Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,6,Mod(1,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, 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("1089.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.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: | \(174.657979776\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 363) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1089.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 9.00000 | 1.59099 | 0.795495 | − | 0.605960i | \(-0.207211\pi\) | ||||
0.795495 | + | 0.605960i | \(0.207211\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 49.0000 | 1.53125 | ||||||||
\(5\) | −24.0000 | −0.429325 | −0.214663 | − | 0.976688i | \(-0.568865\pi\) | ||||
−0.214663 | + | 0.976688i | \(0.568865\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 72.0000 | 0.555376 | 0.277688 | − | 0.960671i | \(-0.410432\pi\) | ||||
0.277688 | + | 0.960671i | \(0.410432\pi\) | |||||||
\(8\) | 153.000 | 0.845214 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −216.000 | −0.683052 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 306.000 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(14\) | 648.000 | 0.883598 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −191.000 | −0.186523 | ||||||||
\(17\) | −1206.00 | −1.01210 | −0.506052 | − | 0.862503i | \(-0.668896\pi\) | ||||
−0.506052 | + | 0.862503i | \(0.668896\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −774.000 | −0.491878 | −0.245939 | − | 0.969285i | \(-0.579096\pi\) | ||||
−0.245939 | + | 0.969285i | \(0.579096\pi\) | |||||||
\(20\) | −1176.00 | −0.657404 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4626.00 | 1.82342 | 0.911709 | − | 0.410838i | \(-0.134764\pi\) | ||||
0.911709 | + | 0.410838i | \(0.134764\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2549.00 | −0.815680 | ||||||||
\(26\) | 2754.00 | 0.798970 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3528.00 | 0.850420 | ||||||||
\(29\) | 7686.00 | 1.69709 | 0.848546 | − | 0.529122i | \(-0.177478\pi\) | ||||
0.848546 | + | 0.529122i | \(0.177478\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5428.00 | 1.01446 | 0.507231 | − | 0.861810i | \(-0.330669\pi\) | ||||
0.507231 | + | 0.861810i | \(0.330669\pi\) | |||||||
\(32\) | −6615.00 | −1.14197 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −10854.0 | −1.61025 | ||||||||
\(35\) | −1728.00 | −0.238437 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3454.00 | 0.414780 | 0.207390 | − | 0.978258i | \(-0.433503\pi\) | ||||
0.207390 | + | 0.978258i | \(0.433503\pi\) | |||||||
\(38\) | −6966.00 | −0.782572 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3672.00 | −0.362871 | ||||||||
\(41\) | −7866.00 | −0.730793 | −0.365396 | − | 0.930852i | \(-0.619067\pi\) | ||||
−0.365396 | + | 0.930852i | \(0.619067\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 15786.0 | 1.30197 | 0.650985 | − | 0.759091i | \(-0.274356\pi\) | ||||
0.650985 | + | 0.759091i | \(0.274356\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 41634.0 | 2.90104 | ||||||||
\(47\) | 6402.00 | 0.422738 | 0.211369 | − | 0.977406i | \(-0.432208\pi\) | ||||
0.211369 | + | 0.977406i | \(0.432208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11623.0 | −0.691557 | ||||||||
\(50\) | −22941.0 | −1.29774 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 14994.0 | 0.768970 | ||||||||
\(53\) | 21684.0 | 1.06035 | 0.530176 | − | 0.847888i | \(-0.322126\pi\) | ||||
0.530176 | + | 0.847888i | \(0.322126\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11016.0 | 0.469412 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 69174.0 | 2.70006 | ||||||||
\(59\) | 27420.0 | 1.02550 | 0.512752 | − | 0.858537i | \(-0.328626\pi\) | ||||
0.512752 | + | 0.858537i | \(0.328626\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 52866.0 | 1.81908 | 0.909540 | − | 0.415616i | \(-0.136434\pi\) | ||||
0.909540 | + | 0.415616i | \(0.136434\pi\) | |||||||
\(62\) | 48852.0 | 1.61400 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −53423.0 | −1.63034 | ||||||||
\(65\) | −7344.00 | −0.215600 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 25012.0 | 0.680709 | 0.340354 | − | 0.940297i | \(-0.389453\pi\) | ||||
0.340354 | + | 0.940297i | \(0.389453\pi\) | |||||||
\(68\) | −59094.0 | −1.54978 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −15552.0 | −0.379351 | ||||||||
\(71\) | −65058.0 | −1.53163 | −0.765817 | − | 0.643059i | \(-0.777665\pi\) | ||||
−0.765817 | + | 0.643059i | \(0.777665\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −26676.0 | −0.585887 | −0.292943 | − | 0.956130i | \(-0.594635\pi\) | ||||
−0.292943 | + | 0.956130i | \(0.594635\pi\) | |||||||
\(74\) | 31086.0 | 0.659911 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −37926.0 | −0.753187 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −18612.0 | −0.335525 | −0.167763 | − | 0.985827i | \(-0.553654\pi\) | ||||
−0.167763 | + | 0.985827i | \(0.553654\pi\) | |||||||
\(80\) | 4584.00 | 0.0800792 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −70794.0 | −1.16268 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28944.0 | 0.434521 | ||||||||
\(86\) | 142074. | 2.07142 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 41670.0 | 0.557633 | 0.278817 | − | 0.960344i | \(-0.410058\pi\) | ||||
0.278817 | + | 0.960344i | \(0.410058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 22032.0 | 0.278901 | ||||||||
\(92\) | 226674. | 2.79211 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 57618.0 | 0.672572 | ||||||||
\(95\) | 18576.0 | 0.211175 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 40694.0 | 0.439138 | 0.219569 | − | 0.975597i | \(-0.429535\pi\) | ||||
0.219569 | + | 0.975597i | \(0.429535\pi\) | |||||||
\(98\) | −104607. | −1.10026 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −124901. | −1.24901 | ||||||||
\(101\) | 76554.0 | 0.746731 | 0.373366 | − | 0.927684i | \(-0.378204\pi\) | ||||
0.373366 | + | 0.927684i | \(0.378204\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −81748.0 | −0.759249 | −0.379624 | − | 0.925141i | \(-0.623947\pi\) | ||||
−0.379624 | + | 0.925141i | \(0.623947\pi\) | |||||||
\(104\) | 46818.0 | 0.424453 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 195156. | 1.68701 | ||||||||
\(107\) | 53748.0 | 0.453840 | 0.226920 | − | 0.973913i | \(-0.427134\pi\) | ||||
0.226920 | + | 0.973913i | \(0.427134\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −213390. | −1.72031 | −0.860157 | − | 0.510029i | \(-0.829635\pi\) | ||||
−0.860157 | + | 0.510029i | \(0.829635\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −13752.0 | −0.103591 | ||||||||
\(113\) | 141594. | 1.04315 | 0.521577 | − | 0.853204i | \(-0.325344\pi\) | ||||
0.521577 | + | 0.853204i | \(0.325344\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −111024. | −0.782839 | ||||||||
\(116\) | 376614. | 2.59867 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 246780. | 1.63157 | ||||||||
\(119\) | −86832.0 | −0.562098 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 475794. | 2.89414 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 265972. | 1.55339 | ||||||||
\(125\) | 136176. | 0.779517 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 196812. | 1.08279 | 0.541393 | − | 0.840770i | \(-0.317897\pi\) | ||||
0.541393 | + | 0.840770i | \(0.317897\pi\) | |||||||
\(128\) | −269127. | −1.45189 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −66096.0 | −0.343018 | ||||||||
\(131\) | 68436.0 | 0.348423 | 0.174211 | − | 0.984708i | \(-0.444262\pi\) | ||||
0.174211 | + | 0.984708i | \(0.444262\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −55728.0 | −0.273177 | ||||||||
\(134\) | 225108. | 1.08300 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −184518. | −0.855444 | ||||||||
\(137\) | 106806. | 0.486177 | 0.243088 | − | 0.970004i | \(-0.421839\pi\) | ||||
0.243088 | + | 0.970004i | \(0.421839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 362322. | 1.59059 | 0.795294 | − | 0.606224i | \(-0.207316\pi\) | ||||
0.795294 | + | 0.606224i | \(0.207316\pi\) | |||||||
\(140\) | −84672.0 | −0.365107 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −585522. | −2.43681 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −184464. | −0.728604 | ||||||||
\(146\) | −240084. | −0.932140 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 169246. | 0.635132 | ||||||||
\(149\) | 149814. | 0.552824 | 0.276412 | − | 0.961039i | \(-0.410855\pi\) | ||||
0.276412 | + | 0.961039i | \(0.410855\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −335772. | −1.19840 | −0.599200 | − | 0.800599i | \(-0.704515\pi\) | ||||
−0.599200 | + | 0.800599i | \(0.704515\pi\) | |||||||
\(152\) | −118422. | −0.415742 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −130272. | −0.435534 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 155458. | 0.503343 | 0.251671 | − | 0.967813i | \(-0.419020\pi\) | ||||
0.251671 | + | 0.967813i | \(0.419020\pi\) | |||||||
\(158\) | −167508. | −0.533818 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 158760. | 0.490277 | ||||||||
\(161\) | 333072. | 1.01268 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −213964. | −0.630771 | −0.315385 | − | 0.948964i | \(-0.602134\pi\) | ||||
−0.315385 | + | 0.948964i | \(0.602134\pi\) | |||||||
\(164\) | −385434. | −1.11903 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 425880. | 1.18167 | 0.590835 | − | 0.806793i | \(-0.298798\pi\) | ||||
0.590835 | + | 0.806793i | \(0.298798\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −277657. | −0.747811 | ||||||||
\(170\) | 260496. | 0.691319 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 773514. | 1.99364 | ||||||||
\(173\) | 723438. | 1.83775 | 0.918874 | − | 0.394551i | \(-0.129100\pi\) | ||||
0.918874 | + | 0.394551i | \(0.129100\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −183528. | −0.453009 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 375030. | 0.887189 | ||||||||
\(179\) | −620112. | −1.44656 | −0.723282 | − | 0.690553i | \(-0.757367\pi\) | ||||
−0.723282 | + | 0.690553i | \(0.757367\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 584354. | 1.32580 | 0.662902 | − | 0.748706i | \(-0.269324\pi\) | ||||
0.662902 | + | 0.748706i | \(0.269324\pi\) | |||||||
\(182\) | 198288. | 0.443729 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 707778. | 1.54118 | ||||||||
\(185\) | −82896.0 | −0.178076 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 313698. | 0.647317 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 167184. | 0.335978 | ||||||||
\(191\) | −206310. | −0.409201 | −0.204601 | − | 0.978846i | \(-0.565590\pi\) | ||||
−0.204601 | + | 0.978846i | \(0.565590\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 915300. | 1.76877 | 0.884383 | − | 0.466763i | \(-0.154580\pi\) | ||||
0.884383 | + | 0.466763i | \(0.154580\pi\) | |||||||
\(194\) | 366246. | 0.698664 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −569527. | −1.05895 | ||||||||
\(197\) | 219978. | 0.403844 | 0.201922 | − | 0.979402i | \(-0.435281\pi\) | ||||
0.201922 | + | 0.979402i | \(0.435281\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 563056. | 1.00790 | 0.503952 | − | 0.863732i | \(-0.331879\pi\) | ||||
0.503952 | + | 0.863732i | \(0.331879\pi\) | |||||||
\(200\) | −389997. | −0.689424 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 688986. | 1.18804 | ||||||||
\(203\) | 553392. | 0.942525 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 188784. | 0.313748 | ||||||||
\(206\) | −735732. | −1.20796 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −58446.0 | −0.0936691 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 220662. | 0.341210 | 0.170605 | − | 0.985340i | \(-0.445428\pi\) | ||||
0.170605 | + | 0.985340i | \(0.445428\pi\) | |||||||
\(212\) | 1.06252e6 | 1.62366 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 483732. | 0.722055 | ||||||||
\(215\) | −378864. | −0.558968 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 390816. | 0.563408 | ||||||||
\(218\) | −1.92051e6 | −2.73700 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −369036. | −0.508262 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.28150e6 | −1.72566 | −0.862830 | − | 0.505495i | \(-0.831310\pi\) | ||||
−0.862830 | + | 0.505495i | \(0.831310\pi\) | |||||||
\(224\) | −476280. | −0.634223 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.27435e6 | 1.65965 | ||||||||
\(227\) | 1.45480e6 | 1.87386 | 0.936931 | − | 0.349515i | \(-0.113654\pi\) | ||||
0.936931 | + | 0.349515i | \(0.113654\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4382.00 | −0.00552184 | −0.00276092 | − | 0.999996i | \(-0.500879\pi\) | ||||
−0.00276092 | + | 0.999996i | \(0.500879\pi\) | |||||||
\(230\) | −999216. | −1.24549 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.17596e6 | 1.43441 | ||||||||
\(233\) | −1.07231e6 | −1.29399 | −0.646997 | − | 0.762493i | \(-0.723975\pi\) | ||||
−0.646997 | + | 0.762493i | \(0.723975\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −153648. | −0.181492 | ||||||||
\(236\) | 1.34358e6 | 1.57030 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −781488. | −0.894293 | ||||||||
\(239\) | 828648. | 0.938373 | 0.469186 | − | 0.883099i | \(-0.344547\pi\) | ||||
0.469186 | + | 0.883099i | \(0.344547\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −601200. | −0.666770 | −0.333385 | − | 0.942791i | \(-0.608191\pi\) | ||||
−0.333385 | + | 0.942791i | \(0.608191\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.59043e6 | 2.78547 | ||||||||
\(245\) | 278952. | 0.296903 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −236844. | −0.247013 | ||||||||
\(248\) | 830484. | 0.857437 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.22558e6 | 1.24020 | ||||||||
\(251\) | −1.13940e6 | −1.14154 | −0.570771 | − | 0.821109i | \(-0.693356\pi\) | ||||
−0.570771 | + | 0.821109i | \(0.693356\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.77131e6 | 1.72270 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −712607. | −0.679595 | ||||||||
\(257\) | 466542. | 0.440614 | 0.220307 | − | 0.975431i | \(-0.429294\pi\) | ||||
0.220307 | + | 0.975431i | \(0.429294\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 248688. | 0.230359 | ||||||||
\(260\) | −359856. | −0.330138 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 615924. | 0.554337 | ||||||||
\(263\) | −720504. | −0.642313 | −0.321157 | − | 0.947026i | \(-0.604072\pi\) | ||||
−0.321157 | + | 0.947026i | \(0.604072\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −520416. | −0.455235 | ||||||||
\(266\) | −501552. | −0.434622 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.22559e6 | 1.04234 | ||||||||
\(269\) | 1.22492e6 | 1.03212 | 0.516058 | − | 0.856554i | \(-0.327399\pi\) | ||||
0.516058 | + | 0.856554i | \(0.327399\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.37840e6 | −1.14013 | −0.570064 | − | 0.821601i | \(-0.693081\pi\) | ||||
−0.570064 | + | 0.821601i | \(0.693081\pi\) | |||||||
\(272\) | 230346. | 0.188781 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 961254. | 0.773503 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.33627e6 | −1.82947 | −0.914733 | − | 0.404059i | \(-0.867599\pi\) | ||||
−0.914733 | + | 0.404059i | \(0.867599\pi\) | |||||||
\(278\) | 3.26090e6 | 2.53061 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −264384. | −0.201530 | ||||||||
\(281\) | −2.37652e6 | −1.79546 | −0.897731 | − | 0.440545i | \(-0.854785\pi\) | ||||
−0.897731 | + | 0.440545i | \(0.854785\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.11433e6 | −0.827077 | −0.413539 | − | 0.910487i | \(-0.635707\pi\) | ||||
−0.413539 | + | 0.910487i | \(0.635707\pi\) | |||||||
\(284\) | −3.18784e6 | −2.34531 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −566352. | −0.405865 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34579.0 | 0.0243539 | ||||||||
\(290\) | −1.66018e6 | −1.15920 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.30712e6 | −0.897139 | ||||||||
\(293\) | −558558. | −0.380101 | −0.190051 | − | 0.981774i | \(-0.560865\pi\) | ||||
−0.190051 | + | 0.981774i | \(0.560865\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −658080. | −0.440275 | ||||||||
\(296\) | 528462. | 0.350578 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.34833e6 | 0.879537 | ||||||||
\(299\) | 1.41556e6 | 0.915691 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.13659e6 | 0.723083 | ||||||||
\(302\) | −3.02195e6 | −1.90664 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 147834. | 0.0917467 | ||||||||
\(305\) | −1.26878e6 | −0.780977 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.22369e6 | −0.741015 | −0.370507 | − | 0.928830i | \(-0.620816\pi\) | ||||
−0.370507 | + | 0.928830i | \(0.620816\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.17245e6 | −0.692930 | ||||||||
\(311\) | 1.91858e6 | 1.12481 | 0.562404 | − | 0.826863i | \(-0.309877\pi\) | ||||
0.562404 | + | 0.826863i | \(0.309877\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −801626. | −0.462499 | −0.231250 | − | 0.972894i | \(-0.574281\pi\) | ||||
−0.231250 | + | 0.972894i | \(0.574281\pi\) | |||||||
\(314\) | 1.39912e6 | 0.800814 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −911988. | −0.513773 | ||||||||
\(317\) | 2.34522e6 | 1.31080 | 0.655398 | − | 0.755283i | \(-0.272501\pi\) | ||||
0.655398 | + | 0.755283i | \(0.272501\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.28215e6 | 0.699946 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.99765e6 | 1.61117 | ||||||||
\(323\) | 933444. | 0.497831 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −779994. | −0.409622 | ||||||||
\(326\) | −1.92568e6 | −1.00355 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.20350e6 | −0.617676 | ||||||||
\(329\) | 460944. | 0.234779 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.31005e6 | 1.66060 | 0.830300 | − | 0.557317i | \(-0.188169\pi\) | ||||
0.830300 | + | 0.557317i | \(0.188169\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.83292e6 | 1.88002 | ||||||||
\(335\) | −600288. | −0.292245 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.44803e6 | 0.694548 | 0.347274 | − | 0.937764i | \(-0.387107\pi\) | ||||
0.347274 | + | 0.937764i | \(0.387107\pi\) | |||||||
\(338\) | −2.49891e6 | −1.18976 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.41826e6 | 0.665361 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.04696e6 | −0.939451 | ||||||||
\(344\) | 2.41526e6 | 1.10044 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.51094e6 | 2.92384 | ||||||||
\(347\) | 391752. | 0.174658 | 0.0873288 | − | 0.996180i | \(-0.472167\pi\) | ||||
0.0873288 | + | 0.996180i | \(0.472167\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.65603e6 | −1.16726 | −0.583632 | − | 0.812019i | \(-0.698369\pi\) | ||||
−0.583632 | + | 0.812019i | \(0.698369\pi\) | |||||||
\(350\) | −1.65175e6 | −0.720734 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.40614e6 | 0.600610 | 0.300305 | − | 0.953843i | \(-0.402912\pi\) | ||||
0.300305 | + | 0.953843i | \(0.402912\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.56139e6 | 0.657569 | ||||||||
\(356\) | 2.04183e6 | 0.853876 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.58101e6 | −2.30147 | ||||||||
\(359\) | −3.14755e6 | −1.28895 | −0.644476 | − | 0.764624i | \(-0.722924\pi\) | ||||
−0.644476 | + | 0.764624i | \(0.722924\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.87702e6 | −0.758057 | ||||||||
\(362\) | 5.25919e6 | 2.10934 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.07957e6 | 0.427068 | ||||||||
\(365\) | 640224. | 0.251536 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.74806e6 | −0.677470 | −0.338735 | − | 0.940882i | \(-0.609999\pi\) | ||||
−0.338735 | + | 0.940882i | \(0.609999\pi\) | |||||||
\(368\) | −883566. | −0.340110 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −746064. | −0.283316 | ||||||||
\(371\) | 1.56125e6 | 0.588894 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.30925e6 | 1.23156 | 0.615782 | − | 0.787917i | \(-0.288840\pi\) | ||||
0.615782 | + | 0.787917i | \(0.288840\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 979506. | 0.357304 | ||||||||
\(377\) | 2.35192e6 | 0.852253 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.10254e6 | −1.46708 | −0.733542 | − | 0.679644i | \(-0.762134\pi\) | ||||
−0.733542 | + | 0.679644i | \(0.762134\pi\) | |||||||
\(380\) | 910224. | 0.323362 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.85679e6 | −0.651035 | ||||||||
\(383\) | 1.12151e6 | 0.390668 | 0.195334 | − | 0.980737i | \(-0.437421\pi\) | ||||
0.195334 | + | 0.980737i | \(0.437421\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.23770e6 | 2.81409 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.99401e6 | 0.672430 | ||||||||
\(389\) | 3.08818e6 | 1.03473 | 0.517366 | − | 0.855764i | \(-0.326913\pi\) | ||||
0.517366 | + | 0.855764i | \(0.326913\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.57896e6 | −1.84549 | ||||||||
\(392\) | −1.77832e6 | −0.584513 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.97980e6 | 0.642512 | ||||||||
\(395\) | 446688. | 0.144049 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 506594. | 0.161318 | 0.0806592 | − | 0.996742i | \(-0.474297\pi\) | ||||
0.0806592 | + | 0.996742i | \(0.474297\pi\) | |||||||
\(398\) | 5.06750e6 | 1.60356 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 486859. | 0.152143 | ||||||||
\(401\) | 2.44671e6 | 0.759839 | 0.379919 | − | 0.925020i | \(-0.375952\pi\) | ||||
0.379919 | + | 0.925020i | \(0.375952\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.66097e6 | 0.509447 | ||||||||
\(404\) | 3.75115e6 | 1.14343 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.98053e6 | 1.49955 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.48818e6 | −0.735483 | −0.367742 | − | 0.929928i | \(-0.619869\pi\) | ||||
−0.367742 | + | 0.929928i | \(0.619869\pi\) | |||||||
\(410\) | 1.69906e6 | 0.499170 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.00565e6 | −1.16260 | ||||||||
\(413\) | 1.97424e6 | 0.569541 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.02419e6 | −0.573480 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −405672. | −0.112886 | −0.0564430 | − | 0.998406i | \(-0.517976\pi\) | ||||
−0.0564430 | + | 0.998406i | \(0.517976\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.36275e6 | −1.19965 | −0.599825 | − | 0.800131i | \(-0.704763\pi\) | ||||
−0.599825 | + | 0.800131i | \(0.704763\pi\) | |||||||
\(422\) | 1.98596e6 | 0.542861 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.31765e6 | 0.896223 | ||||||||
\(425\) | 3.07409e6 | 0.825553 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.80635e6 | 1.01027 | ||||||||
\(428\) | 2.63365e6 | 0.694943 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.40978e6 | −0.889313 | ||||||||
\(431\) | −5.71615e6 | −1.48221 | −0.741106 | − | 0.671388i | \(-0.765699\pi\) | ||||
−0.741106 | + | 0.671388i | \(0.765699\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.84150e6 | −1.49729 | −0.748643 | − | 0.662973i | \(-0.769294\pi\) | ||||
−0.748643 | + | 0.662973i | \(0.769294\pi\) | |||||||
\(434\) | 3.51734e6 | 0.896377 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.04561e7 | −2.63423 | ||||||||
\(437\) | −3.58052e6 | −0.896898 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 393336. | 0.0974097 | 0.0487049 | − | 0.998813i | \(-0.484491\pi\) | ||||
0.0487049 | + | 0.998813i | \(0.484491\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.32132e6 | −0.808641 | ||||||||
\(443\) | 1.65260e6 | 0.400092 | 0.200046 | − | 0.979787i | \(-0.435891\pi\) | ||||
0.200046 | + | 0.979787i | \(0.435891\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.00008e6 | −0.239406 | ||||||||
\(446\) | −1.15335e7 | −2.74551 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.84646e6 | −0.905453 | ||||||||
\(449\) | −1.73199e6 | −0.405443 | −0.202721 | − | 0.979236i | \(-0.564979\pi\) | ||||
−0.202721 | + | 0.979236i | \(0.564979\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.93811e6 | 1.59733 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.30932e7 | 2.98130 | ||||||||
\(455\) | −528768. | −0.119739 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.66489e6 | −1.26882 | −0.634411 | − | 0.772996i | \(-0.718757\pi\) | ||||
−0.634411 | + | 0.772996i | \(0.718757\pi\) | |||||||
\(458\) | −39438.0 | −0.00878519 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.44018e6 | −1.19872 | ||||||||
\(461\) | −827982. | −0.181455 | −0.0907274 | − | 0.995876i | \(-0.528919\pi\) | ||||
−0.0907274 | + | 0.995876i | \(0.528919\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.24255e6 | −0.702965 | −0.351483 | − | 0.936194i | \(-0.614322\pi\) | ||||
−0.351483 | + | 0.936194i | \(0.614322\pi\) | |||||||
\(464\) | −1.46803e6 | −0.316547 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.65083e6 | −2.05873 | ||||||||
\(467\) | 6.29414e6 | 1.33550 | 0.667751 | − | 0.744385i | \(-0.267257\pi\) | ||||
0.667751 | + | 0.744385i | \(0.267257\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.80086e6 | 0.378050 | ||||||||
\(470\) | −1.38283e6 | −0.288752 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.19526e6 | 0.866770 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.97293e6 | 0.401215 | ||||||||
\(476\) | −4.25477e6 | −0.860713 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.45783e6 | 1.49294 | ||||||||
\(479\) | −7.28863e6 | −1.45147 | −0.725734 | − | 0.687976i | \(-0.758500\pi\) | ||||
−0.725734 | + | 0.687976i | \(0.758500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.05692e6 | 0.208296 | ||||||||
\(482\) | −5.41080e6 | −1.06083 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −976656. | −0.188533 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.01570e6 | −0.385126 | −0.192563 | − | 0.981285i | \(-0.561680\pi\) | ||||
−0.192563 | + | 0.981285i | \(0.561680\pi\) | |||||||
\(488\) | 8.08850e6 | 1.53751 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.51057e6 | 0.472369 | ||||||||
\(491\) | −538596. | −0.100823 | −0.0504115 | − | 0.998729i | \(-0.516053\pi\) | ||||
−0.0504115 | + | 0.998729i | \(0.516053\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.26932e6 | −1.71763 | ||||||||
\(494\) | −2.13160e6 | −0.392995 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.03675e6 | −0.189221 | ||||||||
\(497\) | −4.68418e6 | −0.850633 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.15588e6 | 0.926939 | 0.463469 | − | 0.886113i | \(-0.346604\pi\) | ||||
0.463469 | + | 0.886113i | \(0.346604\pi\) | |||||||
\(500\) | 6.67262e6 | 1.19364 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.02546e7 | −1.81618 | ||||||||
\(503\) | −4.64962e6 | −0.819402 | −0.409701 | − | 0.912220i | \(-0.634367\pi\) | ||||
−0.409701 | + | 0.912220i | \(0.634367\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.83730e6 | −0.320591 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.64379e6 | 1.65801 | ||||||||
\(509\) | −6.73988e6 | −1.15308 | −0.576538 | − | 0.817070i | \(-0.695597\pi\) | ||||
−0.576538 | + | 0.817070i | \(0.695597\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.92067e6 | −0.325388 | ||||||||
\(512\) | 2.19860e6 | 0.370656 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.19888e6 | 0.701012 | ||||||||
\(515\) | 1.96195e6 | 0.325965 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.23819e6 | 0.366499 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.12363e6 | −0.182228 | ||||||||
\(521\) | 2.62743e6 | 0.424069 | 0.212035 | − | 0.977262i | \(-0.431991\pi\) | ||||
0.212035 | + | 0.977262i | \(0.431991\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.18041e6 | −1.30774 | −0.653869 | − | 0.756608i | \(-0.726855\pi\) | ||||
−0.653869 | + | 0.756608i | \(0.726855\pi\) | |||||||
\(524\) | 3.35336e6 | 0.533522 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.48454e6 | −1.02191 | ||||||||
\(527\) | −6.54617e6 | −1.02674 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.49635e7 | 2.32485 | ||||||||
\(530\) | −4.68374e6 | −0.724275 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.73067e6 | −0.418302 | ||||||||
\(533\) | −2.40700e6 | −0.366993 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.28995e6 | −0.194845 | ||||||||
\(536\) | 3.82684e6 | 0.575344 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.10243e7 | 1.64209 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.44510e6 | 0.946752 | 0.473376 | − | 0.880860i | \(-0.343035\pi\) | ||||
0.473376 | + | 0.880860i | \(0.343035\pi\) | |||||||
\(542\) | −1.24056e7 | −1.81393 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.97769e6 | 1.15579 | ||||||||
\(545\) | 5.12136e6 | 0.738574 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.72241e6 | 0.960631 | 0.480315 | − | 0.877096i | \(-0.340522\pi\) | ||||
0.480315 | + | 0.877096i | \(0.340522\pi\) | |||||||
\(548\) | 5.23349e6 | 0.744458 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.94896e6 | −0.834761 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.34006e6 | −0.186343 | ||||||||
\(554\) | −2.10265e7 | −2.91066 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.77538e7 | 2.43559 | ||||||||
\(557\) | 2.71874e6 | 0.371304 | 0.185652 | − | 0.982616i | \(-0.440560\pi\) | ||||
0.185652 | + | 0.982616i | \(0.440560\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.83052e6 | 0.653829 | ||||||||
\(560\) | 330048. | 0.0444741 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.13887e7 | −2.85656 | ||||||||
\(563\) | −817848. | −0.108743 | −0.0543715 | − | 0.998521i | \(-0.517316\pi\) | ||||
−0.0543715 | + | 0.998521i | \(0.517316\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.39826e6 | −0.447852 | ||||||||
\(566\) | −1.00289e7 | −1.31587 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.95387e6 | −1.29456 | ||||||||
\(569\) | −8.33672e6 | −1.07948 | −0.539740 | − | 0.841832i | \(-0.681477\pi\) | ||||
−0.539740 | + | 0.841832i | \(0.681477\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.20715e6 | −1.05342 | −0.526711 | − | 0.850044i | \(-0.676575\pi\) | ||||
−0.526711 | + | 0.850044i | \(0.676575\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.09717e6 | −0.645727 | ||||||||
\(575\) | −1.17917e7 | −1.48732 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −605126. | −0.0756670 | −0.0378335 | − | 0.999284i | \(-0.512046\pi\) | ||||
−0.0378335 | + | 0.999284i | \(0.512046\pi\) | |||||||
\(578\) | 311211. | 0.0387468 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.03874e6 | −1.11568 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −4.08143e6 | −0.495199 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.02702e6 | −0.604737 | ||||||||
\(587\) | 1.00479e7 | 1.20359 | 0.601797 | − | 0.798649i | \(-0.294452\pi\) | ||||
0.601797 | + | 0.798649i | \(0.294452\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.20127e6 | −0.498991 | ||||||||
\(590\) | −5.92272e6 | −0.700473 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −659714. | −0.0773662 | ||||||||
\(593\) | 2.95609e6 | 0.345208 | 0.172604 | − | 0.984991i | \(-0.444782\pi\) | ||||
0.172604 | + | 0.984991i | \(0.444782\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.08397e6 | 0.241323 | ||||||||
\(596\) | 7.34089e6 | 0.846511 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.27400e7 | 1.45686 | ||||||||
\(599\) | 1.27169e7 | 1.44815 | 0.724075 | − | 0.689722i | \(-0.242267\pi\) | ||||
0.724075 | + | 0.689722i | \(0.242267\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.62535e7 | 1.83553 | 0.917763 | − | 0.397128i | \(-0.129993\pi\) | ||||
0.917763 | + | 0.397128i | \(0.129993\pi\) | |||||||
\(602\) | 1.02293e7 | 1.15042 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.64528e7 | −1.83505 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.20900e7 | −1.33185 | −0.665923 | − | 0.746020i | \(-0.731962\pi\) | ||||
−0.665923 | + | 0.746020i | \(0.731962\pi\) | |||||||
\(608\) | 5.12001e6 | 0.561710 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.14191e7 | −1.24253 | ||||||||
\(611\) | 1.95901e6 | 0.212292 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.83160e6 | −0.304355 | −0.152177 | − | 0.988353i | \(-0.548629\pi\) | ||||
−0.152177 | + | 0.988353i | \(0.548629\pi\) | |||||||
\(614\) | −1.10132e7 | −1.17895 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.62285e6 | 0.171619 | 0.0858095 | − | 0.996312i | \(-0.472652\pi\) | ||||
0.0858095 | + | 0.996312i | \(0.472652\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.25560e6 | 0.131712 | 0.0658561 | − | 0.997829i | \(-0.479022\pi\) | ||||
0.0658561 | + | 0.997829i | \(0.479022\pi\) | |||||||
\(620\) | −6.38333e6 | −0.666911 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.72672e7 | 1.78956 | ||||||||
\(623\) | 3.00024e6 | 0.309696 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.69740e6 | 0.481014 | ||||||||
\(626\) | −7.21463e6 | −0.735832 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.61744e6 | 0.770744 | ||||||||
\(629\) | −4.16552e6 | −0.419801 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −579044. | −0.0578946 | −0.0289473 | − | 0.999581i | \(-0.509216\pi\) | ||||
−0.0289473 | + | 0.999581i | \(0.509216\pi\) | |||||||
\(632\) | −2.84764e6 | −0.283591 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.11070e7 | 2.08547 | ||||||||
\(635\) | −4.72349e6 | −0.464867 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.55664e6 | −0.347289 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.45905e6 | 0.623331 | ||||||||
\(641\) | 1.12839e7 | 1.08471 | 0.542354 | − | 0.840150i | \(-0.317533\pi\) | ||||
0.542354 | + | 0.840150i | \(0.317533\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.60866e7 | 1.53439 | 0.767196 | − | 0.641413i | \(-0.221652\pi\) | ||||
0.767196 | + | 0.641413i | \(0.221652\pi\) | |||||||
\(644\) | 1.63205e7 | 1.55067 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.40100e6 | 0.792044 | ||||||||
\(647\) | −7.80003e6 | −0.732547 | −0.366274 | − | 0.930507i | \(-0.619367\pi\) | ||||
−0.366274 | + | 0.930507i | \(0.619367\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −7.01995e6 | −0.651704 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.04842e7 | −0.965868 | ||||||||
\(653\) | 3.81000e6 | 0.349657 | 0.174828 | − | 0.984599i | \(-0.444063\pi\) | ||||
0.174828 | + | 0.984599i | \(0.444063\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.64246e6 | −0.149587 | ||||||||
\(656\) | 1.50241e6 | 0.136310 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.14850e6 | 0.373530 | ||||||||
\(659\) | −2.82564e6 | −0.253456 | −0.126728 | − | 0.991937i | \(-0.540448\pi\) | ||||
−0.126728 | + | 0.991937i | \(0.540448\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.52399e7 | −1.35668 | −0.678340 | − | 0.734748i | \(-0.737300\pi\) | ||||
−0.678340 | + | 0.734748i | \(0.737300\pi\) | |||||||
\(662\) | 2.97905e7 | 2.64200 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.33747e6 | 0.117282 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.55554e7 | 3.09451 | ||||||||
\(668\) | 2.08681e7 | 1.80943 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.40259e6 | −0.464960 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.33261e7 | −1.13414 | −0.567068 | − | 0.823671i | \(-0.691922\pi\) | ||||
−0.567068 | + | 0.823671i | \(0.691922\pi\) | |||||||
\(674\) | 1.30323e7 | 1.10502 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.36052e7 | −1.14509 | ||||||||
\(677\) | 9.75076e6 | 0.817649 | 0.408824 | − | 0.912613i | \(-0.365939\pi\) | ||||
0.408824 | + | 0.912613i | \(0.365939\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.92997e6 | 0.243887 | ||||||||
\(680\) | 4.42843e6 | 0.367263 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.79889e6 | −0.311605 | −0.155803 | − | 0.987788i | \(-0.549796\pi\) | ||||
−0.155803 | + | 0.987788i | \(0.549796\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.56334e6 | −0.208728 | ||||||||
\(686\) | −1.84226e7 | −1.49466 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.01513e6 | −0.242848 | ||||||||
\(689\) | 6.63530e6 | 0.532492 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.04595e7 | 0.833328 | 0.416664 | − | 0.909060i | \(-0.363199\pi\) | ||||
0.416664 | + | 0.909060i | \(0.363199\pi\) | |||||||
\(692\) | 3.54485e7 | 2.81405 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.52577e6 | 0.277879 | ||||||||
\(695\) | −8.69573e6 | −0.682879 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.48640e6 | 0.739638 | ||||||||
\(698\) | −2.39042e7 | −1.85710 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.99287e6 | −0.693671 | ||||||||
\(701\) | 2.79859e6 | 0.215102 | 0.107551 | − | 0.994200i | \(-0.465699\pi\) | ||||
0.107551 | + | 0.994200i | \(0.465699\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.67340e6 | −0.204021 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.26553e7 | 0.955564 | ||||||||
\(707\) | 5.51189e6 | 0.414717 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.45413e7 | −1.83350 | −0.916752 | − | 0.399457i | \(-0.869199\pi\) | ||||
−0.916752 | + | 0.399457i | \(0.869199\pi\) | |||||||
\(710\) | 1.40525e7 | 1.04619 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.37551e6 | 0.471319 | ||||||||
\(713\) | 2.51099e7 | 1.84979 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.03855e7 | −2.21505 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.83280e7 | −2.05071 | ||||||||
\(719\) | 4.81287e6 | 0.347202 | 0.173601 | − | 0.984816i | \(-0.444460\pi\) | ||||
0.173601 | + | 0.984816i | \(0.444460\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.88586e6 | −0.421669 | ||||||||
\(722\) | −1.68932e7 | −1.20606 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.86333e7 | 2.03014 | ||||||||
\(725\) | −1.95916e7 | −1.38428 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.22938e7 | 0.862677 | 0.431339 | − | 0.902190i | \(-0.358041\pi\) | ||||
0.431339 | + | 0.902190i | \(0.358041\pi\) | |||||||
\(728\) | 3.37090e6 | 0.235731 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.76202e6 | 0.400191 | ||||||||
\(731\) | −1.90379e7 | −1.31773 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.60411e6 | 0.179019 | 0.0895097 | − | 0.995986i | \(-0.471470\pi\) | ||||
0.0895097 | + | 0.995986i | \(0.471470\pi\) | |||||||
\(734\) | −1.57325e7 | −1.07785 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.06010e7 | −2.08229 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.85178e7 | −1.24732 | −0.623661 | − | 0.781695i | \(-0.714355\pi\) | ||||
−0.623661 | + | 0.781695i | \(0.714355\pi\) | |||||||
\(740\) | −4.06190e6 | −0.272678 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.40512e7 | 0.936925 | ||||||||
\(743\) | −3.01104e6 | −0.200099 | −0.100049 | − | 0.994982i | \(-0.531900\pi\) | ||||
−0.100049 | + | 0.994982i | \(0.531900\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.59554e6 | −0.237341 | ||||||||
\(746\) | 2.97832e7 | 1.95941 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.86986e6 | 0.252052 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.41805e7 | 0.917470 | 0.458735 | − | 0.888573i | \(-0.348303\pi\) | ||||
0.458735 | + | 0.888573i | \(0.348303\pi\) | |||||||
\(752\) | −1.22278e6 | −0.0788505 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.11672e7 | 1.35593 | ||||||||
\(755\) | 8.05853e6 | 0.514504 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.79645e6 | −0.494490 | −0.247245 | − | 0.968953i | \(-0.579525\pi\) | ||||
−0.247245 | + | 0.968953i | \(0.579525\pi\) | |||||||
\(758\) | −3.69229e7 | −2.33412 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.84213e6 | 0.178488 | ||||||||
\(761\) | 1.09794e7 | 0.687252 | 0.343626 | − | 0.939107i | \(-0.388345\pi\) | ||||
0.343626 | + | 0.939107i | \(0.388345\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.53641e7 | −0.955422 | ||||||||
\(764\) | −1.01092e7 | −0.626589 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.00936e7 | 0.621549 | ||||||||
\(767\) | 8.39052e6 | 0.514992 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.88030e7 | −1.14660 | −0.573299 | − | 0.819347i | \(-0.694336\pi\) | ||||
−0.573299 | + | 0.819347i | \(0.694336\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.48497e7 | 2.70842 | ||||||||
\(773\) | 1.21929e7 | 0.733935 | 0.366967 | − | 0.930234i | \(-0.380396\pi\) | ||||
0.366967 | + | 0.930234i | \(0.380396\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.38360e7 | −0.827476 | ||||||||
\(776\) | 6.22618e6 | 0.371165 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.77936e7 | 1.64625 | ||||||||
\(779\) | 6.08828e6 | 0.359461 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.02106e7 | −2.93615 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.21999e6 | 0.128992 | ||||||||
\(785\) | −3.73099e6 | −0.216098 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.75304e7 | 1.58444 | 0.792221 | − | 0.610234i | \(-0.208925\pi\) | ||||
0.792221 | + | 0.610234i | \(0.208925\pi\) | |||||||
\(788\) | 1.07789e7 | 0.618386 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.02019e6 | 0.229181 | ||||||||
\(791\) | 1.01948e7 | 0.579343 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.61770e7 | 0.913513 | ||||||||
\(794\) | 4.55935e6 | 0.256656 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.75897e7 | 1.54335 | ||||||||
\(797\) | −2.46936e7 | −1.37701 | −0.688507 | − | 0.725230i | \(-0.741733\pi\) | ||||
−0.688507 | + | 0.725230i | \(0.741733\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.72081e6 | −0.427854 | ||||||||
\(800\) | 1.68616e7 | 0.931483 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.20204e7 | 1.20890 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.99373e6 | −0.434770 | ||||||||
\(806\) | 1.49487e7 | 0.810525 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.17128e7 | 0.631148 | ||||||||
\(809\) | −2.40376e7 | −1.29128 | −0.645639 | − | 0.763642i | \(-0.723409\pi\) | ||||
−0.645639 | + | 0.763642i | \(0.723409\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.38751e6 | 0.180854 | 0.0904271 | − | 0.995903i | \(-0.471177\pi\) | ||||
0.0904271 | + | 0.995903i | \(0.471177\pi\) | |||||||
\(812\) | 2.71162e7 | 1.44324 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.13514e6 | 0.270806 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.22184e7 | −0.640410 | ||||||||
\(818\) | −2.23936e7 | −1.17015 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.25042e6 | 0.480426 | ||||||||
\(821\) | −2.68551e6 | −0.139049 | −0.0695247 | − | 0.997580i | \(-0.522148\pi\) | ||||
−0.0695247 | + | 0.997580i | \(0.522148\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.52561e7 | 0.785134 | 0.392567 | − | 0.919723i | \(-0.371587\pi\) | ||||
0.392567 | + | 0.919723i | \(0.371587\pi\) | |||||||
\(824\) | −1.25074e7 | −0.641727 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.77682e7 | 0.906134 | ||||||||
\(827\) | −2.51270e7 | −1.27755 | −0.638773 | − | 0.769395i | \(-0.720558\pi\) | ||||
−0.638773 | + | 0.769395i | \(0.720558\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.00676e7 | 1.51954 | 0.759770 | − | 0.650191i | \(-0.225311\pi\) | ||||
0.759770 | + | 0.650191i | \(0.225311\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.63474e7 | −0.818731 | ||||||||
\(833\) | 1.40173e7 | 0.699927 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.02211e7 | −0.507320 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.65105e6 | −0.179600 | ||||||||
\(839\) | −3.77681e7 | −1.85234 | −0.926170 | − | 0.377107i | \(-0.876919\pi\) | ||||
−0.926170 | + | 0.377107i | \(0.876919\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.85634e7 | 1.88012 | ||||||||
\(842\) | −3.92647e7 | −1.90863 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.08124e7 | 0.522477 | ||||||||
\(845\) | 6.66377e6 | 0.321054 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.14164e6 | −0.197780 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.76668e7 | 1.31345 | ||||||||
\(851\) | 1.59782e7 | 0.756317 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −254934. | −0.0119965 | −0.00599826 | − | 0.999982i | \(-0.501909\pi\) | ||||
−0.00599826 | + | 0.999982i | \(0.501909\pi\) | |||||||
\(854\) | 3.42572e7 | 1.60734 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.22344e6 | 0.383592 | ||||||||
\(857\) | −4.24942e6 | −0.197641 | −0.0988207 | − | 0.995105i | \(-0.531507\pi\) | ||||
−0.0988207 | + | 0.995105i | \(0.531507\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.24416e7 | −1.03770 | −0.518850 | − | 0.854865i | \(-0.673640\pi\) | ||||
−0.518850 | + | 0.854865i | \(0.673640\pi\) | |||||||
\(860\) | −1.85643e7 | −0.855920 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.14454e7 | −2.35819 | ||||||||
\(863\) | −2.01011e6 | −0.0918742 | −0.0459371 | − | 0.998944i | \(-0.514627\pi\) | ||||
−0.0459371 | + | 0.998944i | \(0.514627\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.73625e7 | −0.788991 | ||||||||
\(866\) | −5.25735e7 | −2.38217 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.91500e7 | 0.862718 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.65367e6 | 0.341841 | ||||||||
\(872\) | −3.26487e7 | −1.45403 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.22247e7 | −1.42696 | ||||||||
\(875\) | 9.80467e6 | 0.432925 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.26086e6 | −0.318778 | −0.159389 | − | 0.987216i | \(-0.550952\pi\) | ||||
−0.159389 | + | 0.987216i | \(0.550952\pi\) | |||||||
\(878\) | 3.54002e6 | 0.154978 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.04800e7 | 1.75712 | 0.878558 | − | 0.477636i | \(-0.158506\pi\) | ||||
0.878558 | + | 0.477636i | \(0.158506\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.00636e7 | −0.865979 | −0.432990 | − | 0.901399i | \(-0.642541\pi\) | ||||
−0.432990 | + | 0.901399i | \(0.642541\pi\) | |||||||
\(884\) | −1.80828e7 | −0.778277 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.48734e7 | 0.636542 | ||||||||
\(887\) | 1.42543e7 | 0.608325 | 0.304163 | − | 0.952620i | \(-0.401623\pi\) | ||||
0.304163 | + | 0.952620i | \(0.401623\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.41705e7 | 0.601353 | ||||||||
\(890\) | −9.00072e6 | −0.380892 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.27933e7 | −2.64242 | ||||||||
\(893\) | −4.95515e6 | −0.207935 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.48827e7 | 0.621046 | ||||||||
\(896\) | −1.93771e7 | −0.806343 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.55879e7 | −0.645055 | ||||||||
\(899\) | 4.17196e7 | 1.72163 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.61509e7 | −1.07319 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.16639e7 | 0.881689 | ||||||||
\(905\) | −1.40245e7 | −0.569201 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.25752e7 | −1.31483 | −0.657413 | − | 0.753530i | \(-0.728349\pi\) | ||||
−0.657413 | + | 0.753530i | \(0.728349\pi\) | |||||||
\(908\) | 7.12850e7 | 2.86935 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.75891e6 | −0.190504 | ||||||||
\(911\) | −7.00624e6 | −0.279698 | −0.139849 | − | 0.990173i | \(-0.544662\pi\) | ||||
−0.139849 | + | 0.990173i | \(0.544662\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −5.09840e7 | −2.01868 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −214718. | −0.00845531 | ||||||||
\(917\) | 4.92739e6 | 0.193506 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.17803e7 | −0.850695 | −0.425348 | − | 0.905030i | \(-0.639848\pi\) | ||||
−0.425348 | + | 0.905030i | \(0.639848\pi\) | |||||||
\(920\) | −1.69867e7 | −0.661666 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.45184e6 | −0.288693 | ||||||||
\(923\) | −1.99077e7 | −0.769162 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.80425e6 | −0.338328 | ||||||||
\(926\) | −2.91829e7 | −1.11841 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.08429e7 | −1.93803 | ||||||||
\(929\) | 4.88614e7 | 1.85749 | 0.928745 | − | 0.370720i | \(-0.120889\pi\) | ||||
0.928745 | + | 0.370720i | \(0.120889\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.99620e6 | 0.340161 | ||||||||
\(932\) | −5.25434e7 | −1.98143 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.66473e7 | 2.12477 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.16064e6 | −0.0431866 | −0.0215933 | − | 0.999767i | \(-0.506874\pi\) | ||||
−0.0215933 | + | 0.999767i | \(0.506874\pi\) | |||||||
\(938\) | 1.62078e7 | 0.601473 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.52875e6 | −0.277909 | ||||||||
\(941\) | −4.50576e7 | −1.65880 | −0.829400 | − | 0.558656i | \(-0.811317\pi\) | ||||
−0.829400 | + | 0.558656i | \(0.811317\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.63881e7 | −1.33254 | ||||||||
\(944\) | −5.23722e6 | −0.191281 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.06091e7 | 0.384418 | 0.192209 | − | 0.981354i | \(-0.438435\pi\) | ||||
0.192209 | + | 0.981354i | \(0.438435\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.16286e6 | −0.294223 | ||||||||
\(950\) | 1.77563e7 | 0.638329 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.32853e7 | −0.475093 | ||||||||
\(953\) | 3.63059e7 | 1.29493 | 0.647463 | − | 0.762097i | \(-0.275830\pi\) | ||||
0.647463 | + | 0.762097i | \(0.275830\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.95144e6 | 0.175680 | ||||||||
\(956\) | 4.06038e7 | 1.43688 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.55977e7 | −2.30927 | ||||||||
\(959\) | 7.69003e6 | 0.270011 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 834033. | 0.0291323 | ||||||||
\(962\) | 9.51232e6 | 0.331397 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.94588e7 | −1.02099 | ||||||||
\(965\) | −2.19672e7 | −0.759375 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.10387e7 | 0.723524 | 0.361762 | − | 0.932270i | \(-0.382175\pi\) | ||||
0.361762 | + | 0.932270i | \(0.382175\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.78990e6 | −0.299954 | ||||||||
\(971\) | −3.58180e7 | −1.21914 | −0.609570 | − | 0.792732i | \(-0.708658\pi\) | ||||
−0.609570 | + | 0.792732i | \(0.708658\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.60872e7 | 0.883375 | ||||||||
\(974\) | −1.81413e7 | −0.612731 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.00974e7 | −0.339301 | ||||||||
\(977\) | 1.22823e6 | 0.0411664 | 0.0205832 | − | 0.999788i | \(-0.493448\pi\) | ||||
0.0205832 | + | 0.999788i | \(0.493448\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.36686e7 | 0.454632 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.84736e6 | −0.160408 | ||||||||
\(983\) | −3.68929e6 | −0.121775 | −0.0608876 | − | 0.998145i | \(-0.519393\pi\) | ||||
−0.0608876 | + | 0.998145i | \(0.519393\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.27947e6 | −0.173380 | ||||||||
\(986\) | −8.34238e7 | −2.73274 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.16054e7 | −0.378239 | ||||||||
\(989\) | 7.30260e7 | 2.37403 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.24253e7 | 0.401905 | 0.200952 | − | 0.979601i | \(-0.435596\pi\) | ||||
0.200952 | + | 0.979601i | \(0.435596\pi\) | |||||||
\(992\) | −3.59062e7 | −1.15849 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.21576e7 | −1.35335 | ||||||||
\(995\) | −1.35133e7 | −0.432718 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.87328e7 | 0.915462 | 0.457731 | − | 0.889091i | \(-0.348662\pi\) | ||||
0.457731 | + | 0.889091i | \(0.348662\pi\) | |||||||
\(998\) | 4.64029e7 | 1.47475 | ||||||||
\(999\) | 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 | 1089.6.a.i.1.1 | 1 | ||
3.2 | odd | 2 | 363.6.a.a.1.1 | ✓ | 1 | ||
11.10 | odd | 2 | 1089.6.a.a.1.1 | 1 | |||
33.32 | even | 2 | 363.6.a.e.1.1 | yes | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.6.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
363.6.a.e.1.1 | yes | 1 | 33.32 | even | 2 | ||
1089.6.a.a.1.1 | 1 | 11.10 | odd | 2 | |||
1089.6.a.i.1.1 | 1 | 1.1 | even | 1 | trivial |