Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1075,6,Mod(1,1075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1075.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1075 = 5^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1075.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(172.412606299\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | no (minimal twist has level 215) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.25 | ||
Character | \(\chi\) | \(=\) | 1075.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.00353772 | −0.000625387 0 | −0.000312693 | − | 1.00000i | \(-0.500100\pi\) | ||||
−0.000312693 | 1.00000i | \(0.500100\pi\) | ||||||||
\(3\) | 4.42609 | 0.283934 | 0.141967 | − | 0.989871i | \(-0.454657\pi\) | ||||
0.141967 | + | 0.989871i | \(0.454657\pi\) | |||||||
\(4\) | −32.0000 | −1.00000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.0156583 | −0.000177569 0 | ||||||||
\(7\) | 78.1807 | 0.603051 | 0.301526 | − | 0.953458i | \(-0.402504\pi\) | ||||
0.301526 | + | 0.953458i | \(0.402504\pi\) | |||||||
\(8\) | 0.226414 | 0.00125077 | ||||||||
\(9\) | −223.410 | −0.919382 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 343.479 | 0.855890 | 0.427945 | − | 0.903805i | \(-0.359238\pi\) | ||||
0.427945 | + | 0.903805i | \(0.359238\pi\) | |||||||
\(12\) | −141.635 | −0.283934 | ||||||||
\(13\) | 1056.05 | 1.73310 | 0.866552 | − | 0.499087i | \(-0.166331\pi\) | ||||
0.866552 | + | 0.499087i | \(0.166331\pi\) | |||||||
\(14\) | −0.276582 | −0.000377140 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1024.00 | 0.999999 | ||||||||
\(17\) | 1468.63 | 1.23251 | 0.616255 | − | 0.787547i | \(-0.288649\pi\) | ||||
0.616255 | + | 0.787547i | \(0.288649\pi\) | |||||||
\(18\) | 0.790361 | 0.000574969 0 | ||||||||
\(19\) | 1056.43 | 0.671362 | 0.335681 | − | 0.941976i | \(-0.391034\pi\) | ||||
0.335681 | + | 0.941976i | \(0.391034\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 346.035 | 0.171227 | ||||||||
\(22\) | −1.21513 | −0.000535263 0 | ||||||||
\(23\) | −1494.08 | −0.588917 | −0.294458 | − | 0.955664i | \(-0.595139\pi\) | ||||
−0.294458 | + | 0.955664i | \(0.595139\pi\) | |||||||
\(24\) | 1.00213 | 0.000355137 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.73600 | −0.00108386 | ||||||||
\(27\) | −2064.37 | −0.544978 | ||||||||
\(28\) | −2501.78 | −0.603051 | ||||||||
\(29\) | 3072.92 | 0.678510 | 0.339255 | − | 0.940694i | \(-0.389825\pi\) | ||||
0.339255 | + | 0.940694i | \(0.389825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9435.69 | 1.76347 | 0.881737 | − | 0.471741i | \(-0.156374\pi\) | ||||
0.881737 | + | 0.471741i | \(0.156374\pi\) | |||||||
\(32\) | −10.8679 | −0.00187616 | ||||||||
\(33\) | 1520.27 | 0.243016 | ||||||||
\(34\) | −5.19561 | −0.000770795 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7149.11 | 0.919381 | ||||||||
\(37\) | −8632.32 | −1.03663 | −0.518314 | − | 0.855190i | \(-0.673440\pi\) | ||||
−0.518314 | + | 0.855190i | \(0.673440\pi\) | |||||||
\(38\) | −3.73735 | −0.000419861 0 | ||||||||
\(39\) | 4674.16 | 0.492087 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18021.5 | −1.67429 | −0.837145 | − | 0.546981i | \(-0.815777\pi\) | ||||
−0.837145 | + | 0.546981i | \(0.815777\pi\) | |||||||
\(42\) | −1.22418 | −0.000107083 0 | ||||||||
\(43\) | −1849.00 | −0.152499 | ||||||||
\(44\) | −10991.3 | −0.855890 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.28564 | 0.000368301 0 | ||||||||
\(47\) | 12673.8 | 0.836876 | 0.418438 | − | 0.908245i | \(-0.362578\pi\) | ||||
0.418438 | + | 0.908245i | \(0.362578\pi\) | |||||||
\(48\) | 4532.31 | 0.283934 | ||||||||
\(49\) | −10694.8 | −0.636329 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6500.29 | 0.349951 | ||||||||
\(52\) | −33793.5 | −1.73310 | ||||||||
\(53\) | −8709.02 | −0.425872 | −0.212936 | − | 0.977066i | \(-0.568303\pi\) | ||||
−0.212936 | + | 0.977066i | \(0.568303\pi\) | |||||||
\(54\) | 7.30318 | 0.000340822 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 17.7012 | 0.000754281 0 | ||||||||
\(57\) | 4675.86 | 0.190622 | ||||||||
\(58\) | −10.8711 | −0.000424331 0 | ||||||||
\(59\) | −17359.9 | −0.649257 | −0.324628 | − | 0.945842i | \(-0.605239\pi\) | ||||
−0.324628 | + | 0.945842i | \(0.605239\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 41529.3 | 1.42899 | 0.714497 | − | 0.699638i | \(-0.246656\pi\) | ||||
0.714497 | + | 0.699638i | \(0.246656\pi\) | |||||||
\(62\) | −33.3808 | −0.00110285 | ||||||||
\(63\) | −17466.3 | −0.554434 | ||||||||
\(64\) | −32767.9 | −0.999998 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.37829 | −0.000151979 0 | ||||||||
\(67\) | −8888.44 | −0.241902 | −0.120951 | − | 0.992659i | \(-0.538594\pi\) | ||||
−0.120951 | + | 0.992659i | \(0.538594\pi\) | |||||||
\(68\) | −46996.2 | −1.23251 | ||||||||
\(69\) | −6612.93 | −0.167213 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11586.9 | 0.272786 | 0.136393 | − | 0.990655i | \(-0.456449\pi\) | ||||
0.136393 | + | 0.990655i | \(0.456449\pi\) | |||||||
\(72\) | −50.5831 | −0.00114994 | ||||||||
\(73\) | −75620.5 | −1.66086 | −0.830428 | − | 0.557126i | \(-0.811904\pi\) | ||||
−0.830428 | + | 0.557126i | \(0.811904\pi\) | |||||||
\(74\) | 30.5387 | 0.000648294 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −33805.7 | −0.671361 | ||||||||
\(77\) | 26853.4 | 0.516146 | ||||||||
\(78\) | −16.5359 | −0.000307745 0 | ||||||||
\(79\) | 62221.3 | 1.12169 | 0.560843 | − | 0.827922i | \(-0.310477\pi\) | ||||
0.560843 | + | 0.827922i | \(0.310477\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 45151.5 | 0.764644 | ||||||||
\(82\) | 63.7550 | 0.00104708 | ||||||||
\(83\) | 104528. | 1.66547 | 0.832736 | − | 0.553671i | \(-0.186773\pi\) | ||||
0.832736 | + | 0.553671i | \(0.186773\pi\) | |||||||
\(84\) | −11073.1 | −0.171227 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.54125 | 9.53706e−5 0 | ||||||||
\(87\) | 13601.0 | 0.192652 | ||||||||
\(88\) | 77.7685 | 0.00107053 | ||||||||
\(89\) | 16370.8 | 0.219076 | 0.109538 | − | 0.993983i | \(-0.465063\pi\) | ||||
0.109538 | + | 0.993983i | \(0.465063\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 82562.4 | 1.04515 | ||||||||
\(92\) | 47810.5 | 0.588917 | ||||||||
\(93\) | 41763.2 | 0.500710 | ||||||||
\(94\) | −44.8363 | −0.000523371 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −48.1022 | −0.000532705 0 | ||||||||
\(97\) | −14099.6 | −0.152152 | −0.0760759 | − | 0.997102i | \(-0.524239\pi\) | ||||
−0.0760759 | + | 0.997102i | \(0.524239\pi\) | |||||||
\(98\) | 37.8352 | 0.000397952 0 | ||||||||
\(99\) | −76736.5 | −0.786890 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 73684.5 | 0.718742 | 0.359371 | − | 0.933195i | \(-0.382991\pi\) | ||||
0.359371 | + | 0.933195i | \(0.382991\pi\) | |||||||
\(102\) | −22.9962 | −0.000218855 0 | ||||||||
\(103\) | 28407.3 | 0.263838 | 0.131919 | − | 0.991260i | \(-0.457886\pi\) | ||||
0.131919 | + | 0.991260i | \(0.457886\pi\) | |||||||
\(104\) | 239.104 | 0.00216772 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 30.8101 | 0.000266335 0 | ||||||||
\(107\) | −38692.0 | −0.326710 | −0.163355 | − | 0.986567i | \(-0.552232\pi\) | ||||
−0.163355 | + | 0.986567i | \(0.552232\pi\) | |||||||
\(108\) | 66059.9 | 0.544977 | ||||||||
\(109\) | 75524.3 | 0.608864 | 0.304432 | − | 0.952534i | \(-0.401533\pi\) | ||||
0.304432 | + | 0.952534i | \(0.401533\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −38207.4 | −0.294334 | ||||||||
\(112\) | 80056.9 | 0.603051 | ||||||||
\(113\) | −105450. | −0.776875 | −0.388438 | − | 0.921475i | \(-0.626985\pi\) | ||||
−0.388438 | + | 0.921475i | \(0.626985\pi\) | |||||||
\(114\) | −16.5419 | −0.000119213 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −98333.4 | −0.678510 | ||||||||
\(117\) | −235931. | −1.59338 | ||||||||
\(118\) | 61.4144 | 0.000406037 0 | ||||||||
\(119\) | 114819. | 0.743267 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −43073.3 | −0.267451 | ||||||||
\(122\) | −146.919 | −0.000893674 0 | ||||||||
\(123\) | −79764.7 | −0.475388 | ||||||||
\(124\) | −301942. | −1.76347 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 61.7910 | 0.000346736 0 | ||||||||
\(127\) | −151292. | −0.832352 | −0.416176 | − | 0.909284i | \(-0.636630\pi\) | ||||
−0.416176 | + | 0.909284i | \(0.636630\pi\) | |||||||
\(128\) | 463.696 | 0.00250154 | ||||||||
\(129\) | −8183.84 | −0.0432995 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 160063. | 0.814914 | 0.407457 | − | 0.913224i | \(-0.366416\pi\) | ||||
0.407457 | + | 0.913224i | \(0.366416\pi\) | |||||||
\(132\) | −48648.6 | −0.243016 | ||||||||
\(133\) | 82592.4 | 0.404866 | ||||||||
\(134\) | 31.4448 | 0.000151282 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 332.519 | 0.00154159 | ||||||||
\(137\) | 243141. | 1.10677 | 0.553384 | − | 0.832926i | \(-0.313336\pi\) | ||||
0.553384 | + | 0.832926i | \(0.313336\pi\) | |||||||
\(138\) | 23.3947 | 0.000104573 0 | ||||||||
\(139\) | 213863. | 0.938857 | 0.469429 | − | 0.882970i | \(-0.344460\pi\) | ||||
0.469429 | + | 0.882970i | \(0.344460\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 56095.3 | 0.237618 | ||||||||
\(142\) | −40.9913 | −0.000170597 0 | ||||||||
\(143\) | 362729. | 1.48335 | ||||||||
\(144\) | −228771. | −0.919380 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 267.524 | 0.00103868 | ||||||||
\(147\) | −47336.1 | −0.180675 | ||||||||
\(148\) | 276234. | 1.03663 | ||||||||
\(149\) | −121710. | −0.449117 | −0.224558 | − | 0.974461i | \(-0.572094\pi\) | ||||
−0.224558 | + | 0.974461i | \(0.572094\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −464982. | −1.65956 | −0.829782 | − | 0.558088i | \(-0.811535\pi\) | ||||
−0.829782 | + | 0.558088i | \(0.811535\pi\) | |||||||
\(152\) | 239.191 | 0.000839721 0 | ||||||||
\(153\) | −328106. | −1.13315 | ||||||||
\(154\) | −94.9999 | −0.000322791 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −149573. | −0.492087 | ||||||||
\(157\) | −239887. | −0.776707 | −0.388354 | − | 0.921510i | \(-0.626956\pi\) | ||||
−0.388354 | + | 0.921510i | \(0.626956\pi\) | |||||||
\(158\) | −220.122 | −0.000701488 0 | ||||||||
\(159\) | −38546.9 | −0.120920 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −116808. | −0.355147 | ||||||||
\(162\) | −159.733 | −0.000478198 0 | ||||||||
\(163\) | 509936. | 1.50330 | 0.751651 | − | 0.659561i | \(-0.229258\pi\) | ||||
0.751651 | + | 0.659561i | \(0.229258\pi\) | |||||||
\(164\) | 576687. | 1.67429 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −369.791 | −0.00104156 | ||||||||
\(167\) | 567512. | 1.57465 | 0.787325 | − | 0.616538i | \(-0.211465\pi\) | ||||
0.787325 | + | 0.616538i | \(0.211465\pi\) | |||||||
\(168\) | 78.3472 | 0.000214166 0 | ||||||||
\(169\) | 743940. | 2.00365 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −236017. | −0.617238 | ||||||||
\(172\) | 59168.0 | 0.152499 | ||||||||
\(173\) | 192003. | 0.487746 | 0.243873 | − | 0.969807i | \(-0.421582\pi\) | ||||
0.243873 | + | 0.969807i | \(0.421582\pi\) | |||||||
\(174\) | −48.1166 | −0.000120482 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 351722. | 0.855889 | ||||||||
\(177\) | −76836.4 | −0.184346 | ||||||||
\(178\) | −57.9154 | −0.000137007 0 | ||||||||
\(179\) | 181703. | 0.423867 | 0.211933 | − | 0.977284i | \(-0.432024\pi\) | ||||
0.211933 | + | 0.977284i | \(0.432024\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 160168. | 0.363395 | 0.181698 | − | 0.983354i | \(-0.441841\pi\) | ||||
0.181698 | + | 0.983354i | \(0.441841\pi\) | |||||||
\(182\) | −292.083 | −0.000653623 0 | ||||||||
\(183\) | 183813. | 0.405740 | ||||||||
\(184\) | −338.281 | −0.000736601 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −147.747 | −0.000313138 0 | ||||||||
\(187\) | 504443. | 1.05489 | ||||||||
\(188\) | −405561. | −0.836876 | ||||||||
\(189\) | −161394. | −0.328650 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −795626. | −1.57807 | −0.789034 | − | 0.614349i | \(-0.789419\pi\) | ||||
−0.789034 | + | 0.614349i | \(0.789419\pi\) | |||||||
\(192\) | −145034. | −0.283933 | ||||||||
\(193\) | 142218. | 0.274828 | 0.137414 | − | 0.990514i | \(-0.456121\pi\) | ||||
0.137414 | + | 0.990514i | \(0.456121\pi\) | |||||||
\(194\) | 49.8804 | 9.51537e−5 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 342233. | 0.636329 | ||||||||
\(197\) | −613720. | −1.12669 | −0.563345 | − | 0.826222i | \(-0.690486\pi\) | ||||
−0.563345 | + | 0.826222i | \(0.690486\pi\) | |||||||
\(198\) | 271.472 | 0.000492111 0 | ||||||||
\(199\) | 95621.6 | 0.171168 | 0.0855841 | − | 0.996331i | \(-0.472724\pi\) | ||||
0.0855841 | + | 0.996331i | \(0.472724\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −39341.1 | −0.0686841 | ||||||||
\(202\) | −260.675 | −0.000449492 0 | ||||||||
\(203\) | 240243. | 0.409176 | ||||||||
\(204\) | −208009. | −0.349951 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −100.497 | −0.000165001 0 | ||||||||
\(207\) | 333792. | 0.541439 | ||||||||
\(208\) | 1.08139e6 | 1.73310 | ||||||||
\(209\) | 362861. | 0.574612 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.09309e6 | −1.69024 | −0.845120 | − | 0.534576i | \(-0.820471\pi\) | ||||
−0.845120 | + | 0.534576i | \(0.820471\pi\) | |||||||
\(212\) | 278688. | 0.425872 | ||||||||
\(213\) | 51284.8 | 0.0774533 | ||||||||
\(214\) | 136.882 | 0.000204320 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −467.403 | −0.000681643 0 | ||||||||
\(217\) | 737688. | 1.06347 | ||||||||
\(218\) | −267.184 | −0.000380776 0 | ||||||||
\(219\) | −334703. | −0.471574 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.55094e6 | 2.13607 | ||||||||
\(222\) | 135.167 | 0.000184073 0 | ||||||||
\(223\) | −69717.1 | −0.0938808 | −0.0469404 | − | 0.998898i | \(-0.514947\pi\) | ||||
−0.0469404 | + | 0.998898i | \(0.514947\pi\) | |||||||
\(224\) | −849.658 | −0.00113142 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 373.054 | 0.000485848 0 | ||||||||
\(227\) | −72397.0 | −0.0932515 | −0.0466258 | − | 0.998912i | \(-0.514847\pi\) | ||||
−0.0466258 | + | 0.998912i | \(0.514847\pi\) | |||||||
\(228\) | −149627. | −0.190622 | ||||||||
\(229\) | −773691. | −0.974942 | −0.487471 | − | 0.873139i | \(-0.662081\pi\) | ||||
−0.487471 | + | 0.873139i | \(0.662081\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 118856. | 0.146551 | ||||||||
\(232\) | 695.752 | 0.000848662 0 | ||||||||
\(233\) | 1.17517e6 | 1.41812 | 0.709060 | − | 0.705149i | \(-0.249120\pi\) | ||||
0.709060 | + | 0.705149i | \(0.249120\pi\) | |||||||
\(234\) | 834.658 | 0.000996481 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 555516. | 0.649257 | ||||||||
\(237\) | 275397. | 0.318485 | ||||||||
\(238\) | −406.196 | −0.000464829 0 | ||||||||
\(239\) | 1.59060e6 | 1.80122 | 0.900608 | − | 0.434633i | \(-0.143122\pi\) | ||||
0.900608 | + | 0.434633i | \(0.143122\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 863760. | 0.957967 | 0.478984 | − | 0.877824i | \(-0.341005\pi\) | ||||
0.478984 | + | 0.877824i | \(0.341005\pi\) | |||||||
\(242\) | 152.381 | 0.000167261 0 | ||||||||
\(243\) | 701487. | 0.762086 | ||||||||
\(244\) | −1.32894e6 | −1.42899 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 282.185 | 0.000297301 0 | ||||||||
\(247\) | 1.11564e6 | 1.16354 | ||||||||
\(248\) | 2136.37 | 0.00220571 | ||||||||
\(249\) | 462650. | 0.472884 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −373603. | −0.374306 | −0.187153 | − | 0.982331i | \(-0.559926\pi\) | ||||
−0.187153 | + | 0.982331i | \(0.559926\pi\) | |||||||
\(252\) | 558922. | 0.554434 | ||||||||
\(253\) | −513184. | −0.504048 | ||||||||
\(254\) | 535.229 | 0.000520542 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.04857e6 | 0.999996 | ||||||||
\(257\) | 1.56964e6 | 1.48241 | 0.741204 | − | 0.671280i | \(-0.234255\pi\) | ||||
0.741204 | + | 0.671280i | \(0.234255\pi\) | |||||||
\(258\) | 28.9522 | 2.70789e−5 0 | ||||||||
\(259\) | −674881. | −0.625140 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −686520. | −0.623809 | ||||||||
\(262\) | −566.257 | −0.000509636 0 | ||||||||
\(263\) | −121397. | −0.108222 | −0.0541112 | − | 0.998535i | \(-0.517233\pi\) | ||||
−0.0541112 | + | 0.998535i | \(0.517233\pi\) | |||||||
\(264\) | 344.210 | 0.000303958 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −292.189 | −0.000253198 0 | ||||||||
\(267\) | 72458.8 | 0.0622032 | ||||||||
\(268\) | 284430. | 0.241901 | ||||||||
\(269\) | −1.32256e6 | −1.11438 | −0.557192 | − | 0.830383i | \(-0.688121\pi\) | ||||
−0.557192 | + | 0.830383i | \(0.688121\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −681839. | −0.563974 | −0.281987 | − | 0.959418i | \(-0.590993\pi\) | ||||
−0.281987 | + | 0.959418i | \(0.590993\pi\) | |||||||
\(272\) | 1.50388e6 | 1.23251 | ||||||||
\(273\) | 365429. | 0.296754 | ||||||||
\(274\) | −860.166 | −0.000692159 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 211614. | 0.167213 | ||||||||
\(277\) | −1.34688e6 | −1.05470 | −0.527351 | − | 0.849647i | \(-0.676815\pi\) | ||||
−0.527351 | + | 0.849647i | \(0.676815\pi\) | |||||||
\(278\) | −756.589 | −0.000587149 0 | ||||||||
\(279\) | −2.10802e6 | −1.62131 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −426288. | −0.322060 | −0.161030 | − | 0.986949i | \(-0.551482\pi\) | ||||
−0.161030 | + | 0.986949i | \(0.551482\pi\) | |||||||
\(282\) | −198.450 | −0.000148603 0 | ||||||||
\(283\) | 891682. | 0.661826 | 0.330913 | − | 0.943661i | \(-0.392643\pi\) | ||||
0.330913 | + | 0.943661i | \(0.392643\pi\) | |||||||
\(284\) | −370782. | −0.272786 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1283.24 | −0.000927666 0 | ||||||||
\(287\) | −1.40893e6 | −1.00968 | ||||||||
\(288\) | 2427.99 | 0.00172491 | ||||||||
\(289\) | 737019. | 0.519080 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −62406.1 | −0.0432011 | ||||||||
\(292\) | 2.41985e6 | 1.66086 | ||||||||
\(293\) | 1.65642e6 | 1.12720 | 0.563601 | − | 0.826047i | \(-0.309416\pi\) | ||||
0.563601 | + | 0.826047i | \(0.309416\pi\) | |||||||
\(294\) | 167.462 | 0.000112992 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1954.48 | −0.00129659 | ||||||||
\(297\) | −709068. | −0.466441 | ||||||||
\(298\) | 430.575 | 0.000280872 0 | ||||||||
\(299\) | −1.57782e6 | −1.02065 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −144556. | −0.0919645 | ||||||||
\(302\) | 1644.98 | 0.00103787 | ||||||||
\(303\) | 326135. | 0.204075 | ||||||||
\(304\) | 1.08178e6 | 0.671361 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1160.75 | 0.000708655 0 | ||||||||
\(307\) | 413794. | 0.250575 | 0.125288 | − | 0.992120i | \(-0.460015\pi\) | ||||
0.125288 | + | 0.992120i | \(0.460015\pi\) | |||||||
\(308\) | −859309. | −0.516146 | ||||||||
\(309\) | 125734. | 0.0749126 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.24054e6 | 0.727296 | 0.363648 | − | 0.931536i | \(-0.381531\pi\) | ||||
0.363648 | + | 0.931536i | \(0.381531\pi\) | |||||||
\(312\) | 1058.30 | 0.000615489 0 | ||||||||
\(313\) | 1.63545e6 | 0.943575 | 0.471787 | − | 0.881712i | \(-0.343609\pi\) | ||||
0.471787 | + | 0.881712i | \(0.343609\pi\) | |||||||
\(314\) | 848.653 | 0.000485742 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.99108e6 | −1.12169 | ||||||||
\(317\) | −2.54854e6 | −1.42444 | −0.712219 | − | 0.701957i | \(-0.752310\pi\) | ||||
−0.712219 | + | 0.701957i | \(0.752310\pi\) | |||||||
\(318\) | 136.368 | 7.56216e−5 0 | ||||||||
\(319\) | 1.05548e6 | 0.580730 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −171254. | −0.0927639 | ||||||||
\(322\) | 413.235 | 0.000222104 0 | ||||||||
\(323\) | 1.55150e6 | 0.827460 | ||||||||
\(324\) | −1.44485e6 | −0.764644 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1804.01 | −0.000940145 0 | ||||||||
\(327\) | 334278. | 0.172877 | ||||||||
\(328\) | −4080.32 | −0.00209416 | ||||||||
\(329\) | 990844. | 0.504680 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −466025. | −0.233797 | −0.116899 | − | 0.993144i | \(-0.537295\pi\) | ||||
−0.116899 | + | 0.993144i | \(0.537295\pi\) | |||||||
\(332\) | −3.34489e6 | −1.66547 | ||||||||
\(333\) | 1.92854e6 | 0.953057 | ||||||||
\(334\) | −2007.70 | −0.000984766 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 354339. | 0.171227 | ||||||||
\(337\) | −1.93053e6 | −0.925980 | −0.462990 | − | 0.886364i | \(-0.653223\pi\) | ||||
−0.462990 | + | 0.886364i | \(0.653223\pi\) | |||||||
\(338\) | −2631.85 | −0.00125306 | ||||||||
\(339\) | −466732. | −0.220581 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.24096e6 | 1.50934 | ||||||||
\(342\) | 834.961 | 0.000386012 0 | ||||||||
\(343\) | −2.15011e6 | −0.986791 | ||||||||
\(344\) | −418.640 | −0.000190741 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −679.254 | −0.000305030 0 | ||||||||
\(347\) | 1.86530e6 | 0.831622 | 0.415811 | − | 0.909451i | \(-0.363498\pi\) | ||||
0.415811 | + | 0.909451i | \(0.363498\pi\) | |||||||
\(348\) | −435233. | −0.192652 | ||||||||
\(349\) | 2.46427e6 | 1.08299 | 0.541496 | − | 0.840703i | \(-0.317858\pi\) | ||||
0.541496 | + | 0.840703i | \(0.317858\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.18007e6 | −0.944503 | ||||||||
\(352\) | −3732.88 | −0.00160579 | ||||||||
\(353\) | 162393. | 0.0693635 | 0.0346818 | − | 0.999398i | \(-0.488958\pi\) | ||||
0.0346818 | + | 0.999398i | \(0.488958\pi\) | |||||||
\(354\) | 271.826 | 0.000115288 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −523866. | −0.219076 | ||||||||
\(357\) | 508197. | 0.211039 | ||||||||
\(358\) | −642.814 | −0.000265081 0 | ||||||||
\(359\) | −4.55649e6 | −1.86593 | −0.932963 | − | 0.359972i | \(-0.882786\pi\) | ||||
−0.932963 | + | 0.359972i | \(0.882786\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.36006e6 | −0.549273 | ||||||||
\(362\) | −566.630 | −0.000227263 0 | ||||||||
\(363\) | −190647. | −0.0759386 | ||||||||
\(364\) | −2.64200e6 | −1.04515 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −650.278 | −0.000253744 0 | ||||||||
\(367\) | 809982. | 0.313914 | 0.156957 | − | 0.987605i | \(-0.449832\pi\) | ||||
0.156957 | + | 0.987605i | \(0.449832\pi\) | |||||||
\(368\) | −1.52994e6 | −0.588916 | ||||||||
\(369\) | 4.02617e6 | 1.53931 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −680877. | −0.256823 | ||||||||
\(372\) | −1.33642e6 | −0.500710 | ||||||||
\(373\) | 1.09407e6 | 0.407169 | 0.203585 | − | 0.979057i | \(-0.434741\pi\) | ||||
0.203585 | + | 0.979057i | \(0.434741\pi\) | |||||||
\(374\) | −1784.58 | −0.000659716 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2869.52 | 0.00104674 | ||||||||
\(377\) | 3.24514e6 | 1.17593 | ||||||||
\(378\) | 570.967 | 0.000205533 0 | ||||||||
\(379\) | 2.79365e6 | 0.999021 | 0.499510 | − | 0.866308i | \(-0.333513\pi\) | ||||
0.499510 | + | 0.866308i | \(0.333513\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −669633. | −0.236333 | ||||||||
\(382\) | 2814.71 | 0.000986903 0 | ||||||||
\(383\) | −1.08096e6 | −0.376540 | −0.188270 | − | 0.982117i | \(-0.560288\pi\) | ||||
−0.188270 | + | 0.982117i | \(0.560288\pi\) | |||||||
\(384\) | 2052.36 | 0.000710274 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −503.127 | −0.000171874 0 | ||||||||
\(387\) | 413085. | 0.140204 | ||||||||
\(388\) | 451187. | 0.152152 | ||||||||
\(389\) | 5.14305e6 | 1.72324 | 0.861621 | − | 0.507552i | \(-0.169449\pi\) | ||||
0.861621 | + | 0.507552i | \(0.169449\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.19425e6 | −0.725846 | ||||||||
\(392\) | −2421.45 | −0.000795903 0 | ||||||||
\(393\) | 708452. | 0.231382 | ||||||||
\(394\) | 2171.17 | 0.000704617 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.45557e6 | 0.786890 | ||||||||
\(397\) | −1.54920e6 | −0.493322 | −0.246661 | − | 0.969102i | \(-0.579333\pi\) | ||||
−0.246661 | + | 0.969102i | \(0.579333\pi\) | |||||||
\(398\) | −338.283 | −0.000107046 0 | ||||||||
\(399\) | 365562. | 0.114955 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.99982e6 | 1.24217 | 0.621083 | − | 0.783744i | \(-0.286693\pi\) | ||||
0.621083 | + | 0.783744i | \(0.286693\pi\) | |||||||
\(402\) | 139.178 | 4.29541e−5 0 | ||||||||
\(403\) | 9.96452e6 | 3.05628 | ||||||||
\(404\) | −2.35790e6 | −0.718742 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −849.913 | −0.000255894 0 | ||||||||
\(407\) | −2.96502e6 | −0.887241 | ||||||||
\(408\) | 1471.76 | 0.000437710 0 | ||||||||
\(409\) | −6.41702e6 | −1.89682 | −0.948408 | − | 0.317053i | \(-0.897307\pi\) | ||||
−0.948408 | + | 0.317053i | \(0.897307\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.07616e6 | 0.314249 | ||||||||
\(412\) | −909035. | −0.263838 | ||||||||
\(413\) | −1.35721e6 | −0.391535 | ||||||||
\(414\) | −1180.86 | −0.000338609 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −11477.0 | −0.00325158 | ||||||||
\(417\) | 946579. | 0.266573 | ||||||||
\(418\) | −1283.70 | −0.000359355 0 | ||||||||
\(419\) | 3.66292e6 | 1.01928 | 0.509638 | − | 0.860389i | \(-0.329779\pi\) | ||||
0.509638 | + | 0.860389i | \(0.329779\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.49763e6 | 0.686787 | 0.343394 | − | 0.939192i | \(-0.388424\pi\) | ||||
0.343394 | + | 0.939192i | \(0.388424\pi\) | |||||||
\(422\) | 3867.04 | 0.00105705 | ||||||||
\(423\) | −2.83144e6 | −0.769409 | ||||||||
\(424\) | −1971.85 | −0.000532670 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −181.431 | −4.84383e−5 0 | ||||||||
\(427\) | 3.24679e6 | 0.861757 | ||||||||
\(428\) | 1.23814e6 | 0.326709 | ||||||||
\(429\) | 1.60547e6 | 0.421173 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.03126e6 | 0.526711 | 0.263356 | − | 0.964699i | \(-0.415171\pi\) | ||||
0.263356 | + | 0.964699i | \(0.415171\pi\) | |||||||
\(432\) | −2.11391e6 | −0.544977 | ||||||||
\(433\) | 5.93651e6 | 1.52164 | 0.760819 | − | 0.648964i | \(-0.224798\pi\) | ||||
0.760819 | + | 0.648964i | \(0.224798\pi\) | |||||||
\(434\) | −2609.74 | −0.000665078 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.41678e6 | −0.608864 | ||||||||
\(437\) | −1.57839e6 | −0.395376 | ||||||||
\(438\) | 1184.09 | 0.000294916 0 | ||||||||
\(439\) | 6.21806e6 | 1.53990 | 0.769952 | − | 0.638102i | \(-0.220280\pi\) | ||||
0.769952 | + | 0.638102i | \(0.220280\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.38932e6 | 0.585029 | ||||||||
\(442\) | −5486.80 | −0.00133587 | ||||||||
\(443\) | 2.82973e6 | 0.685071 | 0.342536 | − | 0.939505i | \(-0.388714\pi\) | ||||
0.342536 | + | 0.939505i | \(0.388714\pi\) | |||||||
\(444\) | 1.22264e6 | 0.294334 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 246.640 | 5.87118e−5 0 | ||||||||
\(447\) | −538698. | −0.127519 | ||||||||
\(448\) | −2.56182e6 | −0.603050 | ||||||||
\(449\) | 2.43580e6 | 0.570197 | 0.285099 | − | 0.958498i | \(-0.407974\pi\) | ||||
0.285099 | + | 0.958498i | \(0.407974\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.18999e6 | −1.43301 | ||||||||
\(452\) | 3.37441e6 | 0.776875 | ||||||||
\(453\) | −2.05805e6 | −0.471207 | ||||||||
\(454\) | 256.121 | 5.83183e−5 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1058.68 | 0.000238425 0 | ||||||||
\(457\) | 3.89311e6 | 0.871979 | 0.435990 | − | 0.899952i | \(-0.356398\pi\) | ||||
0.435990 | + | 0.899952i | \(0.356398\pi\) | |||||||
\(458\) | 2737.10 | 0.000609716 0 | ||||||||
\(459\) | −3.03180e6 | −0.671690 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.41045e6 | −0.309105 | −0.154553 | − | 0.987985i | \(-0.549394\pi\) | ||||
−0.154553 | + | 0.987985i | \(0.549394\pi\) | |||||||
\(462\) | −420.478 | −9.16513e−5 0 | ||||||||
\(463\) | 7.46201e6 | 1.61772 | 0.808860 | − | 0.588001i | \(-0.200085\pi\) | ||||
0.808860 | + | 0.588001i | \(0.200085\pi\) | |||||||
\(464\) | 3.14667e6 | 0.678509 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4157.44 | −0.000886873 0 | ||||||||
\(467\) | 226020. | 0.0479574 | 0.0239787 | − | 0.999712i | \(-0.492367\pi\) | ||||
0.0239787 | + | 0.999712i | \(0.492367\pi\) | |||||||
\(468\) | 7.54979e6 | 1.59338 | ||||||||
\(469\) | −694905. | −0.145879 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.06176e6 | −0.220534 | ||||||||
\(472\) | −3930.52 | −0.000812073 0 | ||||||||
\(473\) | −635092. | −0.130522 | ||||||||
\(474\) | −974.279 | −0.000199176 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.67419e6 | −0.743266 | ||||||||
\(477\) | 1.94568e6 | 0.391539 | ||||||||
\(478\) | −5627.09 | −0.00112646 | ||||||||
\(479\) | 3.60908e6 | 0.718717 | 0.359358 | − | 0.933200i | \(-0.382996\pi\) | ||||
0.359358 | + | 0.933200i | \(0.382996\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.11613e6 | −1.79658 | ||||||||
\(482\) | −3055.74 | −0.000599100 0 | ||||||||
\(483\) | −517004. | −0.100838 | ||||||||
\(484\) | 1.37835e6 | 0.267451 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2481.67 | −0.000476598 0 | ||||||||
\(487\) | −3.25236e6 | −0.621407 | −0.310704 | − | 0.950507i | \(-0.600565\pi\) | ||||
−0.310704 | + | 0.950507i | \(0.600565\pi\) | |||||||
\(488\) | 9402.83 | 0.00178735 | ||||||||
\(489\) | 2.25702e6 | 0.426839 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.44360e6 | −0.644628 | −0.322314 | − | 0.946633i | \(-0.604461\pi\) | ||||
−0.322314 | + | 0.946633i | \(0.604461\pi\) | |||||||
\(492\) | 2.55247e6 | 0.475387 | ||||||||
\(493\) | 4.51298e6 | 0.836270 | ||||||||
\(494\) | −3946.82 | −0.000727662 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.66213e6 | 1.76347 | ||||||||
\(497\) | 905874. | 0.164504 | ||||||||
\(498\) | −1636.73 | −0.000295735 0 | ||||||||
\(499\) | 5.93248e6 | 1.06656 | 0.533279 | − | 0.845939i | \(-0.320959\pi\) | ||||
0.533279 | + | 0.845939i | \(0.320959\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.51186e6 | 0.447097 | ||||||||
\(502\) | 1321.70 | 0.000234086 0 | ||||||||
\(503\) | 8.79043e6 | 1.54914 | 0.774569 | − | 0.632489i | \(-0.217967\pi\) | ||||
0.774569 | + | 0.632489i | \(0.217967\pi\) | |||||||
\(504\) | −3954.62 | −0.000693472 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1815.50 | 0.000315225 0 | ||||||||
\(507\) | 3.29275e6 | 0.568904 | ||||||||
\(508\) | 4.84134e6 | 0.832351 | ||||||||
\(509\) | −9.23965e6 | −1.58074 | −0.790371 | − | 0.612629i | \(-0.790112\pi\) | ||||
−0.790371 | + | 0.612629i | \(0.790112\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.91206e6 | −1.00158 | ||||||||
\(512\) | −18547.8 | −0.00312693 | ||||||||
\(513\) | −2.18086e6 | −0.365877 | ||||||||
\(514\) | −5552.95 | −0.000927078 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 261883. | 0.0432995 | ||||||||
\(517\) | 4.35317e6 | 0.716275 | ||||||||
\(518\) | 2387.54 | 0.000390955 0 | ||||||||
\(519\) | 849824. | 0.138488 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.38904e6 | −0.224192 | −0.112096 | − | 0.993697i | \(-0.535756\pi\) | ||||
−0.112096 | + | 0.993697i | \(0.535756\pi\) | |||||||
\(522\) | 2428.72 | 0.000390122 0 | ||||||||
\(523\) | −8.64626e6 | −1.38221 | −0.691105 | − | 0.722755i | \(-0.742876\pi\) | ||||
−0.691105 | + | 0.722755i | \(0.742876\pi\) | |||||||
\(524\) | −5.12200e6 | −0.814913 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 429.468 | 6.76809e−5 0 | ||||||||
\(527\) | 1.38575e7 | 2.17350 | ||||||||
\(528\) | 1.55675e6 | 0.243016 | ||||||||
\(529\) | −4.20407e6 | −0.653177 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.87836e6 | 0.596915 | ||||||||
\(532\) | −2.64296e6 | −0.404865 | ||||||||
\(533\) | −1.90315e7 | −2.90172 | ||||||||
\(534\) | −256.339 | −3.89011e−5 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2012.47 | −0.000302564 0 | ||||||||
\(537\) | 804234. | 0.120350 | ||||||||
\(538\) | 4678.85 | 0.000696921 0 | ||||||||
\(539\) | −3.67343e6 | −0.544628 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.59194e6 | 0.674533 | 0.337267 | − | 0.941409i | \(-0.390498\pi\) | ||||
0.337267 | + | 0.941409i | \(0.390498\pi\) | |||||||
\(542\) | 2412.16 | 0.000352702 0 | ||||||||
\(543\) | 708918. | 0.103180 | ||||||||
\(544\) | −15960.9 | −0.00231238 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1292.79 | −0.000185586 0 | ||||||||
\(547\) | 2.30374e6 | 0.329204 | 0.164602 | − | 0.986360i | \(-0.447366\pi\) | ||||
0.164602 | + | 0.986360i | \(0.447366\pi\) | |||||||
\(548\) | −7.78051e6 | −1.10677 | ||||||||
\(549\) | −9.27806e6 | −1.31379 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.24632e6 | 0.455526 | ||||||||
\(552\) | −1497.26 | −0.000209146 0 | ||||||||
\(553\) | 4.86450e6 | 0.676434 | ||||||||
\(554\) | 4764.89 | 0.000659597 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.84363e6 | −0.938857 | ||||||||
\(557\) | −8.88996e6 | −1.21412 | −0.607061 | − | 0.794656i | \(-0.707651\pi\) | ||||
−0.607061 | + | 0.794656i | \(0.707651\pi\) | |||||||
\(558\) | 7457.60 | 0.00101394 | ||||||||
\(559\) | −1.95263e6 | −0.264296 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.23271e6 | 0.299520 | ||||||||
\(562\) | 1508.09 | 0.000201412 0 | ||||||||
\(563\) | −67473.0 | −0.00897138 | −0.00448569 | − | 0.999990i | \(-0.501428\pi\) | ||||
−0.00448569 | + | 0.999990i | \(0.501428\pi\) | |||||||
\(564\) | −1.79505e6 | −0.237618 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3154.52 | −0.000413897 0 | ||||||||
\(567\) | 3.52997e6 | 0.461120 | ||||||||
\(568\) | 2623.44 | 0.000341194 0 | ||||||||
\(569\) | −1.40102e7 | −1.81411 | −0.907057 | − | 0.421007i | \(-0.861677\pi\) | ||||
−0.907057 | + | 0.421007i | \(0.861677\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.48697e6 | 0.960983 | 0.480492 | − | 0.876999i | \(-0.340458\pi\) | ||||
0.480492 | + | 0.876999i | \(0.340458\pi\) | |||||||
\(572\) | −1.16073e7 | −1.48335 | ||||||||
\(573\) | −3.52152e6 | −0.448067 | ||||||||
\(574\) | 4984.41 | 0.000631442 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.32067e6 | 0.919379 | ||||||||
\(577\) | −8.22787e6 | −1.02884 | −0.514420 | − | 0.857538i | \(-0.671993\pi\) | ||||
−0.514420 | + | 0.857538i | \(0.671993\pi\) | |||||||
\(578\) | −2607.37 | −0.000324626 0 | ||||||||
\(579\) | 629469. | 0.0780329 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.17207e6 | 1.00436 | ||||||||
\(582\) | 220.775 | 2.70174e−5 0 | ||||||||
\(583\) | −2.99136e6 | −0.364500 | ||||||||
\(584\) | −17121.5 | −0.00207736 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5859.96 | −0.000704937 0 | ||||||||
\(587\) | 3.61821e6 | 0.433409 | 0.216705 | − | 0.976237i | \(-0.430469\pi\) | ||||
0.216705 | + | 0.976237i | \(0.430469\pi\) | |||||||
\(588\) | 1.51475e6 | 0.180675 | ||||||||
\(589\) | 9.96814e6 | 1.18393 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.71638e6 | −0.319906 | ||||||||
\(592\) | −8.83949e6 | −1.03663 | ||||||||
\(593\) | −7.99199e6 | −0.933293 | −0.466646 | − | 0.884444i | \(-0.654538\pi\) | ||||
−0.466646 | + | 0.884444i | \(0.654538\pi\) | |||||||
\(594\) | 2508.49 | 0.000291706 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.89471e6 | 0.449116 | ||||||||
\(597\) | 423230. | 0.0486005 | ||||||||
\(598\) | 5581.88 | 0.000638303 0 | ||||||||
\(599\) | −6.36161e6 | −0.724436 | −0.362218 | − | 0.932093i | \(-0.617980\pi\) | ||||
−0.362218 | + | 0.932093i | \(0.617980\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.73298e6 | 0.308638 | 0.154319 | − | 0.988021i | \(-0.450682\pi\) | ||||
0.154319 | + | 0.988021i | \(0.450682\pi\) | |||||||
\(602\) | 511.399 | 5.75134e−5 0 | ||||||||
\(603\) | 1.98576e6 | 0.222400 | ||||||||
\(604\) | 1.48794e7 | 1.65956 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1153.77 | −0.000127626 0 | ||||||||
\(607\) | 1.59118e7 | 1.75286 | 0.876428 | − | 0.481532i | \(-0.159920\pi\) | ||||
0.876428 | + | 0.481532i | \(0.159920\pi\) | |||||||
\(608\) | −11481.1 | −0.00125958 | ||||||||
\(609\) | 1.06334e6 | 0.116179 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.33841e7 | 1.45039 | ||||||||
\(612\) | 1.04994e7 | 1.13315 | ||||||||
\(613\) | −1.23223e7 | −1.32447 | −0.662234 | − | 0.749297i | \(-0.730391\pi\) | ||||
−0.662234 | + | 0.749297i | \(0.730391\pi\) | |||||||
\(614\) | −1463.89 | −0.000156706 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6079.99 | 0.000645582 0 | ||||||||
\(617\) | 5.19439e6 | 0.549315 | 0.274658 | − | 0.961542i | \(-0.411436\pi\) | ||||
0.274658 | + | 0.961542i | \(0.411436\pi\) | |||||||
\(618\) | −444.810 | −4.68494e−5 0 | ||||||||
\(619\) | 1.15468e6 | 0.121125 | 0.0605624 | − | 0.998164i | \(-0.480711\pi\) | ||||
0.0605624 | + | 0.998164i | \(0.480711\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.08434e6 | 0.320946 | ||||||||
\(622\) | −4388.70 | −0.000454841 0 | ||||||||
\(623\) | 1.27988e6 | 0.132114 | ||||||||
\(624\) | 4.78633e6 | 0.492086 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5785.76 | −0.000590099 0 | ||||||||
\(627\) | 1.60606e6 | 0.163152 | ||||||||
\(628\) | 7.67638e6 | 0.776707 | ||||||||
\(629\) | −1.26777e7 | −1.27765 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.68764e6 | −0.768634 | −0.384317 | − | 0.923201i | \(-0.625563\pi\) | ||||
−0.384317 | + | 0.923201i | \(0.625563\pi\) | |||||||
\(632\) | 14087.8 | 0.00140297 | ||||||||
\(633\) | −4.83810e6 | −0.479917 | ||||||||
\(634\) | 9016.03 | 0.000890825 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.23350e6 | 0.120920 | ||||||||
\(637\) | −1.12942e7 | −1.10282 | ||||||||
\(638\) | −3734.00 | −0.000363181 0 | ||||||||
\(639\) | −2.58863e6 | −0.250795 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.71146e6 | 0.164522 | 0.0822608 | − | 0.996611i | \(-0.473786\pi\) | ||||
0.0822608 | + | 0.996611i | \(0.473786\pi\) | |||||||
\(642\) | 605.850 | 5.80133e−5 0 | ||||||||
\(643\) | 356593. | 0.0340131 | 0.0170065 | − | 0.999855i | \(-0.494586\pi\) | ||||
0.0170065 | + | 0.999855i | \(0.494586\pi\) | |||||||
\(644\) | 3.73786e6 | 0.355147 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5488.79 | −0.000517482 0 | ||||||||
\(647\) | −1.26524e7 | −1.18826 | −0.594132 | − | 0.804368i | \(-0.702504\pi\) | ||||
−0.594132 | + | 0.804368i | \(0.702504\pi\) | |||||||
\(648\) | 10222.9 | 0.000956396 0 | ||||||||
\(649\) | −5.96275e6 | −0.555693 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.26508e6 | 0.301954 | ||||||||
\(652\) | −1.63179e7 | −1.50330 | ||||||||
\(653\) | −8.05675e6 | −0.739396 | −0.369698 | − | 0.929152i | \(-0.620539\pi\) | ||||
−0.369698 | + | 0.929152i | \(0.620539\pi\) | |||||||
\(654\) | −1182.58 | −0.000108115 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.84540e7 | −1.67429 | ||||||||
\(657\) | 1.68943e7 | 1.52696 | ||||||||
\(658\) | −3505.33 | −0.000315620 0 | ||||||||
\(659\) | 2.71544e6 | 0.243572 | 0.121786 | − | 0.992556i | \(-0.461138\pi\) | ||||
0.121786 | + | 0.992556i | \(0.461138\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.04028e7 | −0.926076 | −0.463038 | − | 0.886339i | \(-0.653241\pi\) | ||||
−0.463038 | + | 0.886339i | \(0.653241\pi\) | |||||||
\(662\) | 1648.67 | 0.000146214 0 | ||||||||
\(663\) | 6.86461e6 | 0.606502 | ||||||||
\(664\) | 23666.6 | 0.00208313 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6822.65 | −0.000596029 0 | ||||||||
\(667\) | −4.59118e6 | −0.399586 | ||||||||
\(668\) | −1.81604e7 | −1.57465 | ||||||||
\(669\) | −308574. | −0.0266560 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.42644e7 | 1.22306 | ||||||||
\(672\) | −3760.66 | −0.000321249 0 | ||||||||
\(673\) | 1.16759e7 | 0.993697 | 0.496849 | − | 0.867837i | \(-0.334490\pi\) | ||||
0.496849 | + | 0.867837i | \(0.334490\pi\) | |||||||
\(674\) | 6829.67 | 0.000579095 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.38061e7 | −2.00365 | ||||||||
\(677\) | 2.24509e7 | 1.88262 | 0.941309 | − | 0.337546i | \(-0.109597\pi\) | ||||
0.941309 | + | 0.337546i | \(0.109597\pi\) | |||||||
\(678\) | 1651.17 | 0.000137949 0 | ||||||||
\(679\) | −1.10232e6 | −0.0917553 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −320436. | −0.0264773 | ||||||||
\(682\) | −11465.6 | −0.000943922 0 | ||||||||
\(683\) | 1.60650e7 | 1.31774 | 0.658871 | − | 0.752256i | \(-0.271034\pi\) | ||||
0.658871 | + | 0.752256i | \(0.271034\pi\) | |||||||
\(684\) | 7.55253e6 | 0.617237 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7606.48 | 0.000617126 0 | ||||||||
\(687\) | −3.42443e6 | −0.276819 | ||||||||
\(688\) | −1.89337e6 | −0.152498 | ||||||||
\(689\) | −9.19713e6 | −0.738081 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −901705. | −0.0718405 | −0.0359202 | − | 0.999355i | \(-0.511436\pi\) | ||||
−0.0359202 | + | 0.999355i | \(0.511436\pi\) | |||||||
\(692\) | −6.14410e6 | −0.487745 | ||||||||
\(693\) | −5.99931e6 | −0.474535 | ||||||||
\(694\) | −6598.92 | −0.000520085 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3079.46 | 0.000240964 0 | ||||||||
\(697\) | −2.64669e7 | −2.06358 | ||||||||
\(698\) | −8717.92 | −0.000677289 0 | ||||||||
\(699\) | 5.20143e6 | 0.402652 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.78394e6 | 0.598280 | 0.299140 | − | 0.954209i | \(-0.403300\pi\) | ||||
0.299140 | + | 0.954209i | \(0.403300\pi\) | |||||||
\(702\) | 7712.49 | 0.000590679 0 | ||||||||
\(703\) | −9.11944e6 | −0.695953 | ||||||||
\(704\) | −1.12551e7 | −0.855888 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −574.502 | −4.33790e−5 0 | ||||||||
\(707\) | 5.76071e6 | 0.433438 | ||||||||
\(708\) | 2.45876e6 | 0.184346 | ||||||||
\(709\) | 9.67167e6 | 0.722580 | 0.361290 | − | 0.932453i | \(-0.382336\pi\) | ||||
0.361290 | + | 0.932453i | \(0.382336\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.39008e7 | −1.03126 | ||||||||
\(712\) | 3706.59 | 0.000274015 0 | ||||||||
\(713\) | −1.40977e7 | −1.03854 | ||||||||
\(714\) | −1797.86 | −0.000131981 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.81449e6 | −0.423866 | ||||||||
\(717\) | 7.04013e6 | 0.511426 | ||||||||
\(718\) | 16119.6 | 0.00116693 | ||||||||
\(719\) | 6.86720e6 | 0.495402 | 0.247701 | − | 0.968837i | \(-0.420325\pi\) | ||||
0.247701 | + | 0.968837i | \(0.420325\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.22091e6 | 0.159108 | ||||||||
\(722\) | 4811.50 | 0.000343508 0 | ||||||||
\(723\) | 3.82308e6 | 0.271999 | ||||||||
\(724\) | −5.12537e6 | −0.363395 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 674.454 | 4.74910e−5 0 | ||||||||
\(727\) | −6.13088e6 | −0.430216 | −0.215108 | − | 0.976590i | \(-0.569010\pi\) | ||||
−0.215108 | + | 0.976590i | \(0.569010\pi\) | |||||||
\(728\) | 18693.3 | 0.00130725 | ||||||||
\(729\) | −7.86696e6 | −0.548262 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.71550e6 | −0.187956 | ||||||||
\(732\) | −5.88201e6 | −0.405740 | ||||||||
\(733\) | −2.82167e7 | −1.93975 | −0.969876 | − | 0.243597i | \(-0.921672\pi\) | ||||
−0.969876 | + | 0.243597i | \(0.921672\pi\) | |||||||
\(734\) | −2865.49 | −0.000196318 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16237.5 | 0.00110490 | ||||||||
\(737\) | −3.05299e6 | −0.207041 | ||||||||
\(738\) | −14243.5 | −0.000962665 0 | ||||||||
\(739\) | 2.52195e7 | 1.69874 | 0.849368 | − | 0.527802i | \(-0.176984\pi\) | ||||
0.849368 | + | 0.527802i | \(0.176984\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.93792e6 | 0.330368 | ||||||||
\(742\) | 2408.75 | 0.000160614 0 | ||||||||
\(743\) | 1.13603e6 | 0.0754949 | 0.0377475 | − | 0.999287i | \(-0.487982\pi\) | ||||
0.0377475 | + | 0.999287i | \(0.487982\pi\) | |||||||
\(744\) | 9455.78 | 0.000626275 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3870.53 | −0.000254638 0 | ||||||||
\(747\) | −2.33526e7 | −1.53120 | ||||||||
\(748\) | −1.61422e7 | −1.05489 | ||||||||
\(749\) | −3.02497e6 | −0.197023 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.35844e7 | 0.878905 | 0.439453 | − | 0.898266i | \(-0.355172\pi\) | ||||
0.439453 | + | 0.898266i | \(0.355172\pi\) | |||||||
\(752\) | 1.29779e7 | 0.836875 | ||||||||
\(753\) | −1.65360e6 | −0.106278 | ||||||||
\(754\) | −11480.4 | −0.000735410 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.16461e6 | 0.328649 | ||||||||
\(757\) | 2.47876e7 | 1.57215 | 0.786076 | − | 0.618130i | \(-0.212109\pi\) | ||||
0.786076 | + | 0.618130i | \(0.212109\pi\) | |||||||
\(758\) | −9883.17 | −0.000624774 0 | ||||||||
\(759\) | −2.27140e6 | −0.143116 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.67533e7 | −1.67462 | −0.837308 | − | 0.546732i | \(-0.815872\pi\) | ||||
−0.837308 | + | 0.546732i | \(0.815872\pi\) | |||||||
\(762\) | 2368.97 | 0.000147799 0 | ||||||||
\(763\) | 5.90454e6 | 0.367177 | ||||||||
\(764\) | 2.54600e7 | 1.57807 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3824.12 | 0.000235483 0 | ||||||||
\(767\) | −1.83328e7 | −1.12523 | ||||||||
\(768\) | 4.64108e6 | 0.283933 | ||||||||
\(769\) | −2.06950e7 | −1.26197 | −0.630986 | − | 0.775794i | \(-0.717350\pi\) | ||||
−0.630986 | + | 0.775794i | \(0.717350\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.94738e6 | 0.420906 | ||||||||
\(772\) | −4.55096e6 | −0.274828 | ||||||||
\(773\) | −1.54618e7 | −0.930701 | −0.465350 | − | 0.885127i | \(-0.654072\pi\) | ||||
−0.465350 | + | 0.885127i | \(0.654072\pi\) | |||||||
\(774\) | −1461.38 | −8.76820e−5 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3192.35 | −0.000190307 0 | ||||||||
\(777\) | −2.98708e6 | −0.177499 | ||||||||
\(778\) | −18194.7 | −0.00107769 | ||||||||
\(779\) | −1.90384e7 | −1.12405 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.97986e6 | 0.233475 | ||||||||
\(782\) | 7762.65 | 0.000453934 0 | ||||||||
\(783\) | −6.34365e6 | −0.369773 | ||||||||
\(784\) | −1.09514e7 | −0.636328 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2506.31 | −0.000144703 0 | ||||||||
\(787\) | −1.53082e7 | −0.881021 | −0.440511 | − | 0.897747i | \(-0.645203\pi\) | ||||
−0.440511 | + | 0.897747i | \(0.645203\pi\) | |||||||
\(788\) | 1.96390e7 | 1.12669 | ||||||||
\(789\) | −537313. | −0.0307280 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.24417e6 | −0.468496 | ||||||||
\(792\) | −17374.2 | −0.000984221 0 | ||||||||
\(793\) | 4.38569e7 | 2.47660 | ||||||||
\(794\) | 5480.63 | 0.000308517 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.05989e6 | −0.171168 | ||||||||
\(797\) | 9.44001e6 | 0.526413 | 0.263207 | − | 0.964740i | \(-0.415220\pi\) | ||||
0.263207 | + | 0.964740i | \(0.415220\pi\) | |||||||
\(798\) | −1293.26 | −7.18914e−5 0 | ||||||||
\(799\) | 1.86131e7 | 1.03146 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.65740e6 | −0.201415 | ||||||||
\(802\) | −14150.3 | −0.000776835 0 | ||||||||
\(803\) | −2.59740e7 | −1.42151 | ||||||||
\(804\) | 1.25891e6 | 0.0686841 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −35251.7 | −0.00191136 | ||||||||
\(807\) | −5.85378e6 | −0.316412 | ||||||||
\(808\) | 16683.2 | 0.000898983 0 | ||||||||
\(809\) | 6.62446e6 | 0.355860 | 0.177930 | − | 0.984043i | \(-0.443060\pi\) | ||||
0.177930 | + | 0.984043i | \(0.443060\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.51429e7 | −0.808455 | −0.404228 | − | 0.914658i | \(-0.632460\pi\) | ||||
−0.404228 | + | 0.914658i | \(0.632460\pi\) | |||||||
\(812\) | −7.68777e6 | −0.409176 | ||||||||
\(813\) | −3.01788e6 | −0.160131 | ||||||||
\(814\) | 10489.4 | 0.000554869 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.65629e6 | 0.349951 | ||||||||
\(817\) | −1.95334e6 | −0.102382 | ||||||||
\(818\) | 22701.6 | 0.00118624 | ||||||||
\(819\) | −1.84452e7 | −0.960892 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 219211. | 0.0113502 | 0.00567512 | − | 0.999984i | \(-0.498194\pi\) | ||||
0.00567512 | + | 0.999984i | \(0.498194\pi\) | |||||||
\(822\) | −3807.17 | −0.000196527 0 | ||||||||
\(823\) | −3.47564e7 | −1.78869 | −0.894346 | − | 0.447375i | \(-0.852359\pi\) | ||||
−0.894346 | + | 0.447375i | \(0.852359\pi\) | |||||||
\(824\) | 6431.83 | 0.000330002 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4801.42 | 0.000244861 0 | ||||||||
\(827\) | −3.26993e7 | −1.66255 | −0.831275 | − | 0.555861i | \(-0.812389\pi\) | ||||
−0.831275 | + | 0.555861i | \(0.812389\pi\) | |||||||
\(828\) | −1.06813e7 | −0.541439 | ||||||||
\(829\) | 3.49311e7 | 1.76533 | 0.882664 | − | 0.470004i | \(-0.155748\pi\) | ||||
0.882664 | + | 0.470004i | \(0.155748\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.96142e6 | −0.299466 | ||||||||
\(832\) | −3.46044e7 | −1.73310 | ||||||||
\(833\) | −1.57067e7 | −0.784281 | ||||||||
\(834\) | −3348.73 | −0.000166712 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.16116e7 | −0.574612 | ||||||||
\(837\) | −1.94788e7 | −0.961054 | ||||||||
\(838\) | −12958.4 | −0.000637442 0 | ||||||||
\(839\) | 2.60569e7 | 1.27796 | 0.638982 | − | 0.769222i | \(-0.279356\pi\) | ||||
0.638982 | + | 0.769222i | \(0.279356\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.10683e7 | −0.539624 | ||||||||
\(842\) | −8835.91 | −0.000429508 0 | ||||||||
\(843\) | −1.88679e6 | −0.0914438 | ||||||||
\(844\) | 3.49788e7 | 1.69024 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10016.9 | 0.000481178 0 | ||||||||
\(847\) | −3.36750e6 | −0.161287 | ||||||||
\(848\) | −8.91802e6 | −0.425872 | ||||||||
\(849\) | 3.94667e6 | 0.187915 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.28974e7 | 0.610488 | ||||||||
\(852\) | −1.64111e6 | −0.0774532 | ||||||||
\(853\) | −1.36792e7 | −0.643709 | −0.321854 | − | 0.946789i | \(-0.604306\pi\) | ||||
−0.321854 | + | 0.946789i | \(0.604306\pi\) | |||||||
\(854\) | −11486.2 | −0.000538932 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8760.42 | −0.000408640 0 | ||||||||
\(857\) | 7.35615e6 | 0.342136 | 0.171068 | − | 0.985259i | \(-0.445278\pi\) | ||||
0.171068 | + | 0.985259i | \(0.445278\pi\) | |||||||
\(858\) | −5679.72 | −0.000263396 0 | ||||||||
\(859\) | 7.11286e6 | 0.328898 | 0.164449 | − | 0.986386i | \(-0.447415\pi\) | ||||
0.164449 | + | 0.986386i | \(0.447415\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.23606e6 | −0.286683 | ||||||||
\(862\) | −7186.03 | −0.000329398 0 | ||||||||
\(863\) | −2.93200e7 | −1.34010 | −0.670050 | − | 0.742316i | \(-0.733727\pi\) | ||||
−0.670050 | + | 0.742316i | \(0.733727\pi\) | |||||||
\(864\) | 22435.3 | 0.00102246 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −21001.7 | −0.000951612 0 | ||||||||
\(867\) | 3.26211e6 | 0.147384 | ||||||||
\(868\) | −2.36060e7 | −1.06347 | ||||||||
\(869\) | 2.13717e7 | 0.960040 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.38661e6 | −0.419241 | ||||||||
\(872\) | 17099.8 | 0.000761551 0 | ||||||||
\(873\) | 3.14998e6 | 0.139886 | ||||||||
\(874\) | 5583.90 | 0.000247263 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.07105e7 | 0.471573 | ||||||||
\(877\) | −3.15641e7 | −1.38578 | −0.692890 | − | 0.721044i | \(-0.743663\pi\) | ||||
−0.692890 | + | 0.721044i | \(0.743663\pi\) | |||||||
\(878\) | −21997.8 | −0.000963036 0 | ||||||||
\(879\) | 7.33147e6 | 0.320051 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.85426e7 | 1.23895 | 0.619475 | − | 0.785017i | \(-0.287346\pi\) | ||||
0.619475 | + | 0.785017i | \(0.287346\pi\) | |||||||
\(882\) | −8452.74 | −0.000365869 0 | ||||||||
\(883\) | −1.51806e7 | −0.655222 | −0.327611 | − | 0.944813i | \(-0.606244\pi\) | ||||
−0.327611 | + | 0.944813i | \(0.606244\pi\) | |||||||
\(884\) | −4.96301e7 | −2.13607 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10010.8 | −0.000428435 0 | ||||||||
\(887\) | 1.32033e7 | 0.563474 | 0.281737 | − | 0.959492i | \(-0.409089\pi\) | ||||
0.281737 | + | 0.959492i | \(0.409089\pi\) | |||||||
\(888\) | −8650.71 | −0.000368145 0 | ||||||||
\(889\) | −1.18281e7 | −0.501951 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.55086e7 | 0.654451 | ||||||||
\(892\) | 2.23094e6 | 0.0938808 | ||||||||
\(893\) | 1.33890e7 | 0.561847 | ||||||||
\(894\) | 1905.76 | 7.97490e−5 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 36252.1 | 0.00150856 | ||||||||
\(897\) | −6.98356e6 | −0.289798 | ||||||||
\(898\) | −8617.17 | −0.000356594 0 | ||||||||
\(899\) | 2.89951e7 | 1.19654 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.27903e7 | −0.524892 | ||||||||
\(902\) | 21898.5 | 0.000896185 0 | ||||||||
\(903\) | −639819. | −0.0261118 | ||||||||
\(904\) | −23875.4 | −0.000971695 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7280.82 | 0.000294686 0 | ||||||||
\(907\) | 3.96521e7 | 1.60047 | 0.800236 | − | 0.599685i | \(-0.204707\pi\) | ||||
0.800236 | + | 0.599685i | \(0.204707\pi\) | |||||||
\(908\) | 2.31670e6 | 0.0932515 | ||||||||
\(909\) | −1.64618e7 | −0.660798 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.22945e6 | 0.0490810 | 0.0245405 | − | 0.999699i | \(-0.492188\pi\) | ||||
0.0245405 | + | 0.999699i | \(0.492188\pi\) | |||||||
\(912\) | 4.78807e6 | 0.190622 | ||||||||
\(913\) | 3.59031e7 | 1.42546 | ||||||||
\(914\) | −13772.7 | −0.000545324 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.47581e7 | 0.974942 | ||||||||
\(917\) | 1.25138e7 | 0.491435 | ||||||||
\(918\) | 10725.7 | 0.000420066 0 | ||||||||
\(919\) | −9.08804e6 | −0.354961 | −0.177481 | − | 0.984124i | \(-0.556795\pi\) | ||||
−0.177481 | + | 0.984124i | \(0.556795\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.83149e6 | 0.0711468 | ||||||||
\(922\) | 4989.79 | 0.000193310 0 | ||||||||
\(923\) | 1.22363e7 | 0.472767 | ||||||||
\(924\) | −3.80338e6 | −0.146551 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −26398.5 | −0.00101170 | ||||||||
\(927\) | −6.34648e6 | −0.242568 | ||||||||
\(928\) | −33396.1 | −0.00127299 | ||||||||
\(929\) | −4.99370e7 | −1.89838 | −0.949190 | − | 0.314704i | \(-0.898095\pi\) | ||||
−0.949190 | + | 0.314704i | \(0.898095\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.12983e7 | −0.427207 | ||||||||
\(932\) | −3.76056e7 | −1.41812 | ||||||||
\(933\) | 5.49076e6 | 0.206504 | ||||||||
\(934\) | −799.597 | −2.99919e−5 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −53418.1 | −0.00199296 | ||||||||
\(937\) | 3.54310e7 | 1.31836 | 0.659180 | − | 0.751985i | \(-0.270903\pi\) | ||||
0.659180 | + | 0.751985i | \(0.270903\pi\) | |||||||
\(938\) | 2458.38 | 9.12309e−5 0 | ||||||||
\(939\) | 7.23865e6 | 0.267913 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.82105e7 | 0.670421 | 0.335211 | − | 0.942143i | \(-0.391193\pi\) | ||||
0.335211 | + | 0.942143i | \(0.391193\pi\) | |||||||
\(942\) | 3756.22 | 0.000137919 0 | ||||||||
\(943\) | 2.69255e7 | 0.986017 | ||||||||
\(944\) | −1.77765e7 | −0.649256 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2246.78 | 8.16268e−5 0 | ||||||||
\(947\) | 2.99743e7 | 1.08611 | 0.543056 | − | 0.839697i | \(-0.317267\pi\) | ||||
0.543056 | + | 0.839697i | \(0.317267\pi\) | |||||||
\(948\) | −8.81271e6 | −0.318485 | ||||||||
\(949\) | −7.98587e7 | −2.87844 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.12801e7 | −0.404446 | ||||||||
\(952\) | 25996.5 | 0.000929658 0 | ||||||||
\(953\) | −4.88225e7 | −1.74136 | −0.870679 | − | 0.491851i | \(-0.836320\pi\) | ||||
−0.870679 | + | 0.491851i | \(0.836320\pi\) | |||||||
\(954\) | −6883.27 | −0.000244863 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.08991e7 | −1.80121 | ||||||||
\(957\) | 4.67166e6 | 0.164889 | ||||||||
\(958\) | −12767.9 | −0.000449476 0 | ||||||||
\(959\) | 1.90089e7 | 0.667439 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.04030e7 | 2.10984 | ||||||||
\(962\) | 32250.3 | 0.00112356 | ||||||||
\(963\) | 8.64417e6 | 0.300371 | ||||||||
\(964\) | −2.76403e7 | −0.957967 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1829.01 | 6.30630e−5 0 | ||||||||
\(967\) | 5.21957e7 | 1.79502 | 0.897508 | − | 0.440999i | \(-0.145376\pi\) | ||||
0.897508 | + | 0.440999i | \(0.145376\pi\) | |||||||
\(968\) | −9752.41 | −0.000334521 0 | ||||||||
\(969\) | 6.86710e6 | 0.234944 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.63198e7 | −0.895849 | −0.447924 | − | 0.894071i | \(-0.647837\pi\) | ||||
−0.447924 | + | 0.894071i | \(0.647837\pi\) | |||||||
\(972\) | −2.24476e7 | −0.762086 | ||||||||
\(973\) | 1.67200e7 | 0.566179 | ||||||||
\(974\) | 11505.9 | 0.000388620 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.25260e7 | 1.42899 | ||||||||
\(977\) | −3.95342e6 | −0.132506 | −0.0662532 | − | 0.997803i | \(-0.521105\pi\) | ||||
−0.0662532 | + | 0.997803i | \(0.521105\pi\) | |||||||
\(978\) | −7984.72 | −0.000266939 0 | ||||||||
\(979\) | 5.62303e6 | 0.187505 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.68729e7 | −0.559779 | ||||||||
\(982\) | 12182.5 | 0.000403142 0 | ||||||||
\(983\) | 4.78744e7 | 1.58023 | 0.790114 | − | 0.612960i | \(-0.210021\pi\) | ||||
0.790114 | + | 0.612960i | \(0.210021\pi\) | |||||||
\(984\) | −18059.9 | −0.000594602 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −15965.7 | −0.000522992 0 | ||||||||
\(987\) | 4.38557e6 | 0.143296 | ||||||||
\(988\) | −3.57004e7 | −1.16354 | ||||||||
\(989\) | 2.76255e6 | 0.0898090 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.72624e6 | −0.282256 | −0.141128 | − | 0.989991i | \(-0.545073\pi\) | ||||
−0.141128 | + | 0.989991i | \(0.545073\pi\) | |||||||
\(992\) | −102546. | −0.00330856 | ||||||||
\(993\) | −2.06267e6 | −0.0663830 | ||||||||
\(994\) | −3204.73 | −0.000102879 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.48048e7 | −0.472884 | ||||||||
\(997\) | 4.45976e6 | 0.142093 | 0.0710467 | − | 0.997473i | \(-0.477366\pi\) | ||||
0.0710467 | + | 0.997473i | \(0.477366\pi\) | |||||||
\(998\) | −20987.5 | −0.000667012 0 | ||||||||
\(999\) | 1.78203e7 | 0.564939 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1075.6.a.l.1.25 | 52 | ||
5.2 | odd | 4 | 215.6.b.a.44.52 | ✓ | 104 | ||
5.3 | odd | 4 | 215.6.b.a.44.53 | yes | 104 | ||
5.4 | even | 2 | 1075.6.a.k.1.28 | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
215.6.b.a.44.52 | ✓ | 104 | 5.2 | odd | 4 | ||
215.6.b.a.44.53 | yes | 104 | 5.3 | odd | 4 | ||
1075.6.a.k.1.28 | 52 | 5.4 | even | 2 | |||
1075.6.a.l.1.25 | 52 | 1.1 | even | 1 | trivial |