Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,10,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.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: | \(46.8682610909\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 7 x^{14} - 7002 x^{13} + 56252 x^{12} + 19365525 x^{11} - 172593791 x^{10} + \cdots + 15\!\cdots\!80 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{13}\cdot 3^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(25.4969\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 26.4969 | 1.17101 | 0.585505 | − | 0.810669i | \(-0.300896\pi\) | ||||
0.585505 | + | 0.810669i | \(0.300896\pi\) | |||||||
\(3\) | −277.459 | −1.97767 | −0.988835 | − | 0.149017i | \(-0.952389\pi\) | ||||
−0.988835 | + | 0.149017i | \(0.952389\pi\) | |||||||
\(4\) | 190.088 | 0.371265 | ||||||||
\(5\) | 2398.86 | 1.71648 | 0.858241 | − | 0.513247i | \(-0.171557\pi\) | ||||
0.858241 | + | 0.513247i | \(0.171557\pi\) | |||||||
\(6\) | −7351.82 | −2.31587 | ||||||||
\(7\) | −2401.00 | −0.377964 | ||||||||
\(8\) | −8529.69 | −0.736255 | ||||||||
\(9\) | 57300.7 | 2.91118 | ||||||||
\(10\) | 63562.4 | 2.01002 | ||||||||
\(11\) | −76819.0 | −1.58198 | −0.790991 | − | 0.611828i | \(-0.790435\pi\) | ||||
−0.790991 | + | 0.611828i | \(0.790435\pi\) | |||||||
\(12\) | −52741.6 | −0.734240 | ||||||||
\(13\) | 28561.0 | 0.277350 | ||||||||
\(14\) | −63619.2 | −0.442600 | ||||||||
\(15\) | −665585. | −3.39463 | ||||||||
\(16\) | −323336. | −1.23343 | ||||||||
\(17\) | −291393. | −0.846174 | −0.423087 | − | 0.906089i | \(-0.639053\pi\) | ||||
−0.423087 | + | 0.906089i | \(0.639053\pi\) | |||||||
\(18\) | 1.51829e6 | 3.40902 | ||||||||
\(19\) | 459049. | 0.808106 | 0.404053 | − | 0.914736i | \(-0.367601\pi\) | ||||
0.404053 | + | 0.914736i | \(0.367601\pi\) | |||||||
\(20\) | 455993. | 0.637270 | ||||||||
\(21\) | 666180. | 0.747489 | ||||||||
\(22\) | −2.03547e6 | −1.85252 | ||||||||
\(23\) | 711333. | 0.530027 | 0.265013 | − | 0.964245i | \(-0.414624\pi\) | ||||
0.265013 | + | 0.964245i | \(0.414624\pi\) | |||||||
\(24\) | 2.36664e6 | 1.45607 | ||||||||
\(25\) | 3.80139e6 | 1.94631 | ||||||||
\(26\) | 756779. | 0.324780 | ||||||||
\(27\) | −1.04374e7 | −3.77967 | ||||||||
\(28\) | −456401. | −0.140325 | ||||||||
\(29\) | 2.48029e6 | 0.651195 | 0.325598 | − | 0.945508i | \(-0.394435\pi\) | ||||
0.325598 | + | 0.945508i | \(0.394435\pi\) | |||||||
\(30\) | −1.76360e7 | −3.97515 | ||||||||
\(31\) | −108503. | −0.0211015 | −0.0105508 | − | 0.999944i | \(-0.503358\pi\) | ||||
−0.0105508 | + | 0.999944i | \(0.503358\pi\) | |||||||
\(32\) | −4.20020e6 | −0.708101 | ||||||||
\(33\) | 2.13141e7 | 3.12864 | ||||||||
\(34\) | −7.72103e6 | −0.990878 | ||||||||
\(35\) | −5.75966e6 | −0.648769 | ||||||||
\(36\) | 1.08922e7 | 1.08082 | ||||||||
\(37\) | 1.04971e7 | 0.920792 | 0.460396 | − | 0.887714i | \(-0.347707\pi\) | ||||
0.460396 | + | 0.887714i | \(0.347707\pi\) | |||||||
\(38\) | 1.21634e7 | 0.946300 | ||||||||
\(39\) | −7.92452e6 | −0.548507 | ||||||||
\(40\) | −2.04615e7 | −1.26377 | ||||||||
\(41\) | 2.35016e7 | 1.29888 | 0.649442 | − | 0.760411i | \(-0.275003\pi\) | ||||
0.649442 | + | 0.760411i | \(0.275003\pi\) | |||||||
\(42\) | 1.76517e7 | 0.875317 | ||||||||
\(43\) | 1.77396e7 | 0.791291 | 0.395645 | − | 0.918403i | \(-0.370521\pi\) | ||||
0.395645 | + | 0.918403i | \(0.370521\pi\) | |||||||
\(44\) | −1.46024e7 | −0.587335 | ||||||||
\(45\) | 1.37456e8 | 4.99698 | ||||||||
\(46\) | 1.88482e7 | 0.620667 | ||||||||
\(47\) | 2.24965e7 | 0.672474 | 0.336237 | − | 0.941777i | \(-0.390846\pi\) | ||||
0.336237 | + | 0.941777i | \(0.390846\pi\) | |||||||
\(48\) | 8.97125e7 | 2.43931 | ||||||||
\(49\) | 5.76480e6 | 0.142857 | ||||||||
\(50\) | 1.00725e8 | 2.27915 | ||||||||
\(51\) | 8.08498e7 | 1.67345 | ||||||||
\(52\) | 5.42910e6 | 0.102970 | ||||||||
\(53\) | 2.78805e7 | 0.485354 | 0.242677 | − | 0.970107i | \(-0.421975\pi\) | ||||
0.242677 | + | 0.970107i | \(0.421975\pi\) | |||||||
\(54\) | −2.76558e8 | −4.42604 | ||||||||
\(55\) | −1.84278e8 | −2.71544 | ||||||||
\(56\) | 2.04798e7 | 0.278278 | ||||||||
\(57\) | −1.27368e8 | −1.59817 | ||||||||
\(58\) | 6.57201e7 | 0.762556 | ||||||||
\(59\) | 9.28208e7 | 0.997266 | 0.498633 | − | 0.866813i | \(-0.333836\pi\) | ||||
0.498633 | + | 0.866813i | \(0.333836\pi\) | |||||||
\(60\) | −1.26520e8 | −1.26031 | ||||||||
\(61\) | −1.75471e7 | −0.162264 | −0.0811319 | − | 0.996703i | \(-0.525854\pi\) | ||||
−0.0811319 | + | 0.996703i | \(0.525854\pi\) | |||||||
\(62\) | −2.87500e6 | −0.0247101 | ||||||||
\(63\) | −1.37579e8 | −1.10032 | ||||||||
\(64\) | 5.42553e7 | 0.404233 | ||||||||
\(65\) | 6.85137e7 | 0.476067 | ||||||||
\(66\) | 5.64760e8 | 3.66367 | ||||||||
\(67\) | 7.32976e7 | 0.444379 | 0.222189 | − | 0.975004i | \(-0.428680\pi\) | ||||
0.222189 | + | 0.975004i | \(0.428680\pi\) | |||||||
\(68\) | −5.53903e7 | −0.314155 | ||||||||
\(69\) | −1.97366e8 | −1.04822 | ||||||||
\(70\) | −1.52613e8 | −0.759716 | ||||||||
\(71\) | 3.79736e8 | 1.77345 | 0.886726 | − | 0.462295i | \(-0.152974\pi\) | ||||
0.886726 | + | 0.462295i | \(0.152974\pi\) | |||||||
\(72\) | −4.88757e8 | −2.14337 | ||||||||
\(73\) | −2.09156e8 | −0.862022 | −0.431011 | − | 0.902347i | \(-0.641843\pi\) | ||||
−0.431011 | + | 0.902347i | \(0.641843\pi\) | |||||||
\(74\) | 2.78141e8 | 1.07826 | ||||||||
\(75\) | −1.05473e9 | −3.84916 | ||||||||
\(76\) | 8.72597e7 | 0.300022 | ||||||||
\(77\) | 1.84442e8 | 0.597933 | ||||||||
\(78\) | −2.09975e8 | −0.642307 | ||||||||
\(79\) | −2.44184e8 | −0.705335 | −0.352667 | − | 0.935749i | \(-0.614725\pi\) | ||||
−0.352667 | + | 0.935749i | \(0.614725\pi\) | |||||||
\(80\) | −7.75636e8 | −2.11716 | ||||||||
\(81\) | 1.76810e9 | 4.56377 | ||||||||
\(82\) | 6.22721e8 | 1.52101 | ||||||||
\(83\) | −3.43460e8 | −0.794372 | −0.397186 | − | 0.917738i | \(-0.630013\pi\) | ||||
−0.397186 | + | 0.917738i | \(0.630013\pi\) | |||||||
\(84\) | 1.26633e8 | 0.277517 | ||||||||
\(85\) | −6.99011e8 | −1.45244 | ||||||||
\(86\) | 4.70045e8 | 0.926610 | ||||||||
\(87\) | −6.88179e8 | −1.28785 | ||||||||
\(88\) | 6.55242e8 | 1.16474 | ||||||||
\(89\) | −5.92819e8 | −1.00154 | −0.500769 | − | 0.865581i | \(-0.666949\pi\) | ||||
−0.500769 | + | 0.865581i | \(0.666949\pi\) | |||||||
\(90\) | 3.64217e9 | 5.85152 | ||||||||
\(91\) | −6.85750e7 | −0.104828 | ||||||||
\(92\) | 1.35216e8 | 0.196781 | ||||||||
\(93\) | 3.01052e7 | 0.0417319 | ||||||||
\(94\) | 5.96089e8 | 0.787474 | ||||||||
\(95\) | 1.10119e9 | 1.38710 | ||||||||
\(96\) | 1.16539e9 | 1.40039 | ||||||||
\(97\) | 7.56337e7 | 0.0867446 | 0.0433723 | − | 0.999059i | \(-0.486190\pi\) | ||||
0.0433723 | + | 0.999059i | \(0.486190\pi\) | |||||||
\(98\) | 1.52750e8 | 0.167287 | ||||||||
\(99\) | −4.40178e9 | −4.60543 | ||||||||
\(100\) | 7.22598e8 | 0.722598 | ||||||||
\(101\) | −6.85104e8 | −0.655104 | −0.327552 | − | 0.944833i | \(-0.606224\pi\) | ||||
−0.327552 | + | 0.944833i | \(0.606224\pi\) | |||||||
\(102\) | 2.14227e9 | 1.95963 | ||||||||
\(103\) | 6.50294e8 | 0.569302 | 0.284651 | − | 0.958631i | \(-0.408122\pi\) | ||||
0.284651 | + | 0.958631i | \(0.408122\pi\) | |||||||
\(104\) | −2.43616e8 | −0.204200 | ||||||||
\(105\) | 1.59807e9 | 1.28305 | ||||||||
\(106\) | 7.38747e8 | 0.568354 | ||||||||
\(107\) | −5.07743e8 | −0.374470 | −0.187235 | − | 0.982315i | \(-0.559953\pi\) | ||||
−0.187235 | + | 0.982315i | \(0.559953\pi\) | |||||||
\(108\) | −1.98402e9 | −1.40326 | ||||||||
\(109\) | 1.50664e9 | 1.02233 | 0.511164 | − | 0.859483i | \(-0.329215\pi\) | ||||
0.511164 | + | 0.859483i | \(0.329215\pi\) | |||||||
\(110\) | −4.88280e9 | −3.17981 | ||||||||
\(111\) | −2.91252e9 | −1.82102 | ||||||||
\(112\) | 7.76329e8 | 0.466192 | ||||||||
\(113\) | 1.80858e9 | 1.04348 | 0.521740 | − | 0.853105i | \(-0.325283\pi\) | ||||
0.521740 | + | 0.853105i | \(0.325283\pi\) | |||||||
\(114\) | −3.37485e9 | −1.87147 | ||||||||
\(115\) | 1.70639e9 | 0.909782 | ||||||||
\(116\) | 4.71473e8 | 0.241766 | ||||||||
\(117\) | 1.63656e9 | 0.807415 | ||||||||
\(118\) | 2.45947e9 | 1.16781 | ||||||||
\(119\) | 6.99635e8 | 0.319824 | ||||||||
\(120\) | 5.67723e9 | 2.49932 | ||||||||
\(121\) | 3.54321e9 | 1.50267 | ||||||||
\(122\) | −4.64945e8 | −0.190013 | ||||||||
\(123\) | −6.52074e9 | −2.56876 | ||||||||
\(124\) | −2.06251e7 | −0.00783427 | ||||||||
\(125\) | 4.43372e9 | 1.62433 | ||||||||
\(126\) | −3.64542e9 | −1.28849 | ||||||||
\(127\) | −1.90701e9 | −0.650482 | −0.325241 | − | 0.945631i | \(-0.605445\pi\) | ||||
−0.325241 | + | 0.945631i | \(0.605445\pi\) | |||||||
\(128\) | 3.58810e9 | 1.18146 | ||||||||
\(129\) | −4.92202e9 | −1.56491 | ||||||||
\(130\) | 1.81540e9 | 0.557479 | ||||||||
\(131\) | −2.39027e9 | −0.709130 | −0.354565 | − | 0.935031i | \(-0.615371\pi\) | ||||
−0.354565 | + | 0.935031i | \(0.615371\pi\) | |||||||
\(132\) | 4.05156e9 | 1.16155 | ||||||||
\(133\) | −1.10218e9 | −0.305435 | ||||||||
\(134\) | 1.94216e9 | 0.520372 | ||||||||
\(135\) | −2.50378e10 | −6.48774 | ||||||||
\(136\) | 2.48549e9 | 0.622999 | ||||||||
\(137\) | 1.84094e9 | 0.446474 | 0.223237 | − | 0.974764i | \(-0.428338\pi\) | ||||
0.223237 | + | 0.974764i | \(0.428338\pi\) | |||||||
\(138\) | −5.22960e9 | −1.22747 | ||||||||
\(139\) | 8.26362e9 | 1.87760 | 0.938802 | − | 0.344457i | \(-0.111937\pi\) | ||||
0.938802 | + | 0.344457i | \(0.111937\pi\) | |||||||
\(140\) | −1.09484e9 | −0.240865 | ||||||||
\(141\) | −6.24187e9 | −1.32993 | ||||||||
\(142\) | 1.00618e10 | 2.07673 | ||||||||
\(143\) | −2.19403e9 | −0.438763 | ||||||||
\(144\) | −1.85273e10 | −3.59072 | ||||||||
\(145\) | 5.94986e9 | 1.11777 | ||||||||
\(146\) | −5.54200e9 | −1.00944 | ||||||||
\(147\) | −1.59950e9 | −0.282524 | ||||||||
\(148\) | 1.99537e9 | 0.341858 | ||||||||
\(149\) | 2.80217e9 | 0.465754 | 0.232877 | − | 0.972506i | \(-0.425186\pi\) | ||||
0.232877 | + | 0.972506i | \(0.425186\pi\) | |||||||
\(150\) | −2.79471e10 | −4.50741 | ||||||||
\(151\) | 2.12154e9 | 0.332089 | 0.166044 | − | 0.986118i | \(-0.446901\pi\) | ||||
0.166044 | + | 0.986118i | \(0.446901\pi\) | |||||||
\(152\) | −3.91555e9 | −0.594972 | ||||||||
\(153\) | −1.66970e10 | −2.46336 | ||||||||
\(154\) | 4.88716e9 | 0.700186 | ||||||||
\(155\) | −2.60283e8 | −0.0362204 | ||||||||
\(156\) | −1.50635e9 | −0.203642 | ||||||||
\(157\) | −1.32649e10 | −1.74243 | −0.871217 | − | 0.490899i | \(-0.836669\pi\) | ||||
−0.871217 | + | 0.490899i | \(0.836669\pi\) | |||||||
\(158\) | −6.47013e9 | −0.825954 | ||||||||
\(159\) | −7.73569e9 | −0.959869 | ||||||||
\(160\) | −1.00757e10 | −1.21544 | ||||||||
\(161\) | −1.70791e9 | −0.200331 | ||||||||
\(162\) | 4.68492e10 | 5.34422 | ||||||||
\(163\) | 1.20868e10 | 1.34112 | 0.670561 | − | 0.741855i | \(-0.266054\pi\) | ||||
0.670561 | + | 0.741855i | \(0.266054\pi\) | |||||||
\(164\) | 4.46737e9 | 0.482231 | ||||||||
\(165\) | 5.11296e10 | 5.37025 | ||||||||
\(166\) | −9.10063e9 | −0.930218 | ||||||||
\(167\) | 8.10121e9 | 0.805983 | 0.402992 | − | 0.915204i | \(-0.367970\pi\) | ||||
0.402992 | + | 0.915204i | \(0.367970\pi\) | |||||||
\(168\) | −5.68231e9 | −0.550342 | ||||||||
\(169\) | 8.15731e8 | 0.0769231 | ||||||||
\(170\) | −1.85216e10 | −1.70082 | ||||||||
\(171\) | 2.63038e10 | 2.35254 | ||||||||
\(172\) | 3.37208e9 | 0.293779 | ||||||||
\(173\) | 6.17802e9 | 0.524375 | 0.262187 | − | 0.965017i | \(-0.415556\pi\) | ||||
0.262187 | + | 0.965017i | \(0.415556\pi\) | |||||||
\(174\) | −1.82346e10 | −1.50808 | ||||||||
\(175\) | −9.12713e9 | −0.735636 | ||||||||
\(176\) | 2.48383e10 | 1.95126 | ||||||||
\(177\) | −2.57540e10 | −1.97226 | ||||||||
\(178\) | −1.57079e10 | −1.17281 | ||||||||
\(179\) | 8.89717e9 | 0.647759 | 0.323879 | − | 0.946098i | \(-0.395013\pi\) | ||||
0.323879 | + | 0.946098i | \(0.395013\pi\) | |||||||
\(180\) | 2.61287e10 | 1.85521 | ||||||||
\(181\) | 1.03368e10 | 0.715868 | 0.357934 | − | 0.933747i | \(-0.383481\pi\) | ||||
0.357934 | + | 0.933747i | \(0.383481\pi\) | |||||||
\(182\) | −1.81703e9 | −0.122755 | ||||||||
\(183\) | 4.86862e9 | 0.320904 | ||||||||
\(184\) | −6.06745e9 | −0.390235 | ||||||||
\(185\) | 2.51810e10 | 1.58052 | ||||||||
\(186\) | 7.97695e8 | 0.0488685 | ||||||||
\(187\) | 2.23845e10 | 1.33863 | ||||||||
\(188\) | 4.27632e9 | 0.249666 | ||||||||
\(189\) | 2.50601e10 | 1.42858 | ||||||||
\(190\) | 2.91783e10 | 1.62431 | ||||||||
\(191\) | 1.12240e9 | 0.0610238 | 0.0305119 | − | 0.999534i | \(-0.490286\pi\) | ||||
0.0305119 | + | 0.999534i | \(0.490286\pi\) | |||||||
\(192\) | −1.50536e10 | −0.799440 | ||||||||
\(193\) | −1.30436e10 | −0.676692 | −0.338346 | − | 0.941022i | \(-0.609867\pi\) | ||||
−0.338346 | + | 0.941022i | \(0.609867\pi\) | |||||||
\(194\) | 2.00406e9 | 0.101579 | ||||||||
\(195\) | −1.90098e10 | −0.941502 | ||||||||
\(196\) | 1.09582e9 | 0.0530379 | ||||||||
\(197\) | 2.00026e10 | 0.946212 | 0.473106 | − | 0.881005i | \(-0.343133\pi\) | ||||
0.473106 | + | 0.881005i | \(0.343133\pi\) | |||||||
\(198\) | −1.16634e11 | −5.39300 | ||||||||
\(199\) | −1.18798e10 | −0.536995 | −0.268497 | − | 0.963280i | \(-0.586527\pi\) | ||||
−0.268497 | + | 0.963280i | \(0.586527\pi\) | |||||||
\(200\) | −3.24247e10 | −1.43298 | ||||||||
\(201\) | −2.03371e10 | −0.878834 | ||||||||
\(202\) | −1.81532e10 | −0.767134 | ||||||||
\(203\) | −5.95517e9 | −0.246129 | ||||||||
\(204\) | 1.53686e10 | 0.621294 | ||||||||
\(205\) | 5.63770e10 | 2.22951 | ||||||||
\(206\) | 1.72308e10 | 0.666658 | ||||||||
\(207\) | 4.07599e10 | 1.54300 | ||||||||
\(208\) | −9.23479e9 | −0.342091 | ||||||||
\(209\) | −3.52637e10 | −1.27841 | ||||||||
\(210\) | 4.23440e10 | 1.50247 | ||||||||
\(211\) | −3.92872e10 | −1.36452 | −0.682260 | − | 0.731110i | \(-0.739003\pi\) | ||||
−0.682260 | + | 0.731110i | \(0.739003\pi\) | |||||||
\(212\) | 5.29973e9 | 0.180195 | ||||||||
\(213\) | −1.05361e11 | −3.50730 | ||||||||
\(214\) | −1.34536e10 | −0.438508 | ||||||||
\(215\) | 4.25548e10 | 1.35824 | ||||||||
\(216\) | 8.90275e10 | 2.78280 | ||||||||
\(217\) | 2.60516e8 | 0.00797563 | ||||||||
\(218\) | 3.99213e10 | 1.19716 | ||||||||
\(219\) | 5.80324e10 | 1.70479 | ||||||||
\(220\) | −3.50290e10 | −1.00815 | ||||||||
\(221\) | −8.32248e9 | −0.234686 | ||||||||
\(222\) | −7.71728e10 | −2.13244 | ||||||||
\(223\) | −6.01989e10 | −1.63011 | −0.815054 | − | 0.579384i | \(-0.803293\pi\) | ||||
−0.815054 | + | 0.579384i | \(0.803293\pi\) | |||||||
\(224\) | 1.00847e10 | 0.267637 | ||||||||
\(225\) | 2.17822e11 | 5.66605 | ||||||||
\(226\) | 4.79217e10 | 1.22192 | ||||||||
\(227\) | −4.01885e10 | −1.00458 | −0.502291 | − | 0.864699i | \(-0.667509\pi\) | ||||
−0.502291 | + | 0.864699i | \(0.667509\pi\) | |||||||
\(228\) | −2.42110e10 | −0.593344 | ||||||||
\(229\) | −1.10241e10 | −0.264900 | −0.132450 | − | 0.991190i | \(-0.542284\pi\) | ||||
−0.132450 | + | 0.991190i | \(0.542284\pi\) | |||||||
\(230\) | 4.52140e10 | 1.06536 | ||||||||
\(231\) | −5.11753e10 | −1.18251 | ||||||||
\(232\) | −2.11561e10 | −0.479446 | ||||||||
\(233\) | −1.12011e10 | −0.248977 | −0.124489 | − | 0.992221i | \(-0.539729\pi\) | ||||
−0.124489 | + | 0.992221i | \(0.539729\pi\) | |||||||
\(234\) | 4.33640e10 | 0.945491 | ||||||||
\(235\) | 5.39660e10 | 1.15429 | ||||||||
\(236\) | 1.76441e10 | 0.370250 | ||||||||
\(237\) | 6.77511e10 | 1.39492 | ||||||||
\(238\) | 1.85382e10 | 0.374517 | ||||||||
\(239\) | −7.26906e10 | −1.44108 | −0.720540 | − | 0.693414i | \(-0.756106\pi\) | ||||
−0.720540 | + | 0.693414i | \(0.756106\pi\) | |||||||
\(240\) | 2.15207e11 | 4.18703 | ||||||||
\(241\) | 2.78685e10 | 0.532154 | 0.266077 | − | 0.963952i | \(-0.414272\pi\) | ||||
0.266077 | + | 0.963952i | \(0.414272\pi\) | |||||||
\(242\) | 9.38842e10 | 1.75964 | ||||||||
\(243\) | −2.85136e11 | −5.24595 | ||||||||
\(244\) | −3.33550e9 | −0.0602429 | ||||||||
\(245\) | 1.38289e10 | 0.245212 | ||||||||
\(246\) | −1.72780e11 | −3.00805 | ||||||||
\(247\) | 1.31109e10 | 0.224128 | ||||||||
\(248\) | 9.25497e8 | 0.0155361 | ||||||||
\(249\) | 9.52960e10 | 1.57101 | ||||||||
\(250\) | 1.17480e11 | 1.90210 | ||||||||
\(251\) | −7.50781e10 | −1.19394 | −0.596968 | − | 0.802265i | \(-0.703628\pi\) | ||||
−0.596968 | + | 0.802265i | \(0.703628\pi\) | |||||||
\(252\) | −2.61521e10 | −0.408511 | ||||||||
\(253\) | −5.46439e10 | −0.838493 | ||||||||
\(254\) | −5.05298e10 | −0.761721 | ||||||||
\(255\) | 1.93947e11 | 2.87245 | ||||||||
\(256\) | 6.72950e10 | 0.979272 | ||||||||
\(257\) | −9.16533e10 | −1.31054 | −0.655268 | − | 0.755396i | \(-0.727444\pi\) | ||||
−0.655268 | + | 0.755396i | \(0.727444\pi\) | |||||||
\(258\) | −1.30418e11 | −1.83253 | ||||||||
\(259\) | −2.52035e10 | −0.348027 | ||||||||
\(260\) | 1.30236e10 | 0.176747 | ||||||||
\(261\) | 1.42122e11 | 1.89574 | ||||||||
\(262\) | −6.33348e10 | −0.830398 | ||||||||
\(263\) | 4.94093e10 | 0.636807 | 0.318404 | − | 0.947955i | \(-0.396853\pi\) | ||||
0.318404 | + | 0.947955i | \(0.396853\pi\) | |||||||
\(264\) | −1.81803e11 | −2.30347 | ||||||||
\(265\) | 6.68812e10 | 0.833101 | ||||||||
\(266\) | −2.92043e10 | −0.357668 | ||||||||
\(267\) | 1.64483e11 | 1.98071 | ||||||||
\(268\) | 1.39330e10 | 0.164982 | ||||||||
\(269\) | −1.57496e10 | −0.183394 | −0.0916968 | − | 0.995787i | \(-0.529229\pi\) | ||||
−0.0916968 | + | 0.995787i | \(0.529229\pi\) | |||||||
\(270\) | −6.63424e11 | −7.59721 | ||||||||
\(271\) | 1.36371e11 | 1.53589 | 0.767946 | − | 0.640514i | \(-0.221279\pi\) | ||||
0.767946 | + | 0.640514i | \(0.221279\pi\) | |||||||
\(272\) | 9.42178e10 | 1.04369 | ||||||||
\(273\) | 1.90268e10 | 0.207316 | ||||||||
\(274\) | 4.87792e10 | 0.522826 | ||||||||
\(275\) | −2.92019e11 | −3.07903 | ||||||||
\(276\) | −3.75169e10 | −0.389167 | ||||||||
\(277\) | 4.56765e10 | 0.466159 | 0.233079 | − | 0.972458i | \(-0.425120\pi\) | ||||
0.233079 | + | 0.972458i | \(0.425120\pi\) | |||||||
\(278\) | 2.18961e11 | 2.19869 | ||||||||
\(279\) | −6.21730e9 | −0.0614303 | ||||||||
\(280\) | 4.91281e10 | 0.477660 | ||||||||
\(281\) | −1.26483e11 | −1.21019 | −0.605095 | − | 0.796153i | \(-0.706865\pi\) | ||||
−0.605095 | + | 0.796153i | \(0.706865\pi\) | |||||||
\(282\) | −1.65391e11 | −1.55736 | ||||||||
\(283\) | 1.06887e11 | 0.990572 | 0.495286 | − | 0.868730i | \(-0.335063\pi\) | ||||
0.495286 | + | 0.868730i | \(0.335063\pi\) | |||||||
\(284\) | 7.21832e10 | 0.658421 | ||||||||
\(285\) | −3.05537e11 | −2.74322 | ||||||||
\(286\) | −5.81350e10 | −0.513796 | ||||||||
\(287\) | −5.64274e10 | −0.490932 | ||||||||
\(288\) | −2.40674e11 | −2.06141 | ||||||||
\(289\) | −3.36778e10 | −0.283990 | ||||||||
\(290\) | 1.57653e11 | 1.30891 | ||||||||
\(291\) | −2.09853e10 | −0.171552 | ||||||||
\(292\) | −3.97581e10 | −0.320039 | ||||||||
\(293\) | 1.88608e11 | 1.49505 | 0.747525 | − | 0.664234i | \(-0.231242\pi\) | ||||
0.747525 | + | 0.664234i | \(0.231242\pi\) | |||||||
\(294\) | −4.23818e10 | −0.330839 | ||||||||
\(295\) | 2.22664e11 | 1.71179 | ||||||||
\(296\) | −8.95370e10 | −0.677938 | ||||||||
\(297\) | 8.01789e11 | 5.97938 | ||||||||
\(298\) | 7.42489e10 | 0.545402 | ||||||||
\(299\) | 2.03164e10 | 0.147003 | ||||||||
\(300\) | −2.00491e11 | −1.42906 | ||||||||
\(301\) | −4.25928e10 | −0.299080 | ||||||||
\(302\) | 5.62142e10 | 0.388879 | ||||||||
\(303\) | 1.90089e11 | 1.29558 | ||||||||
\(304\) | −1.48427e11 | −0.996740 | ||||||||
\(305\) | −4.20931e10 | −0.278523 | ||||||||
\(306\) | −4.42420e11 | −2.88462 | ||||||||
\(307\) | −1.56897e11 | −1.00807 | −0.504035 | − | 0.863683i | \(-0.668152\pi\) | ||||
−0.504035 | + | 0.863683i | \(0.668152\pi\) | |||||||
\(308\) | 3.50603e10 | 0.221992 | ||||||||
\(309\) | −1.80430e11 | −1.12589 | ||||||||
\(310\) | −6.89671e9 | −0.0424145 | ||||||||
\(311\) | 3.09817e11 | 1.87795 | 0.938974 | − | 0.343989i | \(-0.111778\pi\) | ||||
0.938974 | + | 0.343989i | \(0.111778\pi\) | |||||||
\(312\) | 6.75936e10 | 0.403841 | ||||||||
\(313\) | 7.61815e10 | 0.448642 | 0.224321 | − | 0.974515i | \(-0.427984\pi\) | ||||
0.224321 | + | 0.974515i | \(0.427984\pi\) | |||||||
\(314\) | −3.51480e11 | −2.04041 | ||||||||
\(315\) | −3.30032e11 | −1.88868 | ||||||||
\(316\) | −4.64164e10 | −0.261866 | ||||||||
\(317\) | −1.55190e11 | −0.863170 | −0.431585 | − | 0.902072i | \(-0.642046\pi\) | ||||
−0.431585 | + | 0.902072i | \(0.642046\pi\) | |||||||
\(318\) | −2.04972e11 | −1.12402 | ||||||||
\(319\) | −1.90533e11 | −1.03018 | ||||||||
\(320\) | 1.30151e11 | 0.693859 | ||||||||
\(321\) | 1.40878e11 | 0.740578 | ||||||||
\(322\) | −4.52544e10 | −0.234590 | ||||||||
\(323\) | −1.33764e11 | −0.683798 | ||||||||
\(324\) | 3.36094e11 | 1.69437 | ||||||||
\(325\) | 1.08571e11 | 0.539810 | ||||||||
\(326\) | 3.20264e11 | 1.57047 | ||||||||
\(327\) | −4.18031e11 | −2.02183 | ||||||||
\(328\) | −2.00461e11 | −0.956310 | ||||||||
\(329\) | −5.40142e10 | −0.254171 | ||||||||
\(330\) | 1.35478e12 | 6.28862 | ||||||||
\(331\) | −3.05827e10 | −0.140039 | −0.0700195 | − | 0.997546i | \(-0.522306\pi\) | ||||
−0.0700195 | + | 0.997546i | \(0.522306\pi\) | |||||||
\(332\) | −6.52875e10 | −0.294923 | ||||||||
\(333\) | 6.01491e11 | 2.68059 | ||||||||
\(334\) | 2.14657e11 | 0.943814 | ||||||||
\(335\) | 1.75831e11 | 0.762768 | ||||||||
\(336\) | −2.15400e11 | −0.921973 | ||||||||
\(337\) | −2.62984e11 | −1.11070 | −0.555348 | − | 0.831618i | \(-0.687415\pi\) | ||||
−0.555348 | + | 0.831618i | \(0.687415\pi\) | |||||||
\(338\) | 2.16144e10 | 0.0900777 | ||||||||
\(339\) | −5.01806e11 | −2.06366 | ||||||||
\(340\) | −1.32873e11 | −0.539241 | ||||||||
\(341\) | 8.33509e9 | 0.0333823 | ||||||||
\(342\) | 6.96971e11 | 2.75485 | ||||||||
\(343\) | −1.38413e10 | −0.0539949 | ||||||||
\(344\) | −1.51313e11 | −0.582592 | ||||||||
\(345\) | −4.73453e11 | −1.79925 | ||||||||
\(346\) | 1.63699e11 | 0.614048 | ||||||||
\(347\) | 1.11251e11 | 0.411928 | 0.205964 | − | 0.978560i | \(-0.433967\pi\) | ||||
0.205964 | + | 0.978560i | \(0.433967\pi\) | |||||||
\(348\) | −1.30814e11 | −0.478134 | ||||||||
\(349\) | 3.04891e11 | 1.10009 | 0.550047 | − | 0.835134i | \(-0.314610\pi\) | ||||
0.550047 | + | 0.835134i | \(0.314610\pi\) | |||||||
\(350\) | −2.41841e11 | −0.861438 | ||||||||
\(351\) | −2.98102e11 | −1.04829 | ||||||||
\(352\) | 3.22655e11 | 1.12020 | ||||||||
\(353\) | −5.08802e11 | −1.74407 | −0.872033 | − | 0.489448i | \(-0.837198\pi\) | ||||
−0.872033 | + | 0.489448i | \(0.837198\pi\) | |||||||
\(354\) | −6.82402e11 | −2.30954 | ||||||||
\(355\) | 9.10933e11 | 3.04410 | ||||||||
\(356\) | −1.12688e11 | −0.371836 | ||||||||
\(357\) | −1.94120e11 | −0.632505 | ||||||||
\(358\) | 2.35748e11 | 0.758532 | ||||||||
\(359\) | 4.65758e11 | 1.47991 | 0.739955 | − | 0.672656i | \(-0.234847\pi\) | ||||
0.739955 | + | 0.672656i | \(0.234847\pi\) | |||||||
\(360\) | −1.17246e12 | −3.67905 | ||||||||
\(361\) | −1.11961e11 | −0.346965 | ||||||||
\(362\) | 2.73894e11 | 0.838289 | ||||||||
\(363\) | −9.83097e11 | −2.97178 | ||||||||
\(364\) | −1.30353e10 | −0.0389192 | ||||||||
\(365\) | −5.01736e11 | −1.47964 | ||||||||
\(366\) | 1.29003e11 | 0.375782 | ||||||||
\(367\) | 3.53772e11 | 1.01795 | 0.508975 | − | 0.860781i | \(-0.330024\pi\) | ||||
0.508975 | + | 0.860781i | \(0.330024\pi\) | |||||||
\(368\) | −2.29999e11 | −0.653750 | ||||||||
\(369\) | 1.34666e12 | 3.78128 | ||||||||
\(370\) | 6.67220e11 | 1.85081 | ||||||||
\(371\) | −6.69410e10 | −0.183447 | ||||||||
\(372\) | 5.72263e9 | 0.0154936 | ||||||||
\(373\) | 2.71566e11 | 0.726415 | 0.363208 | − | 0.931708i | \(-0.381682\pi\) | ||||
0.363208 | + | 0.931708i | \(0.381682\pi\) | |||||||
\(374\) | 5.93122e11 | 1.56755 | ||||||||
\(375\) | −1.23018e12 | −3.21238 | ||||||||
\(376\) | −1.91888e11 | −0.495112 | ||||||||
\(377\) | 7.08395e10 | 0.180609 | ||||||||
\(378\) | 6.64017e11 | 1.67288 | ||||||||
\(379\) | 2.57514e11 | 0.641097 | 0.320548 | − | 0.947232i | \(-0.396133\pi\) | ||||
0.320548 | + | 0.947232i | \(0.396133\pi\) | |||||||
\(380\) | 2.09324e11 | 0.514982 | ||||||||
\(381\) | 5.29116e11 | 1.28644 | ||||||||
\(382\) | 2.97403e10 | 0.0714595 | ||||||||
\(383\) | 6.05972e10 | 0.143899 | 0.0719496 | − | 0.997408i | \(-0.477078\pi\) | ||||
0.0719496 | + | 0.997408i | \(0.477078\pi\) | |||||||
\(384\) | −9.95553e11 | −2.33654 | ||||||||
\(385\) | 4.42451e11 | 1.02634 | ||||||||
\(386\) | −3.45617e11 | −0.792413 | ||||||||
\(387\) | 1.01649e12 | 2.30359 | ||||||||
\(388\) | 1.43770e10 | 0.0322053 | ||||||||
\(389\) | 1.65406e11 | 0.366250 | 0.183125 | − | 0.983090i | \(-0.441379\pi\) | ||||
0.183125 | + | 0.983090i | \(0.441379\pi\) | |||||||
\(390\) | −5.03701e11 | −1.10251 | ||||||||
\(391\) | −2.07278e11 | −0.448495 | ||||||||
\(392\) | −4.91720e10 | −0.105179 | ||||||||
\(393\) | 6.63202e11 | 1.40242 | ||||||||
\(394\) | 5.30008e11 | 1.10802 | ||||||||
\(395\) | −5.85762e11 | −1.21069 | ||||||||
\(396\) | −8.36725e11 | −1.70984 | ||||||||
\(397\) | −4.13695e11 | −0.835840 | −0.417920 | − | 0.908484i | \(-0.637241\pi\) | ||||
−0.417920 | + | 0.908484i | \(0.637241\pi\) | |||||||
\(398\) | −3.14778e11 | −0.628827 | ||||||||
\(399\) | 3.05810e11 | 0.604050 | ||||||||
\(400\) | −1.22912e12 | −2.40063 | ||||||||
\(401\) | 5.58295e11 | 1.07824 | 0.539118 | − | 0.842230i | \(-0.318758\pi\) | ||||
0.539118 | + | 0.842230i | \(0.318758\pi\) | |||||||
\(402\) | −5.38871e11 | −1.02912 | ||||||||
\(403\) | −3.09895e9 | −0.00585252 | ||||||||
\(404\) | −1.30230e11 | −0.243217 | ||||||||
\(405\) | 4.24141e12 | 7.83363 | ||||||||
\(406\) | −1.57794e11 | −0.288219 | ||||||||
\(407\) | −8.06377e11 | −1.45668 | ||||||||
\(408\) | −6.89623e11 | −1.23209 | ||||||||
\(409\) | −5.70882e11 | −1.00877 | −0.504384 | − | 0.863480i | \(-0.668280\pi\) | ||||
−0.504384 | + | 0.863480i | \(0.668280\pi\) | |||||||
\(410\) | 1.49382e12 | 2.61078 | ||||||||
\(411\) | −5.10785e11 | −0.882979 | ||||||||
\(412\) | 1.23613e11 | 0.211362 | ||||||||
\(413\) | −2.22863e11 | −0.376931 | ||||||||
\(414\) | 1.08001e12 | 1.80687 | ||||||||
\(415\) | −8.23910e11 | −1.36353 | ||||||||
\(416\) | −1.19962e11 | −0.196392 | ||||||||
\(417\) | −2.29282e12 | −3.71328 | ||||||||
\(418\) | −9.34381e11 | −1.49703 | ||||||||
\(419\) | −8.23728e11 | −1.30563 | −0.652816 | − | 0.757517i | \(-0.726412\pi\) | ||||
−0.652816 | + | 0.757517i | \(0.726412\pi\) | |||||||
\(420\) | 3.03774e11 | 0.476352 | ||||||||
\(421\) | 4.81803e11 | 0.747481 | 0.373741 | − | 0.927533i | \(-0.378075\pi\) | ||||
0.373741 | + | 0.927533i | \(0.378075\pi\) | |||||||
\(422\) | −1.04099e12 | −1.59787 | ||||||||
\(423\) | 1.28907e12 | 1.95769 | ||||||||
\(424\) | −2.37812e11 | −0.357344 | ||||||||
\(425\) | −1.10770e12 | −1.64692 | ||||||||
\(426\) | −2.79175e12 | −4.10709 | ||||||||
\(427\) | 4.21307e10 | 0.0613300 | ||||||||
\(428\) | −9.65158e10 | −0.139028 | ||||||||
\(429\) | 6.08753e11 | 0.867728 | ||||||||
\(430\) | 1.12757e12 | 1.59051 | ||||||||
\(431\) | 2.96390e11 | 0.413729 | 0.206865 | − | 0.978370i | \(-0.433674\pi\) | ||||
0.206865 | + | 0.978370i | \(0.433674\pi\) | |||||||
\(432\) | 3.37477e12 | 4.66195 | ||||||||
\(433\) | 1.61523e11 | 0.220820 | 0.110410 | − | 0.993886i | \(-0.464784\pi\) | ||||
0.110410 | + | 0.993886i | \(0.464784\pi\) | |||||||
\(434\) | 6.90287e9 | 0.00933955 | ||||||||
\(435\) | −1.65084e12 | −2.21057 | ||||||||
\(436\) | 2.86394e11 | 0.379555 | ||||||||
\(437\) | 3.26537e11 | 0.428318 | ||||||||
\(438\) | 1.53768e12 | 1.99633 | ||||||||
\(439\) | 8.16317e11 | 1.04898 | 0.524491 | − | 0.851416i | \(-0.324256\pi\) | ||||
0.524491 | + | 0.851416i | \(0.324256\pi\) | |||||||
\(440\) | 1.57183e12 | 1.99926 | ||||||||
\(441\) | 3.30327e11 | 0.415882 | ||||||||
\(442\) | −2.20520e11 | −0.274820 | ||||||||
\(443\) | 5.85838e11 | 0.722704 | 0.361352 | − | 0.932429i | \(-0.382315\pi\) | ||||
0.361352 | + | 0.932429i | \(0.382315\pi\) | |||||||
\(444\) | −5.53634e11 | −0.676082 | ||||||||
\(445\) | −1.42209e12 | −1.71912 | ||||||||
\(446\) | −1.59509e12 | −1.90887 | ||||||||
\(447\) | −7.77488e11 | −0.921107 | ||||||||
\(448\) | −1.30267e11 | −0.152786 | ||||||||
\(449\) | −4.39931e10 | −0.0510830 | −0.0255415 | − | 0.999674i | \(-0.508131\pi\) | ||||
−0.0255415 | + | 0.999674i | \(0.508131\pi\) | |||||||
\(450\) | 5.77162e12 | 6.63501 | ||||||||
\(451\) | −1.80537e12 | −2.05481 | ||||||||
\(452\) | 3.43788e11 | 0.387408 | ||||||||
\(453\) | −5.88640e11 | −0.656762 | ||||||||
\(454\) | −1.06487e12 | −1.17638 | ||||||||
\(455\) | −1.64502e11 | −0.179936 | ||||||||
\(456\) | 1.08641e12 | 1.17666 | ||||||||
\(457\) | 1.31992e12 | 1.41555 | 0.707776 | − | 0.706437i | \(-0.249699\pi\) | ||||
0.707776 | + | 0.706437i | \(0.249699\pi\) | |||||||
\(458\) | −2.92104e11 | −0.310200 | ||||||||
\(459\) | 3.04138e12 | 3.19826 | ||||||||
\(460\) | 3.24363e11 | 0.337770 | ||||||||
\(461\) | 1.22900e12 | 1.26735 | 0.633677 | − | 0.773598i | \(-0.281545\pi\) | ||||
0.633677 | + | 0.773598i | \(0.281545\pi\) | |||||||
\(462\) | −1.35599e12 | −1.38474 | ||||||||
\(463\) | −1.27424e12 | −1.28866 | −0.644328 | − | 0.764750i | \(-0.722863\pi\) | ||||
−0.644328 | + | 0.764750i | \(0.722863\pi\) | |||||||
\(464\) | −8.01966e11 | −0.803202 | ||||||||
\(465\) | 7.22180e10 | 0.0716320 | ||||||||
\(466\) | −2.96795e11 | −0.291555 | ||||||||
\(467\) | −1.29483e12 | −1.25976 | −0.629880 | − | 0.776692i | \(-0.716896\pi\) | ||||
−0.629880 | + | 0.776692i | \(0.716896\pi\) | |||||||
\(468\) | 3.11091e11 | 0.299765 | ||||||||
\(469\) | −1.75988e11 | −0.167959 | ||||||||
\(470\) | 1.42993e12 | 1.35168 | ||||||||
\(471\) | 3.68048e12 | 3.44596 | ||||||||
\(472\) | −7.91732e11 | −0.734242 | ||||||||
\(473\) | −1.36274e12 | −1.25181 | ||||||||
\(474\) | 1.79520e12 | 1.63346 | ||||||||
\(475\) | 1.74503e12 | 1.57283 | ||||||||
\(476\) | 1.32992e11 | 0.118739 | ||||||||
\(477\) | 1.59757e12 | 1.41295 | ||||||||
\(478\) | −1.92608e12 | −1.68752 | ||||||||
\(479\) | 2.12991e11 | 0.184864 | 0.0924318 | − | 0.995719i | \(-0.470536\pi\) | ||||
0.0924318 | + | 0.995719i | \(0.470536\pi\) | |||||||
\(480\) | 2.79559e12 | 2.40374 | ||||||||
\(481\) | 2.99808e11 | 0.255382 | ||||||||
\(482\) | 7.38431e11 | 0.623158 | ||||||||
\(483\) | 4.73876e11 | 0.396189 | ||||||||
\(484\) | 6.73521e11 | 0.557888 | ||||||||
\(485\) | 1.81434e11 | 0.148896 | ||||||||
\(486\) | −7.55524e12 | −6.14306 | ||||||||
\(487\) | 4.56414e11 | 0.367688 | 0.183844 | − | 0.982955i | \(-0.441146\pi\) | ||||
0.183844 | + | 0.982955i | \(0.441146\pi\) | |||||||
\(488\) | 1.49672e11 | 0.119468 | ||||||||
\(489\) | −3.35360e12 | −2.65230 | ||||||||
\(490\) | 3.66424e11 | 0.287145 | ||||||||
\(491\) | 2.93744e11 | 0.228088 | 0.114044 | − | 0.993476i | \(-0.463620\pi\) | ||||
0.114044 | + | 0.993476i | \(0.463620\pi\) | |||||||
\(492\) | −1.23951e12 | −0.953693 | ||||||||
\(493\) | −7.22740e11 | −0.551024 | ||||||||
\(494\) | 3.47399e11 | 0.262457 | ||||||||
\(495\) | −1.05592e13 | −7.90514 | ||||||||
\(496\) | 3.50829e10 | 0.0260272 | ||||||||
\(497\) | −9.11747e11 | −0.670302 | ||||||||
\(498\) | 2.52505e12 | 1.83966 | ||||||||
\(499\) | 1.32402e12 | 0.955962 | 0.477981 | − | 0.878370i | \(-0.341369\pi\) | ||||
0.477981 | + | 0.878370i | \(0.341369\pi\) | |||||||
\(500\) | 8.42796e11 | 0.603056 | ||||||||
\(501\) | −2.24776e12 | −1.59397 | ||||||||
\(502\) | −1.98934e12 | −1.39811 | ||||||||
\(503\) | −6.97884e11 | −0.486102 | −0.243051 | − | 0.970014i | \(-0.578148\pi\) | ||||
−0.243051 | + | 0.970014i | \(0.578148\pi\) | |||||||
\(504\) | 1.17351e12 | 0.810117 | ||||||||
\(505\) | −1.64347e12 | −1.12447 | ||||||||
\(506\) | −1.44790e12 | −0.981884 | ||||||||
\(507\) | −2.26332e11 | −0.152128 | ||||||||
\(508\) | −3.62498e11 | −0.241501 | ||||||||
\(509\) | −1.38012e11 | −0.0911355 | −0.0455678 | − | 0.998961i | \(-0.514510\pi\) | ||||
−0.0455678 | + | 0.998961i | \(0.514510\pi\) | |||||||
\(510\) | 5.13900e12 | 3.36367 | ||||||||
\(511\) | 5.02184e11 | 0.325814 | ||||||||
\(512\) | −5.39961e10 | −0.0347254 | ||||||||
\(513\) | −4.79127e12 | −3.05438 | ||||||||
\(514\) | −2.42853e12 | −1.53465 | ||||||||
\(515\) | 1.55996e12 | 0.977196 | ||||||||
\(516\) | −9.35616e11 | −0.580997 | ||||||||
\(517\) | −1.72816e12 | −1.06384 | ||||||||
\(518\) | −6.67817e11 | −0.407543 | ||||||||
\(519\) | −1.71415e12 | −1.03704 | ||||||||
\(520\) | −5.84401e11 | −0.350506 | ||||||||
\(521\) | 1.16892e12 | 0.695050 | 0.347525 | − | 0.937671i | \(-0.387022\pi\) | ||||
0.347525 | + | 0.937671i | \(0.387022\pi\) | |||||||
\(522\) | 3.76580e12 | 2.21994 | ||||||||
\(523\) | 1.56229e12 | 0.913068 | 0.456534 | − | 0.889706i | \(-0.349091\pi\) | ||||
0.456534 | + | 0.889706i | \(0.349091\pi\) | |||||||
\(524\) | −4.54361e11 | −0.263275 | ||||||||
\(525\) | 2.53241e12 | 1.45485 | ||||||||
\(526\) | 1.30920e12 | 0.745708 | ||||||||
\(527\) | 3.16171e10 | 0.0178556 | ||||||||
\(528\) | −6.89162e12 | −3.85895 | ||||||||
\(529\) | −1.29516e12 | −0.719072 | ||||||||
\(530\) | 1.77215e12 | 0.975570 | ||||||||
\(531\) | 5.31869e12 | 2.90322 | ||||||||
\(532\) | −2.09511e11 | −0.113398 | ||||||||
\(533\) | 6.71230e11 | 0.360246 | ||||||||
\(534\) | 4.35830e12 | 2.31943 | ||||||||
\(535\) | −1.21800e12 | −0.642771 | ||||||||
\(536\) | −6.25206e11 | −0.327176 | ||||||||
\(537\) | −2.46860e12 | −1.28105 | ||||||||
\(538\) | −4.17316e11 | −0.214756 | ||||||||
\(539\) | −4.42846e11 | −0.225997 | ||||||||
\(540\) | −4.75937e12 | −2.40867 | ||||||||
\(541\) | −1.98015e12 | −0.993827 | −0.496914 | − | 0.867800i | \(-0.665533\pi\) | ||||
−0.496914 | + | 0.867800i | \(0.665533\pi\) | |||||||
\(542\) | 3.61342e12 | 1.79855 | ||||||||
\(543\) | −2.86805e12 | −1.41575 | ||||||||
\(544\) | 1.22391e12 | 0.599177 | ||||||||
\(545\) | 3.61421e12 | 1.75481 | ||||||||
\(546\) | 5.04151e11 | 0.242769 | ||||||||
\(547\) | 2.69781e12 | 1.28845 | 0.644226 | − | 0.764835i | \(-0.277180\pi\) | ||||
0.644226 | + | 0.764835i | \(0.277180\pi\) | |||||||
\(548\) | 3.49940e11 | 0.165760 | ||||||||
\(549\) | −1.00546e12 | −0.472379 | ||||||||
\(550\) | −7.73761e12 | −3.60558 | ||||||||
\(551\) | 1.13858e12 | 0.526235 | ||||||||
\(552\) | 1.68347e12 | 0.771756 | ||||||||
\(553\) | 5.86286e11 | 0.266591 | ||||||||
\(554\) | 1.21029e12 | 0.545877 | ||||||||
\(555\) | −6.98671e12 | −3.12575 | ||||||||
\(556\) | 1.57081e12 | 0.697089 | ||||||||
\(557\) | −1.98888e12 | −0.875509 | −0.437754 | − | 0.899095i | \(-0.644226\pi\) | ||||
−0.437754 | + | 0.899095i | \(0.644226\pi\) | |||||||
\(558\) | −1.64739e11 | −0.0719355 | ||||||||
\(559\) | 5.06661e11 | 0.219465 | ||||||||
\(560\) | 1.86230e12 | 0.800210 | ||||||||
\(561\) | −6.21080e12 | −2.64737 | ||||||||
\(562\) | −3.35141e12 | −1.41714 | ||||||||
\(563\) | 2.31950e12 | 0.972986 | 0.486493 | − | 0.873685i | \(-0.338276\pi\) | ||||
0.486493 | + | 0.873685i | \(0.338276\pi\) | |||||||
\(564\) | −1.18650e12 | −0.493757 | ||||||||
\(565\) | 4.33852e12 | 1.79111 | ||||||||
\(566\) | 2.83218e12 | 1.15997 | ||||||||
\(567\) | −4.24520e12 | −1.72494 | ||||||||
\(568\) | −3.23903e12 | −1.30571 | ||||||||
\(569\) | 3.73307e12 | 1.49300 | 0.746502 | − | 0.665383i | \(-0.231732\pi\) | ||||
0.746502 | + | 0.665383i | \(0.231732\pi\) | |||||||
\(570\) | −8.09578e12 | −3.21234 | ||||||||
\(571\) | 5.07920e11 | 0.199955 | 0.0999777 | − | 0.994990i | \(-0.468123\pi\) | ||||
0.0999777 | + | 0.994990i | \(0.468123\pi\) | |||||||
\(572\) | −4.17058e11 | −0.162897 | ||||||||
\(573\) | −3.11421e11 | −0.120685 | ||||||||
\(574\) | −1.49515e12 | −0.574887 | ||||||||
\(575\) | 2.70405e12 | 1.03160 | ||||||||
\(576\) | 3.10886e12 | 1.17679 | ||||||||
\(577\) | −1.32703e12 | −0.498412 | −0.249206 | − | 0.968451i | \(-0.580170\pi\) | ||||
−0.249206 | + | 0.968451i | \(0.580170\pi\) | |||||||
\(578\) | −8.92359e11 | −0.332556 | ||||||||
\(579\) | 3.61908e12 | 1.33827 | ||||||||
\(580\) | 1.13100e12 | 0.414987 | ||||||||
\(581\) | 8.24646e11 | 0.300245 | ||||||||
\(582\) | −5.56046e11 | −0.200889 | ||||||||
\(583\) | −2.14175e12 | −0.767821 | ||||||||
\(584\) | 1.78404e12 | 0.634668 | ||||||||
\(585\) | 3.92588e12 | 1.38591 | ||||||||
\(586\) | 4.99753e12 | 1.75072 | ||||||||
\(587\) | 1.49468e12 | 0.519607 | 0.259804 | − | 0.965661i | \(-0.416342\pi\) | ||||
0.259804 | + | 0.965661i | \(0.416342\pi\) | |||||||
\(588\) | −3.04045e11 | −0.104891 | ||||||||
\(589\) | −4.98083e10 | −0.0170523 | ||||||||
\(590\) | 5.89991e12 | 2.00452 | ||||||||
\(591\) | −5.54991e12 | −1.87130 | ||||||||
\(592\) | −3.39409e12 | −1.13573 | ||||||||
\(593\) | 5.13938e12 | 1.70673 | 0.853364 | − | 0.521316i | \(-0.174559\pi\) | ||||
0.853364 | + | 0.521316i | \(0.174559\pi\) | |||||||
\(594\) | 2.12449e13 | 7.00191 | ||||||||
\(595\) | 1.67832e12 | 0.548971 | ||||||||
\(596\) | 5.32658e11 | 0.172918 | ||||||||
\(597\) | 3.29616e12 | 1.06200 | ||||||||
\(598\) | 5.38322e11 | 0.172142 | ||||||||
\(599\) | 5.91186e12 | 1.87631 | 0.938153 | − | 0.346222i | \(-0.112536\pi\) | ||||
0.938153 | + | 0.346222i | \(0.112536\pi\) | |||||||
\(600\) | 8.99652e12 | 2.83396 | ||||||||
\(601\) | −2.59431e12 | −0.811123 | −0.405561 | − | 0.914068i | \(-0.632924\pi\) | ||||
−0.405561 | + | 0.914068i | \(0.632924\pi\) | |||||||
\(602\) | −1.12858e12 | −0.350226 | ||||||||
\(603\) | 4.20000e12 | 1.29366 | ||||||||
\(604\) | 4.03278e11 | 0.123293 | ||||||||
\(605\) | 8.49966e12 | 2.57930 | ||||||||
\(606\) | 5.03676e12 | 1.51714 | ||||||||
\(607\) | −9.72998e11 | −0.290913 | −0.145456 | − | 0.989365i | \(-0.546465\pi\) | ||||
−0.145456 | + | 0.989365i | \(0.546465\pi\) | |||||||
\(608\) | −1.92810e12 | −0.572221 | ||||||||
\(609\) | 1.65232e12 | 0.486761 | ||||||||
\(610\) | −1.11534e12 | −0.326153 | ||||||||
\(611\) | 6.42524e11 | 0.186511 | ||||||||
\(612\) | −3.17390e12 | −0.914560 | ||||||||
\(613\) | −3.42096e12 | −0.978535 | −0.489267 | − | 0.872134i | \(-0.662736\pi\) | ||||
−0.489267 | + | 0.872134i | \(0.662736\pi\) | |||||||
\(614\) | −4.15728e12 | −1.18046 | ||||||||
\(615\) | −1.56423e13 | −4.40924 | ||||||||
\(616\) | −1.57324e12 | −0.440231 | ||||||||
\(617\) | 3.21416e12 | 0.892863 | 0.446431 | − | 0.894818i | \(-0.352695\pi\) | ||||
0.446431 | + | 0.894818i | \(0.352695\pi\) | |||||||
\(618\) | −4.78085e12 | −1.31843 | ||||||||
\(619\) | 6.18766e12 | 1.69402 | 0.847010 | − | 0.531577i | \(-0.178400\pi\) | ||||
0.847010 | + | 0.531577i | \(0.178400\pi\) | |||||||
\(620\) | −4.94767e10 | −0.0134474 | ||||||||
\(621\) | −7.42445e12 | −2.00333 | ||||||||
\(622\) | 8.20920e12 | 2.19910 | ||||||||
\(623\) | 1.42336e12 | 0.378545 | ||||||||
\(624\) | 2.56228e12 | 0.676543 | ||||||||
\(625\) | 3.21127e12 | 0.841816 | ||||||||
\(626\) | 2.01858e12 | 0.525364 | ||||||||
\(627\) | 9.78425e12 | 2.52827 | ||||||||
\(628\) | −2.52150e12 | −0.646905 | ||||||||
\(629\) | −3.05878e12 | −0.779150 | ||||||||
\(630\) | −8.74484e12 | −2.21167 | ||||||||
\(631\) | −1.41212e12 | −0.354601 | −0.177301 | − | 0.984157i | \(-0.556737\pi\) | ||||
−0.177301 | + | 0.984157i | \(0.556737\pi\) | |||||||
\(632\) | 2.08281e12 | 0.519306 | ||||||||
\(633\) | 1.09006e13 | 2.69857 | ||||||||
\(634\) | −4.11205e12 | −1.01078 | ||||||||
\(635\) | −4.57463e12 | −1.11654 | ||||||||
\(636\) | −1.47046e12 | −0.356366 | ||||||||
\(637\) | 1.64648e11 | 0.0396214 | ||||||||
\(638\) | −5.04855e12 | −1.20635 | ||||||||
\(639\) | 2.17591e13 | 5.16283 | ||||||||
\(640\) | 8.60735e12 | 2.02796 | ||||||||
\(641\) | −2.12051e12 | −0.496110 | −0.248055 | − | 0.968746i | \(-0.579791\pi\) | ||||
−0.248055 | + | 0.968746i | \(0.579791\pi\) | |||||||
\(642\) | 3.73284e12 | 0.867224 | ||||||||
\(643\) | −4.00523e12 | −0.924012 | −0.462006 | − | 0.886877i | \(-0.652870\pi\) | ||||
−0.462006 | + | 0.886877i | \(0.652870\pi\) | |||||||
\(644\) | −3.24653e11 | −0.0743761 | ||||||||
\(645\) | −1.18072e13 | −2.68614 | ||||||||
\(646\) | −3.54434e12 | −0.800734 | ||||||||
\(647\) | −5.78356e12 | −1.29755 | −0.648777 | − | 0.760978i | \(-0.724719\pi\) | ||||
−0.648777 | + | 0.760978i | \(0.724719\pi\) | |||||||
\(648\) | −1.50813e13 | −3.36010 | ||||||||
\(649\) | −7.13040e12 | −1.57766 | ||||||||
\(650\) | 2.87681e12 | 0.632123 | ||||||||
\(651\) | −7.22825e10 | −0.0157732 | ||||||||
\(652\) | 2.29756e12 | 0.497912 | ||||||||
\(653\) | −8.00952e12 | −1.72384 | −0.861920 | − | 0.507044i | \(-0.830738\pi\) | ||||
−0.861920 | + | 0.507044i | \(0.830738\pi\) | |||||||
\(654\) | −1.10765e13 | −2.36758 | ||||||||
\(655\) | −5.73391e12 | −1.21721 | ||||||||
\(656\) | −7.59891e12 | −1.60208 | ||||||||
\(657\) | −1.19848e13 | −2.50950 | ||||||||
\(658\) | −1.43121e12 | −0.297637 | ||||||||
\(659\) | −1.35625e11 | −0.0280127 | −0.0140063 | − | 0.999902i | \(-0.504459\pi\) | ||||
−0.0140063 | + | 0.999902i | \(0.504459\pi\) | |||||||
\(660\) | 9.71911e12 | 1.99379 | ||||||||
\(661\) | 8.30109e12 | 1.69133 | 0.845666 | − | 0.533713i | \(-0.179204\pi\) | ||||
0.845666 | + | 0.533713i | \(0.179204\pi\) | |||||||
\(662\) | −8.10347e11 | −0.163987 | ||||||||
\(663\) | 2.30915e12 | 0.464132 | ||||||||
\(664\) | 2.92960e12 | 0.584861 | ||||||||
\(665\) | −2.64397e12 | −0.524274 | ||||||||
\(666\) | 1.59377e13 | 3.13900 | ||||||||
\(667\) | 1.76431e12 | 0.345151 | ||||||||
\(668\) | 1.53994e12 | 0.299233 | ||||||||
\(669\) | 1.67027e13 | 3.22382 | ||||||||
\(670\) | 4.65897e12 | 0.893210 | ||||||||
\(671\) | 1.34795e12 | 0.256699 | ||||||||
\(672\) | −2.79809e12 | −0.529298 | ||||||||
\(673\) | 1.36269e12 | 0.256053 | 0.128027 | − | 0.991771i | \(-0.459136\pi\) | ||||
0.128027 | + | 0.991771i | \(0.459136\pi\) | |||||||
\(674\) | −6.96828e12 | −1.30064 | ||||||||
\(675\) | −3.96765e13 | −7.35642 | ||||||||
\(676\) | 1.55060e11 | 0.0285589 | ||||||||
\(677\) | 4.36285e12 | 0.798218 | 0.399109 | − | 0.916904i | \(-0.369320\pi\) | ||||
0.399109 | + | 0.916904i | \(0.369320\pi\) | |||||||
\(678\) | −1.32963e13 | −2.41656 | ||||||||
\(679\) | −1.81597e11 | −0.0327864 | ||||||||
\(680\) | 5.96234e12 | 1.06937 | ||||||||
\(681\) | 1.11507e13 | 1.98673 | ||||||||
\(682\) | 2.20854e11 | 0.0390910 | ||||||||
\(683\) | −3.17805e12 | −0.558815 | −0.279408 | − | 0.960173i | \(-0.590138\pi\) | ||||
−0.279408 | + | 0.960173i | \(0.590138\pi\) | |||||||
\(684\) | 5.00004e12 | 0.873416 | ||||||||
\(685\) | 4.41615e12 | 0.766365 | ||||||||
\(686\) | −3.66752e11 | −0.0632286 | ||||||||
\(687\) | 3.05873e12 | 0.523884 | ||||||||
\(688\) | −5.73585e12 | −0.976000 | ||||||||
\(689\) | 7.96294e11 | 0.134613 | ||||||||
\(690\) | −1.25451e13 | −2.10694 | ||||||||
\(691\) | −1.03260e13 | −1.72299 | −0.861494 | − | 0.507768i | \(-0.830471\pi\) | ||||
−0.861494 | + | 0.507768i | \(0.830471\pi\) | |||||||
\(692\) | 1.17437e12 | 0.194682 | ||||||||
\(693\) | 1.05687e13 | 1.74069 | ||||||||
\(694\) | 2.94781e12 | 0.482372 | ||||||||
\(695\) | 1.98233e13 | 3.22287 | ||||||||
\(696\) | 5.86995e12 | 0.948185 | ||||||||
\(697\) | −6.84821e12 | −1.09908 | ||||||||
\(698\) | 8.07867e12 | 1.28822 | ||||||||
\(699\) | 3.10785e12 | 0.492394 | ||||||||
\(700\) | −1.73496e12 | −0.273116 | ||||||||
\(701\) | −6.94497e12 | −1.08627 | −0.543137 | − | 0.839644i | \(-0.682764\pi\) | ||||
−0.543137 | + | 0.839644i | \(0.682764\pi\) | |||||||
\(702\) | −7.89879e12 | −1.22756 | ||||||||
\(703\) | 4.81869e12 | 0.744097 | ||||||||
\(704\) | −4.16784e12 | −0.639490 | ||||||||
\(705\) | −1.49734e13 | −2.28280 | ||||||||
\(706\) | −1.34817e13 | −2.04232 | ||||||||
\(707\) | 1.64494e12 | 0.247606 | ||||||||
\(708\) | −4.89552e12 | −0.732233 | ||||||||
\(709\) | 9.72796e12 | 1.44582 | 0.722909 | − | 0.690943i | \(-0.242805\pi\) | ||||
0.722909 | + | 0.690943i | \(0.242805\pi\) | |||||||
\(710\) | 2.41369e13 | 3.56467 | ||||||||
\(711\) | −1.39919e13 | −2.05335 | ||||||||
\(712\) | 5.05656e12 | 0.737387 | ||||||||
\(713\) | −7.71818e10 | −0.0111844 | ||||||||
\(714\) | −5.14360e12 | −0.740670 | ||||||||
\(715\) | −5.26316e12 | −0.753129 | ||||||||
\(716\) | 1.69124e12 | 0.240490 | ||||||||
\(717\) | 2.01687e13 | 2.84998 | ||||||||
\(718\) | 1.23412e13 | 1.73299 | ||||||||
\(719\) | 8.85585e12 | 1.23581 | 0.617903 | − | 0.786254i | \(-0.287982\pi\) | ||||
0.617903 | + | 0.786254i | \(0.287982\pi\) | |||||||
\(720\) | −4.44445e13 | −6.16341 | ||||||||
\(721\) | −1.56136e12 | −0.215176 | ||||||||
\(722\) | −2.96663e12 | −0.406299 | ||||||||
\(723\) | −7.73239e12 | −1.05243 | ||||||||
\(724\) | 1.96490e12 | 0.265777 | ||||||||
\(725\) | 9.42854e12 | 1.26743 | ||||||||
\(726\) | −2.60491e13 | −3.47998 | ||||||||
\(727\) | −6.27985e12 | −0.833767 | −0.416883 | − | 0.908960i | \(-0.636878\pi\) | ||||
−0.416883 | + | 0.908960i | \(0.636878\pi\) | |||||||
\(728\) | 5.84923e11 | 0.0771805 | ||||||||
\(729\) | 4.43123e13 | 5.81099 | ||||||||
\(730\) | −1.32945e13 | −1.73268 | ||||||||
\(731\) | −5.16920e12 | −0.669569 | ||||||||
\(732\) | 9.25464e11 | 0.119141 | ||||||||
\(733\) | 5.07216e12 | 0.648970 | 0.324485 | − | 0.945891i | \(-0.394809\pi\) | ||||
0.324485 | + | 0.945891i | \(0.394809\pi\) | |||||||
\(734\) | 9.37389e12 | 1.19203 | ||||||||
\(735\) | −3.83697e12 | −0.484948 | ||||||||
\(736\) | −2.98774e12 | −0.375313 | ||||||||
\(737\) | −5.63065e12 | −0.702999 | ||||||||
\(738\) | 3.56823e13 | 4.42792 | ||||||||
\(739\) | 1.32468e13 | 1.63385 | 0.816923 | − | 0.576747i | \(-0.195678\pi\) | ||||
0.816923 | + | 0.576747i | \(0.195678\pi\) | |||||||
\(740\) | 4.78661e12 | 0.586793 | ||||||||
\(741\) | −3.63774e12 | −0.443252 | ||||||||
\(742\) | −1.77373e12 | −0.214818 | ||||||||
\(743\) | −2.80783e12 | −0.338003 | −0.169002 | − | 0.985616i | \(-0.554054\pi\) | ||||
−0.169002 | + | 0.985616i | \(0.554054\pi\) | |||||||
\(744\) | −2.56788e11 | −0.0307253 | ||||||||
\(745\) | 6.72200e12 | 0.799458 | ||||||||
\(746\) | 7.19566e12 | 0.850640 | ||||||||
\(747\) | −1.96805e13 | −2.31256 | ||||||||
\(748\) | 4.25503e12 | 0.496987 | ||||||||
\(749\) | 1.21909e12 | 0.141536 | ||||||||
\(750\) | −3.25959e13 | −3.76173 | ||||||||
\(751\) | 7.26416e12 | 0.833309 | 0.416654 | − | 0.909065i | \(-0.363203\pi\) | ||||
0.416654 | + | 0.909065i | \(0.363203\pi\) | |||||||
\(752\) | −7.27393e12 | −0.829448 | ||||||||
\(753\) | 2.08311e13 | 2.36121 | ||||||||
\(754\) | 1.87703e12 | 0.211495 | ||||||||
\(755\) | 5.08926e12 | 0.570024 | ||||||||
\(756\) | 4.76363e12 | 0.530383 | ||||||||
\(757\) | −3.92411e12 | −0.434320 | −0.217160 | − | 0.976136i | \(-0.569679\pi\) | ||||
−0.217160 | + | 0.976136i | \(0.569679\pi\) | |||||||
\(758\) | 6.82332e12 | 0.750731 | ||||||||
\(759\) | 1.51615e13 | 1.65826 | ||||||||
\(760\) | −9.39284e12 | −1.02126 | ||||||||
\(761\) | −1.38205e13 | −1.49380 | −0.746901 | − | 0.664935i | \(-0.768459\pi\) | ||||
−0.746901 | + | 0.664935i | \(0.768459\pi\) | |||||||
\(762\) | 1.40200e13 | 1.50643 | ||||||||
\(763\) | −3.61744e12 | −0.386404 | ||||||||
\(764\) | 2.13355e11 | 0.0226560 | ||||||||
\(765\) | −4.00538e13 | −4.22831 | ||||||||
\(766\) | 1.60564e12 | 0.168507 | ||||||||
\(767\) | 2.65105e12 | 0.276592 | ||||||||
\(768\) | −1.86716e13 | −1.93668 | ||||||||
\(769\) | −4.53896e12 | −0.468045 | −0.234023 | − | 0.972231i | \(-0.575189\pi\) | ||||
−0.234023 | + | 0.972231i | \(0.575189\pi\) | |||||||
\(770\) | 1.17236e13 | 1.20186 | ||||||||
\(771\) | 2.54301e13 | 2.59181 | ||||||||
\(772\) | −2.47944e12 | −0.251232 | ||||||||
\(773\) | −1.40549e13 | −1.41586 | −0.707931 | − | 0.706281i | \(-0.750371\pi\) | ||||
−0.707931 | + | 0.706281i | \(0.750371\pi\) | |||||||
\(774\) | 2.69339e13 | 2.69752 | ||||||||
\(775\) | −4.12462e11 | −0.0410702 | ||||||||
\(776\) | −6.45132e11 | −0.0638662 | ||||||||
\(777\) | 6.99296e12 | 0.688282 | ||||||||
\(778\) | 4.38274e12 | 0.428882 | ||||||||
\(779\) | 1.07884e13 | 1.04964 | ||||||||
\(780\) | −3.61353e12 | −0.349547 | ||||||||
\(781\) | −2.91710e13 | −2.80557 | ||||||||
\(782\) | −5.49223e12 | −0.525192 | ||||||||
\(783\) | −2.58877e13 | −2.46131 | ||||||||
\(784\) | −1.86397e12 | −0.176204 | ||||||||
\(785\) | −3.18206e13 | −2.99086 | ||||||||
\(786\) | 1.75728e13 | 1.64225 | ||||||||
\(787\) | −1.34638e13 | −1.25107 | −0.625536 | − | 0.780195i | \(-0.715120\pi\) | ||||
−0.625536 | + | 0.780195i | \(0.715120\pi\) | |||||||
\(788\) | 3.80225e12 | 0.351296 | ||||||||
\(789\) | −1.37091e13 | −1.25939 | ||||||||
\(790\) | −1.55209e13 | −1.41774 | ||||||||
\(791\) | −4.34239e12 | −0.394398 | ||||||||
\(792\) | 3.75458e13 | 3.39077 | ||||||||
\(793\) | −5.01164e11 | −0.0450039 | ||||||||
\(794\) | −1.09617e13 | −0.978777 | ||||||||
\(795\) | −1.85568e13 | −1.64760 | ||||||||
\(796\) | −2.25820e12 | −0.199368 | ||||||||
\(797\) | −1.42488e13 | −1.25088 | −0.625439 | − | 0.780273i | \(-0.715080\pi\) | ||||
−0.625439 | + | 0.780273i | \(0.715080\pi\) | |||||||
\(798\) | 8.10302e12 | 0.707349 | ||||||||
\(799\) | −6.55534e12 | −0.569029 | ||||||||
\(800\) | −1.59666e13 | −1.37819 | ||||||||
\(801\) | −3.39689e13 | −2.91565 | ||||||||
\(802\) | 1.47931e13 | 1.26263 | ||||||||
\(803\) | 1.60672e13 | 1.36370 | ||||||||
\(804\) | −3.86584e12 | −0.326281 | ||||||||
\(805\) | −4.09703e12 | −0.343865 | ||||||||
\(806\) | −8.21128e10 | −0.00685336 | ||||||||
\(807\) | 4.36987e12 | 0.362692 | ||||||||
\(808\) | 5.84372e12 | 0.482324 | ||||||||
\(809\) | 6.34414e12 | 0.520720 | 0.260360 | − | 0.965512i | \(-0.416159\pi\) | ||||
0.260360 | + | 0.965512i | \(0.416159\pi\) | |||||||
\(810\) | 1.12384e14 | 9.17326 | ||||||||
\(811\) | 2.31379e13 | 1.87815 | 0.939073 | − | 0.343719i | \(-0.111687\pi\) | ||||
0.939073 | + | 0.343719i | \(0.111687\pi\) | |||||||
\(812\) | −1.13201e12 | −0.0913790 | ||||||||
\(813\) | −3.78375e13 | −3.03749 | ||||||||
\(814\) | −2.13665e13 | −1.70578 | ||||||||
\(815\) | 2.89946e13 | 2.30201 | ||||||||
\(816\) | −2.61416e13 | −2.06408 | ||||||||
\(817\) | 8.14336e12 | 0.639447 | ||||||||
\(818\) | −1.51266e13 | −1.18128 | ||||||||
\(819\) | −3.92939e12 | −0.305174 | ||||||||
\(820\) | 1.07166e13 | 0.827740 | ||||||||
\(821\) | 9.70997e12 | 0.745888 | 0.372944 | − | 0.927854i | \(-0.378348\pi\) | ||||
0.372944 | + | 0.927854i | \(0.378348\pi\) | |||||||
\(822\) | −1.35343e13 | −1.03398 | ||||||||
\(823\) | −5.67650e12 | −0.431302 | −0.215651 | − | 0.976471i | \(-0.569187\pi\) | ||||
−0.215651 | + | 0.976471i | \(0.569187\pi\) | |||||||
\(824\) | −5.54681e12 | −0.419151 | ||||||||
\(825\) | 8.10234e13 | 6.08930 | ||||||||
\(826\) | −5.90518e12 | −0.441390 | ||||||||
\(827\) | 8.76966e12 | 0.651941 | 0.325970 | − | 0.945380i | \(-0.394309\pi\) | ||||
0.325970 | + | 0.945380i | \(0.394309\pi\) | |||||||
\(828\) | 7.74796e12 | 0.572863 | ||||||||
\(829\) | −9.89738e12 | −0.727821 | −0.363911 | − | 0.931434i | \(-0.618559\pi\) | ||||
−0.363911 | + | 0.931434i | \(0.618559\pi\) | |||||||
\(830\) | −2.18311e13 | −1.59670 | ||||||||
\(831\) | −1.26734e13 | −0.921908 | ||||||||
\(832\) | 1.54959e12 | 0.112114 | ||||||||
\(833\) | −1.67982e12 | −0.120882 | ||||||||
\(834\) | −6.07527e13 | −4.34829 | ||||||||
\(835\) | 1.94336e13 | 1.38346 | ||||||||
\(836\) | −6.70320e12 | −0.474629 | ||||||||
\(837\) | 1.13249e12 | 0.0797570 | ||||||||
\(838\) | −2.18263e13 | −1.52891 | ||||||||
\(839\) | 5.43436e12 | 0.378634 | 0.189317 | − | 0.981916i | \(-0.439373\pi\) | ||||
0.189317 | + | 0.981916i | \(0.439373\pi\) | |||||||
\(840\) | −1.36310e13 | −0.944653 | ||||||||
\(841\) | −8.35531e12 | −0.575945 | ||||||||
\(842\) | 1.27663e13 | 0.875308 | ||||||||
\(843\) | 3.50939e13 | 2.39336 | ||||||||
\(844\) | −7.46801e12 | −0.506599 | ||||||||
\(845\) | 1.95682e12 | 0.132037 | ||||||||
\(846\) | 3.41563e13 | 2.29247 | ||||||||
\(847\) | −8.50725e12 | −0.567955 | ||||||||
\(848\) | −9.01474e12 | −0.598649 | ||||||||
\(849\) | −2.96568e13 | −1.95902 | ||||||||
\(850\) | −2.93506e13 | −1.92856 | ||||||||
\(851\) | 7.46694e12 | 0.488044 | ||||||||
\(852\) | −2.00279e13 | −1.30214 | ||||||||
\(853\) | −5.85034e12 | −0.378364 | −0.189182 | − | 0.981942i | \(-0.560584\pi\) | ||||
−0.189182 | + | 0.981942i | \(0.560584\pi\) | |||||||
\(854\) | 1.11633e12 | 0.0718180 | ||||||||
\(855\) | 6.30992e13 | 4.03809 | ||||||||
\(856\) | 4.33089e12 | 0.275705 | ||||||||
\(857\) | 2.25901e13 | 1.43056 | 0.715278 | − | 0.698840i | \(-0.246300\pi\) | ||||
0.715278 | + | 0.698840i | \(0.246300\pi\) | |||||||
\(858\) | 1.61301e13 | 1.01612 | ||||||||
\(859\) | −2.68487e13 | −1.68249 | −0.841246 | − | 0.540652i | \(-0.818178\pi\) | ||||
−0.841246 | + | 0.540652i | \(0.818178\pi\) | |||||||
\(860\) | 8.08915e12 | 0.504266 | ||||||||
\(861\) | 1.56563e13 | 0.970901 | ||||||||
\(862\) | 7.85343e12 | 0.484481 | ||||||||
\(863\) | 1.71044e13 | 1.04968 | 0.524842 | − | 0.851199i | \(-0.324124\pi\) | ||||
0.524842 | + | 0.851199i | \(0.324124\pi\) | |||||||
\(864\) | 4.38391e13 | 2.67639 | ||||||||
\(865\) | 1.48202e13 | 0.900080 | ||||||||
\(866\) | 4.27985e12 | 0.258582 | ||||||||
\(867\) | 9.34422e12 | 0.561639 | ||||||||
\(868\) | 4.95209e10 | 0.00296108 | ||||||||
\(869\) | 1.87580e13 | 1.11583 | ||||||||
\(870\) | −4.37423e13 | −2.58860 | ||||||||
\(871\) | 2.09345e12 | 0.123249 | ||||||||
\(872\) | −1.28512e13 | −0.752694 | ||||||||
\(873\) | 4.33386e12 | 0.252529 | ||||||||
\(874\) | 8.65224e12 | 0.501565 | ||||||||
\(875\) | −1.06454e13 | −0.613938 | ||||||||
\(876\) | 1.10312e13 | 0.632931 | ||||||||
\(877\) | 9.99257e12 | 0.570400 | 0.285200 | − | 0.958468i | \(-0.407940\pi\) | ||||
0.285200 | + | 0.958468i | \(0.407940\pi\) | |||||||
\(878\) | 2.16299e13 | 1.22837 | ||||||||
\(879\) | −5.23310e13 | −2.95671 | ||||||||
\(880\) | 5.95836e13 | 3.34930 | ||||||||
\(881\) | −2.34044e13 | −1.30890 | −0.654449 | − | 0.756106i | \(-0.727100\pi\) | ||||
−0.654449 | + | 0.756106i | \(0.727100\pi\) | |||||||
\(882\) | 8.75265e12 | 0.487002 | ||||||||
\(883\) | 2.46363e13 | 1.36381 | 0.681904 | − | 0.731442i | \(-0.261152\pi\) | ||||
0.681904 | + | 0.731442i | \(0.261152\pi\) | |||||||
\(884\) | −1.58200e12 | −0.0871309 | ||||||||
\(885\) | −6.17801e13 | −3.38535 | ||||||||
\(886\) | 1.55229e13 | 0.846294 | ||||||||
\(887\) | −1.97388e12 | −0.107069 | −0.0535346 | − | 0.998566i | \(-0.517049\pi\) | ||||
−0.0535346 | + | 0.998566i | \(0.517049\pi\) | |||||||
\(888\) | 2.48429e13 | 1.34074 | ||||||||
\(889\) | 4.57872e12 | 0.245859 | ||||||||
\(890\) | −3.76810e13 | −2.01311 | ||||||||
\(891\) | −1.35823e14 | −7.21980 | ||||||||
\(892\) | −1.14431e13 | −0.605203 | ||||||||
\(893\) | 1.03270e13 | 0.543430 | ||||||||
\(894\) | −2.06011e13 | −1.07863 | ||||||||
\(895\) | 2.13430e13 | 1.11187 | ||||||||
\(896\) | −8.61504e12 | −0.446551 | ||||||||
\(897\) | −5.63697e12 | −0.290723 | ||||||||
\(898\) | −1.16568e12 | −0.0598187 | ||||||||
\(899\) | −2.69119e11 | −0.0137412 | ||||||||
\(900\) | 4.14053e13 | 2.10361 | ||||||||
\(901\) | −8.12418e12 | −0.410694 | ||||||||
\(902\) | −4.78368e13 | −2.40621 | ||||||||
\(903\) | 1.18178e13 | 0.591481 | ||||||||
\(904\) | −1.54266e13 | −0.768267 | ||||||||
\(905\) | 2.47965e13 | 1.22878 | ||||||||
\(906\) | −1.55972e13 | −0.769075 | ||||||||
\(907\) | −2.09991e13 | −1.03031 | −0.515156 | − | 0.857097i | \(-0.672266\pi\) | ||||
−0.515156 | + | 0.857097i | \(0.672266\pi\) | |||||||
\(908\) | −7.63934e12 | −0.372966 | ||||||||
\(909\) | −3.92569e13 | −1.90712 | ||||||||
\(910\) | −4.35879e12 | −0.210707 | ||||||||
\(911\) | 3.25895e12 | 0.156764 | 0.0783818 | − | 0.996923i | \(-0.475025\pi\) | ||||
0.0783818 | + | 0.996923i | \(0.475025\pi\) | |||||||
\(912\) | 4.11825e13 | 1.97122 | ||||||||
\(913\) | 2.63842e13 | 1.25668 | ||||||||
\(914\) | 3.49739e13 | 1.65763 | ||||||||
\(915\) | 1.16791e13 | 0.550827 | ||||||||
\(916\) | −2.09554e12 | −0.0983481 | ||||||||
\(917\) | 5.73903e12 | 0.268026 | ||||||||
\(918\) | 8.05873e13 | 3.74520 | ||||||||
\(919\) | −3.55979e13 | −1.64628 | −0.823142 | − | 0.567835i | \(-0.807781\pi\) | ||||
−0.823142 | + | 0.567835i | \(0.807781\pi\) | |||||||
\(920\) | −1.45549e13 | −0.669831 | ||||||||
\(921\) | 4.35324e13 | 1.99363 | ||||||||
\(922\) | 3.25648e13 | 1.48408 | ||||||||
\(923\) | 1.08456e13 | 0.491867 | ||||||||
\(924\) | −9.72779e12 | −0.439026 | ||||||||
\(925\) | 3.99036e13 | 1.79215 | ||||||||
\(926\) | −3.37635e13 | −1.50903 | ||||||||
\(927\) | 3.72623e13 | 1.65734 | ||||||||
\(928\) | −1.04177e13 | −0.461112 | ||||||||
\(929\) | −1.74409e12 | −0.0768244 | −0.0384122 | − | 0.999262i | \(-0.512230\pi\) | ||||
−0.0384122 | + | 0.999262i | \(0.512230\pi\) | |||||||
\(930\) | 1.91356e12 | 0.0838818 | ||||||||
\(931\) | 2.64633e12 | 0.115444 | ||||||||
\(932\) | −2.12919e12 | −0.0924366 | ||||||||
\(933\) | −8.59616e13 | −3.71396 | ||||||||
\(934\) | −3.43091e13 | −1.47519 | ||||||||
\(935\) | 5.36973e13 | 2.29774 | ||||||||
\(936\) | −1.39594e13 | −0.594463 | ||||||||
\(937\) | 6.94275e12 | 0.294241 | 0.147121 | − | 0.989119i | \(-0.452999\pi\) | ||||
0.147121 | + | 0.989119i | \(0.452999\pi\) | |||||||
\(938\) | −4.66313e12 | −0.196682 | ||||||||
\(939\) | −2.11373e13 | −0.887266 | ||||||||
\(940\) | 1.02583e13 | 0.428547 | ||||||||
\(941\) | −9.17701e12 | −0.381547 | −0.190773 | − | 0.981634i | \(-0.561100\pi\) | ||||
−0.190773 | + | 0.981634i | \(0.561100\pi\) | |||||||
\(942\) | 9.75213e13 | 4.03525 | ||||||||
\(943\) | 1.67175e13 | 0.688443 | ||||||||
\(944\) | −3.00123e13 | −1.23006 | ||||||||
\(945\) | 6.01157e13 | 2.45214 | ||||||||
\(946\) | −3.61084e13 | −1.46588 | ||||||||
\(947\) | 3.03420e13 | 1.22594 | 0.612971 | − | 0.790105i | \(-0.289974\pi\) | ||||
0.612971 | + | 0.790105i | \(0.289974\pi\) | |||||||
\(948\) | 1.28787e13 | 0.517885 | ||||||||
\(949\) | −5.97371e12 | −0.239082 | ||||||||
\(950\) | 4.62378e13 | 1.84180 | ||||||||
\(951\) | 4.30588e13 | 1.70707 | ||||||||
\(952\) | −5.96767e12 | −0.235472 | ||||||||
\(953\) | 2.76636e13 | 1.08640 | 0.543201 | − | 0.839603i | \(-0.317212\pi\) | ||||
0.543201 | + | 0.839603i | \(0.317212\pi\) | |||||||
\(954\) | 4.23307e13 | 1.65458 | ||||||||
\(955\) | 2.69249e12 | 0.104746 | ||||||||
\(956\) | −1.38176e13 | −0.535023 | ||||||||
\(957\) | 5.28652e13 | 2.03735 | ||||||||
\(958\) | 5.64361e12 | 0.216477 | ||||||||
\(959\) | −4.42009e12 | −0.168751 | ||||||||
\(960\) | −3.61115e13 | −1.37222 | ||||||||
\(961\) | −2.64278e13 | −0.999555 | ||||||||
\(962\) | 7.94399e12 | 0.299055 | ||||||||
\(963\) | −2.90940e13 | −1.09015 | ||||||||
\(964\) | 5.29747e12 | 0.197570 | ||||||||
\(965\) | −3.12898e13 | −1.16153 | ||||||||
\(966\) | 1.25563e13 | 0.463942 | ||||||||
\(967\) | 6.69223e12 | 0.246123 | 0.123061 | − | 0.992399i | \(-0.460729\pi\) | ||||
0.123061 | + | 0.992399i | \(0.460729\pi\) | |||||||
\(968\) | −3.02225e13 | −1.10635 | ||||||||
\(969\) | 3.71141e13 | 1.35233 | ||||||||
\(970\) | 4.80746e12 | 0.174358 | ||||||||
\(971\) | −2.87538e13 | −1.03803 | −0.519013 | − | 0.854766i | \(-0.673701\pi\) | ||||
−0.519013 | + | 0.854766i | \(0.673701\pi\) | |||||||
\(972\) | −5.42009e13 | −1.94764 | ||||||||
\(973\) | −1.98410e13 | −0.709668 | ||||||||
\(974\) | 1.20936e13 | 0.430566 | ||||||||
\(975\) | −3.01242e13 | −1.06756 | ||||||||
\(976\) | 5.67361e12 | 0.200141 | ||||||||
\(977\) | −1.71791e13 | −0.603219 | −0.301609 | − | 0.953432i | \(-0.597524\pi\) | ||||
−0.301609 | + | 0.953432i | \(0.597524\pi\) | |||||||
\(978\) | −8.88602e13 | −3.10587 | ||||||||
\(979\) | 4.55398e13 | 1.58441 | ||||||||
\(980\) | 2.62871e12 | 0.0910386 | ||||||||
\(981\) | 8.63315e13 | 2.97618 | ||||||||
\(982\) | 7.78332e12 | 0.267093 | ||||||||
\(983\) | −4.52401e13 | −1.54537 | −0.772685 | − | 0.634789i | \(-0.781087\pi\) | ||||
−0.772685 | + | 0.634789i | \(0.781087\pi\) | |||||||
\(984\) | 5.56199e13 | 1.89126 | ||||||||
\(985\) | 4.79834e13 | 1.62416 | ||||||||
\(986\) | −1.91504e13 | −0.645255 | ||||||||
\(987\) | 1.49867e13 | 0.502667 | ||||||||
\(988\) | 2.49222e12 | 0.0832110 | ||||||||
\(989\) | 1.26188e13 | 0.419405 | ||||||||
\(990\) | −2.79788e14 | −9.25700 | ||||||||
\(991\) | −4.49657e13 | −1.48098 | −0.740491 | − | 0.672066i | \(-0.765407\pi\) | ||||
−0.740491 | + | 0.672066i | \(0.765407\pi\) | |||||||
\(992\) | 4.55735e11 | 0.0149420 | ||||||||
\(993\) | 8.48544e12 | 0.276951 | ||||||||
\(994\) | −2.41585e13 | −0.784930 | ||||||||
\(995\) | −2.84979e13 | −0.921742 | ||||||||
\(996\) | 1.81146e13 | 0.583260 | ||||||||
\(997\) | 4.39312e13 | 1.40814 | 0.704069 | − | 0.710132i | \(-0.251365\pi\) | ||||
0.704069 | + | 0.710132i | \(0.251365\pi\) | |||||||
\(998\) | 3.50824e13 | 1.11944 | ||||||||
\(999\) | −1.09562e14 | −3.48029 |
(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 | 91.10.a.d.1.11 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.10.a.d.1.11 | ✓ | 15 | 1.1 | even | 1 | trivial |