Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,6,Mod(1,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, 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("400.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.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: | \(64.1535279252\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.47217.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 38x - 24 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 200) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-5.30760\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.1 |
$q$-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 | ||||||||
\(3\) | −19.0934 | −1.22484 | −0.612420 | − | 0.790532i | \(-0.709804\pi\) | ||||
−0.612420 | + | 0.790532i | \(0.709804\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −210.117 | −1.62075 | −0.810376 | − | 0.585911i | \(-0.800737\pi\) | ||||
−0.810376 | + | 0.585911i | \(0.800737\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 121.557 | 0.500234 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.2768 | 0.0455426 | 0.0227713 | − | 0.999741i | \(-0.492751\pi\) | ||||
0.0227713 | + | 0.999741i | \(0.492751\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 834.918 | 1.37021 | 0.685103 | − | 0.728447i | \(-0.259757\pi\) | ||||
0.685103 | + | 0.728447i | \(0.259757\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −292.543 | −0.245509 | −0.122755 | − | 0.992437i | \(-0.539173\pi\) | ||||
−0.122755 | + | 0.992437i | \(0.539173\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2287.27 | 1.45356 | 0.726779 | − | 0.686871i | \(-0.241016\pi\) | ||||
0.726779 | + | 0.686871i | \(0.241016\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4011.84 | 1.98516 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3788.91 | −1.49346 | −0.746731 | − | 0.665126i | \(-0.768378\pi\) | ||||
−0.746731 | + | 0.665126i | \(0.768378\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2318.76 | 0.612133 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4554.90 | 1.00574 | 0.502868 | − | 0.864363i | \(-0.332278\pi\) | ||||
0.502868 | + | 0.864363i | \(0.332278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1458.49 | 0.272584 | 0.136292 | − | 0.990669i | \(-0.456481\pi\) | ||||
0.136292 | + | 0.990669i | \(0.456481\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −348.965 | −0.0557824 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5509.69 | 0.661642 | 0.330821 | − | 0.943693i | \(-0.392674\pi\) | ||||
0.330821 | + | 0.943693i | \(0.392674\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15941.4 | −1.67828 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −616.780 | −0.0573021 | −0.0286511 | − | 0.999589i | \(-0.509121\pi\) | ||||
−0.0286511 | + | 0.999589i | \(0.509121\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −15866.5 | −1.30861 | −0.654303 | − | 0.756232i | \(-0.727038\pi\) | ||||
−0.654303 | + | 0.756232i | \(0.727038\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 29157.2 | 1.92531 | 0.962655 | − | 0.270730i | \(-0.0872650\pi\) | ||||
0.962655 | + | 0.270730i | \(0.0872650\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 27342.2 | 1.62683 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5585.64 | 0.300710 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −36944.9 | −1.80661 | −0.903305 | − | 0.428998i | \(-0.858867\pi\) | ||||
−0.903305 | + | 0.428998i | \(0.858867\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −43671.6 | −1.78038 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −18713.3 | −0.699874 | −0.349937 | − | 0.936773i | \(-0.613797\pi\) | ||||
−0.349937 | + | 0.936773i | \(0.613797\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 33063.9 | 1.13770 | 0.568852 | − | 0.822440i | \(-0.307388\pi\) | ||||
0.568852 | + | 0.822440i | \(0.307388\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −25541.2 | −0.810755 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5592.37 | −0.152198 | −0.0760990 | − | 0.997100i | \(-0.524246\pi\) | ||||
−0.0760990 | + | 0.997100i | \(0.524246\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 72343.0 | 1.82925 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −31534.1 | −0.742394 | −0.371197 | − | 0.928554i | \(-0.621053\pi\) | ||||
−0.371197 | + | 0.928554i | \(0.621053\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 86147.7 | 1.89207 | 0.946034 | − | 0.324067i | \(-0.105050\pi\) | ||||
0.946034 | + | 0.324067i | \(0.105050\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3840.26 | −0.0738132 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 34527.0 | 0.622430 | 0.311215 | − | 0.950340i | \(-0.399264\pi\) | ||||
0.311215 | + | 0.950340i | \(0.399264\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −73811.2 | −1.25000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −89370.3 | −1.42396 | −0.711980 | − | 0.702199i | \(-0.752201\pi\) | ||||
−0.711980 | + | 0.702199i | \(0.752201\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −86968.5 | −1.23187 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 45489.4 | 0.608745 | 0.304373 | − | 0.952553i | \(-0.401553\pi\) | ||||
0.304373 | + | 0.952553i | \(0.401553\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −175431. | −2.22076 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −27847.6 | −0.333872 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −133312. | −1.43860 | −0.719302 | − | 0.694697i | \(-0.755538\pi\) | ||||
−0.719302 | + | 0.694697i | \(0.755538\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2221.67 | 0.0227820 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −67742.9 | −0.660785 | −0.330393 | − | 0.943844i | \(-0.607181\pi\) | ||||
−0.330393 | + | 0.943844i | \(0.607181\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −62032.7 | −0.576139 | −0.288070 | − | 0.957609i | \(-0.593013\pi\) | ||||
−0.288070 | + | 0.957609i | \(0.593013\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 22529.0 | 0.190231 | 0.0951156 | − | 0.995466i | \(-0.469678\pi\) | ||||
0.0951156 | + | 0.995466i | \(0.469678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −212316. | −1.71166 | −0.855829 | − | 0.517259i | \(-0.826953\pi\) | ||||
−0.855829 | + | 0.517259i | \(0.826953\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −105199. | −0.810406 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −198742. | −1.46417 | −0.732087 | − | 0.681211i | \(-0.761454\pi\) | ||||
−0.732087 | + | 0.681211i | \(0.761454\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 101490. | 0.685423 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 61468.4 | 0.397910 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −160717. | −0.997926 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11776.4 | 0.0701860 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −84802.8 | −0.466553 | −0.233276 | − | 0.972410i | \(-0.574945\pi\) | ||||
−0.233276 | + | 0.972410i | \(0.574945\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 302944. | 1.60283 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 220540. | 1.12282 | 0.561410 | − | 0.827538i | \(-0.310259\pi\) | ||||
0.561410 | + | 0.827538i | \(0.310259\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −480594. | −2.35586 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −46832.2 | −0.213178 | −0.106589 | − | 0.994303i | \(-0.533993\pi\) | ||||
−0.106589 | + | 0.994303i | \(0.533993\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 169151. | 0.742569 | 0.371284 | − | 0.928519i | \(-0.378917\pi\) | ||||
0.371284 | + | 0.928519i | \(0.378917\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −556709. | −2.35820 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15259.6 | 0.0624027 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −522055. | −1.99261 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −280036. | −1.03335 | −0.516675 | − | 0.856181i | \(-0.672831\pi\) | ||||
−0.516675 | + | 0.856181i | \(0.672831\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −98970.7 | −0.353235 | −0.176618 | − | 0.984280i | \(-0.556516\pi\) | ||||
−0.176618 | + | 0.984280i | \(0.556516\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −35560.7 | −0.122812 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 31033.4 | 0.100480 | 0.0502401 | − | 0.998737i | \(-0.484001\pi\) | ||||
0.0502401 | + | 0.998737i | \(0.484001\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 705402. | 2.21281 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 796114. | 2.42053 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 98784.1 | 0.291218 | 0.145609 | − | 0.989342i | \(-0.453486\pi\) | ||||
0.145609 | + | 0.989342i | \(0.453486\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 418435. | 1.16101 | 0.580506 | − | 0.814256i | \(-0.302855\pi\) | ||||
0.580506 | + | 0.814256i | \(0.302855\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 325796. | 0.877462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 278033. | 0.727120 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −284193. | −0.721934 | −0.360967 | − | 0.932579i | \(-0.617553\pi\) | ||||
−0.360967 | + | 0.932579i | \(0.617553\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 357299. | 0.857233 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 783123. | 1.82683 | 0.913414 | − | 0.407032i | \(-0.133436\pi\) | ||||
0.913414 | + | 0.407032i | \(0.133436\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −64283.0 | −0.145848 | −0.0729238 | − | 0.997338i | \(-0.523233\pi\) | ||||
−0.0729238 | + | 0.997338i | \(0.523233\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −631302. | −1.39351 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5346.75 | −0.0111811 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −487211. | −0.992116 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 112334. | 0.222806 | 0.111403 | − | 0.993775i | \(-0.464465\pi\) | ||||
0.111403 | + | 0.993775i | \(0.464465\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −161036. | −0.311193 | −0.155596 | − | 0.987821i | \(-0.549730\pi\) | ||||
−0.155596 | + | 0.987821i | \(0.549730\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 456071. | 0.837273 | 0.418636 | − | 0.908154i | \(-0.362508\pi\) | ||||
0.418636 | + | 0.908154i | \(0.362508\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −569030. | −1.01860 | −0.509299 | − | 0.860590i | \(-0.670095\pi\) | ||||
−0.509299 | + | 0.860590i | \(0.670095\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 106777. | 0.186418 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −957064. | −1.63005 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −460568. | −0.747081 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 41803.8 | 0.0661988 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −402226. | −0.621963 | −0.310981 | − | 0.950416i | \(-0.600658\pi\) | ||||
−0.310981 | + | 0.950416i | \(0.600658\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 602092. | 0.909314 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −306455. | −0.441791 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.64485e6 | −2.31748 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −244250. | −0.336398 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.24567e6 | 1.67742 | 0.838709 | − | 0.544579i | \(-0.183311\pi\) | ||||
0.838709 | + | 0.544579i | \(0.183311\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 475220. | 0.612111 | 0.306055 | − | 0.952014i | \(-0.400991\pi\) | ||||
0.306055 | + | 0.952014i | \(0.400991\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −399176. | −0.503009 | −0.251505 | − | 0.967856i | \(-0.580925\pi\) | ||||
−0.251505 | + | 0.967856i | \(0.580925\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 73323.5 | 0.0904094 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 280117. | 0.338026 | 0.169013 | − | 0.985614i | \(-0.445942\pi\) | ||||
0.169013 | + | 0.985614i | \(0.445942\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −659236. | −0.762378 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −190860. | −0.216133 | −0.108067 | − | 0.994144i | \(-0.534466\pi\) | ||||
−0.108067 | + | 0.994144i | \(0.534466\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −31402.5 | −0.0348275 | −0.0174137 | − | 0.999848i | \(-0.505543\pi\) | ||||
−0.0174137 | + | 0.999848i | \(0.505543\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 845847. | 0.918917 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.90968e6 | 1.99167 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.70638e6 | 1.74412 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −47989.7 | −0.0480799 | −0.0240400 | − | 0.999711i | \(-0.507653\pi\) | ||||
−0.0240400 | + | 0.999711i | \(0.507653\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −69248.9 | −0.0680161 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.79852e6 | −1.69857 | −0.849284 | − | 0.527937i | \(-0.822966\pi\) | ||||
−0.849284 | + | 0.527937i | \(0.822966\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.15768e6 | −1.07236 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 553680. | 0.503104 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 967118. | 0.862164 | 0.431082 | − | 0.902313i | \(-0.358132\pi\) | ||||
0.431082 | + | 0.902313i | \(0.358132\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −868547. | −0.745616 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 878552. | 0.740264 | 0.370132 | − | 0.928979i | \(-0.379312\pi\) | ||||
0.370132 | + | 0.928979i | \(0.379312\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.19503e6 | −0.988455 | −0.494228 | − | 0.869333i | \(-0.664549\pi\) | ||||
−0.494228 | + | 0.869333i | \(0.664549\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.34956e6 | 2.72008 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 850774. | 0.666215 | 0.333108 | − | 0.942889i | \(-0.391903\pi\) | ||||
0.333108 | + | 0.942889i | \(0.391903\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 177290. | 0.136356 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.05422e6 | −0.796462 | −0.398231 | − | 0.917285i | \(-0.630376\pi\) | ||||
−0.398231 | + | 0.917285i | \(0.630376\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −226845. | −0.168369 | −0.0841846 | − | 0.996450i | \(-0.526829\pi\) | ||||
−0.0841846 | + | 0.996450i | \(0.526829\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 129596. | 0.0928725 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.33428e6 | −0.939725 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.54538e6 | 1.76206 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.64442e6 | 1.11904 | 0.559519 | − | 0.828818i | \(-0.310986\pi\) | ||||
0.559519 | + | 0.828818i | \(0.310986\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 42379.4 | 0.0278781 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.16343e6 | −2.04635 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.33382e6 | 2.12093 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.29344e6 | 0.809356 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.09665e6 | −1.26964 | −0.634820 | − | 0.772660i | \(-0.718926\pi\) | ||||
−0.634820 | + | 0.772660i | \(0.718926\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.18441e6 | 0.705678 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.46148e6 | −0.856825 | −0.428413 | − | 0.903583i | \(-0.640927\pi\) | ||||
−0.428413 | + | 0.903583i | \(0.640927\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.03377e6 | 0.596437 | 0.298219 | − | 0.954498i | \(-0.403608\pi\) | ||||
0.298219 | + | 0.954498i | \(0.403608\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 148727. | 0.0831272 | 0.0415636 | − | 0.999136i | \(-0.486766\pi\) | ||||
0.0415636 | + | 0.999136i | \(0.486766\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 83248.9 | 0.0458038 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −430154. | −0.233003 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −669125. | −0.356862 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.05383e6 | 2.09651 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.12642e6 | −3.12045 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.54319e6 | −0.774194 | −0.387097 | − | 0.922039i | \(-0.626522\pi\) | ||||
−0.387097 | + | 0.922039i | \(0.626522\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 669741. | 0.330976 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.22154e6 | 1.54522 | 0.772608 | − | 0.634883i | \(-0.218952\pi\) | ||||
0.772608 | + | 0.634883i | \(0.218952\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.79465e6 | 1.79338 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26656.6 | 0.0124142 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.21363e6 | −1.01594 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 217036. | 0.0967626 | 0.0483813 | − | 0.998829i | \(-0.484594\pi\) | ||||
0.0483813 | + | 0.998829i | \(0.484594\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −37149.9 | −0.0163265 | −0.00816326 | − | 0.999967i | \(-0.502598\pi\) | ||||
−0.00816326 | + | 0.999967i | \(0.502598\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.93597e6 | 0.838748 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.92411e6 | −1.24898 | −0.624492 | − | 0.781031i | \(-0.714694\pi\) | ||||
−0.624492 | + | 0.781031i | \(0.714694\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.17364e6 | −0.487376 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.55303e6 | −0.635980 | −0.317990 | − | 0.948094i | \(-0.603008\pi\) | ||||
−0.317990 | + | 0.948094i | \(0.603008\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.75549e6 | 1.11283 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.06863e6 | 1.22230 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 413541. | 0.160271 | 0.0801353 | − | 0.996784i | \(-0.474465\pi\) | ||||
0.0801353 | + | 0.996784i | \(0.474465\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −74973.9 | −0.0286645 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.76275e6 | 2.92807 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.06546e6 | −0.768677 | −0.384338 | − | 0.923192i | \(-0.625570\pi\) | ||||
−0.384338 | + | 0.923192i | \(0.625570\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.80297e6 | 1.37807 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.27742e6 | −0.814412 | −0.407206 | − | 0.913336i | \(-0.633497\pi\) | ||||
−0.407206 | + | 0.913336i | \(0.633497\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.61917e6 | 0.571453 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.88095e6 | 1.00355 | 0.501774 | − | 0.864999i | \(-0.332681\pi\) | ||||
0.501774 | + | 0.864999i | \(0.332681\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.92868e6 | −0.654610 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 634299. | 0.212530 | 0.106265 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106265 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.10842e6 | 0.366659 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.21086e6 | −1.37527 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.36800e6 | 1.39093 | 0.695466 | − | 0.718559i | \(-0.255198\pi\) | ||||
0.695466 | + | 0.718559i | \(0.255198\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.17616e6 | 2.88555 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.50000e6 | −1.70806 | −0.854028 | − | 0.520228i | \(-0.825847\pi\) | ||||
−0.854028 | + | 0.520228i | \(0.825847\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.21772e6 | 0.373496 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 100699. | 0.0301329 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.21295e6 | 0.949721 | 0.474860 | − | 0.880061i | \(-0.342499\pi\) | ||||
0.474860 | + | 0.880061i | \(0.342499\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 894184. | 0.261109 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.93198e6 | 1.13432 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.22966e6 | −0.909528 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −890973. | −0.247930 | −0.123965 | − | 0.992287i | \(-0.539561\pi\) | ||||
−0.123965 | + | 0.992287i | \(0.539561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.87922e6 | −0.791716 | −0.395858 | − | 0.918312i | \(-0.629553\pi\) | ||||
−0.395858 | + | 0.918312i | \(0.629553\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.54426e6 | 0.963106 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.94729e6 | −1.84394 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −291357. | −0.0764333 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.29450e6 | −1.63218 | −0.816090 | − | 0.577924i | \(-0.803863\pi\) | ||||
−0.816090 | + | 0.577924i | \(0.803863\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.96375e6 | −1.52862 | −0.764311 | − | 0.644848i | \(-0.776921\pi\) | ||||
−0.764311 | + | 0.644848i | \(0.776921\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.66623e6 | −2.17084 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.91648e6 | 1.21757 | 0.608784 | − | 0.793336i | \(-0.291658\pi\) | ||||
0.608784 | + | 0.793336i | \(0.291658\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.32363e6 | 0.813798 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.53513e6 | −1.34004 | −0.670021 | − | 0.742342i | \(-0.733715\pi\) | ||||
−0.670021 | + | 0.742342i | \(0.733715\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.34683e6 | 1.26569 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.20215e6 | −1.68596 | −0.842978 | − | 0.537948i | \(-0.819200\pi\) | ||||
−0.842978 | + | 0.537948i | \(0.819200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11272.7 | −0.00260969 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.88968e6 | 0.432657 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.49984e6 | 1.23185 | 0.615927 | − | 0.787803i | \(-0.288782\pi\) | ||||
0.615927 | + | 0.787803i | \(0.288782\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −678338. | −0.150285 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.79223e6 | −0.831078 | −0.415539 | − | 0.909575i | \(-0.636407\pi\) | ||||
−0.415539 | + | 0.909575i | \(0.636407\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.78947e6 | 1.03833 | 0.519164 | − | 0.854674i | \(-0.326243\pi\) | ||||
0.519164 | + | 0.854674i | \(0.326243\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.62497e6 | −1.19352 | −0.596758 | − | 0.802422i | \(-0.703545\pi\) | ||||
−0.596758 | + | 0.802422i | \(0.703545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.17505e6 | 0.246675 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −592532. | −0.123072 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −289988. | −0.0595973 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.49090e6 | −0.903728 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −760544. | −0.151456 | −0.0757278 | − | 0.997129i | \(-0.524128\pi\) | ||||
−0.0757278 | + | 0.997129i | \(0.524128\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.60014e6 | 0.906586 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.52005e7 | −2.96476 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.52969e6 | 0.483332 | 0.241666 | − | 0.970360i | \(-0.422306\pi\) | ||||
0.241666 | + | 0.970360i | \(0.422306\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.88612e6 | −0.356695 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.83619e6 | −0.905316 | −0.452658 | − | 0.891684i | \(-0.649524\pi\) | ||||
−0.452658 | + | 0.891684i | \(0.649524\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.33251e6 | −0.246918 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.62585e6 | 1.20324 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.17357e6 | −1.64925 | −0.824626 | − | 0.565678i | \(-0.808615\pi\) | ||||
−0.824626 | + | 0.565678i | \(0.808615\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.98933e6 | −1.42205 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.02119e7 | −1.79964 | −0.899820 | − | 0.436262i | \(-0.856302\pi\) | ||||
−0.899820 | + | 0.436262i | \(0.856302\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.22054e6 | −1.07475 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.61475e6 | 1.13167 | 0.565834 | − | 0.824519i | \(-0.308554\pi\) | ||||
0.565834 | + | 0.824519i | \(0.308554\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.81011e7 | −3.06657 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.30362e6 | 0.889772 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 532899. | 0.0876836 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.42620e6 | 0.884254 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.91327e6 | −1.60001 | −0.800005 | − | 0.599993i | \(-0.795170\pi\) | ||||
−0.800005 | + | 0.599993i | \(0.795170\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.66698e6 | 0.746074 | 0.373037 | − | 0.927816i | \(-0.378316\pi\) | ||||
0.373037 | + | 0.927816i | \(0.378316\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −426673. | −0.0669220 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.91946e6 | 1.23043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.27473e6 | −0.350101 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −514961. | −0.0785157 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.49525e7 | −2.23757 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 499727. | 0.0740902 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.47136e6 | −0.216136 | −0.108068 | − | 0.994144i | \(-0.534466\pi\) | ||||
−0.108068 | + | 0.994144i | \(0.534466\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.22738e6 | 0.178640 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.55704e6 | 0.651200 | 0.325600 | − | 0.945508i | \(-0.394434\pi\) | ||||
0.325600 | + | 0.945508i | \(0.394434\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.01915e6 | 0.569119 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.04183e7 | 1.46190 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.25470e6 | −1.00880 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.05967e7 | −1.44721 | −0.723605 | − | 0.690215i | \(-0.757516\pi\) | ||||
−0.723605 | + | 0.690215i | \(0.757516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.32472e7 | −1.79306 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 102087. | 0.0136951 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.17451e6 | −0.289129 | −0.144564 | − | 0.989495i | \(-0.546178\pi\) | ||||
−0.144564 | + | 0.989495i | \(0.546178\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.55090e7 | 2.02594 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.36030e6 | 1.21202 | 0.606009 | − | 0.795458i | \(-0.292769\pi\) | ||||
0.606009 | + | 0.795458i | \(0.292769\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.64209e6 | −0.210770 | −0.105385 | − | 0.994432i | \(-0.533607\pi\) | ||||
−0.105385 | + | 0.994432i | \(0.533607\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.14484e6 | −0.272902 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.20742e6 | −0.651153 | −0.325576 | − | 0.945516i | \(-0.605558\pi\) | ||||
−0.325576 | + | 0.945516i | \(0.605558\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.07472e6 | 0.381161 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.87782e7 | 2.30789 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −675233. | −0.0822777 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.06067e7 | −1.27053 | −0.635267 | − | 0.772292i | \(-0.719110\pi\) | ||||
−0.635267 | + | 0.772292i | \(0.719110\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.33596e6 | 0.396217 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.70794e6 | −1.02553 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.99180e6 | 0.232600 | 0.116300 | − | 0.993214i | \(-0.462897\pi\) | ||||
0.116300 | + | 0.993214i | \(0.462897\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.08647e7 | 1.24762 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.16108e7 | 1.32219 | 0.661095 | − | 0.750303i | \(-0.270092\pi\) | ||||
0.661095 | + | 0.750303i | \(0.270092\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −628490. | −0.0709761 | −0.0354881 | − | 0.999370i | \(-0.511299\pi\) | ||||
−0.0354881 | + | 0.999370i | \(0.511299\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −679791. | −0.0761346 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −707145. | −0.0778998 | −0.0389499 | − | 0.999241i | \(-0.512401\pi\) | ||||
−0.0389499 | + | 0.999241i | \(0.512401\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.82736e7 | 1.99655 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.43439e7 | 2.63807 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.37228e7 | −1.47500 | −0.737500 | − | 0.675347i | \(-0.763994\pi\) | ||||
−0.737500 | + | 0.675347i | \(0.763994\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.47885e7 | −1.56390 | −0.781952 | − | 0.623339i | \(-0.785776\pi\) | ||||
−0.781952 | + | 0.623339i | \(0.785776\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.72872e6 | −0.286241 | −0.143121 | − | 0.989705i | \(-0.545714\pi\) | ||||
−0.143121 | + | 0.989705i | \(0.545714\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.78556e6 | −0.914198 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.55811e6 | −0.986624 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −798176. | −0.0810830 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.61183e6 | −0.162439 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.75522e6 | −0.575425 | −0.287713 | − | 0.957717i | \(-0.592895\pi\) | ||||
−0.287713 | + | 0.957717i | \(0.592895\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.67986e6 | 0.761805 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.28285e7 | 2.22910 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.83319e6 | −0.371371 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.94835e6 | 0.379551 | 0.189776 | − | 0.981827i | \(-0.439224\pi\) | ||||
0.189776 | + | 0.981827i | \(0.439224\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.12977e7 | −1.07761 | −0.538804 | − | 0.842431i | \(-0.681124\pi\) | ||||
−0.538804 | + | 0.842431i | \(0.681124\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.60010e7 | 1.50275 | 0.751376 | − | 0.659875i | \(-0.229391\pi\) | ||||
0.751376 | + | 0.659875i | \(0.229391\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −342018. | −0.0318741 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.85125e6 | 0.541124 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.51457e6 | −0.781412 | −0.390706 | − | 0.920516i | \(-0.627769\pi\) | ||||
−0.390706 | + | 0.920516i | \(0.627769\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.04719e7 | 0.946477 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.15442e7 | −1.03550 | −0.517751 | − | 0.855531i | \(-0.673231\pi\) | ||||
−0.517751 | + | 0.855531i | \(0.673231\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.51328e7 | 1.34715 | 0.673576 | − | 0.739118i | \(-0.264757\pi\) | ||||
0.673576 | + | 0.739118i | \(0.264757\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.66355e6 | 0.412034 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.72581e7 | −1.50203 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.37841e7 | −2.05457 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 604301. | 0.0518140 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.82845e7 | 1.55613 | 0.778063 | − | 0.628187i | \(-0.216203\pi\) | ||||
0.778063 | + | 0.628187i | \(0.216203\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.67653e6 | 0.308295 | 0.154147 | − | 0.988048i | \(-0.450737\pi\) | ||||
0.154147 | + | 0.988048i | \(0.450737\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.80112e7 | 2.33162 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.07355e6 | −0.749738 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.19937e6 | −0.0983784 | −0.0491892 | − | 0.998789i | \(-0.515664\pi\) | ||||
−0.0491892 | + | 0.998789i | \(0.515664\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.62162e6 | 0.616106 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.08460e7 | −2.47543 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.32762e7 | −1.05774 | −0.528868 | − | 0.848704i | \(-0.677383\pi\) | ||||
−0.528868 | + | 0.848704i | \(0.677383\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −466810. | −0.0369239 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 180435. | 0.0140682 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.34839e6 | −0.414028 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.25654e6 | 0.711466 | 0.355733 | − | 0.934588i | \(-0.384231\pi\) | ||||
0.355733 | + | 0.934588i | \(0.384231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.26021e7 | 0.961736 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.42339e7 | 1.07097 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.58869e6 | −0.716381 | −0.358190 | − | 0.933649i | \(-0.616606\pi\) | ||||
−0.358190 | + | 0.933649i | \(0.616606\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.19699e6 | 0.311361 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.52610e6 | −0.407094 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.64417e6 | 0.264728 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.17477e6 | −0.0847483 | −0.0423741 | − | 0.999102i | \(-0.513492\pi\) | ||||
−0.0423741 | + | 0.999102i | \(0.513492\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.30341e7 | 0.933778 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 599581. | 0.0426581 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.68157e7 | −1.17999 | −0.589997 | − | 0.807405i | \(-0.700871\pi\) | ||||
−0.589997 | + | 0.807405i | \(0.700871\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.78606e6 | 0.124473 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.64163e6 | 0.321275 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.18574e6 | 0.356493 | 0.178247 | − | 0.983986i | \(-0.442958\pi\) | ||||
0.178247 | + | 0.983986i | \(0.442958\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −102210. | −0.00693149 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.07382e7 | 0.723302 | 0.361651 | − | 0.932313i | \(-0.382213\pi\) | ||||
0.361651 | + | 0.932313i | \(0.382213\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.64622e7 | −2.43948 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.88845e7 | 1.25497 | 0.627487 | − | 0.778627i | \(-0.284084\pi\) | ||||
0.627487 | + | 0.778627i | \(0.284084\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.08636e7 | −0.712314 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.73372e6 | −0.308318 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.40163e6 | −0.478881 | −0.239440 | − | 0.970911i | \(-0.576964\pi\) | ||||
−0.239440 | + | 0.970911i | \(0.576964\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 916286. | 0.0588903 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.24822e6 | 0.459718 | 0.229859 | − | 0.973224i | \(-0.426173\pi\) | ||||
0.229859 | + | 0.973224i | \(0.426173\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.32220e6 | 0.0833089 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.50511e6 | 0.344591 | 0.172296 | − | 0.985045i | \(-0.444882\pi\) | ||||
0.172296 | + | 0.985045i | \(0.444882\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.46113e7 | 2.77417 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.56241e7 | −0.958970 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.81612e7 | 1.10746 | 0.553730 | − | 0.832696i | \(-0.313204\pi\) | ||||
0.553730 | + | 0.832696i | \(0.313204\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.43398e7 | 2.08047 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.39969e6 | −0.445415 | −0.222707 | − | 0.974885i | \(-0.571489\pi\) | ||||
−0.222707 | + | 0.974885i | \(0.571489\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.21040e7 | 1.31347 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.41074e6 | −0.0832920 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −576341. | −0.0338105 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.05617e7 | 0.615645 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.85122e7 | 1.06542 | 0.532709 | − | 0.846298i | \(-0.321174\pi\) | ||||
0.532709 | + | 0.846298i | \(0.321174\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.84655e7 | −1.05601 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.17590e7 | 2.37306 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.76057e7 | 1.55889 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.68656e7 | −0.940493 | −0.470247 | − | 0.882535i | \(-0.655835\pi\) | ||||
−0.470247 | + | 0.882535i | \(0.655835\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.52974e6 | −0.472682 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.52955e6 | 0.304515 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.57450e6 | 0.0861697 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.67745e7 | −0.906706 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.53056e6 | −0.297097 | −0.148548 | − | 0.988905i | \(-0.547460\pi\) | ||||
−0.148548 | + | 0.988905i | \(0.547460\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.91422e7 | −1.55586 | −0.777929 | − | 0.628353i | \(-0.783730\pi\) | ||||
−0.777929 | + | 0.628353i | \(0.783730\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.28172e7 | 1.21070 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.62908e7 | −1.90214 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.13248e7 | −1.11090 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.44892e7 | −0.750216 | −0.375108 | − | 0.926981i | \(-0.622394\pi\) | ||||
−0.375108 | + | 0.926981i | \(0.622394\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.71404e7 | 1.39674 | 0.698371 | − | 0.715736i | \(-0.253908\pi\) | ||||
0.698371 | + | 0.715736i | \(0.253908\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.01025e7 | −1.53052 | −0.765259 | − | 0.643722i | \(-0.777389\pi\) | ||||
−0.765259 | + | 0.643722i | \(0.777389\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.47022e7 | −1.24839 | −0.624194 | − | 0.781269i | \(-0.714573\pi\) | ||||
−0.624194 | + | 0.781269i | \(0.714573\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.62441e7 | −0.816008 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.99878e6 | −0.399403 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.38190e6 | 0.166858 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.23647e7 | −0.606428 | −0.303214 | − | 0.952922i | \(-0.598060\pi\) | ||||
−0.303214 | + | 0.952922i | \(0.598060\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 236010. | 0.0115064 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.01286e7 | 0.975539 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.37694e7 | 1.61739 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.33123e6 | 0.206225 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.08757e7 | −0.988137 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.20993e7 | −0.569363 | −0.284681 | − | 0.958622i | \(-0.591888\pi\) | ||||
−0.284681 | + | 0.958622i | \(0.591888\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.86289e6 | −0.319194 | −0.159597 | − | 0.987182i | \(-0.551020\pi\) | ||||
−0.159597 | + | 0.987182i | \(0.551020\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.52569e7 | 1.16788 | 0.583938 | − | 0.811798i | \(-0.301511\pi\) | ||||
0.583938 | + | 0.811798i | \(0.301511\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.47443e6 | −0.113754 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.45114e6 | 0.112032 | 0.0560159 | − | 0.998430i | \(-0.482160\pi\) | ||||
0.0560159 | + | 0.998430i | \(0.482160\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.54758e7 | 1.15101 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 631041. | 0.0283471 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.66917e6 | −0.208542 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.62050e7 | −0.719639 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.14652e7 | 0.942401 | 0.471201 | − | 0.882026i | \(-0.343821\pi\) | ||||
0.471201 | + | 0.882026i | \(0.343821\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.13976e7 | −1.37064 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.68815e7 | 0.732775 | 0.366388 | − | 0.930462i | \(-0.380594\pi\) | ||||
0.366388 | + | 0.930462i | \(0.380594\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.37649e7 | −1.45735 | −0.728676 | − | 0.684859i | \(-0.759864\pi\) | ||||
−0.728676 | + | 0.684859i | \(0.759864\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.20696e7 | 1.36862 | 0.684312 | − | 0.729189i | \(-0.260103\pi\) | ||||
0.684312 | + | 0.729189i | \(0.260103\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.78185e7 | 0.756166 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.34903e6 | −0.0569282 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.66902e7 | 2.79855 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.04005e7 | 2.50645 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.64330e6 | 0.274148 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.08080e7 | 0.443540 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.36538e7 | −2.59780 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.29290e7 | 0.521853 | 0.260926 | − | 0.965359i | \(-0.415972\pi\) | ||||
0.260926 | + | 0.965359i | \(0.415972\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.23461e6 | −0.330547 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.00076e6 | −0.159715 | −0.0798577 | − | 0.996806i | \(-0.525447\pi\) | ||||
−0.0798577 | + | 0.996806i | \(0.525447\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.63340e6 | −0.0648508 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.63393e7 | −1.81981 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.55409e7 | −0.997581 | −0.498790 | − | 0.866723i | \(-0.666222\pi\) | ||||
−0.498790 | + | 0.866723i | \(0.666222\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.00321e7 | 1.55511 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.63284e7 | −1.01723 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.54050e6 | −0.288204 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.98080e7 | −1.13316 | −0.566582 | − | 0.824005i | \(-0.691735\pi\) | ||||
−0.566582 | + | 0.824005i | \(0.691735\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.25389e7 | 2.36470 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.79046e7 | 1.04947 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.52937e7 | 1.31325 | 0.656627 | − | 0.754216i | \(-0.271983\pi\) | ||||
0.656627 | + | 0.754216i | \(0.271983\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.97382e7 | −0.730540 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.71557e7 | 1.73604 | 0.868020 | − | 0.496529i | \(-0.165392\pi\) | ||||
0.868020 | + | 0.496529i | \(0.165392\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.33692e6 | 0.0855785 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.56893e7 | −1.65554 | −0.827770 | − | 0.561067i | \(-0.810391\pi\) | ||||
−0.827770 | + | 0.561067i | \(0.810391\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.19263e7 | 2.59252 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.83971e6 | −0.101818 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.47162e7 | −0.881556 | −0.440778 | − | 0.897616i | \(-0.645297\pi\) | ||||
−0.440778 | + | 0.897616i | \(0.645297\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.58950e6 | −0.0561024 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.84024e6 | 0.345509 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.65019e7 | −0.925698 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.73855e6 | 0.0951602 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.56789e6 | −0.0883102 | −0.0441551 | − | 0.999025i | \(-0.514060\pi\) | ||||
−0.0441551 | + | 0.999025i | \(0.514060\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.27758e7 | 0.437099 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.46122e7 | −1.17810 | −0.589049 | − | 0.808097i | \(-0.700498\pi\) | ||||
−0.589049 | + | 0.808097i | \(0.700498\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.55414e7 | −1.20352 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.51384e7 | −1.84807 | −0.924034 | − | 0.382309i | \(-0.875129\pi\) | ||||
−0.924034 | + | 0.382309i | \(0.875129\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 831400. | 0.0277238 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.58085e7 | −0.856230 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.37599e7 | −1.11434 | −0.557169 | − | 0.830399i | \(-0.688113\pi\) | ||||
−0.557169 | + | 0.830399i | \(0.688113\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.16974e8 | 3.82205 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.01166e7 | 1.95435 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.25256e7 | 0.405150 | 0.202575 | − | 0.979267i | \(-0.435069\pi\) | ||||
0.202575 | + | 0.979267i | \(0.435069\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.94647e7 | 0.948265 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.02324e7 | −0.963240 | −0.481620 | − | 0.876380i | \(-0.659952\pi\) | ||||
−0.481620 | + | 0.876380i | \(0.659952\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.27757e7 | 0.405013 |
(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 | 400.6.a.y.1.1 | 3 | ||
4.3 | odd | 2 | 200.6.a.h.1.3 | ✓ | 3 | ||
5.2 | odd | 4 | 400.6.c.p.49.5 | 6 | |||
5.3 | odd | 4 | 400.6.c.p.49.2 | 6 | |||
5.4 | even | 2 | 400.6.a.x.1.3 | 3 | |||
20.3 | even | 4 | 200.6.c.g.49.5 | 6 | |||
20.7 | even | 4 | 200.6.c.g.49.2 | 6 | |||
20.19 | odd | 2 | 200.6.a.i.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.6.a.h.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
200.6.a.i.1.1 | yes | 3 | 20.19 | odd | 2 | ||
200.6.c.g.49.2 | 6 | 20.7 | even | 4 | |||
200.6.c.g.49.5 | 6 | 20.3 | even | 4 | |||
400.6.a.x.1.3 | 3 | 5.4 | even | 2 | |||
400.6.a.y.1.1 | 3 | 1.1 | even | 1 | trivial | ||
400.6.c.p.49.2 | 6 | 5.3 | odd | 4 | |||
400.6.c.p.49.5 | 6 | 5.2 | odd | 4 |