Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −26.9492 | −1.19100 | −0.595498 | − | 0.803357i | \(-0.703045\pi\) | ||||
−0.595498 | + | 0.803357i | \(0.703045\pi\) | |||||||
\(3\) | 20.4039 | 0.145434 | 0.0727172 | − | 0.997353i | \(-0.476833\pi\) | ||||
0.0727172 | + | 0.997353i | \(0.476833\pi\) | |||||||
\(4\) | 214.258 | 0.418472 | ||||||||
\(5\) | 1220.88 | 0.873592 | 0.436796 | − | 0.899561i | \(-0.356113\pi\) | ||||
0.436796 | + | 0.899561i | \(0.356113\pi\) | |||||||
\(6\) | −549.868 | −0.173212 | ||||||||
\(7\) | −4892.40 | −0.770160 | −0.385080 | − | 0.922883i | \(-0.625826\pi\) | ||||
−0.385080 | + | 0.922883i | \(0.625826\pi\) | |||||||
\(8\) | 8023.91 | 0.692598 | ||||||||
\(9\) | −19266.7 | −0.978849 | ||||||||
\(10\) | −32901.7 | −1.04044 | ||||||||
\(11\) | 90391.9 | 1.86150 | 0.930749 | − | 0.365659i | \(-0.119156\pi\) | ||||
0.930749 | + | 0.365659i | \(0.119156\pi\) | |||||||
\(12\) | 4371.69 | 0.0608602 | ||||||||
\(13\) | 114220. | 1.10916 | 0.554582 | − | 0.832129i | \(-0.312878\pi\) | ||||
0.554582 | + | 0.832129i | \(0.312878\pi\) | |||||||
\(14\) | 131846. | 0.917258 | ||||||||
\(15\) | 24910.7 | 0.127050 | ||||||||
\(16\) | −325938. | −1.24335 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 519221. | 1.16581 | ||||||||
\(19\) | 864034. | 1.52104 | 0.760518 | − | 0.649317i | \(-0.224945\pi\) | ||||
0.760518 | + | 0.649317i | \(0.224945\pi\) | |||||||
\(20\) | 261583. | 0.365574 | ||||||||
\(21\) | −99824.0 | −0.112008 | ||||||||
\(22\) | −2.43599e6 | −2.21704 | ||||||||
\(23\) | 1.60148e6 | 1.19329 | 0.596646 | − | 0.802505i | \(-0.296500\pi\) | ||||
0.596646 | + | 0.802505i | \(0.296500\pi\) | |||||||
\(24\) | 163719. | 0.100728 | ||||||||
\(25\) | −462573. | −0.236837 | ||||||||
\(26\) | −3.07812e6 | −1.32101 | ||||||||
\(27\) | −794725. | −0.287793 | ||||||||
\(28\) | −1.04823e6 | −0.322290 | ||||||||
\(29\) | 1.73683e6 | 0.456002 | 0.228001 | − | 0.973661i | \(-0.426781\pi\) | ||||
0.228001 | + | 0.973661i | \(0.426781\pi\) | |||||||
\(30\) | −671323. | −0.151316 | ||||||||
\(31\) | −1.24125e6 | −0.241397 | −0.120699 | − | 0.992689i | \(-0.538513\pi\) | ||||
−0.120699 | + | 0.992689i | \(0.538513\pi\) | |||||||
\(32\) | 4.67550e6 | 0.788231 | ||||||||
\(33\) | 1.84435e6 | 0.270726 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.97305e6 | −0.672806 | ||||||||
\(36\) | −4.12803e6 | −0.409621 | ||||||||
\(37\) | −762881. | −0.0669189 | −0.0334595 | − | 0.999440i | \(-0.510652\pi\) | ||||
−0.0334595 | + | 0.999440i | \(0.510652\pi\) | |||||||
\(38\) | −2.32850e7 | −1.81155 | ||||||||
\(39\) | 2.33052e6 | 0.161311 | ||||||||
\(40\) | 9.79625e6 | 0.605048 | ||||||||
\(41\) | 2.60499e7 | 1.43972 | 0.719862 | − | 0.694117i | \(-0.244205\pi\) | ||||
0.719862 | + | 0.694117i | \(0.244205\pi\) | |||||||
\(42\) | 2.69017e6 | 0.133401 | ||||||||
\(43\) | 4.19945e7 | 1.87320 | 0.936599 | − | 0.350402i | \(-0.113955\pi\) | ||||
0.936599 | + | 0.350402i | \(0.113955\pi\) | |||||||
\(44\) | 1.93672e7 | 0.778984 | ||||||||
\(45\) | −2.35223e7 | −0.855114 | ||||||||
\(46\) | −4.31586e7 | −1.42121 | ||||||||
\(47\) | 1.74865e7 | 0.522713 | 0.261357 | − | 0.965242i | \(-0.415830\pi\) | ||||
0.261357 | + | 0.965242i | \(0.415830\pi\) | |||||||
\(48\) | −6.65039e6 | −0.180826 | ||||||||
\(49\) | −1.64180e7 | −0.406853 | ||||||||
\(50\) | 1.24659e7 | 0.282072 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.44724e7 | 0.464154 | ||||||||
\(53\) | 3.19270e7 | 0.555797 | 0.277898 | − | 0.960610i | \(-0.410362\pi\) | ||||
0.277898 | + | 0.960610i | \(0.410362\pi\) | |||||||
\(54\) | 2.14172e7 | 0.342760 | ||||||||
\(55\) | 1.10358e8 | 1.62619 | ||||||||
\(56\) | −3.92562e7 | −0.533411 | ||||||||
\(57\) | 1.76296e7 | 0.221211 | ||||||||
\(58\) | −4.68062e7 | −0.543097 | ||||||||
\(59\) | −8.87378e7 | −0.953398 | −0.476699 | − | 0.879066i | \(-0.658167\pi\) | ||||
−0.476699 | + | 0.879066i | \(0.658167\pi\) | |||||||
\(60\) | 5.33731e6 | 0.0531670 | ||||||||
\(61\) | 8.13726e7 | 0.752478 | 0.376239 | − | 0.926523i | \(-0.377217\pi\) | ||||
0.376239 | + | 0.926523i | \(0.377217\pi\) | |||||||
\(62\) | 3.34507e7 | 0.287503 | ||||||||
\(63\) | 9.42604e7 | 0.753870 | ||||||||
\(64\) | 4.08791e7 | 0.304573 | ||||||||
\(65\) | 1.39449e8 | 0.968956 | ||||||||
\(66\) | −4.97036e7 | −0.322433 | ||||||||
\(67\) | 1.53073e8 | 0.928027 | 0.464014 | − | 0.885828i | \(-0.346409\pi\) | ||||
0.464014 | + | 0.885828i | \(0.346409\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.26764e7 | 0.173546 | ||||||||
\(70\) | 1.60969e8 | 0.801309 | ||||||||
\(71\) | −3.08494e8 | −1.44074 | −0.720368 | − | 0.693593i | \(-0.756027\pi\) | ||||
−0.720368 | + | 0.693593i | \(0.756027\pi\) | |||||||
\(72\) | −1.54594e8 | −0.677948 | ||||||||
\(73\) | −2.12590e8 | −0.876173 | −0.438086 | − | 0.898933i | \(-0.644344\pi\) | ||||
−0.438086 | + | 0.898933i | \(0.644344\pi\) | |||||||
\(74\) | 2.05590e7 | 0.0797002 | ||||||||
\(75\) | −9.43827e6 | −0.0344443 | ||||||||
\(76\) | 1.85126e8 | 0.636511 | ||||||||
\(77\) | −4.42234e8 | −1.43365 | ||||||||
\(78\) | −6.28057e7 | −0.192120 | ||||||||
\(79\) | −3.93764e8 | −1.13740 | −0.568702 | − | 0.822544i | \(-0.692554\pi\) | ||||
−0.568702 | + | 0.822544i | \(0.692554\pi\) | |||||||
\(80\) | −3.97931e8 | −1.08618 | ||||||||
\(81\) | 3.63011e8 | 0.936994 | ||||||||
\(82\) | −7.02024e8 | −1.71471 | ||||||||
\(83\) | −6.17768e8 | −1.42881 | −0.714404 | − | 0.699734i | \(-0.753302\pi\) | ||||
−0.714404 | + | 0.699734i | \(0.753302\pi\) | |||||||
\(84\) | −2.13881e7 | −0.0468721 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.13172e9 | −2.23097 | ||||||||
\(87\) | 3.54381e7 | 0.0663184 | ||||||||
\(88\) | 7.25296e8 | 1.28927 | ||||||||
\(89\) | 7.46742e8 | 1.26158 | 0.630791 | − | 0.775953i | \(-0.282730\pi\) | ||||
0.630791 | + | 0.775953i | \(0.282730\pi\) | |||||||
\(90\) | 6.33908e8 | 1.01844 | ||||||||
\(91\) | −5.58808e8 | −0.854233 | ||||||||
\(92\) | 3.43129e8 | 0.499359 | ||||||||
\(93\) | −2.53264e7 | −0.0351075 | ||||||||
\(94\) | −4.71248e8 | −0.622549 | ||||||||
\(95\) | 1.05488e9 | 1.32876 | ||||||||
\(96\) | 9.53984e7 | 0.114636 | ||||||||
\(97\) | 1.98363e7 | 0.0227503 | 0.0113751 | − | 0.999935i | \(-0.496379\pi\) | ||||
0.0113751 | + | 0.999935i | \(0.496379\pi\) | |||||||
\(98\) | 4.42452e8 | 0.484561 | ||||||||
\(99\) | −1.74155e9 | −1.82212 | ||||||||
\(100\) | −9.91097e7 | −0.0991097 | ||||||||
\(101\) | −5.44823e8 | −0.520966 | −0.260483 | − | 0.965478i | \(-0.583882\pi\) | ||||
−0.260483 | + | 0.965478i | \(0.583882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.08729e9 | 0.951871 | 0.475935 | − | 0.879480i | \(-0.342110\pi\) | ||||
0.475935 | + | 0.879480i | \(0.342110\pi\) | |||||||
\(104\) | 9.16488e8 | 0.768204 | ||||||||
\(105\) | −1.21873e8 | −0.0978491 | ||||||||
\(106\) | −8.60405e8 | −0.661952 | ||||||||
\(107\) | −9.36864e8 | −0.690955 | −0.345477 | − | 0.938427i | \(-0.612283\pi\) | ||||
−0.345477 | + | 0.938427i | \(0.612283\pi\) | |||||||
\(108\) | −1.70276e8 | −0.120433 | ||||||||
\(109\) | −2.94426e8 | −0.199782 | −0.0998910 | − | 0.994998i | \(-0.531849\pi\) | ||||
−0.0998910 | + | 0.994998i | \(0.531849\pi\) | |||||||
\(110\) | −2.97405e9 | −1.93679 | ||||||||
\(111\) | −1.55657e7 | −0.00973231 | ||||||||
\(112\) | 1.59462e9 | 0.957581 | ||||||||
\(113\) | −1.06461e9 | −0.614237 | −0.307119 | − | 0.951671i | \(-0.599365\pi\) | ||||
−0.307119 | + | 0.951671i | \(0.599365\pi\) | |||||||
\(114\) | −4.75104e8 | −0.263461 | ||||||||
\(115\) | 1.95522e9 | 1.04245 | ||||||||
\(116\) | 3.72129e8 | 0.190824 | ||||||||
\(117\) | −2.20063e9 | −1.08570 | ||||||||
\(118\) | 2.39141e9 | 1.13549 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.99881e8 | 0.0879948 | ||||||||
\(121\) | 5.81275e9 | 2.46517 | ||||||||
\(122\) | −2.19292e9 | −0.896199 | ||||||||
\(123\) | 5.31520e8 | 0.209385 | ||||||||
\(124\) | −2.65948e8 | −0.101018 | ||||||||
\(125\) | −2.94928e9 | −1.08049 | ||||||||
\(126\) | −2.54024e9 | −0.897857 | ||||||||
\(127\) | −6.56388e8 | −0.223895 | −0.111947 | − | 0.993714i | \(-0.535709\pi\) | ||||
−0.111947 | + | 0.993714i | \(0.535709\pi\) | |||||||
\(128\) | −3.49552e9 | −1.15098 | ||||||||
\(129\) | 8.56850e8 | 0.272428 | ||||||||
\(130\) | −3.75802e9 | −1.15402 | ||||||||
\(131\) | −4.18207e9 | −1.24071 | −0.620355 | − | 0.784321i | \(-0.713011\pi\) | ||||
−0.620355 | + | 0.784321i | \(0.713011\pi\) | |||||||
\(132\) | 3.95165e8 | 0.113291 | ||||||||
\(133\) | −4.22720e9 | −1.17144 | ||||||||
\(134\) | −4.12518e9 | −1.10528 | ||||||||
\(135\) | −9.70265e8 | −0.251413 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.88438e8 | −0.118459 | −0.0592293 | − | 0.998244i | \(-0.518864\pi\) | ||||
−0.0592293 | + | 0.998244i | \(0.518864\pi\) | |||||||
\(138\) | −8.80602e8 | −0.206692 | ||||||||
\(139\) | −4.99993e9 | −1.13605 | −0.568025 | − | 0.823011i | \(-0.692292\pi\) | ||||
−0.568025 | + | 0.823011i | \(0.692292\pi\) | |||||||
\(140\) | −1.27977e9 | −0.281550 | ||||||||
\(141\) | 3.56793e8 | 0.0760205 | ||||||||
\(142\) | 8.31366e9 | 1.71591 | ||||||||
\(143\) | 1.03245e10 | 2.06471 | ||||||||
\(144\) | 6.27974e9 | 1.21705 | ||||||||
\(145\) | 2.12047e9 | 0.398360 | ||||||||
\(146\) | 5.72912e9 | 1.04352 | ||||||||
\(147\) | −3.34991e8 | −0.0591705 | ||||||||
\(148\) | −1.63453e8 | −0.0280037 | ||||||||
\(149\) | 3.59475e9 | 0.597489 | 0.298745 | − | 0.954333i | \(-0.403432\pi\) | ||||
0.298745 | + | 0.954333i | \(0.403432\pi\) | |||||||
\(150\) | 2.54354e8 | 0.0410230 | ||||||||
\(151\) | −1.10303e9 | −0.172660 | −0.0863298 | − | 0.996267i | \(-0.527514\pi\) | ||||
−0.0863298 | + | 0.996267i | \(0.527514\pi\) | |||||||
\(152\) | 6.93293e9 | 1.05347 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.19178e10 | 1.70747 | ||||||||
\(155\) | −1.51542e9 | −0.210883 | ||||||||
\(156\) | 4.99332e8 | 0.0675039 | ||||||||
\(157\) | −8.13616e9 | −1.06874 | −0.534368 | − | 0.845252i | \(-0.679451\pi\) | ||||
−0.534368 | + | 0.845252i | \(0.679451\pi\) | |||||||
\(158\) | 1.06116e10 | 1.35464 | ||||||||
\(159\) | 6.51434e8 | 0.0808320 | ||||||||
\(160\) | 5.70824e9 | 0.688592 | ||||||||
\(161\) | −7.83509e9 | −0.919025 | ||||||||
\(162\) | −9.78283e9 | −1.11596 | ||||||||
\(163\) | 3.43437e9 | 0.381068 | 0.190534 | − | 0.981681i | \(-0.438978\pi\) | ||||
0.190534 | + | 0.981681i | \(0.438978\pi\) | |||||||
\(164\) | 5.58139e9 | 0.602484 | ||||||||
\(165\) | 2.25173e9 | 0.236504 | ||||||||
\(166\) | 1.66483e10 | 1.70170 | ||||||||
\(167\) | 4.41406e8 | 0.0439151 | 0.0219575 | − | 0.999759i | \(-0.493010\pi\) | ||||
0.0219575 | + | 0.999759i | \(0.493010\pi\) | |||||||
\(168\) | −8.00979e8 | −0.0775763 | ||||||||
\(169\) | 2.44162e9 | 0.230244 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.66471e10 | −1.48886 | ||||||||
\(172\) | 8.99763e9 | 0.783881 | ||||||||
\(173\) | 1.16031e10 | 0.984838 | 0.492419 | − | 0.870358i | \(-0.336113\pi\) | ||||
0.492419 | + | 0.870358i | \(0.336113\pi\) | |||||||
\(174\) | −9.55028e8 | −0.0789849 | ||||||||
\(175\) | 2.26309e9 | 0.182403 | ||||||||
\(176\) | −2.94621e10 | −2.31450 | ||||||||
\(177\) | −1.81059e9 | −0.138657 | ||||||||
\(178\) | −2.01241e10 | −1.50254 | ||||||||
\(179\) | −1.11368e9 | −0.0810816 | −0.0405408 | − | 0.999178i | \(-0.512908\pi\) | ||||
−0.0405408 | + | 0.999178i | \(0.512908\pi\) | |||||||
\(180\) | −5.03984e9 | −0.357841 | ||||||||
\(181\) | 2.27345e10 | 1.57446 | 0.787229 | − | 0.616661i | \(-0.211515\pi\) | ||||
0.787229 | + | 0.616661i | \(0.211515\pi\) | |||||||
\(182\) | 1.50594e10 | 1.01739 | ||||||||
\(183\) | 1.66032e9 | 0.109436 | ||||||||
\(184\) | 1.28501e10 | 0.826471 | ||||||||
\(185\) | −9.31387e8 | −0.0584598 | ||||||||
\(186\) | 6.82525e8 | 0.0418129 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.74662e9 | 0.218741 | ||||||||
\(189\) | 3.88811e9 | 0.221646 | ||||||||
\(190\) | −2.84282e10 | −1.58255 | ||||||||
\(191\) | −1.39886e10 | −0.760544 | −0.380272 | − | 0.924875i | \(-0.624170\pi\) | ||||
−0.380272 | + | 0.924875i | \(0.624170\pi\) | |||||||
\(192\) | 8.34092e8 | 0.0442954 | ||||||||
\(193\) | 3.49366e10 | 1.81248 | 0.906238 | − | 0.422767i | \(-0.138941\pi\) | ||||
0.906238 | + | 0.422767i | \(0.138941\pi\) | |||||||
\(194\) | −5.34571e8 | −0.0270955 | ||||||||
\(195\) | 2.84529e9 | 0.140920 | ||||||||
\(196\) | −3.51768e9 | −0.170257 | ||||||||
\(197\) | −1.47793e10 | −0.699126 | −0.349563 | − | 0.936913i | \(-0.613670\pi\) | ||||
−0.349563 | + | 0.936913i | \(0.613670\pi\) | |||||||
\(198\) | 4.69334e10 | 2.17014 | ||||||||
\(199\) | 1.24263e10 | 0.561700 | 0.280850 | − | 0.959752i | \(-0.409384\pi\) | ||||
0.280850 | + | 0.959752i | \(0.409384\pi\) | |||||||
\(200\) | −3.71164e9 | −0.164033 | ||||||||
\(201\) | 3.12327e9 | 0.134967 | ||||||||
\(202\) | 1.46825e10 | 0.620469 | ||||||||
\(203\) | −8.49728e9 | −0.351195 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.18039e10 | 1.25773 | ||||||||
\(206\) | −2.93016e10 | −1.13367 | ||||||||
\(207\) | −3.08552e10 | −1.16805 | ||||||||
\(208\) | −3.72285e10 | −1.37908 | ||||||||
\(209\) | 7.81017e10 | 2.83140 | ||||||||
\(210\) | 3.28438e9 | 0.116538 | ||||||||
\(211\) | 3.46615e10 | 1.20386 | 0.601931 | − | 0.798548i | \(-0.294398\pi\) | ||||
0.601931 | + | 0.798548i | \(0.294398\pi\) | |||||||
\(212\) | 6.84059e9 | 0.232585 | ||||||||
\(213\) | −6.29447e9 | −0.209532 | ||||||||
\(214\) | 2.52477e10 | 0.822925 | ||||||||
\(215\) | 5.12703e10 | 1.63641 | ||||||||
\(216\) | −6.37680e9 | −0.199325 | ||||||||
\(217\) | 6.07271e9 | 0.185915 | ||||||||
\(218\) | 7.93453e9 | 0.237940 | ||||||||
\(219\) | −4.33766e9 | −0.127426 | ||||||||
\(220\) | 2.36450e10 | 0.680515 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.19483e8 | 0.0115911 | ||||||||
\(223\) | −3.38261e10 | −0.915966 | −0.457983 | − | 0.888961i | \(-0.651428\pi\) | ||||
−0.457983 | + | 0.888961i | \(0.651428\pi\) | |||||||
\(224\) | −2.28745e10 | −0.607064 | ||||||||
\(225\) | 8.91224e9 | 0.231828 | ||||||||
\(226\) | 2.86903e10 | 0.731554 | ||||||||
\(227\) | −1.62331e10 | −0.405775 | −0.202887 | − | 0.979202i | \(-0.565033\pi\) | ||||
−0.202887 | + | 0.979202i | \(0.565033\pi\) | |||||||
\(228\) | 3.77729e9 | 0.0925706 | ||||||||
\(229\) | 5.53406e10 | 1.32979 | 0.664896 | − | 0.746936i | \(-0.268476\pi\) | ||||
0.664896 | + | 0.746936i | \(0.268476\pi\) | |||||||
\(230\) | −5.26915e10 | −1.24155 | ||||||||
\(231\) | −9.02328e9 | −0.208502 | ||||||||
\(232\) | 1.39362e10 | 0.315826 | ||||||||
\(233\) | 3.33712e10 | 0.741772 | 0.370886 | − | 0.928678i | \(-0.379054\pi\) | ||||
0.370886 | + | 0.928678i | \(0.379054\pi\) | |||||||
\(234\) | 5.93052e10 | 1.29307 | ||||||||
\(235\) | 2.13490e10 | 0.456638 | ||||||||
\(236\) | −1.90127e10 | −0.398970 | ||||||||
\(237\) | −8.03432e9 | −0.165418 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.77200e10 | 1.54079 | 0.770393 | − | 0.637569i | \(-0.220060\pi\) | ||||
0.770393 | + | 0.637569i | \(0.220060\pi\) | |||||||
\(240\) | −8.11934e9 | −0.157968 | ||||||||
\(241\) | −2.18341e10 | −0.416925 | −0.208463 | − | 0.978030i | \(-0.566846\pi\) | ||||
−0.208463 | + | 0.978030i | \(0.566846\pi\) | |||||||
\(242\) | −1.56649e11 | −2.93601 | ||||||||
\(243\) | 2.30494e10 | 0.424064 | ||||||||
\(244\) | 1.74347e10 | 0.314891 | ||||||||
\(245\) | −2.00444e10 | −0.355424 | ||||||||
\(246\) | −1.43240e10 | −0.249377 | ||||||||
\(247\) | 9.86896e10 | 1.68708 | ||||||||
\(248\) | −9.95970e9 | −0.167191 | ||||||||
\(249\) | −1.26049e10 | −0.207798 | ||||||||
\(250\) | 7.94807e10 | 1.28686 | ||||||||
\(251\) | 1.67155e10 | 0.265819 | 0.132910 | − | 0.991128i | \(-0.457568\pi\) | ||||
0.132910 | + | 0.991128i | \(0.457568\pi\) | |||||||
\(252\) | 2.01960e10 | 0.315474 | ||||||||
\(253\) | 1.44761e11 | 2.22131 | ||||||||
\(254\) | 1.76891e10 | 0.266658 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.32711e10 | 1.06624 | ||||||||
\(257\) | 1.17094e11 | 1.67431 | 0.837156 | − | 0.546964i | \(-0.184217\pi\) | ||||
0.837156 | + | 0.546964i | \(0.184217\pi\) | |||||||
\(258\) | −2.30914e10 | −0.324460 | ||||||||
\(259\) | 3.73232e9 | 0.0515383 | ||||||||
\(260\) | 2.98779e10 | 0.405481 | ||||||||
\(261\) | −3.34630e10 | −0.446357 | ||||||||
\(262\) | 1.12703e11 | 1.47768 | ||||||||
\(263\) | −1.02193e11 | −1.31710 | −0.658551 | − | 0.752536i | \(-0.728830\pi\) | ||||
−0.658551 | + | 0.752536i | \(0.728830\pi\) | |||||||
\(264\) | 1.47989e10 | 0.187504 | ||||||||
\(265\) | 3.89790e10 | 0.485540 | ||||||||
\(266\) | 1.13920e11 | 1.39518 | ||||||||
\(267\) | 1.52364e10 | 0.183477 | ||||||||
\(268\) | 3.27970e10 | 0.388353 | ||||||||
\(269\) | 1.53946e11 | 1.79260 | 0.896299 | − | 0.443450i | \(-0.146246\pi\) | ||||
0.896299 | + | 0.443450i | \(0.146246\pi\) | |||||||
\(270\) | 2.61478e10 | 0.299432 | ||||||||
\(271\) | 4.06059e10 | 0.457328 | 0.228664 | − | 0.973505i | \(-0.426564\pi\) | ||||
0.228664 | + | 0.973505i | \(0.426564\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.14019e10 | −0.124235 | ||||||||
\(274\) | 1.31630e10 | 0.141084 | ||||||||
\(275\) | −4.18128e10 | −0.440872 | ||||||||
\(276\) | 7.00117e9 | 0.0726239 | ||||||||
\(277\) | 1.48740e11 | 1.51799 | 0.758993 | − | 0.651099i | \(-0.225692\pi\) | ||||
0.758993 | + | 0.651099i | \(0.225692\pi\) | |||||||
\(278\) | 1.34744e11 | 1.35303 | ||||||||
\(279\) | 2.39148e10 | 0.236292 | ||||||||
\(280\) | −4.79272e10 | −0.465984 | ||||||||
\(281\) | −1.82559e11 | −1.74673 | −0.873365 | − | 0.487067i | \(-0.838067\pi\) | ||||
−0.873365 | + | 0.487067i | \(0.838067\pi\) | |||||||
\(282\) | −9.61528e9 | −0.0905401 | ||||||||
\(283\) | 1.13202e11 | 1.04909 | 0.524546 | − | 0.851382i | \(-0.324235\pi\) | ||||
0.524546 | + | 0.851382i | \(0.324235\pi\) | |||||||
\(284\) | −6.60972e10 | −0.602907 | ||||||||
\(285\) | 2.15237e10 | 0.193248 | ||||||||
\(286\) | −2.78237e11 | −2.45906 | ||||||||
\(287\) | −1.27447e11 | −1.10882 | ||||||||
\(288\) | −9.00815e10 | −0.771559 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −5.71448e10 | −0.474445 | ||||||||
\(291\) | 4.04737e8 | 0.00330868 | ||||||||
\(292\) | −4.55490e10 | −0.366654 | ||||||||
\(293\) | −9.88878e10 | −0.783860 | −0.391930 | − | 0.919995i | \(-0.628192\pi\) | ||||
−0.391930 | + | 0.919995i | \(0.628192\pi\) | |||||||
\(294\) | 9.02773e9 | 0.0704718 | ||||||||
\(295\) | −1.08338e11 | −0.832881 | ||||||||
\(296\) | −6.12129e9 | −0.0463479 | ||||||||
\(297\) | −7.18367e10 | −0.535725 | ||||||||
\(298\) | −9.68755e10 | −0.711608 | ||||||||
\(299\) | 1.82920e11 | 1.32356 | ||||||||
\(300\) | −2.02222e9 | −0.0144140 | ||||||||
\(301\) | −2.05454e11 | −1.44266 | ||||||||
\(302\) | 2.97257e10 | 0.205637 | ||||||||
\(303\) | −1.11165e10 | −0.0757664 | ||||||||
\(304\) | −2.81621e11 | −1.89119 | ||||||||
\(305\) | 9.93463e10 | 0.657359 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.32346e11 | −0.850334 | −0.425167 | − | 0.905115i | \(-0.639785\pi\) | ||||
−0.425167 | + | 0.905115i | \(0.639785\pi\) | |||||||
\(308\) | −9.47519e10 | −0.599943 | ||||||||
\(309\) | 2.21849e10 | 0.138435 | ||||||||
\(310\) | 4.08394e10 | 0.251161 | ||||||||
\(311\) | −2.91738e11 | −1.76836 | −0.884181 | − | 0.467144i | \(-0.845283\pi\) | ||||
−0.884181 | + | 0.467144i | \(0.845283\pi\) | |||||||
\(312\) | 1.86999e10 | 0.111723 | ||||||||
\(313\) | 2.79377e10 | 0.164528 | 0.0822642 | − | 0.996611i | \(-0.473785\pi\) | ||||
0.0822642 | + | 0.996611i | \(0.473785\pi\) | |||||||
\(314\) | 2.19263e11 | 1.27286 | ||||||||
\(315\) | 1.15081e11 | 0.658575 | ||||||||
\(316\) | −8.43670e10 | −0.475971 | ||||||||
\(317\) | −2.06834e11 | −1.15041 | −0.575207 | − | 0.818008i | \(-0.695079\pi\) | ||||
−0.575207 | + | 0.818008i | \(0.695079\pi\) | |||||||
\(318\) | −1.75556e10 | −0.0962706 | ||||||||
\(319\) | 1.56996e11 | 0.848847 | ||||||||
\(320\) | 4.99085e10 | 0.266072 | ||||||||
\(321\) | −1.91157e10 | −0.100489 | ||||||||
\(322\) | 2.11149e11 | 1.09456 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 7.77778e10 | 0.392106 | ||||||||
\(325\) | −5.28349e10 | −0.262691 | ||||||||
\(326\) | −9.25534e10 | −0.453851 | ||||||||
\(327\) | −6.00743e9 | −0.0290552 | ||||||||
\(328\) | 2.09022e11 | 0.997149 | ||||||||
\(329\) | −8.55512e10 | −0.402573 | ||||||||
\(330\) | −6.06822e10 | −0.281675 | ||||||||
\(331\) | −2.13845e11 | −0.979203 | −0.489601 | − | 0.871946i | \(-0.662858\pi\) | ||||
−0.489601 | + | 0.871946i | \(0.662858\pi\) | |||||||
\(332\) | −1.32361e11 | −0.597916 | ||||||||
\(333\) | 1.46982e10 | 0.0655035 | ||||||||
\(334\) | −1.18955e10 | −0.0523027 | ||||||||
\(335\) | 1.86884e11 | 0.810717 | ||||||||
\(336\) | 3.25364e10 | 0.139265 | ||||||||
\(337\) | −2.72147e11 | −1.14939 | −0.574697 | − | 0.818366i | \(-0.694880\pi\) | ||||
−0.574697 | + | 0.818366i | \(0.694880\pi\) | |||||||
\(338\) | −6.57996e10 | −0.274219 | ||||||||
\(339\) | −2.17221e10 | −0.0893312 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.12199e11 | −0.449361 | ||||||||
\(342\) | 4.48625e11 | 1.77323 | ||||||||
\(343\) | 2.77750e11 | 1.08350 | ||||||||
\(344\) | 3.36960e11 | 1.29737 | ||||||||
\(345\) | 3.98940e10 | 0.151608 | ||||||||
\(346\) | −3.12693e11 | −1.17294 | ||||||||
\(347\) | 1.46260e11 | 0.541555 | 0.270777 | − | 0.962642i | \(-0.412719\pi\) | ||||
0.270777 | + | 0.962642i | \(0.412719\pi\) | |||||||
\(348\) | 7.59288e9 | 0.0277524 | ||||||||
\(349\) | −1.97033e11 | −0.710927 | −0.355464 | − | 0.934690i | \(-0.615677\pi\) | ||||
−0.355464 | + | 0.934690i | \(0.615677\pi\) | |||||||
\(350\) | −6.09884e10 | −0.217241 | ||||||||
\(351\) | −9.07731e10 | −0.319209 | ||||||||
\(352\) | 4.22628e11 | 1.46729 | ||||||||
\(353\) | 1.79594e11 | 0.615610 | 0.307805 | − | 0.951449i | \(-0.400406\pi\) | ||||
0.307805 | + | 0.951449i | \(0.400406\pi\) | |||||||
\(354\) | 4.87940e10 | 0.165140 | ||||||||
\(355\) | −3.76635e11 | −1.25861 | ||||||||
\(356\) | 1.59995e11 | 0.527937 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.00128e10 | 0.0965679 | ||||||||
\(359\) | 2.48013e11 | 0.788043 | 0.394021 | − | 0.919101i | \(-0.371084\pi\) | ||||
0.394021 | + | 0.919101i | \(0.371084\pi\) | |||||||
\(360\) | −1.88741e11 | −0.592250 | ||||||||
\(361\) | 4.23867e11 | 1.31355 | ||||||||
\(362\) | −6.12675e11 | −1.87517 | ||||||||
\(363\) | 1.18603e11 | 0.358521 | ||||||||
\(364\) | −1.19729e11 | −0.357473 | ||||||||
\(365\) | −2.59547e11 | −0.765417 | ||||||||
\(366\) | −4.47442e10 | −0.130338 | ||||||||
\(367\) | 5.21437e11 | 1.50039 | 0.750195 | − | 0.661216i | \(-0.229959\pi\) | ||||
0.750195 | + | 0.661216i | \(0.229959\pi\) | |||||||
\(368\) | −5.21983e11 | −1.48368 | ||||||||
\(369\) | −5.01896e11 | −1.40927 | ||||||||
\(370\) | 2.51001e10 | 0.0696254 | ||||||||
\(371\) | −1.56200e11 | −0.428053 | ||||||||
\(372\) | −5.42637e9 | −0.0146915 | ||||||||
\(373\) | −5.99693e11 | −1.60413 | −0.802065 | − | 0.597237i | \(-0.796265\pi\) | ||||
−0.802065 | + | 0.597237i | \(0.796265\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.01768e10 | −0.157141 | ||||||||
\(376\) | 1.40310e11 | 0.362030 | ||||||||
\(377\) | 1.98380e11 | 0.505781 | ||||||||
\(378\) | −1.04781e11 | −0.263980 | ||||||||
\(379\) | 9.27561e10 | 0.230922 | 0.115461 | − | 0.993312i | \(-0.463165\pi\) | ||||
0.115461 | + | 0.993312i | \(0.463165\pi\) | |||||||
\(380\) | 2.26017e11 | 0.556051 | ||||||||
\(381\) | −1.33929e10 | −0.0325620 | ||||||||
\(382\) | 3.76981e11 | 0.905805 | ||||||||
\(383\) | 6.05110e11 | 1.43694 | 0.718472 | − | 0.695555i | \(-0.244842\pi\) | ||||
0.718472 | + | 0.695555i | \(0.244842\pi\) | |||||||
\(384\) | −7.13221e10 | −0.167392 | ||||||||
\(385\) | −5.39915e11 | −1.25243 | ||||||||
\(386\) | −9.41511e11 | −2.15865 | ||||||||
\(387\) | −8.09094e11 | −1.83358 | ||||||||
\(388\) | 4.25007e9 | 0.00952036 | ||||||||
\(389\) | 7.62830e11 | 1.68910 | 0.844548 | − | 0.535480i | \(-0.179869\pi\) | ||||
0.844548 | + | 0.535480i | \(0.179869\pi\) | |||||||
\(390\) | −7.66783e10 | −0.167835 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.31737e11 | −0.281786 | ||||||||
\(393\) | −8.53304e10 | −0.180442 | ||||||||
\(394\) | 3.98290e11 | 0.832657 | ||||||||
\(395\) | −4.80740e11 | −0.993627 | ||||||||
\(396\) | −3.73141e11 | −0.762508 | ||||||||
\(397\) | −8.86527e10 | −0.179116 | −0.0895580 | − | 0.995982i | \(-0.528545\pi\) | ||||
−0.0895580 | + | 0.995982i | \(0.528545\pi\) | |||||||
\(398\) | −3.34880e11 | −0.668983 | ||||||||
\(399\) | −8.62513e10 | −0.170368 | ||||||||
\(400\) | 1.50770e11 | 0.294472 | ||||||||
\(401\) | 6.95370e11 | 1.34297 | 0.671485 | − | 0.741019i | \(-0.265657\pi\) | ||||
0.671485 | + | 0.741019i | \(0.265657\pi\) | |||||||
\(402\) | −8.41696e10 | −0.160745 | ||||||||
\(403\) | −1.41775e11 | −0.267749 | ||||||||
\(404\) | −1.16733e11 | −0.218010 | ||||||||
\(405\) | 4.43193e11 | 0.818550 | ||||||||
\(406\) | 2.28995e11 | 0.418271 | ||||||||
\(407\) | −6.89583e10 | −0.124569 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.29107e11 | −0.581543 | −0.290771 | − | 0.956793i | \(-0.593912\pi\) | ||||
−0.290771 | + | 0.956793i | \(0.593912\pi\) | |||||||
\(410\) | −8.57088e11 | −1.49795 | ||||||||
\(411\) | −9.96602e9 | −0.0172280 | ||||||||
\(412\) | 2.32960e11 | 0.398331 | ||||||||
\(413\) | 4.34141e11 | 0.734269 | ||||||||
\(414\) | 8.31522e11 | 1.39115 | ||||||||
\(415\) | −7.54221e11 | −1.24819 | ||||||||
\(416\) | 5.34034e11 | 0.874277 | ||||||||
\(417\) | −1.02018e11 | −0.165221 | ||||||||
\(418\) | −2.10477e12 | −3.37219 | ||||||||
\(419\) | 7.10268e10 | 0.112579 | 0.0562897 | − | 0.998414i | \(-0.482073\pi\) | ||||
0.0562897 | + | 0.998414i | \(0.482073\pi\) | |||||||
\(420\) | −2.61123e10 | −0.0409471 | ||||||||
\(421\) | −6.19951e11 | −0.961807 | −0.480904 | − | 0.876773i | \(-0.659691\pi\) | ||||
−0.480904 | + | 0.876773i | \(0.659691\pi\) | |||||||
\(422\) | −9.34099e11 | −1.43379 | ||||||||
\(423\) | −3.36908e11 | −0.511657 | ||||||||
\(424\) | 2.56179e11 | 0.384944 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.69631e11 | 0.249552 | ||||||||
\(427\) | −3.98108e11 | −0.579529 | ||||||||
\(428\) | −2.00730e11 | −0.289145 | ||||||||
\(429\) | 2.10660e11 | 0.300279 | ||||||||
\(430\) | −1.38169e12 | −1.94896 | ||||||||
\(431\) | −5.72129e11 | −0.798631 | −0.399316 | − | 0.916814i | \(-0.630752\pi\) | ||||
−0.399316 | + | 0.916814i | \(0.630752\pi\) | |||||||
\(432\) | 2.59031e11 | 0.357828 | ||||||||
\(433\) | 1.85587e10 | 0.0253718 | 0.0126859 | − | 0.999920i | \(-0.495962\pi\) | ||||
0.0126859 | + | 0.999920i | \(0.495962\pi\) | |||||||
\(434\) | −1.63654e11 | −0.221424 | ||||||||
\(435\) | 4.32657e10 | 0.0579352 | ||||||||
\(436\) | −6.30829e10 | −0.0836032 | ||||||||
\(437\) | 1.38373e12 | 1.81504 | ||||||||
\(438\) | 1.16896e11 | 0.151763 | ||||||||
\(439\) | −1.96136e11 | −0.252038 | −0.126019 | − | 0.992028i | \(-0.540220\pi\) | ||||
−0.126019 | + | 0.992028i | \(0.540220\pi\) | |||||||
\(440\) | 8.85501e11 | 1.12629 | ||||||||
\(441\) | 3.16320e11 | 0.398248 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.73153e11 | 0.213606 | 0.106803 | − | 0.994280i | \(-0.465939\pi\) | ||||
0.106803 | + | 0.994280i | \(0.465939\pi\) | |||||||
\(444\) | −3.33508e9 | −0.00407270 | ||||||||
\(445\) | 9.11684e11 | 1.10211 | ||||||||
\(446\) | 9.11584e11 | 1.09091 | ||||||||
\(447\) | 7.33468e10 | 0.0868955 | ||||||||
\(448\) | −1.99997e11 | −0.234570 | ||||||||
\(449\) | −2.19116e11 | −0.254428 | −0.127214 | − | 0.991875i | \(-0.540604\pi\) | ||||
−0.127214 | + | 0.991875i | \(0.540604\pi\) | |||||||
\(450\) | −2.40177e11 | −0.276106 | ||||||||
\(451\) | 2.35470e12 | 2.68004 | ||||||||
\(452\) | −2.28100e11 | −0.257041 | ||||||||
\(453\) | −2.25061e10 | −0.0251106 | ||||||||
\(454\) | 4.37468e11 | 0.483276 | ||||||||
\(455\) | −6.82239e11 | −0.746251 | ||||||||
\(456\) | 1.41459e11 | 0.153210 | ||||||||
\(457\) | 4.00079e11 | 0.429065 | 0.214532 | − | 0.976717i | \(-0.431177\pi\) | ||||
0.214532 | + | 0.976717i | \(0.431177\pi\) | |||||||
\(458\) | −1.49138e12 | −1.58378 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.18920e11 | 0.436236 | ||||||||
\(461\) | 6.96330e11 | 0.718061 | 0.359030 | − | 0.933326i | \(-0.383107\pi\) | ||||
0.359030 | + | 0.933326i | \(0.383107\pi\) | |||||||
\(462\) | 2.43170e11 | 0.248325 | ||||||||
\(463\) | 1.04638e12 | 1.05821 | 0.529106 | − | 0.848556i | \(-0.322527\pi\) | ||||
0.529106 | + | 0.848556i | \(0.322527\pi\) | |||||||
\(464\) | −5.66099e11 | −0.566972 | ||||||||
\(465\) | −3.09205e10 | −0.0306696 | ||||||||
\(466\) | −8.99327e11 | −0.883448 | ||||||||
\(467\) | 1.17010e12 | 1.13840 | 0.569202 | − | 0.822198i | \(-0.307252\pi\) | ||||
0.569202 | + | 0.822198i | \(0.307252\pi\) | |||||||
\(468\) | −4.71502e11 | −0.454336 | ||||||||
\(469\) | −7.48893e11 | −0.714730 | ||||||||
\(470\) | −5.75338e11 | −0.543854 | ||||||||
\(471\) | −1.66009e11 | −0.155431 | ||||||||
\(472\) | −7.12024e11 | −0.660322 | ||||||||
\(473\) | 3.79596e12 | 3.48695 | ||||||||
\(474\) | 2.16518e11 | 0.197012 | ||||||||
\(475\) | −3.99678e11 | −0.360238 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.15127e11 | −0.544041 | ||||||||
\(478\) | −2.09449e12 | −1.83507 | ||||||||
\(479\) | 1.23985e12 | 1.07611 | 0.538057 | − | 0.842908i | \(-0.319158\pi\) | ||||
0.538057 | + | 0.842908i | \(0.319158\pi\) | |||||||
\(480\) | 1.16470e11 | 0.100145 | ||||||||
\(481\) | −8.71359e10 | −0.0742240 | ||||||||
\(482\) | 5.88410e11 | 0.496556 | ||||||||
\(483\) | −1.59866e11 | −0.133658 | ||||||||
\(484\) | 1.24543e12 | 1.03161 | ||||||||
\(485\) | 2.42177e10 | 0.0198745 | ||||||||
\(486\) | −6.21162e11 | −0.505058 | ||||||||
\(487\) | 1.21764e12 | 0.980934 | 0.490467 | − | 0.871460i | \(-0.336826\pi\) | ||||
0.490467 | + | 0.871460i | \(0.336826\pi\) | |||||||
\(488\) | 6.52926e11 | 0.521165 | ||||||||
\(489\) | 7.00744e10 | 0.0554204 | ||||||||
\(490\) | 5.40181e11 | 0.423309 | ||||||||
\(491\) | 6.56579e11 | 0.509824 | 0.254912 | − | 0.966964i | \(-0.417954\pi\) | ||||
0.254912 | + | 0.966964i | \(0.417954\pi\) | |||||||
\(492\) | 1.13882e11 | 0.0876219 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −2.65960e12 | −2.00930 | ||||||||
\(495\) | −2.12623e12 | −1.59179 | ||||||||
\(496\) | 4.04571e11 | 0.300142 | ||||||||
\(497\) | 1.50928e12 | 1.10960 | ||||||||
\(498\) | 3.39690e11 | 0.247486 | ||||||||
\(499\) | −1.66940e12 | −1.20534 | −0.602669 | − | 0.797991i | \(-0.705896\pi\) | ||||
−0.602669 | + | 0.797991i | \(0.705896\pi\) | |||||||
\(500\) | −6.31906e11 | −0.452155 | ||||||||
\(501\) | 9.00639e9 | 0.00638676 | ||||||||
\(502\) | −4.50468e11 | −0.316590 | ||||||||
\(503\) | −4.93759e11 | −0.343922 | −0.171961 | − | 0.985104i | \(-0.555010\pi\) | ||||
−0.171961 | + | 0.985104i | \(0.555010\pi\) | |||||||
\(504\) | 7.56337e11 | 0.522129 | ||||||||
\(505\) | −6.65165e11 | −0.455112 | ||||||||
\(506\) | −3.90119e12 | −2.64557 | ||||||||
\(507\) | 4.98185e10 | 0.0334854 | ||||||||
\(508\) | −1.40636e11 | −0.0936937 | ||||||||
\(509\) | −2.29659e12 | −1.51654 | −0.758268 | − | 0.651943i | \(-0.773954\pi\) | ||||
−0.758268 | + | 0.651943i | \(0.773954\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.04008e12 | 0.674793 | ||||||||
\(512\) | −1.84892e11 | −0.118906 | ||||||||
\(513\) | −6.86669e11 | −0.437743 | ||||||||
\(514\) | −3.15559e12 | −1.99410 | ||||||||
\(515\) | 1.32745e12 | 0.831546 | ||||||||
\(516\) | 1.83587e11 | 0.114003 | ||||||||
\(517\) | 1.58064e12 | 0.973029 | ||||||||
\(518\) | −1.00583e11 | −0.0613819 | ||||||||
\(519\) | 2.36747e11 | 0.143229 | ||||||||
\(520\) | 1.11892e12 | 0.671097 | ||||||||
\(521\) | 1.03325e12 | 0.614377 | 0.307188 | − | 0.951649i | \(-0.400612\pi\) | ||||
0.307188 | + | 0.951649i | \(0.400612\pi\) | |||||||
\(522\) | 9.01800e11 | 0.531610 | ||||||||
\(523\) | 8.50931e11 | 0.497321 | 0.248660 | − | 0.968591i | \(-0.420010\pi\) | ||||
0.248660 | + | 0.968591i | \(0.420010\pi\) | |||||||
\(524\) | −8.96040e11 | −0.519202 | ||||||||
\(525\) | 4.61758e10 | 0.0265276 | ||||||||
\(526\) | 2.75401e12 | 1.56866 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −6.01142e11 | −0.336608 | ||||||||
\(529\) | 7.63587e11 | 0.423944 | ||||||||
\(530\) | −1.05045e12 | −0.578276 | ||||||||
\(531\) | 1.70968e12 | 0.933233 | ||||||||
\(532\) | −9.05710e11 | −0.490215 | ||||||||
\(533\) | 2.97541e12 | 1.59689 | ||||||||
\(534\) | −4.10609e11 | −0.218521 | ||||||||
\(535\) | −1.14380e12 | −0.603613 | ||||||||
\(536\) | 1.22824e12 | 0.642750 | ||||||||
\(537\) | −2.27234e10 | −0.0117921 | ||||||||
\(538\) | −4.14872e12 | −2.13498 | ||||||||
\(539\) | −1.48405e12 | −0.757357 | ||||||||
\(540\) | −2.07887e11 | −0.105209 | ||||||||
\(541\) | −1.53052e12 | −0.768161 | −0.384080 | − | 0.923300i | \(-0.625481\pi\) | ||||
−0.384080 | + | 0.923300i | \(0.625481\pi\) | |||||||
\(542\) | −1.09430e12 | −0.544676 | ||||||||
\(543\) | 4.63871e11 | 0.228980 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.59459e11 | −0.174528 | ||||||||
\(546\) | 3.07271e11 | 0.147963 | ||||||||
\(547\) | 1.12770e12 | 0.538579 | 0.269289 | − | 0.963059i | \(-0.413211\pi\) | ||||
0.269289 | + | 0.963059i | \(0.413211\pi\) | |||||||
\(548\) | −1.04651e11 | −0.0495716 | ||||||||
\(549\) | −1.56778e12 | −0.736562 | ||||||||
\(550\) | 1.12682e12 | 0.525077 | ||||||||
\(551\) | 1.50068e12 | 0.693596 | ||||||||
\(552\) | 2.62193e11 | 0.120197 | ||||||||
\(553\) | 1.92645e12 | 0.875983 | ||||||||
\(554\) | −4.00841e12 | −1.80792 | ||||||||
\(555\) | −1.90039e10 | −0.00850207 | ||||||||
\(556\) | −1.07127e12 | −0.475405 | ||||||||
\(557\) | 1.25702e12 | 0.553340 | 0.276670 | − | 0.960965i | \(-0.410769\pi\) | ||||
0.276670 | + | 0.960965i | \(0.410769\pi\) | |||||||
\(558\) | −6.44485e11 | −0.281422 | ||||||||
\(559\) | 4.79659e12 | 2.07768 | ||||||||
\(560\) | 1.94684e12 | 0.836535 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.91982e12 | 2.08035 | ||||||||
\(563\) | 1.88611e12 | 0.791185 | 0.395593 | − | 0.918426i | \(-0.370539\pi\) | ||||
0.395593 | + | 0.918426i | \(0.370539\pi\) | |||||||
\(564\) | 7.64457e10 | 0.0318124 | ||||||||
\(565\) | −1.29976e12 | −0.536593 | ||||||||
\(566\) | −3.05069e12 | −1.24947 | ||||||||
\(567\) | −1.77599e12 | −0.721635 | ||||||||
\(568\) | −2.47533e12 | −0.997850 | ||||||||
\(569\) | −2.29668e12 | −0.918535 | −0.459267 | − | 0.888298i | \(-0.651888\pi\) | ||||
−0.459267 | + | 0.888298i | \(0.651888\pi\) | |||||||
\(570\) | −5.80046e11 | −0.230158 | ||||||||
\(571\) | 5.17537e11 | 0.203741 | 0.101871 | − | 0.994798i | \(-0.467517\pi\) | ||||
0.101871 | + | 0.994798i | \(0.467517\pi\) | |||||||
\(572\) | 2.21211e12 | 0.864021 | ||||||||
\(573\) | −2.85422e11 | −0.110609 | ||||||||
\(574\) | 3.43458e12 | 1.32060 | ||||||||
\(575\) | −7.40801e11 | −0.282616 | ||||||||
\(576\) | −7.87604e11 | −0.298131 | ||||||||
\(577\) | −4.42858e12 | −1.66331 | −0.831656 | − | 0.555291i | \(-0.812607\pi\) | ||||
−0.831656 | + | 0.555291i | \(0.812607\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.12842e11 | 0.263596 | ||||||||
\(580\) | 4.54326e11 | 0.166702 | ||||||||
\(581\) | 3.02237e12 | 1.10041 | ||||||||
\(582\) | −1.09073e10 | −0.00394062 | ||||||||
\(583\) | 2.88594e12 | 1.03461 | ||||||||
\(584\) | −1.70580e12 | −0.606835 | ||||||||
\(585\) | −2.68671e12 | −0.948462 | ||||||||
\(586\) | 2.66494e12 | 0.933574 | ||||||||
\(587\) | −3.58678e12 | −1.24690 | −0.623452 | − | 0.781861i | \(-0.714270\pi\) | ||||
−0.623452 | + | 0.781861i | \(0.714270\pi\) | |||||||
\(588\) | −7.17744e10 | −0.0247612 | ||||||||
\(589\) | −1.07248e12 | −0.367174 | ||||||||
\(590\) | 2.91963e12 | 0.991958 | ||||||||
\(591\) | −3.01555e11 | −0.101677 | ||||||||
\(592\) | 2.48652e11 | 0.0832039 | ||||||||
\(593\) | −5.90244e12 | −1.96013 | −0.980067 | − | 0.198667i | \(-0.936339\pi\) | ||||
−0.980067 | + | 0.198667i | \(0.936339\pi\) | |||||||
\(594\) | 1.93594e12 | 0.638047 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.70202e11 | 0.250033 | ||||||||
\(597\) | 2.53546e11 | 0.0816906 | ||||||||
\(598\) | −4.92955e12 | −1.57635 | ||||||||
\(599\) | 8.98381e10 | 0.0285128 | 0.0142564 | − | 0.999898i | \(-0.495462\pi\) | ||||
0.0142564 | + | 0.999898i | \(0.495462\pi\) | |||||||
\(600\) | −7.57319e10 | −0.0238560 | ||||||||
\(601\) | 3.87756e10 | 0.0121234 | 0.00606168 | − | 0.999982i | \(-0.498070\pi\) | ||||
0.00606168 | + | 0.999982i | \(0.498070\pi\) | |||||||
\(602\) | 5.53681e12 | 1.71821 | ||||||||
\(603\) | −2.94920e12 | −0.908398 | ||||||||
\(604\) | −2.36332e11 | −0.0722532 | ||||||||
\(605\) | 7.09668e12 | 2.15356 | ||||||||
\(606\) | 2.99581e11 | 0.0902375 | ||||||||
\(607\) | −4.02539e12 | −1.20353 | −0.601767 | − | 0.798672i | \(-0.705536\pi\) | ||||
−0.601767 | + | 0.798672i | \(0.705536\pi\) | |||||||
\(608\) | 4.03979e12 | 1.19893 | ||||||||
\(609\) | −1.73377e11 | −0.0510758 | ||||||||
\(610\) | −2.67730e12 | −0.782912 | ||||||||
\(611\) | 1.99731e12 | 0.579774 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.68203e12 | −0.481128 | −0.240564 | − | 0.970633i | \(-0.577332\pi\) | ||||
−0.240564 | + | 0.970633i | \(0.577332\pi\) | |||||||
\(614\) | 3.56663e12 | 1.01274 | ||||||||
\(615\) | 6.48923e11 | 0.182917 | ||||||||
\(616\) | −3.54844e12 | −0.992943 | ||||||||
\(617\) | 3.08394e12 | 0.856689 | 0.428344 | − | 0.903616i | \(-0.359097\pi\) | ||||
0.428344 | + | 0.903616i | \(0.359097\pi\) | |||||||
\(618\) | −5.97866e11 | −0.164875 | ||||||||
\(619\) | 5.43988e11 | 0.148930 | 0.0744649 | − | 0.997224i | \(-0.476275\pi\) | ||||
0.0744649 | + | 0.997224i | \(0.476275\pi\) | |||||||
\(620\) | −3.24691e11 | −0.0882485 | ||||||||
\(621\) | −1.27274e12 | −0.343420 | ||||||||
\(622\) | 7.86210e12 | 2.10611 | ||||||||
\(623\) | −3.65336e12 | −0.971620 | ||||||||
\(624\) | −7.59605e11 | −0.200566 | ||||||||
\(625\) | −2.69726e12 | −0.707071 | ||||||||
\(626\) | −7.52898e11 | −0.195953 | ||||||||
\(627\) | 1.59358e12 | 0.411784 | ||||||||
\(628\) | −1.74323e12 | −0.447236 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −3.10133e12 | −0.784360 | ||||||||
\(631\) | 4.83979e12 | 1.21533 | 0.607665 | − | 0.794193i | \(-0.292106\pi\) | ||||
0.607665 | + | 0.794193i | \(0.292106\pi\) | |||||||
\(632\) | −3.15953e12 | −0.787763 | ||||||||
\(633\) | 7.07229e11 | 0.175083 | ||||||||
\(634\) | 5.57399e12 | 1.37014 | ||||||||
\(635\) | −8.01373e11 | −0.195593 | ||||||||
\(636\) | 1.39575e11 | 0.0338259 | ||||||||
\(637\) | −1.87526e12 | −0.451267 | ||||||||
\(638\) | −4.23090e12 | −1.01097 | ||||||||
\(639\) | 5.94366e12 | 1.41026 | ||||||||
\(640\) | −4.26761e12 | −1.00548 | ||||||||
\(641\) | −4.45073e11 | −0.104129 | −0.0520643 | − | 0.998644i | \(-0.516580\pi\) | ||||
−0.0520643 | + | 0.998644i | \(0.516580\pi\) | |||||||
\(642\) | 5.15151e11 | 0.119682 | ||||||||
\(643\) | −6.18246e12 | −1.42630 | −0.713152 | − | 0.701010i | \(-0.752733\pi\) | ||||
−0.713152 | + | 0.701010i | \(0.752733\pi\) | |||||||
\(644\) | −1.67873e12 | −0.384586 | ||||||||
\(645\) | 1.04611e12 | 0.237990 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.44313e11 | 0.0996828 | 0.0498414 | − | 0.998757i | \(-0.484128\pi\) | ||||
0.0498414 | + | 0.998757i | \(0.484128\pi\) | |||||||
\(648\) | 2.91276e12 | 0.648960 | ||||||||
\(649\) | −8.02118e12 | −1.77475 | ||||||||
\(650\) | 1.42386e12 | 0.312864 | ||||||||
\(651\) | 1.23907e11 | 0.0270384 | ||||||||
\(652\) | 7.35839e11 | 0.159466 | ||||||||
\(653\) | 6.17383e12 | 1.32876 | 0.664378 | − | 0.747397i | \(-0.268697\pi\) | ||||
0.664378 | + | 0.747397i | \(0.268697\pi\) | |||||||
\(654\) | 1.61895e11 | 0.0346046 | ||||||||
\(655\) | −5.10581e12 | −1.08387 | ||||||||
\(656\) | −8.49065e12 | −1.79008 | ||||||||
\(657\) | 4.09590e12 | 0.857640 | ||||||||
\(658\) | 2.30553e12 | 0.479463 | ||||||||
\(659\) | 7.68232e12 | 1.58675 | 0.793374 | − | 0.608735i | \(-0.208323\pi\) | ||||
0.793374 | + | 0.608735i | \(0.208323\pi\) | |||||||
\(660\) | 4.82450e11 | 0.0989702 | ||||||||
\(661\) | −7.12469e12 | −1.45164 | −0.725821 | − | 0.687884i | \(-0.758540\pi\) | ||||
−0.725821 | + | 0.687884i | \(0.758540\pi\) | |||||||
\(662\) | 5.76294e12 | 1.16623 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.95691e12 | −0.989589 | ||||||||
\(665\) | −5.16091e12 | −1.02336 | ||||||||
\(666\) | −3.96104e11 | −0.0780144 | ||||||||
\(667\) | 2.78150e12 | 0.544143 | ||||||||
\(668\) | 9.45745e10 | 0.0183772 | ||||||||
\(669\) | −6.90183e11 | −0.133213 | ||||||||
\(670\) | −5.03635e12 | −0.965561 | ||||||||
\(671\) | 7.35542e12 | 1.40074 | ||||||||
\(672\) | −4.66728e11 | −0.0882880 | ||||||||
\(673\) | −1.48990e12 | −0.279956 | −0.139978 | − | 0.990155i | \(-0.544703\pi\) | ||||
−0.139978 | + | 0.990155i | \(0.544703\pi\) | |||||||
\(674\) | 7.33414e12 | 1.36892 | ||||||||
\(675\) | 3.67618e11 | 0.0681600 | ||||||||
\(676\) | 5.23136e11 | 0.0963505 | ||||||||
\(677\) | −2.00832e12 | −0.367438 | −0.183719 | − | 0.982979i | \(-0.558814\pi\) | ||||
−0.183719 | + | 0.982979i | \(0.558814\pi\) | |||||||
\(678\) | 5.85393e11 | 0.106393 | ||||||||
\(679\) | −9.70470e10 | −0.0175214 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.31218e11 | −0.0590136 | ||||||||
\(682\) | 3.02368e12 | 0.535187 | ||||||||
\(683\) | 4.93569e12 | 0.867870 | 0.433935 | − | 0.900944i | \(-0.357125\pi\) | ||||
0.433935 | + | 0.900944i | \(0.357125\pi\) | |||||||
\(684\) | −3.56676e12 | −0.623048 | ||||||||
\(685\) | −5.96325e11 | −0.103484 | ||||||||
\(686\) | −7.48512e12 | −1.29045 | ||||||||
\(687\) | 1.12916e12 | 0.193398 | ||||||||
\(688\) | −1.36876e13 | −2.32905 | ||||||||
\(689\) | 3.64668e12 | 0.616470 | ||||||||
\(690\) | −1.07511e12 | −0.180565 | ||||||||
\(691\) | 1.12902e13 | 1.88387 | 0.941934 | − | 0.335798i | \(-0.109006\pi\) | ||||
0.941934 | + | 0.335798i | \(0.109006\pi\) | |||||||
\(692\) | 2.48604e12 | 0.412127 | ||||||||
\(693\) | 8.52037e12 | 1.40333 | ||||||||
\(694\) | −3.94158e12 | −0.644990 | ||||||||
\(695\) | −6.10433e12 | −0.992444 | ||||||||
\(696\) | 2.84352e11 | 0.0459320 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 5.30988e12 | 0.846711 | ||||||||
\(699\) | 6.80903e11 | 0.107879 | ||||||||
\(700\) | 4.84884e11 | 0.0763303 | ||||||||
\(701\) | −6.20736e12 | −0.970904 | −0.485452 | − | 0.874263i | \(-0.661345\pi\) | ||||
−0.485452 | + | 0.874263i | \(0.661345\pi\) | |||||||
\(702\) | 2.44626e12 | 0.380177 | ||||||||
\(703\) | −6.59155e11 | −0.101786 | ||||||||
\(704\) | 3.69514e12 | 0.566962 | ||||||||
\(705\) | 4.35602e11 | 0.0664109 | ||||||||
\(706\) | −4.83991e12 | −0.733189 | ||||||||
\(707\) | 2.66550e12 | 0.401227 | ||||||||
\(708\) | −3.87934e11 | −0.0580240 | ||||||||
\(709\) | 1.90163e12 | 0.282629 | 0.141315 | − | 0.989965i | \(-0.454867\pi\) | ||||
0.141315 | + | 0.989965i | \(0.454867\pi\) | |||||||
\(710\) | 1.01500e13 | 1.49901 | ||||||||
\(711\) | 7.58653e12 | 1.11335 | ||||||||
\(712\) | 5.99179e12 | 0.873769 | ||||||||
\(713\) | −1.98784e12 | −0.288057 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.26050e13 | 1.80371 | ||||||||
\(716\) | −2.38615e11 | −0.0339304 | ||||||||
\(717\) | 1.58579e12 | 0.224083 | ||||||||
\(718\) | −6.68375e12 | −0.938556 | ||||||||
\(719\) | −4.62958e12 | −0.646043 | −0.323022 | − | 0.946392i | \(-0.604699\pi\) | ||||
−0.323022 | + | 0.946392i | \(0.604699\pi\) | |||||||
\(720\) | 7.66682e12 | 1.06321 | ||||||||
\(721\) | −5.31946e12 | −0.733093 | ||||||||
\(722\) | −1.14229e13 | −1.56443 | ||||||||
\(723\) | −4.45500e11 | −0.0606353 | ||||||||
\(724\) | 4.87103e12 | 0.658866 | ||||||||
\(725\) | −8.03411e11 | −0.107998 | ||||||||
\(726\) | −3.19624e12 | −0.426997 | ||||||||
\(727\) | −4.11644e11 | −0.0546533 | −0.0273267 | − | 0.999627i | \(-0.508699\pi\) | ||||
−0.0273267 | + | 0.999627i | \(0.508699\pi\) | |||||||
\(728\) | −4.48383e12 | −0.591640 | ||||||||
\(729\) | −6.67484e12 | −0.875320 | ||||||||
\(730\) | 6.99458e12 | 0.911609 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 3.55736e11 | 0.0457960 | ||||||||
\(733\) | −4.17503e11 | −0.0534185 | −0.0267093 | − | 0.999643i | \(-0.508503\pi\) | ||||
−0.0267093 | + | 0.999643i | \(0.508503\pi\) | |||||||
\(734\) | −1.40523e13 | −1.78696 | ||||||||
\(735\) | −4.08984e11 | −0.0516909 | ||||||||
\(736\) | 7.48773e12 | 0.940589 | ||||||||
\(737\) | 1.38365e13 | 1.72752 | ||||||||
\(738\) | 1.35257e13 | 1.67844 | ||||||||
\(739\) | 9.55303e12 | 1.17826 | 0.589130 | − | 0.808038i | \(-0.299471\pi\) | ||||
0.589130 | + | 0.808038i | \(0.299471\pi\) | |||||||
\(740\) | −1.99557e11 | −0.0244638 | ||||||||
\(741\) | 2.01365e12 | 0.245359 | ||||||||
\(742\) | 4.20945e12 | 0.509809 | ||||||||
\(743\) | −5.13979e12 | −0.618722 | −0.309361 | − | 0.950945i | \(-0.600115\pi\) | ||||
−0.309361 | + | 0.950945i | \(0.600115\pi\) | |||||||
\(744\) | −2.03217e11 | −0.0243154 | ||||||||
\(745\) | 4.38876e12 | 0.521962 | ||||||||
\(746\) | 1.61612e13 | 1.91051 | ||||||||
\(747\) | 1.19023e13 | 1.39859 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.58352e12 | 0.532146 | ||||||||
\(750\) | 1.62171e12 | 0.187154 | ||||||||
\(751\) | 7.08291e12 | 0.812516 | 0.406258 | − | 0.913758i | \(-0.366833\pi\) | ||||
0.406258 | + | 0.913758i | \(0.366833\pi\) | |||||||
\(752\) | −5.69952e12 | −0.649917 | ||||||||
\(753\) | 3.41060e11 | 0.0386593 | ||||||||
\(754\) | −5.34618e12 | −0.602383 | ||||||||
\(755\) | −1.34667e12 | −0.150834 | ||||||||
\(756\) | 8.33058e11 | 0.0927528 | ||||||||
\(757\) | −9.55210e12 | −1.05722 | −0.528612 | − | 0.848863i | \(-0.677287\pi\) | ||||
−0.528612 | + | 0.848863i | \(0.677287\pi\) | |||||||
\(758\) | −2.49970e12 | −0.275028 | ||||||||
\(759\) | 2.95368e12 | 0.323055 | ||||||||
\(760\) | 8.46429e12 | 0.920300 | ||||||||
\(761\) | −8.35916e12 | −0.903508 | −0.451754 | − | 0.892143i | \(-0.649201\pi\) | ||||
−0.451754 | + | 0.892143i | \(0.649201\pi\) | |||||||
\(762\) | 3.60927e11 | 0.0387812 | ||||||||
\(763\) | 1.44045e12 | 0.153864 | ||||||||
\(764\) | −2.99716e12 | −0.318266 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.63072e13 | −1.71140 | ||||||||
\(767\) | −1.01356e13 | −1.05747 | ||||||||
\(768\) | 1.49502e12 | 0.155067 | ||||||||
\(769\) | −4.20920e10 | −0.00434041 | −0.00217021 | − | 0.999998i | \(-0.500691\pi\) | ||||
−0.00217021 | + | 0.999998i | \(0.500691\pi\) | |||||||
\(770\) | 1.45503e13 | 1.49163 | ||||||||
\(771\) | 2.38918e12 | 0.243503 | ||||||||
\(772\) | 7.48543e12 | 0.758470 | ||||||||
\(773\) | −1.22458e12 | −0.123362 | −0.0616808 | − | 0.998096i | \(-0.519646\pi\) | ||||
−0.0616808 | + | 0.998096i | \(0.519646\pi\) | |||||||
\(774\) | 2.18044e13 | 2.18378 | ||||||||
\(775\) | 5.74169e11 | 0.0571719 | ||||||||
\(776\) | 1.59164e11 | 0.0157568 | ||||||||
\(777\) | 7.61538e10 | 0.00749544 | ||||||||
\(778\) | −2.05576e13 | −2.01171 | ||||||||
\(779\) | 2.25080e13 | 2.18987 | ||||||||
\(780\) | 6.09626e11 | 0.0589709 | ||||||||
\(781\) | −2.78854e13 | −2.68192 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.38030e12 | −0.131234 | ||||||||
\(784\) | 5.35124e12 | 0.505863 | ||||||||
\(785\) | −9.93329e12 | −0.933640 | ||||||||
\(786\) | 2.29958e12 | 0.214906 | ||||||||
\(787\) | 1.03160e13 | 0.958570 | 0.479285 | − | 0.877659i | \(-0.340896\pi\) | ||||
0.479285 | + | 0.877659i | \(0.340896\pi\) | |||||||
\(788\) | −3.16658e12 | −0.292565 | ||||||||
\(789\) | −2.08513e12 | −0.191552 | ||||||||
\(790\) | 1.29555e13 | 1.18341 | ||||||||
\(791\) | 5.20848e12 | 0.473061 | ||||||||
\(792\) | −1.39741e13 | −1.26200 | ||||||||
\(793\) | 9.29435e12 | 0.834621 | ||||||||
\(794\) | 2.38912e12 | 0.213327 | ||||||||
\(795\) | 7.95324e11 | 0.0706142 | ||||||||
\(796\) | 2.66244e12 | 0.235056 | ||||||||
\(797\) | 1.05845e13 | 0.929196 | 0.464598 | − | 0.885522i | \(-0.346199\pi\) | ||||
0.464598 | + | 0.885522i | \(0.346199\pi\) | |||||||
\(798\) | 2.32440e12 | 0.202907 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −2.16276e12 | −0.186682 | ||||||||
\(801\) | −1.43872e13 | −1.23490 | ||||||||
\(802\) | −1.87396e13 | −1.59947 | ||||||||
\(803\) | −1.92164e13 | −1.63099 | ||||||||
\(804\) | 6.69185e11 | 0.0564799 | ||||||||
\(805\) | −9.56572e12 | −0.802853 | ||||||||
\(806\) | 3.82073e12 | 0.318888 | ||||||||
\(807\) | 3.14110e12 | 0.260705 | ||||||||
\(808\) | −4.37161e12 | −0.360820 | ||||||||
\(809\) | 5.95200e12 | 0.488534 | 0.244267 | − | 0.969708i | \(-0.421453\pi\) | ||||
0.244267 | + | 0.969708i | \(0.421453\pi\) | |||||||
\(810\) | −1.19437e13 | −0.974890 | ||||||||
\(811\) | 1.22320e13 | 0.992896 | 0.496448 | − | 0.868066i | \(-0.334637\pi\) | ||||
0.496448 | + | 0.868066i | \(0.334637\pi\) | |||||||
\(812\) | −1.82061e12 | −0.146965 | ||||||||
\(813\) | 8.28519e11 | 0.0665112 | ||||||||
\(814\) | 1.85837e12 | 0.148362 | ||||||||
\(815\) | 4.19296e12 | 0.332898 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.62846e13 | 2.84920 | ||||||||
\(818\) | 8.86915e12 | 0.692615 | ||||||||
\(819\) | 1.07664e13 | 0.836165 | ||||||||
\(820\) | 6.81422e12 | 0.526325 | ||||||||
\(821\) | −6.29236e12 | −0.483359 | −0.241679 | − | 0.970356i | \(-0.577698\pi\) | ||||
−0.241679 | + | 0.970356i | \(0.577698\pi\) | |||||||
\(822\) | 2.68576e11 | 0.0205184 | ||||||||
\(823\) | −3.82855e12 | −0.290894 | −0.145447 | − | 0.989366i | \(-0.546462\pi\) | ||||
−0.145447 | + | 0.989366i | \(0.546462\pi\) | |||||||
\(824\) | 8.72432e12 | 0.659263 | ||||||||
\(825\) | −8.53144e11 | −0.0641179 | ||||||||
\(826\) | −1.16997e13 | −0.874512 | ||||||||
\(827\) | 6.54281e12 | 0.486395 | 0.243198 | − | 0.969977i | \(-0.421804\pi\) | ||||
0.243198 | + | 0.969977i | \(0.421804\pi\) | |||||||
\(828\) | −6.61097e12 | −0.488797 | ||||||||
\(829\) | 1.48419e13 | 1.09142 | 0.545711 | − | 0.837973i | \(-0.316260\pi\) | ||||
0.545711 | + | 0.837973i | \(0.316260\pi\) | |||||||
\(830\) | 2.03256e13 | 1.48660 | ||||||||
\(831\) | 3.03487e12 | 0.220767 | ||||||||
\(832\) | 4.66919e12 | 0.337821 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.74930e12 | 0.196777 | ||||||||
\(835\) | 5.38904e11 | 0.0383639 | ||||||||
\(836\) | 1.67339e13 | 1.18486 | ||||||||
\(837\) | 9.86454e11 | 0.0694724 | ||||||||
\(838\) | −1.91411e12 | −0.134082 | ||||||||
\(839\) | 1.53149e13 | 1.06705 | 0.533526 | − | 0.845784i | \(-0.320867\pi\) | ||||
0.533526 | + | 0.845784i | \(0.320867\pi\) | |||||||
\(840\) | −9.77900e11 | −0.0677701 | ||||||||
\(841\) | −1.14906e13 | −0.792062 | ||||||||
\(842\) | 1.67072e13 | 1.14551 | ||||||||
\(843\) | −3.72492e12 | −0.254035 | ||||||||
\(844\) | 7.42649e12 | 0.503782 | ||||||||
\(845\) | 2.98093e12 | 0.201139 | ||||||||
\(846\) | 9.07938e12 | 0.609382 | ||||||||
\(847\) | −2.84383e13 | −1.89858 | ||||||||
\(848\) | −1.04062e13 | −0.691052 | ||||||||
\(849\) | 2.30975e12 | 0.152574 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.22174e12 | −0.0798538 | ||||||||
\(852\) | −1.34864e12 | −0.0876834 | ||||||||
\(853\) | 1.38576e13 | 0.896224 | 0.448112 | − | 0.893977i | \(-0.352097\pi\) | ||||
0.448112 | + | 0.893977i | \(0.352097\pi\) | |||||||
\(854\) | 1.07287e13 | 0.690216 | ||||||||
\(855\) | −2.03241e13 | −1.30066 | ||||||||
\(856\) | −7.51731e12 | −0.478554 | ||||||||
\(857\) | −2.49616e13 | −1.58073 | −0.790367 | − | 0.612634i | \(-0.790110\pi\) | ||||
−0.790367 | + | 0.612634i | \(0.790110\pi\) | |||||||
\(858\) | −5.67712e12 | −0.357631 | ||||||||
\(859\) | −2.53111e13 | −1.58614 | −0.793071 | − | 0.609130i | \(-0.791519\pi\) | ||||
−0.793071 | + | 0.609130i | \(0.791519\pi\) | |||||||
\(860\) | 1.09850e13 | 0.684792 | ||||||||
\(861\) | −2.60041e12 | −0.161260 | ||||||||
\(862\) | 1.54184e13 | 0.951167 | ||||||||
\(863\) | −1.28027e13 | −0.785692 | −0.392846 | − | 0.919604i | \(-0.628509\pi\) | ||||
−0.392846 | + | 0.919604i | \(0.628509\pi\) | |||||||
\(864\) | −3.71574e12 | −0.226847 | ||||||||
\(865\) | 1.41660e13 | 0.860347 | ||||||||
\(866\) | −5.00140e11 | −0.0302177 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.30112e12 | 0.0778001 | ||||||||
\(869\) | −3.55931e13 | −2.11727 | ||||||||
\(870\) | −1.16598e12 | −0.0690006 | ||||||||
\(871\) | 1.74839e13 | 1.02933 | ||||||||
\(872\) | −2.36244e12 | −0.138369 | ||||||||
\(873\) | −3.82179e11 | −0.0222691 | ||||||||
\(874\) | −3.72905e13 | −2.16170 | ||||||||
\(875\) | 1.44291e13 | 0.832151 | ||||||||
\(876\) | −9.29376e11 | −0.0533240 | ||||||||
\(877\) | −3.41529e13 | −1.94953 | −0.974763 | − | 0.223240i | \(-0.928336\pi\) | ||||
−0.974763 | + | 0.223240i | \(0.928336\pi\) | |||||||
\(878\) | 5.28570e12 | 0.300177 | ||||||||
\(879\) | −2.01769e12 | −0.114000 | ||||||||
\(880\) | −3.59698e13 | −2.02193 | ||||||||
\(881\) | −1.43259e13 | −0.801181 | −0.400591 | − | 0.916257i | \(-0.631195\pi\) | ||||
−0.400591 | + | 0.916257i | \(0.631195\pi\) | |||||||
\(882\) | −8.52457e12 | −0.474312 | ||||||||
\(883\) | −2.75197e13 | −1.52342 | −0.761711 | − | 0.647916i | \(-0.775641\pi\) | ||||
−0.761711 | + | 0.647916i | \(0.775641\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.21052e12 | −0.121130 | ||||||||
\(886\) | −4.66634e12 | −0.254404 | ||||||||
\(887\) | 1.55573e13 | 0.843877 | 0.421938 | − | 0.906624i | \(-0.361350\pi\) | ||||
0.421938 | + | 0.906624i | \(0.361350\pi\) | |||||||
\(888\) | −1.24898e11 | −0.00674058 | ||||||||
\(889\) | 3.21132e12 | 0.172435 | ||||||||
\(890\) | −2.45691e13 | −1.31261 | ||||||||
\(891\) | 3.28132e13 | 1.74421 | ||||||||
\(892\) | −7.24749e12 | −0.383306 | ||||||||
\(893\) | 1.51090e13 | 0.795066 | ||||||||
\(894\) | −1.97664e12 | −0.103492 | ||||||||
\(895\) | −1.35967e12 | −0.0708322 | ||||||||
\(896\) | 1.71015e13 | 0.886436 | ||||||||
\(897\) | 3.73229e12 | 0.192490 | ||||||||
\(898\) | 5.90499e12 | 0.303023 | ||||||||
\(899\) | −2.15585e12 | −0.110078 | ||||||||
\(900\) | 1.90951e12 | 0.0970134 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −6.34573e13 | −3.19192 | ||||||||
\(903\) | −4.19205e12 | −0.209813 | ||||||||
\(904\) | −8.54231e12 | −0.425419 | ||||||||
\(905\) | 2.77561e13 | 1.37543 | ||||||||
\(906\) | 6.06520e11 | 0.0299067 | ||||||||
\(907\) | 1.46031e13 | 0.716494 | 0.358247 | − | 0.933627i | \(-0.383375\pi\) | ||||
0.358247 | + | 0.933627i | \(0.383375\pi\) | |||||||
\(908\) | −3.47807e12 | −0.169805 | ||||||||
\(909\) | 1.04969e13 | 0.509947 | ||||||||
\(910\) | 1.83858e13 | 0.888783 | ||||||||
\(911\) | 1.79784e12 | 0.0864807 | 0.0432404 | − | 0.999065i | \(-0.486232\pi\) | ||||
0.0432404 | + | 0.999065i | \(0.486232\pi\) | |||||||
\(912\) | −5.74616e12 | −0.275043 | ||||||||
\(913\) | −5.58412e13 | −2.65972 | ||||||||
\(914\) | −1.07818e13 | −0.511014 | ||||||||
\(915\) | 2.02705e12 | 0.0956026 | ||||||||
\(916\) | 1.18571e13 | 0.556481 | ||||||||
\(917\) | 2.04604e13 | 0.955545 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.20132e12 | −0.286790 | −0.143395 | − | 0.989666i | \(-0.545802\pi\) | ||||
−0.143395 | + | 0.989666i | \(0.545802\pi\) | |||||||
\(920\) | 1.56885e13 | 0.721998 | ||||||||
\(921\) | −2.70038e12 | −0.123668 | ||||||||
\(922\) | −1.87655e13 | −0.855207 | ||||||||
\(923\) | −3.52361e13 | −1.59801 | ||||||||
\(924\) | −1.93331e12 | −0.0872523 | ||||||||
\(925\) | 3.52888e11 | 0.0158489 | ||||||||
\(926\) | −2.81989e13 | −1.26033 | ||||||||
\(927\) | −2.09485e13 | −0.931737 | ||||||||
\(928\) | 8.12057e12 | 0.359435 | ||||||||
\(929\) | −4.48551e12 | −0.197579 | −0.0987896 | − | 0.995108i | \(-0.531497\pi\) | ||||
−0.0987896 | + | 0.995108i | \(0.531497\pi\) | |||||||
\(930\) | 8.33282e11 | 0.0365274 | ||||||||
\(931\) | −1.41857e13 | −0.618839 | ||||||||
\(932\) | 7.15004e12 | 0.310411 | ||||||||
\(933\) | −5.95259e12 | −0.257181 | ||||||||
\(934\) | −3.15332e13 | −1.35583 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.76577e13 | −0.751956 | ||||||||
\(937\) | 3.19604e13 | 1.35451 | 0.677257 | − | 0.735746i | \(-0.263168\pi\) | ||||
0.677257 | + | 0.735746i | \(0.263168\pi\) | |||||||
\(938\) | 2.01820e13 | 0.851240 | ||||||||
\(939\) | 5.70037e11 | 0.0239281 | ||||||||
\(940\) | 4.57419e12 | 0.191090 | ||||||||
\(941\) | 3.68931e13 | 1.53388 | 0.766941 | − | 0.641718i | \(-0.221778\pi\) | ||||
0.766941 | + | 0.641718i | \(0.221778\pi\) | |||||||
\(942\) | 4.47381e12 | 0.185118 | ||||||||
\(943\) | 4.17184e13 | 1.71801 | ||||||||
\(944\) | 2.89230e13 | 1.18541 | ||||||||
\(945\) | 4.74693e12 | 0.193629 | ||||||||
\(946\) | −1.02298e14 | −4.15295 | ||||||||
\(947\) | −3.52895e13 | −1.42584 | −0.712920 | − | 0.701246i | \(-0.752628\pi\) | ||||
−0.712920 | + | 0.701246i | \(0.752628\pi\) | |||||||
\(948\) | −1.72141e12 | −0.0692226 | ||||||||
\(949\) | −2.42819e13 | −0.971819 | ||||||||
\(950\) | 1.07710e13 | 0.429042 | ||||||||
\(951\) | −4.22021e12 | −0.167310 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.19331e11 | 0.00468634 | 0.00234317 | − | 0.999997i | \(-0.499254\pi\) | ||||
0.00234317 | + | 0.999997i | \(0.499254\pi\) | |||||||
\(954\) | 1.65771e13 | 0.647951 | ||||||||
\(955\) | −1.70784e13 | −0.664405 | ||||||||
\(956\) | 1.66521e13 | 0.644776 | ||||||||
\(957\) | 3.20332e12 | 0.123452 | ||||||||
\(958\) | −3.34129e13 | −1.28165 | ||||||||
\(959\) | 2.38963e12 | 0.0912321 | ||||||||
\(960\) | 1.01833e12 | 0.0386961 | ||||||||
\(961\) | −2.48989e13 | −0.941727 | ||||||||
\(962\) | 2.34824e12 | 0.0884005 | ||||||||
\(963\) | 1.80503e13 | 0.676340 | ||||||||
\(964\) | −4.67812e12 | −0.174471 | ||||||||
\(965\) | 4.26534e13 | 1.58336 | ||||||||
\(966\) | 4.30826e12 | 0.159186 | ||||||||
\(967\) | −3.07077e13 | −1.12935 | −0.564674 | − | 0.825314i | \(-0.690998\pi\) | ||||
−0.564674 | + | 0.825314i | \(0.690998\pi\) | |||||||
\(968\) | 4.66410e13 | 1.70737 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.52648e11 | −0.0236704 | ||||||||
\(971\) | −2.09057e13 | −0.754706 | −0.377353 | − | 0.926069i | \(-0.623166\pi\) | ||||
−0.377353 | + | 0.926069i | \(0.623166\pi\) | |||||||
\(972\) | 4.93851e12 | 0.177459 | ||||||||
\(973\) | 2.44617e13 | 0.874940 | ||||||||
\(974\) | −3.28145e13 | −1.16829 | ||||||||
\(975\) | −1.07804e12 | −0.0382043 | ||||||||
\(976\) | −2.65224e13 | −0.935596 | ||||||||
\(977\) | −1.72144e12 | −0.0604459 | −0.0302230 | − | 0.999543i | \(-0.509622\pi\) | ||||
−0.0302230 | + | 0.999543i | \(0.509622\pi\) | |||||||
\(978\) | −1.88845e12 | −0.0660055 | ||||||||
\(979\) | 6.74994e13 | 2.34843 | ||||||||
\(980\) | −4.29467e12 | −0.148735 | ||||||||
\(981\) | 5.67261e12 | 0.195556 | ||||||||
\(982\) | −1.76942e13 | −0.607198 | ||||||||
\(983\) | 2.07042e13 | 0.707241 | 0.353621 | − | 0.935389i | \(-0.384950\pi\) | ||||
0.353621 | + | 0.935389i | \(0.384950\pi\) | |||||||
\(984\) | 4.26486e12 | 0.145020 | ||||||||
\(985\) | −1.80438e13 | −0.610751 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.74558e12 | −0.0585479 | ||||||||
\(988\) | 2.11450e13 | 0.705995 | ||||||||
\(989\) | 6.72533e13 | 2.23527 | ||||||||
\(990\) | 5.73001e13 | 1.89582 | ||||||||
\(991\) | −4.22967e13 | −1.39308 | −0.696539 | − | 0.717519i | \(-0.745278\pi\) | ||||
−0.696539 | + | 0.717519i | \(0.745278\pi\) | |||||||
\(992\) | −5.80348e12 | −0.190277 | ||||||||
\(993\) | −4.36326e12 | −0.142410 | ||||||||
\(994\) | −4.06738e13 | −1.32153 | ||||||||
\(995\) | 1.51711e13 | 0.490697 | ||||||||
\(996\) | −2.70069e12 | −0.0869575 | ||||||||
\(997\) | −5.58372e13 | −1.78976 | −0.894882 | − | 0.446303i | \(-0.852740\pi\) | ||||
−0.894882 | + | 0.446303i | \(0.852740\pi\) | |||||||
\(998\) | 4.49891e13 | 1.43555 | ||||||||
\(999\) | 6.06280e11 | 0.0192588 |
(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 | 289.10.a.h.1.8 | yes | 36 | |
17.16 | even | 2 | 289.10.a.g.1.8 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.g.1.8 | ✓ | 36 | 17.16 | even | 2 | ||
289.10.a.h.1.8 | yes | 36 | 1.1 | even | 1 | trivial |