Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,6,Mod(1,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("160.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.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: | \(25.6614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.39180.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 36x - 24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.688934\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.755735 | −0.0484804 | −0.0242402 | − | 0.999706i | \(-0.507717\pi\) | ||||
−0.0242402 | + | 0.999706i | \(0.507717\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −172.424 | −1.33001 | −0.665003 | − | 0.746841i | \(-0.731570\pi\) | ||||
−0.665003 | + | 0.746841i | \(0.731570\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −242.429 | −0.997650 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 391.540 | 0.975651 | 0.487825 | − | 0.872941i | \(-0.337790\pi\) | ||||
0.487825 | + | 0.872941i | \(0.337790\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 149.245 | 0.244930 | 0.122465 | − | 0.992473i | \(-0.460920\pi\) | ||||
0.122465 | + | 0.992473i | \(0.460920\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 18.8934 | 0.0216811 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1187.74 | 0.996776 | 0.498388 | − | 0.866954i | \(-0.333925\pi\) | ||||
0.498388 | + | 0.866954i | \(0.333925\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 685.033 | 0.435339 | 0.217670 | − | 0.976023i | \(-0.430155\pi\) | ||||
0.217670 | + | 0.976023i | \(0.430155\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 130.307 | 0.0644792 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 996.236 | 0.392684 | 0.196342 | − | 0.980536i | \(-0.437094\pi\) | ||||
0.196342 | + | 0.980536i | \(0.437094\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 366.856 | 0.0968469 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8769.13 | −1.93625 | −0.968125 | − | 0.250466i | \(-0.919416\pi\) | ||||
−0.968125 | + | 0.250466i | \(0.919416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9525.61 | 1.78028 | 0.890140 | − | 0.455686i | \(-0.150606\pi\) | ||||
0.890140 | + | 0.455686i | \(0.150606\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −295.901 | −0.0473000 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4310.61 | 0.594796 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10226.8 | 1.22811 | 0.614054 | − | 0.789264i | \(-0.289538\pi\) | ||||
0.614054 | + | 0.789264i | \(0.289538\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −112.790 | −0.0118743 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 32.6496 | 0.00303332 | 0.00151666 | − | 0.999999i | \(-0.499517\pi\) | ||||
0.00151666 | + | 0.999999i | \(0.499517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10321.5 | 0.851279 | 0.425639 | − | 0.904893i | \(-0.360049\pi\) | ||||
0.425639 | + | 0.904893i | \(0.360049\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6060.72 | 0.446162 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 16931.7 | 1.11804 | 0.559018 | − | 0.829156i | \(-0.311178\pi\) | ||||
0.559018 | + | 0.829156i | \(0.311178\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12923.1 | 0.768914 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −897.614 | −0.0483242 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −22287.0 | −1.08984 | −0.544919 | − | 0.838489i | \(-0.683439\pi\) | ||||
−0.544919 | + | 0.838489i | \(0.683439\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9788.50 | −0.436324 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −517.704 | −0.0211054 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 44251.2 | 1.65499 | 0.827494 | − | 0.561474i | \(-0.189766\pi\) | ||||
0.827494 | + | 0.561474i | \(0.189766\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −21743.1 | −0.748165 | −0.374083 | − | 0.927395i | \(-0.622042\pi\) | ||||
−0.374083 | + | 0.927395i | \(0.622042\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 41800.6 | 1.32688 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3731.13 | −0.109536 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20709.0 | 0.563600 | 0.281800 | − | 0.959473i | \(-0.409068\pi\) | ||||
0.281800 | + | 0.959473i | \(0.409068\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −752.891 | −0.0190375 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15379.5 | 0.362073 | 0.181037 | − | 0.983476i | \(-0.442055\pi\) | ||||
0.181037 | + | 0.983476i | \(0.442055\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 57995.4 | 1.27376 | 0.636878 | − | 0.770964i | \(-0.280225\pi\) | ||||
0.636878 | + | 0.770964i | \(0.280225\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −472.335 | −0.00969609 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −67511.0 | −1.29762 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −62466.5 | −1.12611 | −0.563054 | − | 0.826420i | \(-0.690374\pi\) | ||||
−0.563054 | + | 0.826420i | \(0.690374\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 58633.0 | 0.992954 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −43578.7 | −0.694351 | −0.347175 | − | 0.937800i | \(-0.612859\pi\) | ||||
−0.347175 | + | 0.937800i | \(0.612859\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −29693.4 | −0.445772 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6627.14 | 0.0938703 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 66297.9 | 0.887207 | 0.443603 | − | 0.896223i | \(-0.353700\pi\) | ||||
0.443603 | + | 0.896223i | \(0.353700\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25733.5 | −0.325758 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7198.84 | −0.0863088 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −17125.8 | −0.194690 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12264.3 | −0.132346 | −0.0661732 | − | 0.997808i | \(-0.521079\pi\) | ||||
−0.0661732 | + | 0.997808i | \(0.521079\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −94920.6 | −0.973358 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −37376.8 | −0.364584 | −0.182292 | − | 0.983244i | \(-0.558352\pi\) | ||||
−0.182292 | + | 0.983244i | \(0.558352\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 41642.9 | 0.386765 | 0.193383 | − | 0.981123i | \(-0.438054\pi\) | ||||
0.193383 | + | 0.981123i | \(0.438054\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3257.68 | −0.0288360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −69664.7 | −0.588239 | −0.294119 | − | 0.955769i | \(-0.595026\pi\) | ||||
−0.294119 | + | 0.955769i | \(0.595026\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −88554.2 | −0.713909 | −0.356954 | − | 0.934122i | \(-0.616185\pi\) | ||||
−0.356954 | + | 0.934122i | \(0.616185\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7728.78 | −0.0595392 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 77809.3 | 0.573239 | 0.286619 | − | 0.958045i | \(-0.407469\pi\) | ||||
0.286619 | + | 0.958045i | \(0.407469\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24905.9 | −0.175613 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −36181.4 | −0.244355 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −204795. | −1.32572 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7747.38 | −0.0481051 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −24.6744 | −0.000147057 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −294580. | −1.62067 | −0.810333 | − | 0.585970i | \(-0.800714\pi\) | ||||
−0.810333 | + | 0.585970i | \(0.800714\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7800.32 | −0.0412704 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 173565. | 0.883658 | 0.441829 | − | 0.897099i | \(-0.354330\pi\) | ||||
0.441829 | + | 0.897099i | \(0.354330\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −118116. | −0.579003 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9171.39 | −0.0433113 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 346072. | 1.57531 | 0.787653 | − | 0.616119i | \(-0.211296\pi\) | ||||
0.787653 | + | 0.616119i | \(0.211296\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −329344. | −1.44581 | −0.722907 | − | 0.690945i | \(-0.757195\pi\) | ||||
−0.722907 | + | 0.690945i | \(0.757195\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12795.9 | −0.0542029 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 58435.5 | 0.238966 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 219228. | 0.865918 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9766.47 | −0.0372773 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 83495.2 | 0.308103 | 0.154052 | − | 0.988063i | \(-0.450768\pi\) | ||||
0.154052 | + | 0.988063i | \(0.450768\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −155105. | −0.553585 | −0.276792 | − | 0.960930i | \(-0.589271\pi\) | ||||
−0.276792 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −287941. | −0.994433 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −238140. | −0.796166 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −60634.6 | −0.196323 | −0.0981615 | − | 0.995170i | \(-0.531296\pi\) | ||||
−0.0981615 | + | 0.995170i | \(0.531296\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16843.1 | 0.0528358 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −171775. | −0.522271 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 528292. | 1.55742 | 0.778708 | − | 0.627387i | \(-0.215875\pi\) | ||||
0.778708 | + | 0.627387i | \(0.215875\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7397.52 | 0.0211532 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 681927. | 1.89211 | 0.946056 | − | 0.324002i | \(-0.105029\pi\) | ||||
0.946056 | + | 0.324002i | \(0.105029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −349019. | −0.940009 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −166072. | −0.434316 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −148111. | −0.376245 | −0.188122 | − | 0.982146i | \(-0.560240\pi\) | ||||
−0.188122 | + | 0.982146i | \(0.560240\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −107765. | −0.266001 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −33442.2 | −0.0802346 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −650289. | −1.51696 | −0.758480 | − | 0.651697i | \(-0.774058\pi\) | ||||
−0.758480 | + | 0.651697i | \(0.774058\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 315052. | 0.714803 | 0.357401 | − | 0.933951i | \(-0.383663\pi\) | ||||
0.357401 | + | 0.933951i | \(0.383663\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16432.1 | 0.0362714 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −255671. | −0.549227 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 465046. | 0.972506 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −63254.8 | −0.128807 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 851610. | 1.68911 | 0.844554 | − | 0.535471i | \(-0.179866\pi\) | ||||
0.844554 | + | 0.535471i | \(0.179866\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 916910. | 1.77188 | 0.885938 | − | 0.463804i | \(-0.153516\pi\) | ||||
0.885938 | + | 0.463804i | \(0.153516\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2819.75 | 0.00531036 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 595345. | 1.09296 | 0.546479 | − | 0.837473i | \(-0.315968\pi\) | ||||
0.546479 | + | 0.837473i | \(0.315968\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −159504. | −0.285522 | −0.142761 | − | 0.989757i | \(-0.545598\pi\) | ||||
−0.142761 | + | 0.989757i | \(0.545598\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15650.5 | −0.0273236 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.51201e6 | 2.57522 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −816.239 | −0.00135654 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −241516. | −0.391761 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 268218. | 0.424739 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 776648. | 1.20093 | 0.600466 | − | 0.799650i | \(-0.294982\pi\) | ||||
0.600466 | + | 0.799650i | \(0.294982\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11622.8 | −0.0175535 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −258038. | −0.380703 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.64245e6 | −2.36778 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −43829.2 | −0.0617523 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 177264. | 0.244141 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 969846. | 1.30599 | 0.652996 | − | 0.757361i | \(-0.273512\pi\) | ||||
0.652996 | + | 0.757361i | \(0.273512\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −151518. | −0.199530 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 32926.6 | 0.0424113 | 0.0212057 | − | 0.999775i | \(-0.493250\pi\) | ||||
0.0212057 | + | 0.999775i | \(0.493250\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 730255. | 0.920208 | 0.460104 | − | 0.887865i | \(-0.347812\pi\) | ||||
0.460104 | + | 0.887865i | \(0.347812\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 51020.5 | 0.0629092 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −550888. | −0.664774 | −0.332387 | − | 0.943143i | \(-0.607854\pi\) | ||||
−0.332387 | + | 0.943143i | \(0.607854\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −423292. | −0.500001 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 47208.2 | 0.0545942 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −996266. | −1.12819 | −0.564093 | − | 0.825711i | \(-0.690774\pi\) | ||||
−0.564093 | + | 0.825711i | \(0.690774\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −953235. | −1.05720 | −0.528600 | − | 0.848871i | \(-0.677283\pi\) | ||||
−0.528600 | + | 0.848871i | \(0.677283\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −133457. | −0.144986 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −323078. | −0.343869 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 102238. | 0.106628 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 32933.9 | 0.0336624 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 780609. | 0.782077 | 0.391038 | − | 0.920374i | \(-0.372116\pi\) | ||||
0.391038 | + | 0.920374i | \(0.372116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 390066. | 0.383122 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 22440.4 | 0.0216112 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −340539. | −0.321614 | −0.160807 | − | 0.986986i | \(-0.551410\pi\) | ||||
−0.160807 | + | 0.986986i | \(0.551410\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.76335e6 | −1.63339 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.12589e6 | 1.93170 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.05298e6 | 1.83018 | 0.915092 | − | 0.403246i | \(-0.132118\pi\) | ||||
0.915092 | + | 0.403246i | \(0.132118\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 557175. | 0.487390 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −50103.7 | −0.0430122 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 98629.8 | 0.0831050 | 0.0415525 | − | 0.999136i | \(-0.486770\pi\) | ||||
0.0415525 | + | 0.999136i | \(0.486770\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.17220e6 | 0.969565 | 0.484783 | − | 0.874635i | \(-0.338899\pi\) | ||||
0.484783 | + | 0.874635i | \(0.338899\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19447.7 | 0.0157929 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 244713. | 0.195130 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.13901e6 | 0.891923 | 0.445962 | − | 0.895052i | \(-0.352862\pi\) | ||||
0.445962 | + | 0.895052i | \(0.352862\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.30928e6 | −1.77610 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.33128e6 | −1.00578 | −0.502889 | − | 0.864351i | \(-0.667730\pi\) | ||||
−0.502889 | + | 0.864351i | \(0.667730\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −921840. | −0.684210 | −0.342105 | − | 0.939662i | \(-0.611140\pi\) | ||||
−0.342105 | + | 0.939662i | \(0.611140\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12942.6 | 0.00943864 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5629.58 | −0.00403433 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9140.20 | −0.00643741 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9268.54 | 0.00641621 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.64240e6 | −1.11766 | −0.558831 | − | 0.829281i | \(-0.688750\pi\) | ||||
−0.558831 | + | 0.829281i | \(0.688750\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.10628e6 | −0.740134 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 143639. | 0.0944888 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 148684. | 0.0961801 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.77968e6 | −1.13221 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 28246.9 | 0.0176752 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 543578. | 0.334590 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −810866. | −0.491025 | −0.245512 | − | 0.969393i | \(-0.578956\pi\) | ||||
−0.245512 | + | 0.969393i | \(0.578956\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −31471.0 | −0.0187506 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.67678e6 | −0.983050 | −0.491525 | − | 0.870864i | \(-0.663560\pi\) | ||||
−0.491525 | + | 0.870864i | \(0.663560\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.43902e6 | 0.830242 | 0.415121 | − | 0.909766i | \(-0.363739\pi\) | ||||
0.415121 | + | 0.909766i | \(0.363739\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.04502e6 | −0.593398 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 783839. | 0.438105 | 0.219053 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219053 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.43347e6 | −1.88910 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 52648.1 | 0.0285181 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 813639. | 0.433936 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 93278.3 | 0.0489860 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 66923.5 | 0.0346106 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.91943e6 | −1.48699 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.30343e6 | −1.65728 | −0.828638 | − | 0.559785i | \(-0.810884\pi\) | ||||
−0.828638 | + | 0.559785i | \(0.810884\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.47928e6 | −1.22522 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −517724. | −0.252050 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.17037e6 | 1.04102 | 0.520510 | − | 0.853856i | \(-0.325742\pi\) | ||||
0.520510 | + | 0.853856i | \(0.325742\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −58803.2 | −0.0277909 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.72966e6 | 1.73693 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 669673. | 0.307346 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18822.3 | 0.00851382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.26327e6 | 0.563215 | 0.281607 | − | 0.959530i | \(-0.409132\pi\) | ||||
0.281607 | + | 0.959530i | \(0.409132\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.84682e6 | −0.811636 | −0.405818 | − | 0.913954i | \(-0.633013\pi\) | ||||
−0.405818 | + | 0.913954i | \(0.633013\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 54751.5 | 0.0237207 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.82123e6 | 1.63217 | 0.816087 | − | 0.577929i | \(-0.196139\pi\) | ||||
0.816087 | + | 0.577929i | \(0.196139\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −384488. | −0.161924 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 154770. | 0.0642714 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.71131e6 | 0.700798 | 0.350399 | − | 0.936600i | \(-0.386046\pi\) | ||||
0.350399 | + | 0.936600i | \(0.386046\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.00683e6 | −0.810480 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5854.97 | 0.00233216 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.44989e6 | −0.569641 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.72599e6 | −0.668919 | −0.334460 | − | 0.942410i | \(-0.608554\pi\) | ||||
−0.334460 | + | 0.942410i | \(0.608554\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7915.20 | −0.00302619 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.84282e6 | 1.44949 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 732009. | 0.272423 | 0.136212 | − | 0.990680i | \(-0.456507\pi\) | ||||
0.136212 | + | 0.990680i | \(0.456507\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11808.4 | 0.00433622 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.30875e6 | −0.474246 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.07751e6 | −1.10053 | −0.550264 | − | 0.834991i | \(-0.685473\pi\) | ||||
−0.550264 | + | 0.834991i | \(0.685473\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 222624. | 0.0785706 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.26468e6 | 0.440540 | 0.220270 | − | 0.975439i | \(-0.429306\pi\) | ||||
0.220270 | + | 0.975439i | \(0.429306\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.68778e6 | 0.580314 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.50223e6 | −0.849278 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.65533e6 | 1.22476 | 0.612382 | − | 0.790562i | \(-0.290212\pi\) | ||||
0.612382 | + | 0.790562i | \(0.290212\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.18327e6 | 0.391418 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −131169. | −0.0428401 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.56166e6 | 0.503610 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.99465e6 | −1.59048 | −0.795241 | − | 0.606294i | \(-0.792655\pi\) | ||||
−0.795241 | + | 0.606294i | \(0.792655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 89264.7 | 0.0280703 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 298037. | 0.0925570 | 0.0462785 | − | 0.998929i | \(-0.485264\pi\) | ||||
0.0462785 | + | 0.998929i | \(0.485264\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.42165e6 | 0.436045 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.46582e6 | −0.444063 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.00421e6 | 1.19821 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.26110e6 | 0.963954 | 0.481977 | − | 0.876184i | \(-0.339919\pi\) | ||||
0.481977 | + | 0.876184i | \(0.339919\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −261539. | −0.0763715 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.62998e6 | −2.20114 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.08947e6 | 0.310523 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 248897. | 0.0700937 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.24623e6 | 0.346786 | 0.173393 | − | 0.984853i | \(-0.444527\pi\) | ||||
0.173393 | + | 0.984853i | \(0.444527\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.88625e6 | −0.518674 | −0.259337 | − | 0.965787i | \(-0.583504\pi\) | ||||
−0.259337 | + | 0.965787i | \(0.583504\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.10473e6 | −1.11541 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 742335. | 0.199355 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.74905e6 | 0.995064 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −44161.8 | −0.0115852 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.30534e6 | 0.857082 | 0.428541 | − | 0.903522i | \(-0.359028\pi\) | ||||
0.428541 | + | 0.903522i | \(0.359028\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.61270e6 | 1.95128 | 0.975639 | − | 0.219384i | \(-0.0704048\pi\) | ||||
0.975639 | + | 0.219384i | \(0.0704048\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −165679. | −0.0419801 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 682455. | 0.170951 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.45916e6 | 1.35196 | 0.675982 | − | 0.736918i | \(-0.263720\pi\) | ||||
0.675982 | + | 0.736918i | \(0.263720\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.13294e6 | −0.767107 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.09261e6 | 1.23291 | 0.616454 | − | 0.787391i | \(-0.288569\pi\) | ||||
0.616454 | + | 0.787391i | \(0.288569\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.65745e6 | −0.396771 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −63100.3 | −0.0149370 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.83842e6 | 1.36672 | 0.683360 | − | 0.730082i | \(-0.260518\pi\) | ||||
0.683360 | + | 0.730082i | \(0.260518\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12783.6 | 0.00295946 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 117219. | 0.0268380 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 643338. | 0.145684 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.06917e6 | −1.13539 | −0.567697 | − | 0.823238i | \(-0.692165\pi\) | ||||
−0.567697 | + | 0.823238i | \(0.692165\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 435728. | 0.0965347 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.10777e6 | 1.33854 | 0.669269 | − | 0.743021i | \(-0.266608\pi\) | ||||
0.669269 | + | 0.743021i | \(0.266608\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.29238e6 | −0.930563 | −0.465282 | − | 0.885163i | \(-0.654047\pi\) | ||||
−0.465282 | + | 0.885163i | \(0.654047\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 179971. | 0.0385985 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.64461e6 | −0.348957 | −0.174478 | − | 0.984661i | \(-0.555824\pi\) | ||||
−0.174478 | + | 0.984661i | \(0.555824\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.57073e6 | −0.749591 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 45823.7 | 0.00951783 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.04128e6 | 0.830551 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 428146. | 0.0870678 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.40301e6 | 1.08728 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.11578e6 | 1.61619 | 0.808093 | − | 0.589055i | \(-0.200500\pi\) | ||||
0.808093 | + | 0.589055i | \(0.200500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.52631e6 | 0.300801 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 129817. | 0.0253199 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 306607. | 0.0591871 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.11681e6 | −1.16870 | −0.584350 | − | 0.811502i | \(-0.698650\pi\) | ||||
−0.584350 | + | 0.811502i | \(0.698650\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −399249. | −0.0755042 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.78707e6 | 1.27051 | 0.635256 | − | 0.772301i | \(-0.280895\pi\) | ||||
0.635256 | + | 0.772301i | \(0.280895\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.04154e7 | −1.93001 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.37302e6 | 0.435299 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.65180e6 | −0.481560 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.07689e6 | 1.09252 | 0.546260 | − | 0.837615i | \(-0.316051\pi\) | ||||
0.546260 | + | 0.837615i | \(0.316051\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −515357. | −0.0917305 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.89757e6 | 0.334410 | 0.167205 | − | 0.985922i | \(-0.446526\pi\) | ||||
0.167205 | + | 0.985922i | \(0.446526\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 934419. | 0.163047 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 263766. | 0.0455721 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.07101e6 | −1.20973 | −0.604863 | − | 0.796330i | \(-0.706772\pi\) | ||||
−0.604863 | + | 0.796330i | \(0.706772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.99982e6 | −1.69410 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 251308. | 0.0421613 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.04107e6 | −0.172967 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.62944e6 | 1.09081 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 111932. | 0.0182405 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.99273e6 | −1.29003 | −0.645017 | − | 0.764169i | \(-0.723150\pi\) | ||||
−0.645017 | + | 0.764169i | \(0.723150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.04897e7 | −1.67691 | −0.838453 | − | 0.544974i | \(-0.816540\pi\) | ||||
−0.838453 | + | 0.544974i | \(0.816540\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 81442.0 | 0.0128958 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.13139e7 | 1.77454 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.44386e6 | −0.845800 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.07278e7 | −1.65110 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4872.79 | 0.000742951 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.74162e6 | 0.263068 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 491447. | 0.0735429 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.05992e6 | 0.750191 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.56741e6 | 0.964719 | 0.482359 | − | 0.875973i | \(-0.339780\pi\) | ||||
0.482359 | + | 0.875973i | \(0.339780\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −238096. | −0.0346540 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.21385e6 | 0.319270 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.90324e6 | 0.843573 | 0.421786 | − | 0.906695i | \(-0.361403\pi\) | ||||
0.421786 | + | 0.906695i | \(0.361403\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.27116e6 | 0.746407 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.00715e6 | −0.842926 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.07707e7 | 1.49773 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 193219. | 0.0266268 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.34903e6 | 0.457384 | 0.228692 | − | 0.973499i | \(-0.426555\pi\) | ||||
0.228692 | + | 0.973499i | \(0.426555\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.54044e6 | 0.208504 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −351452. | −0.0471475 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.34193e7 | −1.78426 | −0.892132 | − | 0.451774i | \(-0.850791\pi\) | ||||
−0.892132 | + | 0.451774i | \(0.850791\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.94523e6 | −0.256360 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.01097e7 | −1.32063 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.38493e7 | −1.79327 | −0.896635 | − | 0.442770i | \(-0.853996\pi\) | ||||
−0.896635 | + | 0.442770i | \(0.853996\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.24337e6 | −1.05807 | −0.529035 | − | 0.848600i | \(-0.677446\pi\) | ||||
−0.529035 | + | 0.848600i | \(0.677446\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −643592. | −0.0818887 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 622648. | 0.0785367 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.90608e6 | 1.23869 | 0.619345 | − | 0.785119i | \(-0.287398\pi\) | ||||
0.619345 | + | 0.785119i | \(0.287398\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −692941. | −0.0859013 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.51402e6 | 0.923490 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.72625e6 | −1.06330 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 904534. | 0.109279 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.29572e7 | −1.55209 | −0.776044 | − | 0.630679i | \(-0.782776\pi\) | ||||
−0.776044 | + | 0.630679i | \(0.782776\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.52536e6 | 0.775026 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −449923. | −0.0529871 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.95284e6 | −0.695164 | −0.347582 | − | 0.937650i | \(-0.612997\pi\) | ||||
−0.347582 | + | 0.937650i | \(0.612997\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.11986e6 | 0.592879 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 120543. | 0.0138423 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.48855e6 | 0.283387 | 0.141694 | − | 0.989911i | \(-0.454745\pi\) | ||||
0.141694 | + | 0.989911i | \(0.454745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.34152e7 | −1.51499 | −0.757497 | − | 0.652838i | \(-0.773578\pi\) | ||||
−0.757497 | + | 0.652838i | \(0.773578\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.02045e6 | −0.562276 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 193685. | 0.0215133 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.49423e6 | −0.935734 | −0.467867 | − | 0.883799i | \(-0.654977\pi\) | ||||
−0.467867 | + | 0.883799i | \(0.654977\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.14268e6 | −0.124848 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.52698e6 | 0.273841 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.36612e7 | −1.46837 | −0.734187 | − | 0.678948i | \(-0.762436\pi\) | ||||
−0.734187 | + | 0.678948i | \(0.762436\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 616.861 | 6.57657e−5 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.43013e7 | −1.51238 | −0.756191 | − | 0.654351i | \(-0.772942\pi\) | ||||
−0.756191 | + | 0.654351i | \(0.772942\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.03774e7 | 1.08858 | 0.544292 | − | 0.838896i | \(-0.316798\pi\) | ||||
0.544292 | + | 0.838896i | \(0.316798\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 365475. | 0.0380302 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.14314e7 | −1.17999 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −202702. | −0.0205915 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.21468e7 | 1.22415 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.91347e6 | 0.791214 | 0.395607 | − | 0.918420i | \(-0.370534\pi\) | ||||
0.395607 | + | 0.918420i | \(0.370534\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −586941. | −0.0582217 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.36449e6 | 0.724784 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.92872e6 | 0.188330 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.72844e6 | −0.361222 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.70174e6 | −0.548103 | −0.274052 | − | 0.961715i | \(-0.588364\pi\) | ||||
−0.274052 | + | 0.961715i | \(0.588364\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.06376e6 | −0.292232 | −0.146116 | − | 0.989267i | \(-0.546677\pi\) | ||||
−0.146116 | + | 0.989267i | \(0.546677\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 195008. | 0.0184567 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.36482e6 | 0.128178 | 0.0640890 | − | 0.997944i | \(-0.479586\pi\) | ||||
0.0640890 | + | 0.997944i | \(0.479586\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.73261e7 | 1.61469 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.24125e6 | 0.114791 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.58212e6 | 0.787610 | 0.393805 | − | 0.919194i | \(-0.371158\pi\) | ||||
0.393805 | + | 0.919194i | \(0.371158\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.33913e6 | −0.395184 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.40598e7 | −1.27076 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.84222e7 | 1.65245 | 0.826224 | − | 0.563342i | \(-0.190485\pi\) | ||||
0.826224 | + | 0.563342i | \(0.190485\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.69479e7 | 1.50873 | 0.754367 | − | 0.656453i | \(-0.227944\pi\) | ||||
0.754367 | + | 0.656453i | \(0.227944\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −133965. | −0.0118360 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.95291e6 | 0.258938 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.73613e6 | −0.760334 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −732947. | −0.0633151 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.51331e6 | −0.729948 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.18245e6 | 0.100634 | 0.0503172 | − | 0.998733i | \(-0.483977\pi\) | ||||
0.0503172 | + | 0.998733i | \(0.483977\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 229285. | 0.0193694 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.34424e6 | −0.364285 | −0.182143 | − | 0.983272i | \(-0.558303\pi\) | ||||
−0.182143 | + | 0.983272i | \(0.558303\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.11466e6 | 0.176021 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24883.8 | −0.00205612 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.03260e7 | −0.846991 | −0.423495 | − | 0.905898i | \(-0.639197\pi\) | ||||
−0.423495 | + | 0.905898i | \(0.639197\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.65180e6 | −0.704498 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −551880. | −0.0446121 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.32623e6 | −0.266934 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.07013e7 | −1.64931 | −0.824656 | − | 0.565635i | \(-0.808631\pi\) | ||||
−0.824656 | + | 0.565635i | \(0.808631\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.63666e7 | 1.29457 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.23360e6 | 0.646588 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38779.1 | 0.00302354 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 416326. | 0.0322285 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.75116e6 | −0.211457 | −0.105728 | − | 0.994395i | \(-0.533717\pi\) | ||||
−0.105728 | + | 0.994395i | \(0.533717\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.00572e6 | 0.534643 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 319897. | 0.0242403 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.44466e6 | 0.484899 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.07210e6 | −0.304230 | −0.152115 | − | 0.988363i | \(-0.548608\pi\) | ||||
−0.152115 | + | 0.988363i | \(0.548608\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.51437e7 | 1.12346 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.48976e6 | 0.699087 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.46089e6 | −0.106869 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 752914. | 0.0546950 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.75553e7 | 1.26645 | 0.633223 | − | 0.773970i | \(-0.281732\pi\) | ||||
0.633223 | + | 0.773970i | \(0.281732\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.18024e6 | −0.514400 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 720394. | 0.0512536 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.48071e6 | −0.387250 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.46241e7 | 1.02620 | 0.513101 | − | 0.858328i | \(-0.328496\pi\) | ||||
0.513101 | + | 0.858328i | \(0.328496\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.41470e7 | −0.985925 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.22592e7 | 0.848534 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.54961e7 | −1.06528 | −0.532639 | − | 0.846342i | \(-0.678800\pi\) | ||||
−0.532639 | + | 0.846342i | \(0.678800\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 244162. | 0.0166709 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.10839e6 | 0.549877 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.39408e6 | 0.228619 | 0.114309 | − | 0.993445i | \(-0.463535\pi\) | ||||
0.114309 | + | 0.993445i | \(0.463535\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −77264.9 | −0.00516936 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.94591e6 | −0.262225 | −0.131113 | − | 0.991367i | \(-0.541855\pi\) | ||||
−0.131113 | + | 0.991367i | \(0.541855\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.08738e6 | −0.137788 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.05647e7 | 0.692719 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.20119e7 | 0.782360 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −824656. | −0.0533547 | −0.0266774 | − | 0.999644i | \(-0.508493\pi\) | ||||
−0.0266774 | + | 0.999644i | \(0.508493\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −589934. | −0.0379154 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.87763e6 | 0.247571 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.53800e7 | −0.975474 | −0.487737 | − | 0.872991i | \(-0.662177\pi\) | ||||
−0.487737 | + | 0.872991i | \(0.662177\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −294787. | −0.0185739 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.06295e6 | 0.504699 | 0.252349 | − | 0.967636i | \(-0.418797\pi\) | ||||
0.252349 | + | 0.967636i | \(0.418797\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.52689e7 | 0.949502 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.19854e6 | 0.444724 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.60429e6 | 0.405357 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.12351e7 | −0.685110 | −0.342555 | − | 0.939498i | \(-0.611292\pi\) | ||||
−0.342555 | + | 0.939498i | \(0.611292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 257358. | 0.0155920 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 554517. | 0.0333784 | 0.0166892 | − | 0.999861i | \(-0.494687\pi\) | ||||
0.0166892 | + | 0.999861i | \(0.494687\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.95351e6 | 0.356056 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.33263e6 | 0.0791875 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22366.0 | 0.00132052 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.02169e6 | 0.353257 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.21701e6 | −0.187520 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.51586e6 | 0.0877983 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.56812e7 | 0.902492 | 0.451246 | − | 0.892400i | \(-0.350980\pi\) | ||||
0.451246 | + | 0.892400i | \(0.350980\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.55151e6 | −0.0887281 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.34162e7 | −0.762410 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.24506e6 | −0.183248 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −421077. | −0.0236289 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.44267e7 | 1.91977 | 0.959885 | − | 0.280393i | \(-0.0904647\pi\) | ||||
0.959885 | + | 0.280393i | \(0.0904647\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.01104e7 | 1.11443 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.60725e7 | −0.885122 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.27075e7 | 1.24274 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.29438e6 | 0.233567 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −74538.0 | −0.00402897 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.20856e7 | 0.649230 | 0.324615 | − | 0.945846i | \(-0.394765\pi\) | ||||
0.324615 | + | 0.945846i | \(0.394765\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.20419e6 | 0.331232 | 0.165616 | − | 0.986190i | \(-0.447039\pi\) | ||||
0.165616 | + | 0.986190i | \(0.447039\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −885870. | −0.0470050 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.32073e7 | −0.696498 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.07057e6 | 0.370595 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.23855e6 | 0.324993 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.59426e7 | −1.34325 | −0.671624 | − | 0.740892i | \(-0.734403\pi\) | ||||
−0.671624 | + | 0.740892i | \(0.734403\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.30743e6 | −0.376067 | −0.188034 | − | 0.982163i | \(-0.560211\pi\) | ||||
−0.188034 | + | 0.982163i | \(0.560211\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −184938. | −0.00946000 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.22800e7 | −0.624357 | −0.312179 | − | 0.950023i | \(-0.601059\pi\) | ||||
−0.312179 | + | 0.950023i | \(0.601059\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.21244e7 | −1.62349 | −0.811743 | − | 0.584014i | \(-0.801481\pi\) | ||||
−0.811743 | + | 0.584014i | \(0.801481\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −860789. | −0.0432408 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.53493e7 | 0.766435 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.70482e7 | −0.846178 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.49452e6 | 0.172415 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.36956e6 | −0.312395 | −0.156198 | − | 0.987726i | \(-0.549924\pi\) | ||||
−0.156198 | + | 0.987726i | \(0.549924\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.63865e7 | 2.74907 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.00609e6 | 0.0487606 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.72547e6 | 0.420385 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.33584e6 | 0.0639801 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 696667. | 0.0331708 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.01883e7 | 0.482258 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.05840e7 | −1.90978 | −0.954889 | − | 0.296964i | \(-0.904026\pi\) | ||||
−0.954889 | + | 0.296964i | \(0.904026\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.15180e6 | 0.194232 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.30412e6 | 0.153675 | 0.0768376 | − | 0.997044i | \(-0.475518\pi\) | ||||
0.0768376 | + | 0.997044i | \(0.475518\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.45392e7 | −0.672292 | −0.336146 | − | 0.941810i | \(-0.609124\pi\) | ||||
−0.336146 | + | 0.941810i | \(0.609124\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4254.47 | 0.000195586 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.28020e7 | 1.04219 | 0.521094 | − | 0.853499i | \(-0.325524\pi\) | ||||
0.521094 | + | 0.853499i | \(0.325524\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.70276e6 | 0.168262 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6907.58 | 0.000312089 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.44582e7 | −1.09869 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.09072e6 | 0.138043 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.97321e6 | 0.132035 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.69413e6 | 0.118959 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.93150e6 | −0.348222 | −0.174111 | − | 0.984726i | \(-0.555705\pi\) | ||||
−0.174111 | + | 0.984726i | \(0.555705\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.24122e6 | 0.0541848 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.31349e7 | −1.43829 | −0.719144 | − | 0.694861i | \(-0.755466\pi\) | ||||
−0.719144 | + | 0.694861i | \(0.755466\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.25079e7 | −0.971479 | −0.485740 | − | 0.874104i | \(-0.661450\pi\) | ||||
−0.485740 | + | 0.874104i | \(0.661450\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 836055. | 0.0358820 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.66717e7 | −1.56503 | −0.782515 | − | 0.622632i | \(-0.786063\pi\) | ||||
−0.782515 | + | 0.622632i | \(0.786063\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.07927e7 | 2.15549 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.29572e7 | 0.968777 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.15988e7 | 0.486725 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.62572e7 | 0.678405 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −112365. | −0.00466285 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.35313e7 | −3.44707 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.64711e7 | −1.08632 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.34497e6 | 0.0548898 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.87631e6 | −0.319670 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.40388e6 | −0.0970274 | −0.0485137 | − | 0.998823i | \(-0.515448\pi\) | ||||
−0.0485137 | + | 0.998823i | \(0.515448\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.06120e6 | 0.363728 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 467873. | 0.0186781 | 0.00933904 | − | 0.999956i | \(-0.497027\pi\) | ||||
0.00933904 | + | 0.999956i | \(0.497027\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.70628e7 | −0.677444 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −410801. | −0.0162211 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.99268e7 | −1.17527 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.59601e7 | −1.01395 | −0.506976 | − | 0.861960i | \(-0.669237\pi\) | ||||
−0.506976 | + | 0.861960i | \(0.669237\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 612800. | 0.0238051 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.29532e6 | 0.0886827 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.39177e6 | 0.245622 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.00954e7 | −0.385856 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.52441e6 | −0.171998 | −0.0859989 | − | 0.996295i | \(-0.527408\pi\) | ||||
−0.0859989 | + | 0.996295i | \(0.527408\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.85278e6 | 0.334738 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.26720e6 | 0.0476587 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.16262e7 | −0.434918 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.69269e7 | 1.00193 | 0.500964 | − | 0.865468i | \(-0.332979\pi\) | ||||
0.500964 | + | 0.865468i | \(0.332979\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.08751e6 | −0.0402505 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.38789e6 | −0.0510953 | −0.0255477 | − | 0.999674i | \(-0.508133\pi\) | ||||
−0.0255477 | + | 0.999674i | \(0.508133\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32526.7 | 0.00119113 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.58137e6 | 0.0576042 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.10208e7 | −0.399335 | −0.199667 | − | 0.979864i | \(-0.563986\pi\) | ||||
−0.199667 | + | 0.979864i | \(0.563986\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.65555e6 | 0.311982 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −592375. | −0.0212396 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.09536e7 | −0.390683 | −0.195342 | − | 0.980735i | \(-0.562582\pi\) | ||||
−0.195342 | + | 0.980735i | \(0.562582\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.12902e7 | −0.755392 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.59479e6 | 0.0915847 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.96712e7 | −2.09517 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.21081e7 | 2.16940 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.68887e7 | 0.586856 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.29227e7 | −0.792407 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.52685e7 | 1.21289 | 0.606443 | − | 0.795127i | \(-0.292596\pi\) | ||||
0.606443 | + | 0.795127i | \(0.292596\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −614895. | −0.0210374 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.58480e7 | −1.22016 | −0.610079 | − | 0.792340i | \(-0.708862\pi\) | ||||
−0.610079 | + | 0.792340i | \(0.708862\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.67869e7 | 1.92294 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −70493.7 | −0.00237487 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.95941e6 | −0.300292 | −0.150146 | − | 0.988664i | \(-0.547974\pi\) | ||||
−0.150146 | + | 0.988664i | \(0.547974\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.59583e7 | 0.865604 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.14681e7 | 0.712231 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.94666e6 | 0.229294 | 0.114647 | − | 0.993406i | \(-0.463426\pi\) | ||||
0.114647 | + | 0.993406i | \(0.463426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.48836e7 | −0.488785 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.20632e6 | 0.0720901 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.02827e7 | 0.334283 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.72743e6 | −0.249949 | −0.124974 | − | 0.992160i | \(-0.539885\pi\) | ||||
−0.124974 | + | 0.992160i | \(0.539885\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.49652e6 | 0.0803455 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.98761e6 | 0.127690 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.32625e7 | −1.37840 | −0.689198 | − | 0.724573i | \(-0.742037\pi\) | ||||
−0.689198 | + | 0.724573i | \(0.742037\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.75177e6 | 0.118939 |
(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 | 160.6.a.g.1.2 | yes | 3 | |
4.3 | odd | 2 | 160.6.a.f.1.2 | ✓ | 3 | ||
5.2 | odd | 4 | 800.6.c.j.449.4 | 6 | |||
5.3 | odd | 4 | 800.6.c.j.449.3 | 6 | |||
5.4 | even | 2 | 800.6.a.n.1.2 | 3 | |||
8.3 | odd | 2 | 320.6.a.y.1.2 | 3 | |||
8.5 | even | 2 | 320.6.a.x.1.2 | 3 | |||
20.3 | even | 4 | 800.6.c.k.449.4 | 6 | |||
20.7 | even | 4 | 800.6.c.k.449.3 | 6 | |||
20.19 | odd | 2 | 800.6.a.o.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.a.f.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
160.6.a.g.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
320.6.a.x.1.2 | 3 | 8.5 | even | 2 | |||
320.6.a.y.1.2 | 3 | 8.3 | odd | 2 | |||
800.6.a.n.1.2 | 3 | 5.4 | even | 2 | |||
800.6.a.o.1.2 | 3 | 20.19 | odd | 2 | |||
800.6.c.j.449.3 | 6 | 5.3 | odd | 4 | |||
800.6.c.j.449.4 | 6 | 5.2 | odd | 4 | |||
800.6.c.k.449.3 | 6 | 20.7 | even | 4 | |||
800.6.c.k.449.4 | 6 | 20.3 | even | 4 |