Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,84,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, 84, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 84);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 84 \) |
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: | \(43.6272128266\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} + \cdots + 22\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{82}\cdot 3^{30}\cdot 5^{8}\cdot 7^{4}\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.58823e11\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.76211e12 | −1.20972 | −0.604862 | − | 0.796330i | \(-0.706772\pi\) | ||||
−0.604862 | + | 0.796330i | \(0.706772\pi\) | |||||||
\(3\) | −6.68720e19 | −1.05855 | −0.529276 | − | 0.848450i | \(-0.677536\pi\) | ||||
−0.529276 | + | 0.848450i | \(0.677536\pi\) | |||||||
\(4\) | 4.48205e24 | 0.463434 | ||||||||
\(5\) | 1.95538e28 | 0.192299 | 0.0961494 | − | 0.995367i | \(-0.469347\pi\) | ||||
0.0961494 | + | 0.995367i | \(0.469347\pi\) | |||||||
\(6\) | 2.51580e32 | 1.28056 | ||||||||
\(7\) | 1.66208e35 | 1.40956 | 0.704778 | − | 0.709428i | \(-0.251047\pi\) | ||||
0.704778 | + | 0.709428i | \(0.251047\pi\) | |||||||
\(8\) | 1.95229e37 | 0.649098 | ||||||||
\(9\) | 4.81025e38 | 0.120532 | ||||||||
\(10\) | −7.35637e40 | −0.232629 | ||||||||
\(11\) | 1.57715e43 | 0.955163 | 0.477582 | − | 0.878587i | \(-0.341514\pi\) | ||||
0.477582 | + | 0.878587i | \(0.341514\pi\) | |||||||
\(12\) | −2.99724e44 | −0.490569 | ||||||||
\(13\) | 1.54355e46 | 0.911740 | 0.455870 | − | 0.890046i | \(-0.349328\pi\) | ||||
0.455870 | + | 0.890046i | \(0.349328\pi\) | |||||||
\(14\) | −6.25291e47 | −1.70518 | ||||||||
\(15\) | −1.30760e48 | −0.203558 | ||||||||
\(16\) | −1.16795e50 | −1.24866 | ||||||||
\(17\) | −2.86818e50 | −0.247728 | −0.123864 | − | 0.992299i | \(-0.539529\pi\) | ||||
−0.123864 | + | 0.992299i | \(0.539529\pi\) | |||||||
\(18\) | −1.80967e51 | −0.145811 | ||||||||
\(19\) | 1.03565e53 | 0.884988 | 0.442494 | − | 0.896771i | \(-0.354094\pi\) | ||||
0.442494 | + | 0.896771i | \(0.354094\pi\) | |||||||
\(20\) | 8.76414e52 | 0.0891178 | ||||||||
\(21\) | −1.11146e55 | −1.49209 | ||||||||
\(22\) | −5.93342e55 | −1.15548 | ||||||||
\(23\) | −2.08646e56 | −0.642252 | −0.321126 | − | 0.947036i | \(-0.604061\pi\) | ||||
−0.321126 | + | 0.947036i | \(0.604061\pi\) | |||||||
\(24\) | −1.30554e57 | −0.687104 | ||||||||
\(25\) | −9.95741e57 | −0.963021 | ||||||||
\(26\) | −5.80700e58 | −1.10295 | ||||||||
\(27\) | 2.34708e59 | 0.930962 | ||||||||
\(28\) | 7.44952e59 | 0.653236 | ||||||||
\(29\) | 6.67410e60 | 1.36419 | 0.682096 | − | 0.731262i | \(-0.261069\pi\) | ||||
0.682096 | + | 0.731262i | \(0.261069\pi\) | |||||||
\(30\) | 4.91935e60 | 0.246250 | ||||||||
\(31\) | −1.54744e62 | −1.98657 | −0.993284 | − | 0.115701i | \(-0.963089\pi\) | ||||
−0.993284 | + | 0.115701i | \(0.963089\pi\) | |||||||
\(32\) | 2.50582e62 | 0.861441 | ||||||||
\(33\) | −1.05467e63 | −1.01109 | ||||||||
\(34\) | 1.07904e63 | 0.299683 | ||||||||
\(35\) | 3.25000e63 | 0.271056 | ||||||||
\(36\) | 2.15598e63 | 0.0558587 | ||||||||
\(37\) | 2.28009e65 | 1.89488 | 0.947438 | − | 0.319941i | \(-0.103663\pi\) | ||||
0.947438 | + | 0.319941i | \(0.103663\pi\) | |||||||
\(38\) | −3.89622e65 | −1.07059 | ||||||||
\(39\) | −1.03220e66 | −0.965125 | ||||||||
\(40\) | 3.81748e65 | 0.124821 | ||||||||
\(41\) | 3.48018e66 | 0.408387 | 0.204193 | − | 0.978931i | \(-0.434543\pi\) | ||||
0.204193 | + | 0.978931i | \(0.434543\pi\) | |||||||
\(42\) | 4.18145e67 | 1.80502 | ||||||||
\(43\) | 4.05016e67 | 0.658462 | 0.329231 | − | 0.944249i | \(-0.393210\pi\) | ||||
0.329231 | + | 0.944249i | \(0.393210\pi\) | |||||||
\(44\) | 7.06889e67 | 0.442655 | ||||||||
\(45\) | 9.40588e66 | 0.0231782 | ||||||||
\(46\) | 7.84950e68 | 0.776949 | ||||||||
\(47\) | 2.43131e69 | 0.985777 | 0.492889 | − | 0.870092i | \(-0.335941\pi\) | ||||
0.492889 | + | 0.870092i | \(0.335941\pi\) | |||||||
\(48\) | 7.81032e69 | 1.32177 | ||||||||
\(49\) | 1.37211e70 | 0.986849 | ||||||||
\(50\) | 3.74608e70 | 1.16499 | ||||||||
\(51\) | 1.91801e70 | 0.262233 | ||||||||
\(52\) | 6.91827e70 | 0.422531 | ||||||||
\(53\) | −3.24750e71 | −0.899706 | −0.449853 | − | 0.893103i | \(-0.648524\pi\) | ||||
−0.449853 | + | 0.893103i | \(0.648524\pi\) | |||||||
\(54\) | −8.82998e71 | −1.12621 | ||||||||
\(55\) | 3.08394e71 | 0.183677 | ||||||||
\(56\) | 3.24486e72 | 0.914940 | ||||||||
\(57\) | −6.92558e72 | −0.936806 | ||||||||
\(58\) | −2.51087e73 | −1.65030 | ||||||||
\(59\) | −3.03695e73 | −0.981929 | −0.490964 | − | 0.871180i | \(-0.663355\pi\) | ||||
−0.490964 | + | 0.871180i | \(0.663355\pi\) | |||||||
\(60\) | −5.86075e72 | −0.0943358 | ||||||||
\(61\) | −6.07893e73 | −0.492764 | −0.246382 | − | 0.969173i | \(-0.579242\pi\) | ||||
−0.246382 | + | 0.969173i | \(0.579242\pi\) | |||||||
\(62\) | 5.82164e74 | 2.40320 | ||||||||
\(63\) | 7.99500e73 | 0.169897 | ||||||||
\(64\) | 1.86857e74 | 0.206557 | ||||||||
\(65\) | 3.01823e74 | 0.175327 | ||||||||
\(66\) | 3.96780e75 | 1.22314 | ||||||||
\(67\) | −5.36442e75 | −0.885969 | −0.442984 | − | 0.896529i | \(-0.646080\pi\) | ||||
−0.442984 | + | 0.896529i | \(0.646080\pi\) | |||||||
\(68\) | −1.28553e75 | −0.114806 | ||||||||
\(69\) | 1.39526e76 | 0.679858 | ||||||||
\(70\) | −1.22268e76 | −0.327903 | ||||||||
\(71\) | −8.80285e76 | −1.31039 | −0.655197 | − | 0.755458i | \(-0.727414\pi\) | ||||
−0.655197 | + | 0.755458i | \(0.727414\pi\) | |||||||
\(72\) | 9.39100e75 | 0.0782372 | ||||||||
\(73\) | −1.58272e76 | −0.0743887 | −0.0371943 | − | 0.999308i | \(-0.511842\pi\) | ||||
−0.0371943 | + | 0.999308i | \(0.511842\pi\) | |||||||
\(74\) | −8.57795e77 | −2.29228 | ||||||||
\(75\) | 6.65872e77 | 1.01941 | ||||||||
\(76\) | 4.64183e77 | 0.410133 | ||||||||
\(77\) | 2.62135e78 | 1.34636 | ||||||||
\(78\) | 3.88325e78 | 1.16753 | ||||||||
\(79\) | 9.61180e77 | 0.170326 | 0.0851629 | − | 0.996367i | \(-0.472859\pi\) | ||||
0.0851629 | + | 0.996367i | \(0.472859\pi\) | |||||||
\(80\) | −2.28379e78 | −0.240116 | ||||||||
\(81\) | −1.76151e79 | −1.10600 | ||||||||
\(82\) | −1.30928e79 | −0.494035 | ||||||||
\(83\) | 6.23836e79 | 1.42341 | 0.711704 | − | 0.702479i | \(-0.247924\pi\) | ||||
0.711704 | + | 0.702479i | \(0.247924\pi\) | |||||||
\(84\) | −4.98164e79 | −0.691484 | ||||||||
\(85\) | −5.60839e78 | −0.0476379 | ||||||||
\(86\) | −1.52371e80 | −0.796558 | ||||||||
\(87\) | −4.46310e80 | −1.44407 | ||||||||
\(88\) | 3.07906e80 | 0.619994 | ||||||||
\(89\) | 3.80332e80 | 0.479157 | 0.239578 | − | 0.970877i | \(-0.422991\pi\) | ||||
0.239578 | + | 0.970877i | \(0.422991\pi\) | |||||||
\(90\) | −3.53859e79 | −0.0280393 | ||||||||
\(91\) | 2.56550e81 | 1.28515 | ||||||||
\(92\) | −9.35165e80 | −0.297641 | ||||||||
\(93\) | 1.03480e82 | 2.10289 | ||||||||
\(94\) | −9.14684e81 | −1.19252 | ||||||||
\(95\) | 2.02509e81 | 0.170182 | ||||||||
\(96\) | −1.67569e82 | −0.911880 | ||||||||
\(97\) | −8.03314e81 | −0.284353 | −0.142177 | − | 0.989841i | \(-0.545410\pi\) | ||||
−0.142177 | + | 0.989841i | \(0.545410\pi\) | |||||||
\(98\) | −5.16202e82 | −1.19382 | ||||||||
\(99\) | 7.58650e81 | 0.115128 | ||||||||
\(100\) | −4.46296e82 | −0.446296 | ||||||||
\(101\) | 2.79563e83 | 1.84988 | 0.924939 | − | 0.380116i | \(-0.124116\pi\) | ||||
0.924939 | + | 0.380116i | \(0.124116\pi\) | |||||||
\(102\) | −7.21575e82 | −0.317230 | ||||||||
\(103\) | −2.74147e83 | −0.803969 | −0.401984 | − | 0.915646i | \(-0.631679\pi\) | ||||
−0.401984 | + | 0.915646i | \(0.631679\pi\) | |||||||
\(104\) | 3.01346e83 | 0.591809 | ||||||||
\(105\) | −2.17334e83 | −0.286927 | ||||||||
\(106\) | 1.22174e84 | 1.08840 | ||||||||
\(107\) | 4.90933e82 | 0.0296207 | 0.0148103 | − | 0.999890i | \(-0.495286\pi\) | ||||
0.0148103 | + | 0.999890i | \(0.495286\pi\) | |||||||
\(108\) | 1.05198e84 | 0.431439 | ||||||||
\(109\) | 2.89032e84 | 0.808624 | 0.404312 | − | 0.914621i | \(-0.367511\pi\) | ||||
0.404312 | + | 0.914621i | \(0.367511\pi\) | |||||||
\(110\) | −1.16021e84 | −0.222198 | ||||||||
\(111\) | −1.52474e85 | −2.00582 | ||||||||
\(112\) | −1.94122e85 | −1.76006 | ||||||||
\(113\) | 3.23999e84 | 0.203136 | 0.101568 | − | 0.994829i | \(-0.467614\pi\) | ||||
0.101568 | + | 0.994829i | \(0.467614\pi\) | |||||||
\(114\) | 2.60548e85 | 1.13328 | ||||||||
\(115\) | −4.07984e84 | −0.123504 | ||||||||
\(116\) | 2.99137e85 | 0.632213 | ||||||||
\(117\) | 7.42485e84 | 0.109894 | ||||||||
\(118\) | 1.14254e86 | 1.18786 | ||||||||
\(119\) | −4.76713e85 | −0.349187 | ||||||||
\(120\) | −2.55282e85 | −0.132129 | ||||||||
\(121\) | −2.39007e85 | −0.0876634 | ||||||||
\(122\) | 2.28696e86 | 0.596109 | ||||||||
\(123\) | −2.32727e86 | −0.432299 | ||||||||
\(124\) | −6.93571e86 | −0.920642 | ||||||||
\(125\) | −3.96887e86 | −0.377487 | ||||||||
\(126\) | −3.00781e86 | −0.205529 | ||||||||
\(127\) | 2.95189e87 | 1.45293 | 0.726467 | − | 0.687201i | \(-0.241161\pi\) | ||||
0.726467 | + | 0.687201i | \(0.241161\pi\) | |||||||
\(128\) | −3.12645e87 | −1.11132 | ||||||||
\(129\) | −2.70842e87 | −0.697017 | ||||||||
\(130\) | −1.13549e87 | −0.212097 | ||||||||
\(131\) | 8.76943e87 | 1.19183 | 0.595913 | − | 0.803049i | \(-0.296790\pi\) | ||||
0.595913 | + | 0.803049i | \(0.296790\pi\) | |||||||
\(132\) | −4.72711e87 | −0.468573 | ||||||||
\(133\) | 1.72133e88 | 1.24744 | ||||||||
\(134\) | 2.01815e88 | 1.07178 | ||||||||
\(135\) | 4.58945e87 | 0.179023 | ||||||||
\(136\) | −5.59951e87 | −0.160800 | ||||||||
\(137\) | −3.81478e88 | −0.808287 | −0.404144 | − | 0.914696i | \(-0.632430\pi\) | ||||
−0.404144 | + | 0.914696i | \(0.632430\pi\) | |||||||
\(138\) | −5.24912e88 | −0.822440 | ||||||||
\(139\) | −1.12530e89 | −1.30663 | −0.653315 | − | 0.757086i | \(-0.726622\pi\) | ||||
−0.653315 | + | 0.757086i | \(0.726622\pi\) | |||||||
\(140\) | 1.45667e88 | 0.125617 | ||||||||
\(141\) | −1.62586e89 | −1.04350 | ||||||||
\(142\) | 3.31173e89 | 1.58522 | ||||||||
\(143\) | 2.43441e89 | 0.870861 | ||||||||
\(144\) | −5.61813e88 | −0.150504 | ||||||||
\(145\) | 1.30504e89 | 0.262333 | ||||||||
\(146\) | 5.95438e88 | 0.0899898 | ||||||||
\(147\) | −9.17556e89 | −1.04463 | ||||||||
\(148\) | 1.02195e90 | 0.878149 | ||||||||
\(149\) | 1.73231e90 | 1.12563 | 0.562815 | − | 0.826583i | \(-0.309718\pi\) | ||||
0.562815 | + | 0.826583i | \(0.309718\pi\) | |||||||
\(150\) | −2.50508e90 | −1.23320 | ||||||||
\(151\) | 8.38919e89 | 0.313456 | 0.156728 | − | 0.987642i | \(-0.449905\pi\) | ||||
0.156728 | + | 0.987642i | \(0.449905\pi\) | |||||||
\(152\) | 2.02189e90 | 0.574444 | ||||||||
\(153\) | −1.37966e89 | −0.0298593 | ||||||||
\(154\) | −9.86181e90 | −1.62872 | ||||||||
\(155\) | −3.02584e90 | −0.382015 | ||||||||
\(156\) | −4.62638e90 | −0.447271 | ||||||||
\(157\) | 6.87875e90 | 0.510122 | 0.255061 | − | 0.966925i | \(-0.417904\pi\) | ||||
0.255061 | + | 0.966925i | \(0.417904\pi\) | |||||||
\(158\) | −3.61606e90 | −0.206047 | ||||||||
\(159\) | 2.17167e91 | 0.952386 | ||||||||
\(160\) | 4.89983e90 | 0.165654 | ||||||||
\(161\) | −3.46786e91 | −0.905291 | ||||||||
\(162\) | 6.62699e91 | 1.33796 | ||||||||
\(163\) | 9.29918e91 | 1.45432 | 0.727158 | − | 0.686470i | \(-0.240841\pi\) | ||||
0.727158 | + | 0.686470i | \(0.240841\pi\) | |||||||
\(164\) | 1.55984e91 | 0.189260 | ||||||||
\(165\) | −2.06229e91 | −0.194431 | ||||||||
\(166\) | −2.34694e92 | −1.72193 | ||||||||
\(167\) | −4.16853e91 | −0.238369 | −0.119184 | − | 0.992872i | \(-0.538028\pi\) | ||||
−0.119184 | + | 0.992872i | \(0.538028\pi\) | |||||||
\(168\) | −2.16990e92 | −0.968511 | ||||||||
\(169\) | −4.83603e91 | −0.168729 | ||||||||
\(170\) | 2.10994e91 | 0.0576287 | ||||||||
\(171\) | 4.98172e91 | 0.106670 | ||||||||
\(172\) | 1.81530e92 | 0.305154 | ||||||||
\(173\) | 4.60190e92 | 0.608169 | 0.304084 | − | 0.952645i | \(-0.401650\pi\) | ||||
0.304084 | + | 0.952645i | \(0.401650\pi\) | |||||||
\(174\) | 1.67907e93 | 1.74693 | ||||||||
\(175\) | −1.65500e93 | −1.35743 | ||||||||
\(176\) | −1.84204e93 | −1.19268 | ||||||||
\(177\) | 2.03087e93 | 1.03942 | ||||||||
\(178\) | −1.43085e93 | −0.579647 | ||||||||
\(179\) | 4.63689e93 | 1.48876 | 0.744382 | − | 0.667754i | \(-0.232744\pi\) | ||||
0.744382 | + | 0.667754i | \(0.232744\pi\) | |||||||
\(180\) | 4.21577e91 | 0.0107416 | ||||||||
\(181\) | 3.06896e93 | 0.621341 | 0.310671 | − | 0.950518i | \(-0.399446\pi\) | ||||
0.310671 | + | 0.950518i | \(0.399446\pi\) | |||||||
\(182\) | −9.65168e93 | −1.55468 | ||||||||
\(183\) | 4.06510e93 | 0.521617 | ||||||||
\(184\) | −4.07338e93 | −0.416885 | ||||||||
\(185\) | 4.45845e93 | 0.364382 | ||||||||
\(186\) | −3.89304e94 | −2.54391 | ||||||||
\(187\) | −4.52355e93 | −0.236621 | ||||||||
\(188\) | 1.08973e94 | 0.456842 | ||||||||
\(189\) | 3.90103e94 | 1.31224 | ||||||||
\(190\) | −7.61860e93 | −0.205874 | ||||||||
\(191\) | 8.40728e94 | 1.82714 | 0.913568 | − | 0.406686i | \(-0.133316\pi\) | ||||
0.913568 | + | 0.406686i | \(0.133316\pi\) | |||||||
\(192\) | −1.24955e94 | −0.218651 | ||||||||
\(193\) | −9.56818e93 | −0.134959 | −0.0674794 | − | 0.997721i | \(-0.521496\pi\) | ||||
−0.0674794 | + | 0.997721i | \(0.521496\pi\) | |||||||
\(194\) | 3.02215e94 | 0.343989 | ||||||||
\(195\) | −2.01835e94 | −0.185592 | ||||||||
\(196\) | 6.14986e94 | 0.457339 | ||||||||
\(197\) | −2.10092e95 | −1.26491 | −0.632456 | − | 0.774596i | \(-0.717953\pi\) | ||||
−0.632456 | + | 0.774596i | \(0.717953\pi\) | |||||||
\(198\) | −2.85412e94 | −0.139273 | ||||||||
\(199\) | −1.13664e95 | −0.450010 | −0.225005 | − | 0.974358i | \(-0.572240\pi\) | ||||
−0.225005 | + | 0.974358i | \(0.572240\pi\) | |||||||
\(200\) | −1.94397e95 | −0.625095 | ||||||||
\(201\) | 3.58729e95 | 0.937844 | ||||||||
\(202\) | −1.05175e96 | −2.23784 | ||||||||
\(203\) | 1.10929e96 | 1.92291 | ||||||||
\(204\) | 8.59661e94 | 0.121528 | ||||||||
\(205\) | 6.80509e94 | 0.0785323 | ||||||||
\(206\) | 1.03137e96 | 0.972581 | ||||||||
\(207\) | −1.00364e95 | −0.0774121 | ||||||||
\(208\) | −1.80279e96 | −1.13846 | ||||||||
\(209\) | 1.63338e96 | 0.845308 | ||||||||
\(210\) | 8.17633e95 | 0.347103 | ||||||||
\(211\) | −1.71697e96 | −0.598468 | −0.299234 | − | 0.954180i | \(-0.596731\pi\) | ||||
−0.299234 | + | 0.954180i | \(0.596731\pi\) | |||||||
\(212\) | −1.45555e96 | −0.416954 | ||||||||
\(213\) | 5.88664e96 | 1.38712 | ||||||||
\(214\) | −1.84694e95 | −0.0358329 | ||||||||
\(215\) | 7.91961e95 | 0.126622 | ||||||||
\(216\) | 4.58219e96 | 0.604285 | ||||||||
\(217\) | −2.57196e97 | −2.80018 | ||||||||
\(218\) | −1.08737e97 | −0.978213 | ||||||||
\(219\) | 1.05840e96 | 0.0787443 | ||||||||
\(220\) | 1.38224e96 | 0.0851220 | ||||||||
\(221\) | −4.42717e96 | −0.225864 | ||||||||
\(222\) | 5.73625e97 | 2.42649 | ||||||||
\(223\) | −1.09963e97 | −0.386008 | −0.193004 | − | 0.981198i | \(-0.561823\pi\) | ||||
−0.193004 | + | 0.981198i | \(0.561823\pi\) | |||||||
\(224\) | 4.16486e97 | 1.21425 | ||||||||
\(225\) | −4.78976e96 | −0.116075 | ||||||||
\(226\) | −1.21892e97 | −0.245739 | ||||||||
\(227\) | 7.81227e97 | 1.31131 | 0.655653 | − | 0.755062i | \(-0.272393\pi\) | ||||
0.655653 | + | 0.755062i | \(0.272393\pi\) | |||||||
\(228\) | −3.10408e97 | −0.434147 | ||||||||
\(229\) | −1.50776e98 | −1.75858 | −0.879288 | − | 0.476291i | \(-0.841981\pi\) | ||||
−0.879288 | + | 0.476291i | \(0.841981\pi\) | |||||||
\(230\) | 1.53488e97 | 0.149406 | ||||||||
\(231\) | −1.75295e98 | −1.42519 | ||||||||
\(232\) | 1.30298e98 | 0.885494 | ||||||||
\(233\) | 9.20166e96 | 0.0523113 | 0.0261557 | − | 0.999658i | \(-0.491673\pi\) | ||||
0.0261557 | + | 0.999658i | \(0.491673\pi\) | |||||||
\(234\) | −2.79331e97 | −0.132942 | ||||||||
\(235\) | 4.75414e97 | 0.189564 | ||||||||
\(236\) | −1.36118e98 | −0.455059 | ||||||||
\(237\) | −6.42760e97 | −0.180299 | ||||||||
\(238\) | 1.79345e98 | 0.422420 | ||||||||
\(239\) | 2.98788e98 | 0.591357 | 0.295679 | − | 0.955287i | \(-0.404454\pi\) | ||||
0.295679 | + | 0.955287i | \(0.404454\pi\) | |||||||
\(240\) | 1.52722e98 | 0.254176 | ||||||||
\(241\) | −9.04678e97 | −0.126703 | −0.0633515 | − | 0.997991i | \(-0.520179\pi\) | ||||
−0.0633515 | + | 0.997991i | \(0.520179\pi\) | |||||||
\(242\) | 8.99172e97 | 0.106049 | ||||||||
\(243\) | 2.41274e98 | 0.239801 | ||||||||
\(244\) | −2.72461e98 | −0.228364 | ||||||||
\(245\) | 2.68300e98 | 0.189770 | ||||||||
\(246\) | 8.75542e98 | 0.522962 | ||||||||
\(247\) | 1.59857e99 | 0.806880 | ||||||||
\(248\) | −3.02105e99 | −1.28948 | ||||||||
\(249\) | −4.17172e99 | −1.50675 | ||||||||
\(250\) | 1.49313e99 | 0.456655 | ||||||||
\(251\) | 2.57941e99 | 0.668437 | 0.334219 | − | 0.942496i | \(-0.391528\pi\) | ||||
0.334219 | + | 0.942496i | \(0.391528\pi\) | |||||||
\(252\) | 3.58340e98 | 0.0787360 | ||||||||
\(253\) | −3.29067e99 | −0.613456 | ||||||||
\(254\) | −1.11053e100 | −1.75765 | ||||||||
\(255\) | 3.75044e98 | 0.0504272 | ||||||||
\(256\) | 9.95489e99 | 1.13783 | ||||||||
\(257\) | −4.68226e99 | −0.455230 | −0.227615 | − | 0.973751i | \(-0.573093\pi\) | ||||
−0.227615 | + | 0.973751i | \(0.573093\pi\) | |||||||
\(258\) | 1.01894e100 | 0.843198 | ||||||||
\(259\) | 3.78969e100 | 2.67093 | ||||||||
\(260\) | 1.35279e99 | 0.0812523 | ||||||||
\(261\) | 3.21041e99 | 0.164429 | ||||||||
\(262\) | −3.29915e100 | −1.44178 | ||||||||
\(263\) | 1.03753e100 | 0.387114 | 0.193557 | − | 0.981089i | \(-0.437998\pi\) | ||||
0.193557 | + | 0.981089i | \(0.437998\pi\) | |||||||
\(264\) | −2.05903e100 | −0.656296 | ||||||||
\(265\) | −6.35011e99 | −0.173012 | ||||||||
\(266\) | −6.47582e100 | −1.50906 | ||||||||
\(267\) | −2.54335e100 | −0.507212 | ||||||||
\(268\) | −2.40436e100 | −0.410588 | ||||||||
\(269\) | 9.23197e100 | 1.35075 | 0.675375 | − | 0.737475i | \(-0.263982\pi\) | ||||
0.675375 | + | 0.737475i | \(0.263982\pi\) | |||||||
\(270\) | −1.72660e100 | −0.216569 | ||||||||
\(271\) | 1.13749e101 | 1.22383 | 0.611917 | − | 0.790922i | \(-0.290399\pi\) | ||||
0.611917 | + | 0.790922i | \(0.290399\pi\) | |||||||
\(272\) | 3.34989e100 | 0.309329 | ||||||||
\(273\) | −1.71560e101 | −1.36040 | ||||||||
\(274\) | 1.43516e101 | 0.977805 | ||||||||
\(275\) | −1.57044e101 | −0.919842 | ||||||||
\(276\) | 6.25363e100 | 0.315069 | ||||||||
\(277\) | −9.66258e100 | −0.418970 | −0.209485 | − | 0.977812i | \(-0.567179\pi\) | ||||
−0.209485 | + | 0.977812i | \(0.567179\pi\) | |||||||
\(278\) | 4.23349e101 | 1.58066 | ||||||||
\(279\) | −7.44357e100 | −0.239446 | ||||||||
\(280\) | 6.34494e100 | 0.175942 | ||||||||
\(281\) | −1.19538e101 | −0.285885 | −0.142943 | − | 0.989731i | \(-0.545656\pi\) | ||||
−0.142943 | + | 0.989731i | \(0.545656\pi\) | |||||||
\(282\) | 6.11668e101 | 1.26234 | ||||||||
\(283\) | −5.03803e101 | −0.897684 | −0.448842 | − | 0.893611i | \(-0.648163\pi\) | ||||
−0.448842 | + | 0.893611i | \(0.648163\pi\) | |||||||
\(284\) | −3.94548e101 | −0.607280 | ||||||||
\(285\) | −1.35422e101 | −0.180147 | ||||||||
\(286\) | −9.15853e101 | −1.05350 | ||||||||
\(287\) | 5.78433e101 | 0.575644 | ||||||||
\(288\) | 1.20536e101 | 0.103831 | ||||||||
\(289\) | −1.25822e102 | −0.938631 | ||||||||
\(290\) | −4.90971e101 | −0.317350 | ||||||||
\(291\) | 5.37192e101 | 0.301003 | ||||||||
\(292\) | −7.09386e100 | −0.0344742 | ||||||||
\(293\) | 9.31769e101 | 0.392918 | 0.196459 | − | 0.980512i | \(-0.437056\pi\) | ||||
0.196459 | + | 0.980512i | \(0.437056\pi\) | |||||||
\(294\) | 3.45194e102 | 1.26372 | ||||||||
\(295\) | −5.93841e101 | −0.188824 | ||||||||
\(296\) | 4.45140e102 | 1.22996 | ||||||||
\(297\) | 3.70171e102 | 0.889221 | ||||||||
\(298\) | −6.51714e102 | −1.36170 | ||||||||
\(299\) | −3.22056e102 | −0.585567 | ||||||||
\(300\) | 2.98447e102 | 0.472428 | ||||||||
\(301\) | 6.73167e102 | 0.928140 | ||||||||
\(302\) | −3.15611e102 | −0.379196 | ||||||||
\(303\) | −1.86949e103 | −1.95819 | ||||||||
\(304\) | −1.20959e103 | −1.10505 | ||||||||
\(305\) | −1.18866e102 | −0.0947580 | ||||||||
\(306\) | 5.19045e101 | 0.0361215 | ||||||||
\(307\) | 2.81336e102 | 0.170995 | 0.0854973 | − | 0.996338i | \(-0.472752\pi\) | ||||
0.0854973 | + | 0.996338i | \(0.472752\pi\) | |||||||
\(308\) | 1.17490e103 | 0.623947 | ||||||||
\(309\) | 1.83328e103 | 0.851043 | ||||||||
\(310\) | 1.13835e103 | 0.462133 | ||||||||
\(311\) | 7.00646e102 | 0.248853 | 0.124426 | − | 0.992229i | \(-0.460291\pi\) | ||||
0.124426 | + | 0.992229i | \(0.460291\pi\) | |||||||
\(312\) | −2.01516e103 | −0.626460 | ||||||||
\(313\) | 3.43919e103 | 0.936194 | 0.468097 | − | 0.883677i | \(-0.344940\pi\) | ||||
0.468097 | + | 0.883677i | \(0.344940\pi\) | |||||||
\(314\) | −2.58786e103 | −0.617107 | ||||||||
\(315\) | 1.56333e102 | 0.0326710 | ||||||||
\(316\) | 4.30806e102 | 0.0789347 | ||||||||
\(317\) | −8.71226e102 | −0.140014 | −0.0700070 | − | 0.997547i | \(-0.522302\pi\) | ||||
−0.0700070 | + | 0.997547i | \(0.522302\pi\) | |||||||
\(318\) | −8.17005e103 | −1.15212 | ||||||||
\(319\) | 1.05261e104 | 1.30303 | ||||||||
\(320\) | 3.65377e102 | 0.0397207 | ||||||||
\(321\) | −3.28296e102 | −0.0313550 | ||||||||
\(322\) | 1.30465e104 | 1.09515 | ||||||||
\(323\) | −2.97042e103 | −0.219237 | ||||||||
\(324\) | −7.89518e103 | −0.512559 | ||||||||
\(325\) | −1.53697e104 | −0.878025 | ||||||||
\(326\) | −3.49845e104 | −1.75932 | ||||||||
\(327\) | −1.93282e104 | −0.855971 | ||||||||
\(328\) | 6.79432e103 | 0.265083 | ||||||||
\(329\) | 4.04102e104 | 1.38951 | ||||||||
\(330\) | 7.75857e103 | 0.235209 | ||||||||
\(331\) | 1.74091e104 | 0.465495 | 0.232747 | − | 0.972537i | \(-0.425228\pi\) | ||||
0.232747 | + | 0.972537i | \(0.425228\pi\) | |||||||
\(332\) | 2.79607e104 | 0.659655 | ||||||||
\(333\) | 1.09678e104 | 0.228394 | ||||||||
\(334\) | 1.56825e104 | 0.288360 | ||||||||
\(335\) | −1.04895e104 | −0.170371 | ||||||||
\(336\) | 1.29813e105 | 1.86312 | ||||||||
\(337\) | −1.17971e105 | −1.49670 | −0.748350 | − | 0.663304i | \(-0.769154\pi\) | ||||
−0.748350 | + | 0.663304i | \(0.769154\pi\) | |||||||
\(338\) | 1.81937e104 | 0.204116 | ||||||||
\(339\) | −2.16664e104 | −0.215030 | ||||||||
\(340\) | −2.51371e103 | −0.0220770 | ||||||||
\(341\) | −2.44055e105 | −1.89750 | ||||||||
\(342\) | −1.87418e104 | −0.129041 | ||||||||
\(343\) | −3.03907e103 | −0.0185368 | ||||||||
\(344\) | 7.90708e104 | 0.427406 | ||||||||
\(345\) | 2.72827e104 | 0.130736 | ||||||||
\(346\) | −1.73129e105 | −0.735717 | ||||||||
\(347\) | 9.62166e104 | 0.362725 | 0.181362 | − | 0.983416i | \(-0.441949\pi\) | ||||
0.181362 | + | 0.983416i | \(0.441949\pi\) | |||||||
\(348\) | −2.00039e105 | −0.669230 | ||||||||
\(349\) | −8.73629e104 | −0.259461 | −0.129730 | − | 0.991549i | \(-0.541411\pi\) | ||||
−0.129730 | + | 0.991549i | \(0.541411\pi\) | |||||||
\(350\) | 6.22628e105 | 1.64212 | ||||||||
\(351\) | 3.62284e105 | 0.848796 | ||||||||
\(352\) | 3.95206e105 | 0.822816 | ||||||||
\(353\) | 1.21464e105 | 0.224801 | 0.112401 | − | 0.993663i | \(-0.464146\pi\) | ||||
0.112401 | + | 0.993663i | \(0.464146\pi\) | |||||||
\(354\) | −7.64036e105 | −1.25741 | ||||||||
\(355\) | −1.72129e105 | −0.251987 | ||||||||
\(356\) | 1.70467e105 | 0.222057 | ||||||||
\(357\) | 3.18787e105 | 0.369633 | ||||||||
\(358\) | −1.74445e106 | −1.80099 | ||||||||
\(359\) | 1.68929e106 | 1.55340 | 0.776702 | − | 0.629869i | \(-0.216891\pi\) | ||||
0.776702 | + | 0.629869i | \(0.216891\pi\) | |||||||
\(360\) | 1.83630e104 | 0.0150449 | ||||||||
\(361\) | −2.96893e105 | −0.216796 | ||||||||
\(362\) | −1.15458e106 | −0.751652 | ||||||||
\(363\) | 1.59829e105 | 0.0927963 | ||||||||
\(364\) | 1.14987e106 | 0.595581 | ||||||||
\(365\) | −3.09483e104 | −0.0143049 | ||||||||
\(366\) | −1.52934e106 | −0.631013 | ||||||||
\(367\) | −3.04040e106 | −1.12018 | −0.560092 | − | 0.828430i | \(-0.689234\pi\) | ||||
−0.560092 | + | 0.828430i | \(0.689234\pi\) | |||||||
\(368\) | 2.43689e106 | 0.801957 | ||||||||
\(369\) | 1.67405e105 | 0.0492238 | ||||||||
\(370\) | −1.67732e106 | −0.440802 | ||||||||
\(371\) | −5.39759e106 | −1.26819 | ||||||||
\(372\) | 4.63805e106 | 0.974548 | ||||||||
\(373\) | 7.73158e106 | 1.45329 | 0.726644 | − | 0.687014i | \(-0.241079\pi\) | ||||
0.726644 | + | 0.687014i | \(0.241079\pi\) | |||||||
\(374\) | 1.70181e106 | 0.286246 | ||||||||
\(375\) | 2.65407e106 | 0.399589 | ||||||||
\(376\) | 4.74662e106 | 0.639866 | ||||||||
\(377\) | 1.03018e107 | 1.24379 | ||||||||
\(378\) | −1.46761e107 | −1.58745 | ||||||||
\(379\) | 1.33873e107 | 1.29767 | 0.648836 | − | 0.760929i | \(-0.275256\pi\) | ||||
0.648836 | + | 0.760929i | \(0.275256\pi\) | |||||||
\(380\) | 9.07656e105 | 0.0788682 | ||||||||
\(381\) | −1.97399e107 | −1.53801 | ||||||||
\(382\) | −3.16291e107 | −2.21033 | ||||||||
\(383\) | −2.43713e107 | −1.52802 | −0.764010 | − | 0.645204i | \(-0.776772\pi\) | ||||
−0.764010 | + | 0.645204i | \(0.776772\pi\) | |||||||
\(384\) | 2.09072e107 | 1.17639 | ||||||||
\(385\) | 5.12575e106 | 0.258903 | ||||||||
\(386\) | 3.59965e106 | 0.163263 | ||||||||
\(387\) | 1.94823e106 | 0.0793660 | ||||||||
\(388\) | −3.60049e106 | −0.131779 | ||||||||
\(389\) | 2.96841e107 | 0.976371 | 0.488186 | − | 0.872740i | \(-0.337659\pi\) | ||||
0.488186 | + | 0.872740i | \(0.337659\pi\) | |||||||
\(390\) | 7.59325e106 | 0.224516 | ||||||||
\(391\) | 5.98435e106 | 0.159104 | ||||||||
\(392\) | 2.67875e107 | 0.640561 | ||||||||
\(393\) | −5.86429e107 | −1.26161 | ||||||||
\(394\) | 7.90388e107 | 1.53020 | ||||||||
\(395\) | 1.87948e106 | 0.0327535 | ||||||||
\(396\) | 3.40031e106 | 0.0533542 | ||||||||
\(397\) | −7.61528e107 | −1.07617 | −0.538084 | − | 0.842891i | \(-0.680852\pi\) | ||||
−0.538084 | + | 0.842891i | \(0.680852\pi\) | |||||||
\(398\) | 4.27618e107 | 0.544388 | ||||||||
\(399\) | −1.15108e108 | −1.32048 | ||||||||
\(400\) | 1.16298e108 | 1.20249 | ||||||||
\(401\) | 1.83663e108 | 1.71210 | 0.856051 | − | 0.516891i | \(-0.172911\pi\) | ||||
0.856051 | + | 0.516891i | \(0.172911\pi\) | |||||||
\(402\) | −1.34958e108 | −1.13453 | ||||||||
\(403\) | −2.38855e108 | −1.81123 | ||||||||
\(404\) | 1.25302e108 | 0.857295 | ||||||||
\(405\) | −3.44443e107 | −0.212683 | ||||||||
\(406\) | −4.17326e108 | −2.32619 | ||||||||
\(407\) | 3.59605e108 | 1.80991 | ||||||||
\(408\) | 3.74451e107 | 0.170215 | ||||||||
\(409\) | 2.54069e107 | 0.104336 | 0.0521680 | − | 0.998638i | \(-0.483387\pi\) | ||||
0.0521680 | + | 0.998638i | \(0.483387\pi\) | |||||||
\(410\) | −2.56015e107 | −0.0950025 | ||||||||
\(411\) | 2.55102e108 | 0.855614 | ||||||||
\(412\) | −1.22874e108 | −0.372586 | ||||||||
\(413\) | −5.04765e108 | −1.38408 | ||||||||
\(414\) | 3.77581e107 | 0.0936474 | ||||||||
\(415\) | 1.21984e108 | 0.273720 | ||||||||
\(416\) | 3.86785e108 | 0.785410 | ||||||||
\(417\) | 7.52508e108 | 1.38314 | ||||||||
\(418\) | −6.14494e108 | −1.02259 | ||||||||
\(419\) | 1.24138e109 | 1.87079 | 0.935393 | − | 0.353609i | \(-0.115046\pi\) | ||||
0.935393 | + | 0.353609i | \(0.115046\pi\) | |||||||
\(420\) | −9.74102e107 | −0.132972 | ||||||||
\(421\) | −1.01700e109 | −1.25781 | −0.628904 | − | 0.777483i | \(-0.716496\pi\) | ||||
−0.628904 | + | 0.777483i | \(0.716496\pi\) | |||||||
\(422\) | 6.45943e108 | 0.723981 | ||||||||
\(423\) | 1.16952e108 | 0.118818 | ||||||||
\(424\) | −6.34006e108 | −0.583997 | ||||||||
\(425\) | 2.85596e108 | 0.238568 | ||||||||
\(426\) | −2.21462e109 | −1.67803 | ||||||||
\(427\) | −1.01037e109 | −0.694579 | ||||||||
\(428\) | 2.20039e107 | 0.0137272 | ||||||||
\(429\) | −1.62794e109 | −0.921851 | ||||||||
\(430\) | −2.97944e108 | −0.153177 | ||||||||
\(431\) | 1.04249e109 | 0.486703 | 0.243352 | − | 0.969938i | \(-0.421753\pi\) | ||||
0.243352 | + | 0.969938i | \(0.421753\pi\) | |||||||
\(432\) | −2.74128e109 | −1.16246 | ||||||||
\(433\) | 3.20495e109 | 1.23474 | 0.617368 | − | 0.786674i | \(-0.288199\pi\) | ||||
0.617368 | + | 0.786674i | \(0.288199\pi\) | |||||||
\(434\) | 9.67601e109 | 3.38745 | ||||||||
\(435\) | −8.72708e108 | −0.277693 | ||||||||
\(436\) | 1.29546e109 | 0.374744 | ||||||||
\(437\) | −2.16084e109 | −0.568386 | ||||||||
\(438\) | −3.98181e108 | −0.0952589 | ||||||||
\(439\) | −1.87780e109 | −0.408669 | −0.204335 | − | 0.978901i | \(-0.565503\pi\) | ||||
−0.204335 | + | 0.978901i | \(0.565503\pi\) | |||||||
\(440\) | 6.02075e108 | 0.119224 | ||||||||
\(441\) | 6.60018e108 | 0.118947 | ||||||||
\(442\) | 1.66555e109 | 0.273233 | ||||||||
\(443\) | −5.14989e109 | −0.769207 | −0.384604 | − | 0.923082i | \(-0.625662\pi\) | ||||
−0.384604 | + | 0.923082i | \(0.625662\pi\) | |||||||
\(444\) | −6.83398e109 | −0.929566 | ||||||||
\(445\) | 7.43695e108 | 0.0921413 | ||||||||
\(446\) | 4.13694e109 | 0.466964 | ||||||||
\(447\) | −1.15843e110 | −1.19154 | ||||||||
\(448\) | 3.10570e109 | 0.291154 | ||||||||
\(449\) | 8.93975e109 | 0.764016 | 0.382008 | − | 0.924159i | \(-0.375233\pi\) | ||||
0.382008 | + | 0.924159i | \(0.375233\pi\) | |||||||
\(450\) | 1.80196e109 | 0.140419 | ||||||||
\(451\) | 5.48878e109 | 0.390076 | ||||||||
\(452\) | 1.45218e109 | 0.0941402 | ||||||||
\(453\) | −5.61002e109 | −0.331810 | ||||||||
\(454\) | −2.93906e110 | −1.58632 | ||||||||
\(455\) | 5.01653e109 | 0.247133 | ||||||||
\(456\) | −1.35207e110 | −0.608079 | ||||||||
\(457\) | −5.58235e109 | −0.229242 | −0.114621 | − | 0.993409i | \(-0.536565\pi\) | ||||
−0.114621 | + | 0.993409i | \(0.536565\pi\) | |||||||
\(458\) | 5.67237e110 | 2.12739 | ||||||||
\(459\) | −6.73185e109 | −0.230626 | ||||||||
\(460\) | −1.82861e109 | −0.0572361 | ||||||||
\(461\) | 2.21966e110 | 0.634891 | 0.317445 | − | 0.948277i | \(-0.397175\pi\) | ||||
0.317445 | + | 0.948277i | \(0.397175\pi\) | |||||||
\(462\) | 6.59479e110 | 1.72409 | ||||||||
\(463\) | −6.75566e109 | −0.161457 | −0.0807285 | − | 0.996736i | \(-0.525725\pi\) | ||||
−0.0807285 | + | 0.996736i | \(0.525725\pi\) | |||||||
\(464\) | −7.79502e110 | −1.70342 | ||||||||
\(465\) | 2.02344e110 | 0.404383 | ||||||||
\(466\) | −3.46177e109 | −0.0632823 | ||||||||
\(467\) | 3.66494e110 | 0.612937 | 0.306469 | − | 0.951881i | \(-0.400853\pi\) | ||||
0.306469 | + | 0.951881i | \(0.400853\pi\) | |||||||
\(468\) | 3.32786e109 | 0.0509286 | ||||||||
\(469\) | −8.91608e110 | −1.24882 | ||||||||
\(470\) | −1.78856e110 | −0.229320 | ||||||||
\(471\) | −4.59996e110 | −0.539990 | ||||||||
\(472\) | −5.92902e110 | −0.637367 | ||||||||
\(473\) | 6.38772e110 | 0.628939 | ||||||||
\(474\) | 2.41813e110 | 0.218112 | ||||||||
\(475\) | −1.03124e111 | −0.852263 | ||||||||
\(476\) | −2.13665e110 | −0.161825 | ||||||||
\(477\) | −1.56213e110 | −0.108444 | ||||||||
\(478\) | −1.12407e111 | −0.715380 | ||||||||
\(479\) | 2.39386e111 | 1.39693 | 0.698465 | − | 0.715644i | \(-0.253867\pi\) | ||||
0.698465 | + | 0.715644i | \(0.253867\pi\) | |||||||
\(480\) | −3.27662e110 | −0.175353 | ||||||||
\(481\) | 3.51943e111 | 1.72763 | ||||||||
\(482\) | 3.40350e110 | 0.153276 | ||||||||
\(483\) | 2.31903e111 | 0.958298 | ||||||||
\(484\) | −1.07124e110 | −0.0406262 | ||||||||
\(485\) | −1.57079e110 | −0.0546808 | ||||||||
\(486\) | −9.07700e110 | −0.290093 | ||||||||
\(487\) | 2.38100e111 | 0.698726 | 0.349363 | − | 0.936988i | \(-0.386398\pi\) | ||||
0.349363 | + | 0.936988i | \(0.386398\pi\) | |||||||
\(488\) | −1.18678e111 | −0.319852 | ||||||||
\(489\) | −6.21855e111 | −1.53947 | ||||||||
\(490\) | −1.00937e111 | −0.229569 | ||||||||
\(491\) | −2.91833e111 | −0.609891 | −0.304945 | − | 0.952370i | \(-0.598638\pi\) | ||||
−0.304945 | + | 0.952370i | \(0.598638\pi\) | |||||||
\(492\) | −1.04309e111 | −0.200342 | ||||||||
\(493\) | −1.91425e111 | −0.337949 | ||||||||
\(494\) | −6.01400e111 | −0.976102 | ||||||||
\(495\) | 1.48345e110 | 0.0221390 | ||||||||
\(496\) | 1.80733e112 | 2.48055 | ||||||||
\(497\) | −1.46310e112 | −1.84707 | ||||||||
\(498\) | 1.56944e112 | 1.82275 | ||||||||
\(499\) | 2.64463e111 | 0.282613 | 0.141307 | − | 0.989966i | \(-0.454870\pi\) | ||||
0.141307 | + | 0.989966i | \(0.454870\pi\) | |||||||
\(500\) | −1.77887e111 | −0.174940 | ||||||||
\(501\) | 2.78758e111 | 0.252326 | ||||||||
\(502\) | −9.70401e111 | −0.808625 | ||||||||
\(503\) | −1.45072e112 | −1.11304 | −0.556520 | − | 0.830834i | \(-0.687864\pi\) | ||||
−0.556520 | + | 0.830834i | \(0.687864\pi\) | |||||||
\(504\) | 1.56086e111 | 0.110280 | ||||||||
\(505\) | 5.46653e111 | 0.355729 | ||||||||
\(506\) | 1.23799e112 | 0.742113 | ||||||||
\(507\) | 3.23395e111 | 0.178609 | ||||||||
\(508\) | 1.32305e112 | 0.673339 | ||||||||
\(509\) | −2.78815e111 | −0.130776 | −0.0653880 | − | 0.997860i | \(-0.520829\pi\) | ||||
−0.0653880 | + | 0.997860i | \(0.520829\pi\) | |||||||
\(510\) | −1.41096e111 | −0.0610030 | ||||||||
\(511\) | −2.63061e111 | −0.104855 | ||||||||
\(512\) | −7.21417e111 | −0.265145 | ||||||||
\(513\) | 2.43075e112 | 0.823891 | ||||||||
\(514\) | 1.76152e112 | 0.550703 | ||||||||
\(515\) | −5.36063e111 | −0.154602 | ||||||||
\(516\) | −1.21393e112 | −0.323021 | ||||||||
\(517\) | 3.83455e112 | 0.941578 | ||||||||
\(518\) | −1.42572e113 | −3.23109 | ||||||||
\(519\) | −3.07738e112 | −0.643778 | ||||||||
\(520\) | 5.89246e111 | 0.113804 | ||||||||
\(521\) | −2.73888e112 | −0.488436 | −0.244218 | − | 0.969720i | \(-0.578531\pi\) | ||||
−0.244218 | + | 0.969720i | \(0.578531\pi\) | |||||||
\(522\) | −1.20779e112 | −0.198914 | ||||||||
\(523\) | 1.03362e112 | 0.157232 | 0.0786159 | − | 0.996905i | \(-0.474950\pi\) | ||||
0.0786159 | + | 0.996905i | \(0.474950\pi\) | |||||||
\(524\) | 3.93051e112 | 0.552332 | ||||||||
\(525\) | 1.10673e113 | 1.43691 | ||||||||
\(526\) | −3.90331e112 | −0.468301 | ||||||||
\(527\) | 4.43833e112 | 0.492129 | ||||||||
\(528\) | 1.23181e113 | 1.26251 | ||||||||
\(529\) | −6.20050e112 | −0.587512 | ||||||||
\(530\) | 2.38898e112 | 0.209297 | ||||||||
\(531\) | −1.46085e112 | −0.118354 | ||||||||
\(532\) | 7.71508e112 | 0.578106 | ||||||||
\(533\) | 5.37183e112 | 0.372343 | ||||||||
\(534\) | 9.56838e112 | 0.613587 | ||||||||
\(535\) | 9.59962e110 | 0.00569603 | ||||||||
\(536\) | −1.04729e113 | −0.575080 | ||||||||
\(537\) | −3.10078e113 | −1.57593 | ||||||||
\(538\) | −3.47317e113 | −1.63403 | ||||||||
\(539\) | 2.16402e113 | 0.942602 | ||||||||
\(540\) | 2.05701e112 | 0.0829653 | ||||||||
\(541\) | 3.60651e113 | 1.34710 | 0.673551 | − | 0.739141i | \(-0.264768\pi\) | ||||
0.673551 | + | 0.739141i | \(0.264768\pi\) | |||||||
\(542\) | −4.27937e113 | −1.48050 | ||||||||
\(543\) | −2.05227e113 | −0.657722 | ||||||||
\(544\) | −7.18713e112 | −0.213403 | ||||||||
\(545\) | 5.65169e112 | 0.155498 | ||||||||
\(546\) | 6.45427e113 | 1.64571 | ||||||||
\(547\) | −5.93233e113 | −1.40201 | −0.701006 | − | 0.713156i | \(-0.747265\pi\) | ||||
−0.701006 | + | 0.713156i | \(0.747265\pi\) | |||||||
\(548\) | −1.70980e113 | −0.374587 | ||||||||
\(549\) | −2.92412e112 | −0.0593940 | ||||||||
\(550\) | 5.90815e113 | 1.11276 | ||||||||
\(551\) | 6.91201e113 | 1.20729 | ||||||||
\(552\) | 2.72395e113 | 0.441294 | ||||||||
\(553\) | 1.59755e113 | 0.240084 | ||||||||
\(554\) | 3.63517e113 | 0.506838 | ||||||||
\(555\) | −2.98146e113 | −0.385718 | ||||||||
\(556\) | −5.04364e113 | −0.605536 | ||||||||
\(557\) | −1.60497e114 | −1.78845 | −0.894226 | − | 0.447615i | \(-0.852273\pi\) | ||||
−0.894226 | + | 0.447615i | \(0.852273\pi\) | |||||||
\(558\) | 2.80035e113 | 0.289663 | ||||||||
\(559\) | 6.25161e113 | 0.600347 | ||||||||
\(560\) | −3.79584e113 | −0.338458 | ||||||||
\(561\) | 3.02499e113 | 0.250476 | ||||||||
\(562\) | 4.49713e113 | 0.345843 | ||||||||
\(563\) | 1.36019e114 | 0.971632 | 0.485816 | − | 0.874061i | \(-0.338522\pi\) | ||||
0.485816 | + | 0.874061i | \(0.338522\pi\) | |||||||
\(564\) | −7.28721e113 | −0.483591 | ||||||||
\(565\) | 6.33541e112 | 0.0390629 | ||||||||
\(566\) | 1.89536e114 | 1.08595 | ||||||||
\(567\) | −2.92776e114 | −1.55898 | ||||||||
\(568\) | −1.71857e114 | −0.850573 | ||||||||
\(569\) | −2.49280e114 | −1.14691 | −0.573454 | − | 0.819238i | \(-0.694397\pi\) | ||||
−0.573454 | + | 0.819238i | \(0.694397\pi\) | |||||||
\(570\) | 5.09471e113 | 0.217928 | ||||||||
\(571\) | 2.45827e114 | 0.977758 | 0.488879 | − | 0.872352i | \(-0.337406\pi\) | ||||
0.488879 | + | 0.872352i | \(0.337406\pi\) | |||||||
\(572\) | 1.09112e114 | 0.403586 | ||||||||
\(573\) | −5.62212e114 | −1.93412 | ||||||||
\(574\) | −2.17613e114 | −0.696371 | ||||||||
\(575\) | 2.07758e114 | 0.618503 | ||||||||
\(576\) | 8.98828e112 | 0.0248968 | ||||||||
\(577\) | 6.41691e114 | 1.65398 | 0.826990 | − | 0.562217i | \(-0.190052\pi\) | ||||
0.826990 | + | 0.562217i | \(0.190052\pi\) | |||||||
\(578\) | 4.73355e114 | 1.13548 | ||||||||
\(579\) | 6.39843e113 | 0.142861 | ||||||||
\(580\) | 5.84927e113 | 0.121574 | ||||||||
\(581\) | 1.03686e115 | 2.00637 | ||||||||
\(582\) | −2.02097e114 | −0.364130 | ||||||||
\(583\) | −5.12181e114 | −0.859366 | ||||||||
\(584\) | −3.08994e113 | −0.0482855 | ||||||||
\(585\) | 1.45184e113 | 0.0211325 | ||||||||
\(586\) | −3.50541e114 | −0.475322 | ||||||||
\(587\) | −5.70812e114 | −0.721127 | −0.360563 | − | 0.932735i | \(-0.617416\pi\) | ||||
−0.360563 | + | 0.932735i | \(0.617416\pi\) | |||||||
\(588\) | −4.11253e114 | −0.484117 | ||||||||
\(589\) | −1.60260e115 | −1.75809 | ||||||||
\(590\) | 2.23410e114 | 0.228425 | ||||||||
\(591\) | 1.40493e115 | 1.33898 | ||||||||
\(592\) | −2.66303e115 | −2.36606 | ||||||||
\(593\) | 2.38483e115 | 1.97555 | 0.987775 | − | 0.155885i | \(-0.0498229\pi\) | ||||
0.987775 | + | 0.155885i | \(0.0498229\pi\) | |||||||
\(594\) | −1.39262e115 | −1.07571 | ||||||||
\(595\) | −9.32157e113 | −0.0671483 | ||||||||
\(596\) | 7.76431e114 | 0.521654 | ||||||||
\(597\) | 7.60097e114 | 0.476359 | ||||||||
\(598\) | 1.21161e115 | 0.708375 | ||||||||
\(599\) | −8.39829e114 | −0.458118 | −0.229059 | − | 0.973412i | \(-0.573565\pi\) | ||||
−0.229059 | + | 0.973412i | \(0.573565\pi\) | |||||||
\(600\) | 1.29997e115 | 0.661695 | ||||||||
\(601\) | 1.94245e115 | 0.922698 | 0.461349 | − | 0.887219i | \(-0.347366\pi\) | ||||
0.461349 | + | 0.887219i | \(0.347366\pi\) | |||||||
\(602\) | −2.53253e115 | −1.12279 | ||||||||
\(603\) | −2.58042e114 | −0.106788 | ||||||||
\(604\) | 3.76008e114 | 0.145266 | ||||||||
\(605\) | −4.67351e113 | −0.0168576 | ||||||||
\(606\) | 7.03324e115 | 2.36887 | ||||||||
\(607\) | −5.08563e115 | −1.59961 | −0.799805 | − | 0.600260i | \(-0.795064\pi\) | ||||
−0.799805 | + | 0.600260i | \(0.795064\pi\) | |||||||
\(608\) | 2.59514e115 | 0.762365 | ||||||||
\(609\) | −7.41802e115 | −2.03550 | ||||||||
\(610\) | 4.47189e114 | 0.114631 | ||||||||
\(611\) | 3.75284e115 | 0.898773 | ||||||||
\(612\) | −6.18373e113 | −0.0138378 | ||||||||
\(613\) | −8.90445e114 | −0.186208 | −0.0931039 | − | 0.995656i | \(-0.529679\pi\) | ||||
−0.0931039 | + | 0.995656i | \(0.529679\pi\) | |||||||
\(614\) | −1.05842e115 | −0.206856 | ||||||||
\(615\) | −4.55070e114 | −0.0831305 | ||||||||
\(616\) | 5.11764e115 | 0.873917 | ||||||||
\(617\) | −6.82203e115 | −1.08913 | −0.544565 | − | 0.838719i | \(-0.683305\pi\) | ||||
−0.544565 | + | 0.838719i | \(0.683305\pi\) | |||||||
\(618\) | −6.89699e115 | −1.02953 | ||||||||
\(619\) | 3.57057e115 | 0.498398 | 0.249199 | − | 0.968452i | \(-0.419833\pi\) | ||||
0.249199 | + | 0.968452i | \(0.419833\pi\) | |||||||
\(620\) | −1.35620e115 | −0.177039 | ||||||||
\(621\) | −4.89710e115 | −0.597913 | ||||||||
\(622\) | −2.63591e115 | −0.301043 | ||||||||
\(623\) | 6.32141e115 | 0.675398 | ||||||||
\(624\) | 1.20556e116 | 1.20512 | ||||||||
\(625\) | 9.51965e115 | 0.890431 | ||||||||
\(626\) | −1.29386e116 | −1.13254 | ||||||||
\(627\) | −1.09227e116 | −0.894803 | ||||||||
\(628\) | 3.08309e115 | 0.236408 | ||||||||
\(629\) | −6.53970e115 | −0.469414 | ||||||||
\(630\) | −5.88142e114 | −0.0395229 | ||||||||
\(631\) | 2.68414e116 | 1.68883 | 0.844416 | − | 0.535687i | \(-0.179947\pi\) | ||||
0.844416 | + | 0.535687i | \(0.179947\pi\) | |||||||
\(632\) | 1.87650e115 | 0.110558 | ||||||||
\(633\) | 1.14817e116 | 0.633509 | ||||||||
\(634\) | 3.27765e115 | 0.169378 | ||||||||
\(635\) | 5.77208e115 | 0.279398 | ||||||||
\(636\) | 9.73353e115 | 0.441367 | ||||||||
\(637\) | 2.11791e116 | 0.899750 | ||||||||
\(638\) | −3.96002e116 | −1.57630 | ||||||||
\(639\) | −4.23439e115 | −0.157945 | ||||||||
\(640\) | −6.11342e115 | −0.213705 | ||||||||
\(641\) | −4.40590e116 | −1.44353 | −0.721766 | − | 0.692137i | \(-0.756669\pi\) | ||||
−0.721766 | + | 0.692137i | \(0.756669\pi\) | |||||||
\(642\) | 1.23509e115 | 0.0379310 | ||||||||
\(643\) | −1.91871e116 | −0.552400 | −0.276200 | − | 0.961100i | \(-0.589075\pi\) | ||||
−0.276200 | + | 0.961100i | \(0.589075\pi\) | |||||||
\(644\) | −1.55432e116 | −0.419542 | ||||||||
\(645\) | −5.29600e115 | −0.134036 | ||||||||
\(646\) | 1.11750e116 | 0.265216 | ||||||||
\(647\) | −4.37850e116 | −0.974536 | −0.487268 | − | 0.873253i | \(-0.662006\pi\) | ||||
−0.487268 | + | 0.873253i | \(0.662006\pi\) | |||||||
\(648\) | −3.43898e116 | −0.717905 | ||||||||
\(649\) | −4.78974e116 | −0.937902 | ||||||||
\(650\) | 5.78226e116 | 1.06217 | ||||||||
\(651\) | 1.71992e117 | 2.96414 | ||||||||
\(652\) | 4.16794e116 | 0.673979 | ||||||||
\(653\) | 3.03451e116 | 0.460459 | 0.230230 | − | 0.973136i | \(-0.426052\pi\) | ||||
0.230230 | + | 0.973136i | \(0.426052\pi\) | |||||||
\(654\) | 7.27147e116 | 1.03549 | ||||||||
\(655\) | 1.71476e116 | 0.229187 | ||||||||
\(656\) | −4.06468e116 | −0.509937 | ||||||||
\(657\) | −7.61330e114 | −0.00896623 | ||||||||
\(658\) | −1.52028e117 | −1.68092 | ||||||||
\(659\) | −1.18132e116 | −0.122637 | −0.0613186 | − | 0.998118i | \(-0.519531\pi\) | ||||
−0.0613186 | + | 0.998118i | \(0.519531\pi\) | |||||||
\(660\) | −9.24331e115 | −0.0901061 | ||||||||
\(661\) | −1.93365e116 | −0.177018 | −0.0885092 | − | 0.996075i | \(-0.528210\pi\) | ||||
−0.0885092 | + | 0.996075i | \(0.528210\pi\) | |||||||
\(662\) | −6.54950e116 | −0.563120 | ||||||||
\(663\) | 2.96054e116 | 0.239089 | ||||||||
\(664\) | 1.21791e117 | 0.923931 | ||||||||
\(665\) | 3.36585e116 | 0.239882 | ||||||||
\(666\) | −4.12621e116 | −0.276293 | ||||||||
\(667\) | −1.39253e117 | −0.876156 | ||||||||
\(668\) | −1.86836e116 | −0.110468 | ||||||||
\(669\) | 7.35347e116 | 0.408610 | ||||||||
\(670\) | 3.94626e116 | 0.206102 | ||||||||
\(671\) | −9.58741e116 | −0.470670 | ||||||||
\(672\) | −2.78513e117 | −1.28535 | ||||||||
\(673\) | 6.98440e116 | 0.303043 | 0.151521 | − | 0.988454i | \(-0.451583\pi\) | ||||
0.151521 | + | 0.988454i | \(0.451583\pi\) | |||||||
\(674\) | 4.43820e117 | 1.81059 | ||||||||
\(675\) | −2.33708e117 | −0.896536 | ||||||||
\(676\) | −2.16754e116 | −0.0781949 | ||||||||
\(677\) | −9.10436e116 | −0.308901 | −0.154451 | − | 0.988001i | \(-0.549361\pi\) | ||||
−0.154451 | + | 0.988001i | \(0.549361\pi\) | |||||||
\(678\) | 8.15114e116 | 0.260128 | ||||||||
\(679\) | −1.33517e117 | −0.400812 | ||||||||
\(680\) | −1.09492e116 | −0.0309216 | ||||||||
\(681\) | −5.22422e117 | −1.38809 | ||||||||
\(682\) | 9.18161e117 | 2.29545 | ||||||||
\(683\) | 3.36570e117 | 0.791800 | 0.395900 | − | 0.918294i | \(-0.370433\pi\) | ||||
0.395900 | + | 0.918294i | \(0.370433\pi\) | |||||||
\(684\) | 2.23284e116 | 0.0494343 | ||||||||
\(685\) | −7.45935e116 | −0.155433 | ||||||||
\(686\) | 1.14333e116 | 0.0224244 | ||||||||
\(687\) | 1.00827e118 | 1.86154 | ||||||||
\(688\) | −4.73038e117 | −0.822197 | ||||||||
\(689\) | −5.01267e117 | −0.820298 | ||||||||
\(690\) | −1.02640e117 | −0.158154 | ||||||||
\(691\) | −1.14140e117 | −0.165614 | −0.0828071 | − | 0.996566i | \(-0.526389\pi\) | ||||
−0.0828071 | + | 0.996566i | \(0.526389\pi\) | |||||||
\(692\) | 2.06260e117 | 0.281846 | ||||||||
\(693\) | 1.26093e117 | 0.162279 | ||||||||
\(694\) | −3.61977e117 | −0.438797 | ||||||||
\(695\) | −2.20039e117 | −0.251264 | ||||||||
\(696\) | −8.71327e117 | −0.937341 | ||||||||
\(697\) | −9.98177e116 | −0.101169 | ||||||||
\(698\) | 3.28669e117 | 0.313876 | ||||||||
\(699\) | −6.15334e116 | −0.0553742 | ||||||||
\(700\) | −7.41779e117 | −0.629080 | ||||||||
\(701\) | −1.37335e118 | −1.09770 | −0.548851 | − | 0.835920i | \(-0.684935\pi\) | ||||
−0.548851 | + | 0.835920i | \(0.684935\pi\) | |||||||
\(702\) | −1.36295e118 | −1.02681 | ||||||||
\(703\) | 2.36137e118 | 1.67694 | ||||||||
\(704\) | 2.94702e117 | 0.197296 | ||||||||
\(705\) | −3.17919e117 | −0.200663 | ||||||||
\(706\) | −4.56962e117 | −0.271947 | ||||||||
\(707\) | 4.64656e118 | 2.60751 | ||||||||
\(708\) | 9.10248e117 | 0.481703 | ||||||||
\(709\) | −1.80564e118 | −0.901181 | −0.450591 | − | 0.892731i | \(-0.648787\pi\) | ||||
−0.450591 | + | 0.892731i | \(0.648787\pi\) | |||||||
\(710\) | 6.47570e117 | 0.304835 | ||||||||
\(711\) | 4.62351e116 | 0.0205298 | ||||||||
\(712\) | 7.42518e117 | 0.311019 | ||||||||
\(713\) | 3.22868e118 | 1.27588 | ||||||||
\(714\) | −1.19931e118 | −0.447154 | ||||||||
\(715\) | 4.76021e117 | 0.167466 | ||||||||
\(716\) | 2.07828e118 | 0.689943 | ||||||||
\(717\) | −1.99805e118 | −0.625982 | ||||||||
\(718\) | −6.35529e118 | −1.87919 | ||||||||
\(719\) | −1.93376e118 | −0.539703 | −0.269851 | − | 0.962902i | \(-0.586975\pi\) | ||||
−0.269851 | + | 0.962902i | \(0.586975\pi\) | |||||||
\(720\) | −1.09856e117 | −0.0289418 | ||||||||
\(721\) | −4.55654e118 | −1.13324 | ||||||||
\(722\) | 1.11694e118 | 0.262263 | ||||||||
\(723\) | 6.04976e117 | 0.134122 | ||||||||
\(724\) | 1.37552e118 | 0.287950 | ||||||||
\(725\) | −6.64567e118 | −1.31375 | ||||||||
\(726\) | −6.01294e117 | −0.112258 | ||||||||
\(727\) | 5.50038e118 | 0.969873 | 0.484937 | − | 0.874549i | \(-0.338843\pi\) | ||||
0.484937 | + | 0.874549i | \(0.338843\pi\) | |||||||
\(728\) | 5.00859e118 | 0.834187 | ||||||||
\(729\) | 5.41645e118 | 0.852163 | ||||||||
\(730\) | 1.16431e117 | 0.0173049 | ||||||||
\(731\) | −1.16166e118 | −0.163120 | ||||||||
\(732\) | 1.82200e118 | 0.241735 | ||||||||
\(733\) | −7.49231e118 | −0.939292 | −0.469646 | − | 0.882855i | \(-0.655618\pi\) | ||||
−0.469646 | + | 0.882855i | \(0.655618\pi\) | |||||||
\(734\) | 1.14383e119 | 1.35511 | ||||||||
\(735\) | −1.79417e118 | −0.200881 | ||||||||
\(736\) | −5.22830e118 | −0.553262 | ||||||||
\(737\) | −8.46051e118 | −0.846245 | ||||||||
\(738\) | −6.29797e117 | −0.0595472 | ||||||||
\(739\) | −8.09019e117 | −0.0723127 | −0.0361564 | − | 0.999346i | \(-0.511511\pi\) | ||||
−0.0361564 | + | 0.999346i | \(0.511511\pi\) | |||||||
\(740\) | 1.99830e118 | 0.168867 | ||||||||
\(741\) | −1.06900e119 | −0.854124 | ||||||||
\(742\) | 2.03063e119 | 1.53416 | ||||||||
\(743\) | 1.54577e119 | 1.10435 | 0.552177 | − | 0.833727i | \(-0.313797\pi\) | ||||
0.552177 | + | 0.833727i | \(0.313797\pi\) | |||||||
\(744\) | 2.02024e119 | 1.36498 | ||||||||
\(745\) | 3.38733e118 | 0.216457 | ||||||||
\(746\) | −2.90870e119 | −1.75808 | ||||||||
\(747\) | 3.00081e118 | 0.171567 | ||||||||
\(748\) | −2.02748e118 | −0.109658 | ||||||||
\(749\) | 8.15968e117 | 0.0417520 | ||||||||
\(750\) | −9.98488e118 | −0.483393 | ||||||||
\(751\) | 1.41537e119 | 0.648354 | 0.324177 | − | 0.945997i | \(-0.394913\pi\) | ||||
0.324177 | + | 0.945997i | \(0.394913\pi\) | |||||||
\(752\) | −2.83965e119 | −1.23090 | ||||||||
\(753\) | −1.72490e119 | −0.707576 | ||||||||
\(754\) | −3.87565e119 | −1.50464 | ||||||||
\(755\) | 1.64041e118 | 0.0602773 | ||||||||
\(756\) | 1.74846e119 | 0.608138 | ||||||||
\(757\) | 2.40708e119 | 0.792521 | 0.396261 | − | 0.918138i | \(-0.370308\pi\) | ||||
0.396261 | + | 0.918138i | \(0.370308\pi\) | |||||||
\(758\) | −5.03643e119 | −1.56982 | ||||||||
\(759\) | 2.20054e119 | 0.649375 | ||||||||
\(760\) | 3.95356e118 | 0.110465 | ||||||||
\(761\) | −5.04788e119 | −1.33550 | −0.667752 | − | 0.744383i | \(-0.732744\pi\) | ||||
−0.667752 | + | 0.744383i | \(0.732744\pi\) | |||||||
\(762\) | 7.42636e119 | 1.86056 | ||||||||
\(763\) | 4.80394e119 | 1.13980 | ||||||||
\(764\) | 3.76819e119 | 0.846756 | ||||||||
\(765\) | −2.69777e117 | −0.00574190 | ||||||||
\(766\) | 9.16874e119 | 1.84848 | ||||||||
\(767\) | −4.68769e119 | −0.895264 | ||||||||
\(768\) | −6.65703e119 | −1.20445 | ||||||||
\(769\) | −1.69583e118 | −0.0290697 | −0.0145348 | − | 0.999894i | \(-0.504627\pi\) | ||||
−0.0145348 | + | 0.999894i | \(0.504627\pi\) | |||||||
\(770\) | −1.92836e119 | −0.313201 | ||||||||
\(771\) | 3.13112e119 | 0.481885 | ||||||||
\(772\) | −4.28851e118 | −0.0625444 | ||||||||
\(773\) | 2.48383e119 | 0.343299 | 0.171650 | − | 0.985158i | \(-0.445090\pi\) | ||||
0.171650 | + | 0.985158i | \(0.445090\pi\) | |||||||
\(774\) | −7.32944e118 | −0.0960110 | ||||||||
\(775\) | 1.54085e120 | 1.91311 | ||||||||
\(776\) | −1.56830e119 | −0.184573 | ||||||||
\(777\) | −2.53424e120 | −2.82732 | ||||||||
\(778\) | −1.11675e120 | −1.18114 | ||||||||
\(779\) | 3.60424e119 | 0.361417 | ||||||||
\(780\) | −9.04636e118 | −0.0860097 | ||||||||
\(781\) | −1.38834e120 | −1.25164 | ||||||||
\(782\) | −2.25138e119 | −0.192472 | ||||||||
\(783\) | 1.56647e120 | 1.27001 | ||||||||
\(784\) | −1.60255e120 | −1.23224 | ||||||||
\(785\) | 1.34506e119 | 0.0980958 | ||||||||
\(786\) | 2.20621e120 | 1.52620 | ||||||||
\(787\) | 2.35369e120 | 1.54454 | 0.772269 | − | 0.635296i | \(-0.219122\pi\) | ||||
0.772269 | + | 0.635296i | \(0.219122\pi\) | |||||||
\(788\) | −9.41643e119 | −0.586203 | ||||||||
\(789\) | −6.93819e119 | −0.409780 | ||||||||
\(790\) | −7.07079e118 | −0.0396227 | ||||||||
\(791\) | 5.38510e119 | 0.286332 | ||||||||
\(792\) | 1.48111e119 | 0.0747293 | ||||||||
\(793\) | −9.38313e119 | −0.449273 | ||||||||
\(794\) | 2.86495e120 | 1.30187 | ||||||||
\(795\) | 4.24644e119 | 0.183143 | ||||||||
\(796\) | −5.09450e119 | −0.208550 | ||||||||
\(797\) | −1.42809e120 | −0.554927 | −0.277463 | − | 0.960736i | \(-0.589494\pi\) | ||||
−0.277463 | + | 0.960736i | \(0.589494\pi\) | |||||||
\(798\) | 4.33051e120 | 1.59742 | ||||||||
\(799\) | −6.97342e119 | −0.244205 | ||||||||
\(800\) | −2.49514e120 | −0.829585 | ||||||||
\(801\) | 1.82949e119 | 0.0577538 | ||||||||
\(802\) | −6.90959e120 | −2.07117 | ||||||||
\(803\) | −2.49620e119 | −0.0710533 | ||||||||
\(804\) | 1.60784e120 | 0.434628 | ||||||||
\(805\) | −6.78100e119 | −0.174086 | ||||||||
\(806\) | 8.98598e120 | 2.19109 | ||||||||
\(807\) | −6.17360e120 | −1.42984 | ||||||||
\(808\) | 5.45789e120 | 1.20075 | ||||||||
\(809\) | −3.58829e120 | −0.749935 | −0.374967 | − | 0.927038i | \(-0.622346\pi\) | ||||
−0.374967 | + | 0.927038i | \(0.622346\pi\) | |||||||
\(810\) | 1.29583e120 | 0.257288 | ||||||||
\(811\) | 4.55375e119 | 0.0859021 | 0.0429510 | − | 0.999077i | \(-0.486324\pi\) | ||||
0.0429510 | + | 0.999077i | \(0.486324\pi\) | |||||||
\(812\) | 4.97188e120 | 0.891139 | ||||||||
\(813\) | −7.60664e120 | −1.29549 | ||||||||
\(814\) | −1.35287e121 | −2.18950 | ||||||||
\(815\) | 1.81835e120 | 0.279664 | ||||||||
\(816\) | −2.24014e120 | −0.327441 | ||||||||
\(817\) | 4.19454e120 | 0.582732 | ||||||||
\(818\) | −9.55835e119 | −0.126218 | ||||||||
\(819\) | 1.23407e120 | 0.154902 | ||||||||
\(820\) | 3.05008e119 | 0.0363945 | ||||||||
\(821\) | 6.38182e120 | 0.723941 | 0.361971 | − | 0.932189i | \(-0.382104\pi\) | ||||
0.361971 | + | 0.932189i | \(0.382104\pi\) | |||||||
\(822\) | −9.59720e120 | −1.03506 | ||||||||
\(823\) | 1.21516e121 | 1.24607 | 0.623034 | − | 0.782195i | \(-0.285900\pi\) | ||||
0.623034 | + | 0.782195i | \(0.285900\pi\) | |||||||
\(824\) | −5.35215e120 | −0.521854 | ||||||||
\(825\) | 1.05018e121 | 0.973701 | ||||||||
\(826\) | 1.89898e121 | 1.67436 | ||||||||
\(827\) | 7.06562e120 | 0.592477 | 0.296239 | − | 0.955114i | \(-0.404268\pi\) | ||||
0.296239 | + | 0.955114i | \(0.404268\pi\) | |||||||
\(828\) | −4.49837e119 | −0.0358754 | ||||||||
\(829\) | 3.78118e119 | 0.0286823 | 0.0143412 | − | 0.999897i | \(-0.495435\pi\) | ||||
0.0143412 | + | 0.999897i | \(0.495435\pi\) | |||||||
\(830\) | −4.58917e120 | −0.331126 | ||||||||
\(831\) | 6.46156e120 | 0.443501 | ||||||||
\(832\) | 2.88423e120 | 0.188326 | ||||||||
\(833\) | −3.93545e120 | −0.244470 | ||||||||
\(834\) | −2.83102e121 | −1.67321 | ||||||||
\(835\) | −8.15107e119 | −0.0458380 | ||||||||
\(836\) | 7.32088e120 | 0.391744 | ||||||||
\(837\) | −3.63197e121 | −1.84942 | ||||||||
\(838\) | −4.67022e121 | −2.26314 | ||||||||
\(839\) | 1.95436e120 | 0.0901329 | 0.0450664 | − | 0.998984i | \(-0.485650\pi\) | ||||
0.0450664 | + | 0.998984i | \(0.485650\pi\) | |||||||
\(840\) | −4.24299e120 | −0.186244 | ||||||||
\(841\) | 2.06086e121 | 0.861021 | ||||||||
\(842\) | 3.82606e121 | 1.52160 | ||||||||
\(843\) | 7.99371e120 | 0.302625 | ||||||||
\(844\) | −7.69555e120 | −0.277350 | ||||||||
\(845\) | −9.45630e119 | −0.0324465 | ||||||||
\(846\) | −4.39986e120 | −0.143737 | ||||||||
\(847\) | −3.97249e120 | −0.123567 | ||||||||
\(848\) | 3.79292e121 | 1.12343 | ||||||||
\(849\) | 3.36903e121 | 0.950246 | ||||||||
\(850\) | −1.07444e121 | −0.288601 | ||||||||
\(851\) | −4.75733e121 | −1.21699 | ||||||||
\(852\) | 2.63842e121 | 0.642838 | ||||||||
\(853\) | 5.99716e120 | 0.139175 | 0.0695874 | − | 0.997576i | \(-0.477832\pi\) | ||||
0.0695874 | + | 0.997576i | \(0.477832\pi\) | |||||||
\(854\) | 3.80111e121 | 0.840249 | ||||||||
\(855\) | 9.74118e119 | 0.0205125 | ||||||||
\(856\) | 9.58443e119 | 0.0192267 | ||||||||
\(857\) | −6.42993e121 | −1.22886 | −0.614429 | − | 0.788972i | \(-0.710614\pi\) | ||||
−0.614429 | + | 0.788972i | \(0.710614\pi\) | |||||||
\(858\) | 6.12449e121 | 1.11519 | ||||||||
\(859\) | 2.36235e121 | 0.409852 | 0.204926 | − | 0.978777i | \(-0.434305\pi\) | ||||
0.204926 | + | 0.978777i | \(0.434305\pi\) | |||||||
\(860\) | 3.54961e120 | 0.0586807 | ||||||||
\(861\) | −3.86809e121 | −0.609349 | ||||||||
\(862\) | −3.92195e121 | −0.588777 | ||||||||
\(863\) | −3.26016e121 | −0.466435 | −0.233218 | − | 0.972425i | \(-0.574925\pi\) | ||||
−0.233218 | + | 0.972425i | \(0.574925\pi\) | |||||||
\(864\) | 5.88136e121 | 0.801969 | ||||||||
\(865\) | 8.99848e120 | 0.116950 | ||||||||
\(866\) | −1.20574e122 | −1.49369 | ||||||||
\(867\) | 8.41394e121 | 0.993589 | ||||||||
\(868\) | −1.15277e122 | −1.29770 | ||||||||
\(869\) | 1.51593e121 | 0.162689 | ||||||||
\(870\) | 3.28322e121 | 0.335932 | ||||||||
\(871\) | −8.28024e121 | −0.807773 | ||||||||
\(872\) | 5.64275e121 | 0.524876 | ||||||||
\(873\) | −3.86414e120 | −0.0342737 | ||||||||
\(874\) | 8.12932e121 | 0.687590 | ||||||||
\(875\) | −6.59657e121 | −0.532089 | ||||||||
\(876\) | 4.74380e120 | 0.0364927 | ||||||||
\(877\) | 5.81721e121 | 0.426807 | 0.213404 | − | 0.976964i | \(-0.431545\pi\) | ||||
0.213404 | + | 0.976964i | \(0.431545\pi\) | |||||||
\(878\) | 7.06450e121 | 0.494378 | ||||||||
\(879\) | −6.23092e121 | −0.415924 | ||||||||
\(880\) | −3.60189e121 | −0.229350 | ||||||||
\(881\) | −8.70995e121 | −0.529073 | −0.264536 | − | 0.964376i | \(-0.585219\pi\) | ||||
−0.264536 | + | 0.964376i | \(0.585219\pi\) | |||||||
\(882\) | −2.48306e121 | −0.143893 | ||||||||
\(883\) | 1.15838e122 | 0.640442 | 0.320221 | − | 0.947343i | \(-0.396243\pi\) | ||||
0.320221 | + | 0.947343i | \(0.396243\pi\) | |||||||
\(884\) | −1.98428e121 | −0.104673 | ||||||||
\(885\) | 3.97113e121 | 0.199880 | ||||||||
\(886\) | 1.93744e122 | 0.930529 | ||||||||
\(887\) | 8.70278e121 | 0.398867 | 0.199433 | − | 0.979911i | \(-0.436090\pi\) | ||||
0.199433 | + | 0.979911i | \(0.436090\pi\) | |||||||
\(888\) | −2.97674e122 | −1.30198 | ||||||||
\(889\) | 4.90627e122 | 2.04799 | ||||||||
\(890\) | −2.79786e121 | −0.111466 | ||||||||
\(891\) | −2.77817e122 | −1.05641 | ||||||||
\(892\) | −4.92862e121 | −0.178889 | ||||||||
\(893\) | 2.51798e122 | 0.872402 | ||||||||
\(894\) | 4.35814e122 | 1.44143 | ||||||||
\(895\) | 9.06690e121 | 0.286288 | ||||||||
\(896\) | −5.19641e122 | −1.56646 | ||||||||
\(897\) | 2.15365e122 | 0.619854 | ||||||||
\(898\) | −3.36323e122 | −0.924249 | ||||||||
\(899\) | −1.03278e123 | −2.71006 | ||||||||
\(900\) | −2.14680e121 | −0.0537931 | ||||||||
\(901\) | 9.31440e121 | 0.222883 | ||||||||
\(902\) | −2.06494e122 | −0.471884 | ||||||||
\(903\) | −4.50160e122 | −0.982484 | ||||||||
\(904\) | 6.32539e121 | 0.131855 | ||||||||
\(905\) | 6.00099e121 | 0.119483 | ||||||||
\(906\) | 2.11055e122 | 0.401398 | ||||||||
\(907\) | 4.66008e122 | 0.846625 | 0.423313 | − | 0.905984i | \(-0.360867\pi\) | ||||
0.423313 | + | 0.905984i | \(0.360867\pi\) | |||||||
\(908\) | 3.50150e122 | 0.607703 | ||||||||
\(909\) | 1.34477e122 | 0.222970 | ||||||||
\(910\) | −1.88727e122 | −0.298963 | ||||||||
\(911\) | −2.69220e122 | −0.407469 | −0.203735 | − | 0.979026i | \(-0.565308\pi\) | ||||
−0.203735 | + | 0.979026i | \(0.565308\pi\) | |||||||
\(912\) | 8.08874e122 | 1.16976 | ||||||||
\(913\) | 9.83885e122 | 1.35959 | ||||||||
\(914\) | 2.10014e122 | 0.277320 | ||||||||
\(915\) | 7.94884e121 | 0.100306 | ||||||||
\(916\) | −6.75788e122 | −0.814983 | ||||||||
\(917\) | 1.45755e123 | 1.67994 | ||||||||
\(918\) | 2.53259e122 | 0.278994 | ||||||||
\(919\) | −4.70853e122 | −0.495783 | −0.247891 | − | 0.968788i | \(-0.579738\pi\) | ||||
−0.247891 | + | 0.968788i | \(0.579738\pi\) | |||||||
\(920\) | −7.96503e121 | −0.0801664 | ||||||||
\(921\) | −1.88135e122 | −0.181007 | ||||||||
\(922\) | −8.35062e122 | −0.768043 | ||||||||
\(923\) | −1.35876e123 | −1.19474 | ||||||||
\(924\) | −7.85681e122 | −0.660480 | ||||||||
\(925\) | −2.27038e123 | −1.82480 | ||||||||
\(926\) | 2.54155e122 | 0.195319 | ||||||||
\(927\) | −1.31872e122 | −0.0969042 | ||||||||
\(928\) | 1.67241e123 | 1.17517 | ||||||||
\(929\) | 2.03493e123 | 1.36740 | 0.683702 | − | 0.729761i | \(-0.260369\pi\) | ||||
0.683702 | + | 0.729761i | \(0.260369\pi\) | |||||||
\(930\) | −7.61240e122 | −0.489192 | ||||||||
\(931\) | 1.42102e123 | 0.873350 | ||||||||
\(932\) | 4.12424e121 | 0.0242428 | ||||||||
\(933\) | −4.68536e122 | −0.263424 | ||||||||
\(934\) | −1.37879e123 | −0.741486 | ||||||||
\(935\) | −8.84529e121 | −0.0455019 | ||||||||
\(936\) | 1.44955e122 | 0.0713320 | ||||||||
\(937\) | −3.17058e123 | −1.49261 | −0.746305 | − | 0.665605i | \(-0.768174\pi\) | ||||
−0.746305 | + | 0.665605i | \(0.768174\pi\) | |||||||
\(938\) | 3.35433e123 | 1.51073 | ||||||||
\(939\) | −2.29985e123 | −0.991010 | ||||||||
\(940\) | 2.13083e122 | 0.0878503 | ||||||||
\(941\) | 6.89910e122 | 0.272159 | 0.136080 | − | 0.990698i | \(-0.456550\pi\) | ||||
0.136080 | + | 0.990698i | \(0.456550\pi\) | |||||||
\(942\) | 1.73055e123 | 0.653240 | ||||||||
\(943\) | −7.26127e122 | −0.262287 | ||||||||
\(944\) | 3.54701e123 | 1.22610 | ||||||||
\(945\) | 7.62801e122 | 0.252343 | ||||||||
\(946\) | −2.40313e123 | −0.760843 | ||||||||
\(947\) | −1.35585e123 | −0.410855 | −0.205428 | − | 0.978672i | \(-0.565859\pi\) | ||||
−0.205428 | + | 0.978672i | \(0.565859\pi\) | |||||||
\(948\) | −2.88089e122 | −0.0835565 | ||||||||
\(949\) | −2.44301e122 | −0.0678231 | ||||||||
\(950\) | 3.87962e123 | 1.03100 | ||||||||
\(951\) | 5.82606e122 | 0.148212 | ||||||||
\(952\) | −9.30682e122 | −0.226656 | ||||||||
\(953\) | 6.10390e123 | 1.42315 | 0.711577 | − | 0.702608i | \(-0.247981\pi\) | ||||
0.711577 | + | 0.702608i | \(0.247981\pi\) | |||||||
\(954\) | 5.87690e122 | 0.131187 | ||||||||
\(955\) | 1.64395e123 | 0.351356 | ||||||||
\(956\) | 1.33918e123 | 0.274055 | ||||||||
\(957\) | −7.03900e123 | −1.37932 | ||||||||
\(958\) | −9.00595e123 | −1.68990 | ||||||||
\(959\) | −6.34045e123 | −1.13933 | ||||||||
\(960\) | −2.44335e122 | −0.0420464 | ||||||||
\(961\) | 1.78780e124 | 2.94645 | ||||||||
\(962\) | −1.32405e124 | −2.08996 | ||||||||
\(963\) | 2.36151e121 | 0.00357025 | ||||||||
\(964\) | −4.05482e122 | −0.0587184 | ||||||||
\(965\) | −1.87095e122 | −0.0259524 | ||||||||
\(966\) | −8.72444e123 | −1.15928 | ||||||||
\(967\) | 6.41485e123 | 0.816559 | 0.408280 | − | 0.912857i | \(-0.366129\pi\) | ||||
0.408280 | + | 0.912857i | \(0.366129\pi\) | |||||||
\(968\) | −4.66612e122 | −0.0569021 | ||||||||
\(969\) | 1.98638e123 | 0.232073 | ||||||||
\(970\) | 5.90947e122 | 0.0661487 | ||||||||
\(971\) | 3.86744e123 | 0.414787 | 0.207394 | − | 0.978258i | \(-0.433502\pi\) | ||||
0.207394 | + | 0.978258i | \(0.433502\pi\) | |||||||
\(972\) | 1.08140e123 | 0.111132 | ||||||||
\(973\) | −1.87033e124 | −1.84177 | ||||||||
\(974\) | −8.95756e123 | −0.845266 | ||||||||
\(975\) | 1.02781e124 | 0.929435 | ||||||||
\(976\) | 7.09990e123 | 0.615297 | ||||||||
\(977\) | 1.43586e124 | 1.19258 | 0.596292 | − | 0.802768i | \(-0.296640\pi\) | ||||
0.596292 | + | 0.802768i | \(0.296640\pi\) | |||||||
\(978\) | 2.33948e124 | 1.86233 | ||||||||
\(979\) | 5.99842e123 | 0.457673 | ||||||||
\(980\) | 1.20253e123 | 0.0879458 | ||||||||
\(981\) | 1.39032e123 | 0.0974653 | ||||||||
\(982\) | 1.09791e124 | 0.737800 | ||||||||
\(983\) | −1.00422e124 | −0.646933 | −0.323466 | − | 0.946240i | \(-0.604848\pi\) | ||||
−0.323466 | + | 0.946240i | \(0.604848\pi\) | |||||||
\(984\) | −4.54350e123 | −0.280604 | ||||||||
\(985\) | −4.10810e123 | −0.243241 | ||||||||
\(986\) | 7.20161e123 | 0.408825 | ||||||||
\(987\) | −2.70231e124 | −1.47087 | ||||||||
\(988\) | 7.16489e123 | 0.373935 | ||||||||
\(989\) | −8.45051e123 | −0.422899 | ||||||||
\(990\) | −5.58091e122 | −0.0267821 | ||||||||
\(991\) | −3.50545e124 | −1.61319 | −0.806597 | − | 0.591102i | \(-0.798693\pi\) | ||||
−0.806597 | + | 0.591102i | \(0.798693\pi\) | |||||||
\(992\) | −3.87760e124 | −1.71131 | ||||||||
\(993\) | −1.16418e124 | −0.492750 | ||||||||
\(994\) | 5.50435e124 | 2.23445 | ||||||||
\(995\) | −2.22258e123 | −0.0865364 | ||||||||
\(996\) | −1.86979e124 | −0.698279 | ||||||||
\(997\) | −1.71517e124 | −0.614410 | −0.307205 | − | 0.951643i | \(-0.599394\pi\) | ||||
−0.307205 | + | 0.951643i | \(0.599394\pi\) | |||||||
\(998\) | −9.94939e123 | −0.341884 | ||||||||
\(999\) | 5.35156e124 | 1.76406 |
(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 | 1.84.a.a.1.2 | ✓ | 7 | |
3.2 | odd | 2 | 9.84.a.c.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.84.a.a.1.2 | ✓ | 7 | 1.1 | even | 1 | trivial | |
9.84.a.c.1.6 | 7 | 3.2 | odd | 2 |