Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,10,Mod(1,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("384.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(197.773761087\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 3854x^{3} + 12258x^{2} + 2877633x + 16772643 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{29}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(44.2229\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1251.33 | −0.895376 | −0.447688 | − | 0.894190i | \(-0.647752\pi\) | ||||
−0.447688 | + | 0.894190i | \(0.647752\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 561.535 | 0.0883966 | 0.0441983 | − | 0.999023i | \(-0.485927\pi\) | ||||
0.0441983 | + | 0.999023i | \(0.485927\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 80532.1 | 1.65845 | 0.829224 | − | 0.558917i | \(-0.188783\pi\) | ||||
0.829224 | + | 0.558917i | \(0.188783\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 119077. | 1.15633 | 0.578165 | − | 0.815920i | \(-0.303769\pi\) | ||||
0.578165 | + | 0.815920i | \(0.303769\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −101357. | −0.516945 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −603707. | −1.75310 | −0.876549 | − | 0.481313i | \(-0.840160\pi\) | ||||
−0.876549 | + | 0.481313i | \(0.840160\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 722380. | 1.27167 | 0.635835 | − | 0.771825i | \(-0.280656\pi\) | ||||
0.635835 | + | 0.771825i | \(0.280656\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 45484.3 | 0.0510358 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 229161. | 0.170752 | 0.0853760 | − | 0.996349i | \(-0.472791\pi\) | ||||
0.0853760 | + | 0.996349i | \(0.472791\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −387309. | −0.198302 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.34286e6 | 1.92786 | 0.963928 | − | 0.266165i | \(-0.0857564\pi\) | ||||
0.963928 | + | 0.266165i | \(0.0857564\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.26391e6 | 0.829239 | 0.414620 | − | 0.909995i | \(-0.363915\pi\) | ||||
0.414620 | + | 0.909995i | \(0.363915\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.52310e6 | 0.957505 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −702663. | −0.0791482 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.01156e7 | −0.887323 | −0.443662 | − | 0.896194i | \(-0.646321\pi\) | ||||
−0.443662 | + | 0.896194i | \(0.646321\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.64521e6 | 0.667607 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.68312e7 | −0.930224 | −0.465112 | − | 0.885252i | \(-0.653986\pi\) | ||||
−0.465112 | + | 0.885252i | \(0.653986\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.63523e7 | −0.729410 | −0.364705 | − | 0.931123i | \(-0.618830\pi\) | ||||
−0.364705 | + | 0.931123i | \(0.618830\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.20995e6 | −0.298459 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.92462e7 | 1.47208 | 0.736041 | − | 0.676936i | \(-0.236693\pi\) | ||||
0.736041 | + | 0.676936i | \(0.236693\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.00383e7 | −0.992186 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.89003e7 | −1.01215 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.72617e7 | −1.51909 | −0.759543 | − | 0.650457i | \(-0.774577\pi\) | ||||
−0.759543 | + | 0.650457i | \(0.774577\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00772e8 | −1.48493 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.85128e7 | 0.734199 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.14769e8 | 1.23308 | 0.616541 | − | 0.787323i | \(-0.288533\pi\) | ||||
0.616541 | + | 0.787323i | \(0.288533\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.21503e7 | 0.112358 | 0.0561790 | − | 0.998421i | \(-0.482108\pi\) | ||||
0.0561790 | + | 0.998421i | \(0.482108\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.68423e6 | 0.0294655 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.49004e8 | −1.03535 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.43537e8 | −1.47648 | −0.738241 | − | 0.674537i | \(-0.764343\pi\) | ||||
−0.738241 | + | 0.674537i | \(0.764343\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.85620e7 | 0.0985837 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.05574e8 | 0.493056 | 0.246528 | − | 0.969136i | \(-0.420710\pi\) | ||||
0.246528 | + | 0.969136i | \(0.420710\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.19551e7 | −0.131700 | −0.0658502 | − | 0.997830i | \(-0.520976\pi\) | ||||
−0.0658502 | + | 0.997830i | \(0.520976\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.13721e7 | −0.114490 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.52216e7 | 0.146601 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.34767e8 | 1.54470 | 0.772348 | − | 0.635200i | \(-0.219082\pi\) | ||||
0.772348 | + | 0.635200i | \(0.219082\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.54300e8 | 1.74459 | 0.872294 | − | 0.488983i | \(-0.162632\pi\) | ||||
0.872294 | + | 0.488983i | \(0.162632\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.55434e8 | 1.56968 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.94772e8 | 1.11305 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.93697e8 | −1.00302 | −0.501510 | − | 0.865152i | \(-0.667222\pi\) | ||||
−0.501510 | + | 0.865152i | \(0.667222\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.68658e7 | 0.102216 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.45376e8 | 0.478762 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.03932e8 | −1.13862 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.63848e8 | −0.876060 | −0.438030 | − | 0.898960i | \(-0.644324\pi\) | ||||
−0.438030 | + | 0.898960i | \(0.644324\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.28371e8 | 0.552816 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.64929e9 | −1.57707 | −0.788536 | − | 0.614989i | \(-0.789160\pi\) | ||||
−0.788536 | + | 0.614989i | \(0.789160\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.77578e8 | 0.680732 | 0.340366 | − | 0.940293i | \(-0.389449\pi\) | ||||
0.340366 | + | 0.940293i | \(0.389449\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.69157e7 | −0.0456962 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.08863e9 | −0.802887 | −0.401443 | − | 0.915884i | \(-0.631491\pi\) | ||||
−0.401443 | + | 0.915884i | \(0.631491\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.28952e9 | 0.875002 | 0.437501 | − | 0.899218i | \(-0.355864\pi\) | ||||
0.437501 | + | 0.899218i | \(0.355864\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.19360e8 | −0.512296 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.76262e9 | 1.01697 | 0.508483 | − | 0.861072i | \(-0.330207\pi\) | ||||
0.508483 | + | 0.861072i | \(0.330207\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.86755e8 | −0.152887 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.81262e8 | 0.385443 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.39003e8 | −0.154968 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.12747e9 | 1.75045 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.36333e9 | −0.537065 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.92865e9 | 1.07293 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.81850e9 | −0.620293 | −0.310147 | − | 0.950689i | \(-0.600378\pi\) | ||||
−0.310147 | + | 0.950689i | \(0.600378\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.32454e9 | −0.421125 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.95102e9 | 1.46884 | 0.734418 | − | 0.678697i | \(-0.237455\pi\) | ||||
0.734418 | + | 0.678697i | \(0.237455\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.05642e8 | 0.112411 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.65006e8 | −0.172315 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.04562e9 | 0.981165 | 0.490583 | − | 0.871395i | \(-0.336784\pi\) | ||||
0.490583 | + | 0.871395i | \(0.336784\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.05001e9 | 1.37464 | 0.687321 | − | 0.726354i | \(-0.258787\pi\) | ||||
0.687321 | + | 0.726354i | \(0.258787\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.98894e9 | 0.849907 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.58950e9 | 1.91771 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.18831e9 | −1.72615 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.24310e9 | −0.572839 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.15234e9 | 0.523955 | 0.261978 | − | 0.965074i | \(-0.415625\pi\) | ||||
0.261978 | + | 0.965074i | \(0.415625\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.09017e8 | 0.0483711 | 0.0241855 | − | 0.999707i | \(-0.492301\pi\) | ||||
0.0241855 | + | 0.999707i | \(0.492301\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.96092e9 | −0.584366 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.33553e9 | −0.742481 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.07723e10 | −1.41501 | −0.707506 | − | 0.706707i | \(-0.750180\pi\) | ||||
−0.707506 | + | 0.706707i | \(0.750180\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.06820e9 | −0.877045 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.28682e8 | 0.0150939 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.36455e9 | −0.595236 | −0.297618 | − | 0.954685i | \(-0.596192\pi\) | ||||
−0.297618 | + | 0.954685i | \(0.596192\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.16252e9 | −0.857327 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.33915e10 | 1.33231 | 0.666154 | − | 0.745814i | \(-0.267939\pi\) | ||||
0.666154 | + | 0.745814i | \(0.267939\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.57476e9 | 0.337099 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.73953e9 | 0.423890 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.95779e9 | 0.590559 | 0.295280 | − | 0.955411i | \(-0.404587\pi\) | ||||
0.295280 | + | 0.955411i | \(0.404587\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.17488e8 | −0.0175293 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.29632e9 | 0.711920 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.35492e10 | −0.986451 | −0.493225 | − | 0.869902i | \(-0.664182\pi\) | ||||
−0.493225 | + | 0.869902i | \(0.664182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.02270e10 | 0.708261 | 0.354130 | − | 0.935196i | \(-0.384777\pi\) | ||||
0.354130 | + | 0.935196i | \(0.384777\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.84177e8 | 0.0648699 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.26578e10 | 0.794488 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.86178e10 | −2.90742 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.98423e8 | 0.0170119 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.80601e9 | 0.206928 | 0.103464 | − | 0.994633i | \(-0.467007\pi\) | ||||
0.103464 | + | 0.994633i | \(0.467007\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.58965e10 | 0.824695 | 0.412348 | − | 0.911027i | \(-0.364709\pi\) | ||||
0.412348 | + | 0.911027i | \(0.364709\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.20693e10 | −0.597759 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.49591e10 | −0.707630 | −0.353815 | − | 0.935315i | \(-0.615116\pi\) | ||||
−0.353815 | + | 0.935315i | \(0.615116\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.22732e8 | 0.0281489 | 0.0140745 | − | 0.999901i | \(-0.495520\pi\) | ||||
0.0140745 | + | 0.999901i | \(0.495520\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.97265e10 | −0.852448 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.12328e9 | 0.170416 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.10613e10 | 0.832900 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.50353e9 | 0.0569173 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.81747e10 | 2.10900 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.01982e10 | 0.701523 | 0.350761 | − | 0.936465i | \(-0.385923\pi\) | ||||
0.350761 | + | 0.936465i | \(0.385923\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.55153e9 | 0.284666 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.04621e10 | 0.653096 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.39433e9 | 0.0733020 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.58836e9 | −0.0760372 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.18874e10 | −2.02716 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.61462e10 | −0.437218 | −0.218609 | − | 0.975813i | \(-0.570152\pi\) | ||||
−0.218609 | + | 0.975813i | \(0.570152\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.54114e9 | −0.0661008 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.36800e10 | 0.341955 | 0.170978 | − | 0.985275i | \(-0.445307\pi\) | ||||
0.170978 | + | 0.985275i | \(0.445307\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.10441e10 | 1.70714 | 0.853569 | − | 0.520980i | \(-0.174433\pi\) | ||||
0.853569 | + | 0.520980i | \(0.174433\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.66295e9 | 0.0846403 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.55113e9 | 0.212302 | 0.106151 | − | 0.994350i | \(-0.466147\pi\) | ||||
0.106151 | + | 0.994350i | \(0.466147\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.16230e10 | −1.31807 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.33162e10 | 0.891831 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.30873e10 | −0.457702 | −0.228851 | − | 0.973461i | \(-0.573497\pi\) | ||||
−0.228851 | + | 0.973461i | \(0.573497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.68503e10 | −0.321759 | −0.160880 | − | 0.986974i | \(-0.551433\pi\) | ||||
−0.160880 | + | 0.986974i | \(0.551433\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.01009e10 | 0.888379 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.60186e10 | 1.47047 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.10983e10 | 1.00724 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.76046e10 | −0.279959 | −0.139980 | − | 0.990154i | \(-0.544704\pi\) | ||||
−0.139980 | + | 0.990154i | \(0.544704\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.84548e10 | 0.283183 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.11901e10 | 0.906256 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.74568e10 | −0.249613 | −0.124806 | − | 0.992181i | \(-0.539831\pi\) | ||||
−0.124806 | + | 0.992181i | \(0.539831\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.68024e9 | −0.0784364 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.81765e10 | 0.642618 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.18217e10 | 0.667899 | 0.333950 | − | 0.942591i | \(-0.391618\pi\) | ||||
0.333950 | + | 0.942591i | \(0.391618\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.09193e11 | 1.36015 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.80894e10 | −0.579094 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.56192e11 | 1.81876 | 0.909379 | − | 0.415970i | \(-0.136558\pi\) | ||||
0.909379 | + | 0.415970i | \(0.136558\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.59149e10 | 0.629746 | 0.314873 | − | 0.949134i | \(-0.398038\pi\) | ||||
0.314873 | + | 0.949134i | \(0.398038\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.41613e9 | 0.0590143 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.11908e10 | −0.328874 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.68080e10 | 0.171536 | 0.0857682 | − | 0.996315i | \(-0.472666\pi\) | ||||
0.0857682 | + | 0.996315i | \(0.472666\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.79755e10 | 0.276413 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.76924e10 | 0.264961 | 0.132481 | − | 0.991186i | \(-0.457706\pi\) | ||||
0.132481 | + | 0.991186i | \(0.457706\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.56295e9 | 0.0886243 | 0.0443122 | − | 0.999018i | \(-0.485890\pi\) | ||||
0.0443122 | + | 0.999018i | \(0.485890\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.32185e10 | −0.657384 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.45131e9 | −0.0822287 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.45874e11 | 2.07335 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.18716e10 | −0.505793 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.50049e11 | 1.18940 | 0.594700 | − | 0.803947i | \(-0.297271\pi\) | ||||
0.594700 | + | 0.803947i | \(0.297271\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.43614e11 | −1.10407 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.27980e10 | 0.319168 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.72877e10 | 0.197446 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.18241e9 | −0.0644774 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.33593e11 | −0.910522 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.52040e10 | −0.100603 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.83624e10 | −0.374982 | −0.187491 | − | 0.982266i | \(-0.560036\pi\) | ||||
−0.187491 | + | 0.982266i | \(0.560036\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.29838e10 | 0.393021 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.08426e11 | 1.26337 | 0.631685 | − | 0.775225i | \(-0.282364\pi\) | ||||
0.631685 | + | 0.775225i | \(0.282364\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.10734e10 | −0.241886 | −0.120943 | − | 0.992659i | \(-0.538592\pi\) | ||||
−0.120943 | + | 0.992659i | \(0.538592\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.61017e9 | −0.0263827 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.35043e10 | 0.297593 | 0.148796 | − | 0.988868i | \(-0.452460\pi\) | ||||
0.148796 | + | 0.988868i | \(0.452460\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.91336e11 | 3.19725 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.81793e10 | −0.463547 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.36106e11 | −2.22936 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.61195e10 | −0.229303 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.04451e11 | 0.505183 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.76535e10 | 0.130127 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.06052e11 | −0.485615 | −0.242808 | − | 0.970074i | \(-0.578068\pi\) | ||||
−0.242808 | + | 0.970074i | \(0.578068\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.63681e10 | −0.295774 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.04744e11 | 1.32201 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.09163e11 | −0.461042 | −0.230521 | − | 0.973067i | \(-0.574043\pi\) | ||||
−0.230521 | + | 0.973067i | \(0.574043\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.42772e11 | 0.587145 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.43381e11 | 1.37525 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.51429e10 | −0.176103 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.32272e10 | −0.0882694 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.61488e11 | −0.597939 | −0.298970 | − | 0.954263i | \(-0.596643\pi\) | ||||
−0.298970 | + | 0.954263i | \(0.596643\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.05572e11 | 1.82418 | 0.912091 | − | 0.409987i | \(-0.134467\pi\) | ||||
0.912091 | + | 0.409987i | \(0.134467\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.32822e10 | 0.222536 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.61940e11 | −0.555096 | −0.277548 | − | 0.960712i | \(-0.589522\pi\) | ||||
−0.277548 | + | 0.960712i | \(0.589522\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.32108e11 | −0.441470 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.74592e10 | −0.0894708 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.90648e11 | 0.923513 | 0.461756 | − | 0.887007i | \(-0.347219\pi\) | ||||
0.461756 | + | 0.887007i | \(0.347219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.99145e11 | 0.617144 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.34325e11 | 1.01062 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.99862e10 | 0.117921 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.37994e11 | 0.397065 | 0.198533 | − | 0.980094i | \(-0.436382\pi\) | ||||
0.198533 | + | 0.980094i | \(0.436382\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.10430e11 | −0.310075 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.90005e10 | −0.134282 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.34309e11 | −0.359265 | −0.179632 | − | 0.983734i | \(-0.557491\pi\) | ||||
−0.179632 | + | 0.983734i | \(0.557491\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.37220e11 | 0.619457 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.74364e11 | 2.22924 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.43415e11 | −1.10391 | −0.551955 | − | 0.833874i | \(-0.686118\pi\) | ||||
−0.551955 | + | 0.833874i | \(0.686118\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.47299e11 | −0.358126 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.08821e11 | −1.44576 | −0.722878 | − | 0.690976i | \(-0.757181\pi\) | ||||
−0.722878 | + | 0.690976i | \(0.757181\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.65869e10 | −0.131263 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.07288e11 | −0.243137 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.16458e11 | 0.479293 | 0.239646 | − | 0.970860i | \(-0.422968\pi\) | ||||
0.239646 | + | 0.970860i | \(0.422968\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.38346e11 | −0.299345 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.01032e11 | 0.848033 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.69168e11 | −1.38308 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.65679e11 | −1.74904 | −0.874520 | − | 0.484989i | \(-0.838824\pi\) | ||||
−0.874520 | + | 0.484989i | \(0.838824\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.28570e10 | 0.0649007 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.77629e10 | −0.0922445 | −0.0461223 | − | 0.998936i | \(-0.514686\pi\) | ||||
−0.0461223 | + | 0.998936i | \(0.514686\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.07732e11 | 0.958874 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.38655e10 | −0.0994862 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.14626e11 | −1.47158 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.58925e11 | 1.16434 | 0.582172 | − | 0.813066i | \(-0.302203\pi\) | ||||
0.582172 | + | 0.813066i | \(0.302203\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.27695e11 | 0.566476 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.44470e10 | 0.109000 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.43875e11 | −1.56206 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.90051e11 | 0.793650 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.54261e11 | −0.561514 | −0.280757 | − | 0.959779i | \(-0.590585\pi\) | ||||
−0.280757 | + | 0.959779i | \(0.590585\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.97395e11 | 0.926812 | 0.463406 | − | 0.886146i | \(-0.346627\pi\) | ||||
0.463406 | + | 0.886146i | \(0.346627\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.23104e11 | 0.490694 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.33821e11 | 0.347643 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.82284e9 | 0.00993207 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.76749e11 | 1.10719 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.12658e11 | 1.27397 | 0.636987 | − | 0.770875i | \(-0.280181\pi\) | ||||
0.636987 | + | 0.770875i | \(0.280181\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.10826e11 | 0.561645 | 0.280823 | − | 0.959760i | \(-0.409393\pi\) | ||||
0.280823 | + | 0.959760i | \(0.409393\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.44253e11 | −0.996596 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.65541e11 | 0.217140 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.04423e11 | 0.391190 | 0.195595 | − | 0.980685i | \(-0.437336\pi\) | ||||
0.195595 | + | 0.980685i | \(0.437336\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.62691e11 | −0.330729 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.08842e12 | 1.34270 | 0.671352 | − | 0.741139i | \(-0.265714\pi\) | ||||
0.671352 | + | 0.741139i | \(0.265714\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.42908e11 | 0.898080 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.55339e11 | 0.302506 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.78713e11 | −1.13644 | −0.568220 | − | 0.822876i | \(-0.692368\pi\) | ||||
−0.568220 | + | 0.822876i | \(0.692368\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.35545e12 | −1.54273 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.50304e10 | 0.0279271 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.36708e10 | −0.0915214 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.55228e11 | 0.595454 | 0.297727 | − | 0.954651i | \(-0.403771\pi\) | ||||
0.297727 | + | 0.954651i | \(0.403771\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.20835e11 | −0.337384 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.08518e12 | −1.11905 | −0.559524 | − | 0.828814i | \(-0.689016\pi\) | ||||
−0.559524 | + | 0.828814i | \(0.689016\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.82120e11 | 0.689837 | 0.344918 | − | 0.938633i | \(-0.387907\pi\) | ||||
0.344918 | + | 0.938633i | \(0.387907\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.32178e11 | −0.428671 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.55597e12 | 1.51382 | 0.756911 | − | 0.653518i | \(-0.226708\pi\) | ||||
0.756911 | + | 0.653518i | \(0.226708\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.36755e11 | −0.130516 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.72556e11 | −0.816957 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.31689e12 | −1.20969 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.79784e11 | −0.252175 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.72524e11 | −0.506362 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.60423e11 | 0.660002 | 0.330001 | − | 0.943981i | \(-0.392951\pi\) | ||||
0.330001 | + | 0.943981i | \(0.392951\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.20453e12 | −1.02604 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.04232e10 | 0.00871446 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.55822e11 | 0.784403 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.67749e12 | −1.35139 | −0.675693 | − | 0.737183i | \(-0.736155\pi\) | ||||
−0.675693 | + | 0.737183i | \(0.736155\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.34528e11 | −0.343659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.47048e12 | 1.91829 | 0.959145 | − | 0.282914i | \(-0.0913010\pi\) | ||||
0.959145 | + | 0.282914i | \(0.0913010\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.43294e12 | −3.37972 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.61164e11 | −0.494978 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.92838e10 | 0.0435845 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.96398e11 | 0.575013 | 0.287507 | − | 0.957779i | \(-0.407174\pi\) | ||||
0.287507 | + | 0.957779i | \(0.407174\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.08471e12 | 0.769209 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.33174e12 | −0.927605 | −0.463803 | − | 0.885939i | \(-0.653515\pi\) | ||||
−0.463803 | + | 0.885939i | \(0.653515\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.06380e12 | 1.41207 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.89556e11 | 0.194624 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.57766e12 | −1.04180 | −0.520898 | − | 0.853619i | \(-0.674403\pi\) | ||||
−0.520898 | + | 0.853619i | \(0.674403\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.79439e10 | −0.0116419 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.83902e11 | 0.244733 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.73003e11 | −0.609511 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.96590e12 | 2.44137 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.63581e11 | 0.340960 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.00242e12 | −0.596044 | −0.298022 | − | 0.954559i | \(-0.596327\pi\) | ||||
−0.298022 | + | 0.954559i | \(0.596327\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.90824e11 | −0.286859 | −0.143429 | − | 0.989661i | \(-0.545813\pi\) | ||||
−0.143429 | + | 0.989661i | \(0.545813\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.76165e10 | −0.0101205 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.57415e12 | −1.45374 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.74864e12 | −0.970844 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.53002e11 | 0.411027 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.00420e12 | −1.07565 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.36223e12 | 0.718885 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.09749e12 | −0.569528 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.22437e12 | −1.64549 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.88983e12 | −1.95228 | −0.976141 | − | 0.217139i | \(-0.930327\pi\) | ||||
−0.976141 | + | 0.217139i | \(0.930327\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.28384e11 | 0.408915 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.61361e12 | −0.783456 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.08571e12 | 0.996117 | 0.498059 | − | 0.867143i | \(-0.334046\pi\) | ||||
0.498059 | + | 0.867143i | \(0.334046\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.97183e10 | 0.0374526 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.30433e12 | 2.45160 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.00291e11 | 0.136546 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.02529e12 | 0.458698 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.11503e12 | 0.490840 | 0.245420 | − | 0.969417i | \(-0.421074\pi\) | ||||
0.245420 | + | 0.969417i | \(0.421074\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.94718e12 | −0.843438 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.93804e12 | −1.67860 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.53114e12 | 0.642283 | 0.321142 | − | 0.947031i | \(-0.395933\pi\) | ||||
0.321142 | + | 0.947031i | \(0.395933\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.20561e12 | −0.910566 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.41722e10 | 0.00982185 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.50044e12 | 1.39997 | 0.699983 | − | 0.714159i | \(-0.253191\pi\) | ||||
0.699983 | + | 0.714159i | \(0.253191\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.49783e12 | −0.589658 | −0.294829 | − | 0.955550i | \(-0.595263\pi\) | ||||
−0.294829 | + | 0.955550i | \(0.595263\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.08287e11 | 0.119470 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.87562e10 | −0.0338605 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.78055e12 | −1.41992 | −0.709961 | − | 0.704241i | \(-0.751287\pi\) | ||||
−0.709961 | + | 0.704241i | \(0.751287\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.28762e12 | 0.476138 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.23566e11 | 0.154216 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.02737e12 | −2.51932 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.77614e11 | −0.345117 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.05765e12 | 1.41060 | 0.705298 | − | 0.708911i | \(-0.250813\pi\) | ||||
0.705298 | + | 0.708911i | \(0.250813\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.08016e12 | 1.05452 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.21168e12 | −0.408550 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.66492e11 | 0.0552900 | 0.0276450 | − | 0.999618i | \(-0.491199\pi\) | ||||
0.0276450 | + | 0.999618i | \(0.491199\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.24203e11 | 0.138754 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.04413e10 | 0.0162518 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.82896e12 | 0.897855 | 0.448928 | − | 0.893568i | \(-0.351806\pi\) | ||||
0.448928 | + | 0.893568i | \(0.351806\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.28549e12 | −1.65253 | −0.826266 | − | 0.563280i | \(-0.809539\pi\) | ||||
−0.826266 | + | 0.563280i | \(0.809539\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.59785e12 | −0.492161 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.16481e12 | −1.56731 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.17198e12 | −1.24736 | −0.623682 | − | 0.781678i | \(-0.714364\pi\) | ||||
−0.623682 | + | 0.781678i | \(0.714364\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.33985e11 | 0.0983897 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.86407e12 | 1.70221 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.86672e12 | −0.819999 | −0.410000 | − | 0.912086i | \(-0.634471\pi\) | ||||
−0.410000 | + | 0.912086i | \(0.634471\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.70597e12 | 0.480875 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.49703e12 | 0.415859 | 0.207930 | − | 0.978144i | \(-0.433328\pi\) | ||||
0.207930 | + | 0.978144i | \(0.433328\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.86995e12 | 1.60704 | 0.803520 | − | 0.595277i | \(-0.202958\pi\) | ||||
0.803520 | + | 0.595277i | \(0.202958\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.21786e11 | 0.0328612 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.33382e11 | −0.0886636 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.90823e12 | −0.762374 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.71215e12 | 1.21763 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.10683e12 | 1.55556 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.13958e11 | −0.103950 | −0.0519749 | − | 0.998648i | \(-0.516552\pi\) | ||||
−0.0519749 | + | 0.998648i | \(0.516552\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.63605e12 | 0.405024 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.27554e12 | 0.555396 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.76763e12 | −1.14729 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.92674e11 | 0.164352 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.29223e12 | −1.70608 | −0.853040 | − | 0.521845i | \(-0.825244\pi\) | ||||
−0.853040 | + | 0.521845i | \(0.825244\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.25513e12 | −1.67377 | −0.836885 | − | 0.547379i | \(-0.815626\pi\) | ||||
−0.836885 | + | 0.547379i | \(0.815626\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.65743e12 | 0.377065 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.45684e12 | −0.999902 | −0.499951 | − | 0.866054i | \(-0.666649\pi\) | ||||
−0.499951 | + | 0.866054i | \(0.666649\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.24262e12 | 2.04500 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.93941e11 | 0.0423209 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.47800e11 | −0.0963773 | −0.0481886 | − | 0.998838i | \(-0.515345\pi\) | ||||
−0.0481886 | + | 0.998838i | \(0.515345\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.19533e12 | −1.31516 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.09657e11 | −0.0439001 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.30424e12 | 0.889021 | 0.444510 | − | 0.895774i | \(-0.353378\pi\) | ||||
0.444510 | + | 0.895774i | \(0.353378\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.41518e11 | −0.110333 | −0.0551666 | − | 0.998477i | \(-0.517569\pi\) | ||||
−0.0551666 | + | 0.998477i | \(0.517569\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.82288e12 | −1.17038 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.07590e11 | −0.100650 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.68270e12 | 0.329185 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.30784e12 | −0.252428 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.78491e11 | 0.186340 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.18075e12 | 1.53718 | 0.768591 | − | 0.639740i | \(-0.220958\pi\) | ||||
0.768591 | + | 0.639740i | \(0.220958\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.05832e11 | −0.0381633 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.69000e12 | 0.858073 | 0.429036 | − | 0.903287i | \(-0.358853\pi\) | ||||
0.429036 | + | 0.903287i | \(0.358853\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.28927e11 | −0.0774408 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.10808e12 | 0.197428 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.17085e12 | −1.08506 | −0.542528 | − | 0.840038i | \(-0.682533\pi\) | ||||
−0.542528 | + | 0.840038i | \(0.682533\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.06238e12 | −0.878512 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.75457e12 | 0.985616 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.03908e13 | −1.75656 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.51124e12 | −0.919597 | −0.459799 | − | 0.888023i | \(-0.652078\pi\) | ||||
−0.459799 | + | 0.888023i | \(0.652078\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.96699e11 | 0.0488671 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.57053e12 | −1.23082 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.01611e13 | 1.63077 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.73642e11 | 0.122572 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.87462e12 | −1.23168 | −0.615841 | − | 0.787871i | \(-0.711183\pi\) | ||||
−0.615841 | + | 0.787871i | \(0.711183\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.30727e12 | −1.12838 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.99146e12 | −0.760986 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.26135e11 | −0.139408 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.87402e12 | −1.31890 | −0.659451 | − | 0.751747i | \(-0.729211\pi\) | ||||
−0.659451 | + | 0.751747i | \(0.729211\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.50861e12 | 0.514899 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.77121e11 | 0.141594 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.19996e13 | −1.71707 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.87007e12 | −0.264255 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.24721e12 | −1.01132 | −0.505662 | − | 0.862731i | \(-0.668752\pi\) | ||||
−0.505662 | + | 0.862731i | \(0.668752\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.36637e11 | 0.0601745 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.36487e12 | −0.185768 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.84396e12 | −0.382298 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.22078e12 | 0.958693 | 0.479346 | − | 0.877626i | \(-0.340874\pi\) | ||||
0.479346 | + | 0.877626i | \(0.340874\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.87202e12 | 1.27873 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.93345e12 | −1.27096 | −0.635480 | − | 0.772117i | \(-0.719198\pi\) | ||||
−0.635480 | + | 0.772117i | \(0.719198\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.05818e12 | 0.512906 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.96125e13 | −2.44867 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.09416e12 | 0.258292 | 0.129146 | − | 0.991626i | \(-0.458776\pi\) | ||||
0.129146 | + | 0.991626i | \(0.458776\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.96751e12 | 0.848976 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.98254e10 | −0.00359035 | −0.00179518 | − | 0.999998i | \(-0.500571\pi\) | ||||
−0.00179518 | + | 0.999998i | \(0.500571\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.94460e12 | −0.469137 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.94896e12 | 0.581529 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.11306e11 | −0.0709725 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.54090e13 | 1.76765 | 0.883823 | − | 0.467821i | \(-0.154961\pi\) | ||||
0.883823 | + | 0.467821i | \(0.154961\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.42597e12 | −0.161635 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.86681e11 | −0.0433103 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.80995e11 | 0.0643044 | 0.0321522 | − | 0.999483i | \(-0.489764\pi\) | ||||
0.0321522 | + | 0.999483i | \(0.489764\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.49484e12 | 0.163496 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.96002e12 | 0.536108 | 0.268054 | − | 0.963404i | \(-0.413619\pi\) | ||||
0.268054 | + | 0.963404i | \(0.413619\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.24111e11 | 0.0773472 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.95640e12 | 0.523227 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.36664e13 | 1.42585 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.42174e13 | 1.46606 | 0.733032 | − | 0.680194i | \(-0.238104\pi\) | ||||
0.733032 | + | 0.680194i | \(0.238104\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.41400e12 | −0.144114 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.34947e12 | 0.941844 | 0.470922 | − | 0.882175i | \(-0.343921\pi\) | ||||
0.470922 | + | 0.882175i | \(0.343921\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.65145e12 | −0.164440 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.60099e11 | −0.0452853 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.21585e13 | −1.18294 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.50213e12 | 0.817708 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.90230e12 | 0.371016 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.34797e13 | 1.26697 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.37342e12 | −0.313461 | −0.156731 | − | 0.987641i | \(-0.550095\pi\) | ||||
−0.156731 | + | 0.987641i | \(0.550095\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.19756e12 | 0.385612 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.89775e11 | 0.0898964 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.44682e12 | 0.129923 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.84462e12 | 0.785284 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.69600e13 | 1.48890 | 0.744448 | − | 0.667680i | \(-0.232713\pi\) | ||||
0.744448 | + | 0.667680i | \(0.232713\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.97303e13 | −2.58070 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.89524e12 | −0.334340 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.57341e12 | −0.218418 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.61023e11 | −0.0135147 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.26516e13 | 1.05006 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.04004e13 | −0.853652 | −0.426826 | − | 0.904334i | \(-0.640368\pi\) | ||||
−0.426826 | + | 0.904334i | \(0.640368\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.07761e12 | −0.0874717 | −0.0437359 | − | 0.999043i | \(-0.513926\pi\) | ||||
−0.0437359 | + | 0.999043i | \(0.513926\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.52911e12 | 0.363584 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.71280e12 | 0.532959 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.18126e13 | −0.927568 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.38706e11 | 0.0340719 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.51220e12 | 0.116162 | 0.0580812 | − | 0.998312i | \(-0.481502\pi\) | ||||
0.0580812 | + | 0.998312i | \(0.481502\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.40763e12 | 0.334893 | 0.167446 | − | 0.985881i | \(-0.446448\pi\) | ||||
0.167446 | + | 0.985881i | \(0.446448\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.52646e12 | −0.189876 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.34950e13 | −1.00323 | −0.501613 | − | 0.865092i | \(-0.667260\pi\) | ||||
−0.501613 | + | 0.865092i | \(0.667260\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.57710e13 | −1.89512 | −0.947558 | − | 0.319585i | \(-0.896456\pi\) | ||||
−0.947558 | + | 0.319585i | \(0.896456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.36145e12 | 0.0990366 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.41714e13 | 1.73940 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.67571e13 | −1.19292 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.26601e12 | 0.159587 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.79371e12 | 0.264323 | 0.132161 | − | 0.991228i | \(-0.457808\pi\) | ||||
0.132161 | + | 0.991228i | \(0.457808\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.94105e13 | 2.71663 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.24308e12 | 0.152975 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.47319e12 | −0.301830 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.31772e12 | 0.154734 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.74599e11 | 0.0511673 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.31809e12 | −0.151512 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.12640e12 | −0.590240 | −0.295120 | − | 0.955460i | \(-0.595360\pi\) | ||||
−0.295120 | + | 0.955460i | \(0.595360\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.93070e12 | −0.379541 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.91982e12 | −0.311555 | −0.155778 | − | 0.987792i | \(-0.549788\pi\) | ||||
−0.155778 | + | 0.987792i | \(0.549788\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.92238e12 | −0.496462 | −0.248231 | − | 0.968701i | \(-0.579849\pi\) | ||||
−0.248231 | + | 0.968701i | \(0.579849\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.65556e11 | −0.0474748 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.91668e12 | 0.178995 | 0.0894975 | − | 0.995987i | \(-0.471474\pi\) | ||||
0.0894975 | + | 0.995987i | \(0.471474\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.70646e12 | −0.528773 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.99158e13 | 1.19705 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.30659e13 | 2.56180 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.89996e13 | −1.70730 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.01160e12 | −0.292020 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.64454e12 | 0.0948435 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.56703e12 | −0.374861 | −0.187431 | − | 0.982278i | \(-0.560016\pi\) | ||||
−0.187431 | + | 0.982278i | \(0.560016\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.21540e13 | 0.686701 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.07579e13 | −0.601640 | −0.300820 | − | 0.953681i | \(-0.597260\pi\) | ||||
−0.300820 | + | 0.953681i | \(0.597260\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.76747e13 | −1.53201 | −0.766003 | − | 0.642837i | \(-0.777757\pi\) | ||||
−0.766003 | + | 0.642837i | \(0.777757\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.16327e13 | −0.637436 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.30611e13 | 1.25090 | 0.625451 | − | 0.780264i | \(-0.284915\pi\) | ||||
0.625451 | + | 0.780264i | \(0.284915\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.02115e12 | −0.0548318 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.46664e12 | 0.184272 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.55744e13 | 1.87200 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.69545e13 | 0.883244 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.21031e12 | 0.113995 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.13093e13 | 1.59865 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.26805e13 | 2.66311 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.43775e11 | −0.0372260 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.27973e13 | −0.634160 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.86843e12 | 0.336996 | 0.168498 | − | 0.985702i | \(-0.446108\pi\) | ||||
0.168498 | + | 0.985702i | \(0.446108\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.08210e13 | −0.525690 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.69252e13 | 1.77619 | 0.888096 | − | 0.459659i | \(-0.152028\pi\) | ||||
0.888096 | + | 0.459659i | \(0.152028\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.07453e13 | 2.89331 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.23153e12 | −0.0580829 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.78017e12 | 0.129840 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.23010e13 | −0.568880 | −0.284440 | − | 0.958694i | \(-0.591808\pi\) | ||||
−0.284440 | + | 0.958694i | \(0.591808\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.72735e12 | −0.216496 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.25715e13 | 0.570135 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.91785e12 | 0.175958 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.10169e12 | 0.226911 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.34100e13 | 0.590689 | 0.295345 | − | 0.955391i | \(-0.404566\pi\) | ||||
0.295345 | + | 0.955391i | \(0.404566\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.89228e13 | −1.26173 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.68825e13 | 0.729407 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.08367e13 | 2.60323 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.18685e13 | 0.502998 | 0.251499 | − | 0.967858i | \(-0.419077\pi\) | ||||
0.251499 | + | 0.967858i | \(0.419077\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.32695e12 | −0.139653 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.42000e13 | 0.590385 | 0.295193 | − | 0.955438i | \(-0.404616\pi\) | ||||
0.295193 | + | 0.955438i | \(0.404616\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.85706e12 | −0.158838 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.73424e11 | −0.0152321 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.04481e13 | −0.826185 | −0.413092 | − | 0.910689i | \(-0.635551\pi\) | ||||
−0.413092 | + | 0.910689i | \(0.635551\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.80510e12 | −0.152289 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.33385e12 | 0.171815 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.34108e13 | 0.919387 | 0.459694 | − | 0.888078i | \(-0.347959\pi\) | ||||
0.459694 | + | 0.888078i | \(0.347959\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.76256e12 | −0.185279 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.78982e13 | 1.84593 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.27176e12 | 0.0867317 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.25873e12 | −0.312362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.14252e12 | −0.267629 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.98917e13 | −0.738412 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.10773e13 | −1.14294 | −0.571471 | − | 0.820622i | \(-0.693627\pi\) | ||||
−0.571471 | + | 0.820622i | \(0.693627\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.53246e13 | −1.28712 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.30119e13 | 1.19175 | 0.595874 | − | 0.803078i | \(-0.296806\pi\) | ||||
0.595874 | + | 0.803078i | \(0.296806\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.39729e12 | 0.121514 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.73568e12 | −0.132388 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.09262e12 | 0.0734791 | 0.0367396 | − | 0.999325i | \(-0.488303\pi\) | ||||
0.0367396 | + | 0.999325i | \(0.488303\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.78116e13 | −1.66346 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.46054e12 | 0.291667 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.01778e13 | −0.347666 | −0.173833 | − | 0.984775i | \(-0.555615\pi\) | ||||
−0.173833 | + | 0.984775i | \(0.555615\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.87186e13 | 0.633595 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.23993e12 | 0.0751290 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.74732e12 | −0.124548 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.55312e13 | 1.49961 | 0.749803 | − | 0.661661i | \(-0.230148\pi\) | ||||
0.749803 | + | 0.661661i | \(0.230148\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.59020e12 | −0.280370 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.79240e11 | −0.0252039 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.73400e13 | −1.83793 | −0.918966 | − | 0.394337i | \(-0.870974\pi\) | ||||
−0.918966 | + | 0.394337i | \(0.870974\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.37582e12 | −0.170765 |
(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 | 384.10.a.p.1.2 | yes | 5 | |
4.3 | odd | 2 | 384.10.a.l.1.2 | yes | 5 | ||
8.3 | odd | 2 | 384.10.a.m.1.4 | yes | 5 | ||
8.5 | even | 2 | 384.10.a.i.1.4 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.10.a.i.1.4 | ✓ | 5 | 8.5 | even | 2 | ||
384.10.a.l.1.2 | yes | 5 | 4.3 | odd | 2 | ||
384.10.a.m.1.4 | yes | 5 | 8.3 | odd | 2 | ||
384.10.a.p.1.2 | yes | 5 | 1.1 | even | 1 | trivial |