Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,6,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, 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("441.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(70.7292645375\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{19}, \sqrt{69})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 71x^{2} + 72x - 15 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.705587\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.71780 | −1.54110 | −0.770552 | − | 0.637377i | \(-0.780019\pi\) | ||||
−0.770552 | + | 0.637377i | \(0.780019\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 44.0000 | 1.37500 | ||||||||
\(5\) | −99.6795 | −1.78312 | −0.891560 | − | 0.452902i | \(-0.850389\pi\) | ||||
−0.891560 | + | 0.452902i | \(0.850389\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −104.614 | −0.577914 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 868.986 | 2.74797 | ||||||||
\(11\) | −374.865 | −0.934100 | −0.467050 | − | 0.884231i | \(-0.654683\pi\) | ||||
−0.467050 | + | 0.884231i | \(0.654683\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 868.986 | 1.42611 | 0.713057 | − | 0.701106i | \(-0.247310\pi\) | ||||
0.713057 | + | 0.701106i | \(0.247310\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −496.000 | −0.484375 | ||||||||
\(17\) | 1096.47 | 0.920187 | 0.460094 | − | 0.887870i | \(-0.347816\pi\) | ||||
0.460094 | + | 0.887870i | \(0.347816\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −868.986 | −0.552241 | −0.276120 | − | 0.961123i | \(-0.589049\pi\) | ||||
−0.276120 | + | 0.961123i | \(0.589049\pi\) | |||||||
\(20\) | −4385.90 | −2.45179 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3268.00 | 1.43955 | ||||||||
\(23\) | −2972.77 | −1.17177 | −0.585884 | − | 0.810395i | \(-0.699253\pi\) | ||||
−0.585884 | + | 0.810395i | \(0.699253\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6811.00 | 2.17952 | ||||||||
\(26\) | −7575.64 | −2.19779 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4515.82 | −0.997107 | −0.498553 | − | 0.866859i | \(-0.666135\pi\) | ||||
−0.498553 | + | 0.866859i | \(0.666135\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9558.84 | −1.78649 | −0.893246 | − | 0.449568i | \(-0.851578\pi\) | ||||
−0.893246 | + | 0.449568i | \(0.851578\pi\) | |||||||
\(32\) | 7671.66 | 1.32439 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9558.84 | −1.41810 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5466.00 | −0.656395 | −0.328198 | − | 0.944609i | \(-0.606441\pi\) | ||||
−0.328198 | + | 0.944609i | \(0.606441\pi\) | |||||||
\(38\) | 7575.64 | 0.851060 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 10427.8 | 1.03049 | ||||||||
\(41\) | −9868.27 | −0.916814 | −0.458407 | − | 0.888742i | \(-0.651580\pi\) | ||||
−0.458407 | + | 0.888742i | \(0.651580\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12540.0 | 1.03425 | 0.517126 | − | 0.855909i | \(-0.327002\pi\) | ||||
0.517126 | + | 0.855909i | \(0.327002\pi\) | |||||||
\(44\) | −16494.1 | −1.28439 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 25916.0 | 1.80582 | ||||||||
\(47\) | 9967.95 | 0.658205 | 0.329102 | − | 0.944294i | \(-0.393254\pi\) | ||||
0.329102 | + | 0.944294i | \(0.393254\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −59376.9 | −3.35887 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 38235.4 | 1.96091 | ||||||||
\(53\) | 15151.5 | 0.740912 | 0.370456 | − | 0.928850i | \(-0.379201\pi\) | ||||
0.370456 | + | 0.928850i | \(0.379201\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 37366.4 | 1.66561 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 39368.0 | 1.53664 | ||||||||
\(59\) | −42662.8 | −1.59558 | −0.797792 | − | 0.602933i | \(-0.793999\pi\) | ||||
−0.797792 | + | 0.602933i | \(0.793999\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −47794.2 | −1.64456 | −0.822282 | − | 0.569080i | \(-0.807299\pi\) | ||||
−0.822282 | + | 0.569080i | \(0.807299\pi\) | |||||||
\(62\) | 83332.1 | 2.75317 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −51008.0 | −1.55664 | ||||||||
\(65\) | −86620.0 | −2.54293 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −29996.0 | −0.816350 | −0.408175 | − | 0.912904i | \(-0.633835\pi\) | ||||
−0.408175 | + | 0.912904i | \(0.633835\pi\) | |||||||
\(68\) | 48244.9 | 1.26526 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −61469.2 | −1.44714 | −0.723572 | − | 0.690249i | \(-0.757501\pi\) | ||||
−0.723572 | + | 0.690249i | \(0.757501\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −48663.2 | −1.06879 | −0.534396 | − | 0.845234i | \(-0.679461\pi\) | ||||
−0.534396 | + | 0.845234i | \(0.679461\pi\) | |||||||
\(74\) | 47651.5 | 1.01157 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −38235.4 | −0.759331 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 80168.0 | 1.44522 | 0.722609 | − | 0.691257i | \(-0.242943\pi\) | ||||
0.722609 | + | 0.691257i | \(0.242943\pi\) | |||||||
\(80\) | 49441.0 | 0.863699 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 86029.6 | 1.41291 | ||||||||
\(83\) | −30701.3 | −0.489172 | −0.244586 | − | 0.969628i | \(-0.578652\pi\) | ||||
−0.244586 | + | 0.969628i | \(0.578652\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −109296. | −1.64080 | ||||||||
\(86\) | −109321. | −1.59389 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 39216.0 | 0.539829 | ||||||||
\(89\) | 20833.0 | 0.278790 | 0.139395 | − | 0.990237i | \(-0.455484\pi\) | ||||
0.139395 | + | 0.990237i | \(0.455484\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −130802. | −1.61118 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −86898.6 | −1.01436 | ||||||||
\(95\) | 86620.0 | 0.984712 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −133824. | −1.44412 | −0.722061 | − | 0.691829i | \(-0.756805\pi\) | ||||
−0.722061 | + | 0.691829i | \(0.756805\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 299684. | 2.99684 | ||||||||
\(101\) | −106358. | −1.03745 | −0.518725 | − | 0.854941i | \(-0.673593\pi\) | ||||
−0.518725 | + | 0.854941i | \(0.673593\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 47794.2 | 0.443897 | 0.221949 | − | 0.975058i | \(-0.428758\pi\) | ||||
0.221949 | + | 0.975058i | \(0.428758\pi\) | |||||||
\(104\) | −90907.7 | −0.824171 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −132088. | −1.14182 | ||||||||
\(107\) | 102983. | 0.869576 | 0.434788 | − | 0.900533i | \(-0.356823\pi\) | ||||
0.434788 | + | 0.900533i | \(0.356823\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 73854.0 | 0.595399 | 0.297699 | − | 0.954660i | \(-0.403781\pi\) | ||||
0.297699 | + | 0.954660i | \(0.403781\pi\) | |||||||
\(110\) | −325753. | −2.56688 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 29535.9 | 0.217598 | 0.108799 | − | 0.994064i | \(-0.465300\pi\) | ||||
0.108799 | + | 0.994064i | \(0.465300\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 296324. | 2.08940 | ||||||||
\(116\) | −198696. | −1.37102 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 371926. | 2.45896 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −20527.0 | −0.127457 | ||||||||
\(122\) | 416660. | 2.53444 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −420589. | −2.45643 | ||||||||
\(125\) | −367419. | −2.10323 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 175120. | 0.963444 | 0.481722 | − | 0.876324i | \(-0.340012\pi\) | ||||
0.481722 | + | 0.876324i | \(0.340012\pi\) | |||||||
\(128\) | 199184. | 1.07456 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 755136. | 3.91892 | ||||||||
\(131\) | 144735. | 0.736876 | 0.368438 | − | 0.929652i | \(-0.379893\pi\) | ||||
0.368438 | + | 0.929652i | \(0.379893\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 261499. | 1.25808 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −114706. | −0.531789 | ||||||||
\(137\) | 172229. | 0.783979 | 0.391989 | − | 0.919970i | \(-0.371787\pi\) | ||||
0.391989 | + | 0.919970i | \(0.371787\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19117.7 | −0.0839263 | −0.0419632 | − | 0.999119i | \(-0.513361\pi\) | ||||
−0.0419632 | + | 0.999119i | \(0.513361\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 535876. | 2.23020 | ||||||||
\(143\) | −325753. | −1.33213 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 450135. | 1.77796 | ||||||||
\(146\) | 424236. | 1.64712 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −240504. | −0.902543 | ||||||||
\(149\) | 9118.82 | 0.0336491 | 0.0168245 | − | 0.999858i | \(-0.494644\pi\) | ||||
0.0168245 | + | 0.999858i | \(0.494644\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 310200. | 1.10713 | 0.553566 | − | 0.832805i | \(-0.313267\pi\) | ||||
0.553566 | + | 0.832805i | \(0.313267\pi\) | |||||||
\(152\) | 90907.7 | 0.319148 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 952820. | 3.18553 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −258089. | −0.835641 | −0.417821 | − | 0.908530i | \(-0.637206\pi\) | ||||
−0.417821 | + | 0.908530i | \(0.637206\pi\) | |||||||
\(158\) | −698888. | −2.22723 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −764707. | −2.36154 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 126556. | 0.373090 | 0.186545 | − | 0.982446i | \(-0.440271\pi\) | ||||
0.186545 | + | 0.982446i | \(0.440271\pi\) | |||||||
\(164\) | −434204. | −1.26062 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 267648. | 0.753864 | ||||||||
\(167\) | 342100. | 0.949209 | 0.474605 | − | 0.880199i | \(-0.342591\pi\) | ||||
0.474605 | + | 0.880199i | \(0.342591\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 383843. | 1.03380 | ||||||||
\(170\) | 952820. | 2.52865 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 551760. | 1.42210 | ||||||||
\(173\) | 187497. | 0.476299 | 0.238149 | − | 0.971229i | \(-0.423459\pi\) | ||||
0.238149 | + | 0.971229i | \(0.423459\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 185933. | 0.452455 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −181618. | −0.429644 | ||||||||
\(179\) | 127829. | 0.298193 | 0.149096 | − | 0.988823i | \(-0.452364\pi\) | ||||
0.149096 | + | 0.988823i | \(0.452364\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 219853. | 0.498812 | 0.249406 | − | 0.968399i | \(-0.419765\pi\) | ||||
0.249406 | + | 0.968399i | \(0.419765\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 310992. | 0.677181 | ||||||||
\(185\) | 544848. | 1.17043 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −411030. | −0.859547 | ||||||||
\(188\) | 438590. | 0.905032 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −755136. | −1.51754 | ||||||||
\(191\) | 116130. | 0.230335 | 0.115168 | − | 0.993346i | \(-0.463259\pi\) | ||||
0.115168 | + | 0.993346i | \(0.463259\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −306306. | −0.591919 | −0.295959 | − | 0.955200i | \(-0.595639\pi\) | ||||
−0.295959 | + | 0.955200i | \(0.595639\pi\) | |||||||
\(194\) | 1.16665e6 | 2.22554 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 360202. | 0.661273 | 0.330636 | − | 0.943758i | \(-0.392737\pi\) | ||||
0.330636 | + | 0.943758i | \(0.392737\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 229412. | 0.410661 | 0.205331 | − | 0.978693i | \(-0.434173\pi\) | ||||
0.205331 | + | 0.978693i | \(0.434173\pi\) | |||||||
\(200\) | −712523. | −1.25957 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 927208. | 1.59882 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 983664. | 1.63479 | ||||||||
\(206\) | −416660. | −0.684091 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −431017. | −0.690774 | ||||||||
\(209\) | 325753. | 0.515848 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.21031e6 | −1.87150 | −0.935750 | − | 0.352664i | \(-0.885276\pi\) | ||||
−0.935750 | + | 0.352664i | \(0.885276\pi\) | |||||||
\(212\) | 666667. | 1.01875 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −897788. | −1.34011 | ||||||||
\(215\) | −1.24998e6 | −1.84420 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −643844. | −0.917571 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.64412e6 | 2.29022 | ||||||||
\(221\) | 952820. | 1.31229 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 745590. | 1.00401 | 0.502005 | − | 0.864865i | \(-0.332596\pi\) | ||||
0.502005 | + | 0.864865i | \(0.332596\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −257488. | −0.335340 | ||||||||
\(227\) | −140349. | −0.180777 | −0.0903886 | − | 0.995907i | \(-0.528811\pi\) | ||||
−0.0903886 | + | 0.995907i | \(0.528811\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −774266. | −0.975667 | −0.487833 | − | 0.872937i | \(-0.662213\pi\) | ||||
−0.487833 | + | 0.872937i | \(0.662213\pi\) | |||||||
\(230\) | −2.58329e6 | −3.21999 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 472416. | 0.576242 | ||||||||
\(233\) | −1.03550e6 | −1.24957 | −0.624785 | − | 0.780797i | \(-0.714813\pi\) | ||||
−0.624785 | + | 0.780797i | \(0.714813\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −993600. | −1.17366 | ||||||||
\(236\) | −1.87716e6 | −2.19393 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.11622e6 | 1.26402 | 0.632011 | − | 0.774960i | \(-0.282230\pi\) | ||||
0.632011 | + | 0.774960i | \(0.282230\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.44425e6 | −1.60177 | −0.800887 | − | 0.598816i | \(-0.795638\pi\) | ||||
−0.800887 | + | 0.598816i | \(0.795638\pi\) | |||||||
\(242\) | 178950. | 0.196424 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.10295e6 | −2.26128 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −755136. | −0.787558 | ||||||||
\(248\) | 999985. | 1.03244 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.20308e6 | 3.24129 | ||||||||
\(251\) | 216105. | 0.216511 | 0.108256 | − | 0.994123i | \(-0.465473\pi\) | ||||
0.108256 | + | 0.994123i | \(0.465473\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.11439e6 | 1.09455 | ||||||||
\(254\) | −1.52666e6 | −1.48477 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −104192. | −0.0993652 | ||||||||
\(257\) | 1.28517e6 | 1.21374 | 0.606872 | − | 0.794800i | \(-0.292424\pi\) | ||||
0.606872 | + | 0.794800i | \(0.292424\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.81128e6 | −3.49653 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.26177e6 | −1.13560 | ||||||||
\(263\) | 1.47794e6 | 1.31755 | 0.658774 | − | 0.752341i | \(-0.271075\pi\) | ||||
0.658774 | + | 0.752341i | \(0.271075\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.51030e6 | −1.32114 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.31982e6 | −1.12248 | ||||||||
\(269\) | 2.28176e6 | 1.92260 | 0.961302 | − | 0.275497i | \(-0.0888423\pi\) | ||||
0.961302 | + | 0.275497i | \(0.0888423\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.09058e6 | −0.902055 | −0.451028 | − | 0.892510i | \(-0.648942\pi\) | ||||
−0.451028 | + | 0.892510i | \(0.648942\pi\) | |||||||
\(272\) | −543851. | −0.445716 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.50146e6 | −1.20819 | ||||||||
\(275\) | −2.55321e6 | −2.03589 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −256234. | −0.200649 | −0.100325 | − | 0.994955i | \(-0.531988\pi\) | ||||
−0.100325 | + | 0.994955i | \(0.531988\pi\) | |||||||
\(278\) | 166664. | 0.129339 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −889041. | −0.671670 | −0.335835 | − | 0.941921i | \(-0.609018\pi\) | ||||
−0.335835 | + | 0.941921i | \(0.609018\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −496191. | −0.368284 | −0.184142 | − | 0.982900i | \(-0.558951\pi\) | ||||
−0.184142 | + | 0.982900i | \(0.558951\pi\) | |||||||
\(284\) | −2.70464e6 | −1.98982 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.83984e6 | 2.05296 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −217601. | −0.153256 | ||||||||
\(290\) | −3.92418e6 | −2.74002 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.14118e6 | −1.46959 | ||||||||
\(293\) | 731348. | 0.497686 | 0.248843 | − | 0.968544i | \(-0.419950\pi\) | ||||
0.248843 | + | 0.968544i | \(0.419950\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.25261e6 | 2.84512 | ||||||||
\(296\) | 571818. | 0.379340 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −79496.0 | −0.0518567 | ||||||||
\(299\) | −2.58329e6 | −1.67107 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.70426e6 | −1.70621 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 431017. | 0.267492 | ||||||||
\(305\) | 4.76410e6 | 2.93246 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 66911.9 | 0.0405189 | 0.0202594 | − | 0.999795i | \(-0.493551\pi\) | ||||
0.0202594 | + | 0.999795i | \(0.493551\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.30650e6 | −4.90923 | ||||||||
\(311\) | 302627. | 0.177422 | 0.0887108 | − | 0.996057i | \(-0.471725\pi\) | ||||
0.0887108 | + | 0.996057i | \(0.471725\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.01324e6 | 0.584589 | 0.292294 | − | 0.956328i | \(-0.405581\pi\) | ||||
0.292294 | + | 0.956328i | \(0.405581\pi\) | |||||||
\(314\) | 2.24997e6 | 1.28781 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.52739e6 | 1.98717 | ||||||||
\(317\) | −638474. | −0.356858 | −0.178429 | − | 0.983953i | \(-0.557101\pi\) | ||||
−0.178429 | + | 0.983953i | \(0.557101\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.69282e6 | 0.931398 | ||||||||
\(320\) | 5.08445e6 | 2.77568 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −952820. | −0.508165 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.91866e6 | 3.10824 | ||||||||
\(326\) | −1.10329e6 | −0.574970 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.03235e6 | 0.529840 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.63905e6 | 1.32397 | 0.661985 | − | 0.749517i | \(-0.269714\pi\) | ||||
0.661985 | + | 0.749517i | \(0.269714\pi\) | |||||||
\(332\) | −1.35086e6 | −0.672611 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.98236e6 | −1.46283 | ||||||||
\(335\) | 2.98999e6 | 1.45565 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −455070. | −0.218275 | −0.109137 | − | 0.994027i | \(-0.534809\pi\) | ||||
−0.109137 | + | 0.994027i | \(0.534809\pi\) | |||||||
\(338\) | −3.34627e6 | −1.59319 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.80902e6 | −2.25611 | ||||||||
\(341\) | 3.58328e6 | 1.66876 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.31185e6 | −0.597709 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.63456e6 | −0.734025 | ||||||||
\(347\) | 1.30756e6 | 0.582957 | 0.291479 | − | 0.956577i | \(-0.405853\pi\) | ||||
0.291479 | + | 0.956577i | \(0.405853\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.05234e6 | 0.462480 | 0.231240 | − | 0.972897i | \(-0.425722\pi\) | ||||
0.231240 | + | 0.972897i | \(0.425722\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.87584e6 | −1.23711 | ||||||||
\(353\) | 1.17333e6 | 0.501167 | 0.250583 | − | 0.968095i | \(-0.419378\pi\) | ||||
0.250583 | + | 0.968095i | \(0.419378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.12722e6 | 2.58043 | ||||||||
\(356\) | 916653. | 0.383336 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.11439e6 | −0.459546 | ||||||||
\(359\) | 2.98746e6 | 1.22339 | 0.611696 | − | 0.791093i | \(-0.290488\pi\) | ||||
0.611696 | + | 0.791093i | \(0.290488\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.72096e6 | −0.695030 | ||||||||
\(362\) | −1.91664e6 | −0.768721 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.85072e6 | 1.90579 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.98236e6 | −1.15583 | −0.577916 | − | 0.816096i | \(-0.696134\pi\) | ||||
−0.577916 | + | 0.816096i | \(0.696134\pi\) | |||||||
\(368\) | 1.47449e6 | 0.567575 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.74988e6 | −1.80376 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.58662e6 | −0.590473 | −0.295237 | − | 0.955424i | \(-0.595398\pi\) | ||||
−0.295237 | + | 0.955424i | \(0.595398\pi\) | |||||||
\(374\) | 3.58328e6 | 1.32465 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.04278e6 | −0.380386 | ||||||||
\(377\) | −3.92418e6 | −1.42199 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.27168e6 | 0.454756 | 0.227378 | − | 0.973807i | \(-0.426985\pi\) | ||||
0.227378 | + | 0.973807i | \(0.426985\pi\) | |||||||
\(380\) | 3.81128e6 | 1.35398 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.01240e6 | −0.354970 | ||||||||
\(383\) | −5.13589e6 | −1.78903 | −0.894517 | − | 0.447035i | \(-0.852480\pi\) | ||||
−0.894517 | + | 0.447035i | \(0.852480\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.67031e6 | 0.912208 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.88825e6 | −1.98567 | ||||||||
\(389\) | −4.92655e6 | −1.65070 | −0.825351 | − | 0.564619i | \(-0.809023\pi\) | ||||
−0.825351 | + | 0.564619i | \(0.809023\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.25957e6 | −1.07825 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.14017e6 | −1.01909 | ||||||||
\(395\) | −7.99111e6 | −2.57700 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −219853. | −0.0700095 | −0.0350047 | − | 0.999387i | \(-0.511145\pi\) | ||||
−0.0350047 | + | 0.999387i | \(0.511145\pi\) | |||||||
\(398\) | −1.99997e6 | −0.632872 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.37826e6 | −1.05570 | ||||||||
\(401\) | −3.18796e6 | −0.990038 | −0.495019 | − | 0.868882i | \(-0.664839\pi\) | ||||
−0.495019 | + | 0.868882i | \(0.664839\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.30650e6 | −2.54774 | ||||||||
\(404\) | −4.67975e6 | −1.42649 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.04901e6 | 0.613139 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.54265e6 | −0.751586 | −0.375793 | − | 0.926704i | \(-0.622630\pi\) | ||||
−0.375793 | + | 0.926704i | \(0.622630\pi\) | |||||||
\(410\) | −8.57538e6 | −2.51938 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.10295e6 | 0.610358 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.06029e6 | 0.872252 | ||||||||
\(416\) | 6.66656e6 | 1.88873 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.83984e6 | −0.794976 | ||||||||
\(419\) | −3.57132e6 | −0.993787 | −0.496893 | − | 0.867812i | \(-0.665526\pi\) | ||||
−0.496893 | + | 0.867812i | \(0.665526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 991750. | 0.272707 | 0.136354 | − | 0.990660i | \(-0.456462\pi\) | ||||
0.136354 | + | 0.990660i | \(0.456462\pi\) | |||||||
\(422\) | 1.05512e7 | 2.88417 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.58506e6 | −0.428184 | ||||||||
\(425\) | 7.46809e6 | 2.00557 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.53127e6 | 1.19567 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.08971e7 | 2.84210 | ||||||||
\(431\) | 3.40602e6 | 0.883189 | 0.441595 | − | 0.897215i | \(-0.354413\pi\) | ||||
0.441595 | + | 0.897215i | \(0.354413\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.74266e6 | 1.98459 | 0.992294 | − | 0.123902i | \(-0.0395409\pi\) | ||||
0.992294 | + | 0.123902i | \(0.0395409\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.24958e6 | 0.818673 | ||||||||
\(437\) | 2.58329e6 | 0.647098 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.31753e6 | −1.56454 | −0.782268 | − | 0.622942i | \(-0.785937\pi\) | ||||
−0.782268 | + | 0.622942i | \(0.785937\pi\) | |||||||
\(440\) | −3.90903e6 | −0.962581 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.30650e6 | −2.02238 | ||||||||
\(443\) | 485712. | 0.117590 | 0.0587949 | − | 0.998270i | \(-0.481274\pi\) | ||||
0.0587949 | + | 0.998270i | \(0.481274\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.07662e6 | −0.497116 | ||||||||
\(446\) | −6.49990e6 | −1.54728 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.18374e6 | 1.21347 | 0.606733 | − | 0.794906i | \(-0.292480\pi\) | ||||
0.606733 | + | 0.794906i | \(0.292480\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.69927e6 | 0.856396 | ||||||||
\(452\) | 1.29958e6 | 0.299197 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.22353e6 | 0.278596 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.55690e6 | 1.46862 | 0.734308 | − | 0.678817i | \(-0.237507\pi\) | ||||
0.734308 | + | 0.678817i | \(0.237507\pi\) | |||||||
\(458\) | 6.74990e6 | 1.50360 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.30383e7 | 2.87293 | ||||||||
\(461\) | −4.15893e6 | −0.911442 | −0.455721 | − | 0.890123i | \(-0.650619\pi\) | ||||
−0.455721 | + | 0.890123i | \(0.650619\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.62854e6 | 1.22023 | 0.610117 | − | 0.792311i | \(-0.291123\pi\) | ||||
0.610117 | + | 0.792311i | \(0.291123\pi\) | |||||||
\(464\) | 2.23985e6 | 0.482973 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.02728e6 | 1.92572 | ||||||||
\(467\) | −4.20727e6 | −0.892706 | −0.446353 | − | 0.894857i | \(-0.647277\pi\) | ||||
−0.446353 | + | 0.894857i | \(0.647277\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.66200e6 | 1.80873 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.46311e6 | 0.922110 | ||||||||
\(473\) | −4.70081e6 | −0.966095 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.91866e6 | −1.20362 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.73096e6 | −1.94799 | ||||||||
\(479\) | −7.10954e6 | −1.41580 | −0.707901 | − | 0.706311i | \(-0.750358\pi\) | ||||
−0.707901 | + | 0.706311i | \(0.750358\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.74988e6 | −0.936094 | ||||||||
\(482\) | 1.25907e7 | 2.46850 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −903188. | −0.175253 | ||||||||
\(485\) | 1.33395e7 | 2.57504 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.03615e6 | 1.34435 | 0.672176 | − | 0.740392i | \(-0.265360\pi\) | ||||
0.672176 | + | 0.740392i | \(0.265360\pi\) | |||||||
\(488\) | 4.99992e6 | 0.950416 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.08668e6 | 0.203422 | 0.101711 | − | 0.994814i | \(-0.467568\pi\) | ||||
0.101711 | + | 0.994814i | \(0.467568\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.95148e6 | −0.917525 | ||||||||
\(494\) | 6.58312e6 | 1.21371 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.74119e6 | 0.865332 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.05896e6 | 0.549948 | 0.274974 | − | 0.961452i | \(-0.411331\pi\) | ||||
0.274974 | + | 0.961452i | \(0.411331\pi\) | |||||||
\(500\) | −1.61664e7 | −2.89194 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.88396e6 | −0.333666 | ||||||||
\(503\) | 6.23236e6 | 1.09833 | 0.549165 | − | 0.835714i | \(-0.314946\pi\) | ||||
0.549165 | + | 0.835714i | \(0.314946\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.06017e7 | 1.84990 | ||||||||
\(506\) | −9.71501e6 | −1.68681 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.70528e6 | 1.32474 | ||||||||
\(509\) | 6.14574e6 | 1.05143 | 0.525714 | − | 0.850661i | \(-0.323798\pi\) | ||||
0.525714 | + | 0.850661i | \(0.323798\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −5.46557e6 | −0.921426 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.12038e7 | −1.87050 | ||||||||
\(515\) | −4.76410e6 | −0.791522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.73664e6 | −0.614829 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.06163e6 | 1.46960 | ||||||||
\(521\) | 6.78050e6 | 1.09438 | 0.547189 | − | 0.837009i | \(-0.315698\pi\) | ||||
0.547189 | + | 0.837009i | \(0.315698\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.90134e6 | −0.303952 | −0.151976 | − | 0.988384i | \(-0.548564\pi\) | ||||
−0.151976 | + | 0.988384i | \(0.548564\pi\) | |||||||
\(524\) | 6.36832e6 | 1.01320 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.28844e7 | −2.03048 | ||||||||
\(527\) | −1.04810e7 | −1.64391 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.40101e6 | 0.373040 | ||||||||
\(530\) | 1.31665e7 | 2.03601 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.57538e6 | −1.30748 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.02653e7 | −1.55056 | ||||||||
\(536\) | 3.13799e6 | 0.471780 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.98919e7 | −2.96293 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.04950e6 | 1.32933 | 0.664663 | − | 0.747143i | \(-0.268575\pi\) | ||||
0.664663 | + | 0.747143i | \(0.268575\pi\) | |||||||
\(542\) | 9.50743e6 | 1.39016 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.41178e6 | 1.21868 | ||||||||
\(545\) | −7.36173e6 | −1.06167 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.91721e6 | 0.273969 | 0.136985 | − | 0.990573i | \(-0.456259\pi\) | ||||
0.136985 | + | 0.990573i | \(0.456259\pi\) | |||||||
\(548\) | 7.57807e6 | 1.07797 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.22583e7 | 3.13752 | ||||||||
\(551\) | 3.92418e6 | 0.550643 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.23380e6 | 0.309221 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −841178. | −0.115399 | ||||||||
\(557\) | −2.62380e6 | −0.358337 | −0.179169 | − | 0.983818i | \(-0.557341\pi\) | ||||
−0.179169 | + | 0.983818i | \(0.557341\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.08971e7 | 1.47496 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.75048e6 | 1.03511 | ||||||||
\(563\) | −1.07498e7 | −1.42932 | −0.714662 | − | 0.699470i | \(-0.753420\pi\) | ||||
−0.714662 | + | 0.699470i | \(0.753420\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.94412e6 | −0.388003 | ||||||||
\(566\) | 4.32569e6 | 0.567563 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.43051e6 | 0.836324 | ||||||||
\(569\) | −914671. | −0.118436 | −0.0592181 | − | 0.998245i | \(-0.518861\pi\) | ||||
−0.0592181 | + | 0.998245i | \(0.518861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.24616e6 | 0.673367 | 0.336683 | − | 0.941618i | \(-0.390695\pi\) | ||||
0.336683 | + | 0.941618i | \(0.390695\pi\) | |||||||
\(572\) | −1.43331e7 | −1.83168 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.02475e7 | −2.55389 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.15471e7 | 1.44389 | 0.721943 | − | 0.691953i | \(-0.243249\pi\) | ||||
0.721943 | + | 0.691953i | \(0.243249\pi\) | |||||||
\(578\) | 1.89700e6 | 0.236183 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.98059e7 | 2.44470 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.67978e6 | −0.692087 | ||||||||
\(584\) | 5.09083e6 | 0.617670 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.37575e6 | −0.766985 | ||||||||
\(587\) | 5.01428e6 | 0.600638 | 0.300319 | − | 0.953839i | \(-0.402907\pi\) | ||||
0.300319 | + | 0.953839i | \(0.402907\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.30650e6 | 0.986574 | ||||||||
\(590\) | −3.70734e7 | −4.38462 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.71114e6 | 0.317941 | ||||||||
\(593\) | −4.82778e6 | −0.563781 | −0.281890 | − | 0.959447i | \(-0.590961\pi\) | ||||
−0.281890 | + | 0.959447i | \(0.590961\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 401228. | 0.0462674 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.25206e7 | 2.57530 | ||||||||
\(599\) | −9.24522e6 | −1.05281 | −0.526405 | − | 0.850234i | \(-0.676460\pi\) | ||||
−0.526405 | + | 0.850234i | \(0.676460\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.60455e6 | −0.407066 | −0.203533 | − | 0.979068i | \(-0.565242\pi\) | ||||
−0.203533 | + | 0.979068i | \(0.565242\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.36488e7 | 1.52231 | ||||||||
\(605\) | 2.04612e6 | 0.227270 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.34988e6 | 0.809671 | 0.404835 | − | 0.914390i | \(-0.367329\pi\) | ||||
0.404835 | + | 0.914390i | \(0.367329\pi\) | |||||||
\(608\) | −6.66656e6 | −0.731380 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.15325e7 | −4.51922 | ||||||||
\(611\) | 8.66200e6 | 0.938675 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.52374e7 | −1.63780 | −0.818898 | − | 0.573940i | \(-0.805414\pi\) | ||||
−0.818898 | + | 0.573940i | \(0.805414\pi\) | |||||||
\(614\) | −583324. | −0.0624438 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.13748e7 | −1.20290 | −0.601450 | − | 0.798910i | \(-0.705410\pi\) | ||||
−0.601450 | + | 0.798910i | \(0.705410\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.50074e7 | 1.57427 | 0.787133 | − | 0.616783i | \(-0.211564\pi\) | ||||
0.787133 | + | 0.616783i | \(0.211564\pi\) | |||||||
\(620\) | 4.19241e7 | 4.38010 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.63824e6 | −0.273425 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.53397e7 | 1.57079 | ||||||||
\(626\) | −8.83320e6 | −0.900911 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.13559e7 | −1.14901 | ||||||||
\(629\) | −5.99333e6 | −0.604006 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.06654e6 | −0.406586 | −0.203293 | − | 0.979118i | \(-0.565164\pi\) | ||||
−0.203293 | + | 0.979118i | \(0.565164\pi\) | |||||||
\(632\) | −8.38666e6 | −0.835211 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.56609e6 | 0.549955 | ||||||||
\(635\) | −1.74559e7 | −1.71794 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.47577e7 | −1.43538 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.98546e7 | −1.91607 | ||||||||
\(641\) | 9.79786e6 | 0.941860 | 0.470930 | − | 0.882171i | \(-0.343918\pi\) | ||||
0.470930 | + | 0.882171i | \(0.343918\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −678678. | −0.0647346 | −0.0323673 | − | 0.999476i | \(-0.510305\pi\) | ||||
−0.0323673 | + | 0.999476i | \(0.510305\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.30650e6 | 0.783135 | ||||||||
\(647\) | 1.51545e7 | 1.42325 | 0.711623 | − | 0.702561i | \(-0.247960\pi\) | ||||
0.711623 | + | 0.702561i | \(0.247960\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.59928e7 | 1.49044 | ||||||||
\(650\) | −5.15977e7 | −4.79013 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.56846e6 | 0.512999 | ||||||||
\(653\) | −6.64999e6 | −0.610292 | −0.305146 | − | 0.952306i | \(-0.598705\pi\) | ||||
−0.305146 | + | 0.952306i | \(0.598705\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.44271e7 | −1.31394 | ||||||||
\(656\) | 4.89466e6 | 0.444082 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.20368e6 | −0.825559 | −0.412780 | − | 0.910831i | \(-0.635442\pi\) | ||||
−0.412780 | + | 0.910831i | \(0.635442\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.24361e7 | −1.10708 | −0.553540 | − | 0.832823i | \(-0.686723\pi\) | ||||
−0.553540 | + | 0.832823i | \(0.686723\pi\) | |||||||
\(662\) | −2.30067e7 | −2.04037 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.21177e6 | 0.282699 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.34245e7 | 1.16838 | ||||||||
\(668\) | 1.50524e7 | 1.30516 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.60661e7 | −2.24331 | ||||||||
\(671\) | 1.79164e7 | 1.53619 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.53297e6 | −0.811317 | −0.405659 | − | 0.914025i | \(-0.632958\pi\) | ||||
−0.405659 | + | 0.914025i | \(0.632958\pi\) | |||||||
\(674\) | 3.96721e6 | 0.336384 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.68891e7 | 1.42148 | ||||||||
\(677\) | 6.45494e6 | 0.541279 | 0.270639 | − | 0.962681i | \(-0.412765\pi\) | ||||
0.270639 | + | 0.962681i | \(0.412765\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.14338e7 | 0.948244 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.12383e7 | −2.57174 | ||||||||
\(683\) | −4.39884e6 | −0.360816 | −0.180408 | − | 0.983592i | \(-0.557742\pi\) | ||||
−0.180408 | + | 0.983592i | \(0.557742\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.71677e7 | −1.39793 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.21984e6 | −0.500966 | ||||||||
\(689\) | 1.31665e7 | 1.05663 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.30559e7 | 1.83691 | 0.918454 | − | 0.395528i | \(-0.129438\pi\) | ||||
0.918454 | + | 0.395528i | \(0.129438\pi\) | |||||||
\(692\) | 8.24987e6 | 0.654911 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.13990e7 | −0.898397 | ||||||||
\(695\) | 1.90564e6 | 0.149651 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.08203e7 | −0.843641 | ||||||||
\(698\) | −9.17410e6 | −0.712730 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.69755e7 | −1.30475 | −0.652374 | − | 0.757898i | \(-0.726227\pi\) | ||||
−0.652374 | + | 0.757898i | \(0.726227\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.74988e6 | 0.362488 | ||||||||
\(704\) | 1.91211e7 | 1.45406 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.02288e7 | −0.772350 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.61369e6 | 0.269982 | 0.134991 | − | 0.990847i | \(-0.456899\pi\) | ||||
0.134991 | + | 0.990847i | \(0.456899\pi\) | |||||||
\(710\) | −5.34158e7 | −3.97671 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.17942e6 | −0.161117 | ||||||||
\(713\) | 2.84162e7 | 2.09335 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.24708e7 | 2.37536 | ||||||||
\(716\) | 5.62448e6 | 0.410015 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.60441e7 | −1.88537 | ||||||||
\(719\) | −5.66778e6 | −0.408875 | −0.204437 | − | 0.978880i | \(-0.565536\pi\) | ||||
−0.204437 | + | 0.978880i | \(0.565536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.50030e7 | 1.07111 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.67355e6 | 0.685866 | ||||||||
\(725\) | −3.07572e7 | −2.17321 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.72919e7 | 1.21341 | 0.606705 | − | 0.794927i | \(-0.292491\pi\) | ||||
0.606705 | + | 0.794927i | \(0.292491\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.22876e7 | −2.93701 | ||||||||
\(731\) | 1.37498e7 | 0.951705 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.37427e6 | 0.231964 | 0.115982 | − | 0.993251i | \(-0.462999\pi\) | ||||
0.115982 | + | 0.993251i | \(0.462999\pi\) | |||||||
\(734\) | 2.59996e7 | 1.78126 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.28061e7 | −1.55187 | ||||||||
\(737\) | 1.12445e7 | 0.762553 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.16148e7 | 1.45593 | 0.727964 | − | 0.685616i | \(-0.240467\pi\) | ||||
0.727964 | + | 0.685616i | \(0.240467\pi\) | |||||||
\(740\) | 2.39733e7 | 1.60934 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.51151e7 | 1.00447 | 0.502237 | − | 0.864730i | \(-0.332510\pi\) | ||||
0.502237 | + | 0.864730i | \(0.332510\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −908959. | −0.0600003 | ||||||||
\(746\) | 1.38318e7 | 0.909981 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.80853e7 | −1.18188 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.45624e7 | 1.58917 | 0.794587 | − | 0.607151i | \(-0.207688\pi\) | ||||
0.794587 | + | 0.607151i | \(0.207688\pi\) | |||||||
\(752\) | −4.94410e6 | −0.318818 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.42102e7 | 2.19143 | ||||||||
\(755\) | −3.09206e7 | −1.97415 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.02916e6 | 0.128699 | 0.0643496 | − | 0.997927i | \(-0.479503\pi\) | ||||
0.0643496 | + | 0.997927i | \(0.479503\pi\) | |||||||
\(758\) | −1.10862e7 | −0.700826 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.06163e6 | −0.569079 | ||||||||
\(761\) | 5.94179e6 | 0.371926 | 0.185963 | − | 0.982557i | \(-0.440460\pi\) | ||||
0.185963 | + | 0.982557i | \(0.440460\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.10971e6 | 0.316711 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.47736e7 | 2.75709 | ||||||||
\(767\) | −3.70734e7 | −2.27548 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.07928e6 | 0.0658140 | 0.0329070 | − | 0.999458i | \(-0.489523\pi\) | ||||
0.0329070 | + | 0.999458i | \(0.489523\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.34775e7 | −0.813889 | ||||||||
\(773\) | 1.84656e6 | 0.111151 | 0.0555757 | − | 0.998454i | \(-0.482301\pi\) | ||||
0.0555757 | + | 0.998454i | \(0.482301\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.51053e7 | −3.89369 | ||||||||
\(776\) | 1.39998e7 | 0.834578 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.29487e7 | 2.54390 | ||||||||
\(779\) | 8.57538e6 | 0.506302 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.30427e7 | 1.35178 | ||||||||
\(782\) | 2.84162e7 | 1.66169 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.57262e7 | 1.49005 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.32764e7 | 0.764086 | 0.382043 | − | 0.924145i | \(-0.375221\pi\) | ||||
0.382043 | + | 0.924145i | \(0.375221\pi\) | |||||||
\(788\) | 1.58489e7 | 0.909250 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.96648e7 | 3.97142 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.15325e7 | −2.34534 | ||||||||
\(794\) | 1.91664e6 | 0.107892 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.00941e7 | 0.564659 | ||||||||
\(797\) | 8.63793e6 | 0.481686 | 0.240843 | − | 0.970564i | \(-0.422576\pi\) | ||||
0.240843 | + | 0.970564i | \(0.422576\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.09296e7 | 0.605672 | ||||||||
\(800\) | 5.22517e7 | 2.88653 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.77920e7 | 1.52575 | ||||||||
\(803\) | 1.82421e7 | 0.998360 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.24144e7 | 3.92633 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.11265e7 | 0.599556 | ||||||||
\(809\) | 2.39614e6 | 0.128718 | 0.0643592 | − | 0.997927i | \(-0.479500\pi\) | ||||
0.0643592 | + | 0.997927i | \(0.479500\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.79547e6 | −0.362800 | −0.181400 | − | 0.983409i | \(-0.558063\pi\) | ||||
−0.181400 | + | 0.983409i | \(0.558063\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.78629e7 | −0.944910 | ||||||||
\(815\) | −1.26150e7 | −0.665265 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.08971e7 | −0.571156 | ||||||||
\(818\) | 2.21663e7 | 1.15827 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.32812e7 | 2.24784 | ||||||||
\(821\) | 2.64758e6 | 0.137085 | 0.0685426 | − | 0.997648i | \(-0.478165\pi\) | ||||
0.0685426 | + | 0.997648i | \(0.478165\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.40725e7 | −1.23886 | −0.619430 | − | 0.785052i | \(-0.712636\pi\) | ||||
−0.619430 | + | 0.785052i | \(0.712636\pi\) | |||||||
\(824\) | −4.99992e6 | −0.256534 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.55007e6 | 0.0788110 | 0.0394055 | − | 0.999223i | \(-0.487454\pi\) | ||||
0.0394055 | + | 0.999223i | \(0.487454\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.64111e7 | −1.33475 | −0.667375 | − | 0.744722i | \(-0.732582\pi\) | ||||
−0.667375 | + | 0.744722i | \(0.732582\pi\) | |||||||
\(830\) | −2.66790e7 | −1.34423 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.43252e7 | −2.21995 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.41004e7 | −1.69255 | ||||||||
\(836\) | 1.43331e7 | 0.709292 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.11340e7 | 1.53153 | ||||||||
\(839\) | 1.47573e7 | 0.723775 | 0.361887 | − | 0.932222i | \(-0.382132\pi\) | ||||
0.361887 | + | 0.932222i | \(0.382132\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −118525. | −0.00577856 | ||||||||
\(842\) | −8.64588e6 | −0.420270 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.32536e7 | −2.57331 | ||||||||
\(845\) | −3.82613e7 | −1.84339 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.51516e6 | −0.358879 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.51053e7 | −3.09079 | ||||||||
\(851\) | 1.62492e7 | 0.769143 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.12722e6 | 0.288331 | 0.144165 | − | 0.989554i | \(-0.453950\pi\) | ||||
0.144165 | + | 0.989554i | \(0.453950\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.07735e7 | −0.502540 | ||||||||
\(857\) | −3.88119e7 | −1.80515 | −0.902574 | − | 0.430534i | \(-0.858325\pi\) | ||||
−0.902574 | + | 0.430534i | \(0.858325\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.09339e6 | −0.0967980 | −0.0483990 | − | 0.998828i | \(-0.515412\pi\) | ||||
−0.0483990 | + | 0.998828i | \(0.515412\pi\) | |||||||
\(860\) | −5.49992e7 | −2.53577 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.96930e7 | −1.36109 | ||||||||
\(863\) | 4.08889e7 | 1.86887 | 0.934434 | − | 0.356137i | \(-0.115906\pi\) | ||||
0.934434 | + | 0.356137i | \(0.115906\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.86896e7 | −0.849298 | ||||||||
\(866\) | −6.74990e7 | −3.05846 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.00522e7 | −1.34998 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.60661e7 | −1.16421 | ||||||||
\(872\) | −7.72613e6 | −0.344089 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.25206e7 | −0.997245 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.65515e7 | 0.726670 | 0.363335 | − | 0.931659i | \(-0.381638\pi\) | ||||
0.363335 | + | 0.931659i | \(0.381638\pi\) | |||||||
\(878\) | 5.50749e7 | 2.41111 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.85337e7 | −0.806782 | ||||||||
\(881\) | −1.48157e7 | −0.643104 | −0.321552 | − | 0.946892i | \(-0.604205\pi\) | ||||
−0.321552 | + | 0.946892i | \(0.604205\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.52632e7 | 1.09040 | 0.545202 | − | 0.838305i | \(-0.316453\pi\) | ||||
0.545202 | + | 0.838305i | \(0.316453\pi\) | |||||||
\(884\) | 4.19241e7 | 1.80440 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.23434e6 | −0.181218 | ||||||||
\(887\) | 3.23328e7 | 1.37986 | 0.689930 | − | 0.723877i | \(-0.257641\pi\) | ||||
0.689930 | + | 0.723877i | \(0.257641\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.81036e7 | 0.766107 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.28059e7 | 1.38051 | ||||||||
\(893\) | −8.66200e6 | −0.363488 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.27419e7 | −0.531714 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.51908e7 | −1.87008 | ||||||||
\(899\) | 4.31660e7 | 1.78132 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.66133e7 | 0.681778 | ||||||||
\(902\) | −3.22495e7 | −1.31980 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.08986e6 | −0.125753 | ||||||||
\(905\) | −2.19149e7 | −0.889442 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.10034e7 | 0.444129 | 0.222065 | − | 0.975032i | \(-0.428720\pi\) | ||||
0.222065 | + | 0.975032i | \(0.428720\pi\) | |||||||
\(908\) | −6.17534e6 | −0.248569 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.12930e7 | 1.64847 | 0.824234 | − | 0.566249i | \(-0.191606\pi\) | ||||
0.824234 | + | 0.566249i | \(0.191606\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.15088e7 | 0.456935 | ||||||||
\(914\) | −5.71617e7 | −2.26329 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.40677e7 | −1.34154 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.78206e6 | 0.147720 | 0.0738601 | − | 0.997269i | \(-0.476468\pi\) | ||||
0.0738601 | + | 0.997269i | \(0.476468\pi\) | |||||||
\(920\) | −3.09995e7 | −1.20750 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.62567e7 | 1.40463 | ||||||||
\(923\) | −5.34158e7 | −2.06379 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.72289e7 | −1.43063 | ||||||||
\(926\) | −4.90684e7 | −1.88051 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.46438e7 | −1.32055 | ||||||||
\(929\) | −1.47979e7 | −0.562550 | −0.281275 | − | 0.959627i | \(-0.590757\pi\) | ||||
−0.281275 | + | 0.959627i | \(0.590757\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.55620e7 | −1.71816 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.66781e7 | 1.37575 | ||||||||
\(935\) | 4.09713e7 | 1.53268 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.07412e7 | 1.14386 | 0.571929 | − | 0.820303i | \(-0.306195\pi\) | ||||
0.571929 | + | 0.820303i | \(0.306195\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.37184e7 | −1.61378 | ||||||||
\(941\) | −2.56871e7 | −0.945673 | −0.472837 | − | 0.881150i | \(-0.656770\pi\) | ||||
−0.472837 | + | 0.881150i | \(0.656770\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.93361e7 | 1.07429 | ||||||||
\(944\) | 2.11608e7 | 0.772861 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.09807e7 | 1.48885 | ||||||||
\(947\) | 6.25960e6 | 0.226815 | 0.113407 | − | 0.993549i | \(-0.463823\pi\) | ||||
0.113407 | + | 0.993549i | \(0.463823\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.22876e7 | −1.52422 | ||||||||
\(950\) | 5.15977e7 | 1.85490 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.65561e7 | 0.947180 | 0.473590 | − | 0.880746i | \(-0.342958\pi\) | ||||
0.473590 | + | 0.880746i | \(0.342958\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.15758e7 | −0.410715 | ||||||||
\(956\) | 4.91136e7 | 1.73803 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.19795e7 | 2.18190 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.27423e7 | 2.19155 | ||||||||
\(962\) | 4.14085e7 | 1.44262 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.35472e7 | −2.20244 | ||||||||
\(965\) | 3.05324e7 | 1.05546 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.33142e7 | −1.14568 | −0.572841 | − | 0.819667i | \(-0.694159\pi\) | ||||
−0.572841 | + | 0.819667i | \(0.694159\pi\) | |||||||
\(968\) | 2.14740e6 | 0.0736589 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.16291e8 | −3.96841 | ||||||||
\(971\) | −4.04061e6 | −0.137530 | −0.0687652 | − | 0.997633i | \(-0.521906\pi\) | ||||
−0.0687652 | + | 0.997633i | \(0.521906\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.13398e7 | −2.07178 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.37059e7 | 0.796586 | ||||||||
\(977\) | 1.10096e7 | 0.369008 | 0.184504 | − | 0.982832i | \(-0.440932\pi\) | ||||
0.184504 | + | 0.982832i | \(0.440932\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.80957e6 | −0.260418 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.47348e6 | −0.313495 | ||||||||
\(983\) | −2.74119e7 | −0.904804 | −0.452402 | − | 0.891814i | \(-0.649433\pi\) | ||||
−0.452402 | + | 0.891814i | \(0.649433\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.59047e7 | −1.17913 | ||||||||
\(986\) | 4.31660e7 | 1.41400 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.32260e7 | −1.08289 | ||||||||
\(989\) | −3.72785e7 | −1.21190 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.29977e7 | 0.743875 | 0.371938 | − | 0.928258i | \(-0.378694\pi\) | ||||
0.371938 | + | 0.928258i | \(0.378694\pi\) | |||||||
\(992\) | −7.33322e7 | −2.36600 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.28677e7 | −0.732259 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.23347e7 | 1.66744 | 0.833722 | − | 0.552184i | \(-0.186205\pi\) | ||||
0.833722 | + | 0.552184i | \(0.186205\pi\) | |||||||
\(998\) | −2.66674e7 | −0.847527 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.6.a.y.1.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 441.6.a.y.1.4 | yes | 4 | |
7.6 | odd | 2 | inner | 441.6.a.y.1.2 | yes | 4 | |
21.20 | even | 2 | inner | 441.6.a.y.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.6.a.y.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
441.6.a.y.1.2 | yes | 4 | 7.6 | odd | 2 | inner | |
441.6.a.y.1.3 | yes | 4 | 21.20 | even | 2 | inner | |
441.6.a.y.1.4 | yes | 4 | 3.2 | odd | 2 | inner |