Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [275,6,Mod(1,275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(275, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("275.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.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: | \(44.1055504486\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 352 x^{12} + 47255 x^{10} - 3018020 x^{8} + 93670492 x^{6} - 1312532272 x^{4} + \cdots - 10706454784 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{2}\cdot 5^{8} \) |
Twist minimal: | no (minimal twist has level 55) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(3.98693\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 275.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.98693 | 0.704796 | 0.352398 | − | 0.935850i | \(-0.385366\pi\) | ||||
0.352398 | + | 0.935850i | \(0.385366\pi\) | |||||||
\(3\) | −2.19418 | −0.140757 | −0.0703783 | − | 0.997520i | \(-0.522421\pi\) | ||||
−0.0703783 | + | 0.997520i | \(0.522421\pi\) | |||||||
\(4\) | −16.1044 | −0.503262 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −8.74803 | −0.0992047 | ||||||||
\(7\) | −90.9095 | −0.701236 | −0.350618 | − | 0.936519i | \(-0.614028\pi\) | ||||
−0.350618 | + | 0.936519i | \(0.614028\pi\) | |||||||
\(8\) | −191.789 | −1.05949 | ||||||||
\(9\) | −238.186 | −0.980188 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 35.3359 | 0.0708375 | ||||||||
\(13\) | −533.632 | −0.875757 | −0.437878 | − | 0.899034i | \(-0.644270\pi\) | ||||
−0.437878 | + | 0.899034i | \(0.644270\pi\) | |||||||
\(14\) | −362.450 | −0.494228 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −249.308 | −0.243465 | ||||||||
\(17\) | 1599.02 | 1.34193 | 0.670966 | − | 0.741488i | \(-0.265879\pi\) | ||||
0.670966 | + | 0.741488i | \(0.265879\pi\) | |||||||
\(18\) | −949.629 | −0.690832 | ||||||||
\(19\) | 2530.14 | 1.60791 | 0.803953 | − | 0.594692i | \(-0.202726\pi\) | ||||
0.803953 | + | 0.594692i | \(0.202726\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 199.472 | 0.0987035 | ||||||||
\(22\) | −482.418 | −0.212504 | ||||||||
\(23\) | 3015.96 | 1.18879 | 0.594396 | − | 0.804173i | \(-0.297391\pi\) | ||||
0.594396 | + | 0.804173i | \(0.297391\pi\) | |||||||
\(24\) | 420.819 | 0.149131 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2127.55 | −0.617230 | ||||||||
\(27\) | 1055.81 | 0.278724 | ||||||||
\(28\) | 1464.04 | 0.352906 | ||||||||
\(29\) | −8585.18 | −1.89563 | −0.947817 | − | 0.318816i | \(-0.896715\pi\) | ||||
−0.947817 | + | 0.318816i | \(0.896715\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5151.17 | 0.962724 | 0.481362 | − | 0.876522i | \(-0.340142\pi\) | ||||
0.481362 | + | 0.876522i | \(0.340142\pi\) | |||||||
\(32\) | 5143.27 | 0.887901 | ||||||||
\(33\) | 265.496 | 0.0424397 | ||||||||
\(34\) | 6375.17 | 0.945789 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3835.84 | 0.493292 | ||||||||
\(37\) | −10772.3 | −1.29362 | −0.646808 | − | 0.762653i | \(-0.723896\pi\) | ||||
−0.646808 | + | 0.762653i | \(0.723896\pi\) | |||||||
\(38\) | 10087.5 | 1.13325 | ||||||||
\(39\) | 1170.88 | 0.123269 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3608.14 | 0.335215 | 0.167608 | − | 0.985854i | \(-0.446396\pi\) | ||||
0.167608 | + | 0.985854i | \(0.446396\pi\) | |||||||
\(42\) | 795.279 | 0.0695659 | ||||||||
\(43\) | 9224.88 | 0.760834 | 0.380417 | − | 0.924815i | \(-0.375781\pi\) | ||||
0.380417 | + | 0.924815i | \(0.375781\pi\) | |||||||
\(44\) | 1948.63 | 0.151739 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12024.4 | 0.837856 | ||||||||
\(47\) | −14482.8 | −0.956330 | −0.478165 | − | 0.878270i | \(-0.658698\pi\) | ||||
−0.478165 | + | 0.878270i | \(0.658698\pi\) | |||||||
\(48\) | 547.025 | 0.0342692 | ||||||||
\(49\) | −8542.47 | −0.508269 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3508.53 | −0.188886 | ||||||||
\(52\) | 8593.82 | 0.440736 | ||||||||
\(53\) | 14087.6 | 0.688884 | 0.344442 | − | 0.938808i | \(-0.388068\pi\) | ||||
0.344442 | + | 0.938808i | \(0.388068\pi\) | |||||||
\(54\) | 4209.43 | 0.196444 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 17435.4 | 0.742955 | ||||||||
\(57\) | −5551.58 | −0.226323 | ||||||||
\(58\) | −34228.5 | −1.33603 | ||||||||
\(59\) | 47154.1 | 1.76356 | 0.881778 | − | 0.471665i | \(-0.156347\pi\) | ||||
0.881778 | + | 0.471665i | \(0.156347\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11407.2 | 0.392512 | 0.196256 | − | 0.980553i | \(-0.437122\pi\) | ||||
0.196256 | + | 0.980553i | \(0.437122\pi\) | |||||||
\(62\) | 20537.4 | 0.678524 | ||||||||
\(63\) | 21653.3 | 0.687342 | ||||||||
\(64\) | 28483.7 | 0.869254 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1058.51 | 0.0299113 | ||||||||
\(67\) | 16964.5 | 0.461693 | 0.230846 | − | 0.972990i | \(-0.425851\pi\) | ||||
0.230846 | + | 0.972990i | \(0.425851\pi\) | |||||||
\(68\) | −25751.2 | −0.675344 | ||||||||
\(69\) | −6617.55 | −0.167330 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 70000.1 | 1.64798 | 0.823992 | − | 0.566602i | \(-0.191742\pi\) | ||||
0.823992 | + | 0.566602i | \(0.191742\pi\) | |||||||
\(72\) | 45681.3 | 1.03850 | ||||||||
\(73\) | 14601.9 | 0.320702 | 0.160351 | − | 0.987060i | \(-0.448737\pi\) | ||||
0.160351 | + | 0.987060i | \(0.448737\pi\) | |||||||
\(74\) | −42948.5 | −0.911735 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −40746.4 | −0.809199 | ||||||||
\(77\) | 11000.0 | 0.211431 | ||||||||
\(78\) | 4668.23 | 0.0868792 | ||||||||
\(79\) | 36856.2 | 0.664421 | 0.332210 | − | 0.943205i | \(-0.392206\pi\) | ||||
0.332210 | + | 0.943205i | \(0.392206\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 55562.5 | 0.940955 | ||||||||
\(82\) | 14385.4 | 0.236258 | ||||||||
\(83\) | −48596.1 | −0.774294 | −0.387147 | − | 0.922018i | \(-0.626539\pi\) | ||||
−0.387147 | + | 0.922018i | \(0.626539\pi\) | |||||||
\(84\) | −3212.37 | −0.0496738 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 36778.9 | 0.536233 | ||||||||
\(87\) | 18837.4 | 0.266823 | ||||||||
\(88\) | 23206.4 | 0.319449 | ||||||||
\(89\) | −48077.2 | −0.643375 | −0.321687 | − | 0.946846i | \(-0.604250\pi\) | ||||
−0.321687 | + | 0.946846i | \(0.604250\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 48512.2 | 0.614112 | ||||||||
\(92\) | −48570.2 | −0.598274 | ||||||||
\(93\) | −11302.6 | −0.135510 | ||||||||
\(94\) | −57741.9 | −0.674018 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −11285.2 | −0.124978 | ||||||||
\(97\) | −153399. | −1.65536 | −0.827682 | − | 0.561198i | \(-0.810341\pi\) | ||||
−0.827682 | + | 0.561198i | \(0.810341\pi\) | |||||||
\(98\) | −34058.2 | −0.358226 | ||||||||
\(99\) | 28820.5 | 0.295538 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 25004.5 | 0.243902 | 0.121951 | − | 0.992536i | \(-0.461085\pi\) | ||||
0.121951 | + | 0.992536i | \(0.461085\pi\) | |||||||
\(102\) | −13988.3 | −0.133126 | ||||||||
\(103\) | −137496. | −1.27701 | −0.638507 | − | 0.769616i | \(-0.720448\pi\) | ||||
−0.638507 | + | 0.769616i | \(0.720448\pi\) | |||||||
\(104\) | 102345. | 0.927859 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 56166.1 | 0.485523 | ||||||||
\(107\) | −220391. | −1.86095 | −0.930474 | − | 0.366358i | \(-0.880604\pi\) | ||||
−0.930474 | + | 0.366358i | \(0.880604\pi\) | |||||||
\(108\) | −17003.1 | −0.140272 | ||||||||
\(109\) | 225704. | 1.81959 | 0.909796 | − | 0.415056i | \(-0.136238\pi\) | ||||
0.909796 | + | 0.415056i | \(0.136238\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 23636.4 | 0.182085 | ||||||||
\(112\) | 22664.4 | 0.170726 | ||||||||
\(113\) | 98344.0 | 0.724522 | 0.362261 | − | 0.932077i | \(-0.382005\pi\) | ||||
0.362261 | + | 0.932077i | \(0.382005\pi\) | |||||||
\(114\) | −22133.8 | −0.159512 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 138259. | 0.954001 | ||||||||
\(117\) | 127103. | 0.858406 | ||||||||
\(118\) | 188000. | 1.24295 | ||||||||
\(119\) | −145366. | −0.941011 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 45479.6 | 0.276641 | ||||||||
\(123\) | −7916.90 | −0.0471838 | ||||||||
\(124\) | −82956.5 | −0.484503 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 86330.3 | 0.484436 | ||||||||
\(127\) | 22651.8 | 0.124622 | 0.0623108 | − | 0.998057i | \(-0.480153\pi\) | ||||
0.0623108 | + | 0.998057i | \(0.480153\pi\) | |||||||
\(128\) | −51022.2 | −0.275254 | ||||||||
\(129\) | −20241.0 | −0.107092 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 45526.9 | 0.231787 | 0.115894 | − | 0.993262i | \(-0.463027\pi\) | ||||
0.115894 | + | 0.993262i | \(0.463027\pi\) | |||||||
\(132\) | −4275.65 | −0.0213583 | ||||||||
\(133\) | −230014. | −1.12752 | ||||||||
\(134\) | 67636.1 | 0.325399 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −306674. | −1.42177 | ||||||||
\(137\) | 97204.5 | 0.442471 | 0.221235 | − | 0.975220i | \(-0.428991\pi\) | ||||
0.221235 | + | 0.975220i | \(0.428991\pi\) | |||||||
\(138\) | −26383.7 | −0.117934 | ||||||||
\(139\) | −4897.20 | −0.0214986 | −0.0107493 | − | 0.999942i | \(-0.503422\pi\) | ||||
−0.0107493 | + | 0.999942i | \(0.503422\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 31777.8 | 0.134610 | ||||||||
\(142\) | 279086. | 1.16149 | ||||||||
\(143\) | 64569.5 | 0.264051 | ||||||||
\(144\) | 59381.5 | 0.238641 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 58216.6 | 0.226029 | ||||||||
\(147\) | 18743.7 | 0.0715421 | ||||||||
\(148\) | 173482. | 0.651028 | ||||||||
\(149\) | 72021.5 | 0.265764 | 0.132882 | − | 0.991132i | \(-0.457577\pi\) | ||||
0.132882 | + | 0.991132i | \(0.457577\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 120149. | 0.428822 | 0.214411 | − | 0.976743i | \(-0.431217\pi\) | ||||
0.214411 | + | 0.976743i | \(0.431217\pi\) | |||||||
\(152\) | −485253. | −1.70357 | ||||||||
\(153\) | −380863. | −1.31535 | ||||||||
\(154\) | 43856.4 | 0.149015 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −18856.4 | −0.0620364 | ||||||||
\(157\) | 147799. | 0.478545 | 0.239273 | − | 0.970952i | \(-0.423091\pi\) | ||||
0.239273 | + | 0.970952i | \(0.423091\pi\) | |||||||
\(158\) | 146943. | 0.468281 | ||||||||
\(159\) | −30910.6 | −0.0969650 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −274179. | −0.833623 | ||||||||
\(162\) | 221524. | 0.663182 | ||||||||
\(163\) | 47145.7 | 0.138987 | 0.0694933 | − | 0.997582i | \(-0.477862\pi\) | ||||
0.0694933 | + | 0.997582i | \(0.477862\pi\) | |||||||
\(164\) | −58106.9 | −0.168701 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −193749. | −0.545720 | ||||||||
\(167\) | 181485. | 0.503559 | 0.251779 | − | 0.967785i | \(-0.418984\pi\) | ||||
0.251779 | + | 0.967785i | \(0.418984\pi\) | |||||||
\(168\) | −38256.4 | −0.104576 | ||||||||
\(169\) | −86529.8 | −0.233050 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −602643. | −1.57605 | ||||||||
\(172\) | −148561. | −0.382899 | ||||||||
\(173\) | 680704. | 1.72919 | 0.864596 | − | 0.502468i | \(-0.167575\pi\) | ||||
0.864596 | + | 0.502468i | \(0.167575\pi\) | |||||||
\(174\) | 75103.4 | 0.188056 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 30166.2 | 0.0734073 | ||||||||
\(177\) | −103464. | −0.248232 | ||||||||
\(178\) | −191680. | −0.453448 | ||||||||
\(179\) | 372370. | 0.868646 | 0.434323 | − | 0.900757i | \(-0.356988\pi\) | ||||
0.434323 | + | 0.900757i | \(0.356988\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −187574. | −0.425575 | −0.212788 | − | 0.977098i | \(-0.568254\pi\) | ||||
−0.212788 | + | 0.977098i | \(0.568254\pi\) | |||||||
\(182\) | 193415. | 0.432824 | ||||||||
\(183\) | −25029.3 | −0.0552487 | ||||||||
\(184\) | −578427. | −1.25952 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −45062.6 | −0.0955067 | ||||||||
\(187\) | −193481. | −0.404608 | ||||||||
\(188\) | 233237. | 0.481285 | ||||||||
\(189\) | −95982.8 | −0.195452 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 327121. | 0.648821 | 0.324411 | − | 0.945916i | \(-0.394834\pi\) | ||||
0.324411 | + | 0.945916i | \(0.394834\pi\) | |||||||
\(192\) | −62498.3 | −0.122353 | ||||||||
\(193\) | −593369. | −1.14665 | −0.573326 | − | 0.819327i | \(-0.694347\pi\) | ||||
−0.573326 | + | 0.819327i | \(0.694347\pi\) | |||||||
\(194\) | −611591. | −1.16669 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 137571. | 0.255792 | ||||||||
\(197\) | 699226. | 1.28367 | 0.641833 | − | 0.766844i | \(-0.278174\pi\) | ||||
0.641833 | + | 0.766844i | \(0.278174\pi\) | |||||||
\(198\) | 114905. | 0.208294 | ||||||||
\(199\) | 203765. | 0.364751 | 0.182376 | − | 0.983229i | \(-0.441621\pi\) | ||||
0.182376 | + | 0.983229i | \(0.441621\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −37223.0 | −0.0649863 | ||||||||
\(202\) | 99691.2 | 0.171901 | ||||||||
\(203\) | 780474. | 1.32929 | ||||||||
\(204\) | 56502.7 | 0.0950592 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −548185. | −0.900035 | ||||||||
\(207\) | −718358. | −1.16524 | ||||||||
\(208\) | 133039. | 0.213216 | ||||||||
\(209\) | −306147. | −0.484802 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −395743. | −0.611937 | −0.305969 | − | 0.952042i | \(-0.598980\pi\) | ||||
−0.305969 | + | 0.952042i | \(0.598980\pi\) | |||||||
\(212\) | −226872. | −0.346690 | ||||||||
\(213\) | −153593. | −0.231965 | ||||||||
\(214\) | −878683. | −1.31159 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −202492. | −0.295307 | ||||||||
\(217\) | −468290. | −0.675096 | ||||||||
\(218\) | 899868. | 1.28244 | ||||||||
\(219\) | −32039.1 | −0.0451409 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −853287. | −1.17521 | ||||||||
\(222\) | 94236.6 | 0.128333 | ||||||||
\(223\) | 477978. | 0.643644 | 0.321822 | − | 0.946800i | \(-0.395705\pi\) | ||||
0.321822 | + | 0.946800i | \(0.395705\pi\) | |||||||
\(224\) | −467572. | −0.622628 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 392091. | 0.510641 | ||||||||
\(227\) | −588034. | −0.757422 | −0.378711 | − | 0.925515i | \(-0.623633\pi\) | ||||
−0.378711 | + | 0.925515i | \(0.623633\pi\) | |||||||
\(228\) | 89404.9 | 0.113900 | ||||||||
\(229\) | 388983. | 0.490165 | 0.245082 | − | 0.969502i | \(-0.421185\pi\) | ||||
0.245082 | + | 0.969502i | \(0.421185\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24136.1 | −0.0297602 | ||||||||
\(232\) | 1.64654e6 | 2.00841 | ||||||||
\(233\) | −501987. | −0.605763 | −0.302882 | − | 0.953028i | \(-0.597949\pi\) | ||||
−0.302882 | + | 0.953028i | \(0.597949\pi\) | |||||||
\(234\) | 506753. | 0.605001 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −759388. | −0.887531 | ||||||||
\(237\) | −80869.1 | −0.0935216 | ||||||||
\(238\) | −579563. | −0.663221 | ||||||||
\(239\) | 481013. | 0.544705 | 0.272353 | − | 0.962197i | \(-0.412198\pi\) | ||||
0.272353 | + | 0.962197i | \(0.412198\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −463041. | −0.513544 | −0.256772 | − | 0.966472i | \(-0.582659\pi\) | ||||
−0.256772 | + | 0.966472i | \(0.582659\pi\) | |||||||
\(242\) | 58372.6 | 0.0640724 | ||||||||
\(243\) | −378475. | −0.411170 | ||||||||
\(244\) | −183706. | −0.197537 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −31564.1 | −0.0332549 | ||||||||
\(247\) | −1.35016e6 | −1.40814 | ||||||||
\(248\) | −987937. | −1.02000 | ||||||||
\(249\) | 106628. | 0.108987 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 401567. | 0.402321 | 0.201161 | − | 0.979558i | \(-0.435529\pi\) | ||||
0.201161 | + | 0.979558i | \(0.435529\pi\) | |||||||
\(252\) | −348714. | −0.345914 | ||||||||
\(253\) | −364931. | −0.358434 | ||||||||
\(254\) | 90311.0 | 0.0878328 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.11490e6 | −1.06325 | ||||||||
\(257\) | 1.25197e6 | 1.18240 | 0.591198 | − | 0.806527i | \(-0.298655\pi\) | ||||
0.591198 | + | 0.806527i | \(0.298655\pi\) | |||||||
\(258\) | −80699.5 | −0.0754783 | ||||||||
\(259\) | 979306. | 0.907129 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.04487e6 | 1.85808 | ||||||||
\(262\) | 181513. | 0.163363 | ||||||||
\(263\) | −1.27396e6 | −1.13571 | −0.567853 | − | 0.823130i | \(-0.692226\pi\) | ||||
−0.567853 | + | 0.823130i | \(0.692226\pi\) | |||||||
\(264\) | −50919.1 | −0.0449646 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −917049. | −0.794673 | ||||||||
\(267\) | 105490. | 0.0905593 | ||||||||
\(268\) | −273202. | −0.232353 | ||||||||
\(269\) | 863140. | 0.727278 | 0.363639 | − | 0.931540i | \(-0.381534\pi\) | ||||
0.363639 | + | 0.931540i | \(0.381534\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −265882. | −0.219920 | −0.109960 | − | 0.993936i | \(-0.535072\pi\) | ||||
−0.109960 | + | 0.993936i | \(0.535072\pi\) | |||||||
\(272\) | −398647. | −0.326713 | ||||||||
\(273\) | −106444. | −0.0864403 | ||||||||
\(274\) | 387547. | 0.311852 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 106572. | 0.0842110 | ||||||||
\(277\) | 269789. | 0.211264 | 0.105632 | − | 0.994405i | \(-0.466313\pi\) | ||||
0.105632 | + | 0.994405i | \(0.466313\pi\) | |||||||
\(278\) | −19524.8 | −0.0151521 | ||||||||
\(279\) | −1.22693e6 | −0.943650 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 453679. | 0.342754 | 0.171377 | − | 0.985206i | \(-0.445178\pi\) | ||||
0.171377 | + | 0.985206i | \(0.445178\pi\) | |||||||
\(282\) | 126696. | 0.0948724 | ||||||||
\(283\) | −10472.1 | −0.00777264 | −0.00388632 | − | 0.999992i | \(-0.501237\pi\) | ||||
−0.00388632 | + | 0.999992i | \(0.501237\pi\) | |||||||
\(284\) | −1.12731e6 | −0.829368 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 257434. | 0.186102 | ||||||||
\(287\) | −328014. | −0.235065 | ||||||||
\(288\) | −1.22505e6 | −0.870309 | ||||||||
\(289\) | 1.13700e6 | 0.800784 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 336585. | 0.233003 | ||||||||
\(292\) | −235154. | −0.161397 | ||||||||
\(293\) | 339136. | 0.230783 | 0.115392 | − | 0.993320i | \(-0.463188\pi\) | ||||
0.115392 | + | 0.993320i | \(0.463188\pi\) | |||||||
\(294\) | 74729.8 | 0.0504226 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.06601e6 | 1.37058 | ||||||||
\(297\) | −127753. | −0.0840386 | ||||||||
\(298\) | 287145. | 0.187310 | ||||||||
\(299\) | −1.60941e6 | −1.04109 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −838629. | −0.533524 | ||||||||
\(302\) | 479025. | 0.302232 | ||||||||
\(303\) | −54864.3 | −0.0343308 | ||||||||
\(304\) | −630784. | −0.391468 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.51847e6 | −0.927051 | ||||||||
\(307\) | −821082. | −0.497211 | −0.248605 | − | 0.968605i | \(-0.579972\pi\) | ||||
−0.248605 | + | 0.968605i | \(0.579972\pi\) | |||||||
\(308\) | −177149. | −0.106405 | ||||||||
\(309\) | 301690. | 0.179748 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.41897e6 | 1.41817 | 0.709087 | − | 0.705121i | \(-0.249107\pi\) | ||||
0.709087 | + | 0.705121i | \(0.249107\pi\) | |||||||
\(312\) | −224562. | −0.130602 | ||||||||
\(313\) | −433767. | −0.250263 | −0.125131 | − | 0.992140i | \(-0.539935\pi\) | ||||
−0.125131 | + | 0.992140i | \(0.539935\pi\) | |||||||
\(314\) | 589265. | 0.337277 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −593547. | −0.334378 | ||||||||
\(317\) | 2.12363e6 | 1.18695 | 0.593473 | − | 0.804854i | \(-0.297757\pi\) | ||||
0.593473 | + | 0.804854i | \(0.297757\pi\) | |||||||
\(318\) | −123238. | −0.0683406 | ||||||||
\(319\) | 1.03881e6 | 0.571555 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 483577. | 0.261941 | ||||||||
\(322\) | −1.09313e6 | −0.587534 | ||||||||
\(323\) | 4.04574e6 | 2.15770 | ||||||||
\(324\) | −894800. | −0.473547 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 187966. | 0.0979572 | ||||||||
\(327\) | −495236. | −0.256119 | ||||||||
\(328\) | −692001. | −0.355158 | ||||||||
\(329\) | 1.31662e6 | 0.670613 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 763933. | 0.383253 | 0.191626 | − | 0.981468i | \(-0.438624\pi\) | ||||
0.191626 | + | 0.981468i | \(0.438624\pi\) | |||||||
\(332\) | 782611. | 0.389673 | ||||||||
\(333\) | 2.56581e6 | 1.26799 | ||||||||
\(334\) | 723569. | 0.354906 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −49729.8 | −0.0240308 | ||||||||
\(337\) | −1.99588e6 | −0.957324 | −0.478662 | − | 0.877999i | \(-0.658878\pi\) | ||||
−0.478662 | + | 0.877999i | \(0.658878\pi\) | |||||||
\(338\) | −344988. | −0.164253 | ||||||||
\(339\) | −215784. | −0.101981 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −623292. | −0.290272 | ||||||||
\(342\) | −2.40270e6 | −1.11079 | ||||||||
\(343\) | 2.30451e6 | 1.05765 | ||||||||
\(344\) | −1.76923e6 | −0.806098 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.71392e6 | 1.21873 | ||||||||
\(347\) | 651996. | 0.290684 | 0.145342 | − | 0.989381i | \(-0.453572\pi\) | ||||
0.145342 | + | 0.989381i | \(0.453572\pi\) | |||||||
\(348\) | −303365. | −0.134282 | ||||||||
\(349\) | 274136. | 0.120477 | 0.0602383 | − | 0.998184i | \(-0.480814\pi\) | ||||
0.0602383 | + | 0.998184i | \(0.480814\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −563412. | −0.244095 | ||||||||
\(352\) | −622336. | −0.267712 | ||||||||
\(353\) | −2.59169e6 | −1.10700 | −0.553498 | − | 0.832851i | \(-0.686707\pi\) | ||||
−0.553498 | + | 0.832851i | \(0.686707\pi\) | |||||||
\(354\) | −412505. | −0.174953 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 774254. | 0.323786 | ||||||||
\(357\) | 318958. | 0.132454 | ||||||||
\(358\) | 1.48461e6 | 0.612218 | ||||||||
\(359\) | 1.82934e6 | 0.749132 | 0.374566 | − | 0.927200i | \(-0.377792\pi\) | ||||
0.374566 | + | 0.927200i | \(0.377792\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.92552e6 | 1.58536 | ||||||||
\(362\) | −747845. | −0.299944 | ||||||||
\(363\) | −32125.0 | −0.0127961 | ||||||||
\(364\) | −781260. | −0.309059 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −99790.2 | −0.0389390 | ||||||||
\(367\) | 1.90734e6 | 0.739203 | 0.369601 | − | 0.929190i | \(-0.379494\pi\) | ||||
0.369601 | + | 0.929190i | \(0.379494\pi\) | |||||||
\(368\) | −751902. | −0.289429 | ||||||||
\(369\) | −859407. | −0.328574 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.28069e6 | −0.483070 | ||||||||
\(372\) | 182021. | 0.0681969 | ||||||||
\(373\) | 3.03699e6 | 1.13024 | 0.565122 | − | 0.825008i | \(-0.308829\pi\) | ||||
0.565122 | + | 0.825008i | \(0.308829\pi\) | |||||||
\(374\) | −771395. | −0.285166 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.77764e6 | 1.01323 | ||||||||
\(377\) | 4.58133e6 | 1.66011 | ||||||||
\(378\) | −382677. | −0.137753 | ||||||||
\(379\) | 3.09949e6 | 1.10839 | 0.554195 | − | 0.832387i | \(-0.313026\pi\) | ||||
0.554195 | + | 0.832387i | \(0.313026\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −49702.0 | −0.0175413 | ||||||||
\(382\) | 1.30421e6 | 0.457287 | ||||||||
\(383\) | −5.38627e6 | −1.87625 | −0.938127 | − | 0.346292i | \(-0.887441\pi\) | ||||
−0.938127 | + | 0.346292i | \(0.887441\pi\) | |||||||
\(384\) | 111952. | 0.0387438 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.36572e6 | −0.808156 | ||||||||
\(387\) | −2.19723e6 | −0.745760 | ||||||||
\(388\) | 2.47040e6 | 0.833082 | ||||||||
\(389\) | 3.81576e6 | 1.27852 | 0.639260 | − | 0.768991i | \(-0.279241\pi\) | ||||
0.639260 | + | 0.768991i | \(0.279241\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.82257e6 | 1.59528 | ||||||||
\(392\) | 1.63835e6 | 0.538507 | ||||||||
\(393\) | −99894.1 | −0.0326256 | ||||||||
\(394\) | 2.78776e6 | 0.904723 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −464136. | −0.148733 | ||||||||
\(397\) | 187812. | 0.0598063 | 0.0299032 | − | 0.999553i | \(-0.490480\pi\) | ||||
0.0299032 | + | 0.999553i | \(0.490480\pi\) | |||||||
\(398\) | 812397. | 0.257075 | ||||||||
\(399\) | 504691. | 0.158706 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.01719e6 | 0.626448 | 0.313224 | − | 0.949679i | \(-0.398591\pi\) | ||||
0.313224 | + | 0.949679i | \(0.398591\pi\) | |||||||
\(402\) | −148406. | −0.0458021 | ||||||||
\(403\) | −2.74883e6 | −0.843112 | ||||||||
\(404\) | −402683. | −0.122747 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.11169e6 | 0.936875 | ||||||||
\(407\) | 1.30345e6 | 0.390040 | ||||||||
\(408\) | 672896. | 0.200123 | ||||||||
\(409\) | 4.21012e6 | 1.24447 | 0.622237 | − | 0.782829i | \(-0.286224\pi\) | ||||
0.622237 | + | 0.782829i | \(0.286224\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −213284. | −0.0622807 | ||||||||
\(412\) | 2.21428e6 | 0.642673 | ||||||||
\(413\) | −4.28675e6 | −1.23667 | ||||||||
\(414\) | −2.86404e6 | −0.821256 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.74461e6 | −0.777585 | ||||||||
\(417\) | 10745.3 | 0.00302607 | ||||||||
\(418\) | −1.22059e6 | −0.341687 | ||||||||
\(419\) | −4.57372e6 | −1.27273 | −0.636363 | − | 0.771390i | \(-0.719562\pi\) | ||||
−0.636363 | + | 0.771390i | \(0.719562\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.03432e6 | −1.10934 | −0.554670 | − | 0.832070i | \(-0.687156\pi\) | ||||
−0.554670 | + | 0.832070i | \(0.687156\pi\) | |||||||
\(422\) | −1.57780e6 | −0.431291 | ||||||||
\(423\) | 3.44959e6 | 0.937383 | ||||||||
\(424\) | −2.70184e6 | −0.729868 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −612363. | −0.163488 | ||||||||
\(427\) | −1.03702e6 | −0.275244 | ||||||||
\(428\) | 3.54926e6 | 0.936545 | ||||||||
\(429\) | −141677. | −0.0371669 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 306364. | 0.0794411 | 0.0397205 | − | 0.999211i | \(-0.487353\pi\) | ||||
0.0397205 | + | 0.999211i | \(0.487353\pi\) | |||||||
\(432\) | −263221. | −0.0678595 | ||||||||
\(433\) | 2.76255e6 | 0.708093 | 0.354046 | − | 0.935228i | \(-0.384806\pi\) | ||||
0.354046 | + | 0.935228i | \(0.384806\pi\) | |||||||
\(434\) | −1.86704e6 | −0.475805 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.63483e6 | −0.915732 | ||||||||
\(437\) | 7.63080e6 | 1.91147 | ||||||||
\(438\) | −127738. | −0.0318151 | ||||||||
\(439\) | 1.84274e6 | 0.456356 | 0.228178 | − | 0.973619i | \(-0.426723\pi\) | ||||
0.228178 | + | 0.973619i | \(0.426723\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.03469e6 | 0.498199 | ||||||||
\(442\) | −3.40199e6 | −0.828281 | ||||||||
\(443\) | −574713. | −0.139137 | −0.0695684 | − | 0.997577i | \(-0.522162\pi\) | ||||
−0.0695684 | + | 0.997577i | \(0.522162\pi\) | |||||||
\(444\) | −380650. | −0.0916365 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.90566e6 | 0.453638 | ||||||||
\(447\) | −158028. | −0.0374080 | ||||||||
\(448\) | −2.58944e6 | −0.609552 | ||||||||
\(449\) | 5.24929e6 | 1.22881 | 0.614404 | − | 0.788991i | \(-0.289396\pi\) | ||||
0.614404 | + | 0.788991i | \(0.289396\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −436585. | −0.101071 | ||||||||
\(452\) | −1.58377e6 | −0.364625 | ||||||||
\(453\) | −263628. | −0.0603596 | ||||||||
\(454\) | −2.34445e6 | −0.533828 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.06473e6 | 0.239788 | ||||||||
\(457\) | −7.46219e6 | −1.67138 | −0.835691 | − | 0.549200i | \(-0.814932\pi\) | ||||
−0.835691 | + | 0.549200i | \(0.814932\pi\) | |||||||
\(458\) | 1.55085e6 | 0.345466 | ||||||||
\(459\) | 1.68825e6 | 0.374029 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.68536e6 | −0.588506 | −0.294253 | − | 0.955728i | \(-0.595071\pi\) | ||||
−0.294253 | + | 0.955728i | \(0.595071\pi\) | |||||||
\(462\) | −96228.7 | −0.0209749 | ||||||||
\(463\) | 6.34877e6 | 1.37638 | 0.688188 | − | 0.725533i | \(-0.258407\pi\) | ||||
0.688188 | + | 0.725533i | \(0.258407\pi\) | |||||||
\(464\) | 2.14035e6 | 0.461519 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.00139e6 | −0.426940 | ||||||||
\(467\) | 4.68768e6 | 0.994641 | 0.497320 | − | 0.867567i | \(-0.334317\pi\) | ||||
0.497320 | + | 0.867567i | \(0.334317\pi\) | |||||||
\(468\) | −2.04692e6 | −0.432003 | ||||||||
\(469\) | −1.54223e6 | −0.323755 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −324298. | −0.0673584 | ||||||||
\(472\) | −9.04362e6 | −1.86848 | ||||||||
\(473\) | −1.11621e6 | −0.229400 | ||||||||
\(474\) | −322419. | −0.0659137 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.34103e6 | 0.473576 | ||||||||
\(477\) | −3.35546e6 | −0.675236 | ||||||||
\(478\) | 1.91776e6 | 0.383906 | ||||||||
\(479\) | −795999. | −0.158516 | −0.0792581 | − | 0.996854i | \(-0.525255\pi\) | ||||
−0.0792581 | + | 0.996854i | \(0.525255\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.74846e6 | 1.13289 | ||||||||
\(482\) | −1.84611e6 | −0.361944 | ||||||||
\(483\) | 601598. | 0.117338 | ||||||||
\(484\) | −235784. | −0.0457511 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.50895e6 | −0.289791 | ||||||||
\(487\) | 1.83464e6 | 0.350532 | 0.175266 | − | 0.984521i | \(-0.443921\pi\) | ||||
0.175266 | + | 0.984521i | \(0.443921\pi\) | |||||||
\(488\) | −2.18777e6 | −0.415864 | ||||||||
\(489\) | −103446. | −0.0195633 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.40439e6 | −1.01168 | −0.505840 | − | 0.862627i | \(-0.668817\pi\) | ||||
−0.505840 | + | 0.862627i | \(0.668817\pi\) | |||||||
\(492\) | 127497. | 0.0237458 | ||||||||
\(493\) | −1.37278e7 | −2.54381 | ||||||||
\(494\) | −5.38301e6 | −0.992448 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.28423e6 | −0.234389 | ||||||||
\(497\) | −6.36367e6 | −1.15562 | ||||||||
\(498\) | 425120. | 0.0768136 | ||||||||
\(499\) | −3.85216e6 | −0.692553 | −0.346277 | − | 0.938132i | \(-0.612554\pi\) | ||||
−0.346277 | + | 0.938132i | \(0.612554\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −398211. | −0.0708792 | ||||||||
\(502\) | 1.60102e6 | 0.283555 | ||||||||
\(503\) | 5.01187e6 | 0.883242 | 0.441621 | − | 0.897202i | \(-0.354404\pi\) | ||||
0.441621 | + | 0.897202i | \(0.354404\pi\) | |||||||
\(504\) | −4.15287e6 | −0.728235 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.45495e6 | −0.252623 | ||||||||
\(507\) | 189862. | 0.0328033 | ||||||||
\(508\) | −364793. | −0.0627173 | ||||||||
\(509\) | −8.08491e6 | −1.38319 | −0.691594 | − | 0.722287i | \(-0.743091\pi\) | ||||
−0.691594 | + | 0.722287i | \(0.743091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.32745e6 | −0.224887 | ||||||||
\(512\) | −2.81232e6 | −0.474121 | ||||||||
\(513\) | 2.67134e6 | 0.448163 | ||||||||
\(514\) | 4.99153e6 | 0.833347 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 325970. | 0.0538955 | ||||||||
\(517\) | 1.75242e6 | 0.288344 | ||||||||
\(518\) | 3.90442e6 | 0.639341 | ||||||||
\(519\) | −1.49359e6 | −0.243395 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.18229e6 | 0.675025 | 0.337513 | − | 0.941321i | \(-0.390414\pi\) | ||||
0.337513 | + | 0.941321i | \(0.390414\pi\) | |||||||
\(522\) | 8.15273e6 | 1.30956 | ||||||||
\(523\) | −6.29712e6 | −1.00667 | −0.503336 | − | 0.864091i | \(-0.667894\pi\) | ||||
−0.503336 | + | 0.864091i | \(0.667894\pi\) | |||||||
\(524\) | −733183. | −0.116650 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.07919e6 | −0.800442 | ||||||||
\(527\) | 8.23681e6 | 1.29191 | ||||||||
\(528\) | −66190.1 | −0.0103326 | ||||||||
\(529\) | 2.65966e6 | 0.413225 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.12314e7 | −1.72861 | ||||||||
\(532\) | 3.70423e6 | 0.567439 | ||||||||
\(533\) | −1.92542e6 | −0.293567 | ||||||||
\(534\) | 420581. | 0.0638258 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.25359e6 | −0.489160 | ||||||||
\(537\) | −817047. | −0.122268 | ||||||||
\(538\) | 3.44128e6 | 0.512583 | ||||||||
\(539\) | 1.03364e6 | 0.153249 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −863454. | −0.126837 | −0.0634185 | − | 0.997987i | \(-0.520200\pi\) | ||||
−0.0634185 | + | 0.997987i | \(0.520200\pi\) | |||||||
\(542\) | −1.06005e6 | −0.154999 | ||||||||
\(543\) | 411571. | 0.0599025 | ||||||||
\(544\) | 8.22418e6 | 1.19150 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −424386. | −0.0609228 | ||||||||
\(547\) | 2.32481e6 | 0.332215 | 0.166108 | − | 0.986108i | \(-0.446880\pi\) | ||||
0.166108 | + | 0.986108i | \(0.446880\pi\) | |||||||
\(548\) | −1.56542e6 | −0.222679 | ||||||||
\(549\) | −2.71702e6 | −0.384736 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.17217e7 | −3.04800 | ||||||||
\(552\) | 1.26917e6 | 0.177285 | ||||||||
\(553\) | −3.35058e6 | −0.465916 | ||||||||
\(554\) | 1.07563e6 | 0.148898 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 78866.4 | 0.0108194 | ||||||||
\(557\) | 2.37211e6 | 0.323964 | 0.161982 | − | 0.986794i | \(-0.448211\pi\) | ||||
0.161982 | + | 0.986794i | \(0.448211\pi\) | |||||||
\(558\) | −4.89170e6 | −0.665081 | ||||||||
\(559\) | −4.92269e6 | −0.666305 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 424532. | 0.0569512 | ||||||||
\(562\) | 1.80878e6 | 0.241572 | ||||||||
\(563\) | −3.70497e6 | −0.492621 | −0.246311 | − | 0.969191i | \(-0.579218\pi\) | ||||
−0.246311 | + | 0.969191i | \(0.579218\pi\) | |||||||
\(564\) | −511763. | −0.0677440 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −41751.6 | −0.00547813 | ||||||||
\(567\) | −5.05115e6 | −0.659831 | ||||||||
\(568\) | −1.34252e7 | −1.74603 | ||||||||
\(569\) | −4.79504e6 | −0.620886 | −0.310443 | − | 0.950592i | \(-0.600477\pi\) | ||||
−0.310443 | + | 0.950592i | \(0.600477\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.37138e7 | 1.76023 | 0.880114 | − | 0.474763i | \(-0.157466\pi\) | ||||
0.880114 | + | 0.474763i | \(0.157466\pi\) | |||||||
\(572\) | −1.03985e6 | −0.132887 | ||||||||
\(573\) | −717762. | −0.0913259 | ||||||||
\(574\) | −1.30777e6 | −0.165673 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.78441e6 | −0.852031 | ||||||||
\(577\) | −5.34197e6 | −0.667977 | −0.333989 | − | 0.942577i | \(-0.608395\pi\) | ||||
−0.333989 | + | 0.942577i | \(0.608395\pi\) | |||||||
\(578\) | 4.53313e6 | 0.564390 | ||||||||
\(579\) | 1.30196e6 | 0.161399 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.41784e6 | 0.542963 | ||||||||
\(582\) | 1.34194e6 | 0.164220 | ||||||||
\(583\) | −1.70460e6 | −0.207706 | ||||||||
\(584\) | −2.80047e6 | −0.339781 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.35211e6 | 0.162655 | ||||||||
\(587\) | −5.07416e6 | −0.607811 | −0.303906 | − | 0.952702i | \(-0.598291\pi\) | ||||
−0.303906 | + | 0.952702i | \(0.598291\pi\) | |||||||
\(588\) | −301856. | −0.0360045 | ||||||||
\(589\) | 1.30332e7 | 1.54797 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.53423e6 | −0.180684 | ||||||||
\(592\) | 2.68562e6 | 0.314949 | ||||||||
\(593\) | 7.73891e6 | 0.903739 | 0.451870 | − | 0.892084i | \(-0.350757\pi\) | ||||
0.451870 | + | 0.892084i | \(0.350757\pi\) | |||||||
\(594\) | −509341. | −0.0592301 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.15986e6 | −0.133749 | ||||||||
\(597\) | −447097. | −0.0513412 | ||||||||
\(598\) | −6.41661e6 | −0.733758 | ||||||||
\(599\) | 5.04688e6 | 0.574720 | 0.287360 | − | 0.957823i | \(-0.407222\pi\) | ||||
0.287360 | + | 0.957823i | \(0.407222\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.89498e6 | −0.552796 | −0.276398 | − | 0.961043i | \(-0.589141\pi\) | ||||
−0.276398 | + | 0.961043i | \(0.589141\pi\) | |||||||
\(602\) | −3.34355e6 | −0.376025 | ||||||||
\(603\) | −4.04069e6 | −0.452545 | ||||||||
\(604\) | −1.93493e6 | −0.215810 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −218740. | −0.0241962 | ||||||||
\(607\) | 9.09514e6 | 1.00193 | 0.500965 | − | 0.865467i | \(-0.332978\pi\) | ||||
0.500965 | + | 0.865467i | \(0.332978\pi\) | |||||||
\(608\) | 1.30132e7 | 1.42766 | ||||||||
\(609\) | −1.71250e6 | −0.187106 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.72849e6 | 0.837513 | ||||||||
\(612\) | 6.13357e6 | 0.661964 | ||||||||
\(613\) | 1.68653e7 | 1.81277 | 0.906385 | − | 0.422452i | \(-0.138830\pi\) | ||||
0.906385 | + | 0.422452i | \(0.138830\pi\) | |||||||
\(614\) | −3.27360e6 | −0.350432 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.10969e6 | −0.224009 | ||||||||
\(617\) | −1.33815e7 | −1.41512 | −0.707560 | − | 0.706654i | \(-0.750204\pi\) | ||||
−0.707560 | + | 0.706654i | \(0.750204\pi\) | |||||||
\(618\) | 1.20282e6 | 0.126686 | ||||||||
\(619\) | 1.36962e7 | 1.43672 | 0.718360 | − | 0.695671i | \(-0.244893\pi\) | ||||
0.718360 | + | 0.695671i | \(0.244893\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.18427e6 | 0.331345 | ||||||||
\(622\) | 9.64426e6 | 0.999523 | ||||||||
\(623\) | 4.37067e6 | 0.451157 | ||||||||
\(624\) | −291910. | −0.0300115 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.72940e6 | −0.176384 | ||||||||
\(627\) | 671741. | 0.0682391 | ||||||||
\(628\) | −2.38022e6 | −0.240834 | ||||||||
\(629\) | −1.72251e7 | −1.73594 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.04869e6 | −0.104851 | −0.0524254 | − | 0.998625i | \(-0.516695\pi\) | ||||
−0.0524254 | + | 0.998625i | \(0.516695\pi\) | |||||||
\(632\) | −7.06861e6 | −0.703949 | ||||||||
\(633\) | 868330. | 0.0861342 | ||||||||
\(634\) | 8.46676e6 | 0.836554 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 497797. | 0.0487988 | ||||||||
\(637\) | 4.55854e6 | 0.445120 | ||||||||
\(638\) | 4.14165e6 | 0.402830 | ||||||||
\(639\) | −1.66730e7 | −1.61533 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.66293e6 | −0.928889 | −0.464444 | − | 0.885602i | \(-0.653746\pi\) | ||||
−0.464444 | + | 0.885602i | \(0.653746\pi\) | |||||||
\(642\) | 1.92799e6 | 0.184615 | ||||||||
\(643\) | 8.87055e6 | 0.846102 | 0.423051 | − | 0.906106i | \(-0.360959\pi\) | ||||
0.423051 | + | 0.906106i | \(0.360959\pi\) | |||||||
\(644\) | 4.41549e6 | 0.419531 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.61301e7 | 1.52074 | ||||||||
\(647\) | 1.95886e6 | 0.183969 | 0.0919843 | − | 0.995760i | \(-0.470679\pi\) | ||||
0.0919843 | + | 0.995760i | \(0.470679\pi\) | |||||||
\(648\) | −1.06563e7 | −0.996936 | ||||||||
\(649\) | −5.70564e6 | −0.531732 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.02751e6 | 0.0950242 | ||||||||
\(652\) | −759252. | −0.0699467 | ||||||||
\(653\) | 1.06165e7 | 0.974311 | 0.487155 | − | 0.873315i | \(-0.338035\pi\) | ||||
0.487155 | + | 0.873315i | \(0.338035\pi\) | |||||||
\(654\) | −1.97447e6 | −0.180512 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −899537. | −0.0816130 | ||||||||
\(657\) | −3.47795e6 | −0.314348 | ||||||||
\(658\) | 5.24928e6 | 0.472645 | ||||||||
\(659\) | 549361. | 0.0492770 | 0.0246385 | − | 0.999696i | \(-0.492157\pi\) | ||||
0.0246385 | + | 0.999696i | \(0.492157\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.35330e7 | −1.20473 | −0.602365 | − | 0.798221i | \(-0.705775\pi\) | ||||
−0.602365 | + | 0.798221i | \(0.705775\pi\) | |||||||
\(662\) | 3.04575e6 | 0.270115 | ||||||||
\(663\) | 1.87226e6 | 0.165418 | ||||||||
\(664\) | 9.32018e6 | 0.820360 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.02297e7 | 0.893671 | ||||||||
\(667\) | −2.58925e7 | −2.25351 | ||||||||
\(668\) | −2.92271e6 | −0.253422 | ||||||||
\(669\) | −1.04877e6 | −0.0905972 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.38027e6 | −0.118347 | ||||||||
\(672\) | 1.02594e6 | 0.0876389 | ||||||||
\(673\) | 1.81588e7 | 1.54543 | 0.772714 | − | 0.634755i | \(-0.218899\pi\) | ||||
0.772714 | + | 0.634755i | \(0.218899\pi\) | |||||||
\(674\) | −7.95742e6 | −0.674718 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.39351e6 | 0.117285 | ||||||||
\(677\) | 8.73920e6 | 0.732824 | 0.366412 | − | 0.930453i | \(-0.380586\pi\) | ||||
0.366412 | + | 0.930453i | \(0.380586\pi\) | |||||||
\(678\) | −860316. | −0.0718760 | ||||||||
\(679\) | 1.39454e7 | 1.16080 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.29025e6 | 0.106612 | ||||||||
\(682\) | −2.48502e6 | −0.204583 | ||||||||
\(683\) | −7.60223e6 | −0.623575 | −0.311788 | − | 0.950152i | \(-0.600928\pi\) | ||||
−0.311788 | + | 0.950152i | \(0.600928\pi\) | |||||||
\(684\) | 9.70521e6 | 0.793167 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.18790e6 | 0.745429 | ||||||||
\(687\) | −853498. | −0.0689939 | ||||||||
\(688\) | −2.29983e6 | −0.185236 | ||||||||
\(689\) | −7.51758e6 | −0.603295 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.58643e6 | −0.445081 | −0.222541 | − | 0.974923i | \(-0.571435\pi\) | ||||
−0.222541 | + | 0.974923i | \(0.571435\pi\) | |||||||
\(692\) | −1.09623e7 | −0.870237 | ||||||||
\(693\) | −2.62005e6 | −0.207242 | ||||||||
\(694\) | 2.59946e6 | 0.204873 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.61280e6 | −0.282697 | ||||||||
\(697\) | 5.76948e6 | 0.449836 | ||||||||
\(698\) | 1.09296e6 | 0.0849114 | ||||||||
\(699\) | 1.10145e6 | 0.0852652 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.78672e7 | 1.37329 | 0.686645 | − | 0.726993i | \(-0.259083\pi\) | ||||
0.686645 | + | 0.726993i | \(0.259083\pi\) | |||||||
\(702\) | −2.24629e6 | −0.172037 | ||||||||
\(703\) | −2.72555e7 | −2.08001 | ||||||||
\(704\) | −3.44653e6 | −0.262090 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.03329e7 | −0.780206 | ||||||||
\(707\) | −2.27315e6 | −0.171033 | ||||||||
\(708\) | 1.66623e6 | 0.124926 | ||||||||
\(709\) | −1.16435e7 | −0.869894 | −0.434947 | − | 0.900456i | \(-0.643233\pi\) | ||||
−0.434947 | + | 0.900456i | \(0.643233\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.77862e6 | −0.651257 | ||||||||
\(712\) | 9.22067e6 | 0.681652 | ||||||||
\(713\) | 1.55357e7 | 1.14448 | ||||||||
\(714\) | 1.27166e6 | 0.0933527 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.99680e6 | −0.437157 | ||||||||
\(717\) | −1.05543e6 | −0.0766709 | ||||||||
\(718\) | 7.29345e6 | 0.527985 | ||||||||
\(719\) | −1.67754e7 | −1.21018 | −0.605090 | − | 0.796157i | \(-0.706863\pi\) | ||||
−0.605090 | + | 0.796157i | \(0.706863\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.24997e7 | 0.895488 | ||||||||
\(722\) | 1.56508e7 | 1.11736 | ||||||||
\(723\) | 1.01600e6 | 0.0722846 | ||||||||
\(724\) | 3.02077e6 | 0.214176 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −128080. | −0.00901861 | ||||||||
\(727\) | 2.15242e7 | 1.51039 | 0.755197 | − | 0.655498i | \(-0.227541\pi\) | ||||
0.755197 | + | 0.655498i | \(0.227541\pi\) | |||||||
\(728\) | −9.30410e6 | −0.650648 | ||||||||
\(729\) | −1.26712e7 | −0.883080 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.47507e7 | 1.02099 | ||||||||
\(732\) | 403083. | 0.0278046 | ||||||||
\(733\) | 5.66516e6 | 0.389450 | 0.194725 | − | 0.980858i | \(-0.437619\pi\) | ||||
0.194725 | + | 0.980858i | \(0.437619\pi\) | |||||||
\(734\) | 7.60444e6 | 0.520987 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.55119e7 | 1.05553 | ||||||||
\(737\) | −2.05270e6 | −0.139206 | ||||||||
\(738\) | −3.42640e6 | −0.231578 | ||||||||
\(739\) | 2.04439e7 | 1.37706 | 0.688530 | − | 0.725208i | \(-0.258256\pi\) | ||||
0.688530 | + | 0.725208i | \(0.258256\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.96250e6 | 0.198204 | ||||||||
\(742\) | −5.10603e6 | −0.340466 | ||||||||
\(743\) | −2.00010e7 | −1.32917 | −0.664583 | − | 0.747214i | \(-0.731391\pi\) | ||||
−0.664583 | + | 0.747214i | \(0.731391\pi\) | |||||||
\(744\) | 2.16771e6 | 0.143572 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.21083e7 | 0.796591 | ||||||||
\(747\) | 1.15749e7 | 0.758954 | ||||||||
\(748\) | 3.11590e6 | 0.203624 | ||||||||
\(749\) | 2.00356e7 | 1.30496 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.47046e7 | 0.951381 | 0.475690 | − | 0.879613i | \(-0.342198\pi\) | ||||
0.475690 | + | 0.879613i | \(0.342198\pi\) | |||||||
\(752\) | 3.61067e6 | 0.232832 | ||||||||
\(753\) | −881108. | −0.0566294 | ||||||||
\(754\) | 1.82654e7 | 1.17004 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.54575e6 | 0.0983634 | ||||||||
\(757\) | −6.06609e6 | −0.384742 | −0.192371 | − | 0.981322i | \(-0.561618\pi\) | ||||
−0.192371 | + | 0.981322i | \(0.561618\pi\) | |||||||
\(758\) | 1.23574e7 | 0.781188 | ||||||||
\(759\) | 800723. | 0.0504520 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.60732e7 | 1.00610 | 0.503048 | − | 0.864258i | \(-0.332212\pi\) | ||||
0.503048 | + | 0.864258i | \(0.332212\pi\) | |||||||
\(762\) | −198158. | −0.0123630 | ||||||||
\(763\) | −2.05187e7 | −1.27596 | ||||||||
\(764\) | −5.26809e6 | −0.326527 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.14747e7 | −1.32238 | ||||||||
\(767\) | −2.51629e7 | −1.54445 | ||||||||
\(768\) | 2.44629e6 | 0.149660 | ||||||||
\(769\) | 1.37349e7 | 0.837547 | 0.418773 | − | 0.908091i | \(-0.362460\pi\) | ||||
0.418773 | + | 0.908091i | \(0.362460\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.74705e6 | −0.166430 | ||||||||
\(772\) | 9.55585e6 | 0.577067 | ||||||||
\(773\) | −2.30727e7 | −1.38883 | −0.694416 | − | 0.719573i | \(-0.744337\pi\) | ||||
−0.694416 | + | 0.719573i | \(0.744337\pi\) | |||||||
\(774\) | −8.76021e6 | −0.525608 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.94202e7 | 1.75385 | ||||||||
\(777\) | −2.14877e6 | −0.127684 | ||||||||
\(778\) | 1.52132e7 | 0.901096 | ||||||||
\(779\) | 9.12911e6 | 0.538995 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.47001e6 | −0.496886 | ||||||||
\(782\) | 1.92272e7 | 1.12435 | ||||||||
\(783\) | −9.06429e6 | −0.528359 | ||||||||
\(784\) | 2.12970e6 | 0.123745 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −398271. | −0.0229944 | ||||||||
\(787\) | −6.11082e6 | −0.351692 | −0.175846 | − | 0.984418i | \(-0.556266\pi\) | ||||
−0.175846 | + | 0.984418i | \(0.556266\pi\) | |||||||
\(788\) | −1.12606e7 | −0.646021 | ||||||||
\(789\) | 2.79529e6 | 0.159858 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.94040e6 | −0.508061 | ||||||||
\(792\) | −5.52744e6 | −0.313120 | ||||||||
\(793\) | −6.08723e6 | −0.343745 | ||||||||
\(794\) | 748793. | 0.0421513 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.28151e6 | −0.183566 | ||||||||
\(797\) | −2.96316e7 | −1.65238 | −0.826188 | − | 0.563395i | \(-0.809495\pi\) | ||||
−0.826188 | + | 0.563395i | \(0.809495\pi\) | |||||||
\(798\) | 2.01217e6 | 0.111855 | ||||||||
\(799\) | −2.31582e7 | −1.28333 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.14513e7 | 0.630628 | ||||||||
\(802\) | 8.04238e6 | 0.441518 | ||||||||
\(803\) | −1.76683e6 | −0.0966952 | ||||||||
\(804\) | 599455. | 0.0327052 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.09594e7 | −0.594222 | ||||||||
\(807\) | −1.89388e6 | −0.102369 | ||||||||
\(808\) | −4.79559e6 | −0.258412 | ||||||||
\(809\) | −2.07185e7 | −1.11298 | −0.556489 | − | 0.830855i | \(-0.687852\pi\) | ||||
−0.556489 | + | 0.830855i | \(0.687852\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.27788e6 | 0.228390 | 0.114195 | − | 0.993458i | \(-0.463571\pi\) | ||||
0.114195 | + | 0.993458i | \(0.463571\pi\) | |||||||
\(812\) | −1.25691e7 | −0.668979 | ||||||||
\(813\) | 583392. | 0.0309552 | ||||||||
\(814\) | 5.19677e6 | 0.274898 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 874703. | 0.0459870 | ||||||||
\(817\) | 2.33403e7 | 1.22335 | ||||||||
\(818\) | 1.67854e7 | 0.877100 | ||||||||
\(819\) | −1.15549e7 | −0.601945 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.14051e7 | −0.590531 | −0.295265 | − | 0.955415i | \(-0.595408\pi\) | ||||
−0.295265 | + | 0.955415i | \(0.595408\pi\) | |||||||
\(822\) | −850348. | −0.0438952 | ||||||||
\(823\) | 3.13322e7 | 1.61247 | 0.806233 | − | 0.591598i | \(-0.201503\pi\) | ||||
0.806233 | + | 0.591598i | \(0.201503\pi\) | |||||||
\(824\) | 2.63701e7 | 1.35299 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.70910e7 | −0.871599 | ||||||||
\(827\) | 1.84821e7 | 0.939696 | 0.469848 | − | 0.882747i | \(-0.344309\pi\) | ||||
0.469848 | + | 0.882747i | \(0.344309\pi\) | |||||||
\(828\) | 1.15687e7 | 0.586421 | ||||||||
\(829\) | 2.73374e7 | 1.38156 | 0.690782 | − | 0.723063i | \(-0.257266\pi\) | ||||
0.690782 | + | 0.723063i | \(0.257266\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −591965. | −0.0297368 | ||||||||
\(832\) | −1.51998e7 | −0.761255 | ||||||||
\(833\) | −1.36596e7 | −0.682062 | ||||||||
\(834\) | 42840.8 | 0.00213276 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.93032e6 | 0.243983 | ||||||||
\(837\) | 5.43864e6 | 0.268335 | ||||||||
\(838\) | −1.82351e7 | −0.897012 | ||||||||
\(839\) | 3.10089e6 | 0.152083 | 0.0760417 | − | 0.997105i | \(-0.475772\pi\) | ||||
0.0760417 | + | 0.997105i | \(0.475772\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.31941e7 | 2.59342 | ||||||||
\(842\) | −1.60845e7 | −0.781859 | ||||||||
\(843\) | −995452. | −0.0482449 | ||||||||
\(844\) | 6.37320e6 | 0.307965 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.37533e7 | 0.660664 | ||||||||
\(847\) | −1.33101e6 | −0.0637487 | ||||||||
\(848\) | −3.51214e6 | −0.167719 | ||||||||
\(849\) | 22977.7 | 0.00109405 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.24889e7 | −1.53784 | ||||||||
\(852\) | 2.47352e6 | 0.116739 | ||||||||
\(853\) | −1.43661e7 | −0.676032 | −0.338016 | − | 0.941140i | \(-0.609756\pi\) | ||||
−0.338016 | + | 0.941140i | \(0.609756\pi\) | |||||||
\(854\) | −4.13452e6 | −0.193991 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.22685e7 | 1.97166 | ||||||||
\(857\) | 1.49076e7 | 0.693353 | 0.346677 | − | 0.937985i | \(-0.387310\pi\) | ||||
0.346677 | + | 0.937985i | \(0.387310\pi\) | |||||||
\(858\) | −564856. | −0.0261951 | ||||||||
\(859\) | −4.03264e7 | −1.86469 | −0.932344 | − | 0.361571i | \(-0.882240\pi\) | ||||
−0.932344 | + | 0.361571i | \(0.882240\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 719721. | 0.0330869 | ||||||||
\(862\) | 1.22145e6 | 0.0559898 | ||||||||
\(863\) | −327785. | −0.0149817 | −0.00749086 | − | 0.999972i | \(-0.502384\pi\) | ||||
−0.00749086 | + | 0.999972i | \(0.502384\pi\) | |||||||
\(864\) | 5.43030e6 | 0.247480 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.10141e7 | 0.499061 | ||||||||
\(867\) | −2.49478e6 | −0.112716 | ||||||||
\(868\) | 7.54153e6 | 0.339751 | ||||||||
\(869\) | −4.45960e6 | −0.200330 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.05278e6 | −0.404331 | ||||||||
\(872\) | −4.32876e7 | −1.92785 | ||||||||
\(873\) | 3.65374e7 | 1.62257 | ||||||||
\(874\) | 3.04235e7 | 1.34719 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 515970. | 0.0227177 | ||||||||
\(877\) | −1.74545e7 | −0.766317 | −0.383159 | − | 0.923683i | \(-0.625164\pi\) | ||||
−0.383159 | + | 0.923683i | \(0.625164\pi\) | |||||||
\(878\) | 7.34688e6 | 0.321638 | ||||||||
\(879\) | −744124. | −0.0324843 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.31899e7 | −1.44068 | −0.720339 | − | 0.693622i | \(-0.756014\pi\) | ||||
−0.720339 | + | 0.693622i | \(0.756014\pi\) | |||||||
\(882\) | 8.11218e6 | 0.351128 | ||||||||
\(883\) | −97139.3 | −0.00419269 | −0.00209635 | − | 0.999998i | \(-0.500667\pi\) | ||||
−0.00209635 | + | 0.999998i | \(0.500667\pi\) | |||||||
\(884\) | 1.37417e7 | 0.591438 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.29134e6 | −0.0980631 | ||||||||
\(887\) | −1.86238e6 | −0.0794803 | −0.0397401 | − | 0.999210i | \(-0.512653\pi\) | ||||
−0.0397401 | + | 0.999210i | \(0.512653\pi\) | |||||||
\(888\) | −4.53320e6 | −0.192918 | ||||||||
\(889\) | −2.05926e6 | −0.0873890 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.72306e6 | −0.283709 | ||||||||
\(892\) | −7.69755e6 | −0.323922 | ||||||||
\(893\) | −3.66435e7 | −1.53769 | ||||||||
\(894\) | −630046. | −0.0263650 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.63840e6 | 0.193018 | ||||||||
\(897\) | 3.53134e6 | 0.146541 | ||||||||
\(898\) | 2.09285e7 | 0.866060 | ||||||||
\(899\) | −4.42237e7 | −1.82497 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.25263e7 | 0.924437 | ||||||||
\(902\) | −1.74063e6 | −0.0712346 | ||||||||
\(903\) | 1.84010e6 | 0.0750970 | ||||||||
\(904\) | −1.88613e7 | −0.767627 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.05107e6 | −0.0425412 | ||||||||
\(907\) | 3.38081e7 | 1.36459 | 0.682295 | − | 0.731077i | \(-0.260982\pi\) | ||||
0.682295 | + | 0.731077i | \(0.260982\pi\) | |||||||
\(908\) | 9.46994e6 | 0.381182 | ||||||||
\(909\) | −5.95571e6 | −0.239069 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.30899e7 | −1.72020 | −0.860102 | − | 0.510123i | \(-0.829600\pi\) | ||||
−0.860102 | + | 0.510123i | \(0.829600\pi\) | |||||||
\(912\) | 1.38405e6 | 0.0551017 | ||||||||
\(913\) | 5.88013e6 | 0.233458 | ||||||||
\(914\) | −2.97512e7 | −1.17798 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.26434e6 | −0.246681 | ||||||||
\(917\) | −4.13883e6 | −0.162538 | ||||||||
\(918\) | 6.73095e6 | 0.263615 | ||||||||
\(919\) | 1.53572e7 | 0.599824 | 0.299912 | − | 0.953967i | \(-0.403043\pi\) | ||||
0.299912 | + | 0.953967i | \(0.403043\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.80160e6 | 0.0699857 | ||||||||
\(922\) | −1.07064e7 | −0.414777 | ||||||||
\(923\) | −3.73543e7 | −1.44323 | ||||||||
\(924\) | 388697. | 0.0149772 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.53121e7 | 0.970064 | ||||||||
\(927\) | 3.27495e7 | 1.25171 | ||||||||
\(928\) | −4.41559e7 | −1.68313 | ||||||||
\(929\) | 3.93862e7 | 1.49729 | 0.748644 | − | 0.662972i | \(-0.230705\pi\) | ||||
0.748644 | + | 0.662972i | \(0.230705\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.16137e7 | −0.817248 | ||||||||
\(932\) | 8.08420e6 | 0.304858 | ||||||||
\(933\) | −5.30765e6 | −0.199617 | ||||||||
\(934\) | 1.86895e7 | 0.701019 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.43770e7 | −0.909476 | ||||||||
\(937\) | −3.81263e7 | −1.41865 | −0.709325 | − | 0.704882i | \(-0.751000\pi\) | ||||
−0.709325 | + | 0.704882i | \(0.751000\pi\) | |||||||
\(938\) | −6.14876e6 | −0.228182 | ||||||||
\(939\) | 951762. | 0.0352261 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.40994e7 | 1.62352 | 0.811761 | − | 0.583989i | \(-0.198509\pi\) | ||||
0.811761 | + | 0.583989i | \(0.198509\pi\) | |||||||
\(942\) | −1.29295e6 | −0.0474739 | ||||||||
\(943\) | 1.08820e7 | 0.398501 | ||||||||
\(944\) | −1.17559e7 | −0.429363 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.45025e6 | −0.161680 | ||||||||
\(947\) | −3.53205e7 | −1.27983 | −0.639915 | − | 0.768446i | \(-0.721031\pi\) | ||||
−0.639915 | + | 0.768446i | \(0.721031\pi\) | |||||||
\(948\) | 1.30235e6 | 0.0470659 | ||||||||
\(949\) | −7.79202e6 | −0.280857 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.65962e6 | −0.167070 | ||||||||
\(952\) | 2.78795e7 | 0.996995 | ||||||||
\(953\) | 1.95033e7 | 0.695626 | 0.347813 | − | 0.937564i | \(-0.386924\pi\) | ||||
0.347813 | + | 0.937564i | \(0.386924\pi\) | |||||||
\(954\) | −1.33780e7 | −0.475904 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.74642e6 | −0.274130 | ||||||||
\(957\) | −2.27933e6 | −0.0804501 | ||||||||
\(958\) | −3.17359e6 | −0.111722 | ||||||||
\(959\) | −8.83680e6 | −0.310276 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.09459e6 | −0.0731630 | ||||||||
\(962\) | 2.29187e7 | 0.798458 | ||||||||
\(963\) | 5.24939e7 | 1.82408 | ||||||||
\(964\) | 7.45700e6 | 0.258447 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.39853e6 | 0.0826993 | ||||||||
\(967\) | −9.54346e6 | −0.328201 | −0.164100 | − | 0.986444i | \(-0.552472\pi\) | ||||
−0.164100 | + | 0.986444i | \(0.552472\pi\) | |||||||
\(968\) | −2.80798e6 | −0.0963176 | ||||||||
\(969\) | −8.87707e6 | −0.303711 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.16714e7 | −1.41837 | −0.709186 | − | 0.705021i | \(-0.750938\pi\) | ||||
−0.709186 | + | 0.705021i | \(0.750938\pi\) | |||||||
\(972\) | 6.09511e6 | 0.206926 | ||||||||
\(973\) | 445201. | 0.0150756 | ||||||||
\(974\) | 7.31457e6 | 0.247054 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.84389e6 | −0.0955628 | ||||||||
\(977\) | 2.59092e7 | 0.868395 | 0.434197 | − | 0.900818i | \(-0.357032\pi\) | ||||
0.434197 | + | 0.900818i | \(0.357032\pi\) | |||||||
\(978\) | −412432. | −0.0137881 | ||||||||
\(979\) | 5.81734e6 | 0.193985 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.37595e7 | −1.78354 | ||||||||
\(982\) | −2.15469e7 | −0.713028 | ||||||||
\(983\) | 1.17591e6 | 0.0388143 | 0.0194071 | − | 0.999812i | \(-0.493822\pi\) | ||||
0.0194071 | + | 0.999812i | \(0.493822\pi\) | |||||||
\(984\) | 1.51837e6 | 0.0499909 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.47319e7 | −1.79287 | ||||||||
\(987\) | −2.88891e6 | −0.0943931 | ||||||||
\(988\) | 2.17436e7 | 0.708662 | ||||||||
\(989\) | 2.78219e7 | 0.904472 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.35602e7 | −1.08553 | −0.542763 | − | 0.839886i | \(-0.682622\pi\) | ||||
−0.542763 | + | 0.839886i | \(0.682622\pi\) | |||||||
\(992\) | 2.64939e7 | 0.854803 | ||||||||
\(993\) | −1.67621e6 | −0.0539454 | ||||||||
\(994\) | −2.53715e7 | −0.814480 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.71719e6 | −0.0548491 | ||||||||
\(997\) | 4.73106e7 | 1.50737 | 0.753686 | − | 0.657235i | \(-0.228274\pi\) | ||||
0.753686 | + | 0.657235i | \(0.228274\pi\) | |||||||
\(998\) | −1.53583e7 | −0.488109 | ||||||||
\(999\) | −1.13735e7 | −0.360562 |
(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 | 275.6.a.l.1.10 | 14 | ||
5.2 | odd | 4 | 55.6.b.b.34.10 | yes | 14 | ||
5.3 | odd | 4 | 55.6.b.b.34.5 | ✓ | 14 | ||
5.4 | even | 2 | inner | 275.6.a.l.1.5 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.6.b.b.34.5 | ✓ | 14 | 5.3 | odd | 4 | ||
55.6.b.b.34.10 | yes | 14 | 5.2 | odd | 4 | ||
275.6.a.l.1.5 | 14 | 5.4 | even | 2 | inner | ||
275.6.a.l.1.10 | 14 | 1.1 | even | 1 | trivial |