Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,64,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 64, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 64);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 64 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(25.1360966918\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2 x^{4} + \cdots - 35\!\cdots\!34 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{37}\cdot 3^{17}\cdot 5^{3}\cdot 7^{2}\cdot 13 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-6.41810e7\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.72250e9 | 1.55499 | 0.777493 | − | 0.628891i | \(-0.216491\pi\) | ||||
0.777493 | + | 0.628891i | \(0.216491\pi\) | |||||||
\(3\) | 8.02316e14 | 0.749939 | 0.374970 | − | 0.927037i | \(-0.377653\pi\) | ||||
0.374970 | + | 0.927037i | \(0.377653\pi\) | |||||||
\(4\) | 1.30786e19 | 1.41798 | ||||||||
\(5\) | 1.36438e22 | 1.31033 | 0.655166 | − | 0.755485i | \(-0.272599\pi\) | ||||
0.655166 | + | 0.755485i | \(0.272599\pi\) | |||||||
\(6\) | 3.78894e24 | 1.16615 | ||||||||
\(7\) | 4.00095e26 | 0.958463 | 0.479231 | − | 0.877689i | \(-0.340915\pi\) | ||||
0.479231 | + | 0.877689i | \(0.340915\pi\) | |||||||
\(8\) | 1.82063e28 | 0.649959 | ||||||||
\(9\) | −5.00850e29 | −0.437591 | ||||||||
\(10\) | 6.44329e31 | 2.03755 | ||||||||
\(11\) | −8.56884e32 | −1.34602 | −0.673012 | − | 0.739632i | \(-0.735000\pi\) | ||||
−0.673012 | + | 0.739632i | \(0.735000\pi\) | |||||||
\(12\) | 1.04932e34 | 1.06340 | ||||||||
\(13\) | 2.07398e35 | 1.68884 | 0.844421 | − | 0.535680i | \(-0.179945\pi\) | ||||
0.844421 | + | 0.535680i | \(0.179945\pi\) | |||||||
\(14\) | 1.88945e36 | 1.49040 | ||||||||
\(15\) | 1.09467e37 | 0.982669 | ||||||||
\(16\) | −3.46497e37 | −0.407306 | ||||||||
\(17\) | −5.37140e38 | −0.935291 | −0.467645 | − | 0.883916i | \(-0.654898\pi\) | ||||
−0.467645 | + | 0.883916i | \(0.654898\pi\) | |||||||
\(18\) | −2.36526e39 | −0.680448 | ||||||||
\(19\) | −4.25177e39 | −0.222757 | −0.111379 | − | 0.993778i | \(-0.535527\pi\) | ||||
−0.111379 | + | 0.993778i | \(0.535527\pi\) | |||||||
\(20\) | 1.78442e41 | 1.85803 | ||||||||
\(21\) | 3.21003e41 | 0.718789 | ||||||||
\(22\) | −4.04663e42 | −2.09305 | ||||||||
\(23\) | 7.22439e42 | 0.921243 | 0.460621 | − | 0.887597i | \(-0.347627\pi\) | ||||
0.460621 | + | 0.887597i | \(0.347627\pi\) | |||||||
\(24\) | 1.46072e43 | 0.487430 | ||||||||
\(25\) | 7.77338e43 | 0.716967 | ||||||||
\(26\) | 9.79436e44 | 2.62613 | ||||||||
\(27\) | −1.32014e45 | −1.07811 | ||||||||
\(28\) | 5.23268e45 | 1.35908 | ||||||||
\(29\) | 6.34966e45 | 0.546027 | 0.273013 | − | 0.962010i | \(-0.411980\pi\) | ||||
0.273013 | + | 0.962010i | \(0.411980\pi\) | |||||||
\(30\) | 5.16956e46 | 1.52804 | ||||||||
\(31\) | 1.09199e47 | 1.14902 | 0.574508 | − | 0.818499i | \(-0.305193\pi\) | ||||
0.574508 | + | 0.818499i | \(0.305193\pi\) | |||||||
\(32\) | −3.31556e47 | −1.28331 | ||||||||
\(33\) | −6.87492e47 | −1.00944 | ||||||||
\(34\) | −2.53664e48 | −1.45436 | ||||||||
\(35\) | 5.45883e48 | 1.25590 | ||||||||
\(36\) | −6.55041e48 | −0.620497 | ||||||||
\(37\) | −2.36747e49 | −0.946087 | −0.473043 | − | 0.881039i | \(-0.656845\pi\) | ||||
−0.473043 | + | 0.881039i | \(0.656845\pi\) | |||||||
\(38\) | −2.00790e49 | −0.346384 | ||||||||
\(39\) | 1.66399e50 | 1.26653 | ||||||||
\(40\) | 2.48403e50 | 0.851662 | ||||||||
\(41\) | 2.67628e50 | 0.421542 | 0.210771 | − | 0.977535i | \(-0.432403\pi\) | ||||
0.210771 | + | 0.977535i | \(0.432403\pi\) | |||||||
\(42\) | 1.51594e51 | 1.11771 | ||||||||
\(43\) | −2.12019e51 | −0.744936 | −0.372468 | − | 0.928045i | \(-0.621488\pi\) | ||||
−0.372468 | + | 0.928045i | \(0.621488\pi\) | |||||||
\(44\) | −1.12068e52 | −1.90864 | ||||||||
\(45\) | −6.83350e51 | −0.573389 | ||||||||
\(46\) | 3.41171e52 | 1.43252 | ||||||||
\(47\) | −3.01357e52 | −0.642686 | −0.321343 | − | 0.946963i | \(-0.604134\pi\) | ||||
−0.321343 | + | 0.946963i | \(0.604134\pi\) | |||||||
\(48\) | −2.78000e52 | −0.305454 | ||||||||
\(49\) | −1.41752e52 | −0.0813493 | ||||||||
\(50\) | 3.67097e53 | 1.11487 | ||||||||
\(51\) | −4.30956e53 | −0.701411 | ||||||||
\(52\) | 2.71247e54 | 2.39475 | ||||||||
\(53\) | −1.69213e52 | −0.00819867 | −0.00409934 | − | 0.999992i | \(-0.501305\pi\) | ||||
−0.00409934 | + | 0.999992i | \(0.501305\pi\) | |||||||
\(54\) | −6.23436e54 | −1.67644 | ||||||||
\(55\) | −1.16912e55 | −1.76374 | ||||||||
\(56\) | 7.28424e54 | 0.622962 | ||||||||
\(57\) | −3.41127e54 | −0.167054 | ||||||||
\(58\) | 2.99863e55 | 0.849064 | ||||||||
\(59\) | −7.40118e54 | −0.122310 | −0.0611551 | − | 0.998128i | \(-0.519478\pi\) | ||||
−0.0611551 | + | 0.998128i | \(0.519478\pi\) | |||||||
\(60\) | 1.43167e56 | 1.39341 | ||||||||
\(61\) | −2.87222e56 | −1.66084 | −0.830420 | − | 0.557137i | \(-0.811900\pi\) | ||||
−0.830420 | + | 0.557137i | \(0.811900\pi\) | |||||||
\(62\) | 5.15693e56 | 1.78670 | ||||||||
\(63\) | −2.00388e56 | −0.419415 | ||||||||
\(64\) | −1.24619e57 | −1.58823 | ||||||||
\(65\) | 2.82970e57 | 2.21294 | ||||||||
\(66\) | −3.24668e57 | −1.56966 | ||||||||
\(67\) | −2.05697e57 | −0.619258 | −0.309629 | − | 0.950857i | \(-0.600205\pi\) | ||||
−0.309629 | + | 0.950857i | \(0.600205\pi\) | |||||||
\(68\) | −7.02504e57 | −1.32623 | ||||||||
\(69\) | 5.79624e57 | 0.690876 | ||||||||
\(70\) | 2.57793e58 | 1.95291 | ||||||||
\(71\) | 2.18652e58 | 1.05954 | 0.529768 | − | 0.848142i | \(-0.322279\pi\) | ||||
0.529768 | + | 0.848142i | \(0.322279\pi\) | |||||||
\(72\) | −9.11860e57 | −0.284416 | ||||||||
\(73\) | −1.91991e58 | −0.387803 | −0.193902 | − | 0.981021i | \(-0.562114\pi\) | ||||
−0.193902 | + | 0.981021i | \(0.562114\pi\) | |||||||
\(74\) | −1.11804e59 | −1.47115 | ||||||||
\(75\) | 6.23671e58 | 0.537682 | ||||||||
\(76\) | −5.56072e58 | −0.315866 | ||||||||
\(77\) | −3.42835e59 | −1.29011 | ||||||||
\(78\) | 7.85818e59 | 1.96944 | ||||||||
\(79\) | −1.43780e59 | −0.241237 | −0.120618 | − | 0.992699i | \(-0.538488\pi\) | ||||
−0.120618 | + | 0.992699i | \(0.538488\pi\) | |||||||
\(80\) | −4.72755e59 | −0.533705 | ||||||||
\(81\) | −4.85917e59 | −0.370923 | ||||||||
\(82\) | 1.26387e60 | 0.655492 | ||||||||
\(83\) | 2.96542e60 | 1.04985 | 0.524924 | − | 0.851149i | \(-0.324094\pi\) | ||||
0.524924 | + | 0.851149i | \(0.324094\pi\) | |||||||
\(84\) | 4.19827e60 | 1.01923 | ||||||||
\(85\) | −7.32865e60 | −1.22554 | ||||||||
\(86\) | −1.00126e61 | −1.15837 | ||||||||
\(87\) | 5.09444e60 | 0.409487 | ||||||||
\(88\) | −1.56007e61 | −0.874861 | ||||||||
\(89\) | −3.32533e60 | −0.130632 | −0.0653161 | − | 0.997865i | \(-0.520806\pi\) | ||||
−0.0653161 | + | 0.997865i | \(0.520806\pi\) | |||||||
\(90\) | −3.22712e61 | −0.891612 | ||||||||
\(91\) | 8.29790e61 | 1.61869 | ||||||||
\(92\) | 9.44848e61 | 1.30631 | ||||||||
\(93\) | 8.76123e61 | 0.861692 | ||||||||
\(94\) | −1.42316e62 | −0.999368 | ||||||||
\(95\) | −5.80104e61 | −0.291886 | ||||||||
\(96\) | −2.66013e62 | −0.962408 | ||||||||
\(97\) | −5.80025e61 | −0.151404 | −0.0757020 | − | 0.997130i | \(-0.524120\pi\) | ||||
−0.0757020 | + | 0.997130i | \(0.524120\pi\) | |||||||
\(98\) | −6.69425e61 | −0.126497 | ||||||||
\(99\) | 4.29170e62 | 0.589008 | ||||||||
\(100\) | 1.01665e63 | 1.01665 | ||||||||
\(101\) | −1.95277e63 | −1.42734 | −0.713671 | − | 0.700481i | \(-0.752969\pi\) | ||||
−0.713671 | + | 0.700481i | \(0.752969\pi\) | |||||||
\(102\) | −2.03519e63 | −1.09069 | ||||||||
\(103\) | 1.61718e63 | 0.637363 | 0.318682 | − | 0.947862i | \(-0.396760\pi\) | ||||
0.318682 | + | 0.947862i | \(0.396760\pi\) | |||||||
\(104\) | 3.77594e63 | 1.09768 | ||||||||
\(105\) | 4.37971e63 | 0.941851 | ||||||||
\(106\) | −7.99107e61 | −0.0127488 | ||||||||
\(107\) | 2.02228e63 | 0.240023 | 0.120011 | − | 0.992773i | \(-0.461707\pi\) | ||||
0.120011 | + | 0.992773i | \(0.461707\pi\) | |||||||
\(108\) | −1.72656e64 | −1.52874 | ||||||||
\(109\) | 2.99199e64 | 1.98164 | 0.990821 | − | 0.135180i | \(-0.0431613\pi\) | ||||
0.990821 | + | 0.135180i | \(0.0431613\pi\) | |||||||
\(110\) | −5.52115e64 | −2.74259 | ||||||||
\(111\) | −1.89946e64 | −0.709508 | ||||||||
\(112\) | −1.38632e64 | −0.390387 | ||||||||
\(113\) | 8.58568e64 | 1.82727 | 0.913637 | − | 0.406531i | \(-0.133262\pi\) | ||||
0.913637 | + | 0.406531i | \(0.133262\pi\) | |||||||
\(114\) | −1.61097e64 | −0.259767 | ||||||||
\(115\) | 9.85683e64 | 1.20713 | ||||||||
\(116\) | 8.30447e64 | 0.774257 | ||||||||
\(117\) | −1.03875e65 | −0.739022 | ||||||||
\(118\) | −3.49520e64 | −0.190191 | ||||||||
\(119\) | −2.14907e65 | −0.896441 | ||||||||
\(120\) | 1.99298e65 | 0.638695 | ||||||||
\(121\) | 3.28986e65 | 0.811779 | ||||||||
\(122\) | −1.35640e66 | −2.58259 | ||||||||
\(123\) | 2.14723e65 | 0.316131 | ||||||||
\(124\) | 1.42817e66 | 1.62929 | ||||||||
\(125\) | −4.18681e65 | −0.370866 | ||||||||
\(126\) | −9.46329e65 | −0.652184 | ||||||||
\(127\) | 1.13001e66 | 0.607104 | 0.303552 | − | 0.952815i | \(-0.401827\pi\) | ||||
0.303552 | + | 0.952815i | \(0.401827\pi\) | |||||||
\(128\) | −2.82704e66 | −1.18636 | ||||||||
\(129\) | −1.70106e66 | −0.558657 | ||||||||
\(130\) | 1.33633e67 | 3.44110 | ||||||||
\(131\) | 4.17132e66 | 0.843776 | 0.421888 | − | 0.906648i | \(-0.361368\pi\) | ||||
0.421888 | + | 0.906648i | \(0.361368\pi\) | |||||||
\(132\) | −8.99143e66 | −1.43136 | ||||||||
\(133\) | −1.70111e66 | −0.213504 | ||||||||
\(134\) | −9.71403e66 | −0.962938 | ||||||||
\(135\) | −1.80118e67 | −1.41268 | ||||||||
\(136\) | −9.77932e66 | −0.607901 | ||||||||
\(137\) | 1.55906e67 | 0.769422 | 0.384711 | − | 0.923037i | \(-0.374301\pi\) | ||||
0.384711 | + | 0.923037i | \(0.374301\pi\) | |||||||
\(138\) | 2.73727e67 | 1.07430 | ||||||||
\(139\) | −2.06837e67 | −0.646640 | −0.323320 | − | 0.946290i | \(-0.604799\pi\) | ||||
−0.323320 | + | 0.946290i | \(0.604799\pi\) | |||||||
\(140\) | 7.13938e67 | 1.78085 | ||||||||
\(141\) | −2.41784e67 | −0.481976 | ||||||||
\(142\) | 1.03258e68 | 1.64757 | ||||||||
\(143\) | −1.77716e68 | −2.27322 | ||||||||
\(144\) | 1.73543e67 | 0.178233 | ||||||||
\(145\) | 8.66337e67 | 0.715476 | ||||||||
\(146\) | −9.06678e67 | −0.603029 | ||||||||
\(147\) | −1.13730e67 | −0.0610071 | ||||||||
\(148\) | −3.09632e68 | −1.34154 | ||||||||
\(149\) | 2.12773e68 | 0.745675 | 0.372838 | − | 0.927897i | \(-0.378385\pi\) | ||||
0.372838 | + | 0.927897i | \(0.378385\pi\) | |||||||
\(150\) | 2.94528e68 | 0.836089 | ||||||||
\(151\) | −2.22182e68 | −0.511606 | −0.255803 | − | 0.966729i | \(-0.582340\pi\) | ||||
−0.255803 | + | 0.966729i | \(0.582340\pi\) | |||||||
\(152\) | −7.74089e67 | −0.144783 | ||||||||
\(153\) | 2.69026e68 | 0.409275 | ||||||||
\(154\) | −1.61904e69 | −2.00611 | ||||||||
\(155\) | 1.48989e69 | 1.50559 | ||||||||
\(156\) | 2.17626e69 | 1.79592 | ||||||||
\(157\) | 3.83578e68 | 0.258830 | 0.129415 | − | 0.991591i | \(-0.458690\pi\) | ||||
0.129415 | + | 0.991591i | \(0.458690\pi\) | |||||||
\(158\) | −6.78998e68 | −0.375120 | ||||||||
\(159\) | −1.35762e67 | −0.00614851 | ||||||||
\(160\) | −4.52370e69 | −1.68157 | ||||||||
\(161\) | 2.89044e69 | 0.882977 | ||||||||
\(162\) | −2.29474e69 | −0.576781 | ||||||||
\(163\) | −7.56737e69 | −1.56688 | −0.783439 | − | 0.621468i | \(-0.786537\pi\) | ||||
−0.783439 | + | 0.621468i | \(0.786537\pi\) | |||||||
\(164\) | 3.50020e69 | 0.597740 | ||||||||
\(165\) | −9.38003e69 | −1.32270 | ||||||||
\(166\) | 1.40042e70 | 1.63250 | ||||||||
\(167\) | 1.31868e70 | 1.27225 | 0.636124 | − | 0.771587i | \(-0.280537\pi\) | ||||
0.636124 | + | 0.771587i | \(0.280537\pi\) | |||||||
\(168\) | 5.84427e69 | 0.467184 | ||||||||
\(169\) | 2.79329e70 | 1.85219 | ||||||||
\(170\) | −3.46095e70 | −1.90570 | ||||||||
\(171\) | 2.12950e69 | 0.0974765 | ||||||||
\(172\) | −2.77291e70 | −1.05631 | ||||||||
\(173\) | −4.13644e70 | −1.31273 | −0.656364 | − | 0.754445i | \(-0.727906\pi\) | ||||
−0.656364 | + | 0.754445i | \(0.727906\pi\) | |||||||
\(174\) | 2.40585e70 | 0.636747 | ||||||||
\(175\) | 3.11009e70 | 0.687186 | ||||||||
\(176\) | 2.96908e70 | 0.548243 | ||||||||
\(177\) | −5.93809e69 | −0.0917252 | ||||||||
\(178\) | −1.57039e70 | −0.203131 | ||||||||
\(179\) | −1.07726e71 | −1.16802 | −0.584009 | − | 0.811747i | \(-0.698517\pi\) | ||||
−0.584009 | + | 0.811747i | \(0.698517\pi\) | |||||||
\(180\) | −8.93726e70 | −0.813056 | ||||||||
\(181\) | 8.24880e70 | 0.630254 | 0.315127 | − | 0.949049i | \(-0.397953\pi\) | ||||
0.315127 | + | 0.949049i | \(0.397953\pi\) | |||||||
\(182\) | 3.91868e71 | 2.51705 | ||||||||
\(183\) | −2.30443e71 | −1.24553 | ||||||||
\(184\) | 1.31529e71 | 0.598770 | ||||||||
\(185\) | −3.23014e71 | −1.23969 | ||||||||
\(186\) | 4.13749e71 | 1.33992 | ||||||||
\(187\) | 4.60267e71 | 1.25892 | ||||||||
\(188\) | −3.94133e71 | −0.911318 | ||||||||
\(189\) | −5.28182e71 | −1.03332 | ||||||||
\(190\) | −2.73954e71 | −0.453878 | ||||||||
\(191\) | 2.79537e70 | 0.0392544 | 0.0196272 | − | 0.999807i | \(-0.493752\pi\) | ||||
0.0196272 | + | 0.999807i | \(0.493752\pi\) | |||||||
\(192\) | −9.99836e71 | −1.19108 | ||||||||
\(193\) | −2.20841e71 | −0.223370 | −0.111685 | − | 0.993744i | \(-0.535625\pi\) | ||||
−0.111685 | + | 0.993744i | \(0.535625\pi\) | |||||||
\(194\) | −2.73917e71 | −0.235431 | ||||||||
\(195\) | 2.27032e72 | 1.65957 | ||||||||
\(196\) | −1.85392e71 | −0.115352 | ||||||||
\(197\) | 2.04182e72 | 1.08226 | 0.541130 | − | 0.840939i | \(-0.317997\pi\) | ||||
0.541130 | + | 0.840939i | \(0.317997\pi\) | |||||||
\(198\) | 2.02675e72 | 0.915899 | ||||||||
\(199\) | −5.99449e71 | −0.231143 | −0.115571 | − | 0.993299i | \(-0.536870\pi\) | ||||
−0.115571 | + | 0.993299i | \(0.536870\pi\) | |||||||
\(200\) | 1.41524e72 | 0.466000 | ||||||||
\(201\) | −1.65034e72 | −0.464406 | ||||||||
\(202\) | −9.22195e72 | −2.21950 | ||||||||
\(203\) | 2.54047e72 | 0.523346 | ||||||||
\(204\) | −5.63630e72 | −0.994590 | ||||||||
\(205\) | 3.65148e72 | 0.552359 | ||||||||
\(206\) | 7.63715e72 | 0.991091 | ||||||||
\(207\) | −3.61833e72 | −0.403127 | ||||||||
\(208\) | −7.18629e72 | −0.687875 | ||||||||
\(209\) | 3.64328e72 | 0.299836 | ||||||||
\(210\) | 2.06832e73 | 1.46457 | ||||||||
\(211\) | −2.24768e73 | −1.37037 | −0.685183 | − | 0.728371i | \(-0.740278\pi\) | ||||
−0.685183 | + | 0.728371i | \(0.740278\pi\) | |||||||
\(212\) | −2.21307e71 | −0.0116256 | ||||||||
\(213\) | 1.75428e73 | 0.794588 | ||||||||
\(214\) | 9.55021e72 | 0.373232 | ||||||||
\(215\) | −2.89275e73 | −0.976112 | ||||||||
\(216\) | −2.40348e73 | −0.700725 | ||||||||
\(217\) | 4.36901e73 | 1.10129 | ||||||||
\(218\) | 1.41297e74 | 3.08143 | ||||||||
\(219\) | −1.54038e73 | −0.290829 | ||||||||
\(220\) | −1.52904e74 | −2.50095 | ||||||||
\(221\) | −1.11402e74 | −1.57956 | ||||||||
\(222\) | −8.97021e73 | −1.10327 | ||||||||
\(223\) | 1.34223e74 | 1.43293 | 0.716464 | − | 0.697624i | \(-0.245759\pi\) | ||||
0.716464 | + | 0.697624i | \(0.245759\pi\) | |||||||
\(224\) | −1.32654e74 | −1.23001 | ||||||||
\(225\) | −3.89329e73 | −0.313738 | ||||||||
\(226\) | 4.05458e74 | 2.84139 | ||||||||
\(227\) | 8.28902e73 | 0.505462 | 0.252731 | − | 0.967537i | \(-0.418671\pi\) | ||||
0.252731 | + | 0.967537i | \(0.418671\pi\) | |||||||
\(228\) | −4.46146e73 | −0.236880 | ||||||||
\(229\) | −1.94712e74 | −0.900688 | −0.450344 | − | 0.892855i | \(-0.648699\pi\) | ||||
−0.450344 | + | 0.892855i | \(0.648699\pi\) | |||||||
\(230\) | 4.65488e74 | 1.87708 | ||||||||
\(231\) | −2.75062e74 | −0.967507 | ||||||||
\(232\) | 1.15604e74 | 0.354895 | ||||||||
\(233\) | 1.85040e74 | 0.496083 | 0.248041 | − | 0.968749i | \(-0.420213\pi\) | ||||
0.248041 | + | 0.968749i | \(0.420213\pi\) | |||||||
\(234\) | −4.90550e74 | −1.14917 | ||||||||
\(235\) | −4.11166e74 | −0.842131 | ||||||||
\(236\) | −9.67970e73 | −0.173434 | ||||||||
\(237\) | −1.15357e74 | −0.180913 | ||||||||
\(238\) | −1.01490e75 | −1.39395 | ||||||||
\(239\) | 1.17037e75 | 1.40861 | 0.704303 | − | 0.709900i | \(-0.251260\pi\) | ||||
0.704303 | + | 0.709900i | \(0.251260\pi\) | |||||||
\(240\) | −3.79299e74 | −0.400246 | ||||||||
\(241\) | 1.07492e75 | 0.995035 | 0.497517 | − | 0.867454i | \(-0.334245\pi\) | ||||
0.497517 | + | 0.867454i | \(0.334245\pi\) | |||||||
\(242\) | 1.55363e75 | 1.26231 | ||||||||
\(243\) | 1.12112e75 | 0.799936 | ||||||||
\(244\) | −3.75646e75 | −2.35505 | ||||||||
\(245\) | −1.93404e74 | −0.106595 | ||||||||
\(246\) | 1.01403e75 | 0.491579 | ||||||||
\(247\) | −8.81809e74 | −0.376202 | ||||||||
\(248\) | 1.98811e75 | 0.746814 | ||||||||
\(249\) | 2.37921e75 | 0.787323 | ||||||||
\(250\) | −1.97722e75 | −0.576692 | ||||||||
\(251\) | 3.30820e75 | 0.850882 | 0.425441 | − | 0.904986i | \(-0.360119\pi\) | ||||
0.425441 | + | 0.904986i | \(0.360119\pi\) | |||||||
\(252\) | −2.62079e75 | −0.594723 | ||||||||
\(253\) | −6.19046e75 | −1.24001 | ||||||||
\(254\) | 5.33644e75 | 0.944039 | ||||||||
\(255\) | −5.87989e75 | −0.919081 | ||||||||
\(256\) | −1.85665e75 | −0.256549 | ||||||||
\(257\) | −3.83510e75 | −0.468688 | −0.234344 | − | 0.972154i | \(-0.575294\pi\) | ||||
−0.234344 | + | 0.972154i | \(0.575294\pi\) | |||||||
\(258\) | −8.03327e75 | −0.868704 | ||||||||
\(259\) | −9.47215e75 | −0.906789 | ||||||||
\(260\) | 3.70085e76 | 3.13792 | ||||||||
\(261\) | −3.18023e75 | −0.238936 | ||||||||
\(262\) | 1.96990e76 | 1.31206 | ||||||||
\(263\) | 1.43118e76 | 0.845448 | 0.422724 | − | 0.906258i | \(-0.361074\pi\) | ||||
0.422724 | + | 0.906258i | \(0.361074\pi\) | |||||||
\(264\) | −1.25167e76 | −0.656092 | ||||||||
\(265\) | −2.30871e74 | −0.0107430 | ||||||||
\(266\) | −8.03350e75 | −0.331996 | ||||||||
\(267\) | −2.66797e75 | −0.0979662 | ||||||||
\(268\) | −2.69023e76 | −0.878098 | ||||||||
\(269\) | 4.09775e75 | 0.118946 | 0.0594728 | − | 0.998230i | \(-0.481058\pi\) | ||||
0.0594728 | + | 0.998230i | \(0.481058\pi\) | |||||||
\(270\) | −8.50605e76 | −2.19669 | ||||||||
\(271\) | −1.28815e76 | −0.296097 | −0.148049 | − | 0.988980i | \(-0.547299\pi\) | ||||
−0.148049 | + | 0.988980i | \(0.547299\pi\) | |||||||
\(272\) | 1.86118e76 | 0.380949 | ||||||||
\(273\) | 6.65754e76 | 1.21392 | ||||||||
\(274\) | 7.36265e76 | 1.19644 | ||||||||
\(275\) | −6.66088e76 | −0.965055 | ||||||||
\(276\) | 7.58067e76 | 0.979651 | ||||||||
\(277\) | 4.42046e76 | 0.509747 | 0.254874 | − | 0.966974i | \(-0.417966\pi\) | ||||
0.254874 | + | 0.966974i | \(0.417966\pi\) | |||||||
\(278\) | −9.76789e76 | −1.00552 | ||||||||
\(279\) | −5.46924e76 | −0.502799 | ||||||||
\(280\) | 9.93849e76 | 0.816286 | ||||||||
\(281\) | −3.12493e76 | −0.229399 | −0.114699 | − | 0.993400i | \(-0.536591\pi\) | ||||
−0.114699 | + | 0.993400i | \(0.536591\pi\) | |||||||
\(282\) | −1.14182e77 | −0.749466 | ||||||||
\(283\) | 2.35005e77 | 1.37976 | 0.689881 | − | 0.723923i | \(-0.257663\pi\) | ||||
0.689881 | + | 0.723923i | \(0.257663\pi\) | |||||||
\(284\) | 2.85966e77 | 1.50241 | ||||||||
\(285\) | −4.65427e76 | −0.218896 | ||||||||
\(286\) | −8.39264e77 | −3.53483 | ||||||||
\(287\) | 1.07077e77 | 0.404032 | ||||||||
\(288\) | 1.66060e77 | 0.561567 | ||||||||
\(289\) | −4.13043e76 | −0.125231 | ||||||||
\(290\) | 4.09127e77 | 1.11256 | ||||||||
\(291\) | −4.65364e76 | −0.113544 | ||||||||
\(292\) | −2.51098e77 | −0.549899 | ||||||||
\(293\) | −4.60913e77 | −0.906335 | −0.453167 | − | 0.891425i | \(-0.649706\pi\) | ||||
−0.453167 | + | 0.891425i | \(0.649706\pi\) | |||||||
\(294\) | −5.37091e76 | −0.0948652 | ||||||||
\(295\) | −1.00980e77 | −0.160267 | ||||||||
\(296\) | −4.31029e77 | −0.614918 | ||||||||
\(297\) | 1.13121e78 | 1.45116 | ||||||||
\(298\) | 1.00482e78 | 1.15951 | ||||||||
\(299\) | 1.49832e78 | 1.55583 | ||||||||
\(300\) | 8.15674e77 | 0.762425 | ||||||||
\(301\) | −8.48279e77 | −0.713993 | ||||||||
\(302\) | −1.04926e78 | −0.795541 | ||||||||
\(303\) | −1.56674e78 | −1.07042 | ||||||||
\(304\) | 1.47323e77 | 0.0907302 | ||||||||
\(305\) | −3.91881e78 | −2.17625 | ||||||||
\(306\) | 1.27048e78 | 0.636417 | ||||||||
\(307\) | 3.47715e77 | 0.157168 | 0.0785841 | − | 0.996907i | \(-0.474960\pi\) | ||||
0.0785841 | + | 0.996907i | \(0.474960\pi\) | |||||||
\(308\) | −4.48380e78 | −1.82936 | ||||||||
\(309\) | 1.29749e78 | 0.477984 | ||||||||
\(310\) | 7.03602e78 | 2.34117 | ||||||||
\(311\) | −1.27935e78 | −0.384626 | −0.192313 | − | 0.981334i | \(-0.561599\pi\) | ||||
−0.192313 | + | 0.981334i | \(0.561599\pi\) | |||||||
\(312\) | 3.02950e78 | 0.823193 | ||||||||
\(313\) | 2.55012e77 | 0.0626490 | 0.0313245 | − | 0.999509i | \(-0.490027\pi\) | ||||
0.0313245 | + | 0.999509i | \(0.490027\pi\) | |||||||
\(314\) | 1.81145e78 | 0.402478 | ||||||||
\(315\) | −2.73405e78 | −0.549572 | ||||||||
\(316\) | −1.88043e78 | −0.342070 | ||||||||
\(317\) | 8.57182e78 | 1.41158 | 0.705791 | − | 0.708420i | \(-0.250592\pi\) | ||||
0.705791 | + | 0.708420i | \(0.250592\pi\) | |||||||
\(318\) | −6.41137e76 | −0.00956085 | ||||||||
\(319\) | −5.44093e78 | −0.734965 | ||||||||
\(320\) | −1.70027e79 | −2.08111 | ||||||||
\(321\) | 1.62251e78 | 0.180002 | ||||||||
\(322\) | 1.36501e79 | 1.37302 | ||||||||
\(323\) | 2.28380e78 | 0.208343 | ||||||||
\(324\) | −6.35511e78 | −0.525963 | ||||||||
\(325\) | 1.61218e79 | 1.21084 | ||||||||
\(326\) | −3.57369e79 | −2.43648 | ||||||||
\(327\) | 2.40052e79 | 1.48611 | ||||||||
\(328\) | 4.87251e78 | 0.273985 | ||||||||
\(329\) | −1.20572e79 | −0.615991 | ||||||||
\(330\) | −4.42971e79 | −2.05677 | ||||||||
\(331\) | −1.19633e78 | −0.0504973 | −0.0252486 | − | 0.999681i | \(-0.508038\pi\) | ||||
−0.0252486 | + | 0.999681i | \(0.508038\pi\) | |||||||
\(332\) | 3.87836e79 | 1.48867 | ||||||||
\(333\) | 1.18575e79 | 0.413999 | ||||||||
\(334\) | 6.22748e79 | 1.97833 | ||||||||
\(335\) | −2.80649e79 | −0.811433 | ||||||||
\(336\) | −1.11227e79 | −0.292767 | ||||||||
\(337\) | −6.02075e79 | −1.44314 | −0.721571 | − | 0.692340i | \(-0.756580\pi\) | ||||
−0.721571 | + | 0.692340i | \(0.756580\pi\) | |||||||
\(338\) | 1.31913e80 | 2.88013 | ||||||||
\(339\) | 6.88843e79 | 1.37034 | ||||||||
\(340\) | −9.58484e79 | −1.73780 | ||||||||
\(341\) | −9.35711e79 | −1.54660 | ||||||||
\(342\) | 1.00565e79 | 0.151575 | ||||||||
\(343\) | −7.53887e79 | −1.03643 | ||||||||
\(344\) | −3.86008e79 | −0.484178 | ||||||||
\(345\) | 7.90829e79 | 0.905277 | ||||||||
\(346\) | −1.95343e80 | −2.04127 | ||||||||
\(347\) | 1.32734e80 | 1.26650 | 0.633248 | − | 0.773949i | \(-0.281721\pi\) | ||||
0.633248 | + | 0.773949i | \(0.281721\pi\) | |||||||
\(348\) | 6.66281e79 | 0.580646 | ||||||||
\(349\) | −5.81469e79 | −0.462941 | −0.231471 | − | 0.972842i | \(-0.574354\pi\) | ||||
−0.231471 | + | 0.972842i | \(0.574354\pi\) | |||||||
\(350\) | 1.46874e80 | 1.06857 | ||||||||
\(351\) | −2.73795e80 | −1.82075 | ||||||||
\(352\) | 2.84105e80 | 1.72737 | ||||||||
\(353\) | 2.98209e80 | 1.65813 | 0.829064 | − | 0.559154i | \(-0.188874\pi\) | ||||
0.829064 | + | 0.559154i | \(0.188874\pi\) | |||||||
\(354\) | −2.80426e79 | −0.142632 | ||||||||
\(355\) | 2.98325e80 | 1.38834 | ||||||||
\(356\) | −4.34907e79 | −0.185234 | ||||||||
\(357\) | −1.72424e80 | −0.672277 | ||||||||
\(358\) | −5.08735e80 | −1.81625 | ||||||||
\(359\) | −3.44639e80 | −1.12691 | −0.563455 | − | 0.826147i | \(-0.690528\pi\) | ||||
−0.563455 | + | 0.826147i | \(0.690528\pi\) | |||||||
\(360\) | −1.24413e80 | −0.372680 | ||||||||
\(361\) | −3.46237e80 | −0.950379 | ||||||||
\(362\) | 3.89549e80 | 0.980037 | ||||||||
\(363\) | 2.63951e80 | 0.608785 | ||||||||
\(364\) | 1.08525e81 | 2.29528 | ||||||||
\(365\) | −2.61950e80 | −0.508151 | ||||||||
\(366\) | −1.08827e81 | −1.93678 | ||||||||
\(367\) | 9.05746e80 | 1.47920 | 0.739598 | − | 0.673049i | \(-0.235016\pi\) | ||||
0.739598 | + | 0.673049i | \(0.235016\pi\) | |||||||
\(368\) | −2.50323e80 | −0.375227 | ||||||||
\(369\) | −1.34042e80 | −0.184463 | ||||||||
\(370\) | −1.52543e81 | −1.92770 | ||||||||
\(371\) | −6.77013e78 | −0.00785812 | ||||||||
\(372\) | 1.14585e81 | 1.22187 | ||||||||
\(373\) | 1.52085e80 | 0.149024 | 0.0745121 | − | 0.997220i | \(-0.476260\pi\) | ||||
0.0745121 | + | 0.997220i | \(0.476260\pi\) | |||||||
\(374\) | 2.17361e81 | 1.95761 | ||||||||
\(375\) | −3.35914e80 | −0.278127 | ||||||||
\(376\) | −5.48659e80 | −0.417720 | ||||||||
\(377\) | 1.31691e81 | 0.922153 | ||||||||
\(378\) | −2.49434e81 | −1.60681 | ||||||||
\(379\) | 1.67737e81 | 0.994248 | 0.497124 | − | 0.867680i | \(-0.334389\pi\) | ||||
0.497124 | + | 0.867680i | \(0.334389\pi\) | |||||||
\(380\) | −7.58695e80 | −0.413889 | ||||||||
\(381\) | 9.06622e80 | 0.455291 | ||||||||
\(382\) | 1.32011e80 | 0.0610401 | ||||||||
\(383\) | −1.23141e81 | −0.524372 | −0.262186 | − | 0.965017i | \(-0.584443\pi\) | ||||
−0.262186 | + | 0.965017i | \(0.584443\pi\) | |||||||
\(384\) | −2.26818e81 | −0.889701 | ||||||||
\(385\) | −4.67759e81 | −1.69048 | ||||||||
\(386\) | −1.04292e81 | −0.347337 | ||||||||
\(387\) | 1.06190e81 | 0.325977 | ||||||||
\(388\) | −7.58592e80 | −0.214688 | ||||||||
\(389\) | 1.48659e81 | 0.387954 | 0.193977 | − | 0.981006i | \(-0.437861\pi\) | ||||
0.193977 | + | 0.981006i | \(0.437861\pi\) | |||||||
\(390\) | 1.07216e82 | 2.58061 | ||||||||
\(391\) | −3.88051e81 | −0.861630 | ||||||||
\(392\) | −2.58078e80 | −0.0528738 | ||||||||
\(393\) | 3.34672e81 | 0.632781 | ||||||||
\(394\) | 9.64249e81 | 1.68290 | ||||||||
\(395\) | −1.96170e81 | −0.316100 | ||||||||
\(396\) | 5.61294e81 | 0.835203 | ||||||||
\(397\) | −1.33902e82 | −1.84029 | −0.920146 | − | 0.391576i | \(-0.871930\pi\) | ||||
−0.920146 | + | 0.391576i | \(0.871930\pi\) | |||||||
\(398\) | −2.83090e81 | −0.359424 | ||||||||
\(399\) | −1.36483e81 | −0.160115 | ||||||||
\(400\) | −2.69345e81 | −0.292025 | ||||||||
\(401\) | −5.92318e81 | −0.593618 | −0.296809 | − | 0.954937i | \(-0.595923\pi\) | ||||
−0.296809 | + | 0.954937i | \(0.595923\pi\) | |||||||
\(402\) | −7.79373e81 | −0.722145 | ||||||||
\(403\) | 2.26477e82 | 1.94051 | ||||||||
\(404\) | −2.55395e82 | −2.02395 | ||||||||
\(405\) | −6.62977e81 | −0.486032 | ||||||||
\(406\) | 1.19974e82 | 0.813796 | ||||||||
\(407\) | 2.02865e82 | 1.27345 | ||||||||
\(408\) | −7.84611e81 | −0.455889 | ||||||||
\(409\) | −1.97907e82 | −1.06457 | −0.532287 | − | 0.846564i | \(-0.678667\pi\) | ||||
−0.532287 | + | 0.846564i | \(0.678667\pi\) | |||||||
\(410\) | 1.72441e82 | 0.858912 | ||||||||
\(411\) | 1.25086e82 | 0.577020 | ||||||||
\(412\) | 2.11505e82 | 0.903771 | ||||||||
\(413\) | −2.96118e81 | −0.117230 | ||||||||
\(414\) | −1.70876e82 | −0.626858 | ||||||||
\(415\) | 4.04597e82 | 1.37565 | ||||||||
\(416\) | −6.87641e82 | −2.16732 | ||||||||
\(417\) | −1.65949e82 | −0.484941 | ||||||||
\(418\) | 1.72054e82 | 0.466241 | ||||||||
\(419\) | 5.68402e81 | 0.142861 | 0.0714306 | − | 0.997446i | \(-0.477244\pi\) | ||||
0.0714306 | + | 0.997446i | \(0.477244\pi\) | |||||||
\(420\) | 5.72804e82 | 1.33553 | ||||||||
\(421\) | 6.48979e82 | 1.40393 | 0.701964 | − | 0.712212i | \(-0.252307\pi\) | ||||
0.701964 | + | 0.712212i | \(0.252307\pi\) | |||||||
\(422\) | −1.06147e83 | −2.13090 | ||||||||
\(423\) | 1.50935e82 | 0.281234 | ||||||||
\(424\) | −3.08073e80 | −0.00532880 | ||||||||
\(425\) | −4.17539e82 | −0.670573 | ||||||||
\(426\) | 8.28459e82 | 1.23557 | ||||||||
\(427\) | −1.14916e83 | −1.59185 | ||||||||
\(428\) | 2.64486e82 | 0.340348 | ||||||||
\(429\) | −1.42585e83 | −1.70478 | ||||||||
\(430\) | −1.36610e83 | −1.51784 | ||||||||
\(431\) | 1.31954e83 | 1.36266 | 0.681331 | − | 0.731976i | \(-0.261401\pi\) | ||||
0.681331 | + | 0.731976i | \(0.261401\pi\) | |||||||
\(432\) | 4.57425e82 | 0.439119 | ||||||||
\(433\) | −4.32188e82 | −0.385748 | −0.192874 | − | 0.981224i | \(-0.561781\pi\) | ||||
−0.192874 | + | 0.981224i | \(0.561781\pi\) | |||||||
\(434\) | 2.06326e83 | 1.71249 | ||||||||
\(435\) | 6.95077e82 | 0.536563 | ||||||||
\(436\) | 3.91310e83 | 2.80994 | ||||||||
\(437\) | −3.07164e82 | −0.205213 | ||||||||
\(438\) | −7.27443e82 | −0.452235 | ||||||||
\(439\) | −3.04529e81 | −0.0176196 | −0.00880982 | − | 0.999961i | \(-0.502804\pi\) | ||||
−0.00880982 | + | 0.999961i | \(0.502804\pi\) | |||||||
\(440\) | −2.12853e83 | −1.14636 | ||||||||
\(441\) | 7.09966e81 | 0.0355977 | ||||||||
\(442\) | −5.26095e83 | −2.45619 | ||||||||
\(443\) | 1.28926e83 | 0.560560 | 0.280280 | − | 0.959918i | \(-0.409573\pi\) | ||||
0.280280 | + | 0.959918i | \(0.409573\pi\) | |||||||
\(444\) | −2.48423e83 | −1.00607 | ||||||||
\(445\) | −4.53703e82 | −0.171171 | ||||||||
\(446\) | 6.33869e83 | 2.22819 | ||||||||
\(447\) | 1.70712e83 | 0.559211 | ||||||||
\(448\) | −4.98593e83 | −1.52226 | ||||||||
\(449\) | −4.12515e83 | −1.17403 | −0.587017 | − | 0.809575i | \(-0.699698\pi\) | ||||
−0.587017 | + | 0.809575i | \(0.699698\pi\) | |||||||
\(450\) | −1.83861e83 | −0.487859 | ||||||||
\(451\) | −2.29327e83 | −0.567405 | ||||||||
\(452\) | 1.12289e84 | 2.59104 | ||||||||
\(453\) | −1.78261e83 | −0.383674 | ||||||||
\(454\) | 3.91448e83 | 0.785987 | ||||||||
\(455\) | 1.13215e84 | 2.12102 | ||||||||
\(456\) | −6.21064e82 | −0.108579 | ||||||||
\(457\) | −9.82972e83 | −1.60391 | −0.801957 | − | 0.597382i | \(-0.796208\pi\) | ||||
−0.801957 | + | 0.597382i | \(0.796208\pi\) | |||||||
\(458\) | −9.19525e83 | −1.40056 | ||||||||
\(459\) | 7.09100e83 | 1.00834 | ||||||||
\(460\) | 1.28913e84 | 1.71170 | ||||||||
\(461\) | −1.38498e84 | −1.71737 | −0.858685 | − | 0.512504i | \(-0.828718\pi\) | ||||
−0.858685 | + | 0.512504i | \(0.828718\pi\) | |||||||
\(462\) | −1.29898e84 | −1.50446 | ||||||||
\(463\) | 7.43768e83 | 0.804705 | 0.402352 | − | 0.915485i | \(-0.368193\pi\) | ||||
0.402352 | + | 0.915485i | \(0.368193\pi\) | |||||||
\(464\) | −2.20014e83 | −0.222400 | ||||||||
\(465\) | 1.19537e84 | 1.12910 | ||||||||
\(466\) | 8.73851e83 | 0.771402 | ||||||||
\(467\) | 4.43713e83 | 0.366118 | 0.183059 | − | 0.983102i | \(-0.441400\pi\) | ||||
0.183059 | + | 0.983102i | \(0.441400\pi\) | |||||||
\(468\) | −1.35854e84 | −1.04792 | ||||||||
\(469\) | −8.22984e83 | −0.593536 | ||||||||
\(470\) | −1.94173e84 | −1.30950 | ||||||||
\(471\) | 3.07751e83 | 0.194107 | ||||||||
\(472\) | −1.34748e83 | −0.0794967 | ||||||||
\(473\) | 1.81676e84 | 1.00270 | ||||||||
\(474\) | −5.44772e83 | −0.281317 | ||||||||
\(475\) | −3.30506e83 | −0.159710 | ||||||||
\(476\) | −2.81068e84 | −1.27114 | ||||||||
\(477\) | 8.47502e81 | 0.00358766 | ||||||||
\(478\) | 5.52707e84 | 2.19036 | ||||||||
\(479\) | 3.88526e84 | 1.44162 | 0.720811 | − | 0.693132i | \(-0.243770\pi\) | ||||
0.720811 | + | 0.693132i | \(0.243770\pi\) | |||||||
\(480\) | −3.62944e84 | −1.26107 | ||||||||
\(481\) | −4.91009e84 | −1.59779 | ||||||||
\(482\) | 5.07629e84 | 1.54727 | ||||||||
\(483\) | 2.31905e84 | 0.662179 | ||||||||
\(484\) | 4.30267e84 | 1.15109 | ||||||||
\(485\) | −7.91377e83 | −0.198389 | ||||||||
\(486\) | 5.29449e84 | 1.24389 | ||||||||
\(487\) | −6.87945e84 | −1.51493 | −0.757463 | − | 0.652878i | \(-0.773561\pi\) | ||||
−0.757463 | + | 0.652878i | \(0.773561\pi\) | |||||||
\(488\) | −5.22924e84 | −1.07948 | ||||||||
\(489\) | −6.07143e84 | −1.17506 | ||||||||
\(490\) | −9.13352e83 | −0.165753 | ||||||||
\(491\) | −7.22668e84 | −1.22991 | −0.614953 | − | 0.788564i | \(-0.710825\pi\) | ||||
−0.614953 | + | 0.788564i | \(0.710825\pi\) | |||||||
\(492\) | 2.80827e84 | 0.448269 | ||||||||
\(493\) | −3.41066e84 | −0.510694 | ||||||||
\(494\) | −4.16434e84 | −0.584988 | ||||||||
\(495\) | 5.85552e84 | 0.771795 | ||||||||
\(496\) | −3.78372e84 | −0.468000 | ||||||||
\(497\) | 8.74817e84 | 1.01553 | ||||||||
\(498\) | 1.12358e85 | 1.22428 | ||||||||
\(499\) | 1.29645e85 | 1.32613 | 0.663067 | − | 0.748560i | \(-0.269255\pi\) | ||||
0.663067 | + | 0.748560i | \(0.269255\pi\) | |||||||
\(500\) | −5.47575e84 | −0.525883 | ||||||||
\(501\) | 1.05800e85 | 0.954109 | ||||||||
\(502\) | 1.56229e85 | 1.32311 | ||||||||
\(503\) | −1.26653e85 | −1.00745 | −0.503724 | − | 0.863865i | \(-0.668037\pi\) | ||||
−0.503724 | + | 0.863865i | \(0.668037\pi\) | |||||||
\(504\) | −3.64831e84 | −0.272602 | ||||||||
\(505\) | −2.66433e85 | −1.87029 | ||||||||
\(506\) | −2.92344e85 | −1.92821 | ||||||||
\(507\) | 2.24110e85 | 1.38903 | ||||||||
\(508\) | 1.47789e85 | 0.860864 | ||||||||
\(509\) | 1.58987e85 | 0.870467 | 0.435233 | − | 0.900318i | \(-0.356666\pi\) | ||||
0.435233 | + | 0.900318i | \(0.356666\pi\) | |||||||
\(510\) | −2.77678e85 | −1.42916 | ||||||||
\(511\) | −7.68148e84 | −0.371695 | ||||||||
\(512\) | 1.73068e85 | 0.787433 | ||||||||
\(513\) | 5.61293e84 | 0.240156 | ||||||||
\(514\) | −1.81113e85 | −0.728804 | ||||||||
\(515\) | 2.20646e85 | 0.835157 | ||||||||
\(516\) | −2.22475e85 | −0.792166 | ||||||||
\(517\) | 2.58228e85 | 0.865070 | ||||||||
\(518\) | −4.47322e85 | −1.41004 | ||||||||
\(519\) | −3.31873e85 | −0.984466 | ||||||||
\(520\) | 5.15183e85 | 1.43832 | ||||||||
\(521\) | −3.41495e84 | −0.0897420 | −0.0448710 | − | 0.998993i | \(-0.514288\pi\) | ||||
−0.0448710 | + | 0.998993i | \(0.514288\pi\) | |||||||
\(522\) | −1.50186e85 | −0.371543 | ||||||||
\(523\) | −2.46994e85 | −0.575286 | −0.287643 | − | 0.957738i | \(-0.592872\pi\) | ||||
−0.287643 | + | 0.957738i | \(0.592872\pi\) | |||||||
\(524\) | 5.45549e85 | 1.19646 | ||||||||
\(525\) | 2.49528e85 | 0.515348 | ||||||||
\(526\) | 6.75872e85 | 1.31466 | ||||||||
\(527\) | −5.86553e85 | −1.07466 | ||||||||
\(528\) | 2.38214e85 | 0.411149 | ||||||||
\(529\) | −9.30521e84 | −0.151312 | ||||||||
\(530\) | −1.09029e84 | −0.0167052 | ||||||||
\(531\) | 3.70688e84 | 0.0535218 | ||||||||
\(532\) | −2.22482e85 | −0.302746 | ||||||||
\(533\) | 5.55056e85 | 0.711918 | ||||||||
\(534\) | −1.25995e85 | −0.152336 | ||||||||
\(535\) | 2.75916e85 | 0.314509 | ||||||||
\(536\) | −3.74498e85 | −0.402493 | ||||||||
\(537\) | −8.64303e85 | −0.875943 | ||||||||
\(538\) | 1.93516e85 | 0.184959 | ||||||||
\(539\) | 1.21465e85 | 0.109498 | ||||||||
\(540\) | −2.35569e86 | −2.00315 | ||||||||
\(541\) | −2.40272e86 | −1.92748 | −0.963740 | − | 0.266842i | \(-0.914020\pi\) | ||||
−0.963740 | + | 0.266842i | \(0.914020\pi\) | |||||||
\(542\) | −6.08329e85 | −0.460427 | ||||||||
\(543\) | 6.61815e85 | 0.472652 | ||||||||
\(544\) | 1.78092e86 | 1.20027 | ||||||||
\(545\) | 4.08222e86 | 2.59661 | ||||||||
\(546\) | 3.14402e86 | 1.88763 | ||||||||
\(547\) | −2.76159e86 | −1.56516 | −0.782579 | − | 0.622551i | \(-0.786096\pi\) | ||||
−0.782579 | + | 0.622551i | \(0.786096\pi\) | |||||||
\(548\) | 2.03903e86 | 1.09103 | ||||||||
\(549\) | 1.43855e86 | 0.726769 | ||||||||
\(550\) | −3.14560e86 | −1.50065 | ||||||||
\(551\) | −2.69973e85 | −0.121631 | ||||||||
\(552\) | 1.05528e86 | 0.449042 | ||||||||
\(553\) | −5.75255e85 | −0.231217 | ||||||||
\(554\) | 2.08756e86 | 0.792650 | ||||||||
\(555\) | −2.59159e86 | −0.929690 | ||||||||
\(556\) | −2.70514e86 | −0.916926 | ||||||||
\(557\) | 3.40659e86 | 1.09114 | 0.545571 | − | 0.838065i | \(-0.316313\pi\) | ||||
0.545571 | + | 0.838065i | \(0.316313\pi\) | |||||||
\(558\) | −2.58284e86 | −0.781846 | ||||||||
\(559\) | −4.39724e86 | −1.25808 | ||||||||
\(560\) | −1.89147e86 | −0.511536 | ||||||||
\(561\) | 3.69280e86 | 0.944116 | ||||||||
\(562\) | −1.47575e86 | −0.356712 | ||||||||
\(563\) | −6.77865e86 | −1.54928 | −0.774638 | − | 0.632405i | \(-0.782068\pi\) | ||||
−0.774638 | + | 0.632405i | \(0.782068\pi\) | |||||||
\(564\) | −3.16219e86 | −0.683434 | ||||||||
\(565\) | 1.17141e87 | 2.39433 | ||||||||
\(566\) | 1.10981e87 | 2.14551 | ||||||||
\(567\) | −1.94413e86 | −0.355516 | ||||||||
\(568\) | 3.98084e86 | 0.688656 | ||||||||
\(569\) | −7.28196e86 | −1.19182 | −0.595912 | − | 0.803050i | \(-0.703209\pi\) | ||||
−0.595912 | + | 0.803050i | \(0.703209\pi\) | |||||||
\(570\) | −2.19798e86 | −0.340381 | ||||||||
\(571\) | 1.03258e87 | 1.51316 | 0.756579 | − | 0.653902i | \(-0.226869\pi\) | ||||
0.756579 | + | 0.653902i | \(0.226869\pi\) | |||||||
\(572\) | −2.32428e87 | −3.22339 | ||||||||
\(573\) | 2.24277e85 | 0.0294384 | ||||||||
\(574\) | 5.05670e86 | 0.628265 | ||||||||
\(575\) | 5.61579e86 | 0.660501 | ||||||||
\(576\) | 6.24152e86 | 0.694995 | ||||||||
\(577\) | −3.16007e85 | −0.0333164 | −0.0166582 | − | 0.999861i | \(-0.505303\pi\) | ||||
−0.0166582 | + | 0.999861i | \(0.505303\pi\) | |||||||
\(578\) | −1.95059e86 | −0.194733 | ||||||||
\(579\) | −1.77184e86 | −0.167514 | ||||||||
\(580\) | 1.13305e87 | 1.01453 | ||||||||
\(581\) | 1.18645e87 | 1.00624 | ||||||||
\(582\) | −2.19768e86 | −0.176559 | ||||||||
\(583\) | 1.44996e85 | 0.0110356 | ||||||||
\(584\) | −3.49545e86 | −0.252056 | ||||||||
\(585\) | −1.41726e87 | −0.968363 | ||||||||
\(586\) | −2.17666e87 | −1.40934 | ||||||||
\(587\) | −1.43853e87 | −0.882711 | −0.441356 | − | 0.897332i | \(-0.645502\pi\) | ||||
−0.441356 | + | 0.897332i | \(0.645502\pi\) | |||||||
\(588\) | −1.48743e86 | −0.0865070 | ||||||||
\(589\) | −4.64290e86 | −0.255951 | ||||||||
\(590\) | −4.76880e86 | −0.249213 | ||||||||
\(591\) | 1.63819e87 | 0.811629 | ||||||||
\(592\) | 8.20323e86 | 0.385346 | ||||||||
\(593\) | −2.93573e87 | −1.30765 | −0.653827 | − | 0.756644i | \(-0.726838\pi\) | ||||
−0.653827 | + | 0.756644i | \(0.726838\pi\) | |||||||
\(594\) | 5.34212e87 | 2.25653 | ||||||||
\(595\) | −2.93216e87 | −1.17463 | ||||||||
\(596\) | 2.78278e87 | 1.05736 | ||||||||
\(597\) | −4.80948e86 | −0.173343 | ||||||||
\(598\) | 7.07583e87 | 2.41930 | ||||||||
\(599\) | −1.56895e87 | −0.508938 | −0.254469 | − | 0.967081i | \(-0.581901\pi\) | ||||
−0.254469 | + | 0.967081i | \(0.581901\pi\) | |||||||
\(600\) | 1.13547e87 | 0.349472 | ||||||||
\(601\) | 4.83029e86 | 0.141068 | 0.0705338 | − | 0.997509i | \(-0.477530\pi\) | ||||
0.0705338 | + | 0.997509i | \(0.477530\pi\) | |||||||
\(602\) | −4.00599e87 | −1.11025 | ||||||||
\(603\) | 1.03023e87 | 0.270982 | ||||||||
\(604\) | −2.90583e87 | −0.725450 | ||||||||
\(605\) | 4.48862e87 | 1.06370 | ||||||||
\(606\) | −7.39892e87 | −1.66449 | ||||||||
\(607\) | 4.23483e87 | 0.904465 | 0.452232 | − | 0.891900i | \(-0.350628\pi\) | ||||
0.452232 | + | 0.891900i | \(0.350628\pi\) | |||||||
\(608\) | 1.40970e87 | 0.285867 | ||||||||
\(609\) | 2.03826e87 | 0.392478 | ||||||||
\(610\) | −1.85066e88 | −3.38404 | ||||||||
\(611\) | −6.25009e87 | −1.08540 | ||||||||
\(612\) | 3.51849e87 | 0.580345 | ||||||||
\(613\) | 5.92849e87 | 0.928836 | 0.464418 | − | 0.885616i | \(-0.346263\pi\) | ||||
0.464418 | + | 0.885616i | \(0.346263\pi\) | |||||||
\(614\) | 1.64208e87 | 0.244394 | ||||||||
\(615\) | 2.92964e87 | 0.414236 | ||||||||
\(616\) | −6.24175e87 | −0.838521 | ||||||||
\(617\) | −1.01610e87 | −0.129704 | −0.0648522 | − | 0.997895i | \(-0.520658\pi\) | ||||
−0.0648522 | + | 0.997895i | \(0.520658\pi\) | |||||||
\(618\) | 6.12741e87 | 0.743258 | ||||||||
\(619\) | 1.56773e88 | 1.80724 | 0.903622 | − | 0.428330i | \(-0.140898\pi\) | ||||
0.903622 | + | 0.428330i | \(0.140898\pi\) | |||||||
\(620\) | 1.94857e88 | 2.13490 | ||||||||
\(621\) | −9.53720e87 | −0.993197 | ||||||||
\(622\) | −6.04174e87 | −0.598088 | ||||||||
\(623\) | −1.33045e87 | −0.125206 | ||||||||
\(624\) | −5.76568e87 | −0.515864 | ||||||||
\(625\) | −1.41403e88 | −1.20293 | ||||||||
\(626\) | 1.20429e87 | 0.0974183 | ||||||||
\(627\) | 2.92306e87 | 0.224859 | ||||||||
\(628\) | 5.01666e87 | 0.367017 | ||||||||
\(629\) | 1.27167e88 | 0.884866 | ||||||||
\(630\) | −1.29116e88 | −0.854577 | ||||||||
\(631\) | −5.69991e87 | −0.358875 | −0.179438 | − | 0.983769i | \(-0.557428\pi\) | ||||
−0.179438 | + | 0.983769i | \(0.557428\pi\) | |||||||
\(632\) | −2.61769e87 | −0.156794 | ||||||||
\(633\) | −1.80335e88 | −1.02769 | ||||||||
\(634\) | 4.04804e88 | 2.19499 | ||||||||
\(635\) | 1.54176e88 | 0.795507 | ||||||||
\(636\) | −1.77558e86 | −0.00871848 | ||||||||
\(637\) | −2.93992e87 | −0.137386 | ||||||||
\(638\) | −2.56948e88 | −1.14286 | ||||||||
\(639\) | −1.09512e88 | −0.463644 | ||||||||
\(640\) | −3.85716e88 | −1.55453 | ||||||||
\(641\) | −3.75954e88 | −1.44247 | −0.721236 | − | 0.692690i | \(-0.756426\pi\) | ||||
−0.721236 | + | 0.692690i | \(0.756426\pi\) | |||||||
\(642\) | 7.66229e87 | 0.279902 | ||||||||
\(643\) | 5.08063e88 | 1.76714 | 0.883572 | − | 0.468296i | \(-0.155132\pi\) | ||||
0.883572 | + | 0.468296i | \(0.155132\pi\) | |||||||
\(644\) | 3.78029e88 | 1.25205 | ||||||||
\(645\) | −2.32090e88 | −0.732025 | ||||||||
\(646\) | 1.07852e88 | 0.323970 | ||||||||
\(647\) | −1.87849e88 | −0.537433 | −0.268716 | − | 0.963219i | \(-0.586599\pi\) | ||||
−0.268716 | + | 0.963219i | \(0.586599\pi\) | |||||||
\(648\) | −8.84674e87 | −0.241085 | ||||||||
\(649\) | 6.34196e87 | 0.164632 | ||||||||
\(650\) | 7.61353e88 | 1.88285 | ||||||||
\(651\) | 3.50533e88 | 0.825900 | ||||||||
\(652\) | −9.89705e88 | −2.22181 | ||||||||
\(653\) | 6.60139e87 | 0.141211 | 0.0706057 | − | 0.997504i | \(-0.477507\pi\) | ||||
0.0706057 | + | 0.997504i | \(0.477507\pi\) | |||||||
\(654\) | 1.13365e89 | 2.31088 | ||||||||
\(655\) | 5.69127e88 | 1.10563 | ||||||||
\(656\) | −9.27325e87 | −0.171696 | ||||||||
\(657\) | 9.61588e87 | 0.169699 | ||||||||
\(658\) | −5.69399e88 | −0.957857 | ||||||||
\(659\) | −4.59134e88 | −0.736289 | −0.368145 | − | 0.929768i | \(-0.620007\pi\) | ||||
−0.368145 | + | 0.929768i | \(0.620007\pi\) | |||||||
\(660\) | −1.22678e89 | −1.87556 | ||||||||
\(661\) | −1.18619e89 | −1.72906 | −0.864529 | − | 0.502583i | \(-0.832383\pi\) | ||||
−0.864529 | + | 0.502583i | \(0.832383\pi\) | |||||||
\(662\) | −5.64965e87 | −0.0785226 | ||||||||
\(663\) | −8.93795e88 | −1.18457 | ||||||||
\(664\) | 5.39893e88 | 0.682359 | ||||||||
\(665\) | −2.32097e88 | −0.279761 | ||||||||
\(666\) | 5.59969e88 | 0.643763 | ||||||||
\(667\) | 4.58724e88 | 0.503023 | ||||||||
\(668\) | 1.72465e89 | 1.80403 | ||||||||
\(669\) | 1.07690e89 | 1.07461 | ||||||||
\(670\) | −1.32537e89 | −1.26177 | ||||||||
\(671\) | 2.46116e89 | 2.23553 | ||||||||
\(672\) | −1.06431e89 | −0.922432 | ||||||||
\(673\) | 4.18096e88 | 0.345781 | 0.172890 | − | 0.984941i | \(-0.444689\pi\) | ||||
0.172890 | + | 0.984941i | \(0.444689\pi\) | |||||||
\(674\) | −2.84330e89 | −2.24407 | ||||||||
\(675\) | −1.02619e89 | −0.772967 | ||||||||
\(676\) | 3.65323e89 | 2.62637 | ||||||||
\(677\) | −1.54143e89 | −1.05774 | −0.528872 | − | 0.848702i | \(-0.677385\pi\) | ||||
−0.528872 | + | 0.848702i | \(0.677385\pi\) | |||||||
\(678\) | 3.25306e89 | 2.13087 | ||||||||
\(679\) | −2.32065e88 | −0.145115 | ||||||||
\(680\) | −1.33427e89 | −0.796552 | ||||||||
\(681\) | 6.65041e88 | 0.379066 | ||||||||
\(682\) | −4.41889e89 | −2.40495 | ||||||||
\(683\) | 1.37735e89 | 0.715800 | 0.357900 | − | 0.933760i | \(-0.383493\pi\) | ||||
0.357900 | + | 0.933760i | \(0.383493\pi\) | |||||||
\(684\) | 2.78508e88 | 0.138220 | ||||||||
\(685\) | 2.12715e89 | 1.00820 | ||||||||
\(686\) | −3.56023e89 | −1.61164 | ||||||||
\(687\) | −1.56220e89 | −0.675461 | ||||||||
\(688\) | 7.34641e88 | 0.303416 | ||||||||
\(689\) | −3.50944e87 | −0.0138463 | ||||||||
\(690\) | 3.73469e89 | 1.40769 | ||||||||
\(691\) | −1.04508e89 | −0.376349 | −0.188175 | − | 0.982136i | \(-0.560257\pi\) | ||||
−0.188175 | + | 0.982136i | \(0.560257\pi\) | |||||||
\(692\) | −5.40988e89 | −1.86143 | ||||||||
\(693\) | 1.71709e89 | 0.564542 | ||||||||
\(694\) | 6.26836e89 | 1.96938 | ||||||||
\(695\) | −2.82205e89 | −0.847313 | ||||||||
\(696\) | 9.27507e88 | 0.266150 | ||||||||
\(697\) | −1.43754e89 | −0.394264 | ||||||||
\(698\) | −2.74599e89 | −0.719867 | ||||||||
\(699\) | 1.48461e89 | 0.372032 | ||||||||
\(700\) | 4.06756e89 | 0.974419 | ||||||||
\(701\) | 1.99798e89 | 0.457588 | 0.228794 | − | 0.973475i | \(-0.426522\pi\) | ||||
0.228794 | + | 0.973475i | \(0.426522\pi\) | |||||||
\(702\) | −1.29299e90 | −2.83124 | ||||||||
\(703\) | 1.00660e89 | 0.210747 | ||||||||
\(704\) | 1.06784e90 | 2.13780 | ||||||||
\(705\) | −3.29885e89 | −0.631548 | ||||||||
\(706\) | 1.40829e90 | 2.57837 | ||||||||
\(707\) | −7.81294e89 | −1.36805 | ||||||||
\(708\) | −7.76619e88 | −0.130065 | ||||||||
\(709\) | −5.01550e89 | −0.803449 | −0.401724 | − | 0.915761i | \(-0.631589\pi\) | ||||
−0.401724 | + | 0.915761i | \(0.631589\pi\) | |||||||
\(710\) | 1.40884e90 | 2.15886 | ||||||||
\(711\) | 7.20119e88 | 0.105563 | ||||||||
\(712\) | −6.05419e88 | −0.0849056 | ||||||||
\(713\) | 7.88897e89 | 1.05852 | ||||||||
\(714\) | −8.14270e89 | −1.04538 | ||||||||
\(715\) | −2.42473e90 | −2.97867 | ||||||||
\(716\) | −1.40890e90 | −1.65623 | ||||||||
\(717\) | 9.39007e89 | 1.05637 | ||||||||
\(718\) | −1.62756e90 | −1.75233 | ||||||||
\(719\) | 8.38497e89 | 0.864055 | 0.432028 | − | 0.901860i | \(-0.357798\pi\) | ||||
0.432028 | + | 0.901860i | \(0.357798\pi\) | |||||||
\(720\) | 2.36779e89 | 0.233544 | ||||||||
\(721\) | 6.47028e89 | 0.610889 | ||||||||
\(722\) | −1.63510e90 | −1.47783 | ||||||||
\(723\) | 8.62424e89 | 0.746216 | ||||||||
\(724\) | 1.07883e90 | 0.893690 | ||||||||
\(725\) | 4.93583e89 | 0.391483 | ||||||||
\(726\) | 1.24651e90 | 0.946653 | ||||||||
\(727\) | 1.03681e90 | 0.753988 | 0.376994 | − | 0.926216i | \(-0.376958\pi\) | ||||
0.376994 | + | 0.926216i | \(0.376958\pi\) | |||||||
\(728\) | 1.51074e90 | 1.05208 | ||||||||
\(729\) | 1.45566e90 | 0.970827 | ||||||||
\(730\) | −1.23706e90 | −0.790168 | ||||||||
\(731\) | 1.13884e90 | 0.696732 | ||||||||
\(732\) | −3.01387e90 | −1.76614 | ||||||||
\(733\) | −3.18443e90 | −1.78754 | −0.893771 | − | 0.448523i | \(-0.851950\pi\) | ||||
−0.893771 | + | 0.448523i | \(0.851950\pi\) | |||||||
\(734\) | 4.27738e90 | 2.30013 | ||||||||
\(735\) | −1.55172e89 | −0.0799394 | ||||||||
\(736\) | −2.39529e90 | −1.18224 | ||||||||
\(737\) | 1.76259e90 | 0.833536 | ||||||||
\(738\) | −6.33011e89 | −0.286837 | ||||||||
\(739\) | −3.22969e89 | −0.140236 | −0.0701181 | − | 0.997539i | \(-0.522338\pi\) | ||||
−0.0701181 | + | 0.997539i | \(0.522338\pi\) | |||||||
\(740\) | −4.22457e90 | −1.75786 | ||||||||
\(741\) | −7.07490e89 | −0.282128 | ||||||||
\(742\) | −3.19719e88 | −0.0122193 | ||||||||
\(743\) | −2.59061e90 | −0.948974 | −0.474487 | − | 0.880262i | \(-0.657366\pi\) | ||||
−0.474487 | + | 0.880262i | \(0.657366\pi\) | |||||||
\(744\) | 1.59509e90 | 0.560065 | ||||||||
\(745\) | 2.90304e90 | 0.977081 | ||||||||
\(746\) | 7.18218e89 | 0.231731 | ||||||||
\(747\) | −1.48523e90 | −0.459404 | ||||||||
\(748\) | 6.01964e90 | 1.78513 | ||||||||
\(749\) | 8.09105e89 | 0.230053 | ||||||||
\(750\) | −1.58635e90 | −0.432484 | ||||||||
\(751\) | −5.64788e90 | −1.47648 | −0.738240 | − | 0.674538i | \(-0.764343\pi\) | ||||
−0.738240 | + | 0.674538i | \(0.764343\pi\) | |||||||
\(752\) | 1.04419e90 | 0.261770 | ||||||||
\(753\) | 2.65422e90 | 0.638110 | ||||||||
\(754\) | 6.21909e90 | 1.43394 | ||||||||
\(755\) | −3.03142e90 | −0.670374 | ||||||||
\(756\) | −6.90788e90 | −1.46524 | ||||||||
\(757\) | −2.35445e90 | −0.479037 | −0.239519 | − | 0.970892i | \(-0.576990\pi\) | ||||
−0.239519 | + | 0.970892i | \(0.576990\pi\) | |||||||
\(758\) | 7.92139e90 | 1.54604 | ||||||||
\(759\) | −4.96671e90 | −0.929936 | ||||||||
\(760\) | −1.05615e90 | −0.189714 | ||||||||
\(761\) | 5.15918e89 | 0.0889128 | 0.0444564 | − | 0.999011i | \(-0.485844\pi\) | ||||
0.0444564 | + | 0.999011i | \(0.485844\pi\) | |||||||
\(762\) | 4.28152e90 | 0.707972 | ||||||||
\(763\) | 1.19708e91 | 1.89933 | ||||||||
\(764\) | 3.65595e89 | 0.0556621 | ||||||||
\(765\) | 3.67055e90 | 0.536285 | ||||||||
\(766\) | −5.81531e90 | −0.815392 | ||||||||
\(767\) | −1.53499e90 | −0.206563 | ||||||||
\(768\) | −1.48962e90 | −0.192397 | ||||||||
\(769\) | 3.98793e90 | 0.494388 | 0.247194 | − | 0.968966i | \(-0.420492\pi\) | ||||
0.247194 | + | 0.968966i | \(0.420492\pi\) | |||||||
\(770\) | −2.20899e91 | −2.62867 | ||||||||
\(771\) | −3.07697e90 | −0.351488 | ||||||||
\(772\) | −2.88829e90 | −0.316735 | ||||||||
\(773\) | −5.31617e90 | −0.559687 | −0.279843 | − | 0.960046i | \(-0.590282\pi\) | ||||
−0.279843 | + | 0.960046i | \(0.590282\pi\) | |||||||
\(774\) | 5.01481e90 | 0.506890 | ||||||||
\(775\) | 8.48846e90 | 0.823807 | ||||||||
\(776\) | −1.05601e90 | −0.0984065 | ||||||||
\(777\) | −7.59966e90 | −0.680037 | ||||||||
\(778\) | 7.02043e90 | 0.603263 | ||||||||
\(779\) | −1.13789e90 | −0.0939014 | ||||||||
\(780\) | 2.96926e91 | 2.35325 | ||||||||
\(781\) | −1.87360e91 | −1.42616 | ||||||||
\(782\) | −1.83257e91 | −1.33982 | ||||||||
\(783\) | −8.38245e90 | −0.588675 | ||||||||
\(784\) | 4.91168e89 | 0.0331340 | ||||||||
\(785\) | 5.23348e90 | 0.339153 | ||||||||
\(786\) | 1.58048e91 | 0.983966 | ||||||||
\(787\) | 2.94356e91 | 1.76063 | 0.880315 | − | 0.474389i | \(-0.157331\pi\) | ||||
0.880315 | + | 0.474389i | \(0.157331\pi\) | |||||||
\(788\) | 2.67041e91 | 1.53463 | ||||||||
\(789\) | 1.14826e91 | 0.634035 | ||||||||
\(790\) | −9.26414e90 | −0.491532 | ||||||||
\(791\) | 3.43509e91 | 1.75137 | ||||||||
\(792\) | 7.81359e90 | 0.382831 | ||||||||
\(793\) | −5.95693e91 | −2.80490 | ||||||||
\(794\) | −6.32352e91 | −2.86163 | ||||||||
\(795\) | −1.85232e89 | −0.00805658 | ||||||||
\(796\) | −7.83995e90 | −0.327757 | ||||||||
\(797\) | −4.20154e90 | −0.168838 | −0.0844192 | − | 0.996430i | \(-0.526903\pi\) | ||||
−0.0844192 | + | 0.996430i | \(0.526903\pi\) | |||||||
\(798\) | −6.44541e90 | −0.248977 | ||||||||
\(799\) | 1.61871e91 | 0.601098 | ||||||||
\(800\) | −2.57731e91 | −0.920094 | ||||||||
\(801\) | 1.66549e90 | 0.0571634 | ||||||||
\(802\) | −2.79722e91 | −0.923069 | ||||||||
\(803\) | 1.64514e91 | 0.521992 | ||||||||
\(804\) | −2.15841e91 | −0.658520 | ||||||||
\(805\) | 3.94367e91 | 1.15699 | ||||||||
\(806\) | 1.06954e92 | 3.01746 | ||||||||
\(807\) | 3.28769e90 | 0.0892020 | ||||||||
\(808\) | −3.55527e91 | −0.927714 | ||||||||
\(809\) | 1.39812e91 | 0.350886 | 0.175443 | − | 0.984490i | \(-0.443864\pi\) | ||||
0.175443 | + | 0.984490i | \(0.443864\pi\) | |||||||
\(810\) | −3.13091e91 | −0.755774 | ||||||||
\(811\) | −3.59866e90 | −0.0835571 | −0.0417786 | − | 0.999127i | \(-0.513302\pi\) | ||||
−0.0417786 | + | 0.999127i | \(0.513302\pi\) | |||||||
\(812\) | 3.32258e91 | 0.742096 | ||||||||
\(813\) | −1.03351e91 | −0.222055 | ||||||||
\(814\) | 9.58030e91 | 1.98021 | ||||||||
\(815\) | −1.03248e92 | −2.05313 | ||||||||
\(816\) | 1.49325e91 | 0.285689 | ||||||||
\(817\) | 9.01457e90 | 0.165940 | ||||||||
\(818\) | −9.34613e91 | −1.65540 | ||||||||
\(819\) | −4.15600e91 | −0.708325 | ||||||||
\(820\) | 4.77562e91 | 0.783237 | ||||||||
\(821\) | −2.87760e91 | −0.454173 | −0.227087 | − | 0.973875i | \(-0.572920\pi\) | ||||
−0.227087 | + | 0.973875i | \(0.572920\pi\) | |||||||
\(822\) | 5.90717e91 | 0.897258 | ||||||||
\(823\) | 1.30669e92 | 1.91020 | 0.955098 | − | 0.296290i | \(-0.0957496\pi\) | ||||
0.955098 | + | 0.296290i | \(0.0957496\pi\) | |||||||
\(824\) | 2.94429e91 | 0.414260 | ||||||||
\(825\) | −5.34414e91 | −0.723733 | ||||||||
\(826\) | −1.39841e91 | −0.182291 | ||||||||
\(827\) | −6.67625e91 | −0.837740 | −0.418870 | − | 0.908046i | \(-0.637574\pi\) | ||||
−0.418870 | + | 0.908046i | \(0.637574\pi\) | |||||||
\(828\) | −4.73227e91 | −0.571628 | ||||||||
\(829\) | −1.02129e92 | −1.18763 | −0.593814 | − | 0.804603i | \(-0.702378\pi\) | ||||
−0.593814 | + | 0.804603i | \(0.702378\pi\) | |||||||
\(830\) | 1.91071e92 | 2.13912 | ||||||||
\(831\) | 3.54661e91 | 0.382280 | ||||||||
\(832\) | −2.58457e92 | −2.68227 | ||||||||
\(833\) | 7.61409e90 | 0.0760853 | ||||||||
\(834\) | −7.83693e91 | −0.754077 | ||||||||
\(835\) | 1.79919e92 | 1.66707 | ||||||||
\(836\) | 4.76489e91 | 0.425163 | ||||||||
\(837\) | −1.44158e92 | −1.23876 | ||||||||
\(838\) | 2.68428e91 | 0.222147 | ||||||||
\(839\) | −5.22788e91 | −0.416700 | −0.208350 | − | 0.978054i | \(-0.566809\pi\) | ||||
−0.208350 | + | 0.978054i | \(0.566809\pi\) | |||||||
\(840\) | 7.97382e91 | 0.612165 | ||||||||
\(841\) | −9.49120e91 | −0.701855 | ||||||||
\(842\) | 3.06480e92 | 2.18309 | ||||||||
\(843\) | −2.50718e91 | −0.172035 | ||||||||
\(844\) | −2.93965e92 | −1.94316 | ||||||||
\(845\) | 3.81112e92 | 2.42698 | ||||||||
\(846\) | 7.12788e91 | 0.437314 | ||||||||
\(847\) | 1.31626e92 | 0.778060 | ||||||||
\(848\) | 5.86318e89 | 0.00333936 | ||||||||
\(849\) | 1.88548e92 | 1.03474 | ||||||||
\(850\) | −1.97183e92 | −1.04273 | ||||||||
\(851\) | −1.71035e92 | −0.871575 | ||||||||
\(852\) | 2.29436e92 | 1.12671 | ||||||||
\(853\) | 2.86871e91 | 0.135766 | 0.0678832 | − | 0.997693i | \(-0.478375\pi\) | ||||
0.0678832 | + | 0.997693i | \(0.478375\pi\) | |||||||
\(854\) | −5.42691e92 | −2.47531 | ||||||||
\(855\) | 2.90545e91 | 0.127726 | ||||||||
\(856\) | 3.68182e91 | 0.156005 | ||||||||
\(857\) | 1.42668e92 | 0.582679 | 0.291340 | − | 0.956620i | \(-0.405899\pi\) | ||||
0.291340 | + | 0.956620i | \(0.405899\pi\) | |||||||
\(858\) | −6.73355e92 | −2.65091 | ||||||||
\(859\) | −2.36785e92 | −0.898608 | −0.449304 | − | 0.893379i | \(-0.648328\pi\) | ||||
−0.449304 | + | 0.893379i | \(0.648328\pi\) | |||||||
\(860\) | −3.78331e92 | −1.38411 | ||||||||
\(861\) | 8.59095e91 | 0.303000 | ||||||||
\(862\) | 6.23152e92 | 2.11892 | ||||||||
\(863\) | 3.48284e92 | 1.14181 | 0.570905 | − | 0.821016i | \(-0.306592\pi\) | ||||
0.570905 | + | 0.821016i | \(0.306592\pi\) | |||||||
\(864\) | 4.37701e92 | 1.38355 | ||||||||
\(865\) | −5.64369e92 | −1.72011 | ||||||||
\(866\) | −2.04100e92 | −0.599833 | ||||||||
\(867\) | −3.31391e91 | −0.0939159 | ||||||||
\(868\) | 5.71405e92 | 1.56161 | ||||||||
\(869\) | 1.23202e92 | 0.324711 | ||||||||
\(870\) | 3.28250e92 | 0.834349 | ||||||||
\(871\) | −4.26612e92 | −1.04583 | ||||||||
\(872\) | 5.44729e92 | 1.28799 | ||||||||
\(873\) | 2.90506e91 | 0.0662530 | ||||||||
\(874\) | −1.45058e92 | −0.319104 | ||||||||
\(875\) | −1.67512e92 | −0.355462 | ||||||||
\(876\) | −2.01460e92 | −0.412391 | ||||||||
\(877\) | 7.38143e92 | 1.45765 | 0.728825 | − | 0.684700i | \(-0.240067\pi\) | ||||
0.728825 | + | 0.684700i | \(0.240067\pi\) | |||||||
\(878\) | −1.43814e91 | −0.0273983 | ||||||||
\(879\) | −3.69798e92 | −0.679696 | ||||||||
\(880\) | 4.05096e92 | 0.718380 | ||||||||
\(881\) | −4.66751e92 | −0.798627 | −0.399313 | − | 0.916814i | \(-0.630751\pi\) | ||||
−0.399313 | + | 0.916814i | \(0.630751\pi\) | |||||||
\(882\) | 3.35281e91 | 0.0553540 | ||||||||
\(883\) | −5.66714e92 | −0.902821 | −0.451410 | − | 0.892316i | \(-0.649079\pi\) | ||||
−0.451410 | + | 0.892316i | \(0.649079\pi\) | |||||||
\(884\) | −1.45698e93 | −2.23979 | ||||||||
\(885\) | −8.10183e91 | −0.120190 | ||||||||
\(886\) | 6.08851e92 | 0.871664 | ||||||||
\(887\) | 4.96787e91 | 0.0686398 | 0.0343199 | − | 0.999411i | \(-0.489073\pi\) | ||||
0.0343199 | + | 0.999411i | \(0.489073\pi\) | |||||||
\(888\) | −3.45821e92 | −0.461151 | ||||||||
\(889\) | 4.52110e92 | 0.581887 | ||||||||
\(890\) | −2.14261e92 | −0.266169 | ||||||||
\(891\) | 4.16375e92 | 0.499271 | ||||||||
\(892\) | 1.75545e93 | 2.03187 | ||||||||
\(893\) | 1.28130e92 | 0.143163 | ||||||||
\(894\) | 8.06184e92 | 0.869566 | ||||||||
\(895\) | −1.46979e93 | −1.53049 | ||||||||
\(896\) | −1.13109e93 | −1.13709 | ||||||||
\(897\) | 1.20213e93 | 1.16678 | ||||||||
\(898\) | −1.94810e93 | −1.82561 | ||||||||
\(899\) | 6.93378e92 | 0.627393 | ||||||||
\(900\) | −5.09188e92 | −0.444876 | ||||||||
\(901\) | 9.08910e90 | 0.00766814 | ||||||||
\(902\) | −1.08299e93 | −0.882308 | ||||||||
\(903\) | −6.80588e92 | −0.535452 | ||||||||
\(904\) | 1.56313e93 | 1.18765 | ||||||||
\(905\) | 1.12545e93 | 0.825842 | ||||||||
\(906\) | −8.41835e92 | −0.596608 | ||||||||
\(907\) | 1.79893e93 | 1.23136 | 0.615680 | − | 0.787997i | \(-0.288882\pi\) | ||||
0.615680 | + | 0.787997i | \(0.288882\pi\) | |||||||
\(908\) | 1.08409e93 | 0.716737 | ||||||||
\(909\) | 9.78044e92 | 0.624592 | ||||||||
\(910\) | 5.34658e93 | 3.29816 | ||||||||
\(911\) | −8.99801e92 | −0.536188 | −0.268094 | − | 0.963393i | \(-0.586394\pi\) | ||||
−0.268094 | + | 0.963393i | \(0.586394\pi\) | |||||||
\(912\) | 1.18199e92 | 0.0680421 | ||||||||
\(913\) | −2.54102e93 | −1.41312 | ||||||||
\(914\) | −4.64208e93 | −2.49406 | ||||||||
\(915\) | −3.14412e93 | −1.63206 | ||||||||
\(916\) | −2.54655e93 | −1.27716 | ||||||||
\(917\) | 1.66892e93 | 0.808728 | ||||||||
\(918\) | 3.34872e93 | 1.56796 | ||||||||
\(919\) | −1.85074e93 | −0.837348 | −0.418674 | − | 0.908137i | \(-0.637505\pi\) | ||||
−0.418674 | + | 0.908137i | \(0.637505\pi\) | |||||||
\(920\) | 1.79456e93 | 0.784587 | ||||||||
\(921\) | 2.78977e92 | 0.117867 | ||||||||
\(922\) | −6.54056e93 | −2.67049 | ||||||||
\(923\) | 4.53481e93 | 1.78939 | ||||||||
\(924\) | −3.59743e93 | −1.37191 | ||||||||
\(925\) | −1.84033e93 | −0.678313 | ||||||||
\(926\) | 3.51244e93 | 1.25131 | ||||||||
\(927\) | −8.09966e92 | −0.278904 | ||||||||
\(928\) | −2.10527e93 | −0.700724 | ||||||||
\(929\) | 3.53579e93 | 1.13760 | 0.568802 | − | 0.822475i | \(-0.307407\pi\) | ||||
0.568802 | + | 0.822475i | \(0.307407\pi\) | |||||||
\(930\) | 5.64511e93 | 1.75574 | ||||||||
\(931\) | 6.02699e91 | 0.0181211 | ||||||||
\(932\) | 2.42006e93 | 0.703438 | ||||||||
\(933\) | −1.02645e93 | −0.288446 | ||||||||
\(934\) | 2.09543e93 | 0.569308 | ||||||||
\(935\) | 6.27980e93 | 1.64961 | ||||||||
\(936\) | −1.89118e93 | −0.480334 | ||||||||
\(937\) | 1.39400e93 | 0.342346 | 0.171173 | − | 0.985241i | \(-0.445244\pi\) | ||||
0.171173 | + | 0.985241i | \(0.445244\pi\) | |||||||
\(938\) | −3.88654e93 | −0.922940 | ||||||||
\(939\) | 2.04600e92 | 0.0469829 | ||||||||
\(940\) | −5.37748e93 | −1.19413 | ||||||||
\(941\) | −4.43425e93 | −0.952241 | −0.476120 | − | 0.879380i | \(-0.657957\pi\) | ||||
−0.476120 | + | 0.879380i | \(0.657957\pi\) | |||||||
\(942\) | 1.45335e93 | 0.301834 | ||||||||
\(943\) | 1.93345e93 | 0.388342 | ||||||||
\(944\) | 2.56449e92 | 0.0498176 | ||||||||
\(945\) | −7.20642e93 | −1.35400 | ||||||||
\(946\) | 8.57964e93 | 1.55919 | ||||||||
\(947\) | −7.29795e93 | −1.28285 | −0.641426 | − | 0.767185i | \(-0.721657\pi\) | ||||
−0.641426 | + | 0.767185i | \(0.721657\pi\) | |||||||
\(948\) | −1.50870e93 | −0.256532 | ||||||||
\(949\) | −3.98186e93 | −0.654939 | ||||||||
\(950\) | −1.56081e93 | −0.248346 | ||||||||
\(951\) | 6.87731e93 | 1.05860 | ||||||||
\(952\) | −3.91266e93 | −0.582650 | ||||||||
\(953\) | −5.59234e93 | −0.805689 | −0.402844 | − | 0.915268i | \(-0.631978\pi\) | ||||
−0.402844 | + | 0.915268i | \(0.631978\pi\) | |||||||
\(954\) | 4.00232e91 | 0.00557877 | ||||||||
\(955\) | 3.81396e92 | 0.0514363 | ||||||||
\(956\) | 1.53068e94 | 1.99738 | ||||||||
\(957\) | −4.36535e93 | −0.551179 | ||||||||
\(958\) | 1.83481e94 | 2.24170 | ||||||||
\(959\) | 6.23772e93 | 0.737462 | ||||||||
\(960\) | −1.36416e94 | −1.56071 | ||||||||
\(961\) | 2.89240e93 | 0.320237 | ||||||||
\(962\) | −2.31879e94 | −2.48454 | ||||||||
\(963\) | −1.01286e93 | −0.105032 | ||||||||
\(964\) | 1.40584e94 | 1.41094 | ||||||||
\(965\) | −3.01311e93 | −0.292688 | ||||||||
\(966\) | 1.09517e94 | 1.02968 | ||||||||
\(967\) | −1.35469e94 | −1.23284 | −0.616419 | − | 0.787418i | \(-0.711417\pi\) | ||||
−0.616419 | + | 0.787418i | \(0.711417\pi\) | |||||||
\(968\) | 5.98960e93 | 0.527623 | ||||||||
\(969\) | 1.83233e93 | 0.156244 | ||||||||
\(970\) | −3.73727e93 | −0.308493 | ||||||||
\(971\) | 1.40182e94 | 1.12018 | 0.560088 | − | 0.828433i | \(-0.310767\pi\) | ||||
0.560088 | + | 0.828433i | \(0.310767\pi\) | |||||||
\(972\) | 1.46627e94 | 1.13430 | ||||||||
\(973\) | −8.27547e93 | −0.619781 | ||||||||
\(974\) | −3.24882e94 | −2.35569 | ||||||||
\(975\) | 1.29348e94 | 0.908060 | ||||||||
\(976\) | 9.95217e93 | 0.676470 | ||||||||
\(977\) | 2.67935e94 | 1.76340 | 0.881700 | − | 0.471810i | \(-0.156399\pi\) | ||||
0.881700 | + | 0.471810i | \(0.156399\pi\) | |||||||
\(978\) | −2.86723e94 | −1.82721 | ||||||||
\(979\) | 2.84943e93 | 0.175834 | ||||||||
\(980\) | −2.52946e93 | −0.151149 | ||||||||
\(981\) | −1.49854e94 | −0.867149 | ||||||||
\(982\) | −3.41280e94 | −1.91249 | ||||||||
\(983\) | 1.93233e94 | 1.04868 | 0.524342 | − | 0.851508i | \(-0.324311\pi\) | ||||
0.524342 | + | 0.851508i | \(0.324311\pi\) | |||||||
\(984\) | 3.90930e93 | 0.205472 | ||||||||
\(985\) | 2.78582e94 | 1.41812 | ||||||||
\(986\) | −1.61068e94 | −0.794122 | ||||||||
\(987\) | −9.67365e93 | −0.461956 | ||||||||
\(988\) | −1.15328e94 | −0.533448 | ||||||||
\(989\) | −1.53171e94 | −0.686267 | ||||||||
\(990\) | 2.76527e94 | 1.20013 | ||||||||
\(991\) | −2.43225e94 | −1.02256 | −0.511279 | − | 0.859415i | \(-0.670828\pi\) | ||||
−0.511279 | + | 0.859415i | \(0.670828\pi\) | |||||||
\(992\) | −3.62057e94 | −1.47455 | ||||||||
\(993\) | −9.59833e92 | −0.0378699 | ||||||||
\(994\) | 4.13132e94 | 1.57913 | ||||||||
\(995\) | −8.17878e93 | −0.302874 | ||||||||
\(996\) | 3.11167e94 | 1.11641 | ||||||||
\(997\) | 3.29728e94 | 1.14619 | 0.573097 | − | 0.819487i | \(-0.305742\pi\) | ||||
0.573097 | + | 0.819487i | \(0.305742\pi\) | |||||||
\(998\) | 6.12246e94 | 2.06212 | ||||||||
\(999\) | 3.12540e94 | 1.01998 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1.64.a.a.1.5 | ✓ | 5 | |
3.2 | odd | 2 | 9.64.a.c.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.64.a.a.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
9.64.a.c.1.1 | 5 | 3.2 | odd | 2 |