Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,6,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(85.1638083207\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5 x^{10} - 238 x^{9} + 1067 x^{8} + 20782 x^{7} - 79077 x^{6} - 813818 x^{5} + 2364885 x^{4} + \cdots - 14846072 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(4.20625\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.20625 | −0.566790 | −0.283395 | − | 0.959003i | \(-0.591461\pi\) | ||||
−0.283395 | + | 0.959003i | \(0.591461\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −21.7200 | −0.678749 | ||||||||
\(5\) | −26.7258 | −0.478086 | −0.239043 | − | 0.971009i | \(-0.576834\pi\) | ||||
−0.239043 | + | 0.971009i | \(0.576834\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 39.0273 | 0.301039 | 0.150520 | − | 0.988607i | \(-0.451905\pi\) | ||||
0.150520 | + | 0.988607i | \(0.451905\pi\) | |||||||
\(8\) | 172.240 | 0.951498 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 85.6897 | 0.270974 | ||||||||
\(11\) | 606.405 | 1.51106 | 0.755528 | − | 0.655116i | \(-0.227380\pi\) | ||||
0.755528 | + | 0.655116i | \(0.227380\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −161.707 | −0.265382 | −0.132691 | − | 0.991157i | \(-0.542362\pi\) | ||||
−0.132691 | + | 0.991157i | \(0.542362\pi\) | |||||||
\(14\) | −125.131 | −0.170626 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 142.797 | 0.139450 | ||||||||
\(17\) | 1651.20 | 1.38572 | 0.692861 | − | 0.721071i | \(-0.256350\pi\) | ||||
0.692861 | + | 0.721071i | \(0.256350\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 882.094 | 0.560572 | 0.280286 | − | 0.959917i | \(-0.409571\pi\) | ||||
0.280286 | + | 0.959917i | \(0.409571\pi\) | |||||||
\(20\) | 580.485 | 0.324501 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1944.28 | −0.856451 | ||||||||
\(23\) | −2923.63 | −1.15240 | −0.576199 | − | 0.817309i | \(-0.695465\pi\) | ||||
−0.576199 | + | 0.817309i | \(0.695465\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2410.73 | −0.771433 | ||||||||
\(26\) | 518.474 | 0.150416 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −847.672 | −0.204330 | ||||||||
\(29\) | 7064.00 | 1.55975 | 0.779876 | − | 0.625934i | \(-0.215282\pi\) | ||||
0.779876 | + | 0.625934i | \(0.215282\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2253.17 | −0.421105 | −0.210553 | − | 0.977583i | \(-0.567526\pi\) | ||||
−0.210553 | + | 0.977583i | \(0.567526\pi\) | |||||||
\(32\) | −5969.51 | −1.03054 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5294.14 | −0.785413 | ||||||||
\(35\) | −1043.04 | −0.143923 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7561.88 | −0.908082 | −0.454041 | − | 0.890981i | \(-0.650018\pi\) | ||||
−0.454041 | + | 0.890981i | \(0.650018\pi\) | |||||||
\(38\) | −2828.21 | −0.317726 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4603.25 | −0.454898 | ||||||||
\(41\) | 16708.0 | 1.55226 | 0.776130 | − | 0.630574i | \(-0.217180\pi\) | ||||
0.776130 | + | 0.630574i | \(0.217180\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4502.50 | −0.371349 | −0.185675 | − | 0.982611i | \(-0.559447\pi\) | ||||
−0.185675 | + | 0.982611i | \(0.559447\pi\) | |||||||
\(44\) | −13171.1 | −1.02563 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9373.88 | 0.653168 | ||||||||
\(47\) | −8408.79 | −0.555251 | −0.277625 | − | 0.960689i | \(-0.589547\pi\) | ||||
−0.277625 | + | 0.960689i | \(0.589547\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15283.9 | −0.909375 | ||||||||
\(50\) | 7729.39 | 0.437241 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3512.28 | 0.180128 | ||||||||
\(53\) | −11049.2 | −0.540307 | −0.270154 | − | 0.962817i | \(-0.587075\pi\) | ||||
−0.270154 | + | 0.962817i | \(0.587075\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16206.7 | −0.722416 | ||||||||
\(56\) | 6722.04 | 0.286438 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −22648.9 | −0.884052 | ||||||||
\(59\) | −3481.00 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 34738.9 | 1.19534 | 0.597670 | − | 0.801742i | \(-0.296093\pi\) | ||||
0.597670 | + | 0.801742i | \(0.296093\pi\) | |||||||
\(62\) | 7224.23 | 0.238678 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 14570.2 | 0.444648 | ||||||||
\(65\) | 4321.76 | 0.126875 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −57227.0 | −1.55745 | −0.778724 | − | 0.627366i | \(-0.784133\pi\) | ||||
−0.778724 | + | 0.627366i | \(0.784133\pi\) | |||||||
\(68\) | −35863.9 | −0.940558 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3344.23 | 0.0815740 | ||||||||
\(71\) | −26.9044 | −0.000633398 0 | −0.000316699 | − | 1.00000i | \(-0.500101\pi\) | ||||
−0.000316699 | 1.00000i | \(0.500101\pi\) | ||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 54481.3 | 1.19658 | 0.598288 | − | 0.801281i | \(-0.295848\pi\) | ||||
0.598288 | + | 0.801281i | \(0.295848\pi\) | |||||||
\(74\) | 24245.2 | 0.514692 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −19159.1 | −0.380488 | ||||||||
\(77\) | 23666.3 | 0.454887 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 93190.6 | 1.67998 | 0.839990 | − | 0.542601i | \(-0.182561\pi\) | ||||
0.839990 | + | 0.542601i | \(0.182561\pi\) | |||||||
\(80\) | −3816.37 | −0.0666692 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −53569.9 | −0.879805 | ||||||||
\(83\) | 89600.1 | 1.42762 | 0.713811 | − | 0.700339i | \(-0.246968\pi\) | ||||
0.713811 | + | 0.700339i | \(0.246968\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −44129.6 | −0.662495 | ||||||||
\(86\) | 14436.1 | 0.210477 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 104447. | 1.43777 | ||||||||
\(89\) | 128157. | 1.71502 | 0.857508 | − | 0.514471i | \(-0.172012\pi\) | ||||
0.857508 | + | 0.514471i | \(0.172012\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6311.00 | −0.0798904 | ||||||||
\(92\) | 63501.2 | 0.782190 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 26960.7 | 0.314710 | ||||||||
\(95\) | −23574.7 | −0.268002 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −26665.5 | −0.287753 | −0.143877 | − | 0.989596i | \(-0.545957\pi\) | ||||
−0.143877 | + | 0.989596i | \(0.545957\pi\) | |||||||
\(98\) | 49003.9 | 0.515425 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 52361.0 | 0.523610 | ||||||||
\(101\) | −153961. | −1.50178 | −0.750890 | − | 0.660427i | \(-0.770375\pi\) | ||||
−0.750890 | + | 0.660427i | \(0.770375\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −51991.3 | −0.482878 | −0.241439 | − | 0.970416i | \(-0.577619\pi\) | ||||
−0.241439 | + | 0.970416i | \(0.577619\pi\) | |||||||
\(104\) | −27852.4 | −0.252510 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 35426.4 | 0.306241 | ||||||||
\(107\) | −215950. | −1.82345 | −0.911725 | − | 0.410801i | \(-0.865249\pi\) | ||||
−0.911725 | + | 0.410801i | \(0.865249\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 62561.7 | 0.504362 | 0.252181 | − | 0.967680i | \(-0.418852\pi\) | ||||
0.252181 | + | 0.967680i | \(0.418852\pi\) | |||||||
\(110\) | 51962.6 | 0.409458 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5572.98 | 0.0419800 | ||||||||
\(113\) | −242539. | −1.78684 | −0.893421 | − | 0.449220i | \(-0.851702\pi\) | ||||
−0.893421 | + | 0.449220i | \(0.851702\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 78136.5 | 0.550946 | ||||||||
\(116\) | −153430. | −1.05868 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11160.9 | 0.0737897 | ||||||||
\(119\) | 64441.7 | 0.417157 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 206675. | 1.28329 | ||||||||
\(122\) | −111381. | −0.677506 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 48938.9 | 0.285825 | ||||||||
\(125\) | 147947. | 0.846898 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4520.72 | 0.0248713 | 0.0124356 | − | 0.999923i | \(-0.496042\pi\) | ||||
0.0124356 | + | 0.999923i | \(0.496042\pi\) | |||||||
\(128\) | 144309. | 0.778515 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −13856.6 | −0.0719117 | ||||||||
\(131\) | 201847. | 1.02765 | 0.513823 | − | 0.857896i | \(-0.328229\pi\) | ||||
0.513823 | + | 0.857896i | \(0.328229\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 34425.8 | 0.168754 | ||||||||
\(134\) | 183484. | 0.882746 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 284401. | 1.31851 | ||||||||
\(137\) | −128569. | −0.585242 | −0.292621 | − | 0.956229i | \(-0.594527\pi\) | ||||
−0.292621 | + | 0.956229i | \(0.594527\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 264506. | 1.16118 | 0.580588 | − | 0.814198i | \(-0.302823\pi\) | ||||
0.580588 | + | 0.814198i | \(0.302823\pi\) | |||||||
\(140\) | 22654.7 | 0.0976875 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 86.2620 | 0.000359003 0 | ||||||||
\(143\) | −98060.0 | −0.401007 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −188791. | −0.745697 | ||||||||
\(146\) | −174680. | −0.678207 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 164244. | 0.616360 | ||||||||
\(149\) | 310579. | 1.14606 | 0.573028 | − | 0.819536i | \(-0.305769\pi\) | ||||
0.573028 | + | 0.819536i | \(0.305769\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 150211. | 0.536118 | 0.268059 | − | 0.963402i | \(-0.413618\pi\) | ||||
0.268059 | + | 0.963402i | \(0.413618\pi\) | |||||||
\(152\) | 151932. | 0.533383 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −75880.1 | −0.257826 | ||||||||
\(155\) | 60218.0 | 0.201325 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 381735. | 1.23598 | 0.617992 | − | 0.786185i | \(-0.287947\pi\) | ||||
0.617992 | + | 0.786185i | \(0.287947\pi\) | |||||||
\(158\) | −298792. | −0.952196 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 159540. | 0.492686 | ||||||||
\(161\) | −114101. | −0.346917 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −43367.4 | −0.127848 | −0.0639240 | − | 0.997955i | \(-0.520362\pi\) | ||||
−0.0639240 | + | 0.997955i | \(0.520362\pi\) | |||||||
\(164\) | −362897. | −1.05359 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −287280. | −0.809161 | ||||||||
\(167\) | −227398. | −0.630951 | −0.315475 | − | 0.948934i | \(-0.602164\pi\) | ||||
−0.315475 | + | 0.948934i | \(0.602164\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −345144. | −0.929572 | ||||||||
\(170\) | 141490. | 0.375495 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 97794.2 | 0.252053 | ||||||||
\(173\) | 196716. | 0.499716 | 0.249858 | − | 0.968282i | \(-0.419616\pi\) | ||||
0.249858 | + | 0.968282i | \(0.419616\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −94084.2 | −0.232232 | ||||||||
\(176\) | 86592.7 | 0.210717 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −410904. | −0.972053 | ||||||||
\(179\) | 51846.3 | 0.120944 | 0.0604722 | − | 0.998170i | \(-0.480739\pi\) | ||||
0.0604722 | + | 0.998170i | \(0.480739\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 692422. | 1.57099 | 0.785496 | − | 0.618866i | \(-0.212408\pi\) | ||||
0.785496 | + | 0.618866i | \(0.212408\pi\) | |||||||
\(182\) | 20234.6 | 0.0452810 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −503565. | −1.09651 | ||||||||
\(185\) | 202098. | 0.434142 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.00129e6 | 2.09390 | ||||||||
\(188\) | 182639. | 0.376876 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 75586.4 | 0.151901 | ||||||||
\(191\) | 964737. | 1.91349 | 0.956743 | − | 0.290933i | \(-0.0939658\pi\) | ||||
0.956743 | + | 0.290933i | \(0.0939658\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −305452. | −0.590268 | −0.295134 | − | 0.955456i | \(-0.595364\pi\) | ||||
−0.295134 | + | 0.955456i | \(0.595364\pi\) | |||||||
\(194\) | 85496.1 | 0.163096 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 331965. | 0.617238 | ||||||||
\(197\) | 31988.0 | 0.0587249 | 0.0293624 | − | 0.999569i | \(-0.490652\pi\) | ||||
0.0293624 | + | 0.999569i | \(0.490652\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 428137. | 0.766390 | 0.383195 | − | 0.923668i | \(-0.374824\pi\) | ||||
0.383195 | + | 0.923668i | \(0.374824\pi\) | |||||||
\(200\) | −415223. | −0.734017 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 493636. | 0.851193 | ||||||||
\(203\) | 275689. | 0.469547 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −446535. | −0.742114 | ||||||||
\(206\) | 166697. | 0.273691 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −23091.3 | −0.0370075 | ||||||||
\(209\) | 534906. | 0.847055 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.07522e6 | −1.66261 | −0.831306 | − | 0.555815i | \(-0.812406\pi\) | ||||
−0.831306 | + | 0.555815i | \(0.812406\pi\) | |||||||
\(212\) | 239988. | 0.366733 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 692389. | 1.03351 | ||||||||
\(215\) | 120333. | 0.177537 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −87935.3 | −0.126769 | ||||||||
\(218\) | −200588. | −0.285867 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 352009. | 0.490339 | ||||||||
\(221\) | −267010. | −0.367746 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 541635. | 0.729365 | 0.364682 | − | 0.931132i | \(-0.381178\pi\) | ||||
0.364682 | + | 0.931132i | \(0.381178\pi\) | |||||||
\(224\) | −232974. | −0.310232 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 777641. | 1.01276 | ||||||||
\(227\) | 503824. | 0.648954 | 0.324477 | − | 0.945894i | \(-0.394812\pi\) | ||||
0.324477 | + | 0.945894i | \(0.394812\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 236193. | 0.297631 | 0.148815 | − | 0.988865i | \(-0.452454\pi\) | ||||
0.148815 | + | 0.988865i | \(0.452454\pi\) | |||||||
\(230\) | −250525. | −0.312271 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.21670e6 | 1.48410 | ||||||||
\(233\) | 1.35136e6 | 1.63073 | 0.815366 | − | 0.578946i | \(-0.196536\pi\) | ||||
0.815366 | + | 0.578946i | \(0.196536\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 224732. | 0.265458 | ||||||||
\(236\) | 75607.3 | 0.0883656 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −206616. | −0.236440 | ||||||||
\(239\) | 1.00537e6 | 1.13849 | 0.569245 | − | 0.822168i | \(-0.307235\pi\) | ||||
0.569245 | + | 0.822168i | \(0.307235\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −968910. | −1.07458 | −0.537292 | − | 0.843396i | \(-0.680553\pi\) | ||||
−0.537292 | + | 0.843396i | \(0.680553\pi\) | |||||||
\(242\) | −662653. | −0.727357 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −754528. | −0.811336 | ||||||||
\(245\) | 408474. | 0.434760 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −142641. | −0.148766 | ||||||||
\(248\) | −388086. | −0.400681 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −474355. | −0.480013 | ||||||||
\(251\) | 1.74198e6 | 1.74525 | 0.872626 | − | 0.488390i | \(-0.162416\pi\) | ||||
0.872626 | + | 0.488390i | \(0.162416\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.77290e6 | −1.74134 | ||||||||
\(254\) | −14494.5 | −0.0140968 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −928936. | −0.885902 | ||||||||
\(257\) | 696669. | 0.657951 | 0.328976 | − | 0.944338i | \(-0.393297\pi\) | ||||
0.328976 | + | 0.944338i | \(0.393297\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −295120. | −0.273369 | ||||||||
\(260\) | −93868.6 | −0.0861166 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −647171. | −0.582459 | ||||||||
\(263\) | 894241. | 0.797196 | 0.398598 | − | 0.917126i | \(-0.369497\pi\) | ||||
0.398598 | + | 0.917126i | \(0.369497\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 295299. | 0.258314 | ||||||||
\(266\) | −110377. | −0.0956481 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.24297e6 | 1.05712 | ||||||||
\(269\) | −346103. | −0.291625 | −0.145812 | − | 0.989312i | \(-0.546580\pi\) | ||||
−0.145812 | + | 0.989312i | \(0.546580\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 476055. | 0.393762 | 0.196881 | − | 0.980427i | \(-0.436919\pi\) | ||||
0.196881 | + | 0.980427i | \(0.436919\pi\) | |||||||
\(272\) | 235786. | 0.193239 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 412224. | 0.331709 | ||||||||
\(275\) | −1.46188e6 | −1.16568 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.33986e6 | −1.04920 | −0.524600 | − | 0.851349i | \(-0.675785\pi\) | ||||
−0.524600 | + | 0.851349i | \(0.675785\pi\) | |||||||
\(278\) | −848071. | −0.658143 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −179652. | −0.136942 | ||||||||
\(281\) | −767258. | −0.579663 | −0.289831 | − | 0.957078i | \(-0.593599\pi\) | ||||
−0.289831 | + | 0.957078i | \(0.593599\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 391631. | 0.290677 | 0.145339 | − | 0.989382i | \(-0.453573\pi\) | ||||
0.145339 | + | 0.989382i | \(0.453573\pi\) | |||||||
\(284\) | 584.362 | 0.000429919 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 314405. | 0.227287 | ||||||||
\(287\) | 652067. | 0.467291 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.30659e6 | 0.920227 | ||||||||
\(290\) | 605312. | 0.422653 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.18333e6 | −0.812175 | ||||||||
\(293\) | −1.78575e6 | −1.21521 | −0.607606 | − | 0.794239i | \(-0.707870\pi\) | ||||
−0.607606 | + | 0.794239i | \(0.707870\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 93032.7 | 0.0622415 | ||||||||
\(296\) | −1.30245e6 | −0.864039 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −995791. | −0.649573 | ||||||||
\(299\) | 472772. | 0.305826 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −175720. | −0.111791 | ||||||||
\(302\) | −481615. | −0.303866 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 125960. | 0.0781718 | ||||||||
\(305\) | −928426. | −0.571476 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −927343. | −0.561558 | −0.280779 | − | 0.959772i | \(-0.590593\pi\) | ||||
−0.280779 | + | 0.959772i | \(0.590593\pi\) | |||||||
\(308\) | −514032. | −0.308755 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −193074. | −0.114109 | ||||||||
\(311\) | −766407. | −0.449323 | −0.224661 | − | 0.974437i | \(-0.572128\pi\) | ||||
−0.224661 | + | 0.974437i | \(0.572128\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 226189. | 0.130500 | 0.0652501 | − | 0.997869i | \(-0.479215\pi\) | ||||
0.0652501 | + | 0.997869i | \(0.479215\pi\) | |||||||
\(314\) | −1.22394e6 | −0.700543 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.02410e6 | −1.14029 | ||||||||
\(317\) | −1.08057e6 | −0.603955 | −0.301978 | − | 0.953315i | \(-0.597647\pi\) | ||||
−0.301978 | + | 0.953315i | \(0.597647\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.28364e6 | 2.35687 | ||||||||
\(320\) | −389401. | −0.212580 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 365837. | 0.196629 | ||||||||
\(323\) | 1.45651e6 | 0.776797 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 389833. | 0.204724 | ||||||||
\(326\) | 139047. | 0.0724630 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.87777e6 | 1.47697 | ||||||||
\(329\) | −328172. | −0.167152 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.89963e6 | −1.45470 | −0.727350 | − | 0.686267i | \(-0.759248\pi\) | ||||
−0.727350 | + | 0.686267i | \(0.759248\pi\) | |||||||
\(332\) | −1.94611e6 | −0.968997 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 729094. | 0.357617 | ||||||||
\(335\) | 1.52944e6 | 0.744595 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −204495. | −0.0980863 | −0.0490432 | − | 0.998797i | \(-0.515617\pi\) | ||||
−0.0490432 | + | 0.998797i | \(0.515617\pi\) | |||||||
\(338\) | 1.10662e6 | 0.526872 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 958494. | 0.449668 | ||||||||
\(341\) | −1.36634e6 | −0.636314 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.25242e6 | −0.574797 | ||||||||
\(344\) | −775509. | −0.353338 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −630719. | −0.283234 | ||||||||
\(347\) | −1.14557e6 | −0.510739 | −0.255370 | − | 0.966843i | \(-0.582197\pi\) | ||||
−0.255370 | + | 0.966843i | \(0.582197\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.14511e6 | 1.38220 | 0.691101 | − | 0.722758i | \(-0.257126\pi\) | ||||
0.691101 | + | 0.722758i | \(0.257126\pi\) | |||||||
\(350\) | 301657. | 0.131627 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.61994e6 | −1.55720 | ||||||||
\(353\) | 2.35284e6 | 1.00497 | 0.502487 | − | 0.864584i | \(-0.332418\pi\) | ||||
0.502487 | + | 0.864584i | \(0.332418\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 719.042 | 0.000302819 0 | ||||||||
\(356\) | −2.78357e6 | −1.16407 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −166232. | −0.0685500 | ||||||||
\(359\) | −198560. | −0.0813122 | −0.0406561 | − | 0.999173i | \(-0.512945\pi\) | ||||
−0.0406561 | + | 0.999173i | \(0.512945\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.69801e6 | −0.685759 | ||||||||
\(362\) | −2.22007e6 | −0.890423 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 137075. | 0.0542255 | ||||||||
\(365\) | −1.45606e6 | −0.572067 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.33716e6 | 1.29334 | 0.646669 | − | 0.762771i | \(-0.276162\pi\) | ||||
0.646669 | + | 0.762771i | \(0.276162\pi\) | |||||||
\(368\) | −417485. | −0.160702 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −647975. | −0.246067 | ||||||||
\(371\) | −431220. | −0.162654 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.49695e6 | 1.30142 | 0.650710 | − | 0.759326i | \(-0.274471\pi\) | ||||
0.650710 | + | 0.759326i | \(0.274471\pi\) | |||||||
\(374\) | −3.21039e6 | −1.18680 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.44833e6 | −0.528320 | ||||||||
\(377\) | −1.14230e6 | −0.413930 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.62014e6 | −1.65218 | −0.826089 | − | 0.563539i | \(-0.809439\pi\) | ||||
−0.826089 | + | 0.563539i | \(0.809439\pi\) | |||||||
\(380\) | 512042. | 0.181906 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.09318e6 | −1.08454 | ||||||||
\(383\) | 3.77589e6 | 1.31529 | 0.657645 | − | 0.753328i | \(-0.271553\pi\) | ||||
0.657645 | + | 0.753328i | \(0.271553\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −632502. | −0.217475 | ||||||||
\(386\) | 979353. | 0.334558 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 579174. | 0.195312 | ||||||||
\(389\) | −1.44066e6 | −0.482710 | −0.241355 | − | 0.970437i | \(-0.577592\pi\) | ||||
−0.241355 | + | 0.970437i | \(0.577592\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.82749e6 | −1.59691 | ||||||||
\(392\) | −2.63249e6 | −0.865269 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −102562. | −0.0332846 | ||||||||
\(395\) | −2.49060e6 | −0.803176 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.04765e6 | 1.28892 | 0.644461 | − | 0.764637i | \(-0.277082\pi\) | ||||
0.644461 | + | 0.764637i | \(0.277082\pi\) | |||||||
\(398\) | −1.37271e6 | −0.434382 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −344245. | −0.107576 | ||||||||
\(401\) | 187555. | 0.0582462 | 0.0291231 | − | 0.999576i | \(-0.490729\pi\) | ||||
0.0291231 | + | 0.999576i | \(0.490729\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 364355. | 0.111754 | ||||||||
\(404\) | 3.34402e6 | 1.01933 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −883926. | −0.266134 | ||||||||
\(407\) | −4.58556e6 | −1.37216 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.25079e6 | −0.960906 | −0.480453 | − | 0.877021i | \(-0.659528\pi\) | ||||
−0.480453 | + | 0.877021i | \(0.659528\pi\) | |||||||
\(410\) | 1.43170e6 | 0.420623 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.12925e6 | 0.327753 | ||||||||
\(413\) | −135854. | −0.0391920 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.39464e6 | −0.682526 | ||||||||
\(416\) | 965313. | 0.273486 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.71504e6 | −0.480102 | ||||||||
\(419\) | −3.65412e6 | −1.01683 | −0.508414 | − | 0.861113i | \(-0.669768\pi\) | ||||
−0.508414 | + | 0.861113i | \(0.669768\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.36572e6 | −1.47544 | −0.737722 | − | 0.675105i | \(-0.764098\pi\) | ||||
−0.737722 | + | 0.675105i | \(0.764098\pi\) | |||||||
\(422\) | 3.44742e6 | 0.942351 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.90311e6 | −0.514101 | ||||||||
\(425\) | −3.98059e6 | −1.06899 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.35576e6 | 0.359844 | ||||||||
\(428\) | 4.69043e6 | 1.23767 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −385818. | −0.100626 | ||||||||
\(431\) | 6.87518e6 | 1.78275 | 0.891377 | − | 0.453264i | \(-0.149740\pi\) | ||||
0.891377 | + | 0.453264i | \(0.149740\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40489.0 | 0.0103781 | 0.00518904 | − | 0.999987i | \(-0.498348\pi\) | ||||
0.00518904 | + | 0.999987i | \(0.498348\pi\) | |||||||
\(434\) | 281942. | 0.0718515 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.35884e6 | −0.342335 | ||||||||
\(437\) | −2.57892e6 | −0.646002 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.44389e6 | −1.10053 | −0.550265 | − | 0.834990i | \(-0.685473\pi\) | ||||
−0.550265 | + | 0.834990i | \(0.685473\pi\) | |||||||
\(440\) | −2.79143e6 | −0.687377 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 856101. | 0.208434 | ||||||||
\(443\) | 278084. | 0.0673236 | 0.0336618 | − | 0.999433i | \(-0.489283\pi\) | ||||
0.0336618 | + | 0.999433i | \(0.489283\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.42511e6 | −0.819925 | ||||||||
\(446\) | −1.73662e6 | −0.413397 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 568636. | 0.133856 | ||||||||
\(449\) | −1.07874e6 | −0.252523 | −0.126262 | − | 0.991997i | \(-0.540298\pi\) | ||||
−0.126262 | + | 0.991997i | \(0.540298\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.01318e7 | 2.34555 | ||||||||
\(452\) | 5.26795e6 | 1.21282 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.61538e6 | −0.367821 | ||||||||
\(455\) | 168667. | 0.0381945 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.34460e6 | −0.525144 | −0.262572 | − | 0.964912i | \(-0.584571\pi\) | ||||
−0.262572 | + | 0.964912i | \(0.584571\pi\) | |||||||
\(458\) | −757292. | −0.168694 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.69712e6 | −0.373954 | ||||||||
\(461\) | 8.15879e6 | 1.78802 | 0.894012 | − | 0.448043i | \(-0.147879\pi\) | ||||
0.894012 | + | 0.448043i | \(0.147879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.42287e6 | 1.17565 | 0.587823 | − | 0.808990i | \(-0.299985\pi\) | ||||
0.587823 | + | 0.808990i | \(0.299985\pi\) | |||||||
\(464\) | 1.00872e6 | 0.217508 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.33281e6 | −0.924282 | ||||||||
\(467\) | −8.21137e6 | −1.74230 | −0.871151 | − | 0.491015i | \(-0.836626\pi\) | ||||
−0.871151 | + | 0.491015i | \(0.836626\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.23341e6 | −0.468853 | ||||||||
\(470\) | −720547. | −0.150459 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −599566. | −0.123874 | ||||||||
\(473\) | −2.73034e6 | −0.561130 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.12649e6 | −0.432444 | ||||||||
\(476\) | −1.39967e6 | −0.283145 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.22345e6 | −0.645285 | ||||||||
\(479\) | 5.34027e6 | 1.06347 | 0.531734 | − | 0.846911i | \(-0.321541\pi\) | ||||
0.531734 | + | 0.846911i | \(0.321541\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.22281e6 | 0.240989 | ||||||||
\(482\) | 3.10656e6 | 0.609064 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.48899e6 | −0.871034 | ||||||||
\(485\) | 712658. | 0.137571 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.52006e6 | 0.481492 | 0.240746 | − | 0.970588i | \(-0.422608\pi\) | ||||
0.240746 | + | 0.970588i | \(0.422608\pi\) | |||||||
\(488\) | 5.98341e6 | 1.13736 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.30967e6 | −0.246417 | ||||||||
\(491\) | 8.33075e6 | 1.55948 | 0.779741 | − | 0.626102i | \(-0.215351\pi\) | ||||
0.779741 | + | 0.626102i | \(0.215351\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.16640e7 | 2.16138 | ||||||||
\(494\) | 457343. | 0.0843188 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −321746. | −0.0587232 | ||||||||
\(497\) | −1050.00 | −0.000190678 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.76824e6 | 1.75616 | 0.878082 | − | 0.478510i | \(-0.158823\pi\) | ||||
0.878082 | + | 0.478510i | \(0.158823\pi\) | |||||||
\(500\) | −3.21341e6 | −0.574832 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.58521e6 | −0.989190 | ||||||||
\(503\) | −2.49233e6 | −0.439223 | −0.219612 | − | 0.975587i | \(-0.570479\pi\) | ||||
−0.219612 | + | 0.975587i | \(0.570479\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.11473e6 | 0.717981 | ||||||||
\(506\) | 5.68436e6 | 0.986974 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −98189.9 | −0.0168814 | ||||||||
\(509\) | 7.02509e6 | 1.20187 | 0.600935 | − | 0.799298i | \(-0.294795\pi\) | ||||
0.600935 | + | 0.799298i | \(0.294795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.12626e6 | 0.360216 | ||||||||
\(512\) | −1.63948e6 | −0.276395 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.23369e6 | −0.372920 | ||||||||
\(515\) | 1.38951e6 | 0.230858 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.09913e6 | −0.839015 | ||||||||
\(518\) | 946226. | 0.154942 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 744379. | 0.120722 | ||||||||
\(521\) | 5.27900e6 | 0.852034 | 0.426017 | − | 0.904715i | \(-0.359916\pi\) | ||||
0.426017 | + | 0.904715i | \(0.359916\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −291703. | −0.0466322 | −0.0233161 | − | 0.999728i | \(-0.507422\pi\) | ||||
−0.0233161 | + | 0.999728i | \(0.507422\pi\) | |||||||
\(524\) | −4.38411e6 | −0.697514 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.86716e6 | −0.451843 | ||||||||
\(527\) | −3.72043e6 | −0.583535 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.11127e6 | 0.328023 | ||||||||
\(530\) | −946802. | −0.146410 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −747727. | −0.114542 | ||||||||
\(533\) | −2.70180e6 | −0.411941 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.77145e6 | 0.871767 | ||||||||
\(536\) | −9.85674e6 | −1.48191 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.10969e6 | 0.165290 | ||||||||
\(539\) | −9.26821e6 | −1.37412 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.81999e6 | 0.267347 | 0.133673 | − | 0.991025i | \(-0.457323\pi\) | ||||
0.133673 | + | 0.991025i | \(0.457323\pi\) | |||||||
\(542\) | −1.52635e6 | −0.223180 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.85682e6 | −1.42804 | ||||||||
\(545\) | −1.67201e6 | −0.241128 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.72974e6 | −1.39038 | −0.695189 | − | 0.718827i | \(-0.744679\pi\) | ||||
−0.695189 | + | 0.718827i | \(0.744679\pi\) | |||||||
\(548\) | 2.79252e6 | 0.397232 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.68714e6 | 0.660695 | ||||||||
\(551\) | 6.23112e6 | 0.874353 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.63698e6 | 0.505740 | ||||||||
\(554\) | 4.29591e6 | 0.594676 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.74506e6 | −0.788147 | ||||||||
\(557\) | 3.95131e6 | 0.539638 | 0.269819 | − | 0.962911i | \(-0.413036\pi\) | ||||
0.269819 | + | 0.962911i | \(0.413036\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 728087. | 0.0985494 | ||||||||
\(560\) | −148942. | −0.0200701 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.46002e6 | 0.328547 | ||||||||
\(563\) | 907456. | 0.120658 | 0.0603288 | − | 0.998179i | \(-0.480785\pi\) | ||||
0.0603288 | + | 0.998179i | \(0.480785\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.48207e6 | 0.854265 | ||||||||
\(566\) | −1.25567e6 | −0.164753 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4633.99 | −0.000602677 0 | ||||||||
\(569\) | 4.32375e6 | 0.559861 | 0.279931 | − | 0.960020i | \(-0.409689\pi\) | ||||
0.279931 | + | 0.960020i | \(0.409689\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.76582e6 | −0.226650 | −0.113325 | − | 0.993558i | \(-0.536150\pi\) | ||||
−0.113325 | + | 0.993558i | \(0.536150\pi\) | |||||||
\(572\) | 2.12986e6 | 0.272183 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.09069e6 | −0.264856 | ||||||||
\(575\) | 7.04808e6 | 0.888999 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.97841e6 | 0.622516 | 0.311258 | − | 0.950325i | \(-0.399250\pi\) | ||||
0.311258 | + | 0.950325i | \(0.399250\pi\) | |||||||
\(578\) | −4.18925e6 | −0.521575 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.10054e6 | 0.506141 | ||||||||
\(581\) | 3.49685e6 | 0.429770 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.70028e6 | −0.816435 | ||||||||
\(584\) | 9.38383e6 | 1.13854 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.72556e6 | 0.688769 | ||||||||
\(587\) | −2.55026e6 | −0.305484 | −0.152742 | − | 0.988266i | \(-0.548810\pi\) | ||||
−0.152742 | + | 0.988266i | \(0.548810\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.98751e6 | −0.236060 | ||||||||
\(590\) | −298286. | −0.0352779 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.07981e6 | −0.126632 | ||||||||
\(593\) | −5.95905e6 | −0.695889 | −0.347945 | − | 0.937515i | \(-0.613120\pi\) | ||||
−0.347945 | + | 0.937515i | \(0.613120\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.72226e6 | −0.199437 | ||||||||
\(596\) | −6.74576e6 | −0.777885 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.51582e6 | −0.173339 | ||||||||
\(599\) | −7.34100e6 | −0.835966 | −0.417983 | − | 0.908455i | \(-0.637263\pi\) | ||||
−0.417983 | + | 0.908455i | \(0.637263\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.04285e6 | 0.569495 | 0.284748 | − | 0.958603i | \(-0.408090\pi\) | ||||
0.284748 | + | 0.958603i | \(0.408090\pi\) | |||||||
\(602\) | 563403. | 0.0633619 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.26259e6 | −0.363890 | ||||||||
\(605\) | −5.52358e6 | −0.613524 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.78269e7 | 1.96383 | 0.981916 | − | 0.189318i | \(-0.0606277\pi\) | ||||
0.981916 | + | 0.189318i | \(0.0606277\pi\) | |||||||
\(608\) | −5.26567e6 | −0.577690 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.97676e6 | 0.323906 | ||||||||
\(611\) | 1.35976e6 | 0.147353 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.10977e7 | 1.19284 | 0.596421 | − | 0.802672i | \(-0.296589\pi\) | ||||
0.596421 | + | 0.802672i | \(0.296589\pi\) | |||||||
\(614\) | 2.97329e6 | 0.318285 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.07628e6 | 0.432824 | ||||||||
\(617\) | −6.00790e6 | −0.635345 | −0.317673 | − | 0.948200i | \(-0.602901\pi\) | ||||
−0.317673 | + | 0.948200i | \(0.602901\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.79364e6 | 0.188151 | 0.0940757 | − | 0.995565i | \(-0.470010\pi\) | ||||
0.0940757 | + | 0.995565i | \(0.470010\pi\) | |||||||
\(620\) | −1.30793e6 | −0.136649 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.45729e6 | 0.254672 | ||||||||
\(623\) | 5.00163e6 | 0.516287 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.57952e6 | 0.366543 | ||||||||
\(626\) | −725218. | −0.0739661 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.29127e6 | −0.838923 | ||||||||
\(629\) | −1.24861e7 | −1.25835 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00827e7 | −1.00810 | −0.504052 | − | 0.863673i | \(-0.668158\pi\) | ||||
−0.504052 | + | 0.863673i | \(0.668158\pi\) | |||||||
\(632\) | 1.60511e7 | 1.59850 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.46457e6 | 0.342316 | ||||||||
\(635\) | −120820. | −0.0118906 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.47151e6 | 0.241332 | ||||||||
\(638\) | −1.37344e7 | −1.33585 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.85677e6 | −0.372198 | ||||||||
\(641\) | 5.75277e6 | 0.553009 | 0.276505 | − | 0.961013i | \(-0.410824\pi\) | ||||
0.276505 | + | 0.961013i | \(0.410824\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.46072e6 | −0.520862 | −0.260431 | − | 0.965492i | \(-0.583865\pi\) | ||||
−0.260431 | + | 0.965492i | \(0.583865\pi\) | |||||||
\(644\) | 2.47828e6 | 0.235470 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.66993e6 | −0.440280 | ||||||||
\(647\) | −2.48477e6 | −0.233360 | −0.116680 | − | 0.993170i | \(-0.537225\pi\) | ||||
−0.116680 | + | 0.993170i | \(0.537225\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.11089e6 | −0.196723 | ||||||||
\(650\) | −1.24990e6 | −0.116036 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 941939. | 0.0867768 | ||||||||
\(653\) | 9.47172e6 | 0.869253 | 0.434626 | − | 0.900611i | \(-0.356880\pi\) | ||||
0.434626 | + | 0.900611i | \(0.356880\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.39453e6 | −0.491304 | ||||||||
\(656\) | 2.38585e6 | 0.216463 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.05220e6 | 0.0947402 | ||||||||
\(659\) | −9.34926e6 | −0.838617 | −0.419309 | − | 0.907844i | \(-0.637727\pi\) | ||||
−0.419309 | + | 0.907844i | \(0.637727\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.30563e6 | 0.383295 | 0.191647 | − | 0.981464i | \(-0.438617\pi\) | ||||
0.191647 | + | 0.981464i | \(0.438617\pi\) | |||||||
\(662\) | 9.29694e6 | 0.824509 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.54327e7 | 1.35838 | ||||||||
\(665\) | −920057. | −0.0806790 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.06525e7 | −1.79746 | ||||||||
\(668\) | 4.93908e6 | 0.428258 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.90376e6 | −0.422029 | ||||||||
\(671\) | 2.10658e7 | 1.80623 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.43291e7 | 1.21950 | 0.609748 | − | 0.792595i | \(-0.291271\pi\) | ||||
0.609748 | + | 0.792595i | \(0.291271\pi\) | |||||||
\(674\) | 655662. | 0.0555943 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.49652e6 | 0.630947 | ||||||||
\(677\) | 6.86042e6 | 0.575279 | 0.287640 | − | 0.957739i | \(-0.407129\pi\) | ||||
0.287640 | + | 0.957739i | \(0.407129\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.04068e6 | −0.0866250 | ||||||||
\(680\) | −7.60086e6 | −0.630363 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.38081e6 | 0.360656 | ||||||||
\(683\) | 2.00520e7 | 1.64478 | 0.822388 | − | 0.568927i | \(-0.192641\pi\) | ||||
0.822388 | + | 0.568927i | \(0.192641\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.43612e6 | 0.279796 | ||||||||
\(686\) | 4.01557e6 | 0.325789 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −642943. | −0.0517847 | ||||||||
\(689\) | 1.78674e6 | 0.143388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.21795e7 | 0.970365 | 0.485182 | − | 0.874413i | \(-0.338753\pi\) | ||||
0.485182 | + | 0.874413i | \(0.338753\pi\) | |||||||
\(692\) | −4.27266e6 | −0.339182 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.67299e6 | 0.289482 | ||||||||
\(695\) | −7.06914e6 | −0.555142 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.75881e7 | 2.15100 | ||||||||
\(698\) | −1.00840e7 | −0.783418 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.04351e6 | 0.157627 | ||||||||
\(701\) | −1.23445e7 | −0.948809 | −0.474404 | − | 0.880307i | \(-0.657337\pi\) | ||||
−0.474404 | + | 0.880307i | \(0.657337\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.67029e6 | −0.509045 | ||||||||
\(704\) | 8.83544e6 | 0.671888 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.54378e6 | −0.569609 | ||||||||
\(707\) | −6.00867e6 | −0.452095 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.21727e7 | 1.65654 | 0.828272 | − | 0.560327i | \(-0.189324\pi\) | ||||
0.828272 | + | 0.560327i | \(0.189324\pi\) | |||||||
\(710\) | −2305.42 | −0.000171635 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.20737e7 | 1.63183 | ||||||||
\(713\) | 6.58745e6 | 0.485281 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.62074e6 | 0.191716 | ||||||||
\(716\) | −1.12610e6 | −0.0820909 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 636632. | 0.0460869 | ||||||||
\(719\) | 2.40050e6 | 0.173173 | 0.0865864 | − | 0.996244i | \(-0.472404\pi\) | ||||
0.0865864 | + | 0.996244i | \(0.472404\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.02908e6 | −0.145365 | ||||||||
\(722\) | 5.44423e6 | 0.388681 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.50394e7 | −1.06631 | ||||||||
\(725\) | −1.70294e7 | −1.20325 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.51466e6 | −0.667663 | −0.333831 | − | 0.942633i | \(-0.608342\pi\) | ||||
−0.333831 | + | 0.942633i | \(0.608342\pi\) | |||||||
\(728\) | −1.08700e6 | −0.0760155 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.66848e6 | 0.324242 | ||||||||
\(731\) | −7.43451e6 | −0.514587 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.04964e6 | 0.0721572 | 0.0360786 | − | 0.999349i | \(-0.488513\pi\) | ||||
0.0360786 | + | 0.999349i | \(0.488513\pi\) | |||||||
\(734\) | −1.06998e7 | −0.733050 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.74526e7 | 1.18759 | ||||||||
\(737\) | −3.47027e7 | −2.35339 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.68604e6 | −0.180926 | −0.0904629 | − | 0.995900i | \(-0.528835\pi\) | ||||
−0.0904629 | + | 0.995900i | \(0.528835\pi\) | |||||||
\(740\) | −4.38955e6 | −0.294674 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.38260e6 | 0.0921905 | ||||||||
\(743\) | 2.09335e7 | 1.39114 | 0.695569 | − | 0.718460i | \(-0.255153\pi\) | ||||
0.695569 | + | 0.718460i | \(0.255153\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.30047e6 | −0.547914 | ||||||||
\(746\) | −1.12121e7 | −0.737632 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.17481e7 | −1.42124 | ||||||||
\(749\) | −8.42794e6 | −0.548930 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.59501e7 | 1.67895 | 0.839477 | − | 0.543395i | \(-0.182861\pi\) | ||||
0.839477 | + | 0.543395i | \(0.182861\pi\) | |||||||
\(752\) | −1.20075e6 | −0.0774298 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.66250e6 | 0.234611 | ||||||||
\(755\) | −4.01452e6 | −0.256311 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.97503e6 | −0.569241 | −0.284620 | − | 0.958640i | \(-0.591868\pi\) | ||||
−0.284620 | + | 0.958640i | \(0.591868\pi\) | |||||||
\(758\) | 1.48133e7 | 0.936438 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.06050e6 | −0.255003 | ||||||||
\(761\) | −1.20515e7 | −0.754361 | −0.377180 | − | 0.926140i | \(-0.623106\pi\) | ||||
−0.377180 | + | 0.926140i | \(0.623106\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.44161e6 | 0.151833 | ||||||||
\(764\) | −2.09541e7 | −1.29878 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.21064e7 | −0.745493 | ||||||||
\(767\) | 562903. | 0.0345498 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.32176e7 | 0.806001 | 0.403001 | − | 0.915200i | \(-0.367967\pi\) | ||||
0.403001 | + | 0.915200i | \(0.367967\pi\) | |||||||
\(770\) | 2.02796e6 | 0.123263 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.63440e6 | 0.400644 | ||||||||
\(773\) | 1.10628e7 | 0.665914 | 0.332957 | − | 0.942942i | \(-0.391954\pi\) | ||||
0.332957 | + | 0.942942i | \(0.391954\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.43179e6 | 0.324855 | ||||||||
\(776\) | −4.59285e6 | −0.273797 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.61910e6 | 0.273595 | ||||||||
\(779\) | 1.47380e7 | 0.870152 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16314.9 | −0.000957100 0 | ||||||||
\(782\) | 1.54781e7 | 0.905109 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.18249e6 | −0.126813 | ||||||||
\(785\) | −1.02022e7 | −0.590907 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.33119e7 | −0.766132 | −0.383066 | − | 0.923721i | \(-0.625132\pi\) | ||||
−0.383066 | + | 0.923721i | \(0.625132\pi\) | |||||||
\(788\) | −694779. | −0.0398595 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.98547e6 | 0.455232 | ||||||||
\(791\) | −9.46565e6 | −0.537910 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.61753e6 | −0.317221 | ||||||||
\(794\) | −1.29778e7 | −0.730548 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.29912e6 | −0.520186 | ||||||||
\(797\) | −1.61590e6 | −0.0901089 | −0.0450544 | − | 0.998985i | \(-0.514346\pi\) | ||||
−0.0450544 | + | 0.998985i | \(0.514346\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.38846e7 | −0.769423 | ||||||||
\(800\) | 1.43909e7 | 0.794991 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −601347. | −0.0330133 | ||||||||
\(803\) | 3.30377e7 | 1.80809 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.04945e6 | 0.165856 | ||||||||
\(806\) | −1.16821e6 | −0.0633408 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.65181e7 | −1.42894 | ||||||||
\(809\) | 1.48836e7 | 0.799535 | 0.399768 | − | 0.916617i | \(-0.369091\pi\) | ||||
0.399768 | + | 0.916617i | \(0.369091\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.19912e7 | −1.70796 | −0.853982 | − | 0.520303i | \(-0.825819\pi\) | ||||
−0.853982 | + | 0.520303i | \(0.825819\pi\) | |||||||
\(812\) | −5.98795e6 | −0.318705 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.47024e7 | 0.777728 | ||||||||
\(815\) | 1.15903e6 | 0.0611224 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.97163e6 | −0.208168 | ||||||||
\(818\) | 1.04228e7 | 0.544632 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.69873e6 | 0.503709 | ||||||||
\(821\) | 2.95946e7 | 1.53234 | 0.766169 | − | 0.642640i | \(-0.222161\pi\) | ||||
0.766169 | + | 0.642640i | \(0.222161\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.71026e7 | 0.880163 | 0.440081 | − | 0.897958i | \(-0.354950\pi\) | ||||
0.440081 | + | 0.897958i | \(0.354950\pi\) | |||||||
\(824\) | −8.95496e6 | −0.459458 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 435581. | 0.0222136 | ||||||||
\(827\) | 2.24600e7 | 1.14195 | 0.570974 | − | 0.820968i | \(-0.306566\pi\) | ||||
0.570974 | + | 0.820968i | \(0.306566\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.65000e7 | −1.33924 | −0.669622 | − | 0.742702i | \(-0.733544\pi\) | ||||
−0.669622 | + | 0.742702i | \(0.733544\pi\) | |||||||
\(830\) | 7.67780e6 | 0.386849 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.35611e6 | −0.118001 | ||||||||
\(833\) | −2.52367e7 | −1.26014 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.07740e6 | 0.301649 | ||||||||
\(836\) | −1.16182e7 | −0.574938 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.17160e7 | 0.576328 | ||||||||
\(839\) | −3.38841e7 | −1.66185 | −0.830924 | − | 0.556386i | \(-0.812187\pi\) | ||||
−0.830924 | + | 0.556386i | \(0.812187\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.93890e7 | 1.43283 | ||||||||
\(842\) | 1.72038e7 | 0.836266 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.33537e7 | 1.12850 | ||||||||
\(845\) | 9.22426e6 | 0.444416 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.06598e6 | 0.386321 | ||||||||
\(848\) | −1.57779e6 | −0.0753459 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.27627e7 | 0.605894 | ||||||||
\(851\) | 2.21081e7 | 1.04647 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.88452e6 | −0.0886804 | −0.0443402 | − | 0.999016i | \(-0.514119\pi\) | ||||
−0.0443402 | + | 0.999016i | \(0.514119\pi\) | |||||||
\(854\) | −4.34691e6 | −0.203956 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.71951e7 | −1.73501 | ||||||||
\(857\) | −1.95529e6 | −0.0909407 | −0.0454704 | − | 0.998966i | \(-0.514479\pi\) | ||||
−0.0454704 | + | 0.998966i | \(0.514479\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.15147e7 | −0.532437 | −0.266219 | − | 0.963913i | \(-0.585774\pi\) | ||||
−0.266219 | + | 0.963913i | \(0.585774\pi\) | |||||||
\(860\) | −2.61363e6 | −0.120503 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.20435e7 | −1.01045 | ||||||||
\(863\) | −2.60655e6 | −0.119135 | −0.0595674 | − | 0.998224i | \(-0.518972\pi\) | ||||
−0.0595674 | + | 0.998224i | \(0.518972\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.25739e6 | −0.238908 | ||||||||
\(866\) | −129818. | −0.00588219 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.90995e6 | 0.0860445 | ||||||||
\(869\) | 5.65112e7 | 2.53855 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.25402e6 | 0.413319 | ||||||||
\(872\) | 1.07756e7 | 0.479899 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.26865e6 | 0.366147 | ||||||||
\(875\) | 5.77397e6 | 0.254950 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.54109e7 | 1.55467 | 0.777335 | − | 0.629087i | \(-0.216571\pi\) | ||||
0.777335 | + | 0.629087i | \(0.216571\pi\) | |||||||
\(878\) | 1.42482e7 | 0.623769 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.31426e6 | −0.100741 | ||||||||
\(881\) | −1.78051e7 | −0.772867 | −0.386434 | − | 0.922317i | \(-0.626293\pi\) | ||||
−0.386434 | + | 0.922317i | \(0.626293\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.70288e7 | −1.59822 | −0.799111 | − | 0.601183i | \(-0.794696\pi\) | ||||
−0.799111 | + | 0.601183i | \(0.794696\pi\) | |||||||
\(884\) | 5.79946e6 | 0.249607 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −891607. | −0.0381583 | ||||||||
\(887\) | 3.85936e7 | 1.64705 | 0.823524 | − | 0.567281i | \(-0.192005\pi\) | ||||
0.823524 | + | 0.567281i | \(0.192005\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 176431. | 0.00748723 | ||||||||
\(890\) | 1.09817e7 | 0.464725 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.17643e7 | −0.495056 | ||||||||
\(893\) | −7.41735e6 | −0.311258 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.38564e6 | −0.0578218 | ||||||||
\(896\) | 5.63197e6 | 0.234364 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.45871e6 | 0.143128 | ||||||||
\(899\) | −1.59164e7 | −0.656820 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.82444e7 | −0.748716 | ||||||||
\(902\) | −3.24850e7 | −1.32943 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.17749e7 | −1.70018 | ||||||||
\(905\) | −1.85056e7 | −0.751070 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.11662e6 | −0.367973 | −0.183986 | − | 0.982929i | \(-0.558900\pi\) | ||||
−0.183986 | + | 0.982929i | \(0.558900\pi\) | |||||||
\(908\) | −1.09430e7 | −0.440477 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −540787. | −0.0216483 | ||||||||
\(911\) | 4.35218e7 | 1.73745 | 0.868723 | − | 0.495299i | \(-0.164941\pi\) | ||||
0.868723 | + | 0.495299i | \(0.164941\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.43339e7 | 2.15722 | ||||||||
\(914\) | 7.51737e6 | 0.297646 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.13010e6 | −0.202017 | ||||||||
\(917\) | 7.87753e6 | 0.309362 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.99781e6 | 0.117089 | 0.0585444 | − | 0.998285i | \(-0.481354\pi\) | ||||
0.0585444 | + | 0.998285i | \(0.481354\pi\) | |||||||
\(920\) | 1.34582e7 | 0.524224 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.61591e7 | −1.01343 | ||||||||
\(923\) | 4350.63 | 0.000168092 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.82296e7 | 0.700525 | ||||||||
\(926\) | −1.73871e7 | −0.666344 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.21686e7 | −1.60738 | ||||||||
\(929\) | −2.19993e7 | −0.836313 | −0.418156 | − | 0.908375i | \(-0.637324\pi\) | ||||
−0.418156 | + | 0.908375i | \(0.637324\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.34818e7 | −0.509770 | ||||||||
\(932\) | −2.93516e7 | −1.10686 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.63277e7 | 0.987519 | ||||||||
\(935\) | −2.67604e7 | −1.00107 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.01794e6 | 0.298341 | 0.149171 | − | 0.988811i | \(-0.452340\pi\) | ||||
0.149171 | + | 0.988811i | \(0.452340\pi\) | |||||||
\(938\) | 7.16087e6 | 0.265741 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.88118e6 | −0.180179 | ||||||||
\(941\) | −9.19445e6 | −0.338494 | −0.169247 | − | 0.985574i | \(-0.554134\pi\) | ||||
−0.169247 | + | 0.985574i | \(0.554134\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.88479e7 | −1.78882 | ||||||||
\(944\) | −497076. | −0.0181549 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.75414e6 | 0.318043 | ||||||||
\(947\) | 4.27420e6 | 0.154874 | 0.0774372 | − | 0.996997i | \(-0.475326\pi\) | ||||
0.0774372 | + | 0.996997i | \(0.475326\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.81002e6 | −0.317550 | ||||||||
\(950\) | 6.81806e6 | 0.245105 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.10994e7 | 0.396924 | ||||||||
\(953\) | 5.03679e7 | 1.79648 | 0.898239 | − | 0.439507i | \(-0.144847\pi\) | ||||
0.898239 | + | 0.439507i | \(0.144847\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.57834e7 | −0.914812 | ||||||||
\(956\) | −2.18365e7 | −0.772750 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.71222e7 | −0.602763 | ||||||||
\(959\) | −5.01770e6 | −0.176181 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.35524e7 | −0.822670 | ||||||||
\(962\) | −3.92063e6 | −0.136590 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.10447e7 | 0.729374 | ||||||||
\(965\) | 8.16345e6 | 0.282199 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.89781e6 | −0.0652659 | −0.0326329 | − | 0.999467i | \(-0.510389\pi\) | ||||
−0.0326329 | + | 0.999467i | \(0.510389\pi\) | |||||||
\(968\) | 3.55977e7 | 1.22105 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.28496e6 | −0.0779738 | ||||||||
\(971\) | −2.68041e7 | −0.912331 | −0.456166 | − | 0.889895i | \(-0.650778\pi\) | ||||
−0.456166 | + | 0.889895i | \(0.650778\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.03229e7 | 0.349560 | ||||||||
\(974\) | −8.07994e6 | −0.272905 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.96061e6 | 0.166690 | ||||||||
\(977\) | −4.27764e7 | −1.43373 | −0.716865 | − | 0.697212i | \(-0.754424\pi\) | ||||
−0.716865 | + | 0.697212i | \(0.754424\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.77151e7 | 2.59148 | ||||||||
\(980\) | −8.87205e6 | −0.295093 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.67104e7 | −0.883898 | ||||||||
\(983\) | 3.97908e7 | 1.31340 | 0.656702 | − | 0.754150i | \(-0.271951\pi\) | ||||
0.656702 | + | 0.754150i | \(0.271951\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −854907. | −0.0280756 | ||||||||
\(986\) | −3.73978e7 | −1.22505 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.09816e6 | 0.100975 | ||||||||
\(989\) | 1.31636e7 | 0.427943 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.18022e7 | 0.705207 | 0.352604 | − | 0.935773i | \(-0.385296\pi\) | ||||
0.352604 | + | 0.935773i | \(0.385296\pi\) | |||||||
\(992\) | 1.34503e7 | 0.433964 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3366.57 | 0.000108074 0 | ||||||||
\(995\) | −1.14423e7 | −0.366400 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.61869e7 | −0.834346 | −0.417173 | − | 0.908827i | \(-0.636979\pi\) | ||||
−0.417173 | + | 0.908827i | \(0.636979\pi\) | |||||||
\(998\) | −3.13194e7 | −0.995376 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 531.6.a.b.1.5 | 11 | ||
3.2 | odd | 2 | 177.6.a.a.1.7 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.a.1.7 | ✓ | 11 | 3.2 | odd | 2 | ||
531.6.a.b.1.5 | 11 | 1.1 | even | 1 | trivial |