Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(55.2921495107\) |
Analytic rank: | \(1\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} - 89298188 x^{10} + 64650816672 x^{9} + \cdots - 58\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(15.6681\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 13.6681 | 1.20810 | 0.604049 | − | 0.796948i | \(-0.293553\pi\) | ||||
0.604049 | + | 0.796948i | \(0.293553\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 58.8158 | 0.459498 | ||||||||
\(5\) | −207.404 | −0.742031 | −0.371015 | − | 0.928627i | \(-0.620990\pi\) | ||||
−0.371015 | + | 0.928627i | \(0.620990\pi\) | |||||||
\(6\) | 369.038 | 0.697495 | ||||||||
\(7\) | 882.793 | 0.972782 | 0.486391 | − | 0.873741i | \(-0.338313\pi\) | ||||
0.486391 | + | 0.873741i | \(0.338313\pi\) | |||||||
\(8\) | −945.614 | −0.652978 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −2834.81 | −0.896445 | ||||||||
\(11\) | −3637.21 | −0.823937 | −0.411969 | − | 0.911198i | \(-0.635159\pi\) | ||||
−0.411969 | + | 0.911198i | \(0.635159\pi\) | |||||||
\(12\) | 1588.03 | 0.265292 | ||||||||
\(13\) | 208.023 | 0.0262609 | 0.0131305 | − | 0.999914i | \(-0.495820\pi\) | ||||
0.0131305 | + | 0.999914i | \(0.495820\pi\) | |||||||
\(14\) | 12066.1 | 1.17522 | ||||||||
\(15\) | −5599.90 | −0.428412 | ||||||||
\(16\) | −20453.1 | −1.24836 | ||||||||
\(17\) | −13120.6 | −0.647714 | −0.323857 | − | 0.946106i | \(-0.604980\pi\) | ||||
−0.323857 | + | 0.946106i | \(0.604980\pi\) | |||||||
\(18\) | 9964.01 | 0.402699 | ||||||||
\(19\) | −9914.89 | −0.331627 | −0.165814 | − | 0.986157i | \(-0.553025\pi\) | ||||
−0.165814 | + | 0.986157i | \(0.553025\pi\) | |||||||
\(20\) | −12198.6 | −0.340962 | ||||||||
\(21\) | 23835.4 | 0.561636 | ||||||||
\(22\) | −49713.6 | −0.995396 | ||||||||
\(23\) | −37757.5 | −0.647077 | −0.323538 | − | 0.946215i | \(-0.604872\pi\) | ||||
−0.323538 | + | 0.946215i | \(0.604872\pi\) | |||||||
\(24\) | −25531.6 | −0.376997 | ||||||||
\(25\) | −35108.6 | −0.449391 | ||||||||
\(26\) | 2843.27 | 0.0317257 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 51922.2 | 0.446992 | ||||||||
\(29\) | −98092.3 | −0.746865 | −0.373432 | − | 0.927657i | \(-0.621819\pi\) | ||||
−0.373432 | + | 0.927657i | \(0.621819\pi\) | |||||||
\(30\) | −76539.8 | −0.517563 | ||||||||
\(31\) | 326883. | 1.97073 | 0.985364 | − | 0.170463i | \(-0.0545265\pi\) | ||||
0.985364 | + | 0.170463i | \(0.0545265\pi\) | |||||||
\(32\) | −158516. | −0.855161 | ||||||||
\(33\) | −98204.7 | −0.475700 | ||||||||
\(34\) | −179333. | −0.782501 | ||||||||
\(35\) | −183095. | −0.721834 | ||||||||
\(36\) | 42876.7 | 0.153166 | ||||||||
\(37\) | 39434.0 | 0.127987 | 0.0639934 | − | 0.997950i | \(-0.479616\pi\) | ||||
0.0639934 | + | 0.997950i | \(0.479616\pi\) | |||||||
\(38\) | −135517. | −0.400638 | ||||||||
\(39\) | 5616.63 | 0.0151618 | ||||||||
\(40\) | 196124. | 0.484530 | ||||||||
\(41\) | −719442. | −1.63024 | −0.815121 | − | 0.579291i | \(-0.803330\pi\) | ||||
−0.815121 | + | 0.579291i | \(0.803330\pi\) | |||||||
\(42\) | 325784. | 0.678511 | ||||||||
\(43\) | −878099. | −1.68424 | −0.842120 | − | 0.539290i | \(-0.818693\pi\) | ||||
−0.842120 | + | 0.539290i | \(0.818693\pi\) | |||||||
\(44\) | −213925. | −0.378598 | ||||||||
\(45\) | −151197. | −0.247344 | ||||||||
\(46\) | −516072. | −0.781731 | ||||||||
\(47\) | −158129. | −0.222162 | −0.111081 | − | 0.993811i | \(-0.535431\pi\) | ||||
−0.111081 | + | 0.993811i | \(0.535431\pi\) | |||||||
\(48\) | −552234. | −0.720741 | ||||||||
\(49\) | −44219.7 | −0.0536945 | ||||||||
\(50\) | −479867. | −0.542907 | ||||||||
\(51\) | −354257. | −0.373958 | ||||||||
\(52\) | 12235.0 | 0.0120669 | ||||||||
\(53\) | −1.83479e6 | −1.69286 | −0.846429 | − | 0.532502i | \(-0.821252\pi\) | ||||
−0.846429 | + | 0.532502i | \(0.821252\pi\) | |||||||
\(54\) | 269028. | 0.232498 | ||||||||
\(55\) | 754372. | 0.611387 | ||||||||
\(56\) | −834781. | −0.635206 | ||||||||
\(57\) | −267702. | −0.191465 | ||||||||
\(58\) | −1.34073e6 | −0.902285 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | −329363. | −0.196854 | ||||||||
\(61\) | 3.49764e6 | 1.97297 | 0.986485 | − | 0.163851i | \(-0.0523917\pi\) | ||||
0.986485 | + | 0.163851i | \(0.0523917\pi\) | |||||||
\(62\) | 4.46786e6 | 2.38083 | ||||||||
\(63\) | 643556. | 0.324261 | ||||||||
\(64\) | 451395. | 0.215242 | ||||||||
\(65\) | −43144.8 | −0.0194864 | ||||||||
\(66\) | −1.34227e6 | −0.574692 | ||||||||
\(67\) | −1.00103e6 | −0.406615 | −0.203308 | − | 0.979115i | \(-0.565169\pi\) | ||||
−0.203308 | + | 0.979115i | \(0.565169\pi\) | |||||||
\(68\) | −771700. | −0.297623 | ||||||||
\(69\) | −1.01945e6 | −0.373590 | ||||||||
\(70\) | −2.50255e6 | −0.872046 | ||||||||
\(71\) | 331392. | 0.109885 | 0.0549423 | − | 0.998490i | \(-0.482502\pi\) | ||||
0.0549423 | + | 0.998490i | \(0.482502\pi\) | |||||||
\(72\) | −689352. | −0.217659 | ||||||||
\(73\) | −527191. | −0.158613 | −0.0793063 | − | 0.996850i | \(-0.525271\pi\) | ||||
−0.0793063 | + | 0.996850i | \(0.525271\pi\) | |||||||
\(74\) | 538987. | 0.154620 | ||||||||
\(75\) | −947933. | −0.259456 | ||||||||
\(76\) | −583152. | −0.152382 | ||||||||
\(77\) | −3.21090e6 | −0.801512 | ||||||||
\(78\) | 76768.4 | 0.0183169 | ||||||||
\(79\) | −1.50960e6 | −0.344481 | −0.172241 | − | 0.985055i | \(-0.555101\pi\) | ||||
−0.172241 | + | 0.985055i | \(0.555101\pi\) | |||||||
\(80\) | 4.24206e6 | 0.926321 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −9.83337e6 | −1.96949 | ||||||||
\(83\) | 2.48775e6 | 0.477566 | 0.238783 | − | 0.971073i | \(-0.423252\pi\) | ||||
0.238783 | + | 0.971073i | \(0.423252\pi\) | |||||||
\(84\) | 1.40190e6 | 0.258071 | ||||||||
\(85\) | 2.72127e6 | 0.480623 | ||||||||
\(86\) | −1.20019e7 | −2.03472 | ||||||||
\(87\) | −2.64849e6 | −0.431203 | ||||||||
\(88\) | 3.43940e6 | 0.538013 | ||||||||
\(89\) | 6.37807e6 | 0.959013 | 0.479506 | − | 0.877538i | \(-0.340816\pi\) | ||||
0.479506 | + | 0.877538i | \(0.340816\pi\) | |||||||
\(90\) | −2.06657e6 | −0.298815 | ||||||||
\(91\) | 183641. | 0.0255462 | ||||||||
\(92\) | −2.22074e6 | −0.297331 | ||||||||
\(93\) | 8.82585e6 | 1.13780 | ||||||||
\(94\) | −2.16132e6 | −0.268393 | ||||||||
\(95\) | 2.05639e6 | 0.246078 | ||||||||
\(96\) | −4.27993e6 | −0.493728 | ||||||||
\(97\) | −4.33428e6 | −0.482187 | −0.241094 | − | 0.970502i | \(-0.577506\pi\) | ||||
−0.241094 | + | 0.970502i | \(0.577506\pi\) | |||||||
\(98\) | −604398. | −0.0648682 | ||||||||
\(99\) | −2.65153e6 | −0.274646 | ||||||||
\(100\) | −2.06494e6 | −0.206494 | ||||||||
\(101\) | 6.87221e6 | 0.663700 | 0.331850 | − | 0.943332i | \(-0.392327\pi\) | ||||
0.331850 | + | 0.943332i | \(0.392327\pi\) | |||||||
\(102\) | −4.84200e6 | −0.451777 | ||||||||
\(103\) | 1.71578e6 | 0.154715 | 0.0773574 | − | 0.997003i | \(-0.475352\pi\) | ||||
0.0773574 | + | 0.997003i | \(0.475352\pi\) | |||||||
\(104\) | −196710. | −0.0171478 | ||||||||
\(105\) | −4.94356e6 | −0.416751 | ||||||||
\(106\) | −2.50780e7 | −2.04514 | ||||||||
\(107\) | −7.08886e6 | −0.559414 | −0.279707 | − | 0.960085i | \(-0.590237\pi\) | ||||
−0.279707 | + | 0.960085i | \(0.590237\pi\) | |||||||
\(108\) | 1.15767e6 | 0.0884305 | ||||||||
\(109\) | 2.29535e7 | 1.69768 | 0.848840 | − | 0.528650i | \(-0.177301\pi\) | ||||
0.848840 | + | 0.528650i | \(0.177301\pi\) | |||||||
\(110\) | 1.03108e7 | 0.738614 | ||||||||
\(111\) | 1.06472e6 | 0.0738932 | ||||||||
\(112\) | −1.80559e7 | −1.21438 | ||||||||
\(113\) | −1.69616e7 | −1.10584 | −0.552919 | − | 0.833235i | \(-0.686486\pi\) | ||||
−0.552919 | + | 0.833235i | \(0.686486\pi\) | |||||||
\(114\) | −3.65897e6 | −0.231308 | ||||||||
\(115\) | 7.83105e6 | 0.480151 | ||||||||
\(116\) | −5.76938e6 | −0.343183 | ||||||||
\(117\) | 151649. | 0.00875364 | ||||||||
\(118\) | −2.80713e6 | −0.157281 | ||||||||
\(119\) | −1.15828e7 | −0.630084 | ||||||||
\(120\) | 5.29535e6 | 0.279743 | ||||||||
\(121\) | −6.25787e6 | −0.321127 | ||||||||
\(122\) | 4.78059e7 | 2.38354 | ||||||||
\(123\) | −1.94249e7 | −0.941220 | ||||||||
\(124\) | 1.92259e7 | 0.905546 | ||||||||
\(125\) | 2.34851e7 | 1.07549 | ||||||||
\(126\) | 8.79616e6 | 0.391738 | ||||||||
\(127\) | −1.24664e7 | −0.540044 | −0.270022 | − | 0.962854i | \(-0.587031\pi\) | ||||
−0.270022 | + | 0.962854i | \(0.587031\pi\) | |||||||
\(128\) | 2.64597e7 | 1.11519 | ||||||||
\(129\) | −2.37087e7 | −0.972396 | ||||||||
\(130\) | −589706. | −0.0235415 | ||||||||
\(131\) | 4.68201e7 | 1.81963 | 0.909815 | − | 0.415015i | \(-0.136224\pi\) | ||||
0.909815 | + | 0.415015i | \(0.136224\pi\) | |||||||
\(132\) | −5.77599e6 | −0.218584 | ||||||||
\(133\) | −8.75279e6 | −0.322601 | ||||||||
\(134\) | −1.36821e7 | −0.491231 | ||||||||
\(135\) | −4.08233e6 | −0.142804 | ||||||||
\(136\) | 1.24070e7 | 0.422943 | ||||||||
\(137\) | −1.03397e7 | −0.343545 | −0.171773 | − | 0.985137i | \(-0.554949\pi\) | ||||
−0.171773 | + | 0.985137i | \(0.554949\pi\) | |||||||
\(138\) | −1.39339e7 | −0.451333 | ||||||||
\(139\) | −3.07437e7 | −0.970965 | −0.485483 | − | 0.874246i | \(-0.661356\pi\) | ||||
−0.485483 | + | 0.874246i | \(0.661356\pi\) | |||||||
\(140\) | −1.07689e7 | −0.331682 | ||||||||
\(141\) | −4.26949e6 | −0.128265 | ||||||||
\(142\) | 4.52948e6 | 0.132751 | ||||||||
\(143\) | −756624. | −0.0216374 | ||||||||
\(144\) | −1.49103e7 | −0.416120 | ||||||||
\(145\) | 2.03447e7 | 0.554196 | ||||||||
\(146\) | −7.20567e6 | −0.191619 | ||||||||
\(147\) | −1.19393e6 | −0.0310005 | ||||||||
\(148\) | 2.31934e6 | 0.0588097 | ||||||||
\(149\) | 3.66220e6 | 0.0906963 | 0.0453482 | − | 0.998971i | \(-0.485560\pi\) | ||||
0.0453482 | + | 0.998971i | \(0.485560\pi\) | |||||||
\(150\) | −1.29564e7 | −0.313448 | ||||||||
\(151\) | 7.28781e7 | 1.72257 | 0.861286 | − | 0.508120i | \(-0.169659\pi\) | ||||
0.861286 | + | 0.508120i | \(0.169659\pi\) | |||||||
\(152\) | 9.37565e6 | 0.216545 | ||||||||
\(153\) | −9.56493e6 | −0.215905 | ||||||||
\(154\) | −4.38868e7 | −0.968304 | ||||||||
\(155\) | −6.77968e7 | −1.46234 | ||||||||
\(156\) | 330346. | 0.00696680 | ||||||||
\(157\) | −9.09496e7 | −1.87565 | −0.937826 | − | 0.347106i | \(-0.887164\pi\) | ||||
−0.937826 | + | 0.347106i | \(0.887164\pi\) | |||||||
\(158\) | −2.06332e7 | −0.416167 | ||||||||
\(159\) | −4.95393e7 | −0.977372 | ||||||||
\(160\) | 3.28768e7 | 0.634556 | ||||||||
\(161\) | −3.33320e7 | −0.629465 | ||||||||
\(162\) | 7.26377e6 | 0.134233 | ||||||||
\(163\) | 5.62746e7 | 1.01778 | 0.508892 | − | 0.860830i | \(-0.330055\pi\) | ||||
0.508892 | + | 0.860830i | \(0.330055\pi\) | |||||||
\(164\) | −4.23145e7 | −0.749094 | ||||||||
\(165\) | 2.03680e7 | 0.352984 | ||||||||
\(166\) | 3.40027e7 | 0.576945 | ||||||||
\(167\) | 3.21050e7 | 0.533415 | 0.266707 | − | 0.963778i | \(-0.414064\pi\) | ||||
0.266707 | + | 0.963778i | \(0.414064\pi\) | |||||||
\(168\) | −2.25391e7 | −0.366736 | ||||||||
\(169\) | −6.27052e7 | −0.999310 | ||||||||
\(170\) | 3.71944e7 | 0.580640 | ||||||||
\(171\) | −7.22795e6 | −0.110542 | ||||||||
\(172\) | −5.16461e7 | −0.773905 | ||||||||
\(173\) | 7.85878e7 | 1.15397 | 0.576984 | − | 0.816756i | \(-0.304230\pi\) | ||||
0.576984 | + | 0.816756i | \(0.304230\pi\) | |||||||
\(174\) | −3.61997e7 | −0.520935 | ||||||||
\(175\) | −3.09937e7 | −0.437159 | ||||||||
\(176\) | 7.43923e7 | 1.02857 | ||||||||
\(177\) | −5.54523e6 | −0.0751646 | ||||||||
\(178\) | 8.71759e7 | 1.15858 | ||||||||
\(179\) | −5.87666e7 | −0.765853 | −0.382926 | − | 0.923779i | \(-0.625084\pi\) | ||||
−0.382926 | + | 0.923779i | \(0.625084\pi\) | |||||||
\(180\) | −8.89280e6 | −0.113654 | ||||||||
\(181\) | −4.81650e7 | −0.603749 | −0.301875 | − | 0.953348i | \(-0.597612\pi\) | ||||
−0.301875 | + | 0.953348i | \(0.597612\pi\) | |||||||
\(182\) | 2.51002e6 | 0.0308622 | ||||||||
\(183\) | 9.44362e7 | 1.13909 | ||||||||
\(184\) | 3.57040e7 | 0.422527 | ||||||||
\(185\) | −8.17877e6 | −0.0949701 | ||||||||
\(186\) | 1.20632e8 | 1.37457 | ||||||||
\(187\) | 4.77225e7 | 0.533675 | ||||||||
\(188\) | −9.30049e6 | −0.102083 | ||||||||
\(189\) | 1.73760e7 | 0.187212 | ||||||||
\(190\) | 2.81068e7 | 0.297286 | ||||||||
\(191\) | 1.65487e8 | 1.71849 | 0.859247 | − | 0.511560i | \(-0.170932\pi\) | ||||
0.859247 | + | 0.511560i | \(0.170932\pi\) | |||||||
\(192\) | 1.21877e7 | 0.124270 | ||||||||
\(193\) | −1.11360e8 | −1.11501 | −0.557504 | − | 0.830174i | \(-0.688241\pi\) | ||||
−0.557504 | + | 0.830174i | \(0.688241\pi\) | |||||||
\(194\) | −5.92412e7 | −0.582529 | ||||||||
\(195\) | −1.16491e6 | −0.0112505 | ||||||||
\(196\) | −2.60082e6 | −0.0246725 | ||||||||
\(197\) | 3.64560e7 | 0.339733 | 0.169866 | − | 0.985467i | \(-0.445666\pi\) | ||||
0.169866 | + | 0.985467i | \(0.445666\pi\) | |||||||
\(198\) | −3.62412e7 | −0.331799 | ||||||||
\(199\) | 7.61265e7 | 0.684779 | 0.342389 | − | 0.939558i | \(-0.388764\pi\) | ||||
0.342389 | + | 0.939558i | \(0.388764\pi\) | |||||||
\(200\) | 3.31992e7 | 0.293442 | ||||||||
\(201\) | −2.70277e7 | −0.234760 | ||||||||
\(202\) | 9.39298e7 | 0.801814 | ||||||||
\(203\) | −8.65952e7 | −0.726537 | ||||||||
\(204\) | −2.08359e7 | −0.171833 | ||||||||
\(205\) | 1.49215e8 | 1.20969 | ||||||||
\(206\) | 2.34514e7 | 0.186911 | ||||||||
\(207\) | −2.75252e7 | −0.215692 | ||||||||
\(208\) | −4.25472e6 | −0.0327831 | ||||||||
\(209\) | 3.60625e7 | 0.273240 | ||||||||
\(210\) | −6.75688e7 | −0.503476 | ||||||||
\(211\) | 2.35187e8 | 1.72355 | 0.861775 | − | 0.507291i | \(-0.169353\pi\) | ||||
0.861775 | + | 0.507291i | \(0.169353\pi\) | |||||||
\(212\) | −1.07915e8 | −0.777866 | ||||||||
\(213\) | 8.94757e6 | 0.0634420 | ||||||||
\(214\) | −9.68910e7 | −0.675826 | ||||||||
\(215\) | 1.82121e8 | 1.24976 | ||||||||
\(216\) | −1.86125e7 | −0.125666 | ||||||||
\(217\) | 2.88570e8 | 1.91709 | ||||||||
\(218\) | 3.13730e8 | 2.05096 | ||||||||
\(219\) | −1.42342e7 | −0.0915751 | ||||||||
\(220\) | 4.43690e7 | 0.280931 | ||||||||
\(221\) | −2.72939e6 | −0.0170096 | ||||||||
\(222\) | 1.45526e7 | 0.0892702 | ||||||||
\(223\) | 1.57494e8 | 0.951036 | 0.475518 | − | 0.879706i | \(-0.342261\pi\) | ||||
0.475518 | + | 0.879706i | \(0.342261\pi\) | |||||||
\(224\) | −1.39937e8 | −0.831886 | ||||||||
\(225\) | −2.55942e7 | −0.149797 | ||||||||
\(226\) | −2.31832e8 | −1.33596 | ||||||||
\(227\) | −4.25579e7 | −0.241485 | −0.120742 | − | 0.992684i | \(-0.538527\pi\) | ||||
−0.120742 | + | 0.992684i | \(0.538527\pi\) | |||||||
\(228\) | −1.57451e7 | −0.0879779 | ||||||||
\(229\) | −5.07210e7 | −0.279103 | −0.139551 | − | 0.990215i | \(-0.544566\pi\) | ||||
−0.139551 | + | 0.990215i | \(0.544566\pi\) | |||||||
\(230\) | 1.07035e8 | 0.580069 | ||||||||
\(231\) | −8.66944e7 | −0.462753 | ||||||||
\(232\) | 9.27574e7 | 0.487686 | ||||||||
\(233\) | −2.44954e8 | −1.26864 | −0.634321 | − | 0.773069i | \(-0.718720\pi\) | ||||
−0.634321 | + | 0.773069i | \(0.718720\pi\) | |||||||
\(234\) | 2.07275e6 | 0.0105752 | ||||||||
\(235\) | 3.27966e7 | 0.164851 | ||||||||
\(236\) | −1.20795e7 | −0.0598216 | ||||||||
\(237\) | −4.07591e7 | −0.198886 | ||||||||
\(238\) | −1.58314e8 | −0.761203 | ||||||||
\(239\) | −3.38900e6 | −0.0160575 | −0.00802877 | − | 0.999968i | \(-0.502556\pi\) | ||||
−0.00802877 | + | 0.999968i | \(0.502556\pi\) | |||||||
\(240\) | 1.14536e8 | 0.534812 | ||||||||
\(241\) | 2.42976e8 | 1.11816 | 0.559080 | − | 0.829114i | \(-0.311155\pi\) | ||||
0.559080 | + | 0.829114i | \(0.311155\pi\) | |||||||
\(242\) | −8.55329e7 | −0.387953 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 2.05716e8 | 0.906577 | ||||||||
\(245\) | 9.17134e6 | 0.0398430 | ||||||||
\(246\) | −2.65501e8 | −1.13709 | ||||||||
\(247\) | −2.06253e6 | −0.00870884 | ||||||||
\(248\) | −3.09105e8 | −1.28684 | ||||||||
\(249\) | 6.71692e7 | 0.275723 | ||||||||
\(250\) | 3.20996e8 | 1.29930 | ||||||||
\(251\) | −1.00242e7 | −0.0400120 | −0.0200060 | − | 0.999800i | \(-0.506369\pi\) | ||||
−0.0200060 | + | 0.999800i | \(0.506369\pi\) | |||||||
\(252\) | 3.78513e7 | 0.148997 | ||||||||
\(253\) | 1.37332e8 | 0.533150 | ||||||||
\(254\) | −1.70392e8 | −0.652425 | ||||||||
\(255\) | 7.34742e7 | 0.277488 | ||||||||
\(256\) | 3.03875e8 | 1.13202 | ||||||||
\(257\) | −1.65390e8 | −0.607774 | −0.303887 | − | 0.952708i | \(-0.598285\pi\) | ||||
−0.303887 | + | 0.952708i | \(0.598285\pi\) | |||||||
\(258\) | −3.24052e8 | −1.17475 | ||||||||
\(259\) | 3.48121e7 | 0.124503 | ||||||||
\(260\) | −2.53760e6 | −0.00895397 | ||||||||
\(261\) | −7.15093e7 | −0.248955 | ||||||||
\(262\) | 6.39940e8 | 2.19829 | ||||||||
\(263\) | −3.86525e8 | −1.31019 | −0.655093 | − | 0.755549i | \(-0.727370\pi\) | ||||
−0.655093 | + | 0.755549i | \(0.727370\pi\) | |||||||
\(264\) | 9.28637e7 | 0.310622 | ||||||||
\(265\) | 3.80542e8 | 1.25615 | ||||||||
\(266\) | −1.19634e8 | −0.389734 | ||||||||
\(267\) | 1.72208e8 | 0.553686 | ||||||||
\(268\) | −5.88762e7 | −0.186839 | ||||||||
\(269\) | 2.13282e8 | 0.668070 | 0.334035 | − | 0.942561i | \(-0.391590\pi\) | ||||
0.334035 | + | 0.942561i | \(0.391590\pi\) | |||||||
\(270\) | −5.57975e7 | −0.172521 | ||||||||
\(271\) | −5.08751e7 | −0.155279 | −0.0776396 | − | 0.996981i | \(-0.524738\pi\) | ||||
−0.0776396 | + | 0.996981i | \(0.524738\pi\) | |||||||
\(272\) | 2.68358e8 | 0.808580 | ||||||||
\(273\) | 4.95832e6 | 0.0147491 | ||||||||
\(274\) | −1.41323e8 | −0.415036 | ||||||||
\(275\) | 1.27698e8 | 0.370270 | ||||||||
\(276\) | −5.99599e7 | −0.171664 | ||||||||
\(277\) | −4.14639e8 | −1.17217 | −0.586086 | − | 0.810249i | \(-0.699332\pi\) | ||||
−0.586086 | + | 0.810249i | \(0.699332\pi\) | |||||||
\(278\) | −4.20206e8 | −1.17302 | ||||||||
\(279\) | 2.38298e8 | 0.656909 | ||||||||
\(280\) | 1.73137e8 | 0.471342 | ||||||||
\(281\) | −3.84206e8 | −1.03298 | −0.516491 | − | 0.856293i | \(-0.672762\pi\) | ||||
−0.516491 | + | 0.856293i | \(0.672762\pi\) | |||||||
\(282\) | −5.83556e7 | −0.154957 | ||||||||
\(283\) | 4.66433e8 | 1.22331 | 0.611656 | − | 0.791124i | \(-0.290504\pi\) | ||||
0.611656 | + | 0.791124i | \(0.290504\pi\) | |||||||
\(284\) | 1.94911e7 | 0.0504918 | ||||||||
\(285\) | 5.55224e7 | 0.142073 | ||||||||
\(286\) | −1.03416e7 | −0.0261400 | ||||||||
\(287\) | −6.35118e8 | −1.58587 | ||||||||
\(288\) | −1.15558e8 | −0.285054 | ||||||||
\(289\) | −2.38188e8 | −0.580467 | ||||||||
\(290\) | 2.78073e8 | 0.669523 | ||||||||
\(291\) | −1.17026e8 | −0.278391 | ||||||||
\(292\) | −3.10071e7 | −0.0728823 | ||||||||
\(293\) | −7.57454e8 | −1.75922 | −0.879609 | − | 0.475697i | \(-0.842196\pi\) | ||||
−0.879609 | + | 0.475697i | \(0.842196\pi\) | |||||||
\(294\) | −1.63187e7 | −0.0374517 | ||||||||
\(295\) | 4.25964e7 | 0.0966042 | ||||||||
\(296\) | −3.72894e7 | −0.0835726 | ||||||||
\(297\) | −7.15912e7 | −0.158567 | ||||||||
\(298\) | 5.00551e7 | 0.109570 | ||||||||
\(299\) | −7.85443e6 | −0.0169928 | ||||||||
\(300\) | −5.57535e7 | −0.119220 | ||||||||
\(301\) | −7.75180e8 | −1.63840 | ||||||||
\(302\) | 9.96101e8 | 2.08103 | ||||||||
\(303\) | 1.85550e8 | 0.383187 | ||||||||
\(304\) | 2.02790e8 | 0.413990 | ||||||||
\(305\) | −7.25424e8 | −1.46400 | ||||||||
\(306\) | −1.30734e8 | −0.260834 | ||||||||
\(307\) | −5.11428e8 | −1.00879 | −0.504394 | − | 0.863473i | \(-0.668284\pi\) | ||||
−0.504394 | + | 0.863473i | \(0.668284\pi\) | |||||||
\(308\) | −1.88852e8 | −0.368293 | ||||||||
\(309\) | 4.63261e7 | 0.0893246 | ||||||||
\(310\) | −9.26651e8 | −1.76665 | ||||||||
\(311\) | 4.47095e8 | 0.842826 | 0.421413 | − | 0.906869i | \(-0.361534\pi\) | ||||
0.421413 | + | 0.906869i | \(0.361534\pi\) | |||||||
\(312\) | −5.31116e6 | −0.00990029 | ||||||||
\(313\) | −3.05704e7 | −0.0563503 | −0.0281751 | − | 0.999603i | \(-0.508970\pi\) | ||||
−0.0281751 | + | 0.999603i | \(0.508970\pi\) | |||||||
\(314\) | −1.24310e9 | −2.26597 | ||||||||
\(315\) | −1.33476e8 | −0.240611 | ||||||||
\(316\) | −8.87881e7 | −0.158289 | ||||||||
\(317\) | −2.57462e8 | −0.453948 | −0.226974 | − | 0.973901i | \(-0.572883\pi\) | ||||
−0.226974 | + | 0.973901i | \(0.572883\pi\) | |||||||
\(318\) | −6.77106e8 | −1.18076 | ||||||||
\(319\) | 3.56782e8 | 0.615370 | ||||||||
\(320\) | −9.36211e7 | −0.159716 | ||||||||
\(321\) | −1.91399e8 | −0.322978 | ||||||||
\(322\) | −4.55584e8 | −0.760454 | ||||||||
\(323\) | 1.30089e8 | 0.214800 | ||||||||
\(324\) | 3.12571e7 | 0.0510554 | ||||||||
\(325\) | −7.30341e6 | −0.0118014 | ||||||||
\(326\) | 7.69164e8 | 1.22958 | ||||||||
\(327\) | 6.19744e8 | 0.980156 | ||||||||
\(328\) | 6.80314e8 | 1.06451 | ||||||||
\(329\) | −1.39595e8 | −0.216115 | ||||||||
\(330\) | 2.78391e8 | 0.426439 | ||||||||
\(331\) | 6.68825e8 | 1.01371 | 0.506856 | − | 0.862031i | \(-0.330808\pi\) | ||||
0.506856 | + | 0.862031i | \(0.330808\pi\) | |||||||
\(332\) | 1.46319e8 | 0.219441 | ||||||||
\(333\) | 2.87474e7 | 0.0426623 | ||||||||
\(334\) | 4.38813e8 | 0.644417 | ||||||||
\(335\) | 2.07617e8 | 0.301721 | ||||||||
\(336\) | −4.87509e8 | −0.701124 | ||||||||
\(337\) | 1.47419e7 | 0.0209821 | 0.0104911 | − | 0.999945i | \(-0.496661\pi\) | ||||
0.0104911 | + | 0.999945i | \(0.496661\pi\) | |||||||
\(338\) | −8.57059e8 | −1.20726 | ||||||||
\(339\) | −4.57962e8 | −0.638455 | ||||||||
\(340\) | 1.60053e8 | 0.220846 | ||||||||
\(341\) | −1.18894e9 | −1.62376 | ||||||||
\(342\) | −9.87921e7 | −0.133546 | ||||||||
\(343\) | −7.66055e8 | −1.02502 | ||||||||
\(344\) | 8.30342e8 | 1.09977 | ||||||||
\(345\) | 2.11438e8 | 0.277215 | ||||||||
\(346\) | 1.07414e9 | 1.39410 | ||||||||
\(347\) | −6.05234e8 | −0.777625 | −0.388812 | − | 0.921317i | \(-0.627115\pi\) | ||||
−0.388812 | + | 0.921317i | \(0.627115\pi\) | |||||||
\(348\) | −1.55773e8 | −0.198137 | ||||||||
\(349\) | −1.02679e9 | −1.29298 | −0.646491 | − | 0.762922i | \(-0.723764\pi\) | ||||
−0.646491 | + | 0.762922i | \(0.723764\pi\) | |||||||
\(350\) | −4.23623e8 | −0.528131 | ||||||||
\(351\) | 4.09452e6 | 0.00505392 | ||||||||
\(352\) | 5.76556e8 | 0.704599 | ||||||||
\(353\) | −1.41214e9 | −1.70870 | −0.854352 | − | 0.519695i | \(-0.826046\pi\) | ||||
−0.854352 | + | 0.519695i | \(0.826046\pi\) | |||||||
\(354\) | −7.57926e7 | −0.0908061 | ||||||||
\(355\) | −6.87319e7 | −0.0815378 | ||||||||
\(356\) | 3.75131e8 | 0.440665 | ||||||||
\(357\) | −3.12735e8 | −0.363779 | ||||||||
\(358\) | −8.03226e8 | −0.925224 | ||||||||
\(359\) | −2.89775e8 | −0.330545 | −0.165272 | − | 0.986248i | \(-0.552850\pi\) | ||||
−0.165272 | + | 0.986248i | \(0.552850\pi\) | |||||||
\(360\) | 1.42974e8 | 0.161510 | ||||||||
\(361\) | −7.95567e8 | −0.890023 | ||||||||
\(362\) | −6.58322e8 | −0.729388 | ||||||||
\(363\) | −1.68962e8 | −0.185403 | ||||||||
\(364\) | 1.08010e7 | 0.0117384 | ||||||||
\(365\) | 1.09341e8 | 0.117695 | ||||||||
\(366\) | 1.29076e9 | 1.37614 | ||||||||
\(367\) | −6.11428e8 | −0.645676 | −0.322838 | − | 0.946454i | \(-0.604637\pi\) | ||||
−0.322838 | + | 0.946454i | \(0.604637\pi\) | |||||||
\(368\) | 7.72259e8 | 0.807784 | ||||||||
\(369\) | −5.24473e8 | −0.543414 | ||||||||
\(370\) | −1.11788e8 | −0.114733 | ||||||||
\(371\) | −1.61974e9 | −1.64678 | ||||||||
\(372\) | 5.19099e8 | 0.522817 | ||||||||
\(373\) | 6.09388e7 | 0.0608013 | 0.0304006 | − | 0.999538i | \(-0.490322\pi\) | ||||
0.0304006 | + | 0.999538i | \(0.490322\pi\) | |||||||
\(374\) | 6.52273e8 | 0.644732 | ||||||||
\(375\) | 6.34098e8 | 0.620936 | ||||||||
\(376\) | 1.49529e8 | 0.145067 | ||||||||
\(377\) | −2.04055e7 | −0.0196134 | ||||||||
\(378\) | 2.37496e8 | 0.226170 | ||||||||
\(379\) | −9.94919e8 | −0.938751 | −0.469376 | − | 0.882999i | \(-0.655521\pi\) | ||||
−0.469376 | + | 0.882999i | \(0.655521\pi\) | |||||||
\(380\) | 1.20948e8 | 0.113072 | ||||||||
\(381\) | −3.36593e8 | −0.311794 | ||||||||
\(382\) | 2.26189e9 | 2.07611 | ||||||||
\(383\) | −1.69498e8 | −0.154159 | −0.0770794 | − | 0.997025i | \(-0.524560\pi\) | ||||
−0.0770794 | + | 0.997025i | \(0.524560\pi\) | |||||||
\(384\) | 7.14413e8 | 0.643858 | ||||||||
\(385\) | 6.65954e8 | 0.594746 | ||||||||
\(386\) | −1.52207e9 | −1.34704 | ||||||||
\(387\) | −6.40134e8 | −0.561413 | ||||||||
\(388\) | −2.54924e8 | −0.221564 | ||||||||
\(389\) | −1.92883e8 | −0.166139 | −0.0830694 | − | 0.996544i | \(-0.526472\pi\) | ||||
−0.0830694 | + | 0.996544i | \(0.526472\pi\) | |||||||
\(390\) | −1.59221e7 | −0.0135917 | ||||||||
\(391\) | 4.95402e8 | 0.419120 | ||||||||
\(392\) | 4.18148e7 | 0.0350613 | ||||||||
\(393\) | 1.26414e9 | 1.05056 | ||||||||
\(394\) | 4.98283e8 | 0.410430 | ||||||||
\(395\) | 3.13096e8 | 0.255616 | ||||||||
\(396\) | −1.55952e8 | −0.126199 | ||||||||
\(397\) | 1.91282e9 | 1.53429 | 0.767146 | − | 0.641472i | \(-0.221676\pi\) | ||||
0.767146 | + | 0.641472i | \(0.221676\pi\) | |||||||
\(398\) | 1.04050e9 | 0.827279 | ||||||||
\(399\) | −2.36325e8 | −0.186254 | ||||||||
\(400\) | 7.18081e8 | 0.561001 | ||||||||
\(401\) | 2.01241e8 | 0.155852 | 0.0779258 | − | 0.996959i | \(-0.475170\pi\) | ||||
0.0779258 | + | 0.996959i | \(0.475170\pi\) | |||||||
\(402\) | −3.69416e8 | −0.283612 | ||||||||
\(403\) | 6.79993e7 | 0.0517531 | ||||||||
\(404\) | 4.04195e8 | 0.304969 | ||||||||
\(405\) | −1.10223e8 | −0.0824478 | ||||||||
\(406\) | −1.18359e9 | −0.877727 | ||||||||
\(407\) | −1.43430e8 | −0.105453 | ||||||||
\(408\) | 3.34990e8 | 0.244186 | ||||||||
\(409\) | 3.51133e8 | 0.253770 | 0.126885 | − | 0.991917i | \(-0.459502\pi\) | ||||
0.126885 | + | 0.991917i | \(0.459502\pi\) | |||||||
\(410\) | 2.03948e9 | 1.46142 | ||||||||
\(411\) | −2.79171e8 | −0.198346 | ||||||||
\(412\) | 1.00915e8 | 0.0710912 | ||||||||
\(413\) | −1.81307e8 | −0.126645 | ||||||||
\(414\) | −3.76216e8 | −0.260577 | ||||||||
\(415\) | −5.15968e8 | −0.354368 | ||||||||
\(416\) | −3.29750e7 | −0.0224573 | ||||||||
\(417\) | −8.30079e8 | −0.560587 | ||||||||
\(418\) | 4.92905e8 | 0.330101 | ||||||||
\(419\) | 3.67310e8 | 0.243940 | 0.121970 | − | 0.992534i | \(-0.461079\pi\) | ||||
0.121970 | + | 0.992534i | \(0.461079\pi\) | |||||||
\(420\) | −2.90759e8 | −0.191497 | ||||||||
\(421\) | 1.20983e9 | 0.790202 | 0.395101 | − | 0.918638i | \(-0.370710\pi\) | ||||
0.395101 | + | 0.918638i | \(0.370710\pi\) | |||||||
\(422\) | 3.21454e9 | 2.08222 | ||||||||
\(423\) | −1.15276e8 | −0.0740539 | ||||||||
\(424\) | 1.73500e9 | 1.10540 | ||||||||
\(425\) | 4.60647e8 | 0.291076 | ||||||||
\(426\) | 1.22296e8 | 0.0766440 | ||||||||
\(427\) | 3.08769e9 | 1.91927 | ||||||||
\(428\) | −4.16937e8 | −0.257050 | ||||||||
\(429\) | −2.04289e7 | −0.0124923 | ||||||||
\(430\) | 2.48924e9 | 1.50983 | ||||||||
\(431\) | 6.04724e8 | 0.363820 | 0.181910 | − | 0.983315i | \(-0.441772\pi\) | ||||
0.181910 | + | 0.983315i | \(0.441772\pi\) | |||||||
\(432\) | −4.02579e8 | −0.240247 | ||||||||
\(433\) | −8.36784e8 | −0.495343 | −0.247671 | − | 0.968844i | \(-0.579665\pi\) | ||||
−0.247671 | + | 0.968844i | \(0.579665\pi\) | |||||||
\(434\) | 3.94419e9 | 2.31603 | ||||||||
\(435\) | 5.49308e8 | 0.319965 | ||||||||
\(436\) | 1.35003e9 | 0.780081 | ||||||||
\(437\) | 3.74361e8 | 0.214588 | ||||||||
\(438\) | −1.94553e8 | −0.110632 | ||||||||
\(439\) | −2.70885e9 | −1.52813 | −0.764064 | − | 0.645140i | \(-0.776799\pi\) | ||||
−0.764064 | + | 0.645140i | \(0.776799\pi\) | |||||||
\(440\) | −7.13344e8 | −0.399222 | ||||||||
\(441\) | −3.22362e7 | −0.0178982 | ||||||||
\(442\) | −3.73055e7 | −0.0205492 | ||||||||
\(443\) | −9.58898e8 | −0.524034 | −0.262017 | − | 0.965063i | \(-0.584388\pi\) | ||||
−0.262017 | + | 0.965063i | \(0.584388\pi\) | |||||||
\(444\) | 6.26223e7 | 0.0339538 | ||||||||
\(445\) | −1.32284e9 | −0.711617 | ||||||||
\(446\) | 2.15264e9 | 1.14894 | ||||||||
\(447\) | 9.88793e7 | 0.0523635 | ||||||||
\(448\) | 3.98488e8 | 0.209384 | ||||||||
\(449\) | 1.53949e9 | 0.802630 | 0.401315 | − | 0.915940i | \(-0.368553\pi\) | ||||
0.401315 | + | 0.915940i | \(0.368553\pi\) | |||||||
\(450\) | −3.49823e8 | −0.180969 | ||||||||
\(451\) | 2.61676e9 | 1.34322 | ||||||||
\(452\) | −9.97607e8 | −0.508130 | ||||||||
\(453\) | 1.96771e9 | 0.994528 | ||||||||
\(454\) | −5.81683e8 | −0.291737 | ||||||||
\(455\) | −3.80879e7 | −0.0189560 | ||||||||
\(456\) | 2.53143e8 | 0.125023 | ||||||||
\(457\) | −3.33563e9 | −1.63483 | −0.817413 | − | 0.576052i | \(-0.804592\pi\) | ||||
−0.817413 | + | 0.576052i | \(0.804592\pi\) | |||||||
\(458\) | −6.93258e8 | −0.337183 | ||||||||
\(459\) | −2.58253e8 | −0.124653 | ||||||||
\(460\) | 4.60589e8 | 0.220628 | ||||||||
\(461\) | 2.62350e9 | 1.24718 | 0.623589 | − | 0.781753i | \(-0.285674\pi\) | ||||
0.623589 | + | 0.781753i | \(0.285674\pi\) | |||||||
\(462\) | −1.18494e9 | −0.559050 | ||||||||
\(463\) | −6.85295e8 | −0.320881 | −0.160441 | − | 0.987045i | \(-0.551292\pi\) | ||||
−0.160441 | + | 0.987045i | \(0.551292\pi\) | |||||||
\(464\) | 2.00629e9 | 0.932356 | ||||||||
\(465\) | −1.83051e9 | −0.844283 | ||||||||
\(466\) | −3.34805e9 | −1.53264 | ||||||||
\(467\) | −3.13987e9 | −1.42660 | −0.713301 | − | 0.700858i | \(-0.752801\pi\) | ||||
−0.713301 | + | 0.700858i | \(0.752801\pi\) | |||||||
\(468\) | 8.91935e6 | 0.00402228 | ||||||||
\(469\) | −8.83699e8 | −0.395548 | ||||||||
\(470\) | 4.48266e8 | 0.199156 | ||||||||
\(471\) | −2.45564e9 | −1.08291 | ||||||||
\(472\) | 1.94209e8 | 0.0850105 | ||||||||
\(473\) | 3.19383e9 | 1.38771 | ||||||||
\(474\) | −5.57098e8 | −0.240274 | ||||||||
\(475\) | 3.48098e8 | 0.149030 | ||||||||
\(476\) | −6.81251e8 | −0.289523 | ||||||||
\(477\) | −1.33756e9 | −0.564286 | ||||||||
\(478\) | −4.63211e7 | −0.0193991 | ||||||||
\(479\) | 1.33909e9 | 0.556718 | 0.278359 | − | 0.960477i | \(-0.410210\pi\) | ||||
0.278359 | + | 0.960477i | \(0.410210\pi\) | |||||||
\(480\) | 8.87674e8 | 0.366361 | ||||||||
\(481\) | 8.20319e6 | 0.00336105 | ||||||||
\(482\) | 3.32101e9 | 1.35084 | ||||||||
\(483\) | −8.99965e8 | −0.363422 | ||||||||
\(484\) | −3.68061e8 | −0.147558 | ||||||||
\(485\) | 8.98946e8 | 0.357798 | ||||||||
\(486\) | 1.96122e8 | 0.0774995 | ||||||||
\(487\) | −3.02031e9 | −1.18495 | −0.592476 | − | 0.805588i | \(-0.701849\pi\) | ||||
−0.592476 | + | 0.805588i | \(0.701849\pi\) | |||||||
\(488\) | −3.30741e9 | −1.28831 | ||||||||
\(489\) | 1.51941e9 | 0.587618 | ||||||||
\(490\) | 1.25354e8 | 0.0481342 | ||||||||
\(491\) | −2.38195e9 | −0.908129 | −0.454065 | − | 0.890969i | \(-0.650026\pi\) | ||||
−0.454065 | + | 0.890969i | \(0.650026\pi\) | |||||||
\(492\) | −1.14249e9 | −0.432489 | ||||||||
\(493\) | 1.28703e9 | 0.483754 | ||||||||
\(494\) | −2.81907e7 | −0.0105211 | ||||||||
\(495\) | 5.49937e8 | 0.203796 | ||||||||
\(496\) | −6.68578e9 | −2.46018 | ||||||||
\(497\) | 2.92550e8 | 0.106894 | ||||||||
\(498\) | 9.18072e8 | 0.333100 | ||||||||
\(499\) | 2.51861e9 | 0.907421 | 0.453711 | − | 0.891149i | \(-0.350100\pi\) | ||||
0.453711 | + | 0.891149i | \(0.350100\pi\) | |||||||
\(500\) | 1.38129e9 | 0.494187 | ||||||||
\(501\) | 8.66835e8 | 0.307967 | ||||||||
\(502\) | −1.37011e8 | −0.0483384 | ||||||||
\(503\) | 8.04366e8 | 0.281816 | 0.140908 | − | 0.990023i | \(-0.454998\pi\) | ||||
0.140908 | + | 0.990023i | \(0.454998\pi\) | |||||||
\(504\) | −6.08555e8 | −0.211735 | ||||||||
\(505\) | −1.42532e9 | −0.492486 | ||||||||
\(506\) | 1.87706e9 | 0.644098 | ||||||||
\(507\) | −1.69304e9 | −0.576952 | ||||||||
\(508\) | −7.33223e8 | −0.248149 | ||||||||
\(509\) | −5.19329e9 | −1.74554 | −0.872772 | − | 0.488128i | \(-0.837680\pi\) | ||||
−0.872772 | + | 0.488128i | \(0.837680\pi\) | |||||||
\(510\) | 1.00425e9 | 0.335232 | ||||||||
\(511\) | −4.65400e8 | −0.154296 | ||||||||
\(512\) | 7.66530e8 | 0.252397 | ||||||||
\(513\) | −1.95155e8 | −0.0638217 | ||||||||
\(514\) | −2.26055e9 | −0.734250 | ||||||||
\(515\) | −3.55860e8 | −0.114803 | ||||||||
\(516\) | −1.39444e9 | −0.446815 | ||||||||
\(517\) | 5.75149e8 | 0.183047 | ||||||||
\(518\) | 4.75814e8 | 0.150412 | ||||||||
\(519\) | 2.12187e9 | 0.666243 | ||||||||
\(520\) | 4.07983e7 | 0.0127242 | ||||||||
\(521\) | 4.19746e9 | 1.30033 | 0.650166 | − | 0.759792i | \(-0.274699\pi\) | ||||
0.650166 | + | 0.759792i | \(0.274699\pi\) | |||||||
\(522\) | −9.77393e8 | −0.300762 | ||||||||
\(523\) | −3.75242e9 | −1.14698 | −0.573490 | − | 0.819213i | \(-0.694411\pi\) | ||||
−0.573490 | + | 0.819213i | \(0.694411\pi\) | |||||||
\(524\) | 2.75376e9 | 0.836117 | ||||||||
\(525\) | −8.36829e8 | −0.252394 | ||||||||
\(526\) | −5.28305e9 | −1.58283 | ||||||||
\(527\) | −4.28891e9 | −1.27647 | ||||||||
\(528\) | 2.00859e9 | 0.593845 | ||||||||
\(529\) | −1.97920e9 | −0.581292 | ||||||||
\(530\) | 5.20127e9 | 1.51755 | ||||||||
\(531\) | −1.49721e8 | −0.0433963 | ||||||||
\(532\) | −5.14803e8 | −0.148235 | ||||||||
\(533\) | −1.49661e8 | −0.0428117 | ||||||||
\(534\) | 2.35375e9 | 0.668907 | ||||||||
\(535\) | 1.47026e9 | 0.415102 | ||||||||
\(536\) | 9.46585e8 | 0.265511 | ||||||||
\(537\) | −1.58670e9 | −0.442165 | ||||||||
\(538\) | 2.91516e9 | 0.807093 | ||||||||
\(539\) | 1.60837e8 | 0.0442409 | ||||||||
\(540\) | −2.40106e8 | −0.0656181 | ||||||||
\(541\) | −1.64171e9 | −0.445765 | −0.222882 | − | 0.974845i | \(-0.571547\pi\) | ||||
−0.222882 | + | 0.974845i | \(0.571547\pi\) | |||||||
\(542\) | −6.95364e8 | −0.187592 | ||||||||
\(543\) | −1.30046e9 | −0.348575 | ||||||||
\(544\) | 2.07983e9 | 0.553900 | ||||||||
\(545\) | −4.76064e9 | −1.25973 | ||||||||
\(546\) | 6.77706e7 | 0.0178183 | ||||||||
\(547\) | 6.20746e9 | 1.62166 | 0.810828 | − | 0.585285i | \(-0.199017\pi\) | ||||
0.810828 | + | 0.585285i | \(0.199017\pi\) | |||||||
\(548\) | −6.08135e8 | −0.157858 | ||||||||
\(549\) | 2.54978e9 | 0.657657 | ||||||||
\(550\) | 1.74538e9 | 0.447322 | ||||||||
\(551\) | 9.72574e8 | 0.247681 | ||||||||
\(552\) | 9.64008e8 | 0.243946 | ||||||||
\(553\) | −1.33266e9 | −0.335106 | ||||||||
\(554\) | −5.66732e9 | −1.41610 | ||||||||
\(555\) | −2.20827e8 | −0.0548310 | ||||||||
\(556\) | −1.80821e9 | −0.446157 | ||||||||
\(557\) | 6.02362e9 | 1.47694 | 0.738472 | − | 0.674284i | \(-0.235548\pi\) | ||||
0.738472 | + | 0.674284i | \(0.235548\pi\) | |||||||
\(558\) | 3.25707e9 | 0.793610 | ||||||||
\(559\) | −1.82665e8 | −0.0442297 | ||||||||
\(560\) | 3.74486e9 | 0.901109 | ||||||||
\(561\) | 1.28851e9 | 0.308118 | ||||||||
\(562\) | −5.25136e9 | −1.24794 | ||||||||
\(563\) | −3.76918e9 | −0.890159 | −0.445079 | − | 0.895491i | \(-0.646825\pi\) | ||||
−0.445079 | + | 0.895491i | \(0.646825\pi\) | |||||||
\(564\) | −2.51113e8 | −0.0589376 | ||||||||
\(565\) | 3.51789e9 | 0.820565 | ||||||||
\(566\) | 6.37524e9 | 1.47788 | ||||||||
\(567\) | 4.69152e8 | 0.108087 | ||||||||
\(568\) | −3.13368e8 | −0.0717523 | ||||||||
\(569\) | −5.40701e9 | −1.23045 | −0.615226 | − | 0.788351i | \(-0.710935\pi\) | ||||
−0.615226 | + | 0.788351i | \(0.710935\pi\) | |||||||
\(570\) | 7.58884e8 | 0.171638 | ||||||||
\(571\) | 3.44502e7 | 0.00774399 | 0.00387200 | − | 0.999993i | \(-0.498768\pi\) | ||||
0.00387200 | + | 0.999993i | \(0.498768\pi\) | |||||||
\(572\) | −4.45015e7 | −0.00994233 | ||||||||
\(573\) | 4.46816e9 | 0.992173 | ||||||||
\(574\) | −8.68083e9 | −1.91589 | ||||||||
\(575\) | 1.32561e9 | 0.290790 | ||||||||
\(576\) | 3.29067e8 | 0.0717473 | ||||||||
\(577\) | 1.54181e8 | 0.0334131 | 0.0167065 | − | 0.999860i | \(-0.494682\pi\) | ||||
0.0167065 | + | 0.999860i | \(0.494682\pi\) | |||||||
\(578\) | −3.25557e9 | −0.701261 | ||||||||
\(579\) | −3.00671e9 | −0.643750 | ||||||||
\(580\) | 1.19659e9 | 0.254652 | ||||||||
\(581\) | 2.19617e9 | 0.464567 | ||||||||
\(582\) | −1.59951e9 | −0.336323 | ||||||||
\(583\) | 6.67351e9 | 1.39481 | ||||||||
\(584\) | 4.98519e8 | 0.103571 | ||||||||
\(585\) | −3.14526e7 | −0.00649547 | ||||||||
\(586\) | −1.03529e10 | −2.12531 | ||||||||
\(587\) | 7.89426e9 | 1.61093 | 0.805467 | − | 0.592640i | \(-0.201914\pi\) | ||||
0.805467 | + | 0.592640i | \(0.201914\pi\) | |||||||
\(588\) | −7.02221e7 | −0.0142447 | ||||||||
\(589\) | −3.24101e9 | −0.653547 | ||||||||
\(590\) | 5.82210e8 | 0.116707 | ||||||||
\(591\) | 9.84312e8 | 0.196145 | ||||||||
\(592\) | −8.06549e8 | −0.159774 | ||||||||
\(593\) | 1.93894e9 | 0.381833 | 0.190917 | − | 0.981606i | \(-0.438854\pi\) | ||||
0.190917 | + | 0.981606i | \(0.438854\pi\) | |||||||
\(594\) | −9.78513e8 | −0.191564 | ||||||||
\(595\) | 2.40231e9 | 0.467542 | ||||||||
\(596\) | 2.15395e8 | 0.0416748 | ||||||||
\(597\) | 2.05542e9 | 0.395357 | ||||||||
\(598\) | −1.07355e8 | −0.0205290 | ||||||||
\(599\) | −4.91194e9 | −0.933812 | −0.466906 | − | 0.884307i | \(-0.654631\pi\) | ||||
−0.466906 | + | 0.884307i | \(0.654631\pi\) | |||||||
\(600\) | 8.96379e8 | 0.169419 | ||||||||
\(601\) | −2.50771e9 | −0.471211 | −0.235606 | − | 0.971849i | \(-0.575707\pi\) | ||||
−0.235606 | + | 0.971849i | \(0.575707\pi\) | |||||||
\(602\) | −1.05952e10 | −1.97934 | ||||||||
\(603\) | −7.29748e8 | −0.135538 | ||||||||
\(604\) | 4.28638e9 | 0.791519 | ||||||||
\(605\) | 1.29791e9 | 0.238286 | ||||||||
\(606\) | 2.53610e9 | 0.462928 | ||||||||
\(607\) | −5.17646e8 | −0.0939446 | −0.0469723 | − | 0.998896i | \(-0.514957\pi\) | ||||
−0.0469723 | + | 0.998896i | \(0.514957\pi\) | |||||||
\(608\) | 1.57167e9 | 0.283595 | ||||||||
\(609\) | −2.33807e9 | −0.419466 | ||||||||
\(610\) | −9.91513e9 | −1.76866 | ||||||||
\(611\) | −3.28945e7 | −0.00583417 | ||||||||
\(612\) | −5.62569e8 | −0.0992078 | ||||||||
\(613\) | −2.24783e9 | −0.394141 | −0.197070 | − | 0.980389i | \(-0.563143\pi\) | ||||
−0.197070 | + | 0.980389i | \(0.563143\pi\) | |||||||
\(614\) | −6.99023e9 | −1.21871 | ||||||||
\(615\) | 4.02880e9 | 0.698414 | ||||||||
\(616\) | 3.03627e9 | 0.523370 | ||||||||
\(617\) | −3.82861e9 | −0.656211 | −0.328106 | − | 0.944641i | \(-0.606410\pi\) | ||||
−0.328106 | + | 0.944641i | \(0.606410\pi\) | |||||||
\(618\) | 6.33188e8 | 0.107913 | ||||||||
\(619\) | 1.53060e9 | 0.259385 | 0.129693 | − | 0.991554i | \(-0.458601\pi\) | ||||
0.129693 | + | 0.991554i | \(0.458601\pi\) | |||||||
\(620\) | −3.98753e9 | −0.671943 | ||||||||
\(621\) | −7.43181e8 | −0.124530 | ||||||||
\(622\) | 6.11091e9 | 1.01822 | ||||||||
\(623\) | 5.63052e9 | 0.932911 | ||||||||
\(624\) | −1.14878e8 | −0.0189273 | ||||||||
\(625\) | −2.12804e9 | −0.348658 | ||||||||
\(626\) | −4.17838e8 | −0.0680766 | ||||||||
\(627\) | 9.73689e8 | 0.157755 | ||||||||
\(628\) | −5.34928e9 | −0.861859 | ||||||||
\(629\) | −5.17399e8 | −0.0828988 | ||||||||
\(630\) | −1.82436e9 | −0.290682 | ||||||||
\(631\) | 8.76195e9 | 1.38835 | 0.694174 | − | 0.719807i | \(-0.255770\pi\) | ||||
0.694174 | + | 0.719807i | \(0.255770\pi\) | |||||||
\(632\) | 1.42749e9 | 0.224939 | ||||||||
\(633\) | 6.35004e9 | 0.995092 | ||||||||
\(634\) | −3.51900e9 | −0.548413 | ||||||||
\(635\) | 2.58558e9 | 0.400729 | ||||||||
\(636\) | −2.91369e9 | −0.449101 | ||||||||
\(637\) | −9.19873e6 | −0.00141007 | ||||||||
\(638\) | 4.87652e9 | 0.743426 | ||||||||
\(639\) | 2.41584e8 | 0.0366282 | ||||||||
\(640\) | −5.48785e9 | −0.827508 | ||||||||
\(641\) | −8.85004e9 | −1.32722 | −0.663609 | − | 0.748080i | \(-0.730976\pi\) | ||||
−0.663609 | + | 0.748080i | \(0.730976\pi\) | |||||||
\(642\) | −2.61606e9 | −0.390188 | ||||||||
\(643\) | −1.79228e9 | −0.265869 | −0.132935 | − | 0.991125i | \(-0.542440\pi\) | ||||
−0.132935 | + | 0.991125i | \(0.542440\pi\) | |||||||
\(644\) | −1.96045e9 | −0.289238 | ||||||||
\(645\) | 4.91727e9 | 0.721548 | ||||||||
\(646\) | 1.77807e9 | 0.259499 | ||||||||
\(647\) | −7.01663e9 | −1.01851 | −0.509253 | − | 0.860617i | \(-0.670078\pi\) | ||||
−0.509253 | + | 0.860617i | \(0.670078\pi\) | |||||||
\(648\) | −5.02538e8 | −0.0725531 | ||||||||
\(649\) | 7.47007e8 | 0.107267 | ||||||||
\(650\) | −9.98234e7 | −0.0142572 | ||||||||
\(651\) | 7.79139e9 | 1.10683 | ||||||||
\(652\) | 3.30983e9 | 0.467670 | ||||||||
\(653\) | 5.63028e9 | 0.791287 | 0.395644 | − | 0.918404i | \(-0.370522\pi\) | ||||
0.395644 | + | 0.918404i | \(0.370522\pi\) | |||||||
\(654\) | 8.47070e9 | 1.18412 | ||||||||
\(655\) | −9.71067e9 | −1.35022 | ||||||||
\(656\) | 1.47148e10 | 2.03513 | ||||||||
\(657\) | −3.84322e8 | −0.0528709 | ||||||||
\(658\) | −1.90800e9 | −0.261088 | ||||||||
\(659\) | 2.18357e9 | 0.297214 | 0.148607 | − | 0.988896i | \(-0.452521\pi\) | ||||
0.148607 | + | 0.988896i | \(0.452521\pi\) | |||||||
\(660\) | 1.19796e9 | 0.162196 | ||||||||
\(661\) | 1.27138e10 | 1.71227 | 0.856134 | − | 0.516755i | \(-0.172860\pi\) | ||||
0.856134 | + | 0.516755i | \(0.172860\pi\) | |||||||
\(662\) | 9.14153e9 | 1.22466 | ||||||||
\(663\) | −7.36936e7 | −0.00982047 | ||||||||
\(664\) | −2.35245e9 | −0.311840 | ||||||||
\(665\) | 1.81536e9 | 0.239380 | ||||||||
\(666\) | 3.92921e8 | 0.0515402 | ||||||||
\(667\) | 3.70372e9 | 0.483279 | ||||||||
\(668\) | 1.88828e9 | 0.245103 | ||||||||
\(669\) | 4.25234e9 | 0.549081 | ||||||||
\(670\) | 2.83772e9 | 0.364508 | ||||||||
\(671\) | −1.27216e10 | −1.62560 | ||||||||
\(672\) | −3.77829e9 | −0.480289 | ||||||||
\(673\) | −5.04564e9 | −0.638063 | −0.319031 | − | 0.947744i | \(-0.603358\pi\) | ||||
−0.319031 | + | 0.947744i | \(0.603358\pi\) | |||||||
\(674\) | 2.01494e8 | 0.0253485 | ||||||||
\(675\) | −6.91043e8 | −0.0864853 | ||||||||
\(676\) | −3.68806e9 | −0.459182 | ||||||||
\(677\) | −4.93561e9 | −0.611337 | −0.305668 | − | 0.952138i | \(-0.598880\pi\) | ||||
−0.305668 | + | 0.952138i | \(0.598880\pi\) | |||||||
\(678\) | −6.25945e9 | −0.771316 | ||||||||
\(679\) | −3.82627e9 | −0.469063 | ||||||||
\(680\) | −2.57327e9 | −0.313837 | ||||||||
\(681\) | −1.14906e9 | −0.139421 | ||||||||
\(682\) | −1.62505e10 | −1.96165 | ||||||||
\(683\) | −8.54468e9 | −1.02618 | −0.513090 | − | 0.858335i | \(-0.671499\pi\) | ||||
−0.513090 | + | 0.858335i | \(0.671499\pi\) | |||||||
\(684\) | −4.25118e8 | −0.0507941 | ||||||||
\(685\) | 2.14448e9 | 0.254921 | ||||||||
\(686\) | −1.04705e10 | −1.23832 | ||||||||
\(687\) | −1.36947e9 | −0.161140 | ||||||||
\(688\) | 1.79599e10 | 2.10254 | ||||||||
\(689\) | −3.81679e8 | −0.0444560 | ||||||||
\(690\) | 2.88995e9 | 0.334903 | ||||||||
\(691\) | −2.27573e9 | −0.262390 | −0.131195 | − | 0.991357i | \(-0.541881\pi\) | ||||
−0.131195 | + | 0.991357i | \(0.541881\pi\) | |||||||
\(692\) | 4.62220e9 | 0.530246 | ||||||||
\(693\) | −2.34075e9 | −0.267171 | ||||||||
\(694\) | −8.27237e9 | −0.939446 | ||||||||
\(695\) | 6.37635e9 | 0.720486 | ||||||||
\(696\) | 2.50445e9 | 0.281566 | ||||||||
\(697\) | 9.43952e9 | 1.05593 | ||||||||
\(698\) | −1.40342e10 | −1.56205 | ||||||||
\(699\) | −6.61377e9 | −0.732451 | ||||||||
\(700\) | −1.82292e9 | −0.200874 | ||||||||
\(701\) | 2.18428e8 | 0.0239494 | 0.0119747 | − | 0.999928i | \(-0.496188\pi\) | ||||
0.0119747 | + | 0.999928i | \(0.496188\pi\) | |||||||
\(702\) | 5.59641e7 | 0.00610562 | ||||||||
\(703\) | −3.90984e8 | −0.0424439 | ||||||||
\(704\) | −1.64182e9 | −0.177346 | ||||||||
\(705\) | 8.85508e8 | 0.0951767 | ||||||||
\(706\) | −1.93012e10 | −2.06428 | ||||||||
\(707\) | 6.06674e9 | 0.645636 | ||||||||
\(708\) | −3.26147e8 | −0.0345380 | ||||||||
\(709\) | 1.81988e10 | 1.91770 | 0.958849 | − | 0.283917i | \(-0.0916341\pi\) | ||||
0.958849 | + | 0.283917i | \(0.0916341\pi\) | |||||||
\(710\) | −9.39431e8 | −0.0985056 | ||||||||
\(711\) | −1.10050e9 | −0.114827 | ||||||||
\(712\) | −6.03119e9 | −0.626215 | ||||||||
\(713\) | −1.23423e10 | −1.27521 | ||||||||
\(714\) | −4.27448e9 | −0.439481 | ||||||||
\(715\) | 1.56927e8 | 0.0160556 | ||||||||
\(716\) | −3.45641e9 | −0.351908 | ||||||||
\(717\) | −9.15030e7 | −0.00927083 | ||||||||
\(718\) | −3.96066e9 | −0.399330 | ||||||||
\(719\) | −6.16960e9 | −0.619022 | −0.309511 | − | 0.950896i | \(-0.600165\pi\) | ||||
−0.309511 | + | 0.950896i | \(0.600165\pi\) | |||||||
\(720\) | 3.09246e9 | 0.308774 | ||||||||
\(721\) | 1.51468e9 | 0.150504 | ||||||||
\(722\) | −1.08739e10 | −1.07523 | ||||||||
\(723\) | 6.56035e9 | 0.645570 | ||||||||
\(724\) | −2.83286e9 | −0.277422 | ||||||||
\(725\) | 3.44389e9 | 0.335634 | ||||||||
\(726\) | −2.30939e9 | −0.223985 | ||||||||
\(727\) | 5.20930e9 | 0.502816 | 0.251408 | − | 0.967881i | \(-0.419106\pi\) | ||||
0.251408 | + | 0.967881i | \(0.419106\pi\) | |||||||
\(728\) | −1.73654e8 | −0.0166811 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 1.49448e9 | 0.142188 | ||||||||
\(731\) | 1.15212e10 | 1.09090 | ||||||||
\(732\) | 5.55434e9 | 0.523412 | ||||||||
\(733\) | 9.86561e9 | 0.925252 | 0.462626 | − | 0.886554i | \(-0.346907\pi\) | ||||
0.462626 | + | 0.886554i | \(0.346907\pi\) | |||||||
\(734\) | −8.35704e9 | −0.780039 | ||||||||
\(735\) | 2.47626e8 | 0.0230033 | ||||||||
\(736\) | 5.98516e9 | 0.553355 | ||||||||
\(737\) | 3.64095e9 | 0.335026 | ||||||||
\(738\) | −7.16853e9 | −0.656497 | ||||||||
\(739\) | 6.68716e9 | 0.609517 | 0.304759 | − | 0.952430i | \(-0.401424\pi\) | ||||
0.304759 | + | 0.952430i | \(0.401424\pi\) | |||||||
\(740\) | −4.81041e8 | −0.0436386 | ||||||||
\(741\) | −5.56882e7 | −0.00502805 | ||||||||
\(742\) | −2.21387e10 | −1.98947 | ||||||||
\(743\) | 1.17332e10 | 1.04944 | 0.524719 | − | 0.851275i | \(-0.324170\pi\) | ||||
0.524719 | + | 0.851275i | \(0.324170\pi\) | |||||||
\(744\) | −8.34584e9 | −0.742959 | ||||||||
\(745\) | −7.59553e8 | −0.0672994 | ||||||||
\(746\) | 8.32915e8 | 0.0734539 | ||||||||
\(747\) | 1.81357e9 | 0.159189 | ||||||||
\(748\) | 2.80683e9 | 0.245223 | ||||||||
\(749\) | −6.25800e9 | −0.544188 | ||||||||
\(750\) | 8.66688e9 | 0.750151 | ||||||||
\(751\) | −1.63538e10 | −1.40890 | −0.704448 | − | 0.709756i | \(-0.748805\pi\) | ||||
−0.704448 | + | 0.709756i | \(0.748805\pi\) | |||||||
\(752\) | 3.23423e9 | 0.277338 | ||||||||
\(753\) | −2.70653e8 | −0.0231010 | ||||||||
\(754\) | −2.78903e8 | −0.0236948 | ||||||||
\(755\) | −1.51152e10 | −1.27820 | ||||||||
\(756\) | 1.02198e9 | 0.0860236 | ||||||||
\(757\) | −7.22904e9 | −0.605683 | −0.302841 | − | 0.953041i | \(-0.597935\pi\) | ||||
−0.302841 | + | 0.953041i | \(0.597935\pi\) | |||||||
\(758\) | −1.35986e10 | −1.13410 | ||||||||
\(759\) | 3.70796e9 | 0.307815 | ||||||||
\(760\) | −1.94455e9 | −0.160683 | ||||||||
\(761\) | −1.16317e9 | −0.0956747 | −0.0478373 | − | 0.998855i | \(-0.515233\pi\) | ||||
−0.0478373 | + | 0.998855i | \(0.515233\pi\) | |||||||
\(762\) | −4.60058e9 | −0.376678 | ||||||||
\(763\) | 2.02632e10 | 1.65147 | ||||||||
\(764\) | 9.73328e9 | 0.789646 | ||||||||
\(765\) | 1.98380e9 | 0.160208 | ||||||||
\(766\) | −2.31671e9 | −0.186239 | ||||||||
\(767\) | −4.27236e7 | −0.00341888 | ||||||||
\(768\) | 8.20461e9 | 0.653573 | ||||||||
\(769\) | 2.40619e10 | 1.90804 | 0.954022 | − | 0.299735i | \(-0.0968984\pi\) | ||||
0.954022 | + | 0.299735i | \(0.0968984\pi\) | |||||||
\(770\) | 9.10230e9 | 0.718511 | ||||||||
\(771\) | −4.46552e9 | −0.350899 | ||||||||
\(772\) | −6.54972e9 | −0.512344 | ||||||||
\(773\) | −1.37533e9 | −0.107097 | −0.0535486 | − | 0.998565i | \(-0.517053\pi\) | ||||
−0.0535486 | + | 0.998565i | \(0.517053\pi\) | |||||||
\(774\) | −8.74939e9 | −0.678242 | ||||||||
\(775\) | −1.14764e10 | −0.885627 | ||||||||
\(776\) | 4.09855e9 | 0.314858 | ||||||||
\(777\) | 9.39926e8 | 0.0718820 | ||||||||
\(778\) | −2.63634e9 | −0.200712 | ||||||||
\(779\) | 7.13318e9 | 0.540633 | ||||||||
\(780\) | −6.85151e7 | −0.00516958 | ||||||||
\(781\) | −1.20534e9 | −0.0905381 | ||||||||
\(782\) | 6.77118e9 | 0.506338 | ||||||||
\(783\) | −1.93075e9 | −0.143734 | ||||||||
\(784\) | 9.04432e8 | 0.0670301 | ||||||||
\(785\) | 1.88633e10 | 1.39179 | ||||||||
\(786\) | 1.72784e10 | 1.26918 | ||||||||
\(787\) | 1.62448e10 | 1.18796 | 0.593980 | − | 0.804480i | \(-0.297556\pi\) | ||||
0.593980 | + | 0.804480i | \(0.297556\pi\) | |||||||
\(788\) | 2.14419e9 | 0.156107 | ||||||||
\(789\) | −1.04362e10 | −0.756436 | ||||||||
\(790\) | 4.27941e9 | 0.308809 | ||||||||
\(791\) | −1.49735e10 | −1.07574 | ||||||||
\(792\) | 2.50732e9 | 0.179338 | ||||||||
\(793\) | 7.27590e8 | 0.0518120 | ||||||||
\(794\) | 2.61446e10 | 1.85357 | ||||||||
\(795\) | 1.02746e10 | 0.725240 | ||||||||
\(796\) | 4.47744e9 | 0.314655 | ||||||||
\(797\) | −1.10596e10 | −0.773814 | −0.386907 | − | 0.922119i | \(-0.626457\pi\) | ||||
−0.386907 | + | 0.922119i | \(0.626457\pi\) | |||||||
\(798\) | −3.23011e9 | −0.225013 | ||||||||
\(799\) | 2.07475e9 | 0.143897 | ||||||||
\(800\) | 5.56528e9 | 0.384301 | ||||||||
\(801\) | 4.64961e9 | 0.319671 | ||||||||
\(802\) | 2.75057e9 | 0.188284 | ||||||||
\(803\) | 1.91750e9 | 0.130687 | ||||||||
\(804\) | −1.58966e9 | −0.107872 | ||||||||
\(805\) | 6.91319e9 | 0.467082 | ||||||||
\(806\) | 9.29418e8 | 0.0625228 | ||||||||
\(807\) | 5.75862e9 | 0.385710 | ||||||||
\(808\) | −6.49846e9 | −0.433382 | ||||||||
\(809\) | −2.52839e10 | −1.67890 | −0.839450 | − | 0.543436i | \(-0.817123\pi\) | ||||
−0.839450 | + | 0.543436i | \(0.817123\pi\) | |||||||
\(810\) | −1.50653e9 | −0.0996050 | ||||||||
\(811\) | 7.05869e9 | 0.464677 | 0.232339 | − | 0.972635i | \(-0.425362\pi\) | ||||
0.232339 | + | 0.972635i | \(0.425362\pi\) | |||||||
\(812\) | −5.09317e9 | −0.333843 | ||||||||
\(813\) | −1.37363e9 | −0.0896504 | ||||||||
\(814\) | −1.96041e9 | −0.127398 | ||||||||
\(815\) | −1.16716e10 | −0.755227 | ||||||||
\(816\) | 7.24566e9 | 0.466834 | ||||||||
\(817\) | 8.70625e9 | 0.558540 | ||||||||
\(818\) | 4.79930e9 | 0.306578 | ||||||||
\(819\) | 1.33875e8 | 0.00851539 | ||||||||
\(820\) | 8.77620e9 | 0.555850 | ||||||||
\(821\) | −1.72937e10 | −1.09066 | −0.545328 | − | 0.838223i | \(-0.683595\pi\) | ||||
−0.545328 | + | 0.838223i | \(0.683595\pi\) | |||||||
\(822\) | −3.81572e9 | −0.239621 | ||||||||
\(823\) | 1.28299e10 | 0.802278 | 0.401139 | − | 0.916017i | \(-0.368614\pi\) | ||||
0.401139 | + | 0.916017i | \(0.368614\pi\) | |||||||
\(824\) | −1.62247e9 | −0.101025 | ||||||||
\(825\) | 3.44783e9 | 0.213775 | ||||||||
\(826\) | −2.47812e9 | −0.153000 | ||||||||
\(827\) | 1.83922e10 | 1.13074 | 0.565372 | − | 0.824836i | \(-0.308732\pi\) | ||||
0.565372 | + | 0.824836i | \(0.308732\pi\) | |||||||
\(828\) | −1.61892e9 | −0.0991102 | ||||||||
\(829\) | −4.09547e9 | −0.249668 | −0.124834 | − | 0.992178i | \(-0.539840\pi\) | ||||
−0.124834 | + | 0.992178i | \(0.539840\pi\) | |||||||
\(830\) | −7.05229e9 | −0.428111 | ||||||||
\(831\) | −1.11953e10 | −0.676754 | ||||||||
\(832\) | 9.39006e7 | 0.00565245 | ||||||||
\(833\) | 5.80190e8 | 0.0347787 | ||||||||
\(834\) | −1.13456e10 | −0.677244 | ||||||||
\(835\) | −6.65870e9 | −0.395810 | ||||||||
\(836\) | 2.12105e9 | 0.125553 | ||||||||
\(837\) | 6.43404e9 | 0.379267 | ||||||||
\(838\) | 5.02041e9 | 0.294704 | ||||||||
\(839\) | −1.88735e9 | −0.110328 | −0.0551641 | − | 0.998477i | \(-0.517568\pi\) | ||||
−0.0551641 | + | 0.998477i | \(0.517568\pi\) | |||||||
\(840\) | 4.67469e9 | 0.272130 | ||||||||
\(841\) | −7.62778e9 | −0.442193 | ||||||||
\(842\) | 1.65361e10 | 0.954641 | ||||||||
\(843\) | −1.03736e10 | −0.596392 | ||||||||
\(844\) | 1.38327e10 | 0.791969 | ||||||||
\(845\) | 1.30053e10 | 0.741519 | ||||||||
\(846\) | −1.57560e9 | −0.0894643 | ||||||||
\(847\) | −5.52440e9 | −0.312387 | ||||||||
\(848\) | 3.75272e10 | 2.11330 | ||||||||
\(849\) | 1.25937e10 | 0.706279 | ||||||||
\(850\) | 6.29615e9 | 0.351649 | ||||||||
\(851\) | −1.48893e9 | −0.0828173 | ||||||||
\(852\) | 5.26259e8 | 0.0291515 | ||||||||
\(853\) | 6.81026e8 | 0.0375701 | 0.0187850 | − | 0.999824i | \(-0.494020\pi\) | ||||
0.0187850 | + | 0.999824i | \(0.494020\pi\) | |||||||
\(854\) | 4.22027e10 | 2.31866 | ||||||||
\(855\) | 1.49911e9 | 0.0820259 | ||||||||
\(856\) | 6.70332e9 | 0.365285 | ||||||||
\(857\) | 6.43948e9 | 0.349476 | 0.174738 | − | 0.984615i | \(-0.444092\pi\) | ||||
0.174738 | + | 0.984615i | \(0.444092\pi\) | |||||||
\(858\) | −2.79223e8 | −0.0150919 | ||||||||
\(859\) | 1.88733e10 | 1.01595 | 0.507974 | − | 0.861373i | \(-0.330395\pi\) | ||||
0.507974 | + | 0.861373i | \(0.330395\pi\) | |||||||
\(860\) | 1.07116e10 | 0.574262 | ||||||||
\(861\) | −1.71482e10 | −0.915603 | ||||||||
\(862\) | 8.26541e9 | 0.439530 | ||||||||
\(863\) | 1.84568e10 | 0.977505 | 0.488753 | − | 0.872422i | \(-0.337452\pi\) | ||||
0.488753 | + | 0.872422i | \(0.337452\pi\) | |||||||
\(864\) | −3.12007e9 | −0.164576 | ||||||||
\(865\) | −1.62994e10 | −0.856279 | ||||||||
\(866\) | −1.14372e10 | −0.598422 | ||||||||
\(867\) | −6.43108e9 | −0.335133 | ||||||||
\(868\) | 1.69725e10 | 0.880900 | ||||||||
\(869\) | 5.49072e9 | 0.283831 | ||||||||
\(870\) | 7.50797e9 | 0.386549 | ||||||||
\(871\) | −2.08237e8 | −0.0106781 | ||||||||
\(872\) | −2.17051e10 | −1.10855 | ||||||||
\(873\) | −3.15969e9 | −0.160729 | ||||||||
\(874\) | 5.11679e9 | 0.259243 | ||||||||
\(875\) | 2.07325e10 | 1.04622 | ||||||||
\(876\) | −8.37193e8 | −0.0420786 | ||||||||
\(877\) | 1.79041e10 | 0.896301 | 0.448151 | − | 0.893958i | \(-0.352083\pi\) | ||||
0.448151 | + | 0.893958i | \(0.352083\pi\) | |||||||
\(878\) | −3.70248e10 | −1.84613 | ||||||||
\(879\) | −2.04513e10 | −1.01569 | ||||||||
\(880\) | −1.54293e10 | −0.763230 | ||||||||
\(881\) | −1.86101e10 | −0.916922 | −0.458461 | − | 0.888715i | \(-0.651599\pi\) | ||||
−0.458461 | + | 0.888715i | \(0.651599\pi\) | |||||||
\(882\) | −4.40606e8 | −0.0216227 | ||||||||
\(883\) | −1.45294e10 | −0.710207 | −0.355103 | − | 0.934827i | \(-0.615554\pi\) | ||||
−0.355103 | + | 0.934827i | \(0.615554\pi\) | |||||||
\(884\) | −1.60531e8 | −0.00781586 | ||||||||
\(885\) | 1.15010e9 | 0.0557744 | ||||||||
\(886\) | −1.31063e10 | −0.633084 | ||||||||
\(887\) | −3.46786e9 | −0.166851 | −0.0834256 | − | 0.996514i | \(-0.526586\pi\) | ||||
−0.0834256 | + | 0.996514i | \(0.526586\pi\) | |||||||
\(888\) | −1.00681e9 | −0.0482507 | ||||||||
\(889\) | −1.10053e10 | −0.525345 | ||||||||
\(890\) | −1.80806e10 | −0.859702 | ||||||||
\(891\) | −1.93296e9 | −0.0915486 | ||||||||
\(892\) | 9.26313e9 | 0.436999 | ||||||||
\(893\) | 1.56783e9 | 0.0736749 | ||||||||
\(894\) | 1.35149e9 | 0.0632602 | ||||||||
\(895\) | 1.21884e10 | 0.568286 | ||||||||
\(896\) | 2.33585e10 | 1.08484 | ||||||||
\(897\) | −2.12070e8 | −0.00981081 | ||||||||
\(898\) | 2.10419e10 | 0.969655 | ||||||||
\(899\) | −3.20647e10 | −1.47187 | ||||||||
\(900\) | −1.50534e9 | −0.0688314 | ||||||||
\(901\) | 2.40736e10 | 1.09649 | ||||||||
\(902\) | 3.57660e10 | 1.62274 | ||||||||
\(903\) | −2.09298e10 | −0.945930 | ||||||||
\(904\) | 1.60391e10 | 0.722088 | ||||||||
\(905\) | 9.98961e9 | 0.448001 | ||||||||
\(906\) | 2.68947e10 | 1.20149 | ||||||||
\(907\) | −4.86854e9 | −0.216657 | −0.108329 | − | 0.994115i | \(-0.534550\pi\) | ||||
−0.108329 | + | 0.994115i | \(0.534550\pi\) | |||||||
\(908\) | −2.50308e9 | −0.110962 | ||||||||
\(909\) | 5.00984e9 | 0.221233 | ||||||||
\(910\) | −5.20588e8 | −0.0229007 | ||||||||
\(911\) | 5.41157e9 | 0.237142 | 0.118571 | − | 0.992946i | \(-0.462169\pi\) | ||||
0.118571 | + | 0.992946i | \(0.462169\pi\) | |||||||
\(912\) | 5.47534e9 | 0.239017 | ||||||||
\(913\) | −9.04846e9 | −0.393484 | ||||||||
\(914\) | −4.55916e10 | −1.97503 | ||||||||
\(915\) | −1.95864e10 | −0.845243 | ||||||||
\(916\) | −2.98320e9 | −0.128247 | ||||||||
\(917\) | 4.13325e10 | 1.77010 | ||||||||
\(918\) | −3.52982e9 | −0.150592 | ||||||||
\(919\) | −4.36861e10 | −1.85669 | −0.928343 | − | 0.371724i | \(-0.878767\pi\) | ||||
−0.928343 | + | 0.371724i | \(0.878767\pi\) | |||||||
\(920\) | −7.40515e9 | −0.313528 | ||||||||
\(921\) | −1.38086e10 | −0.582424 | ||||||||
\(922\) | 3.58582e10 | 1.50671 | ||||||||
\(923\) | 6.89371e7 | 0.00288567 | ||||||||
\(924\) | −5.09900e9 | −0.212634 | ||||||||
\(925\) | −1.38448e9 | −0.0575161 | ||||||||
\(926\) | −9.36666e9 | −0.387656 | ||||||||
\(927\) | 1.25081e9 | 0.0515716 | ||||||||
\(928\) | 1.55492e10 | 0.638690 | ||||||||
\(929\) | 1.09031e10 | 0.446164 | 0.223082 | − | 0.974800i | \(-0.428388\pi\) | ||||
0.223082 | + | 0.974800i | \(0.428388\pi\) | |||||||
\(930\) | −2.50196e10 | −1.01998 | ||||||||
\(931\) | 4.38434e8 | 0.0178066 | ||||||||
\(932\) | −1.44072e10 | −0.582939 | ||||||||
\(933\) | 1.20716e10 | 0.486606 | ||||||||
\(934\) | −4.29159e10 | −1.72347 | ||||||||
\(935\) | −9.89782e9 | −0.396003 | ||||||||
\(936\) | −1.43401e8 | −0.00571594 | ||||||||
\(937\) | 3.25215e10 | 1.29146 | 0.645732 | − | 0.763564i | \(-0.276552\pi\) | ||||
0.645732 | + | 0.763564i | \(0.276552\pi\) | |||||||
\(938\) | −1.20785e10 | −0.477861 | ||||||||
\(939\) | −8.25401e8 | −0.0325339 | ||||||||
\(940\) | 1.92896e9 | 0.0757487 | ||||||||
\(941\) | −2.70964e10 | −1.06010 | −0.530052 | − | 0.847965i | \(-0.677828\pi\) | ||||
−0.530052 | + | 0.847965i | \(0.677828\pi\) | |||||||
\(942\) | −3.35638e10 | −1.30826 | ||||||||
\(943\) | 2.71643e10 | 1.05489 | ||||||||
\(944\) | 4.20064e9 | 0.162523 | ||||||||
\(945\) | −3.60385e9 | −0.138917 | ||||||||
\(946\) | 4.36535e10 | 1.67649 | ||||||||
\(947\) | 2.06829e10 | 0.791382 | 0.395691 | − | 0.918384i | \(-0.370505\pi\) | ||||
0.395691 | + | 0.918384i | \(0.370505\pi\) | |||||||
\(948\) | −2.39728e9 | −0.0913880 | ||||||||
\(949\) | −1.09668e8 | −0.00416531 | ||||||||
\(950\) | 4.75783e9 | 0.180043 | ||||||||
\(951\) | −6.95147e9 | −0.262087 | ||||||||
\(952\) | 1.09528e10 | 0.411431 | ||||||||
\(953\) | −3.31031e10 | −1.23892 | −0.619460 | − | 0.785028i | \(-0.712649\pi\) | ||||
−0.619460 | + | 0.785028i | \(0.712649\pi\) | |||||||
\(954\) | −1.82819e10 | −0.681712 | ||||||||
\(955\) | −3.43227e10 | −1.27518 | ||||||||
\(956\) | −1.99327e8 | −0.00737841 | ||||||||
\(957\) | 9.63313e9 | 0.355284 | ||||||||
\(958\) | 1.83027e10 | 0.672569 | ||||||||
\(959\) | −9.12777e9 | −0.334195 | ||||||||
\(960\) | −2.52777e9 | −0.0922121 | ||||||||
\(961\) | 7.93400e10 | 2.88377 | ||||||||
\(962\) | 1.12122e8 | 0.00406048 | ||||||||
\(963\) | −5.16778e9 | −0.186471 | ||||||||
\(964\) | 1.42908e10 | 0.513792 | ||||||||
\(965\) | 2.30965e10 | 0.827370 | ||||||||
\(966\) | −1.23008e10 | −0.439049 | ||||||||
\(967\) | −2.24560e10 | −0.798618 | −0.399309 | − | 0.916816i | \(-0.630750\pi\) | ||||
−0.399309 | + | 0.916816i | \(0.630750\pi\) | |||||||
\(968\) | 5.91752e9 | 0.209689 | ||||||||
\(969\) | 3.51242e9 | 0.124015 | ||||||||
\(970\) | 1.22868e10 | 0.432254 | ||||||||
\(971\) | −1.83485e10 | −0.643182 | −0.321591 | − | 0.946879i | \(-0.604218\pi\) | ||||
−0.321591 | + | 0.946879i | \(0.604218\pi\) | |||||||
\(972\) | 8.43942e8 | 0.0294768 | ||||||||
\(973\) | −2.71403e10 | −0.944538 | ||||||||
\(974\) | −4.12818e10 | −1.43154 | ||||||||
\(975\) | −1.97192e8 | −0.00681355 | ||||||||
\(976\) | −7.15376e10 | −2.46298 | ||||||||
\(977\) | 2.21334e10 | 0.759306 | 0.379653 | − | 0.925129i | \(-0.376043\pi\) | ||||
0.379653 | + | 0.925129i | \(0.376043\pi\) | |||||||
\(978\) | 2.07674e10 | 0.709899 | ||||||||
\(979\) | −2.31984e10 | −0.790166 | ||||||||
\(980\) | 5.39420e8 | 0.0183078 | ||||||||
\(981\) | 1.67331e10 | 0.565893 | ||||||||
\(982\) | −3.25566e10 | −1.09711 | ||||||||
\(983\) | 5.39105e10 | 1.81024 | 0.905121 | − | 0.425155i | \(-0.139780\pi\) | ||||
0.905121 | + | 0.425155i | \(0.139780\pi\) | |||||||
\(984\) | 1.83685e10 | 0.614597 | ||||||||
\(985\) | −7.56112e9 | −0.252092 | ||||||||
\(986\) | 1.75912e10 | 0.584422 | ||||||||
\(987\) | −3.76907e9 | −0.124774 | ||||||||
\(988\) | −1.21309e8 | −0.00400170 | ||||||||
\(989\) | 3.31548e10 | 1.08983 | ||||||||
\(990\) | 7.51657e9 | 0.246205 | ||||||||
\(991\) | −1.06845e10 | −0.348734 | −0.174367 | − | 0.984681i | \(-0.555788\pi\) | ||||
−0.174367 | + | 0.984681i | \(0.555788\pi\) | |||||||
\(992\) | −5.18162e10 | −1.68529 | ||||||||
\(993\) | 1.80583e10 | 0.585267 | ||||||||
\(994\) | 3.99859e9 | 0.129138 | ||||||||
\(995\) | −1.57889e10 | −0.508127 | ||||||||
\(996\) | 3.95061e9 | 0.126694 | ||||||||
\(997\) | −3.63110e10 | −1.16039 | −0.580196 | − | 0.814477i | \(-0.697024\pi\) | ||||
−0.580196 | + | 0.814477i | \(0.697024\pi\) | |||||||
\(998\) | 3.44245e10 | 1.09625 | ||||||||
\(999\) | 7.76180e8 | 0.0246311 |
(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 | 177.8.a.b.1.14 | ✓ | 17 | |
3.2 | odd | 2 | 531.8.a.d.1.4 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.b.1.14 | ✓ | 17 | 1.1 | even | 1 | trivial | |
531.8.a.d.1.4 | 17 | 3.2 | odd | 2 |