Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,7,Mod(113,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.113");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.e (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(69.9364414204\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.9 | ||
Character | \(\chi\) | \(=\) | 304.113 |
Dual form | 304.7.e.f.113.22 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 27.9511i | − | 1.03523i | −0.855615 | − | 0.517613i | \(-0.826821\pi\) | ||
0.855615 | − | 0.517613i | \(-0.173179\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −141.368 | −1.13094 | −0.565472 | − | 0.824768i | \(-0.691306\pi\) | ||||
−0.565472 | + | 0.824768i | \(0.691306\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −302.893 | −0.883069 | −0.441535 | − | 0.897244i | \(-0.645566\pi\) | ||||
−0.441535 | + | 0.897244i | \(0.645566\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −52.2651 | −0.0716943 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1423.94 | −1.06983 | −0.534913 | − | 0.844907i | \(-0.679656\pi\) | ||||
−0.534913 | + | 0.844907i | \(0.679656\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1109.38i | − | 0.504953i | −0.967603 | − | 0.252477i | \(-0.918755\pi\) | ||
0.967603 | − | 0.252477i | \(-0.0812451\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3951.39i | 1.17078i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1818.90 | −0.370222 | −0.185111 | − | 0.982718i | \(-0.559265\pi\) | ||||
−0.185111 | + | 0.982718i | \(0.559265\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6854.30 | − | 253.905i | −0.999315 | − | 0.0370178i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8466.19i | 0.914177i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −14409.0 | −1.18427 | −0.592136 | − | 0.805838i | \(-0.701715\pi\) | ||||
−0.592136 | + | 0.805838i | \(0.701715\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4359.90 | 0.279034 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 18915.5i | − | 0.961007i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6338.49i | 0.259891i | 0.991521 | + | 0.129946i | \(0.0414803\pi\) | ||||
−0.991521 | + | 0.129946i | \(0.958520\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8988.56i | 0.301721i | 0.988555 | + | 0.150860i | \(0.0482044\pi\) | ||||
−0.988555 | + | 0.150860i | \(0.951796\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 39800.7i | 1.10751i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 42819.3 | 0.998701 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 40845.9i | 0.806386i | 0.915115 | + | 0.403193i | \(0.132100\pi\) | ||||
−0.915115 | + | 0.403193i | \(0.867900\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −31008.5 | −0.522741 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 46829.9i | 0.679472i | 0.940521 | + | 0.339736i | \(0.110338\pi\) | ||||
−0.940521 | + | 0.339736i | \(0.889662\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 37009.5 | 0.465487 | 0.232743 | − | 0.972538i | \(-0.425230\pi\) | ||||
0.232743 | + | 0.972538i | \(0.425230\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7388.61 | 0.0810822 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 68823.4 | 0.662892 | 0.331446 | − | 0.943474i | \(-0.392464\pi\) | ||||
0.331446 | + | 0.943474i | \(0.392464\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −25905.0 | −0.220189 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 50840.4i | 0.383264i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9195.15i | 0.0617634i | 0.999523 | + | 0.0308817i | \(0.00983151\pi\) | ||||
−0.999523 | + | 0.0308817i | \(0.990168\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 201299. | 1.20991 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7096.93 | + | 191585.i | −0.0383218 | + | 1.03452i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 154031.i | − | 0.749985i | −0.927028 | − | 0.374992i | \(-0.877645\pi\) | ||
0.927028 | − | 0.374992i | \(-0.122355\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 312647. | 1.37741 | 0.688707 | − | 0.725040i | \(-0.258179\pi\) | ||||
0.688707 | + | 0.725040i | \(0.258179\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15830.7 | 0.0633110 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 156831.i | 0.571074i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 327569.i | − | 1.08913i | −0.838720 | − | 0.544563i | \(-0.816695\pi\) | ||
0.838720 | − | 0.544563i | \(-0.183305\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 402749.i | 1.22599i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 601597.i | − | 1.68086i | −0.541922 | − | 0.840429i | \(-0.682303\pi\) | ||
0.541922 | − | 0.840429i | \(-0.317697\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 277023. | 0.712109 | 0.356055 | − | 0.934465i | \(-0.384122\pi\) | ||||
0.356055 | + | 0.934465i | \(0.384122\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 121864.i | − | 0.288863i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 431301. | 0.944731 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 139958.i | 0.283869i | 0.989876 | + | 0.141934i | \(0.0453322\pi\) | ||||
−0.989876 | + | 0.141934i | \(0.954668\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −566811. | −1.06655 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −676886. | −1.18381 | −0.591904 | − | 0.806008i | \(-0.701624\pi\) | ||||
−0.591904 | + | 0.806008i | \(0.701624\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 257134. | 0.418701 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 177168. | 0.269047 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 412278.i | − | 0.584817i | −0.956293 | − | 0.292409i | \(-0.905543\pi\) | ||
0.956293 | − | 0.292409i | \(-0.0944567\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 336024.i | 0.445909i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 251240. | 0.312349 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 968978. | + | 35894.0i | 1.13017 | + | 0.0418650i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 834434.i | − | 0.914275i | −0.889396 | − | 0.457137i | \(-0.848875\pi\) | ||
0.889396 | − | 0.457137i | \(-0.151125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 74422.4 | 0.0767004 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 729972. | 0.708504 | 0.354252 | − | 0.935150i | \(-0.384736\pi\) | ||||
0.354252 | + | 0.935150i | \(0.384736\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 252659.i | 0.231219i | 0.993295 | + | 0.115609i | \(0.0368821\pi\) | ||||
−0.993295 | + | 0.115609i | \(0.963118\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 1.19685e6i | − | 1.03388i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 2.04228e6i | − | 1.66711i | −0.552435 | − | 0.833556i | \(-0.686301\pi\) | ||
0.552435 | − | 0.833556i | \(-0.313699\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.40931e6i | − | 1.08824i | −0.839006 | − | 0.544122i | \(-0.816863\pi\) | ||
0.839006 | − | 0.544122i | \(-0.183137\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.14169e6 | 0.834792 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.51884e6i | 1.74568i | 0.488003 | + | 0.872842i | \(0.337725\pi\) | ||||
−0.488003 | + | 0.872842i | \(0.662275\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.03698e6 | 1.33934 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 57982.0i | 0.0362023i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 550932. | 0.326932 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 256042. | 0.144529 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.30895e6 | 0.703408 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.59252e6 | 0.815372 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.24362e6i | 1.58350i | 0.610842 | + | 0.791752i | \(0.290831\pi\) | ||||
−0.610842 | + | 0.791752i | \(0.709169\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1.03446e6i | − | 0.481884i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 468655. | 0.208468 | 0.104234 | − | 0.994553i | \(-0.466761\pi\) | ||||
0.104234 | + | 0.994553i | \(0.466761\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.07612e6 | + | 76905.9i | 0.882464 | + | 0.0326892i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.67405e6i | 1.08684i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −643914. | −0.250418 | −0.125209 | − | 0.992130i | \(-0.539960\pi\) | ||||
−0.125209 | + | 0.992130i | \(0.539960\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 355772. | 0.132473 | 0.0662364 | − | 0.997804i | \(-0.478901\pi\) | ||||
0.0662364 | + | 0.997804i | \(0.478901\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 1.92369e6i | − | 0.686244i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.57969e6i | 0.540212i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 896060.i | − | 0.293923i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 724074.i | 0.227945i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −545081. | −0.164779 | −0.0823896 | − | 0.996600i | \(-0.526255\pi\) | ||||
−0.0823896 | + | 0.996600i | \(0.526255\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.20603e6i | 0.350291i | 0.984543 | + | 0.175146i | \(0.0560396\pi\) | ||||
−0.984543 | + | 0.175146i | \(0.943960\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 95065.2 | 0.0265428 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 1.27069e6i | − | 0.341229i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.46765e6 | 1.41287 | 0.706434 | − | 0.707779i | \(-0.250303\pi\) | ||||
0.706434 | + | 0.707779i | \(0.250303\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 257015. | 0.0639391 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.36439e6 | 1.04579 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.43164e6 | 0.561482 | 0.280741 | − | 0.959784i | \(-0.409420\pi\) | ||||
0.280741 | + | 0.959784i | \(0.409420\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 5.62654e6i | − | 1.25253i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.60010e6i | 1.84652i | 0.384177 | + | 0.923260i | \(0.374485\pi\) | ||||
−0.384177 | + | 0.923260i | \(0.625515\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.59608e6 | 0.745022 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 358241. | + | 13270.4i | 0.0716451 | + | 0.00265396i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.20708e6i | 0.426265i | 0.977023 | + | 0.213133i | \(0.0683666\pi\) | ||||
−0.977023 | + | 0.213133i | \(0.931633\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.32058e6 | −0.246406 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.30534e6 | −0.776404 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.69883e6i | 0.644919i | 0.946583 | + | 0.322459i | \(0.104510\pi\) | ||||
−0.946583 | + | 0.322459i | \(0.895490\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.18691e6i | 1.21201i | 0.795461 | + | 0.606005i | \(0.207229\pi\) | ||||
−0.795461 | + | 0.606005i | \(0.792771\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 8.73883e6i | − | 1.42594i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5.77429e6i | − | 0.911977i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.59001e6 | 0.396074 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.72937e6i | 0.848635i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.52887e6 | −0.219417 | −0.109708 | − | 0.993964i | \(-0.534992\pi\) | ||||
−0.109708 | + | 0.993964i | \(0.534992\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.01811e6i | 1.25442i | 0.778849 | + | 0.627211i | \(0.215804\pi\) | ||||
−0.778849 | + | 0.627211i | \(0.784196\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.38360e6 | 0.591191 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.62332e6 | −0.343125 | −0.171562 | − | 0.985173i | \(-0.554881\pi\) | ||||
−0.171562 | + | 0.985173i | \(0.554881\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.27787e6 | −0.669729 | −0.334864 | − | 0.942266i | \(-0.608691\pi\) | ||||
−0.334864 | + | 0.942266i | \(0.608691\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.15592e6 | −1.12749 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.91988e6i | − | 0.229502i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 6.62025e6i | − | 0.768445i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 753090. | 0.0849055 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.76010e6 | + | 361545.i | 1.06909 | + | 0.0396026i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.58144e7i | − | 1.68347i | −0.539891 | − | 0.841735i | \(-0.681535\pi\) | ||
0.539891 | − | 0.841735i | \(-0.318465\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.68153e7 | −1.74007 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.23195e6 | −0.526439 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.72257e6i | − | 0.266440i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 7.74309e6i | − | 0.737194i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.01786e6i | 0.186945i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.14905e6i | 0.554489i | 0.960799 | + | 0.277245i | \(0.0894212\pi\) | ||||
−0.960799 | + | 0.277245i | \(0.910579\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −227871. | −0.0200051 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 8.95249e6i | − | 0.765361i | −0.923881 | − | 0.382680i | \(-0.875001\pi\) | ||
0.923881 | − | 0.382680i | \(-0.124999\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.14151e7 | −0.950548 | −0.475274 | − | 0.879838i | \(-0.657651\pi\) | ||||
−0.475274 | + | 0.879838i | \(0.657651\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 1.20553e7i | − | 0.978011i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.75905e6 | −0.692451 | −0.346226 | − | 0.938151i | \(-0.612537\pi\) | ||||
−0.346226 | + | 0.938151i | \(0.612537\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.72943e6 | −0.749694 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.91199e6 | 0.293868 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.69135e6 | 0.563390 | 0.281695 | − | 0.959504i | \(-0.409103\pi\) | ||||
0.281695 | + | 0.959504i | \(0.409103\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 5.03469e6i | − | 0.359684i | −0.983695 | − | 0.179842i | \(-0.942441\pi\) | ||
0.983695 | − | 0.179842i | \(-0.0575587\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.05359e6i | 0.143119i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.66214e6 | 0.249021 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −281678. | + | 7.60404e6i | −0.0186922 | + | 0.504607i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.89197e7i | 1.22551i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.72919e7 | −1.72589 | −0.862945 | − | 0.505297i | \(-0.831383\pi\) | ||||
−0.862945 | + | 0.505297i | \(0.831383\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.05176e7 | 1.26697 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 7.18720e6i | − | 0.433450i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3.97818e6i | − | 0.234361i | −0.993111 | − | 0.117180i | \(-0.962614\pi\) | ||
0.993111 | − | 0.117180i | \(-0.0373856\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.23719e7i | − | 0.712094i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 331282.i | − | 0.0186327i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.64161e7 | 0.902409 | 0.451205 | − | 0.892420i | \(-0.350994\pi\) | ||||
0.451205 | + | 0.892420i | \(0.350994\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.29990e6i | − | 0.0698509i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.15236e7 | −0.605418 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.00061e7i | 1.54153i | 0.637117 | + | 0.770767i | \(0.280127\pi\) | ||||
−0.637117 | + | 0.770767i | \(0.719873\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.91185e6 | 0.447775 | 0.223888 | − | 0.974615i | \(-0.428125\pi\) | ||||
0.223888 | + | 0.974615i | \(0.428125\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.39224e6 | 0.461616 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.20823e6 | −0.298517 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.77222e6 | −0.177484 | −0.0887418 | − | 0.996055i | \(-0.528285\pi\) | ||||
−0.0887418 | + | 0.996055i | \(0.528285\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 469788.i | − | 0.0216316i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4.13268e6i | − | 0.186257i | −0.995654 | − | 0.0931286i | \(-0.970313\pi\) | ||
0.995654 | − | 0.0931286i | \(-0.0296868\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.57367e6 | −0.422395 | −0.211198 | − | 0.977443i | \(-0.567736\pi\) | ||||
−0.211198 | + | 0.977443i | \(0.567736\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00328e6 | − | 2.70840e7i | 0.0433398 | − | 1.16998i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.41844e7i | − | 0.600021i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.08292e7 | −0.862935 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.33234e7 | −0.946482 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.36722e7i | − | 0.543544i | −0.962362 | − | 0.271772i | \(-0.912390\pi\) | ||
0.962362 | − | 0.271772i | \(-0.0876097\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.17751e7i | 0.848191i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.69345e7i | 1.02811i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.59851e7i | 0.598002i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.12099e7 | −0.411057 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.04035e7i | − | 0.733462i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.41982e7 | −1.55778 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.56154e7i | 1.23090i | 0.788175 | + | 0.615451i | \(0.211026\pi\) | ||||
−0.788175 | + | 0.615451i | \(0.788974\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.06211e6 | 0.239364 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.01481e7 | −1.66714 | −0.833572 | − | 0.552411i | \(-0.813708\pi\) | ||||
−0.833572 | + | 0.552411i | \(0.813708\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.40051e6 | −0.273951 | −0.136975 | − | 0.990574i | \(-0.543738\pi\) | ||||
−0.136975 | + | 0.990574i | \(0.543738\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.23796e6 | −0.0716012 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.76287e7i | 0.867325i | 0.901075 | + | 0.433663i | \(0.142779\pi\) | ||||
−0.901075 | + | 0.433663i | \(0.857221\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 9.02563e6i | − | 0.278039i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.70841e7 | −1.72584 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.24673e7 | + | 461828.i | 0.369969 | + | 0.0137048i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.83679e6i | − | 0.140899i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.93917e7 | −1.12658 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.08461e7 | −0.585380 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.72197e7i | 1.85358i | 0.375575 | + | 0.926792i | \(0.377445\pi\) | ||||
−0.375575 | + | 0.926792i | \(0.622555\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.13481e6i | − | 0.0578132i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.63077e7i | 1.23174i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.50842e7i | − | 0.394124i | −0.980391 | − | 0.197062i | \(-0.936860\pi\) | ||
0.980391 | − | 0.197062i | \(-0.0631400\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.04045e7 | 1.80718 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.27992e7i | − | 0.322789i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.34815e7 | 1.07751 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 5.69358e7i | − | 1.38653i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.85858e6 | 0.212019 | 0.106010 | − | 0.994365i | \(-0.466193\pi\) | ||||
0.106010 | + | 0.994365i | \(0.466193\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.01758e7 | 1.65086 | 0.825432 | − | 0.564502i | \(-0.190932\pi\) | ||||
0.825432 | + | 0.564502i | \(0.190932\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.09845e7 | −0.485263 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.94479e7 | −1.80617 | −0.903084 | − | 0.429463i | \(-0.858703\pi\) | ||||
−0.903084 | + | 0.429463i | \(0.858703\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.50466e7i | 1.90096i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 1.53992e7i | − | 0.338449i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.55216e7 | −1.63225 | −0.816127 | − | 0.577872i | \(-0.803883\pi\) | ||||
−0.816127 | + | 0.577872i | \(0.803883\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.69169e7 | + | 3.48068e6i | 0.997259 | + | 0.0739848i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 7.15665e6i | − | 0.149620i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.91621e7 | −0.805355 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.35966e7 | 0.275062 | 0.137531 | − | 0.990497i | \(-0.456083\pi\) | ||||
0.137531 | + | 0.990497i | \(0.456083\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2.44757e6i | − | 0.0487143i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 2.78514e6i | − | 0.0545413i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 3.44978e7i | − | 0.664759i | −0.943146 | − | 0.332380i | \(-0.892148\pi\) | ||
0.943146 | − | 0.332380i | \(-0.107852\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 4.45128e7i | − | 0.844095i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.03181e6 | 0.131233 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.57185e7i | − | 0.656108i | −0.944659 | − | 0.328054i | \(-0.893607\pi\) | ||
0.944659 | − | 0.328054i | \(-0.106393\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.06629e7 | 1.63929 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.94898e6i | 0.0702893i | 0.999382 | + | 0.0351446i | \(0.0111892\pi\) | ||||
−0.999382 | + | 0.0351446i | \(0.988811\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.09721e7 | −1.06844 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.93430e6 | −0.0333727 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.60746e7 | 1.63215 | 0.816074 | − | 0.577947i | \(-0.196146\pi\) | ||||
0.816074 | + | 0.577947i | \(0.196146\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.62086e7 | 0.438444 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1.30994e7i | − | 0.215812i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1.97856e7i | − | 0.321040i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.60152e7 | 0.415773 | 0.207886 | − | 0.978153i | \(-0.433342\pi\) | ||||
0.207886 | + | 0.978153i | \(0.433342\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.14961e6 | − | 5.80298e7i | 0.0338408 | − | 0.913550i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00439e8i | 1.55765i | 0.627241 | + | 0.778825i | \(0.284184\pi\) | ||||
−0.627241 | + | 0.778825i | \(0.715816\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.97175e6 | 0.152355 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.01289e7 | 1.20621 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.81620e7i | − | 0.862693i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 8.41310e7i | − | 1.22966i | −0.788658 | − | 0.614832i | \(-0.789224\pi\) | ||
0.788658 | − | 0.614832i | \(-0.210776\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.79981e7i | 0.259240i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.66549e7i | 0.662289i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.56900e7 | 1.33882 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 9.94422e6i | − | 0.137139i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.09172e8 | 1.48412 | 0.742058 | − | 0.670336i | \(-0.233850\pi\) | ||||
0.742058 | + | 0.670336i | \(0.233850\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.23025e8i | − | 1.64873i | −0.566061 | − | 0.824363i | \(-0.691533\pi\) | ||
0.566061 | − | 0.824363i | \(-0.308467\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.59707e6 | −0.0475256 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.93023e6 | −0.103304 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.46984e7 | −1.21635 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.41542e7 | 0.559242 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4.81803e7i | − | 0.601780i | −0.953659 | − | 0.300890i | \(-0.902716\pi\) | ||
0.953659 | − | 0.300890i | \(-0.0972838\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.03495e7i | 0.620200i | 0.950704 | + | 0.310100i | \(0.100363\pi\) | ||||
−0.950704 | + | 0.310100i | \(0.899637\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.50459e7 | −0.304276 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.87638e7 | + | 3.65852e6i | 1.18346 | + | 0.0438391i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.27207e8i | 1.50355i | 0.659420 | + | 0.751775i | \(0.270802\pi\) | ||||
−0.659420 | + | 0.751775i | \(0.729198\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.35393e6 | 0.0157863 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.16056e6 | 0.0478565 | 0.0239282 | − | 0.999714i | \(-0.492383\pi\) | ||||
0.0239282 | + | 0.999714i | \(0.492383\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.82829e7i | 0.661395i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.52356e7i | 0.170584i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6.00799e7i | − | 0.663728i | −0.943327 | − | 0.331864i | \(-0.892322\pi\) | ||
0.943327 | − | 0.331864i | \(-0.107678\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6.66829e7i | − | 0.726917i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.37100e7 | 0.362631 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 4.75030e7i | − | 0.504297i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.25241e8 | −1.31219 | −0.656097 | − | 0.754677i | \(-0.727794\pi\) | ||||
−0.656097 | + | 0.754677i | \(0.727794\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.44054e7i | 0.355786i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.99428e7 | −0.611835 | −0.305917 | − | 0.952058i | \(-0.598963\pi\) | ||||
−0.305917 | + | 0.952058i | \(0.598963\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.41095e8 | 1.42157 | 0.710784 | − | 0.703411i | \(-0.248341\pi\) | ||||
0.710784 | + | 0.703411i | \(0.248341\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.55173e7 | −0.353249 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.37901e7 | 0.920887 | 0.460444 | − | 0.887689i | \(-0.347690\pi\) | ||||
0.460444 | + | 0.887689i | \(0.347690\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.92182e7i | 0.961774i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1.52827e8i | − | 1.46264i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.26992e7 | −0.497990 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.98840e7 | − | 1.10700e6i | −0.278842 | − | 0.0103292i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 480586.i | − | 0.00442808i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.04641e6 | 0.0823133 | 0.0411566 | − | 0.999153i | \(-0.486896\pi\) | ||||
0.0411566 | + | 0.999153i | \(0.486896\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.53137e7 | 0.407187 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 1.21990e8i | − | 1.08263i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.17962e8i | 1.03399i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.31773e7i | − | 0.546983i | −0.961874 | − | 0.273492i | \(-0.911821\pi\) | ||
0.961874 | − | 0.273492i | \(-0.0881786\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 6.79670e7i | − | 0.581262i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.12129e8 | 0.947269 | 0.473635 | − | 0.880721i | \(-0.342942\pi\) | ||||
0.473635 | + | 0.880721i | \(0.342942\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.15291e7i | − | 0.0962176i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.05209e7 | −0.0867439 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.82219e8i | 1.48431i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.47216e7 | −0.440410 | −0.220205 | − | 0.975454i | \(-0.570673\pi\) | ||||
−0.220205 | + | 0.975454i | \(0.570673\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.40382e8 | 1.91157 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.65203e7 | −0.679851 | −0.339926 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339926 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.03195e8 | −0.801278 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.00514e8i | − | 0.771267i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.09132e7i | − | 0.0827557i | −0.999144 | − | 0.0413778i | \(-0.986825\pi\) | ||
0.999144 | − | 0.0413778i | \(-0.0131747\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.39081e7 | −0.628842 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.80274e6 | + | 1.29652e8i | −0.0355743 | + | 0.960348i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 3.57179e7i | − | 0.261496i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.80004e7 | −0.709180 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.16904e7 | 0.441281 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.60201e8i | 1.13280i | 0.824131 | + | 0.566399i | \(0.191664\pi\) | ||||
−0.824131 | + | 0.566399i | \(0.808336\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.49611e8i | 1.04582i | 0.852388 | + | 0.522910i | \(0.175154\pi\) | ||||
−0.852388 | + | 0.522910i | \(0.824846\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.69117e7i | 0.255086i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.63493e7i | − | 0.111704i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.95844e7 | 0.402500 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.05046e6i | 0.0537696i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.19523e7 | 0.343102 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.88713e8i | 1.88541i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.03386e8 | 0.667637 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.68872e7 | 0.235564 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.87285e7 | 0.434055 | 0.217028 | − | 0.976165i | \(-0.430364\pi\) | ||||
0.217028 | + | 0.976165i | \(0.430364\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.00882e8 | 1.25471 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.99231e8i | 1.23074i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.72965e8i | 1.05681i | 0.848992 | + | 0.528405i | \(0.177210\pi\) | ||||
−0.848992 | + | 0.528405i | \(0.822790\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.63405e7 | −0.0987527 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.60937e6 | − | 4.34459e7i | 0.00962060 | − | 0.259713i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.23924e7i | − | 0.250676i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.61398e8 | −0.944103 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.16158e8 | 1.25085 | 0.625425 | − | 0.780284i | \(-0.284926\pi\) | ||||
0.625425 | + | 0.780284i | \(0.284926\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.10576e7i | − | 0.235049i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 7.23936e7i | − | 0.410026i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 3.61156e7i | − | 0.202381i | −0.994867 | − | 0.101191i | \(-0.967735\pi\) | ||
0.994867 | − | 0.101191i | \(-0.0322652\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 3.56084e8i | − | 1.97427i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.71683e8 | 0.941841 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 3.09877e8i | − | 1.68210i | −0.540955 | − | 0.841052i | \(-0.681937\pi\) | ||
0.540955 | − | 0.841052i | \(-0.318063\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.07573e7 | −0.0577824 | −0.0288912 | − | 0.999583i | \(-0.509198\pi\) | ||||
−0.0288912 | + | 0.999583i | \(0.509198\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.27336e7i | 0.227146i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.28219e7 | −0.330452 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.31948e8 | 1.72800 | 0.863998 | − | 0.503496i | \(-0.167953\pi\) | ||||
0.863998 | + | 0.503496i | \(0.167953\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.52066e8 | 1.29861 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.05024e8 | 1.04538 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.30933e7i | − | 0.0660761i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 8.19680e6i | − | 0.0409427i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.23251e7 | −0.357581 | −0.178791 | − | 0.983887i | \(-0.557218\pi\) | ||||
−0.178791 | + | 0.983887i | \(0.557218\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.28224e6 | − | 6.16103e7i | 0.0111690 | − | 0.301514i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.33246e7i | 0.355212i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.90059e8 | −0.911430 | −0.455715 | − | 0.890126i | \(-0.650616\pi\) | ||||
−0.455715 | + | 0.890126i | \(0.650616\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.78842e7 | −0.369742 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.47522e8i | 0.693321i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.64594e8i | 1.23112i | 0.788092 | + | 0.615558i | \(0.211069\pi\) | ||||
−0.788092 | + | 0.615558i | \(0.788931\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.02137e8i | − | 1.39181i | −0.718133 | − | 0.695906i | \(-0.755003\pi\) | ||
0.718133 | − | 0.695906i | \(-0.244997\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.71204e7i | 0.0780841i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.61961e7 | −0.163454 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.11107e8i | 0.943921i | 0.881620 | + | 0.471960i | \(0.156453\pi\) | ||||
−0.881620 | + | 0.471960i | \(0.843547\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.36629e7 | −0.237587 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 7.63515e7i | − | 0.334729i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.67466e8 | −1.59528 | −0.797639 | − | 0.603135i | \(-0.793918\pi\) | ||||
−0.797639 | + | 0.603135i | \(0.793918\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.85043e8 | −0.795515 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.32514e8 | −0.564166 | −0.282083 | − | 0.959390i | \(-0.591025\pi\) | ||||
−0.282083 | + | 0.959390i | \(0.591025\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.35214e7 | −0.309986 | −0.154993 | − | 0.987916i | \(-0.549535\pi\) | ||||
−0.154993 | + | 0.987916i | \(0.549535\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.72554e8i | 1.13809i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.24876e8i | 0.516434i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.93255e8 | −1.20117 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.01056e7 | − | 2.72806e8i | 0.0409977 | − | 1.10675i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 7.42946e7i | − | 0.298542i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.74752e7 | −0.228766 | −0.114383 | − | 0.993437i | \(-0.536489\pi\) | ||||
−0.114383 | + | 0.993437i | \(0.536489\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.42030e8 | −1.74277 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 4.58544e8i | − | 1.79085i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.87386e7i | 0.111185i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.14426e7i | 0.120508i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 3.65121e8i | − | 1.38632i | −0.720786 | − | 0.693158i | \(-0.756219\pi\) | ||
0.720786 | − | 0.693158i | \(-0.243781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.80157e8 | −1.05383 | −0.526913 | − | 0.849920i | \(-0.676650\pi\) | ||||
−0.526913 | + | 0.849920i | \(0.676650\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.46239e8i | 0.544984i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.49771e7 | −0.0922208 | −0.0461104 | − | 0.998936i | \(-0.514683\pi\) | ||||
−0.0461104 | + | 0.998936i | \(0.514683\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.19331e8i | 0.802354i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.60988e7 | −0.275826 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.88241e8 | −1.03518 | −0.517591 | − | 0.855628i | \(-0.673171\pi\) | ||||
−0.517591 | + | 0.855628i | \(0.673171\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.62528e7 | −0.235766 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.44786e7 | −0.0510542 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.65298e8i | 1.62583i | 0.582383 | + | 0.812915i | \(0.302120\pi\) | ||||
−0.582383 | + | 0.812915i | \(0.697880\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 4.86400e8i | − | 1.68418i | −0.539336 | − | 0.842091i | \(-0.681325\pi\) | ||
0.539336 | − | 0.842091i | \(-0.318675\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.64014e7 | 0.193530 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.93496e8 | − | 1.08720e7i | −0.998017 | − | 0.0369697i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 9.13316e7i | − | 0.307782i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.71873e8 | 0.574022 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.45190e8 | −1.47359 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.58465e8i | − | 0.519862i | −0.965627 | − | 0.259931i | \(-0.916300\pi\) | ||
0.965627 | − | 0.259931i | \(-0.0836997\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 8.24697e7i | − | 0.268153i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 5.27476e8i | − | 1.69995i | −0.526822 | − | 0.849976i | \(-0.676617\pi\) | ||
0.526822 | − | 0.849976i | \(-0.323383\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.52744e8i | 0.807368i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.50232e8 | −0.792322 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 2.10229e8i | − | 0.659827i | −0.944011 | − | 0.329914i | \(-0.892980\pi\) | ||
0.944011 | − | 0.329914i | \(-0.107020\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.10288e7 | 0.283209 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.19065e8i | 0.984032i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.02009e7 | 0.0311876 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.00384e8 | 1.21351 | 0.606754 | − | 0.794890i | \(-0.292471\pi\) | ||||
0.606754 | + | 0.794890i | \(0.292471\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.25420e7 | −0.0677318 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.02947e7 | −0.149819 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.51790e7i | − | 0.251556i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.44825e8i | 0.716844i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.82964e8 | 0.531145 | 0.265572 | − | 0.964091i | \(-0.414439\pi\) | ||||
0.265572 | + | 0.964091i | \(0.414439\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.03710e7 | − | 2.79970e8i | 0.0298506 | − | 0.805833i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.71948e8i | 0.776103i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.21103e8 | −0.625658 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.49438e7 | −0.210280 | −0.105140 | − | 0.994457i | \(-0.533529\pi\) | ||||
−0.105140 | + | 0.994457i | \(0.533529\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 7.31494e6i | − | 0.0203518i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.29516e8i | − | 0.357319i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.23318e8i | − | 0.610950i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 2.14982e8i | − | 0.583236i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.87906e8 | −1.04361 | −0.521807 | − | 0.853064i | \(-0.674742\pi\) | ||||
−0.521807 | + | 0.853064i | \(0.674742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 7.65286e7i | − | 0.204182i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.40725e8 | −0.372355 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.76352e7i | 0.0725184i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.28037e7 | 0.137423 | 0.0687117 | − | 0.997637i | \(-0.478111\pi\) | ||||
0.0687117 | + | 0.997637i | \(0.478111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.55805e8 | −0.918394 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.73166e7 | −0.172334 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.53898e8 | 0.898599 | 0.449299 | − | 0.893381i | \(-0.351674\pi\) | ||||
0.449299 | + | 0.893381i | \(0.351674\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 1.02361e8i | − | 0.257793i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.66438e8i | 1.16518i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.41903e7 | −0.109495 | −0.0547474 | − | 0.998500i | \(-0.517435\pi\) | ||||
−0.0547474 | + | 0.998500i | \(0.517435\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.12541e8 | + | 7.87320e6i | 0.522383 | + | 0.0193507i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.60498e8i | − | 0.391295i | −0.980674 | − | 0.195647i | \(-0.937319\pi\) | ||
0.980674 | − | 0.195647i | \(-0.0626808\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.70570e7 | 0.186356 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.53775e7 | 0.0848723 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.18593e8i | 1.47217i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.63368e8i | 0.621790i | 0.950444 | + | 0.310895i | \(0.100629\pi\) | ||||
−0.950444 | + | 0.310895i | \(0.899371\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.62840e8i | 1.78669i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.70495e8i | − | 0.396159i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.66664e8 | 0.845241 | 0.422621 | − | 0.906307i | \(-0.361110\pi\) | ||||
0.422621 | + | 0.906307i | \(0.361110\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 5.73490e8i | − | 1.31160i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.04652e7 | −0.0464367 | −0.0232184 | − | 0.999730i | \(-0.507391\pi\) | ||||
−0.0232184 | + | 0.999730i | \(0.507391\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.26869e8i | 0.960995i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.34392e7 | −0.0300184 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.70879e8 | −0.378707 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.44380e8 | 1.63688 | 0.818438 | − | 0.574595i | \(-0.194841\pi\) | ||||
0.818438 | + | 0.574595i | \(0.194841\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.11195e8 | −0.242617 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.08872e8i | 0.452212i | 0.974103 | + | 0.226106i | \(0.0725995\pi\) | ||||
−0.974103 | + | 0.226106i | \(0.927400\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.91892e7i | 0.0841902i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.45809e8 | −0.737179 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.18903e7 | − | 3.20986e8i | 0.0251525 | − | 0.679006i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.56638e8i | 1.79823i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.19896e8 | 0.249757 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.72950e8 | −1.59787 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.18061e8i | 0.857660i | 0.903385 | + | 0.428830i | \(0.141074\pi\) | ||||
−0.903385 | + | 0.428830i | \(0.858926\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 4.58849e8i | − | 0.934198i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 7.62939e8i | − | 1.54156i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.46845e8i | − | 0.695530i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.63336e7 | −0.0723115 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.79777e8i | 1.14521i | 0.819830 | + | 0.572607i | \(0.194068\pi\) | ||||
−0.819830 | + | 0.572607i | \(0.805932\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.25183e8 | −0.245417 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.15478e7i | 0.0419280i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.94463e8 | −0.761833 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.16985e8 | −1.18273 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.38705e8 | 1.59584 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.81512e7 | 0.147601 | 0.0738006 | − | 0.997273i | \(-0.476487\pi\) | ||||
0.0738006 | + | 0.997273i | \(0.476487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.19059e8i | 0.410676i | 0.978691 | + | 0.205338i | \(0.0658293\pi\) | ||||
−0.978691 | + | 0.205338i | \(0.934171\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 2.49096e8i | − | 0.463549i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.43756e8 | −0.635005 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.53674e8 | − | 9.39688e6i | −0.465168 | − | 0.0172313i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 1.75623e7i | − | 0.0319691i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.78671e8 | −0.322867 | −0.161434 | − | 0.986884i | \(-0.551612\pi\) | ||||
−0.161434 | + | 0.986884i | \(0.551612\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.21889e8 | 1.11561 | 0.557806 | − | 0.829971i | \(-0.311643\pi\) | ||||
0.557806 | + | 0.829971i | \(0.311643\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.73527e8i | 0.309033i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.91151e8i | 1.39876i | 0.714750 | + | 0.699380i | \(0.246540\pi\) | ||||
−0.714750 | + | 0.699380i | \(0.753460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.15868e8i | 0.729948i | 0.931018 | + | 0.364974i | \(0.118922\pi\) | ||||
−0.931018 | + | 0.364974i | \(0.881078\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.05438e8i | 0.183736i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.71187e7 | 0.0815189 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.21578e9i | − | 2.08831i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.70023e8 | 0.289956 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.51724e8i | 0.426225i | 0.977028 | + | 0.213112i | \(0.0683601\pi\) | ||||
−0.977028 | + | 0.213112i | \(0.931640\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.54647e8 | 0.932456 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.15513e8 | −0.192818 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.08370e8 | −0.842578 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.75532e7 | −0.127629 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.67595e8i | 0.437275i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 5.88549e8i | − | 0.954980i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.47932e8 | 1.36620 | 0.683099 | − | 0.730325i | \(-0.260632\pi\) | ||||
0.683099 | + | 0.730325i | \(0.260632\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.06438e7 | − | 1.87601e6i | −0.0810266 | − | 0.00300148i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.20056e9i | 1.90740i | 0.300760 | + | 0.953700i | \(0.402760\pi\) | ||||
−0.300760 | + | 0.953700i | \(0.597240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.74459e8 | 1.53739 | 0.768695 | − | 0.639615i | \(-0.220906\pi\) | ||||
0.768695 | + | 0.639615i | \(0.220906\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.96471e8 | −0.621158 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.53525e8i | − | 0.394446i | −0.980359 | − | 0.197223i | \(-0.936808\pi\) | ||
0.980359 | − | 0.197223i | \(-0.0631924\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 3.12010e8i | − | 0.482082i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.82198e8i | 0.893334i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.99292e8i | − | 0.303690i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.63399e8 | −0.549958 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.36118e7i | 0.0655483i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.82364e8 | −0.720030 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 6.12474e8i | − | 0.908007i | −0.891000 | − | 0.454004i | \(-0.849995\pi\) | ||
0.891000 | − | 0.454004i | \(-0.150005\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.82153e8 | −0.562692 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.68417e8 | −0.977507 | −0.488754 | − | 0.872422i | \(-0.662548\pi\) | ||||
−0.488754 | + | 0.872422i | \(0.662548\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.24854e9 | 1.81351 | 0.906753 | − | 0.421661i | \(-0.138553\pi\) | ||||
0.906753 | + | 0.421661i | \(0.138553\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.08638e8 | 0.878070 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.98396e8i | 1.28735i | 0.765298 | + | 0.643676i | \(0.222591\pi\) | ||||
−0.765298 | + | 0.643676i | \(0.777409\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 9.82470e8i | − | 1.39834i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.07104e8 | 1.14103 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.71736e8 | − | 1.74746e7i | −0.662438 | − | 0.0245388i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5.22896e8i | − | 0.729367i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.46802e8 | 0.619067 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.69739e7 | −0.0784146 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.67251e7i | − | 0.0228662i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.13329e8i | 0.425537i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.01600e9i | − | 1.37072i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.08672e8i | − | 0.279668i | −0.990175 | − | 0.139834i | \(-0.955343\pi\) | ||
0.990175 | − | 0.139834i | \(-0.0446569\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.81521e7 | −0.0507957 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.37374e9i | − | 1.81697i | −0.417913 | − | 0.908487i | \(-0.637238\pi\) | ||
0.417913 | − | 0.908487i | \(-0.362762\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.63845e8 | 1.26647 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.23539e9i | 1.61265i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.41952e8 | −0.184092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.38508e8 | 0.178455 | 0.0892276 | − | 0.996011i | \(-0.471560\pi\) | ||||
0.0892276 | + | 0.996011i | \(0.471560\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.95492e8 | 1.27426 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.67402e8 | −0.848755 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.78084e8i | 0.225009i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 1.32053e7i | − | 0.0165771i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.89511e8 | −0.610542 | −0.305271 | − | 0.952266i | \(-0.598747\pi\) | ||||
−0.305271 | + | 0.952266i | \(0.598747\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.77561e8 | + | 6.57741e6i | 0.220038 | + | 0.00815090i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.40169e9i | 1.72587i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.66144e8 | −0.447937 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.43426e9 | 1.74345 | 0.871724 | − | 0.489997i | \(-0.163002\pi\) | ||||
0.871724 | + | 0.489997i | \(0.163002\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.34804e8i | 0.283601i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.10210e9i | − | 1.32268i | −0.750087 | − | 0.661339i | \(-0.769989\pi\) | ||
0.750087 | − | 0.661339i | \(-0.230011\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 6.74774e8i | − | 0.804680i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 8.09949e8i | − | 0.959759i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.54268e9 | −1.81646 | −0.908229 | − | 0.418473i | \(-0.862565\pi\) | ||||
−0.908229 | + | 0.418473i | \(0.862565\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 3.07324e8i | − | 0.359582i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.72252e8 | 0.897878 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.20290e8i | 0.138980i | 0.997583 | + | 0.0694899i | \(0.0221372\pi\) | ||||
−0.997583 | + | 0.0694899i | \(0.977863\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.16133e8 | 0.248148 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.52276e8 | −0.287833 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.95037e8 | 0.221137 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.06710e8 | 0.908965 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.06740e8i | 0.119522i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.27487e9i | − | 1.41868i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.40392e9 | 1.55261 | 0.776306 | − | 0.630357i | \(-0.217091\pi\) | ||||
0.776306 | + | 0.630357i | \(0.217091\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.29086e7 | − | 3.48475e8i | 0.0141876 | − | 0.383001i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 6.57153e8i | − | 0.717808i | −0.933374 | − | 0.358904i | \(-0.883150\pi\) | ||
0.933374 | − | 0.358904i | \(-0.116850\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.07761e8 | −0.116983 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.35194e8 | −0.145862 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.55873e8i | − | 0.167143i | −0.996502 | − | 0.0835714i | \(-0.973367\pi\) | ||
0.996502 | − | 0.0835714i | \(-0.0266327\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.87059e8i | 0.625653i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.36577e7i | 0.0780209i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 5.23668e7i | − | 0.0551309i | −0.999620 | − | 0.0275655i | \(-0.991225\pi\) | ||
0.999620 | − | 0.0275655i | \(-0.00877547\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.70853e8 | 0.388055 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.82672e8i | 0.606001i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.33271e8 | −0.551263 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.96783e8i | 0.202193i | 0.994877 | + | 0.101097i | \(0.0322351\pi\) | ||||
−0.994877 | + | 0.101097i | \(0.967765\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.87886e9 | 1.91888 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.46121e8 | 0.757426 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.85567e9 | −1.87247 | −0.936236 | − | 0.351371i | \(-0.885715\pi\) | ||||
−0.936236 | + | 0.351371i | \(0.885715\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.72620e8 | 0.774942 |
(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 | 304.7.e.f.113.9 | 30 | ||
4.3 | odd | 2 | 152.7.e.a.113.22 | yes | 30 | ||
19.18 | odd | 2 | inner | 304.7.e.f.113.22 | 30 | ||
76.75 | even | 2 | 152.7.e.a.113.9 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.7.e.a.113.9 | ✓ | 30 | 76.75 | even | 2 | ||
152.7.e.a.113.22 | yes | 30 | 4.3 | odd | 2 | ||
304.7.e.f.113.9 | 30 | 1.1 | even | 1 | trivial | ||
304.7.e.f.113.22 | 30 | 19.18 | odd | 2 | inner |