Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,6,Mod(1,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, 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("363.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.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: | \(58.2193265921\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 363.1 |
$q$-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 | \(0.207211\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 49.0000 | 1.53125 | ||||||||
\(5\) | 24.0000 | 0.429325 | 0.214663 | − | 0.976688i | \(-0.431135\pi\) | ||||
0.214663 | + | 0.976688i | \(0.431135\pi\) | |||||||
\(6\) | −81.0000 | −0.918559 | ||||||||
\(7\) | −72.0000 | −0.555376 | −0.277688 | − | 0.960671i | \(-0.589568\pi\) | ||||
−0.277688 | + | 0.960671i | \(0.589568\pi\) | |||||||
\(8\) | 153.000 | 0.845214 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 216.000 | 0.683052 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −441.000 | −0.884068 | ||||||||
\(13\) | −306.000 | −0.502184 | −0.251092 | − | 0.967963i | \(-0.580790\pi\) | ||||
−0.251092 | + | 0.967963i | \(0.580790\pi\) | |||||||
\(14\) | −648.000 | −0.883598 | ||||||||
\(15\) | −216.000 | −0.247871 | ||||||||
\(16\) | −191.000 | −0.186523 | ||||||||
\(17\) | −1206.00 | −1.01210 | −0.506052 | − | 0.862503i | \(-0.668896\pi\) | ||||
−0.506052 | + | 0.862503i | \(0.668896\pi\) | |||||||
\(18\) | 729.000 | 0.530330 | ||||||||
\(19\) | 774.000 | 0.491878 | 0.245939 | − | 0.969285i | \(-0.420904\pi\) | ||||
0.245939 | + | 0.969285i | \(0.420904\pi\) | |||||||
\(20\) | 1176.00 | 0.657404 | ||||||||
\(21\) | 648.000 | 0.320647 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4626.00 | −1.82342 | −0.911709 | − | 0.410838i | \(-0.865236\pi\) | ||||
−0.911709 | + | 0.410838i | \(0.865236\pi\) | |||||||
\(24\) | −1377.00 | −0.487984 | ||||||||
\(25\) | −2549.00 | −0.815680 | ||||||||
\(26\) | −2754.00 | −0.798970 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −3528.00 | −0.850420 | ||||||||
\(29\) | 7686.00 | 1.69709 | 0.848546 | − | 0.529122i | \(-0.177478\pi\) | ||||
0.848546 | + | 0.529122i | \(0.177478\pi\) | |||||||
\(30\) | −1944.00 | −0.394360 | ||||||||
\(31\) | 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 | ||||||||
\(36\) | 3969.00 | 0.510417 | ||||||||
\(37\) | 3454.00 | 0.414780 | 0.207390 | − | 0.978258i | \(-0.433503\pi\) | ||||
0.207390 | + | 0.978258i | \(0.433503\pi\) | |||||||
\(38\) | 6966.00 | 0.782572 | ||||||||
\(39\) | 2754.00 | 0.289936 | ||||||||
\(40\) | 3672.00 | 0.362871 | ||||||||
\(41\) | −7866.00 | −0.730793 | −0.365396 | − | 0.930852i | \(-0.619067\pi\) | ||||
−0.365396 | + | 0.930852i | \(0.619067\pi\) | |||||||
\(42\) | 5832.00 | 0.510146 | ||||||||
\(43\) | −15786.0 | −1.30197 | −0.650985 | − | 0.759091i | \(-0.725644\pi\) | ||||
−0.650985 | + | 0.759091i | \(0.725644\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1944.00 | 0.143108 | ||||||||
\(46\) | −41634.0 | −2.90104 | ||||||||
\(47\) | −6402.00 | −0.422738 | −0.211369 | − | 0.977406i | \(-0.567792\pi\) | ||||
−0.211369 | + | 0.977406i | \(0.567792\pi\) | |||||||
\(48\) | 1719.00 | 0.107689 | ||||||||
\(49\) | −11623.0 | −0.691557 | ||||||||
\(50\) | −22941.0 | −1.29774 | ||||||||
\(51\) | 10854.0 | 0.584338 | ||||||||
\(52\) | −14994.0 | −0.768970 | ||||||||
\(53\) | −21684.0 | −1.06035 | −0.530176 | − | 0.847888i | \(-0.677874\pi\) | ||||
−0.530176 | + | 0.847888i | \(0.677874\pi\) | |||||||
\(54\) | −6561.00 | −0.306186 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −11016.0 | −0.469412 | ||||||||
\(57\) | −6966.00 | −0.283986 | ||||||||
\(58\) | 69174.0 | 2.70006 | ||||||||
\(59\) | −27420.0 | −1.02550 | −0.512752 | − | 0.858537i | \(-0.671374\pi\) | ||||
−0.512752 | + | 0.858537i | \(0.671374\pi\) | |||||||
\(60\) | −10584.0 | −0.379552 | ||||||||
\(61\) | −52866.0 | −1.81908 | −0.909540 | − | 0.415616i | \(-0.863566\pi\) | ||||
−0.909540 | + | 0.415616i | \(0.863566\pi\) | |||||||
\(62\) | 48852.0 | 1.61400 | ||||||||
\(63\) | −5832.00 | −0.185125 | ||||||||
\(64\) | −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 | ||||||||
\(69\) | 41634.0 | 1.05275 | ||||||||
\(70\) | −15552.0 | −0.379351 | ||||||||
\(71\) | 65058.0 | 1.53163 | 0.765817 | − | 0.643059i | \(-0.222335\pi\) | ||||
0.765817 | + | 0.643059i | \(0.222335\pi\) | |||||||
\(72\) | 12393.0 | 0.281738 | ||||||||
\(73\) | 26676.0 | 0.585887 | 0.292943 | − | 0.956130i | \(-0.405365\pi\) | ||||
0.292943 | + | 0.956130i | \(0.405365\pi\) | |||||||
\(74\) | 31086.0 | 0.659911 | ||||||||
\(75\) | 22941.0 | 0.470933 | ||||||||
\(76\) | 37926.0 | 0.753187 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 24786.0 | 0.461286 | ||||||||
\(79\) | 18612.0 | 0.335525 | 0.167763 | − | 0.985827i | \(-0.446346\pi\) | ||||
0.167763 | + | 0.985827i | \(0.446346\pi\) | |||||||
\(80\) | −4584.00 | −0.0800792 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −70794.0 | −1.16268 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 31752.0 | 0.490990 | ||||||||
\(85\) | −28944.0 | −0.434521 | ||||||||
\(86\) | −142074. | −2.07142 | ||||||||
\(87\) | −69174.0 | −0.979817 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −41670.0 | −0.557633 | −0.278817 | − | 0.960344i | \(-0.589942\pi\) | ||||
−0.278817 | + | 0.960344i | \(0.589942\pi\) | |||||||
\(90\) | 17496.0 | 0.227684 | ||||||||
\(91\) | 22032.0 | 0.278901 | ||||||||
\(92\) | −226674. | −2.79211 | ||||||||
\(93\) | −48852.0 | −0.585700 | ||||||||
\(94\) | −57618.0 | −0.672572 | ||||||||
\(95\) | 18576.0 | 0.211175 | ||||||||
\(96\) | 59535.0 | 0.659317 | ||||||||
\(97\) | 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 | \(0.378204\pi\) | |||||||
\(102\) | 97686.0 | 0.929677 | ||||||||
\(103\) | −81748.0 | −0.759249 | −0.379624 | − | 0.925141i | \(-0.623947\pi\) | ||||
−0.379624 | + | 0.925141i | \(0.623947\pi\) | |||||||
\(104\) | −46818.0 | −0.424453 | ||||||||
\(105\) | 15552.0 | 0.137662 | ||||||||
\(106\) | −195156. | −1.68701 | ||||||||
\(107\) | 53748.0 | 0.453840 | 0.226920 | − | 0.973913i | \(-0.427134\pi\) | ||||
0.226920 | + | 0.973913i | \(0.427134\pi\) | |||||||
\(108\) | −35721.0 | −0.294689 | ||||||||
\(109\) | 213390. | 1.72031 | 0.860157 | − | 0.510029i | \(-0.170365\pi\) | ||||
0.860157 | + | 0.510029i | \(0.170365\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −31086.0 | −0.239473 | ||||||||
\(112\) | 13752.0 | 0.103591 | ||||||||
\(113\) | −141594. | −1.04315 | −0.521577 | − | 0.853204i | \(-0.674656\pi\) | ||||
−0.521577 | + | 0.853204i | \(0.674656\pi\) | |||||||
\(114\) | −62694.0 | −0.451818 | ||||||||
\(115\) | −111024. | −0.782839 | ||||||||
\(116\) | 376614. | 2.59867 | ||||||||
\(117\) | −24786.0 | −0.167395 | ||||||||
\(118\) | −246780. | −1.63157 | ||||||||
\(119\) | 86832.0 | 0.562098 | ||||||||
\(120\) | −33048.0 | −0.209504 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −475794. | −2.89414 | ||||||||
\(123\) | 70794.0 | 0.421923 | ||||||||
\(124\) | 265972. | 1.55339 | ||||||||
\(125\) | −136176. | −0.779517 | ||||||||
\(126\) | −52488.0 | −0.294533 | ||||||||
\(127\) | −196812. | −1.08279 | −0.541393 | − | 0.840770i | \(-0.682103\pi\) | ||||
−0.541393 | + | 0.840770i | \(0.682103\pi\) | |||||||
\(128\) | −269127. | −1.45189 | ||||||||
\(129\) | 142074. | 0.751693 | ||||||||
\(130\) | −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 | ||||||||
\(135\) | −17496.0 | −0.0826236 | ||||||||
\(136\) | −184518. | −0.855444 | ||||||||
\(137\) | −106806. | −0.486177 | −0.243088 | − | 0.970004i | \(-0.578161\pi\) | ||||
−0.243088 | + | 0.970004i | \(0.578161\pi\) | |||||||
\(138\) | 374706. | 1.67492 | ||||||||
\(139\) | −362322. | −1.59059 | −0.795294 | − | 0.606224i | \(-0.792684\pi\) | ||||
−0.795294 | + | 0.606224i | \(0.792684\pi\) | |||||||
\(140\) | −84672.0 | −0.365107 | ||||||||
\(141\) | 57618.0 | 0.244068 | ||||||||
\(142\) | 585522. | 2.43681 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −15471.0 | −0.0621745 | ||||||||
\(145\) | 184464. | 0.728604 | ||||||||
\(146\) | 240084. | 0.932140 | ||||||||
\(147\) | 104607. | 0.399271 | ||||||||
\(148\) | 169246. | 0.635132 | ||||||||
\(149\) | 149814. | 0.552824 | 0.276412 | − | 0.961039i | \(-0.410855\pi\) | ||||
0.276412 | + | 0.961039i | \(0.410855\pi\) | |||||||
\(150\) | 206469. | 0.749250 | ||||||||
\(151\) | 335772. | 1.19840 | 0.599200 | − | 0.800599i | \(-0.295485\pi\) | ||||
0.599200 | + | 0.800599i | \(0.295485\pi\) | |||||||
\(152\) | 118422. | 0.415742 | ||||||||
\(153\) | −97686.0 | −0.337368 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 130272. | 0.435534 | ||||||||
\(156\) | 134946. | 0.443965 | ||||||||
\(157\) | 155458. | 0.503343 | 0.251671 | − | 0.967813i | \(-0.419020\pi\) | ||||
0.251671 | + | 0.967813i | \(0.419020\pi\) | |||||||
\(158\) | 167508. | 0.533818 | ||||||||
\(159\) | 195156. | 0.612194 | ||||||||
\(160\) | −158760. | −0.490277 | ||||||||
\(161\) | 333072. | 1.01268 | ||||||||
\(162\) | 59049.0 | 0.176777 | ||||||||
\(163\) | −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 | \(0.298798\pi\) | |||||||
\(168\) | 99144.0 | 0.271015 | ||||||||
\(169\) | −277657. | −0.747811 | ||||||||
\(170\) | −260496. | −0.691319 | ||||||||
\(171\) | 62694.0 | 0.163959 | ||||||||
\(172\) | −773514. | −1.99364 | ||||||||
\(173\) | 723438. | 1.83775 | 0.918874 | − | 0.394551i | \(-0.129100\pi\) | ||||
0.918874 | + | 0.394551i | \(0.129100\pi\) | |||||||
\(174\) | −622566. | −1.55888 | ||||||||
\(175\) | 183528. | 0.453009 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 246780. | 0.592075 | ||||||||
\(178\) | −375030. | −0.887189 | ||||||||
\(179\) | 620112. | 1.44656 | 0.723282 | − | 0.690553i | \(-0.242633\pi\) | ||||
0.723282 | + | 0.690553i | \(0.242633\pi\) | |||||||
\(180\) | 95256.0 | 0.219135 | ||||||||
\(181\) | 584354. | 1.32580 | 0.662902 | − | 0.748706i | \(-0.269324\pi\) | ||||
0.662902 | + | 0.748706i | \(0.269324\pi\) | |||||||
\(182\) | 198288. | 0.443729 | ||||||||
\(183\) | 475794. | 1.05025 | ||||||||
\(184\) | −707778. | −1.54118 | ||||||||
\(185\) | 82896.0 | 0.178076 | ||||||||
\(186\) | −439668. | −0.931842 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −313698. | −0.647317 | ||||||||
\(189\) | 52488.0 | 0.106882 | ||||||||
\(190\) | 167184. | 0.335978 | ||||||||
\(191\) | 206310. | 0.409201 | 0.204601 | − | 0.978846i | \(-0.434410\pi\) | ||||
0.204601 | + | 0.978846i | \(0.434410\pi\) | |||||||
\(192\) | 480807. | 0.941278 | ||||||||
\(193\) | −915300. | −1.76877 | −0.884383 | − | 0.466763i | \(-0.845420\pi\) | ||||
−0.884383 | + | 0.466763i | \(0.845420\pi\) | |||||||
\(194\) | 366246. | 0.698664 | ||||||||
\(195\) | 66096.0 | 0.124477 | ||||||||
\(196\) | −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 | ||||||||
\(201\) | −225108. | −0.393007 | ||||||||
\(202\) | 688986. | 1.18804 | ||||||||
\(203\) | −553392. | −0.942525 | ||||||||
\(204\) | 531846. | 0.894768 | ||||||||
\(205\) | −188784. | −0.313748 | ||||||||
\(206\) | −735732. | −1.20796 | ||||||||
\(207\) | −374706. | −0.607806 | ||||||||
\(208\) | 58446.0 | 0.0936691 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 139968. | 0.219018 | ||||||||
\(211\) | −220662. | −0.341210 | −0.170605 | − | 0.985340i | \(-0.554572\pi\) | ||||
−0.170605 | + | 0.985340i | \(0.554572\pi\) | |||||||
\(212\) | −1.06252e6 | −1.62366 | ||||||||
\(213\) | −585522. | −0.884289 | ||||||||
\(214\) | 483732. | 0.722055 | ||||||||
\(215\) | −378864. | −0.558968 | ||||||||
\(216\) | −111537. | −0.162661 | ||||||||
\(217\) | −390816. | −0.563408 | ||||||||
\(218\) | 1.92051e6 | 2.73700 | ||||||||
\(219\) | −240084. | −0.338262 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 369036. | 0.508262 | ||||||||
\(222\) | −279774. | −0.381000 | ||||||||
\(223\) | −1.28150e6 | −1.72566 | −0.862830 | − | 0.505495i | \(-0.831310\pi\) | ||||
−0.862830 | + | 0.505495i | \(0.831310\pi\) | |||||||
\(224\) | 476280. | 0.634223 | ||||||||
\(225\) | −206469. | −0.271893 | ||||||||
\(226\) | −1.27435e6 | −1.65965 | ||||||||
\(227\) | 1.45480e6 | 1.87386 | 0.936931 | − | 0.349515i | \(-0.113654\pi\) | ||||
0.936931 | + | 0.349515i | \(0.113654\pi\) | |||||||
\(228\) | −341334. | −0.434853 | ||||||||
\(229\) | −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 | \(0.723975\pi\) | |||||||
\(234\) | −223074. | −0.266323 | ||||||||
\(235\) | −153648. | −0.181492 | ||||||||
\(236\) | −1.34358e6 | −1.57030 | ||||||||
\(237\) | −167508. | −0.193716 | ||||||||
\(238\) | 781488. | 0.894293 | ||||||||
\(239\) | 828648. | 0.938373 | 0.469186 | − | 0.883099i | \(-0.344547\pi\) | ||||
0.469186 | + | 0.883099i | \(0.344547\pi\) | |||||||
\(240\) | 41256.0 | 0.0462337 | ||||||||
\(241\) | 601200. | 0.666770 | 0.333385 | − | 0.942791i | \(-0.391809\pi\) | ||||
0.333385 | + | 0.942791i | \(0.391809\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −2.59043e6 | −2.78547 | ||||||||
\(245\) | −278952. | −0.296903 | ||||||||
\(246\) | 637146. | 0.671276 | ||||||||
\(247\) | −236844. | −0.247013 | ||||||||
\(248\) | 830484. | 0.857437 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.22558e6 | −1.24020 | ||||||||
\(251\) | 1.13940e6 | 1.14154 | 0.570771 | − | 0.821109i | \(-0.306644\pi\) | ||||
0.570771 | + | 0.821109i | \(0.306644\pi\) | |||||||
\(252\) | −285768. | −0.283473 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.77131e6 | −1.72270 | ||||||||
\(255\) | 260496. | 0.250871 | ||||||||
\(256\) | −712607. | −0.679595 | ||||||||
\(257\) | −466542. | −0.440614 | −0.220307 | − | 0.975431i | \(-0.570706\pi\) | ||||
−0.220307 | + | 0.975431i | \(0.570706\pi\) | |||||||
\(258\) | 1.27867e6 | 1.19594 | ||||||||
\(259\) | −248688. | −0.230359 | ||||||||
\(260\) | −359856. | −0.330138 | ||||||||
\(261\) | 622566. | 0.565697 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 375030. | 0.321950 | ||||||||
\(268\) | 1.22559e6 | 1.04234 | ||||||||
\(269\) | −1.22492e6 | −1.03212 | −0.516058 | − | 0.856554i | \(-0.672601\pi\) | ||||
−0.516058 | + | 0.856554i | \(0.672601\pi\) | |||||||
\(270\) | −157464. | −0.131453 | ||||||||
\(271\) | 1.37840e6 | 1.14013 | 0.570064 | − | 0.821601i | \(-0.306919\pi\) | ||||
0.570064 | + | 0.821601i | \(0.306919\pi\) | |||||||
\(272\) | 230346. | 0.188781 | ||||||||
\(273\) | −198288. | −0.161024 | ||||||||
\(274\) | −961254. | −0.773503 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.04007e6 | 1.61202 | ||||||||
\(277\) | 2.33627e6 | 1.82947 | 0.914733 | − | 0.404059i | \(-0.132401\pi\) | ||||
0.914733 | + | 0.404059i | \(0.132401\pi\) | |||||||
\(278\) | −3.26090e6 | −2.53061 | ||||||||
\(279\) | 439668. | 0.338154 | ||||||||
\(280\) | −264384. | −0.201530 | ||||||||
\(281\) | −2.37652e6 | −1.79546 | −0.897731 | − | 0.440545i | \(-0.854785\pi\) | ||||
−0.897731 | + | 0.440545i | \(0.854785\pi\) | |||||||
\(282\) | 518562. | 0.388309 | ||||||||
\(283\) | 1.11433e6 | 0.827077 | 0.413539 | − | 0.910487i | \(-0.364293\pi\) | ||||
0.413539 | + | 0.910487i | \(0.364293\pi\) | |||||||
\(284\) | 3.18784e6 | 2.34531 | ||||||||
\(285\) | −167184. | −0.121922 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 566352. | 0.405865 | ||||||||
\(288\) | −535815. | −0.380657 | ||||||||
\(289\) | 34579.0 | 0.0243539 | ||||||||
\(290\) | 1.66018e6 | 1.15920 | ||||||||
\(291\) | −366246. | −0.253536 | ||||||||
\(292\) | 1.30712e6 | 0.897139 | ||||||||
\(293\) | −558558. | −0.380101 | −0.190051 | − | 0.981774i | \(-0.560865\pi\) | ||||
−0.190051 | + | 0.981774i | \(0.560865\pi\) | |||||||
\(294\) | 941463. | 0.635236 | ||||||||
\(295\) | −658080. | −0.440275 | ||||||||
\(296\) | 528462. | 0.350578 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.34833e6 | 0.879537 | ||||||||
\(299\) | 1.41556e6 | 0.915691 | ||||||||
\(300\) | 1.12411e6 | 0.721116 | ||||||||
\(301\) | 1.13659e6 | 0.723083 | ||||||||
\(302\) | 3.02195e6 | 1.90664 | ||||||||
\(303\) | −688986. | −0.431126 | ||||||||
\(304\) | −147834. | −0.0917467 | ||||||||
\(305\) | −1.26878e6 | −0.780977 | ||||||||
\(306\) | −879174. | −0.536749 | ||||||||
\(307\) | 1.22369e6 | 0.741015 | 0.370507 | − | 0.928830i | \(-0.379184\pi\) | ||||
0.370507 | + | 0.928830i | \(0.379184\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 735732. | 0.438352 | ||||||||
\(310\) | 1.17245e6 | 0.692930 | ||||||||
\(311\) | −1.91858e6 | −1.12481 | −0.562404 | − | 0.826863i | \(-0.690123\pi\) | ||||
−0.562404 | + | 0.826863i | \(0.690123\pi\) | |||||||
\(312\) | 421362. | 0.245058 | ||||||||
\(313\) | −801626. | −0.462499 | −0.231250 | − | 0.972894i | \(-0.574281\pi\) | ||||
−0.231250 | + | 0.972894i | \(0.574281\pi\) | |||||||
\(314\) | 1.39912e6 | 0.800814 | ||||||||
\(315\) | −139968. | −0.0794790 | ||||||||
\(316\) | 911988. | 0.513773 | ||||||||
\(317\) | −2.34522e6 | −1.31080 | −0.655398 | − | 0.755283i | \(-0.727499\pi\) | ||||
−0.655398 | + | 0.755283i | \(0.727499\pi\) | |||||||
\(318\) | 1.75640e6 | 0.973995 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.28215e6 | −0.699946 | ||||||||
\(321\) | −483732. | −0.262025 | ||||||||
\(322\) | 2.99765e6 | 1.61117 | ||||||||
\(323\) | −933444. | −0.497831 | ||||||||
\(324\) | 321489. | 0.170139 | ||||||||
\(325\) | 779994. | 0.409622 | ||||||||
\(326\) | −1.92568e6 | −1.00355 | ||||||||
\(327\) | −1.92051e6 | −0.993224 | ||||||||
\(328\) | −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 | ||||||||
\(333\) | 279774. | 0.138260 | ||||||||
\(334\) | 3.83292e6 | 1.88002 | ||||||||
\(335\) | 600288. | 0.292245 | ||||||||
\(336\) | −123768. | −0.0598081 | ||||||||
\(337\) | −1.44803e6 | −0.694548 | −0.347274 | − | 0.937764i | \(-0.612893\pi\) | ||||
−0.347274 | + | 0.937764i | \(0.612893\pi\) | |||||||
\(338\) | −2.49891e6 | −1.18976 | ||||||||
\(339\) | 1.27435e6 | 0.602266 | ||||||||
\(340\) | −1.41826e6 | −0.665361 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 564246. | 0.260857 | ||||||||
\(343\) | 2.04696e6 | 0.939451 | ||||||||
\(344\) | −2.41526e6 | −1.10044 | ||||||||
\(345\) | 999216. | 0.451972 | ||||||||
\(346\) | 6.51094e6 | 2.92384 | ||||||||
\(347\) | 391752. | 0.174658 | 0.0873288 | − | 0.996180i | \(-0.472167\pi\) | ||||
0.0873288 | + | 0.996180i | \(0.472167\pi\) | |||||||
\(348\) | −3.38953e6 | −1.50034 | ||||||||
\(349\) | 2.65603e6 | 1.16726 | 0.583632 | − | 0.812019i | \(-0.301631\pi\) | ||||
0.583632 | + | 0.812019i | \(0.301631\pi\) | |||||||
\(350\) | 1.65175e6 | 0.720734 | ||||||||
\(351\) | 223074. | 0.0966454 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.40614e6 | −0.600610 | −0.300305 | − | 0.953843i | \(-0.597088\pi\) | ||||
−0.300305 | + | 0.953843i | \(0.597088\pi\) | |||||||
\(354\) | 2.22102e6 | 0.941986 | ||||||||
\(355\) | 1.56139e6 | 0.657569 | ||||||||
\(356\) | −2.04183e6 | −0.853876 | ||||||||
\(357\) | −781488. | −0.324528 | ||||||||
\(358\) | 5.58101e6 | 2.30147 | ||||||||
\(359\) | −3.14755e6 | −1.28895 | −0.644476 | − | 0.764624i | \(-0.722924\pi\) | ||||
−0.644476 | + | 0.764624i | \(0.722924\pi\) | |||||||
\(360\) | 297432. | 0.120957 | ||||||||
\(361\) | −1.87702e6 | −0.758057 | ||||||||
\(362\) | 5.25919e6 | 2.10934 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.07957e6 | 0.427068 | ||||||||
\(365\) | 640224. | 0.251536 | ||||||||
\(366\) | 4.28215e6 | 1.67093 | ||||||||
\(367\) | −1.74806e6 | −0.677470 | −0.338735 | − | 0.940882i | \(-0.609999\pi\) | ||||
−0.338735 | + | 0.940882i | \(0.609999\pi\) | |||||||
\(368\) | 883566. | 0.340110 | ||||||||
\(369\) | −637146. | −0.243598 | ||||||||
\(370\) | 746064. | 0.283316 | ||||||||
\(371\) | 1.56125e6 | 0.588894 | ||||||||
\(372\) | −2.39375e6 | −0.896853 | ||||||||
\(373\) | −3.30925e6 | −1.23156 | −0.615782 | − | 0.787917i | \(-0.711160\pi\) | ||||
−0.615782 | + | 0.787917i | \(0.711160\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.22558e6 | 0.450054 | ||||||||
\(376\) | −979506. | −0.357304 | ||||||||
\(377\) | −2.35192e6 | −0.852253 | ||||||||
\(378\) | 472392. | 0.170049 | ||||||||
\(379\) | −4.10254e6 | −1.46708 | −0.733542 | − | 0.679644i | \(-0.762134\pi\) | ||||
−0.733542 | + | 0.679644i | \(0.762134\pi\) | |||||||
\(380\) | 910224. | 0.323362 | ||||||||
\(381\) | 1.77131e6 | 0.625146 | ||||||||
\(382\) | 1.85679e6 | 0.651035 | ||||||||
\(383\) | −1.12151e6 | −0.390668 | −0.195334 | − | 0.980737i | \(-0.562579\pi\) | ||||
−0.195334 | + | 0.980737i | \(0.562579\pi\) | |||||||
\(384\) | 2.42214e6 | 0.838246 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.23770e6 | −2.81409 | ||||||||
\(387\) | −1.27867e6 | −0.433990 | ||||||||
\(388\) | 1.99401e6 | 0.672430 | ||||||||
\(389\) | −3.08818e6 | −1.03473 | −0.517366 | − | 0.855764i | \(-0.673087\pi\) | ||||
−0.517366 | + | 0.855764i | \(0.673087\pi\) | |||||||
\(390\) | 594864. | 0.198041 | ||||||||
\(391\) | 5.57896e6 | 1.84549 | ||||||||
\(392\) | −1.77832e6 | −0.584513 | ||||||||
\(393\) | −615924. | −0.201162 | ||||||||
\(394\) | 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 | ||||||||
\(399\) | 501552. | 0.157719 | ||||||||
\(400\) | 486859. | 0.152143 | ||||||||
\(401\) | −2.44671e6 | −0.759839 | −0.379919 | − | 0.925020i | \(-0.624048\pi\) | ||||
−0.379919 | + | 0.925020i | \(0.624048\pi\) | |||||||
\(402\) | −2.02597e6 | −0.625271 | ||||||||
\(403\) | −1.66097e6 | −0.509447 | ||||||||
\(404\) | 3.75115e6 | 1.14343 | ||||||||
\(405\) | 157464. | 0.0477028 | ||||||||
\(406\) | −4.98053e6 | −1.49955 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.66066e6 | 0.493891 | ||||||||
\(409\) | 2.48818e6 | 0.735483 | 0.367742 | − | 0.929928i | \(-0.380131\pi\) | ||||
0.367742 | + | 0.929928i | \(0.380131\pi\) | |||||||
\(410\) | −1.69906e6 | −0.499170 | ||||||||
\(411\) | 961254. | 0.280694 | ||||||||
\(412\) | −4.00565e6 | −1.16260 | ||||||||
\(413\) | 1.97424e6 | 0.569541 | ||||||||
\(414\) | −3.37235e6 | −0.967013 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.02419e6 | 0.573480 | ||||||||
\(417\) | 3.26090e6 | 0.918326 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 405672. | 0.112886 | 0.0564430 | − | 0.998406i | \(-0.482024\pi\) | ||||
0.0564430 | + | 0.998406i | \(0.482024\pi\) | |||||||
\(420\) | 762048. | 0.210794 | ||||||||
\(421\) | −4.36275e6 | −1.19965 | −0.599825 | − | 0.800131i | \(-0.704763\pi\) | ||||
−0.599825 | + | 0.800131i | \(0.704763\pi\) | |||||||
\(422\) | −1.98596e6 | −0.542861 | ||||||||
\(423\) | −518562. | −0.140913 | ||||||||
\(424\) | −3.31765e6 | −0.896223 | ||||||||
\(425\) | 3.07409e6 | 0.825553 | ||||||||
\(426\) | −5.26970e6 | −1.40690 | ||||||||
\(427\) | 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 | \(0.765699\pi\) | |||||||
\(432\) | 139239. | 0.0358965 | ||||||||
\(433\) | −5.84150e6 | −1.49729 | −0.748643 | − | 0.662973i | \(-0.769294\pi\) | ||||
−0.748643 | + | 0.662973i | \(0.769294\pi\) | |||||||
\(434\) | −3.51734e6 | −0.896377 | ||||||||
\(435\) | −1.66018e6 | −0.420660 | ||||||||
\(436\) | 1.04561e7 | 2.63423 | ||||||||
\(437\) | −3.58052e6 | −0.896898 | ||||||||
\(438\) | −2.16076e6 | −0.538171 | ||||||||
\(439\) | −393336. | −0.0974097 | −0.0487049 | − | 0.998813i | \(-0.515509\pi\) | ||||
−0.0487049 | + | 0.998813i | \(0.515509\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −941463. | −0.230519 | ||||||||
\(442\) | 3.32132e6 | 0.808641 | ||||||||
\(443\) | −1.65260e6 | −0.400092 | −0.200046 | − | 0.979787i | \(-0.564109\pi\) | ||||
−0.200046 | + | 0.979787i | \(0.564109\pi\) | |||||||
\(444\) | −1.52321e6 | −0.366694 | ||||||||
\(445\) | −1.00008e6 | −0.239406 | ||||||||
\(446\) | −1.15335e7 | −2.74551 | ||||||||
\(447\) | −1.34833e6 | −0.319173 | ||||||||
\(448\) | 3.84646e6 | 0.905453 | ||||||||
\(449\) | 1.73199e6 | 0.405443 | 0.202721 | − | 0.979236i | \(-0.435021\pi\) | ||||
0.202721 | + | 0.979236i | \(0.435021\pi\) | |||||||
\(450\) | −1.85822e6 | −0.432580 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.93811e6 | −1.59733 | ||||||||
\(453\) | −3.02195e6 | −0.691897 | ||||||||
\(454\) | 1.30932e7 | 2.98130 | ||||||||
\(455\) | 528768. | 0.119739 | ||||||||
\(456\) | −1.06580e6 | −0.240028 | ||||||||
\(457\) | 5.66489e6 | 1.26882 | 0.634411 | − | 0.772996i | \(-0.281243\pi\) | ||||
0.634411 | + | 0.772996i | \(0.281243\pi\) | |||||||
\(458\) | −39438.0 | −0.00878519 | ||||||||
\(459\) | 879174. | 0.194779 | ||||||||
\(460\) | −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 | ||||||||
\(465\) | −1.17245e6 | −0.251456 | ||||||||
\(466\) | −9.65083e6 | −2.05873 | ||||||||
\(467\) | −6.29414e6 | −1.33550 | −0.667751 | − | 0.744385i | \(-0.732743\pi\) | ||||
−0.667751 | + | 0.744385i | \(0.732743\pi\) | |||||||
\(468\) | −1.21451e6 | −0.256323 | ||||||||
\(469\) | −1.80086e6 | −0.378050 | ||||||||
\(470\) | −1.38283e6 | −0.288752 | ||||||||
\(471\) | −1.39912e6 | −0.290605 | ||||||||
\(472\) | −4.19526e6 | −0.866770 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.50757e6 | −0.308200 | ||||||||
\(475\) | −1.97293e6 | −0.401215 | ||||||||
\(476\) | 4.25477e6 | 0.860713 | ||||||||
\(477\) | −1.75640e6 | −0.353450 | ||||||||
\(478\) | 7.45783e6 | 1.49294 | ||||||||
\(479\) | −7.28863e6 | −1.45147 | −0.725734 | − | 0.687976i | \(-0.758500\pi\) | ||||
−0.725734 | + | 0.687976i | \(0.758500\pi\) | |||||||
\(480\) | 1.42884e6 | 0.283061 | ||||||||
\(481\) | −1.05692e6 | −0.208296 | ||||||||
\(482\) | 5.41080e6 | 1.06083 | ||||||||
\(483\) | −2.99765e6 | −0.584673 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 976656. | 0.188533 | ||||||||
\(486\) | −531441. | −0.102062 | ||||||||
\(487\) | −2.01570e6 | −0.385126 | −0.192563 | − | 0.981285i | \(-0.561680\pi\) | ||||
−0.192563 | + | 0.981285i | \(0.561680\pi\) | |||||||
\(488\) | −8.08850e6 | −1.53751 | ||||||||
\(489\) | 1.92568e6 | 0.364176 | ||||||||
\(490\) | −2.51057e6 | −0.472369 | ||||||||
\(491\) | −538596. | −0.100823 | −0.0504115 | − | 0.998729i | \(-0.516053\pi\) | ||||
−0.0504115 | + | 0.998729i | \(0.516053\pi\) | |||||||
\(492\) | 3.46891e6 | 0.646070 | ||||||||
\(493\) | −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 | ||||||||
\(501\) | −3.83292e6 | −0.682237 | ||||||||
\(502\) | 1.02546e7 | 1.81618 | ||||||||
\(503\) | −4.64962e6 | −0.819402 | −0.409701 | − | 0.912220i | \(-0.634367\pi\) | ||||
−0.409701 | + | 0.912220i | \(0.634367\pi\) | |||||||
\(504\) | −892296. | −0.156471 | ||||||||
\(505\) | 1.83730e6 | 0.320591 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.49891e6 | 0.431749 | ||||||||
\(508\) | −9.64379e6 | −1.65801 | ||||||||
\(509\) | 6.73988e6 | 1.15308 | 0.576538 | − | 0.817070i | \(-0.304403\pi\) | ||||
0.576538 | + | 0.817070i | \(0.304403\pi\) | |||||||
\(510\) | 2.34446e6 | 0.399133 | ||||||||
\(511\) | −1.92067e6 | −0.325388 | ||||||||
\(512\) | 2.19860e6 | 0.370656 | ||||||||
\(513\) | −564246. | −0.0946619 | ||||||||
\(514\) | −4.19888e6 | −0.701012 | ||||||||
\(515\) | −1.96195e6 | −0.325965 | ||||||||
\(516\) | 6.96163e6 | 1.15103 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.23819e6 | −0.366499 | ||||||||
\(519\) | −6.51094e6 | −1.06102 | ||||||||
\(520\) | −1.12363e6 | −0.182228 | ||||||||
\(521\) | −2.62743e6 | −0.424069 | −0.212035 | − | 0.977262i | \(-0.568009\pi\) | ||||
−0.212035 | + | 0.977262i | \(0.568009\pi\) | |||||||
\(522\) | 5.60309e6 | 0.900019 | ||||||||
\(523\) | 8.18041e6 | 1.30774 | 0.653869 | − | 0.756608i | \(-0.273145\pi\) | ||||
0.653869 | + | 0.756608i | \(0.273145\pi\) | |||||||
\(524\) | 3.35336e6 | 0.533522 | ||||||||
\(525\) | −1.65175e6 | −0.261545 | ||||||||
\(526\) | −6.48454e6 | −1.02191 | ||||||||
\(527\) | −6.54617e6 | −1.02674 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.49635e7 | 2.32485 | ||||||||
\(530\) | −4.68374e6 | −0.724275 | ||||||||
\(531\) | −2.22102e6 | −0.341835 | ||||||||
\(532\) | −2.73067e6 | −0.418302 | ||||||||
\(533\) | 2.40700e6 | 0.366993 | ||||||||
\(534\) | 3.37527e6 | 0.512219 | ||||||||
\(535\) | 1.28995e6 | 0.194845 | ||||||||
\(536\) | 3.82684e6 | 0.575344 | ||||||||
\(537\) | −5.58101e6 | −0.835174 | ||||||||
\(538\) | −1.10243e7 | −1.64209 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −857304. | −0.126517 | ||||||||
\(541\) | −6.44510e6 | −0.946752 | −0.473376 | − | 0.880860i | \(-0.656965\pi\) | ||||
−0.473376 | + | 0.880860i | \(0.656965\pi\) | |||||||
\(542\) | 1.24056e7 | 1.81393 | ||||||||
\(543\) | −5.25919e6 | −0.765454 | ||||||||
\(544\) | 7.97769e6 | 1.15579 | ||||||||
\(545\) | 5.12136e6 | 0.738574 | ||||||||
\(546\) | −1.78459e6 | −0.256187 | ||||||||
\(547\) | −6.72241e6 | −0.960631 | −0.480315 | − | 0.877096i | \(-0.659478\pi\) | ||||
−0.480315 | + | 0.877096i | \(0.659478\pi\) | |||||||
\(548\) | −5.23349e6 | −0.744458 | ||||||||
\(549\) | −4.28215e6 | −0.606360 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.94896e6 | 0.834761 | ||||||||
\(552\) | 6.37000e6 | 0.889799 | ||||||||
\(553\) | −1.34006e6 | −0.186343 | ||||||||
\(554\) | 2.10265e7 | 2.91066 | ||||||||
\(555\) | −746064. | −0.102812 | ||||||||
\(556\) | −1.77538e7 | −2.43559 | ||||||||
\(557\) | 2.71874e6 | 0.371304 | 0.185652 | − | 0.982616i | \(-0.440560\pi\) | ||||
0.185652 | + | 0.982616i | \(0.440560\pi\) | |||||||
\(558\) | 3.95701e6 | 0.537999 | ||||||||
\(559\) | 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 | \(0.517316\pi\) | |||||||
\(564\) | 2.82328e6 | 0.373729 | ||||||||
\(565\) | −3.39826e6 | −0.447852 | ||||||||
\(566\) | 1.00289e7 | 1.31587 | ||||||||
\(567\) | −472392. | −0.0617085 | ||||||||
\(568\) | 9.95387e6 | 1.29456 | ||||||||
\(569\) | −8.33672e6 | −1.07948 | −0.539740 | − | 0.841832i | \(-0.681477\pi\) | ||||
−0.539740 | + | 0.841832i | \(0.681477\pi\) | |||||||
\(570\) | −1.50466e6 | −0.193977 | ||||||||
\(571\) | 8.20715e6 | 1.05342 | 0.526711 | − | 0.850044i | \(-0.323425\pi\) | ||||
0.526711 | + | 0.850044i | \(0.323425\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.85679e6 | −0.236252 | ||||||||
\(574\) | 5.09717e6 | 0.645727 | ||||||||
\(575\) | 1.17917e7 | 1.48732 | ||||||||
\(576\) | −4.32726e6 | −0.543447 | ||||||||
\(577\) | −605126. | −0.0756670 | −0.0378335 | − | 0.999284i | \(-0.512046\pi\) | ||||
−0.0378335 | + | 0.999284i | \(0.512046\pi\) | |||||||
\(578\) | 311211. | 0.0387468 | ||||||||
\(579\) | 8.23770e6 | 1.02120 | ||||||||
\(580\) | 9.03874e6 | 1.11568 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.29621e6 | −0.403374 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.08143e6 | 0.495199 | ||||||||
\(585\) | −594864. | −0.0718668 | ||||||||
\(586\) | −5.02702e6 | −0.604737 | ||||||||
\(587\) | −1.00479e7 | −1.20359 | −0.601797 | − | 0.798649i | \(-0.705548\pi\) | ||||
−0.601797 | + | 0.798649i | \(0.705548\pi\) | |||||||
\(588\) | 5.12574e6 | 0.611383 | ||||||||
\(589\) | 4.20127e6 | 0.498991 | ||||||||
\(590\) | −5.92272e6 | −0.700473 | ||||||||
\(591\) | −1.97980e6 | −0.233159 | ||||||||
\(592\) | −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 | ||||||||
\(597\) | −5.06750e6 | −0.581913 | ||||||||
\(598\) | 1.27400e7 | 1.45686 | ||||||||
\(599\) | −1.27169e7 | −1.44815 | −0.724075 | − | 0.689722i | \(-0.757733\pi\) | ||||
−0.724075 | + | 0.689722i | \(0.757733\pi\) | |||||||
\(600\) | 3.50997e6 | 0.398039 | ||||||||
\(601\) | −1.62535e7 | −1.83553 | −0.917763 | − | 0.397128i | \(-0.870007\pi\) | ||||
−0.917763 | + | 0.397128i | \(0.870007\pi\) | |||||||
\(602\) | 1.02293e7 | 1.15042 | ||||||||
\(603\) | 2.02597e6 | 0.226903 | ||||||||
\(604\) | 1.64528e7 | 1.83505 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.20087e6 | −0.685917 | ||||||||
\(607\) | 1.20900e7 | 1.33185 | 0.665923 | − | 0.746020i | \(-0.268038\pi\) | ||||
0.665923 | + | 0.746020i | \(0.268038\pi\) | |||||||
\(608\) | −5.12001e6 | −0.561710 | ||||||||
\(609\) | 4.98053e6 | 0.544167 | ||||||||
\(610\) | −1.14191e7 | −1.24253 | ||||||||
\(611\) | 1.95901e6 | 0.212292 | ||||||||
\(612\) | −4.78661e6 | −0.516595 | ||||||||
\(613\) | 2.83160e6 | 0.304355 | 0.152177 | − | 0.988353i | \(-0.451371\pi\) | ||||
0.152177 | + | 0.988353i | \(0.451371\pi\) | |||||||
\(614\) | 1.10132e7 | 1.17895 | ||||||||
\(615\) | 1.69906e6 | 0.181142 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.62285e6 | −0.171619 | −0.0858095 | − | 0.996312i | \(-0.527348\pi\) | ||||
−0.0858095 | + | 0.996312i | \(0.527348\pi\) | |||||||
\(618\) | 6.62159e6 | 0.697414 | ||||||||
\(619\) | 1.25560e6 | 0.131712 | 0.0658561 | − | 0.997829i | \(-0.479022\pi\) | ||||
0.0658561 | + | 0.997829i | \(0.479022\pi\) | |||||||
\(620\) | 6.38333e6 | 0.666911 | ||||||||
\(621\) | 3.37235e6 | 0.350917 | ||||||||
\(622\) | −1.72672e7 | −1.78956 | ||||||||
\(623\) | 3.00024e6 | 0.309696 | ||||||||
\(624\) | −526014. | −0.0540799 | ||||||||
\(625\) | 4.69740e6 | 0.481014 | ||||||||
\(626\) | −7.21463e6 | −0.735832 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.61744e6 | 0.770744 | ||||||||
\(629\) | −4.16552e6 | −0.419801 | ||||||||
\(630\) | −1.25971e6 | −0.126450 | ||||||||
\(631\) | −579044. | −0.0578946 | −0.0289473 | − | 0.999581i | \(-0.509216\pi\) | ||||
−0.0289473 | + | 0.999581i | \(0.509216\pi\) | |||||||
\(632\) | 2.84764e6 | 0.283591 | ||||||||
\(633\) | 1.98596e6 | 0.196998 | ||||||||
\(634\) | −2.11070e7 | −2.08547 | ||||||||
\(635\) | −4.72349e6 | −0.464867 | ||||||||
\(636\) | 9.56264e6 | 0.937422 | ||||||||
\(637\) | 3.55664e6 | 0.347289 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.26970e6 | 0.510544 | ||||||||
\(640\) | −6.45905e6 | −0.623331 | ||||||||
\(641\) | −1.12839e7 | −1.08471 | −0.542354 | − | 0.840150i | \(-0.682467\pi\) | ||||
−0.542354 | + | 0.840150i | \(0.682467\pi\) | |||||||
\(642\) | −4.35359e6 | −0.416879 | ||||||||
\(643\) | 1.60866e7 | 1.53439 | 0.767196 | − | 0.641413i | \(-0.221652\pi\) | ||||
0.767196 | + | 0.641413i | \(0.221652\pi\) | |||||||
\(644\) | 1.63205e7 | 1.55067 | ||||||||
\(645\) | 3.40978e6 | 0.322721 | ||||||||
\(646\) | −8.40100e6 | −0.792044 | ||||||||
\(647\) | 7.80003e6 | 0.732547 | 0.366274 | − | 0.930507i | \(-0.380633\pi\) | ||||
0.366274 | + | 0.930507i | \(0.380633\pi\) | |||||||
\(648\) | 1.00383e6 | 0.0939126 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 7.01995e6 | 0.651704 | ||||||||
\(651\) | 3.51734e6 | 0.325284 | ||||||||
\(652\) | −1.04842e7 | −0.965868 | ||||||||
\(653\) | −3.81000e6 | −0.349657 | −0.174828 | − | 0.984599i | \(-0.555937\pi\) | ||||
−0.174828 | + | 0.984599i | \(0.555937\pi\) | |||||||
\(654\) | −1.72846e7 | −1.58021 | ||||||||
\(655\) | 1.64246e6 | 0.149587 | ||||||||
\(656\) | 1.50241e6 | 0.136310 | ||||||||
\(657\) | 2.16076e6 | 0.195296 | ||||||||
\(658\) | 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 | ||||||||
\(663\) | −3.32132e6 | −0.293445 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.33747e6 | −0.117282 | ||||||||
\(666\) | 2.51797e6 | 0.219970 | ||||||||
\(667\) | −3.55554e7 | −3.09451 | ||||||||
\(668\) | 2.08681e7 | 1.80943 | ||||||||
\(669\) | 1.15335e7 | 0.996310 | ||||||||
\(670\) | 5.40259e6 | 0.464960 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −4.28652e6 | −0.366169 | ||||||||
\(673\) | 1.33261e7 | 1.13414 | 0.567068 | − | 0.823671i | \(-0.308078\pi\) | ||||
0.567068 | + | 0.823671i | \(0.308078\pi\) | |||||||
\(674\) | −1.30323e7 | −1.10502 | ||||||||
\(675\) | 1.85822e6 | 0.156978 | ||||||||
\(676\) | −1.36052e7 | −1.14509 | ||||||||
\(677\) | 9.75076e6 | 0.817649 | 0.408824 | − | 0.912613i | \(-0.365939\pi\) | ||||
0.408824 | + | 0.912613i | \(0.365939\pi\) | |||||||
\(678\) | 1.14691e7 | 0.958199 | ||||||||
\(679\) | −2.92997e6 | −0.243887 | ||||||||
\(680\) | −4.42843e6 | −0.367263 | ||||||||
\(681\) | −1.30932e7 | −1.08187 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.79889e6 | 0.311605 | 0.155803 | − | 0.987788i | \(-0.450204\pi\) | ||||
0.155803 | + | 0.987788i | \(0.450204\pi\) | |||||||
\(684\) | 3.07201e6 | 0.251062 | ||||||||
\(685\) | −2.56334e6 | −0.208728 | ||||||||
\(686\) | 1.84226e7 | 1.49466 | ||||||||
\(687\) | 39438.0 | 0.00318803 | ||||||||
\(688\) | 3.01513e6 | 0.242848 | ||||||||
\(689\) | 6.63530e6 | 0.532492 | ||||||||
\(690\) | 8.99294e6 | 0.719083 | ||||||||
\(691\) | 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 | ||||||||
\(696\) | −1.05836e7 | −0.828154 | ||||||||
\(697\) | 9.48640e6 | 0.739638 | ||||||||
\(698\) | 2.39042e7 | 1.85710 | ||||||||
\(699\) | 9.65083e6 | 0.747088 | ||||||||
\(700\) | 8.99287e6 | 0.693671 | ||||||||
\(701\) | 2.79859e6 | 0.215102 | 0.107551 | − | 0.994200i | \(-0.465699\pi\) | ||||
0.107551 | + | 0.994200i | \(0.465699\pi\) | |||||||
\(702\) | 2.00767e6 | 0.153762 | ||||||||
\(703\) | 2.67340e6 | 0.204021 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.38283e6 | 0.104784 | ||||||||
\(706\) | −1.26553e7 | −0.955564 | ||||||||
\(707\) | −5.51189e6 | −0.414717 | ||||||||
\(708\) | 1.20922e7 | 0.906615 | ||||||||
\(709\) | −2.45413e7 | −1.83350 | −0.916752 | − | 0.399457i | \(-0.869199\pi\) | ||||
−0.916752 | + | 0.399457i | \(0.869199\pi\) | |||||||
\(710\) | 1.40525e7 | 1.04619 | ||||||||
\(711\) | 1.50757e6 | 0.111842 | ||||||||
\(712\) | −6.37551e6 | −0.471319 | ||||||||
\(713\) | −2.51099e7 | −1.84979 | ||||||||
\(714\) | −7.03339e6 | −0.516320 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.03855e7 | 2.21505 | ||||||||
\(717\) | −7.45783e6 | −0.541770 | ||||||||
\(718\) | −2.83280e7 | −2.05071 | ||||||||
\(719\) | −4.81287e6 | −0.347202 | −0.173601 | − | 0.984816i | \(-0.555540\pi\) | ||||
−0.173601 | + | 0.984816i | \(0.555540\pi\) | |||||||
\(720\) | −371304. | −0.0266931 | ||||||||
\(721\) | 5.88586e6 | 0.421669 | ||||||||
\(722\) | −1.68932e7 | −1.20606 | ||||||||
\(723\) | −5.41080e6 | −0.384960 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 5.76202e6 | 0.400191 | ||||||||
\(731\) | 1.90379e7 | 1.31773 | ||||||||
\(732\) | 2.33139e7 | 1.60819 | ||||||||
\(733\) | −2.60411e6 | −0.179019 | −0.0895097 | − | 0.995986i | \(-0.528530\pi\) | ||||
−0.0895097 | + | 0.995986i | \(0.528530\pi\) | |||||||
\(734\) | −1.57325e7 | −1.07785 | ||||||||
\(735\) | 2.51057e6 | 0.171417 | ||||||||
\(736\) | 3.06010e7 | 2.08229 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −5.73431e6 | −0.387561 | ||||||||
\(739\) | 1.85178e7 | 1.24732 | 0.623661 | − | 0.781695i | \(-0.285645\pi\) | ||||
0.623661 | + | 0.781695i | \(0.285645\pi\) | |||||||
\(740\) | 4.06190e6 | 0.272678 | ||||||||
\(741\) | 2.13160e6 | 0.142613 | ||||||||
\(742\) | 1.40512e7 | 0.936925 | ||||||||
\(743\) | −3.01104e6 | −0.200099 | −0.100049 | − | 0.994982i | \(-0.531900\pi\) | ||||
−0.100049 | + | 0.994982i | \(0.531900\pi\) | |||||||
\(744\) | −7.47436e6 | −0.495041 | ||||||||
\(745\) | 3.59554e6 | 0.237341 | ||||||||
\(746\) | −2.97832e7 | −1.95941 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.86986e6 | −0.252052 | ||||||||
\(750\) | 1.10303e7 | 0.716032 | ||||||||
\(751\) | 1.41805e7 | 0.917470 | 0.458735 | − | 0.888573i | \(-0.348303\pi\) | ||||
0.458735 | + | 0.888573i | \(0.348303\pi\) | |||||||
\(752\) | 1.22278e6 | 0.0788505 | ||||||||
\(753\) | −1.02546e7 | −0.659070 | ||||||||
\(754\) | −2.11672e7 | −1.35593 | ||||||||
\(755\) | 8.05853e6 | 0.514504 | ||||||||
\(756\) | 2.57191e6 | 0.163663 | ||||||||
\(757\) | −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 | \(0.388345\pi\) | |||||||
\(762\) | 1.59418e7 | 0.994602 | ||||||||
\(763\) | −1.53641e7 | −0.955422 | ||||||||
\(764\) | 1.01092e7 | 0.626589 | ||||||||
\(765\) | −2.34446e6 | −0.144840 | ||||||||
\(766\) | −1.00936e7 | −0.621549 | ||||||||
\(767\) | 8.39052e6 | 0.514992 | ||||||||
\(768\) | 6.41346e6 | 0.392364 | ||||||||
\(769\) | 1.88030e7 | 1.14660 | 0.573299 | − | 0.819347i | \(-0.305664\pi\) | ||||
0.573299 | + | 0.819347i | \(0.305664\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.19888e6 | 0.254388 | ||||||||
\(772\) | −4.48497e7 | −2.70842 | ||||||||
\(773\) | −1.21929e7 | −0.733935 | −0.366967 | − | 0.930234i | \(-0.619604\pi\) | ||||
−0.366967 | + | 0.930234i | \(0.619604\pi\) | |||||||
\(774\) | −1.15080e7 | −0.690474 | ||||||||
\(775\) | −1.38360e7 | −0.827476 | ||||||||
\(776\) | 6.22618e6 | 0.371165 | ||||||||
\(777\) | 2.23819e6 | 0.132998 | ||||||||
\(778\) | −2.77936e7 | −1.64625 | ||||||||
\(779\) | −6.08828e6 | −0.359461 | ||||||||
\(780\) | 3.23870e6 | 0.190605 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 5.02106e7 | 2.93615 | ||||||||
\(783\) | −5.60309e6 | −0.326606 | ||||||||
\(784\) | 2.21999e6 | 0.128992 | ||||||||
\(785\) | 3.73099e6 | 0.216098 | ||||||||
\(786\) | −5.54332e6 | −0.320047 | ||||||||
\(787\) | −2.75304e7 | −1.58444 | −0.792221 | − | 0.610234i | \(-0.791075\pi\) | ||||
−0.792221 | + | 0.610234i | \(0.791075\pi\) | |||||||
\(788\) | 1.07789e7 | 0.618386 | ||||||||
\(789\) | 6.48454e6 | 0.370840 | ||||||||
\(790\) | 4.02019e6 | 0.229181 | ||||||||
\(791\) | 1.01948e7 | 0.579343 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.61770e7 | 0.913513 | ||||||||
\(794\) | 4.55935e6 | 0.256656 | ||||||||
\(795\) | 4.68374e6 | 0.262830 | ||||||||
\(796\) | 2.75897e7 | 1.54335 | ||||||||
\(797\) | 2.46936e7 | 1.37701 | 0.688507 | − | 0.725230i | \(-0.258267\pi\) | ||||
0.688507 | + | 0.725230i | \(0.258267\pi\) | |||||||
\(798\) | 4.51397e6 | 0.250929 | ||||||||
\(799\) | 7.72081e6 | 0.427854 | ||||||||
\(800\) | 1.68616e7 | 0.931483 | ||||||||
\(801\) | −3.37527e6 | −0.185878 | ||||||||
\(802\) | −2.20204e7 | −1.20890 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.10303e7 | −0.601793 | ||||||||
\(805\) | 7.99373e6 | 0.434770 | ||||||||
\(806\) | −1.49487e7 | −0.810525 | ||||||||
\(807\) | 1.10243e7 | 0.595892 | ||||||||
\(808\) | 1.17128e7 | 0.631148 | ||||||||
\(809\) | −2.40376e7 | −1.29128 | −0.645639 | − | 0.763642i | \(-0.723409\pi\) | ||||
−0.645639 | + | 0.763642i | \(0.723409\pi\) | |||||||
\(810\) | 1.41718e6 | 0.0758947 | ||||||||
\(811\) | −3.38751e6 | −0.180854 | −0.0904271 | − | 0.995903i | \(-0.528823\pi\) | ||||
−0.0904271 | + | 0.995903i | \(0.528823\pi\) | |||||||
\(812\) | −2.71162e7 | −1.44324 | ||||||||
\(813\) | −1.24056e7 | −0.658253 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.13514e6 | −0.270806 | ||||||||
\(816\) | −2.07311e6 | −0.108993 | ||||||||
\(817\) | −1.22184e7 | −0.640410 | ||||||||
\(818\) | 2.23936e7 | 1.17015 | ||||||||
\(819\) | 1.78459e6 | 0.0929671 | ||||||||
\(820\) | −9.25042e6 | −0.480426 | ||||||||
\(821\) | −2.68551e6 | −0.139049 | −0.0695247 | − | 0.997580i | \(-0.522148\pi\) | ||||
−0.0695247 | + | 0.997580i | \(0.522148\pi\) | |||||||
\(822\) | 8.65129e6 | 0.446582 | ||||||||
\(823\) | 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 | \(0.720558\pi\) | |||||||
\(828\) | −1.83606e7 | −0.930703 | ||||||||
\(829\) | 3.00676e7 | 1.51954 | 0.759770 | − | 0.650191i | \(-0.225311\pi\) | ||||
0.759770 | + | 0.650191i | \(0.225311\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.10265e7 | −1.05624 | ||||||||
\(832\) | 1.63474e7 | 0.818731 | ||||||||
\(833\) | 1.40173e7 | 0.699927 | ||||||||
\(834\) | 2.93481e7 | 1.46105 | ||||||||
\(835\) | 1.02211e7 | 0.507320 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.95701e6 | −0.195233 | ||||||||
\(838\) | 3.65105e6 | 0.179600 | ||||||||
\(839\) | 3.77681e7 | 1.85234 | 0.926170 | − | 0.377107i | \(-0.123081\pi\) | ||||
0.926170 | + | 0.377107i | \(0.123081\pi\) | |||||||
\(840\) | 2.37946e6 | 0.116354 | ||||||||
\(841\) | 3.85634e7 | 1.88012 | ||||||||
\(842\) | −3.92647e7 | −1.90863 | ||||||||
\(843\) | 2.13887e7 | 1.03661 | ||||||||
\(844\) | −1.08124e7 | −0.522477 | ||||||||
\(845\) | −6.66377e6 | −0.321054 | ||||||||
\(846\) | −4.66706e6 | −0.224191 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.14164e6 | 0.197780 | ||||||||
\(849\) | −1.00289e7 | −0.477513 | ||||||||
\(850\) | 2.76668e7 | 1.31345 | ||||||||
\(851\) | −1.59782e7 | −0.756317 | ||||||||
\(852\) | −2.86906e7 | −1.35407 | ||||||||
\(853\) | 254934. | 0.0119965 | 0.00599826 | − | 0.999982i | \(-0.498091\pi\) | ||||
0.00599826 | + | 0.999982i | \(0.498091\pi\) | |||||||
\(854\) | 3.42572e7 | 1.60734 | ||||||||
\(855\) | 1.50466e6 | 0.0703918 | ||||||||
\(856\) | 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 | ||||||||
\(861\) | −5.09717e6 | −0.234326 | ||||||||
\(862\) | −5.14454e7 | −2.35819 | ||||||||
\(863\) | 2.01011e6 | 0.0918742 | 0.0459371 | − | 0.998944i | \(-0.485373\pi\) | ||||
0.0459371 | + | 0.998944i | \(0.485373\pi\) | |||||||
\(864\) | 4.82234e6 | 0.219772 | ||||||||
\(865\) | 1.73625e7 | 0.788991 | ||||||||
\(866\) | −5.25735e7 | −2.38217 | ||||||||
\(867\) | −311211. | −0.0140607 | ||||||||
\(868\) | −1.91500e7 | −0.862718 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −1.49416e7 | −0.669266 | ||||||||
\(871\) | −7.65367e6 | −0.341841 | ||||||||
\(872\) | 3.26487e7 | 1.45403 | ||||||||
\(873\) | 3.29621e6 | 0.146379 | ||||||||
\(874\) | −3.22247e7 | −1.42696 | ||||||||
\(875\) | 9.80467e6 | 0.432925 | ||||||||
\(876\) | −1.17641e7 | −0.517963 | ||||||||
\(877\) | 7.26086e6 | 0.318778 | 0.159389 | − | 0.987216i | \(-0.449048\pi\) | ||||
0.159389 | + | 0.987216i | \(0.449048\pi\) | |||||||
\(878\) | −3.54002e6 | −0.154978 | ||||||||
\(879\) | 5.02702e6 | 0.219452 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.04800e7 | −1.75712 | −0.878558 | − | 0.477636i | \(-0.841494\pi\) | ||||
−0.878558 | + | 0.477636i | \(0.841494\pi\) | |||||||
\(882\) | −8.47317e6 | −0.366754 | ||||||||
\(883\) | −2.00636e7 | −0.865979 | −0.432990 | − | 0.901399i | \(-0.642541\pi\) | ||||
−0.432990 | + | 0.901399i | \(0.642541\pi\) | |||||||
\(884\) | 1.80828e7 | 0.778277 | ||||||||
\(885\) | 5.92272e6 | 0.254193 | ||||||||
\(886\) | −1.48734e7 | −0.636542 | ||||||||
\(887\) | 1.42543e7 | 0.608325 | 0.304163 | − | 0.952620i | \(-0.401623\pi\) | ||||
0.304163 | + | 0.952620i | \(0.401623\pi\) | |||||||
\(888\) | −4.75616e6 | −0.202406 | ||||||||
\(889\) | 1.41705e7 | 0.601353 | ||||||||
\(890\) | −9.00072e6 | −0.380892 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.27933e7 | −2.64242 | ||||||||
\(893\) | −4.95515e6 | −0.207935 | ||||||||
\(894\) | −1.21349e7 | −0.507801 | ||||||||
\(895\) | 1.48827e7 | 0.621046 | ||||||||
\(896\) | 1.93771e7 | 0.806343 | ||||||||
\(897\) | −1.27400e7 | −0.528675 | ||||||||
\(898\) | 1.55879e7 | 0.645055 | ||||||||
\(899\) | 4.17196e7 | 1.72163 | ||||||||
\(900\) | −1.01170e7 | −0.416337 | ||||||||
\(901\) | 2.61509e7 | 1.07319 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.02293e7 | −0.417472 | ||||||||
\(904\) | −2.16639e7 | −0.881689 | ||||||||
\(905\) | 1.40245e7 | 0.569201 | ||||||||
\(906\) | −2.71975e7 | −1.10080 | ||||||||
\(907\) | −3.25752e7 | −1.31483 | −0.657413 | − | 0.753530i | \(-0.728349\pi\) | ||||
−0.657413 | + | 0.753530i | \(0.728349\pi\) | |||||||
\(908\) | 7.12850e7 | 2.86935 | ||||||||
\(909\) | 6.20087e6 | 0.248910 | ||||||||
\(910\) | 4.75891e6 | 0.190504 | ||||||||
\(911\) | 7.00624e6 | 0.279698 | 0.139849 | − | 0.990173i | \(-0.455338\pi\) | ||||
0.139849 | + | 0.990173i | \(0.455338\pi\) | |||||||
\(912\) | 1.33051e6 | 0.0529700 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 5.09840e7 | 2.01868 | ||||||||
\(915\) | 1.14191e7 | 0.450897 | ||||||||
\(916\) | −214718. | −0.00845531 | ||||||||
\(917\) | −4.92739e6 | −0.193506 | ||||||||
\(918\) | 7.91257e6 | 0.309892 | ||||||||
\(919\) | 2.17803e7 | 0.850695 | 0.425348 | − | 0.905030i | \(-0.360152\pi\) | ||||
0.425348 | + | 0.905030i | \(0.360152\pi\) | |||||||
\(920\) | −1.69867e7 | −0.661666 | ||||||||
\(921\) | −1.10132e7 | −0.427825 | ||||||||
\(922\) | −7.45184e6 | −0.288693 | ||||||||
\(923\) | −1.99077e7 | −0.769162 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.80425e6 | −0.338328 | ||||||||
\(926\) | −2.91829e7 | −1.11841 | ||||||||
\(927\) | −6.62159e6 | −0.253083 | ||||||||
\(928\) | −5.08429e7 | −1.93803 | ||||||||
\(929\) | −4.88614e7 | −1.85749 | −0.928745 | − | 0.370720i | \(-0.879111\pi\) | ||||
−0.928745 | + | 0.370720i | \(0.879111\pi\) | |||||||
\(930\) | −1.05520e7 | −0.400063 | ||||||||
\(931\) | −8.99620e6 | −0.340161 | ||||||||
\(932\) | −5.25434e7 | −1.98143 | ||||||||
\(933\) | 1.72672e7 | 0.649408 | ||||||||
\(934\) | −5.66473e7 | −2.12477 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.79226e6 | −0.141484 | ||||||||
\(937\) | 1.16064e6 | 0.0431866 | 0.0215933 | − | 0.999767i | \(-0.493126\pi\) | ||||
0.0215933 | + | 0.999767i | \(0.493126\pi\) | |||||||
\(938\) | −1.62078e7 | −0.601473 | ||||||||
\(939\) | 7.21463e6 | 0.267024 | ||||||||
\(940\) | −7.52875e6 | −0.277909 | ||||||||
\(941\) | −4.50576e7 | −1.65880 | −0.829400 | − | 0.558656i | \(-0.811317\pi\) | ||||
−0.829400 | + | 0.558656i | \(0.811317\pi\) | |||||||
\(942\) | −1.25921e7 | −0.462350 | ||||||||
\(943\) | 3.63881e7 | 1.33254 | ||||||||
\(944\) | 5.23722e6 | 0.191281 | ||||||||
\(945\) | 1.25971e6 | 0.0458872 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.06091e7 | −0.384418 | −0.192209 | − | 0.981354i | \(-0.561565\pi\) | ||||
−0.192209 | + | 0.981354i | \(0.561565\pi\) | |||||||
\(948\) | −8.20789e6 | −0.296627 | ||||||||
\(949\) | −8.16286e6 | −0.294223 | ||||||||
\(950\) | −1.77563e7 | −0.638329 | ||||||||
\(951\) | 2.11070e7 | 0.756789 | ||||||||
\(952\) | 1.32853e7 | 0.475093 | ||||||||
\(953\) | 3.63059e7 | 1.29493 | 0.647463 | − | 0.762097i | \(-0.275830\pi\) | ||||
0.647463 | + | 0.762097i | \(0.275830\pi\) | |||||||
\(954\) | −1.58076e7 | −0.562336 | ||||||||
\(955\) | 4.95144e6 | 0.175680 | ||||||||
\(956\) | 4.06038e7 | 1.43688 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.55977e7 | −2.30927 | ||||||||
\(959\) | 7.69003e6 | 0.270011 | ||||||||
\(960\) | 1.15394e7 | 0.404114 | ||||||||
\(961\) | 834033. | 0.0291323 | ||||||||
\(962\) | −9.51232e6 | −0.331397 | ||||||||
\(963\) | 4.35359e6 | 0.151280 | ||||||||
\(964\) | 2.94588e7 | 1.02099 | ||||||||
\(965\) | −2.19672e7 | −0.759375 | ||||||||
\(966\) | −2.69788e7 | −0.930209 | ||||||||
\(967\) | −2.10387e7 | −0.723524 | −0.361762 | − | 0.932270i | \(-0.617825\pi\) | ||||
−0.361762 | + | 0.932270i | \(0.617825\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.40100e6 | 0.287423 | ||||||||
\(970\) | 8.78990e6 | 0.299954 | ||||||||
\(971\) | 3.58180e7 | 1.21914 | 0.609570 | − | 0.792732i | \(-0.291342\pi\) | ||||
0.609570 | + | 0.792732i | \(0.291342\pi\) | |||||||
\(972\) | −2.89340e6 | −0.0982297 | ||||||||
\(973\) | 2.60872e7 | 0.883375 | ||||||||
\(974\) | −1.81413e7 | −0.612731 | ||||||||
\(975\) | −7.01995e6 | −0.236495 | ||||||||
\(976\) | 1.00974e7 | 0.339301 | ||||||||
\(977\) | −1.22823e6 | −0.0411664 | −0.0205832 | − | 0.999788i | \(-0.506552\pi\) | ||||
−0.0205832 | + | 0.999788i | \(0.506552\pi\) | |||||||
\(978\) | 1.73311e7 | 0.579400 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.36686e7 | −0.454632 | ||||||||
\(981\) | 1.72846e7 | 0.573438 | ||||||||
\(982\) | −4.84736e6 | −0.160408 | ||||||||
\(983\) | 3.68929e6 | 0.121775 | 0.0608876 | − | 0.998145i | \(-0.480607\pi\) | ||||
0.0608876 | + | 0.998145i | \(0.480607\pi\) | |||||||
\(984\) | 1.08315e7 | 0.356615 | ||||||||
\(985\) | 5.27947e6 | 0.173380 | ||||||||
\(986\) | −8.34238e7 | −2.73274 | ||||||||
\(987\) | −4.14850e6 | −0.135549 | ||||||||
\(988\) | −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 | ||||||||
\(993\) | −2.97905e7 | −0.958747 | ||||||||
\(994\) | −4.21576e7 | −1.35335 | ||||||||
\(995\) | 1.35133e7 | 0.432718 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.87328e7 | −0.915462 | −0.457731 | − | 0.889091i | \(-0.651338\pi\) | ||||
−0.457731 | + | 0.889091i | \(0.651338\pi\) | |||||||
\(998\) | 4.64029e7 | 1.47475 | ||||||||
\(999\) | −2.51797e6 | −0.0798245 |
(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 | 363.6.a.e.1.1 | yes | 1 | |
3.2 | odd | 2 | 1089.6.a.a.1.1 | 1 | |||
11.10 | odd | 2 | 363.6.a.a.1.1 | ✓ | 1 | ||
33.32 | even | 2 | 1089.6.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.6.a.a.1.1 | ✓ | 1 | 11.10 | odd | 2 | ||
363.6.a.e.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
1089.6.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
1089.6.a.i.1.1 | 1 | 33.32 | even | 2 |