Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [471,6,Mod(1,471)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(471, 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("471.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 471 = 3 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 471.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: | \(75.5407791319\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 471.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.01065 | −1.41610 | −0.708048 | − | 0.706164i | \(-0.750424\pi\) | ||||
−0.708048 | + | 0.706164i | \(0.750424\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 32.1705 | 1.00533 | ||||||||
\(5\) | −50.4239 | −0.902011 | −0.451005 | − | 0.892521i | \(-0.648934\pi\) | ||||
−0.451005 | + | 0.892521i | \(0.648934\pi\) | |||||||
\(6\) | 72.0959 | 0.817584 | ||||||||
\(7\) | 130.088 | 1.00344 | 0.501720 | − | 0.865030i | \(-0.332701\pi\) | ||||
0.501720 | + | 0.865030i | \(0.332701\pi\) | |||||||
\(8\) | −1.36618 | −0.00754716 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 403.929 | 1.27733 | ||||||||
\(11\) | −543.858 | −1.35520 | −0.677600 | − | 0.735430i | \(-0.736980\pi\) | ||||
−0.677600 | + | 0.735430i | \(0.736980\pi\) | |||||||
\(12\) | −289.535 | −0.580427 | ||||||||
\(13\) | 881.397 | 1.44648 | 0.723241 | − | 0.690595i | \(-0.242651\pi\) | ||||
0.723241 | + | 0.690595i | \(0.242651\pi\) | |||||||
\(14\) | −1042.09 | −1.42097 | ||||||||
\(15\) | 453.815 | 0.520776 | ||||||||
\(16\) | −1018.51 | −0.994642 | ||||||||
\(17\) | −1152.81 | −0.967469 | −0.483734 | − | 0.875215i | \(-0.660720\pi\) | ||||
−0.483734 | + | 0.875215i | \(0.660720\pi\) | |||||||
\(18\) | −648.863 | −0.472032 | ||||||||
\(19\) | 376.341 | 0.239165 | 0.119582 | − | 0.992824i | \(-0.461844\pi\) | ||||
0.119582 | + | 0.992824i | \(0.461844\pi\) | |||||||
\(20\) | −1622.17 | −0.906818 | ||||||||
\(21\) | −1170.79 | −0.579336 | ||||||||
\(22\) | 4356.65 | 1.91909 | ||||||||
\(23\) | −2808.90 | −1.10718 | −0.553589 | − | 0.832790i | \(-0.686742\pi\) | ||||
−0.553589 | + | 0.832790i | \(0.686742\pi\) | |||||||
\(24\) | 12.2956 | 0.00435736 | ||||||||
\(25\) | −582.428 | −0.186377 | ||||||||
\(26\) | −7060.57 | −2.04836 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 4185.00 | 1.00879 | ||||||||
\(29\) | 2312.72 | 0.510656 | 0.255328 | − | 0.966855i | \(-0.417817\pi\) | ||||
0.255328 | + | 0.966855i | \(0.417817\pi\) | |||||||
\(30\) | −3635.36 | −0.737469 | ||||||||
\(31\) | 3813.41 | 0.712705 | 0.356352 | − | 0.934352i | \(-0.384020\pi\) | ||||
0.356352 | + | 0.934352i | \(0.384020\pi\) | |||||||
\(32\) | 8202.67 | 1.41606 | ||||||||
\(33\) | 4894.72 | 0.782425 | ||||||||
\(34\) | 9234.79 | 1.37003 | ||||||||
\(35\) | −6559.54 | −0.905114 | ||||||||
\(36\) | 2605.81 | 0.335110 | ||||||||
\(37\) | 4805.83 | 0.577117 | 0.288558 | − | 0.957462i | \(-0.406824\pi\) | ||||
0.288558 | + | 0.957462i | \(0.406824\pi\) | |||||||
\(38\) | −3014.74 | −0.338681 | ||||||||
\(39\) | −7932.57 | −0.835127 | ||||||||
\(40\) | 68.8883 | 0.00680762 | ||||||||
\(41\) | 1232.77 | 0.114531 | 0.0572654 | − | 0.998359i | \(-0.481762\pi\) | ||||
0.0572654 | + | 0.998359i | \(0.481762\pi\) | |||||||
\(42\) | 9378.79 | 0.820396 | ||||||||
\(43\) | −9646.49 | −0.795606 | −0.397803 | − | 0.917471i | \(-0.630227\pi\) | ||||
−0.397803 | + | 0.917471i | \(0.630227\pi\) | |||||||
\(44\) | −17496.2 | −1.36242 | ||||||||
\(45\) | −4084.34 | −0.300670 | ||||||||
\(46\) | 22501.2 | 1.56787 | ||||||||
\(47\) | 11853.0 | 0.782678 | 0.391339 | − | 0.920247i | \(-0.372012\pi\) | ||||
0.391339 | + | 0.920247i | \(0.372012\pi\) | |||||||
\(48\) | 9166.62 | 0.574257 | ||||||||
\(49\) | 115.839 | 0.00689230 | ||||||||
\(50\) | 4665.63 | 0.263928 | ||||||||
\(51\) | 10375.3 | 0.558568 | ||||||||
\(52\) | 28355.0 | 1.45419 | ||||||||
\(53\) | 1751.99 | 0.0856725 | 0.0428363 | − | 0.999082i | \(-0.486361\pi\) | ||||
0.0428363 | + | 0.999082i | \(0.486361\pi\) | |||||||
\(54\) | 5839.77 | 0.272528 | ||||||||
\(55\) | 27423.4 | 1.22241 | ||||||||
\(56\) | −177.724 | −0.00757313 | ||||||||
\(57\) | −3387.07 | −0.138082 | ||||||||
\(58\) | −18526.4 | −0.723138 | ||||||||
\(59\) | 21914.2 | 0.819589 | 0.409794 | − | 0.912178i | \(-0.365600\pi\) | ||||
0.409794 | + | 0.912178i | \(0.365600\pi\) | |||||||
\(60\) | 14599.5 | 0.523552 | ||||||||
\(61\) | 23265.5 | 0.800548 | 0.400274 | − | 0.916395i | \(-0.368915\pi\) | ||||
0.400274 | + | 0.916395i | \(0.368915\pi\) | |||||||
\(62\) | −30547.9 | −1.00926 | ||||||||
\(63\) | 10537.1 | 0.334480 | ||||||||
\(64\) | −33116.3 | −1.01063 | ||||||||
\(65\) | −44443.5 | −1.30474 | ||||||||
\(66\) | −39209.9 | −1.10799 | ||||||||
\(67\) | −12277.7 | −0.334140 | −0.167070 | − | 0.985945i | \(-0.553431\pi\) | ||||
−0.167070 | + | 0.985945i | \(0.553431\pi\) | |||||||
\(68\) | −37086.7 | −0.972625 | ||||||||
\(69\) | 25280.1 | 0.639229 | ||||||||
\(70\) | 52546.2 | 1.28173 | ||||||||
\(71\) | 65912.9 | 1.55176 | 0.775880 | − | 0.630881i | \(-0.217306\pi\) | ||||
0.775880 | + | 0.630881i | \(0.217306\pi\) | |||||||
\(72\) | −110.661 | −0.00251572 | ||||||||
\(73\) | −3780.86 | −0.0830392 | −0.0415196 | − | 0.999138i | \(-0.513220\pi\) | ||||
−0.0415196 | + | 0.999138i | \(0.513220\pi\) | |||||||
\(74\) | −38497.8 | −0.817253 | ||||||||
\(75\) | 5241.85 | 0.107605 | ||||||||
\(76\) | 12107.1 | 0.240440 | ||||||||
\(77\) | −70749.3 | −1.35986 | ||||||||
\(78\) | 63545.1 | 1.18262 | ||||||||
\(79\) | 45943.6 | 0.828242 | 0.414121 | − | 0.910222i | \(-0.364089\pi\) | ||||
0.414121 | + | 0.910222i | \(0.364089\pi\) | |||||||
\(80\) | 51357.4 | 0.897178 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −9875.29 | −0.162187 | ||||||||
\(83\) | −42028.6 | −0.669654 | −0.334827 | − | 0.942280i | \(-0.608678\pi\) | ||||
−0.334827 | + | 0.942280i | \(0.608678\pi\) | |||||||
\(84\) | −37665.0 | −0.582424 | ||||||||
\(85\) | 58129.4 | 0.872667 | ||||||||
\(86\) | 77274.7 | 1.12666 | ||||||||
\(87\) | −20814.5 | −0.294827 | ||||||||
\(88\) | 743.009 | 0.0102279 | ||||||||
\(89\) | 39290.8 | 0.525795 | 0.262897 | − | 0.964824i | \(-0.415322\pi\) | ||||
0.262897 | + | 0.964824i | \(0.415322\pi\) | |||||||
\(90\) | 32718.2 | 0.425778 | ||||||||
\(91\) | 114659. | 1.45146 | ||||||||
\(92\) | −90364.0 | −1.11308 | ||||||||
\(93\) | −34320.7 | −0.411480 | ||||||||
\(94\) | −94950.2 | −1.10835 | ||||||||
\(95\) | −18976.6 | −0.215729 | ||||||||
\(96\) | −73824.1 | −0.817561 | ||||||||
\(97\) | −47667.8 | −0.514394 | −0.257197 | − | 0.966359i | \(-0.582799\pi\) | ||||
−0.257197 | + | 0.966359i | \(0.582799\pi\) | |||||||
\(98\) | −927.945 | −0.00976016 | ||||||||
\(99\) | −44052.5 | −0.451733 | ||||||||
\(100\) | −18737.0 | −0.187370 | ||||||||
\(101\) | −56384.0 | −0.549987 | −0.274994 | − | 0.961446i | \(-0.588676\pi\) | ||||
−0.274994 | + | 0.961446i | \(0.588676\pi\) | |||||||
\(102\) | −83113.1 | −0.790987 | ||||||||
\(103\) | 176480. | 1.63909 | 0.819545 | − | 0.573015i | \(-0.194226\pi\) | ||||
0.819545 | + | 0.573015i | \(0.194226\pi\) | |||||||
\(104\) | −1204.15 | −0.0109168 | ||||||||
\(105\) | 59035.8 | 0.522568 | ||||||||
\(106\) | −14034.6 | −0.121321 | ||||||||
\(107\) | 71931.0 | 0.607375 | 0.303687 | − | 0.952772i | \(-0.401782\pi\) | ||||
0.303687 | + | 0.952772i | \(0.401782\pi\) | |||||||
\(108\) | −23452.3 | −0.193476 | ||||||||
\(109\) | −142324. | −1.14739 | −0.573696 | − | 0.819068i | \(-0.694491\pi\) | ||||
−0.573696 | + | 0.819068i | \(0.694491\pi\) | |||||||
\(110\) | −219680. | −1.73104 | ||||||||
\(111\) | −43252.4 | −0.333199 | ||||||||
\(112\) | −132496. | −0.998064 | ||||||||
\(113\) | 137208. | 1.01084 | 0.505421 | − | 0.862873i | \(-0.331337\pi\) | ||||
0.505421 | + | 0.862873i | \(0.331337\pi\) | |||||||
\(114\) | 27132.6 | 0.195537 | ||||||||
\(115\) | 141636. | 0.998686 | ||||||||
\(116\) | 74401.5 | 0.513377 | ||||||||
\(117\) | 71393.2 | 0.482161 | ||||||||
\(118\) | −175547. | −1.16062 | ||||||||
\(119\) | −149967. | −0.970797 | ||||||||
\(120\) | −619.994 | −0.00393038 | ||||||||
\(121\) | 134730. | 0.836568 | ||||||||
\(122\) | −186372. | −1.13365 | ||||||||
\(123\) | −11094.9 | −0.0661244 | ||||||||
\(124\) | 122680. | 0.716503 | ||||||||
\(125\) | 186943. | 1.07012 | ||||||||
\(126\) | −84409.1 | −0.473656 | ||||||||
\(127\) | −284159. | −1.56334 | −0.781669 | − | 0.623694i | \(-0.785631\pi\) | ||||
−0.781669 | + | 0.623694i | \(0.785631\pi\) | |||||||
\(128\) | 2797.90 | 0.0150941 | ||||||||
\(129\) | 86818.4 | 0.459344 | ||||||||
\(130\) | 356021. | 1.84764 | ||||||||
\(131\) | 39819.3 | 0.202729 | 0.101364 | − | 0.994849i | \(-0.467679\pi\) | ||||
0.101364 | + | 0.994849i | \(0.467679\pi\) | |||||||
\(132\) | 157466. | 0.786595 | ||||||||
\(133\) | 48957.4 | 0.239988 | ||||||||
\(134\) | 98352.0 | 0.473175 | ||||||||
\(135\) | 36759.0 | 0.173592 | ||||||||
\(136\) | 1574.95 | 0.00730164 | ||||||||
\(137\) | −288640. | −1.31388 | −0.656939 | − | 0.753944i | \(-0.728149\pi\) | ||||
−0.656939 | + | 0.753944i | \(0.728149\pi\) | |||||||
\(138\) | −202510. | −0.905210 | ||||||||
\(139\) | 287463. | 1.26196 | 0.630979 | − | 0.775800i | \(-0.282653\pi\) | ||||
0.630979 | + | 0.775800i | \(0.282653\pi\) | |||||||
\(140\) | −211024. | −0.909938 | ||||||||
\(141\) | −106677. | −0.451879 | ||||||||
\(142\) | −528005. | −2.19744 | ||||||||
\(143\) | −479355. | −1.96027 | ||||||||
\(144\) | −82499.6 | −0.331547 | ||||||||
\(145\) | −116616. | −0.460617 | ||||||||
\(146\) | 30287.1 | 0.117592 | ||||||||
\(147\) | −1042.55 | −0.00397927 | ||||||||
\(148\) | 154606. | 0.580193 | ||||||||
\(149\) | −246867. | −0.910956 | −0.455478 | − | 0.890247i | \(-0.650532\pi\) | ||||
−0.455478 | + | 0.890247i | \(0.650532\pi\) | |||||||
\(150\) | −41990.6 | −0.152379 | ||||||||
\(151\) | −231949. | −0.827848 | −0.413924 | − | 0.910311i | \(-0.635842\pi\) | ||||
−0.413924 | + | 0.910311i | \(0.635842\pi\) | |||||||
\(152\) | −514.150 | −0.00180502 | ||||||||
\(153\) | −93377.9 | −0.322490 | ||||||||
\(154\) | 566748. | 1.92570 | ||||||||
\(155\) | −192287. | −0.642867 | ||||||||
\(156\) | −255195. | −0.839578 | ||||||||
\(157\) | −24649.0 | −0.0798087 | ||||||||
\(158\) | −368038. | −1.17287 | ||||||||
\(159\) | −15767.9 | −0.0494631 | ||||||||
\(160\) | −413611. | −1.27730 | ||||||||
\(161\) | −365404. | −1.11099 | ||||||||
\(162\) | −52557.9 | −0.157344 | ||||||||
\(163\) | −132246. | −0.389865 | −0.194933 | − | 0.980817i | \(-0.562449\pi\) | ||||
−0.194933 | + | 0.980817i | \(0.562449\pi\) | |||||||
\(164\) | 39658.9 | 0.115141 | ||||||||
\(165\) | −246811. | −0.705756 | ||||||||
\(166\) | 336677. | 0.948294 | ||||||||
\(167\) | −499847. | −1.38690 | −0.693452 | − | 0.720503i | \(-0.743911\pi\) | ||||
−0.693452 | + | 0.720503i | \(0.743911\pi\) | |||||||
\(168\) | 1599.51 | 0.00437235 | ||||||||
\(169\) | 405568. | 1.09231 | ||||||||
\(170\) | −465654. | −1.23578 | ||||||||
\(171\) | 30483.6 | 0.0797216 | ||||||||
\(172\) | −310333. | −0.799847 | ||||||||
\(173\) | 183603. | 0.466406 | 0.233203 | − | 0.972428i | \(-0.425079\pi\) | ||||
0.233203 | + | 0.972428i | \(0.425079\pi\) | |||||||
\(174\) | 166738. | 0.417504 | ||||||||
\(175\) | −75766.8 | −0.187018 | ||||||||
\(176\) | 553926. | 1.34794 | ||||||||
\(177\) | −197228. | −0.473190 | ||||||||
\(178\) | −314745. | −0.744576 | ||||||||
\(179\) | −675753. | −1.57636 | −0.788180 | − | 0.615445i | \(-0.788976\pi\) | ||||
−0.788180 | + | 0.615445i | \(0.788976\pi\) | |||||||
\(180\) | −131395. | −0.302273 | ||||||||
\(181\) | −135576. | −0.307601 | −0.153801 | − | 0.988102i | \(-0.549151\pi\) | ||||
−0.153801 | + | 0.988102i | \(0.549151\pi\) | |||||||
\(182\) | −918494. | −2.05541 | ||||||||
\(183\) | −209389. | −0.462197 | ||||||||
\(184\) | 3837.47 | 0.00835605 | ||||||||
\(185\) | −242329. | −0.520566 | ||||||||
\(186\) | 274931. | 0.582696 | ||||||||
\(187\) | 626967. | 1.31111 | ||||||||
\(188\) | 381317. | 0.786849 | ||||||||
\(189\) | −94834.0 | −0.193112 | ||||||||
\(190\) | 152015. | 0.305494 | ||||||||
\(191\) | −435271. | −0.863329 | −0.431665 | − | 0.902034i | \(-0.642074\pi\) | ||||
−0.431665 | + | 0.902034i | \(0.642074\pi\) | |||||||
\(192\) | 298047. | 0.583488 | ||||||||
\(193\) | 114292. | 0.220862 | 0.110431 | − | 0.993884i | \(-0.464777\pi\) | ||||
0.110431 | + | 0.993884i | \(0.464777\pi\) | |||||||
\(194\) | 381850. | 0.728431 | ||||||||
\(195\) | 399992. | 0.753294 | ||||||||
\(196\) | 3726.60 | 0.00692903 | ||||||||
\(197\) | −350757. | −0.643933 | −0.321967 | − | 0.946751i | \(-0.604344\pi\) | ||||
−0.321967 | + | 0.946751i | \(0.604344\pi\) | |||||||
\(198\) | 352889. | 0.639698 | ||||||||
\(199\) | −317648. | −0.568609 | −0.284304 | − | 0.958734i | \(-0.591763\pi\) | ||||
−0.284304 | + | 0.958734i | \(0.591763\pi\) | |||||||
\(200\) | 795.703 | 0.00140662 | ||||||||
\(201\) | 110499. | 0.192916 | ||||||||
\(202\) | 451673. | 0.778835 | ||||||||
\(203\) | 300857. | 0.512412 | ||||||||
\(204\) | 333780. | 0.561545 | ||||||||
\(205\) | −62161.1 | −0.103308 | ||||||||
\(206\) | −1.41372e6 | −2.32111 | ||||||||
\(207\) | −227521. | −0.369059 | ||||||||
\(208\) | −897715. | −1.43873 | ||||||||
\(209\) | −204676. | −0.324116 | ||||||||
\(210\) | −472916. | −0.740006 | ||||||||
\(211\) | −868366. | −1.34275 | −0.671377 | − | 0.741116i | \(-0.734297\pi\) | ||||
−0.671377 | + | 0.741116i | \(0.734297\pi\) | |||||||
\(212\) | 56362.4 | 0.0861291 | ||||||||
\(213\) | −593216. | −0.895909 | ||||||||
\(214\) | −576215. | −0.860102 | ||||||||
\(215\) | 486414. | 0.717645 | ||||||||
\(216\) | 995.947 | 0.00145245 | ||||||||
\(217\) | 496078. | 0.715156 | ||||||||
\(218\) | 1.14011e6 | 1.62482 | ||||||||
\(219\) | 34027.7 | 0.0479427 | ||||||||
\(220\) | 882227. | 1.22892 | ||||||||
\(221\) | −1.01609e6 | −1.39943 | ||||||||
\(222\) | 346480. | 0.471841 | ||||||||
\(223\) | 110563. | 0.148884 | 0.0744422 | − | 0.997225i | \(-0.476282\pi\) | ||||
0.0744422 | + | 0.997225i | \(0.476282\pi\) | |||||||
\(224\) | 1.06707e6 | 1.42093 | ||||||||
\(225\) | −47176.7 | −0.0621256 | ||||||||
\(226\) | −1.09913e6 | −1.43145 | ||||||||
\(227\) | 482629. | 0.621654 | 0.310827 | − | 0.950467i | \(-0.399394\pi\) | ||||
0.310827 | + | 0.950467i | \(0.399394\pi\) | |||||||
\(228\) | −108964. | −0.138818 | ||||||||
\(229\) | 264468. | 0.333260 | 0.166630 | − | 0.986019i | \(-0.446711\pi\) | ||||
0.166630 | + | 0.986019i | \(0.446711\pi\) | |||||||
\(230\) | −1.13460e6 | −1.41424 | ||||||||
\(231\) | 636743. | 0.785117 | ||||||||
\(232\) | −3159.60 | −0.00385400 | ||||||||
\(233\) | 1.35835e6 | 1.63916 | 0.819581 | − | 0.572963i | \(-0.194206\pi\) | ||||
0.819581 | + | 0.572963i | \(0.194206\pi\) | |||||||
\(234\) | −571906. | −0.682786 | ||||||||
\(235\) | −597674. | −0.705984 | ||||||||
\(236\) | 704992. | 0.823957 | ||||||||
\(237\) | −413493. | −0.478186 | ||||||||
\(238\) | 1.20133e6 | 1.37474 | ||||||||
\(239\) | 188728. | 0.213718 | 0.106859 | − | 0.994274i | \(-0.465921\pi\) | ||||
0.106859 | + | 0.994274i | \(0.465921\pi\) | |||||||
\(240\) | −462217. | −0.517986 | ||||||||
\(241\) | −186252. | −0.206565 | −0.103283 | − | 0.994652i | \(-0.532935\pi\) | ||||
−0.103283 | + | 0.994652i | \(0.532935\pi\) | |||||||
\(242\) | −1.07928e6 | −1.18466 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 748463. | 0.804815 | ||||||||
\(245\) | −5841.05 | −0.00621693 | ||||||||
\(246\) | 88877.6 | 0.0936385 | ||||||||
\(247\) | 331706. | 0.345948 | ||||||||
\(248\) | −5209.82 | −0.00537890 | ||||||||
\(249\) | 378258. | 0.386625 | ||||||||
\(250\) | −1.49754e6 | −1.51540 | ||||||||
\(251\) | 1.47025e6 | 1.47301 | 0.736505 | − | 0.676432i | \(-0.236475\pi\) | ||||
0.736505 | + | 0.676432i | \(0.236475\pi\) | |||||||
\(252\) | 338985. | 0.336263 | ||||||||
\(253\) | 1.52764e6 | 1.50045 | ||||||||
\(254\) | 2.27630e6 | 2.21384 | ||||||||
\(255\) | −523165. | −0.503835 | ||||||||
\(256\) | 1.03731e6 | 0.989256 | ||||||||
\(257\) | −1.28684e6 | −1.21532 | −0.607660 | − | 0.794197i | \(-0.707892\pi\) | ||||
−0.607660 | + | 0.794197i | \(0.707892\pi\) | |||||||
\(258\) | −695472. | −0.650475 | ||||||||
\(259\) | 625180. | 0.579102 | ||||||||
\(260\) | −1.42977e6 | −1.31170 | ||||||||
\(261\) | 187330. | 0.170219 | ||||||||
\(262\) | −318979. | −0.287084 | ||||||||
\(263\) | 1.28504e6 | 1.14559 | 0.572794 | − | 0.819699i | \(-0.305859\pi\) | ||||
0.572794 | + | 0.819699i | \(0.305859\pi\) | |||||||
\(264\) | −6687.08 | −0.00590509 | ||||||||
\(265\) | −88342.2 | −0.0772775 | ||||||||
\(266\) | −392181. | −0.339846 | ||||||||
\(267\) | −353618. | −0.303568 | ||||||||
\(268\) | −394979. | −0.335921 | ||||||||
\(269\) | −213282. | −0.179711 | −0.0898553 | − | 0.995955i | \(-0.528640\pi\) | ||||
−0.0898553 | + | 0.995955i | \(0.528640\pi\) | |||||||
\(270\) | −294464. | −0.245823 | ||||||||
\(271\) | 1.14006e6 | 0.942981 | 0.471490 | − | 0.881871i | \(-0.343716\pi\) | ||||
0.471490 | + | 0.881871i | \(0.343716\pi\) | |||||||
\(272\) | 1.17416e6 | 0.962285 | ||||||||
\(273\) | −1.03193e6 | −0.838000 | ||||||||
\(274\) | 2.31219e6 | 1.86058 | ||||||||
\(275\) | 316758. | 0.252578 | ||||||||
\(276\) | 813276. | 0.642636 | ||||||||
\(277\) | 597548. | 0.467922 | 0.233961 | − | 0.972246i | \(-0.424831\pi\) | ||||
0.233961 | + | 0.972246i | \(0.424831\pi\) | |||||||
\(278\) | −2.30277e6 | −1.78705 | ||||||||
\(279\) | 308886. | 0.237568 | ||||||||
\(280\) | 8961.52 | 0.00683104 | ||||||||
\(281\) | 151453. | 0.114423 | 0.0572113 | − | 0.998362i | \(-0.481779\pi\) | ||||
0.0572113 | + | 0.998362i | \(0.481779\pi\) | |||||||
\(282\) | 854551. | 0.639905 | ||||||||
\(283\) | 785823. | 0.583255 | 0.291628 | − | 0.956532i | \(-0.405803\pi\) | ||||
0.291628 | + | 0.956532i | \(0.405803\pi\) | |||||||
\(284\) | 2.12045e6 | 1.56003 | ||||||||
\(285\) | 170789. | 0.124551 | ||||||||
\(286\) | 3.83994e6 | 2.77594 | ||||||||
\(287\) | 160368. | 0.114925 | ||||||||
\(288\) | 664417. | 0.472019 | ||||||||
\(289\) | −90876.9 | −0.0640042 | ||||||||
\(290\) | 934174. | 0.652278 | ||||||||
\(291\) | 429010. | 0.296985 | ||||||||
\(292\) | −121632. | −0.0834818 | ||||||||
\(293\) | −2.00010e6 | −1.36108 | −0.680538 | − | 0.732713i | \(-0.738254\pi\) | ||||
−0.680538 | + | 0.732713i | \(0.738254\pi\) | |||||||
\(294\) | 8351.51 | 0.00563503 | ||||||||
\(295\) | −1.10500e6 | −0.739278 | ||||||||
\(296\) | −6565.64 | −0.00435559 | ||||||||
\(297\) | 396472. | 0.260808 | ||||||||
\(298\) | 1.97757e6 | 1.29000 | ||||||||
\(299\) | −2.47576e6 | −1.60151 | ||||||||
\(300\) | 168633. | 0.108178 | ||||||||
\(301\) | −1.25489e6 | −0.798343 | ||||||||
\(302\) | 1.85807e6 | 1.17231 | ||||||||
\(303\) | 507456. | 0.317535 | ||||||||
\(304\) | −383308. | −0.237884 | ||||||||
\(305\) | −1.17314e6 | −0.722103 | ||||||||
\(306\) | 748018. | 0.456676 | ||||||||
\(307\) | 1.55974e6 | 0.944511 | 0.472255 | − | 0.881462i | \(-0.343440\pi\) | ||||
0.472255 | + | 0.881462i | \(0.343440\pi\) | |||||||
\(308\) | −2.27604e6 | −1.36711 | ||||||||
\(309\) | −1.58832e6 | −0.946329 | ||||||||
\(310\) | 1.54035e6 | 0.910362 | ||||||||
\(311\) | −201859. | −0.118344 | −0.0591721 | − | 0.998248i | \(-0.518846\pi\) | ||||
−0.0591721 | + | 0.998248i | \(0.518846\pi\) | |||||||
\(312\) | 10837.3 | 0.00630284 | ||||||||
\(313\) | 602644. | 0.347696 | 0.173848 | − | 0.984772i | \(-0.444380\pi\) | ||||
0.173848 | + | 0.984772i | \(0.444380\pi\) | |||||||
\(314\) | 197455. | 0.113017 | ||||||||
\(315\) | −531323. | −0.301705 | ||||||||
\(316\) | 1.47803e6 | 0.832657 | ||||||||
\(317\) | −167035. | −0.0933594 | −0.0466797 | − | 0.998910i | \(-0.514864\pi\) | ||||
−0.0466797 | + | 0.998910i | \(0.514864\pi\) | |||||||
\(318\) | 126311. | 0.0700445 | ||||||||
\(319\) | −1.25779e6 | −0.692041 | ||||||||
\(320\) | 1.66986e6 | 0.911599 | ||||||||
\(321\) | −647379. | −0.350668 | ||||||||
\(322\) | 2.92713e6 | 1.57326 | ||||||||
\(323\) | −433851. | −0.231385 | ||||||||
\(324\) | 211071. | 0.111703 | ||||||||
\(325\) | −513350. | −0.269591 | ||||||||
\(326\) | 1.05938e6 | 0.552087 | ||||||||
\(327\) | 1.28092e6 | 0.662447 | ||||||||
\(328\) | −1684.19 | −0.000864383 0 | ||||||||
\(329\) | 1.54193e6 | 0.785371 | ||||||||
\(330\) | 1.97712e6 | 0.999419 | ||||||||
\(331\) | −3.16373e6 | −1.58719 | −0.793596 | − | 0.608445i | \(-0.791794\pi\) | ||||
−0.793596 | + | 0.608445i | \(0.791794\pi\) | |||||||
\(332\) | −1.35208e6 | −0.673222 | ||||||||
\(333\) | 389272. | 0.192372 | ||||||||
\(334\) | 4.00410e6 | 1.96399 | ||||||||
\(335\) | 619088. | 0.301398 | ||||||||
\(336\) | 1.19247e6 | 0.576232 | ||||||||
\(337\) | 862985. | 0.413932 | 0.206966 | − | 0.978348i | \(-0.433641\pi\) | ||||
0.206966 | + | 0.978348i | \(0.433641\pi\) | |||||||
\(338\) | −3.24886e6 | −1.54682 | ||||||||
\(339\) | −1.23487e6 | −0.583610 | ||||||||
\(340\) | 1.87005e6 | 0.877318 | ||||||||
\(341\) | −2.07395e6 | −0.965858 | ||||||||
\(342\) | −244194. | −0.112894 | ||||||||
\(343\) | −2.17132e6 | −0.996524 | ||||||||
\(344\) | 13178.9 | 0.00600457 | ||||||||
\(345\) | −1.27472e6 | −0.576592 | ||||||||
\(346\) | −1.47078e6 | −0.660476 | ||||||||
\(347\) | −594390. | −0.265001 | −0.132501 | − | 0.991183i | \(-0.542301\pi\) | ||||
−0.132501 | + | 0.991183i | \(0.542301\pi\) | |||||||
\(348\) | −669613. | −0.296398 | ||||||||
\(349\) | −708488. | −0.311364 | −0.155682 | − | 0.987807i | \(-0.549758\pi\) | ||||
−0.155682 | + | 0.987807i | \(0.549758\pi\) | |||||||
\(350\) | 606941. | 0.264836 | ||||||||
\(351\) | −642538. | −0.278376 | ||||||||
\(352\) | −4.46109e6 | −1.91904 | ||||||||
\(353\) | −4.42524e6 | −1.89017 | −0.945084 | − | 0.326827i | \(-0.894020\pi\) | ||||
−0.945084 | + | 0.326827i | \(0.894020\pi\) | |||||||
\(354\) | 1.57992e6 | 0.670082 | ||||||||
\(355\) | −3.32359e6 | −1.39970 | ||||||||
\(356\) | 1.26401e6 | 0.528597 | ||||||||
\(357\) | 1.34970e6 | 0.560490 | ||||||||
\(358\) | 5.41322e6 | 2.23228 | ||||||||
\(359\) | −1.66754e6 | −0.682872 | −0.341436 | − | 0.939905i | \(-0.610913\pi\) | ||||
−0.341436 | + | 0.939905i | \(0.610913\pi\) | |||||||
\(360\) | 5579.95 | 0.00226921 | ||||||||
\(361\) | −2.33447e6 | −0.942800 | ||||||||
\(362\) | 1.08606e6 | 0.435593 | ||||||||
\(363\) | −1.21257e6 | −0.482993 | ||||||||
\(364\) | 3.68864e6 | 1.45919 | ||||||||
\(365\) | 190646. | 0.0749023 | ||||||||
\(366\) | 1.67735e6 | 0.654515 | ||||||||
\(367\) | −1.61412e6 | −0.625562 | −0.312781 | − | 0.949825i | \(-0.601261\pi\) | ||||
−0.312781 | + | 0.949825i | \(0.601261\pi\) | |||||||
\(368\) | 2.86091e6 | 1.10125 | ||||||||
\(369\) | 99854.4 | 0.0381769 | ||||||||
\(370\) | 1.94121e6 | 0.737171 | ||||||||
\(371\) | 227912. | 0.0859673 | ||||||||
\(372\) | −1.10412e6 | −0.413673 | ||||||||
\(373\) | 161337. | 0.0600431 | 0.0300216 | − | 0.999549i | \(-0.490442\pi\) | ||||
0.0300216 | + | 0.999549i | \(0.490442\pi\) | |||||||
\(374\) | −5.02241e6 | −1.85666 | ||||||||
\(375\) | −1.68249e6 | −0.617837 | ||||||||
\(376\) | −16193.3 | −0.00590700 | ||||||||
\(377\) | 2.03842e6 | 0.738654 | ||||||||
\(378\) | 759682. | 0.273465 | ||||||||
\(379\) | −4.76876e6 | −1.70533 | −0.852663 | − | 0.522462i | \(-0.825014\pi\) | ||||
−0.852663 | + | 0.522462i | \(0.825014\pi\) | |||||||
\(380\) | −610487. | −0.216879 | ||||||||
\(381\) | 2.55743e6 | 0.902593 | ||||||||
\(382\) | 3.48681e6 | 1.22256 | ||||||||
\(383\) | −3.60084e6 | −1.25432 | −0.627159 | − | 0.778892i | \(-0.715782\pi\) | ||||
−0.627159 | + | 0.778892i | \(0.715782\pi\) | |||||||
\(384\) | −25181.1 | −0.00871459 | ||||||||
\(385\) | 3.56745e6 | 1.22661 | ||||||||
\(386\) | −915550. | −0.312762 | ||||||||
\(387\) | −781366. | −0.265202 | ||||||||
\(388\) | −1.53350e6 | −0.517135 | ||||||||
\(389\) | 3.19249e6 | 1.06968 | 0.534842 | − | 0.844952i | \(-0.320371\pi\) | ||||
0.534842 | + | 0.844952i | \(0.320371\pi\) | |||||||
\(390\) | −3.20419e6 | −1.06674 | ||||||||
\(391\) | 3.23814e6 | 1.07116 | ||||||||
\(392\) | −158.257 | −5.20173e−5 0 | ||||||||
\(393\) | −358374. | −0.117046 | ||||||||
\(394\) | 2.80979e6 | 0.911871 | ||||||||
\(395\) | −2.31666e6 | −0.747083 | ||||||||
\(396\) | −1.41719e6 | −0.454141 | ||||||||
\(397\) | −965266. | −0.307377 | −0.153688 | − | 0.988119i | \(-0.549115\pi\) | ||||
−0.153688 | + | 0.988119i | \(0.549115\pi\) | |||||||
\(398\) | 2.54457e6 | 0.805205 | ||||||||
\(399\) | −440616. | −0.138557 | ||||||||
\(400\) | 593211. | 0.185378 | ||||||||
\(401\) | 1.22115e6 | 0.379234 | 0.189617 | − | 0.981858i | \(-0.439275\pi\) | ||||
0.189617 | + | 0.981858i | \(0.439275\pi\) | |||||||
\(402\) | −885168. | −0.273187 | ||||||||
\(403\) | 3.36113e6 | 1.03091 | ||||||||
\(404\) | −1.81391e6 | −0.552919 | ||||||||
\(405\) | −330831. | −0.100223 | ||||||||
\(406\) | −2.41006e6 | −0.725625 | ||||||||
\(407\) | −2.61369e6 | −0.782109 | ||||||||
\(408\) | −14174.6 | −0.00421561 | ||||||||
\(409\) | −289200. | −0.0854850 | −0.0427425 | − | 0.999086i | \(-0.513610\pi\) | ||||
−0.0427425 | + | 0.999086i | \(0.513610\pi\) | |||||||
\(410\) | 497951. | 0.146294 | ||||||||
\(411\) | 2.59776e6 | 0.758568 | ||||||||
\(412\) | 5.67746e6 | 1.64783 | ||||||||
\(413\) | 2.85077e6 | 0.822408 | ||||||||
\(414\) | 1.82259e6 | 0.522623 | ||||||||
\(415\) | 2.11925e6 | 0.604035 | ||||||||
\(416\) | 7.22981e6 | 2.04830 | ||||||||
\(417\) | −2.58717e6 | −0.728592 | ||||||||
\(418\) | 1.63959e6 | 0.458980 | ||||||||
\(419\) | 6.51026e6 | 1.81160 | 0.905802 | − | 0.423701i | \(-0.139269\pi\) | ||||
0.905802 | + | 0.423701i | \(0.139269\pi\) | |||||||
\(420\) | 1.89922e6 | 0.525353 | ||||||||
\(421\) | 3.87989e6 | 1.06688 | 0.533439 | − | 0.845839i | \(-0.320900\pi\) | ||||
0.533439 | + | 0.845839i | \(0.320900\pi\) | |||||||
\(422\) | 6.95617e6 | 1.90147 | ||||||||
\(423\) | 960092. | 0.260893 | ||||||||
\(424\) | −2393.54 | −0.000646585 0 | ||||||||
\(425\) | 671431. | 0.180314 | ||||||||
\(426\) | 4.75205e6 | 1.26869 | ||||||||
\(427\) | 3.02656e6 | 0.803302 | ||||||||
\(428\) | 2.31406e6 | 0.610612 | ||||||||
\(429\) | 4.31419e6 | 1.13176 | ||||||||
\(430\) | −3.89649e6 | −1.01626 | ||||||||
\(431\) | −7.38490e6 | −1.91492 | −0.957462 | − | 0.288561i | \(-0.906823\pi\) | ||||
−0.957462 | + | 0.288561i | \(0.906823\pi\) | |||||||
\(432\) | 742496. | 0.191419 | ||||||||
\(433\) | 270737. | 0.0693951 | 0.0346975 | − | 0.999398i | \(-0.488953\pi\) | ||||
0.0346975 | + | 0.999398i | \(0.488953\pi\) | |||||||
\(434\) | −3.97391e6 | −1.01273 | ||||||||
\(435\) | 1.04955e6 | 0.265937 | ||||||||
\(436\) | −4.57864e6 | −1.15351 | ||||||||
\(437\) | −1.05711e6 | −0.264798 | ||||||||
\(438\) | −272584. | −0.0678915 | ||||||||
\(439\) | 1.83338e6 | 0.454037 | 0.227018 | − | 0.973890i | \(-0.427102\pi\) | ||||
0.227018 | + | 0.973890i | \(0.427102\pi\) | |||||||
\(440\) | −37465.4 | −0.00922569 | ||||||||
\(441\) | 9382.95 | 0.00229743 | ||||||||
\(442\) | 8.13952e6 | 1.98172 | ||||||||
\(443\) | 787815. | 0.190728 | 0.0953641 | − | 0.995442i | \(-0.469598\pi\) | ||||
0.0953641 | + | 0.995442i | \(0.469598\pi\) | |||||||
\(444\) | −1.39145e6 | −0.334974 | ||||||||
\(445\) | −1.98120e6 | −0.474273 | ||||||||
\(446\) | −885684. | −0.210835 | ||||||||
\(447\) | 2.22180e6 | 0.525941 | ||||||||
\(448\) | −4.30803e6 | −1.01411 | ||||||||
\(449\) | −2.43718e6 | −0.570521 | −0.285261 | − | 0.958450i | \(-0.592080\pi\) | ||||
−0.285261 | + | 0.958450i | \(0.592080\pi\) | |||||||
\(450\) | 377916. | 0.0879759 | ||||||||
\(451\) | −670451. | −0.155212 | ||||||||
\(452\) | 4.41406e6 | 1.01623 | ||||||||
\(453\) | 2.08754e6 | 0.477958 | ||||||||
\(454\) | −3.86617e6 | −0.880322 | ||||||||
\(455\) | −5.78156e6 | −1.30923 | ||||||||
\(456\) | 4627.35 | 0.00104213 | ||||||||
\(457\) | −5.84362e6 | −1.30886 | −0.654428 | − | 0.756125i | \(-0.727090\pi\) | ||||
−0.654428 | + | 0.756125i | \(0.727090\pi\) | |||||||
\(458\) | −2.11856e6 | −0.471929 | ||||||||
\(459\) | 840401. | 0.186189 | ||||||||
\(460\) | 4.55651e6 | 1.00401 | ||||||||
\(461\) | −3.47871e6 | −0.762371 | −0.381185 | − | 0.924499i | \(-0.624484\pi\) | ||||
−0.381185 | + | 0.924499i | \(0.624484\pi\) | |||||||
\(462\) | −5.10073e6 | −1.11180 | ||||||||
\(463\) | −1.57539e6 | −0.341535 | −0.170768 | − | 0.985311i | \(-0.554625\pi\) | ||||
−0.170768 | + | 0.985311i | \(0.554625\pi\) | |||||||
\(464\) | −2.35554e6 | −0.507920 | ||||||||
\(465\) | 1.73058e6 | 0.371159 | ||||||||
\(466\) | −1.08813e7 | −2.32121 | ||||||||
\(467\) | −5.67553e6 | −1.20424 | −0.602121 | − | 0.798405i | \(-0.705678\pi\) | ||||
−0.602121 | + | 0.798405i | \(0.705678\pi\) | |||||||
\(468\) | 2.29676e6 | 0.484731 | ||||||||
\(469\) | −1.59717e6 | −0.335290 | ||||||||
\(470\) | 4.78776e6 | 0.999741 | ||||||||
\(471\) | 221841. | 0.0460776 | ||||||||
\(472\) | −29938.8 | −0.00618557 | ||||||||
\(473\) | 5.24632e6 | 1.07821 | ||||||||
\(474\) | 3.31235e6 | 0.677158 | ||||||||
\(475\) | −219191. | −0.0445748 | ||||||||
\(476\) | −4.82452e6 | −0.975971 | ||||||||
\(477\) | 141911. | 0.0285575 | ||||||||
\(478\) | −1.51183e6 | −0.302645 | ||||||||
\(479\) | −6.98669e6 | −1.39134 | −0.695669 | − | 0.718362i | \(-0.744892\pi\) | ||||
−0.695669 | + | 0.718362i | \(0.744892\pi\) | |||||||
\(480\) | 3.72250e6 | 0.737448 | ||||||||
\(481\) | 4.23584e6 | 0.834790 | ||||||||
\(482\) | 1.49200e6 | 0.292517 | ||||||||
\(483\) | 3.28864e6 | 0.641428 | ||||||||
\(484\) | 4.33434e6 | 0.841027 | ||||||||
\(485\) | 2.40360e6 | 0.463989 | ||||||||
\(486\) | 473021. | 0.0908426 | ||||||||
\(487\) | 2.29336e6 | 0.438177 | 0.219089 | − | 0.975705i | \(-0.429692\pi\) | ||||
0.219089 | + | 0.975705i | \(0.429692\pi\) | |||||||
\(488\) | −31784.9 | −0.00604187 | ||||||||
\(489\) | 1.19022e6 | 0.225089 | ||||||||
\(490\) | 46790.6 | 0.00880377 | ||||||||
\(491\) | −4.04531e6 | −0.757265 | −0.378632 | − | 0.925547i | \(-0.623606\pi\) | ||||
−0.378632 | + | 0.925547i | \(0.623606\pi\) | |||||||
\(492\) | −356930. | −0.0664768 | ||||||||
\(493\) | −2.66614e6 | −0.494043 | ||||||||
\(494\) | −2.65718e6 | −0.489896 | ||||||||
\(495\) | 2.22130e6 | 0.407468 | ||||||||
\(496\) | −3.88401e6 | −0.708886 | ||||||||
\(497\) | 8.57446e6 | 1.55710 | ||||||||
\(498\) | −3.03009e6 | −0.547498 | ||||||||
\(499\) | −6.10078e6 | −1.09682 | −0.548408 | − | 0.836211i | \(-0.684766\pi\) | ||||
−0.548408 | + | 0.836211i | \(0.684766\pi\) | |||||||
\(500\) | 6.01406e6 | 1.07583 | ||||||||
\(501\) | 4.49863e6 | 0.800729 | ||||||||
\(502\) | −1.17776e7 | −2.08592 | ||||||||
\(503\) | 553552. | 0.0975526 | 0.0487763 | − | 0.998810i | \(-0.484468\pi\) | ||||
0.0487763 | + | 0.998810i | \(0.484468\pi\) | |||||||
\(504\) | −14395.6 | −0.00252438 | ||||||||
\(505\) | 2.84310e6 | 0.496094 | ||||||||
\(506\) | −1.22374e7 | −2.12478 | ||||||||
\(507\) | −3.65011e6 | −0.630647 | ||||||||
\(508\) | −9.14156e6 | −1.57167 | ||||||||
\(509\) | −7.90065e6 | −1.35166 | −0.675831 | − | 0.737056i | \(-0.736215\pi\) | ||||
−0.675831 | + | 0.737056i | \(0.736215\pi\) | |||||||
\(510\) | 4.19089e6 | 0.713478 | ||||||||
\(511\) | −491844. | −0.0833249 | ||||||||
\(512\) | −8.39906e6 | −1.41598 | ||||||||
\(513\) | −274353. | −0.0460273 | ||||||||
\(514\) | 1.03084e7 | 1.72101 | ||||||||
\(515\) | −8.89882e6 | −1.47848 | ||||||||
\(516\) | 2.79300e6 | 0.461792 | ||||||||
\(517\) | −6.44634e6 | −1.06069 | ||||||||
\(518\) | −5.00810e6 | −0.820065 | ||||||||
\(519\) | −1.65242e6 | −0.269279 | ||||||||
\(520\) | 60717.9 | 0.00984710 | ||||||||
\(521\) | −2.40957e6 | −0.388906 | −0.194453 | − | 0.980912i | \(-0.562293\pi\) | ||||
−0.194453 | + | 0.980912i | \(0.562293\pi\) | |||||||
\(522\) | −1.50064e6 | −0.241046 | ||||||||
\(523\) | 3.61719e6 | 0.578252 | 0.289126 | − | 0.957291i | \(-0.406635\pi\) | ||||
0.289126 | + | 0.957291i | \(0.406635\pi\) | |||||||
\(524\) | 1.28101e6 | 0.203809 | ||||||||
\(525\) | 681901. | 0.107975 | ||||||||
\(526\) | −1.02940e7 | −1.62226 | ||||||||
\(527\) | −4.39616e6 | −0.689519 | ||||||||
\(528\) | −4.98534e6 | −0.778233 | ||||||||
\(529\) | 1.45360e6 | 0.225842 | ||||||||
\(530\) | 707678. | 0.109432 | ||||||||
\(531\) | 1.77505e6 | 0.273196 | ||||||||
\(532\) | 1.57499e6 | 0.241267 | ||||||||
\(533\) | 1.08656e6 | 0.165667 | ||||||||
\(534\) | 2.83271e6 | 0.429881 | ||||||||
\(535\) | −3.62705e6 | −0.547859 | ||||||||
\(536\) | 16773.5 | 0.00252181 | ||||||||
\(537\) | 6.08177e6 | 0.910111 | ||||||||
\(538\) | 1.70853e6 | 0.254488 | ||||||||
\(539\) | −62999.9 | −0.00934045 | ||||||||
\(540\) | 1.18256e6 | 0.174517 | ||||||||
\(541\) | 505392. | 0.0742395 | 0.0371198 | − | 0.999311i | \(-0.488182\pi\) | ||||
0.0371198 | + | 0.999311i | \(0.488182\pi\) | |||||||
\(542\) | −9.13259e6 | −1.33535 | ||||||||
\(543\) | 1.22019e6 | 0.177594 | ||||||||
\(544\) | −9.45616e6 | −1.36999 | ||||||||
\(545\) | 7.17654e6 | 1.03496 | ||||||||
\(546\) | 8.26644e6 | 1.18669 | ||||||||
\(547\) | −1.05410e7 | −1.50630 | −0.753152 | − | 0.657847i | \(-0.771467\pi\) | ||||
−0.753152 | + | 0.657847i | \(0.771467\pi\) | |||||||
\(548\) | −9.28570e6 | −1.32088 | ||||||||
\(549\) | 1.88450e6 | 0.266849 | ||||||||
\(550\) | −2.53744e6 | −0.357675 | ||||||||
\(551\) | 870371. | 0.122131 | ||||||||
\(552\) | −34537.3 | −0.00482437 | ||||||||
\(553\) | 5.97670e6 | 0.831092 | ||||||||
\(554\) | −4.78675e6 | −0.662623 | ||||||||
\(555\) | 2.18096e6 | 0.300549 | ||||||||
\(556\) | 9.24784e6 | 1.26868 | ||||||||
\(557\) | −7.63355e6 | −1.04253 | −0.521265 | − | 0.853395i | \(-0.674540\pi\) | ||||
−0.521265 | + | 0.853395i | \(0.674540\pi\) | |||||||
\(558\) | −2.47438e6 | −0.336420 | ||||||||
\(559\) | −8.50239e6 | −1.15083 | ||||||||
\(560\) | 6.68098e6 | 0.900264 | ||||||||
\(561\) | −5.64270e6 | −0.756972 | ||||||||
\(562\) | −1.21324e6 | −0.162033 | ||||||||
\(563\) | 1.07078e7 | 1.42374 | 0.711869 | − | 0.702312i | \(-0.247849\pi\) | ||||
0.711869 | + | 0.702312i | \(0.247849\pi\) | |||||||
\(564\) | −3.43185e6 | −0.454288 | ||||||||
\(565\) | −6.91857e6 | −0.911791 | ||||||||
\(566\) | −6.29495e6 | −0.825946 | ||||||||
\(567\) | 853506. | 0.111493 | ||||||||
\(568\) | −90049.0 | −0.0117114 | ||||||||
\(569\) | 5.44680e6 | 0.705278 | 0.352639 | − | 0.935759i | \(-0.385284\pi\) | ||||
0.352639 | + | 0.935759i | \(0.385284\pi\) | |||||||
\(570\) | −1.36813e6 | −0.176377 | ||||||||
\(571\) | −3.64813e6 | −0.468252 | −0.234126 | − | 0.972206i | \(-0.575223\pi\) | ||||
−0.234126 | + | 0.972206i | \(0.575223\pi\) | |||||||
\(572\) | −1.54211e7 | −1.97072 | ||||||||
\(573\) | 3.91744e6 | 0.498443 | ||||||||
\(574\) | −1.28466e6 | −0.162745 | ||||||||
\(575\) | 1.63598e6 | 0.206352 | ||||||||
\(576\) | −2.68242e6 | −0.336877 | ||||||||
\(577\) | −996401. | −0.124593 | −0.0622967 | − | 0.998058i | \(-0.519842\pi\) | ||||
−0.0622967 | + | 0.998058i | \(0.519842\pi\) | |||||||
\(578\) | 727983. | 0.0906362 | ||||||||
\(579\) | −1.02862e6 | −0.127515 | ||||||||
\(580\) | −3.75161e6 | −0.463072 | ||||||||
\(581\) | −5.46741e6 | −0.671957 | ||||||||
\(582\) | −3.43665e6 | −0.420560 | ||||||||
\(583\) | −952833. | −0.116103 | ||||||||
\(584\) | 5165.34 | 0.000626710 0 | ||||||||
\(585\) | −3.59992e6 | −0.434914 | ||||||||
\(586\) | 1.60221e7 | 1.92741 | ||||||||
\(587\) | 7.17752e6 | 0.859764 | 0.429882 | − | 0.902885i | \(-0.358555\pi\) | ||||
0.429882 | + | 0.902885i | \(0.358555\pi\) | |||||||
\(588\) | −33539.4 | −0.00400048 | ||||||||
\(589\) | 1.43514e6 | 0.170454 | ||||||||
\(590\) | 8.85178e6 | 1.04689 | ||||||||
\(591\) | 3.15681e6 | 0.371775 | ||||||||
\(592\) | −4.89480e6 | −0.574025 | ||||||||
\(593\) | 1.60087e7 | 1.86948 | 0.934739 | − | 0.355334i | \(-0.115633\pi\) | ||||
0.934739 | + | 0.355334i | \(0.115633\pi\) | |||||||
\(594\) | −3.17600e6 | −0.369330 | ||||||||
\(595\) | 7.56193e6 | 0.875669 | ||||||||
\(596\) | −7.94184e6 | −0.915811 | ||||||||
\(597\) | 2.85883e6 | 0.328286 | ||||||||
\(598\) | 1.98324e7 | 2.26790 | ||||||||
\(599\) | −1.24030e6 | −0.141241 | −0.0706205 | − | 0.997503i | \(-0.522498\pi\) | ||||
−0.0706205 | + | 0.997503i | \(0.522498\pi\) | |||||||
\(600\) | −7161.32 | −0.000812111 0 | ||||||||
\(601\) | −1.51872e6 | −0.171511 | −0.0857554 | − | 0.996316i | \(-0.527330\pi\) | ||||
−0.0857554 | + | 0.996316i | \(0.527330\pi\) | |||||||
\(602\) | 1.00525e7 | 1.13053 | ||||||||
\(603\) | −994490. | −0.111380 | ||||||||
\(604\) | −7.46194e6 | −0.832260 | ||||||||
\(605\) | −6.79362e6 | −0.754593 | ||||||||
\(606\) | −4.06506e6 | −0.449661 | ||||||||
\(607\) | −1.65820e7 | −1.82669 | −0.913345 | − | 0.407186i | \(-0.866510\pi\) | ||||
−0.913345 | + | 0.407186i | \(0.866510\pi\) | |||||||
\(608\) | 3.08700e6 | 0.338671 | ||||||||
\(609\) | −2.70771e6 | −0.295841 | ||||||||
\(610\) | 9.39759e6 | 1.02257 | ||||||||
\(611\) | 1.04472e7 | 1.13213 | ||||||||
\(612\) | −3.00402e6 | −0.324208 | ||||||||
\(613\) | −1.45006e7 | −1.55860 | −0.779298 | − | 0.626654i | \(-0.784424\pi\) | ||||
−0.779298 | + | 0.626654i | \(0.784424\pi\) | |||||||
\(614\) | −1.24946e7 | −1.33752 | ||||||||
\(615\) | 559450. | 0.0596449 | ||||||||
\(616\) | 96656.4 | 0.0102631 | ||||||||
\(617\) | 1.93473e6 | 0.204601 | 0.102301 | − | 0.994754i | \(-0.467380\pi\) | ||||
0.102301 | + | 0.994754i | \(0.467380\pi\) | |||||||
\(618\) | 1.27235e7 | 1.34009 | ||||||||
\(619\) | 2.04727e6 | 0.214758 | 0.107379 | − | 0.994218i | \(-0.465754\pi\) | ||||
0.107379 | + | 0.994218i | \(0.465754\pi\) | |||||||
\(620\) | −6.18598e6 | −0.646293 | ||||||||
\(621\) | 2.04769e6 | 0.213076 | ||||||||
\(622\) | 1.61702e6 | 0.167587 | ||||||||
\(623\) | 5.11126e6 | 0.527604 | ||||||||
\(624\) | 8.07943e6 | 0.830653 | ||||||||
\(625\) | −7.60632e6 | −0.778887 | ||||||||
\(626\) | −4.82757e6 | −0.492372 | ||||||||
\(627\) | 1.84208e6 | 0.187129 | ||||||||
\(628\) | −792972. | −0.0802340 | ||||||||
\(629\) | −5.54023e6 | −0.558343 | ||||||||
\(630\) | 4.25624e6 | 0.427243 | ||||||||
\(631\) | −1.25862e7 | −1.25840 | −0.629202 | − | 0.777242i | \(-0.716618\pi\) | ||||
−0.629202 | + | 0.777242i | \(0.716618\pi\) | |||||||
\(632\) | −62767.3 | −0.00625088 | ||||||||
\(633\) | 7.81529e6 | 0.775239 | ||||||||
\(634\) | 1.33806e6 | 0.132206 | ||||||||
\(635\) | 1.43284e7 | 1.41015 | ||||||||
\(636\) | −507262. | −0.0497267 | ||||||||
\(637\) | 102100. | 0.00996959 | ||||||||
\(638\) | 1.00757e7 | 0.979996 | ||||||||
\(639\) | 5.33894e6 | 0.517253 | ||||||||
\(640\) | −141081. | −0.0136150 | ||||||||
\(641\) | 167068. | 0.0160601 | 0.00803004 | − | 0.999968i | \(-0.497444\pi\) | ||||
0.00803004 | + | 0.999968i | \(0.497444\pi\) | |||||||
\(642\) | 5.18593e6 | 0.496580 | ||||||||
\(643\) | −818867. | −0.0781063 | −0.0390531 | − | 0.999237i | \(-0.512434\pi\) | ||||
−0.0390531 | + | 0.999237i | \(0.512434\pi\) | |||||||
\(644\) | −1.17553e7 | −1.11691 | ||||||||
\(645\) | −4.37773e6 | −0.414333 | ||||||||
\(646\) | 3.47543e6 | 0.327663 | ||||||||
\(647\) | 1.96572e7 | 1.84613 | 0.923064 | − | 0.384647i | \(-0.125677\pi\) | ||||
0.923064 | + | 0.384647i | \(0.125677\pi\) | |||||||
\(648\) | −8963.52 | −0.000838573 0 | ||||||||
\(649\) | −1.19182e7 | −1.11071 | ||||||||
\(650\) | 4.11227e6 | 0.381767 | ||||||||
\(651\) | −4.46471e6 | −0.412896 | ||||||||
\(652\) | −4.25444e6 | −0.391943 | ||||||||
\(653\) | 1.87341e6 | 0.171929 | 0.0859647 | − | 0.996298i | \(-0.472603\pi\) | ||||
0.0859647 | + | 0.996298i | \(0.472603\pi\) | |||||||
\(654\) | −1.02610e7 | −0.938089 | ||||||||
\(655\) | −2.00785e6 | −0.182864 | ||||||||
\(656\) | −1.25559e6 | −0.113917 | ||||||||
\(657\) | −306250. | −0.0276797 | ||||||||
\(658\) | −1.23519e7 | −1.11216 | ||||||||
\(659\) | −1.16592e7 | −1.04581 | −0.522907 | − | 0.852390i | \(-0.675153\pi\) | ||||
−0.522907 | + | 0.852390i | \(0.675153\pi\) | |||||||
\(660\) | −7.94004e6 | −0.709517 | ||||||||
\(661\) | −4.42372e6 | −0.393808 | −0.196904 | − | 0.980423i | \(-0.563089\pi\) | ||||
−0.196904 | + | 0.980423i | \(0.563089\pi\) | |||||||
\(662\) | 2.53435e7 | 2.24762 | ||||||||
\(663\) | 9.14478e6 | 0.807959 | ||||||||
\(664\) | 57418.8 | 0.00505398 | ||||||||
\(665\) | −2.46862e6 | −0.216471 | ||||||||
\(666\) | −3.11832e6 | −0.272418 | ||||||||
\(667\) | −6.49621e6 | −0.565386 | ||||||||
\(668\) | −1.60804e7 | −1.39430 | ||||||||
\(669\) | −995070. | −0.0859584 | ||||||||
\(670\) | −4.95930e6 | −0.426808 | ||||||||
\(671\) | −1.26531e7 | −1.08490 | ||||||||
\(672\) | −9.60361e6 | −0.820373 | ||||||||
\(673\) | −1.21247e7 | −1.03189 | −0.515945 | − | 0.856621i | \(-0.672559\pi\) | ||||
−0.515945 | + | 0.856621i | \(0.672559\pi\) | |||||||
\(674\) | −6.91307e6 | −0.586167 | ||||||||
\(675\) | 424590. | 0.0358683 | ||||||||
\(676\) | 1.30473e7 | 1.09813 | ||||||||
\(677\) | 652613. | 0.0547248 | 0.0273624 | − | 0.999626i | \(-0.491289\pi\) | ||||
0.0273624 | + | 0.999626i | \(0.491289\pi\) | |||||||
\(678\) | 9.89214e6 | 0.826449 | ||||||||
\(679\) | −6.20100e6 | −0.516163 | ||||||||
\(680\) | −79415.4 | −0.00658616 | ||||||||
\(681\) | −4.34366e6 | −0.358912 | ||||||||
\(682\) | 1.66137e7 | 1.36775 | ||||||||
\(683\) | −1.42720e7 | −1.17067 | −0.585335 | − | 0.810791i | \(-0.699037\pi\) | ||||
−0.585335 | + | 0.810791i | \(0.699037\pi\) | |||||||
\(684\) | 980675. | 0.0801465 | ||||||||
\(685\) | 1.45544e7 | 1.18513 | ||||||||
\(686\) | 1.73937e7 | 1.41117 | ||||||||
\(687\) | −2.38021e6 | −0.192408 | ||||||||
\(688\) | 9.82508e6 | 0.791344 | ||||||||
\(689\) | 1.54420e6 | 0.123924 | ||||||||
\(690\) | 1.02114e7 | 0.816509 | ||||||||
\(691\) | 8.45754e6 | 0.673828 | 0.336914 | − | 0.941535i | \(-0.390617\pi\) | ||||
0.336914 | + | 0.941535i | \(0.390617\pi\) | |||||||
\(692\) | 5.90660e6 | 0.468891 | ||||||||
\(693\) | −5.73069e6 | −0.453288 | ||||||||
\(694\) | 4.76145e6 | 0.375267 | ||||||||
\(695\) | −1.44950e7 | −1.13830 | ||||||||
\(696\) | 28436.4 | 0.00222511 | ||||||||
\(697\) | −1.42115e6 | −0.110805 | ||||||||
\(698\) | 5.67545e6 | 0.440922 | ||||||||
\(699\) | −1.22252e7 | −0.946371 | ||||||||
\(700\) | −2.43746e6 | −0.188015 | ||||||||
\(701\) | −503720. | −0.0387164 | −0.0193582 | − | 0.999813i | \(-0.506162\pi\) | ||||
−0.0193582 | + | 0.999813i | \(0.506162\pi\) | |||||||
\(702\) | 5.14715e6 | 0.394207 | ||||||||
\(703\) | 1.80863e6 | 0.138026 | ||||||||
\(704\) | 1.80106e7 | 1.36961 | ||||||||
\(705\) | 5.37907e6 | 0.407600 | ||||||||
\(706\) | 3.54491e7 | 2.67666 | ||||||||
\(707\) | −7.33488e6 | −0.551880 | ||||||||
\(708\) | −6.34493e6 | −0.475712 | ||||||||
\(709\) | −5.32900e6 | −0.398135 | −0.199067 | − | 0.979986i | \(-0.563791\pi\) | ||||
−0.199067 | + | 0.979986i | \(0.563791\pi\) | |||||||
\(710\) | 2.66241e7 | 1.98212 | ||||||||
\(711\) | 3.72143e6 | 0.276081 | ||||||||
\(712\) | −53678.4 | −0.00396826 | ||||||||
\(713\) | −1.07115e7 | −0.789091 | ||||||||
\(714\) | −1.08120e7 | −0.793708 | ||||||||
\(715\) | 2.41709e7 | 1.76819 | ||||||||
\(716\) | −2.17393e7 | −1.58476 | ||||||||
\(717\) | −1.69855e6 | −0.123390 | ||||||||
\(718\) | 1.33580e7 | 0.967012 | ||||||||
\(719\) | −1.30821e7 | −0.943749 | −0.471875 | − | 0.881666i | \(-0.656423\pi\) | ||||
−0.471875 | + | 0.881666i | \(0.656423\pi\) | |||||||
\(720\) | 4.15995e6 | 0.299059 | ||||||||
\(721\) | 2.29579e7 | 1.64473 | ||||||||
\(722\) | 1.87006e7 | 1.33510 | ||||||||
\(723\) | 1.67627e6 | 0.119261 | ||||||||
\(724\) | −4.36157e6 | −0.309241 | ||||||||
\(725\) | −1.34699e6 | −0.0951744 | ||||||||
\(726\) | 9.71349e6 | 0.683965 | ||||||||
\(727\) | 2.00785e7 | 1.40895 | 0.704475 | − | 0.709729i | \(-0.251183\pi\) | ||||
0.704475 | + | 0.709729i | \(0.251183\pi\) | |||||||
\(728\) | −156645. | −0.0109544 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −1.52720e6 | −0.106069 | ||||||||
\(731\) | 1.11206e7 | 0.769724 | ||||||||
\(732\) | −6.73617e6 | −0.464660 | ||||||||
\(733\) | 2.37956e7 | 1.63582 | 0.817911 | − | 0.575344i | \(-0.195132\pi\) | ||||
0.817911 | + | 0.575344i | \(0.195132\pi\) | |||||||
\(734\) | 1.29301e7 | 0.885856 | ||||||||
\(735\) | 52569.5 | 0.00358935 | ||||||||
\(736\) | −2.30405e7 | −1.56783 | ||||||||
\(737\) | 6.67730e6 | 0.452827 | ||||||||
\(738\) | −799899. | −0.0540622 | ||||||||
\(739\) | −1.28052e7 | −0.862532 | −0.431266 | − | 0.902225i | \(-0.641933\pi\) | ||||
−0.431266 | + | 0.902225i | \(0.641933\pi\) | |||||||
\(740\) | −7.79585e6 | −0.523340 | ||||||||
\(741\) | −2.98535e6 | −0.199733 | ||||||||
\(742\) | −1.82573e6 | −0.121738 | ||||||||
\(743\) | 2.47381e7 | 1.64397 | 0.821987 | − | 0.569506i | \(-0.192866\pi\) | ||||
0.821987 | + | 0.569506i | \(0.192866\pi\) | |||||||
\(744\) | 46888.3 | 0.00310551 | ||||||||
\(745\) | 1.24480e7 | 0.821692 | ||||||||
\(746\) | −1.29242e6 | −0.0850268 | ||||||||
\(747\) | −3.40432e6 | −0.223218 | ||||||||
\(748\) | 2.01699e7 | 1.31810 | ||||||||
\(749\) | 9.35735e6 | 0.609464 | ||||||||
\(750\) | 1.34778e7 | 0.874916 | ||||||||
\(751\) | −9.84535e6 | −0.636988 | −0.318494 | − | 0.947925i | \(-0.603177\pi\) | ||||
−0.318494 | + | 0.947925i | \(0.603177\pi\) | |||||||
\(752\) | −1.20724e7 | −0.778485 | ||||||||
\(753\) | −1.32322e7 | −0.850443 | ||||||||
\(754\) | −1.63291e7 | −1.04601 | ||||||||
\(755\) | 1.16958e7 | 0.746728 | ||||||||
\(756\) | −3.05086e6 | −0.194141 | ||||||||
\(757\) | −2.16698e7 | −1.37441 | −0.687205 | − | 0.726464i | \(-0.741162\pi\) | ||||
−0.687205 | + | 0.726464i | \(0.741162\pi\) | |||||||
\(758\) | 3.82009e7 | 2.41491 | ||||||||
\(759\) | −1.37488e7 | −0.866284 | ||||||||
\(760\) | 25925.5 | 0.00162814 | ||||||||
\(761\) | 9.62217e6 | 0.602298 | 0.301149 | − | 0.953577i | \(-0.402630\pi\) | ||||
0.301149 | + | 0.953577i | \(0.402630\pi\) | |||||||
\(762\) | −2.04867e7 | −1.27816 | ||||||||
\(763\) | −1.85146e7 | −1.15134 | ||||||||
\(764\) | −1.40029e7 | −0.867930 | ||||||||
\(765\) | 4.70848e6 | 0.290889 | ||||||||
\(766\) | 2.88451e7 | 1.77623 | ||||||||
\(767\) | 1.93151e7 | 1.18552 | ||||||||
\(768\) | −9.33579e6 | −0.571147 | ||||||||
\(769\) | −2.41984e7 | −1.47561 | −0.737804 | − | 0.675015i | \(-0.764137\pi\) | ||||
−0.737804 | + | 0.675015i | \(0.764137\pi\) | |||||||
\(770\) | −2.85776e7 | −1.73700 | ||||||||
\(771\) | 1.15815e7 | 0.701666 | ||||||||
\(772\) | 3.67682e6 | 0.222039 | ||||||||
\(773\) | 2.12900e7 | 1.28152 | 0.640761 | − | 0.767740i | \(-0.278619\pi\) | ||||
0.640761 | + | 0.767740i | \(0.278619\pi\) | |||||||
\(774\) | 6.25925e6 | 0.375552 | ||||||||
\(775\) | −2.22104e6 | −0.132832 | ||||||||
\(776\) | 65122.9 | 0.00388221 | ||||||||
\(777\) | −5.62662e6 | −0.334345 | ||||||||
\(778\) | −2.55739e7 | −1.51478 | ||||||||
\(779\) | 463942. | 0.0273918 | ||||||||
\(780\) | 1.28679e7 | 0.757308 | ||||||||
\(781\) | −3.58472e7 | −2.10295 | ||||||||
\(782\) | −2.59396e7 | −1.51687 | ||||||||
\(783\) | −1.68597e6 | −0.0982757 | ||||||||
\(784\) | −117983. | −0.00685537 | ||||||||
\(785\) | 1.24290e6 | 0.0719883 | ||||||||
\(786\) | 2.87081e6 | 0.165748 | ||||||||
\(787\) | 2.77630e7 | 1.59782 | 0.798912 | − | 0.601448i | \(-0.205409\pi\) | ||||
0.798912 | + | 0.601448i | \(0.205409\pi\) | |||||||
\(788\) | −1.12840e7 | −0.647365 | ||||||||
\(789\) | −1.15654e7 | −0.661406 | ||||||||
\(790\) | 1.85579e7 | 1.05794 | ||||||||
\(791\) | 1.78491e7 | 1.01432 | ||||||||
\(792\) | 60183.7 | 0.00340931 | ||||||||
\(793\) | 2.05061e7 | 1.15798 | ||||||||
\(794\) | 7.73241e6 | 0.435275 | ||||||||
\(795\) | 795079. | 0.0446162 | ||||||||
\(796\) | −1.02189e7 | −0.571639 | ||||||||
\(797\) | 197775. | 0.0110287 | 0.00551436 | − | 0.999985i | \(-0.498245\pi\) | ||||
0.00551436 | + | 0.999985i | \(0.498245\pi\) | |||||||
\(798\) | 3.52962e6 | 0.196210 | ||||||||
\(799\) | −1.36643e7 | −0.757217 | ||||||||
\(800\) | −4.77747e6 | −0.263920 | ||||||||
\(801\) | 3.18256e6 | 0.175265 | ||||||||
\(802\) | −9.78218e6 | −0.537031 | ||||||||
\(803\) | 2.05625e6 | 0.112535 | ||||||||
\(804\) | 3.55481e6 | 0.193944 | ||||||||
\(805\) | 1.84251e7 | 1.00212 | ||||||||
\(806\) | −2.69248e7 | −1.45987 | ||||||||
\(807\) | 1.91954e6 | 0.103756 | ||||||||
\(808\) | 77030.9 | 0.00415084 | ||||||||
\(809\) | −2.30614e7 | −1.23884 | −0.619418 | − | 0.785061i | \(-0.712631\pi\) | ||||
−0.619418 | + | 0.785061i | \(0.712631\pi\) | |||||||
\(810\) | 2.65017e6 | 0.141926 | ||||||||
\(811\) | 2.91077e7 | 1.55402 | 0.777009 | − | 0.629489i | \(-0.216736\pi\) | ||||
0.777009 | + | 0.629489i | \(0.216736\pi\) | |||||||
\(812\) | 9.67872e6 | 0.515143 | ||||||||
\(813\) | −1.02605e7 | −0.544430 | ||||||||
\(814\) | 2.09373e7 | 1.10754 | ||||||||
\(815\) | 6.66838e6 | 0.351663 | ||||||||
\(816\) | −1.05674e7 | −0.555576 | ||||||||
\(817\) | −3.63037e6 | −0.190281 | ||||||||
\(818\) | 2.31668e6 | 0.121055 | ||||||||
\(819\) | 9.28738e6 | 0.483820 | ||||||||
\(820\) | −1.99976e6 | −0.103859 | ||||||||
\(821\) | −1.84168e6 | −0.0953578 | −0.0476789 | − | 0.998863i | \(-0.515182\pi\) | ||||
−0.0476789 | + | 0.998863i | \(0.515182\pi\) | |||||||
\(822\) | −2.08097e7 | −1.07421 | ||||||||
\(823\) | −2.10114e7 | −1.08132 | −0.540660 | − | 0.841241i | \(-0.681826\pi\) | ||||
−0.540660 | + | 0.841241i | \(0.681826\pi\) | |||||||
\(824\) | −241104. | −0.0123705 | ||||||||
\(825\) | −2.85082e6 | −0.145826 | ||||||||
\(826\) | −2.28365e7 | −1.16461 | ||||||||
\(827\) | 2.55214e7 | 1.29760 | 0.648801 | − | 0.760958i | \(-0.275271\pi\) | ||||
0.648801 | + | 0.760958i | \(0.275271\pi\) | |||||||
\(828\) | −7.31948e6 | −0.371026 | ||||||||
\(829\) | −3.43311e7 | −1.73501 | −0.867503 | − | 0.497433i | \(-0.834276\pi\) | ||||
−0.867503 | + | 0.497433i | \(0.834276\pi\) | |||||||
\(830\) | −1.69766e7 | −0.855371 | ||||||||
\(831\) | −5.37794e6 | −0.270155 | ||||||||
\(832\) | −2.91886e7 | −1.46186 | ||||||||
\(833\) | −133541. | −0.00666809 | ||||||||
\(834\) | 2.07249e7 | 1.03176 | ||||||||
\(835\) | 2.52043e7 | 1.25100 | ||||||||
\(836\) | −6.58454e6 | −0.325844 | ||||||||
\(837\) | −2.77998e6 | −0.137160 | ||||||||
\(838\) | −5.21514e7 | −2.56541 | ||||||||
\(839\) | −2.31108e7 | −1.13347 | −0.566735 | − | 0.823900i | \(-0.691794\pi\) | ||||
−0.566735 | + | 0.823900i | \(0.691794\pi\) | |||||||
\(840\) | −80653.7 | −0.00394390 | ||||||||
\(841\) | −1.51625e7 | −0.739231 | ||||||||
\(842\) | −3.10805e7 | −1.51080 | ||||||||
\(843\) | −1.36308e6 | −0.0660619 | ||||||||
\(844\) | −2.79358e7 | −1.34991 | ||||||||
\(845\) | −2.04503e7 | −0.985277 | ||||||||
\(846\) | −7.69096e6 | −0.369449 | ||||||||
\(847\) | 1.75267e7 | 0.839446 | ||||||||
\(848\) | −1.78442e6 | −0.0852135 | ||||||||
\(849\) | −7.07241e6 | −0.336743 | ||||||||
\(850\) | −5.37860e6 | −0.255342 | ||||||||
\(851\) | −1.34991e7 | −0.638971 | ||||||||
\(852\) | −1.90841e7 | −0.900684 | ||||||||
\(853\) | −2.49666e7 | −1.17486 | −0.587432 | − | 0.809274i | \(-0.699861\pi\) | ||||
−0.587432 | + | 0.809274i | \(0.699861\pi\) | |||||||
\(854\) | −2.42447e7 | −1.13755 | ||||||||
\(855\) | −1.53710e6 | −0.0719098 | ||||||||
\(856\) | −98270.9 | −0.00458396 | ||||||||
\(857\) | −1.83322e7 | −0.852632 | −0.426316 | − | 0.904574i | \(-0.640189\pi\) | ||||
−0.426316 | + | 0.904574i | \(0.640189\pi\) | |||||||
\(858\) | −3.45595e7 | −1.60269 | ||||||||
\(859\) | 4.08002e7 | 1.88660 | 0.943298 | − | 0.331946i | \(-0.107705\pi\) | ||||
0.943298 | + | 0.331946i | \(0.107705\pi\) | |||||||
\(860\) | 1.56482e7 | 0.721470 | ||||||||
\(861\) | −1.44332e6 | −0.0663519 | ||||||||
\(862\) | 5.91578e7 | 2.71172 | ||||||||
\(863\) | 3.42668e7 | 1.56620 | 0.783100 | − | 0.621896i | \(-0.213637\pi\) | ||||
0.783100 | + | 0.621896i | \(0.213637\pi\) | |||||||
\(864\) | −5.97975e6 | −0.272520 | ||||||||
\(865\) | −9.25797e6 | −0.420703 | ||||||||
\(866\) | −2.16878e6 | −0.0982701 | ||||||||
\(867\) | 817892. | 0.0369529 | ||||||||
\(868\) | 1.59591e7 | 0.718968 | ||||||||
\(869\) | −2.49868e7 | −1.12243 | ||||||||
\(870\) | −8.40756e6 | −0.376593 | ||||||||
\(871\) | −1.08215e7 | −0.483328 | ||||||||
\(872\) | 194441. | 0.00865956 | ||||||||
\(873\) | −3.86109e6 | −0.171465 | ||||||||
\(874\) | 8.46811e6 | 0.374980 | ||||||||
\(875\) | 2.43190e7 | 1.07381 | ||||||||
\(876\) | 1.09469e6 | 0.0481982 | ||||||||
\(877\) | 3.49651e7 | 1.53509 | 0.767547 | − | 0.640992i | \(-0.221477\pi\) | ||||
0.767547 | + | 0.640992i | \(0.221477\pi\) | |||||||
\(878\) | −1.46866e7 | −0.642960 | ||||||||
\(879\) | 1.80009e7 | 0.785817 | ||||||||
\(880\) | −2.79311e7 | −1.21586 | ||||||||
\(881\) | −3.60062e7 | −1.56292 | −0.781461 | − | 0.623954i | \(-0.785525\pi\) | ||||
−0.781461 | + | 0.623954i | \(0.785525\pi\) | |||||||
\(882\) | −75163.6 | −0.00325339 | ||||||||
\(883\) | −2.04032e6 | −0.0880638 | −0.0440319 | − | 0.999030i | \(-0.514020\pi\) | ||||
−0.0440319 | + | 0.999030i | \(0.514020\pi\) | |||||||
\(884\) | −3.26881e7 | −1.40689 | ||||||||
\(885\) | 9.94501e6 | 0.426822 | ||||||||
\(886\) | −6.31091e6 | −0.270090 | ||||||||
\(887\) | −1.23778e7 | −0.528242 | −0.264121 | − | 0.964490i | \(-0.585082\pi\) | ||||
−0.264121 | + | 0.964490i | \(0.585082\pi\) | |||||||
\(888\) | 59090.7 | 0.00251470 | ||||||||
\(889\) | −3.69657e7 | −1.56872 | ||||||||
\(890\) | 1.58707e7 | 0.671616 | ||||||||
\(891\) | −3.56825e6 | −0.150578 | ||||||||
\(892\) | 3.55688e6 | 0.149678 | ||||||||
\(893\) | 4.46077e6 | 0.187189 | ||||||||
\(894\) | −1.77981e7 | −0.744783 | ||||||||
\(895\) | 3.40741e7 | 1.42189 | ||||||||
\(896\) | 363973. | 0.0151460 | ||||||||
\(897\) | 2.22818e7 | 0.924634 | ||||||||
\(898\) | 1.95234e7 | 0.807913 | ||||||||
\(899\) | 8.81936e6 | 0.363947 | ||||||||
\(900\) | −1.51770e6 | −0.0624567 | ||||||||
\(901\) | −2.01972e6 | −0.0828855 | ||||||||
\(902\) | 5.37075e6 | 0.219796 | ||||||||
\(903\) | 1.12940e7 | 0.460924 | ||||||||
\(904\) | −187451. | −0.00762899 | ||||||||
\(905\) | 6.83630e6 | 0.277460 | ||||||||
\(906\) | −1.67226e7 | −0.676835 | ||||||||
\(907\) | 3.18709e7 | 1.28640 | 0.643199 | − | 0.765699i | \(-0.277607\pi\) | ||||
0.643199 | + | 0.765699i | \(0.277607\pi\) | |||||||
\(908\) | 1.55264e7 | 0.624967 | ||||||||
\(909\) | −4.56711e6 | −0.183329 | ||||||||
\(910\) | 4.63140e7 | 1.85400 | ||||||||
\(911\) | 1.92955e7 | 0.770301 | 0.385150 | − | 0.922854i | \(-0.374150\pi\) | ||||
0.385150 | + | 0.922854i | \(0.374150\pi\) | |||||||
\(912\) | 3.44978e6 | 0.137342 | ||||||||
\(913\) | 2.28576e7 | 0.907515 | ||||||||
\(914\) | 4.68112e7 | 1.85347 | ||||||||
\(915\) | 1.05582e7 | 0.416906 | ||||||||
\(916\) | 8.50807e6 | 0.335037 | ||||||||
\(917\) | 5.18001e6 | 0.203426 | ||||||||
\(918\) | −6.73216e6 | −0.263662 | ||||||||
\(919\) | −1.22903e7 | −0.480035 | −0.240017 | − | 0.970769i | \(-0.577153\pi\) | ||||
−0.240017 | + | 0.970769i | \(0.577153\pi\) | |||||||
\(920\) | −193501. | −0.00753724 | ||||||||
\(921\) | −1.40377e7 | −0.545314 | ||||||||
\(922\) | 2.78668e7 | 1.07959 | ||||||||
\(923\) | 5.80954e7 | 2.24459 | ||||||||
\(924\) | 2.04844e7 | 0.789301 | ||||||||
\(925\) | −2.79905e6 | −0.107561 | ||||||||
\(926\) | 1.26199e7 | 0.483647 | ||||||||
\(927\) | 1.42949e7 | 0.546363 | ||||||||
\(928\) | 1.89705e7 | 0.723117 | ||||||||
\(929\) | 3.75326e7 | 1.42682 | 0.713411 | − | 0.700746i | \(-0.247149\pi\) | ||||
0.713411 | + | 0.700746i | \(0.247149\pi\) | |||||||
\(930\) | −1.38631e7 | −0.525598 | ||||||||
\(931\) | 43594.9 | 0.00164840 | ||||||||
\(932\) | 4.36989e7 | 1.64790 | ||||||||
\(933\) | 1.81673e6 | 0.0683260 | ||||||||
\(934\) | 4.54647e7 | 1.70532 | ||||||||
\(935\) | −3.16141e7 | −1.18264 | ||||||||
\(936\) | −97536.1 | −0.00363895 | ||||||||
\(937\) | −1.81510e7 | −0.675384 | −0.337692 | − | 0.941257i | \(-0.609646\pi\) | ||||
−0.337692 | + | 0.941257i | \(0.609646\pi\) | |||||||
\(938\) | 1.27944e7 | 0.474802 | ||||||||
\(939\) | −5.42380e6 | −0.200743 | ||||||||
\(940\) | −1.92275e7 | −0.709747 | ||||||||
\(941\) | −2.06931e7 | −0.761820 | −0.380910 | − | 0.924612i | \(-0.624389\pi\) | ||||
−0.380910 | + | 0.924612i | \(0.624389\pi\) | |||||||
\(942\) | −1.77709e6 | −0.0652503 | ||||||||
\(943\) | −3.46273e6 | −0.126806 | ||||||||
\(944\) | −2.23199e7 | −0.815197 | ||||||||
\(945\) | 4.78190e6 | 0.174189 | ||||||||
\(946\) | −4.20264e7 | −1.52684 | ||||||||
\(947\) | 3.21751e7 | 1.16585 | 0.582927 | − | 0.812524i | \(-0.301907\pi\) | ||||
0.582927 | + | 0.812524i | \(0.301907\pi\) | |||||||
\(948\) | −1.33023e7 | −0.480735 | ||||||||
\(949\) | −3.33244e6 | −0.120115 | ||||||||
\(950\) | 1.75587e6 | 0.0631223 | ||||||||
\(951\) | 1.50331e6 | 0.0539011 | ||||||||
\(952\) | 204882. | 0.00732676 | ||||||||
\(953\) | −4.74547e7 | −1.69257 | −0.846286 | − | 0.532728i | \(-0.821167\pi\) | ||||
−0.846286 | + | 0.532728i | \(0.821167\pi\) | |||||||
\(954\) | −1.13680e6 | −0.0404402 | ||||||||
\(955\) | 2.19481e7 | 0.778732 | ||||||||
\(956\) | 6.07148e6 | 0.214857 | ||||||||
\(957\) | 1.13201e7 | 0.399550 | ||||||||
\(958\) | 5.59679e7 | 1.97027 | ||||||||
\(959\) | −3.75485e7 | −1.31840 | ||||||||
\(960\) | −1.50287e7 | −0.526312 | ||||||||
\(961\) | −1.40870e7 | −0.492052 | ||||||||
\(962\) | −3.39319e7 | −1.18214 | ||||||||
\(963\) | 5.82641e6 | 0.202458 | ||||||||
\(964\) | −5.99182e6 | −0.207666 | ||||||||
\(965\) | −5.76303e6 | −0.199220 | ||||||||
\(966\) | −2.63441e7 | −0.908325 | ||||||||
\(967\) | 2.00999e6 | 0.0691238 | 0.0345619 | − | 0.999403i | \(-0.488996\pi\) | ||||
0.0345619 | + | 0.999403i | \(0.488996\pi\) | |||||||
\(968\) | −184066. | −0.00631371 | ||||||||
\(969\) | 3.90466e6 | 0.133590 | ||||||||
\(970\) | −1.92544e7 | −0.657053 | ||||||||
\(971\) | −1.73673e7 | −0.591131 | −0.295565 | − | 0.955323i | \(-0.595508\pi\) | ||||
−0.295565 | + | 0.955323i | \(0.595508\pi\) | |||||||
\(972\) | −1.89964e6 | −0.0644919 | ||||||||
\(973\) | 3.73954e7 | 1.26630 | ||||||||
\(974\) | −1.83713e7 | −0.620501 | ||||||||
\(975\) | 4.62015e6 | 0.155648 | ||||||||
\(976\) | −2.36962e7 | −0.796259 | ||||||||
\(977\) | −9.02178e6 | −0.302382 | −0.151191 | − | 0.988505i | \(-0.548311\pi\) | ||||
−0.151191 | + | 0.988505i | \(0.548311\pi\) | |||||||
\(978\) | −9.53441e6 | −0.318747 | ||||||||
\(979\) | −2.13686e7 | −0.712557 | ||||||||
\(980\) | −187910. | −0.00625006 | ||||||||
\(981\) | −1.15282e7 | −0.382464 | ||||||||
\(982\) | 3.24056e7 | 1.07236 | ||||||||
\(983\) | −140546. | −0.00463912 | −0.00231956 | − | 0.999997i | \(-0.500738\pi\) | ||||
−0.00231956 | + | 0.999997i | \(0.500738\pi\) | |||||||
\(984\) | 15157.7 | 0.000499052 0 | ||||||||
\(985\) | 1.76865e7 | 0.580834 | ||||||||
\(986\) | 2.13575e7 | 0.699613 | ||||||||
\(987\) | −1.38774e7 | −0.453434 | ||||||||
\(988\) | 1.06712e7 | 0.347792 | ||||||||
\(989\) | 2.70961e7 | 0.880878 | ||||||||
\(990\) | −1.77940e7 | −0.577015 | ||||||||
\(991\) | −2.19130e6 | −0.0708790 | −0.0354395 | − | 0.999372i | \(-0.511283\pi\) | ||||
−0.0354395 | + | 0.999372i | \(0.511283\pi\) | |||||||
\(992\) | 3.12802e7 | 1.00923 | ||||||||
\(993\) | 2.84736e7 | 0.916366 | ||||||||
\(994\) | −6.86871e7 | −2.20500 | ||||||||
\(995\) | 1.60171e7 | 0.512891 | ||||||||
\(996\) | 1.21688e7 | 0.388685 | ||||||||
\(997\) | −4.42434e7 | −1.40965 | −0.704823 | − | 0.709383i | \(-0.748974\pi\) | ||||
−0.704823 | + | 0.709383i | \(0.748974\pi\) | |||||||
\(998\) | 4.88712e7 | 1.55320 | ||||||||
\(999\) | −3.50345e6 | −0.111066 |
(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 | 471.6.a.b.1.5 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
471.6.a.b.1.5 | ✓ | 30 | 1.1 | even | 1 | trivial |