Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1075,6,Mod(1,1075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1075.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1075 = 5^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1075.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: | \(172.412606299\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + \cdots - 22734604 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-9.70631\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.7063 | −1.89263 | −0.946313 | − | 0.323251i | \(-0.895224\pi\) | ||||
−0.946313 | + | 0.323251i | \(0.895224\pi\) | |||||||
\(3\) | −18.3440 | −1.17677 | −0.588385 | − | 0.808581i | \(-0.700236\pi\) | ||||
−0.588385 | + | 0.808581i | \(0.700236\pi\) | |||||||
\(4\) | 82.6251 | 2.58203 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 196.397 | 2.22719 | ||||||||
\(7\) | 96.4803 | 0.744207 | 0.372103 | − | 0.928191i | \(-0.378637\pi\) | ||||
0.372103 | + | 0.928191i | \(0.378637\pi\) | |||||||
\(8\) | −542.008 | −2.99420 | ||||||||
\(9\) | 93.5034 | 0.384788 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −684.136 | −1.70475 | −0.852376 | − | 0.522930i | \(-0.824839\pi\) | ||||
−0.852376 | + | 0.522930i | \(0.824839\pi\) | |||||||
\(12\) | −1515.68 | −3.03846 | ||||||||
\(13\) | −344.655 | −0.565622 | −0.282811 | − | 0.959176i | \(-0.591267\pi\) | ||||
−0.282811 | + | 0.959176i | \(0.591267\pi\) | |||||||
\(14\) | −1032.95 | −1.40851 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3158.90 | 3.08487 | ||||||||
\(17\) | −1319.32 | −1.10721 | −0.553604 | − | 0.832780i | \(-0.686748\pi\) | ||||
−0.553604 | + | 0.832780i | \(0.686748\pi\) | |||||||
\(18\) | −1001.08 | −0.728260 | ||||||||
\(19\) | 739.016 | 0.469645 | 0.234823 | − | 0.972038i | \(-0.424549\pi\) | ||||
0.234823 | + | 0.972038i | \(0.424549\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1769.84 | −0.875760 | ||||||||
\(22\) | 7324.58 | 3.22646 | ||||||||
\(23\) | −3165.85 | −1.24787 | −0.623937 | − | 0.781474i | \(-0.714468\pi\) | ||||
−0.623937 | + | 0.781474i | \(0.714468\pi\) | |||||||
\(24\) | 9942.61 | 3.52349 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3689.99 | 1.07051 | ||||||||
\(27\) | 2742.37 | 0.723963 | ||||||||
\(28\) | 7971.70 | 1.92157 | ||||||||
\(29\) | 7073.21 | 1.56179 | 0.780893 | − | 0.624665i | \(-0.214765\pi\) | ||||
0.780893 | + | 0.624665i | \(0.214765\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3791.93 | −0.708689 | −0.354345 | − | 0.935115i | \(-0.615296\pi\) | ||||
−0.354345 | + | 0.935115i | \(0.615296\pi\) | |||||||
\(32\) | −16476.0 | −2.84430 | ||||||||
\(33\) | 12549.8 | 2.00610 | ||||||||
\(34\) | 14125.1 | 2.09553 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7725.73 | 0.993536 | ||||||||
\(37\) | 12682.3 | 1.52298 | 0.761489 | − | 0.648177i | \(-0.224469\pi\) | ||||
0.761489 | + | 0.648177i | \(0.224469\pi\) | |||||||
\(38\) | −7912.13 | −0.888863 | ||||||||
\(39\) | 6322.37 | 0.665607 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10882.5 | −1.01105 | −0.505523 | − | 0.862813i | \(-0.668700\pi\) | ||||
−0.505523 | + | 0.862813i | \(0.668700\pi\) | |||||||
\(42\) | 18948.4 | 1.65749 | ||||||||
\(43\) | −1849.00 | −0.152499 | ||||||||
\(44\) | −56526.8 | −4.40173 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 33894.6 | 2.36176 | ||||||||
\(47\) | −3873.59 | −0.255782 | −0.127891 | − | 0.991788i | \(-0.540821\pi\) | ||||
−0.127891 | + | 0.991788i | \(0.540821\pi\) | |||||||
\(48\) | −57947.0 | −3.63018 | ||||||||
\(49\) | −7498.54 | −0.446156 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 24201.7 | 1.30293 | ||||||||
\(52\) | −28477.2 | −1.46046 | ||||||||
\(53\) | −6479.38 | −0.316843 | −0.158421 | − | 0.987372i | \(-0.550640\pi\) | ||||
−0.158421 | + | 0.987372i | \(0.550640\pi\) | |||||||
\(54\) | −29360.7 | −1.37019 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −52293.1 | −2.22830 | ||||||||
\(57\) | −13556.5 | −0.552664 | ||||||||
\(58\) | −75728.0 | −2.95588 | ||||||||
\(59\) | 34750.3 | 1.29966 | 0.649829 | − | 0.760081i | \(-0.274841\pi\) | ||||
0.649829 | + | 0.760081i | \(0.274841\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 26452.9 | 0.910224 | 0.455112 | − | 0.890434i | \(-0.349599\pi\) | ||||
0.455112 | + | 0.890434i | \(0.349599\pi\) | |||||||
\(62\) | 40597.6 | 1.34128 | ||||||||
\(63\) | 9021.24 | 0.286362 | ||||||||
\(64\) | 75311.8 | 2.29833 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −134362. | −3.79680 | ||||||||
\(67\) | 58007.3 | 1.57868 | 0.789342 | − | 0.613953i | \(-0.210422\pi\) | ||||
0.789342 | + | 0.613953i | \(0.210422\pi\) | |||||||
\(68\) | −109009. | −2.85885 | ||||||||
\(69\) | 58074.5 | 1.46846 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −23477.7 | −0.552726 | −0.276363 | − | 0.961053i | \(-0.589129\pi\) | ||||
−0.276363 | + | 0.961053i | \(0.589129\pi\) | |||||||
\(72\) | −50679.6 | −1.15213 | ||||||||
\(73\) | −45184.4 | −0.992388 | −0.496194 | − | 0.868212i | \(-0.665269\pi\) | ||||
−0.496194 | + | 0.868212i | \(0.665269\pi\) | |||||||
\(74\) | −135781. | −2.88243 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 61061.3 | 1.21264 | ||||||||
\(77\) | −66005.7 | −1.26869 | ||||||||
\(78\) | −67689.2 | −1.25975 | ||||||||
\(79\) | 17895.9 | 0.322617 | 0.161308 | − | 0.986904i | \(-0.448429\pi\) | ||||
0.161308 | + | 0.986904i | \(0.448429\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −73027.4 | −1.23673 | ||||||||
\(82\) | 116512. | 1.91353 | ||||||||
\(83\) | −39799.2 | −0.634132 | −0.317066 | − | 0.948403i | \(-0.602698\pi\) | ||||
−0.317066 | + | 0.948403i | \(0.602698\pi\) | |||||||
\(84\) | −146233. | −2.26124 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 19796.0 | 0.288623 | ||||||||
\(87\) | −129751. | −1.83786 | ||||||||
\(88\) | 370808. | 5.10437 | ||||||||
\(89\) | −30802.0 | −0.412197 | −0.206098 | − | 0.978531i | \(-0.566077\pi\) | ||||
−0.206098 | + | 0.978531i | \(0.566077\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −33252.5 | −0.420940 | ||||||||
\(92\) | −261579. | −3.22206 | ||||||||
\(93\) | 69559.2 | 0.833964 | ||||||||
\(94\) | 41471.9 | 0.484099 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 302235. | 3.34709 | ||||||||
\(97\) | −22524.5 | −0.243067 | −0.121533 | − | 0.992587i | \(-0.538781\pi\) | ||||
−0.121533 | + | 0.992587i | \(0.538781\pi\) | |||||||
\(98\) | 80281.7 | 0.844407 | ||||||||
\(99\) | −63969.1 | −0.655968 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 70592.5 | 0.688581 | 0.344290 | − | 0.938863i | \(-0.388120\pi\) | ||||
0.344290 | + | 0.938863i | \(0.388120\pi\) | |||||||
\(102\) | −259111. | −2.46596 | ||||||||
\(103\) | 36628.5 | 0.340193 | 0.170097 | − | 0.985427i | \(-0.445592\pi\) | ||||
0.170097 | + | 0.985427i | \(0.445592\pi\) | |||||||
\(104\) | 186806. | 1.69359 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 69370.2 | 0.599665 | ||||||||
\(107\) | 48388.9 | 0.408588 | 0.204294 | − | 0.978910i | \(-0.434510\pi\) | ||||
0.204294 | + | 0.978910i | \(0.434510\pi\) | |||||||
\(108\) | 226589. | 1.86930 | ||||||||
\(109\) | −75896.0 | −0.611861 | −0.305930 | − | 0.952054i | \(-0.598967\pi\) | ||||
−0.305930 | + | 0.952054i | \(0.598967\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −232645. | −1.79220 | ||||||||
\(112\) | 304772. | 2.29578 | ||||||||
\(113\) | 212156. | 1.56300 | 0.781500 | − | 0.623905i | \(-0.214455\pi\) | ||||
0.781500 | + | 0.623905i | \(0.214455\pi\) | |||||||
\(114\) | 145140. | 1.04599 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 584424. | 4.03258 | ||||||||
\(117\) | −32226.4 | −0.217645 | ||||||||
\(118\) | −372048. | −2.45977 | ||||||||
\(119\) | −127289. | −0.823992 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 306992. | 1.90618 | ||||||||
\(122\) | −283213. | −1.72271 | ||||||||
\(123\) | 199630. | 1.18977 | ||||||||
\(124\) | −313308. | −1.82986 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −96584.3 | −0.541976 | ||||||||
\(127\) | 74547.8 | 0.410134 | 0.205067 | − | 0.978748i | \(-0.434259\pi\) | ||||
0.205067 | + | 0.978748i | \(0.434259\pi\) | |||||||
\(128\) | −279081. | −1.50558 | ||||||||
\(129\) | 33918.1 | 0.179456 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −57691.8 | −0.293722 | −0.146861 | − | 0.989157i | \(-0.546917\pi\) | ||||
−0.146861 | + | 0.989157i | \(0.546917\pi\) | |||||||
\(132\) | 1.03693e6 | 5.17982 | ||||||||
\(133\) | 71300.5 | 0.349513 | ||||||||
\(134\) | −621044. | −2.98786 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 715084. | 3.31520 | ||||||||
\(137\) | 23674.0 | 0.107763 | 0.0538815 | − | 0.998547i | \(-0.482841\pi\) | ||||
0.0538815 | + | 0.998547i | \(0.482841\pi\) | |||||||
\(138\) | −621763. | −2.77925 | ||||||||
\(139\) | 234996. | 1.03163 | 0.515815 | − | 0.856700i | \(-0.327489\pi\) | ||||
0.515815 | + | 0.856700i | \(0.327489\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 71057.3 | 0.300996 | ||||||||
\(142\) | 251360. | 1.04610 | ||||||||
\(143\) | 235791. | 0.964245 | ||||||||
\(144\) | 295368. | 1.18702 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 483758. | 1.87822 | ||||||||
\(147\) | 137554. | 0.525023 | ||||||||
\(148\) | 1.04788e6 | 3.93238 | ||||||||
\(149\) | 236660. | 0.873292 | 0.436646 | − | 0.899633i | \(-0.356166\pi\) | ||||
0.436646 | + | 0.899633i | \(0.356166\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −106852. | −0.381363 | −0.190681 | − | 0.981652i | \(-0.561070\pi\) | ||||
−0.190681 | + | 0.981652i | \(0.561070\pi\) | |||||||
\(152\) | −400553. | −1.40621 | ||||||||
\(153\) | −123361. | −0.426040 | ||||||||
\(154\) | 706678. | 2.40115 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 522386. | 1.71862 | ||||||||
\(157\) | −316009. | −1.02318 | −0.511588 | − | 0.859231i | \(-0.670943\pi\) | ||||
−0.511588 | + | 0.859231i | \(0.670943\pi\) | |||||||
\(158\) | −191599. | −0.610593 | ||||||||
\(159\) | 118858. | 0.372851 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −305442. | −0.928677 | ||||||||
\(162\) | 781855. | 2.34066 | ||||||||
\(163\) | 467943. | 1.37951 | 0.689753 | − | 0.724045i | \(-0.257719\pi\) | ||||
0.689753 | + | 0.724045i | \(0.257719\pi\) | |||||||
\(164\) | −899172. | −2.61056 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 426103. | 1.20017 | ||||||||
\(167\) | −329143. | −0.913258 | −0.456629 | − | 0.889657i | \(-0.650943\pi\) | ||||
−0.456629 | + | 0.889657i | \(0.650943\pi\) | |||||||
\(168\) | 959267. | 2.62220 | ||||||||
\(169\) | −252506. | −0.680072 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 69100.5 | 0.180714 | ||||||||
\(172\) | −152774. | −0.393757 | ||||||||
\(173\) | −197867. | −0.502641 | −0.251321 | − | 0.967904i | \(-0.580865\pi\) | ||||
−0.251321 | + | 0.967904i | \(0.580865\pi\) | |||||||
\(174\) | 1.38916e6 | 3.47839 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.16112e6 | −5.25893 | ||||||||
\(177\) | −637461. | −1.52940 | ||||||||
\(178\) | 329776. | 0.780134 | ||||||||
\(179\) | 71110.2 | 0.165882 | 0.0829410 | − | 0.996554i | \(-0.473569\pi\) | ||||
0.0829410 | + | 0.996554i | \(0.473569\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 111059. | 0.251975 | 0.125987 | − | 0.992032i | \(-0.459790\pi\) | ||||
0.125987 | + | 0.992032i | \(0.459790\pi\) | |||||||
\(182\) | 356011. | 0.796682 | ||||||||
\(183\) | −485252. | −1.07112 | ||||||||
\(184\) | 1.71592e6 | 3.73639 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −744723. | −1.57838 | ||||||||
\(187\) | 902597. | 1.88751 | ||||||||
\(188\) | −320056. | −0.660437 | ||||||||
\(189\) | 264585. | 0.538779 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 620980. | 1.23167 | 0.615835 | − | 0.787875i | \(-0.288819\pi\) | ||||
0.615835 | + | 0.787875i | \(0.288819\pi\) | |||||||
\(192\) | −1.38152e6 | −2.70461 | ||||||||
\(193\) | 725314. | 1.40163 | 0.700814 | − | 0.713344i | \(-0.252820\pi\) | ||||
0.700814 | + | 0.713344i | \(0.252820\pi\) | |||||||
\(194\) | 241154. | 0.460035 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −619568. | −1.15199 | ||||||||
\(197\) | −273782. | −0.502619 | −0.251310 | − | 0.967907i | \(-0.580861\pi\) | ||||
−0.251310 | + | 0.967907i | \(0.580861\pi\) | |||||||
\(198\) | 684873. | 1.24150 | ||||||||
\(199\) | −314223. | −0.562477 | −0.281239 | − | 0.959638i | \(-0.590745\pi\) | ||||
−0.281239 | + | 0.959638i | \(0.590745\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.06409e6 | −1.85775 | ||||||||
\(202\) | −755785. | −1.30323 | ||||||||
\(203\) | 682425. | 1.16229 | ||||||||
\(204\) | 1.99967e6 | 3.36421 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −392156. | −0.643859 | ||||||||
\(207\) | −296018. | −0.480167 | ||||||||
\(208\) | −1.08873e6 | −1.74487 | ||||||||
\(209\) | −505588. | −0.800628 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −540561. | −0.835869 | −0.417935 | − | 0.908477i | \(-0.637246\pi\) | ||||
−0.417935 | + | 0.908477i | \(0.637246\pi\) | |||||||
\(212\) | −535359. | −0.818099 | ||||||||
\(213\) | 430676. | 0.650432 | ||||||||
\(214\) | −518066. | −0.773305 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.48639e6 | −2.16769 | ||||||||
\(217\) | −365846. | −0.527411 | ||||||||
\(218\) | 812566. | 1.15802 | ||||||||
\(219\) | 828864. | 1.16781 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 454712. | 0.626261 | ||||||||
\(222\) | 2.49076e6 | 3.39196 | ||||||||
\(223\) | 231856. | 0.312216 | 0.156108 | − | 0.987740i | \(-0.450105\pi\) | ||||
0.156108 | + | 0.987740i | \(0.450105\pi\) | |||||||
\(224\) | −1.58961e6 | −2.11675 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.27141e6 | −2.95818 | ||||||||
\(227\) | 1.39293e6 | 1.79418 | 0.897090 | − | 0.441848i | \(-0.145677\pi\) | ||||
0.897090 | + | 0.441848i | \(0.145677\pi\) | |||||||
\(228\) | −1.12011e6 | −1.42700 | ||||||||
\(229\) | −565105. | −0.712099 | −0.356050 | − | 0.934467i | \(-0.615877\pi\) | ||||
−0.356050 | + | 0.934467i | \(0.615877\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.21081e6 | 1.49295 | ||||||||
\(232\) | −3.83374e6 | −4.67630 | ||||||||
\(233\) | −237550. | −0.286658 | −0.143329 | − | 0.989675i | \(-0.545781\pi\) | ||||
−0.143329 | + | 0.989675i | \(0.545781\pi\) | |||||||
\(234\) | 345026. | 0.411920 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.87125e6 | 3.35576 | ||||||||
\(237\) | −328284. | −0.379645 | ||||||||
\(238\) | 1.36279e6 | 1.55951 | ||||||||
\(239\) | 1.31472e6 | 1.48881 | 0.744403 | − | 0.667731i | \(-0.232734\pi\) | ||||
0.744403 | + | 0.667731i | \(0.232734\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.03644e6 | 1.14948 | 0.574739 | − | 0.818337i | \(-0.305104\pi\) | ||||
0.574739 | + | 0.818337i | \(0.305104\pi\) | |||||||
\(242\) | −3.28675e6 | −3.60768 | ||||||||
\(243\) | 673222. | 0.731379 | ||||||||
\(244\) | 2.18567e6 | 2.35023 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.13730e6 | −2.25179 | ||||||||
\(247\) | −254706. | −0.265642 | ||||||||
\(248\) | 2.05526e6 | 2.12196 | ||||||||
\(249\) | 730079. | 0.746227 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.67030e6 | −1.67344 | −0.836720 | − | 0.547632i | \(-0.815530\pi\) | ||||
−0.836720 | + | 0.547632i | \(0.815530\pi\) | |||||||
\(252\) | 745381. | 0.739396 | ||||||||
\(253\) | 2.16587e6 | 2.12732 | ||||||||
\(254\) | −798132. | −0.776230 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 577949. | 0.551175 | ||||||||
\(257\) | −311852. | −0.294521 | −0.147261 | − | 0.989098i | \(-0.547046\pi\) | ||||
−0.147261 | + | 0.989098i | \(0.547046\pi\) | |||||||
\(258\) | −363138. | −0.339643 | ||||||||
\(259\) | 1.22359e6 | 1.13341 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 661369. | 0.600956 | ||||||||
\(262\) | 617666. | 0.555905 | ||||||||
\(263\) | 341600. | 0.304529 | 0.152264 | − | 0.988340i | \(-0.451343\pi\) | ||||
0.152264 | + | 0.988340i | \(0.451343\pi\) | |||||||
\(264\) | −6.80210e6 | −6.00667 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −763365. | −0.661498 | ||||||||
\(267\) | 565034. | 0.485061 | ||||||||
\(268\) | 4.79286e6 | 4.07622 | ||||||||
\(269\) | 865544. | 0.729304 | 0.364652 | − | 0.931144i | \(-0.381188\pi\) | ||||
0.364652 | + | 0.931144i | \(0.381188\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.49244e6 | 1.23445 | 0.617226 | − | 0.786786i | \(-0.288256\pi\) | ||||
0.617226 | + | 0.786786i | \(0.288256\pi\) | |||||||
\(272\) | −4.16762e6 | −3.41559 | ||||||||
\(273\) | 609984. | 0.495350 | ||||||||
\(274\) | −253461. | −0.203955 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.79841e6 | 3.79162 | ||||||||
\(277\) | 395961. | 0.310065 | 0.155033 | − | 0.987909i | \(-0.450452\pi\) | ||||
0.155033 | + | 0.987909i | \(0.450452\pi\) | |||||||
\(278\) | −2.51595e6 | −1.95249 | ||||||||
\(279\) | −354558. | −0.272695 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.19634e6 | 1.65934 | 0.829668 | − | 0.558257i | \(-0.188530\pi\) | ||||
0.829668 | + | 0.558257i | \(0.188530\pi\) | |||||||
\(282\) | −760761. | −0.569673 | ||||||||
\(283\) | −562659. | −0.417618 | −0.208809 | − | 0.977956i | \(-0.566959\pi\) | ||||
−0.208809 | + | 0.977956i | \(0.566959\pi\) | |||||||
\(284\) | −1.93985e6 | −1.42716 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.52445e6 | −1.82496 | ||||||||
\(287\) | −1.04995e6 | −0.752427 | ||||||||
\(288\) | −1.54056e6 | −1.09445 | ||||||||
\(289\) | 320758. | 0.225909 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 413190. | 0.286034 | ||||||||
\(292\) | −3.73337e6 | −2.56238 | ||||||||
\(293\) | −2.24866e6 | −1.53022 | −0.765111 | − | 0.643898i | \(-0.777316\pi\) | ||||
−0.765111 | + | 0.643898i | \(0.777316\pi\) | |||||||
\(294\) | −1.47269e6 | −0.993672 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.87391e6 | −4.56010 | ||||||||
\(297\) | −1.87615e6 | −1.23418 | ||||||||
\(298\) | −2.53376e6 | −1.65282 | ||||||||
\(299\) | 1.09113e6 | 0.705826 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −178392. | −0.113490 | ||||||||
\(302\) | 1.14399e6 | 0.721778 | ||||||||
\(303\) | −1.29495e6 | −0.810301 | ||||||||
\(304\) | 2.33448e6 | 1.44879 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.32074e6 | 0.806335 | ||||||||
\(307\) | −2.14795e6 | −1.30070 | −0.650352 | − | 0.759633i | \(-0.725379\pi\) | ||||
−0.650352 | + | 0.759633i | \(0.725379\pi\) | |||||||
\(308\) | −5.45373e6 | −3.27580 | ||||||||
\(309\) | −671914. | −0.400329 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.61384e6 | −1.53242 | −0.766210 | − | 0.642590i | \(-0.777860\pi\) | ||||
−0.766210 | + | 0.642590i | \(0.777860\pi\) | |||||||
\(312\) | −3.42677e6 | −1.99296 | ||||||||
\(313\) | −968697. | −0.558891 | −0.279445 | − | 0.960162i | \(-0.590151\pi\) | ||||
−0.279445 | + | 0.960162i | \(0.590151\pi\) | |||||||
\(314\) | 3.38329e6 | 1.93649 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.47865e6 | 0.833007 | ||||||||
\(317\) | −289378. | −0.161740 | −0.0808700 | − | 0.996725i | \(-0.525770\pi\) | ||||
−0.0808700 | + | 0.996725i | \(0.525770\pi\) | |||||||
\(318\) | −1.27253e6 | −0.705667 | ||||||||
\(319\) | −4.83904e6 | −2.66246 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −887647. | −0.480815 | ||||||||
\(322\) | 3.27016e6 | 1.75764 | ||||||||
\(323\) | −975001. | −0.519995 | ||||||||
\(324\) | −6.03390e6 | −3.19327 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.00994e6 | −2.61089 | ||||||||
\(327\) | 1.39224e6 | 0.720019 | ||||||||
\(328\) | 5.89843e6 | 3.02727 | ||||||||
\(329\) | −373725. | −0.190354 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.74453e6 | 1.37689 | 0.688443 | − | 0.725291i | \(-0.258295\pi\) | ||||
0.688443 | + | 0.725291i | \(0.258295\pi\) | |||||||
\(332\) | −3.28842e6 | −1.63735 | ||||||||
\(333\) | 1.18584e6 | 0.586024 | ||||||||
\(334\) | 3.52391e6 | 1.72846 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.59075e6 | −2.70161 | ||||||||
\(337\) | 1.03816e6 | 0.497956 | 0.248978 | − | 0.968509i | \(-0.419905\pi\) | ||||
0.248978 | + | 0.968509i | \(0.419905\pi\) | |||||||
\(338\) | 2.70341e6 | 1.28712 | ||||||||
\(339\) | −3.89180e6 | −1.83929 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.59420e6 | 1.20814 | ||||||||
\(342\) | −739812. | −0.342023 | ||||||||
\(343\) | −2.34501e6 | −1.07624 | ||||||||
\(344\) | 1.00217e6 | 0.456611 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.11843e6 | 0.951312 | ||||||||
\(347\) | 1.87377e6 | 0.835396 | 0.417698 | − | 0.908586i | \(-0.362837\pi\) | ||||
0.417698 | + | 0.908586i | \(0.362837\pi\) | |||||||
\(348\) | −1.07207e7 | −4.74542 | ||||||||
\(349\) | 46712.6 | 0.0205291 | 0.0102646 | − | 0.999947i | \(-0.496733\pi\) | ||||
0.0102646 | + | 0.999947i | \(0.496733\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −945172. | −0.409490 | ||||||||
\(352\) | 1.12718e7 | 4.84883 | ||||||||
\(353\) | −643022. | −0.274656 | −0.137328 | − | 0.990526i | \(-0.543851\pi\) | ||||
−0.137328 | + | 0.990526i | \(0.543851\pi\) | |||||||
\(354\) | 6.82486e6 | 2.89458 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.54502e6 | −1.06431 | ||||||||
\(357\) | 2.33499e6 | 0.969649 | ||||||||
\(358\) | −761328. | −0.313953 | ||||||||
\(359\) | 361451. | 0.148017 | 0.0740087 | − | 0.997258i | \(-0.476421\pi\) | ||||
0.0740087 | + | 0.997258i | \(0.476421\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.92995e6 | −0.779434 | ||||||||
\(362\) | −1.18903e6 | −0.476894 | ||||||||
\(363\) | −5.63146e6 | −2.24313 | ||||||||
\(364\) | −2.74749e6 | −1.08688 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.19526e6 | 2.02724 | ||||||||
\(367\) | 1.12671e6 | 0.436663 | 0.218332 | − | 0.975875i | \(-0.429939\pi\) | ||||
0.218332 | + | 0.975875i | \(0.429939\pi\) | |||||||
\(368\) | −1.00006e7 | −3.84953 | ||||||||
\(369\) | −1.01756e6 | −0.389038 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −625132. | −0.235796 | ||||||||
\(372\) | 5.74734e6 | 2.15332 | ||||||||
\(373\) | 1.98041e6 | 0.737027 | 0.368514 | − | 0.929622i | \(-0.379867\pi\) | ||||
0.368514 | + | 0.929622i | \(0.379867\pi\) | |||||||
\(374\) | −9.66349e6 | −3.57236 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.09952e6 | 0.765861 | ||||||||
\(377\) | −2.43782e6 | −0.883380 | ||||||||
\(378\) | −2.83273e6 | −1.01971 | ||||||||
\(379\) | −870212. | −0.311191 | −0.155596 | − | 0.987821i | \(-0.549730\pi\) | ||||
−0.155596 | + | 0.987821i | \(0.549730\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.36751e6 | −0.482633 | ||||||||
\(382\) | −6.64841e6 | −2.33109 | ||||||||
\(383\) | 2.78192e6 | 0.969055 | 0.484527 | − | 0.874776i | \(-0.338992\pi\) | ||||
0.484527 | + | 0.874776i | \(0.338992\pi\) | |||||||
\(384\) | 5.11947e6 | 1.77173 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.76544e6 | −2.65276 | ||||||||
\(387\) | −172888. | −0.0586796 | ||||||||
\(388\) | −1.86109e6 | −0.627607 | ||||||||
\(389\) | 5.01979e6 | 1.68195 | 0.840973 | − | 0.541077i | \(-0.181983\pi\) | ||||
0.840973 | + | 0.541077i | \(0.181983\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.17678e6 | 1.38166 | ||||||||
\(392\) | 4.06427e6 | 1.33588 | ||||||||
\(393\) | 1.05830e6 | 0.345643 | ||||||||
\(394\) | 2.93119e6 | 0.951270 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.28545e6 | −1.69373 | ||||||||
\(397\) | 3.26819e6 | 1.04071 | 0.520357 | − | 0.853949i | \(-0.325799\pi\) | ||||
0.520357 | + | 0.853949i | \(0.325799\pi\) | |||||||
\(398\) | 3.36417e6 | 1.06456 | ||||||||
\(399\) | −1.30794e6 | −0.411297 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.63270e6 | 1.12815 | 0.564077 | − | 0.825722i | \(-0.309232\pi\) | ||||
0.564077 | + | 0.825722i | \(0.309232\pi\) | |||||||
\(402\) | 1.13924e7 | 3.51603 | ||||||||
\(403\) | 1.30691e6 | 0.400850 | ||||||||
\(404\) | 5.83271e6 | 1.77794 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.30626e6 | −2.19978 | ||||||||
\(407\) | −8.67643e6 | −2.59630 | ||||||||
\(408\) | −1.31175e7 | −3.90123 | ||||||||
\(409\) | −4.93318e6 | −1.45821 | −0.729103 | − | 0.684404i | \(-0.760063\pi\) | ||||
−0.729103 | + | 0.684404i | \(0.760063\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −434276. | −0.126812 | ||||||||
\(412\) | 3.02643e6 | 0.878391 | ||||||||
\(413\) | 3.35272e6 | 0.967214 | ||||||||
\(414\) | 3.16926e6 | 0.908777 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.67852e6 | 1.60880 | ||||||||
\(417\) | −4.31078e6 | −1.21399 | ||||||||
\(418\) | 5.41298e6 | 1.51529 | ||||||||
\(419\) | 412864. | 0.114887 | 0.0574437 | − | 0.998349i | \(-0.481705\pi\) | ||||
0.0574437 | + | 0.998349i | \(0.481705\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.27168e6 | −0.624656 | −0.312328 | − | 0.949974i | \(-0.601109\pi\) | ||||
−0.312328 | + | 0.949974i | \(0.601109\pi\) | |||||||
\(422\) | 5.78741e6 | 1.58199 | ||||||||
\(423\) | −362194. | −0.0984216 | ||||||||
\(424\) | 3.51188e6 | 0.948690 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.61095e6 | −1.23102 | ||||||||
\(427\) | 2.55218e6 | 0.677395 | ||||||||
\(428\) | 3.99814e6 | 1.05499 | ||||||||
\(429\) | −4.32536e6 | −1.13469 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.37855e6 | −0.357461 | −0.178731 | − | 0.983898i | \(-0.557199\pi\) | ||||
−0.178731 | + | 0.983898i | \(0.557199\pi\) | |||||||
\(432\) | 8.66288e6 | 2.23333 | ||||||||
\(433\) | 4.50720e6 | 1.15528 | 0.577639 | − | 0.816292i | \(-0.303974\pi\) | ||||
0.577639 | + | 0.816292i | \(0.303974\pi\) | |||||||
\(434\) | 3.91687e6 | 0.998193 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.27091e6 | −1.57985 | ||||||||
\(437\) | −2.33961e6 | −0.586058 | ||||||||
\(438\) | −8.87408e6 | −2.21023 | ||||||||
\(439\) | −1.97588e6 | −0.489327 | −0.244663 | − | 0.969608i | \(-0.578677\pi\) | ||||
−0.244663 | + | 0.969608i | \(0.578677\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −701140. | −0.171675 | ||||||||
\(442\) | −4.86829e6 | −1.18528 | ||||||||
\(443\) | 2.75707e6 | 0.667481 | 0.333740 | − | 0.942665i | \(-0.391689\pi\) | ||||
0.333740 | + | 0.942665i | \(0.391689\pi\) | |||||||
\(444\) | −1.92223e7 | −4.62751 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.48232e6 | −0.590909 | ||||||||
\(447\) | −4.34130e6 | −1.02766 | ||||||||
\(448\) | 7.26611e6 | 1.71044 | ||||||||
\(449\) | 5.19837e6 | 1.21689 | 0.608445 | − | 0.793596i | \(-0.291794\pi\) | ||||
0.608445 | + | 0.793596i | \(0.291794\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.44515e6 | 1.72358 | ||||||||
\(452\) | 1.75294e7 | 4.03572 | ||||||||
\(453\) | 1.96009e6 | 0.448777 | ||||||||
\(454\) | −1.49132e7 | −3.39571 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.34775e6 | 1.65479 | ||||||||
\(457\) | −7.85140e6 | −1.75856 | −0.879279 | − | 0.476307i | \(-0.841975\pi\) | ||||
−0.879279 | + | 0.476307i | \(0.841975\pi\) | |||||||
\(458\) | 6.05019e6 | 1.34774 | ||||||||
\(459\) | −3.61807e6 | −0.801578 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 528436. | 0.115808 | 0.0579042 | − | 0.998322i | \(-0.481558\pi\) | ||||
0.0579042 | + | 0.998322i | \(0.481558\pi\) | |||||||
\(462\) | −1.29633e7 | −2.82560 | ||||||||
\(463\) | −825321. | −0.178925 | −0.0894624 | − | 0.995990i | \(-0.528515\pi\) | ||||
−0.0894624 | + | 0.995990i | \(0.528515\pi\) | |||||||
\(464\) | 2.23436e7 | 4.81790 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.54328e6 | 0.542537 | ||||||||
\(467\) | −4.03618e6 | −0.856404 | −0.428202 | − | 0.903683i | \(-0.640853\pi\) | ||||
−0.428202 | + | 0.903683i | \(0.640853\pi\) | |||||||
\(468\) | −2.66271e6 | −0.561966 | ||||||||
\(469\) | 5.59656e6 | 1.17487 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.79688e6 | 1.20404 | ||||||||
\(472\) | −1.88350e7 | −3.89144 | ||||||||
\(473\) | 1.26497e6 | 0.259972 | ||||||||
\(474\) | 3.51471e6 | 0.718527 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.05173e7 | −2.12758 | ||||||||
\(477\) | −605844. | −0.121917 | ||||||||
\(478\) | −1.40758e7 | −2.81775 | ||||||||
\(479\) | −6.39933e6 | −1.27437 | −0.637186 | − | 0.770710i | \(-0.719902\pi\) | ||||
−0.637186 | + | 0.770710i | \(0.719902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.37102e6 | −0.861431 | ||||||||
\(482\) | −1.10964e7 | −2.17553 | ||||||||
\(483\) | 5.60305e6 | 1.09284 | ||||||||
\(484\) | 2.53652e7 | 4.92181 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7.20772e6 | −1.38423 | ||||||||
\(487\) | −4.00561e6 | −0.765326 | −0.382663 | − | 0.923888i | \(-0.624993\pi\) | ||||
−0.382663 | + | 0.923888i | \(0.624993\pi\) | |||||||
\(488\) | −1.43377e7 | −2.72539 | ||||||||
\(489\) | −8.58395e6 | −1.62336 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.31835e6 | −0.995573 | −0.497786 | − | 0.867300i | \(-0.665854\pi\) | ||||
−0.497786 | + | 0.867300i | \(0.665854\pi\) | |||||||
\(492\) | 1.64944e7 | 3.07202 | ||||||||
\(493\) | −9.33185e6 | −1.72922 | ||||||||
\(494\) | 2.72696e6 | 0.502760 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.19783e7 | −2.18621 | ||||||||
\(497\) | −2.26514e6 | −0.411343 | ||||||||
\(498\) | −7.81645e6 | −1.41233 | ||||||||
\(499\) | 172551. | 0.0310217 | 0.0155108 | − | 0.999880i | \(-0.495063\pi\) | ||||
0.0155108 | + | 0.999880i | \(0.495063\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.03781e6 | 1.07470 | ||||||||
\(502\) | 1.78827e7 | 3.16719 | ||||||||
\(503\) | −1.54456e6 | −0.272198 | −0.136099 | − | 0.990695i | \(-0.543457\pi\) | ||||
−0.136099 | + | 0.990695i | \(0.543457\pi\) | |||||||
\(504\) | −4.88959e6 | −0.857425 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.31885e7 | −4.02621 | ||||||||
\(507\) | 4.63197e6 | 0.800288 | ||||||||
\(508\) | 6.15952e6 | 1.05898 | ||||||||
\(509\) | 3.51269e6 | 0.600960 | 0.300480 | − | 0.953788i | \(-0.402853\pi\) | ||||
0.300480 | + | 0.953788i | \(0.402853\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.35941e6 | −0.738542 | ||||||||
\(512\) | 2.74289e6 | 0.462416 | ||||||||
\(513\) | 2.02665e6 | 0.340006 | ||||||||
\(514\) | 3.33879e6 | 0.557418 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.80249e6 | 0.463361 | ||||||||
\(517\) | 2.65007e6 | 0.436044 | ||||||||
\(518\) | −1.31002e7 | −2.14512 | ||||||||
\(519\) | 3.62968e6 | 0.591493 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.33669e6 | −0.215743 | −0.107871 | − | 0.994165i | \(-0.534403\pi\) | ||||
−0.107871 | + | 0.994165i | \(0.534403\pi\) | |||||||
\(522\) | −7.08082e6 | −1.13739 | ||||||||
\(523\) | 1.35607e6 | 0.216784 | 0.108392 | − | 0.994108i | \(-0.465430\pi\) | ||||
0.108392 | + | 0.994108i | \(0.465430\pi\) | |||||||
\(524\) | −4.76679e6 | −0.758399 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.65728e6 | −0.576359 | ||||||||
\(527\) | 5.00278e6 | 0.784666 | ||||||||
\(528\) | 3.96437e7 | 6.18855 | ||||||||
\(529\) | 3.58627e6 | 0.557191 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.24928e6 | 0.500092 | ||||||||
\(532\) | 5.89121e6 | 0.902455 | ||||||||
\(533\) | 3.75073e6 | 0.571870 | ||||||||
\(534\) | −6.04943e6 | −0.918039 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.14404e7 | −4.72690 | ||||||||
\(537\) | −1.30445e6 | −0.195205 | ||||||||
\(538\) | −9.26678e6 | −1.38030 | ||||||||
\(539\) | 5.13003e6 | 0.760585 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.28068e6 | 0.188125 | 0.0940625 | − | 0.995566i | \(-0.470015\pi\) | ||||
0.0940625 | + | 0.995566i | \(0.470015\pi\) | |||||||
\(542\) | −1.59785e7 | −2.33636 | ||||||||
\(543\) | −2.03727e6 | −0.296516 | ||||||||
\(544\) | 2.17371e7 | 3.14923 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.53068e6 | −0.937512 | ||||||||
\(547\) | −1.13222e7 | −1.61793 | −0.808967 | − | 0.587854i | \(-0.799973\pi\) | ||||
−0.808967 | + | 0.587854i | \(0.799973\pi\) | |||||||
\(548\) | 1.95606e6 | 0.278248 | ||||||||
\(549\) | 2.47343e6 | 0.350243 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.22721e6 | 0.733485 | ||||||||
\(552\) | −3.14768e7 | −4.39687 | ||||||||
\(553\) | 1.72661e6 | 0.240093 | ||||||||
\(554\) | −4.23928e6 | −0.586838 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.94166e7 | 2.66371 | ||||||||
\(557\) | 1.13494e7 | 1.55002 | 0.775008 | − | 0.631952i | \(-0.217746\pi\) | ||||
0.775008 | + | 0.631952i | \(0.217746\pi\) | |||||||
\(558\) | 3.79601e6 | 0.516110 | ||||||||
\(559\) | 637267. | 0.0862566 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.65573e7 | −2.22117 | ||||||||
\(562\) | −2.35147e7 | −3.14050 | ||||||||
\(563\) | 8.01199e6 | 1.06529 | 0.532647 | − | 0.846338i | \(-0.321198\pi\) | ||||
0.532647 | + | 0.846338i | \(0.321198\pi\) | |||||||
\(564\) | 5.87112e6 | 0.777182 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.02401e6 | 0.790395 | ||||||||
\(567\) | −7.04571e6 | −0.920380 | ||||||||
\(568\) | 1.27251e7 | 1.65497 | ||||||||
\(569\) | −6.18179e6 | −0.800448 | −0.400224 | − | 0.916417i | \(-0.631068\pi\) | ||||
−0.400224 | + | 0.916417i | \(0.631068\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.84960e6 | 0.622466 | 0.311233 | − | 0.950334i | \(-0.399258\pi\) | ||||
0.311233 | + | 0.950334i | \(0.399258\pi\) | |||||||
\(572\) | 1.94823e7 | 2.48971 | ||||||||
\(573\) | −1.13913e7 | −1.44939 | ||||||||
\(574\) | 1.12411e7 | 1.42406 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.04191e6 | 0.884371 | ||||||||
\(577\) | 1.20012e6 | 0.150067 | 0.0750335 | − | 0.997181i | \(-0.476094\pi\) | ||||
0.0750335 | + | 0.997181i | \(0.476094\pi\) | |||||||
\(578\) | −3.43414e6 | −0.427561 | ||||||||
\(579\) | −1.33052e7 | −1.64939 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.83984e6 | −0.471925 | ||||||||
\(582\) | −4.42374e6 | −0.541355 | ||||||||
\(583\) | 4.43278e6 | 0.540138 | ||||||||
\(584\) | 2.44903e7 | 2.97141 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.40748e7 | 2.89614 | ||||||||
\(587\) | −2.03492e6 | −0.243754 | −0.121877 | − | 0.992545i | \(-0.538891\pi\) | ||||
−0.121877 | + | 0.992545i | \(0.538891\pi\) | |||||||
\(588\) | 1.13654e7 | 1.35563 | ||||||||
\(589\) | −2.80229e6 | −0.332832 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.02226e6 | 0.591467 | ||||||||
\(592\) | 4.00622e7 | 4.69819 | ||||||||
\(593\) | 1.38521e7 | 1.61762 | 0.808812 | − | 0.588067i | \(-0.200111\pi\) | ||||
0.808812 | + | 0.588067i | \(0.200111\pi\) | |||||||
\(594\) | 2.00867e7 | 2.33584 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.95541e7 | 2.25487 | ||||||||
\(597\) | 5.76411e6 | 0.661906 | ||||||||
\(598\) | −1.16819e7 | −1.33586 | ||||||||
\(599\) | −1.64523e7 | −1.87352 | −0.936760 | − | 0.349972i | \(-0.886191\pi\) | ||||
−0.936760 | + | 0.349972i | \(0.886191\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.48314e7 | 1.67493 | 0.837465 | − | 0.546491i | \(-0.184037\pi\) | ||||
0.837465 | + | 0.546491i | \(0.184037\pi\) | |||||||
\(602\) | 1.90992e6 | 0.214795 | ||||||||
\(603\) | 5.42388e6 | 0.607459 | ||||||||
\(604\) | −8.82862e6 | −0.984692 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.38641e7 | 1.53360 | ||||||||
\(607\) | 1.64197e7 | 1.80881 | 0.904404 | − | 0.426677i | \(-0.140316\pi\) | ||||
0.904404 | + | 0.426677i | \(0.140316\pi\) | |||||||
\(608\) | −1.21760e7 | −1.33581 | ||||||||
\(609\) | −1.25184e7 | −1.36775 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.33505e6 | 0.144676 | ||||||||
\(612\) | −1.01927e7 | −1.10005 | ||||||||
\(613\) | −8.77423e6 | −0.943100 | −0.471550 | − | 0.881839i | \(-0.656305\pi\) | ||||
−0.471550 | + | 0.881839i | \(0.656305\pi\) | |||||||
\(614\) | 2.29966e7 | 2.46175 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.57756e7 | 3.79871 | ||||||||
\(617\) | −1.23910e7 | −1.31037 | −0.655183 | − | 0.755470i | \(-0.727409\pi\) | ||||
−0.655183 | + | 0.755470i | \(0.727409\pi\) | |||||||
\(618\) | 7.19372e6 | 0.757674 | ||||||||
\(619\) | −1.58048e6 | −0.165791 | −0.0828957 | − | 0.996558i | \(-0.526417\pi\) | ||||
−0.0828957 | + | 0.996558i | \(0.526417\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.68193e6 | −0.903415 | ||||||||
\(622\) | 2.79846e7 | 2.90030 | ||||||||
\(623\) | −2.97179e6 | −0.306760 | ||||||||
\(624\) | 1.99718e7 | 2.05331 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.03712e7 | 1.05777 | ||||||||
\(627\) | 9.27451e6 | 0.942155 | ||||||||
\(628\) | −2.61103e7 | −2.64188 | ||||||||
\(629\) | −1.67321e7 | −1.68625 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.95881e6 | −0.395814 | −0.197907 | − | 0.980221i | \(-0.563414\pi\) | ||||
−0.197907 | + | 0.980221i | \(0.563414\pi\) | |||||||
\(632\) | −9.69974e6 | −0.965979 | ||||||||
\(633\) | 9.91606e6 | 0.983626 | ||||||||
\(634\) | 3.09817e6 | 0.306113 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.82065e6 | 0.962714 | ||||||||
\(637\) | 2.58441e6 | 0.252356 | ||||||||
\(638\) | 5.18082e7 | 5.03903 | ||||||||
\(639\) | −2.19525e6 | −0.212682 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.19225e6 | 0.787514 | 0.393757 | − | 0.919215i | \(-0.371175\pi\) | ||||
0.393757 | + | 0.919215i | \(0.371175\pi\) | |||||||
\(642\) | 9.50343e6 | 0.910003 | ||||||||
\(643\) | 9.53703e6 | 0.909674 | 0.454837 | − | 0.890575i | \(-0.349697\pi\) | ||||
0.454837 | + | 0.890575i | \(0.349697\pi\) | |||||||
\(644\) | −2.52372e7 | −2.39788 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.04387e7 | 0.984155 | ||||||||
\(647\) | 1.17034e7 | 1.09913 | 0.549566 | − | 0.835450i | \(-0.314793\pi\) | ||||
0.549566 | + | 0.835450i | \(0.314793\pi\) | |||||||
\(648\) | 3.95815e7 | 3.70301 | ||||||||
\(649\) | −2.37740e7 | −2.21559 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.71110e6 | 0.620642 | ||||||||
\(652\) | 3.86638e7 | 3.56193 | ||||||||
\(653\) | −9.87401e6 | −0.906172 | −0.453086 | − | 0.891467i | \(-0.649677\pi\) | ||||
−0.453086 | + | 0.891467i | \(0.649677\pi\) | |||||||
\(654\) | −1.49057e7 | −1.36273 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.43769e7 | −3.11894 | ||||||||
\(657\) | −4.22490e6 | −0.381859 | ||||||||
\(658\) | 4.00122e6 | 0.360270 | ||||||||
\(659\) | 1.87688e7 | 1.68354 | 0.841770 | − | 0.539836i | \(-0.181514\pi\) | ||||
0.841770 | + | 0.539836i | \(0.181514\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.84811e6 | 0.164522 | 0.0822612 | − | 0.996611i | \(-0.473786\pi\) | ||||
0.0822612 | + | 0.996611i | \(0.473786\pi\) | |||||||
\(662\) | −2.93838e7 | −2.60593 | ||||||||
\(663\) | −8.34125e6 | −0.736966 | ||||||||
\(664\) | 2.15715e7 | 1.89872 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.26960e7 | −1.10912 | ||||||||
\(667\) | −2.23927e7 | −1.94891 | ||||||||
\(668\) | −2.71955e7 | −2.35806 | ||||||||
\(669\) | −4.25317e6 | −0.367407 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.80974e7 | −1.55171 | ||||||||
\(672\) | 2.91598e7 | 2.49093 | ||||||||
\(673\) | 3.40289e6 | 0.289608 | 0.144804 | − | 0.989460i | \(-0.453745\pi\) | ||||
0.144804 | + | 0.989460i | \(0.453745\pi\) | |||||||
\(674\) | −1.11149e7 | −0.942445 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.08633e7 | −1.75597 | ||||||||
\(677\) | −2.23309e7 | −1.87255 | −0.936276 | − | 0.351266i | \(-0.885751\pi\) | ||||
−0.936276 | + | 0.351266i | \(0.885751\pi\) | |||||||
\(678\) | 4.16668e7 | 3.48109 | ||||||||
\(679\) | −2.17317e6 | −0.180892 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.55520e7 | −2.11134 | ||||||||
\(682\) | −2.77743e7 | −2.28655 | ||||||||
\(683\) | −7.78181e6 | −0.638306 | −0.319153 | − | 0.947703i | \(-0.603398\pi\) | ||||
−0.319153 | + | 0.947703i | \(0.603398\pi\) | |||||||
\(684\) | 5.70944e6 | 0.466609 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.51064e7 | 2.03692 | ||||||||
\(687\) | 1.03663e7 | 0.837977 | ||||||||
\(688\) | −5.84082e6 | −0.470438 | ||||||||
\(689\) | 2.23315e6 | 0.179213 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.39450e7 | 1.90775 | 0.953873 | − | 0.300211i | \(-0.0970570\pi\) | ||||
0.953873 | + | 0.300211i | \(0.0970570\pi\) | |||||||
\(692\) | −1.63488e7 | −1.29784 | ||||||||
\(693\) | −6.17176e6 | −0.488176 | ||||||||
\(694\) | −2.00612e7 | −1.58109 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.03262e7 | 5.50293 | ||||||||
\(697\) | 1.43576e7 | 1.11944 | ||||||||
\(698\) | −500120. | −0.0388540 | ||||||||
\(699\) | 4.35762e6 | 0.337331 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.24393e6 | −0.479914 | −0.239957 | − | 0.970784i | \(-0.577133\pi\) | ||||
−0.239957 | + | 0.970784i | \(0.577133\pi\) | |||||||
\(702\) | 1.01193e7 | 0.775011 | ||||||||
\(703\) | 9.37242e6 | 0.715259 | ||||||||
\(704\) | −5.15235e7 | −3.91809 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.88439e6 | 0.519821 | ||||||||
\(707\) | 6.81079e6 | 0.512447 | ||||||||
\(708\) | −5.26703e7 | −3.94896 | ||||||||
\(709\) | −9.29599e6 | −0.694513 | −0.347256 | − | 0.937770i | \(-0.612887\pi\) | ||||
−0.347256 | + | 0.937770i | \(0.612887\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.67333e6 | 0.124139 | ||||||||
\(712\) | 1.66950e7 | 1.23420 | ||||||||
\(713\) | 1.20047e7 | 0.884355 | ||||||||
\(714\) | −2.49991e7 | −1.83518 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.87549e6 | 0.428313 | ||||||||
\(717\) | −2.41172e7 | −1.75198 | ||||||||
\(718\) | −3.86980e6 | −0.280142 | ||||||||
\(719\) | 1.77934e7 | 1.28362 | 0.641811 | − | 0.766863i | \(-0.278184\pi\) | ||||
0.641811 | + | 0.766863i | \(0.278184\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.53393e6 | 0.253174 | ||||||||
\(722\) | 2.06627e7 | 1.47518 | ||||||||
\(723\) | −1.90124e7 | −1.35267 | ||||||||
\(724\) | 9.17626e6 | 0.650608 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.02922e7 | 4.24541 | ||||||||
\(727\) | 1.60920e7 | 1.12921 | 0.564604 | − | 0.825362i | \(-0.309029\pi\) | ||||
0.564604 | + | 0.825362i | \(0.309029\pi\) | |||||||
\(728\) | 1.80231e7 | 1.26038 | ||||||||
\(729\) | 5.39607e6 | 0.376061 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.43943e6 | 0.168848 | ||||||||
\(732\) | −4.00940e7 | −2.76568 | ||||||||
\(733\) | −2.32899e7 | −1.60106 | −0.800529 | − | 0.599295i | \(-0.795448\pi\) | ||||
−0.800529 | + | 0.599295i | \(0.795448\pi\) | |||||||
\(734\) | −1.20629e7 | −0.826441 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.21604e7 | 3.54933 | ||||||||
\(737\) | −3.96849e7 | −2.69126 | ||||||||
\(738\) | 1.08943e7 | 0.736304 | ||||||||
\(739\) | −1.68335e7 | −1.13387 | −0.566934 | − | 0.823763i | \(-0.691871\pi\) | ||||
−0.566934 | + | 0.823763i | \(0.691871\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.67233e6 | 0.312599 | ||||||||
\(742\) | 6.69286e6 | 0.446275 | ||||||||
\(743\) | −5.88483e6 | −0.391077 | −0.195538 | − | 0.980696i | \(-0.562645\pi\) | ||||
−0.195538 | + | 0.980696i | \(0.562645\pi\) | |||||||
\(744\) | −3.77017e7 | −2.49706 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.12029e7 | −1.39492 | ||||||||
\(747\) | −3.72137e6 | −0.244006 | ||||||||
\(748\) | 7.45772e7 | 4.87363 | ||||||||
\(749\) | 4.66858e6 | 0.304074 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.45954e7 | −1.59131 | −0.795655 | − | 0.605750i | \(-0.792873\pi\) | ||||
−0.795655 | + | 0.605750i | \(0.792873\pi\) | |||||||
\(752\) | −1.22363e7 | −0.789052 | ||||||||
\(753\) | 3.06400e7 | 1.96925 | ||||||||
\(754\) | 2.61000e7 | 1.67191 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.18613e7 | 1.39114 | ||||||||
\(757\) | −1.55533e7 | −0.986467 | −0.493233 | − | 0.869897i | \(-0.664185\pi\) | ||||
−0.493233 | + | 0.869897i | \(0.664185\pi\) | |||||||
\(758\) | 9.31676e6 | 0.588969 | ||||||||
\(759\) | −3.97309e7 | −2.50336 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.20979e7 | −0.757264 | −0.378632 | − | 0.925547i | \(-0.623605\pi\) | ||||
−0.378632 | + | 0.925547i | \(0.623605\pi\) | |||||||
\(762\) | 1.46410e7 | 0.913445 | ||||||||
\(763\) | −7.32247e6 | −0.455351 | ||||||||
\(764\) | 5.13086e7 | 3.18022 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.97841e7 | −1.83406 | ||||||||
\(767\) | −1.19769e7 | −0.735115 | ||||||||
\(768\) | −1.06019e7 | −0.648606 | ||||||||
\(769\) | 6.89705e6 | 0.420579 | 0.210289 | − | 0.977639i | \(-0.432559\pi\) | ||||
0.210289 | + | 0.977639i | \(0.432559\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.72063e6 | 0.346584 | ||||||||
\(772\) | 5.99291e7 | 3.61905 | ||||||||
\(773\) | −2.76899e7 | −1.66676 | −0.833380 | − | 0.552701i | \(-0.813597\pi\) | ||||
−0.833380 | + | 0.552701i | \(0.813597\pi\) | |||||||
\(774\) | 1.85099e6 | 0.111059 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.22085e7 | 0.727791 | ||||||||
\(777\) | −2.24456e7 | −1.33376 | ||||||||
\(778\) | −5.37435e7 | −3.18329 | ||||||||
\(779\) | −8.04237e6 | −0.474833 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.60620e7 | 0.942261 | ||||||||
\(782\) | −4.47179e7 | −2.61496 | ||||||||
\(783\) | 1.93973e7 | 1.13068 | ||||||||
\(784\) | −2.36872e7 | −1.37633 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.13305e7 | −0.654173 | ||||||||
\(787\) | −2.46071e6 | −0.141620 | −0.0708098 | − | 0.997490i | \(-0.522558\pi\) | ||||
−0.0708098 | + | 0.997490i | \(0.522558\pi\) | |||||||
\(788\) | −2.26213e7 | −1.29778 | ||||||||
\(789\) | −6.26632e6 | −0.358360 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.04689e7 | 1.16320 | ||||||||
\(792\) | 3.46718e7 | 1.96410 | ||||||||
\(793\) | −9.11712e6 | −0.514843 | ||||||||
\(794\) | −3.49903e7 | −1.96968 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.59627e7 | −1.45234 | ||||||||
\(797\) | −1.86050e7 | −1.03749 | −0.518746 | − | 0.854928i | \(-0.673601\pi\) | ||||
−0.518746 | + | 0.854928i | \(0.673601\pi\) | |||||||
\(798\) | 1.40032e7 | 0.778431 | ||||||||
\(799\) | 5.11052e6 | 0.283203 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.88010e6 | −0.158608 | ||||||||
\(802\) | −3.88928e7 | −2.13517 | ||||||||
\(803\) | 3.09123e7 | 1.69177 | ||||||||
\(804\) | −8.79203e7 | −4.79677 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.39922e7 | −0.758660 | ||||||||
\(807\) | −1.58776e7 | −0.858223 | ||||||||
\(808\) | −3.82617e7 | −2.06175 | ||||||||
\(809\) | −2.26776e7 | −1.21822 | −0.609110 | − | 0.793085i | \(-0.708473\pi\) | ||||
−0.609110 | + | 0.793085i | \(0.708473\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.84184e7 | −0.983329 | −0.491665 | − | 0.870785i | \(-0.663611\pi\) | ||||
−0.491665 | + | 0.870785i | \(0.663611\pi\) | |||||||
\(812\) | 5.63855e7 | 3.00108 | ||||||||
\(813\) | −2.73774e7 | −1.45267 | ||||||||
\(814\) | 9.28925e7 | 4.91382 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.64509e7 | 4.01936 | ||||||||
\(817\) | −1.36644e6 | −0.0716202 | ||||||||
\(818\) | 5.28162e7 | 2.75984 | ||||||||
\(819\) | −3.10922e6 | −0.161973 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.39401e7 | 0.721783 | 0.360891 | − | 0.932608i | \(-0.382472\pi\) | ||||
0.360891 | + | 0.932608i | \(0.382472\pi\) | |||||||
\(822\) | 4.64949e6 | 0.240008 | ||||||||
\(823\) | −1.86303e6 | −0.0958781 | −0.0479391 | − | 0.998850i | \(-0.515265\pi\) | ||||
−0.0479391 | + | 0.998850i | \(0.515265\pi\) | |||||||
\(824\) | −1.98529e7 | −1.01861 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.58953e7 | −1.83058 | ||||||||
\(827\) | −1.84625e7 | −0.938698 | −0.469349 | − | 0.883013i | \(-0.655511\pi\) | ||||
−0.469349 | + | 0.883013i | \(0.655511\pi\) | |||||||
\(828\) | −2.44585e7 | −1.23981 | ||||||||
\(829\) | 6.01093e6 | 0.303777 | 0.151889 | − | 0.988398i | \(-0.451464\pi\) | ||||
0.151889 | + | 0.988398i | \(0.451464\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.26353e6 | −0.364876 | ||||||||
\(832\) | −2.59566e7 | −1.29999 | ||||||||
\(833\) | 9.89301e6 | 0.493987 | ||||||||
\(834\) | 4.61526e7 | 2.29763 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.17742e7 | −2.06725 | ||||||||
\(837\) | −1.03989e7 | −0.513065 | ||||||||
\(838\) | −4.42025e6 | −0.217439 | ||||||||
\(839\) | −2.60373e7 | −1.27700 | −0.638500 | − | 0.769622i | \(-0.720445\pi\) | ||||
−0.638500 | + | 0.769622i | \(0.720445\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.95191e7 | 1.43917 | ||||||||
\(842\) | 2.43213e7 | 1.18224 | ||||||||
\(843\) | −4.02898e7 | −1.95266 | ||||||||
\(844\) | −4.46639e7 | −2.15824 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.87776e6 | 0.186275 | ||||||||
\(847\) | 2.96187e7 | 1.41859 | ||||||||
\(848\) | −2.04677e7 | −0.977418 | ||||||||
\(849\) | 1.03214e7 | 0.491441 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.01503e7 | −1.90049 | ||||||||
\(852\) | 3.55847e7 | 1.67944 | ||||||||
\(853\) | −1.81066e7 | −0.852050 | −0.426025 | − | 0.904711i | \(-0.640086\pi\) | ||||
−0.426025 | + | 0.904711i | \(0.640086\pi\) | |||||||
\(854\) | −2.73245e7 | −1.28206 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.62272e7 | −1.22340 | ||||||||
\(857\) | −2.48924e7 | −1.15775 | −0.578874 | − | 0.815417i | \(-0.696508\pi\) | ||||
−0.578874 | + | 0.815417i | \(0.696508\pi\) | |||||||
\(858\) | 4.63087e7 | 2.14755 | ||||||||
\(859\) | −8.53406e6 | −0.394614 | −0.197307 | − | 0.980342i | \(-0.563220\pi\) | ||||
−0.197307 | + | 0.980342i | \(0.563220\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.92603e7 | 0.885434 | ||||||||
\(862\) | 1.47592e7 | 0.676541 | ||||||||
\(863\) | 2.14592e7 | 0.980815 | 0.490407 | − | 0.871493i | \(-0.336848\pi\) | ||||
0.490407 | + | 0.871493i | \(0.336848\pi\) | |||||||
\(864\) | −4.51832e7 | −2.05917 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.82555e7 | −2.18651 | ||||||||
\(867\) | −5.88400e6 | −0.265843 | ||||||||
\(868\) | −3.02281e7 | −1.36179 | ||||||||
\(869\) | −1.22433e7 | −0.549981 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.99925e7 | −0.892939 | ||||||||
\(872\) | 4.11363e7 | 1.83203 | ||||||||
\(873\) | −2.10612e6 | −0.0935292 | ||||||||
\(874\) | 2.50486e7 | 1.10919 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.84850e7 | 3.01533 | ||||||||
\(877\) | −3.45569e7 | −1.51717 | −0.758587 | − | 0.651572i | \(-0.774110\pi\) | ||||
−0.758587 | + | 0.651572i | \(0.774110\pi\) | |||||||
\(878\) | 2.11544e7 | 0.926112 | ||||||||
\(879\) | 4.12495e7 | 1.80072 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 780223. | 0.0338672 | 0.0169336 | − | 0.999857i | \(-0.494610\pi\) | ||||
0.0169336 | + | 0.999857i | \(0.494610\pi\) | |||||||
\(882\) | 7.50662e6 | 0.324917 | ||||||||
\(883\) | 1.51541e7 | 0.654077 | 0.327039 | − | 0.945011i | \(-0.393949\pi\) | ||||
0.327039 | + | 0.945011i | \(0.393949\pi\) | |||||||
\(884\) | 3.75706e7 | 1.61703 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.95181e7 | −1.26329 | ||||||||
\(887\) | 2.42062e7 | 1.03304 | 0.516520 | − | 0.856275i | \(-0.327227\pi\) | ||||
0.516520 | + | 0.856275i | \(0.327227\pi\) | |||||||
\(888\) | 1.26095e8 | 5.36619 | ||||||||
\(889\) | 7.19240e6 | 0.305225 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.99607e7 | 2.10831 | ||||||||
\(892\) | 1.91571e7 | 0.806153 | ||||||||
\(893\) | −2.86265e6 | −0.120127 | ||||||||
\(894\) | 4.64793e7 | 1.94498 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.69258e7 | −1.12047 | ||||||||
\(897\) | −2.00157e7 | −0.830594 | ||||||||
\(898\) | −5.56554e7 | −2.30312 | ||||||||
\(899\) | −2.68211e7 | −1.10682 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.54840e6 | 0.350811 | ||||||||
\(902\) | −7.97101e7 | −3.26210 | ||||||||
\(903\) | 3.27243e6 | 0.133552 | ||||||||
\(904\) | −1.14990e8 | −4.67994 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.09853e7 | −0.849366 | ||||||||
\(907\) | 3.38285e7 | 1.36541 | 0.682706 | − | 0.730693i | \(-0.260803\pi\) | ||||
0.682706 | + | 0.730693i | \(0.260803\pi\) | |||||||
\(908\) | 1.15091e8 | 4.63264 | ||||||||
\(909\) | 6.60064e6 | 0.264958 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.51743e7 | −1.40420 | −0.702101 | − | 0.712077i | \(-0.747755\pi\) | ||||
−0.702101 | + | 0.712077i | \(0.747755\pi\) | |||||||
\(912\) | −4.28238e7 | −1.70490 | ||||||||
\(913\) | 2.72281e7 | 1.08104 | ||||||||
\(914\) | 8.40595e7 | 3.32829 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.66919e7 | −1.83866 | ||||||||
\(917\) | −5.56612e6 | −0.218590 | ||||||||
\(918\) | 3.87362e7 | 1.51709 | ||||||||
\(919\) | 7.15839e6 | 0.279593 | 0.139797 | − | 0.990180i | \(-0.455355\pi\) | ||||
0.139797 | + | 0.990180i | \(0.455355\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.94021e7 | 1.53063 | ||||||||
\(922\) | −5.65760e6 | −0.219182 | ||||||||
\(923\) | 8.09172e6 | 0.312634 | ||||||||
\(924\) | 1.00043e8 | 3.85486 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 8.83615e6 | 0.338638 | ||||||||
\(927\) | 3.42489e6 | 0.130902 | ||||||||
\(928\) | −1.16538e8 | −4.44219 | ||||||||
\(929\) | −4.60865e7 | −1.75200 | −0.876000 | − | 0.482311i | \(-0.839798\pi\) | ||||
−0.876000 | + | 0.482311i | \(0.839798\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.54154e6 | −0.209535 | ||||||||
\(932\) | −1.96276e7 | −0.740162 | ||||||||
\(933\) | 4.79484e7 | 1.80331 | ||||||||
\(934\) | 4.32126e7 | 1.62085 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.74670e7 | 0.651671 | ||||||||
\(937\) | −2.18537e7 | −0.813160 | −0.406580 | − | 0.913615i | \(-0.633279\pi\) | ||||
−0.406580 | + | 0.913615i | \(0.633279\pi\) | |||||||
\(938\) | −5.99185e7 | −2.22359 | ||||||||
\(939\) | 1.77698e7 | 0.657686 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.41230e7 | −0.519941 | −0.259970 | − | 0.965617i | \(-0.583713\pi\) | ||||
−0.259970 | + | 0.965617i | \(0.583713\pi\) | |||||||
\(942\) | −6.20632e7 | −2.27880 | ||||||||
\(943\) | 3.44525e7 | 1.26166 | ||||||||
\(944\) | 1.09773e8 | 4.00927 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.35431e7 | −0.492030 | ||||||||
\(947\) | 1.31237e6 | 0.0475535 | 0.0237768 | − | 0.999717i | \(-0.492431\pi\) | ||||
0.0237768 | + | 0.999717i | \(0.492431\pi\) | |||||||
\(948\) | −2.71245e7 | −0.980258 | ||||||||
\(949\) | 1.55730e7 | 0.561316 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.30836e6 | 0.190331 | ||||||||
\(952\) | 6.89916e7 | 2.46720 | ||||||||
\(953\) | −2.64202e7 | −0.942333 | −0.471167 | − | 0.882044i | \(-0.656167\pi\) | ||||
−0.471167 | + | 0.882044i | \(0.656167\pi\) | |||||||
\(954\) | 6.48636e6 | 0.230744 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.08629e8 | 3.84415 | ||||||||
\(957\) | 8.87675e7 | 3.13310 | ||||||||
\(958\) | 6.85133e7 | 2.41191 | ||||||||
\(959\) | 2.28407e6 | 0.0801979 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.42504e7 | −0.497760 | ||||||||
\(962\) | 4.67975e7 | 1.63037 | ||||||||
\(963\) | 4.52453e6 | 0.157220 | ||||||||
\(964\) | 8.56358e7 | 2.96799 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.99880e7 | −2.06834 | ||||||||
\(967\) | −1.50682e7 | −0.518199 | −0.259099 | − | 0.965851i | \(-0.583426\pi\) | ||||
−0.259099 | + | 0.965851i | \(0.583426\pi\) | |||||||
\(968\) | −1.66392e8 | −5.70747 | ||||||||
\(969\) | 1.78855e7 | 0.611914 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.19475e7 | −1.76814 | −0.884070 | − | 0.467354i | \(-0.845207\pi\) | ||||
−0.884070 | + | 0.467354i | \(0.845207\pi\) | |||||||
\(972\) | 5.56250e7 | 1.88845 | ||||||||
\(973\) | 2.26725e7 | 0.767747 | ||||||||
\(974\) | 4.28853e7 | 1.44848 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.35621e7 | 2.80792 | ||||||||
\(977\) | 3.80206e7 | 1.27433 | 0.637166 | − | 0.770727i | \(-0.280107\pi\) | ||||
0.637166 | + | 0.770727i | \(0.280107\pi\) | |||||||
\(978\) | 9.19025e7 | 3.07242 | ||||||||
\(979\) | 2.10728e7 | 0.702693 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.09654e6 | −0.235437 | ||||||||
\(982\) | 5.69399e7 | 1.88425 | ||||||||
\(983\) | −4.43240e7 | −1.46304 | −0.731518 | − | 0.681822i | \(-0.761188\pi\) | ||||
−0.731518 | + | 0.681822i | \(0.761188\pi\) | |||||||
\(984\) | −1.08201e8 | −3.56241 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.99097e7 | 3.27277 | ||||||||
\(987\) | 6.85563e6 | 0.224003 | ||||||||
\(988\) | −2.10451e7 | −0.685896 | ||||||||
\(989\) | 5.85366e6 | 0.190299 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.06776e7 | 0.345373 | 0.172687 | − | 0.984977i | \(-0.444755\pi\) | ||||
0.172687 | + | 0.984977i | \(0.444755\pi\) | |||||||
\(992\) | 6.24756e7 | 2.01573 | ||||||||
\(993\) | −5.03457e7 | −1.62028 | ||||||||
\(994\) | 2.42513e7 | 0.778518 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.03228e7 | 1.92679 | ||||||||
\(997\) | 2.28612e7 | 0.728386 | 0.364193 | − | 0.931324i | \(-0.381345\pi\) | ||||
0.364193 | + | 0.931324i | \(0.381345\pi\) | |||||||
\(998\) | −1.84738e6 | −0.0587124 | ||||||||
\(999\) | 3.47796e7 | 1.10258 |
(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 | 1075.6.a.b.1.1 | 10 | ||
5.4 | even | 2 | 43.6.a.b.1.10 | ✓ | 10 | ||
15.14 | odd | 2 | 387.6.a.e.1.1 | 10 | |||
20.19 | odd | 2 | 688.6.a.h.1.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.a.b.1.10 | ✓ | 10 | 5.4 | even | 2 | ||
387.6.a.e.1.1 | 10 | 15.14 | odd | 2 | |||
688.6.a.h.1.3 | 10 | 20.19 | odd | 2 | |||
1075.6.a.b.1.1 | 10 | 1.1 | even | 1 | trivial |