Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [342,6,Mod(1,342)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(342, 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("342.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.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: | \(54.8512663760\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 114) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 342.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −21.0000 | −0.375659 | −0.187830 | − | 0.982202i | \(-0.560145\pi\) | ||||
−0.187830 | + | 0.982202i | \(0.560145\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −143.000 | −1.10304 | −0.551520 | − | 0.834162i | \(-0.685952\pi\) | ||||
−0.551520 | + | 0.834162i | \(0.685952\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 84.0000 | 0.265631 | ||||||||
\(11\) | 205.000 | 0.510825 | 0.255413 | − | 0.966832i | \(-0.417789\pi\) | ||||
0.255413 | + | 0.966832i | \(0.417789\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −78.0000 | −0.128008 | −0.0640039 | − | 0.997950i | \(-0.520387\pi\) | ||||
−0.0640039 | + | 0.997950i | \(0.520387\pi\) | |||||||
\(14\) | 572.000 | 0.779966 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 2125.00 | 1.78335 | 0.891675 | − | 0.452676i | \(-0.149531\pi\) | ||||
0.891675 | + | 0.452676i | \(0.149531\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 361.000 | 0.229416 | ||||||||
\(20\) | −336.000 | −0.187830 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −820.000 | −0.361208 | ||||||||
\(23\) | −20.0000 | −0.00788334 | −0.00394167 | − | 0.999992i | \(-0.501255\pi\) | ||||
−0.00394167 | + | 0.999992i | \(0.501255\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2684.00 | −0.858880 | ||||||||
\(26\) | 312.000 | 0.0905151 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2288.00 | −0.551520 | ||||||||
\(29\) | 4866.00 | 1.07443 | 0.537214 | − | 0.843446i | \(-0.319477\pi\) | ||||
0.537214 | + | 0.843446i | \(0.319477\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1098.00 | −0.205210 | −0.102605 | − | 0.994722i | \(-0.532718\pi\) | ||||
−0.102605 | + | 0.994722i | \(0.532718\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8500.00 | −1.26102 | ||||||||
\(35\) | 3003.00 | 0.414367 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −15128.0 | −1.81667 | −0.908337 | − | 0.418238i | \(-0.862648\pi\) | ||||
−0.908337 | + | 0.418238i | \(0.862648\pi\) | |||||||
\(38\) | −1444.00 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1344.00 | 0.132816 | ||||||||
\(41\) | 9400.00 | 0.873310 | 0.436655 | − | 0.899629i | \(-0.356163\pi\) | ||||
0.436655 | + | 0.899629i | \(0.356163\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20073.0 | 1.65555 | 0.827773 | − | 0.561063i | \(-0.189608\pi\) | ||||
0.827773 | + | 0.561063i | \(0.189608\pi\) | |||||||
\(44\) | 3280.00 | 0.255413 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 80.0000 | 0.00557437 | ||||||||
\(47\) | −14105.0 | −0.931383 | −0.465692 | − | 0.884947i | \(-0.654194\pi\) | ||||
−0.465692 | + | 0.884947i | \(0.654194\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3642.00 | 0.216695 | ||||||||
\(50\) | 10736.0 | 0.607320 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1248.00 | −0.0640039 | ||||||||
\(53\) | −26386.0 | −1.29028 | −0.645140 | − | 0.764064i | \(-0.723201\pi\) | ||||
−0.645140 | + | 0.764064i | \(0.723201\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4305.00 | −0.191896 | ||||||||
\(56\) | 9152.00 | 0.389983 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −19464.0 | −0.759735 | ||||||||
\(59\) | 13216.0 | 0.494277 | 0.247138 | − | 0.968980i | \(-0.420510\pi\) | ||||
0.247138 | + | 0.968980i | \(0.420510\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2293.00 | −0.0789004 | −0.0394502 | − | 0.999222i | \(-0.512561\pi\) | ||||
−0.0394502 | + | 0.999222i | \(0.512561\pi\) | |||||||
\(62\) | 4392.00 | 0.145105 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 1638.00 | 0.0480873 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 35976.0 | 0.979097 | 0.489549 | − | 0.871976i | \(-0.337162\pi\) | ||||
0.489549 | + | 0.871976i | \(0.337162\pi\) | |||||||
\(68\) | 34000.0 | 0.891675 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12012.0 | −0.293002 | ||||||||
\(71\) | −10180.0 | −0.239664 | −0.119832 | − | 0.992794i | \(-0.538236\pi\) | ||||
−0.119832 | + | 0.992794i | \(0.538236\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 33109.0 | 0.727175 | 0.363587 | − | 0.931560i | \(-0.381552\pi\) | ||||
0.363587 | + | 0.931560i | \(0.381552\pi\) | |||||||
\(74\) | 60512.0 | 1.28458 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5776.00 | 0.114708 | ||||||||
\(77\) | −29315.0 | −0.563460 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −53888.0 | −0.971459 | −0.485729 | − | 0.874109i | \(-0.661446\pi\) | ||||
−0.485729 | + | 0.874109i | \(0.661446\pi\) | |||||||
\(80\) | −5376.00 | −0.0939149 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −37600.0 | −0.617523 | ||||||||
\(83\) | −75196.0 | −1.19812 | −0.599059 | − | 0.800705i | \(-0.704458\pi\) | ||||
−0.599059 | + | 0.800705i | \(0.704458\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −44625.0 | −0.669932 | ||||||||
\(86\) | −80292.0 | −1.17065 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −13120.0 | −0.180604 | ||||||||
\(89\) | −20618.0 | −0.275913 | −0.137956 | − | 0.990438i | \(-0.544053\pi\) | ||||
−0.137956 | + | 0.990438i | \(0.544053\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11154.0 | 0.141198 | ||||||||
\(92\) | −320.000 | −0.00394167 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 56420.0 | 0.658587 | ||||||||
\(95\) | −7581.00 | −0.0861822 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −84130.0 | −0.907866 | −0.453933 | − | 0.891036i | \(-0.649979\pi\) | ||||
−0.453933 | + | 0.891036i | \(0.649979\pi\) | |||||||
\(98\) | −14568.0 | −0.153227 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −42944.0 | −0.429440 | ||||||||
\(101\) | −163714. | −1.59692 | −0.798459 | − | 0.602050i | \(-0.794351\pi\) | ||||
−0.798459 | + | 0.602050i | \(0.794351\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −139062. | −1.29156 | −0.645781 | − | 0.763523i | \(-0.723468\pi\) | ||||
−0.645781 | + | 0.763523i | \(0.723468\pi\) | |||||||
\(104\) | 4992.00 | 0.0452576 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 105544. | 0.912366 | ||||||||
\(107\) | −124690. | −1.05286 | −0.526432 | − | 0.850217i | \(-0.676470\pi\) | ||||
−0.526432 | + | 0.850217i | \(0.676470\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11836.0 | −0.0954198 | −0.0477099 | − | 0.998861i | \(-0.515192\pi\) | ||||
−0.0477099 | + | 0.998861i | \(0.515192\pi\) | |||||||
\(110\) | 17220.0 | 0.135691 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −36608.0 | −0.275760 | ||||||||
\(113\) | −57674.0 | −0.424897 | −0.212449 | − | 0.977172i | \(-0.568144\pi\) | ||||
−0.212449 | + | 0.977172i | \(0.568144\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 420.000 | 0.00296145 | ||||||||
\(116\) | 77856.0 | 0.537214 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −52864.0 | −0.349506 | ||||||||
\(119\) | −303875. | −1.96711 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −119026. | −0.739058 | ||||||||
\(122\) | 9172.00 | 0.0557910 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −17568.0 | −0.102605 | ||||||||
\(125\) | 121989. | 0.698306 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 134314. | 0.738945 | 0.369472 | − | 0.929242i | \(-0.379538\pi\) | ||||
0.369472 | + | 0.929242i | \(0.379538\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6552.00 | −0.0340029 | ||||||||
\(131\) | 365955. | 1.86316 | 0.931578 | − | 0.363540i | \(-0.118432\pi\) | ||||
0.931578 | + | 0.363540i | \(0.118432\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −51623.0 | −0.253055 | ||||||||
\(134\) | −143904. | −0.692326 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −136000. | −0.630510 | ||||||||
\(137\) | −44763.0 | −0.203759 | −0.101880 | − | 0.994797i | \(-0.532486\pi\) | ||||
−0.101880 | + | 0.994797i | \(0.532486\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −422179. | −1.85336 | −0.926680 | − | 0.375852i | \(-0.877350\pi\) | ||||
−0.926680 | + | 0.375852i | \(0.877350\pi\) | |||||||
\(140\) | 48048.0 | 0.207184 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 40720.0 | 0.169468 | ||||||||
\(143\) | −15990.0 | −0.0653896 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −102186. | −0.403619 | ||||||||
\(146\) | −132436. | −0.514190 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −242048. | −0.908337 | ||||||||
\(149\) | 41741.0 | 0.154027 | 0.0770136 | − | 0.997030i | \(-0.475462\pi\) | ||||
0.0770136 | + | 0.997030i | \(0.475462\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −41240.0 | −0.147189 | −0.0735947 | − | 0.997288i | \(-0.523447\pi\) | ||||
−0.0735947 | + | 0.997288i | \(0.523447\pi\) | |||||||
\(152\) | −23104.0 | −0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 117260. | 0.398426 | ||||||||
\(155\) | 23058.0 | 0.0770890 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −345954. | −1.12013 | −0.560066 | − | 0.828448i | \(-0.689224\pi\) | ||||
−0.560066 | + | 0.828448i | \(0.689224\pi\) | |||||||
\(158\) | 215552. | 0.686925 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 21504.0 | 0.0664078 | ||||||||
\(161\) | 2860.00 | 0.00869564 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −298144. | −0.878936 | −0.439468 | − | 0.898258i | \(-0.644833\pi\) | ||||
−0.439468 | + | 0.898258i | \(0.644833\pi\) | |||||||
\(164\) | 150400. | 0.436655 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 300784. | 0.847197 | ||||||||
\(167\) | 73290.0 | 0.203354 | 0.101677 | − | 0.994817i | \(-0.467579\pi\) | ||||
0.101677 | + | 0.994817i | \(0.467579\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −365209. | −0.983614 | ||||||||
\(170\) | 178500. | 0.473714 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 321168. | 0.827773 | ||||||||
\(173\) | −282102. | −0.716623 | −0.358312 | − | 0.933602i | \(-0.616647\pi\) | ||||
−0.358312 | + | 0.933602i | \(0.616647\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 383812. | 0.947378 | ||||||||
\(176\) | 52480.0 | 0.127706 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 82472.0 | 0.195100 | ||||||||
\(179\) | −193946. | −0.452427 | −0.226213 | − | 0.974078i | \(-0.572635\pi\) | ||||
−0.226213 | + | 0.974078i | \(0.572635\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −283446. | −0.643093 | −0.321547 | − | 0.946894i | \(-0.604203\pi\) | ||||
−0.321547 | + | 0.946894i | \(0.604203\pi\) | |||||||
\(182\) | −44616.0 | −0.0998417 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1280.00 | 0.00278718 | ||||||||
\(185\) | 317688. | 0.682451 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 435625. | 0.910980 | ||||||||
\(188\) | −225680. | −0.465692 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 30324.0 | 0.0609400 | ||||||||
\(191\) | −50495.0 | −0.100153 | −0.0500766 | − | 0.998745i | \(-0.515947\pi\) | ||||
−0.0500766 | + | 0.998745i | \(0.515947\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 231092. | 0.446572 | 0.223286 | − | 0.974753i | \(-0.428322\pi\) | ||||
0.223286 | + | 0.974753i | \(0.428322\pi\) | |||||||
\(194\) | 336520. | 0.641958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 58272.0 | 0.108348 | ||||||||
\(197\) | 452482. | 0.830684 | 0.415342 | − | 0.909665i | \(-0.363662\pi\) | ||||
0.415342 | + | 0.909665i | \(0.363662\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −207199. | −0.370898 | −0.185449 | − | 0.982654i | \(-0.559374\pi\) | ||||
−0.185449 | + | 0.982654i | \(0.559374\pi\) | |||||||
\(200\) | 171776. | 0.303660 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 654856. | 1.12919 | ||||||||
\(203\) | −695838. | −1.18514 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −197400. | −0.328067 | ||||||||
\(206\) | 556248. | 0.913273 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −19968.0 | −0.0320019 | ||||||||
\(209\) | 74005.0 | 0.117191 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 985948. | 1.52457 | 0.762286 | − | 0.647240i | \(-0.224077\pi\) | ||||
0.762286 | + | 0.647240i | \(0.224077\pi\) | |||||||
\(212\) | −422176. | −0.645140 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 498760. | 0.744487 | ||||||||
\(215\) | −421533. | −0.621921 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 157014. | 0.226354 | ||||||||
\(218\) | 47344.0 | 0.0674720 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −68880.0 | −0.0959481 | ||||||||
\(221\) | −165750. | −0.228283 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 177756. | 0.239366 | 0.119683 | − | 0.992812i | \(-0.461812\pi\) | ||||
0.119683 | + | 0.992812i | \(0.461812\pi\) | |||||||
\(224\) | 146432. | 0.194992 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 230696. | 0.300448 | ||||||||
\(227\) | −276382. | −0.355996 | −0.177998 | − | 0.984031i | \(-0.556962\pi\) | ||||
−0.177998 | + | 0.984031i | \(0.556962\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 986125. | 1.24263 | 0.621317 | − | 0.783559i | \(-0.286598\pi\) | ||||
0.621317 | + | 0.783559i | \(0.286598\pi\) | |||||||
\(230\) | −1680.00 | −0.00209406 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −311424. | −0.379867 | ||||||||
\(233\) | 116691. | 0.140815 | 0.0704073 | − | 0.997518i | \(-0.477570\pi\) | ||||
0.0704073 | + | 0.997518i | \(0.477570\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 296205. | 0.349883 | ||||||||
\(236\) | 211456. | 0.247138 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.21550e6 | 1.39095 | ||||||||
\(239\) | 1.25870e6 | 1.42537 | 0.712685 | − | 0.701484i | \(-0.247479\pi\) | ||||
0.712685 | + | 0.701484i | \(0.247479\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −143492. | −0.159142 | −0.0795710 | − | 0.996829i | \(-0.525355\pi\) | ||||
−0.0795710 | + | 0.996829i | \(0.525355\pi\) | |||||||
\(242\) | 476104. | 0.522593 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −36688.0 | −0.0394502 | ||||||||
\(245\) | −76482.0 | −0.0814037 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28158.0 | −0.0293670 | ||||||||
\(248\) | 70272.0 | 0.0725526 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −487956. | −0.493777 | ||||||||
\(251\) | 884163. | 0.885825 | 0.442913 | − | 0.896565i | \(-0.353945\pi\) | ||||
0.442913 | + | 0.896565i | \(0.353945\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4100.00 | −0.00402701 | ||||||||
\(254\) | −537256. | −0.522513 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.04230e6 | −0.984370 | −0.492185 | − | 0.870491i | \(-0.663802\pi\) | ||||
−0.492185 | + | 0.870491i | \(0.663802\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.16330e6 | 2.00386 | ||||||||
\(260\) | 26208.0 | 0.0240437 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.46382e6 | −1.31745 | ||||||||
\(263\) | −998121. | −0.889803 | −0.444901 | − | 0.895580i | \(-0.646761\pi\) | ||||
−0.444901 | + | 0.895580i | \(0.646761\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 554106. | 0.484706 | ||||||||
\(266\) | 206492. | 0.178937 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 575616. | 0.489549 | ||||||||
\(269\) | −1.73550e6 | −1.46232 | −0.731162 | − | 0.682204i | \(-0.761022\pi\) | ||||
−0.731162 | + | 0.682204i | \(0.761022\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.01674e6 | −0.840982 | −0.420491 | − | 0.907297i | \(-0.638142\pi\) | ||||
−0.420491 | + | 0.907297i | \(0.638142\pi\) | |||||||
\(272\) | 544000. | 0.445838 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 179052. | 0.144080 | ||||||||
\(275\) | −550220. | −0.438737 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.37870e6 | −1.07962 | −0.539810 | − | 0.841787i | \(-0.681504\pi\) | ||||
−0.539810 | + | 0.841787i | \(0.681504\pi\) | |||||||
\(278\) | 1.68872e6 | 1.31052 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −192192. | −0.146501 | ||||||||
\(281\) | 2.09789e6 | 1.58495 | 0.792476 | − | 0.609903i | \(-0.208792\pi\) | ||||
0.792476 | + | 0.609903i | \(0.208792\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −215963. | −0.160293 | −0.0801463 | − | 0.996783i | \(-0.525539\pi\) | ||||
−0.0801463 | + | 0.996783i | \(0.525539\pi\) | |||||||
\(284\) | −162880. | −0.119832 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 63960.0 | 0.0462374 | ||||||||
\(287\) | −1.34420e6 | −0.963295 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.09577e6 | 2.18034 | ||||||||
\(290\) | 408744. | 0.285402 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 529744. | 0.363587 | ||||||||
\(293\) | 2.47872e6 | 1.68678 | 0.843389 | − | 0.537304i | \(-0.180557\pi\) | ||||
0.843389 | + | 0.537304i | \(0.180557\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −277536. | −0.185680 | ||||||||
\(296\) | 968192. | 0.642292 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −166964. | −0.108914 | ||||||||
\(299\) | 1560.00 | 0.00100913 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.87044e6 | −1.82613 | ||||||||
\(302\) | 164960. | 0.104079 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 92416.0 | 0.0573539 | ||||||||
\(305\) | 48153.0 | 0.0296397 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 495420. | 0.300004 | 0.150002 | − | 0.988686i | \(-0.452072\pi\) | ||||
0.150002 | + | 0.988686i | \(0.452072\pi\) | |||||||
\(308\) | −469040. | −0.281730 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −92232.0 | −0.0545102 | ||||||||
\(311\) | −2.15964e6 | −1.26614 | −0.633070 | − | 0.774095i | \(-0.718205\pi\) | ||||
−0.633070 | + | 0.774095i | \(0.718205\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.34757e6 | −0.777482 | −0.388741 | − | 0.921347i | \(-0.627090\pi\) | ||||
−0.388741 | + | 0.921347i | \(0.627090\pi\) | |||||||
\(314\) | 1.38382e6 | 0.792053 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −862208. | −0.485729 | ||||||||
\(317\) | 1.01166e6 | 0.565440 | 0.282720 | − | 0.959203i | \(-0.408763\pi\) | ||||
0.282720 | + | 0.959203i | \(0.408763\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 997530. | 0.548844 | ||||||||
\(320\) | −86016.0 | −0.0469574 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11440.0 | −0.00614874 | ||||||||
\(323\) | 767125. | 0.409129 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 209352. | 0.109943 | ||||||||
\(326\) | 1.19258e6 | 0.621501 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −601600. | −0.308762 | ||||||||
\(329\) | 2.01702e6 | 1.02735 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.57062e6 | −0.787954 | −0.393977 | − | 0.919120i | \(-0.628901\pi\) | ||||
−0.393977 | + | 0.919120i | \(0.628901\pi\) | |||||||
\(332\) | −1.20314e6 | −0.599059 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −293160. | −0.143793 | ||||||||
\(335\) | −755496. | −0.367807 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.16228e6 | 1.03714 | 0.518570 | − | 0.855035i | \(-0.326464\pi\) | ||||
0.518570 | + | 0.855035i | \(0.326464\pi\) | |||||||
\(338\) | 1.46084e6 | 0.695520 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −714000. | −0.334966 | ||||||||
\(341\) | −225090. | −0.104826 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.88259e6 | 0.864016 | ||||||||
\(344\) | −1.28467e6 | −0.585324 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.12841e6 | 0.506729 | ||||||||
\(347\) | −4.16873e6 | −1.85858 | −0.929288 | − | 0.369356i | \(-0.879578\pi\) | ||||
−0.929288 | + | 0.369356i | \(0.879578\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 722845. | 0.317674 | 0.158837 | − | 0.987305i | \(-0.449226\pi\) | ||||
0.158837 | + | 0.987305i | \(0.449226\pi\) | |||||||
\(350\) | −1.53525e6 | −0.669898 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −209920. | −0.0903020 | ||||||||
\(353\) | −1.45102e6 | −0.619780 | −0.309890 | − | 0.950772i | \(-0.600292\pi\) | ||||
−0.309890 | + | 0.950772i | \(0.600292\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 213780. | 0.0900319 | ||||||||
\(356\) | −329888. | −0.137956 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 775784. | 0.319914 | ||||||||
\(359\) | −517179. | −0.211790 | −0.105895 | − | 0.994377i | \(-0.533771\pi\) | ||||
−0.105895 | + | 0.994377i | \(0.533771\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 1.13378e6 | 0.454736 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 178464. | 0.0705988 | ||||||||
\(365\) | −695289. | −0.273170 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.59392e6 | −1.39285 | −0.696423 | − | 0.717631i | \(-0.745226\pi\) | ||||
−0.696423 | + | 0.717631i | \(0.745226\pi\) | |||||||
\(368\) | −5120.00 | −0.00197084 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.27075e6 | −0.482566 | ||||||||
\(371\) | 3.77320e6 | 1.42323 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.77578e6 | −0.660870 | −0.330435 | − | 0.943829i | \(-0.607195\pi\) | ||||
−0.330435 | + | 0.943829i | \(0.607195\pi\) | |||||||
\(374\) | −1.74250e6 | −0.644160 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 902720. | 0.329294 | ||||||||
\(377\) | −379548. | −0.137535 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.48464e6 | 0.888516 | 0.444258 | − | 0.895899i | \(-0.353467\pi\) | ||||
0.444258 | + | 0.895899i | \(0.353467\pi\) | |||||||
\(380\) | −121296. | −0.0430911 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 201980. | 0.0708190 | ||||||||
\(383\) | −1.70987e6 | −0.595614 | −0.297807 | − | 0.954626i | \(-0.596255\pi\) | ||||
−0.297807 | + | 0.954626i | \(0.596255\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 615615. | 0.211669 | ||||||||
\(386\) | −924368. | −0.315774 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.34608e6 | −0.453933 | ||||||||
\(389\) | 244715. | 0.0819949 | 0.0409974 | − | 0.999159i | \(-0.486946\pi\) | ||||
0.0409974 | + | 0.999159i | \(0.486946\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42500.0 | −0.0140588 | ||||||||
\(392\) | −233088. | −0.0766134 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.80993e6 | −0.587382 | ||||||||
\(395\) | 1.13165e6 | 0.364938 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.11195e6 | −1.30940 | −0.654698 | − | 0.755890i | \(-0.727204\pi\) | ||||
−0.654698 | + | 0.755890i | \(0.727204\pi\) | |||||||
\(398\) | 828796. | 0.262265 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −687104. | −0.214720 | ||||||||
\(401\) | 1.87955e6 | 0.583704 | 0.291852 | − | 0.956464i | \(-0.405729\pi\) | ||||
0.291852 | + | 0.956464i | \(0.405729\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 85644.0 | 0.0262684 | ||||||||
\(404\) | −2.61942e6 | −0.798459 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.78335e6 | 0.838017 | ||||||||
\(407\) | −3.10124e6 | −0.928003 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.68258e6 | −0.792948 | −0.396474 | − | 0.918046i | \(-0.629766\pi\) | ||||
−0.396474 | + | 0.918046i | \(0.629766\pi\) | |||||||
\(410\) | 789600. | 0.231978 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.22499e6 | −0.645781 | ||||||||
\(413\) | −1.88989e6 | −0.545206 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.57912e6 | 0.450084 | ||||||||
\(416\) | 79872.0 | 0.0226288 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −296020. | −0.0828668 | ||||||||
\(419\) | 5.70599e6 | 1.58780 | 0.793900 | − | 0.608048i | \(-0.208047\pi\) | ||||
0.793900 | + | 0.608048i | \(0.208047\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.24578e6 | −1.16749 | −0.583744 | − | 0.811938i | \(-0.698413\pi\) | ||||
−0.583744 | + | 0.811938i | \(0.698413\pi\) | |||||||
\(422\) | −3.94379e6 | −1.07804 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.68870e6 | 0.456183 | ||||||||
\(425\) | −5.70350e6 | −1.53168 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 327899. | 0.0870303 | ||||||||
\(428\) | −1.99504e6 | −0.526432 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.68613e6 | 0.439765 | ||||||||
\(431\) | 1.28341e6 | 0.332793 | 0.166396 | − | 0.986059i | \(-0.446787\pi\) | ||||
0.166396 | + | 0.986059i | \(0.446787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.39182e6 | −1.63834 | −0.819171 | − | 0.573549i | \(-0.805566\pi\) | ||||
−0.819171 | + | 0.573549i | \(0.805566\pi\) | |||||||
\(434\) | −628056. | −0.160057 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −189376. | −0.0477099 | ||||||||
\(437\) | −7220.00 | −0.00180856 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.27464e6 | 0.315664 | 0.157832 | − | 0.987466i | \(-0.449549\pi\) | ||||
0.157832 | + | 0.987466i | \(0.449549\pi\) | |||||||
\(440\) | 275520. | 0.0678456 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 663000. | 0.161420 | ||||||||
\(443\) | −2.35546e6 | −0.570253 | −0.285126 | − | 0.958490i | \(-0.592036\pi\) | ||||
−0.285126 | + | 0.958490i | \(0.592036\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 432978. | 0.103649 | ||||||||
\(446\) | −711024. | −0.169257 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −585728. | −0.137880 | ||||||||
\(449\) | −7.99412e6 | −1.87135 | −0.935675 | − | 0.352863i | \(-0.885208\pi\) | ||||
−0.935675 | + | 0.352863i | \(0.885208\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.92700e6 | 0.446108 | ||||||||
\(452\) | −922784. | −0.212449 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.10553e6 | 0.251727 | ||||||||
\(455\) | −234234. | −0.0530422 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.03844e6 | −0.680550 | −0.340275 | − | 0.940326i | \(-0.610520\pi\) | ||||
−0.340275 | + | 0.940326i | \(0.610520\pi\) | |||||||
\(458\) | −3.94450e6 | −0.878675 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6720.00 | 0.00148073 | ||||||||
\(461\) | 5.98744e6 | 1.31217 | 0.656084 | − | 0.754688i | \(-0.272212\pi\) | ||||
0.656084 | + | 0.754688i | \(0.272212\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.05385e6 | 1.74603 | 0.873014 | − | 0.487695i | \(-0.162162\pi\) | ||||
0.873014 | + | 0.487695i | \(0.162162\pi\) | |||||||
\(464\) | 1.24570e6 | 0.268607 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −466764. | −0.0995709 | ||||||||
\(467\) | 8.29332e6 | 1.75969 | 0.879845 | − | 0.475261i | \(-0.157646\pi\) | ||||
0.879845 | + | 0.475261i | \(0.157646\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.14457e6 | −1.07998 | ||||||||
\(470\) | −1.18482e6 | −0.247405 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −845824. | −0.174753 | ||||||||
\(473\) | 4.11496e6 | 0.845694 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −968924. | −0.197041 | ||||||||
\(476\) | −4.86200e6 | −0.983553 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.03480e6 | −1.00789 | ||||||||
\(479\) | 4.58472e6 | 0.913007 | 0.456503 | − | 0.889722i | \(-0.349102\pi\) | ||||
0.456503 | + | 0.889722i | \(0.349102\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.17998e6 | 0.232548 | ||||||||
\(482\) | 573968. | 0.112530 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.90442e6 | −0.369529 | ||||||||
\(485\) | 1.76673e6 | 0.341048 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 55304.0 | 0.0105666 | 0.00528329 | − | 0.999986i | \(-0.498318\pi\) | ||||
0.00528329 | + | 0.999986i | \(0.498318\pi\) | |||||||
\(488\) | 146752. | 0.0278955 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 305928. | 0.0575611 | ||||||||
\(491\) | 6.88932e6 | 1.28965 | 0.644826 | − | 0.764329i | \(-0.276930\pi\) | ||||
0.644826 | + | 0.764329i | \(0.276930\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.03402e7 | 1.91608 | ||||||||
\(494\) | 112632. | 0.0207656 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −281088. | −0.0513025 | ||||||||
\(497\) | 1.45574e6 | 0.264358 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.61676e6 | 1.00980 | 0.504899 | − | 0.863179i | \(-0.331530\pi\) | ||||
0.504899 | + | 0.863179i | \(0.331530\pi\) | |||||||
\(500\) | 1.95182e6 | 0.349153 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.53665e6 | −0.626373 | ||||||||
\(503\) | 5.16131e6 | 0.909578 | 0.454789 | − | 0.890599i | \(-0.349715\pi\) | ||||
0.454789 | + | 0.890599i | \(0.349715\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.43799e6 | 0.599897 | ||||||||
\(506\) | 16400.0 | 0.00284753 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.14902e6 | 0.369472 | ||||||||
\(509\) | 1.81839e6 | 0.311094 | 0.155547 | − | 0.987828i | \(-0.450286\pi\) | ||||
0.155547 | + | 0.987828i | \(0.450286\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.73459e6 | −0.802102 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.16918e6 | 0.696055 | ||||||||
\(515\) | 2.92030e6 | 0.485188 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.89152e6 | −0.475774 | ||||||||
\(518\) | −8.65322e6 | −1.41695 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −104832. | −0.0170014 | ||||||||
\(521\) | −1.10957e7 | −1.79085 | −0.895424 | − | 0.445215i | \(-0.853127\pi\) | ||||
−0.895424 | + | 0.445215i | \(0.853127\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.51297e6 | −1.20104 | −0.600520 | − | 0.799610i | \(-0.705040\pi\) | ||||
−0.600520 | + | 0.799610i | \(0.705040\pi\) | |||||||
\(524\) | 5.85528e6 | 0.931578 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.99248e6 | 0.629186 | ||||||||
\(527\) | −2.33325e6 | −0.365961 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.43594e6 | −0.999938 | ||||||||
\(530\) | −2.21642e6 | −0.342739 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −825968. | −0.126527 | ||||||||
\(533\) | −733200. | −0.111790 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.61849e6 | 0.395518 | ||||||||
\(536\) | −2.30246e6 | −0.346163 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.94199e6 | 1.03402 | ||||||||
\(539\) | 746610. | 0.110693 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.15622e6 | 0.463632 | 0.231816 | − | 0.972760i | \(-0.425533\pi\) | ||||
0.231816 | + | 0.972760i | \(0.425533\pi\) | |||||||
\(542\) | 4.06696e6 | 0.594664 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.17600e6 | −0.315255 | ||||||||
\(545\) | 248556. | 0.0358454 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.17063e7 | −1.67283 | −0.836417 | − | 0.548094i | \(-0.815353\pi\) | ||||
−0.836417 | + | 0.548094i | \(0.815353\pi\) | |||||||
\(548\) | −716208. | −0.101880 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.20088e6 | 0.310234 | ||||||||
\(551\) | 1.75663e6 | 0.246491 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.70598e6 | 1.07156 | ||||||||
\(554\) | 5.51481e6 | 0.763407 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.75486e6 | −0.926680 | ||||||||
\(557\) | −5.56111e6 | −0.759493 | −0.379746 | − | 0.925091i | \(-0.623989\pi\) | ||||
−0.379746 | + | 0.925091i | \(0.623989\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.56569e6 | −0.211923 | ||||||||
\(560\) | 768768. | 0.103592 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.39154e6 | −1.12073 | ||||||||
\(563\) | 1.17669e7 | 1.56456 | 0.782280 | − | 0.622928i | \(-0.214057\pi\) | ||||
0.782280 | + | 0.622928i | \(0.214057\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.21115e6 | 0.159617 | ||||||||
\(566\) | 863852. | 0.113344 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 651520. | 0.0847338 | ||||||||
\(569\) | −6.49649e6 | −0.841198 | −0.420599 | − | 0.907247i | \(-0.638180\pi\) | ||||
−0.420599 | + | 0.907247i | \(0.638180\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.15432e6 | −0.918286 | −0.459143 | − | 0.888362i | \(-0.651843\pi\) | ||||
−0.459143 | + | 0.888362i | \(0.651843\pi\) | |||||||
\(572\) | −255840. | −0.0326948 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.37680e6 | 0.681152 | ||||||||
\(575\) | 53680.0 | 0.00677085 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.50781e6 | −1.06385 | −0.531923 | − | 0.846793i | \(-0.678530\pi\) | ||||
−0.531923 | + | 0.846793i | \(0.678530\pi\) | |||||||
\(578\) | −1.23831e7 | −1.54173 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.63498e6 | −0.201809 | ||||||||
\(581\) | 1.07530e7 | 1.32157 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.40913e6 | −0.659107 | ||||||||
\(584\) | −2.11898e6 | −0.257095 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.91486e6 | −1.19273 | ||||||||
\(587\) | 854707. | 0.102382 | 0.0511908 | − | 0.998689i | \(-0.483698\pi\) | ||||
0.0511908 | + | 0.998689i | \(0.483698\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −396378. | −0.0470784 | ||||||||
\(590\) | 1.11014e6 | 0.131295 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.87277e6 | −0.454169 | ||||||||
\(593\) | 5.55213e6 | 0.648370 | 0.324185 | − | 0.945994i | \(-0.394910\pi\) | ||||
0.324185 | + | 0.945994i | \(0.394910\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.38138e6 | 0.738962 | ||||||||
\(596\) | 667856. | 0.0770136 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6240.00 | −0.000713562 0 | ||||||||
\(599\) | 1.30669e6 | 0.148801 | 0.0744003 | − | 0.997228i | \(-0.476296\pi\) | ||||
0.0744003 | + | 0.997228i | \(0.476296\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.94858e6 | −0.897643 | −0.448821 | − | 0.893621i | \(-0.648156\pi\) | ||||
−0.448821 | + | 0.893621i | \(0.648156\pi\) | |||||||
\(602\) | 1.14818e7 | 1.29127 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −659840. | −0.0735947 | ||||||||
\(605\) | 2.49955e6 | 0.277634 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.83746e6 | 0.312578 | 0.156289 | − | 0.987711i | \(-0.450047\pi\) | ||||
0.156289 | + | 0.987711i | \(0.450047\pi\) | |||||||
\(608\) | −369664. | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −192612. | −0.0209584 | ||||||||
\(611\) | 1.10019e6 | 0.119224 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.49674e7 | 1.60877 | 0.804387 | − | 0.594106i | \(-0.202494\pi\) | ||||
0.804387 | + | 0.594106i | \(0.202494\pi\) | |||||||
\(614\) | −1.98168e6 | −0.212135 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.87616e6 | 0.199213 | ||||||||
\(617\) | 3.59751e6 | 0.380443 | 0.190221 | − | 0.981741i | \(-0.439079\pi\) | ||||
0.190221 | + | 0.981741i | \(0.439079\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.74758e6 | 0.707818 | 0.353909 | − | 0.935280i | \(-0.384852\pi\) | ||||
0.353909 | + | 0.935280i | \(0.384852\pi\) | |||||||
\(620\) | 368928. | 0.0385445 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.63858e6 | 0.895295 | ||||||||
\(623\) | 2.94837e6 | 0.304342 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.82573e6 | 0.596555 | ||||||||
\(626\) | 5.39028e6 | 0.549763 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.53526e6 | −0.560066 | ||||||||
\(629\) | −3.21470e7 | −3.23977 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.36044e7 | 1.36021 | 0.680103 | − | 0.733117i | \(-0.261935\pi\) | ||||
0.680103 | + | 0.733117i | \(0.261935\pi\) | |||||||
\(632\) | 3.44883e6 | 0.343463 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.04664e6 | −0.399826 | ||||||||
\(635\) | −2.82059e6 | −0.277592 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −284076. | −0.0277387 | ||||||||
\(638\) | −3.99012e6 | −0.388092 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 344064. | 0.0332039 | ||||||||
\(641\) | −1.91221e7 | −1.83819 | −0.919097 | − | 0.394030i | \(-0.871080\pi\) | ||||
−0.919097 | + | 0.394030i | \(0.871080\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.38738e6 | 0.800016 | 0.400008 | − | 0.916512i | \(-0.369007\pi\) | ||||
0.400008 | + | 0.916512i | \(0.369007\pi\) | |||||||
\(644\) | 45760.0 | 0.00434782 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.06850e6 | −0.289298 | ||||||||
\(647\) | −7.90221e6 | −0.742143 | −0.371072 | − | 0.928604i | \(-0.621010\pi\) | ||||
−0.371072 | + | 0.928604i | \(0.621010\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.70928e6 | 0.252489 | ||||||||
\(650\) | −837408. | −0.0777416 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.77030e6 | −0.439468 | ||||||||
\(653\) | 279213. | 0.0256243 | 0.0128122 | − | 0.999918i | \(-0.495922\pi\) | ||||
0.0128122 | + | 0.999918i | \(0.495922\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.68506e6 | −0.699912 | ||||||||
\(656\) | 2.40640e6 | 0.218327 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.06806e6 | −0.726448 | ||||||||
\(659\) | 6.82671e6 | 0.612348 | 0.306174 | − | 0.951976i | \(-0.400951\pi\) | ||||
0.306174 | + | 0.951976i | \(0.400951\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.85059e7 | 1.64742 | 0.823712 | − | 0.567008i | \(-0.191899\pi\) | ||||
0.823712 | + | 0.567008i | \(0.191899\pi\) | |||||||
\(662\) | 6.28248e6 | 0.557168 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.81254e6 | 0.423599 | ||||||||
\(665\) | 1.08408e6 | 0.0950623 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −97320.0 | −0.00847008 | ||||||||
\(668\) | 1.17264e6 | 0.101677 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.02198e6 | 0.260079 | ||||||||
\(671\) | −470065. | −0.0403043 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.25059e7 | 1.06433 | 0.532166 | − | 0.846640i | \(-0.321378\pi\) | ||||
0.532166 | + | 0.846640i | \(0.321378\pi\) | |||||||
\(674\) | −8.64913e6 | −0.733369 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.84334e6 | −0.491807 | ||||||||
\(677\) | −5.47029e6 | −0.458710 | −0.229355 | − | 0.973343i | \(-0.573662\pi\) | ||||
−0.229355 | + | 0.973343i | \(0.573662\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.20306e7 | 1.00141 | ||||||||
\(680\) | 2.85600e6 | 0.236857 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 900360. | 0.0741234 | ||||||||
\(683\) | −1.02415e7 | −0.840061 | −0.420031 | − | 0.907510i | \(-0.637981\pi\) | ||||
−0.420031 | + | 0.907510i | \(0.637981\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 940023. | 0.0765442 | ||||||||
\(686\) | −7.53038e6 | −0.610951 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.13869e6 | 0.413886 | ||||||||
\(689\) | 2.05811e6 | 0.165166 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.84945e6 | 0.147349 | 0.0736744 | − | 0.997282i | \(-0.476527\pi\) | ||||
0.0736744 | + | 0.997282i | \(0.476527\pi\) | |||||||
\(692\) | −4.51363e6 | −0.358312 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.66749e7 | 1.31421 | ||||||||
\(695\) | 8.86576e6 | 0.696232 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.99750e7 | 1.55742 | ||||||||
\(698\) | −2.89138e6 | −0.224629 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.14099e6 | 0.473689 | ||||||||
\(701\) | −1.65813e7 | −1.27445 | −0.637226 | − | 0.770677i | \(-0.719918\pi\) | ||||
−0.637226 | + | 0.770677i | \(0.719918\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.46121e6 | −0.416774 | ||||||||
\(704\) | 839680. | 0.0638531 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.80409e6 | 0.438250 | ||||||||
\(707\) | 2.34111e7 | 1.76146 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.10501e7 | 0.825562 | 0.412781 | − | 0.910830i | \(-0.364558\pi\) | ||||
0.412781 | + | 0.910830i | \(0.364558\pi\) | |||||||
\(710\) | −855120. | −0.0636621 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.31955e6 | 0.0975498 | ||||||||
\(713\) | 21960.0 | 0.00161774 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 335790. | 0.0245642 | ||||||||
\(716\) | −3.10314e6 | −0.226213 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.06872e6 | 0.149758 | ||||||||
\(719\) | −1.02255e7 | −0.737669 | −0.368835 | − | 0.929495i | \(-0.620243\pi\) | ||||
−0.368835 | + | 0.929495i | \(0.620243\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.98859e7 | 1.42464 | ||||||||
\(722\) | −521284. | −0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.53514e6 | −0.321547 | ||||||||
\(725\) | −1.30603e7 | −0.922804 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.61985e7 | 1.83840 | 0.919202 | − | 0.393787i | \(-0.128835\pi\) | ||||
0.919202 | + | 0.393787i | \(0.128835\pi\) | |||||||
\(728\) | −713856. | −0.0499209 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.78116e6 | 0.193160 | ||||||||
\(731\) | 4.26551e7 | 2.95242 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.56029e7 | −1.76007 | −0.880033 | − | 0.474913i | \(-0.842480\pi\) | ||||
−0.880033 | + | 0.474913i | \(0.842480\pi\) | |||||||
\(734\) | 1.43757e7 | 0.984891 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20480.0 | 0.00139359 | ||||||||
\(737\) | 7.37508e6 | 0.500147 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.10847e7 | −1.42022 | −0.710112 | − | 0.704089i | \(-0.751356\pi\) | ||||
−0.710112 | + | 0.704089i | \(0.751356\pi\) | |||||||
\(740\) | 5.08301e6 | 0.341226 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.50928e7 | −1.00637 | ||||||||
\(743\) | −8.71807e6 | −0.579360 | −0.289680 | − | 0.957124i | \(-0.593549\pi\) | ||||
−0.289680 | + | 0.957124i | \(0.593549\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −876561. | −0.0578617 | ||||||||
\(746\) | 7.10310e6 | 0.467306 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.97000e6 | 0.455490 | ||||||||
\(749\) | 1.78307e7 | 1.16135 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.26501e7 | −0.818452 | −0.409226 | − | 0.912433i | \(-0.634201\pi\) | ||||
−0.409226 | + | 0.912433i | \(0.634201\pi\) | |||||||
\(752\) | −3.61088e6 | −0.232846 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.51819e6 | 0.0972520 | ||||||||
\(755\) | 866040. | 0.0552931 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.69653e6 | −0.361302 | −0.180651 | − | 0.983547i | \(-0.557821\pi\) | ||||
−0.180651 | + | 0.983547i | \(0.557821\pi\) | |||||||
\(758\) | −9.93855e6 | −0.628275 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 485184. | 0.0304700 | ||||||||
\(761\) | 2.51658e7 | 1.57525 | 0.787625 | − | 0.616155i | \(-0.211310\pi\) | ||||
0.787625 | + | 0.616155i | \(0.211310\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.69255e6 | 0.105252 | ||||||||
\(764\) | −807920. | −0.0500766 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.83946e6 | 0.421163 | ||||||||
\(767\) | −1.03085e6 | −0.0632712 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.35673e7 | −1.43713 | −0.718563 | − | 0.695462i | \(-0.755200\pi\) | ||||
−0.718563 | + | 0.695462i | \(0.755200\pi\) | |||||||
\(770\) | −2.46246e6 | −0.149673 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.69747e6 | 0.223286 | ||||||||
\(773\) | −1.61071e7 | −0.969548 | −0.484774 | − | 0.874639i | \(-0.661098\pi\) | ||||
−0.484774 | + | 0.874639i | \(0.661098\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.94703e6 | 0.176251 | ||||||||
\(776\) | 5.38432e6 | 0.320979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −978860. | −0.0579791 | ||||||||
\(779\) | 3.39340e6 | 0.200351 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.08690e6 | −0.122426 | ||||||||
\(782\) | 170000. | 0.00994104 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 932352. | 0.0541739 | ||||||||
\(785\) | 7.26503e6 | 0.420788 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.09622e6 | −0.465956 | −0.232978 | − | 0.972482i | \(-0.574847\pi\) | ||||
−0.232978 | + | 0.972482i | \(0.574847\pi\) | |||||||
\(788\) | 7.23971e6 | 0.415342 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.52659e6 | −0.258050 | ||||||||
\(791\) | 8.24738e6 | 0.468678 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 178854. | 0.0100999 | ||||||||
\(794\) | 1.64478e7 | 0.925883 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.31518e6 | −0.185449 | ||||||||
\(797\) | −2.23729e7 | −1.24760 | −0.623800 | − | 0.781584i | \(-0.714412\pi\) | ||||
−0.623800 | + | 0.781584i | \(0.714412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.99731e7 | −1.66098 | ||||||||
\(800\) | 2.74842e6 | 0.151830 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.51819e6 | −0.412741 | ||||||||
\(803\) | 6.78735e6 | 0.371459 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −60060.0 | −0.00326660 | ||||||||
\(806\) | −342576. | −0.0185746 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.04777e7 | 0.564595 | ||||||||
\(809\) | −915669. | −0.0491889 | −0.0245945 | − | 0.999698i | \(-0.507829\pi\) | ||||
−0.0245945 | + | 0.999698i | \(0.507829\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.00496e7 | −1.60430 | −0.802151 | − | 0.597121i | \(-0.796311\pi\) | ||||
−0.802151 | + | 0.597121i | \(0.796311\pi\) | |||||||
\(812\) | −1.11334e7 | −0.592568 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.24050e7 | 0.656197 | ||||||||
\(815\) | 6.26102e6 | 0.330180 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.24635e6 | 0.379808 | ||||||||
\(818\) | 1.07303e7 | 0.560699 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.15840e6 | −0.164033 | ||||||||
\(821\) | −3.25959e6 | −0.168774 | −0.0843868 | − | 0.996433i | \(-0.526893\pi\) | ||||
−0.0843868 | + | 0.996433i | \(0.526893\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.63514e7 | 1.35614 | 0.678068 | − | 0.734999i | \(-0.262817\pi\) | ||||
0.678068 | + | 0.734999i | \(0.262817\pi\) | |||||||
\(824\) | 8.89997e6 | 0.456636 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.55955e6 | 0.385519 | ||||||||
\(827\) | −3.88895e6 | −0.197728 | −0.0988640 | − | 0.995101i | \(-0.531521\pi\) | ||||
−0.0988640 | + | 0.995101i | \(0.531521\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.49909e7 | −1.26298 | −0.631488 | − | 0.775385i | \(-0.717556\pi\) | ||||
−0.631488 | + | 0.775385i | \(0.717556\pi\) | |||||||
\(830\) | −6.31646e6 | −0.318258 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −319488. | −0.0160010 | ||||||||
\(833\) | 7.73925e6 | 0.386444 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.53909e6 | −0.0763920 | ||||||||
\(836\) | 1.18408e6 | 0.0585956 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.28240e7 | −1.12274 | ||||||||
\(839\) | 2.77733e6 | 0.136214 | 0.0681072 | − | 0.997678i | \(-0.478304\pi\) | ||||
0.0681072 | + | 0.997678i | \(0.478304\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.16681e6 | 0.154394 | ||||||||
\(842\) | 1.69831e7 | 0.825539 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.57752e7 | 0.762286 | ||||||||
\(845\) | 7.66939e6 | 0.369504 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.70207e7 | 0.815210 | ||||||||
\(848\) | −6.75482e6 | −0.322570 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.28140e7 | 1.08306 | ||||||||
\(851\) | 302560. | 0.0143215 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.63379e6 | 0.0768820 | 0.0384410 | − | 0.999261i | \(-0.487761\pi\) | ||||
0.0384410 | + | 0.999261i | \(0.487761\pi\) | |||||||
\(854\) | −1.31160e6 | −0.0615397 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.98016e6 | 0.372244 | ||||||||
\(857\) | −2.45037e7 | −1.13967 | −0.569836 | − | 0.821758i | \(-0.692993\pi\) | ||||
−0.569836 | + | 0.821758i | \(0.692993\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.45576e7 | 0.673143 | 0.336572 | − | 0.941658i | \(-0.390733\pi\) | ||||
0.336572 | + | 0.941658i | \(0.390733\pi\) | |||||||
\(860\) | −6.74453e6 | −0.310961 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.13366e6 | −0.235320 | ||||||||
\(863\) | −1.76706e7 | −0.807651 | −0.403826 | − | 0.914836i | \(-0.632320\pi\) | ||||
−0.403826 | + | 0.914836i | \(0.632320\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.92414e6 | 0.269206 | ||||||||
\(866\) | 2.55673e7 | 1.15848 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.51222e6 | 0.113177 | ||||||||
\(869\) | −1.10470e7 | −0.496245 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.80613e6 | −0.125332 | ||||||||
\(872\) | 757504. | 0.0337360 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 28880.0 | 0.00127885 | ||||||||
\(875\) | −1.74444e7 | −0.770259 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.46464e7 | −1.96014 | −0.980070 | − | 0.198650i | \(-0.936344\pi\) | ||||
−0.980070 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(878\) | −5.09855e6 | −0.223208 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.10208e6 | −0.0479741 | ||||||||
\(881\) | 1.97316e7 | 0.856490 | 0.428245 | − | 0.903663i | \(-0.359132\pi\) | ||||
0.428245 | + | 0.903663i | \(0.359132\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.12686e7 | −0.917989 | −0.458994 | − | 0.888439i | \(-0.651790\pi\) | ||||
−0.458994 | + | 0.888439i | \(0.651790\pi\) | |||||||
\(884\) | −2.65200e6 | −0.114141 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.42186e6 | 0.403230 | ||||||||
\(887\) | 3.40623e7 | 1.45367 | 0.726835 | − | 0.686813i | \(-0.240991\pi\) | ||||
0.726835 | + | 0.686813i | \(0.240991\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.92069e7 | −0.815085 | ||||||||
\(890\) | −1.73191e6 | −0.0732910 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.84410e6 | 0.119683 | ||||||||
\(893\) | −5.09190e6 | −0.213674 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.07287e6 | 0.169958 | ||||||||
\(896\) | 2.34291e6 | 0.0974958 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.19765e7 | 1.32324 | ||||||||
\(899\) | −5.34287e6 | −0.220483 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.60702e7 | −2.30102 | ||||||||
\(902\) | −7.70800e6 | −0.315446 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.69114e6 | 0.150224 | ||||||||
\(905\) | 5.95237e6 | 0.241584 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.59880e7 | −0.645323 | −0.322662 | − | 0.946514i | \(-0.604578\pi\) | ||||
−0.322662 | + | 0.946514i | \(0.604578\pi\) | |||||||
\(908\) | −4.42211e6 | −0.177998 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 936936. | 0.0375065 | ||||||||
\(911\) | −2.70045e7 | −1.07805 | −0.539026 | − | 0.842289i | \(-0.681208\pi\) | ||||
−0.539026 | + | 0.842289i | \(0.681208\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.54152e7 | −0.612029 | ||||||||
\(914\) | 1.21537e7 | 0.481221 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.57780e7 | 0.621317 | ||||||||
\(917\) | −5.23316e7 | −2.05514 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.71840e6 | −0.262408 | −0.131204 | − | 0.991355i | \(-0.541884\pi\) | ||||
−0.131204 | + | 0.991355i | \(0.541884\pi\) | |||||||
\(920\) | −26880.0 | −0.00104703 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.39498e7 | −0.927842 | ||||||||
\(923\) | 794040. | 0.0306788 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.06036e7 | 1.56031 | ||||||||
\(926\) | −3.22154e7 | −1.23463 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.98278e6 | −0.189934 | ||||||||
\(929\) | 1.29929e7 | 0.493933 | 0.246967 | − | 0.969024i | \(-0.420566\pi\) | ||||
0.246967 | + | 0.969024i | \(0.420566\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.31476e6 | 0.0497133 | ||||||||
\(932\) | 1.86706e6 | 0.0704073 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.31733e7 | −1.24429 | ||||||||
\(935\) | −9.14812e6 | −0.342218 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.87830e6 | 0.107099 | 0.0535497 | − | 0.998565i | \(-0.482946\pi\) | ||||
0.0535497 | + | 0.998565i | \(0.482946\pi\) | |||||||
\(938\) | 2.05783e7 | 0.763663 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.73928e6 | 0.174941 | ||||||||
\(941\) | 1.11189e7 | 0.409345 | 0.204672 | − | 0.978831i | \(-0.434387\pi\) | ||||
0.204672 | + | 0.978831i | \(0.434387\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −188000. | −0.00688460 | ||||||||
\(944\) | 3.38330e6 | 0.123569 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.64599e7 | −0.597996 | ||||||||
\(947\) | 1.59967e7 | 0.579638 | 0.289819 | − | 0.957081i | \(-0.406405\pi\) | ||||
0.289819 | + | 0.957081i | \(0.406405\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.58250e6 | −0.0930840 | ||||||||
\(950\) | 3.87570e6 | 0.139329 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.94480e7 | 0.695477 | ||||||||
\(953\) | −3.80244e7 | −1.35622 | −0.678110 | − | 0.734960i | \(-0.737201\pi\) | ||||
−0.678110 | + | 0.734960i | \(0.737201\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.06040e6 | 0.0376235 | ||||||||
\(956\) | 2.01392e7 | 0.712685 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.83389e7 | −0.645593 | ||||||||
\(959\) | 6.40111e6 | 0.224755 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.74235e7 | −0.957889 | ||||||||
\(962\) | −4.71994e6 | −0.164437 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.29587e6 | −0.0795710 | ||||||||
\(965\) | −4.85293e6 | −0.167759 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.60950e6 | 0.0897409 | 0.0448705 | − | 0.998993i | \(-0.485712\pi\) | ||||
0.0448705 | + | 0.998993i | \(0.485712\pi\) | |||||||
\(968\) | 7.61766e6 | 0.261296 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.06692e6 | −0.241158 | ||||||||
\(971\) | −1.40618e7 | −0.478623 | −0.239312 | − | 0.970943i | \(-0.576922\pi\) | ||||
−0.239312 | + | 0.970943i | \(0.576922\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.03716e7 | 2.04433 | ||||||||
\(974\) | −221216. | −0.00747170 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −587008. | −0.0197251 | ||||||||
\(977\) | −4.66346e7 | −1.56305 | −0.781523 | − | 0.623876i | \(-0.785557\pi\) | ||||
−0.781523 | + | 0.623876i | \(0.785557\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.22669e6 | −0.140943 | ||||||||
\(980\) | −1.22371e6 | −0.0407018 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.75573e7 | −0.911922 | ||||||||
\(983\) | 2.96980e6 | 0.0980263 | 0.0490132 | − | 0.998798i | \(-0.484392\pi\) | ||||
0.0490132 | + | 0.998798i | \(0.484392\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.50212e6 | −0.312054 | ||||||||
\(986\) | −4.13610e7 | −1.35487 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −450528. | −0.0146835 | ||||||||
\(989\) | −401460. | −0.0130512 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.88690e7 | 1.25724 | 0.628621 | − | 0.777712i | \(-0.283620\pi\) | ||||
0.628621 | + | 0.777712i | \(0.283620\pi\) | |||||||
\(992\) | 1.12435e6 | 0.0362763 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.82296e6 | −0.186930 | ||||||||
\(995\) | 4.35118e6 | 0.139331 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.92115e7 | −1.56794 | −0.783969 | − | 0.620801i | \(-0.786808\pi\) | ||||
−0.783969 | + | 0.620801i | \(0.786808\pi\) | |||||||
\(998\) | −2.24670e7 | −0.714034 | ||||||||
\(999\) | 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 | 342.6.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 114.6.a.c.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 912.6.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.6.a.c.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
342.6.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
912.6.a.f.1.1 | 1 | 12.11 | even | 2 |