Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,8,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, 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("531.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(165.876448532\) |
Analytic rank: | \(0\) |
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: | \( x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + \cdots + 24\!\cdots\!16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(-13.8304\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 13.8304 | 1.22245 | 0.611224 | − | 0.791458i | \(-0.290678\pi\) | ||||
0.611224 | + | 0.791458i | \(0.290678\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 63.2803 | 0.494377 | ||||||||
\(5\) | 149.469 | 0.534757 | 0.267378 | − | 0.963592i | \(-0.413843\pi\) | ||||
0.267378 | + | 0.963592i | \(0.413843\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.2725 | 0.0157274 | 0.00786370 | − | 0.999969i | \(-0.497497\pi\) | ||||
0.00786370 | + | 0.999969i | \(0.497497\pi\) | |||||||
\(8\) | −895.100 | −0.618097 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2067.22 | 0.653712 | ||||||||
\(11\) | −531.760 | −0.120459 | −0.0602297 | − | 0.998185i | \(-0.519183\pi\) | ||||
−0.0602297 | + | 0.998185i | \(0.519183\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4168.02 | 0.526172 | 0.263086 | − | 0.964772i | \(-0.415260\pi\) | ||||
0.263086 | + | 0.964772i | \(0.415260\pi\) | |||||||
\(14\) | 197.395 | 0.0192259 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −20479.5 | −1.24997 | ||||||||
\(17\) | −4562.28 | −0.225222 | −0.112611 | − | 0.993639i | \(-0.535921\pi\) | ||||
−0.112611 | + | 0.993639i | \(0.535921\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 31839.8 | 1.06496 | 0.532480 | − | 0.846443i | \(-0.321260\pi\) | ||||
0.532480 | + | 0.846443i | \(0.321260\pi\) | |||||||
\(20\) | 9458.44 | 0.264372 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7354.45 | −0.147255 | ||||||||
\(23\) | 56030.4 | 0.960231 | 0.480116 | − | 0.877205i | \(-0.340595\pi\) | ||||
0.480116 | + | 0.877205i | \(0.340595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −55784.0 | −0.714035 | ||||||||
\(26\) | 57645.4 | 0.643217 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 903.168 | 0.00777527 | ||||||||
\(29\) | −52043.8 | −0.396256 | −0.198128 | − | 0.980176i | \(-0.563486\pi\) | ||||
−0.198128 | + | 0.980176i | \(0.563486\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −44036.0 | −0.265486 | −0.132743 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132743 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(32\) | −168667. | −0.909923 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −63098.2 | −0.275322 | ||||||||
\(35\) | 2133.30 | 0.00841033 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11309.5 | 0.0367059 | 0.0183529 | − | 0.999832i | \(-0.494158\pi\) | ||||
0.0183529 | + | 0.999832i | \(0.494158\pi\) | |||||||
\(38\) | 440358. | 1.30186 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −133790. | −0.330531 | ||||||||
\(41\) | 455543. | 1.03225 | 0.516126 | − | 0.856513i | \(-0.327374\pi\) | ||||
0.516126 | + | 0.856513i | \(0.327374\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 177174. | 0.339829 | 0.169915 | − | 0.985459i | \(-0.445651\pi\) | ||||
0.169915 | + | 0.985459i | \(0.445651\pi\) | |||||||
\(44\) | −33649.9 | −0.0595524 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 774923. | 1.17383 | ||||||||
\(47\) | 1.27260e6 | 1.78792 | 0.893960 | − | 0.448147i | \(-0.147916\pi\) | ||||
0.893960 | + | 0.448147i | \(0.147916\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −823339. | −0.999753 | ||||||||
\(50\) | −771516. | −0.872871 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 263753. | 0.260127 | ||||||||
\(53\) | −274388. | −0.253162 | −0.126581 | − | 0.991956i | \(-0.540400\pi\) | ||||
−0.126581 | + | 0.991956i | \(0.540400\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −79481.6 | −0.0644165 | ||||||||
\(56\) | −12775.3 | −0.00972106 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −719787. | −0.484402 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −152764. | −0.0861719 | −0.0430860 | − | 0.999071i | \(-0.513719\pi\) | ||||
−0.0430860 | + | 0.999071i | \(0.513719\pi\) | |||||||
\(62\) | −609036. | −0.324543 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 288642. | 0.137635 | ||||||||
\(65\) | 622989. | 0.281374 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.06545e6 | 0.838984 | 0.419492 | − | 0.907759i | \(-0.362208\pi\) | ||||
0.419492 | + | 0.907759i | \(0.362208\pi\) | |||||||
\(68\) | −288702. | −0.111345 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 29504.4 | 0.0102812 | ||||||||
\(71\) | 1.79110e6 | 0.593904 | 0.296952 | − | 0.954892i | \(-0.404030\pi\) | ||||
0.296952 | + | 0.954892i | \(0.404030\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.32985e6 | 1.00183 | 0.500916 | − | 0.865496i | \(-0.332996\pi\) | ||||
0.500916 | + | 0.865496i | \(0.332996\pi\) | |||||||
\(74\) | 156414. | 0.0448710 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.01483e6 | 0.526492 | ||||||||
\(77\) | −7589.54 | −0.00189451 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.43667e6 | 1.46881 | 0.734406 | − | 0.678710i | \(-0.237461\pi\) | ||||
0.734406 | + | 0.678710i | \(0.237461\pi\) | |||||||
\(80\) | −3.06105e6 | −0.668429 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.30035e6 | 1.26187 | ||||||||
\(83\) | 1.15501e6 | 0.221724 | 0.110862 | − | 0.993836i | \(-0.464639\pi\) | ||||
0.110862 | + | 0.993836i | \(0.464639\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −681919. | −0.120439 | ||||||||
\(86\) | 2.45039e6 | 0.415423 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 475978. | 0.0744556 | ||||||||
\(89\) | −3.69123e6 | −0.555016 | −0.277508 | − | 0.960723i | \(-0.589509\pi\) | ||||
−0.277508 | + | 0.960723i | \(0.589509\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 59488.0 | 0.00827532 | ||||||||
\(92\) | 3.54562e6 | 0.474717 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.76005e7 | 2.18564 | ||||||||
\(95\) | 4.75907e6 | 0.569494 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.33530e6 | 0.704800 | 0.352400 | − | 0.935849i | \(-0.385366\pi\) | ||||
0.352400 | + | 0.935849i | \(0.385366\pi\) | |||||||
\(98\) | −1.13871e7 | −1.22214 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.53003e6 | −0.353003 | ||||||||
\(101\) | −8.28710e6 | −0.800346 | −0.400173 | − | 0.916440i | \(-0.631050\pi\) | ||||
−0.400173 | + | 0.916440i | \(0.631050\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.33969e7 | 1.20802 | 0.604008 | − | 0.796979i | \(-0.293570\pi\) | ||||
0.604008 | + | 0.796979i | \(0.293570\pi\) | |||||||
\(104\) | −3.73079e6 | −0.325225 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.79490e6 | −0.309478 | ||||||||
\(107\) | −7.64708e6 | −0.603466 | −0.301733 | − | 0.953393i | \(-0.597565\pi\) | ||||
−0.301733 | + | 0.953393i | \(0.597565\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.75164e6 | 0.647287 | 0.323644 | − | 0.946179i | \(-0.395092\pi\) | ||||
0.323644 | + | 0.946179i | \(0.395092\pi\) | |||||||
\(110\) | −1.09926e6 | −0.0787458 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −292293. | −0.0196588 | ||||||||
\(113\) | 1.76375e7 | 1.14990 | 0.574952 | − | 0.818187i | \(-0.305021\pi\) | ||||
0.574952 | + | 0.818187i | \(0.305021\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.37480e6 | 0.513490 | ||||||||
\(116\) | −3.29335e6 | −0.195900 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.84048e6 | 0.159149 | ||||||||
\(119\) | −65115.1 | −0.00354215 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.92044e7 | −0.985490 | ||||||||
\(122\) | −2.11278e6 | −0.105341 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.78661e6 | −0.131250 | ||||||||
\(125\) | −2.00152e7 | −0.916592 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.15626e7 | −1.36729 | −0.683643 | − | 0.729817i | \(-0.739605\pi\) | ||||
−0.683643 | + | 0.729817i | \(0.739605\pi\) | |||||||
\(128\) | 2.55814e7 | 1.07817 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.61620e6 | 0.343965 | ||||||||
\(131\) | 1.54251e7 | 0.599485 | 0.299742 | − | 0.954020i | \(-0.403099\pi\) | ||||
0.299742 | + | 0.954020i | \(0.403099\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 454434. | 0.0167490 | ||||||||
\(134\) | 2.85661e7 | 1.02561 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.08370e6 | 0.139209 | ||||||||
\(137\) | −2.73563e6 | −0.0908940 | −0.0454470 | − | 0.998967i | \(-0.514471\pi\) | ||||
−0.0454470 | + | 0.998967i | \(0.514471\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.21140e7 | 0.698418 | 0.349209 | − | 0.937045i | \(-0.386450\pi\) | ||||
0.349209 | + | 0.937045i | \(0.386450\pi\) | |||||||
\(140\) | 134996. | 0.00415788 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.47717e7 | 0.726016 | ||||||||
\(143\) | −2.21638e6 | −0.0633824 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.77893e6 | −0.211900 | ||||||||
\(146\) | 4.60532e7 | 1.22469 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 715666. | 0.0181466 | ||||||||
\(149\) | −4.34797e6 | −0.107680 | −0.0538399 | − | 0.998550i | \(-0.517146\pi\) | ||||
−0.0538399 | + | 0.998550i | \(0.517146\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 642629. | 0.0151894 | 0.00759470 | − | 0.999971i | \(-0.497583\pi\) | ||||
0.00759470 | + | 0.999971i | \(0.497583\pi\) | |||||||
\(152\) | −2.84998e7 | −0.658248 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −104966. | −0.00231594 | ||||||||
\(155\) | −6.58202e6 | −0.141970 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.54519e7 | 0.937354 | 0.468677 | − | 0.883370i | \(-0.344731\pi\) | ||||
0.468677 | + | 0.883370i | \(0.344731\pi\) | |||||||
\(158\) | 8.90218e7 | 1.79555 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.52105e7 | −0.486587 | ||||||||
\(161\) | 799693. | 0.0151019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.12208e7 | 1.64982 | 0.824911 | − | 0.565262i | \(-0.191225\pi\) | ||||
0.824911 | + | 0.565262i | \(0.191225\pi\) | |||||||
\(164\) | 2.88269e7 | 0.510322 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.59743e7 | 0.271045 | ||||||||
\(167\) | 6.56493e7 | 1.09074 | 0.545371 | − | 0.838194i | \(-0.316389\pi\) | ||||
0.545371 | + | 0.838194i | \(0.316389\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.53762e7 | −0.723143 | ||||||||
\(170\) | −9.43122e6 | −0.147230 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.12116e7 | 0.168004 | ||||||||
\(173\) | 1.20346e8 | 1.76714 | 0.883568 | − | 0.468303i | \(-0.155134\pi\) | ||||
0.883568 | + | 0.468303i | \(0.155134\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −796177. | −0.0112299 | ||||||||
\(176\) | 1.08902e7 | 0.150571 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.10512e7 | −0.678478 | ||||||||
\(179\) | 1.33167e7 | 0.173544 | 0.0867722 | − | 0.996228i | \(-0.472345\pi\) | ||||
0.0867722 | + | 0.996228i | \(0.472345\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.20262e7 | 0.150748 | 0.0753741 | − | 0.997155i | \(-0.475985\pi\) | ||||
0.0753741 | + | 0.997155i | \(0.475985\pi\) | |||||||
\(182\) | 822744. | 0.0101161 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.01528e7 | −0.593516 | ||||||||
\(185\) | 1.69041e6 | 0.0196287 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.42603e6 | 0.0271301 | ||||||||
\(188\) | 8.05302e7 | 0.883907 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.58198e7 | 0.696176 | ||||||||
\(191\) | 2.96173e6 | 0.0307559 | 0.0153780 | − | 0.999882i | \(-0.495105\pi\) | ||||
0.0153780 | + | 0.999882i | \(0.495105\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.88812e6 | −0.0889937 | −0.0444968 | − | 0.999010i | \(-0.514168\pi\) | ||||
−0.0444968 | + | 0.999010i | \(0.514168\pi\) | |||||||
\(194\) | 8.76198e7 | 0.861581 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.21012e7 | −0.494255 | ||||||||
\(197\) | −5.08009e7 | −0.473412 | −0.236706 | − | 0.971581i | \(-0.576068\pi\) | ||||
−0.236706 | + | 0.971581i | \(0.576068\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.98854e7 | 0.358780 | 0.179390 | − | 0.983778i | \(-0.442588\pi\) | ||||
0.179390 | + | 0.983778i | \(0.442588\pi\) | |||||||
\(200\) | 4.99323e7 | 0.441343 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.14614e8 | −0.978381 | ||||||||
\(203\) | −742795. | −0.00623208 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.80896e7 | 0.552004 | ||||||||
\(206\) | 1.85284e8 | 1.47674 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.53588e7 | −0.657698 | ||||||||
\(209\) | −1.69311e7 | −0.128284 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.97162e7 | 0.584195 | 0.292098 | − | 0.956389i | \(-0.405647\pi\) | ||||
0.292098 | + | 0.956389i | \(0.405647\pi\) | |||||||
\(212\) | −1.73633e7 | −0.125158 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.05762e8 | −0.737705 | ||||||||
\(215\) | 2.64820e7 | 0.181726 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −628504. | −0.00417541 | ||||||||
\(218\) | 1.21039e8 | 0.791274 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.02962e6 | −0.0318460 | ||||||||
\(221\) | −1.90156e7 | −0.118505 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.35288e8 | 0.816947 | 0.408473 | − | 0.912770i | \(-0.366061\pi\) | ||||
0.408473 | + | 0.912770i | \(0.366061\pi\) | |||||||
\(224\) | −2.40730e6 | −0.0143107 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.43934e8 | 1.40570 | ||||||||
\(227\) | 1.97246e8 | 1.11923 | 0.559613 | − | 0.828754i | \(-0.310950\pi\) | ||||
0.559613 | + | 0.828754i | \(0.310950\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.35002e8 | 0.742875 | 0.371438 | − | 0.928458i | \(-0.378865\pi\) | ||||
0.371438 | + | 0.928458i | \(0.378865\pi\) | |||||||
\(230\) | 1.15827e8 | 0.627715 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.65844e7 | 0.244925 | ||||||||
\(233\) | −1.36315e8 | −0.705988 | −0.352994 | − | 0.935626i | \(-0.614836\pi\) | ||||
−0.352994 | + | 0.935626i | \(0.614836\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.90214e8 | 0.956102 | ||||||||
\(236\) | 1.29964e7 | 0.0643624 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −900569. | −0.00433010 | ||||||||
\(239\) | −1.31494e8 | −0.623038 | −0.311519 | − | 0.950240i | \(-0.600838\pi\) | ||||
−0.311519 | + | 0.950240i | \(0.600838\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.49648e8 | 1.14887 | 0.574433 | − | 0.818552i | \(-0.305223\pi\) | ||||
0.574433 | + | 0.818552i | \(0.305223\pi\) | |||||||
\(242\) | −2.65605e8 | −1.20471 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.66693e6 | −0.0426014 | ||||||||
\(245\) | −1.23064e8 | −0.534624 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.32709e8 | 0.560351 | ||||||||
\(248\) | 3.94166e7 | 0.164096 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.76819e8 | −1.12048 | ||||||||
\(251\) | −3.53873e7 | −0.141250 | −0.0706252 | − | 0.997503i | \(-0.522499\pi\) | ||||
−0.0706252 | + | 0.997503i | \(0.522499\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.97947e7 | −0.115669 | ||||||||
\(254\) | −4.36523e8 | −1.67143 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.16855e8 | 1.18038 | ||||||||
\(257\) | −4.79092e7 | −0.176057 | −0.0880285 | − | 0.996118i | \(-0.528057\pi\) | ||||
−0.0880285 | + | 0.996118i | \(0.528057\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 161414. | 0.000577288 0 | ||||||||
\(260\) | 3.94229e7 | 0.139105 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.13335e8 | 0.732838 | ||||||||
\(263\) | −4.03661e8 | −1.36827 | −0.684135 | − | 0.729355i | \(-0.739820\pi\) | ||||
−0.684135 | + | 0.729355i | \(0.739820\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.10125e7 | −0.135380 | ||||||||
\(266\) | 6.28501e6 | 0.0204748 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.30703e8 | 0.414775 | ||||||||
\(269\) | −1.59050e8 | −0.498196 | −0.249098 | − | 0.968478i | \(-0.580134\pi\) | ||||
−0.249098 | + | 0.968478i | \(0.580134\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.63878e8 | −0.805399 | −0.402700 | − | 0.915332i | \(-0.631928\pi\) | ||||
−0.402700 | + | 0.915332i | \(0.631928\pi\) | |||||||
\(272\) | 9.34331e7 | 0.281520 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.78349e7 | −0.111113 | ||||||||
\(275\) | 2.96637e7 | 0.0860123 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.07781e8 | 1.43548 | 0.717740 | − | 0.696311i | \(-0.245177\pi\) | ||||
0.717740 | + | 0.696311i | \(0.245177\pi\) | |||||||
\(278\) | 3.05846e8 | 0.853779 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.90951e6 | −0.00519840 | ||||||||
\(281\) | −4.01914e8 | −1.08059 | −0.540295 | − | 0.841476i | \(-0.681687\pi\) | ||||
−0.540295 | + | 0.841476i | \(0.681687\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.41538e7 | −0.0371210 | −0.0185605 | − | 0.999828i | \(-0.505908\pi\) | ||||
−0.0185605 | + | 0.999828i | \(0.505908\pi\) | |||||||
\(284\) | 1.13341e8 | 0.293612 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.06535e7 | −0.0774816 | ||||||||
\(287\) | 6.50174e6 | 0.0162346 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.89524e8 | −0.949275 | ||||||||
\(290\) | −1.07586e8 | −0.259037 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.10714e8 | 0.495283 | ||||||||
\(293\) | 5.93471e7 | 0.137836 | 0.0689180 | − | 0.997622i | \(-0.478045\pi\) | ||||
0.0689180 | + | 0.997622i | \(0.478045\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.06978e7 | 0.0696194 | ||||||||
\(296\) | −1.01231e7 | −0.0226878 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.01342e7 | −0.131633 | ||||||||
\(299\) | 2.33535e8 | 0.505247 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.52872e6 | 0.00534463 | ||||||||
\(302\) | 8.88782e6 | 0.0185682 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.52063e8 | −1.33117 | ||||||||
\(305\) | −2.28334e7 | −0.0460810 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.64952e8 | 0.522617 | 0.261308 | − | 0.965255i | \(-0.415846\pi\) | ||||
0.261308 | + | 0.965255i | \(0.415846\pi\) | |||||||
\(308\) | −480268. | −0.000936605 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.10320e7 | −0.173551 | ||||||||
\(311\) | −2.51765e8 | −0.474607 | −0.237304 | − | 0.971436i | \(-0.576264\pi\) | ||||
−0.237304 | + | 0.971436i | \(0.576264\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.78674e8 | 0.329348 | 0.164674 | − | 0.986348i | \(-0.447343\pi\) | ||||
0.164674 | + | 0.986348i | \(0.447343\pi\) | |||||||
\(314\) | 6.28619e8 | 1.14587 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.07314e8 | 0.726147 | ||||||||
\(317\) | −7.62555e8 | −1.34451 | −0.672254 | − | 0.740320i | \(-0.734674\pi\) | ||||
−0.672254 | + | 0.740320i | \(0.734674\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.76748e7 | 0.0477328 | ||||||||
\(320\) | 4.31430e7 | 0.0736013 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.10601e7 | 0.0184613 | ||||||||
\(323\) | −1.45262e8 | −0.239852 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.32509e8 | −0.375705 | ||||||||
\(326\) | 1.26162e9 | 2.01682 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.07757e8 | −0.638032 | ||||||||
\(329\) | 1.81631e7 | 0.0281193 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.94113e8 | 0.597342 | 0.298671 | − | 0.954356i | \(-0.403457\pi\) | ||||
0.298671 | + | 0.954356i | \(0.403457\pi\) | |||||||
\(332\) | 7.30893e7 | 0.109615 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.07957e8 | 1.33338 | ||||||||
\(335\) | 3.08721e8 | 0.448652 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.50464e8 | 0.214155 | 0.107077 | − | 0.994251i | \(-0.465851\pi\) | ||||
0.107077 | + | 0.994251i | \(0.465851\pi\) | |||||||
\(338\) | −6.27571e8 | −0.884004 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.31520e7 | −0.0595422 | ||||||||
\(341\) | 2.34166e7 | 0.0319803 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.35051e7 | −0.0314509 | ||||||||
\(344\) | −1.58589e8 | −0.210047 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.66443e9 | 2.16023 | ||||||||
\(347\) | −1.12645e9 | −1.44730 | −0.723651 | − | 0.690166i | \(-0.757538\pi\) | ||||
−0.723651 | + | 0.690166i | \(0.757538\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.40653e8 | −0.303042 | −0.151521 | − | 0.988454i | \(-0.548417\pi\) | ||||
−0.151521 | + | 0.988454i | \(0.548417\pi\) | |||||||
\(350\) | −1.10115e7 | −0.0137280 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.96902e7 | 0.109609 | ||||||||
\(353\) | 2.62604e8 | 0.317754 | 0.158877 | − | 0.987298i | \(-0.449213\pi\) | ||||
0.158877 | + | 0.987298i | \(0.449213\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.67714e8 | 0.317594 | ||||||||
\(356\) | −2.33582e8 | −0.274387 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.84175e8 | 0.212149 | ||||||||
\(359\) | −1.31180e7 | −0.0149636 | −0.00748179 | − | 0.999972i | \(-0.502382\pi\) | ||||
−0.00748179 | + | 0.999972i | \(0.502382\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.19902e8 | 0.134138 | ||||||||
\(362\) | 1.66327e8 | 0.184282 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.76442e6 | 0.00409113 | ||||||||
\(365\) | 4.97710e8 | 0.535737 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.85308e8 | 0.301288 | 0.150644 | − | 0.988588i | \(-0.451865\pi\) | ||||
0.150644 | + | 0.988588i | \(0.451865\pi\) | |||||||
\(368\) | −1.14747e9 | −1.20026 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.33791e7 | 0.0239951 | ||||||||
\(371\) | −3.91620e6 | −0.00398159 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.76282e8 | −0.175884 | −0.0879420 | − | 0.996126i | \(-0.528029\pi\) | ||||
−0.0879420 | + | 0.996126i | \(0.528029\pi\) | |||||||
\(374\) | 3.35531e7 | 0.0331651 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.13910e9 | −1.10511 | ||||||||
\(377\) | −2.16919e8 | −0.208499 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.69178e9 | −1.59627 | −0.798137 | − | 0.602477i | \(-0.794181\pi\) | ||||
−0.798137 | + | 0.602477i | \(0.794181\pi\) | |||||||
\(380\) | 3.01155e8 | 0.281545 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.09620e7 | 0.0375975 | ||||||||
\(383\) | −2.05814e9 | −1.87189 | −0.935944 | − | 0.352149i | \(-0.885451\pi\) | ||||
−0.935944 | + | 0.352149i | \(0.885451\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.13440e6 | −0.00101310 | ||||||||
\(386\) | −1.22926e8 | −0.108790 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.00900e8 | 0.348437 | ||||||||
\(389\) | −1.26822e9 | −1.09237 | −0.546187 | − | 0.837663i | \(-0.683921\pi\) | ||||
−0.546187 | + | 0.837663i | \(0.683921\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.55626e8 | −0.216265 | ||||||||
\(392\) | 7.36971e8 | 0.617944 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.02597e8 | −0.578722 | ||||||||
\(395\) | 9.62082e8 | 0.785457 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.90127e9 | 1.52502 | 0.762512 | − | 0.646975i | \(-0.223966\pi\) | ||||
0.762512 | + | 0.646975i | \(0.223966\pi\) | |||||||
\(398\) | 5.51632e8 | 0.438590 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.14243e9 | 0.892522 | ||||||||
\(401\) | 1.68338e9 | 1.30370 | 0.651849 | − | 0.758349i | \(-0.273993\pi\) | ||||
0.651849 | + | 0.758349i | \(0.273993\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.83543e8 | −0.139691 | ||||||||
\(404\) | −5.24410e8 | −0.395673 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.02732e7 | −0.00761838 | ||||||||
\(407\) | −6.01391e6 | −0.00442157 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.07416e8 | 0.0776317 | 0.0388159 | − | 0.999246i | \(-0.487641\pi\) | ||||
0.0388159 | + | 0.999246i | \(0.487641\pi\) | |||||||
\(410\) | 9.41707e8 | 0.674795 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.47757e8 | 0.597215 | ||||||||
\(413\) | 2.93127e6 | 0.00204753 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.72638e8 | 0.118568 | ||||||||
\(416\) | −7.03006e8 | −0.478776 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.34164e8 | −0.156821 | ||||||||
\(419\) | −2.36422e8 | −0.157014 | −0.0785071 | − | 0.996914i | \(-0.525015\pi\) | ||||
−0.0785071 | + | 0.996914i | \(0.525015\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.71085e9 | −1.11744 | −0.558722 | − | 0.829355i | \(-0.688708\pi\) | ||||
−0.558722 | + | 0.829355i | \(0.688708\pi\) | |||||||
\(422\) | 1.10251e9 | 0.714148 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.45605e8 | 0.156479 | ||||||||
\(425\) | 2.54502e8 | 0.160816 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.18032e6 | −0.00135526 | ||||||||
\(428\) | −4.83910e8 | −0.298340 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.66258e8 | 0.222150 | ||||||||
\(431\) | −6.46052e8 | −0.388685 | −0.194342 | − | 0.980934i | \(-0.562257\pi\) | ||||
−0.194342 | + | 0.980934i | \(0.562257\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.52351e9 | 1.49382 | 0.746908 | − | 0.664927i | \(-0.231537\pi\) | ||||
0.746908 | + | 0.664927i | \(0.231537\pi\) | |||||||
\(434\) | −8.69247e6 | −0.00510422 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.53807e8 | 0.320004 | ||||||||
\(437\) | 1.78400e9 | 1.02261 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.77473e8 | −0.100117 | −0.0500584 | − | 0.998746i | \(-0.515941\pi\) | ||||
−0.0500584 | + | 0.998746i | \(0.515941\pi\) | |||||||
\(440\) | 7.11440e7 | 0.0398156 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.62994e8 | −0.144867 | ||||||||
\(443\) | −1.83781e9 | −1.00436 | −0.502178 | − | 0.864764i | \(-0.667468\pi\) | ||||
−0.502178 | + | 0.864764i | \(0.667468\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.51724e8 | −0.296798 | ||||||||
\(446\) | 1.87110e9 | 0.998674 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.11964e6 | 0.00216464 | ||||||||
\(449\) | 8.93570e8 | 0.465872 | 0.232936 | − | 0.972492i | \(-0.425167\pi\) | ||||
0.232936 | + | 0.972492i | \(0.425167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.42239e8 | −0.124345 | ||||||||
\(452\) | 1.11610e9 | 0.568487 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.72800e9 | 1.36820 | ||||||||
\(455\) | 8.89161e6 | 0.00442528 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.88094e8 | −0.288231 | −0.144115 | − | 0.989561i | \(-0.546034\pi\) | ||||
−0.144115 | + | 0.989561i | \(0.546034\pi\) | |||||||
\(458\) | 1.86713e9 | 0.908126 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.29960e8 | 0.253858 | ||||||||
\(461\) | 2.65315e9 | 1.26127 | 0.630636 | − | 0.776079i | \(-0.282794\pi\) | ||||
0.630636 | + | 0.776079i | \(0.282794\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.10539e9 | 0.517587 | 0.258793 | − | 0.965933i | \(-0.416675\pi\) | ||||
0.258793 | + | 0.965933i | \(0.416675\pi\) | |||||||
\(464\) | 1.06583e9 | 0.495307 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.88529e9 | −0.863033 | ||||||||
\(467\) | −6.70125e8 | −0.304472 | −0.152236 | − | 0.988344i | \(-0.548647\pi\) | ||||
−0.152236 | + | 0.988344i | \(0.548647\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.94792e7 | 0.0131950 | ||||||||
\(470\) | 2.63073e9 | 1.16878 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.83835e8 | −0.0804694 | ||||||||
\(473\) | −9.42140e7 | −0.0409356 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.77615e9 | −0.760418 | ||||||||
\(476\) | −4.12050e6 | −0.00175116 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.81862e9 | −0.761631 | ||||||||
\(479\) | 9.38891e7 | 0.0390338 | 0.0195169 | − | 0.999810i | \(-0.493787\pi\) | ||||
0.0195169 | + | 0.999810i | \(0.493787\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.71380e7 | 0.0193136 | ||||||||
\(482\) | 3.45274e9 | 1.40443 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.21526e9 | −0.487204 | ||||||||
\(485\) | 9.46931e8 | 0.376896 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.37204e9 | 0.538288 | 0.269144 | − | 0.963100i | \(-0.413259\pi\) | ||||
0.269144 | + | 0.963100i | \(0.413259\pi\) | |||||||
\(488\) | 1.36739e8 | 0.0532626 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.70202e9 | −0.653550 | ||||||||
\(491\) | −3.03791e9 | −1.15822 | −0.579108 | − | 0.815251i | \(-0.696599\pi\) | ||||
−0.579108 | + | 0.815251i | \(0.696599\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.37438e8 | 0.0892455 | ||||||||
\(494\) | 1.83542e9 | 0.685000 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.01834e8 | 0.331849 | ||||||||
\(497\) | 2.55635e7 | 0.00934056 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.44240e9 | −1.24025 | −0.620126 | − | 0.784502i | \(-0.712919\pi\) | ||||
−0.620126 | + | 0.784502i | \(0.712919\pi\) | |||||||
\(500\) | −1.26657e9 | −0.453142 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.89421e8 | −0.172671 | ||||||||
\(503\) | −1.03977e8 | −0.0364291 | −0.0182146 | − | 0.999834i | \(-0.505798\pi\) | ||||
−0.0182146 | + | 0.999834i | \(0.505798\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.23866e9 | −0.427990 | ||||||||
\(506\) | −4.12073e8 | −0.141399 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.99729e9 | −0.675955 | ||||||||
\(509\) | 9.41820e8 | 0.316560 | 0.158280 | − | 0.987394i | \(-0.449405\pi\) | ||||
0.158280 | + | 0.987394i | \(0.449405\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.75253e7 | 0.0157562 | ||||||||
\(512\) | 1.10782e9 | 0.364774 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.62604e8 | −0.215220 | ||||||||
\(515\) | 2.00241e9 | 0.645994 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.76715e8 | −0.215372 | ||||||||
\(518\) | 2.23243e6 | 0.000705704 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.57638e8 | −0.173916 | ||||||||
\(521\) | −9.49236e8 | −0.294064 | −0.147032 | − | 0.989132i | \(-0.546972\pi\) | ||||
−0.147032 | + | 0.989132i | \(0.546972\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.88735e9 | −1.18822 | −0.594111 | − | 0.804383i | \(-0.702496\pi\) | ||||
−0.594111 | + | 0.804383i | \(0.702496\pi\) | |||||||
\(524\) | 9.76104e8 | 0.296372 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.58280e9 | −1.67264 | ||||||||
\(527\) | 2.00904e8 | 0.0597933 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.65425e8 | −0.0779555 | ||||||||
\(530\) | −5.67220e8 | −0.165495 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.87567e7 | 0.00828034 | ||||||||
\(533\) | 1.89871e9 | 0.543142 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.14300e9 | −0.322707 | ||||||||
\(536\) | −1.84879e9 | −0.518574 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.19972e9 | −0.609018 | ||||||||
\(539\) | 4.37819e8 | 0.120430 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.42183e9 | −0.657588 | −0.328794 | − | 0.944402i | \(-0.606642\pi\) | ||||
−0.328794 | + | 0.944402i | \(0.606642\pi\) | |||||||
\(542\) | −3.64955e9 | −0.984558 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.69505e8 | 0.204935 | ||||||||
\(545\) | 1.30810e9 | 0.346141 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.83350e9 | 1.52396 | 0.761980 | − | 0.647600i | \(-0.224227\pi\) | ||||
0.761980 | + | 0.647600i | \(0.224227\pi\) | |||||||
\(548\) | −1.73111e8 | −0.0449359 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.10261e8 | 0.105146 | ||||||||
\(551\) | −1.65706e9 | −0.421996 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.18674e7 | 0.0231006 | ||||||||
\(554\) | 7.02282e9 | 1.75480 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.39938e9 | 0.345282 | ||||||||
\(557\) | −2.32049e9 | −0.568967 | −0.284484 | − | 0.958681i | \(-0.591822\pi\) | ||||
−0.284484 | + | 0.958681i | \(0.591822\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.38465e8 | 0.178809 | ||||||||
\(560\) | −4.36888e7 | −0.0105126 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.55863e9 | −1.32096 | ||||||||
\(563\) | 4.30898e9 | 1.01764 | 0.508821 | − | 0.860873i | \(-0.330082\pi\) | ||||
0.508821 | + | 0.860873i | \(0.330082\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.63626e9 | 0.614919 | ||||||||
\(566\) | −1.95753e8 | −0.0453785 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.60322e9 | −0.367090 | ||||||||
\(569\) | −5.58255e9 | −1.27040 | −0.635198 | − | 0.772349i | \(-0.719082\pi\) | ||||
−0.635198 | + | 0.772349i | \(0.719082\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.36498e9 | 1.20598 | 0.602992 | − | 0.797747i | \(-0.293975\pi\) | ||||
0.602992 | + | 0.797747i | \(0.293975\pi\) | |||||||
\(572\) | −1.40253e8 | −0.0313348 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.99217e7 | 0.0198460 | ||||||||
\(575\) | −3.12560e9 | −0.685639 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.50669e9 | 0.976658 | 0.488329 | − | 0.872660i | \(-0.337607\pi\) | ||||
0.488329 | + | 0.872660i | \(0.337607\pi\) | |||||||
\(578\) | −5.38728e9 | −1.16044 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.92253e8 | −0.104759 | ||||||||
\(581\) | 1.64849e7 | 0.00348714 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.45908e8 | 0.0304958 | ||||||||
\(584\) | −2.98055e9 | −0.619230 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.20794e8 | 0.168497 | ||||||||
\(587\) | −4.94446e9 | −1.00899 | −0.504494 | − | 0.863415i | \(-0.668321\pi\) | ||||
−0.504494 | + | 0.863415i | \(0.668321\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.40210e9 | −0.282732 | ||||||||
\(590\) | 4.24563e8 | 0.0851060 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.31612e8 | −0.0458812 | ||||||||
\(593\) | −7.08369e9 | −1.39498 | −0.697490 | − | 0.716594i | \(-0.745700\pi\) | ||||
−0.697490 | + | 0.716594i | \(0.745700\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.73269e6 | −0.00189419 | ||||||||
\(596\) | −2.75141e8 | −0.0532345 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.22989e9 | 0.617638 | ||||||||
\(599\) | −6.53780e9 | −1.24290 | −0.621452 | − | 0.783452i | \(-0.713457\pi\) | ||||
−0.621452 | + | 0.783452i | \(0.713457\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.66921e9 | −1.06528 | −0.532638 | − | 0.846343i | \(-0.678799\pi\) | ||||
−0.532638 | + | 0.846343i | \(0.678799\pi\) | |||||||
\(602\) | 3.49732e7 | 0.00653353 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.06657e7 | 0.00750930 | ||||||||
\(605\) | −2.87046e9 | −0.526997 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.43054e8 | −0.0622590 | −0.0311295 | − | 0.999515i | \(-0.509910\pi\) | ||||
−0.0311295 | + | 0.999515i | \(0.509910\pi\) | |||||||
\(608\) | −5.37032e9 | −0.969031 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.15796e8 | −0.0563316 | ||||||||
\(611\) | 5.30420e9 | 0.940753 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.95826e9 | −0.343367 | −0.171683 | − | 0.985152i | \(-0.554921\pi\) | ||||
−0.171683 | + | 0.985152i | \(0.554921\pi\) | |||||||
\(614\) | 3.66440e9 | 0.638872 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.79340e6 | 0.00117099 | ||||||||
\(617\) | 1.99932e9 | 0.342676 | 0.171338 | − | 0.985212i | \(-0.445191\pi\) | ||||
0.171338 | + | 0.985212i | \(0.445191\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.57292e9 | 0.266556 | 0.133278 | − | 0.991079i | \(-0.457450\pi\) | ||||
0.133278 | + | 0.991079i | \(0.457450\pi\) | |||||||
\(620\) | −4.16512e8 | −0.0701870 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.48202e9 | −0.580182 | ||||||||
\(623\) | −5.26830e7 | −0.00872896 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.36647e9 | 0.223882 | ||||||||
\(626\) | 2.47113e9 | 0.402611 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.87621e9 | 0.463406 | ||||||||
\(629\) | −5.15969e7 | −0.00826697 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.48635e9 | 0.552419 | 0.276209 | − | 0.961097i | \(-0.410922\pi\) | ||||
0.276209 | + | 0.961097i | \(0.410922\pi\) | |||||||
\(632\) | −5.76146e9 | −0.907869 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.05464e10 | −1.64359 | ||||||||
\(635\) | −4.71762e9 | −0.731165 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.43169e9 | −0.526042 | ||||||||
\(638\) | 3.82753e8 | 0.0583508 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.82362e9 | 0.576561 | ||||||||
\(641\) | −3.27300e9 | −0.490843 | −0.245422 | − | 0.969416i | \(-0.578926\pi\) | ||||
−0.245422 | + | 0.969416i | \(0.578926\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.07236e10 | 1.59075 | 0.795373 | − | 0.606120i | \(-0.207275\pi\) | ||||
0.795373 | + | 0.606120i | \(0.207275\pi\) | |||||||
\(644\) | 5.06048e7 | 0.00746606 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.00903e9 | −0.293206 | ||||||||
\(647\) | −1.13384e10 | −1.64584 | −0.822919 | − | 0.568159i | \(-0.807656\pi\) | ||||
−0.822919 | + | 0.568159i | \(0.807656\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.09212e8 | −0.0156825 | ||||||||
\(650\) | −3.21569e9 | −0.459280 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.77248e9 | 0.815635 | ||||||||
\(653\) | −2.78140e9 | −0.390901 | −0.195451 | − | 0.980714i | \(-0.562617\pi\) | ||||
−0.195451 | + | 0.980714i | \(0.562617\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.30557e9 | 0.320578 | ||||||||
\(656\) | −9.32928e9 | −1.29028 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.51204e8 | 0.0343744 | ||||||||
\(659\) | −8.83123e9 | −1.20205 | −0.601025 | − | 0.799230i | \(-0.705241\pi\) | ||||
−0.601025 | + | 0.799230i | \(0.705241\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.82485e9 | −0.784476 | −0.392238 | − | 0.919864i | \(-0.628299\pi\) | ||||
−0.392238 | + | 0.919864i | \(0.628299\pi\) | |||||||
\(662\) | 5.45075e9 | 0.730219 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.03385e9 | −0.137047 | ||||||||
\(665\) | 6.79238e7 | 0.00895666 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.91603e9 | −0.380497 | ||||||||
\(668\) | 4.15431e9 | 0.539239 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.26974e9 | 0.548454 | ||||||||
\(671\) | 8.12335e7 | 0.0103802 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.42844e9 | 0.433554 | 0.216777 | − | 0.976221i | \(-0.430446\pi\) | ||||
0.216777 | + | 0.976221i | \(0.430446\pi\) | |||||||
\(674\) | 2.08098e9 | 0.261793 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.87142e9 | −0.357506 | ||||||||
\(677\) | −8.10222e9 | −1.00356 | −0.501781 | − | 0.864995i | \(-0.667322\pi\) | ||||
−0.501781 | + | 0.864995i | \(0.667322\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.04206e7 | 0.0110847 | ||||||||
\(680\) | 6.10386e8 | 0.0744429 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.23861e8 | 0.0390943 | ||||||||
\(683\) | −1.95901e9 | −0.235269 | −0.117634 | − | 0.993057i | \(-0.537531\pi\) | ||||
−0.117634 | + | 0.993057i | \(0.537531\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.08892e8 | −0.0486061 | ||||||||
\(686\) | −3.25086e8 | −0.0384471 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.62844e9 | −0.424776 | ||||||||
\(689\) | −1.14365e9 | −0.133207 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.12139e9 | −0.821091 | −0.410546 | − | 0.911840i | \(-0.634662\pi\) | ||||
−0.410546 | + | 0.911840i | \(0.634662\pi\) | |||||||
\(692\) | 7.61552e9 | 0.873632 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.55793e10 | −1.76925 | ||||||||
\(695\) | 3.30536e9 | 0.373484 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.07831e9 | −0.232486 | ||||||||
\(698\) | −3.32833e9 | −0.370453 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.03823e7 | −0.00555182 | ||||||||
\(701\) | 9.01916e9 | 0.988902 | 0.494451 | − | 0.869206i | \(-0.335369\pi\) | ||||
0.494451 | + | 0.869206i | \(0.335369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.60091e8 | 0.0390903 | ||||||||
\(704\) | −1.53488e8 | −0.0165794 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.63193e9 | 0.388437 | ||||||||
\(707\) | −1.18278e8 | −0.0125874 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.63143e10 | −1.71912 | −0.859560 | − | 0.511034i | \(-0.829263\pi\) | ||||
−0.859560 | + | 0.511034i | \(0.829263\pi\) | |||||||
\(710\) | 3.70260e9 | 0.388242 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.30402e9 | 0.343054 | ||||||||
\(713\) | −2.46735e9 | −0.254928 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.31280e8 | −0.0338941 | ||||||||
\(716\) | 8.42684e8 | 0.0857964 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.81427e8 | −0.0182922 | ||||||||
\(719\) | −6.12136e9 | −0.614181 | −0.307091 | − | 0.951680i | \(-0.599355\pi\) | ||||
−0.307091 | + | 0.951680i | \(0.599355\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.91207e8 | 0.0189989 | ||||||||
\(722\) | 1.65829e9 | 0.163976 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.61019e8 | 0.0745265 | ||||||||
\(725\) | 2.90321e9 | 0.282941 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.56648e9 | 0.151201 | 0.0756003 | − | 0.997138i | \(-0.475913\pi\) | ||||
0.0756003 | + | 0.997138i | \(0.475913\pi\) | |||||||
\(728\) | −5.32477e7 | −0.00511495 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.88353e9 | 0.654910 | ||||||||
\(731\) | −8.08318e8 | −0.0765370 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.77128e9 | −0.447477 | −0.223739 | − | 0.974649i | \(-0.571826\pi\) | ||||
−0.223739 | + | 0.974649i | \(0.571826\pi\) | |||||||
\(734\) | 3.94592e9 | 0.368309 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.45046e9 | −0.873737 | ||||||||
\(737\) | −1.09833e9 | −0.101064 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.82555e8 | 0.0804427 | 0.0402213 | − | 0.999191i | \(-0.487194\pi\) | ||||
0.0402213 | + | 0.999191i | \(0.487194\pi\) | |||||||
\(740\) | 1.06970e8 | 0.00970399 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.41627e7 | −0.00486728 | ||||||||
\(743\) | −1.56677e9 | −0.140134 | −0.0700672 | − | 0.997542i | \(-0.522321\pi\) | ||||
−0.0700672 | + | 0.997542i | \(0.522321\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.49886e8 | −0.0575825 | ||||||||
\(746\) | −2.43805e9 | −0.215009 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.53520e8 | 0.0134125 | ||||||||
\(749\) | −1.09143e8 | −0.00949095 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.02135e9 | 0.432594 | 0.216297 | − | 0.976328i | \(-0.430602\pi\) | ||||
0.216297 | + | 0.976328i | \(0.430602\pi\) | |||||||
\(752\) | −2.60621e10 | −2.23484 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.00008e9 | −0.254879 | ||||||||
\(755\) | 9.60531e7 | 0.00812263 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.94352e9 | −0.246622 | −0.123311 | − | 0.992368i | \(-0.539351\pi\) | ||||
−0.123311 | + | 0.992368i | \(0.539351\pi\) | |||||||
\(758\) | −2.33980e10 | −1.95136 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.25984e9 | −0.352002 | ||||||||
\(761\) | 1.87159e10 | 1.53945 | 0.769724 | − | 0.638376i | \(-0.220394\pi\) | ||||
0.769724 | + | 0.638376i | \(0.220394\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.24908e8 | 0.0101801 | ||||||||
\(764\) | 1.87419e8 | 0.0152050 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.84650e10 | −2.28828 | ||||||||
\(767\) | 8.56023e8 | 0.0685017 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.08476e10 | −0.860187 | −0.430093 | − | 0.902784i | \(-0.641519\pi\) | ||||
−0.430093 | + | 0.902784i | \(0.641519\pi\) | |||||||
\(770\) | −1.56892e7 | −0.00123847 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.62443e8 | −0.0439965 | ||||||||
\(773\) | 2.59403e9 | 0.201998 | 0.100999 | − | 0.994887i | \(-0.467796\pi\) | ||||
0.100999 | + | 0.994887i | \(0.467796\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.45651e9 | 0.189567 | ||||||||
\(776\) | −5.67073e9 | −0.435635 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.75400e10 | −1.33537 | ||||||||
\(779\) | 1.45044e10 | 1.09931 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.52435e8 | −0.0715413 | ||||||||
\(782\) | −3.53541e9 | −0.264373 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.68616e10 | 1.24966 | ||||||||
\(785\) | 6.79366e9 | 0.501256 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.06990e10 | −1.51369 | −0.756846 | − | 0.653593i | \(-0.773261\pi\) | ||||
−0.756846 | + | 0.653593i | \(0.773261\pi\) | |||||||
\(788\) | −3.21470e9 | −0.234044 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.33060e10 | 0.960180 | ||||||||
\(791\) | 2.51731e8 | 0.0180850 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.36721e8 | −0.0453412 | ||||||||
\(794\) | 2.62953e10 | 1.86426 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.52396e9 | 0.177373 | ||||||||
\(797\) | 6.06784e9 | 0.424551 | 0.212275 | − | 0.977210i | \(-0.431913\pi\) | ||||
0.212275 | + | 0.977210i | \(0.431913\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.80594e9 | −0.402679 | ||||||||
\(800\) | 9.40891e9 | 0.649718 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.32819e10 | 1.59370 | ||||||||
\(803\) | −1.77068e9 | −0.120680 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.19529e8 | 0.00807586 | ||||||||
\(806\) | −2.53847e9 | −0.170765 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.41778e9 | 0.494691 | ||||||||
\(809\) | 2.20534e10 | 1.46438 | 0.732192 | − | 0.681098i | \(-0.238497\pi\) | ||||
0.732192 | + | 0.681098i | \(0.238497\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.91610e9 | 0.652782 | 0.326391 | − | 0.945235i | \(-0.394167\pi\) | ||||
0.326391 | + | 0.945235i | \(0.394167\pi\) | |||||||
\(812\) | −4.70043e7 | −0.00308100 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.31749e7 | −0.00540514 | ||||||||
\(815\) | 1.36347e10 | 0.882253 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.64119e9 | 0.361904 | ||||||||
\(818\) | 1.48561e9 | 0.0949007 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.30873e9 | 0.272898 | ||||||||
\(821\) | 4.09876e9 | 0.258495 | 0.129247 | − | 0.991612i | \(-0.458744\pi\) | ||||
0.129247 | + | 0.991612i | \(0.458744\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.76087e9 | −0.422769 | −0.211384 | − | 0.977403i | \(-0.567797\pi\) | ||||
−0.211384 | + | 0.977403i | \(0.567797\pi\) | |||||||
\(824\) | −1.19915e10 | −0.746671 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.05407e7 | 0.00250300 | ||||||||
\(827\) | −9.41705e8 | −0.0578956 | −0.0289478 | − | 0.999581i | \(-0.509216\pi\) | ||||
−0.0289478 | + | 0.999581i | \(0.509216\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.36525e10 | 0.832284 | 0.416142 | − | 0.909300i | \(-0.363382\pi\) | ||||
0.416142 | + | 0.909300i | \(0.363382\pi\) | |||||||
\(830\) | 2.38766e9 | 0.144943 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.20306e9 | 0.0724197 | ||||||||
\(833\) | 3.75630e9 | 0.225166 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.81253e9 | 0.583282 | ||||||||
\(836\) | −1.07141e9 | −0.0634209 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.26981e9 | −0.191942 | ||||||||
\(839\) | 2.04480e10 | 1.19532 | 0.597660 | − | 0.801750i | \(-0.296097\pi\) | ||||
0.597660 | + | 0.801750i | \(0.296097\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.45413e10 | −0.842981 | ||||||||
\(842\) | −2.36618e10 | −1.36602 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.04446e9 | 0.288813 | ||||||||
\(845\) | −6.78233e9 | −0.386706 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.74095e8 | −0.0154992 | ||||||||
\(848\) | 5.61932e9 | 0.316445 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.51987e9 | 0.196590 | ||||||||
\(851\) | 6.33673e8 | 0.0352461 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.28799e9 | 0.512389 | 0.256195 | − | 0.966625i | \(-0.417531\pi\) | ||||
0.256195 | + | 0.966625i | \(0.417531\pi\) | |||||||
\(854\) | −3.01547e7 | −0.00165673 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.84490e9 | 0.373000 | ||||||||
\(857\) | 7.57637e9 | 0.411177 | 0.205588 | − | 0.978639i | \(-0.434089\pi\) | ||||
0.205588 | + | 0.978639i | \(0.434089\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.27186e9 | 0.283784 | 0.141892 | − | 0.989882i | \(-0.454681\pi\) | ||||
0.141892 | + | 0.989882i | \(0.454681\pi\) | |||||||
\(860\) | 1.67579e9 | 0.0898412 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.93517e9 | −0.475146 | ||||||||
\(863\) | −2.11332e10 | −1.11925 | −0.559625 | − | 0.828746i | \(-0.689055\pi\) | ||||
−0.559625 | + | 0.828746i | \(0.689055\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.79880e10 | 0.944988 | ||||||||
\(866\) | 3.49012e10 | 1.82611 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.97719e7 | −0.00206423 | ||||||||
\(869\) | −3.42276e9 | −0.176932 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.60885e9 | 0.441450 | ||||||||
\(872\) | −7.83360e9 | −0.400086 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.46734e10 | 1.25008 | ||||||||
\(875\) | −2.85668e8 | −0.0144156 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.67780e10 | 0.839928 | 0.419964 | − | 0.907541i | \(-0.362043\pi\) | ||||
0.419964 | + | 0.907541i | \(0.362043\pi\) | |||||||
\(878\) | −2.45453e9 | −0.122387 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.62774e9 | 0.0805186 | ||||||||
\(881\) | −4.60252e9 | −0.226767 | −0.113384 | − | 0.993551i | \(-0.536169\pi\) | ||||
−0.113384 | + | 0.993551i | \(0.536169\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.60291e10 | −0.783515 | −0.391758 | − | 0.920068i | \(-0.628133\pi\) | ||||
−0.391758 | + | 0.920068i | \(0.628133\pi\) | |||||||
\(884\) | −1.20332e9 | −0.0585864 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.54177e10 | −1.22777 | ||||||||
\(887\) | 3.53761e10 | 1.70207 | 0.851034 | − | 0.525111i | \(-0.175976\pi\) | ||||
0.851034 | + | 0.525111i | \(0.175976\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.50477e8 | −0.0215038 | ||||||||
\(890\) | −7.63057e9 | −0.362820 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.56109e9 | 0.403880 | ||||||||
\(893\) | 4.05192e10 | 1.90406 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.99043e9 | 0.0928040 | ||||||||
\(896\) | 3.65110e8 | 0.0169569 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.23584e10 | 0.569504 | ||||||||
\(899\) | 2.29180e9 | 0.105200 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.25183e9 | 0.0570177 | ||||||||
\(902\) | −3.35027e9 | −0.152005 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.57873e10 | −0.710753 | ||||||||
\(905\) | 1.79754e9 | 0.0806136 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.61497e9 | −0.294376 | −0.147188 | − | 0.989109i | \(-0.547022\pi\) | ||||
−0.147188 | + | 0.989109i | \(0.547022\pi\) | |||||||
\(908\) | 1.24818e10 | 0.553320 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.22975e8 | 0.00540967 | ||||||||
\(911\) | −1.46424e10 | −0.641651 | −0.320826 | − | 0.947138i | \(-0.603960\pi\) | ||||
−0.320826 | + | 0.947138i | \(0.603960\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.14187e8 | −0.0267087 | ||||||||
\(914\) | −8.13359e9 | −0.352347 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.54297e9 | 0.367261 | ||||||||
\(917\) | 2.20155e8 | 0.00942834 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.03688e10 | 1.71570 | 0.857850 | − | 0.513901i | \(-0.171800\pi\) | ||||
0.857850 | + | 0.513901i | \(0.171800\pi\) | |||||||
\(920\) | −7.49629e9 | −0.317387 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.66942e10 | 1.54184 | ||||||||
\(923\) | 7.46534e9 | 0.312495 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.30887e8 | −0.0262093 | ||||||||
\(926\) | 1.52880e10 | 0.632723 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.77806e9 | 0.360563 | ||||||||
\(929\) | 2.36038e10 | 0.965889 | 0.482945 | − | 0.875651i | \(-0.339567\pi\) | ||||
0.482945 | + | 0.875651i | \(0.339567\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.62150e10 | −1.06470 | ||||||||
\(932\) | −8.62604e9 | −0.349024 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.26811e9 | −0.372200 | ||||||||
\(935\) | 3.62617e8 | 0.0145080 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.58838e10 | 1.02787 | 0.513937 | − | 0.857828i | \(-0.328186\pi\) | ||||
0.513937 | + | 0.857828i | \(0.328186\pi\) | |||||||
\(938\) | 4.07709e8 | 0.0161302 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.20368e10 | 0.472675 | ||||||||
\(941\) | −1.53080e10 | −0.598902 | −0.299451 | − | 0.954112i | \(-0.596804\pi\) | ||||
−0.299451 | + | 0.954112i | \(0.596804\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.55242e10 | 0.991201 | ||||||||
\(944\) | −4.20606e9 | −0.162732 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.30302e9 | −0.0500417 | ||||||||
\(947\) | −9.43008e9 | −0.360820 | −0.180410 | − | 0.983592i | \(-0.557742\pi\) | ||||
−0.180410 | + | 0.983592i | \(0.557742\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.38789e10 | 0.527136 | ||||||||
\(950\) | −2.45649e10 | −0.929571 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.82846e7 | 0.00218940 | ||||||||
\(953\) | 2.53714e10 | 0.949555 | 0.474777 | − | 0.880106i | \(-0.342529\pi\) | ||||
0.474777 | + | 0.880106i | \(0.342529\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.42687e8 | 0.0164469 | ||||||||
\(956\) | −8.32100e9 | −0.308016 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.29853e9 | 0.0477168 | ||||||||
\(959\) | −3.90442e7 | −0.00142953 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.55734e10 | −0.929517 | ||||||||
\(962\) | 6.51938e8 | 0.0236099 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.57978e10 | 0.567973 | ||||||||
\(965\) | −1.32850e9 | −0.0475900 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.23509e10 | −0.794883 | −0.397442 | − | 0.917627i | \(-0.630102\pi\) | ||||
−0.397442 | + | 0.917627i | \(0.630102\pi\) | |||||||
\(968\) | 1.71899e10 | 0.609128 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.30964e10 | 0.460736 | ||||||||
\(971\) | 2.51106e10 | 0.880217 | 0.440108 | − | 0.897945i | \(-0.354940\pi\) | ||||
0.440108 | + | 0.897945i | \(0.354940\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.15622e8 | 0.0109843 | ||||||||
\(974\) | 1.89758e10 | 0.658028 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.12852e9 | 0.107712 | ||||||||
\(977\) | 1.40783e10 | 0.482970 | 0.241485 | − | 0.970405i | \(-0.422366\pi\) | ||||
0.241485 | + | 0.970405i | \(0.422366\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.96284e9 | 0.0668569 | ||||||||
\(980\) | −7.78751e9 | −0.264306 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.20155e10 | −1.41586 | ||||||||
\(983\) | 4.03081e10 | 1.35349 | 0.676744 | − | 0.736218i | \(-0.263390\pi\) | ||||
0.676744 | + | 0.736218i | \(0.263390\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.59316e9 | −0.253160 | ||||||||
\(986\) | 3.28387e9 | 0.109098 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.39785e9 | 0.277025 | ||||||||
\(989\) | 9.92713e9 | 0.326315 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.94799e10 | 1.94139 | 0.970694 | − | 0.240318i | \(-0.0772517\pi\) | ||||
0.970694 | + | 0.240318i | \(0.0772517\pi\) | |||||||
\(992\) | 7.42741e9 | 0.241572 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.53554e8 | 0.0114183 | ||||||||
\(995\) | 5.96163e9 | 0.191860 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.24113e10 | 0.396630 | 0.198315 | − | 0.980138i | \(-0.436453\pi\) | ||||
0.198315 | + | 0.980138i | \(0.436453\pi\) | |||||||
\(998\) | −4.76099e10 | −1.51614 | ||||||||
\(999\) | 0 | 0 |
(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 | 531.8.a.c.1.14 | 17 | ||
3.2 | odd | 2 | 177.8.a.c.1.4 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.c.1.4 | ✓ | 17 | 3.2 | odd | 2 | ||
531.8.a.c.1.14 | 17 | 1.1 | even | 1 | trivial |