Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,6,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, 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("225.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(36.0863594579\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{89}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 22 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.21699\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.216991 | −0.0383589 | −0.0191794 | − | 0.999816i | \(-0.506105\pi\) | ||||
−0.0191794 | + | 0.999816i | \(0.506105\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −31.9529 | −0.998529 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 59.2078 | 0.456703 | 0.228351 | − | 0.973579i | \(-0.426667\pi\) | ||||
0.228351 | + | 0.973579i | \(0.426667\pi\) | |||||||
\(8\) | 13.8772 | 0.0766613 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 425.435 | 1.06011 | 0.530056 | − | 0.847963i | \(-0.322171\pi\) | ||||
0.530056 | + | 0.847963i | \(0.322171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1044.23 | −1.71371 | −0.856854 | − | 0.515560i | \(-0.827584\pi\) | ||||
−0.856854 | + | 0.515560i | \(0.827584\pi\) | |||||||
\(14\) | −12.8475 | −0.0175186 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1019.48 | 0.995588 | ||||||||
\(17\) | 948.379 | 0.795902 | 0.397951 | − | 0.917407i | \(-0.369721\pi\) | ||||
0.397951 | + | 0.917407i | \(0.369721\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −328.377 | −0.208684 | −0.104342 | − | 0.994541i | \(-0.533274\pi\) | ||||
−0.104342 | + | 0.994541i | \(0.533274\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −92.3154 | −0.0406647 | ||||||||
\(23\) | 3367.10 | 1.32720 | 0.663599 | − | 0.748088i | \(-0.269028\pi\) | ||||
0.663599 | + | 0.748088i | \(0.269028\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 226.587 | 0.0657359 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1891.86 | −0.456031 | ||||||||
\(29\) | −2299.48 | −0.507732 | −0.253866 | − | 0.967239i | \(-0.581702\pi\) | ||||
−0.253866 | + | 0.967239i | \(0.581702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5144.75 | −0.961524 | −0.480762 | − | 0.876851i | \(-0.659640\pi\) | ||||
−0.480762 | + | 0.876851i | \(0.659640\pi\) | |||||||
\(32\) | −665.288 | −0.114851 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −205.789 | −0.0305299 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9211.93 | −1.10623 | −0.553116 | − | 0.833104i | \(-0.686561\pi\) | ||||
−0.553116 | + | 0.833104i | \(0.686561\pi\) | |||||||
\(38\) | 71.2546 | 0.00800487 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −15170.2 | −1.40939 | −0.704695 | − | 0.709511i | \(-0.748916\pi\) | ||||
−0.704695 | + | 0.709511i | \(0.748916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10119.6 | 0.834629 | 0.417315 | − | 0.908762i | \(-0.362971\pi\) | ||||
0.417315 | + | 0.908762i | \(0.362971\pi\) | |||||||
\(44\) | −13593.9 | −1.05855 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −730.628 | −0.0509098 | ||||||||
\(47\) | −4455.48 | −0.294205 | −0.147103 | − | 0.989121i | \(-0.546995\pi\) | ||||
−0.147103 | + | 0.989121i | \(0.546995\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13301.4 | −0.791423 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 33366.1 | 1.71119 | ||||||||
\(53\) | −20578.6 | −1.00630 | −0.503148 | − | 0.864200i | \(-0.667825\pi\) | ||||
−0.503148 | + | 0.864200i | \(0.667825\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 821.637 | 0.0350114 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 498.965 | 0.0194760 | ||||||||
\(59\) | −44460.5 | −1.66282 | −0.831408 | − | 0.555663i | \(-0.812465\pi\) | ||||
−0.831408 | + | 0.555663i | \(0.812465\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −126.574 | −0.00435531 | −0.00217766 | − | 0.999998i | \(-0.500693\pi\) | ||||
−0.00217766 | + | 0.999998i | \(0.500693\pi\) | |||||||
\(62\) | 1116.36 | 0.0368830 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32479.1 | −0.991182 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −18917.5 | −0.514845 | −0.257422 | − | 0.966299i | \(-0.582873\pi\) | ||||
−0.257422 | + | 0.966299i | \(0.582873\pi\) | |||||||
\(68\) | −30303.5 | −0.794731 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6571.05 | 0.154699 | 0.0773497 | − | 0.997004i | \(-0.475354\pi\) | ||||
0.0773497 | + | 0.997004i | \(0.475354\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5463.86 | 0.120003 | 0.0600015 | − | 0.998198i | \(-0.480889\pi\) | ||||
0.0600015 | + | 0.998198i | \(0.480889\pi\) | |||||||
\(74\) | 1998.90 | 0.0424338 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10492.6 | 0.208377 | ||||||||
\(77\) | 25189.1 | 0.484156 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15391.0 | 0.277460 | 0.138730 | − | 0.990330i | \(-0.455698\pi\) | ||||
0.138730 | + | 0.990330i | \(0.455698\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3291.79 | 0.0540626 | ||||||||
\(83\) | 99222.5 | 1.58094 | 0.790469 | − | 0.612502i | \(-0.209837\pi\) | ||||
0.790469 | + | 0.612502i | \(0.209837\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2195.87 | −0.0320154 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5903.84 | 0.0812695 | ||||||||
\(89\) | −90797.1 | −1.21506 | −0.607529 | − | 0.794297i | \(-0.707839\pi\) | ||||
−0.607529 | + | 0.794297i | \(0.707839\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −61826.4 | −0.782655 | ||||||||
\(92\) | −107589. | −1.32525 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 966.798 | 0.0112854 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −116353. | −1.25559 | −0.627796 | − | 0.778378i | \(-0.716043\pi\) | ||||
−0.627796 | + | 0.778378i | \(0.716043\pi\) | |||||||
\(98\) | 2886.29 | 0.0303581 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −145908. | −1.42323 | −0.711615 | − | 0.702569i | \(-0.752036\pi\) | ||||
−0.711615 | + | 0.702569i | \(0.752036\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −116865. | −1.08540 | −0.542702 | − | 0.839925i | \(-0.682599\pi\) | ||||
−0.542702 | + | 0.839925i | \(0.682599\pi\) | |||||||
\(104\) | −14490.9 | −0.131375 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4465.36 | 0.0386004 | ||||||||
\(107\) | 186064. | 1.57110 | 0.785549 | − | 0.618800i | \(-0.212381\pi\) | ||||
0.785549 | + | 0.618800i | \(0.212381\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −132641. | −1.06933 | −0.534663 | − | 0.845065i | \(-0.679562\pi\) | ||||
−0.534663 | + | 0.845065i | \(0.679562\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 60361.3 | 0.454688 | ||||||||
\(113\) | 29607.7 | 0.218126 | 0.109063 | − | 0.994035i | \(-0.465215\pi\) | ||||
0.109063 | + | 0.994035i | \(0.465215\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 73475.1 | 0.506985 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9647.51 | 0.0637837 | ||||||||
\(119\) | 56151.4 | 0.363491 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19943.9 | 0.123836 | ||||||||
\(122\) | 27.4653 | 0.000167065 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 164390. | 0.960110 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 189319. | 1.04156 | 0.520780 | − | 0.853691i | \(-0.325641\pi\) | ||||
0.520780 | + | 0.853691i | \(0.325641\pi\) | |||||||
\(128\) | 28336.9 | 0.152872 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 107363. | 0.546607 | 0.273304 | − | 0.961928i | \(-0.411884\pi\) | ||||
0.273304 | + | 0.961928i | \(0.411884\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19442.5 | −0.0953064 | ||||||||
\(134\) | 4104.91 | 0.0197489 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13160.8 | 0.0610149 | ||||||||
\(137\) | −173859. | −0.791399 | −0.395700 | − | 0.918380i | \(-0.629498\pi\) | ||||
−0.395700 | + | 0.918380i | \(0.629498\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −30334.0 | −0.133166 | −0.0665830 | − | 0.997781i | \(-0.521210\pi\) | ||||
−0.0665830 | + | 0.997781i | \(0.521210\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1425.86 | −0.00593410 | ||||||||
\(143\) | −444251. | −1.81672 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1185.61 | −0.00460318 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 294348. | 1.10460 | ||||||||
\(149\) | 296104. | 1.09264 | 0.546322 | − | 0.837575i | \(-0.316028\pi\) | ||||
0.546322 | + | 0.837575i | \(0.316028\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 240567. | 0.858605 | 0.429303 | − | 0.903161i | \(-0.358759\pi\) | ||||
0.429303 | + | 0.903161i | \(0.358759\pi\) | |||||||
\(152\) | −4556.94 | −0.0159980 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5465.79 | −0.0185717 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −110903. | −0.359081 | −0.179541 | − | 0.983751i | \(-0.557461\pi\) | ||||
−0.179541 | + | 0.983751i | \(0.557461\pi\) | |||||||
\(158\) | −3339.71 | −0.0106430 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 199358. | 0.606135 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 211488. | 0.623472 | 0.311736 | − | 0.950169i | \(-0.399090\pi\) | ||||
0.311736 | + | 0.950169i | \(0.399090\pi\) | |||||||
\(164\) | 484731. | 1.40732 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −21530.3 | −0.0606430 | ||||||||
\(167\) | −74281.4 | −0.206105 | −0.103053 | − | 0.994676i | \(-0.532861\pi\) | ||||
−0.103053 | + | 0.994676i | \(0.532861\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 719117. | 1.93679 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −323352. | −0.833401 | ||||||||
\(173\) | 386465. | 0.981736 | 0.490868 | − | 0.871234i | \(-0.336680\pi\) | ||||
0.490868 | + | 0.871234i | \(0.336680\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 433723. | 1.05543 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 19702.1 | 0.0466083 | ||||||||
\(179\) | 255550. | 0.596133 | 0.298067 | − | 0.954545i | \(-0.403658\pi\) | ||||
0.298067 | + | 0.954545i | \(0.403658\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −425741. | −0.965937 | −0.482969 | − | 0.875638i | \(-0.660441\pi\) | ||||
−0.482969 | + | 0.875638i | \(0.660441\pi\) | |||||||
\(182\) | 13415.7 | 0.0300218 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 46725.8 | 0.101745 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 403473. | 0.843745 | ||||||||
\(188\) | 142366. | 0.293772 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −380425. | −0.754546 | −0.377273 | − | 0.926102i | \(-0.623138\pi\) | ||||
−0.377273 | + | 0.926102i | \(0.623138\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −226896. | −0.438463 | −0.219231 | − | 0.975673i | \(-0.570355\pi\) | ||||
−0.219231 | + | 0.975673i | \(0.570355\pi\) | |||||||
\(194\) | 25247.5 | 0.0481631 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 425020. | 0.790258 | ||||||||
\(197\) | 68875.2 | 0.126444 | 0.0632219 | − | 0.997999i | \(-0.479862\pi\) | ||||
0.0632219 | + | 0.997999i | \(0.479862\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −597116. | −1.06887 | −0.534437 | − | 0.845209i | \(-0.679476\pi\) | ||||
−0.534437 | + | 0.845209i | \(0.679476\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 31660.6 | 0.0545935 | ||||||||
\(203\) | −136147. | −0.231883 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 25358.6 | 0.0416349 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.06457e6 | −1.70615 | ||||||||
\(209\) | −139703. | −0.221228 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 170817. | 0.264134 | 0.132067 | − | 0.991241i | \(-0.457839\pi\) | ||||
0.132067 | + | 0.991241i | \(0.457839\pi\) | |||||||
\(212\) | 657546. | 1.00482 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −40374.1 | −0.0602655 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −304609. | −0.439131 | ||||||||
\(218\) | 28781.8 | 0.0410182 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −990323. | −1.36394 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −233029. | −0.313796 | −0.156898 | − | 0.987615i | \(-0.550149\pi\) | ||||
−0.156898 | + | 0.987615i | \(0.550149\pi\) | |||||||
\(224\) | −39390.2 | −0.0524527 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6424.58 | −0.00836708 | ||||||||
\(227\) | −174347. | −0.224569 | −0.112284 | − | 0.993676i | \(-0.535817\pi\) | ||||
−0.112284 | + | 0.993676i | \(0.535817\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 322529. | 0.406424 | 0.203212 | − | 0.979135i | \(-0.434862\pi\) | ||||
0.203212 | + | 0.979135i | \(0.434862\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −31910.3 | −0.0389234 | ||||||||
\(233\) | 908890. | 1.09679 | 0.548393 | − | 0.836221i | \(-0.315240\pi\) | ||||
0.548393 | + | 0.836221i | \(0.315240\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.42064e6 | 1.66037 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12184.3 | −0.0139431 | ||||||||
\(239\) | −569964. | −0.645436 | −0.322718 | − | 0.946495i | \(-0.604596\pi\) | ||||
−0.322718 | + | 0.946495i | \(0.604596\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −752854. | −0.834965 | −0.417482 | − | 0.908685i | \(-0.637087\pi\) | ||||
−0.417482 | + | 0.908685i | \(0.637087\pi\) | |||||||
\(242\) | −4327.64 | −0.00475021 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4044.40 | 0.00434891 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 342900. | 0.357623 | ||||||||
\(248\) | −71394.7 | −0.0737117 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −616625. | −0.617784 | −0.308892 | − | 0.951097i | \(-0.599958\pi\) | ||||
−0.308892 | + | 0.951097i | \(0.599958\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.43248e6 | 1.40698 | ||||||||
\(254\) | −41080.4 | −0.0399531 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.03318e6 | 0.985318 | ||||||||
\(257\) | −1.34559e6 | −1.27080 | −0.635402 | − | 0.772181i | \(-0.719166\pi\) | ||||
−0.635402 | + | 0.772181i | \(0.719166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −545418. | −0.505219 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −23296.7 | −0.0209672 | ||||||||
\(263\) | −2.06966e6 | −1.84505 | −0.922527 | − | 0.385932i | \(-0.873880\pi\) | ||||
−0.922527 | + | 0.385932i | \(0.873880\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4218.83 | 0.00365585 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 604469. | 0.514087 | ||||||||
\(269\) | −121636. | −0.102490 | −0.0512448 | − | 0.998686i | \(-0.516319\pi\) | ||||
−0.0512448 | + | 0.998686i | \(0.516319\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.32515e6 | −1.09608 | −0.548040 | − | 0.836452i | \(-0.684626\pi\) | ||||
−0.548040 | + | 0.836452i | \(0.684626\pi\) | |||||||
\(272\) | 966855. | 0.792390 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 37725.7 | 0.0303572 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −790419. | −0.618953 | −0.309477 | − | 0.950907i | \(-0.600154\pi\) | ||||
−0.309477 | + | 0.950907i | \(0.600154\pi\) | |||||||
\(278\) | 6582.20 | 0.00510810 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −52617.8 | −0.0397527 | −0.0198763 | − | 0.999802i | \(-0.506327\pi\) | ||||
−0.0198763 | + | 0.999802i | \(0.506327\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.07971e6 | 0.801386 | 0.400693 | − | 0.916212i | \(-0.368769\pi\) | ||||
0.400693 | + | 0.916212i | \(0.368769\pi\) | |||||||
\(284\) | −209964. | −0.154472 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 96398.2 | 0.0696874 | ||||||||
\(287\) | −898193. | −0.643672 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −520435. | −0.366540 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −174586. | −0.119826 | ||||||||
\(293\) | 1.10695e6 | 0.753286 | 0.376643 | − | 0.926359i | \(-0.377078\pi\) | ||||
0.376643 | + | 0.926359i | \(0.377078\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −127836. | −0.0848052 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −64251.7 | −0.0419126 | ||||||||
\(299\) | −3.51601e6 | −2.27443 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 599161. | 0.381178 | ||||||||
\(302\) | −52200.7 | −0.0329351 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −334774. | −0.207763 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.18684e6 | 1.32425 | 0.662126 | − | 0.749393i | \(-0.269654\pi\) | ||||
0.662126 | + | 0.749393i | \(0.269654\pi\) | |||||||
\(308\) | −804864. | −0.483443 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.43710e6 | −0.842533 | −0.421267 | − | 0.906937i | \(-0.638414\pi\) | ||||
−0.421267 | + | 0.906937i | \(0.638414\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.60637e6 | −0.926799 | −0.463400 | − | 0.886149i | \(-0.653371\pi\) | ||||
−0.463400 | + | 0.886149i | \(0.653371\pi\) | |||||||
\(314\) | 24064.8 | 0.0137739 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −491788. | −0.277052 | ||||||||
\(317\) | 2.71344e6 | 1.51660 | 0.758302 | − | 0.651904i | \(-0.226029\pi\) | ||||
0.758302 | + | 0.651904i | \(0.226029\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −978279. | −0.538253 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −43258.9 | −0.0232507 | ||||||||
\(323\) | −311425. | −0.166092 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −45890.9 | −0.0239157 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −210519. | −0.108046 | ||||||||
\(329\) | −263799. | −0.134364 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 380684. | 0.190983 | 0.0954914 | − | 0.995430i | \(-0.469558\pi\) | ||||
0.0954914 | + | 0.995430i | \(0.469558\pi\) | |||||||
\(332\) | −3.17045e6 | −1.57861 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16118.4 | 0.00790596 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −341423. | −0.163764 | −0.0818820 | − | 0.996642i | \(-0.526093\pi\) | ||||
−0.0818820 | + | 0.996642i | \(0.526093\pi\) | |||||||
\(338\) | −156042. | −0.0742932 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.18876e6 | −1.01932 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.78265e6 | −0.818148 | ||||||||
\(344\) | 140432. | 0.0639838 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −83859.3 | −0.0376583 | ||||||||
\(347\) | 1.59293e6 | 0.710187 | 0.355094 | − | 0.934831i | \(-0.384449\pi\) | ||||
0.355094 | + | 0.934831i | \(0.384449\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.83351e6 | −1.24526 | −0.622632 | − | 0.782515i | \(-0.713937\pi\) | ||||
−0.622632 | + | 0.782515i | \(0.713937\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −283037. | −0.121755 | ||||||||
\(353\) | 921269. | 0.393505 | 0.196752 | − | 0.980453i | \(-0.436961\pi\) | ||||
0.196752 | + | 0.980453i | \(0.436961\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.90123e6 | 1.21327 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −55451.9 | −0.0228670 | ||||||||
\(359\) | −1.08583e6 | −0.444658 | −0.222329 | − | 0.974972i | \(-0.571366\pi\) | ||||
−0.222329 | + | 0.974972i | \(0.571366\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.36827e6 | −0.956451 | ||||||||
\(362\) | 92381.7 | 0.0370523 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.97553e6 | 0.781503 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.80160e6 | −0.698223 | −0.349112 | − | 0.937081i | \(-0.613517\pi\) | ||||
−0.349112 | + | 0.937081i | \(0.613517\pi\) | |||||||
\(368\) | 3.43269e6 | 1.32134 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.21841e6 | −0.459578 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.85933e6 | −1.43628 | −0.718140 | − | 0.695898i | \(-0.755006\pi\) | ||||
−0.718140 | + | 0.695898i | \(0.755006\pi\) | |||||||
\(374\) | −87549.9 | −0.0323651 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −61829.5 | −0.0225541 | ||||||||
\(377\) | 2.40118e6 | 0.870104 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.44044e6 | 0.872711 | 0.436356 | − | 0.899774i | \(-0.356269\pi\) | ||||
0.436356 | + | 0.899774i | \(0.356269\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 82548.6 | 0.0289435 | ||||||||
\(383\) | 1.66772e6 | 0.580934 | 0.290467 | − | 0.956885i | \(-0.406189\pi\) | ||||
0.290467 | + | 0.956885i | \(0.406189\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 49234.2 | 0.0168189 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.71782e6 | 1.25374 | ||||||||
\(389\) | 2.33427e6 | 0.782125 | 0.391063 | − | 0.920364i | \(-0.372108\pi\) | ||||
0.391063 | + | 0.920364i | \(0.372108\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.19328e6 | 1.05632 | ||||||||
\(392\) | −184586. | −0.0606715 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14945.3 | −0.00485024 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.31607e6 | −1.05596 | −0.527981 | − | 0.849256i | \(-0.677051\pi\) | ||||
−0.527981 | + | 0.849256i | \(0.677051\pi\) | |||||||
\(398\) | 129569. | 0.0410008 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.84120e6 | 0.571795 | 0.285898 | − | 0.958260i | \(-0.407708\pi\) | ||||
0.285898 | + | 0.958260i | \(0.407708\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.37229e6 | 1.64777 | ||||||||
\(404\) | 4.66218e6 | 1.42114 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 29542.6 | 0.00889476 | ||||||||
\(407\) | −3.91908e6 | −1.17273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.83672e6 | 1.13410 | 0.567050 | − | 0.823683i | \(-0.308085\pi\) | ||||
0.567050 | + | 0.823683i | \(0.308085\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.73418e6 | 1.08381 | ||||||||
\(413\) | −2.63241e6 | −0.759413 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 694712. | 0.196821 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 30314.2 | 0.00848605 | ||||||||
\(419\) | 4.37456e6 | 1.21731 | 0.608653 | − | 0.793437i | \(-0.291710\pi\) | ||||
0.608653 | + | 0.793437i | \(0.291710\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 76116.4 | 0.0209302 | 0.0104651 | − | 0.999945i | \(-0.496669\pi\) | ||||
0.0104651 | + | 0.999945i | \(0.496669\pi\) | |||||||
\(422\) | −37065.7 | −0.0101319 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −285573. | −0.0771440 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7494.16 | −0.00198908 | ||||||||
\(428\) | −5.94529e6 | −1.56879 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.87872e6 | 1.26506 | 0.632532 | − | 0.774534i | \(-0.282016\pi\) | ||||
0.632532 | + | 0.774534i | \(0.282016\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.13136e6 | −1.05894 | −0.529472 | − | 0.848327i | \(-0.677610\pi\) | ||||
−0.529472 | + | 0.848327i | \(0.677610\pi\) | |||||||
\(434\) | 66097.4 | 0.0168446 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.23825e6 | 1.06775 | ||||||||
\(437\) | −1.10568e6 | −0.276964 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −492071. | −0.121862 | −0.0609308 | − | 0.998142i | \(-0.519407\pi\) | ||||
−0.0609308 | + | 0.998142i | \(0.519407\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 214891. | 0.0523193 | ||||||||
\(443\) | −1.70371e6 | −0.412464 | −0.206232 | − | 0.978503i | \(-0.566120\pi\) | ||||
−0.206232 | + | 0.978503i | \(0.566120\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 50565.1 | 0.0120369 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.92301e6 | −0.452676 | ||||||||
\(449\) | −1.25545e6 | −0.293888 | −0.146944 | − | 0.989145i | \(-0.546944\pi\) | ||||
−0.146944 | + | 0.989145i | \(0.546944\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.45393e6 | −1.49411 | ||||||||
\(452\) | −946051. | −0.217805 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 37831.6 | 0.00861421 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.71886e6 | 1.05693 | 0.528466 | − | 0.848955i | \(-0.322767\pi\) | ||||
0.528466 | + | 0.848955i | \(0.322767\pi\) | |||||||
\(458\) | −69985.7 | −0.0155900 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.00772e6 | 0.220844 | 0.110422 | − | 0.993885i | \(-0.464780\pi\) | ||||
0.110422 | + | 0.993885i | \(0.464780\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.52400e6 | 1.63116 | 0.815580 | − | 0.578645i | \(-0.196418\pi\) | ||||
0.815580 | + | 0.578645i | \(0.196418\pi\) | |||||||
\(464\) | −2.34428e6 | −0.505492 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −197221. | −0.0420714 | ||||||||
\(467\) | 4.77568e6 | 1.01331 | 0.506656 | − | 0.862148i | \(-0.330881\pi\) | ||||
0.506656 | + | 0.862148i | \(0.330881\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.12006e6 | −0.235131 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −616986. | −0.127474 | ||||||||
\(473\) | 4.30525e6 | 0.884800 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.79420e6 | −0.362956 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 123677. | 0.0247582 | ||||||||
\(479\) | 8.09043e6 | 1.61114 | 0.805569 | − | 0.592501i | \(-0.201860\pi\) | ||||
0.805569 | + | 0.592501i | \(0.201860\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.61935e6 | 1.89576 | ||||||||
\(482\) | 163362. | 0.0320283 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −637266. | −0.123654 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −605970. | −0.115779 | −0.0578894 | − | 0.998323i | \(-0.518437\pi\) | ||||
−0.0578894 | + | 0.998323i | \(0.518437\pi\) | |||||||
\(488\) | −1756.49 | −0.000333884 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.91166e6 | −1.29383 | −0.646917 | − | 0.762560i | \(-0.723942\pi\) | ||||
−0.646917 | + | 0.762560i | \(0.723942\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.18078e6 | −0.404105 | ||||||||
\(494\) | −74406.0 | −0.0137180 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.24498e6 | −0.957282 | ||||||||
\(497\) | 389057. | 0.0706517 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.20448e6 | 0.755895 | 0.377947 | − | 0.925827i | \(-0.376630\pi\) | ||||
0.377947 | + | 0.925827i | \(0.376630\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 133802. | 0.0236975 | ||||||||
\(503\) | −7.22627e6 | −1.27349 | −0.636743 | − | 0.771076i | \(-0.719719\pi\) | ||||
−0.636743 | + | 0.771076i | \(0.719719\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −310835. | −0.0539701 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.04929e6 | −1.04003 | ||||||||
\(509\) | 2.81947e6 | 0.482362 | 0.241181 | − | 0.970480i | \(-0.422465\pi\) | ||||
0.241181 | + | 0.970480i | \(0.422465\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 323503. | 0.0548057 | ||||||||
\(512\) | −1.13097e6 | −0.190667 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 291980. | 0.0487466 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.89552e6 | −0.311890 | ||||||||
\(518\) | 118351. | 0.0193796 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.64191e6 | 0.749208 | 0.374604 | − | 0.927185i | \(-0.377779\pi\) | ||||
0.374604 | + | 0.927185i | \(0.377779\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.98997e6 | 0.318121 | 0.159061 | − | 0.987269i | \(-0.449154\pi\) | ||||
0.159061 | + | 0.987269i | \(0.449154\pi\) | |||||||
\(524\) | −3.43055e6 | −0.545803 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 449096. | 0.0707742 | ||||||||
\(527\) | −4.87917e6 | −0.765279 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.90099e6 | 0.761455 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 621243. | 0.0951661 | ||||||||
\(533\) | 1.58411e7 | 2.41528 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −262521. | −0.0394687 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26393.8 | 0.00393139 | ||||||||
\(539\) | −5.65890e6 | −0.838996 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.06167e7 | −1.55954 | −0.779768 | − | 0.626069i | \(-0.784663\pi\) | ||||
−0.779768 | + | 0.626069i | \(0.784663\pi\) | |||||||
\(542\) | 287545. | 0.0420444 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −630945. | −0.0914101 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.25513e7 | −1.79358 | −0.896789 | − | 0.442458i | \(-0.854107\pi\) | ||||
−0.896789 | + | 0.442458i | \(0.854107\pi\) | |||||||
\(548\) | 5.55530e6 | 0.790235 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 755096. | 0.105955 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 911269. | 0.126717 | ||||||||
\(554\) | 171513. | 0.0237423 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 969261. | 0.132970 | ||||||||
\(557\) | 3.98643e6 | 0.544435 | 0.272218 | − | 0.962236i | \(-0.412243\pi\) | ||||
0.272218 | + | 0.962236i | \(0.412243\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.05672e7 | −1.43031 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11417.6 | 0.00152487 | ||||||||
\(563\) | 453419. | 0.0602877 | 0.0301438 | − | 0.999546i | \(-0.490403\pi\) | ||||
0.0301438 | + | 0.999546i | \(0.490403\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −234287. | −0.0307403 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 91187.6 | 0.0118595 | ||||||||
\(569\) | 3.96567e6 | 0.513494 | 0.256747 | − | 0.966479i | \(-0.417349\pi\) | ||||
0.256747 | + | 0.966479i | \(0.417349\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.14150e6 | 0.659932 | 0.329966 | − | 0.943993i | \(-0.392963\pi\) | ||||
0.329966 | + | 0.943993i | \(0.392963\pi\) | |||||||
\(572\) | 1.41951e7 | 1.81405 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 194899. | 0.0246905 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.48527e6 | 1.06103 | 0.530513 | − | 0.847677i | \(-0.321999\pi\) | ||||
0.530513 | + | 0.847677i | \(0.321999\pi\) | |||||||
\(578\) | 112929. | 0.0140601 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.87474e6 | 0.722019 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.75485e6 | −1.06679 | ||||||||
\(584\) | 75822.9 | 0.00919959 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −240198. | −0.0288952 | ||||||||
\(587\) | −1.39429e7 | −1.67016 | −0.835079 | − | 0.550130i | \(-0.814578\pi\) | ||||
−0.835079 | + | 0.550130i | \(0.814578\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.68942e6 | 0.200654 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.39140e6 | −1.10135 | ||||||||
\(593\) | −1.32665e7 | −1.54925 | −0.774623 | − | 0.632423i | \(-0.782060\pi\) | ||||
−0.774623 | + | 0.632423i | \(0.782060\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.46138e6 | −1.09104 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 762942. | 0.0872445 | ||||||||
\(599\) | −1.62821e7 | −1.85415 | −0.927073 | − | 0.374880i | \(-0.877684\pi\) | ||||
−0.927073 | + | 0.374880i | \(0.877684\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.32895e7 | 1.50080 | 0.750398 | − | 0.660987i | \(-0.229862\pi\) | ||||
0.750398 | + | 0.660987i | \(0.229862\pi\) | |||||||
\(602\) | −130012. | −0.0146215 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.68681e6 | −0.857342 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.57179e7 | 1.73151 | 0.865753 | − | 0.500472i | \(-0.166840\pi\) | ||||
0.865753 | + | 0.500472i | \(0.166840\pi\) | |||||||
\(608\) | 218465. | 0.0239675 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.65254e6 | 0.504181 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 910487. | 0.0978639 | 0.0489320 | − | 0.998802i | \(-0.484418\pi\) | ||||
0.0489320 | + | 0.998802i | \(0.484418\pi\) | |||||||
\(614\) | −474523. | −0.0507968 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 349553. | 0.0371160 | ||||||||
\(617\) | −4.73246e6 | −0.500466 | −0.250233 | − | 0.968186i | \(-0.580507\pi\) | ||||
−0.250233 | + | 0.968186i | \(0.580507\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.54970e6 | 0.687060 | 0.343530 | − | 0.939142i | \(-0.388377\pi\) | ||||
0.343530 | + | 0.939142i | \(0.388377\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 311838. | 0.0323186 | ||||||||
\(623\) | −5.37590e6 | −0.554921 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 348568. | 0.0355510 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.54366e6 | 0.358553 | ||||||||
\(629\) | −8.73640e6 | −0.880452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.89272e7 | −1.89240 | −0.946199 | − | 0.323585i | \(-0.895112\pi\) | ||||
−0.946199 | + | 0.323585i | \(0.895112\pi\) | |||||||
\(632\) | 213584. | 0.0212704 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −588791. | −0.0581752 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.38897e7 | 1.35627 | ||||||||
\(638\) | 212277. | 0.0206468 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.61144e6 | −0.539422 | −0.269711 | − | 0.962941i | \(-0.586928\pi\) | ||||
−0.269711 | + | 0.962941i | \(0.586928\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.43672e6 | 0.423190 | 0.211595 | − | 0.977357i | \(-0.432134\pi\) | ||||
0.211595 | + | 0.977357i | \(0.432134\pi\) | |||||||
\(644\) | −6.37008e6 | −0.605243 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 67576.4 | 0.00637109 | ||||||||
\(647\) | 8.38503e6 | 0.787488 | 0.393744 | − | 0.919220i | \(-0.371180\pi\) | ||||
0.393744 | + | 0.919220i | \(0.371180\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.89150e7 | −1.76277 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.75766e6 | −0.622555 | ||||||||
\(653\) | −1.33396e7 | −1.22422 | −0.612112 | − | 0.790771i | \(-0.709680\pi\) | ||||
−0.612112 | + | 0.790771i | \(0.709680\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.54657e7 | −1.40317 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 57242.0 | 0.00515406 | ||||||||
\(659\) | −1.16435e7 | −1.04441 | −0.522205 | − | 0.852820i | \(-0.674890\pi\) | ||||
−0.522205 | + | 0.852820i | \(0.674890\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.52598e7 | 1.35845 | 0.679227 | − | 0.733928i | \(-0.262315\pi\) | ||||
0.679227 | + | 0.733928i | \(0.262315\pi\) | |||||||
\(662\) | −82604.7 | −0.00732588 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.37693e6 | 0.121197 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.74257e6 | −0.673861 | ||||||||
\(668\) | 2.37351e6 | 0.205802 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −53849.0 | −0.00461712 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.38345e6 | 0.713485 | 0.356743 | − | 0.934203i | \(-0.383887\pi\) | ||||
0.356743 | + | 0.934203i | \(0.383887\pi\) | |||||||
\(674\) | 74085.6 | 0.00628180 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.29779e7 | −1.93394 | ||||||||
\(677\) | 4.32488e6 | 0.362662 | 0.181331 | − | 0.983422i | \(-0.441959\pi\) | ||||
0.181331 | + | 0.983422i | \(0.441959\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.88901e6 | −0.573432 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 474940. | 0.0391001 | ||||||||
\(683\) | 1.61800e7 | 1.32717 | 0.663585 | − | 0.748101i | \(-0.269034\pi\) | ||||
0.663585 | + | 0.748101i | \(0.269034\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 386819. | 0.0313832 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.03168e7 | 0.830947 | ||||||||
\(689\) | 2.14887e7 | 1.72450 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.21864e6 | 0.0970913 | 0.0485456 | − | 0.998821i | \(-0.484541\pi\) | ||||
0.0485456 | + | 0.998821i | \(0.484541\pi\) | |||||||
\(692\) | −1.23487e7 | −0.980292 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −345651. | −0.0272420 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.43871e7 | −1.12174 | ||||||||
\(698\) | 614845. | 0.0477669 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 883759. | 0.0679264 | 0.0339632 | − | 0.999423i | \(-0.489187\pi\) | ||||
0.0339632 | + | 0.999423i | \(0.489187\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.02498e6 | 0.230852 | ||||||||
\(704\) | −1.38177e7 | −1.05076 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −199907. | −0.0150944 | ||||||||
\(707\) | −8.63888e6 | −0.649993 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.76739e7 | 1.32043 | 0.660216 | − | 0.751076i | \(-0.270465\pi\) | ||||
0.660216 | + | 0.751076i | \(0.270465\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.26001e6 | −0.0931480 | ||||||||
\(713\) | −1.73229e7 | −1.27613 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.16557e6 | −0.595256 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 235615. | 0.0170566 | ||||||||
\(719\) | −2.08338e6 | −0.150296 | −0.0751480 | − | 0.997172i | \(-0.523943\pi\) | ||||
−0.0751480 | + | 0.997172i | \(0.523943\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.91931e6 | −0.495707 | ||||||||
\(722\) | 513892. | 0.0366884 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.36037e7 | 0.964516 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.02846e7 | 0.721689 | 0.360845 | − | 0.932626i | \(-0.382488\pi\) | ||||
0.360845 | + | 0.932626i | \(0.382488\pi\) | |||||||
\(728\) | −857976. | −0.0599993 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.59725e6 | 0.664283 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.72749e7 | −1.18756 | −0.593782 | − | 0.804626i | \(-0.702366\pi\) | ||||
−0.593782 | + | 0.804626i | \(0.702366\pi\) | |||||||
\(734\) | 390931. | 0.0267831 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.24009e6 | −0.152430 | ||||||||
\(737\) | −8.04816e6 | −0.545793 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.26221e6 | −0.421810 | −0.210905 | − | 0.977507i | \(-0.567641\pi\) | ||||
−0.210905 | + | 0.977507i | \(0.567641\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 264384. | 0.0176289 | ||||||||
\(743\) | 2.49470e7 | 1.65786 | 0.828928 | − | 0.559355i | \(-0.188951\pi\) | ||||
0.828928 | + | 0.559355i | \(0.188951\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 837437. | 0.0550941 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.28922e7 | −0.842503 | ||||||||
\(749\) | 1.10164e7 | 0.717524 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.89546e7 | 1.87334 | 0.936671 | − | 0.350211i | \(-0.113890\pi\) | ||||
0.936671 | + | 0.350211i | \(0.113890\pi\) | |||||||
\(752\) | −4.54229e6 | −0.292907 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −521033. | −0.0333762 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.35091e6 | −0.529656 | −0.264828 | − | 0.964296i | \(-0.585315\pi\) | ||||
−0.264828 | + | 0.964296i | \(0.585315\pi\) | |||||||
\(758\) | −529553. | −0.0334762 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.05602e7 | 1.28696 | 0.643481 | − | 0.765462i | \(-0.277489\pi\) | ||||
0.643481 | + | 0.765462i | \(0.277489\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.85336e6 | −0.488364 | ||||||||
\(764\) | 1.21557e7 | 0.753436 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −361880. | −0.0222840 | ||||||||
\(767\) | 4.64268e7 | 2.84958 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.86907e6 | 0.418873 | 0.209436 | − | 0.977822i | \(-0.432837\pi\) | ||||
0.209436 | + | 0.977822i | \(0.432837\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.24998e6 | 0.437818 | ||||||||
\(773\) | 1.55261e7 | 0.934574 | 0.467287 | − | 0.884106i | \(-0.345232\pi\) | ||||
0.467287 | + | 0.884106i | \(0.345232\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.61465e6 | −0.0962553 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −506514. | −0.0300015 | ||||||||
\(779\) | 4.98153e6 | 0.294116 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.79555e6 | 0.163999 | ||||||||
\(782\) | −692912. | −0.0405192 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.35606e7 | −0.787931 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.54797e6 | −0.319299 | −0.159649 | − | 0.987174i | \(-0.551036\pi\) | ||||
−0.159649 | + | 0.987174i | \(0.551036\pi\) | |||||||
\(788\) | −2.20076e6 | −0.126258 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.75300e6 | 0.0996188 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 132172. | 0.00746373 | ||||||||
\(794\) | 719557. | 0.0405055 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.90796e7 | 1.06730 | ||||||||
\(797\) | 3.72345e6 | 0.207634 | 0.103817 | − | 0.994596i | \(-0.466894\pi\) | ||||
0.103817 | + | 0.994596i | \(0.466894\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.22549e6 | −0.234158 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −399523. | −0.0219334 | ||||||||
\(803\) | 2.32452e6 | 0.127217 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.16574e6 | −0.0632067 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.02479e6 | −0.109107 | ||||||||
\(809\) | 3.24496e7 | 1.74317 | 0.871583 | − | 0.490249i | \(-0.163094\pi\) | ||||
0.871583 | + | 0.490249i | \(0.163094\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.73709e7 | −0.927409 | −0.463704 | − | 0.885990i | \(-0.653480\pi\) | ||||
−0.463704 | + | 0.885990i | \(0.653480\pi\) | |||||||
\(812\) | 4.35030e6 | 0.231541 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 850403. | 0.0449846 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.32305e6 | −0.174173 | ||||||||
\(818\) | −832531. | −0.0435028 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.70074e7 | 1.91615 | 0.958076 | − | 0.286513i | \(-0.0924962\pi\) | ||||
0.958076 | + | 0.286513i | \(0.0924962\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.60977e7 | −1.34308 | −0.671541 | − | 0.740967i | \(-0.734367\pi\) | ||||
−0.671541 | + | 0.740967i | \(0.734367\pi\) | |||||||
\(824\) | −1.62176e6 | −0.0832085 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 571207. | 0.0291302 | ||||||||
\(827\) | −1.76833e7 | −0.899083 | −0.449541 | − | 0.893259i | \(-0.648413\pi\) | ||||
−0.449541 | + | 0.893259i | \(0.648413\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.66610e7 | 1.34738 | 0.673689 | − | 0.739015i | \(-0.264709\pi\) | ||||
0.673689 | + | 0.739015i | \(0.264709\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.39155e7 | 1.69860 | ||||||||
\(833\) | −1.26148e7 | −0.629895 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.46392e6 | 0.220902 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −949239. | −0.0466945 | ||||||||
\(839\) | −6.39212e6 | −0.313502 | −0.156751 | − | 0.987638i | \(-0.550102\pi\) | ||||
−0.156751 | + | 0.987638i | \(0.550102\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.52235e7 | −0.742208 | ||||||||
\(842\) | −16516.5 | −0.000802858 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.45810e6 | −0.263746 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.18084e6 | 0.0565563 | ||||||||
\(848\) | −2.09795e7 | −1.00186 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.10174e7 | −1.46819 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.82139e7 | 1.79824 | 0.899122 | − | 0.437699i | \(-0.144206\pi\) | ||||
0.899122 | + | 0.437699i | \(0.144206\pi\) | |||||||
\(854\) | 1626.16 | 7.62990e−5 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.58204e6 | 0.120442 | ||||||||
\(857\) | −3.44766e7 | −1.60351 | −0.801755 | − | 0.597653i | \(-0.796100\pi\) | ||||
−0.801755 | + | 0.597653i | \(0.796100\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.85135e7 | 0.856063 | 0.428032 | − | 0.903764i | \(-0.359207\pi\) | ||||
0.428032 | + | 0.903764i | \(0.359207\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.05864e6 | −0.0485264 | ||||||||
\(863\) | −2.69763e6 | −0.123298 | −0.0616489 | − | 0.998098i | \(-0.519636\pi\) | ||||
−0.0616489 | + | 0.998098i | \(0.519636\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 896465. | 0.0406199 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.73316e6 | 0.438485 | ||||||||
\(869\) | 6.54788e6 | 0.294138 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.97541e7 | 0.882293 | ||||||||
\(872\) | −1.84068e6 | −0.0819760 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 239921. | 0.0106240 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.83239e7 | −1.24352 | −0.621762 | − | 0.783207i | \(-0.713583\pi\) | ||||
−0.621762 | + | 0.783207i | \(0.713583\pi\) | |||||||
\(878\) | 106775. | 0.00467447 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.28203e7 | −0.990564 | −0.495282 | − | 0.868732i | \(-0.664935\pi\) | ||||
−0.495282 | + | 0.868732i | \(0.664935\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.29055e7 | 0.988638 | 0.494319 | − | 0.869281i | \(-0.335417\pi\) | ||||
0.494319 | + | 0.869281i | \(0.335417\pi\) | |||||||
\(884\) | 3.16437e7 | 1.36194 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 369689. | 0.0158216 | ||||||||
\(887\) | 1.99086e7 | 0.849634 | 0.424817 | − | 0.905279i | \(-0.360338\pi\) | ||||
0.424817 | + | 0.905279i | \(0.360338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.12091e7 | 0.475683 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.44595e6 | 0.313334 | ||||||||
\(893\) | 1.46308e6 | 0.0613958 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.67776e6 | 0.0698169 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 272420. | 0.0112732 | ||||||||
\(899\) | 1.18303e7 | 0.488197 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.95163e7 | −0.800913 | ||||||||
\(902\) | 1.40044e6 | 0.0573124 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 410871. | 0.0167218 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.67681e7 | −1.48407 | −0.742033 | − | 0.670364i | \(-0.766138\pi\) | ||||
−0.742033 | + | 0.670364i | \(0.766138\pi\) | |||||||
\(908\) | 5.57089e6 | 0.224238 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.22729e7 | −0.489948 | −0.244974 | − | 0.969530i | \(-0.578779\pi\) | ||||
−0.244974 | + | 0.969530i | \(0.578779\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.22127e7 | 1.67597 | ||||||||
\(914\) | −1.02395e6 | −0.0405427 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.03057e7 | −0.405826 | ||||||||
\(917\) | 6.35671e6 | 0.249637 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.49398e7 | −0.583522 | −0.291761 | − | 0.956491i | \(-0.594241\pi\) | ||||
−0.291761 | + | 0.956491i | \(0.594241\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −218665. | −0.00847134 | ||||||||
\(923\) | −6.86167e6 | −0.265110 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.63264e6 | −0.0625694 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.52982e6 | 0.0583135 | ||||||||
\(929\) | −5.25145e6 | −0.199637 | −0.0998183 | − | 0.995006i | \(-0.531826\pi\) | ||||
−0.0998183 | + | 0.995006i | \(0.531826\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.36788e6 | 0.165157 | ||||||||
\(932\) | −2.90417e7 | −1.09517 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.03628e6 | −0.0388695 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.30065e7 | 1.22815 | 0.614075 | − | 0.789248i | \(-0.289529\pi\) | ||||
0.614075 | + | 0.789248i | \(0.289529\pi\) | |||||||
\(938\) | 243043. | 0.00901936 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.32700e7 | 0.488538 | 0.244269 | − | 0.969708i | \(-0.421452\pi\) | ||||
0.244269 | + | 0.969708i | \(0.421452\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.10794e7 | −1.87054 | ||||||||
\(944\) | −4.53267e7 | −1.65548 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −934198. | −0.0339399 | ||||||||
\(947\) | 7.08995e6 | 0.256903 | 0.128451 | − | 0.991716i | \(-0.458999\pi\) | ||||
0.128451 | + | 0.991716i | \(0.458999\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.70551e6 | −0.205650 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 779223. | 0.0278657 | ||||||||
\(953\) | −6.20087e6 | −0.221167 | −0.110584 | − | 0.993867i | \(-0.535272\pi\) | ||||
−0.110584 | + | 0.993867i | \(0.535272\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.82120e7 | 0.644486 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.75555e6 | −0.0618015 | ||||||||
\(959\) | −1.02938e7 | −0.361434 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.16066e6 | −0.0754708 | ||||||||
\(962\) | −2.08731e6 | −0.0727191 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.40559e7 | 0.833736 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.19568e7 | 1.09900 | 0.549499 | − | 0.835494i | \(-0.314819\pi\) | ||||
0.549499 | + | 0.835494i | \(0.314819\pi\) | |||||||
\(968\) | 276765. | 0.00949344 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.66750e7 | 1.24831 | 0.624154 | − | 0.781301i | \(-0.285444\pi\) | ||||
0.624154 | + | 0.781301i | \(0.285444\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.79601e6 | −0.0608173 | ||||||||
\(974\) | 131490. | 0.00444114 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −129040. | −0.00433610 | ||||||||
\(977\) | 2.13191e7 | 0.714549 | 0.357275 | − | 0.933999i | \(-0.383706\pi\) | ||||
0.357275 | + | 0.933999i | \(0.383706\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.86283e7 | −1.28810 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.49977e6 | 0.0496300 | ||||||||
\(983\) | −1.02603e7 | −0.338670 | −0.169335 | − | 0.985559i | \(-0.554162\pi\) | ||||
−0.169335 | + | 0.985559i | \(0.554162\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 473208. | 0.0155010 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.09567e7 | −0.357096 | ||||||||
\(989\) | 3.40738e7 | 1.10772 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.92940e7 | 0.947535 | 0.473767 | − | 0.880650i | \(-0.342894\pi\) | ||||
0.473767 | + | 0.880650i | \(0.342894\pi\) | |||||||
\(992\) | 3.42274e6 | 0.110432 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −84421.7 | −0.00271012 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.30440e7 | 0.415596 | 0.207798 | − | 0.978172i | \(-0.433370\pi\) | ||||
0.207798 | + | 0.978172i | \(0.433370\pi\) | |||||||
\(998\) | −912333. | −0.0289953 | ||||||||
\(999\) | 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 | 225.6.a.u.1.1 | 2 | ||
3.2 | odd | 2 | 75.6.a.f.1.2 | 2 | |||
5.2 | odd | 4 | 45.6.b.c.19.2 | 4 | |||
5.3 | odd | 4 | 45.6.b.c.19.3 | 4 | |||
5.4 | even | 2 | 225.6.a.i.1.2 | 2 | |||
15.2 | even | 4 | 15.6.b.a.4.3 | yes | 4 | ||
15.8 | even | 4 | 15.6.b.a.4.2 | ✓ | 4 | ||
15.14 | odd | 2 | 75.6.a.j.1.1 | 2 | |||
20.3 | even | 4 | 720.6.f.h.289.1 | 4 | |||
20.7 | even | 4 | 720.6.f.h.289.4 | 4 | |||
60.23 | odd | 4 | 240.6.f.c.49.2 | 4 | |||
60.47 | odd | 4 | 240.6.f.c.49.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.6.b.a.4.2 | ✓ | 4 | 15.8 | even | 4 | ||
15.6.b.a.4.3 | yes | 4 | 15.2 | even | 4 | ||
45.6.b.c.19.2 | 4 | 5.2 | odd | 4 | |||
45.6.b.c.19.3 | 4 | 5.3 | odd | 4 | |||
75.6.a.f.1.2 | 2 | 3.2 | odd | 2 | |||
75.6.a.j.1.1 | 2 | 15.14 | odd | 2 | |||
225.6.a.i.1.2 | 2 | 5.4 | even | 2 | |||
225.6.a.u.1.1 | 2 | 1.1 | even | 1 | trivial | ||
240.6.f.c.49.2 | 4 | 60.23 | odd | 4 | |||
240.6.f.c.49.3 | 4 | 60.47 | odd | 4 | |||
720.6.f.h.289.1 | 4 | 20.3 | even | 4 | |||
720.6.f.h.289.4 | 4 | 20.7 | even | 4 |