Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1104,6,Mod(1,1104)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1104, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1104.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1104 = 2^{4} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1104.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: | \(177.063737074\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.5333.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 11x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 69) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.49331\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1104.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 59.1123 | 1.05743 | 0.528716 | − | 0.848799i | \(-0.322674\pi\) | ||||
0.528716 | + | 0.848799i | \(0.322674\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 213.331 | 1.64554 | 0.822772 | − | 0.568371i | \(-0.192426\pi\) | ||||
0.822772 | + | 0.568371i | \(0.192426\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −126.528 | −0.315287 | −0.157643 | − | 0.987496i | \(-0.550390\pi\) | ||||
−0.157643 | + | 0.987496i | \(0.550390\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −884.825 | −1.45211 | −0.726054 | − | 0.687638i | \(-0.758648\pi\) | ||||
−0.726054 | + | 0.687638i | \(0.758648\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −532.011 | −0.610509 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1179.98 | −0.990264 | −0.495132 | − | 0.868818i | \(-0.664880\pi\) | ||||
−0.495132 | + | 0.868818i | \(0.664880\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1866.19 | 1.18596 | 0.592981 | − | 0.805216i | \(-0.297951\pi\) | ||||
0.592981 | + | 0.805216i | \(0.297951\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1919.98 | −0.950056 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −529.000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 369.263 | 0.118164 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6786.62 | −1.49851 | −0.749253 | − | 0.662284i | \(-0.769587\pi\) | ||||
−0.749253 | + | 0.662284i | \(0.769587\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5146.34 | 0.961820 | 0.480910 | − | 0.876770i | \(-0.340306\pi\) | ||||
0.480910 | + | 0.876770i | \(0.340306\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1138.75 | 0.182031 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12610.5 | 1.74005 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5137.07 | 0.616895 | 0.308448 | − | 0.951241i | \(-0.400191\pi\) | ||||
0.308448 | + | 0.951241i | \(0.400191\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7963.42 | 0.838375 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12482.7 | 1.15971 | 0.579855 | − | 0.814720i | \(-0.303109\pi\) | ||||
0.579855 | + | 0.814720i | \(0.303109\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4198.66 | −0.346290 | −0.173145 | − | 0.984896i | \(-0.555393\pi\) | ||||
−0.173145 | + | 0.984896i | \(0.555393\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4788.10 | 0.352478 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −23006.9 | −1.51919 | −0.759596 | − | 0.650395i | \(-0.774603\pi\) | ||||
−0.759596 | + | 0.650395i | \(0.774603\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 28703.3 | 1.70782 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10619.8 | 0.571729 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 25175.4 | 1.23108 | 0.615541 | − | 0.788105i | \(-0.288938\pi\) | ||||
0.615541 | + | 0.788105i | \(0.288938\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7479.38 | −0.333395 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16795.7 | −0.684716 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 37118.1 | 1.38821 | 0.694107 | − | 0.719872i | \(-0.255800\pi\) | ||||
0.694107 | + | 0.719872i | \(0.255800\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 26410.4 | 0.908761 | 0.454381 | − | 0.890808i | \(-0.349861\pi\) | ||||
0.454381 | + | 0.890808i | \(0.349861\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 17279.8 | 0.548515 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −52304.0 | −1.53551 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 54398.5 | 1.48047 | 0.740236 | − | 0.672347i | \(-0.234714\pi\) | ||||
0.740236 | + | 0.672347i | \(0.234714\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4761.00 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −35684.7 | −0.840110 | −0.420055 | − | 0.907499i | \(-0.637989\pi\) | ||||
−0.420055 | + | 0.907499i | \(0.637989\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 33937.4 | 0.745369 | 0.372684 | − | 0.927958i | \(-0.378437\pi\) | ||||
0.372684 | + | 0.927958i | \(0.378437\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3323.36 | −0.0682220 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −26992.5 | −0.518819 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 76625.8 | 1.38136 | 0.690681 | − | 0.723160i | \(-0.257311\pi\) | ||||
0.690681 | + | 0.723160i | \(0.257311\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 96627.2 | 1.53959 | 0.769794 | − | 0.638293i | \(-0.220359\pi\) | ||||
0.769794 | + | 0.638293i | \(0.220359\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −69751.1 | −1.04714 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 61079.6 | 0.865163 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 30080.8 | 0.402545 | 0.201273 | − | 0.979535i | \(-0.435492\pi\) | ||||
0.201273 | + | 0.979535i | \(0.435492\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −188761. | −2.38951 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −46317.0 | −0.555307 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 110315. | 1.25408 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14637.2 | −0.157953 | −0.0789766 | − | 0.996876i | \(-0.525165\pi\) | ||||
−0.0789766 | + | 0.996876i | \(0.525165\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10248.8 | −0.105096 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −37693.7 | −0.367676 | −0.183838 | − | 0.982957i | \(-0.558852\pi\) | ||||
−0.183838 | + | 0.982957i | \(0.558852\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −125252. | −1.16330 | −0.581649 | − | 0.813440i | \(-0.697592\pi\) | ||||
−0.581649 | + | 0.813440i | \(0.697592\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −113495. | −1.00462 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −28002.7 | −0.236451 | −0.118225 | − | 0.992987i | \(-0.537721\pi\) | ||||
−0.118225 | + | 0.992987i | \(0.537721\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −64151.4 | −0.517178 | −0.258589 | − | 0.965987i | \(-0.583257\pi\) | ||||
−0.258589 | + | 0.965987i | \(0.583257\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −46233.6 | −0.356165 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −25226.7 | −0.185851 | −0.0929253 | − | 0.995673i | \(-0.529622\pi\) | ||||
−0.0929253 | + | 0.995673i | \(0.529622\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −31270.4 | −0.220490 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −71670.8 | −0.484036 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −251726. | −1.62952 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −145042. | −0.900594 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −112344. | −0.669559 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −162898. | −0.932482 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −35783.9 | −0.196870 | −0.0984348 | − | 0.995144i | \(-0.531384\pi\) | ||||
−0.0984348 | + | 0.995144i | \(0.531384\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 37787.9 | 0.199930 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −78119.6 | −0.397724 | −0.198862 | − | 0.980028i | \(-0.563725\pi\) | ||||
−0.198862 | + | 0.980028i | \(0.563725\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 398116. | 1.95155 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −43092.9 | −0.203503 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −92816.7 | −0.422498 | −0.211249 | − | 0.977432i | \(-0.567753\pi\) | ||||
−0.211249 | + | 0.977432i | \(0.567753\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 417118. | 1.83114 | 0.915570 | − | 0.402159i | \(-0.131740\pi\) | ||||
0.915570 | + | 0.402159i | \(0.131740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 207062. | 0.877106 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 111955. | 0.457831 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −401173. | −1.58457 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −258330. | −0.986009 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 445936. | 1.64553 | 0.822766 | − | 0.568380i | \(-0.192430\pi\) | ||||
0.822766 | + | 0.568380i | \(0.192430\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 260458. | 0.929597 | 0.464799 | − | 0.885416i | \(-0.346127\pi\) | ||||
0.464799 | + | 0.885416i | \(0.346127\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −95578.1 | −0.330088 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 304212. | 1.01706 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 46067.4 | 0.149157 | 0.0745787 | − | 0.997215i | \(-0.476239\pi\) | ||||
0.0745787 | + | 0.997215i | \(0.476239\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −226579. | −0.710765 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −112852. | −0.343120 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −188377. | −0.555341 | −0.277671 | − | 0.960676i | \(-0.589562\pi\) | ||||
−0.277671 | + | 0.960676i | \(0.589562\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 67314.4 | 0.192485 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −203214. | −0.563849 | −0.281924 | − | 0.959437i | \(-0.590973\pi\) | ||||
−0.281924 | + | 0.959437i | \(0.590973\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 411622. | 1.10862 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 151161. | 0.395321 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 158051. | 0.401497 | 0.200749 | − | 0.979643i | \(-0.435663\pi\) | ||||
0.200749 | + | 0.979643i | \(0.435663\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 78775.3 | 0.194444 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −334063. | −0.801485 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −166444. | −0.388271 | −0.194136 | − | 0.980975i | \(-0.562190\pi\) | ||||
−0.194136 | + | 0.980975i | \(0.562190\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 185620. | 0.421141 | 0.210571 | − | 0.977579i | \(-0.432468\pi\) | ||||
0.210571 | + | 0.977579i | \(0.432468\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −237693. | −0.524673 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 303664. | 0.652325 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 149300. | 0.312217 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −155519. | −0.316685 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 769733. | 1.52671 | 0.763356 | − | 0.645978i | \(-0.223550\pi\) | ||||
0.763356 | + | 0.645978i | \(0.223550\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −384145. | −0.742338 | −0.371169 | − | 0.928565i | \(-0.621043\pi\) | ||||
−0.371169 | + | 0.928565i | \(0.621043\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 470736. | 0.886525 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 266048. | 0.488421 | 0.244211 | − | 0.969722i | \(-0.421471\pi\) | ||||
0.244211 | + | 0.969722i | \(0.421471\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 706070. | 1.26391 | 0.631953 | − | 0.775007i | \(-0.282254\pi\) | ||||
0.631953 | + | 0.775007i | \(0.282254\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −489587. | −0.854751 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.44780e6 | −2.46586 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 737882. | 1.22631 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −42849.0 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −236125. | −0.373918 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 290636. | 0.449410 | 0.224705 | − | 0.974427i | \(-0.427858\pi\) | ||||
0.224705 | + | 0.974427i | \(0.427858\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 321162. | 0.485038 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −248192. | −0.366178 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.09788e6 | 1.58272 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −305436. | −0.430339 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.04407e6 | 1.43797 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 574915. | 0.774179 | 0.387089 | − | 0.922042i | \(-0.373481\pi\) | ||||
0.387089 | + | 0.922042i | \(0.373481\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 29910.3 | 0.0393880 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.37363e6 | 1.76931 | 0.884655 | − | 0.466246i | \(-0.154394\pi\) | ||||
0.884655 | + | 0.466246i | \(0.154394\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 870725. | 1.09722 | 0.548608 | − | 0.836080i | \(-0.315158\pi\) | ||||
0.548608 | + | 0.836080i | \(0.315158\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 242932. | 0.299540 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.61732e6 | −1.95166 | −0.975832 | − | 0.218522i | \(-0.929876\pi\) | ||||
−0.975832 | + | 0.218522i | \(0.929876\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.35999e6 | −1.60644 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −689633. | −0.797530 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.65281e6 | 1.87167 | 0.935833 | − | 0.352444i | \(-0.114649\pi\) | ||||
0.935833 | + | 0.352444i | \(0.114649\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 928466. | 1.02973 | 0.514865 | − | 0.857271i | \(-0.327842\pi\) | ||||
0.514865 | + | 0.857271i | \(0.327842\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.69672e6 | 1.80590 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.65125e6 | −1.72215 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −869645. | −0.888881 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 909693. | 0.911403 | 0.455702 | − | 0.890133i | \(-0.349388\pi\) | ||||
0.455702 | + | 0.890133i | \(0.349388\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 66933.5 | 0.0657419 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 627760. | 0.604565 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 52666.7 | 0.0497397 | 0.0248699 | − | 0.999691i | \(-0.492083\pi\) | ||||
0.0248699 | + | 0.999691i | \(0.492083\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.09590e6 | 1.01513 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −549716. | −0.499502 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −464764. | −0.414327 | −0.207164 | − | 0.978306i | \(-0.566423\pi\) | ||||
−0.207164 | + | 0.978306i | \(0.566423\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.48818e6 | 1.30179 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −270727. | −0.232410 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 968420. | 0.815987 | 0.407993 | − | 0.912985i | \(-0.366229\pi\) | ||||
0.407993 | + | 0.912985i | \(0.366229\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.29262e6 | −1.89630 | −0.948152 | − | 0.317817i | \(-0.897050\pi\) | ||||
−0.948152 | + | 0.317817i | \(0.897050\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.69885e6 | 1.37958 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −46722.2 | −0.0372556 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 290954. | 0.227837 | 0.113919 | − | 0.993490i | \(-0.463660\pi\) | ||||
0.113919 | + | 0.993490i | \(0.463660\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 416853. | 0.320607 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −391978. | −0.296139 | −0.148070 | − | 0.988977i | \(-0.547306\pi\) | ||||
−0.148070 | + | 0.988977i | \(0.547306\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −732768. | −0.543877 | −0.271938 | − | 0.962315i | \(-0.587665\pi\) | ||||
−0.271938 | + | 0.962315i | \(0.587665\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −992831. | −0.724041 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.66295e6 | 1.90835 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −27511.7 | −0.0193764 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 131735. | 0.0911944 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.62587e6 | 1.10641 | 0.553207 | − | 0.833044i | \(-0.313404\pi\) | ||||
0.553207 | + | 0.833044i | \(0.313404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.19414e6 | 1.46794 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 92239.1 | 0.0606770 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 468072. | 0.302785 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −895706. | −0.569835 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 339243. | 0.212278 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.56118e6 | 0.960954 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.24581e6 | −0.754406 | −0.377203 | − | 0.926131i | \(-0.623114\pi\) | ||||
−0.377203 | + | 0.926131i | \(0.623114\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.12727e6 | 0.671631 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.26852e6 | 1.91624 | 0.958119 | − | 0.286369i | \(-0.0924483\pi\) | ||||
0.958119 | + | 0.286369i | \(0.0924483\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.70161e6 | 0.981744 | 0.490872 | − | 0.871232i | \(-0.336678\pi\) | ||||
0.490872 | + | 0.871232i | \(0.336678\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.02145e6 | 0.580018 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −908317. | −0.507679 | −0.253840 | − | 0.967246i | \(-0.581694\pi\) | ||||
−0.253840 | + | 0.967246i | \(0.581694\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 858699. | 0.472459 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 252025. | 0.136515 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.20206e6 | −1.17442 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −326733. | −0.171587 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 577362. | 0.298593 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.90809e6 | −2.49990 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.14345e6 | 1.07533 | 0.537666 | − | 0.843158i | \(-0.319306\pi\) | ||||
0.537666 | + | 0.843158i | \(0.319306\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 416103. | 0.205632 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.21562e6 | 1.56550 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 817498. | 0.392114 | 0.196057 | − | 0.980593i | \(-0.437186\pi\) | ||||
0.196057 | + | 0.980593i | \(0.437186\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 227040. | 0.107301 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −651157. | −0.303249 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.53785e6 | 1.16475 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 281434. | 0.127300 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.20207e6 | −1.42760 | −0.713801 | − | 0.700349i | \(-0.753028\pi\) | ||||
−0.713801 | + | 0.700349i | \(0.753028\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.23916e6 | −1.42354 | −0.711768 | − | 0.702415i | \(-0.752105\pi\) | ||||
−0.711768 | + | 0.702415i | \(0.752105\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 645037. | 0.279458 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.72676e6 | −0.737555 | −0.368777 | − | 0.929518i | \(-0.620224\pi\) | ||||
−0.368777 | + | 0.929518i | \(0.620224\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.10940e6 | −0.888360 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.26554e6 | 0.940806 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.12338e6 | −1.27905 | −0.639527 | − | 0.768769i | \(-0.720870\pi\) | ||||
−0.639527 | + | 0.768769i | \(0.720870\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00655e6 | 0.406507 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.30537e6 | 0.519958 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.00612e6 | 0.788177 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.17031e6 | −0.453560 | −0.226780 | − | 0.973946i | \(-0.572820\pi\) | ||||
−0.226780 | + | 0.973946i | \(0.572820\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.01110e6 | 0.386570 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.37070e6 | 2.02580 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −692891. | −0.257865 | −0.128933 | − | 0.991653i | \(-0.541155\pi\) | ||||
−0.128933 | + | 0.991653i | \(0.541155\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.46608e6 | 0.538369 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.00497e6 | 2.17599 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.12163e6 | −0.758702 | −0.379351 | − | 0.925253i | \(-0.623853\pi\) | ||||
−0.379351 | + | 0.925253i | \(0.623853\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 322055. | 0.113663 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 287079. | 0.100001 | 0.0500005 | − | 0.998749i | \(-0.484078\pi\) | ||||
0.0500005 | + | 0.998749i | \(0.484078\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.59559e6 | −0.548616 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −340091. | −0.115430 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 679811. | 0.227779 | 0.113890 | − | 0.993493i | \(-0.463669\pi\) | ||||
0.113890 | + | 0.993493i | \(0.463669\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 624208. | 0.206484 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 703076. | 0.229626 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.52953e6 | 1.46070 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.39917e6 | −1.71930 | −0.859648 | − | 0.510886i | \(-0.829317\pi\) | ||||
−0.859648 | + | 0.510886i | \(0.829317\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.58304e6 | −1.12673 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.17808e6 | −0.676416 | −0.338208 | − | 0.941071i | \(-0.609821\pi\) | ||||
−0.338208 | + | 0.941071i | \(0.609821\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.55361e6 | −1.39667 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 387836. | 0.117493 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −649985. | −0.194499 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −356567. | −0.105398 | −0.0526991 | − | 0.998610i | \(-0.516782\pi\) | ||||
−0.0526991 | + | 0.998610i | \(0.516782\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 835350. | 0.243929 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.91847e6 | 2.28437 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.71186e6 | 1.62801 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.75406e6 | −1.05721 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.82634e6 | −1.06475 | −0.532376 | − | 0.846508i | \(-0.678701\pi\) | ||||
−0.532376 | + | 0.846508i | \(0.678701\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.00814e6 | −0.827167 | −0.413584 | − | 0.910466i | \(-0.635723\pi\) | ||||
−0.413584 | + | 0.910466i | \(0.635723\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.86356e6 | −0.506397 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −435721. | −0.117014 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.63416e6 | 1.49541 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.00760e6 | −0.264329 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −577809. | −0.149827 | −0.0749136 | − | 0.997190i | \(-0.523868\pi\) | ||||
−0.0749136 | + | 0.997190i | \(0.523868\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.21909e6 | 1.85039 | 0.925194 | − | 0.379494i | \(-0.123902\pi\) | ||||
0.925194 | + | 0.379494i | \(0.123902\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.61055e6 | 0.914852 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −987212. | −0.247290 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 760935. | 0.188446 | 0.0942229 | − | 0.995551i | \(-0.469963\pi\) | ||||
0.0942229 | + | 0.995551i | \(0.469963\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.32497e6 | 0.569273 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.96892e6 | 1.68716 | 0.843580 | − | 0.537003i | \(-0.180444\pi\) | ||||
0.843580 | + | 0.537003i | \(0.180444\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.77815e6 | 0.425665 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.01342e6 | −0.950049 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.48897e6 | 1.28492 | 0.642458 | − | 0.766321i | \(-0.277915\pi\) | ||||
0.642458 | + | 0.766321i | \(0.277915\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.57942e6 | −0.365641 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.34412e6 | −0.536703 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.11581e7 | −2.52675 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.49968e6 | −0.559879 | −0.279940 | − | 0.960018i | \(-0.590314\pi\) | ||||
−0.279940 | + | 0.960018i | \(0.590314\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 860203. | 0.190576 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.10339e6 | −1.77588 | −0.887942 | − | 0.459956i | \(-0.847865\pi\) | ||||
−0.887942 | + | 0.459956i | \(0.847865\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.71421e6 | 1.02201 | 0.511007 | − | 0.859577i | \(-0.329273\pi\) | ||||
0.511007 | + | 0.859577i | \(0.329273\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.73791e6 | −0.587200 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.03346e6 | 0.219281 | 0.109641 | − | 0.993971i | \(-0.465030\pi\) | ||||
0.109641 | + | 0.993971i | \(0.465030\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.16049e7 | 2.43618 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −414607. | −0.0861161 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 531249. | 0.109181 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 689113. | 0.140138 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.03921e6 | 0.410360 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.13020e6 | −0.225069 | −0.112534 | − | 0.993648i | \(-0.535897\pi\) | ||||
−0.112534 | + | 0.993648i | \(0.535897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.54541e6 | −0.895798 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.01567e6 | 0.198100 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −865238. | −0.167025 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 793366. | 0.151583 | 0.0757916 | − | 0.997124i | \(-0.475852\pi\) | ||||
0.0757916 | + | 0.997124i | \(0.475852\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.69540e6 | 0.320626 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.66618e6 | 0.686294 | 0.343147 | − | 0.939282i | \(-0.388507\pi\) | ||||
0.343147 | + | 0.939282i | \(0.388507\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.00805e6 | 1.48392 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −605829. | −0.111132 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.61267e6 | −1.38244 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.08658e6 | 0.914480 | 0.457240 | − | 0.889343i | \(-0.348838\pi\) | ||||
0.457240 | + | 0.889343i | \(0.348838\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.82893e6 | 0.325538 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.49233e6 | −1.14414 | −0.572072 | − | 0.820203i | \(-0.693860\pi\) | ||||
−0.572072 | + | 0.820203i | \(0.693860\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.22816e6 | −0.388793 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.70460e6 | −0.640061 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.58035e6 | −0.954700 | −0.477350 | − | 0.878713i | \(-0.658403\pi\) | ||||
−0.477350 | + | 0.878713i | \(0.658403\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.23991e6 | 1.22654 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.36045e6 | −0.228239 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.40393e6 | −1.23011 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.91102e6 | 0.478981 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.42246e6 | −0.231804 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.02579e6 | −0.649766 | −0.324883 | − | 0.945754i | \(-0.605325\pi\) | ||||
−0.324883 | + | 0.945754i | \(0.605325\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.41059e6 | 1.50440 | 0.752198 | − | 0.658937i | \(-0.228993\pi\) | ||||
0.752198 | + | 0.658937i | \(0.228993\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −708978. | −0.112262 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.07256e6 | −0.952457 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.00657e6 | 0.462738 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.10450e7 | −1.68402 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.65531e6 | −0.250031 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.49800e6 | 0.224169 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.63178e6 | −0.538453 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.68147e6 | −0.393894 | −0.196947 | − | 0.980414i | \(-0.563103\pi\) | ||||
−0.196947 | + | 0.980414i | \(0.563103\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.67058e6 | −0.243146 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.79214e6 | −0.546881 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.74676e6 | −1.24991 | −0.624955 | − | 0.780660i | \(-0.714883\pi\) | ||||
−0.624955 | + | 0.780660i | \(0.714883\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.13924e6 | 0.302920 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.26651e7 | −1.77717 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.63467e7 | 2.27309 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.73298e6 | −0.376620 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.07905e6 | 0.283940 | 0.141970 | − | 0.989871i | \(-0.454656\pi\) | ||||
0.141970 | + | 0.989871i | \(0.454656\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.71508e6 | 0.502850 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.34370e6 | −0.180259 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.52157e6 | −1.13305 | −0.566524 | − | 0.824045i | \(-0.691712\pi\) | ||||
−0.566524 | + | 0.824045i | \(0.691712\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.49121e6 | −0.196524 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.39967e6 | 0.182838 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.58526e6 | 0.852692 | 0.426346 | − | 0.904560i | \(-0.359801\pi\) | ||||
0.426346 | + | 0.904560i | \(0.359801\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.31614e6 | 0.810702 | 0.405351 | − | 0.914161i | \(-0.367149\pi\) | ||||
0.405351 | + | 0.914161i | \(0.367149\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.92760e6 | −0.881447 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −195340. | −0.0246389 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.48677e6 | 0.561040 | 0.280520 | − | 0.959848i | \(-0.409493\pi\) | ||||
0.280520 | + | 0.959848i | \(0.409493\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.45730e6 | 0.428589 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.06136e7 | 2.53346 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.18540e6 | −0.388144 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.23663e6 | −0.511836 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.42328e6 | 0.889203 | 0.444601 | − | 0.895729i | \(-0.353345\pi\) | ||||
0.444601 | + | 0.895729i | \(0.353345\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.60402e6 | 1.14068 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.39443e6 | −0.281990 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.02182e6 | 0.819998 | 0.409999 | − | 0.912086i | \(-0.365529\pi\) | ||||
0.409999 | + | 0.912086i | \(0.365529\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.48801e7 | −1.72311 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.35463e6 | −0.729717 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.02165e6 | −0.571846 | −0.285923 | − | 0.958253i | \(-0.592300\pi\) | ||||
−0.285923 | + | 0.958253i | \(0.592300\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.66921e6 | 0.527300 | 0.263650 | − | 0.964618i | \(-0.415074\pi\) | ||||
0.263650 | + | 0.964618i | \(0.415074\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.40628e6 | 0.493491 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.57374e6 | −0.952318 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.48942e7 | 1.64076 | 0.820380 | − | 0.571819i | \(-0.193762\pi\) | ||||
0.820380 | + | 0.571819i | \(0.193762\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.30302e7 | 1.42366 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.03570e7 | 2.20603 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.09408e7 | 1.17598 | 0.587989 | − | 0.808869i | \(-0.299920\pi\) | ||||
0.587989 | + | 0.808869i | \(0.299920\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.64093e6 | −0.708013 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.42199e6 | −0.679136 | −0.339568 | − | 0.940582i | \(-0.610281\pi\) | ||||
−0.339568 | + | 0.940582i | \(0.610281\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.05345e6 | 0.320305 | 0.160152 | − | 0.987092i | \(-0.448801\pi\) | ||||
0.160152 | + | 0.987092i | \(0.448801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 385641. | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.41719e6 | 0.662406 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.07832e7 | −1.10420 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.12513e6 | 0.215882 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.06162e6 | −0.610889 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.05012e7 | −1.04994 | −0.524971 | − | 0.851120i | \(-0.675924\pi\) | ||||
−0.524971 | + | 0.851120i | \(0.675924\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.61572e6 | −0.259467 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.11527e6 | −0.208176 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.53974e7 | −2.47994 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.89046e6 | −0.280037 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.57928e7 | −1.51815 | −0.759073 | − | 0.651006i | \(-0.774347\pi\) | ||||
−0.759073 | + | 0.651006i | \(0.774347\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −551159. | −0.0525714 | −0.0262857 | − | 0.999654i | \(-0.508368\pi\) | ||||
−0.0262857 | + | 0.999654i | \(0.508368\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.23373e6 | 0.211413 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.12498e7 | −1.05653 | −0.528267 | − | 0.849078i | \(-0.677158\pi\) | ||||
−0.528267 | + | 0.849078i | \(0.677158\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.69649e6 | −0.437685 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.88088e6 | −0.913783 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.56046e6 | −0.234982 | −0.117491 | − | 0.993074i | \(-0.537485\pi\) | ||||
−0.117491 | + | 0.993074i | \(0.537485\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.61783e6 | −0.420566 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.74893e6 | 0.248456 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 734143. | 0.0658518 | 0.0329259 | − | 0.999458i | \(-0.489517\pi\) | ||||
0.0329259 | + | 0.999458i | \(0.489517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.92354e7 | 1.71237 | 0.856185 | − | 0.516670i | \(-0.172828\pi\) | ||||
0.856185 | + | 0.516670i | \(0.172828\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.39666e6 | −0.830213 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.35336e7 | 2.06364 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.59012e6 | 0.312460 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.17423e6 | −0.446972 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.34166e6 | −0.286520 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.20397e7 | 1.02465 | 0.512326 | − | 0.858791i | \(-0.328784\pi\) | ||||
0.512326 | + | 0.858791i | \(0.328784\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −269192. | −0.0227407 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 99259.2 | 0.00832337 | 0.00416168 | − | 0.999991i | \(-0.498675\pi\) | ||||
0.00416168 | + | 0.999991i | \(0.498675\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.12257e6 | −0.259919 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.23626e7 | −1.02151 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.22059e6 | −0.756323 | −0.378161 | − | 0.925740i | \(-0.623444\pi\) | ||||
−0.378161 | + | 0.925740i | \(0.623444\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.48661e6 | −0.446763 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.83652e6 | −0.633478 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.22758e7 | −1.78766 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.77887e7 | 1.41726 | 0.708629 | − | 0.705581i | \(-0.249314\pi\) | ||||
0.708629 | + | 0.705581i | \(0.249314\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.18639e6 | −0.172940 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.46568e7 | 1.93631 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.47293e7 | −1.14842 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.45558e7 | 1.12679 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.60390e7 | 1.23277 | 0.616384 | − | 0.787446i | \(-0.288597\pi\) | ||||
0.616384 | + | 0.787446i | \(0.288597\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.58673e6 | 0.731614 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.22399e7 | 0.927480 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.04125e6 | −0.605028 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.64673e7 | −1.23029 | −0.615145 | − | 0.788414i | \(-0.710903\pi\) | ||||
−0.615145 | + | 0.788414i | \(0.710903\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.20669e6 | 0.460454 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.72241e6 | −0.200553 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.61794e6 | 0.484125 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.48753e7 | −1.08061 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.48538e6 | −0.395717 | −0.197859 | − | 0.980231i | \(-0.563399\pi\) | ||||
−0.197859 | + | 0.980231i | \(0.563399\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.67202e7 | −1.91426 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.35619e6 | −0.594515 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.50604e6 | −0.177070 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.75484e7 | 1.93313 | 0.966563 | − | 0.256431i | \(-0.0825465\pi\) | ||||
0.966563 | + | 0.256431i | \(0.0825465\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.95432e6 | 0.342918 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.51233e7 | 1.03965 | 0.519825 | − | 0.854273i | \(-0.325997\pi\) | ||||
0.519825 | + | 0.854273i | \(0.325997\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.52705e7 | −1.04264 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.88295e6 | −0.466773 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.56004e7 | 1.05081 | 0.525405 | − | 0.850852i | \(-0.323914\pi\) | ||||
0.525405 | + | 0.850852i | \(0.323914\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.48612e7 | 0.994281 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.77279e6 | −0.117811 | −0.0589053 | − | 0.998264i | \(-0.518761\pi\) | ||||
−0.0589053 | + | 0.998264i | \(0.518761\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.63603e7 | 1.74004 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.82681e6 | 0.513196 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.97386e6 | −0.389090 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.07089e6 | −0.328083 | −0.164042 | − | 0.986453i | \(-0.552453\pi\) | ||||
−0.164042 | + | 0.986453i | \(0.552453\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.18724e6 | −0.526199 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.53962e7 | 0.982987 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −733561. | −0.0465261 | −0.0232631 | − | 0.999729i | \(-0.507406\pi\) | ||||
−0.0232631 | + | 0.999729i | \(0.507406\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −602401. | −0.0379561 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.90077e6 | 0.181573 | 0.0907866 | − | 0.995870i | \(-0.471062\pi\) | ||||
0.0907866 | + | 0.995870i | \(0.471062\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.36855e7 | −0.851039 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.64984e6 | −0.349046 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.28431e7 | −2.01584 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.02882e6 | −0.367635 | −0.183817 | − | 0.982960i | \(-0.558846\pi\) | ||||
−0.183817 | + | 0.982960i | \(0.558846\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −474001. | −0.0287173 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.48827e7 | 0.895844 | 0.447922 | − | 0.894073i | \(-0.352164\pi\) | ||||
0.447922 | + | 0.894073i | \(0.352164\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.90035e6 | 0.113653 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.86309e6 | −0.586085 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.32951e7 | 1.37537 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.51512e6 | 0.264876 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.94745e6 | 0.288388 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.72315e6 | 0.157724 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.19846e7 | −1.26526 | −0.632631 | − | 0.774453i | \(-0.718025\pi\) | ||||
−0.632631 | + | 0.774453i | \(0.718025\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.18288e6 | 0.239212 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.38164e6 | −0.305825 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.33685e7 | −1.31962 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.33936e7 | −0.751586 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.92578e6 | −0.163153 | −0.0815765 | − | 0.996667i | \(-0.525995\pi\) | ||||
−0.0815765 | + | 0.996667i | \(0.525995\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.71476e7 | 1.50440 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.43655e6 | 0.134182 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.29404e6 | −0.235005 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.67096e6 | −0.362826 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.71578e6 | −0.471110 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.36363e6 | −0.126972 | −0.0634860 | − | 0.997983i | \(-0.520222\pi\) | ||||
−0.0634860 | + | 0.997983i | \(0.520222\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.40226e7 | 0.748648 | 0.374324 | − | 0.927298i | \(-0.377875\pi\) | ||||
0.374324 | + | 0.927298i | \(0.377875\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.06335e7 | 1.09483 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.11354e7 | −0.587236 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.83548e6 | −0.410686 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.52896e7 | −0.796503 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.57170e7 | 1.84934 | 0.924670 | − | 0.380769i | \(-0.124341\pi\) | ||||
0.924670 | + | 0.380769i | \(0.124341\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.15100e7 | 0.592344 | 0.296172 | − | 0.955135i | \(-0.404290\pi\) | ||||
0.296172 | + | 0.955135i | \(0.404290\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 420499. | 0.0215095 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.24864e7 | 0.634854 | 0.317427 | − | 0.948283i | \(-0.397181\pi\) | ||||
0.317427 | + | 0.948283i | \(0.397181\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.13398e7 | −0.573087 | −0.286544 | − | 0.958067i | \(-0.592506\pi\) | ||||
−0.286544 | + | 0.958067i | \(0.592506\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.61858e6 | −0.131542 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.38692e7 | −1.69119 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.20125e7 | −0.596232 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.75168e6 | −0.185102 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.91430e7 | −1.42932 | −0.714659 | − | 0.699473i | \(-0.753418\pi\) | ||||
−0.714659 | + | 0.699473i | \(0.753418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.55471e7 | 1.24552 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.52780e6 | 0.170976 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.43319e7 | 1.17229 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.09419e7 | −1.48197 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.59491e6 | 0.314007 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.71751e6 | −0.128632 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.77420e6 | −0.459948 | −0.229974 | − | 0.973197i | \(-0.573864\pi\) | ||||
−0.229974 | + | 0.973197i | \(0.573864\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.93548e6 | 0.418025 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.33262e7 | −1.08491 | −0.542453 | − | 0.840086i | \(-0.682504\pi\) | ||||
−0.542453 | + | 0.840086i | \(0.682504\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.14340e7 | 0.528708 | 0.264354 | − | 0.964426i | \(-0.414841\pi\) | ||||
0.264354 | + | 0.964426i | \(0.414841\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.39666e7 | −1.10179 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.70458e6 | 0.352145 | 0.176073 | − | 0.984377i | \(-0.443661\pi\) | ||||
0.176073 | + | 0.984377i | \(0.443661\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.34277e6 | 0.424556 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 247605. | 0.0111870 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.69534e6 | −0.435525 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.81332e7 | −2.14981 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.18561e6 | −0.0526511 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.47513e7 | −1.53444 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.42476e7 | 0.625520 | 0.312760 | − | 0.949832i | \(-0.398746\pi\) | ||||
0.312760 | + | 0.949832i | \(0.398746\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.46328e7 | −0.638788 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.76114e7 | −0.764459 | −0.382230 | − | 0.924067i | \(-0.624844\pi\) | ||||
−0.382230 | + | 0.924067i | \(0.624844\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.40461e6 | 0.405919 | 0.202959 | − | 0.979187i | \(-0.434944\pi\) | ||||
0.202959 | + | 0.979187i | \(0.434944\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.97472e7 | −0.847517 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.38034e7 | −0.589086 | −0.294543 | − | 0.955638i | \(-0.595167\pi\) | ||||
−0.294543 | + | 0.955638i | \(0.595167\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.63383e6 | −0.323958 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −830152. | −0.0350319 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.29351e7 | −1.80170 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.83888e6 | −0.410571 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.21265e6 | −0.174813 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.49262e7 | −1.44129 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.97064e7 | −1.21910 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.06135e6 | 0.328994 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.09724e7 | 0.445328 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −802157. | −0.0323773 | −0.0161887 | − | 0.999869i | \(-0.505153\pi\) | ||||
−0.0161887 | + | 0.999869i | \(0.505153\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.05319e6 | −0.122559 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.80457e6 | −0.191804 | −0.0959022 | − | 0.995391i | \(-0.530574\pi\) | ||||
−0.0959022 | + | 0.995391i | \(0.530574\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.22261e7 | −0.485412 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.40506e7 | −0.554807 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.66654e7 | −0.654473 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.84366e7 | −1.11068 | −0.555339 | − | 0.831624i | \(-0.687412\pi\) | ||||
−0.555339 | + | 0.831624i | \(0.687412\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.12123e7 | 0.435556 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.15747e7 | 1.21993 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.89693e6 | 0.0728948 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.01454e7 | −0.387766 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.06040e6 | 0.192374 | 0.0961868 | − | 0.995363i | \(-0.469335\pi\) | ||||
0.0961868 | + | 0.995363i | \(0.469335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.35657e7 | 2.02541 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.94166e7 | −1.10634 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.82549e6 | 0.330149 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.27197e7 | 0.473291 | 0.236646 | − | 0.971596i | \(-0.423952\pi\) | ||||
0.236646 | + | 0.971596i | \(0.423952\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.53145e7 | −0.566810 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.66122e7 | −0.611581 | −0.305790 | − | 0.952099i | \(-0.598921\pi\) | ||||
−0.305790 | + | 0.952099i | \(0.598921\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.60335e6 | −0.241816 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.19306e6 | −0.334873 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.77751e7 | −1.73112 | −0.865558 | − | 0.500808i | \(-0.833036\pi\) | ||||
−0.865558 | + | 0.500808i | \(0.833036\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.00286e7 | −1.08236 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.17485e6 | 0.293109 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.77139e7 | −1.34514 | −0.672572 | − | 0.740032i | \(-0.734810\pi\) | ||||
−0.672572 | + | 0.740032i | \(0.734810\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.55007e7 | 1.61439 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.72829e6 | −0.272775 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.98007e7 | −0.695239 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.14436e6 | −0.0749014 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.26822e6 | −0.0788169 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.27077e7 | −0.784973 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.36407e7 | 0.469105 | 0.234553 | − | 0.972103i | \(-0.424638\pi\) | ||||
0.234553 | + | 0.972103i | \(0.424638\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.98185e7 | 0.678050 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.96602e7 | 1.34992 | 0.674958 | − | 0.737856i | \(-0.264162\pi\) | ||||
0.674958 | + | 0.737856i | \(0.264162\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.89843e7 | 3.01322 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.94059e6 | 0.0990658 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.70600e6 | −0.325315 | −0.162657 | − | 0.986683i | \(-0.552007\pi\) | ||||
−0.162657 | + | 0.986683i | \(0.552007\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.80608e6 | −0.126917 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.19626e6 | −0.172393 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.88398e7 | 0.951937 | 0.475969 | − | 0.879462i | \(-0.342098\pi\) | ||||
0.475969 | + | 0.879462i | \(0.342098\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.57267e7 | 0.516473 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.41728e7 | 1.44332 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.22109e6 | 0.0722064 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.94595e7 | −1.27634 | −0.638172 | − | 0.769894i | \(-0.720309\pi\) | ||||
−0.638172 | + | 0.769894i | \(0.720309\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.92910e7 | −0.620844 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.17374e7 | 1.33650 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.61342e7 | 1.15128 | 0.575639 | − | 0.817704i | \(-0.304753\pi\) | ||||
0.575639 | + | 0.817704i | \(0.304753\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.74492e6 | −0.118722 |
(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 | 1104.6.a.i.1.3 | 3 | ||
4.3 | odd | 2 | 69.6.a.b.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 207.6.a.c.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.6.a.b.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
207.6.a.c.1.2 | 3 | 12.11 | even | 2 | |||
1104.6.a.i.1.3 | 3 | 1.1 | even | 1 | trivial |