Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,6,Mod(1,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.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: | \(91.4187772934\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2696x^{2} + 13833x + 894635 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(44.4607\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.1 |
$q$-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 | ||||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | 53.8996 | 0.415758 | 0.207879 | − | 0.978155i | \(-0.433344\pi\) | ||||
0.207879 | + | 0.978155i | \(0.433344\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 100.000 | 0.316228 | ||||||||
\(11\) | 137.824 | 0.343434 | 0.171717 | − | 0.985146i | \(-0.445069\pi\) | ||||
0.171717 | + | 0.985146i | \(0.445069\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | 121.743 | 0.199795 | 0.0998974 | − | 0.994998i | \(-0.468149\pi\) | ||||
0.0998974 | + | 0.994998i | \(0.468149\pi\) | |||||||
\(14\) | −215.598 | −0.293985 | ||||||||
\(15\) | 225.000 | 0.258199 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1682.47 | −1.41197 | −0.705985 | − | 0.708227i | \(-0.749495\pi\) | ||||
−0.705985 | + | 0.708227i | \(0.749495\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | −400.000 | −0.223607 | ||||||||
\(21\) | −485.096 | −0.240038 | ||||||||
\(22\) | −551.295 | −0.242844 | ||||||||
\(23\) | 2915.75 | 1.14929 | 0.574647 | − | 0.818401i | \(-0.305139\pi\) | ||||
0.574647 | + | 0.818401i | \(0.305139\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −486.970 | −0.141276 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 862.394 | 0.207879 | ||||||||
\(29\) | −7935.40 | −1.75216 | −0.876081 | − | 0.482165i | \(-0.839851\pi\) | ||||
−0.876081 | + | 0.482165i | \(0.839851\pi\) | |||||||
\(30\) | −900.000 | −0.182574 | ||||||||
\(31\) | 4745.53 | 0.886912 | 0.443456 | − | 0.896296i | \(-0.353752\pi\) | ||||
0.443456 | + | 0.896296i | \(0.353752\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −1240.41 | −0.198281 | ||||||||
\(34\) | 6729.89 | 0.998414 | ||||||||
\(35\) | −1347.49 | −0.185933 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −7300.69 | −0.876718 | −0.438359 | − | 0.898800i | \(-0.644440\pi\) | ||||
−0.438359 | + | 0.898800i | \(0.644440\pi\) | |||||||
\(38\) | 1444.00 | 0.162221 | ||||||||
\(39\) | −1095.68 | −0.115352 | ||||||||
\(40\) | 1600.00 | 0.158114 | ||||||||
\(41\) | 3813.41 | 0.354286 | 0.177143 | − | 0.984185i | \(-0.443315\pi\) | ||||
0.177143 | + | 0.984185i | \(0.443315\pi\) | |||||||
\(42\) | 1940.39 | 0.169732 | ||||||||
\(43\) | 19360.9 | 1.59681 | 0.798406 | − | 0.602119i | \(-0.205677\pi\) | ||||
0.798406 | + | 0.602119i | \(0.205677\pi\) | |||||||
\(44\) | 2205.18 | 0.171717 | ||||||||
\(45\) | −2025.00 | −0.149071 | ||||||||
\(46\) | −11663.0 | −0.812674 | ||||||||
\(47\) | 28117.9 | 1.85668 | 0.928341 | − | 0.371729i | \(-0.121235\pi\) | ||||
0.928341 | + | 0.371729i | \(0.121235\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | −13901.8 | −0.827145 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | 15142.2 | 0.815201 | ||||||||
\(52\) | 1947.88 | 0.0998974 | ||||||||
\(53\) | −5284.18 | −0.258397 | −0.129199 | − | 0.991619i | \(-0.541240\pi\) | ||||
−0.129199 | + | 0.991619i | \(0.541240\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | −3445.60 | −0.153588 | ||||||||
\(56\) | −3449.57 | −0.146993 | ||||||||
\(57\) | 3249.00 | 0.132453 | ||||||||
\(58\) | 31741.6 | 1.23897 | ||||||||
\(59\) | −17547.2 | −0.656262 | −0.328131 | − | 0.944632i | \(-0.606419\pi\) | ||||
−0.328131 | + | 0.944632i | \(0.606419\pi\) | |||||||
\(60\) | 3600.00 | 0.129099 | ||||||||
\(61\) | 21622.1 | 0.744001 | 0.372000 | − | 0.928233i | \(-0.378672\pi\) | ||||
0.372000 | + | 0.928233i | \(0.378672\pi\) | |||||||
\(62\) | −18982.1 | −0.627142 | ||||||||
\(63\) | 4365.87 | 0.138586 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −3043.56 | −0.0893509 | ||||||||
\(66\) | 4961.66 | 0.140206 | ||||||||
\(67\) | −12374.8 | −0.336783 | −0.168392 | − | 0.985720i | \(-0.553857\pi\) | ||||
−0.168392 | + | 0.985720i | \(0.553857\pi\) | |||||||
\(68\) | −26919.6 | −0.705985 | ||||||||
\(69\) | −26241.8 | −0.663546 | ||||||||
\(70\) | 5389.96 | 0.131474 | ||||||||
\(71\) | −43271.2 | −1.01872 | −0.509358 | − | 0.860555i | \(-0.670117\pi\) | ||||
−0.509358 | + | 0.860555i | \(0.670117\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | 9339.19 | 0.205117 | 0.102559 | − | 0.994727i | \(-0.467297\pi\) | ||||
0.102559 | + | 0.994727i | \(0.467297\pi\) | |||||||
\(74\) | 29202.8 | 0.619933 | ||||||||
\(75\) | −5625.00 | −0.115470 | ||||||||
\(76\) | −5776.00 | −0.114708 | ||||||||
\(77\) | 7428.65 | 0.142785 | ||||||||
\(78\) | 4382.73 | 0.0815659 | ||||||||
\(79\) | 96543.7 | 1.74043 | 0.870214 | − | 0.492673i | \(-0.163980\pi\) | ||||
0.870214 | + | 0.492673i | \(0.163980\pi\) | |||||||
\(80\) | −6400.00 | −0.111803 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −15253.6 | −0.250518 | ||||||||
\(83\) | 25220.6 | 0.401846 | 0.200923 | − | 0.979607i | \(-0.435606\pi\) | ||||
0.200923 | + | 0.979607i | \(0.435606\pi\) | |||||||
\(84\) | −7761.54 | −0.120019 | ||||||||
\(85\) | 42061.8 | 0.631452 | ||||||||
\(86\) | −77443.5 | −1.12912 | ||||||||
\(87\) | 71418.6 | 1.01161 | ||||||||
\(88\) | −8820.73 | −0.121422 | ||||||||
\(89\) | 27191.0 | 0.363873 | 0.181936 | − | 0.983310i | \(-0.441763\pi\) | ||||
0.181936 | + | 0.983310i | \(0.441763\pi\) | |||||||
\(90\) | 8100.00 | 0.105409 | ||||||||
\(91\) | 6561.88 | 0.0830662 | ||||||||
\(92\) | 46652.1 | 0.574647 | ||||||||
\(93\) | −42709.8 | −0.512059 | ||||||||
\(94\) | −112471. | −1.31287 | ||||||||
\(95\) | 9025.00 | 0.102598 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | 119760. | 1.29235 | 0.646177 | − | 0.763187i | \(-0.276367\pi\) | ||||
0.646177 | + | 0.763187i | \(0.276367\pi\) | |||||||
\(98\) | 55607.3 | 0.584880 | ||||||||
\(99\) | 11163.7 | 0.114478 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | −46475.9 | −0.453340 | −0.226670 | − | 0.973972i | \(-0.572784\pi\) | ||||
−0.226670 | + | 0.973972i | \(0.572784\pi\) | |||||||
\(102\) | −60569.0 | −0.576434 | ||||||||
\(103\) | −141512. | −1.31432 | −0.657160 | − | 0.753751i | \(-0.728243\pi\) | ||||
−0.657160 | + | 0.753751i | \(0.728243\pi\) | |||||||
\(104\) | −7791.52 | −0.0706381 | ||||||||
\(105\) | 12127.4 | 0.107348 | ||||||||
\(106\) | 21136.7 | 0.182714 | ||||||||
\(107\) | 4716.62 | 0.0398264 | 0.0199132 | − | 0.999802i | \(-0.493661\pi\) | ||||
0.0199132 | + | 0.999802i | \(0.493661\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | −54152.0 | −0.436565 | −0.218282 | − | 0.975886i | \(-0.570045\pi\) | ||||
−0.218282 | + | 0.975886i | \(0.570045\pi\) | |||||||
\(110\) | 13782.4 | 0.108603 | ||||||||
\(111\) | 65706.2 | 0.506173 | ||||||||
\(112\) | 13798.3 | 0.103939 | ||||||||
\(113\) | 122125. | 0.899723 | 0.449861 | − | 0.893098i | \(-0.351473\pi\) | ||||
0.449861 | + | 0.893098i | \(0.351473\pi\) | |||||||
\(114\) | −12996.0 | −0.0936586 | ||||||||
\(115\) | −72893.9 | −0.513980 | ||||||||
\(116\) | −126966. | −0.876081 | ||||||||
\(117\) | 9861.15 | 0.0665983 | ||||||||
\(118\) | 70188.7 | 0.464047 | ||||||||
\(119\) | −90684.6 | −0.587038 | ||||||||
\(120\) | −14400.0 | −0.0912871 | ||||||||
\(121\) | −142056. | −0.882053 | ||||||||
\(122\) | −86488.4 | −0.526088 | ||||||||
\(123\) | −34320.7 | −0.204547 | ||||||||
\(124\) | 75928.5 | 0.443456 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | −17463.5 | −0.0979951 | ||||||||
\(127\) | 4664.23 | 0.0256608 | 0.0128304 | − | 0.999918i | \(-0.495916\pi\) | ||||
0.0128304 | + | 0.999918i | \(0.495916\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −174248. | −0.921920 | ||||||||
\(130\) | 12174.3 | 0.0631806 | ||||||||
\(131\) | −352988. | −1.79714 | −0.898570 | − | 0.438831i | \(-0.855393\pi\) | ||||
−0.898570 | + | 0.438831i | \(0.855393\pi\) | |||||||
\(132\) | −19846.6 | −0.0991407 | ||||||||
\(133\) | −19457.8 | −0.0953814 | ||||||||
\(134\) | 49499.1 | 0.238142 | ||||||||
\(135\) | 18225.0 | 0.0860663 | ||||||||
\(136\) | 107678. | 0.499207 | ||||||||
\(137\) | −352202. | −1.60321 | −0.801604 | − | 0.597855i | \(-0.796020\pi\) | ||||
−0.801604 | + | 0.597855i | \(0.796020\pi\) | |||||||
\(138\) | 104967. | 0.469198 | ||||||||
\(139\) | 274159. | 1.20355 | 0.601777 | − | 0.798664i | \(-0.294459\pi\) | ||||
0.601777 | + | 0.798664i | \(0.294459\pi\) | |||||||
\(140\) | −21559.8 | −0.0929663 | ||||||||
\(141\) | −253061. | −1.07196 | ||||||||
\(142\) | 173085. | 0.720341 | ||||||||
\(143\) | 16779.0 | 0.0686162 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 198385. | 0.783590 | ||||||||
\(146\) | −37356.8 | −0.145040 | ||||||||
\(147\) | 125116. | 0.477553 | ||||||||
\(148\) | −116811. | −0.438359 | ||||||||
\(149\) | 106435. | 0.392751 | 0.196375 | − | 0.980529i | \(-0.437083\pi\) | ||||
0.196375 | + | 0.980529i | \(0.437083\pi\) | |||||||
\(150\) | 22500.0 | 0.0816497 | ||||||||
\(151\) | 210268. | 0.750466 | 0.375233 | − | 0.926931i | \(-0.377563\pi\) | ||||
0.375233 | + | 0.926931i | \(0.377563\pi\) | |||||||
\(152\) | 23104.0 | 0.0811107 | ||||||||
\(153\) | −136280. | −0.470657 | ||||||||
\(154\) | −29714.6 | −0.100964 | ||||||||
\(155\) | −118638. | −0.396639 | ||||||||
\(156\) | −17530.9 | −0.0576758 | ||||||||
\(157\) | −80915.2 | −0.261988 | −0.130994 | − | 0.991383i | \(-0.541817\pi\) | ||||
−0.130994 | + | 0.991383i | \(0.541817\pi\) | |||||||
\(158\) | −386175. | −1.23067 | ||||||||
\(159\) | 47557.6 | 0.149186 | ||||||||
\(160\) | 25600.0 | 0.0790569 | ||||||||
\(161\) | 157158. | 0.477828 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −378773. | −1.11663 | −0.558315 | − | 0.829629i | \(-0.688552\pi\) | ||||
−0.558315 | + | 0.829629i | \(0.688552\pi\) | |||||||
\(164\) | 61014.5 | 0.177143 | ||||||||
\(165\) | 31010.4 | 0.0886742 | ||||||||
\(166\) | −100882. | −0.284148 | ||||||||
\(167\) | −505883. | −1.40365 | −0.701825 | − | 0.712349i | \(-0.747631\pi\) | ||||
−0.701825 | + | 0.712349i | \(0.747631\pi\) | |||||||
\(168\) | 31046.2 | 0.0848662 | ||||||||
\(169\) | −356472. | −0.960082 | ||||||||
\(170\) | −168247. | −0.446504 | ||||||||
\(171\) | −29241.0 | −0.0764719 | ||||||||
\(172\) | 309774. | 0.798406 | ||||||||
\(173\) | −430633. | −1.09394 | −0.546968 | − | 0.837153i | \(-0.684218\pi\) | ||||
−0.546968 | + | 0.837153i | \(0.684218\pi\) | |||||||
\(174\) | −285675. | −0.715317 | ||||||||
\(175\) | 33687.3 | 0.0831516 | ||||||||
\(176\) | 35282.9 | 0.0858584 | ||||||||
\(177\) | 157925. | 0.378893 | ||||||||
\(178\) | −108764. | −0.257297 | ||||||||
\(179\) | −212623. | −0.495996 | −0.247998 | − | 0.968761i | \(-0.579773\pi\) | ||||
−0.247998 | + | 0.968761i | \(0.579773\pi\) | |||||||
\(180\) | −32400.0 | −0.0745356 | ||||||||
\(181\) | −675316. | −1.53218 | −0.766091 | − | 0.642732i | \(-0.777801\pi\) | ||||
−0.766091 | + | 0.642732i | \(0.777801\pi\) | |||||||
\(182\) | −26247.5 | −0.0587367 | ||||||||
\(183\) | −194599. | −0.429549 | ||||||||
\(184\) | −186608. | −0.406337 | ||||||||
\(185\) | 182517. | 0.392080 | ||||||||
\(186\) | 170839. | 0.362080 | ||||||||
\(187\) | −231885. | −0.484918 | ||||||||
\(188\) | 449886. | 0.928341 | ||||||||
\(189\) | −39292.8 | −0.0800126 | ||||||||
\(190\) | −36100.0 | −0.0725476 | ||||||||
\(191\) | −499269. | −0.990264 | −0.495132 | − | 0.868818i | \(-0.664880\pi\) | ||||
−0.495132 | + | 0.868818i | \(0.664880\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | 196074. | 0.378903 | 0.189451 | − | 0.981890i | \(-0.439329\pi\) | ||||
0.189451 | + | 0.981890i | \(0.439329\pi\) | |||||||
\(194\) | −479039. | −0.913833 | ||||||||
\(195\) | 27392.1 | 0.0515868 | ||||||||
\(196\) | −222429. | −0.413573 | ||||||||
\(197\) | 370392. | 0.679980 | 0.339990 | − | 0.940429i | \(-0.389576\pi\) | ||||
0.339990 | + | 0.940429i | \(0.389576\pi\) | |||||||
\(198\) | −44654.9 | −0.0809481 | ||||||||
\(199\) | −618794. | −1.10768 | −0.553839 | − | 0.832624i | \(-0.686838\pi\) | ||||
−0.553839 | + | 0.832624i | \(0.686838\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | 111373. | 0.194442 | ||||||||
\(202\) | 185903. | 0.320560 | ||||||||
\(203\) | −427715. | −0.728475 | ||||||||
\(204\) | 242276. | 0.407601 | ||||||||
\(205\) | −95335.2 | −0.158441 | ||||||||
\(206\) | 566049. | 0.929365 | ||||||||
\(207\) | 236176. | 0.383098 | ||||||||
\(208\) | 31166.1 | 0.0499487 | ||||||||
\(209\) | −49754.4 | −0.0787891 | ||||||||
\(210\) | −48509.6 | −0.0759067 | ||||||||
\(211\) | −62599.0 | −0.0967968 | −0.0483984 | − | 0.998828i | \(-0.515412\pi\) | ||||
−0.0483984 | + | 0.998828i | \(0.515412\pi\) | |||||||
\(212\) | −84546.8 | −0.129199 | ||||||||
\(213\) | 389441. | 0.588156 | ||||||||
\(214\) | −18866.5 | −0.0281615 | ||||||||
\(215\) | −484022. | −0.714116 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | 255782. | 0.368741 | ||||||||
\(218\) | 216608. | 0.308698 | ||||||||
\(219\) | −84052.7 | −0.118424 | ||||||||
\(220\) | −55129.5 | −0.0767941 | ||||||||
\(221\) | −204828. | −0.282104 | ||||||||
\(222\) | −262825. | −0.357918 | ||||||||
\(223\) | 1.14948e6 | 1.54789 | 0.773946 | − | 0.633251i | \(-0.218280\pi\) | ||||
0.773946 | + | 0.633251i | \(0.218280\pi\) | |||||||
\(224\) | −55193.2 | −0.0734963 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | −488500. | −0.636200 | ||||||||
\(227\) | −558920. | −0.719921 | −0.359960 | − | 0.932968i | \(-0.617210\pi\) | ||||
−0.359960 | + | 0.932968i | \(0.617210\pi\) | |||||||
\(228\) | 51984.0 | 0.0662266 | ||||||||
\(229\) | −1.57296e6 | −1.98211 | −0.991057 | − | 0.133440i | \(-0.957398\pi\) | ||||
−0.991057 | + | 0.133440i | \(0.957398\pi\) | |||||||
\(230\) | 291575. | 0.363439 | ||||||||
\(231\) | −66857.9 | −0.0824371 | ||||||||
\(232\) | 507866. | 0.619483 | ||||||||
\(233\) | −383408. | −0.462670 | −0.231335 | − | 0.972874i | \(-0.574309\pi\) | ||||
−0.231335 | + | 0.972874i | \(0.574309\pi\) | |||||||
\(234\) | −39444.6 | −0.0470921 | ||||||||
\(235\) | −702947. | −0.830334 | ||||||||
\(236\) | −280755. | −0.328131 | ||||||||
\(237\) | −868893. | −1.00484 | ||||||||
\(238\) | 362738. | 0.415098 | ||||||||
\(239\) | −317773. | −0.359850 | −0.179925 | − | 0.983680i | \(-0.557586\pi\) | ||||
−0.179925 | + | 0.983680i | \(0.557586\pi\) | |||||||
\(240\) | 57600.0 | 0.0645497 | ||||||||
\(241\) | −1.30913e6 | −1.45191 | −0.725955 | − | 0.687742i | \(-0.758602\pi\) | ||||
−0.725955 | + | 0.687742i | \(0.758602\pi\) | |||||||
\(242\) | 568222. | 0.623706 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 345954. | 0.372000 | ||||||||
\(245\) | 347546. | 0.369911 | ||||||||
\(246\) | 137283. | 0.144637 | ||||||||
\(247\) | −43949.1 | −0.0458361 | ||||||||
\(248\) | −303714. | −0.313571 | ||||||||
\(249\) | −226985. | −0.232006 | ||||||||
\(250\) | 62500.0 | 0.0632456 | ||||||||
\(251\) | −584074. | −0.585172 | −0.292586 | − | 0.956239i | \(-0.594516\pi\) | ||||
−0.292586 | + | 0.956239i | \(0.594516\pi\) | |||||||
\(252\) | 69853.9 | 0.0692930 | ||||||||
\(253\) | 401861. | 0.394706 | ||||||||
\(254\) | −18656.9 | −0.0181450 | ||||||||
\(255\) | −378556. | −0.364569 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −538075. | −0.508171 | −0.254085 | − | 0.967182i | \(-0.581774\pi\) | ||||
−0.254085 | + | 0.967182i | \(0.581774\pi\) | |||||||
\(258\) | 696991. | 0.651896 | ||||||||
\(259\) | −393504. | −0.364502 | ||||||||
\(260\) | −48697.0 | −0.0446755 | ||||||||
\(261\) | −642768. | −0.584054 | ||||||||
\(262\) | 1.41195e6 | 1.27077 | ||||||||
\(263\) | 320542. | 0.285757 | 0.142878 | − | 0.989740i | \(-0.454364\pi\) | ||||
0.142878 | + | 0.989740i | \(0.454364\pi\) | |||||||
\(264\) | 79386.5 | 0.0701031 | ||||||||
\(265\) | 132104. | 0.115559 | ||||||||
\(266\) | 77831.0 | 0.0674448 | ||||||||
\(267\) | −244719. | −0.210082 | ||||||||
\(268\) | −197996. | −0.168392 | ||||||||
\(269\) | −786706. | −0.662875 | −0.331437 | − | 0.943477i | \(-0.607534\pi\) | ||||
−0.331437 | + | 0.943477i | \(0.607534\pi\) | |||||||
\(270\) | −72900.0 | −0.0608581 | ||||||||
\(271\) | 1.21805e6 | 1.00750 | 0.503748 | − | 0.863851i | \(-0.331954\pi\) | ||||
0.503748 | + | 0.863851i | \(0.331954\pi\) | |||||||
\(272\) | −430713. | −0.352993 | ||||||||
\(273\) | −59056.9 | −0.0479583 | ||||||||
\(274\) | 1.40881e6 | 1.13364 | ||||||||
\(275\) | 86139.9 | 0.0686867 | ||||||||
\(276\) | −419869. | −0.331773 | ||||||||
\(277\) | −673677. | −0.527537 | −0.263768 | − | 0.964586i | \(-0.584965\pi\) | ||||
−0.263768 | + | 0.964586i | \(0.584965\pi\) | |||||||
\(278\) | −1.09664e6 | −0.851042 | ||||||||
\(279\) | 384388. | 0.295637 | ||||||||
\(280\) | 86239.4 | 0.0657371 | ||||||||
\(281\) | 246097. | 0.185927 | 0.0929633 | − | 0.995670i | \(-0.470366\pi\) | ||||
0.0929633 | + | 0.995670i | \(0.470366\pi\) | |||||||
\(282\) | 1.01224e6 | 0.757988 | ||||||||
\(283\) | 2.46217e6 | 1.82748 | 0.913739 | − | 0.406301i | \(-0.133182\pi\) | ||||
0.913739 | + | 0.406301i | \(0.133182\pi\) | |||||||
\(284\) | −692340. | −0.509358 | ||||||||
\(285\) | −81225.0 | −0.0592349 | ||||||||
\(286\) | −67116.1 | −0.0485190 | ||||||||
\(287\) | 205541. | 0.147297 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | 1.41086e6 | 0.993660 | ||||||||
\(290\) | −793540. | −0.554082 | ||||||||
\(291\) | −1.07784e6 | −0.746141 | ||||||||
\(292\) | 149427. | 0.102559 | ||||||||
\(293\) | −1.50307e6 | −1.02285 | −0.511423 | − | 0.859329i | \(-0.670882\pi\) | ||||
−0.511423 | + | 0.859329i | \(0.670882\pi\) | |||||||
\(294\) | −500466. | −0.337681 | ||||||||
\(295\) | 438679. | 0.293489 | ||||||||
\(296\) | 467244. | 0.309967 | ||||||||
\(297\) | −100474. | −0.0660938 | ||||||||
\(298\) | −425738. | −0.277717 | ||||||||
\(299\) | 354971. | 0.229623 | ||||||||
\(300\) | −90000.0 | −0.0577350 | ||||||||
\(301\) | 1.04354e6 | 0.663887 | ||||||||
\(302\) | −841072. | −0.530660 | ||||||||
\(303\) | 418283. | 0.261736 | ||||||||
\(304\) | −92416.0 | −0.0573539 | ||||||||
\(305\) | −540552. | −0.332727 | ||||||||
\(306\) | 545121. | 0.332805 | ||||||||
\(307\) | −1.22912e6 | −0.744302 | −0.372151 | − | 0.928172i | \(-0.621380\pi\) | ||||
−0.372151 | + | 0.928172i | \(0.621380\pi\) | |||||||
\(308\) | 118858. | 0.0713926 | ||||||||
\(309\) | 1.27361e6 | 0.758823 | ||||||||
\(310\) | 474553. | 0.280466 | ||||||||
\(311\) | −2.22112e6 | −1.30218 | −0.651090 | − | 0.759001i | \(-0.725688\pi\) | ||||
−0.651090 | + | 0.759001i | \(0.725688\pi\) | |||||||
\(312\) | 70123.7 | 0.0407829 | ||||||||
\(313\) | 2.16477e6 | 1.24897 | 0.624485 | − | 0.781037i | \(-0.285309\pi\) | ||||
0.624485 | + | 0.781037i | \(0.285309\pi\) | |||||||
\(314\) | 323661. | 0.185253 | ||||||||
\(315\) | −109147. | −0.0619775 | ||||||||
\(316\) | 1.54470e6 | 0.870214 | ||||||||
\(317\) | 2.05697e6 | 1.14969 | 0.574844 | − | 0.818263i | \(-0.305063\pi\) | ||||
0.574844 | + | 0.818263i | \(0.305063\pi\) | |||||||
\(318\) | −190230. | −0.105490 | ||||||||
\(319\) | −1.09369e6 | −0.601751 | ||||||||
\(320\) | −102400. | −0.0559017 | ||||||||
\(321\) | −42449.6 | −0.0229938 | ||||||||
\(322\) | −628632. | −0.337876 | ||||||||
\(323\) | 607372. | 0.323928 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 76089.1 | 0.0399590 | ||||||||
\(326\) | 1.51509e6 | 0.789577 | ||||||||
\(327\) | 487368. | 0.252051 | ||||||||
\(328\) | −244058. | −0.125259 | ||||||||
\(329\) | 1.51554e6 | 0.771931 | ||||||||
\(330\) | −124041. | −0.0627021 | ||||||||
\(331\) | 3.09668e6 | 1.55355 | 0.776776 | − | 0.629776i | \(-0.216854\pi\) | ||||
0.776776 | + | 0.629776i | \(0.216854\pi\) | |||||||
\(332\) | 403529. | 0.200923 | ||||||||
\(333\) | −591356. | −0.292239 | ||||||||
\(334\) | 2.02353e6 | 0.992531 | ||||||||
\(335\) | 309370. | 0.150614 | ||||||||
\(336\) | −124185. | −0.0600095 | ||||||||
\(337\) | −672599. | −0.322613 | −0.161306 | − | 0.986904i | \(-0.551571\pi\) | ||||
−0.161306 | + | 0.986904i | \(0.551571\pi\) | |||||||
\(338\) | 1.42589e6 | 0.678881 | ||||||||
\(339\) | −1.09913e6 | −0.519455 | ||||||||
\(340\) | 672989. | 0.315726 | ||||||||
\(341\) | 654048. | 0.304595 | ||||||||
\(342\) | 116964. | 0.0540738 | ||||||||
\(343\) | −1.65519e6 | −0.759650 | ||||||||
\(344\) | −1.23910e6 | −0.564558 | ||||||||
\(345\) | 656045. | 0.296747 | ||||||||
\(346\) | 1.72253e6 | 0.773530 | ||||||||
\(347\) | 1.35102e6 | 0.602334 | 0.301167 | − | 0.953571i | \(-0.402624\pi\) | ||||
0.301167 | + | 0.953571i | \(0.402624\pi\) | |||||||
\(348\) | 1.14270e6 | 0.505805 | ||||||||
\(349\) | −4.25648e6 | −1.87063 | −0.935313 | − | 0.353821i | \(-0.884882\pi\) | ||||
−0.935313 | + | 0.353821i | \(0.884882\pi\) | |||||||
\(350\) | −134749. | −0.0587970 | ||||||||
\(351\) | −88750.3 | −0.0384505 | ||||||||
\(352\) | −141132. | −0.0607110 | ||||||||
\(353\) | 2.85917e6 | 1.22125 | 0.610623 | − | 0.791921i | \(-0.290919\pi\) | ||||
0.610623 | + | 0.791921i | \(0.290919\pi\) | |||||||
\(354\) | −631698. | −0.267918 | ||||||||
\(355\) | 1.08178e6 | 0.455584 | ||||||||
\(356\) | 435056. | 0.181936 | ||||||||
\(357\) | 816161. | 0.338926 | ||||||||
\(358\) | 850492. | 0.350722 | ||||||||
\(359\) | −2.57491e6 | −1.05445 | −0.527226 | − | 0.849725i | \(-0.676768\pi\) | ||||
−0.527226 | + | 0.849725i | \(0.676768\pi\) | |||||||
\(360\) | 129600. | 0.0527046 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 2.70126e6 | 1.08342 | ||||||||
\(363\) | 1.27850e6 | 0.509254 | ||||||||
\(364\) | 104990. | 0.0415331 | ||||||||
\(365\) | −233480. | −0.0917312 | ||||||||
\(366\) | 778396. | 0.303737 | ||||||||
\(367\) | 1.96392e6 | 0.761129 | 0.380565 | − | 0.924754i | \(-0.375730\pi\) | ||||
0.380565 | + | 0.924754i | \(0.375730\pi\) | |||||||
\(368\) | 746433. | 0.287324 | ||||||||
\(369\) | 308886. | 0.118095 | ||||||||
\(370\) | −730069. | −0.277242 | ||||||||
\(371\) | −284815. | −0.107431 | ||||||||
\(372\) | −683357. | −0.256030 | ||||||||
\(373\) | −281558. | −0.104784 | −0.0523921 | − | 0.998627i | \(-0.516685\pi\) | ||||
−0.0523921 | + | 0.998627i | \(0.516685\pi\) | |||||||
\(374\) | 927539. | 0.342889 | ||||||||
\(375\) | 140625. | 0.0516398 | ||||||||
\(376\) | −1.79954e6 | −0.656437 | ||||||||
\(377\) | −966077. | −0.350073 | ||||||||
\(378\) | 157171. | 0.0565775 | ||||||||
\(379\) | −1.77889e6 | −0.636138 | −0.318069 | − | 0.948068i | \(-0.603034\pi\) | ||||
−0.318069 | + | 0.948068i | \(0.603034\pi\) | |||||||
\(380\) | 144400. | 0.0512989 | ||||||||
\(381\) | −41978.1 | −0.0148153 | ||||||||
\(382\) | 1.99707e6 | 0.700222 | ||||||||
\(383\) | −4.32645e6 | −1.50707 | −0.753537 | − | 0.657406i | \(-0.771654\pi\) | ||||
−0.753537 | + | 0.657406i | \(0.771654\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | −185716. | −0.0638555 | ||||||||
\(386\) | −784298. | −0.267925 | ||||||||
\(387\) | 1.56823e6 | 0.532271 | ||||||||
\(388\) | 1.91616e6 | 0.646177 | ||||||||
\(389\) | −2.81212e6 | −0.942237 | −0.471119 | − | 0.882070i | \(-0.656150\pi\) | ||||
−0.471119 | + | 0.882070i | \(0.656150\pi\) | |||||||
\(390\) | −109568. | −0.0364774 | ||||||||
\(391\) | −4.90568e6 | −1.62277 | ||||||||
\(392\) | 889717. | 0.292440 | ||||||||
\(393\) | 3.17689e6 | 1.03758 | ||||||||
\(394\) | −1.48157e6 | −0.480818 | ||||||||
\(395\) | −2.41359e6 | −0.778343 | ||||||||
\(396\) | 178620. | 0.0572389 | ||||||||
\(397\) | 5.04595e6 | 1.60682 | 0.803408 | − | 0.595428i | \(-0.203018\pi\) | ||||
0.803408 | + | 0.595428i | \(0.203018\pi\) | |||||||
\(398\) | 2.47518e6 | 0.783247 | ||||||||
\(399\) | 175120. | 0.0550685 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | −5.90706e6 | −1.83447 | −0.917235 | − | 0.398347i | \(-0.869584\pi\) | ||||
−0.917235 | + | 0.398347i | \(0.869584\pi\) | |||||||
\(402\) | −445492. | −0.137491 | ||||||||
\(403\) | 577733. | 0.177200 | ||||||||
\(404\) | −743614. | −0.226670 | ||||||||
\(405\) | −164025. | −0.0496904 | ||||||||
\(406\) | 1.71086e6 | 0.515110 | ||||||||
\(407\) | −1.00621e6 | −0.301094 | ||||||||
\(408\) | −969104. | −0.288217 | ||||||||
\(409\) | 4.41096e6 | 1.30384 | 0.651921 | − | 0.758287i | \(-0.273963\pi\) | ||||
0.651921 | + | 0.758287i | \(0.273963\pi\) | |||||||
\(410\) | 381341. | 0.112035 | ||||||||
\(411\) | 3.16981e6 | 0.925613 | ||||||||
\(412\) | −2.26420e6 | −0.657160 | ||||||||
\(413\) | −945786. | −0.272846 | ||||||||
\(414\) | −944704. | −0.270891 | ||||||||
\(415\) | −630514. | −0.179711 | ||||||||
\(416\) | −124664. | −0.0353191 | ||||||||
\(417\) | −2.46743e6 | −0.694873 | ||||||||
\(418\) | 199018. | 0.0557123 | ||||||||
\(419\) | 5.36398e6 | 1.49263 | 0.746315 | − | 0.665593i | \(-0.231821\pi\) | ||||
0.746315 | + | 0.665593i | \(0.231821\pi\) | |||||||
\(420\) | 194039. | 0.0536741 | ||||||||
\(421\) | 2.81350e6 | 0.773646 | 0.386823 | − | 0.922154i | \(-0.373572\pi\) | ||||
0.386823 | + | 0.922154i | \(0.373572\pi\) | |||||||
\(422\) | 250396. | 0.0684457 | ||||||||
\(423\) | 2.27755e6 | 0.618894 | ||||||||
\(424\) | 338187. | 0.0913572 | ||||||||
\(425\) | −1.05155e6 | −0.282394 | ||||||||
\(426\) | −1.55776e6 | −0.415889 | ||||||||
\(427\) | 1.16542e6 | 0.309324 | ||||||||
\(428\) | 75465.9 | 0.0199132 | ||||||||
\(429\) | −151011. | −0.0396156 | ||||||||
\(430\) | 1.93609e6 | 0.504956 | ||||||||
\(431\) | −3.66733e6 | −0.950949 | −0.475475 | − | 0.879729i | \(-0.657724\pi\) | ||||
−0.475475 | + | 0.879729i | \(0.657724\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | −3.19336e6 | −0.818519 | −0.409259 | − | 0.912418i | \(-0.634213\pi\) | ||||
−0.409259 | + | 0.912418i | \(0.634213\pi\) | |||||||
\(434\) | −1.02313e6 | −0.260739 | ||||||||
\(435\) | −1.78547e6 | −0.452406 | ||||||||
\(436\) | −866432. | −0.218282 | ||||||||
\(437\) | −1.05259e6 | −0.263666 | ||||||||
\(438\) | 336211. | 0.0837387 | ||||||||
\(439\) | 4.84345e6 | 1.19948 | 0.599741 | − | 0.800194i | \(-0.295270\pi\) | ||||
0.599741 | + | 0.800194i | \(0.295270\pi\) | |||||||
\(440\) | 220518. | 0.0543016 | ||||||||
\(441\) | −1.12605e6 | −0.275715 | ||||||||
\(442\) | 819314. | 0.199478 | ||||||||
\(443\) | 3.82748e6 | 0.926624 | 0.463312 | − | 0.886195i | \(-0.346661\pi\) | ||||
0.463312 | + | 0.886195i | \(0.346661\pi\) | |||||||
\(444\) | 1.05130e6 | 0.253087 | ||||||||
\(445\) | −679774. | −0.162729 | ||||||||
\(446\) | −4.59794e6 | −1.09453 | ||||||||
\(447\) | −957912. | −0.226755 | ||||||||
\(448\) | 220773. | 0.0519697 | ||||||||
\(449\) | −4.55005e6 | −1.06512 | −0.532562 | − | 0.846391i | \(-0.678771\pi\) | ||||
−0.532562 | + | 0.846391i | \(0.678771\pi\) | |||||||
\(450\) | −202500. | −0.0471405 | ||||||||
\(451\) | 525579. | 0.121674 | ||||||||
\(452\) | 1.95400e6 | 0.449861 | ||||||||
\(453\) | −1.89241e6 | −0.433282 | ||||||||
\(454\) | 2.23568e6 | 0.509061 | ||||||||
\(455\) | −164047. | −0.0371484 | ||||||||
\(456\) | −207936. | −0.0468293 | ||||||||
\(457\) | 3.90722e6 | 0.875139 | 0.437570 | − | 0.899185i | \(-0.355839\pi\) | ||||
0.437570 | + | 0.899185i | \(0.355839\pi\) | |||||||
\(458\) | 6.29183e6 | 1.40157 | ||||||||
\(459\) | 1.22652e6 | 0.271734 | ||||||||
\(460\) | −1.16630e6 | −0.256990 | ||||||||
\(461\) | 5.26269e6 | 1.15333 | 0.576667 | − | 0.816979i | \(-0.304353\pi\) | ||||
0.576667 | + | 0.816979i | \(0.304353\pi\) | |||||||
\(462\) | 267431. | 0.0582918 | ||||||||
\(463\) | 7.16926e6 | 1.55425 | 0.777127 | − | 0.629344i | \(-0.216676\pi\) | ||||
0.777127 | + | 0.629344i | \(0.216676\pi\) | |||||||
\(464\) | −2.03146e6 | −0.438040 | ||||||||
\(465\) | 1.06774e6 | 0.229000 | ||||||||
\(466\) | 1.53363e6 | 0.327157 | ||||||||
\(467\) | −6.62872e6 | −1.40649 | −0.703246 | − | 0.710947i | \(-0.748267\pi\) | ||||
−0.703246 | + | 0.710947i | \(0.748267\pi\) | |||||||
\(468\) | 157778. | 0.0332991 | ||||||||
\(469\) | −666996. | −0.140020 | ||||||||
\(470\) | 2.81179e6 | 0.587135 | ||||||||
\(471\) | 728237. | 0.151259 | ||||||||
\(472\) | 1.12302e6 | 0.232024 | ||||||||
\(473\) | 2.66839e6 | 0.548399 | ||||||||
\(474\) | 3.47557e6 | 0.710527 | ||||||||
\(475\) | −225625. | −0.0458831 | ||||||||
\(476\) | −1.45095e6 | −0.293519 | ||||||||
\(477\) | −428018. | −0.0861324 | ||||||||
\(478\) | 1.27109e6 | 0.254453 | ||||||||
\(479\) | 58865.9 | 0.0117226 | 0.00586131 | − | 0.999983i | \(-0.498134\pi\) | ||||
0.00586131 | + | 0.999983i | \(0.498134\pi\) | |||||||
\(480\) | −230400. | −0.0456435 | ||||||||
\(481\) | −888805. | −0.175164 | ||||||||
\(482\) | 5.23651e6 | 1.02666 | ||||||||
\(483\) | −1.41442e6 | −0.275874 | ||||||||
\(484\) | −2.27289e6 | −0.441027 | ||||||||
\(485\) | −2.99400e6 | −0.577959 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | −9.46054e6 | −1.80756 | −0.903782 | − | 0.427994i | \(-0.859221\pi\) | ||||
−0.903782 | + | 0.427994i | \(0.859221\pi\) | |||||||
\(488\) | −1.38381e6 | −0.263044 | ||||||||
\(489\) | 3.40895e6 | 0.644687 | ||||||||
\(490\) | −1.39018e6 | −0.261566 | ||||||||
\(491\) | 5.67252e6 | 1.06187 | 0.530936 | − | 0.847412i | \(-0.321840\pi\) | ||||
0.530936 | + | 0.847412i | \(0.321840\pi\) | |||||||
\(492\) | −549131. | −0.102273 | ||||||||
\(493\) | 1.33511e7 | 2.47400 | ||||||||
\(494\) | 175796. | 0.0324110 | ||||||||
\(495\) | −279093. | −0.0511961 | ||||||||
\(496\) | 1.21486e6 | 0.221728 | ||||||||
\(497\) | −2.33230e6 | −0.423539 | ||||||||
\(498\) | 907941. | 0.164053 | ||||||||
\(499\) | −9.98280e6 | −1.79474 | −0.897368 | − | 0.441282i | \(-0.854524\pi\) | ||||
−0.897368 | + | 0.441282i | \(0.854524\pi\) | |||||||
\(500\) | −250000. | −0.0447214 | ||||||||
\(501\) | 4.55295e6 | 0.810398 | ||||||||
\(502\) | 2.33630e6 | 0.413779 | ||||||||
\(503\) | −242940. | −0.0428133 | −0.0214067 | − | 0.999771i | \(-0.506814\pi\) | ||||
−0.0214067 | + | 0.999771i | \(0.506814\pi\) | |||||||
\(504\) | −279416. | −0.0489975 | ||||||||
\(505\) | 1.16190e6 | 0.202740 | ||||||||
\(506\) | −1.60744e6 | −0.279100 | ||||||||
\(507\) | 3.20825e6 | 0.554304 | ||||||||
\(508\) | 74627.7 | 0.0128304 | ||||||||
\(509\) | 2.35453e6 | 0.402818 | 0.201409 | − | 0.979507i | \(-0.435448\pi\) | ||||
0.201409 | + | 0.979507i | \(0.435448\pi\) | |||||||
\(510\) | 1.51422e6 | 0.257789 | ||||||||
\(511\) | 503379. | 0.0852791 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 263169. | 0.0441511 | ||||||||
\(514\) | 2.15230e6 | 0.359331 | ||||||||
\(515\) | 3.53781e6 | 0.587782 | ||||||||
\(516\) | −2.78797e6 | −0.460960 | ||||||||
\(517\) | 3.87531e6 | 0.637647 | ||||||||
\(518\) | 1.57402e6 | 0.257742 | ||||||||
\(519\) | 3.87570e6 | 0.631585 | ||||||||
\(520\) | 194788. | 0.0315903 | ||||||||
\(521\) | −3.09311e6 | −0.499230 | −0.249615 | − | 0.968345i | \(-0.580304\pi\) | ||||
−0.249615 | + | 0.968345i | \(0.580304\pi\) | |||||||
\(522\) | 2.57107e6 | 0.412988 | ||||||||
\(523\) | −2.49646e6 | −0.399089 | −0.199544 | − | 0.979889i | \(-0.563946\pi\) | ||||
−0.199544 | + | 0.979889i | \(0.563946\pi\) | |||||||
\(524\) | −5.64781e6 | −0.898570 | ||||||||
\(525\) | −303185. | −0.0480076 | ||||||||
\(526\) | −1.28217e6 | −0.202060 | ||||||||
\(527\) | −7.98422e6 | −1.25229 | ||||||||
\(528\) | −317546. | −0.0495704 | ||||||||
\(529\) | 2.06528e6 | 0.320878 | ||||||||
\(530\) | −528418. | −0.0817123 | ||||||||
\(531\) | −1.42132e6 | −0.218754 | ||||||||
\(532\) | −311324. | −0.0476907 | ||||||||
\(533\) | 464254. | 0.0707844 | ||||||||
\(534\) | 978875. | 0.148551 | ||||||||
\(535\) | −117915. | −0.0178109 | ||||||||
\(536\) | 791986. | 0.119071 | ||||||||
\(537\) | 1.91361e6 | 0.286363 | ||||||||
\(538\) | 3.14682e6 | 0.468723 | ||||||||
\(539\) | −1.91600e6 | −0.284069 | ||||||||
\(540\) | 291600. | 0.0430331 | ||||||||
\(541\) | 4.37052e6 | 0.642007 | 0.321003 | − | 0.947078i | \(-0.395980\pi\) | ||||
0.321003 | + | 0.947078i | \(0.395980\pi\) | |||||||
\(542\) | −4.87221e6 | −0.712407 | ||||||||
\(543\) | 6.07784e6 | 0.884606 | ||||||||
\(544\) | 1.72285e6 | 0.249603 | ||||||||
\(545\) | 1.35380e6 | 0.195238 | ||||||||
\(546\) | 236228. | 0.0339117 | ||||||||
\(547\) | −6.23499e6 | −0.890980 | −0.445490 | − | 0.895287i | \(-0.646970\pi\) | ||||
−0.445490 | + | 0.895287i | \(0.646970\pi\) | |||||||
\(548\) | −5.63523e6 | −0.801604 | ||||||||
\(549\) | 1.75139e6 | 0.248000 | ||||||||
\(550\) | −344560. | −0.0485688 | ||||||||
\(551\) | 2.86468e6 | 0.401973 | ||||||||
\(552\) | 1.67947e6 | 0.234599 | ||||||||
\(553\) | 5.20367e6 | 0.723597 | ||||||||
\(554\) | 2.69471e6 | 0.373025 | ||||||||
\(555\) | −1.64266e6 | −0.226368 | ||||||||
\(556\) | 4.38655e6 | 0.601777 | ||||||||
\(557\) | −2.20103e6 | −0.300599 | −0.150299 | − | 0.988641i | \(-0.548024\pi\) | ||||
−0.150299 | + | 0.988641i | \(0.548024\pi\) | |||||||
\(558\) | −1.53755e6 | −0.209047 | ||||||||
\(559\) | 2.35704e6 | 0.319035 | ||||||||
\(560\) | −344957. | −0.0464831 | ||||||||
\(561\) | 2.08696e6 | 0.279968 | ||||||||
\(562\) | −984390. | −0.131470 | ||||||||
\(563\) | 4.50252e6 | 0.598667 | 0.299333 | − | 0.954149i | \(-0.403236\pi\) | ||||
0.299333 | + | 0.954149i | \(0.403236\pi\) | |||||||
\(564\) | −4.04897e6 | −0.535978 | ||||||||
\(565\) | −3.05313e6 | −0.402368 | ||||||||
\(566\) | −9.84869e6 | −1.29222 | ||||||||
\(567\) | 353635. | 0.0461953 | ||||||||
\(568\) | 2.76936e6 | 0.360171 | ||||||||
\(569\) | −1.96946e6 | −0.255015 | −0.127508 | − | 0.991838i | \(-0.540698\pi\) | ||||
−0.127508 | + | 0.991838i | \(0.540698\pi\) | |||||||
\(570\) | 324900. | 0.0418854 | ||||||||
\(571\) | −6.98166e6 | −0.896124 | −0.448062 | − | 0.894002i | \(-0.647886\pi\) | ||||
−0.448062 | + | 0.894002i | \(0.647886\pi\) | |||||||
\(572\) | 268465. | 0.0343081 | ||||||||
\(573\) | 4.49342e6 | 0.571729 | ||||||||
\(574\) | −822165. | −0.104155 | ||||||||
\(575\) | 1.82235e6 | 0.229859 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 9.73499e6 | 1.21729 | 0.608647 | − | 0.793441i | \(-0.291712\pi\) | ||||
0.608647 | + | 0.793441i | \(0.291712\pi\) | |||||||
\(578\) | −5.64342e6 | −0.702624 | ||||||||
\(579\) | −1.76467e6 | −0.218760 | ||||||||
\(580\) | 3.17416e6 | 0.391795 | ||||||||
\(581\) | 1.35938e6 | 0.167071 | ||||||||
\(582\) | 4.31135e6 | 0.527602 | ||||||||
\(583\) | −728286. | −0.0887422 | ||||||||
\(584\) | −597708. | −0.0725199 | ||||||||
\(585\) | −246529. | −0.0297836 | ||||||||
\(586\) | 6.01228e6 | 0.723262 | ||||||||
\(587\) | −7.02206e6 | −0.841142 | −0.420571 | − | 0.907260i | \(-0.638170\pi\) | ||||
−0.420571 | + | 0.907260i | \(0.638170\pi\) | |||||||
\(588\) | 2.00186e6 | 0.238776 | ||||||||
\(589\) | −1.71314e6 | −0.203472 | ||||||||
\(590\) | −1.75472e6 | −0.207528 | ||||||||
\(591\) | −3.33353e6 | −0.392587 | ||||||||
\(592\) | −1.86898e6 | −0.219179 | ||||||||
\(593\) | 1.11700e7 | 1.30442 | 0.652209 | − | 0.758039i | \(-0.273842\pi\) | ||||
0.652209 | + | 0.758039i | \(0.273842\pi\) | |||||||
\(594\) | 401894. | 0.0467354 | ||||||||
\(595\) | 2.26711e6 | 0.262531 | ||||||||
\(596\) | 1.70295e6 | 0.196375 | ||||||||
\(597\) | 5.56915e6 | 0.639518 | ||||||||
\(598\) | −1.41989e6 | −0.162368 | ||||||||
\(599\) | −1.30059e7 | −1.48106 | −0.740531 | − | 0.672023i | \(-0.765426\pi\) | ||||
−0.740531 | + | 0.672023i | \(0.765426\pi\) | |||||||
\(600\) | 360000. | 0.0408248 | ||||||||
\(601\) | −1.44799e7 | −1.63524 | −0.817618 | − | 0.575761i | \(-0.804706\pi\) | ||||
−0.817618 | + | 0.575761i | \(0.804706\pi\) | |||||||
\(602\) | −4.17417e6 | −0.469439 | ||||||||
\(603\) | −1.00236e6 | −0.112261 | ||||||||
\(604\) | 3.36429e6 | 0.375233 | ||||||||
\(605\) | 3.55139e6 | 0.394466 | ||||||||
\(606\) | −1.67313e6 | −0.185075 | ||||||||
\(607\) | −1.30604e7 | −1.43875 | −0.719375 | − | 0.694622i | \(-0.755572\pi\) | ||||
−0.719375 | + | 0.694622i | \(0.755572\pi\) | |||||||
\(608\) | 369664. | 0.0405554 | ||||||||
\(609\) | 3.84944e6 | 0.420585 | ||||||||
\(610\) | 2.16221e6 | 0.235274 | ||||||||
\(611\) | 3.42314e6 | 0.370956 | ||||||||
\(612\) | −2.18048e6 | −0.235328 | ||||||||
\(613\) | −1.34776e7 | −1.44864 | −0.724320 | − | 0.689464i | \(-0.757846\pi\) | ||||
−0.724320 | + | 0.689464i | \(0.757846\pi\) | |||||||
\(614\) | 4.91649e6 | 0.526301 | ||||||||
\(615\) | 858017. | 0.0914762 | ||||||||
\(616\) | −475434. | −0.0504822 | ||||||||
\(617\) | −1.15779e6 | −0.122438 | −0.0612192 | − | 0.998124i | \(-0.519499\pi\) | ||||
−0.0612192 | + | 0.998124i | \(0.519499\pi\) | |||||||
\(618\) | −5.09444e6 | −0.536569 | ||||||||
\(619\) | −5.82236e6 | −0.610763 | −0.305381 | − | 0.952230i | \(-0.598784\pi\) | ||||
−0.305381 | + | 0.952230i | \(0.598784\pi\) | |||||||
\(620\) | −1.89821e6 | −0.198320 | ||||||||
\(621\) | −2.12559e6 | −0.221182 | ||||||||
\(622\) | 8.88447e6 | 0.920780 | ||||||||
\(623\) | 1.46558e6 | 0.151283 | ||||||||
\(624\) | −280495. | −0.0288379 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −8.65910e6 | −0.883155 | ||||||||
\(627\) | 447790. | 0.0454889 | ||||||||
\(628\) | −1.29464e6 | −0.130994 | ||||||||
\(629\) | 1.22832e7 | 1.23790 | ||||||||
\(630\) | 436587. | 0.0438247 | ||||||||
\(631\) | −1.40805e6 | −0.140781 | −0.0703907 | − | 0.997519i | \(-0.522425\pi\) | ||||
−0.0703907 | + | 0.997519i | \(0.522425\pi\) | |||||||
\(632\) | −6.17880e6 | −0.615334 | ||||||||
\(633\) | 563391. | 0.0558857 | ||||||||
\(634\) | −8.22788e6 | −0.812952 | ||||||||
\(635\) | −116606. | −0.0114759 | ||||||||
\(636\) | 760921. | 0.0745928 | ||||||||
\(637\) | −1.69244e6 | −0.165259 | ||||||||
\(638\) | 4.37475e6 | 0.425502 | ||||||||
\(639\) | −3.50497e6 | −0.339572 | ||||||||
\(640\) | 409600. | 0.0395285 | ||||||||
\(641\) | −6.81024e6 | −0.654662 | −0.327331 | − | 0.944910i | \(-0.606149\pi\) | ||||
−0.327331 | + | 0.944910i | \(0.606149\pi\) | |||||||
\(642\) | 169798. | 0.0162591 | ||||||||
\(643\) | 1.17675e7 | 1.12242 | 0.561210 | − | 0.827674i | \(-0.310336\pi\) | ||||
0.561210 | + | 0.827674i | \(0.310336\pi\) | |||||||
\(644\) | 2.51453e6 | 0.238914 | ||||||||
\(645\) | 4.35620e6 | 0.412295 | ||||||||
\(646\) | −2.42949e6 | −0.229052 | ||||||||
\(647\) | −1.66768e7 | −1.56621 | −0.783106 | − | 0.621888i | \(-0.786366\pi\) | ||||
−0.783106 | + | 0.621888i | \(0.786366\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | −2.41842e6 | −0.225382 | ||||||||
\(650\) | −304356. | −0.0282552 | ||||||||
\(651\) | −2.30204e6 | −0.212893 | ||||||||
\(652\) | −6.06036e6 | −0.558315 | ||||||||
\(653\) | 798441. | 0.0732757 | 0.0366378 | − | 0.999329i | \(-0.488335\pi\) | ||||
0.0366378 | + | 0.999329i | \(0.488335\pi\) | |||||||
\(654\) | −1.94947e6 | −0.178227 | ||||||||
\(655\) | 8.82470e6 | 0.803705 | ||||||||
\(656\) | 976233. | 0.0885714 | ||||||||
\(657\) | 756474. | 0.0683724 | ||||||||
\(658\) | −6.06217e6 | −0.545837 | ||||||||
\(659\) | −1.71609e7 | −1.53931 | −0.769655 | − | 0.638460i | \(-0.779572\pi\) | ||||
−0.769655 | + | 0.638460i | \(0.779572\pi\) | |||||||
\(660\) | 496166. | 0.0443371 | ||||||||
\(661\) | 5.15051e6 | 0.458508 | 0.229254 | − | 0.973367i | \(-0.426371\pi\) | ||||
0.229254 | + | 0.973367i | \(0.426371\pi\) | |||||||
\(662\) | −1.23867e7 | −1.09853 | ||||||||
\(663\) | 1.84346e6 | 0.162873 | ||||||||
\(664\) | −1.61412e6 | −0.142074 | ||||||||
\(665\) | 486444. | 0.0426559 | ||||||||
\(666\) | 2.36542e6 | 0.206644 | ||||||||
\(667\) | −2.31377e7 | −2.01375 | ||||||||
\(668\) | −8.09413e6 | −0.701825 | ||||||||
\(669\) | −1.03454e7 | −0.893676 | ||||||||
\(670\) | −1.23748e6 | −0.106500 | ||||||||
\(671\) | 2.98004e6 | 0.255515 | ||||||||
\(672\) | 496739. | 0.0424331 | ||||||||
\(673\) | −1.53735e7 | −1.30839 | −0.654193 | − | 0.756328i | \(-0.726992\pi\) | ||||
−0.654193 | + | 0.756328i | \(0.726992\pi\) | |||||||
\(674\) | 2.69040e6 | 0.228122 | ||||||||
\(675\) | −455625. | −0.0384900 | ||||||||
\(676\) | −5.70355e6 | −0.480041 | ||||||||
\(677\) | −2.02918e7 | −1.70156 | −0.850782 | − | 0.525518i | \(-0.823871\pi\) | ||||
−0.850782 | + | 0.525518i | \(0.823871\pi\) | |||||||
\(678\) | 4.39650e6 | 0.367310 | ||||||||
\(679\) | 6.45501e6 | 0.537307 | ||||||||
\(680\) | −2.69196e6 | −0.223252 | ||||||||
\(681\) | 5.03028e6 | 0.415646 | ||||||||
\(682\) | −2.61619e6 | −0.215381 | ||||||||
\(683\) | −5.88954e6 | −0.483092 | −0.241546 | − | 0.970389i | \(-0.577654\pi\) | ||||
−0.241546 | + | 0.970389i | \(0.577654\pi\) | |||||||
\(684\) | −467856. | −0.0382360 | ||||||||
\(685\) | 8.80504e6 | 0.716977 | ||||||||
\(686\) | 6.62078e6 | 0.537154 | ||||||||
\(687\) | 1.41566e7 | 1.14437 | ||||||||
\(688\) | 4.95638e6 | 0.399203 | ||||||||
\(689\) | −643309. | −0.0516264 | ||||||||
\(690\) | −2.62418e6 | −0.209832 | ||||||||
\(691\) | 4.05114e6 | 0.322762 | 0.161381 | − | 0.986892i | \(-0.448405\pi\) | ||||
0.161381 | + | 0.986892i | \(0.448405\pi\) | |||||||
\(692\) | −6.89013e6 | −0.546968 | ||||||||
\(693\) | 601721. | 0.0475951 | ||||||||
\(694\) | −5.40407e6 | −0.425915 | ||||||||
\(695\) | −6.85398e6 | −0.538246 | ||||||||
\(696\) | −4.57079e6 | −0.357658 | ||||||||
\(697\) | −6.41595e6 | −0.500241 | ||||||||
\(698\) | 1.70259e7 | 1.32273 | ||||||||
\(699\) | 3.45067e6 | 0.267123 | ||||||||
\(700\) | 538996. | 0.0415758 | ||||||||
\(701\) | −9.46762e6 | −0.727689 | −0.363844 | − | 0.931460i | \(-0.618536\pi\) | ||||
−0.363844 | + | 0.931460i | \(0.618536\pi\) | |||||||
\(702\) | 355001. | 0.0271886 | ||||||||
\(703\) | 2.63555e6 | 0.201133 | ||||||||
\(704\) | 564527. | 0.0429292 | ||||||||
\(705\) | 6.32652e6 | 0.479393 | ||||||||
\(706\) | −1.14367e7 | −0.863552 | ||||||||
\(707\) | −2.50503e6 | −0.188480 | ||||||||
\(708\) | 2.52679e6 | 0.189446 | ||||||||
\(709\) | −1.01721e7 | −0.759971 | −0.379985 | − | 0.924992i | \(-0.624071\pi\) | ||||
−0.379985 | + | 0.924992i | \(0.624071\pi\) | |||||||
\(710\) | −4.32712e6 | −0.322146 | ||||||||
\(711\) | 7.82004e6 | 0.580143 | ||||||||
\(712\) | −1.74022e6 | −0.128649 | ||||||||
\(713\) | 1.38368e7 | 1.01932 | ||||||||
\(714\) | −3.26465e6 | −0.239657 | ||||||||
\(715\) | −419476. | −0.0306861 | ||||||||
\(716\) | −3.40197e6 | −0.247998 | ||||||||
\(717\) | 2.85995e6 | 0.207760 | ||||||||
\(718\) | 1.02997e7 | 0.745610 | ||||||||
\(719\) | 2.09519e7 | 1.51147 | 0.755736 | − | 0.654876i | \(-0.227279\pi\) | ||||
0.755736 | + | 0.654876i | \(0.227279\pi\) | |||||||
\(720\) | −518400. | −0.0372678 | ||||||||
\(721\) | −7.62746e6 | −0.546439 | ||||||||
\(722\) | −521284. | −0.0372161 | ||||||||
\(723\) | 1.17822e7 | 0.838260 | ||||||||
\(724\) | −1.08051e7 | −0.766091 | ||||||||
\(725\) | −4.95963e6 | −0.350432 | ||||||||
\(726\) | −5.11400e6 | −0.360097 | ||||||||
\(727\) | −6.38429e6 | −0.447999 | −0.223999 | − | 0.974589i | \(-0.571911\pi\) | ||||
−0.223999 | + | 0.974589i | \(0.571911\pi\) | |||||||
\(728\) | −419960. | −0.0293684 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 933919. | 0.0648638 | ||||||||
\(731\) | −3.25741e7 | −2.25465 | ||||||||
\(732\) | −3.11358e6 | −0.214774 | ||||||||
\(733\) | 3.31675e6 | 0.228010 | 0.114005 | − | 0.993480i | \(-0.463632\pi\) | ||||
0.114005 | + | 0.993480i | \(0.463632\pi\) | |||||||
\(734\) | −7.85568e6 | −0.538200 | ||||||||
\(735\) | −3.12791e6 | −0.213568 | ||||||||
\(736\) | −2.98573e6 | −0.203169 | ||||||||
\(737\) | −1.70554e6 | −0.115663 | ||||||||
\(738\) | −1.23554e6 | −0.0835059 | ||||||||
\(739\) | 2.06970e7 | 1.39411 | 0.697055 | − | 0.717017i | \(-0.254493\pi\) | ||||
0.697055 | + | 0.717017i | \(0.254493\pi\) | |||||||
\(740\) | 2.92028e6 | 0.196040 | ||||||||
\(741\) | 395542. | 0.0264635 | ||||||||
\(742\) | 1.13926e6 | 0.0759649 | ||||||||
\(743\) | −429578. | −0.0285476 | −0.0142738 | − | 0.999898i | \(-0.504544\pi\) | ||||
−0.0142738 | + | 0.999898i | \(0.504544\pi\) | |||||||
\(744\) | 2.73343e6 | 0.181040 | ||||||||
\(745\) | −2.66087e6 | −0.175644 | ||||||||
\(746\) | 1.12623e6 | 0.0740936 | ||||||||
\(747\) | 2.04287e6 | 0.133949 | ||||||||
\(748\) | −3.71016e6 | −0.242459 | ||||||||
\(749\) | 254224. | 0.0165582 | ||||||||
\(750\) | −562500. | −0.0365148 | ||||||||
\(751\) | 1.31135e7 | 0.848434 | 0.424217 | − | 0.905561i | \(-0.360549\pi\) | ||||
0.424217 | + | 0.905561i | \(0.360549\pi\) | |||||||
\(752\) | 7.19817e6 | 0.464171 | ||||||||
\(753\) | 5.25667e6 | 0.337849 | ||||||||
\(754\) | 3.86431e6 | 0.247539 | ||||||||
\(755\) | −5.25670e6 | −0.335619 | ||||||||
\(756\) | −628685. | −0.0400063 | ||||||||
\(757\) | −8.63134e6 | −0.547442 | −0.273721 | − | 0.961809i | \(-0.588255\pi\) | ||||
−0.273721 | + | 0.961809i | \(0.588255\pi\) | |||||||
\(758\) | 7.11557e6 | 0.449818 | ||||||||
\(759\) | −3.61675e6 | −0.227884 | ||||||||
\(760\) | −577600. | −0.0362738 | ||||||||
\(761\) | 3.32766e6 | 0.208294 | 0.104147 | − | 0.994562i | \(-0.466789\pi\) | ||||
0.104147 | + | 0.994562i | \(0.466789\pi\) | |||||||
\(762\) | 167912. | 0.0104760 | ||||||||
\(763\) | −2.91877e6 | −0.181505 | ||||||||
\(764\) | −7.98830e6 | −0.495132 | ||||||||
\(765\) | 3.40701e6 | 0.210484 | ||||||||
\(766\) | 1.73058e7 | 1.06566 | ||||||||
\(767\) | −2.13624e6 | −0.131118 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | −2.21676e6 | −0.135177 | −0.0675886 | − | 0.997713i | \(-0.521531\pi\) | ||||
−0.0675886 | + | 0.997713i | \(0.521531\pi\) | |||||||
\(770\) | 742865. | 0.0451526 | ||||||||
\(771\) | 4.84267e6 | 0.293393 | ||||||||
\(772\) | 3.13719e6 | 0.189451 | ||||||||
\(773\) | 2.32932e7 | 1.40210 | 0.701052 | − | 0.713110i | \(-0.252714\pi\) | ||||
0.701052 | + | 0.713110i | \(0.252714\pi\) | |||||||
\(774\) | −6.27292e6 | −0.376372 | ||||||||
\(775\) | 2.96596e6 | 0.177382 | ||||||||
\(776\) | −7.66463e6 | −0.456916 | ||||||||
\(777\) | 3.54154e6 | 0.210445 | ||||||||
\(778\) | 1.12485e7 | 0.666262 | ||||||||
\(779\) | −1.37664e6 | −0.0812787 | ||||||||
\(780\) | 438273. | 0.0257934 | ||||||||
\(781\) | −5.96381e6 | −0.349861 | ||||||||
\(782\) | 1.96227e7 | 1.14747 | ||||||||
\(783\) | 5.78491e6 | 0.337204 | ||||||||
\(784\) | −3.55887e6 | −0.206786 | ||||||||
\(785\) | 2.02288e6 | 0.117164 | ||||||||
\(786\) | −1.27076e7 | −0.733679 | ||||||||
\(787\) | −3.33148e7 | −1.91735 | −0.958673 | − | 0.284512i | \(-0.908168\pi\) | ||||
−0.958673 | + | 0.284512i | \(0.908168\pi\) | |||||||
\(788\) | 5.92627e6 | 0.339990 | ||||||||
\(789\) | −2.88488e6 | −0.164982 | ||||||||
\(790\) | 9.65437e6 | 0.550372 | ||||||||
\(791\) | 6.58249e6 | 0.374067 | ||||||||
\(792\) | −714479. | −0.0404740 | ||||||||
\(793\) | 2.63233e6 | 0.148647 | ||||||||
\(794\) | −2.01838e7 | −1.13619 | ||||||||
\(795\) | −1.18894e6 | −0.0667178 | ||||||||
\(796\) | −9.90071e6 | −0.553839 | ||||||||
\(797\) | 2.73232e7 | 1.52365 | 0.761826 | − | 0.647782i | \(-0.224303\pi\) | ||||
0.761826 | + | 0.647782i | \(0.224303\pi\) | |||||||
\(798\) | −700479. | −0.0389393 | ||||||||
\(799\) | −4.73075e7 | −2.62158 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | 2.20247e6 | 0.121291 | ||||||||
\(802\) | 2.36282e7 | 1.29717 | ||||||||
\(803\) | 1.28716e6 | 0.0704441 | ||||||||
\(804\) | 1.78197e6 | 0.0972210 | ||||||||
\(805\) | −3.92895e6 | −0.213691 | ||||||||
\(806\) | −2.31093e6 | −0.125300 | ||||||||
\(807\) | 7.08035e6 | 0.382711 | ||||||||
\(808\) | 2.97446e6 | 0.160280 | ||||||||
\(809\) | −1.92098e7 | −1.03193 | −0.515966 | − | 0.856609i | \(-0.672567\pi\) | ||||
−0.515966 | + | 0.856609i | \(0.672567\pi\) | |||||||
\(810\) | 656100. | 0.0351364 | ||||||||
\(811\) | −3.35126e7 | −1.78919 | −0.894595 | − | 0.446878i | \(-0.852536\pi\) | ||||
−0.894595 | + | 0.446878i | \(0.852536\pi\) | |||||||
\(812\) | −6.84344e6 | −0.364237 | ||||||||
\(813\) | −1.09625e7 | −0.581678 | ||||||||
\(814\) | 4.02484e6 | 0.212906 | ||||||||
\(815\) | 9.46931e6 | 0.499372 | ||||||||
\(816\) | 3.87642e6 | 0.203800 | ||||||||
\(817\) | −6.98928e6 | −0.366334 | ||||||||
\(818\) | −1.76439e7 | −0.921956 | ||||||||
\(819\) | 531512. | 0.0276887 | ||||||||
\(820\) | −1.52536e6 | −0.0792207 | ||||||||
\(821\) | −2.27808e7 | −1.17953 | −0.589767 | − | 0.807573i | \(-0.700780\pi\) | ||||
−0.589767 | + | 0.807573i | \(0.700780\pi\) | |||||||
\(822\) | −1.26793e7 | −0.654507 | ||||||||
\(823\) | 1.06573e6 | 0.0548464 | 0.0274232 | − | 0.999624i | \(-0.491270\pi\) | ||||
0.0274232 | + | 0.999624i | \(0.491270\pi\) | |||||||
\(824\) | 9.05679e6 | 0.464682 | ||||||||
\(825\) | −775259. | −0.0396563 | ||||||||
\(826\) | 3.78314e6 | 0.192931 | ||||||||
\(827\) | 1.60398e6 | 0.0815520 | 0.0407760 | − | 0.999168i | \(-0.487017\pi\) | ||||
0.0407760 | + | 0.999168i | \(0.487017\pi\) | |||||||
\(828\) | 3.77882e6 | 0.191549 | ||||||||
\(829\) | 1.47136e7 | 0.743589 | 0.371794 | − | 0.928315i | \(-0.378743\pi\) | ||||
0.371794 | + | 0.928315i | \(0.378743\pi\) | |||||||
\(830\) | 2.52206e6 | 0.127075 | ||||||||
\(831\) | 6.06310e6 | 0.304573 | ||||||||
\(832\) | 498658. | 0.0249743 | ||||||||
\(833\) | 2.33894e7 | 1.16790 | ||||||||
\(834\) | 9.86973e6 | 0.491349 | ||||||||
\(835\) | 1.26471e7 | 0.627732 | ||||||||
\(836\) | −796071. | −0.0393945 | ||||||||
\(837\) | −3.45949e6 | −0.170686 | ||||||||
\(838\) | −2.14559e7 | −1.05545 | ||||||||
\(839\) | 3.57233e7 | 1.75205 | 0.876026 | − | 0.482263i | \(-0.160185\pi\) | ||||
0.876026 | + | 0.482263i | \(0.160185\pi\) | |||||||
\(840\) | −776154. | −0.0379533 | ||||||||
\(841\) | 4.24595e7 | 2.07007 | ||||||||
\(842\) | −1.12540e7 | −0.547050 | ||||||||
\(843\) | −2.21488e6 | −0.107345 | ||||||||
\(844\) | −1.00158e6 | −0.0483984 | ||||||||
\(845\) | 8.91179e6 | 0.429362 | ||||||||
\(846\) | −9.11019e6 | −0.437624 | ||||||||
\(847\) | −7.65674e6 | −0.366721 | ||||||||
\(848\) | −1.35275e6 | −0.0645993 | ||||||||
\(849\) | −2.21595e7 | −1.05510 | ||||||||
\(850\) | 4.20618e6 | 0.199683 | ||||||||
\(851\) | −2.12870e7 | −1.00761 | ||||||||
\(852\) | 6.23106e6 | 0.294078 | ||||||||
\(853\) | −9.51318e6 | −0.447665 | −0.223832 | − | 0.974628i | \(-0.571857\pi\) | ||||
−0.223832 | + | 0.974628i | \(0.571857\pi\) | |||||||
\(854\) | −4.66169e6 | −0.218725 | ||||||||
\(855\) | 731025. | 0.0341993 | ||||||||
\(856\) | −301864. | −0.0140808 | ||||||||
\(857\) | 1.32585e6 | 0.0616656 | 0.0308328 | − | 0.999525i | \(-0.490184\pi\) | ||||
0.0308328 | + | 0.999525i | \(0.490184\pi\) | |||||||
\(858\) | 604045. | 0.0280125 | ||||||||
\(859\) | −1.00800e7 | −0.466099 | −0.233049 | − | 0.972465i | \(-0.574870\pi\) | ||||
−0.233049 | + | 0.972465i | \(0.574870\pi\) | |||||||
\(860\) | −7.74435e6 | −0.357058 | ||||||||
\(861\) | −1.84987e6 | −0.0850420 | ||||||||
\(862\) | 1.46693e7 | 0.672423 | ||||||||
\(863\) | 1.91198e7 | 0.873887 | 0.436944 | − | 0.899489i | \(-0.356061\pi\) | ||||
0.436944 | + | 0.899489i | \(0.356061\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 1.07658e7 | 0.489223 | ||||||||
\(866\) | 1.27735e7 | 0.578780 | ||||||||
\(867\) | −1.26977e7 | −0.573690 | ||||||||
\(868\) | 4.09252e6 | 0.184370 | ||||||||
\(869\) | 1.33060e7 | 0.597722 | ||||||||
\(870\) | 7.14186e6 | 0.319899 | ||||||||
\(871\) | −1.50654e6 | −0.0672875 | ||||||||
\(872\) | 3.46573e6 | 0.154349 | ||||||||
\(873\) | 9.70054e6 | 0.430785 | ||||||||
\(874\) | 4.21035e6 | 0.186440 | ||||||||
\(875\) | −842181. | −0.0371865 | ||||||||
\(876\) | −1.34484e6 | −0.0592122 | ||||||||
\(877\) | 2.15867e7 | 0.947735 | 0.473867 | − | 0.880596i | \(-0.342858\pi\) | ||||
0.473867 | + | 0.880596i | \(0.342858\pi\) | |||||||
\(878\) | −1.93738e7 | −0.848162 | ||||||||
\(879\) | 1.35276e7 | 0.590541 | ||||||||
\(880\) | −882073. | −0.0383970 | ||||||||
\(881\) | 4.57781e7 | 1.98709 | 0.993546 | − | 0.113433i | \(-0.0361846\pi\) | ||||
0.993546 | + | 0.113433i | \(0.0361846\pi\) | |||||||
\(882\) | 4.50419e6 | 0.194960 | ||||||||
\(883\) | −1.24168e6 | −0.0535931 | −0.0267966 | − | 0.999641i | \(-0.508531\pi\) | ||||
−0.0267966 | + | 0.999641i | \(0.508531\pi\) | |||||||
\(884\) | −3.27726e6 | −0.141052 | ||||||||
\(885\) | −3.94811e6 | −0.169446 | ||||||||
\(886\) | −1.53099e7 | −0.655222 | ||||||||
\(887\) | 2.34585e7 | 1.00113 | 0.500567 | − | 0.865698i | \(-0.333125\pi\) | ||||
0.500567 | + | 0.865698i | \(0.333125\pi\) | |||||||
\(888\) | −4.20520e6 | −0.178959 | ||||||||
\(889\) | 251400. | 0.0106687 | ||||||||
\(890\) | 2.71910e6 | 0.115067 | ||||||||
\(891\) | 904262. | 0.0381593 | ||||||||
\(892\) | 1.83917e7 | 0.773946 | ||||||||
\(893\) | −1.01506e7 | −0.425952 | ||||||||
\(894\) | 3.83165e6 | 0.160340 | ||||||||
\(895\) | 5.31558e6 | 0.221816 | ||||||||
\(896\) | −883091. | −0.0367482 | ||||||||
\(897\) | −3.19474e6 | −0.132573 | ||||||||
\(898\) | 1.82002e7 | 0.753157 | ||||||||
\(899\) | −3.76577e7 | −1.55401 | ||||||||
\(900\) | 810000. | 0.0333333 | ||||||||
\(901\) | 8.89048e6 | 0.364849 | ||||||||
\(902\) | −2.10231e6 | −0.0860362 | ||||||||
\(903\) | −9.39189e6 | −0.383295 | ||||||||
\(904\) | −7.81600e6 | −0.318100 | ||||||||
\(905\) | 1.68829e7 | 0.685213 | ||||||||
\(906\) | 7.56965e6 | 0.306376 | ||||||||
\(907\) | 3.96914e7 | 1.60206 | 0.801028 | − | 0.598626i | \(-0.204287\pi\) | ||||
0.801028 | + | 0.598626i | \(0.204287\pi\) | |||||||
\(908\) | −8.94271e6 | −0.359960 | ||||||||
\(909\) | −3.76455e6 | −0.151113 | ||||||||
\(910\) | 656188. | 0.0262679 | ||||||||
\(911\) | 1.58251e7 | 0.631757 | 0.315879 | − | 0.948800i | \(-0.397701\pi\) | ||||
0.315879 | + | 0.948800i | \(0.397701\pi\) | |||||||
\(912\) | 831744. | 0.0331133 | ||||||||
\(913\) | 3.47600e6 | 0.138007 | ||||||||
\(914\) | −1.56289e7 | −0.618817 | ||||||||
\(915\) | 4.86497e6 | 0.192100 | ||||||||
\(916\) | −2.51673e7 | −0.991057 | ||||||||
\(917\) | −1.90259e7 | −0.747175 | ||||||||
\(918\) | −4.90609e6 | −0.192145 | ||||||||
\(919\) | 2.09138e7 | 0.816855 | 0.408428 | − | 0.912791i | \(-0.366077\pi\) | ||||
0.408428 | + | 0.912791i | \(0.366077\pi\) | |||||||
\(920\) | 4.66521e6 | 0.181719 | ||||||||
\(921\) | 1.10621e7 | 0.429723 | ||||||||
\(922\) | −2.10507e7 | −0.815530 | ||||||||
\(923\) | −5.26795e6 | −0.203534 | ||||||||
\(924\) | −1.06973e6 | −0.0412185 | ||||||||
\(925\) | −4.56293e6 | −0.175344 | ||||||||
\(926\) | −2.86770e7 | −1.09902 | ||||||||
\(927\) | −1.14625e7 | −0.438107 | ||||||||
\(928\) | 8.12585e6 | 0.309741 | ||||||||
\(929\) | 2.94233e7 | 1.11854 | 0.559270 | − | 0.828985i | \(-0.311081\pi\) | ||||
0.559270 | + | 0.828985i | \(0.311081\pi\) | |||||||
\(930\) | −4.27098e6 | −0.161927 | ||||||||
\(931\) | 5.01856e6 | 0.189760 | ||||||||
\(932\) | −6.13453e6 | −0.231335 | ||||||||
\(933\) | 1.99901e7 | 0.751814 | ||||||||
\(934\) | 2.65149e7 | 0.994540 | ||||||||
\(935\) | 5.79712e6 | 0.216862 | ||||||||
\(936\) | −631113. | −0.0235460 | ||||||||
\(937\) | −3.29112e7 | −1.22460 | −0.612301 | − | 0.790625i | \(-0.709756\pi\) | ||||
−0.612301 | + | 0.790625i | \(0.709756\pi\) | |||||||
\(938\) | 2.66798e6 | 0.0990093 | ||||||||
\(939\) | −1.94830e7 | −0.721093 | ||||||||
\(940\) | −1.12471e7 | −0.415167 | ||||||||
\(941\) | −9.35784e6 | −0.344510 | −0.172255 | − | 0.985052i | \(-0.555105\pi\) | ||||
−0.172255 | + | 0.985052i | \(0.555105\pi\) | |||||||
\(942\) | −2.91295e6 | −0.106956 | ||||||||
\(943\) | 1.11190e7 | 0.407179 | ||||||||
\(944\) | −4.49208e6 | −0.164065 | ||||||||
\(945\) | 982320. | 0.0357827 | ||||||||
\(946\) | −1.06736e7 | −0.387777 | ||||||||
\(947\) | 1.02869e7 | 0.372742 | 0.186371 | − | 0.982479i | \(-0.440327\pi\) | ||||
0.186371 | + | 0.982479i | \(0.440327\pi\) | |||||||
\(948\) | −1.39023e7 | −0.502418 | ||||||||
\(949\) | 1.13698e6 | 0.0409813 | ||||||||
\(950\) | 902500. | 0.0324443 | ||||||||
\(951\) | −1.85127e7 | −0.663772 | ||||||||
\(952\) | 5.80381e6 | 0.207549 | ||||||||
\(953\) | −1.10120e7 | −0.392767 | −0.196383 | − | 0.980527i | \(-0.562920\pi\) | ||||
−0.196383 | + | 0.980527i | \(0.562920\pi\) | |||||||
\(954\) | 1.71207e6 | 0.0609048 | ||||||||
\(955\) | 1.24817e7 | 0.442859 | ||||||||
\(956\) | −5.08436e6 | −0.179925 | ||||||||
\(957\) | 9.84319e6 | 0.347421 | ||||||||
\(958\) | −235464. | −0.00828915 | ||||||||
\(959\) | −1.89835e7 | −0.666546 | ||||||||
\(960\) | 921600. | 0.0322749 | ||||||||
\(961\) | −6.10908e6 | −0.213387 | ||||||||
\(962\) | 3.55522e6 | 0.123859 | ||||||||
\(963\) | 382046. | 0.0132755 | ||||||||
\(964\) | −2.09461e7 | −0.725955 | ||||||||
\(965\) | −4.90186e6 | −0.169450 | ||||||||
\(966\) | 5.65769e6 | 0.195073 | ||||||||
\(967\) | −1.85043e7 | −0.636366 | −0.318183 | − | 0.948029i | \(-0.603073\pi\) | ||||
−0.318183 | + | 0.948029i | \(0.603073\pi\) | |||||||
\(968\) | 9.09156e6 | 0.311853 | ||||||||
\(969\) | −5.46635e6 | −0.187020 | ||||||||
\(970\) | 1.19760e7 | 0.408678 | ||||||||
\(971\) | 4.72576e6 | 0.160851 | 0.0804255 | − | 0.996761i | \(-0.474372\pi\) | ||||
0.0804255 | + | 0.996761i | \(0.474372\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | 1.47771e7 | 0.500387 | ||||||||
\(974\) | 3.78422e7 | 1.27814 | ||||||||
\(975\) | −684802. | −0.0230703 | ||||||||
\(976\) | 5.53526e6 | 0.186000 | ||||||||
\(977\) | 2.27688e6 | 0.0763140 | 0.0381570 | − | 0.999272i | \(-0.487851\pi\) | ||||
0.0381570 | + | 0.999272i | \(0.487851\pi\) | |||||||
\(978\) | −1.36358e7 | −0.455863 | ||||||||
\(979\) | 3.74757e6 | 0.124966 | ||||||||
\(980\) | 5.56073e6 | 0.184955 | ||||||||
\(981\) | −4.38631e6 | −0.145522 | ||||||||
\(982\) | −2.26901e7 | −0.750857 | ||||||||
\(983\) | 3.13944e7 | 1.03626 | 0.518130 | − | 0.855302i | \(-0.326628\pi\) | ||||
0.518130 | + | 0.855302i | \(0.326628\pi\) | |||||||
\(984\) | 2.19652e6 | 0.0723183 | ||||||||
\(985\) | −9.25980e6 | −0.304096 | ||||||||
\(986\) | −5.34044e7 | −1.74938 | ||||||||
\(987\) | −1.36399e7 | −0.445674 | ||||||||
\(988\) | −703185. | −0.0229180 | ||||||||
\(989\) | 5.64516e7 | 1.83521 | ||||||||
\(990\) | 1.11637e6 | 0.0362011 | ||||||||
\(991\) | −5.51463e7 | −1.78374 | −0.891871 | − | 0.452290i | \(-0.850607\pi\) | ||||
−0.891871 | + | 0.452290i | \(0.850607\pi\) | |||||||
\(992\) | −4.85942e6 | −0.156785 | ||||||||
\(993\) | −2.78701e7 | −0.896944 | ||||||||
\(994\) | 9.32921e6 | 0.299488 | ||||||||
\(995\) | 1.54699e7 | 0.495369 | ||||||||
\(996\) | −3.63176e6 | −0.116003 | ||||||||
\(997\) | −4.29716e7 | −1.36913 | −0.684564 | − | 0.728953i | \(-0.740007\pi\) | ||||
−0.684564 | + | 0.728953i | \(0.740007\pi\) | |||||||
\(998\) | 3.99312e7 | 1.26907 | ||||||||
\(999\) | 5.32220e6 | 0.168724 |
(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 | 570.6.a.i.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.6.a.i.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial |