Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [102,6,Mod(1,102)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(102, 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("102.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 102 = 2 \cdot 3 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 102.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: | \(16.3591496209\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 102.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | −188.000 | −1.45015 | −0.725075 | − | 0.688670i | \(-0.758195\pi\) | ||||
−0.725075 | + | 0.688670i | \(0.758195\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 100.000 | 0.316228 | ||||||||
\(11\) | 135.000 | 0.336397 | 0.168198 | − | 0.985753i | \(-0.446205\pi\) | ||||
0.168198 | + | 0.985753i | \(0.446205\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | −1113.00 | −1.82657 | −0.913286 | − | 0.407319i | \(-0.866464\pi\) | ||||
−0.913286 | + | 0.407319i | \(0.866464\pi\) | |||||||
\(14\) | −752.000 | −1.02541 | ||||||||
\(15\) | −225.000 | −0.258199 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 289.000 | 0.242536 | ||||||||
\(18\) | 324.000 | 0.235702 | ||||||||
\(19\) | −929.000 | −0.590380 | −0.295190 | − | 0.955439i | \(-0.595383\pi\) | ||||
−0.295190 | + | 0.955439i | \(0.595383\pi\) | |||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | 1692.00 | 0.837244 | ||||||||
\(22\) | 540.000 | 0.237869 | ||||||||
\(23\) | −1701.00 | −0.670478 | −0.335239 | − | 0.942133i | \(-0.608817\pi\) | ||||
−0.335239 | + | 0.942133i | \(0.608817\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | −2500.00 | −0.800000 | ||||||||
\(26\) | −4452.00 | −1.29158 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −3008.00 | −0.725075 | ||||||||
\(29\) | −4670.00 | −1.03115 | −0.515575 | − | 0.856844i | \(-0.672422\pi\) | ||||
−0.515575 | + | 0.856844i | \(0.672422\pi\) | |||||||
\(30\) | −900.000 | −0.182574 | ||||||||
\(31\) | −5490.00 | −1.02605 | −0.513025 | − | 0.858374i | \(-0.671475\pi\) | ||||
−0.513025 | + | 0.858374i | \(0.671475\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | −1215.00 | −0.194219 | ||||||||
\(34\) | 1156.00 | 0.171499 | ||||||||
\(35\) | −4700.00 | −0.648527 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 10808.0 | 1.29790 | 0.648950 | − | 0.760831i | \(-0.275209\pi\) | ||||
0.648950 | + | 0.760831i | \(0.275209\pi\) | |||||||
\(38\) | −3716.00 | −0.417462 | ||||||||
\(39\) | 10017.0 | 1.05457 | ||||||||
\(40\) | 1600.00 | 0.158114 | ||||||||
\(41\) | 8911.00 | 0.827879 | 0.413939 | − | 0.910304i | \(-0.364153\pi\) | ||||
0.413939 | + | 0.910304i | \(0.364153\pi\) | |||||||
\(42\) | 6768.00 | 0.592021 | ||||||||
\(43\) | −11839.0 | −0.976436 | −0.488218 | − | 0.872722i | \(-0.662353\pi\) | ||||
−0.488218 | + | 0.872722i | \(0.662353\pi\) | |||||||
\(44\) | 2160.00 | 0.168198 | ||||||||
\(45\) | 2025.00 | 0.149071 | ||||||||
\(46\) | −6804.00 | −0.474100 | ||||||||
\(47\) | −8578.00 | −0.566424 | −0.283212 | − | 0.959057i | \(-0.591400\pi\) | ||||
−0.283212 | + | 0.959057i | \(0.591400\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | 18537.0 | 1.10293 | ||||||||
\(50\) | −10000.0 | −0.565685 | ||||||||
\(51\) | −2601.00 | −0.140028 | ||||||||
\(52\) | −17808.0 | −0.913286 | ||||||||
\(53\) | 35606.0 | 1.74114 | 0.870570 | − | 0.492045i | \(-0.163751\pi\) | ||||
0.870570 | + | 0.492045i | \(0.163751\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | 3375.00 | 0.150441 | ||||||||
\(56\) | −12032.0 | −0.512705 | ||||||||
\(57\) | 8361.00 | 0.340856 | ||||||||
\(58\) | −18680.0 | −0.729133 | ||||||||
\(59\) | 6138.00 | 0.229560 | 0.114780 | − | 0.993391i | \(-0.463384\pi\) | ||||
0.114780 | + | 0.993391i | \(0.463384\pi\) | |||||||
\(60\) | −3600.00 | −0.129099 | ||||||||
\(61\) | 19688.0 | 0.677450 | 0.338725 | − | 0.940885i | \(-0.390004\pi\) | ||||
0.338725 | + | 0.940885i | \(0.390004\pi\) | |||||||
\(62\) | −21960.0 | −0.725526 | ||||||||
\(63\) | −15228.0 | −0.483383 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −27825.0 | −0.816868 | ||||||||
\(66\) | −4860.00 | −0.137333 | ||||||||
\(67\) | −14724.0 | −0.400718 | −0.200359 | − | 0.979723i | \(-0.564211\pi\) | ||||
−0.200359 | + | 0.979723i | \(0.564211\pi\) | |||||||
\(68\) | 4624.00 | 0.121268 | ||||||||
\(69\) | 15309.0 | 0.387101 | ||||||||
\(70\) | −18800.0 | −0.458578 | ||||||||
\(71\) | 48396.0 | 1.13937 | 0.569683 | − | 0.821864i | \(-0.307066\pi\) | ||||
0.569683 | + | 0.821864i | \(0.307066\pi\) | |||||||
\(72\) | 5184.00 | 0.117851 | ||||||||
\(73\) | 10322.0 | 0.226703 | 0.113351 | − | 0.993555i | \(-0.463841\pi\) | ||||
0.113351 | + | 0.993555i | \(0.463841\pi\) | |||||||
\(74\) | 43232.0 | 0.917753 | ||||||||
\(75\) | 22500.0 | 0.461880 | ||||||||
\(76\) | −14864.0 | −0.295190 | ||||||||
\(77\) | −25380.0 | −0.487826 | ||||||||
\(78\) | 40068.0 | 0.745695 | ||||||||
\(79\) | 77710.0 | 1.40091 | 0.700453 | − | 0.713698i | \(-0.252981\pi\) | ||||
0.700453 | + | 0.713698i | \(0.252981\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 35644.0 | 0.585399 | ||||||||
\(83\) | −108258. | −1.72490 | −0.862452 | − | 0.506139i | \(-0.831072\pi\) | ||||
−0.862452 | + | 0.506139i | \(0.831072\pi\) | |||||||
\(84\) | 27072.0 | 0.418622 | ||||||||
\(85\) | 7225.00 | 0.108465 | ||||||||
\(86\) | −47356.0 | −0.690445 | ||||||||
\(87\) | 42030.0 | 0.595335 | ||||||||
\(88\) | 8640.00 | 0.118934 | ||||||||
\(89\) | −116488. | −1.55886 | −0.779428 | − | 0.626491i | \(-0.784490\pi\) | ||||
−0.779428 | + | 0.626491i | \(0.784490\pi\) | |||||||
\(90\) | 8100.00 | 0.105409 | ||||||||
\(91\) | 209244. | 2.64880 | ||||||||
\(92\) | −27216.0 | −0.335239 | ||||||||
\(93\) | 49410.0 | 0.592390 | ||||||||
\(94\) | −34312.0 | −0.400522 | ||||||||
\(95\) | −23225.0 | −0.264026 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | 10524.0 | 0.113567 | 0.0567834 | − | 0.998387i | \(-0.481916\pi\) | ||||
0.0567834 | + | 0.998387i | \(0.481916\pi\) | |||||||
\(98\) | 74148.0 | 0.779892 | ||||||||
\(99\) | 10935.0 | 0.112132 | ||||||||
\(100\) | −40000.0 | −0.400000 | ||||||||
\(101\) | 122896. | 1.19877 | 0.599383 | − | 0.800462i | \(-0.295413\pi\) | ||||
0.599383 | + | 0.800462i | \(0.295413\pi\) | |||||||
\(102\) | −10404.0 | −0.0990148 | ||||||||
\(103\) | 66661.0 | 0.619126 | 0.309563 | − | 0.950879i | \(-0.399817\pi\) | ||||
0.309563 | + | 0.950879i | \(0.399817\pi\) | |||||||
\(104\) | −71232.0 | −0.645791 | ||||||||
\(105\) | 42300.0 | 0.374427 | ||||||||
\(106\) | 142424. | 1.23117 | ||||||||
\(107\) | −162285. | −1.37031 | −0.685155 | − | 0.728397i | \(-0.740266\pi\) | ||||
−0.685155 | + | 0.728397i | \(0.740266\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | 125500. | 1.01176 | 0.505880 | − | 0.862604i | \(-0.331168\pi\) | ||||
0.505880 | + | 0.862604i | \(0.331168\pi\) | |||||||
\(110\) | 13500.0 | 0.106378 | ||||||||
\(111\) | −97272.0 | −0.749343 | ||||||||
\(112\) | −48128.0 | −0.362537 | ||||||||
\(113\) | 77029.0 | 0.567490 | 0.283745 | − | 0.958900i | \(-0.408423\pi\) | ||||
0.283745 | + | 0.958900i | \(0.408423\pi\) | |||||||
\(114\) | 33444.0 | 0.241022 | ||||||||
\(115\) | −42525.0 | −0.299847 | ||||||||
\(116\) | −74720.0 | −0.515575 | ||||||||
\(117\) | −90153.0 | −0.608857 | ||||||||
\(118\) | 24552.0 | 0.162324 | ||||||||
\(119\) | −54332.0 | −0.351713 | ||||||||
\(120\) | −14400.0 | −0.0912871 | ||||||||
\(121\) | −142826. | −0.886837 | ||||||||
\(122\) | 78752.0 | 0.479029 | ||||||||
\(123\) | −80199.0 | −0.477976 | ||||||||
\(124\) | −87840.0 | −0.513025 | ||||||||
\(125\) | −140625. | −0.804984 | ||||||||
\(126\) | −60912.0 | −0.341803 | ||||||||
\(127\) | −256117. | −1.40906 | −0.704529 | − | 0.709675i | \(-0.748842\pi\) | ||||
−0.704529 | + | 0.709675i | \(0.748842\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 106551. | 0.563746 | ||||||||
\(130\) | −111300. | −0.577613 | ||||||||
\(131\) | −288335. | −1.46798 | −0.733988 | − | 0.679162i | \(-0.762343\pi\) | ||||
−0.733988 | + | 0.679162i | \(0.762343\pi\) | |||||||
\(132\) | −19440.0 | −0.0971094 | ||||||||
\(133\) | 174652. | 0.856139 | ||||||||
\(134\) | −58896.0 | −0.283350 | ||||||||
\(135\) | −18225.0 | −0.0860663 | ||||||||
\(136\) | 18496.0 | 0.0857493 | ||||||||
\(137\) | −144366. | −0.657148 | −0.328574 | − | 0.944478i | \(-0.606568\pi\) | ||||
−0.328574 | + | 0.944478i | \(0.606568\pi\) | |||||||
\(138\) | 61236.0 | 0.273722 | ||||||||
\(139\) | −165682. | −0.727341 | −0.363671 | − | 0.931528i | \(-0.618477\pi\) | ||||
−0.363671 | + | 0.931528i | \(0.618477\pi\) | |||||||
\(140\) | −75200.0 | −0.324263 | ||||||||
\(141\) | 77202.0 | 0.327025 | ||||||||
\(142\) | 193584. | 0.805654 | ||||||||
\(143\) | −150255. | −0.614453 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | −116750. | −0.461144 | ||||||||
\(146\) | 41288.0 | 0.160303 | ||||||||
\(147\) | −166833. | −0.636779 | ||||||||
\(148\) | 172928. | 0.648950 | ||||||||
\(149\) | −276306. | −1.01959 | −0.509794 | − | 0.860297i | \(-0.670278\pi\) | ||||
−0.509794 | + | 0.860297i | \(0.670278\pi\) | |||||||
\(150\) | 90000.0 | 0.326599 | ||||||||
\(151\) | 554808. | 1.98016 | 0.990080 | − | 0.140504i | \(-0.0448722\pi\) | ||||
0.990080 | + | 0.140504i | \(0.0448722\pi\) | |||||||
\(152\) | −59456.0 | −0.208731 | ||||||||
\(153\) | 23409.0 | 0.0808452 | ||||||||
\(154\) | −101520. | −0.344945 | ||||||||
\(155\) | −137250. | −0.458863 | ||||||||
\(156\) | 160272. | 0.527286 | ||||||||
\(157\) | −403605. | −1.30679 | −0.653397 | − | 0.757015i | \(-0.726657\pi\) | ||||
−0.653397 | + | 0.757015i | \(0.726657\pi\) | |||||||
\(158\) | 310840. | 0.990591 | ||||||||
\(159\) | −320454. | −1.00525 | ||||||||
\(160\) | 25600.0 | 0.0790569 | ||||||||
\(161\) | 319788. | 0.972294 | ||||||||
\(162\) | 26244.0 | 0.0785674 | ||||||||
\(163\) | −446490. | −1.31626 | −0.658132 | − | 0.752903i | \(-0.728653\pi\) | ||||
−0.658132 | + | 0.752903i | \(0.728653\pi\) | |||||||
\(164\) | 142576. | 0.413939 | ||||||||
\(165\) | −30375.0 | −0.0868573 | ||||||||
\(166\) | −433032. | −1.21969 | ||||||||
\(167\) | 194423. | 0.539457 | 0.269728 | − | 0.962936i | \(-0.413066\pi\) | ||||
0.269728 | + | 0.962936i | \(0.413066\pi\) | |||||||
\(168\) | 108288. | 0.296011 | ||||||||
\(169\) | 867476. | 2.33637 | ||||||||
\(170\) | 28900.0 | 0.0766965 | ||||||||
\(171\) | −75249.0 | −0.196793 | ||||||||
\(172\) | −189424. | −0.488218 | ||||||||
\(173\) | 80365.0 | 0.204151 | 0.102076 | − | 0.994777i | \(-0.467452\pi\) | ||||
0.102076 | + | 0.994777i | \(0.467452\pi\) | |||||||
\(174\) | 168120. | 0.420965 | ||||||||
\(175\) | 470000. | 1.16012 | ||||||||
\(176\) | 34560.0 | 0.0840992 | ||||||||
\(177\) | −55242.0 | −0.132537 | ||||||||
\(178\) | −465952. | −1.10228 | ||||||||
\(179\) | 39258.0 | 0.0915789 | 0.0457895 | − | 0.998951i | \(-0.485420\pi\) | ||||
0.0457895 | + | 0.998951i | \(0.485420\pi\) | |||||||
\(180\) | 32400.0 | 0.0745356 | ||||||||
\(181\) | −225662. | −0.511991 | −0.255995 | − | 0.966678i | \(-0.582403\pi\) | ||||
−0.255995 | + | 0.966678i | \(0.582403\pi\) | |||||||
\(182\) | 836976. | 1.87299 | ||||||||
\(183\) | −177192. | −0.391126 | ||||||||
\(184\) | −108864. | −0.237050 | ||||||||
\(185\) | 270200. | 0.580438 | ||||||||
\(186\) | 197640. | 0.418883 | ||||||||
\(187\) | 39015.0 | 0.0815882 | ||||||||
\(188\) | −137248. | −0.283212 | ||||||||
\(189\) | 137052. | 0.279081 | ||||||||
\(190\) | −92900.0 | −0.186695 | ||||||||
\(191\) | −163502. | −0.324295 | −0.162147 | − | 0.986767i | \(-0.551842\pi\) | ||||
−0.162147 | + | 0.986767i | \(0.551842\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | −449706. | −0.869031 | −0.434516 | − | 0.900664i | \(-0.643080\pi\) | ||||
−0.434516 | + | 0.900664i | \(0.643080\pi\) | |||||||
\(194\) | 42096.0 | 0.0803039 | ||||||||
\(195\) | 250425. | 0.471619 | ||||||||
\(196\) | 296592. | 0.551467 | ||||||||
\(197\) | 452233. | 0.830227 | 0.415113 | − | 0.909770i | \(-0.363742\pi\) | ||||
0.415113 | + | 0.909770i | \(0.363742\pi\) | |||||||
\(198\) | 43740.0 | 0.0792895 | ||||||||
\(199\) | −37228.0 | −0.0666403 | −0.0333202 | − | 0.999445i | \(-0.510608\pi\) | ||||
−0.0333202 | + | 0.999445i | \(0.510608\pi\) | |||||||
\(200\) | −160000. | −0.282843 | ||||||||
\(201\) | 132516. | 0.231355 | ||||||||
\(202\) | 491584. | 0.847655 | ||||||||
\(203\) | 877960. | 1.49532 | ||||||||
\(204\) | −41616.0 | −0.0700140 | ||||||||
\(205\) | 222775. | 0.370239 | ||||||||
\(206\) | 266644. | 0.437788 | ||||||||
\(207\) | −137781. | −0.223493 | ||||||||
\(208\) | −284928. | −0.456643 | ||||||||
\(209\) | −125415. | −0.198602 | ||||||||
\(210\) | 169200. | 0.264760 | ||||||||
\(211\) | −124402. | −0.192363 | −0.0961814 | − | 0.995364i | \(-0.530663\pi\) | ||||
−0.0961814 | + | 0.995364i | \(0.530663\pi\) | |||||||
\(212\) | 569696. | 0.870570 | ||||||||
\(213\) | −435564. | −0.657814 | ||||||||
\(214\) | −649140. | −0.968956 | ||||||||
\(215\) | −295975. | −0.436676 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 1.03212e6 | 1.48792 | ||||||||
\(218\) | 502000. | 0.715422 | ||||||||
\(219\) | −92898.0 | −0.130887 | ||||||||
\(220\) | 54000.0 | 0.0752206 | ||||||||
\(221\) | −321657. | −0.443009 | ||||||||
\(222\) | −389088. | −0.529865 | ||||||||
\(223\) | −1.20463e6 | −1.62216 | −0.811078 | − | 0.584938i | \(-0.801119\pi\) | ||||
−0.811078 | + | 0.584938i | \(0.801119\pi\) | |||||||
\(224\) | −192512. | −0.256353 | ||||||||
\(225\) | −202500. | −0.266667 | ||||||||
\(226\) | 308116. | 0.401276 | ||||||||
\(227\) | 819497. | 1.05556 | 0.527780 | − | 0.849381i | \(-0.323025\pi\) | ||||
0.527780 | + | 0.849381i | \(0.323025\pi\) | |||||||
\(228\) | 133776. | 0.170428 | ||||||||
\(229\) | 366454. | 0.461775 | 0.230888 | − | 0.972980i | \(-0.425837\pi\) | ||||
0.230888 | + | 0.972980i | \(0.425837\pi\) | |||||||
\(230\) | −170100. | −0.212024 | ||||||||
\(231\) | 228420. | 0.281646 | ||||||||
\(232\) | −298880. | −0.364567 | ||||||||
\(233\) | 762015. | 0.919547 | 0.459773 | − | 0.888036i | \(-0.347931\pi\) | ||||
0.459773 | + | 0.888036i | \(0.347931\pi\) | |||||||
\(234\) | −360612. | −0.430527 | ||||||||
\(235\) | −214450. | −0.253312 | ||||||||
\(236\) | 98208.0 | 0.114780 | ||||||||
\(237\) | −699390. | −0.808814 | ||||||||
\(238\) | −217328. | −0.248699 | ||||||||
\(239\) | −278752. | −0.315663 | −0.157831 | − | 0.987466i | \(-0.550450\pi\) | ||||
−0.157831 | + | 0.987466i | \(0.550450\pi\) | |||||||
\(240\) | −57600.0 | −0.0645497 | ||||||||
\(241\) | 379920. | 0.421356 | 0.210678 | − | 0.977555i | \(-0.432433\pi\) | ||||
0.210678 | + | 0.977555i | \(0.432433\pi\) | |||||||
\(242\) | −571304. | −0.627089 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 315008. | 0.338725 | ||||||||
\(245\) | 463425. | 0.493247 | ||||||||
\(246\) | −320796. | −0.337980 | ||||||||
\(247\) | 1.03398e6 | 1.07837 | ||||||||
\(248\) | −351360. | −0.362763 | ||||||||
\(249\) | 974322. | 0.995873 | ||||||||
\(250\) | −562500. | −0.569210 | ||||||||
\(251\) | 976572. | 0.978408 | 0.489204 | − | 0.872169i | \(-0.337287\pi\) | ||||
0.489204 | + | 0.872169i | \(0.337287\pi\) | |||||||
\(252\) | −243648. | −0.241692 | ||||||||
\(253\) | −229635. | −0.225547 | ||||||||
\(254\) | −1.02447e6 | −0.996355 | ||||||||
\(255\) | −65025.0 | −0.0626224 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 907308. | 0.856884 | 0.428442 | − | 0.903569i | \(-0.359063\pi\) | ||||
0.428442 | + | 0.903569i | \(0.359063\pi\) | |||||||
\(258\) | 426204. | 0.398628 | ||||||||
\(259\) | −2.03190e6 | −1.88215 | ||||||||
\(260\) | −445200. | −0.408434 | ||||||||
\(261\) | −378270. | −0.343717 | ||||||||
\(262\) | −1.15334e6 | −1.03802 | ||||||||
\(263\) | −1.59365e6 | −1.42070 | −0.710351 | − | 0.703848i | \(-0.751464\pi\) | ||||
−0.710351 | + | 0.703848i | \(0.751464\pi\) | |||||||
\(264\) | −77760.0 | −0.0686667 | ||||||||
\(265\) | 890150. | 0.778661 | ||||||||
\(266\) | 698608. | 0.605382 | ||||||||
\(267\) | 1.04839e6 | 0.900006 | ||||||||
\(268\) | −235584. | −0.200359 | ||||||||
\(269\) | 1.24870e6 | 1.05215 | 0.526074 | − | 0.850439i | \(-0.323663\pi\) | ||||
0.526074 | + | 0.850439i | \(0.323663\pi\) | |||||||
\(270\) | −72900.0 | −0.0608581 | ||||||||
\(271\) | 62459.0 | 0.0516621 | 0.0258310 | − | 0.999666i | \(-0.491777\pi\) | ||||
0.0258310 | + | 0.999666i | \(0.491777\pi\) | |||||||
\(272\) | 73984.0 | 0.0606339 | ||||||||
\(273\) | −1.88320e6 | −1.52929 | ||||||||
\(274\) | −577464. | −0.464674 | ||||||||
\(275\) | −337500. | −0.269118 | ||||||||
\(276\) | 244944. | 0.193550 | ||||||||
\(277\) | 1.14635e6 | 0.897669 | 0.448835 | − | 0.893615i | \(-0.351839\pi\) | ||||
0.448835 | + | 0.893615i | \(0.351839\pi\) | |||||||
\(278\) | −662728. | −0.514308 | ||||||||
\(279\) | −444690. | −0.342016 | ||||||||
\(280\) | −300800. | −0.229289 | ||||||||
\(281\) | −2.14530e6 | −1.62077 | −0.810387 | − | 0.585896i | \(-0.800743\pi\) | ||||
−0.810387 | + | 0.585896i | \(0.800743\pi\) | |||||||
\(282\) | 308808. | 0.231241 | ||||||||
\(283\) | −1.72019e6 | −1.27676 | −0.638380 | − | 0.769721i | \(-0.720395\pi\) | ||||
−0.638380 | + | 0.769721i | \(0.720395\pi\) | |||||||
\(284\) | 774336. | 0.569683 | ||||||||
\(285\) | 209025. | 0.152435 | ||||||||
\(286\) | −601020. | −0.434484 | ||||||||
\(287\) | −1.67527e6 | −1.20055 | ||||||||
\(288\) | 82944.0 | 0.0589256 | ||||||||
\(289\) | 83521.0 | 0.0588235 | ||||||||
\(290\) | −467000. | −0.326078 | ||||||||
\(291\) | −94716.0 | −0.0655678 | ||||||||
\(292\) | 165152. | 0.113351 | ||||||||
\(293\) | −1.43433e6 | −0.976069 | −0.488035 | − | 0.872824i | \(-0.662286\pi\) | ||||
−0.488035 | + | 0.872824i | \(0.662286\pi\) | |||||||
\(294\) | −667332. | −0.450271 | ||||||||
\(295\) | 153450. | 0.102663 | ||||||||
\(296\) | 691712. | 0.458877 | ||||||||
\(297\) | −98415.0 | −0.0647396 | ||||||||
\(298\) | −1.10522e6 | −0.720957 | ||||||||
\(299\) | 1.89321e6 | 1.22468 | ||||||||
\(300\) | 360000. | 0.230940 | ||||||||
\(301\) | 2.22573e6 | 1.41598 | ||||||||
\(302\) | 2.21923e6 | 1.40018 | ||||||||
\(303\) | −1.10606e6 | −0.692108 | ||||||||
\(304\) | −237824. | −0.147595 | ||||||||
\(305\) | 492200. | 0.302965 | ||||||||
\(306\) | 93636.0 | 0.0571662 | ||||||||
\(307\) | 1.94190e6 | 1.17593 | 0.587964 | − | 0.808887i | \(-0.299930\pi\) | ||||
0.587964 | + | 0.808887i | \(0.299930\pi\) | |||||||
\(308\) | −406080. | −0.243913 | ||||||||
\(309\) | −599949. | −0.357452 | ||||||||
\(310\) | −549000. | −0.324465 | ||||||||
\(311\) | 739368. | 0.433471 | 0.216735 | − | 0.976230i | \(-0.430459\pi\) | ||||
0.216735 | + | 0.976230i | \(0.430459\pi\) | |||||||
\(312\) | 641088. | 0.372847 | ||||||||
\(313\) | −2.10696e6 | −1.21561 | −0.607806 | − | 0.794086i | \(-0.707950\pi\) | ||||
−0.607806 | + | 0.794086i | \(0.707950\pi\) | |||||||
\(314\) | −1.61442e6 | −0.924043 | ||||||||
\(315\) | −380700. | −0.216176 | ||||||||
\(316\) | 1.24336e6 | 0.700453 | ||||||||
\(317\) | 2.71118e6 | 1.51534 | 0.757671 | − | 0.652637i | \(-0.226337\pi\) | ||||
0.757671 | + | 0.652637i | \(0.226337\pi\) | |||||||
\(318\) | −1.28182e6 | −0.710817 | ||||||||
\(319\) | −630450. | −0.346876 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | 1.46056e6 | 0.791149 | ||||||||
\(322\) | 1.27915e6 | 0.687515 | ||||||||
\(323\) | −268481. | −0.143188 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 2.78250e6 | 1.46126 | ||||||||
\(326\) | −1.78596e6 | −0.930739 | ||||||||
\(327\) | −1.12950e6 | −0.584140 | ||||||||
\(328\) | 570304. | 0.292699 | ||||||||
\(329\) | 1.61266e6 | 0.821399 | ||||||||
\(330\) | −121500. | −0.0614174 | ||||||||
\(331\) | −23965.0 | −0.0120229 | −0.00601143 | − | 0.999982i | \(-0.501914\pi\) | ||||
−0.00601143 | + | 0.999982i | \(0.501914\pi\) | |||||||
\(332\) | −1.73213e6 | −0.862452 | ||||||||
\(333\) | 875448. | 0.432633 | ||||||||
\(334\) | 777692. | 0.381453 | ||||||||
\(335\) | −368100. | −0.179207 | ||||||||
\(336\) | 433152. | 0.209311 | ||||||||
\(337\) | −2.95570e6 | −1.41771 | −0.708853 | − | 0.705357i | \(-0.750787\pi\) | ||||
−0.708853 | + | 0.705357i | \(0.750787\pi\) | |||||||
\(338\) | 3.46990e6 | 1.65206 | ||||||||
\(339\) | −693261. | −0.327640 | ||||||||
\(340\) | 115600. | 0.0542326 | ||||||||
\(341\) | −741150. | −0.345160 | ||||||||
\(342\) | −300996. | −0.139154 | ||||||||
\(343\) | −325240. | −0.149269 | ||||||||
\(344\) | −757696. | −0.345222 | ||||||||
\(345\) | 382725. | 0.173117 | ||||||||
\(346\) | 321460. | 0.144357 | ||||||||
\(347\) | −1.99041e6 | −0.887400 | −0.443700 | − | 0.896175i | \(-0.646334\pi\) | ||||
−0.443700 | + | 0.896175i | \(0.646334\pi\) | |||||||
\(348\) | 672480. | 0.297667 | ||||||||
\(349\) | 475581. | 0.209007 | 0.104504 | − | 0.994525i | \(-0.466675\pi\) | ||||
0.104504 | + | 0.994525i | \(0.466675\pi\) | |||||||
\(350\) | 1.88000e6 | 0.820328 | ||||||||
\(351\) | 811377. | 0.351524 | ||||||||
\(352\) | 138240. | 0.0594671 | ||||||||
\(353\) | −1.98088e6 | −0.846099 | −0.423049 | − | 0.906107i | \(-0.639040\pi\) | ||||
−0.423049 | + | 0.906107i | \(0.639040\pi\) | |||||||
\(354\) | −220968. | −0.0937176 | ||||||||
\(355\) | 1.20990e6 | 0.509540 | ||||||||
\(356\) | −1.86381e6 | −0.779428 | ||||||||
\(357\) | 488988. | 0.203062 | ||||||||
\(358\) | 157032. | 0.0647561 | ||||||||
\(359\) | −3.20778e6 | −1.31362 | −0.656808 | − | 0.754058i | \(-0.728094\pi\) | ||||
−0.656808 | + | 0.754058i | \(0.728094\pi\) | |||||||
\(360\) | 129600. | 0.0527046 | ||||||||
\(361\) | −1.61306e6 | −0.651451 | ||||||||
\(362\) | −902648. | −0.362032 | ||||||||
\(363\) | 1.28543e6 | 0.512016 | ||||||||
\(364\) | 3.34790e6 | 1.32440 | ||||||||
\(365\) | 258050. | 0.101385 | ||||||||
\(366\) | −708768. | −0.276568 | ||||||||
\(367\) | 491980. | 0.190670 | 0.0953350 | − | 0.995445i | \(-0.469608\pi\) | ||||
0.0953350 | + | 0.995445i | \(0.469608\pi\) | |||||||
\(368\) | −435456. | −0.167620 | ||||||||
\(369\) | 721791. | 0.275960 | ||||||||
\(370\) | 1.08080e6 | 0.410432 | ||||||||
\(371\) | −6.69393e6 | −2.52491 | ||||||||
\(372\) | 790560. | 0.296195 | ||||||||
\(373\) | 1.81206e6 | 0.674373 | 0.337186 | − | 0.941438i | \(-0.390525\pi\) | ||||
0.337186 | + | 0.941438i | \(0.390525\pi\) | |||||||
\(374\) | 156060. | 0.0576916 | ||||||||
\(375\) | 1.26562e6 | 0.464758 | ||||||||
\(376\) | −548992. | −0.200261 | ||||||||
\(377\) | 5.19771e6 | 1.88347 | ||||||||
\(378\) | 548208. | 0.197340 | ||||||||
\(379\) | 4.61391e6 | 1.64995 | 0.824976 | − | 0.565168i | \(-0.191189\pi\) | ||||
0.824976 | + | 0.565168i | \(0.191189\pi\) | |||||||
\(380\) | −371600. | −0.132013 | ||||||||
\(381\) | 2.30505e6 | 0.813520 | ||||||||
\(382\) | −654008. | −0.229311 | ||||||||
\(383\) | −3.44867e6 | −1.20131 | −0.600655 | − | 0.799508i | \(-0.705093\pi\) | ||||
−0.600655 | + | 0.799508i | \(0.705093\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | −634500. | −0.218162 | ||||||||
\(386\) | −1.79882e6 | −0.614498 | ||||||||
\(387\) | −958959. | −0.325479 | ||||||||
\(388\) | 168384. | 0.0567834 | ||||||||
\(389\) | −515080. | −0.172584 | −0.0862920 | − | 0.996270i | \(-0.527502\pi\) | ||||
−0.0862920 | + | 0.996270i | \(0.527502\pi\) | |||||||
\(390\) | 1.00170e6 | 0.333485 | ||||||||
\(391\) | −491589. | −0.162615 | ||||||||
\(392\) | 1.18637e6 | 0.389946 | ||||||||
\(393\) | 2.59502e6 | 0.847537 | ||||||||
\(394\) | 1.80893e6 | 0.587059 | ||||||||
\(395\) | 1.94275e6 | 0.626504 | ||||||||
\(396\) | 174960. | 0.0560662 | ||||||||
\(397\) | −3.42470e6 | −1.09055 | −0.545275 | − | 0.838257i | \(-0.683575\pi\) | ||||
−0.545275 | + | 0.838257i | \(0.683575\pi\) | |||||||
\(398\) | −148912. | −0.0471218 | ||||||||
\(399\) | −1.57187e6 | −0.494292 | ||||||||
\(400\) | −640000. | −0.200000 | ||||||||
\(401\) | 2.46651e6 | 0.765987 | 0.382994 | − | 0.923751i | \(-0.374893\pi\) | ||||
0.382994 | + | 0.923751i | \(0.374893\pi\) | |||||||
\(402\) | 530064. | 0.163592 | ||||||||
\(403\) | 6.11037e6 | 1.87415 | ||||||||
\(404\) | 1.96634e6 | 0.599383 | ||||||||
\(405\) | 164025. | 0.0496904 | ||||||||
\(406\) | 3.51184e6 | 1.05735 | ||||||||
\(407\) | 1.45908e6 | 0.436609 | ||||||||
\(408\) | −166464. | −0.0495074 | ||||||||
\(409\) | −5.40107e6 | −1.59651 | −0.798254 | − | 0.602320i | \(-0.794243\pi\) | ||||
−0.798254 | + | 0.602320i | \(0.794243\pi\) | |||||||
\(410\) | 891100. | 0.261798 | ||||||||
\(411\) | 1.29929e6 | 0.379405 | ||||||||
\(412\) | 1.06658e6 | 0.309563 | ||||||||
\(413\) | −1.15394e6 | −0.332897 | ||||||||
\(414\) | −551124. | −0.158033 | ||||||||
\(415\) | −2.70645e6 | −0.771400 | ||||||||
\(416\) | −1.13971e6 | −0.322895 | ||||||||
\(417\) | 1.49114e6 | 0.419931 | ||||||||
\(418\) | −501660. | −0.140433 | ||||||||
\(419\) | 1.16768e6 | 0.324930 | 0.162465 | − | 0.986714i | \(-0.448055\pi\) | ||||
0.162465 | + | 0.986714i | \(0.448055\pi\) | |||||||
\(420\) | 676800. | 0.187213 | ||||||||
\(421\) | −468257. | −0.128759 | −0.0643797 | − | 0.997925i | \(-0.520507\pi\) | ||||
−0.0643797 | + | 0.997925i | \(0.520507\pi\) | |||||||
\(422\) | −497608. | −0.136021 | ||||||||
\(423\) | −694818. | −0.188808 | ||||||||
\(424\) | 2.27878e6 | 0.615586 | ||||||||
\(425\) | −722500. | −0.194029 | ||||||||
\(426\) | −1.74226e6 | −0.465145 | ||||||||
\(427\) | −3.70134e6 | −0.982403 | ||||||||
\(428\) | −2.59656e6 | −0.685155 | ||||||||
\(429\) | 1.35230e6 | 0.354755 | ||||||||
\(430\) | −1.18390e6 | −0.308776 | ||||||||
\(431\) | −3.86744e6 | −1.00284 | −0.501419 | − | 0.865205i | \(-0.667188\pi\) | ||||
−0.501419 | + | 0.865205i | \(0.667188\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | −4.33460e6 | −1.11104 | −0.555520 | − | 0.831503i | \(-0.687481\pi\) | ||||
−0.555520 | + | 0.831503i | \(0.687481\pi\) | |||||||
\(434\) | 4.12848e6 | 1.05212 | ||||||||
\(435\) | 1.05075e6 | 0.266242 | ||||||||
\(436\) | 2.00800e6 | 0.505880 | ||||||||
\(437\) | 1.58023e6 | 0.395837 | ||||||||
\(438\) | −371592. | −0.0925510 | ||||||||
\(439\) | −5.76408e6 | −1.42748 | −0.713738 | − | 0.700412i | \(-0.752999\pi\) | ||||
−0.713738 | + | 0.700412i | \(0.752999\pi\) | |||||||
\(440\) | 216000. | 0.0531890 | ||||||||
\(441\) | 1.50150e6 | 0.367644 | ||||||||
\(442\) | −1.28663e6 | −0.313255 | ||||||||
\(443\) | 4.91399e6 | 1.18967 | 0.594833 | − | 0.803849i | \(-0.297218\pi\) | ||||
0.594833 | + | 0.803849i | \(0.297218\pi\) | |||||||
\(444\) | −1.55635e6 | −0.374671 | ||||||||
\(445\) | −2.91220e6 | −0.697142 | ||||||||
\(446\) | −4.81853e6 | −1.14704 | ||||||||
\(447\) | 2.48675e6 | 0.588659 | ||||||||
\(448\) | −770048. | −0.181269 | ||||||||
\(449\) | 920726. | 0.215533 | 0.107767 | − | 0.994176i | \(-0.465630\pi\) | ||||
0.107767 | + | 0.994176i | \(0.465630\pi\) | |||||||
\(450\) | −810000. | −0.188562 | ||||||||
\(451\) | 1.20298e6 | 0.278496 | ||||||||
\(452\) | 1.23246e6 | 0.283745 | ||||||||
\(453\) | −4.99327e6 | −1.14325 | ||||||||
\(454\) | 3.27799e6 | 0.746393 | ||||||||
\(455\) | 5.23110e6 | 1.18458 | ||||||||
\(456\) | 535104. | 0.120511 | ||||||||
\(457\) | −514955. | −0.115340 | −0.0576698 | − | 0.998336i | \(-0.518367\pi\) | ||||
−0.0576698 | + | 0.998336i | \(0.518367\pi\) | |||||||
\(458\) | 1.46582e6 | 0.326524 | ||||||||
\(459\) | −210681. | −0.0466760 | ||||||||
\(460\) | −680400. | −0.149924 | ||||||||
\(461\) | −6.11783e6 | −1.34074 | −0.670371 | − | 0.742026i | \(-0.733865\pi\) | ||||
−0.670371 | + | 0.742026i | \(0.733865\pi\) | |||||||
\(462\) | 913680. | 0.199154 | ||||||||
\(463\) | 7.85456e6 | 1.70282 | 0.851411 | − | 0.524499i | \(-0.175747\pi\) | ||||
0.851411 | + | 0.524499i | \(0.175747\pi\) | |||||||
\(464\) | −1.19552e6 | −0.257788 | ||||||||
\(465\) | 1.23525e6 | 0.264925 | ||||||||
\(466\) | 3.04806e6 | 0.650218 | ||||||||
\(467\) | −2.50736e6 | −0.532015 | −0.266008 | − | 0.963971i | \(-0.585705\pi\) | ||||
−0.266008 | + | 0.963971i | \(0.585705\pi\) | |||||||
\(468\) | −1.44245e6 | −0.304429 | ||||||||
\(469\) | 2.76811e6 | 0.581101 | ||||||||
\(470\) | −857800. | −0.179119 | ||||||||
\(471\) | 3.63244e6 | 0.754478 | ||||||||
\(472\) | 392832. | 0.0811618 | ||||||||
\(473\) | −1.59826e6 | −0.328470 | ||||||||
\(474\) | −2.79756e6 | −0.571918 | ||||||||
\(475\) | 2.32250e6 | 0.472304 | ||||||||
\(476\) | −869312. | −0.175856 | ||||||||
\(477\) | 2.88409e6 | 0.580380 | ||||||||
\(478\) | −1.11501e6 | −0.223207 | ||||||||
\(479\) | −256969. | −0.0511731 | −0.0255866 | − | 0.999673i | \(-0.508145\pi\) | ||||
−0.0255866 | + | 0.999673i | \(0.508145\pi\) | |||||||
\(480\) | −230400. | −0.0456435 | ||||||||
\(481\) | −1.20293e7 | −2.37071 | ||||||||
\(482\) | 1.51968e6 | 0.297944 | ||||||||
\(483\) | −2.87809e6 | −0.561354 | ||||||||
\(484\) | −2.28522e6 | −0.443419 | ||||||||
\(485\) | 263100. | 0.0507886 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | 1.47589e6 | 0.281989 | 0.140994 | − | 0.990010i | \(-0.454970\pi\) | ||||
0.140994 | + | 0.990010i | \(0.454970\pi\) | |||||||
\(488\) | 1.26003e6 | 0.239515 | ||||||||
\(489\) | 4.01841e6 | 0.759945 | ||||||||
\(490\) | 1.85370e6 | 0.348778 | ||||||||
\(491\) | 1.88665e6 | 0.353174 | 0.176587 | − | 0.984285i | \(-0.443494\pi\) | ||||
0.176587 | + | 0.984285i | \(0.443494\pi\) | |||||||
\(492\) | −1.28318e6 | −0.238988 | ||||||||
\(493\) | −1.34963e6 | −0.250091 | ||||||||
\(494\) | 4.13591e6 | 0.762524 | ||||||||
\(495\) | 273375. | 0.0501471 | ||||||||
\(496\) | −1.40544e6 | −0.256512 | ||||||||
\(497\) | −9.09845e6 | −1.65225 | ||||||||
\(498\) | 3.89729e6 | 0.704189 | ||||||||
\(499\) | −1.00548e7 | −1.80768 | −0.903841 | − | 0.427869i | \(-0.859265\pi\) | ||||
−0.903841 | + | 0.427869i | \(0.859265\pi\) | |||||||
\(500\) | −2.25000e6 | −0.402492 | ||||||||
\(501\) | −1.74981e6 | −0.311455 | ||||||||
\(502\) | 3.90629e6 | 0.691839 | ||||||||
\(503\) | −6.05457e6 | −1.06700 | −0.533499 | − | 0.845801i | \(-0.679123\pi\) | ||||
−0.533499 | + | 0.845801i | \(0.679123\pi\) | |||||||
\(504\) | −974592. | −0.170902 | ||||||||
\(505\) | 3.07240e6 | 0.536104 | ||||||||
\(506\) | −918540. | −0.159486 | ||||||||
\(507\) | −7.80728e6 | −1.34890 | ||||||||
\(508\) | −4.09787e6 | −0.704529 | ||||||||
\(509\) | 7.26288e6 | 1.24255 | 0.621276 | − | 0.783592i | \(-0.286615\pi\) | ||||
0.621276 | + | 0.783592i | \(0.286615\pi\) | |||||||
\(510\) | −260100. | −0.0442807 | ||||||||
\(511\) | −1.94054e6 | −0.328753 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 677241. | 0.113619 | ||||||||
\(514\) | 3.62923e6 | 0.605908 | ||||||||
\(515\) | 1.66653e6 | 0.276881 | ||||||||
\(516\) | 1.70482e6 | 0.281873 | ||||||||
\(517\) | −1.15803e6 | −0.190543 | ||||||||
\(518\) | −8.12762e6 | −1.33088 | ||||||||
\(519\) | −723285. | −0.117867 | ||||||||
\(520\) | −1.78080e6 | −0.288806 | ||||||||
\(521\) | −1.90029e6 | −0.306708 | −0.153354 | − | 0.988171i | \(-0.549008\pi\) | ||||
−0.153354 | + | 0.988171i | \(0.549008\pi\) | |||||||
\(522\) | −1.51308e6 | −0.243044 | ||||||||
\(523\) | 5.24950e6 | 0.839197 | 0.419598 | − | 0.907710i | \(-0.362171\pi\) | ||||
0.419598 | + | 0.907710i | \(0.362171\pi\) | |||||||
\(524\) | −4.61336e6 | −0.733988 | ||||||||
\(525\) | −4.23000e6 | −0.669795 | ||||||||
\(526\) | −6.37459e6 | −1.00459 | ||||||||
\(527\) | −1.58661e6 | −0.248853 | ||||||||
\(528\) | −311040. | −0.0485547 | ||||||||
\(529\) | −3.54294e6 | −0.550459 | ||||||||
\(530\) | 3.56060e6 | 0.550597 | ||||||||
\(531\) | 497178. | 0.0765201 | ||||||||
\(532\) | 2.79443e6 | 0.428070 | ||||||||
\(533\) | −9.91794e6 | −1.51218 | ||||||||
\(534\) | 4.19357e6 | 0.636401 | ||||||||
\(535\) | −4.05712e6 | −0.612821 | ||||||||
\(536\) | −942336. | −0.141675 | ||||||||
\(537\) | −353322. | −0.0528731 | ||||||||
\(538\) | 4.99480e6 | 0.743981 | ||||||||
\(539\) | 2.50250e6 | 0.371023 | ||||||||
\(540\) | −291600. | −0.0430331 | ||||||||
\(541\) | 1.19372e7 | 1.75351 | 0.876757 | − | 0.480933i | \(-0.159702\pi\) | ||||
0.876757 | + | 0.480933i | \(0.159702\pi\) | |||||||
\(542\) | 249836. | 0.0365306 | ||||||||
\(543\) | 2.03096e6 | 0.295598 | ||||||||
\(544\) | 295936. | 0.0428746 | ||||||||
\(545\) | 3.13750e6 | 0.452473 | ||||||||
\(546\) | −7.53278e6 | −1.08137 | ||||||||
\(547\) | 3.92109e6 | 0.560323 | 0.280161 | − | 0.959953i | \(-0.409612\pi\) | ||||
0.280161 | + | 0.959953i | \(0.409612\pi\) | |||||||
\(548\) | −2.30986e6 | −0.328574 | ||||||||
\(549\) | 1.59473e6 | 0.225817 | ||||||||
\(550\) | −1.35000e6 | −0.190295 | ||||||||
\(551\) | 4.33843e6 | 0.608770 | ||||||||
\(552\) | 979776. | 0.136861 | ||||||||
\(553\) | −1.46095e7 | −2.03152 | ||||||||
\(554\) | 4.58538e6 | 0.634748 | ||||||||
\(555\) | −2.43180e6 | −0.335116 | ||||||||
\(556\) | −2.65091e6 | −0.363671 | ||||||||
\(557\) | 8.62416e6 | 1.17782 | 0.588910 | − | 0.808199i | \(-0.299557\pi\) | ||||
0.588910 | + | 0.808199i | \(0.299557\pi\) | |||||||
\(558\) | −1.77876e6 | −0.241842 | ||||||||
\(559\) | 1.31768e7 | 1.78353 | ||||||||
\(560\) | −1.20320e6 | −0.162132 | ||||||||
\(561\) | −351135. | −0.0471050 | ||||||||
\(562\) | −8.58120e6 | −1.14606 | ||||||||
\(563\) | −1.20126e6 | −0.159723 | −0.0798614 | − | 0.996806i | \(-0.525448\pi\) | ||||
−0.0798614 | + | 0.996806i | \(0.525448\pi\) | |||||||
\(564\) | 1.23523e6 | 0.163512 | ||||||||
\(565\) | 1.92572e6 | 0.253789 | ||||||||
\(566\) | −6.88074e6 | −0.902806 | ||||||||
\(567\) | −1.23347e6 | −0.161128 | ||||||||
\(568\) | 3.09734e6 | 0.402827 | ||||||||
\(569\) | −1.10716e6 | −0.143360 | −0.0716800 | − | 0.997428i | \(-0.522836\pi\) | ||||
−0.0716800 | + | 0.997428i | \(0.522836\pi\) | |||||||
\(570\) | 836100. | 0.107788 | ||||||||
\(571\) | 1.30319e7 | 1.67270 | 0.836349 | − | 0.548198i | \(-0.184686\pi\) | ||||
0.836349 | + | 0.548198i | \(0.184686\pi\) | |||||||
\(572\) | −2.40408e6 | −0.307227 | ||||||||
\(573\) | 1.47152e6 | 0.187232 | ||||||||
\(574\) | −6.70107e6 | −0.848916 | ||||||||
\(575\) | 4.25250e6 | 0.536383 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 8.13114e6 | 1.01674 | 0.508372 | − | 0.861137i | \(-0.330247\pi\) | ||||
0.508372 | + | 0.861137i | \(0.330247\pi\) | |||||||
\(578\) | 334084. | 0.0415945 | ||||||||
\(579\) | 4.04735e6 | 0.501735 | ||||||||
\(580\) | −1.86800e6 | −0.230572 | ||||||||
\(581\) | 2.03525e7 | 2.50137 | ||||||||
\(582\) | −378864. | −0.0463635 | ||||||||
\(583\) | 4.80681e6 | 0.585714 | ||||||||
\(584\) | 660608. | 0.0801515 | ||||||||
\(585\) | −2.25382e6 | −0.272289 | ||||||||
\(586\) | −5.73733e6 | −0.690185 | ||||||||
\(587\) | 1.68467e6 | 0.201799 | 0.100900 | − | 0.994897i | \(-0.467828\pi\) | ||||
0.100900 | + | 0.994897i | \(0.467828\pi\) | |||||||
\(588\) | −2.66933e6 | −0.318389 | ||||||||
\(589\) | 5.10021e6 | 0.605759 | ||||||||
\(590\) | 613800. | 0.0725934 | ||||||||
\(591\) | −4.07010e6 | −0.479332 | ||||||||
\(592\) | 2.76685e6 | 0.324475 | ||||||||
\(593\) | −113022. | −0.0131986 | −0.00659928 | − | 0.999978i | \(-0.502101\pi\) | ||||
−0.00659928 | + | 0.999978i | \(0.502101\pi\) | |||||||
\(594\) | −393660. | −0.0457778 | ||||||||
\(595\) | −1.35830e6 | −0.157291 | ||||||||
\(596\) | −4.42090e6 | −0.509794 | ||||||||
\(597\) | 335052. | 0.0384748 | ||||||||
\(598\) | 7.57285e6 | 0.865977 | ||||||||
\(599\) | 8.26813e6 | 0.941543 | 0.470772 | − | 0.882255i | \(-0.343976\pi\) | ||||
0.470772 | + | 0.882255i | \(0.343976\pi\) | |||||||
\(600\) | 1.44000e6 | 0.163299 | ||||||||
\(601\) | −7.67922e6 | −0.867224 | −0.433612 | − | 0.901100i | \(-0.642761\pi\) | ||||
−0.433612 | + | 0.901100i | \(0.642761\pi\) | |||||||
\(602\) | 8.90293e6 | 1.00125 | ||||||||
\(603\) | −1.19264e6 | −0.133573 | ||||||||
\(604\) | 8.87693e6 | 0.990080 | ||||||||
\(605\) | −3.57065e6 | −0.396606 | ||||||||
\(606\) | −4.42426e6 | −0.489394 | ||||||||
\(607\) | 2.95861e6 | 0.325924 | 0.162962 | − | 0.986632i | \(-0.447895\pi\) | ||||
0.162962 | + | 0.986632i | \(0.447895\pi\) | |||||||
\(608\) | −951296. | −0.104365 | ||||||||
\(609\) | −7.90164e6 | −0.863324 | ||||||||
\(610\) | 1.96880e6 | 0.214228 | ||||||||
\(611\) | 9.54731e6 | 1.03461 | ||||||||
\(612\) | 374544. | 0.0404226 | ||||||||
\(613\) | −1.12745e7 | −1.21185 | −0.605924 | − | 0.795523i | \(-0.707196\pi\) | ||||
−0.605924 | + | 0.795523i | \(0.707196\pi\) | |||||||
\(614\) | 7.76760e6 | 0.831507 | ||||||||
\(615\) | −2.00498e6 | −0.213757 | ||||||||
\(616\) | −1.62432e6 | −0.172472 | ||||||||
\(617\) | 1.63830e7 | 1.73252 | 0.866262 | − | 0.499589i | \(-0.166516\pi\) | ||||
0.866262 | + | 0.499589i | \(0.166516\pi\) | |||||||
\(618\) | −2.39980e6 | −0.252757 | ||||||||
\(619\) | 3.35390e6 | 0.351823 | 0.175911 | − | 0.984406i | \(-0.443713\pi\) | ||||
0.175911 | + | 0.984406i | \(0.443713\pi\) | |||||||
\(620\) | −2.19600e6 | −0.229432 | ||||||||
\(621\) | 1.24003e6 | 0.129034 | ||||||||
\(622\) | 2.95747e6 | 0.306510 | ||||||||
\(623\) | 2.18997e7 | 2.26058 | ||||||||
\(624\) | 2.56435e6 | 0.263643 | ||||||||
\(625\) | 4.29688e6 | 0.440000 | ||||||||
\(626\) | −8.42782e6 | −0.859567 | ||||||||
\(627\) | 1.12874e6 | 0.114663 | ||||||||
\(628\) | −6.45768e6 | −0.653397 | ||||||||
\(629\) | 3.12351e6 | 0.314787 | ||||||||
\(630\) | −1.52280e6 | −0.152859 | ||||||||
\(631\) | 1.51263e7 | 1.51237 | 0.756185 | − | 0.654358i | \(-0.227061\pi\) | ||||
0.756185 | + | 0.654358i | \(0.227061\pi\) | |||||||
\(632\) | 4.97344e6 | 0.495295 | ||||||||
\(633\) | 1.11962e6 | 0.111061 | ||||||||
\(634\) | 1.08447e7 | 1.07151 | ||||||||
\(635\) | −6.40292e6 | −0.630150 | ||||||||
\(636\) | −5.12726e6 | −0.502624 | ||||||||
\(637\) | −2.06317e7 | −2.01459 | ||||||||
\(638\) | −2.52180e6 | −0.245278 | ||||||||
\(639\) | 3.92008e6 | 0.379789 | ||||||||
\(640\) | 409600. | 0.0395285 | ||||||||
\(641\) | −1.24739e7 | −1.19910 | −0.599551 | − | 0.800336i | \(-0.704654\pi\) | ||||
−0.599551 | + | 0.800336i | \(0.704654\pi\) | |||||||
\(642\) | 5.84226e6 | 0.559427 | ||||||||
\(643\) | −1.08684e7 | −1.03667 | −0.518334 | − | 0.855178i | \(-0.673448\pi\) | ||||
−0.518334 | + | 0.855178i | \(0.673448\pi\) | |||||||
\(644\) | 5.11661e6 | 0.486147 | ||||||||
\(645\) | 2.66378e6 | 0.252115 | ||||||||
\(646\) | −1.07392e6 | −0.101249 | ||||||||
\(647\) | 3.37275e6 | 0.316755 | 0.158377 | − | 0.987379i | \(-0.449374\pi\) | ||||
0.158377 | + | 0.987379i | \(0.449374\pi\) | |||||||
\(648\) | 419904. | 0.0392837 | ||||||||
\(649\) | 828630. | 0.0772234 | ||||||||
\(650\) | 1.11300e7 | 1.03327 | ||||||||
\(651\) | −9.28908e6 | −0.859054 | ||||||||
\(652\) | −7.14384e6 | −0.658132 | ||||||||
\(653\) | 1.77220e7 | 1.62641 | 0.813203 | − | 0.581981i | \(-0.197722\pi\) | ||||
0.813203 | + | 0.581981i | \(0.197722\pi\) | |||||||
\(654\) | −4.51800e6 | −0.413049 | ||||||||
\(655\) | −7.20838e6 | −0.656499 | ||||||||
\(656\) | 2.28122e6 | 0.206970 | ||||||||
\(657\) | 836082. | 0.0755676 | ||||||||
\(658\) | 6.45066e6 | 0.580817 | ||||||||
\(659\) | 1.27338e7 | 1.14221 | 0.571103 | − | 0.820878i | \(-0.306516\pi\) | ||||
0.571103 | + | 0.820878i | \(0.306516\pi\) | |||||||
\(660\) | −486000. | −0.0434287 | ||||||||
\(661\) | −1.72968e7 | −1.53980 | −0.769898 | − | 0.638167i | \(-0.779693\pi\) | ||||
−0.769898 | + | 0.638167i | \(0.779693\pi\) | |||||||
\(662\) | −95860.0 | −0.00850144 | ||||||||
\(663\) | 2.89491e6 | 0.255771 | ||||||||
\(664\) | −6.92851e6 | −0.609845 | ||||||||
\(665\) | 4.36630e6 | 0.382877 | ||||||||
\(666\) | 3.50179e6 | 0.305918 | ||||||||
\(667\) | 7.94367e6 | 0.691364 | ||||||||
\(668\) | 3.11077e6 | 0.269728 | ||||||||
\(669\) | 1.08417e7 | 0.936552 | ||||||||
\(670\) | −1.47240e6 | −0.126718 | ||||||||
\(671\) | 2.65788e6 | 0.227892 | ||||||||
\(672\) | 1.73261e6 | 0.148005 | ||||||||
\(673\) | −1.34307e7 | −1.14303 | −0.571517 | − | 0.820590i | \(-0.693645\pi\) | ||||
−0.571517 | + | 0.820590i | \(0.693645\pi\) | |||||||
\(674\) | −1.18228e7 | −1.00247 | ||||||||
\(675\) | 1.82250e6 | 0.153960 | ||||||||
\(676\) | 1.38796e7 | 1.16818 | ||||||||
\(677\) | −1.75486e7 | −1.47153 | −0.735767 | − | 0.677235i | \(-0.763178\pi\) | ||||
−0.735767 | + | 0.677235i | \(0.763178\pi\) | |||||||
\(678\) | −2.77304e6 | −0.231677 | ||||||||
\(679\) | −1.97851e6 | −0.164689 | ||||||||
\(680\) | 462400. | 0.0383482 | ||||||||
\(681\) | −7.37547e6 | −0.609428 | ||||||||
\(682\) | −2.96460e6 | −0.244065 | ||||||||
\(683\) | −1.61614e7 | −1.32565 | −0.662824 | − | 0.748775i | \(-0.730642\pi\) | ||||
−0.662824 | + | 0.748775i | \(0.730642\pi\) | |||||||
\(684\) | −1.20398e6 | −0.0983967 | ||||||||
\(685\) | −3.60915e6 | −0.293886 | ||||||||
\(686\) | −1.30096e6 | −0.105549 | ||||||||
\(687\) | −3.29809e6 | −0.266606 | ||||||||
\(688\) | −3.03078e6 | −0.244109 | ||||||||
\(689\) | −3.96295e7 | −3.18032 | ||||||||
\(690\) | 1.53090e6 | 0.122412 | ||||||||
\(691\) | 1.13905e7 | 0.907498 | 0.453749 | − | 0.891129i | \(-0.350086\pi\) | ||||
0.453749 | + | 0.891129i | \(0.350086\pi\) | |||||||
\(692\) | 1.28584e6 | 0.102076 | ||||||||
\(693\) | −2.05578e6 | −0.162609 | ||||||||
\(694\) | −7.96165e6 | −0.627486 | ||||||||
\(695\) | −4.14205e6 | −0.325277 | ||||||||
\(696\) | 2.68992e6 | 0.210483 | ||||||||
\(697\) | 2.57528e6 | 0.200790 | ||||||||
\(698\) | 1.90232e6 | 0.147790 | ||||||||
\(699\) | −6.85814e6 | −0.530900 | ||||||||
\(700\) | 7.52000e6 | 0.580060 | ||||||||
\(701\) | −2.22903e7 | −1.71325 | −0.856626 | − | 0.515938i | \(-0.827443\pi\) | ||||
−0.856626 | + | 0.515938i | \(0.827443\pi\) | |||||||
\(702\) | 3.24551e6 | 0.248565 | ||||||||
\(703\) | −1.00406e7 | −0.766254 | ||||||||
\(704\) | 552960. | 0.0420496 | ||||||||
\(705\) | 1.93005e6 | 0.146250 | ||||||||
\(706\) | −7.92351e6 | −0.598282 | ||||||||
\(707\) | −2.31044e7 | −1.73839 | ||||||||
\(708\) | −883872. | −0.0662684 | ||||||||
\(709\) | 1.24843e7 | 0.932715 | 0.466357 | − | 0.884596i | \(-0.345566\pi\) | ||||
0.466357 | + | 0.884596i | \(0.345566\pi\) | |||||||
\(710\) | 4.83960e6 | 0.360299 | ||||||||
\(711\) | 6.29451e6 | 0.466969 | ||||||||
\(712\) | −7.45523e6 | −0.551139 | ||||||||
\(713\) | 9.33849e6 | 0.687944 | ||||||||
\(714\) | 1.95595e6 | 0.143586 | ||||||||
\(715\) | −3.75638e6 | −0.274792 | ||||||||
\(716\) | 628128. | 0.0457895 | ||||||||
\(717\) | 2.50877e6 | 0.182248 | ||||||||
\(718\) | −1.28311e7 | −0.928867 | ||||||||
\(719\) | −1.44584e7 | −1.04303 | −0.521515 | − | 0.853242i | \(-0.674633\pi\) | ||||
−0.521515 | + | 0.853242i | \(0.674633\pi\) | |||||||
\(720\) | 518400. | 0.0372678 | ||||||||
\(721\) | −1.25323e7 | −0.897825 | ||||||||
\(722\) | −6.45223e6 | −0.460646 | ||||||||
\(723\) | −3.41928e6 | −0.243270 | ||||||||
\(724\) | −3.61059e6 | −0.255995 | ||||||||
\(725\) | 1.16750e7 | 0.824920 | ||||||||
\(726\) | 5.14174e6 | 0.362050 | ||||||||
\(727\) | 8.35149e6 | 0.586041 | 0.293020 | − | 0.956106i | \(-0.405340\pi\) | ||||
0.293020 | + | 0.956106i | \(0.405340\pi\) | |||||||
\(728\) | 1.33916e7 | 0.936493 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 1.03220e6 | 0.0716897 | ||||||||
\(731\) | −3.42147e6 | −0.236821 | ||||||||
\(732\) | −2.83507e6 | −0.195563 | ||||||||
\(733\) | 1.58985e7 | 1.09294 | 0.546470 | − | 0.837479i | \(-0.315971\pi\) | ||||
0.546470 | + | 0.837479i | \(0.315971\pi\) | |||||||
\(734\) | 1.96792e6 | 0.134824 | ||||||||
\(735\) | −4.17082e6 | −0.284776 | ||||||||
\(736\) | −1.74182e6 | −0.118525 | ||||||||
\(737\) | −1.98774e6 | −0.134800 | ||||||||
\(738\) | 2.88716e6 | 0.195133 | ||||||||
\(739\) | −109329. | −0.00736418 | −0.00368209 | − | 0.999993i | \(-0.501172\pi\) | ||||
−0.00368209 | + | 0.999993i | \(0.501172\pi\) | |||||||
\(740\) | 4.32320e6 | 0.290219 | ||||||||
\(741\) | −9.30579e6 | −0.622598 | ||||||||
\(742\) | −2.67757e7 | −1.78538 | ||||||||
\(743\) | 9.80891e6 | 0.651852 | 0.325926 | − | 0.945395i | \(-0.394324\pi\) | ||||
0.325926 | + | 0.945395i | \(0.394324\pi\) | |||||||
\(744\) | 3.16224e6 | 0.209441 | ||||||||
\(745\) | −6.90765e6 | −0.455974 | ||||||||
\(746\) | 7.24823e6 | 0.476854 | ||||||||
\(747\) | −8.76890e6 | −0.574968 | ||||||||
\(748\) | 624240. | 0.0407941 | ||||||||
\(749\) | 3.05096e7 | 1.98715 | ||||||||
\(750\) | 5.06250e6 | 0.328634 | ||||||||
\(751\) | 1.74987e7 | 1.13216 | 0.566078 | − | 0.824352i | \(-0.308460\pi\) | ||||
0.566078 | + | 0.824352i | \(0.308460\pi\) | |||||||
\(752\) | −2.19597e6 | −0.141606 | ||||||||
\(753\) | −8.78915e6 | −0.564884 | ||||||||
\(754\) | 2.07908e7 | 1.33181 | ||||||||
\(755\) | 1.38702e7 | 0.885555 | ||||||||
\(756\) | 2.19283e6 | 0.139541 | ||||||||
\(757\) | 1.67029e7 | 1.05938 | 0.529691 | − | 0.848191i | \(-0.322308\pi\) | ||||
0.529691 | + | 0.848191i | \(0.322308\pi\) | |||||||
\(758\) | 1.84556e7 | 1.16669 | ||||||||
\(759\) | 2.06672e6 | 0.130220 | ||||||||
\(760\) | −1.48640e6 | −0.0933473 | ||||||||
\(761\) | −2.24151e6 | −0.140307 | −0.0701536 | − | 0.997536i | \(-0.522349\pi\) | ||||
−0.0701536 | + | 0.997536i | \(0.522349\pi\) | |||||||
\(762\) | 9.22021e6 | 0.575246 | ||||||||
\(763\) | −2.35940e7 | −1.46720 | ||||||||
\(764\) | −2.61603e6 | −0.162147 | ||||||||
\(765\) | 585225. | 0.0361551 | ||||||||
\(766\) | −1.37947e7 | −0.849454 | ||||||||
\(767\) | −6.83159e6 | −0.419308 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | −1.31165e7 | −0.799837 | −0.399919 | − | 0.916551i | \(-0.630962\pi\) | ||||
−0.399919 | + | 0.916551i | \(0.630962\pi\) | |||||||
\(770\) | −2.53800e6 | −0.154264 | ||||||||
\(771\) | −8.16577e6 | −0.494722 | ||||||||
\(772\) | −7.19530e6 | −0.434516 | ||||||||
\(773\) | −2.82980e7 | −1.70336 | −0.851680 | − | 0.524063i | \(-0.824416\pi\) | ||||
−0.851680 | + | 0.524063i | \(0.824416\pi\) | |||||||
\(774\) | −3.83584e6 | −0.230148 | ||||||||
\(775\) | 1.37250e7 | 0.820839 | ||||||||
\(776\) | 673536. | 0.0401519 | ||||||||
\(777\) | 1.82871e7 | 1.08666 | ||||||||
\(778\) | −2.06032e6 | −0.122035 | ||||||||
\(779\) | −8.27832e6 | −0.488763 | ||||||||
\(780\) | 4.00680e6 | 0.235809 | ||||||||
\(781\) | 6.53346e6 | 0.383280 | ||||||||
\(782\) | −1.96636e6 | −0.114986 | ||||||||
\(783\) | 3.40443e6 | 0.198445 | ||||||||
\(784\) | 4.74547e6 | 0.275733 | ||||||||
\(785\) | −1.00901e7 | −0.584416 | ||||||||
\(786\) | 1.03801e7 | 0.599299 | ||||||||
\(787\) | −2.31191e6 | −0.133056 | −0.0665279 | − | 0.997785i | \(-0.521192\pi\) | ||||
−0.0665279 | + | 0.997785i | \(0.521192\pi\) | |||||||
\(788\) | 7.23573e6 | 0.415113 | ||||||||
\(789\) | 1.43428e7 | 0.820243 | ||||||||
\(790\) | 7.77100e6 | 0.443006 | ||||||||
\(791\) | −1.44815e7 | −0.822945 | ||||||||
\(792\) | 699840. | 0.0396448 | ||||||||
\(793\) | −2.19127e7 | −1.23741 | ||||||||
\(794\) | −1.36988e7 | −0.771136 | ||||||||
\(795\) | −8.01135e6 | −0.449560 | ||||||||
\(796\) | −595648. | −0.0333202 | ||||||||
\(797\) | −4.14006e6 | −0.230867 | −0.115433 | − | 0.993315i | \(-0.536826\pi\) | ||||
−0.115433 | + | 0.993315i | \(0.536826\pi\) | |||||||
\(798\) | −6.28747e6 | −0.349517 | ||||||||
\(799\) | −2.47904e6 | −0.137378 | ||||||||
\(800\) | −2.56000e6 | −0.141421 | ||||||||
\(801\) | −9.43553e6 | −0.519619 | ||||||||
\(802\) | 9.86603e6 | 0.541635 | ||||||||
\(803\) | 1.39347e6 | 0.0762621 | ||||||||
\(804\) | 2.12026e6 | 0.115677 | ||||||||
\(805\) | 7.99470e6 | 0.434823 | ||||||||
\(806\) | 2.44415e7 | 1.32523 | ||||||||
\(807\) | −1.12383e7 | −0.607458 | ||||||||
\(808\) | 7.86534e6 | 0.423828 | ||||||||
\(809\) | 3.97495e6 | 0.213531 | 0.106765 | − | 0.994284i | \(-0.465951\pi\) | ||||
0.106765 | + | 0.994284i | \(0.465951\pi\) | |||||||
\(810\) | 656100. | 0.0351364 | ||||||||
\(811\) | 8.40205e6 | 0.448573 | 0.224286 | − | 0.974523i | \(-0.427995\pi\) | ||||
0.224286 | + | 0.974523i | \(0.427995\pi\) | |||||||
\(812\) | 1.40474e7 | 0.747661 | ||||||||
\(813\) | −562131. | −0.0298271 | ||||||||
\(814\) | 5.83632e6 | 0.308729 | ||||||||
\(815\) | −1.11622e7 | −0.588651 | ||||||||
\(816\) | −665856. | −0.0350070 | ||||||||
\(817\) | 1.09984e7 | 0.576469 | ||||||||
\(818\) | −2.16043e7 | −1.12890 | ||||||||
\(819\) | 1.69488e7 | 0.882934 | ||||||||
\(820\) | 3.56440e6 | 0.185119 | ||||||||
\(821\) | −1.91180e7 | −0.989886 | −0.494943 | − | 0.868925i | \(-0.664811\pi\) | ||||
−0.494943 | + | 0.868925i | \(0.664811\pi\) | |||||||
\(822\) | 5.19718e6 | 0.268280 | ||||||||
\(823\) | −2.00766e7 | −1.03322 | −0.516608 | − | 0.856222i | \(-0.672806\pi\) | ||||
−0.516608 | + | 0.856222i | \(0.672806\pi\) | |||||||
\(824\) | 4.26630e6 | 0.218894 | ||||||||
\(825\) | 3.03750e6 | 0.155375 | ||||||||
\(826\) | −4.61578e6 | −0.235394 | ||||||||
\(827\) | −787327. | −0.0400305 | −0.0200153 | − | 0.999800i | \(-0.506371\pi\) | ||||
−0.0200153 | + | 0.999800i | \(0.506371\pi\) | |||||||
\(828\) | −2.20450e6 | −0.111746 | ||||||||
\(829\) | 2.59446e7 | 1.31118 | 0.655588 | − | 0.755119i | \(-0.272421\pi\) | ||||
0.655588 | + | 0.755119i | \(0.272421\pi\) | |||||||
\(830\) | −1.08258e7 | −0.545462 | ||||||||
\(831\) | −1.03171e7 | −0.518270 | ||||||||
\(832\) | −4.55885e6 | −0.228321 | ||||||||
\(833\) | 5.35719e6 | 0.267501 | ||||||||
\(834\) | 5.96455e6 | 0.296936 | ||||||||
\(835\) | 4.86058e6 | 0.241252 | ||||||||
\(836\) | −2.00664e6 | −0.0993010 | ||||||||
\(837\) | 4.00221e6 | 0.197463 | ||||||||
\(838\) | 4.67074e6 | 0.229760 | ||||||||
\(839\) | −1.64947e7 | −0.808984 | −0.404492 | − | 0.914541i | \(-0.632552\pi\) | ||||
−0.404492 | + | 0.914541i | \(0.632552\pi\) | |||||||
\(840\) | 2.70720e6 | 0.132380 | ||||||||
\(841\) | 1.29775e6 | 0.0632705 | ||||||||
\(842\) | −1.87303e6 | −0.0910467 | ||||||||
\(843\) | 1.93077e7 | 0.935754 | ||||||||
\(844\) | −1.99043e6 | −0.0961814 | ||||||||
\(845\) | 2.16869e7 | 1.04485 | ||||||||
\(846\) | −2.77927e6 | −0.133507 | ||||||||
\(847\) | 2.68513e7 | 1.28605 | ||||||||
\(848\) | 9.11514e6 | 0.435285 | ||||||||
\(849\) | 1.54817e7 | 0.737138 | ||||||||
\(850\) | −2.89000e6 | −0.137199 | ||||||||
\(851\) | −1.83844e7 | −0.870213 | ||||||||
\(852\) | −6.96902e6 | −0.328907 | ||||||||
\(853\) | −4.05828e6 | −0.190972 | −0.0954859 | − | 0.995431i | \(-0.530440\pi\) | ||||
−0.0954859 | + | 0.995431i | \(0.530440\pi\) | |||||||
\(854\) | −1.48054e7 | −0.694664 | ||||||||
\(855\) | −1.88122e6 | −0.0880087 | ||||||||
\(856\) | −1.03862e7 | −0.484478 | ||||||||
\(857\) | −1.93630e7 | −0.900575 | −0.450288 | − | 0.892884i | \(-0.648679\pi\) | ||||
−0.450288 | + | 0.892884i | \(0.648679\pi\) | |||||||
\(858\) | 5.40918e6 | 0.250849 | ||||||||
\(859\) | 1.83312e7 | 0.847632 | 0.423816 | − | 0.905748i | \(-0.360690\pi\) | ||||
0.423816 | + | 0.905748i | \(0.360690\pi\) | |||||||
\(860\) | −4.73560e6 | −0.218338 | ||||||||
\(861\) | 1.50774e7 | 0.693137 | ||||||||
\(862\) | −1.54698e7 | −0.709113 | ||||||||
\(863\) | −3.14626e7 | −1.43803 | −0.719015 | − | 0.694994i | \(-0.755407\pi\) | ||||
−0.719015 | + | 0.694994i | \(0.755407\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | 2.00912e6 | 0.0912991 | ||||||||
\(866\) | −1.73384e7 | −0.785623 | ||||||||
\(867\) | −751689. | −0.0339618 | ||||||||
\(868\) | 1.65139e7 | 0.743962 | ||||||||
\(869\) | 1.04908e7 | 0.471261 | ||||||||
\(870\) | 4.20300e6 | 0.188261 | ||||||||
\(871\) | 1.63878e7 | 0.731940 | ||||||||
\(872\) | 8.03200e6 | 0.357711 | ||||||||
\(873\) | 852444. | 0.0378556 | ||||||||
\(874\) | 6.32092e6 | 0.279899 | ||||||||
\(875\) | 2.64375e7 | 1.16735 | ||||||||
\(876\) | −1.48637e6 | −0.0654434 | ||||||||
\(877\) | −2.78956e7 | −1.22472 | −0.612360 | − | 0.790579i | \(-0.709780\pi\) | ||||
−0.612360 | + | 0.790579i | \(0.709780\pi\) | |||||||
\(878\) | −2.30563e7 | −1.00938 | ||||||||
\(879\) | 1.29090e7 | 0.563534 | ||||||||
\(880\) | 864000. | 0.0376103 | ||||||||
\(881\) | 3.96320e7 | 1.72031 | 0.860153 | − | 0.510036i | \(-0.170368\pi\) | ||||
0.860153 | + | 0.510036i | \(0.170368\pi\) | |||||||
\(882\) | 6.00599e6 | 0.259964 | ||||||||
\(883\) | 3.45310e7 | 1.49042 | 0.745208 | − | 0.666832i | \(-0.232350\pi\) | ||||
0.745208 | + | 0.666832i | \(0.232350\pi\) | |||||||
\(884\) | −5.14651e6 | −0.221504 | ||||||||
\(885\) | −1.38105e6 | −0.0592722 | ||||||||
\(886\) | 1.96560e7 | 0.841221 | ||||||||
\(887\) | −4.02361e7 | −1.71715 | −0.858573 | − | 0.512692i | \(-0.828648\pi\) | ||||
−0.858573 | + | 0.512692i | \(0.828648\pi\) | |||||||
\(888\) | −6.22541e6 | −0.264933 | ||||||||
\(889\) | 4.81500e7 | 2.04335 | ||||||||
\(890\) | −1.16488e7 | −0.492954 | ||||||||
\(891\) | 885735. | 0.0373774 | ||||||||
\(892\) | −1.92741e7 | −0.811078 | ||||||||
\(893\) | 7.96896e6 | 0.334405 | ||||||||
\(894\) | 9.94702e6 | 0.416245 | ||||||||
\(895\) | 981450. | 0.0409553 | ||||||||
\(896\) | −3.08019e6 | −0.128176 | ||||||||
\(897\) | −1.70389e7 | −0.707068 | ||||||||
\(898\) | 3.68290e6 | 0.152405 | ||||||||
\(899\) | 2.56383e7 | 1.05801 | ||||||||
\(900\) | −3.24000e6 | −0.133333 | ||||||||
\(901\) | 1.02901e7 | 0.422288 | ||||||||
\(902\) | 4.81194e6 | 0.196926 | ||||||||
\(903\) | −2.00316e7 | −0.817516 | ||||||||
\(904\) | 4.92986e6 | 0.200638 | ||||||||
\(905\) | −5.64155e6 | −0.228969 | ||||||||
\(906\) | −1.99731e7 | −0.808397 | ||||||||
\(907\) | −3.50673e6 | −0.141542 | −0.0707708 | − | 0.997493i | \(-0.522546\pi\) | ||||
−0.0707708 | + | 0.997493i | \(0.522546\pi\) | |||||||
\(908\) | 1.31120e7 | 0.527780 | ||||||||
\(909\) | 9.95458e6 | 0.399589 | ||||||||
\(910\) | 2.09244e7 | 0.837625 | ||||||||
\(911\) | 2.71634e7 | 1.08439 | 0.542197 | − | 0.840251i | \(-0.317593\pi\) | ||||
0.542197 | + | 0.840251i | \(0.317593\pi\) | |||||||
\(912\) | 2.14042e6 | 0.0852140 | ||||||||
\(913\) | −1.46148e7 | −0.580252 | ||||||||
\(914\) | −2.05982e6 | −0.0815575 | ||||||||
\(915\) | −4.42980e6 | −0.174917 | ||||||||
\(916\) | 5.86326e6 | 0.230888 | ||||||||
\(917\) | 5.42070e7 | 2.12879 | ||||||||
\(918\) | −842724. | −0.0330049 | ||||||||
\(919\) | 3.61774e7 | 1.41302 | 0.706510 | − | 0.707703i | \(-0.250269\pi\) | ||||
0.706510 | + | 0.707703i | \(0.250269\pi\) | |||||||
\(920\) | −2.72160e6 | −0.106012 | ||||||||
\(921\) | −1.74771e7 | −0.678923 | ||||||||
\(922\) | −2.44713e7 | −0.948047 | ||||||||
\(923\) | −5.38647e7 | −2.08114 | ||||||||
\(924\) | 3.65472e6 | 0.140823 | ||||||||
\(925\) | −2.70200e7 | −1.03832 | ||||||||
\(926\) | 3.14182e7 | 1.20408 | ||||||||
\(927\) | 5.39954e6 | 0.206375 | ||||||||
\(928\) | −4.78208e6 | −0.182283 | ||||||||
\(929\) | 5.76520e6 | 0.219167 | 0.109583 | − | 0.993978i | \(-0.465048\pi\) | ||||
0.109583 | + | 0.993978i | \(0.465048\pi\) | |||||||
\(930\) | 4.94100e6 | 0.187330 | ||||||||
\(931\) | −1.72209e7 | −0.651150 | ||||||||
\(932\) | 1.21922e7 | 0.459773 | ||||||||
\(933\) | −6.65431e6 | −0.250264 | ||||||||
\(934\) | −1.00294e7 | −0.376192 | ||||||||
\(935\) | 975375. | 0.0364874 | ||||||||
\(936\) | −5.76979e6 | −0.215264 | ||||||||
\(937\) | −1.41673e7 | −0.527155 | −0.263578 | − | 0.964638i | \(-0.584902\pi\) | ||||
−0.263578 | + | 0.964638i | \(0.584902\pi\) | |||||||
\(938\) | 1.10724e7 | 0.410900 | ||||||||
\(939\) | 1.89626e7 | 0.701833 | ||||||||
\(940\) | −3.43120e6 | −0.126656 | ||||||||
\(941\) | −3.59561e7 | −1.32373 | −0.661864 | − | 0.749624i | \(-0.730234\pi\) | ||||
−0.661864 | + | 0.749624i | \(0.730234\pi\) | |||||||
\(942\) | 1.45298e7 | 0.533497 | ||||||||
\(943\) | −1.51576e7 | −0.555075 | ||||||||
\(944\) | 1.57133e6 | 0.0573901 | ||||||||
\(945\) | 3.42630e6 | 0.124809 | ||||||||
\(946\) | −6.39306e6 | −0.232263 | ||||||||
\(947\) | −1.70356e7 | −0.617280 | −0.308640 | − | 0.951179i | \(-0.599874\pi\) | ||||
−0.308640 | + | 0.951179i | \(0.599874\pi\) | |||||||
\(948\) | −1.11902e7 | −0.404407 | ||||||||
\(949\) | −1.14884e7 | −0.414089 | ||||||||
\(950\) | 9.29000e6 | 0.333969 | ||||||||
\(951\) | −2.44006e7 | −0.874883 | ||||||||
\(952\) | −3.47725e6 | −0.124349 | ||||||||
\(953\) | −1.91214e7 | −0.682003 | −0.341002 | − | 0.940063i | \(-0.610766\pi\) | ||||
−0.341002 | + | 0.940063i | \(0.610766\pi\) | |||||||
\(954\) | 1.15363e7 | 0.410390 | ||||||||
\(955\) | −4.08755e6 | −0.145029 | ||||||||
\(956\) | −4.46003e6 | −0.157831 | ||||||||
\(957\) | 5.67405e6 | 0.200269 | ||||||||
\(958\) | −1.02788e6 | −0.0361849 | ||||||||
\(959\) | 2.71408e7 | 0.952963 | ||||||||
\(960\) | −921600. | −0.0322749 | ||||||||
\(961\) | 1.51095e6 | 0.0527766 | ||||||||
\(962\) | −4.81172e7 | −1.67634 | ||||||||
\(963\) | −1.31451e7 | −0.456770 | ||||||||
\(964\) | 6.07872e6 | 0.210678 | ||||||||
\(965\) | −1.12426e7 | −0.388643 | ||||||||
\(966\) | −1.15124e7 | −0.396937 | ||||||||
\(967\) | 5.27790e7 | 1.81508 | 0.907538 | − | 0.419969i | \(-0.137959\pi\) | ||||
0.907538 | + | 0.419969i | \(0.137959\pi\) | |||||||
\(968\) | −9.14086e6 | −0.313544 | ||||||||
\(969\) | 2.41633e6 | 0.0826697 | ||||||||
\(970\) | 1.05240e6 | 0.0359130 | ||||||||
\(971\) | 4.11049e7 | 1.39909 | 0.699546 | − | 0.714588i | \(-0.253386\pi\) | ||||
0.699546 | + | 0.714588i | \(0.253386\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | 3.11482e7 | 1.05475 | ||||||||
\(974\) | 5.90356e6 | 0.199396 | ||||||||
\(975\) | −2.50425e7 | −0.843657 | ||||||||
\(976\) | 5.04013e6 | 0.169362 | ||||||||
\(977\) | −6.94601e6 | −0.232809 | −0.116404 | − | 0.993202i | \(-0.537137\pi\) | ||||
−0.116404 | + | 0.993202i | \(0.537137\pi\) | |||||||
\(978\) | 1.60736e7 | 0.537362 | ||||||||
\(979\) | −1.57259e7 | −0.524395 | ||||||||
\(980\) | 7.41480e6 | 0.246623 | ||||||||
\(981\) | 1.01655e7 | 0.337253 | ||||||||
\(982\) | 7.54662e6 | 0.249732 | ||||||||
\(983\) | −3.57573e7 | −1.18027 | −0.590134 | − | 0.807306i | \(-0.700925\pi\) | ||||
−0.590134 | + | 0.807306i | \(0.700925\pi\) | |||||||
\(984\) | −5.13274e6 | −0.168990 | ||||||||
\(985\) | 1.13058e7 | 0.371289 | ||||||||
\(986\) | −5.39852e6 | −0.176841 | ||||||||
\(987\) | −1.45140e7 | −0.474235 | ||||||||
\(988\) | 1.65436e7 | 0.539186 | ||||||||
\(989\) | 2.01381e7 | 0.654679 | ||||||||
\(990\) | 1.09350e6 | 0.0354594 | ||||||||
\(991\) | 4.09547e7 | 1.32471 | 0.662353 | − | 0.749192i | \(-0.269558\pi\) | ||||
0.662353 | + | 0.749192i | \(0.269558\pi\) | |||||||
\(992\) | −5.62176e6 | −0.181382 | ||||||||
\(993\) | 215685. | 0.00694140 | ||||||||
\(994\) | −3.63938e7 | −1.16832 | ||||||||
\(995\) | −930700. | −0.0298025 | ||||||||
\(996\) | 1.55892e7 | 0.497937 | ||||||||
\(997\) | 2.10064e7 | 0.669288 | 0.334644 | − | 0.942345i | \(-0.391384\pi\) | ||||
0.334644 | + | 0.942345i | \(0.391384\pi\) | |||||||
\(998\) | −4.02192e7 | −1.27822 | ||||||||
\(999\) | −7.87903e6 | −0.249781 |
(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 | 102.6.a.d.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 306.6.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 816.6.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
102.6.a.d.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
306.6.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
816.6.a.d.1.1 | 1 | 4.3 | odd | 2 |