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: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + 1488374176 x^{9} + 42885295136 x^{8} + \cdots - 23\!\cdots\!32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(19.7363\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 19.7363 | 1.74446 | 0.872230 | − | 0.489096i | \(-0.162673\pi\) | ||||
0.872230 | + | 0.489096i | \(0.162673\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 261.522 | 2.04314 | ||||||||
\(5\) | 90.5952 | 0.324123 | 0.162062 | − | 0.986781i | \(-0.448186\pi\) | ||||
0.162062 | + | 0.986781i | \(0.448186\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −807.818 | −0.890165 | −0.445083 | − | 0.895490i | \(-0.646826\pi\) | ||||
−0.445083 | + | 0.895490i | \(0.646826\pi\) | |||||||
\(8\) | 2635.23 | 1.81971 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1788.01 | 0.565420 | ||||||||
\(11\) | −4971.97 | −1.12630 | −0.563150 | − | 0.826355i | \(-0.690411\pi\) | ||||
−0.563150 | + | 0.826355i | \(0.690411\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2921.19 | −0.368773 | −0.184386 | − | 0.982854i | \(-0.559030\pi\) | ||||
−0.184386 | + | 0.982854i | \(0.559030\pi\) | |||||||
\(14\) | −15943.4 | −1.55286 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 18534.9 | 1.13128 | ||||||||
\(17\) | 29331.0 | 1.44795 | 0.723977 | − | 0.689824i | \(-0.242312\pi\) | ||||
0.723977 | + | 0.689824i | \(0.242312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8907.94 | 0.297948 | 0.148974 | − | 0.988841i | \(-0.452403\pi\) | ||||
0.148974 | + | 0.988841i | \(0.452403\pi\) | |||||||
\(20\) | 23692.6 | 0.662229 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −98128.3 | −1.96479 | ||||||||
\(23\) | 21320.0 | 0.365376 | 0.182688 | − | 0.983171i | \(-0.441520\pi\) | ||||
0.182688 | + | 0.983171i | \(0.441520\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −69917.5 | −0.894944 | ||||||||
\(26\) | −57653.6 | −0.643309 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −211262. | −1.81873 | ||||||||
\(29\) | −144361. | −1.09915 | −0.549575 | − | 0.835444i | \(-0.685210\pi\) | ||||
−0.549575 | + | 0.835444i | \(0.685210\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 124102. | 0.748190 | 0.374095 | − | 0.927390i | \(-0.377953\pi\) | ||||
0.374095 | + | 0.927390i | \(0.377953\pi\) | |||||||
\(32\) | 28500.9 | 0.153757 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 578885. | 2.52590 | ||||||||
\(35\) | −73184.5 | −0.288523 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 249110. | 0.808510 | 0.404255 | − | 0.914646i | \(-0.367531\pi\) | ||||
0.404255 | + | 0.914646i | \(0.367531\pi\) | |||||||
\(38\) | 175810. | 0.519757 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 238739. | 0.589812 | ||||||||
\(41\) | −769960. | −1.74472 | −0.872358 | − | 0.488867i | \(-0.837410\pi\) | ||||
−0.872358 | + | 0.488867i | \(0.837410\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −214862. | −0.412116 | −0.206058 | − | 0.978540i | \(-0.566064\pi\) | ||||
−0.206058 | + | 0.978540i | \(0.566064\pi\) | |||||||
\(44\) | −1.30028e6 | −2.30119 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 420778. | 0.637383 | ||||||||
\(47\) | −826532. | −1.16123 | −0.580614 | − | 0.814179i | \(-0.697187\pi\) | ||||
−0.580614 | + | 0.814179i | \(0.697187\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −170973. | −0.207606 | ||||||||
\(50\) | −1.37991e6 | −1.56119 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −763956. | −0.753454 | ||||||||
\(53\) | −791662. | −0.730423 | −0.365211 | − | 0.930925i | \(-0.619003\pi\) | ||||
−0.365211 | + | 0.930925i | \(0.619003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −450437. | −0.365060 | ||||||||
\(56\) | −2.12879e6 | −1.61985 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.84915e6 | −1.91742 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.23090e6 | −1.25842 | −0.629210 | − | 0.777236i | \(-0.716621\pi\) | ||||
−0.629210 | + | 0.777236i | \(0.716621\pi\) | |||||||
\(62\) | 2.44931e6 | 1.30519 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.80996e6 | −0.863057 | ||||||||
\(65\) | −264646. | −0.119528 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −60136.4 | −0.0244273 | −0.0122137 | − | 0.999925i | \(-0.503888\pi\) | ||||
−0.0122137 | + | 0.999925i | \(0.503888\pi\) | |||||||
\(68\) | 7.67069e6 | 2.95837 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.44439e6 | −0.503317 | ||||||||
\(71\) | −3.73452e6 | −1.23831 | −0.619157 | − | 0.785268i | \(-0.712525\pi\) | ||||
−0.619157 | + | 0.785268i | \(0.712525\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 476492. | 0.143359 | 0.0716796 | − | 0.997428i | \(-0.477164\pi\) | ||||
0.0716796 | + | 0.997428i | \(0.477164\pi\) | |||||||
\(74\) | 4.91652e6 | 1.41041 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.32962e6 | 0.608748 | ||||||||
\(77\) | 4.01645e6 | 1.00259 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.82860e6 | 0.417277 | 0.208638 | − | 0.977993i | \(-0.433097\pi\) | ||||
0.208638 | + | 0.977993i | \(0.433097\pi\) | |||||||
\(80\) | 1.67917e6 | 0.366674 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.51962e7 | −3.04359 | ||||||||
\(83\) | −4.01281e6 | −0.770327 | −0.385164 | − | 0.922848i | \(-0.625855\pi\) | ||||
−0.385164 | + | 0.922848i | \(0.625855\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.65724e6 | 0.469316 | ||||||||
\(86\) | −4.24058e6 | −0.718920 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.31023e7 | −2.04955 | ||||||||
\(89\) | −5.38781e6 | −0.810116 | −0.405058 | − | 0.914291i | \(-0.632749\pi\) | ||||
−0.405058 | + | 0.914291i | \(0.632749\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.35979e6 | 0.328269 | ||||||||
\(92\) | 5.57565e6 | 0.746514 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.63127e7 | −2.02571 | ||||||||
\(95\) | 807017. | 0.0965717 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.52550e7 | −1.69711 | −0.848556 | − | 0.529106i | \(-0.822527\pi\) | ||||
−0.848556 | + | 0.529106i | \(0.822527\pi\) | |||||||
\(98\) | −3.37437e6 | −0.362160 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.82850e7 | −1.82850 | ||||||||
\(101\) | 1.51903e7 | 1.46703 | 0.733517 | − | 0.679671i | \(-0.237877\pi\) | ||||
0.733517 | + | 0.679671i | \(0.237877\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.35870e6 | −0.663546 | −0.331773 | − | 0.943359i | \(-0.607647\pi\) | ||||
−0.331773 | + | 0.943359i | \(0.607647\pi\) | |||||||
\(104\) | −7.69802e6 | −0.671061 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.56245e7 | −1.27419 | ||||||||
\(107\) | 3.56527e6 | 0.281352 | 0.140676 | − | 0.990056i | \(-0.455072\pi\) | ||||
0.140676 | + | 0.990056i | \(0.455072\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.51208e7 | 1.11836 | 0.559179 | − | 0.829047i | \(-0.311116\pi\) | ||||
0.559179 | + | 0.829047i | \(0.311116\pi\) | |||||||
\(110\) | −8.88996e6 | −0.636833 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.49728e7 | −1.00703 | ||||||||
\(113\) | 2.38727e7 | 1.55642 | 0.778212 | − | 0.628002i | \(-0.216127\pi\) | ||||
0.778212 | + | 0.628002i | \(0.216127\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.93149e6 | 0.118427 | ||||||||
\(116\) | −3.77536e7 | −2.24572 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.05342e6 | −0.227109 | ||||||||
\(119\) | −2.36941e7 | −1.28892 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.23332e6 | 0.268552 | ||||||||
\(122\) | −4.40297e7 | −2.19526 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.24553e7 | 1.52866 | ||||||||
\(125\) | −1.34119e7 | −0.614195 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.26438e6 | 0.271372 | 0.135686 | − | 0.990752i | \(-0.456676\pi\) | ||||
0.135686 | + | 0.990752i | \(0.456676\pi\) | |||||||
\(128\) | −3.93701e7 | −1.65933 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.22314e6 | −0.208511 | ||||||||
\(131\) | 2.94087e7 | 1.14295 | 0.571474 | − | 0.820620i | \(-0.306372\pi\) | ||||
0.571474 | + | 0.820620i | \(0.306372\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.19600e6 | −0.265222 | ||||||||
\(134\) | −1.18687e6 | −0.0426124 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.72938e7 | 2.63486 | ||||||||
\(137\) | 4.62523e6 | 0.153678 | 0.0768390 | − | 0.997044i | \(-0.475517\pi\) | ||||
0.0768390 | + | 0.997044i | \(0.475517\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.29866e7 | −0.410152 | −0.205076 | − | 0.978746i | \(-0.565744\pi\) | ||||
−0.205076 | + | 0.978746i | \(0.565744\pi\) | |||||||
\(140\) | −1.91393e7 | −0.589493 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.37056e7 | −2.16019 | ||||||||
\(143\) | 1.45241e7 | 0.415349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.30784e7 | −0.356260 | ||||||||
\(146\) | 9.40419e6 | 0.250084 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.51478e7 | 1.65190 | ||||||||
\(149\) | 6.03191e7 | 1.49384 | 0.746918 | − | 0.664917i | \(-0.231533\pi\) | ||||
0.746918 | + | 0.664917i | \(0.231533\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.08405e6 | −0.214714 | −0.107357 | − | 0.994221i | \(-0.534239\pi\) | ||||
−0.107357 | + | 0.994221i | \(0.534239\pi\) | |||||||
\(152\) | 2.34745e7 | 0.542180 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.92699e7 | 1.74898 | ||||||||
\(155\) | 1.12430e7 | 0.242506 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.23075e7 | 1.07874 | 0.539368 | − | 0.842070i | \(-0.318663\pi\) | ||||
0.539368 | + | 0.842070i | \(0.318663\pi\) | |||||||
\(158\) | 3.60898e7 | 0.727923 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.58205e6 | 0.0498361 | ||||||||
\(161\) | −1.72227e7 | −0.325245 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.85380e7 | 0.335280 | 0.167640 | − | 0.985848i | \(-0.446385\pi\) | ||||
0.167640 | + | 0.985848i | \(0.446385\pi\) | |||||||
\(164\) | −2.01361e8 | −3.56470 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.91980e7 | −1.34380 | ||||||||
\(167\) | −1.04169e7 | −0.173074 | −0.0865369 | − | 0.996249i | \(-0.527580\pi\) | ||||
−0.0865369 | + | 0.996249i | \(0.527580\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.42151e7 | −0.864007 | ||||||||
\(170\) | 5.24442e7 | 0.818703 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.61911e7 | −0.842011 | ||||||||
\(173\) | −7.37218e7 | −1.08252 | −0.541259 | − | 0.840856i | \(-0.682052\pi\) | ||||
−0.541259 | + | 0.840856i | \(0.682052\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.64806e7 | 0.796648 | ||||||||
\(176\) | −9.21549e7 | −1.27416 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.06335e8 | −1.41321 | ||||||||
\(179\) | 9.01187e7 | 1.17444 | 0.587218 | − | 0.809429i | \(-0.300223\pi\) | ||||
0.587218 | + | 0.809429i | \(0.300223\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.95539e7 | 0.746509 | 0.373255 | − | 0.927729i | \(-0.378242\pi\) | ||||
0.373255 | + | 0.927729i | \(0.378242\pi\) | |||||||
\(182\) | 4.65736e7 | 0.572651 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.61831e7 | 0.664880 | ||||||||
\(185\) | 2.25682e7 | 0.262057 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.45833e8 | −1.63083 | ||||||||
\(188\) | −2.16156e8 | −2.37255 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.59275e7 | 0.168465 | ||||||||
\(191\) | −8.79003e7 | −0.912795 | −0.456398 | − | 0.889776i | \(-0.650861\pi\) | ||||
−0.456398 | + | 0.889776i | \(0.650861\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.19947e7 | 0.921112 | 0.460556 | − | 0.887631i | \(-0.347650\pi\) | ||||
0.460556 | + | 0.887631i | \(0.347650\pi\) | |||||||
\(194\) | −3.01077e8 | −2.96054 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.47131e7 | −0.424168 | ||||||||
\(197\) | 9.51132e7 | 0.886357 | 0.443179 | − | 0.896433i | \(-0.353851\pi\) | ||||
0.443179 | + | 0.896433i | \(0.353851\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.84642e7 | −0.885712 | −0.442856 | − | 0.896593i | \(-0.646035\pi\) | ||||
−0.442856 | + | 0.896593i | \(0.646035\pi\) | |||||||
\(200\) | −1.84249e8 | −1.62854 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.99800e8 | 2.55918 | ||||||||
\(203\) | 1.16618e8 | 0.978425 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.97547e7 | −0.565503 | ||||||||
\(206\) | −1.45234e8 | −1.15753 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.41440e7 | −0.417185 | ||||||||
\(209\) | −4.42900e7 | −0.335578 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.85405e8 | −1.35873 | −0.679364 | − | 0.733802i | \(-0.737744\pi\) | ||||
−0.679364 | + | 0.733802i | \(0.737744\pi\) | |||||||
\(212\) | −2.07037e8 | −1.49236 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.03654e7 | 0.490807 | ||||||||
\(215\) | −1.94655e7 | −0.133576 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.00252e8 | −0.666013 | ||||||||
\(218\) | 2.98428e8 | 1.95093 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.17799e8 | −0.745869 | ||||||||
\(221\) | −8.56814e7 | −0.533966 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.33953e7 | −0.322431 | −0.161215 | − | 0.986919i | \(-0.551541\pi\) | ||||
−0.161215 | + | 0.986919i | \(0.551541\pi\) | |||||||
\(224\) | −2.30236e7 | −0.136869 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.71160e8 | 2.71512 | ||||||||
\(227\) | 7.79437e7 | 0.442273 | 0.221137 | − | 0.975243i | \(-0.429023\pi\) | ||||
0.221137 | + | 0.975243i | \(0.429023\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.50546e7 | −0.137868 | −0.0689340 | − | 0.997621i | \(-0.521960\pi\) | ||||
−0.0689340 | + | 0.997621i | \(0.521960\pi\) | |||||||
\(230\) | 3.81205e7 | 0.206591 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.80424e8 | −2.00014 | ||||||||
\(233\) | −2.23037e8 | −1.15513 | −0.577567 | − | 0.816344i | \(-0.695998\pi\) | ||||
−0.577567 | + | 0.816344i | \(0.695998\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.48799e7 | −0.376381 | ||||||||
\(236\) | −5.37111e7 | −0.265994 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.67634e8 | −2.24847 | ||||||||
\(239\) | 1.46524e8 | 0.694249 | 0.347124 | − | 0.937819i | \(-0.387158\pi\) | ||||
0.347124 | + | 0.937819i | \(0.387158\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.35245e7 | −0.246316 | −0.123158 | − | 0.992387i | \(-0.539302\pi\) | ||||
−0.123158 | + | 0.992387i | \(0.539302\pi\) | |||||||
\(242\) | 1.03286e8 | 0.468478 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.83429e8 | −2.57113 | ||||||||
\(245\) | −1.54893e7 | −0.0672900 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.60218e7 | −0.109875 | ||||||||
\(248\) | 3.27037e8 | 1.36149 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.64702e8 | −1.07144 | ||||||||
\(251\) | 3.32032e8 | 1.32532 | 0.662661 | − | 0.748919i | \(-0.269427\pi\) | ||||
0.662661 | + | 0.748919i | \(0.269427\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.06002e8 | −0.411523 | ||||||||
\(254\) | 1.23636e8 | 0.473398 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.45345e8 | −2.03157 | ||||||||
\(257\) | −3.09916e8 | −1.13888 | −0.569441 | − | 0.822032i | \(-0.692840\pi\) | ||||
−0.569441 | + | 0.822032i | \(0.692840\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.01236e8 | −0.719708 | ||||||||
\(260\) | −6.92108e7 | −0.244212 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.80419e8 | 1.99383 | ||||||||
\(263\) | 8.42828e7 | 0.285689 | 0.142845 | − | 0.989745i | \(-0.454375\pi\) | ||||
0.142845 | + | 0.989745i | \(0.454375\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.17208e7 | −0.236747 | ||||||||
\(266\) | −1.42022e8 | −0.462670 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.57270e7 | −0.0499084 | ||||||||
\(269\) | 1.91871e8 | 0.601001 | 0.300501 | − | 0.953782i | \(-0.402846\pi\) | ||||
0.300501 | + | 0.953782i | \(0.402846\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.09645e6 | −0.0216595 | −0.0108298 | − | 0.999941i | \(-0.503447\pi\) | ||||
−0.0108298 | + | 0.999941i | \(0.503447\pi\) | |||||||
\(272\) | 5.43646e8 | 1.63804 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.12851e7 | 0.268085 | ||||||||
\(275\) | 3.47628e8 | 1.00798 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.59631e8 | −0.733968 | −0.366984 | − | 0.930227i | \(-0.619610\pi\) | ||||
−0.366984 | + | 0.930227i | \(0.619610\pi\) | |||||||
\(278\) | −2.56308e8 | −0.715493 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.92858e8 | −0.525030 | ||||||||
\(281\) | 4.92572e7 | 0.132433 | 0.0662167 | − | 0.997805i | \(-0.478907\pi\) | ||||
0.0662167 | + | 0.997805i | \(0.478907\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.62830e8 | −0.427053 | −0.213526 | − | 0.976937i | \(-0.568495\pi\) | ||||
−0.213526 | + | 0.976937i | \(0.568495\pi\) | |||||||
\(284\) | −9.76658e8 | −2.53005 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.86652e8 | 0.724559 | ||||||||
\(287\) | 6.21988e8 | 1.55309 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.49966e8 | 1.09657 | ||||||||
\(290\) | −2.58120e8 | −0.621482 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.24613e8 | 0.292903 | ||||||||
\(293\) | 5.14011e8 | 1.19381 | 0.596905 | − | 0.802312i | \(-0.296397\pi\) | ||||
0.596905 | + | 0.802312i | \(0.296397\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.86064e7 | −0.0421973 | ||||||||
\(296\) | 6.56462e8 | 1.47126 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.19048e9 | 2.60594 | ||||||||
\(299\) | −6.22799e7 | −0.134741 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.73569e8 | 0.366852 | ||||||||
\(302\) | −1.79286e8 | −0.374560 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.65108e8 | 0.337062 | ||||||||
\(305\) | −2.02109e8 | −0.407883 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.27895e8 | 0.252272 | 0.126136 | − | 0.992013i | \(-0.459742\pi\) | ||||
0.126136 | + | 0.992013i | \(0.459742\pi\) | |||||||
\(308\) | 1.05039e9 | 2.04844 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.21896e8 | 0.423042 | ||||||||
\(311\) | −6.02895e8 | −1.13653 | −0.568264 | − | 0.822846i | \(-0.692385\pi\) | ||||
−0.568264 | + | 0.822846i | \(0.692385\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.09308e8 | −1.49179 | −0.745897 | − | 0.666061i | \(-0.767979\pi\) | ||||
−0.745897 | + | 0.666061i | \(0.767979\pi\) | |||||||
\(314\) | 1.03236e9 | 1.88181 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.78219e8 | 0.852555 | ||||||||
\(317\) | −9.39100e7 | −0.165579 | −0.0827893 | − | 0.996567i | \(-0.526383\pi\) | ||||
−0.0827893 | + | 0.996567i | \(0.526383\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.17759e8 | 1.23797 | ||||||||
\(320\) | −1.63974e8 | −0.279737 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.39912e8 | −0.567376 | ||||||||
\(323\) | 2.61278e8 | 0.431415 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.04243e8 | 0.330031 | ||||||||
\(326\) | 3.65873e8 | 0.584882 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.02902e9 | −3.17489 | ||||||||
\(329\) | 6.67688e8 | 1.03368 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.98609e8 | 1.51355 | 0.756776 | − | 0.653674i | \(-0.226773\pi\) | ||||
0.756776 | + | 0.653674i | \(0.226773\pi\) | |||||||
\(332\) | −1.04944e9 | −1.57389 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.05591e8 | −0.301920 | ||||||||
\(335\) | −5.44807e6 | −0.00791746 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.07195e9 | 1.52570 | 0.762851 | − | 0.646575i | \(-0.223799\pi\) | ||||
0.762851 | + | 0.646575i | \(0.223799\pi\) | |||||||
\(338\) | −1.07001e9 | −1.50722 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.94927e8 | 0.958878 | ||||||||
\(341\) | −6.17030e8 | −0.842687 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.03388e8 | 1.07497 | ||||||||
\(344\) | −5.66210e8 | −0.749934 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.45500e9 | −1.88841 | ||||||||
\(347\) | 1.06764e9 | 1.37174 | 0.685869 | − | 0.727725i | \(-0.259422\pi\) | ||||
0.685869 | + | 0.727725i | \(0.259422\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.09465e9 | −1.37843 | −0.689216 | − | 0.724556i | \(-0.742045\pi\) | ||||
−0.689216 | + | 0.724556i | \(0.742045\pi\) | |||||||
\(350\) | 1.11472e9 | 1.38972 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.41706e8 | −0.173176 | ||||||||
\(353\) | 2.65164e8 | 0.320851 | 0.160426 | − | 0.987048i | \(-0.448713\pi\) | ||||
0.160426 | + | 0.987048i | \(0.448713\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.38330e8 | −0.401366 | ||||||||
\(356\) | −1.40903e9 | −1.65518 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.77861e9 | 2.04876 | ||||||||
\(359\) | 7.74082e8 | 0.882992 | 0.441496 | − | 0.897263i | \(-0.354448\pi\) | ||||
0.441496 | + | 0.897263i | \(0.354448\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.14520e8 | −0.911227 | ||||||||
\(362\) | 1.17537e9 | 1.30226 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.17138e8 | 0.670699 | ||||||||
\(365\) | 4.31679e7 | 0.0464660 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.18045e8 | 0.652663 | 0.326331 | − | 0.945255i | \(-0.394187\pi\) | ||||
0.326331 | + | 0.945255i | \(0.394187\pi\) | |||||||
\(368\) | 3.95164e8 | 0.413342 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.45413e8 | 0.457148 | ||||||||
\(371\) | 6.39519e8 | 0.650197 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.27726e7 | −0.0227212 | −0.0113606 | − | 0.999935i | \(-0.503616\pi\) | ||||
−0.0113606 | + | 0.999935i | \(0.503616\pi\) | |||||||
\(374\) | −2.87820e9 | −2.84492 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.17810e9 | −2.11310 | ||||||||
\(377\) | 4.21707e8 | 0.405337 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.75855e8 | −0.920763 | −0.460382 | − | 0.887721i | \(-0.652287\pi\) | ||||
−0.460382 | + | 0.887721i | \(0.652287\pi\) | |||||||
\(380\) | 2.11053e8 | 0.197310 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.73483e9 | −1.59233 | ||||||||
\(383\) | 8.32929e8 | 0.757552 | 0.378776 | − | 0.925488i | \(-0.376345\pi\) | ||||
0.378776 | + | 0.925488i | \(0.376345\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.63871e8 | 0.324964 | ||||||||
\(386\) | 1.81564e9 | 1.60684 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.98951e9 | −3.46744 | ||||||||
\(389\) | 1.77468e8 | 0.152861 | 0.0764304 | − | 0.997075i | \(-0.475648\pi\) | ||||
0.0764304 | + | 0.997075i | \(0.475648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.25336e8 | 0.529048 | ||||||||
\(392\) | −4.50552e8 | −0.377784 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.87718e9 | 1.54621 | ||||||||
\(395\) | 1.65663e8 | 0.135249 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.50894e9 | −1.21033 | −0.605166 | − | 0.796099i | \(-0.706893\pi\) | ||||
−0.605166 | + | 0.796099i | \(0.706893\pi\) | |||||||
\(398\) | −1.94332e9 | −1.54509 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.29591e9 | −1.01243 | ||||||||
\(401\) | −1.77996e9 | −1.37850 | −0.689248 | − | 0.724525i | \(-0.742059\pi\) | ||||
−0.689248 | + | 0.724525i | \(0.742059\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.62525e8 | −0.275912 | ||||||||
\(404\) | 3.97258e9 | 2.99736 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.30160e9 | 1.70682 | ||||||||
\(407\) | −1.23857e9 | −0.910625 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.01746e9 | 0.735335 | 0.367667 | − | 0.929957i | \(-0.380157\pi\) | ||||
0.367667 | + | 0.929957i | \(0.380157\pi\) | |||||||
\(410\) | −1.37670e9 | −0.986497 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.92446e9 | −1.35572 | ||||||||
\(413\) | 1.65909e8 | 0.115890 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.63541e8 | −0.249681 | ||||||||
\(416\) | −8.32568e7 | −0.0567013 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.74122e8 | −0.585403 | ||||||||
\(419\) | 1.28968e9 | 0.856514 | 0.428257 | − | 0.903657i | \(-0.359128\pi\) | ||||
0.428257 | + | 0.903657i | \(0.359128\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.35636e8 | 0.349851 | 0.174925 | − | 0.984582i | \(-0.444032\pi\) | ||||
0.174925 | + | 0.984582i | \(0.444032\pi\) | |||||||
\(422\) | −3.65921e9 | −2.37025 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.08621e9 | −1.32916 | ||||||||
\(425\) | −2.05075e9 | −1.29584 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.80216e9 | 1.12020 | ||||||||
\(428\) | 9.32397e8 | 0.574841 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.84176e8 | −0.233019 | ||||||||
\(431\) | 2.75089e9 | 1.65502 | 0.827509 | − | 0.561452i | \(-0.189757\pi\) | ||||
0.827509 | + | 0.561452i | \(0.189757\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.00172e8 | 0.473670 | 0.236835 | − | 0.971550i | \(-0.423890\pi\) | ||||
0.236835 | + | 0.971550i | \(0.423890\pi\) | |||||||
\(434\) | −1.97860e9 | −1.16183 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.95441e9 | 2.28496 | ||||||||
\(437\) | 1.89917e8 | 0.108863 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.72445e8 | 0.435754 | 0.217877 | − | 0.975976i | \(-0.430087\pi\) | ||||
0.217877 | + | 0.975976i | \(0.430087\pi\) | |||||||
\(440\) | −1.18700e9 | −0.664305 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.69104e9 | −0.931483 | ||||||||
\(443\) | −2.85561e9 | −1.56058 | −0.780289 | − | 0.625419i | \(-0.784928\pi\) | ||||
−0.780289 | + | 0.625419i | \(0.784928\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.88110e8 | −0.262577 | ||||||||
\(446\) | −1.05383e9 | −0.562467 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.46212e9 | 0.768263 | ||||||||
\(449\) | −1.99990e9 | −1.04267 | −0.521334 | − | 0.853352i | \(-0.674566\pi\) | ||||
−0.521334 | + | 0.853352i | \(0.674566\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.82822e9 | 1.96507 | ||||||||
\(452\) | 6.24324e9 | 3.17999 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.53832e9 | 0.771528 | ||||||||
\(455\) | 2.13786e8 | 0.106399 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.08512e9 | −0.531829 | −0.265915 | − | 0.963997i | \(-0.585674\pi\) | ||||
−0.265915 | + | 0.963997i | \(0.585674\pi\) | |||||||
\(458\) | −4.94485e8 | −0.240505 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.05127e8 | 0.241962 | ||||||||
\(461\) | 3.43732e9 | 1.63405 | 0.817027 | − | 0.576600i | \(-0.195621\pi\) | ||||
0.817027 | + | 0.576600i | \(0.195621\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.83083e9 | −1.32550 | −0.662750 | − | 0.748840i | \(-0.730611\pi\) | ||||
−0.662750 | + | 0.748840i | \(0.730611\pi\) | |||||||
\(464\) | −2.67572e9 | −1.24345 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.40194e9 | −2.01508 | ||||||||
\(467\) | 1.27289e9 | 0.578337 | 0.289169 | − | 0.957278i | \(-0.406621\pi\) | ||||
0.289169 | + | 0.957278i | \(0.406621\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.85793e7 | 0.0217443 | ||||||||
\(470\) | −1.47785e9 | −0.656581 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.41221e8 | −0.236907 | ||||||||
\(473\) | 1.06829e9 | 0.464167 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.22821e8 | −0.266646 | ||||||||
\(476\) | −6.19652e9 | −2.63344 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.89184e9 | 1.21109 | ||||||||
\(479\) | 1.83875e9 | 0.764448 | 0.382224 | − | 0.924070i | \(-0.375158\pi\) | ||||
0.382224 | + | 0.924070i | \(0.375158\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.27699e8 | −0.298156 | ||||||||
\(482\) | −1.05638e9 | −0.429689 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.36863e9 | 0.548689 | ||||||||
\(485\) | −1.38203e9 | −0.550073 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.80837e9 | −0.709473 | −0.354736 | − | 0.934966i | \(-0.615429\pi\) | ||||
−0.354736 | + | 0.934966i | \(0.615429\pi\) | |||||||
\(488\) | −5.87893e9 | −2.28996 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.05701e8 | −0.117385 | ||||||||
\(491\) | −3.14661e9 | −1.19966 | −0.599829 | − | 0.800128i | \(-0.704765\pi\) | ||||
−0.599829 | + | 0.800128i | \(0.704765\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.23425e9 | −1.59152 | ||||||||
\(494\) | −5.13575e8 | −0.191672 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.30021e9 | 0.846412 | ||||||||
\(497\) | 3.01681e9 | 1.10230 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.26779e9 | 0.817056 | 0.408528 | − | 0.912746i | \(-0.366042\pi\) | ||||
0.408528 | + | 0.912746i | \(0.366042\pi\) | |||||||
\(500\) | −3.50752e9 | −1.25489 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.55308e9 | 2.31197 | ||||||||
\(503\) | −1.65622e9 | −0.580270 | −0.290135 | − | 0.956986i | \(-0.593700\pi\) | ||||
−0.290135 | + | 0.956986i | \(0.593700\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.37616e9 | 0.475500 | ||||||||
\(506\) | −2.09210e9 | −0.717885 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.63827e9 | 0.554451 | ||||||||
\(509\) | −5.27031e9 | −1.77143 | −0.885715 | − | 0.464229i | \(-0.846332\pi\) | ||||
−0.885715 | + | 0.464229i | \(0.846332\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.84919e8 | −0.127613 | ||||||||
\(512\) | −5.72373e9 | −1.88466 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.11660e9 | −1.98673 | ||||||||
\(515\) | −6.66663e8 | −0.215071 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.10949e9 | 1.30789 | ||||||||
\(518\) | −3.97165e9 | −1.25550 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.97403e8 | −0.217507 | ||||||||
\(521\) | 1.06833e9 | 0.330957 | 0.165478 | − | 0.986213i | \(-0.447083\pi\) | ||||
0.165478 | + | 0.986213i | \(0.447083\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.88919e9 | −1.49445 | −0.747225 | − | 0.664572i | \(-0.768614\pi\) | ||||
−0.747225 | + | 0.664572i | \(0.768614\pi\) | |||||||
\(524\) | 7.69102e9 | 2.33520 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.66343e9 | 0.498374 | ||||||||
\(527\) | 3.64002e9 | 1.08335 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.95028e9 | −0.866500 | ||||||||
\(530\) | −1.41550e9 | −0.412995 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.88191e9 | −0.541887 | ||||||||
\(533\) | 2.24920e9 | 0.643404 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.22997e8 | 0.0911927 | ||||||||
\(536\) | −1.58473e8 | −0.0444507 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.78682e9 | 1.04842 | ||||||||
\(539\) | 8.50070e8 | 0.233827 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.76671e9 | 0.751231 | 0.375615 | − | 0.926776i | \(-0.377431\pi\) | ||||
0.375615 | + | 0.926776i | \(0.377431\pi\) | |||||||
\(542\) | −1.40058e8 | −0.0377842 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.35960e8 | 0.222633 | ||||||||
\(545\) | 1.36987e9 | 0.362486 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.33645e9 | −1.39411 | −0.697054 | − | 0.717018i | \(-0.745506\pi\) | ||||
−0.697054 | + | 0.717018i | \(0.745506\pi\) | |||||||
\(548\) | 1.20960e9 | 0.313986 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.86089e9 | 1.75837 | ||||||||
\(551\) | −1.28596e9 | −0.327489 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.47718e9 | −0.371445 | ||||||||
\(554\) | −5.12416e9 | −1.28038 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.39629e9 | −0.837998 | ||||||||
\(557\) | 4.61945e8 | 0.113265 | 0.0566326 | − | 0.998395i | \(-0.481964\pi\) | ||||
0.0566326 | + | 0.998395i | \(0.481964\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.27653e8 | 0.151977 | ||||||||
\(560\) | −1.35647e9 | −0.326400 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.72156e8 | 0.231025 | ||||||||
\(563\) | −5.71818e9 | −1.35045 | −0.675224 | − | 0.737612i | \(-0.735953\pi\) | ||||
−0.675224 | + | 0.737612i | \(0.735953\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.16276e9 | 0.504473 | ||||||||
\(566\) | −3.21366e9 | −0.744976 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.84131e9 | −2.25338 | ||||||||
\(569\) | 5.60950e9 | 1.27653 | 0.638265 | − | 0.769816i | \(-0.279652\pi\) | ||||
0.638265 | + | 0.769816i | \(0.279652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.21411e9 | 0.722494 | 0.361247 | − | 0.932470i | \(-0.382351\pi\) | ||||
0.361247 | + | 0.932470i | \(0.382351\pi\) | |||||||
\(572\) | 3.79837e9 | 0.848615 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.22757e10 | 2.70930 | ||||||||
\(575\) | −1.49064e9 | −0.326991 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.42295e9 | 0.525085 | 0.262543 | − | 0.964920i | \(-0.415439\pi\) | ||||
0.262543 | + | 0.964920i | \(0.415439\pi\) | |||||||
\(578\) | 8.88068e9 | 1.91293 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.42029e9 | −0.727889 | ||||||||
\(581\) | 3.24162e9 | 0.685718 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.93612e9 | 0.822675 | ||||||||
\(584\) | 1.25567e9 | 0.260873 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.01447e10 | 2.08255 | ||||||||
\(587\) | 8.83936e9 | 1.80380 | 0.901898 | − | 0.431949i | \(-0.142174\pi\) | ||||
0.901898 | + | 0.431949i | \(0.142174\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.10549e9 | 0.222921 | ||||||||
\(590\) | −3.67221e8 | −0.0736114 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.61723e9 | 0.914651 | ||||||||
\(593\) | 2.57682e9 | 0.507450 | 0.253725 | − | 0.967276i | \(-0.418344\pi\) | ||||
0.253725 | + | 0.967276i | \(0.418344\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.14657e9 | −0.417769 | ||||||||
\(596\) | 1.57748e10 | 3.05211 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.22917e9 | −0.235050 | ||||||||
\(599\) | 6.40768e9 | 1.21817 | 0.609084 | − | 0.793106i | \(-0.291537\pi\) | ||||
0.609084 | + | 0.793106i | \(0.291537\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.70821e9 | 0.508887 | 0.254443 | − | 0.967088i | \(-0.418108\pi\) | ||||
0.254443 | + | 0.967088i | \(0.418108\pi\) | |||||||
\(602\) | 3.42562e9 | 0.639958 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.37568e9 | −0.438691 | ||||||||
\(605\) | 4.74114e8 | 0.0870439 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.53113e9 | −1.54827 | −0.774134 | − | 0.633022i | \(-0.781814\pi\) | ||||
−0.774134 | + | 0.633022i | \(0.781814\pi\) | |||||||
\(608\) | 2.53885e8 | 0.0458114 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.98888e9 | −0.711535 | ||||||||
\(611\) | 2.41446e9 | 0.428229 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.93110e9 | −0.513947 | −0.256973 | − | 0.966418i | \(-0.582725\pi\) | ||||
−0.256973 | + | 0.966418i | \(0.582725\pi\) | |||||||
\(614\) | 2.52418e9 | 0.440079 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.05843e10 | 1.82443 | ||||||||
\(617\) | −7.69933e9 | −1.31964 | −0.659819 | − | 0.751425i | \(-0.729367\pi\) | ||||
−0.659819 | + | 0.751425i | \(0.729367\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.43713e9 | 0.243545 | 0.121772 | − | 0.992558i | \(-0.461142\pi\) | ||||
0.121772 | + | 0.992558i | \(0.461142\pi\) | |||||||
\(620\) | 2.94030e9 | 0.495473 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.18989e10 | −1.98263 | ||||||||
\(623\) | 4.35237e9 | 0.721137 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.24725e9 | 0.695869 | ||||||||
\(626\) | −1.59728e10 | −2.60237 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.36796e10 | 2.20401 | ||||||||
\(629\) | 7.30664e9 | 1.17069 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.31824e9 | −1.15959 | −0.579794 | − | 0.814763i | \(-0.696867\pi\) | ||||
−0.579794 | + | 0.814763i | \(0.696867\pi\) | |||||||
\(632\) | 4.81878e9 | 0.759325 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.85344e9 | −0.288845 | ||||||||
\(635\) | 5.67523e8 | 0.0879580 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.99444e8 | 0.0765595 | ||||||||
\(638\) | 1.41659e10 | 2.15959 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.56674e9 | −0.537826 | ||||||||
\(641\) | −1.21948e10 | −1.82883 | −0.914414 | − | 0.404779i | \(-0.867348\pi\) | ||||
−0.914414 | + | 0.404779i | \(0.867348\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.07659e10 | 1.59702 | 0.798510 | − | 0.601982i | \(-0.205622\pi\) | ||||
0.798510 | + | 0.601982i | \(0.205622\pi\) | |||||||
\(644\) | −4.50411e9 | −0.664521 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.15667e9 | 0.752585 | ||||||||
\(647\) | 1.11488e10 | 1.61831 | 0.809156 | − | 0.587594i | \(-0.199925\pi\) | ||||
0.809156 | + | 0.587594i | \(0.199925\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.02114e9 | 0.146632 | ||||||||
\(650\) | 4.03100e9 | 0.575726 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.84810e9 | 0.685023 | ||||||||
\(653\) | −1.17825e10 | −1.65593 | −0.827965 | − | 0.560780i | \(-0.810502\pi\) | ||||
−0.827965 | + | 0.560780i | \(0.810502\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.66429e9 | 0.370456 | ||||||||
\(656\) | −1.42711e10 | −1.97376 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.31777e10 | 1.80322 | ||||||||
\(659\) | 1.18824e10 | 1.61736 | 0.808680 | − | 0.588249i | \(-0.200182\pi\) | ||||
0.808680 | + | 0.588249i | \(0.200182\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.51347e9 | −0.473185 | −0.236592 | − | 0.971609i | \(-0.576031\pi\) | ||||
−0.236592 | + | 0.971609i | \(0.576031\pi\) | |||||||
\(662\) | 1.97089e10 | 2.64033 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.05747e10 | −1.40178 | ||||||||
\(665\) | −6.51923e8 | −0.0859648 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.07778e9 | −0.401603 | ||||||||
\(668\) | −2.72425e9 | −0.353614 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.07525e8 | −0.0138117 | ||||||||
\(671\) | 1.10920e10 | 1.41736 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.05934e8 | −0.0892712 | −0.0446356 | − | 0.999003i | \(-0.514213\pi\) | ||||
−0.0446356 | + | 0.999003i | \(0.514213\pi\) | |||||||
\(674\) | 2.11563e10 | 2.66152 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.41784e10 | −1.76529 | ||||||||
\(677\) | 1.39303e10 | 1.72544 | 0.862720 | − | 0.505681i | \(-0.168759\pi\) | ||||
0.862720 | + | 0.505681i | \(0.168759\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.23232e10 | 1.51071 | ||||||||
\(680\) | 7.00245e9 | 0.854021 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.21779e10 | −1.47003 | ||||||||
\(683\) | 2.00962e9 | 0.241347 | 0.120673 | − | 0.992692i | \(-0.461495\pi\) | ||||
0.120673 | + | 0.992692i | \(0.461495\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.19024e8 | 0.0498106 | ||||||||
\(686\) | 1.58559e10 | 1.87524 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.98244e9 | −0.466219 | ||||||||
\(689\) | 2.31260e9 | 0.269360 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.48060e9 | −0.170712 | −0.0853558 | − | 0.996351i | \(-0.527203\pi\) | ||||
−0.0853558 | + | 0.996351i | \(0.527203\pi\) | |||||||
\(692\) | −1.92799e10 | −2.21173 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.10712e10 | 2.39294 | ||||||||
\(695\) | −1.17653e9 | −0.132940 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.25837e10 | −2.52627 | ||||||||
\(698\) | −2.16043e10 | −2.40462 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.47709e10 | 1.62766 | ||||||||
\(701\) | 9.38403e9 | 1.02891 | 0.514454 | − | 0.857518i | \(-0.327995\pi\) | ||||
0.514454 | + | 0.857518i | \(0.327995\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.21906e9 | 0.240894 | ||||||||
\(704\) | 8.99908e9 | 0.972061 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.23337e9 | 0.559712 | ||||||||
\(707\) | −1.22710e10 | −1.30590 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.90748e9 | 0.622501 | 0.311251 | − | 0.950328i | \(-0.399252\pi\) | ||||
0.311251 | + | 0.950328i | \(0.399252\pi\) | |||||||
\(710\) | −6.67738e9 | −0.700167 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.41981e10 | −1.47418 | ||||||||
\(713\) | 2.64585e9 | 0.273371 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.31581e9 | 0.134624 | ||||||||
\(716\) | 2.35680e10 | 2.39954 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.52775e10 | 1.54034 | ||||||||
\(719\) | 1.54549e10 | 1.55065 | 0.775327 | − | 0.631560i | \(-0.217585\pi\) | ||||
0.775327 | + | 0.631560i | \(0.217585\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.94450e9 | 0.590665 | ||||||||
\(722\) | −1.60756e10 | −1.58960 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.55746e10 | 1.52522 | ||||||||
\(725\) | 1.00934e10 | 0.983678 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.56689e8 | −0.0151240 | −0.00756201 | − | 0.999971i | \(-0.502407\pi\) | ||||
−0.00756201 | + | 0.999971i | \(0.502407\pi\) | |||||||
\(728\) | 6.21860e9 | 0.597355 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.51975e8 | 0.0810581 | ||||||||
\(731\) | −6.30211e9 | −0.596726 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.57137e9 | 0.710086 | 0.355043 | − | 0.934850i | \(-0.384466\pi\) | ||||
0.355043 | + | 0.934850i | \(0.384466\pi\) | |||||||
\(734\) | 1.21979e10 | 1.13854 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.07640e8 | 0.0561790 | ||||||||
\(737\) | 2.98996e8 | 0.0275125 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.72084e9 | −0.703734 | −0.351867 | − | 0.936050i | \(-0.614453\pi\) | ||||
−0.351867 | + | 0.936050i | \(0.614453\pi\) | |||||||
\(740\) | 5.90208e9 | 0.535419 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.26217e10 | 1.13424 | ||||||||
\(743\) | −5.80399e9 | −0.519118 | −0.259559 | − | 0.965727i | \(-0.583577\pi\) | ||||
−0.259559 | + | 0.965727i | \(0.583577\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.46462e9 | 0.484187 | ||||||||
\(746\) | −4.49446e8 | −0.0396362 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.81384e10 | −3.33202 | ||||||||
\(749\) | −2.88009e9 | −0.250450 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00286e10 | 0.863975 | 0.431987 | − | 0.901880i | \(-0.357813\pi\) | ||||
0.431987 | + | 0.901880i | \(0.357813\pi\) | |||||||
\(752\) | −1.53197e10 | −1.31367 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.32294e9 | 0.707093 | ||||||||
\(755\) | −8.22971e8 | −0.0695938 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.32049e10 | −1.10637 | −0.553184 | − | 0.833059i | \(-0.686587\pi\) | ||||
−0.553184 | + | 0.833059i | \(0.686587\pi\) | |||||||
\(758\) | −1.92598e10 | −1.60623 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.12667e9 | 0.175733 | ||||||||
\(761\) | −2.09392e10 | −1.72232 | −0.861161 | − | 0.508332i | \(-0.830262\pi\) | ||||
−0.861161 | + | 0.508332i | \(0.830262\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.22148e10 | −0.995523 | ||||||||
\(764\) | −2.29878e10 | −1.86497 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.64390e10 | 1.32152 | ||||||||
\(767\) | 5.99952e8 | 0.0480101 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.74920e10 | 1.38706 | 0.693532 | − | 0.720426i | \(-0.256054\pi\) | ||||
0.693532 | + | 0.720426i | \(0.256054\pi\) | |||||||
\(770\) | 7.18147e9 | 0.566886 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.40586e10 | 1.88196 | ||||||||
\(773\) | −1.87442e10 | −1.45962 | −0.729808 | − | 0.683652i | \(-0.760390\pi\) | ||||
−0.729808 | + | 0.683652i | \(0.760390\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.67689e9 | −0.669589 | ||||||||
\(776\) | −4.02003e10 | −3.08826 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.50256e9 | 0.266659 | ||||||||
\(779\) | −6.85876e9 | −0.519834 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.85679e10 | 1.39471 | ||||||||
\(782\) | 1.23418e10 | 0.922902 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.16896e9 | −0.234861 | ||||||||
\(785\) | 4.73881e9 | 0.349644 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.93622e10 | −1.41594 | −0.707968 | − | 0.706245i | \(-0.750388\pi\) | ||||
−0.707968 | + | 0.706245i | \(0.750388\pi\) | |||||||
\(788\) | 2.48742e10 | 1.81095 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.26957e9 | 0.235937 | ||||||||
\(791\) | −1.92848e10 | −1.38547 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.51689e9 | 0.464071 | ||||||||
\(794\) | −2.97809e10 | −2.11138 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.57505e10 | −1.80963 | ||||||||
\(797\) | −2.19937e10 | −1.53884 | −0.769420 | − | 0.638744i | \(-0.779454\pi\) | ||||
−0.769420 | + | 0.638744i | \(0.779454\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.42430e10 | −1.68141 | ||||||||
\(800\) | −1.99271e9 | −0.137604 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.51299e10 | −2.40473 | ||||||||
\(803\) | −2.36910e9 | −0.161465 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.56029e9 | −0.105419 | ||||||||
\(806\) | −7.15491e9 | −0.481318 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.00298e10 | 2.66958 | ||||||||
\(809\) | −9.05373e9 | −0.601185 | −0.300592 | − | 0.953753i | \(-0.597184\pi\) | ||||
−0.300592 | + | 0.953753i | \(0.597184\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.27877e9 | −0.150012 | −0.0750062 | − | 0.997183i | \(-0.523898\pi\) | ||||
−0.0750062 | + | 0.997183i | \(0.523898\pi\) | |||||||
\(812\) | 3.04980e10 | 1.99906 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.44448e10 | −1.58855 | ||||||||
\(815\) | 1.67946e9 | 0.108672 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.91398e9 | −0.122789 | ||||||||
\(818\) | 2.00809e10 | 1.28276 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.82424e10 | −1.15540 | ||||||||
\(821\) | −1.34643e10 | −0.849148 | −0.424574 | − | 0.905393i | \(-0.639576\pi\) | ||||
−0.424574 | + | 0.905393i | \(0.639576\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.64535e10 | 1.02887 | 0.514434 | − | 0.857530i | \(-0.328002\pi\) | ||||
0.514434 | + | 0.857530i | \(0.328002\pi\) | |||||||
\(824\) | −1.93919e10 | −1.20746 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.27443e9 | 0.202165 | ||||||||
\(827\) | −1.52598e10 | −0.938165 | −0.469082 | − | 0.883154i | \(-0.655415\pi\) | ||||
−0.469082 | + | 0.883154i | \(0.655415\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.06615e10 | −0.649946 | −0.324973 | − | 0.945723i | \(-0.605355\pi\) | ||||
−0.324973 | + | 0.945723i | \(0.605355\pi\) | |||||||
\(830\) | −7.17496e9 | −0.435558 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.28725e9 | 0.318272 | ||||||||
\(833\) | −5.01479e9 | −0.300604 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.43722e8 | −0.0560972 | ||||||||
\(836\) | −1.15828e10 | −0.685633 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.54536e10 | 1.49415 | ||||||||
\(839\) | 1.09099e10 | 0.637757 | 0.318878 | − | 0.947796i | \(-0.396694\pi\) | ||||
0.318878 | + | 0.947796i | \(0.396694\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.59025e9 | 0.208132 | ||||||||
\(842\) | 1.05715e10 | 0.610300 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.84874e10 | −2.77607 | ||||||||
\(845\) | −4.91163e9 | −0.280045 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.22757e9 | −0.239056 | ||||||||
\(848\) | −1.46734e10 | −0.826312 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.04742e10 | −2.26054 | ||||||||
\(851\) | 5.31103e9 | 0.295410 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.09781e10 | −1.70897 | −0.854483 | − | 0.519480i | \(-0.826126\pi\) | ||||
−0.854483 | + | 0.519480i | \(0.826126\pi\) | |||||||
\(854\) | 3.55680e10 | 1.95415 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.39531e9 | 0.511980 | ||||||||
\(857\) | −4.23395e9 | −0.229781 | −0.114890 | − | 0.993378i | \(-0.536652\pi\) | ||||
−0.114890 | + | 0.993378i | \(0.536652\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.85088e10 | 0.996329 | 0.498165 | − | 0.867082i | \(-0.334007\pi\) | ||||
0.498165 | + | 0.867082i | \(0.334007\pi\) | |||||||
\(860\) | −5.09064e9 | −0.272915 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.42924e10 | 2.88711 | ||||||||
\(863\) | 1.05929e10 | 0.561020 | 0.280510 | − | 0.959851i | \(-0.409496\pi\) | ||||
0.280510 | + | 0.959851i | \(0.409496\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.67884e9 | −0.350869 | ||||||||
\(866\) | 1.57924e10 | 0.826298 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.62180e10 | −1.36076 | ||||||||
\(869\) | −9.09175e9 | −0.469979 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.75670e8 | 0.00900812 | ||||||||
\(872\) | 3.98467e10 | 2.03509 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.74827e9 | 0.189907 | ||||||||
\(875\) | 1.08344e10 | 0.546735 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.90824e9 | −0.496018 | −0.248009 | − | 0.968758i | \(-0.579776\pi\) | ||||
−0.248009 | + | 0.968758i | \(0.579776\pi\) | |||||||
\(878\) | 1.52452e10 | 0.760156 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.34879e9 | −0.412985 | ||||||||
\(881\) | −1.77972e9 | −0.0876873 | −0.0438437 | − | 0.999038i | \(-0.513960\pi\) | ||||
−0.0438437 | + | 0.999038i | \(0.513960\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.07682e10 | 1.50397 | 0.751985 | − | 0.659180i | \(-0.229096\pi\) | ||||
0.751985 | + | 0.659180i | \(0.229096\pi\) | |||||||
\(884\) | −2.24076e10 | −1.09097 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.63591e10 | −2.72236 | ||||||||
\(887\) | 6.77910e9 | 0.326167 | 0.163083 | − | 0.986612i | \(-0.447856\pi\) | ||||
0.163083 | + | 0.986612i | \(0.447856\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.06048e9 | −0.241566 | ||||||||
\(890\) | −9.63348e9 | −0.458056 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.39640e10 | −0.658771 | ||||||||
\(893\) | −7.36270e9 | −0.345985 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.16432e9 | 0.380662 | ||||||||
\(896\) | 3.18039e10 | 1.47707 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.94707e10 | −1.81889 | ||||||||
\(899\) | −1.79155e10 | −0.822374 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.32202e10 | −1.05762 | ||||||||
\(902\) | 7.55549e10 | 3.42799 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.29101e10 | 2.83225 | ||||||||
\(905\) | 5.39530e9 | 0.241961 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.35163e10 | 1.49153 | 0.745763 | − | 0.666211i | \(-0.232085\pi\) | ||||
0.745763 | + | 0.666211i | \(0.232085\pi\) | |||||||
\(908\) | 2.03840e10 | 0.903626 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.21935e9 | 0.185610 | ||||||||
\(911\) | −2.19745e10 | −0.962953 | −0.481476 | − | 0.876459i | \(-0.659899\pi\) | ||||
−0.481476 | + | 0.876459i | \(0.659899\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.99516e10 | 0.867619 | ||||||||
\(914\) | −2.14163e10 | −0.927755 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.55233e9 | −0.281683 | ||||||||
\(917\) | −2.37569e10 | −1.01741 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.02526e10 | 0.435741 | 0.217871 | − | 0.975978i | \(-0.430089\pi\) | ||||
0.217871 | + | 0.975978i | \(0.430089\pi\) | |||||||
\(920\) | 5.08992e9 | 0.215503 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.78399e10 | 2.85054 | ||||||||
\(923\) | 1.09093e10 | 0.456656 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.74172e10 | −0.723571 | ||||||||
\(926\) | −5.58701e10 | −2.31228 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.11443e9 | −0.169002 | ||||||||
\(929\) | 3.38955e10 | 1.38703 | 0.693517 | − | 0.720440i | \(-0.256060\pi\) | ||||
0.693517 | + | 0.720440i | \(0.256060\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.52301e9 | −0.0618557 | ||||||||
\(932\) | −5.83292e10 | −2.36010 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.51221e10 | 1.00889 | ||||||||
\(935\) | −1.32117e10 | −0.528591 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.25645e9 | −0.208739 | −0.104370 | − | 0.994539i | \(-0.533283\pi\) | ||||
−0.104370 | + | 0.994539i | \(0.533283\pi\) | |||||||
\(938\) | 9.58776e8 | 0.0379321 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.95827e10 | −0.768999 | ||||||||
\(941\) | −2.78632e10 | −1.09010 | −0.545052 | − | 0.838402i | \(-0.683490\pi\) | ||||
−0.545052 | + | 0.838402i | \(0.683490\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.64156e10 | −0.637477 | ||||||||
\(944\) | −3.80668e9 | −0.147280 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.10840e10 | 0.809720 | ||||||||
\(947\) | −2.23930e10 | −0.856817 | −0.428409 | − | 0.903585i | \(-0.640926\pi\) | ||||
−0.428409 | + | 0.903585i | \(0.640926\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.39193e9 | −0.0528670 | ||||||||
\(950\) | −1.22922e10 | −0.465154 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.24393e10 | −2.34546 | ||||||||
\(953\) | 4.95205e9 | 0.185336 | 0.0926680 | − | 0.995697i | \(-0.470460\pi\) | ||||
0.0926680 | + | 0.995697i | \(0.470460\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.96334e9 | −0.295858 | ||||||||
\(956\) | 3.83191e10 | 1.41845 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.62901e10 | 1.33355 | ||||||||
\(959\) | −3.73635e9 | −0.136799 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.21114e10 | −0.440211 | ||||||||
\(962\) | −1.43621e10 | −0.520122 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.39978e10 | −0.503258 | ||||||||
\(965\) | 8.33428e9 | 0.298554 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.63566e9 | 0.0937338 | 0.0468669 | − | 0.998901i | \(-0.485076\pi\) | ||||
0.0468669 | + | 0.998901i | \(0.485076\pi\) | |||||||
\(968\) | 1.37910e10 | 0.488688 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.72761e10 | −0.959581 | ||||||||
\(971\) | −2.95178e10 | −1.03471 | −0.517353 | − | 0.855772i | \(-0.673082\pi\) | ||||
−0.517353 | + | 0.855772i | \(0.673082\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.04908e10 | 0.365103 | ||||||||
\(974\) | −3.56905e10 | −1.23765 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.13494e10 | −1.42362 | ||||||||
\(977\) | −3.98464e9 | −0.136697 | −0.0683483 | − | 0.997662i | \(-0.521773\pi\) | ||||
−0.0683483 | + | 0.997662i | \(0.521773\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.67880e10 | 0.912434 | ||||||||
\(980\) | −4.05079e9 | −0.137483 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.21024e10 | −2.09275 | ||||||||
\(983\) | 2.75939e10 | 0.926566 | 0.463283 | − | 0.886210i | \(-0.346671\pi\) | ||||
0.463283 | + | 0.886210i | \(0.346671\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.61680e9 | 0.287289 | ||||||||
\(986\) | −8.35684e10 | −2.77634 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.80528e9 | −0.224490 | ||||||||
\(989\) | −4.58086e9 | −0.150577 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.84374e8 | 0.0256015 | 0.0128008 | − | 0.999918i | \(-0.495925\pi\) | ||||
0.0128008 | + | 0.999918i | \(0.495925\pi\) | |||||||
\(992\) | 3.53702e9 | 0.115039 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.95408e10 | 1.92292 | ||||||||
\(995\) | −8.92038e9 | −0.287080 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.21987e9 | 0.262683 | 0.131342 | − | 0.991337i | \(-0.458072\pi\) | ||||
0.131342 | + | 0.991337i | \(0.458072\pi\) | |||||||
\(998\) | 4.47579e10 | 1.42532 | ||||||||
\(999\) | 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.b.1.16 | 16 | ||
3.2 | odd | 2 | 177.8.a.a.1.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.a.1.1 | ✓ | 16 | 3.2 | odd | 2 | ||
531.8.a.b.1.16 | 16 | 1.1 | even | 1 | trivial |