||||||
\(989\) | −4.04028e18 | −0.137289 | ||||||||
\(990\) | 2.46313e18 | 0.0831493 | ||||||||
\(991\) | −1.40952e19 | −0.472706 | −0.236353 | − | 0.971667i | \(-0.575952\pi\) | ||||
−0.236353 | + | 0.971667i | \(0.575952\pi\) | |||||||
\(992\) | 9.99613e18 | 0.333047 | ||||||||
\(993\) | −7.99918e18 | −0.264774 | ||||||||
\(994\) | 5.26555e17 | 0.0173154 | ||||||||
\(995\) | −7.87239e19 | −2.57192 | ||||||||
\(996\) | 1.57884e19 | 0.512452 | ||||||||
\(997\) | −3.49134e19 | −1.12583 | −0.562917 | − | 0.826514i | \(-0.690321\pi\) | ||||
−0.562917 | + | 0.826514i | \(0.690321\pi\) | |||||||
\(998\) | −3.01146e18 | −0.0964781 | ||||||||
\(999\) | −8.60809e18 | −0.273988 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.14.a.a.1.16 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.a.1.16 | ✓ | 30 | 1.1 | even | 1 | trivial |